# Entrants' Sample Solutions

## Beagle 0.9.22

Peter Baumgartner
NICTA and Australian National University

### Sample solution for DAT013=1

% SZS status Theorem for DAT013=1.p

% SZS output start CNFRefutation for DAT013=1.p
tff(f_77, negated_conjecture, ~(![U:array, Va:$int, Wa:$int]: ((![Xa:$int]: (($lesseq(Va, Xa) & $lesseq(Xa, Wa)) =>$greater(read(U, Xa), 0))) => (![Ya:$int]: (($lesseq($sum(Va, 3), Ya) &$lesseq(Ya, Wa)) => $greater(read(U, Ya), 0))))), file('DAT013=1.p', co1)). tff(c_9, plain, ($lesseq(skF_4, skF_3)), inference(cnfTransformation, [status(thm)], [f_77])).
tff(c_7, plain, (~$greater(read(skF_1, skF_4), 0)), inference(cnfTransformation, [status(thm)], [f_77])). tff(c_13, plain, (![X_1a:$int]: ($greater(read(skF_1, X_1a), 0) | ~$lesseq(skF_2, X_1a) | ~$lesseq(X_1a, skF_3))), inference(cnfTransformation, [status(thm)], [f_77])). tff(c_11, plain, ($lesseq($sum(skF_2, 3), skF_4)), inference(cnfTransformation, [status(thm)], [f_77])). tff(c_10, plain, (~$less(skF_3, skF_4)), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_9])).
tff(c_21, plain, (~$less(0, read(skF_1, skF_4))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_7])). tff(c_24, plain, (read(skF_1, skF_4)=skE_1), inference(define, [status(thm), theory('equality')], [c_21])). tff(c_23, plain, (~$less(0, read(skF_1, skF_4))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_7])).
tff(c_26, plain, (~$less(0, skE_1)), inference(demodulation, [status(thm), theory('equality')], [c_24, c_23])). tff(c_30, plain, (read(skF_1, skF_4)=skE_1), inference(define, [status(thm), theory('equality')], [c_21])). tff(c_68, plain, (![X_15a:$int]: ($less(0, read(skF_1, X_15a)) |$less(X_15a, skF_2) | $less(skF_3, X_15a))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_13])). tff(c_70, plain, ($less(0, skE_1) | $less(skF_4, skF_2) |$less(skF_3, skF_4)), inference(superposition, [status(thm), theory('equality')], [c_30, c_68])).
tff(c_73, plain, ($less(skF_4, skF_2) |$less(skF_3, skF_4)), inference(negUnitSimplification, [status(thm)], [c_26, c_70])).
tff(c_75, plain, ($less(skF_4, skF_2)), inference(negUnitSimplification, [status(thm)], [c_10, c_73])). tff(c_12, plain, (~$less(skF_4, $sum(3, skF_2))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_11])). tff(c_77, plain,$false, inference(close, [status(thm), theory('LIA')], [c_75, c_12])).
% SZS output end CNFRefutation for DAT013=1.p


## CVC4 1.5

Andrew Reynolds
EPFL, Switzerland

CVC4 uses the SMT2 format for models. In this format, the model for function and predicate symbols are provided using the define-fun command. All models produced by CVC4 are finite. In other words, for unsorted inputs, the input is interpreted as a problem having a single uninterpreted sort, $$unsorted, which all models interpret as a finite set. In the output of these models, the domain elements of$$unsorted are named @uc___unsorted_0, ..., @uc___unsorted_n, where n is finite. The cardinality of $$unsorted is specified in a line of the form "; cardinality of$$unsorted is n". For instance, the cardinality of $$unsorted is 4 in the model for NLP042+1, and 2 in the model for SWV017+1. For proofs, CVC4 provides the (fresh) skolem constants it used when witnessing the negation of universally quantified formulas, and a set of tuples of ground terms it used for instantiating universal quantified formulas. The corresponding ground instances of these formulas, along with the ground formulas from the input (if any), are unsatisfiable at the ground level. ### Sample solution for DAT013=1 % SZS status Theorem for DAT013=1 % SZS output start Proof for DAT013=1 Skolem constants of (let ((_let_0 (* (- 1) X))) (let ((_let_1 (* (- 1) BOUND_VAR IABLE_345))) (forall ((U array) (V Int) (W Int) (BOUND_VARIABLE_345 Int)) (or (n ot (forall ((X Int)) (or (>= (+ V _let_0) 1) (not (>= (+ W _let_0) 0)) (>= (read U X) 1)) )) (>= (+ V _let_1) (- 2)) (not (>= (+ W _let_1) 0)) (>= (read U BOUND _VARIABLE_345) 1)) ))) : ( skv_1, skv_2, skv_3, skv_4 ) Instantiations of (forall ((X Int)) (or (not (>= (+ X (* (- 1) skv_2)) 0)) (>= ( + X (* (- 1) skv_3)) 1) (>= (read skv_1 X) 1)) ) : ( skv_4 ) % SZS output end Proof for DAT013=1  ### Sample solution for SEU140+2 % SZS status Theorem for SEU140+2 % SZS output start Proof for SEU140+2 Skolem constants of (forall ((A$$unsorted)) (not (empty A)) ) :
( skv_1 )

Skolem constants of (forall ((A $$unsorted)) (empty A) ) : ( skv_2 ) Skolem constants of (forall ((A$$unsorted) (B $$unsorted) (C$$unsorted)) (or (not (subset A B)) (not (disjoint B C)) (disjoint A C)) ) :
( skv_3, skv_4, skv_5 )

Skolem constants of (forall ((C $$unsorted)) (or (not (in C skv_3)) (not (in C skv_5))) ) : ( skv_6 ) Skolem constants of (forall ((C$$unsorted)) (not (in C (set_intersection2 skv_3 skv_5))) ) :
( skv_7 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (= (= A B) (and (subset A B) (subset B A))) ) :
( skv_3, skv_4 )
( skv_4, skv_3 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (= (proper_subset A B) (and (subset A B) (not (= A B)))) ) :
( skv_3, skv_4 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (subset (set_intersection2 A B) A) ) :
( skv_3, skv_4 )
( skv_3, skv_5 )
( skv_4, skv_5 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (subset (set_difference A B) A) ) :
( skv_3, skv_4 )
( skv_4, skv_3 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (or (not (in A B)) (not (in B A))) ) :
( skv_3, skv_6 )
( skv_5, skv_6 )
( (set_intersection2 skv_3 skv_5), skv_7 )
( skv_6, skv_3 )
( skv_6, skv_5 )
( skv_7, (set_intersection2 skv_3 skv_5) )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (= (set_union2 B A) (set_union2 A B)) ) :
( skv_3, skv_4 )
( skv_3, (set_difference skv_4 skv_3) )
( skv_4, skv_3 )
( (set_difference skv_4 skv_3), skv_3 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (= (set_intersection2 B A) (set_intersection2 A B)) ) :
( skv_3, skv_4 )
( skv_3, skv_5 )
( skv_4, skv_3 )
( skv_4, skv_5 )
( skv_5, skv_3 )
( skv_5, skv_4 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (= (subset A B) (forall ((C $$unsorted)) (or (not (in C A)) (in C B)) )) ) : ( skv_3, skv_4 ) ( skv_4, skv_3 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (= (disjoint A B) (= empty_set (set_intersection2 A B))) ) : ( skv_3, skv_4 ) ( skv_3, skv_5 ) ( skv_4, skv_5 ) ( skv_5, skv_3 ) ( skv_5, skv_4 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (or (empty A) (not (empty (set_union2 A B)))) ) : ( skv_3, skv_4 ) ( skv_3, (set_difference skv_4 skv_3) ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (or (empty A) (not (empty (set_union2 B A)))) ) : ( skv_4, skv_3 ) ( (set_difference skv_4 skv_3), skv_3 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (= (= empty_set (set_difference A B)) (subset A B)) ) : ( skv_3, skv_4 ) ( skv_4, skv_3 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (or (not (disjoint A B)) (disjoint B A)) ) : ( skv_4, skv_5 ) ( skv_5, skv_3 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (or (not (subset A B)) (= B (set_union2 A B))) ) : ( skv_3, skv_4 ) ( skv_3, (set_difference skv_4 skv_3) ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (or (not (subset A B)) (= A (set_intersection2 A B))) ) : ( skv_3, skv_4 ) ( skv_3, skv_5 ) ( skv_4, skv_5 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (= (= empty_set (set_difference A B)) (subset A B)) ) : ( skv_3, skv_4 ) ( skv_4, skv_3 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (= (set_union2 A B) (set_union2 A (set_difference B A))) ) : ( skv_3, (set_difference skv_4 skv_3) ) ( skv_4, skv_3 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (or (disjoint A B) (not (forall ((C$$unsorted)) (or (not (in C A)) (not (in C B))) ))) ) :
( skv_3, skv_5 )
( skv_5, skv_3 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted) (BOUND_VARIABLE_789 $$unsorted)) (or (not (disjoint A B)) (not (in BOUND_VARIABLE_789 A)) (not (in BOUND_VARIABLE_789 B))) ) : ( skv_5, skv_4, skv_6 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (= (set_difference A B) (set_difference (set_union2 A B) B)) ) : ( skv_3, skv_4 ) ( skv_3, (set_difference skv_4 skv_3) ) ( skv_4, skv_3 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (or (not (subset A B)) (= B (set_union2 A (set_difference B A)))) ) : ( skv_3, skv_4 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (= (set_intersection2 A B) (set_difference A (set_difference A B))) ) : ( skv_3, skv_4 ) ( skv_3, skv_5 ) ( skv_4, skv_3 ) ( skv_4, skv_5 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (or (disjoint A B) (not (forall ((C$$unsorted)) (not (in C (set_intersection2 A B))) ))) ) :
( skv_3, skv_5 )
( skv_5, skv_3 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted) (BOUND_VARIABLE_829 $$unsorted)) (or (not (in BOUND_VARIABLE_829 (set_intersection2 A B))) (not (disjoint A B))) ) : ( skv_3, skv_4, skv_6 ) Instantiations of (forall ((A$$unsorted) (B $$unsorted)) (or (not (subset A B)) (not (proper_subset B A))) ) : ( skv_3, skv_4 ) Instantiations of (forall ((A$$unsorted)) (or (not (empty A)) (= empty_set A)) ) :
( skv_1 )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (or (not (in A B)) (not (empty B))) ) :
( skv_6, skv_3 )
( skv_6, skv_5 )
( skv_7, (set_intersection2 skv_3 skv_5) )

Instantiations of (forall ((A $$unsorted) (B$$unsorted)) (or (not (empty A)) (= A B) (not (empty B))) ) :
( empty_set, skv_1 )
( skv_1, empty_set )

Instantiations of (forall ((A $$unsorted) (B$$unsorted) (C $$unsorted)) (or (not (subset A B)) (not (subset C B)) (subset (set_union2 A C) B)) ) : ( skv_3, skv_3, (set_difference skv_4 skv_3) ) Instantiations of (forall ((C$$unsorted)) (or (not (in C skv_3)) (in C skv_4)) ) :
( skv_6 )

% SZS output end Proof for SEU140+2


### Sample solution for NLP042+1

% SZS status CounterSatisfiable for NLP042+1
% SZS output start FiniteModel for NLP042+1
(define-fun woman (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unsorte d_0$x1) (= @uc___unsorted_1 $x2))) (define-fun female (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unsort
ed_0 $x1) (= @uc___unsorted_1$x2)))
(define-fun human_person (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___ unsorted_0$x1) (= @uc___unsorted_1 $x2))) (define-fun animate (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unsor
ted_0 $x1) (= @uc___unsorted_1$x2)))
(define-fun human (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unsorte d_0$x1) (= @uc___unsorted_1 $x2))) (define-fun organism (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unso
rted_0 $x1) (= @uc___unsorted_1$x2)))
(define-fun living (($x1 $$unsorted) (x2$$unsorted)) Bool (not (and (= @uc___u nsorted_0$x1) (= @uc___unsorted_2 $x2)))) (define-fun impartial (($x1 $$unsorted) (x2$$unsorted)) Bool true)
(define-fun entity (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @uc___u nsorted_0$x1) (= @uc___unsorted_2 $x2)) true (and (= @uc___unsorted_0$x1) (= @
uc___unsorted_1 $x2)))) (define-fun mia_forename (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @
uc___unsorted_0 $x1) (= @uc___unsorted_3$x2)) false (ite (and (= @uc___unsorted
_0 $x1) (= @uc___unsorted_2$x2)) false (not (and (= @uc___unsorted_0 $x1) (= @u c___unsorted_1$x2))))))
(define-fun forename (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @uc__ _unsorted_0$x1) (= @uc___unsorted_3 $x2)) false (ite (and (= @uc___unsorted_0$
x1) (= @uc___unsorted_2 $x2)) false (not (and (= @uc___unsorted_0$x1) (= @uc___
unsorted_1 $x2)))))) (define-fun abstraction (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @u
c___unsorted_0 $x1) (= @uc___unsorted_3$x2)) false (ite (and (= @uc___unsorted_
0 $x1) (= @uc___unsorted_2$x2)) false (not (and (= @uc___unsorted_0 $x1) (= @uc ___unsorted_1$x2))))))
(define-fun unisex (($x1 $$unsorted) (x2$$unsorted)) Bool (not (and (= @uc___u nsorted_0$x1) (= @uc___unsorted_1 $x2)))) (define-fun general (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @uc___
unsorted_0 $x1) (= @uc___unsorted_3$x2)) false (ite (and (= @uc___unsorted_0 $x 1) (= @uc___unsorted_2$x2)) false (not (and (= @uc___unsorted_0 $x1) (= @uc___u nsorted_1$x2))))))
(define-fun nonhuman (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @uc__ _unsorted_0$x1) (= @uc___unsorted_1 $x2)) false (ite (and (= @uc___unsorted_0$
x1) (= @uc___unsorted_3 $x2)) false (not (and (= @uc___unsorted_0$x1) (= @uc___
unsorted_2 $x2)))))) (define-fun thing (($x1 $$unsorted) (x2$$unsorted)) Bool true)
(define-fun relation (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @uc__ _unsorted_0$x1) (= @uc___unsorted_3 $x2)) false (ite (and (= @uc___unsorted_0$
x1) (= @uc___unsorted_2 $x2)) false (not (and (= @uc___unsorted_0$x1) (= @uc___
unsorted_1 $x2)))))) (define-fun relname (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @uc___
unsorted_0 $x1) (= @uc___unsorted_3$x2)) false (ite (and (= @uc___unsorted_0 $x 1) (= @uc___unsorted_2$x2)) false (not (and (= @uc___unsorted_0 $x1) (= @uc___u nsorted_1$x2))))))
(define-fun object (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unsort ed_0$x1) (= @uc___unsorted_2 $x2))) (define-fun nonliving (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___uns
orted_0 $x1) (= @uc___unsorted_2$x2)))
(define-fun existent (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @uc__ _unsorted_0$x1) (= @uc___unsorted_2 $x2)) true (and (= @uc___unsorted_0$x1) (=
@uc___unsorted_1 $x2)))) (define-fun specific (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @uc__
_unsorted_0 $x1) (= @uc___unsorted_3$x2)) true (ite (and (= @uc___unsorted_0 $x 1) (= @uc___unsorted_2$x2)) true (and (= @uc___unsorted_0 $x1) (= @uc___unsorte d_1$x2)))))
(define-fun substance_matter (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @u c___unsorted_0$x1) (= @uc___unsorted_2 $x2))) (define-fun food (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unsorted
_0 $x1) (= @uc___unsorted_2$x2)))
(define-fun beverage (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unso rted_0$x1) (= @uc___unsorted_2 $x2))) (define-fun shake_beverage (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc_
__unsorted_0 $x1) (= @uc___unsorted_2$x2)))
(define-fun order (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unsorte d_0$x1) (= @uc___unsorted_3 $x2))) (define-fun event (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unsorte
d_0 $x1) (= @uc___unsorted_3$x2)))
(define-fun eventuality (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___u nsorted_0$x1) (= @uc___unsorted_3 $x2))) (define-fun nonexistent (($x1 $$unsorted) (x2$$unsorted)) Bool (ite (and (= @u
c___unsorted_0 $x1) (= @uc___unsorted_2$x2)) false (not (and (= @uc___unsorted_
0 $x1) (= @uc___unsorted_1$x2)))))
(define-fun singleton (($x1 $$unsorted) (x2$$unsorted)) Bool true) (define-fun act (($x1 $$unsorted) (x2$$unsorted)) Bool (and (= @uc___unsorted_
0 $x1) (= @uc___unsorted_3$x2)))
(define-fun of (($x1 $$unsorted) (x2$$unsorted) ($x3 $$unsorted)) Bool true) (define-fun nonreflexive ((x1$$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___ unsorted_0 x1) (= @uc___unsorted_3 x2))) (define-fun agent ((x1$$unsorted) ($x2 $$unsorted) (x3$$unsorted)) Bool (ite
(and (= @uc___unsorted_0 $x1) (= @uc___unsorted_3$x2) (= @uc___unsorted_2 $x3) ) false (ite (and (= @uc___unsorted_0$x1) (= @uc___unsorted_3 $x2) (= @uc___uns orted_3$x3)) false (not (and (= @uc___unsorted_0 $x1) (= @uc___unsorted_3$x2)
(= @uc___unsorted_0 $x3)))))) (define-fun patient (($x1 $$unsorted) (x2$$unsorted) ($x3 $$unsorted)) Bool (n ot (and (= @uc___unsorted_0 x1) (= @uc___unsorted_3 x2) (= @uc___unsorted_1 x 3)))) (define-fun actual_world ((_ufmt_1$$unsorted)) Bool true) (define-fun past ((_ufmt_1 $$unsorted) (_ufmt_2$$unsorted)) Bool true) ; cardinality of $$unsorted is 4 (declare-sort$$unsorted 0) ; rep: @uc___unsorted_0 ; rep: @uc___unsorted_1 ; rep: @uc___unsorted_2 ; rep: @uc___unsorted_3 % SZS output end FiniteModel for NLP042+1  ### Sample solution for SWV017+1 % SZS status Satisfiable for SWV017+1 % SZS output start FiniteModel for SWV017+1 (define-fun at () $$unsorted @uc___unsorted_0) (define-fun t ()$$unsorted @uc___unsorted_0) (define-fun key (($x1 $$unsorted) (x2$$unsorted)) $$unsorted @uc___unsorted_0) (define-fun a_holds ((x1$$unsorted)) Bool true)
(define-fun a () $$unsorted @uc___unsorted_0) (define-fun party_of_protocol ((x1$$unsorted)) Bool true)
(define-fun b () $$unsorted @uc___unsorted_0) (define-fun an_a_nonce ()$$unsorted @uc___unsorted_0)
(define-fun pair (($x1 $$unsorted) (x2$$unsorted)) $$unsorted @uc___unsorted_0 ) (define-fun sent ((x1$$unsorted) ($x2 $$unsorted) (x3$$unsorted)) $$unsorted @uc___unsorted_0) (define-fun message ((x1$$unsorted)) Bool true)
(define-fun a_stored (($x1 $$unsorted)) Bool true) (define-fun quadruple ((x1$$unsorted) ($x2 $$unsorted) (x3$$unsorted) ($x4$
$unsorted)) $$unsorted @uc___unsorted_0) (define-fun encrypt ((x1$$unsorted) ($x2 $$unsorted))$$unsorted @uc___unsorte
d_0)
(define-fun triple (($x1 $$unsorted) (x2$$unsorted) ($x3 $$unsorted))$$unsort
ed @uc___unsorted_0)
(define-fun bt () $$unsorted @uc___unsorted_0) (define-fun b_holds ((x1$$unsorted)) Bool true)
(define-fun fresh_to_b (($x1 $$unsorted)) Bool true) (define-fun generate_b_nonce ((x1$$unsorted)) $$unsorted @uc___unsorted_0) (define-fun generate_expiration_time ((x1$$unsorted)) $$unsorted @uc___unsorte d_0) (define-fun b_stored ((x1$$unsorted)) Bool true) (define-fun a_key (($x1 $$unsorted)) Bool (= @uc___unsorted_1 x1)) (define-fun t_holds ((x1$$unsorted)) Bool true)
(define-fun a_nonce (($x1 $$unsorted)) Bool (not (= @uc___unsorted_1 x1))) (define-fun generate_key ((x1$$unsorted)) $$unsorted @uc___unsorted_1) (define-fun intruder_message ((x1$$unsorted)) Bool true) (define-fun intruder_holds (($x1 $$unsorted)) Bool true) (define-fun an_intruder_nonce ()$$unsorted @uc___unsorted_0)
(define-fun fresh_intruder_nonce (($x1 $$unsorted)) Bool true) (define-fun generate_intruder_nonce ((x1$$unsorted)) $$unsorted @uc___unsorted _0) ; cardinality of$$unsorted is 2 (declare-sort $$unsorted 0) ; rep: @uc___unsorted_0 ; rep: @uc___unsorted_1 % SZS output end FiniteModel for SWV017+1  ## E 1.9.1 Stephan Schulz DHBW Stuttgart, Germany ### Sample solution for SEU140+2 # No SInE strategy applied # Trying AutoSched0 for 151 seconds # AutoSched0-Mode selected heuristic G_E___107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y # and selection function SelectMaxLComplexAvoidPosPred. # # Presaturation interreduction done # Proof found! # SZS status Theorem # SZS output start CNFRefutation. fof(c_0_0, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t3_xboole_0)). fof(c_0_1, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t63_xboole_1)). fof(c_0_2, axiom, (![X1]:![X2]:![X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2)))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', d4_xboole_0)). fof(c_0_3, axiom, (![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', d1_xboole_0)). fof(c_0_4, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', l32_xboole_1)). fof(c_0_5, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_0])). fof(c_0_6, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[c_0_1])). fof(c_0_7, plain, (![X1]:![X2]:![X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~in(X4,X2))))), inference(fof_simplification,[status(thm)],[c_0_2])). fof(c_0_8, plain, (![X1]:(X1=empty_set<=>![X2]:~in(X2,X1))), inference(fof_simplification,[status(thm)],[c_0_3])). fof(c_0_9, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X9,X7)|~in(X9,X8))|~disjoint(X7,X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])])). fof(c_0_10, negated_conjecture, (((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])). fof(c_0_11, plain, (![X5]:![X6]:![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:(((((in(X8,X5)|~in(X8,X7))|X7!=set_difference(X5,X6))&((~in(X8,X6)|~in(X8,X7))|X7!=set_difference(X5,X6)))&(((~in(X9,X5)|in(X9,X6))|in(X9,X7))|X7!=set_difference(X5,X6)))&(((~in(esk5_3(X10,X11,X12),X12)|(~in(esk5_3(X10,X11,X12),X10)|in(esk5_3(X10,X11,X12),X11)))|X12=set_difference(X10,X11))&(((in(esk5_3(X10,X11,X12),X10)|in(esk5_3(X10,X11,X12),X12))|X12=set_difference(X10,X11))&((~in(esk5_3(X10,X11,X12),X11)|in(esk5_3(X10,X11,X12),X12))|X12=set_difference(X10,X11)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])])). fof(c_0_12, lemma, (![X3]:![X4]:![X5]:![X6]:((set_difference(X3,X4)!=empty_set|subset(X3,X4))&(~subset(X5,X6)|set_difference(X5,X6)=empty_set))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])). fof(c_0_13, plain, (![X3]:![X4]:![X5]:((X3!=empty_set|~in(X4,X3))&(in(esk1_1(X5),X5)|X5=empty_set))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])). cnf(c_0_14,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_15,negated_conjecture,(disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_16,negated_conjecture,(~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_17,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_18,plain,(in(X4,X1)|in(X4,X3)|X1!=set_difference(X2,X3)|~in(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_19,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_20,negated_conjecture,(subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_21,plain,(~in(X1,X2)|X2!=empty_set), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_22,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)), inference(spm,[status(thm)],[c_0_14, c_0_15])). cnf(c_0_23,negated_conjecture,(in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_16, c_0_17])). cnf(c_0_24,plain,(in(X1,set_difference(X2,X3))|in(X1,X3)|~in(X1,X2)), inference(er,[status(thm)],[c_0_18])). cnf(c_0_25,negated_conjecture,(set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_19, c_0_20])). cnf(c_0_26,plain,(~in(X1,empty_set)), inference(er,[status(thm)],[c_0_21])). cnf(c_0_27,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_28,negated_conjecture,(~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_22, c_0_23])). cnf(c_0_29,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25]), c_0_26])). cnf(c_0_30,negated_conjecture,(in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_16, c_0_27])). cnf(c_0_31,negated_conjecture,(false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30])]), ['proof']). # SZS output end CNFRefutation.  ### Sample solution for NLP042+1 # No SInE strategy applied # Trying AutoSched0 for 151 seconds # AutoSched0-Mode selected heuristic H_____047_C18_F1_AE_R8_CS_SP_S2S # and selection function SelectNewComplexAHP. # # No proof found! # SZS status CounterSatisfiable # SZS output start Saturation. fof(c_0_0, conjecture, (~(?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', co1)). fof(c_0_1, axiom, (![X1]:![X2]:(shake_beverage(X1,X2)=>beverage(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax27)). fof(c_0_2, axiom, (![X1]:![X2]:(beverage(X1,X2)=>food(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax26)). fof(c_0_3, axiom, (![X1]:![X2]:(food(X1,X2)=>substance_matter(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax25)). fof(c_0_4, axiom, (![X1]:![X2]:(forename(X1,X2)=>relname(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax16)). fof(c_0_5, axiom, (![X1]:![X2]:(woman(X1,X2)=>human_person(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax8)). fof(c_0_6, axiom, (![X1]:![X2]:(substance_matter(X1,X2)=>object(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax24)). fof(c_0_7, axiom, (![X1]:![X2]:(relname(X1,X2)=>relation(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax15)). fof(c_0_8, axiom, (![X1]:![X2]:(human_person(X1,X2)=>organism(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax7)). fof(c_0_9, axiom, (![X1]:![X2]:(object(X1,X2)=>entity(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax23)). fof(c_0_10, axiom, (![X1]:![X2]:(relation(X1,X2)=>abstraction(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax14)). fof(c_0_11, axiom, (![X1]:![X2]:(event(X1,X2)=>eventuality(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax34)). fof(c_0_12, axiom, (![X1]:![X2]:(organism(X1,X2)=>entity(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax6)). fof(c_0_13, axiom, (![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax38)). fof(c_0_14, axiom, (![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax41)). fof(c_0_15, axiom, (![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax40)). fof(c_0_16, axiom, (![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax39)). fof(c_0_17, axiom, (![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax37)). fof(c_0_18, axiom, (![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax42)). fof(c_0_19, axiom, (![X1]:![X2]:(entity(X1,X2)=>specific(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax21)). fof(c_0_20, axiom, (![X1]:![X2]:(object(X1,X2)=>nonliving(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax19)). fof(c_0_21, axiom, (![X1]:![X2]:(object(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax17)). fof(c_0_22, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>nonhuman(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax12)). fof(c_0_23, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax10)). fof(c_0_24, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>nonexistent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax30)). fof(c_0_25, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>specific(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax31)). fof(c_0_26, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax29)). fof(c_0_27, axiom, (![X1]:![X2]:![X3]:![X4]:(((nonreflexive(X1,X2)&agent(X1,X2,X3))&patient(X1,X2,X4))=>X3!=X4)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax44)). fof(c_0_28, axiom, (![X1]:![X2]:(entity(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax22)). fof(c_0_29, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax13)). fof(c_0_30, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax33)). fof(c_0_31, axiom, (![X1]:![X2]:![X3]:(((entity(X1,X2)&forename(X1,X3))&of(X1,X3,X2))=>~(?[X4]:((forename(X1,X4)&X4!=X3)&of(X1,X4,X2))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax43)). fof(c_0_32, axiom, (![X1]:![X2]:(order(X1,X2)=>act(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax36)). fof(c_0_33, axiom, (![X1]:![X2]:(thing(X1,X2)=>singleton(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax32)). fof(c_0_34, axiom, (![X1]:![X2]:(entity(X1,X2)=>existent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax20)). fof(c_0_35, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>general(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax11)). fof(c_0_36, axiom, (![X1]:![X2]:(object(X1,X2)=>impartial(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax18)). fof(c_0_37, axiom, (![X1]:![X2]:(organism(X1,X2)=>impartial(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax5)). fof(c_0_38, axiom, (![X1]:![X2]:(organism(X1,X2)=>living(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax4)). fof(c_0_39, axiom, (![X1]:![X2]:(human_person(X1,X2)=>human(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax3)). fof(c_0_40, axiom, (![X1]:![X2]:(human_person(X1,X2)=>animate(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax2)). fof(c_0_41, axiom, (![X1]:![X2]:(act(X1,X2)=>event(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax35)). fof(c_0_42, axiom, (![X1]:![X2]:(woman(X1,X2)=>female(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax1)). fof(c_0_43, axiom, (![X1]:![X2]:(order(X1,X2)=>event(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax28)). fof(c_0_44, axiom, (![X1]:![X2]:(mia_forename(X1,X2)=>forename(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax9)). fof(c_0_45, negated_conjecture, (~(~(?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5)))))), inference(assume_negation,[status(cth)],[c_0_0])). fof(c_0_46, plain, (![X3]:![X4]:(~shake_beverage(X3,X4)|beverage(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])). fof(c_0_47, negated_conjecture, ((actual_world(esk1_0)&((((((((((of(esk1_0,esk3_0,esk2_0)&woman(esk1_0,esk2_0))&mia_forename(esk1_0,esk3_0))&forename(esk1_0,esk3_0))&shake_beverage(esk1_0,esk4_0))&event(esk1_0,esk5_0))&agent(esk1_0,esk5_0,esk2_0))&patient(esk1_0,esk5_0,esk4_0))&past(esk1_0,esk5_0))&nonreflexive(esk1_0,esk5_0))&order(esk1_0,esk5_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])). fof(c_0_48, plain, (![X3]:![X4]:(~beverage(X3,X4)|food(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])). cnf(c_0_49,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_50,negated_conjecture,(shake_beverage(esk1_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_47])). fof(c_0_51, plain, (![X3]:![X4]:(~food(X3,X4)|substance_matter(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])). cnf(c_0_52,plain,(food(X1,X2)|~beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_53,negated_conjecture,(beverage(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_49, c_0_50]), ['final']). fof(c_0_54, plain, (![X3]:![X4]:(~forename(X3,X4)|relname(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])). fof(c_0_55, plain, (![X3]:![X4]:(~woman(X3,X4)|human_person(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])). fof(c_0_56, plain, (![X3]:![X4]:(~substance_matter(X3,X4)|object(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])). cnf(c_0_57,plain,(substance_matter(X1,X2)|~food(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_51])). cnf(c_0_58,negated_conjecture,(food(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_52, c_0_53]), ['final']). fof(c_0_59, plain, (![X3]:![X4]:(~relname(X3,X4)|relation(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])). cnf(c_0_60,plain,(relname(X1,X2)|~forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_54])). cnf(c_0_61,negated_conjecture,(forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_47])). fof(c_0_62, plain, (![X3]:![X4]:(~human_person(X3,X4)|organism(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])). cnf(c_0_63,plain,(human_person(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_55])). cnf(c_0_64,negated_conjecture,(woman(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47])). fof(c_0_65, plain, (![X3]:![X4]:(~object(X3,X4)|entity(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])). cnf(c_0_66,plain,(object(X1,X2)|~substance_matter(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_56])). cnf(c_0_67,negated_conjecture,(substance_matter(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_57, c_0_58]), ['final']). fof(c_0_68, plain, (![X3]:![X4]:(~relation(X3,X4)|abstraction(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])). cnf(c_0_69,plain,(relation(X1,X2)|~relname(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_59])). cnf(c_0_70,negated_conjecture,(relname(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_60, c_0_61]), ['final']). fof(c_0_71, plain, (![X3]:![X4]:(~event(X3,X4)|eventuality(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])). fof(c_0_72, plain, (![X3]:![X4]:(~organism(X3,X4)|entity(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])). cnf(c_0_73,plain,(organism(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_62])). cnf(c_0_74,negated_conjecture,(human_person(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_63, c_0_64]), ['final']). fof(c_0_75, plain, (![X1]:![X2]:(existent(X1,X2)=>~nonexistent(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_13])). fof(c_0_76, plain, (![X1]:![X2]:(specific(X1,X2)=>~general(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_14])). fof(c_0_77, plain, (![X1]:![X2]:(nonliving(X1,X2)=>~living(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_15])). fof(c_0_78, plain, (![X1]:![X2]:(nonhuman(X1,X2)=>~human(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_16])). fof(c_0_79, plain, (![X1]:![X2]:(animate(X1,X2)=>~nonliving(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_17])). fof(c_0_80, plain, (![X1]:![X2]:(unisex(X1,X2)=>~female(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_18])). fof(c_0_81, plain, (![X3]:![X4]:(~entity(X3,X4)|specific(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])). cnf(c_0_82,plain,(entity(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_83,negated_conjecture,(object(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_66, c_0_67]), ['final']). fof(c_0_84, plain, (![X3]:![X4]:(~object(X3,X4)|nonliving(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])). fof(c_0_85, plain, (![X3]:![X4]:(~object(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])). fof(c_0_86, plain, (![X3]:![X4]:(~abstraction(X3,X4)|nonhuman(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])). cnf(c_0_87,plain,(abstraction(X1,X2)|~relation(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_68])). cnf(c_0_88,negated_conjecture,(relation(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_69, c_0_70]), ['final']). fof(c_0_89, plain, (![X3]:![X4]:(~abstraction(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])). fof(c_0_90, plain, (![X3]:![X4]:(~eventuality(X3,X4)|nonexistent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])). cnf(c_0_91,plain,(eventuality(X1,X2)|~event(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_71])). cnf(c_0_92,negated_conjecture,(event(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47])). fof(c_0_93, plain, (![X3]:![X4]:(~eventuality(X3,X4)|specific(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])). cnf(c_0_94,plain,(entity(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_72])). cnf(c_0_95,negated_conjecture,(organism(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_73, c_0_74]), ['final']). fof(c_0_96, plain, (![X3]:![X4]:(~eventuality(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])). fof(c_0_97, plain, (![X5]:![X6]:![X7]:![X8]:(((~nonreflexive(X5,X6)|~agent(X5,X6,X7))|~patient(X5,X6,X8))|X7!=X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])). fof(c_0_98, plain, (![X3]:![X4]:(~entity(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])). fof(c_0_99, plain, (![X3]:![X4]:(~abstraction(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])). fof(c_0_100, plain, (![X3]:![X4]:(~eventuality(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])). fof(c_0_101, plain, (![X5]:![X6]:![X7]:![X8]:(((~entity(X5,X6)|~forename(X5,X7))|~of(X5,X7,X6))|((~forename(X5,X8)|X8=X7)|~of(X5,X8,X6)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])). fof(c_0_102, plain, (![X3]:![X4]:(~order(X3,X4)|act(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])). fof(c_0_103, plain, (![X3]:![X4]:(~thing(X3,X4)|singleton(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])). fof(c_0_104, plain, (![X3]:![X4]:(~entity(X3,X4)|existent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])). fof(c_0_105, plain, (![X3]:![X4]:(~abstraction(X3,X4)|general(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])). fof(c_0_106, plain, (![X3]:![X4]:(~object(X3,X4)|impartial(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])). fof(c_0_107, plain, (![X3]:![X4]:(~organism(X3,X4)|impartial(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])). fof(c_0_108, plain, (![X3]:![X4]:(~organism(X3,X4)|living(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])). fof(c_0_109, plain, (![X3]:![X4]:(~human_person(X3,X4)|human(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])). fof(c_0_110, plain, (![X3]:![X4]:(~human_person(X3,X4)|animate(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])). fof(c_0_111, plain, (![X3]:![X4]:(~act(X3,X4)|event(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])). fof(c_0_112, plain, (![X3]:![X4]:(~woman(X3,X4)|female(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])). fof(c_0_113, plain, (![X3]:![X4]:(~order(X3,X4)|event(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])). fof(c_0_114, plain, (![X3]:![X4]:(~mia_forename(X3,X4)|forename(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])). fof(c_0_115, plain, (![X3]:![X4]:(~existent(X3,X4)|~nonexistent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])). fof(c_0_116, plain, (![X3]:![X4]:(~specific(X3,X4)|~general(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])). fof(c_0_117, plain, (![X3]:![X4]:(~nonliving(X3,X4)|~living(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])). fof(c_0_118, plain, (![X3]:![X4]:(~nonhuman(X3,X4)|~human(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])). fof(c_0_119, plain, (![X3]:![X4]:(~animate(X3,X4)|~nonliving(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])). fof(c_0_120, plain, (![X3]:![X4]:(~unisex(X3,X4)|~female(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])])). cnf(c_0_121,plain,(specific(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_81])). cnf(c_0_122,negated_conjecture,(entity(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_82, c_0_83]), ['final']). cnf(c_0_123,plain,(nonliving(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_124,plain,(unisex(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_85])). cnf(c_0_125,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_86])). cnf(c_0_126,negated_conjecture,(abstraction(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_87, c_0_88]), ['final']). cnf(c_0_127,plain,(unisex(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_89])). cnf(c_0_128,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_129,negated_conjecture,(eventuality(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_91, c_0_92]), ['final']). cnf(c_0_130,plain,(specific(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_93])). cnf(c_0_131,negated_conjecture,(entity(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_94, c_0_95]), ['final']). cnf(c_0_132,plain,(unisex(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_96])). cnf(c_0_133,plain,(X1!=X2|~patient(X3,X4,X2)|~agent(X3,X4,X1)|~nonreflexive(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_97])). cnf(c_0_134,plain,(thing(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_98])). cnf(c_0_135,plain,(thing(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_99])). cnf(c_0_136,plain,(thing(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_100])). cnf(c_0_137,plain,(X2=X4|~of(X1,X2,X3)|~forename(X1,X2)|~of(X1,X4,X3)|~forename(X1,X4)|~entity(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_101])). cnf(c_0_138,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_139,plain,(act(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_102])). cnf(c_0_140,plain,(singleton(X1,X2)|~thing(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_103])). cnf(c_0_141,plain,(existent(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_104])). cnf(c_0_142,plain,(general(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_105])). cnf(c_0_143,plain,(impartial(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_106])). cnf(c_0_144,plain,(impartial(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_107])). cnf(c_0_145,plain,(living(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_108])). cnf(c_0_146,plain,(human(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_109])). cnf(c_0_147,plain,(animate(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_110])). cnf(c_0_148,plain,(event(X1,X2)|~act(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_111])). cnf(c_0_149,plain,(female(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_112])). cnf(c_0_150,plain,(event(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_113])). cnf(c_0_151,plain,(forename(X1,X2)|~mia_forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_114])). cnf(c_0_152,plain,(~nonexistent(X1,X2)|~existent(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_115])). cnf(c_0_153,plain,(~general(X1,X2)|~specific(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_116])). cnf(c_0_154,plain,(~living(X1,X2)|~nonliving(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_117])). cnf(c_0_155,plain,(~human(X1,X2)|~nonhuman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_118])). cnf(c_0_156,plain,(~nonliving(X1,X2)|~animate(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_119])). cnf(c_0_157,plain,(~female(X1,X2)|~unisex(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_120])). cnf(c_0_158,negated_conjecture,(specific(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_121, c_0_122]), ['final']). cnf(c_0_159,negated_conjecture,(nonliving(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_123, c_0_83]), ['final']). cnf(c_0_160,negated_conjecture,(unisex(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_124, c_0_83]), ['final']). cnf(c_0_161,negated_conjecture,(nonhuman(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_125, c_0_126]), ['final']). cnf(c_0_162,negated_conjecture,(unisex(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_127, c_0_126]), ['final']). cnf(c_0_163,negated_conjecture,(nonexistent(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_128, c_0_129]), ['final']). cnf(c_0_164,negated_conjecture,(specific(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_130, c_0_129]), ['final']). cnf(c_0_165,negated_conjecture,(specific(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_121, c_0_131]), ['final']). cnf(c_0_166,negated_conjecture,(unisex(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_132, c_0_129]), ['final']). cnf(c_0_167,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)), inference(er,[status(thm)],[c_0_133]), ['final']). cnf(c_0_168,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_169,negated_conjecture,(nonreflexive(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_170,negated_conjecture,(thing(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_134, c_0_122]), ['final']). cnf(c_0_171,negated_conjecture,(thing(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_135, c_0_126]), ['final']). cnf(c_0_172,negated_conjecture,(thing(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_136, c_0_129]), ['final']). cnf(c_0_173,negated_conjecture,(order(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_174,negated_conjecture,(thing(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_134, c_0_131]), ['final']). cnf(c_0_175,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_176,negated_conjecture,(past(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_177,negated_conjecture,(mia_forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_178,negated_conjecture,(actual_world(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_179,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_138]), c_0_61]), c_0_131])]), ['final']). cnf(c_0_180,plain,(X1=X2|~of(X3,X2,X4)|~of(X3,X1,X4)|~forename(X3,X2)|~forename(X3,X1)|~entity(X3,X4)), c_0_137, ['final']). cnf(c_0_181,plain,(act(X1,X2)|~order(X1,X2)), c_0_139, ['final']). cnf(c_0_182,plain,(singleton(X1,X2)|~thing(X1,X2)), c_0_140, ['final']). cnf(c_0_183,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)), c_0_128, ['final']). cnf(c_0_184,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)), c_0_49, ['final']). cnf(c_0_185,plain,(specific(X1,X2)|~eventuality(X1,X2)), c_0_130, ['final']). cnf(c_0_186,plain,(specific(X1,X2)|~entity(X1,X2)), c_0_121, ['final']). cnf(c_0_187,plain,(existent(X1,X2)|~entity(X1,X2)), c_0_141, ['final']). cnf(c_0_188,plain,(nonliving(X1,X2)|~object(X1,X2)), c_0_123, ['final']). cnf(c_0_189,plain,(relname(X1,X2)|~forename(X1,X2)), c_0_60, ['final']). cnf(c_0_190,plain,(thing(X1,X2)|~eventuality(X1,X2)), c_0_136, ['final']). cnf(c_0_191,plain,(thing(X1,X2)|~abstraction(X1,X2)), c_0_135, ['final']). cnf(c_0_192,plain,(thing(X1,X2)|~entity(X1,X2)), c_0_134, ['final']). cnf(c_0_193,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)), c_0_125, ['final']). cnf(c_0_194,plain,(general(X1,X2)|~abstraction(X1,X2)), c_0_142, ['final']). cnf(c_0_195,plain,(unisex(X1,X2)|~eventuality(X1,X2)), c_0_132, ['final']). cnf(c_0_196,plain,(unisex(X1,X2)|~object(X1,X2)), c_0_124, ['final']). cnf(c_0_197,plain,(unisex(X1,X2)|~abstraction(X1,X2)), c_0_127, ['final']). cnf(c_0_198,plain,(impartial(X1,X2)|~object(X1,X2)), c_0_143, ['final']). cnf(c_0_199,plain,(impartial(X1,X2)|~organism(X1,X2)), c_0_144, ['final']). cnf(c_0_200,plain,(living(X1,X2)|~organism(X1,X2)), c_0_145, ['final']). cnf(c_0_201,plain,(organism(X1,X2)|~human_person(X1,X2)), c_0_73, ['final']). cnf(c_0_202,plain,(human(X1,X2)|~human_person(X1,X2)), c_0_146, ['final']). cnf(c_0_203,plain,(animate(X1,X2)|~human_person(X1,X2)), c_0_147, ['final']). cnf(c_0_204,plain,(eventuality(X1,X2)|~event(X1,X2)), c_0_91, ['final']). cnf(c_0_205,plain,(event(X1,X2)|~act(X1,X2)), c_0_148, ['final']). cnf(c_0_206,plain,(female(X1,X2)|~woman(X1,X2)), c_0_149, ['final']). cnf(c_0_207,plain,(event(X1,X2)|~order(X1,X2)), c_0_150, ['final']). cnf(c_0_208,plain,(food(X1,X2)|~beverage(X1,X2)), c_0_52, ['final']). cnf(c_0_209,plain,(substance_matter(X1,X2)|~food(X1,X2)), c_0_57, ['final']). cnf(c_0_210,plain,(object(X1,X2)|~substance_matter(X1,X2)), c_0_66, ['final']). cnf(c_0_211,plain,(relation(X1,X2)|~relname(X1,X2)), c_0_69, ['final']). cnf(c_0_212,plain,(abstraction(X1,X2)|~relation(X1,X2)), c_0_87, ['final']). cnf(c_0_213,plain,(forename(X1,X2)|~mia_forename(X1,X2)), c_0_151, ['final']). cnf(c_0_214,plain,(entity(X1,X2)|~object(X1,X2)), c_0_82, ['final']). cnf(c_0_215,plain,(entity(X1,X2)|~organism(X1,X2)), c_0_94, ['final']). cnf(c_0_216,plain,(human_person(X1,X2)|~woman(X1,X2)), c_0_63, ['final']). cnf(c_0_217,plain,(~nonexistent(X1,X2)|~existent(X1,X2)), c_0_152, ['final']). cnf(c_0_218,plain,(~specific(X1,X2)|~general(X1,X2)), c_0_153, ['final']). cnf(c_0_219,plain,(~nonliving(X1,X2)|~living(X1,X2)), c_0_154, ['final']). cnf(c_0_220,plain,(~nonhuman(X1,X2)|~human(X1,X2)), c_0_155, ['final']). cnf(c_0_221,plain,(~nonliving(X1,X2)|~animate(X1,X2)), c_0_156, ['final']). cnf(c_0_222,plain,(~unisex(X1,X2)|~female(X1,X2)), c_0_157, ['final']). cnf(c_0_223,negated_conjecture,(~general(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_153, c_0_158]), ['final']). cnf(c_0_224,negated_conjecture,(~living(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_154, c_0_159]), ['final']). cnf(c_0_225,negated_conjecture,(~animate(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_156, c_0_159]), ['final']). cnf(c_0_226,negated_conjecture,(~female(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_157, c_0_160]), ['final']). cnf(c_0_227,negated_conjecture,(~human(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_155, c_0_161]), ['final']). cnf(c_0_228,negated_conjecture,(~female(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_157, c_0_162]), ['final']). cnf(c_0_229,negated_conjecture,(~existent(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_152, c_0_163]), ['final']). cnf(c_0_230,negated_conjecture,(~general(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_153, c_0_164]), ['final']). cnf(c_0_231,negated_conjecture,(~general(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_153, c_0_165]), ['final']). cnf(c_0_232,negated_conjecture,(~female(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_157, c_0_166]), ['final']). cnf(c_0_233,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167, c_0_168]), c_0_169])]), ['final']). cnf(c_0_234,negated_conjecture,(singleton(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_140, c_0_170]), ['final']). cnf(c_0_235,negated_conjecture,(existent(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_141, c_0_122]), ['final']). cnf(c_0_236,negated_conjecture,(impartial(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_143, c_0_83]), ['final']). cnf(c_0_237,negated_conjecture,(singleton(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_140, c_0_171]), ['final']). cnf(c_0_238,negated_conjecture,(general(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_142, c_0_126]), ['final']). cnf(c_0_239,negated_conjecture,(singleton(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_140, c_0_172]), ['final']). cnf(c_0_240,negated_conjecture,(act(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_139, c_0_173]), ['final']). cnf(c_0_241,negated_conjecture,(singleton(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_140, c_0_174]), ['final']). cnf(c_0_242,negated_conjecture,(existent(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_141, c_0_131]), ['final']). cnf(c_0_243,negated_conjecture,(impartial(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_144, c_0_95]), ['final']). cnf(c_0_244,negated_conjecture,(living(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_145, c_0_95]), ['final']). cnf(c_0_245,negated_conjecture,(human(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_146, c_0_74]), ['final']). cnf(c_0_246,negated_conjecture,(animate(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_147, c_0_74]), ['final']). cnf(c_0_247,negated_conjecture,(female(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_149, c_0_64]), ['final']). cnf(c_0_248,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)), c_0_168, ['final']). cnf(c_0_249,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)), c_0_175, ['final']). cnf(c_0_250,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)), c_0_138, ['final']). cnf(c_0_251,negated_conjecture,(past(esk1_0,esk5_0)), c_0_176, ['final']). cnf(c_0_252,negated_conjecture,(nonreflexive(esk1_0,esk5_0)), c_0_169, ['final']). cnf(c_0_253,negated_conjecture,(event(esk1_0,esk5_0)), c_0_92, ['final']). cnf(c_0_254,negated_conjecture,(order(esk1_0,esk5_0)), c_0_173, ['final']). cnf(c_0_255,negated_conjecture,(shake_beverage(esk1_0,esk4_0)), c_0_50, ['final']). cnf(c_0_256,negated_conjecture,(forename(esk1_0,esk3_0)), c_0_61, ['final']). cnf(c_0_257,negated_conjecture,(mia_forename(esk1_0,esk3_0)), c_0_177, ['final']). cnf(c_0_258,negated_conjecture,(woman(esk1_0,esk2_0)), c_0_64, ['final']). cnf(c_0_259,negated_conjecture,(actual_world(esk1_0)), c_0_178, ['final']). # SZS output end Saturation.  ### Sample solution for SWV017+1 # No SInE strategy applied # Trying AutoSched0 for 151 seconds # AutoSched0-Mode selected heuristic H_____047_C18_F1_PI_AE_R8_CS_SP_S2S # and selection function SelectNewComplexAHP. # # No proof found! # SZS status Satisfiable # SZS output start Saturation. fof(c_0_0, axiom, (![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:((((message(sent(X1,t,triple(X1,X2,encrypt(triple(X3,X4,X5),X6))))&t_holds(key(X6,X1)))&t_holds(key(X7,X3)))&a_nonce(X4))=>message(sent(t,X3,triple(encrypt(quadruple(X1,X4,generate_key(X4),X5),X7),encrypt(triple(X3,generate_key(X4),X5),X6),X2))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', server_t_generates_key)). fof(c_0_1, axiom, (![X1]:![X2]:((message(sent(X1,b,pair(X1,X2)))&fresh_to_b(X2))=>(message(sent(b,t,triple(b,generate_b_nonce(X2),encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))))&b_stored(pair(X1,X2))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', b_creates_freash_nonces_in_time)). fof(c_0_2, axiom, (t_holds(key(bt,b))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', t_holds_key_bt_for_b)). fof(c_0_3, axiom, (![X1]:![X2]:![X3]:(message(sent(X1,X2,X3))=>intruder_message(X3))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_can_record)). fof(c_0_4, axiom, (message(sent(a,b,pair(a,an_a_nonce)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_sent_message_i_to_b)). fof(c_0_5, axiom, (fresh_to_b(an_a_nonce)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', nonce_a_is_fresh_to_b)). fof(c_0_6, axiom, (![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:((message(sent(t,a,triple(encrypt(quadruple(X5,X6,X3,X2),at),X4,X1)))&a_stored(pair(X5,X6)))=>(message(sent(a,X5,pair(X4,encrypt(X1,X3))))&a_holds(key(X3,X5))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_forwards_secure)). fof(c_0_7, axiom, (t_holds(key(at,a))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', t_holds_key_at_for_a)). fof(c_0_8, axiom, (![X1]:![X2]:![X3]:(((intruder_message(X1)&party_of_protocol(X2))&party_of_protocol(X3))=>message(sent(X2,X3,X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_message_sent)). fof(c_0_9, axiom, (![X1]:![X2]:![X3]:(intruder_message(triple(X1,X2,X3))=>((intruder_message(X1)&intruder_message(X2))&intruder_message(X3)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_decomposes_triples)). fof(c_0_10, axiom, (a_stored(pair(b,an_a_nonce))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_stored_message_i)). fof(c_0_11, axiom, (a_nonce(an_a_nonce)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', an_a_nonce_is_a_nonce)). fof(c_0_12, axiom, (party_of_protocol(b)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', b_is_party_of_protocol)). fof(c_0_13, axiom, (![X1]:![X2]:((intruder_message(X1)&intruder_message(X2))=>intruder_message(pair(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_composes_pairs)). fof(c_0_14, axiom, (party_of_protocol(t)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', t_is_party_of_protocol)). fof(c_0_15, axiom, (![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))=>intruder_message(triple(X1,X2,X3)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_composes_triples)). fof(c_0_16, axiom, (party_of_protocol(a)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_is_party_of_protocol)). fof(c_0_17, axiom, (![X2]:![X4]:![X5]:(((message(sent(X4,b,pair(encrypt(triple(X4,X2,generate_expiration_time(X5)),bt),encrypt(generate_b_nonce(X5),X2))))&a_key(X2))&b_stored(pair(X4,X5)))=>b_holds(key(X2,X4)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', b_accepts_secure_session_key)). fof(c_0_18, axiom, (![X1]:![X2]:(intruder_message(pair(X1,X2))=>(intruder_message(X1)&intruder_message(X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_decomposes_pairs)). fof(c_0_19, axiom, (![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(encrypt(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_key_encrypts)). fof(c_0_20, axiom, (![X2]:![X3]:((intruder_message(X2)&party_of_protocol(X3))=>intruder_holds(key(X2,X3)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_holds_key)). fof(c_0_21, axiom, (![X1]:a_key(generate_key(X1))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', generated_keys_are_keys)). fof(c_0_22, axiom, (![X1]:~(a_nonce(generate_key(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', generated_keys_are_not_nonces)). fof(c_0_23, axiom, (![X1]:(fresh_intruder_nonce(X1)=>(fresh_to_b(X1)&intruder_message(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', fresh_intruder_nonces_are_fresh_to_b)). fof(c_0_24, axiom, (![X1]:(fresh_intruder_nonce(X1)=>fresh_intruder_nonce(generate_intruder_nonce(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', can_generate_more_fresh_intruder_nonces)). fof(c_0_25, axiom, (![X1]:![X2]:![X3]:(((intruder_message(encrypt(X1,X2))&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_interception)). fof(c_0_26, axiom, (![X1]:![X2]:![X3]:![X4]:(intruder_message(quadruple(X1,X2,X3,X4))=>(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))&intruder_message(X4)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_decomposes_quadruples)). fof(c_0_27, axiom, (![X1]:![X2]:![X3]:![X4]:((((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))&intruder_message(X4))=>intruder_message(quadruple(X1,X2,X3,X4)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_composes_quadruples)). fof(c_0_28, axiom, (![X1]:~((a_key(X1)&a_nonce(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', nothing_is_a_nonce_and_a_key)). fof(c_0_29, axiom, (![X1]:(a_nonce(generate_expiration_time(X1))&a_nonce(generate_b_nonce(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', generated_times_and_nonces_are_nonces)). fof(c_0_30, axiom, (fresh_intruder_nonce(an_intruder_nonce)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', an_intruder_nonce_is_a_fresh_intruder_nonce)). fof(c_0_31, axiom, (b_holds(key(bt,t))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', b_hold_key_bt_for_t)). fof(c_0_32, axiom, (a_holds(key(at,t))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_holds_key_at_for_t)). fof(c_0_33, plain, (![X8]:![X9]:![X10]:![X11]:![X12]:![X13]:![X14]:((((~message(sent(X8,t,triple(X8,X9,encrypt(triple(X10,X11,X12),X13))))|~t_holds(key(X13,X8)))|~t_holds(key(X14,X10)))|~a_nonce(X11))|message(sent(t,X10,triple(encrypt(quadruple(X8,X11,generate_key(X11),X12),X14),encrypt(triple(X10,generate_key(X11),X12),X13),X9))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_0])])). fof(c_0_34, plain, (![X3]:![X4]:((message(sent(b,t,triple(b,generate_b_nonce(X4),encrypt(triple(X3,X4,generate_expiration_time(X4)),bt))))|(~message(sent(X3,b,pair(X3,X4)))|~fresh_to_b(X4)))&(b_stored(pair(X3,X4))|(~message(sent(X3,b,pair(X3,X4)))|~fresh_to_b(X4))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])). cnf(c_0_35,plain,(message(sent(t,X1,triple(encrypt(quadruple(X2,X3,generate_key(X3),X4),X5),encrypt(triple(X1,generate_key(X3),X4),X6),X7)))|~a_nonce(X3)|~t_holds(key(X5,X1))|~t_holds(key(X6,X2))|~message(sent(X2,t,triple(X2,X7,encrypt(triple(X1,X3,X4),X6))))), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_36,plain,(t_holds(key(bt,b))), inference(split_conjunct,[status(thm)],[c_0_2])). fof(c_0_37, plain, (![X4]:![X5]:![X6]:(~message(sent(X4,X5,X6))|intruder_message(X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])). cnf(c_0_38,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_39,plain,(message(sent(a,b,pair(a,an_a_nonce)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_40,plain,(fresh_to_b(an_a_nonce)), inference(split_conjunct,[status(thm)],[c_0_5])). fof(c_0_41, plain, (![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:((message(sent(a,X11,pair(X10,encrypt(X7,X9))))|(~message(sent(t,a,triple(encrypt(quadruple(X11,X12,X9,X8),at),X10,X7)))|~a_stored(pair(X11,X12))))&(a_holds(key(X9,X11))|(~message(sent(t,a,triple(encrypt(quadruple(X11,X12,X9,X8),at),X10,X7)))|~a_stored(pair(X11,X12)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])). cnf(c_0_42,plain,(message(sent(t,X1,triple(encrypt(quadruple(b,X2,generate_key(X2),X3),X4),encrypt(triple(X1,generate_key(X2),X3),bt),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(b,t,triple(b,X5,encrypt(triple(X1,X2,X3),bt))))), inference(spm,[status(thm)],[c_0_35, c_0_36]), ['final']). cnf(c_0_43,plain,(t_holds(key(at,a))), inference(split_conjunct,[status(thm)],[c_0_7])). fof(c_0_44, plain, (![X4]:![X5]:![X6]:(((~intruder_message(X4)|~party_of_protocol(X5))|~party_of_protocol(X6))|message(sent(X5,X6,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])). fof(c_0_45, plain, (![X4]:![X5]:![X6]:(((intruder_message(X4)|~intruder_message(triple(X4,X5,X6)))&(intruder_message(X5)|~intruder_message(triple(X4,X5,X6))))&(intruder_message(X6)|~intruder_message(triple(X4,X5,X6))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])). cnf(c_0_46,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_47,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_40])]), ['final']). cnf(c_0_48,plain,(message(sent(a,X1,pair(X5,encrypt(X6,X3))))|~a_stored(pair(X1,X2))|~message(sent(t,a,triple(encrypt(quadruple(X1,X2,X3,X4),at),X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_49,plain,(a_stored(pair(b,an_a_nonce))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_50,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(a,X1,X2),bt))))), inference(spm,[status(thm)],[c_0_42, c_0_43]), ['final']). cnf(c_0_51,plain,(a_nonce(an_a_nonce)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_52,plain,(b_stored(pair(X2,X1))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_53,plain,(message(sent(X1,X2,X3))|~party_of_protocol(X2)|~party_of_protocol(X1)|~intruder_message(X3)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_54,plain,(party_of_protocol(b)), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_55, plain, (![X3]:![X4]:((~intruder_message(X3)|~intruder_message(X4))|intruder_message(pair(X3,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])). cnf(c_0_56,plain,(party_of_protocol(t)), inference(split_conjunct,[status(thm)],[c_0_14])). fof(c_0_57, plain, (![X4]:![X5]:![X6]:(((~intruder_message(X4)|~intruder_message(X5))|~intruder_message(X6))|intruder_message(triple(X4,X5,X6)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])). cnf(c_0_58,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_45])). cnf(c_0_59,plain,(intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))), inference(spm,[status(thm)],[c_0_46, c_0_47]), ['final']). cnf(c_0_60,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2)))), inference(spm,[status(thm)],[c_0_48, c_0_49]), ['final']). cnf(c_0_61,plain,(party_of_protocol(a)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_62,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_47]), c_0_51])]), ['final']). fof(c_0_63, plain, (![X6]:![X7]:![X8]:(((~message(sent(X7,b,pair(encrypt(triple(X7,X6,generate_expiration_time(X8)),bt),encrypt(generate_b_nonce(X8),X6))))|~a_key(X6))|~b_stored(pair(X7,X8)))|b_holds(key(X6,X7)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])). cnf(c_0_64,plain,(b_stored(pair(X1,X2))|~intruder_message(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_54])]), ['final']). cnf(c_0_65,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_55])). fof(c_0_66, plain, (![X3]:![X4]:((intruder_message(X3)|~intruder_message(pair(X3,X4)))&(intruder_message(X4)|~intruder_message(pair(X3,X4))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])). cnf(c_0_67,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_53]), c_0_56]), c_0_54])]), ['final']). cnf(c_0_68,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_57])). cnf(c_0_69,plain,(intruder_message(b)), inference(spm,[status(thm)],[c_0_58, c_0_59]), ['final']). cnf(c_0_70,plain,(intruder_message(X3)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_45])). cnf(c_0_71,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(pair(X2,X1))|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_53]), c_0_54])]), ['final']). cnf(c_0_72,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_53]), c_0_61]), c_0_56])]), ['final']). cnf(c_0_73,plain,(intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))), inference(spm,[status(thm)],[c_0_46, c_0_62]), ['final']). cnf(c_0_74,plain,(b_holds(key(X1,X2))|~b_stored(pair(X2,X3))|~a_key(X1)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))), inference(split_conjunct,[status(thm)],[c_0_63])). cnf(c_0_75,plain,(b_stored(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_64, c_0_65]), ['final']). fof(c_0_76, plain, (![X4]:![X5]:![X6]:(((~intruder_message(X4)|~intruder_holds(key(X5,X6)))|~party_of_protocol(X6))|intruder_message(encrypt(X4,X5)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])). fof(c_0_77, plain, (![X4]:![X5]:((~intruder_message(X4)|~party_of_protocol(X5))|intruder_holds(key(X4,X5)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])). cnf(c_0_78,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_66])). cnf(c_0_79,plain,(intruder_message(pair(a,an_a_nonce))), inference(spm,[status(thm)],[c_0_46, c_0_39]), ['final']). cnf(c_0_80,plain,(b_stored(pair(a,an_a_nonce))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_39]), c_0_40])]), ['final']). cnf(c_0_81,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(a,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_69])]), ['final']). cnf(c_0_82,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_70, c_0_59]), ['final']). cnf(c_0_83,plain,(message(sent(t,X1,triple(encrypt(quadruple(a,X2,generate_key(X2),X3),X4),encrypt(triple(X1,generate_key(X2),X3),at),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(a,t,triple(a,X5,encrypt(triple(X1,X2,X3),at))))), inference(spm,[status(thm)],[c_0_35, c_0_43]), ['final']). cnf(c_0_84,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_71, c_0_65]), ['final']). cnf(c_0_85,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X3,X4),at))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_72, c_0_68]), ['final']). cnf(c_0_86,plain,(intruder_message(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at))), inference(spm,[status(thm)],[c_0_58, c_0_73]), ['final']). cnf(c_0_87,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_74, c_0_75]), ['final']). cnf(c_0_88,plain,(intruder_message(encrypt(X1,X2))|~party_of_protocol(X3)|~intruder_holds(key(X2,X3))|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_76])). cnf(c_0_89,plain,(intruder_holds(key(X1,X2))|~party_of_protocol(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_77])). cnf(c_0_90,plain,(intruder_message(a)), inference(spm,[status(thm)],[c_0_78, c_0_79]), ['final']). cnf(c_0_91,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))))), inference(spm,[status(thm)],[c_0_60, c_0_62]), ['final']). cnf(c_0_92,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(b,X1,X2),bt))))), inference(spm,[status(thm)],[c_0_42, c_0_36]), ['final']). cnf(c_0_93,plain,(b_holds(key(X1,a))|~a_key(X1)|~message(sent(a,b,pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1))))), inference(spm,[status(thm)],[c_0_74, c_0_80]), ['final']). cnf(c_0_94,plain,(a_holds(key(X3,X1))|~a_stored(pair(X1,X2))|~message(sent(t,a,triple(encrypt(quadruple(X1,X2,X3,X4),at),X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_95,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1)))|~intruder_message(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_51])]), ['final']). cnf(c_0_96,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(a,X1,X2),at))))), inference(spm,[status(thm)],[c_0_83, c_0_43]), ['final']). cnf(c_0_97,plain,(intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt)))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_46, c_0_84]), ['final']). cnf(c_0_98,plain,(message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_85, c_0_86]), ['final']). cnf(c_0_99,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(b,X1,X2),at))))), inference(spm,[status(thm)],[c_0_83, c_0_36]), ['final']). cnf(c_0_100,plain,(b_holds(key(X1,X2))|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_53]), c_0_54])]), ['final']). cnf(c_0_101,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X3)), inference(spm,[status(thm)],[c_0_88, c_0_89])). cnf(c_0_102,plain,(intruder_message(X2)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_45])). cnf(c_0_103,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_84]), c_0_90]), c_0_61])]), ['final']). fof(c_0_104, plain, (![X2]:a_key(generate_key(X2))), inference(variable_rename,[status(thm)],[c_0_21])). cnf(c_0_105,plain,(intruder_message(X2)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_66])). cnf(c_0_106,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))), inference(spm,[status(thm)],[c_0_46, c_0_91]), ['final']). cnf(c_0_107,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_53]), c_0_56]), c_0_54])]), ['final']). cnf(c_0_108,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_84]), c_0_69]), c_0_54])]), ['final']). cnf(c_0_109,plain,(b_holds(key(X1,a))|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|~a_key(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_53]), c_0_54]), c_0_61])]), ['final']). cnf(c_0_110,plain,(a_holds(key(X1,b))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4)))), inference(spm,[status(thm)],[c_0_94, c_0_49]), ['final']). fof(c_0_111, plain, (![X1]:~a_nonce(generate_key(X1))), inference(fof_simplification,[status(thm)],[c_0_22])). fof(c_0_112, plain, (![X2]:((fresh_to_b(X2)|~fresh_intruder_nonce(X2))&(intruder_message(X2)|~fresh_intruder_nonce(X2)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])). cnf(c_0_113,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)))))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_60, c_0_95]), ['final']). cnf(c_0_114,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(a,X1,X2),at)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_53]), c_0_56]), c_0_61])]), ['final']). cnf(c_0_115,plain,(intruder_message(encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_70, c_0_97]), ['final']). cnf(c_0_116,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_46, c_0_98]), ['final']). cnf(c_0_117,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(b,X1,X2),at)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_53]), c_0_56]), c_0_61])]), ['final']). cnf(c_0_118,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(encrypt(generate_b_nonce(X3),X1))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_100, c_0_65]), ['final']). cnf(c_0_119,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_101, c_0_54]), ['final']). cnf(c_0_120,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_102, c_0_97]), ['final']). cnf(c_0_121,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_103]), ['final']). cnf(c_0_122,plain,(a_key(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_104])). cnf(c_0_123,plain,(intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))), inference(spm,[status(thm)],[c_0_105, c_0_106]), ['final']). cnf(c_0_124,plain,(intruder_message(an_a_nonce)), inference(spm,[status(thm)],[c_0_105, c_0_79]), ['final']). cnf(c_0_125,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(b,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_68]), c_0_69])]), ['final']). cnf(c_0_126,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_108]), ['final']). cnf(c_0_127,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1))|~a_key(X1)), inference(spm,[status(thm)],[c_0_109, c_0_65]), ['final']). cnf(c_0_128,plain,(intruder_message(generate_b_nonce(an_a_nonce))), inference(spm,[status(thm)],[c_0_102, c_0_59]), ['final']). cnf(c_0_129,plain,(a_holds(key(X1,b))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_53]), c_0_61]), c_0_56])]), ['final']). fof(c_0_130, plain, (![X2]:(~fresh_intruder_nonce(X2)|fresh_intruder_nonce(generate_intruder_nonce(X2)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])). fof(c_0_131, plain, (![X4]:![X5]:![X6]:(((~intruder_message(encrypt(X4,X5))|~intruder_holds(key(X5,X6)))|~party_of_protocol(X6))|intruder_message(X5))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])). fof(c_0_132, plain, (![X5]:![X6]:![X7]:![X8]:((((intruder_message(X5)|~intruder_message(quadruple(X5,X6,X7,X8)))&(intruder_message(X6)|~intruder_message(quadruple(X5,X6,X7,X8))))&(intruder_message(X7)|~intruder_message(quadruple(X5,X6,X7,X8))))&(intruder_message(X8)|~intruder_message(quadruple(X5,X6,X7,X8))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])). fof(c_0_133, plain, (![X5]:![X6]:![X7]:![X8]:((((~intruder_message(X5)|~intruder_message(X6))|~intruder_message(X7))|~intruder_message(X8))|intruder_message(quadruple(X5,X6,X7,X8)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])). fof(c_0_134, plain, (![X2]:(~a_key(X2)|~a_nonce(X2))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])). fof(c_0_135, plain, (![X2]:~a_nonce(generate_key(X2))), inference(variable_rename,[status(thm)],[c_0_111])). fof(c_0_136, plain, (![X2]:![X3]:(a_nonce(generate_expiration_time(X2))&a_nonce(generate_b_nonce(X3)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_29])])])). cnf(c_0_137,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_71, c_0_106]), ['final']). cnf(c_0_138,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_112])). cnf(c_0_139,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_46, c_0_113]), ['final']). cnf(c_0_140,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(a,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_68]), c_0_90])]), ['final']). cnf(c_0_141,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_115]), c_0_90]), c_0_61])]), ['final']). cnf(c_0_142,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_71, c_0_116]), ['final']). cnf(c_0_143,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(b,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_68]), c_0_90])]), ['final']). cnf(c_0_144,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_119]), c_0_120]), ['final']). cnf(c_0_145,plain,(intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_102, c_0_121]), ['final']). cnf(c_0_146,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_64, c_0_106]), ['final']). cnf(c_0_147,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_98]), c_0_90])]), ['final']). cnf(c_0_148,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_116]), c_0_122])]), c_0_120]), ['final']). cnf(c_0_149,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_105, c_0_116])). cnf(c_0_150,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(encrypt(X2,generate_key(an_a_nonce)))|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_64, c_0_116]), ['final']). cnf(c_0_151,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_98]), c_0_90])]), ['final']). cnf(c_0_152,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_123]), c_0_124]), c_0_122]), c_0_40])]), ['final']). cnf(c_0_153,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_115]), c_0_69]), c_0_54])]), ['final']). cnf(c_0_154,plain,(intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_102, c_0_126]), ['final']). cnf(c_0_155,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~a_key(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_119]), c_0_128])]), ['final']). cnf(c_0_156,plain,(a_holds(key(X1,b))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X1,X2),at))|~intruder_message(X3)|~intruder_message(X4)), inference(spm,[status(thm)],[c_0_129, c_0_68]), ['final']). cnf(c_0_157,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_112])). cnf(c_0_158,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_130])). cnf(c_0_159,plain,(intruder_message(X1)|~party_of_protocol(X2)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_131])). cnf(c_0_160,plain,(intruder_message(X1)|~intruder_message(quadruple(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_132])). cnf(c_0_161,plain,(intruder_message(X2)|~intruder_message(quadruple(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_132])). cnf(c_0_162,plain,(intruder_message(quadruple(X1,X2,X3,X4))|~intruder_message(X4)|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_133])). cnf(c_0_163,plain,(intruder_message(X3)|~intruder_message(quadruple(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_132])). cnf(c_0_164,plain,(intruder_message(X4)|~intruder_message(quadruple(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_132])). cnf(c_0_165,plain,(~a_nonce(X1)|~a_key(X1)), inference(split_conjunct,[status(thm)],[c_0_134])). cnf(c_0_166,plain,(~a_nonce(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_135])). cnf(c_0_167,plain,(fresh_intruder_nonce(an_intruder_nonce)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_168,plain,(b_holds(key(bt,t))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_169,plain,(a_holds(key(at,t))), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_170,plain,(a_nonce(generate_expiration_time(X1))), inference(split_conjunct,[status(thm)],[c_0_136])). cnf(c_0_171,plain,(a_nonce(generate_b_nonce(X1))), inference(split_conjunct,[status(thm)],[c_0_136])). cnf(c_0_172,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_137, c_0_138]), ['final']). cnf(c_0_173,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_71, c_0_139]), ['final']). cnf(c_0_174,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_140, c_0_119]), ['final']). cnf(c_0_175,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_141]), ['final']). cnf(c_0_176,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_64, c_0_139]), ['final']). cnf(c_0_177,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_142, c_0_138]), ['final']). cnf(c_0_178,plain,(intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_46, c_0_95]), ['final']). cnf(c_0_179,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_143, c_0_119]), ['final']). cnf(c_0_180,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_81, c_0_119]), ['final']). cnf(c_0_181,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_145]), c_0_90]), c_0_122]), c_0_61])]), ['final']). cnf(c_0_182,plain,(intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_58, c_0_121]), ['final']). cnf(c_0_183,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_146, c_0_138]), ['final']). cnf(c_0_184,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_125, c_0_119]), ['final']). cnf(c_0_185,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_147, c_0_138]), ['final']). cnf(c_0_186,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)|~intruder_message(X2)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_119]), c_0_58]), ['final']). cnf(c_0_187,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(generate_key(an_a_nonce))|~intruder_message(X1)|~fresh_to_b(generate_key(an_a_nonce))|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_148, c_0_115]), ['final']). cnf(c_0_188,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_149, c_0_73]), ['final']). cnf(c_0_189,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X2,generate_key(an_a_nonce)))|~intruder_message(X2)|~intruder_message(X1)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_150, c_0_138]), ['final']). cnf(c_0_190,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_151, c_0_138]), ['final']). cnf(c_0_191,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_119]), c_0_58]), ['final']). cnf(c_0_192,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_153]), ['final']). cnf(c_0_193,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_144, c_0_115]), ['final']). cnf(c_0_194,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_119]), c_0_102]), c_0_58]), ['final']). cnf(c_0_195,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_154]), c_0_69]), c_0_122]), c_0_54])]), ['final']). cnf(c_0_196,plain,(intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_58, c_0_126]), ['final']). cnf(c_0_197,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_70, c_0_126]), ['final']). cnf(c_0_198,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(quadruple(b,an_a_nonce,X3,X4))|~intruder_message(at)|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_85, c_0_119]), ['final']). cnf(c_0_199,plain,(b_holds(key(X1,a))|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_119]), c_0_102]), ['final']). cnf(c_0_200,plain,(b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_82]), c_0_124])]), ['final']). cnf(c_0_201,plain,(a_holds(key(X1,b))|~intruder_message(quadruple(b,an_a_nonce,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~intruder_message(X4)), inference(spm,[status(thm)],[c_0_156, c_0_119]), ['final']). cnf(c_0_202,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(spm,[status(thm)],[c_0_157, c_0_158]), ['final']). cnf(c_0_203,plain,(message(sent(t,X1,triple(encrypt(quadruple(X2,X3,generate_key(X3),X4),X5),encrypt(triple(X1,generate_key(X3),X4),X6),X7)))|~a_nonce(X3)|~t_holds(key(X6,X2))|~t_holds(key(X5,X1))|~message(sent(X2,t,triple(X2,X7,encrypt(triple(X1,X3,X4),X6))))), c_0_35, ['final']). cnf(c_0_204,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))), c_0_38, ['final']). cnf(c_0_205,plain,(message(sent(a,X1,pair(X2,encrypt(X3,X4))))|~a_stored(pair(X1,X5))|~message(sent(t,a,triple(encrypt(quadruple(X1,X5,X4,X6),at),X2,X3)))), c_0_48, ['final']). cnf(c_0_206,plain,(b_holds(key(X1,X2))|~a_key(X1)|~b_stored(pair(X2,X3))|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))), c_0_74, ['final']). cnf(c_0_207,plain,(a_holds(key(X1,X2))|~a_stored(pair(X2,X3))|~message(sent(t,a,triple(encrypt(quadruple(X2,X3,X1,X4),at),X5,X6)))), c_0_94, ['final']). cnf(c_0_208,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~message(sent(X1,b,pair(X1,X2)))), c_0_52, ['final']). cnf(c_0_209,plain,(intruder_message(X1)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))|~party_of_protocol(X2)), c_0_159, ['final']). cnf(c_0_210,plain,(intruder_message(encrypt(X1,X2))|~intruder_holds(key(X2,X3))|~intruder_message(X1)|~party_of_protocol(X3)), c_0_88, ['final']). cnf(c_0_211,plain,(intruder_message(X1)|~intruder_message(quadruple(X1,X2,X3,X4))), c_0_160, ['final']). cnf(c_0_212,plain,(intruder_message(X1)|~intruder_message(quadruple(X2,X1,X3,X4))), c_0_161, ['final']). cnf(c_0_213,plain,(intruder_message(quadruple(X1,X2,X3,X4))|~intruder_message(X4)|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), c_0_162, ['final']). cnf(c_0_214,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), c_0_68, ['final']). cnf(c_0_215,plain,(message(sent(X1,X2,X3))|~intruder_message(X3)|~party_of_protocol(X2)|~party_of_protocol(X1)), c_0_53, ['final']). cnf(c_0_216,plain,(intruder_holds(key(X1,X2))|~intruder_message(X1)|~party_of_protocol(X2)), c_0_89, ['final']). cnf(c_0_217,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)), c_0_65, ['final']). cnf(c_0_218,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), c_0_158, ['final']). cnf(c_0_219,plain,(intruder_message(X1)|~intruder_message(quadruple(X2,X3,X1,X4))), c_0_163, ['final']). cnf(c_0_220,plain,(intruder_message(X1)|~intruder_message(quadruple(X2,X3,X4,X1))), c_0_164, ['final']). cnf(c_0_221,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))), c_0_58, ['final']). cnf(c_0_222,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))), c_0_46, ['final']). cnf(c_0_223,plain,(intruder_message(X1)|~intruder_message(triple(X2,X1,X3))), c_0_102, ['final']). cnf(c_0_224,plain,(intruder_message(X1)|~intruder_message(triple(X2,X3,X1))), c_0_70, ['final']). cnf(c_0_225,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))), c_0_78, ['final']). cnf(c_0_226,plain,(intruder_message(X1)|~intruder_message(pair(X2,X1))), c_0_105, ['final']). cnf(c_0_227,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)), c_0_138, ['final']). cnf(c_0_228,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)), c_0_157, ['final']). cnf(c_0_229,plain,(~a_nonce(X1)|~a_key(X1)), c_0_165, ['final']). cnf(c_0_230,plain,(~a_nonce(generate_key(X1))), c_0_166, ['final']). cnf(c_0_231,plain,(b_holds(key(generate_key(an_a_nonce),b))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_154]), c_0_69]), c_0_54]), c_0_124]), c_0_51]), c_0_40])]), ['final']). cnf(c_0_232,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_78, c_0_106]), ['final']). cnf(c_0_233,plain,(b_holds(key(generate_key(an_a_nonce),a))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_91]), c_0_124]), c_0_90]), c_0_122]), c_0_40]), c_0_61])]), ['final']). cnf(c_0_234,plain,(a_holds(key(generate_key(an_a_nonce),b))), inference(spm,[status(thm)],[c_0_110, c_0_62]), ['final']). cnf(c_0_235,plain,(intruder_message(an_intruder_nonce)), inference(spm,[status(thm)],[c_0_157, c_0_167]), ['final']). cnf(c_0_236,plain,(message(sent(a,b,pair(a,an_a_nonce)))), c_0_39, ['final']). cnf(c_0_237,plain,(t_holds(key(bt,b))), c_0_36, ['final']). cnf(c_0_238,plain,(t_holds(key(at,a))), c_0_43, ['final']). cnf(c_0_239,plain,(b_holds(key(bt,t))), c_0_168, ['final']). cnf(c_0_240,plain,(a_stored(pair(b,an_a_nonce))), c_0_49, ['final']). cnf(c_0_241,plain,(a_holds(key(at,t))), c_0_169, ['final']). cnf(c_0_242,plain,(a_nonce(generate_expiration_time(X1))), c_0_170, ['final']). cnf(c_0_243,plain,(a_nonce(generate_b_nonce(X1))), c_0_171, ['final']). cnf(c_0_244,plain,(a_key(generate_key(X1))), c_0_122, ['final']). cnf(c_0_245,plain,(fresh_intruder_nonce(an_intruder_nonce)), c_0_167, ['final']). cnf(c_0_246,plain,(a_nonce(an_a_nonce)), c_0_51, ['final']). cnf(c_0_247,plain,(fresh_to_b(an_a_nonce)), c_0_40, ['final']). cnf(c_0_248,plain,(party_of_protocol(b)), c_0_54, ['final']). cnf(c_0_249,plain,(party_of_protocol(a)), c_0_61, ['final']). cnf(c_0_250,plain,(party_of_protocol(t)), c_0_56, ['final']). # SZS output end Saturation.  ## ePrincess 1.0 Peter Backeman Uppsala University, Sweden The proof trees are built top-down, with the first line(s) stating what formulas are assumed (this is after preprocessing and simplification has been applied). Afterwards each step is presented one-by-one stating from what formula(s) and by what kind of reasoning it is derived. Alpha-rule is simply breaking a conjunction in its pieces, and beta-rule is breaking a disjunction into two branches. Every formula is written in TPTP-like negation normal form and is contained between "% SZS output start Proof for xxxx" and "% SZS output end Proof for xxxx". ### Sample solution for SEU140+2 % SZS output start Proof for SEU140+2 Assumed formulas after preprocessing and simplification: | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & disjoint(v1, v2) = 0 & disjoint(v0, v2) = v3 & subset(v0, v1) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_difference(v8, v9) = v11) | ~ (set_difference(v7, v9) = v10) | ~ (subset(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ~ (set_intersection2(v8, v9) = v11) | ~ (set_intersection2(v7, v9) = v10) | ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v8) = v11) | ~ (set_union2(v7, v9) = v10) | ? [v12] : ? [v13] : (subset(v9, v8) = v13 & subset(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v7, v10) = v11) | ~ (set_intersection2(v8, v9) = v10) | ? [v12] : ? [v13] : (subset(v7, v9) = v13 & subset(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | (v11 = 0 & ~ (v13 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | (v13 = 0 & v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v13 & in(v10, v8) = v12 & (v13 = 0 | ( ~ (v12 = 0) & ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_difference(v8, v7) = v9) | ~ (set_union2(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (set_difference(v7, v8) = v9) | ~ (subset(v9, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v9, v7) = v10) | ~ (set_intersection2(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v9) = v10) | ~ (subset(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v9) = v10) | ~ (set_union2(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (disjoint(v10, v9) = v8) | ~ (disjoint(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_intersection2(v10, v9) = v8) | ~ (set_intersection2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (proper_subset(v10, v9) = v8) | ~ (proper_subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v7, v8) = v9) | set_difference(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v7) = v9) | ~ (set_union2(v7, v9) = v10) | set_union2(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v9) = v10) | ~ (set_difference(v7, v8) = v9) | set_intersection2(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v7) = 0) | ? [v11] : ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & (v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v7) = 0) | ? [v11] : ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_difference(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0) & (v12 = 0 | (v13 = 0 & ~ (v14 = 0))))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)) & (v12 = 0 | (v14 = 0 & v13 = 0)))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_union2(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v12 = 0) | ( ~ (v14 = 0) & ~ (v13 = 0))) & (v14 = 0 | v13 = 0 | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (set_intersection2(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (proper_subset(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : ? [v11] : (set_intersection2(v7, v8) = v10 & in(v11, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : ( ~ (v10 = empty_set) & set_intersection2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : (in(v10, v8) = 0 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (disjoint(v7, v8) = 0) | ~ (in(v9, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | set_intersection2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ? [v10] : ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ? [v10] : ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (empty(v8) = 0) | ~ (empty(v7) = 0)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_difference(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (subset(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & subset(v8, v7) = v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_intersection2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_difference(empty_set, v7) = v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_intersection2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(empty_set, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | disjoint(v8, v7) = 0) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | set_intersection2(v7, v8) = empty_set) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | ? [v9] : (set_intersection2(v7, v8) = v9 & ! [v10] : ~ (in(v10, v9) = 0))) & ! [v7] : ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (proper_subset(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & subset(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (proper_subset(v7, v8) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (proper_subset(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & proper_subset(v8, v7) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : (v7 = empty_set | ~ (empty(v7) = 0)) & ! [v7] : (v7 = empty_set | ~ (subset(v7, empty_set) = 0)) & ! [v7] : ~ (proper_subset(v7, v7) = 0) & ! [v7] : ~ (in(v7, empty_set) = 0) & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : ? [v10] : ? [v11] : (in(v9, v8) = v11 & in(v9, v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)) & (v11 = 0 | v10 = 0))) & ? [v7] : (v7 = empty_set | ? [v8] : in(v8, v7) = 0)) | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields: | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & disjoint(all_0_5_5, all_0_4_4) = 0 & disjoint(all_0_6_6, all_0_4_4) = all_0_3_3 & subset(all_0_6_6, all_0_5_5) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : ~ (proper_subset(v0, v0) = 0) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) | | Applying alpha-rule on (1) yields: | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) | (8) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) | (11) ! [v0] : ~ (proper_subset(v0, v0) = 0) | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) | (13) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) | (16) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) | (19) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) | (20) disjoint(all_0_6_6, all_0_4_4) = all_0_3_3 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) | (22) empty(empty_set) = 0 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) | (24) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) | (31) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) | (32) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) | (40) empty(all_0_0_0) = 0 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) | (43) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) | (45) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) | (47) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) | (49) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) | (51) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) | (52) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) | (53) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) | (54) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) | (55) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) | (57) ! [v0] : ~ (in(v0, empty_set) = 0) | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) | (61) empty(all_0_2_2) = all_0_1_1 | (62) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) | (63) ~ (all_0_1_1 = 0) | (64) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) | (65) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) | (66) ~ (all_0_3_3 = 0) | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) | (68) disjoint(all_0_5_5, all_0_4_4) = 0 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) | (70) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) | (71) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) | (72) subset(all_0_6_6, all_0_5_5) = 0 | (73) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) | (74) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) | (76) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) | | Instantiating formula (52) with all_0_4_4, all_0_5_5 and discharging atoms disjoint(all_0_5_5, all_0_4_4) = 0, yields: | (78) disjoint(all_0_4_4, all_0_5_5) = 0 | | Instantiating formula (65) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms disjoint(all_0_6_6, all_0_4_4) = all_0_3_3, yields: | (79) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_6_6, all_0_4_4) = v0) | | Instantiating formula (15) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms disjoint(all_0_6_6, all_0_4_4) = all_0_3_3, yields: | (80) all_0_3_3 = 0 | ? [v0] : (in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = 0) | +-Applying beta-rule and splitting (79), into two cases. |-Branch one: | (81) all_0_3_3 = 0 | all_0_3_3| Equations (81) can reduce 66 to: to| (82) false false| false|-The branch is then unsatisfiable |-Branch two: | (66) ~ (all_0_3_3 = 0) | (84) ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_6_6, all_0_4_4) = v0) | v0+-Applying beta-rule and splitting (80), into two cases. cases|-Branch one: one| (81) all_0_3_3 = 0 all_0_3_3| 81| Equations (81) can reduce 66 to: 66| (82) false 82| false|-The branch is then unsatisfiable unsatisfiable|-Branch two: two| (66) ~ (all_0_3_3 = 0) all_0_3_3| (88) ? [v0] : (in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = 0) all_0_6_6| v0| Instantiating (88) with all_33_0_15 yields: all_33_0_15| (89) in(all_33_0_15, all_0_4_4) = 0 & in(all_33_0_15, all_0_6_6) = 0 all_33_0_15| all_0_6_6| Applying alpha-rule on (89) yields: 89| (90) in(all_33_0_15, all_0_4_4) = 0 all_33_0_15| (91) in(all_33_0_15, all_0_6_6) = 0 all_33_0_15| all_0_6_6| Instantiating formula (14) with all_33_0_15, all_0_5_5, all_0_4_4 and discharging atoms disjoint(all_0_4_4, all_0_5_5) = 0, in(all_33_0_15, all_0_4_4) = 0, yields: all_0_4_4| (92) ? [v0] : ( ~ (v0 = 0) & in(all_33_0_15, all_0_5_5) = v0) all_0_5_5| v0| Instantiating formula (41) with all_33_0_15, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, in(all_33_0_15, all_0_6_6) = 0, yields: all_0_6_6| (93) in(all_33_0_15, all_0_5_5) = 0 all_33_0_15| all_0_5_5| Instantiating (92) with all_80_0_21 yields: all_80_0_21| (94) ~ (all_80_0_21 = 0) & in(all_33_0_15, all_0_5_5) = all_80_0_21 all_0_5_5| all_80_0_21| Applying alpha-rule on (94) yields: 94| (95) ~ (all_80_0_21 = 0) 95| (96) in(all_33_0_15, all_0_5_5) = all_80_0_21 all_0_5_5| all_80_0_21| Instantiating formula (38) with all_33_0_15, all_0_5_5, 0, all_80_0_21 and discharging atoms in(all_33_0_15, all_0_5_5) = all_80_0_21, in(all_33_0_15, all_0_5_5) = 0, yields: all_0_5_5| (97) all_80_0_21 = 0 97| all_80_0_21| Equations (97) can reduce 95 to: 95| (82) false 82| false|-The branch is then unsatisfiable % SZS output end Proof for SEU140+2  ## ET 0.2 Josef Urban Radboud University Nijmegen, The Netherlands ### Sample solution for SEU140+2 # No SInE strategy applied # Trying AutoSched4 for 1 seconds # AutoSched4-Mode selected heuristic G_E___042_C18_F1_PI_AE_Q4_CS_SP_PS_S4S # and selection function SelectNewComplexAHPNS. # # Presaturation interreduction done # Proof found! # SZS status Theorem # SZS output start CNFRefutation. fof(c_0_0, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), file('/tmp/SystemOnTPTP11427/SEU140+2.tptp', t3_xboole_0)). fof(c_0_1, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('/tmp/SystemOnTPTP11427/SEU140+2.tptp', t63_xboole_1)). fof(c_0_2, axiom, (![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2)))), file('/tmp/SystemOnTPTP11427/SEU140+2.tptp', d3_tarski)). fof(c_0_3, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), file('/tmp/SystemOnTPTP11427/SEU140+2.tptp', symmetry_r1_xboole_0)). fof(c_0_4, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_0])). fof(c_0_5, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[c_0_1])). fof(c_0_6, axiom, (![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2)))), c_0_2). fof(c_0_7, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X9,X7)|~in(X9,X8))|~disjoint(X7,X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])])). fof(c_0_8, negated_conjecture, (((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])). fof(c_0_9, plain, (![X4]:![X5]:![X6]:![X7]:![X8]:((~subset(X4,X5)|(~in(X6,X4)|in(X6,X5)))&((in(esk3_2(X7,X8),X7)|subset(X7,X8))&(~in(esk3_2(X7,X8),X8)|subset(X7,X8))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])])). cnf(c_0_10,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_11,negated_conjecture,(disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_12,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_13,negated_conjecture,(subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_8])). fof(c_0_14, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), c_0_3). cnf(c_0_15,lemma,(~in(X3,X2)|~in(X3,X1)|~disjoint(X1,X2)), c_0_10). cnf(c_0_16,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_11). cnf(c_0_17,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_18,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)), c_0_12). cnf(c_0_19,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_13). cnf(c_0_20,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_7])). fof(c_0_21, plain, (![X3]:![X4]:(~disjoint(X3,X4)|disjoint(X4,X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])). cnf(c_0_22,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_15). cnf(c_0_23,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_16). cnf(c_0_24,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_17). cnf(c_0_25,plain,(in(X1,X2)|~subset(X3,X2)|~in(X1,X3)), c_0_18). cnf(c_0_26,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_19). cnf(c_0_27,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_20). cnf(c_0_28,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_29,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_22). cnf(c_0_30,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_23). cnf(c_0_31,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_24). cnf(c_0_32,plain,(in(X1,X2)|~subset(X3,X2)|~in(X1,X3)), c_0_25). cnf(c_0_33,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_26). cnf(c_0_34,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_27). cnf(c_0_35,negated_conjecture,(~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_36,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_28). cnf(c_0_37,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)), inference(spm,[status(thm)],[c_0_29, c_0_30, theory(equality)])). cnf(c_0_38,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_31). cnf(c_0_39,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)), inference(spm,[status(thm)],[c_0_32, c_0_33, theory(equality)])). cnf(c_0_40,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_34). cnf(c_0_41,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_35). cnf(c_0_42,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_36). cnf(c_0_43,lemma,(disjoint(esk13_0,X1)|~in(esk9_2(esk13_0,X1),esk12_0)), inference(spm,[status(thm)],[c_0_37, c_0_38, theory(equality)])). cnf(c_0_44,lemma,(disjoint(X1,esk11_0)|in(esk9_2(X1,esk11_0),esk12_0)), inference(spm,[status(thm)],[c_0_39, c_0_40, theory(equality)])). cnf(c_0_45,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_41). cnf(c_0_46,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_42). cnf(c_0_47,lemma,(disjoint(esk13_0,esk11_0)), inference(spm,[status(thm)],[c_0_43, c_0_44, theory(equality)])). cnf(c_0_48,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_45). cnf(c_0_49,lemma,(false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47, theory(equality)]), c_0_48, theory(equality)]), ['proof']). # SZS output end CNFRefutation.  ## Geo-III 2015E Hans de Nivelle University of Wroclaw, Poland In proofs, exists(X,Y) denotes existential resolution, resolve(X,Y) is standard hyperresolution. + denotes Horn clause resolution. mergings( ) means that variables are merged by instantiation. A model is just a list of flat atoms. Elements in the model have form E0, E1, E2, ... etc. Atoms of form #_{T} Ei mean that element Ei is introduced. The other atoms have form p_{T}( E1, E2, E3, E4 ), where T is the truth value, and p the predicate name. At CASC, only T is possible, because CASC is two-valued. ### Sample solution for SEU140+2 % SZS status Theorem for /home/nivelle/TPTP-v6.1.0/Problems/SEU/SEU140+2.p % SZS output start Refutation for /home/nivelle/TPTP-v6.1.0/Problems/SEU/SEU140+2.p RuleSystem INPUT: Initial Rules: #0: input, references = 6, size of lhs = 2: in_{F}(V0,V1), in_{F}(V1,V0) | FALSE (used 0 times, uses = {}) #1: input, references = 3, size of lhs = 2: proper_subset_{F}(V0,V1), proper_subset_{F}(V1,V0) | FALSE (used 0 times, uses = {}) #2: input, references = 4, size of lhs = 3: P_set_union2_{F}(V0,V1,V2), P_set_union2_{F}(V1,V0,V3), V2 == V3 | FALSE (used 0 times, uses = {}) #3: input, references = 5, size of lhs = 3: P_set_intersection2_{F}(V0,V1,V2), P_set_intersection2_{F}(V1,V0,V3), V2 == V3 | FALSE (used 0 times, uses = {}) #4: input, references = 3, size of lhs = 1: #_{F} V1 | pppp0_{T}(V1,V1) (used 0 times, uses = {}) #5: input, references = 3, size of lhs = 2: pppp0_{F}(V0,V1), V0 == V1 | FALSE (used 0 times, uses = {}) #6: input, references = 3, size of lhs = 1: pppp0_{F}(V0,V1) | subset_{T}(V0,V1) (used 0 times, uses = {}) #7: input, references = 3, size of lhs = 1: pppp0_{F}(V0,V1) | subset_{T}(V1,V0) (used 0 times, uses = {}) #8: input, references = 3, size of lhs = 2: subset_{F}(V0,V1), subset_{F}(V1,V0) | pppp0_{T}(V0,V1) (used 0 times, uses = {}) #9: input, references = 3, size of lhs = 1: P_empty_set_{F}(V0) | pppp1_{T}(V0) (used 0 times, uses = {}) #10: input, references = 3, size of lhs = 3: pppp1_{F}(V1), P_empty_set_{F}(V0), V1 == V0 | FALSE (used 0 times, uses = {}) #11: input, references = 5, size of lhs = 3: P_empty_set_{F}(V0), pppp1_{F}(V1), in_{F}(V2,V1) | FALSE (used 0 times, uses = {}) #12: input, references = 4, size of lhs = 2: P_empty_set_{F}(V0), #_{F} V1 | pppp1_{T}(V1), pppp23_{T}(V1) (used 0 times, uses = {}) #13: input, references = 3, size of lhs = 1: pppp23_{F}(V0) | EXISTS V1: pppp10_{T}(V0,V1) (used 0 times, uses = {}) #14: input, references = 3, size of lhs = 1: pppp10_{F}(V0,V1) | in_{T}(V1,V0) (used 0 times, uses = {}) #15: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), P_set_union2_{F}(V1,V2,V4) | pppp3_{T}(V1,V2,V4) (used 0 times, uses = {}) #16: input, references = 3, size of lhs = 4: P_empty_set_{F}(V0), pppp3_{F}(V1,V2,V3), P_set_union2_{F}(V1,V2,V4), V3 == V4 | FALSE (used 0 times, uses = {}) #17: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V4,V3), pppp3_{F}(V1,V2,V3) | pppp2_{T}(V1,V2,V4) (used 0 times, uses = {}) #18: input, references = 7, size of lhs = 3: P_empty_set_{F}(V0), pppp2_{F}(V1,V2,V4), pppp3_{F}(V1,V2,V3) | in_{T}(V4,V3) (used 0 times, uses = {}) #19: input, references = 4, size of lhs = 4: P_empty_set_{F}(V0), #_{F} V1, #_{F} V2, #_{F} V3 | pppp3_{T}(V1,V2,V3), pppp24_{T}(V1,V2,V3) (used 0 times, uses = {}) #20: input, references = 3, size of lhs = 1: pppp24_{F}(V0,V1,V2) | EXISTS V3: pppp11_{T}(V0,V1,V2,V3) (used 0 times, uses = {}) #21: input, references = 4, size of lhs = 3: in_{F}(V3,V2), pppp11_{F}(V0,V1,V2,V3), pppp2_{F}(V0,V1,V3) | FALSE (used 0 times, uses = {}) #22: input, references = 6, size of lhs = 1: pppp11_{F}(V0,V1,V2,V3) | in_{T}(V3,V2), pppp2_{T}(V0,V1,V3) (used 0 times, uses = {}) #23: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), pppp2_{F}(V1,V2,V3) | in_{T}(V3,V1), in_{T}(V3,V2) (used 0 times, uses = {}) #24: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V3,V1), #_{F} V2 | pppp2_{T}(V1,V2,V3) (used 0 times, uses = {}) #25: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V3,V2), #_{F} V1 | pppp2_{T}(V1,V2,V3) (used 0 times, uses = {}) #26: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), subset_{F}(V1,V2) | pppp4_{T}(V1,V2) (used 0 times, uses = {}) #27: input, references = 4, size of lhs = 2: P_empty_set_{F}(V0), pppp4_{F}(V1,V2) | subset_{T}(V1,V2) (used 0 times, uses = {}) #28: input, references = 7, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V3,V1), pppp4_{F}(V1,V2) | in_{T}(V3,V2) (used 0 times, uses = {}) #29: input, references = 5, size of lhs = 3: P_empty_set_{F}(V0), #_{F} V1, #_{F} V2 | pppp4_{T}(V1,V2), pppp25_{T}(V1,V2) (used 0 times, uses = {}) #30: input, references = 3, size of lhs = 1: pppp25_{F}(V0,V1) | EXISTS V2: pppp12_{T}(V0,V1,V2) (used 0 times, uses = {}) #31: input, references = 3, size of lhs = 2: in_{F}(V2,V1), pppp12_{F}(V0,V1,V2) | FALSE (used 0 times, uses = {}) #32: input, references = 3, size of lhs = 1: pppp12_{F}(V0,V1,V2) | in_{T}(V2,V0) (used 0 times, uses = {}) #33: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V4) | pppp6_{T}(V1,V2,V4) (used 0 times, uses = {}) #34: input, references = 3, size of lhs = 4: P_empty_set_{F}(V0), pppp6_{F}(V1,V2,V3), P_set_intersection2_{F}(V1,V2,V4), V3 == V4 | FALSE (used 0 times, uses = {}) #35: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V4,V3), pppp6_{F}(V1,V2,V3) | pppp5_{T}(V1,V2,V4) (used 0 times, uses = {}) #36: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), pppp5_{F}(V1,V2,V4), pppp6_{F}(V1,V2,V3) | in_{T}(V4,V3) (used 0 times, uses = {}) #37: input, references = 4, size of lhs = 4: P_empty_set_{F}(V0), #_{F} V1, #_{F} V2, #_{F} V3 | pppp6_{T}(V1,V2,V3), pppp26_{T}(V1,V2,V3) (used 0 times, uses = {}) #38: input, references = 3, size of lhs = 1: pppp26_{F}(V0,V1,V2) | EXISTS V3: pppp13_{T}(V0,V1,V2,V3) (used 0 times, uses = {}) #39: input, references = 3, size of lhs = 3: in_{F}(V3,V2), pppp13_{F}(V0,V1,V2,V3), pppp5_{F}(V0,V1,V3) | FALSE (used 0 times, uses = {}) #40: input, references = 4, size of lhs = 1: pppp13_{F}(V0,V1,V2,V3) | in_{T}(V3,V2), pppp5_{T}(V0,V1,V3) (used 0 times, uses = {}) #41: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), pppp5_{F}(V1,V2,V3) | in_{T}(V3,V1) (used 0 times, uses = {}) #42: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), pppp5_{F}(V1,V2,V3) | in_{T}(V3,V2) (used 0 times, uses = {}) #43: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V3,V2), in_{F}(V3,V1) | pppp5_{T}(V1,V2,V3) (used 0 times, uses = {}) #44: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V4) | pppp8_{T}(V1,V2,V4) (used 0 times, uses = {}) #45: input, references = 3, size of lhs = 4: P_empty_set_{F}(V0), pppp8_{F}(V1,V2,V3), P_set_difference_{F}(V1,V2,V4), V3 == V4 | FALSE (used 0 times, uses = {}) #46: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V4,V3), pppp8_{F}(V1,V2,V3) | pppp7_{T}(V1,V2,V4) (used 0 times, uses = {}) #47: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), pppp7_{F}(V1,V2,V4), pppp8_{F}(V1,V2,V3) | in_{T}(V4,V3) (used 0 times, uses = {}) #48: input, references = 4, size of lhs = 4: P_empty_set_{F}(V0), #_{F} V1, #_{F} V2, #_{F} V3 | pppp8_{T}(V1,V2,V3), pppp27_{T}(V1,V2,V3) (used 0 times, uses = {}) #49: input, references = 3, size of lhs = 1: pppp27_{F}(V0,V1,V2) | EXISTS V3: pppp14_{T}(V0,V1,V2,V3) (used 0 times, uses = {}) #50: input, references = 3, size of lhs = 3: in_{F}(V3,V2), pppp14_{F}(V0,V1,V2,V3), pppp7_{F}(V0,V1,V3) | FALSE (used 0 times, uses = {}) #51: input, references = 5, size of lhs = 1: pppp14_{F}(V0,V1,V2,V3) | in_{T}(V3,V2), pppp7_{T}(V0,V1,V3) (used 0 times, uses = {}) #52: input, references = 6, size of lhs = 2: P_empty_set_{F}(V0), pppp7_{F}(V1,V2,V3) | in_{T}(V3,V1) (used 0 times, uses = {}) #53: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V3,V2), pppp7_{F}(V1,V2,V3) | FALSE (used 0 times, uses = {}) #54: input, references = 5, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V3,V1), #_{F} V2 | pppp7_{T}(V1,V2,V3), in_{T}(V3,V2) (used 0 times, uses = {}) #55: input, references = 4, size of lhs = 4: P_empty_set_{F}(V0), disjoint_{F}(V1,V2), P_set_intersection2_{F}(V1,V2,V3), V3 == V0 | FALSE (used 0 times, uses = {}) #56: input, references = 4, size of lhs = 2: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V0) | disjoint_{T}(V1,V2) (used 0 times, uses = {}) #57: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), proper_subset_{F}(V1,V2) | pppp9_{T}(V1,V2) (used 0 times, uses = {}) #58: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), pppp9_{F}(V1,V2) | proper_subset_{T}(V1,V2) (used 0 times, uses = {}) #59: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), pppp9_{F}(V1,V2) | subset_{T}(V1,V2) (used 0 times, uses = {}) #60: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), pppp9_{F}(V2,V2) | FALSE (used 0 times, uses = {}) #61: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), subset_{F}(V1,V2), V1 == V2 | pppp9_{T}(V1,V2) (used 0 times, uses = {}) #62: input, references = 3, size of lhs = 1: P_empty_set_{F}(V0) | empty_{T}(V0) (used 0 times, uses = {}) #63: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), empty_{F}(V3), P_set_union2_{F}(V1,V2,V3) | empty_{T}(V1) (used 0 times, uses = {}) #64: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), empty_{F}(V3), P_set_union2_{F}(V2,V1,V3) | empty_{T}(V1) (used 0 times, uses = {}) #65: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), P_set_union2_{F}(V1,V1,V2), V2 == V1 | FALSE (used 0 times, uses = {}) #66: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V1,V2), V2 == V1 | FALSE (used 0 times, uses = {}) #67: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), proper_subset_{F}(V1,V1) | FALSE (used 0 times, uses = {}) #68: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V0) | subset_{T}(V1,V2) (used 0 times, uses = {}) #69: input, references = 4, size of lhs = 4: P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_difference_{F}(V1,V2,V3), V3 == V0 | FALSE (used 0 times, uses = {}) #70: input, references = 4, size of lhs = 1: P_empty_set_{F}(V0) | EXISTS V1: pppp15_{T}(V1) (used 0 times, uses = {}) #71: input, references = 5, size of lhs = 1: pppp15_{F}(V0) | empty_{T}(V0) (used 0 times, uses = {}) #72: input, references = 3, size of lhs = 1: P_empty_set_{F}(V0) | EXISTS V1: pppp16_{T}(V1) (used 0 times, uses = {}) #73: input, references = 3, size of lhs = 2: pppp16_{F}(V0), empty_{F}(V0) | FALSE (used 0 times, uses = {}) #74: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), #_{F} V1 | subset_{T}(V1,V1) (used 0 times, uses = {}) #75: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), disjoint_{F}(V1,V2) | disjoint_{T}(V2,V1) (used 0 times, uses = {}) #76: input, references = 4, size of lhs = 4: P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_union2_{F}(V1,V2,V3), V3 == V2 | FALSE (used 0 times, uses = {}) #77: input, references = 5, size of lhs = 2: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3) | subset_{T}(V3,V1) (used 0 times, uses = {}) #78: input, references = 4, size of lhs = 4: P_empty_set_{F}(V0), subset_{F}(V1,V3), subset_{F}(V1,V2), P_set_intersection2_{F}(V3,V2,V4) | subset_{T}(V1,V4) (used 0 times, uses = {}) #79: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), P_set_union2_{F}(V1,V0,V2), V2 == V1 | FALSE (used 0 times, uses = {}) #80: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), subset_{F}(V3,V1), subset_{F}(V1,V2) | subset_{T}(V3,V2) (used 0 times, uses = {}) #81: input, references = 3, size of lhs = 4: P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_intersection2_{F}(V1,V3,V4), P_set_intersection2_{F}(V2,V3,V5) | subset_{T}(V4,V5) (used 0 times, uses = {}) #82: input, references = 5, size of lhs = 4: P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_intersection2_{F}(V1,V2,V3), V3 == V1 | FALSE (used 0 times, uses = {}) #83: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V0,V2), V2 == V0 | FALSE (used 0 times, uses = {}) #84: input, references = 3, size of lhs = 4: P_empty_set_{F}(V0), #_{F} V1, #_{F} V2, V1 == V2 | EXISTS V3: pppp17_{T}(V1,V2,V3) (used 0 times, uses = {}) #85: input, references = 3, size of lhs = 3: in_{F}(V2,V1), in_{F}(V2,V0), pppp17_{F}(V0,V1,V2) | FALSE (used 0 times, uses = {}) #86: input, references = 4, size of lhs = 1: pppp17_{F}(V0,V1,V2) | in_{T}(V2,V0), in_{T}(V2,V1) (used 0 times, uses = {}) #87: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), #_{F} V1 | subset_{T}(V0,V1) (used 0 times, uses = {}) #88: input, references = 3, size of lhs = 4: P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_difference_{F}(V1,V3,V4), P_set_difference_{F}(V2,V3,V5) | subset_{T}(V4,V5) (used 0 times, uses = {}) #89: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V3) | subset_{T}(V3,V1) (used 0 times, uses = {}) #90: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V0) | subset_{T}(V1,V2) (used 0 times, uses = {}) #91: input, references = 3, size of lhs = 4: P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_difference_{F}(V1,V2,V3), V3 == V0 | FALSE (used 0 times, uses = {}) #92: input, references = 3, size of lhs = 5: P_empty_set_{F}(V0), P_set_difference_{F}(V2,V1,V3), P_set_union2_{F}(V1,V3,V4), P_set_union2_{F}(V1,V2,V5), V4 == V5 | FALSE (used 0 times, uses = {}) #93: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), P_set_difference_{F}(V1,V0,V2), V2 == V1 | FALSE (used 0 times, uses = {}) #94: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), #_{F} V1, #_{F} V2 | disjoint_{T}(V1,V2), pppp28_{T}(V1,V2) (used 0 times, uses = {}) #95: input, references = 3, size of lhs = 1: pppp28_{F}(V0,V1) | EXISTS V2: pppp18_{T}(V0,V1,V2) (used 0 times, uses = {}) #96: input, references = 7, size of lhs = 4: P_empty_set_{F}(V0), in_{F}(V3,V1), in_{F}(V3,V2), disjoint_{F}(V1,V2) | FALSE (used 0 times, uses = {}) #97: input, references = 3, size of lhs = 1: pppp18_{F}(V0,V1,V2) | in_{T}(V2,V1) (used 0 times, uses = {}) #98: input, references = 3, size of lhs = 1: pppp18_{F}(V0,V1,V2) | in_{T}(V2,V0) (used 0 times, uses = {}) #99: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), subset_{F}(V1,V0), V1 == V0 | FALSE (used 0 times, uses = {}) #100: input, references = 3, size of lhs = 5: P_empty_set_{F}(V0), P_set_union2_{F}(V1,V2,V3), P_set_difference_{F}(V3,V2,V4), P_set_difference_{F}(V1,V2,V5), V4 == V5 | FALSE (used 0 times, uses = {}) #101: input, references = 3, size of lhs = 5: P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_difference_{F}(V2,V1,V3), P_set_union2_{F}(V1,V3,V4), V2 == V4 | FALSE (used 0 times, uses = {}) #102: input, references = 4, size of lhs = 5: P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V3), P_set_difference_{F}(V1,V3,V4), P_set_intersection2_{F}(V1,V2,V5), V4 == V5 | FALSE (used 0 times, uses = {}) #103: input, references = 4, size of lhs = 3: P_empty_set_{F}(V0), P_set_difference_{F}(V0,V1,V2), V2 == V0 | FALSE (used 0 times, uses = {}) #104: input, references = 4, size of lhs = 2: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3) | disjoint_{T}(V1,V2), pppp29_{T}(V3) (used 0 times, uses = {}) #105: input, references = 3, size of lhs = 1: pppp29_{F}(V0) | EXISTS V1: pppp19_{T}(V0,V1) (used 0 times, uses = {}) #106: input, references = 3, size of lhs = 4: P_empty_set_{F}(V0), in_{F}(V4,V3), disjoint_{F}(V1,V2), P_set_intersection2_{F}(V1,V2,V3) | FALSE (used 0 times, uses = {}) #107: input, references = 3, size of lhs = 1: pppp19_{F}(V0,V1) | in_{T}(V1,V0) (used 0 times, uses = {}) #108: input, references = 3, size of lhs = 3: P_empty_set_{F}(V0), subset_{F}(V1,V2), proper_subset_{F}(V2,V1) | FALSE (used 0 times, uses = {}) #109: input, references = 4, size of lhs = 1: P_empty_set_{F}(V0) | EXISTS V1: pppp22_{T}(V1) (used 0 times, uses = {}) #110: input, references = 4, size of lhs = 1: pppp22_{F}(V0) | EXISTS V1: pppp21_{T}(V0,V1) (used 0 times, uses = {}) #111: input, references = 4, size of lhs = 1: pppp21_{F}(V0,V1) | EXISTS V2: pppp20_{T}(V2,V0,V1) (used 0 times, uses = {}) #112: input, references = 4, size of lhs = 1: pppp21_{F}(V0,V1) | disjoint_{T}(V0,V1) (used 0 times, uses = {}) #113: input, references = 4, size of lhs = 2: disjoint_{F}(V0,V2), pppp20_{F}(V0,V1,V2) | FALSE (used 0 times, uses = {}) #114: input, references = 4, size of lhs = 1: pppp20_{F}(V0,V1,V2) | subset_{T}(V0,V1) (used 0 times, uses = {}) #115: input, references = 4, size of lhs = 3: empty_{F}(V1), P_empty_set_{F}(V0), V1 == V0 | FALSE (used 0 times, uses = {}) #116: input, references = 5, size of lhs = 3: P_empty_set_{F}(V0), empty_{F}(V1), in_{F}(V2,V1) | FALSE (used 0 times, uses = {}) #117: input, references = 3, size of lhs = 2: P_empty_set_{F}(V0), P_set_union2_{F}(V1,V2,V3) | subset_{T}(V1,V3) (used 0 times, uses = {}) #118: input, references = 4, size of lhs = 4: P_empty_set_{F}(V0), empty_{F}(V2), empty_{F}(V1), V2 == V1 | FALSE (used 0 times, uses = {}) #119: input, references = 3, size of lhs = 4: P_empty_set_{F}(V0), subset_{F}(V3,V1), subset_{F}(V2,V1), P_set_union2_{F}(V3,V2,V4) | subset_{T}(V4,V1) (used 0 times, uses = {}) #120: input, references = 5, size of lhs = 2: #_{F} V0, #_{F} V1 | EXISTS V2: P_set_union2_{T}(V0,V1,V2) (used 0 times, uses = {}) #121: input, references = 8, size of lhs = 2: #_{F} V0, #_{F} V1 | EXISTS V2: P_set_intersection2_{T}(V0,V1,V2) (used 0 times, uses = {}) #122: input, references = 4, size of lhs = 0: TRUE | EXISTS V0: P_empty_set_{T}(V0) (used 0 times, uses = {}) #123: input, references = 5, size of lhs = 2: #_{F} V0, #_{F} V1 | EXISTS V2: P_set_difference_{T}(V0,V1,V2) (used 0 times, uses = {}) number of initial rules = 124 Simplifiers: #124: unsound, references = 3, size of lhs = 3: P_set_union2_{F}(V0,V1,V2), P_set_union2_{F}(V0,V1,V5), V2 == V5 | FALSE (used 0 times, uses = {}) #125: unsound, references = 3, size of lhs = 3: P_set_intersection2_{F}(V0,V1,V2), P_set_intersection2_{F}(V0,V1,V5), V2 == V5 | FALSE (used 0 times, uses = {}) #126: unsound, references = 3, size of lhs = 3: P_empty_set_{F}(V0), P_empty_set_{F}(V1), V0 == V1 | FALSE (used 0 times, uses = {}) #127: unsound, references = 3, size of lhs = 3: P_set_difference_{F}(V0,V1,V2), P_set_difference_{F}(V0,V1,V5), V2 == V5 | FALSE (used 0 times, uses = {}) #128: unsound, references = 3, size of lhs = 3: pppp10_{F}(V0,V1), pppp10_{F}(V0,V3), V1 == V3 | FALSE (used 0 times, uses = {}) #129: unsound, references = 3, size of lhs = 3: pppp11_{F}(V0,V1,V2,V3), pppp11_{F}(V0,V1,V2,V7), V3 == V7 | FALSE (used 0 times, uses = {}) #130: unsound, references = 3, size of lhs = 3: pppp12_{F}(V0,V1,V2), pppp12_{F}(V0,V1,V5), V2 == V5 | FALSE (used 0 times, uses = {}) #131: unsound, references = 3, size of lhs = 3: pppp13_{F}(V0,V1,V2,V3), pppp13_{F}(V0,V1,V2,V7), V3 == V7 | FALSE (used 0 times, uses = {}) #132: unsound, references = 3, size of lhs = 3: pppp14_{F}(V0,V1,V2,V3), pppp14_{F}(V0,V1,V2,V7), V3 == V7 | FALSE (used 0 times, uses = {}) #133: unsound, references = 3, size of lhs = 3: pppp15_{F}(V0), pppp15_{F}(V1), V0 == V1 | FALSE (used 0 times, uses = {}) #134: unsound, references = 3, size of lhs = 3: pppp16_{F}(V0), pppp16_{F}(V1), V0 == V1 | FALSE (used 0 times, uses = {}) #135: unsound, references = 3, size of lhs = 3: pppp17_{F}(V0,V1,V2), pppp17_{F}(V0,V1,V5), V2 == V5 | FALSE (used 0 times, uses = {}) #136: unsound, references = 3, size of lhs = 3: pppp18_{F}(V0,V1,V2), pppp18_{F}(V0,V1,V5), V2 == V5 | FALSE (used 0 times, uses = {}) #137: unsound, references = 3, size of lhs = 3: pppp19_{F}(V0,V1), pppp19_{F}(V0,V3), V1 == V3 | FALSE (used 0 times, uses = {}) #138: unsound, references = 3, size of lhs = 3: pppp20_{F}(V0,V1,V2), pppp20_{F}(V3,V1,V2), V0 == V3 | FALSE (used 0 times, uses = {}) #139: unsound, references = 3, size of lhs = 3: pppp20_{F}(V0,V1,V2), pppp20_{F}(V3,V1,V5), V2 == V5 | FALSE (used 0 times, uses = {}) #140: unsound, references = 3, size of lhs = 3: pppp20_{F}(V0,V1,V2), pppp20_{F}(V3,V4,V5), V1 == V4 | FALSE (used 0 times, uses = {}) #141: unsound, references = 3, size of lhs = 3: pppp21_{F}(V0,V1), pppp21_{F}(V0,V3), V1 == V3 | FALSE (used 0 times, uses = {}) #142: unsound, references = 3, size of lhs = 3: pppp21_{F}(V0,V1), pppp21_{F}(V2,V3), V0 == V2 | FALSE (used 0 times, uses = {}) #143: unsound, references = 3, size of lhs = 3: pppp22_{F}(V0), pppp22_{F}(V1), V0 == V1 | FALSE (used 0 times, uses = {}) number of simplifiers = 20 Learnt: #151: mergings( V0 == V2; #147 ), references = 1, size of lhs = 1: P_empty_set_{F}(V0) | pppp15_{T}(V0) (used 0 times, uses = {}) #153: mergings( V0 == V2; #148 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), empty_{F}(V1) | pppp15_{T}(V1) (used 0 times, uses = {}) #157: exists( #120, #65 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), #_{F} V1 | P_set_union2_{T}(V1,V1,V1) (used 0 times, uses = {}) #158: exists( #120, #79 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), #_{F} V1 | P_set_union2_{T}(V1,V0,V1) (used 0 times, uses = {}) #159: exists( #120, #76 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), subset_{F}(V1,V2) | P_set_union2_{T}(V1,V2,V2) (used 0 times, uses = {}) #163: exists( #121, #66 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), #_{F} V1 | P_set_intersection2_{T}(V1,V1,V1) (used 0 times, uses = {}) #164: exists( #121, #83 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), #_{F} V1 | P_set_intersection2_{T}(V1,V0,V0) (used 0 times, uses = {}) #165: exists( #121, #82 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), subset_{F}(V1,V2) | P_set_intersection2_{T}(V1,V2,V1) (used 0 times, uses = {}) #169: exists( #123, #93 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), #_{F} V1 | P_set_difference_{T}(V1,V0,V1) (used 0 times, uses = {}) #170: exists( #123, #103 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), #_{F} V1 | P_set_difference_{T}(V0,V1,V0) (used 0 times, uses = {}) #171: exists( #123, #69 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), subset_{F}(V1,V2) | P_set_difference_{T}(V1,V2,V0) (used 0 times, uses = {}) #174: mergings( V0 == V3; #172 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3), V3 == V0 | pppp28_{T}(V1,V2) (used 0 times, uses = {}) #179: mergings( V0 == V2; #176 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), #_{F} V1, V1 == V0 | pppp23_{T}(V1) (used 0 times, uses = {}) #182: mergings( V0 == V2, V1 == V2; #177 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), in_{F}(V1,V0) | pppp23_{T}(V0) (used 0 times, uses = {}) #185: mergings( V0 == V4; #183 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), P_set_union2_{F}(V1,V2,V3), #_{F} V4, V4 == V3 | pppp24_{T}(V1,V2,V4) (used 0 times, uses = {}) #191: mergings( V3 == V5, V0 == V4; #186 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3), V3 == V0 | pppp29_{T}(V3) (used 0 times, uses = {}) #194: mergings( V0 == V4, V3 == V4; #187 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), in_{F}(V1,V2), in_{F}(V1,V3), P_set_intersection2_{F}(V2,V3,V0) | pppp29_{T}(V0) (used 0 times, uses = {}) #198: mergings( V6 == V3, V0 == V4, V3 == V4; #188 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), in_{F}(V1,V0), P_set_intersection2_{F}(V2,V3,V0) | pppp29_{T}(V0) (used 0 times, uses = {}) #204: mergings( V0 == V4; #202 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3), #_{F} V4, V4 == V3 | pppp26_{T}(V1,V2,V4) (used 0 times, uses = {}) #208: mergings( V0 == V4; #206 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V3), #_{F} V4, V4 == V3 | pppp27_{T}(V1,V2,V4) (used 0 times, uses = {}) #212: disj( #22, #18+#0 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), pppp3_{F}(V1,V2,V3), pppp11_{F}(V1,V2,V4,V3) | in_{T}(V3,V4) (used 0 times, uses = {}) #229: exists( #120, #2 ), references = 1, size of lhs = 1: P_set_union2_{F}(V0,V1,V2) | P_set_union2_{T}(V1,V0,V2) (used 0 times, uses = {}) #243: exists( #121, #3 ), references = 3, size of lhs = 1: P_set_intersection2_{F}(V0,V1,V2) | P_set_intersection2_{T}(V1,V0,V2) (used 0 times, uses = {}) #259: mergings( V0 == V3; #255 ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), in_{F}(V1,V2) | pppp25_{T}(V2,V1) (used 0 times, uses = {}) #261: mergings( V0 == V3; #256 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), in_{F}(V1,V2), pppp2_{F}(V3,V4,V1), pppp11_{F}(V3,V4,V5,V1) | pppp25_{T}(V2,V5) (used 0 times, uses = {}) #300: mergings( V4 == V5; #296 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), pppp1_{F}(V1), pppp3_{F}(V2,V3,V1), pppp11_{F}(V2,V3,V4,V5) | in_{T}(V5,V4) (used 0 times, uses = {}) #302: mergings( V4 == V5; #297 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), empty_{F}(V1), pppp3_{F}(V2,V3,V1), pppp11_{F}(V2,V3,V4,V5) | in_{T}(V5,V4) (used 0 times, uses = {}) #304: mergings( V4 == V5; #298 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), disjoint_{F}(V1,V1), pppp3_{F}(V2,V3,V1), pppp11_{F}(V2,V3,V4,V5) | in_{T}(V5,V4) (used 0 times, uses = {}) #316: disj( #22, input ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), pppp1_{F}(V1), pppp11_{F}(V2,V3,V1,V4) | pppp2_{T}(V2,V3,V4) (used 0 times, uses = {}) #317: disj( #22, input ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), empty_{F}(V1), pppp11_{F}(V2,V3,V1,V4) | pppp2_{T}(V2,V3,V4) (used 0 times, uses = {}) #318: disj( #22, input ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), disjoint_{F}(V1,V1), pppp11_{F}(V2,V3,V1,V4) | pppp2_{T}(V2,V3,V4) (used 0 times, uses = {}) #370: mergings( V0 == V4; #367 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), in_{F}(V1,V2), in_{F}(V3,V1), pppp8_{F}(V2,V4,V3) | in_{T}(V1,V4) (used 0 times, uses = {}) #377: disj( #54, input ), references = 1, size of lhs = 2: P_empty_set_{F}(V0), in_{F}(V1,V2) | pppp7_{T}(V2,V1,V1) (used 0 times, uses = {}) #378: disj( #54, input ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), in_{F}(V1,V2), pppp7_{F}(V3,V4,V1), pppp14_{F}(V3,V4,V5,V1) | pppp7_{T}(V2,V5,V1) (used 0 times, uses = {}) #432: disj( #40, input ), references = 1, size of lhs = 1: pppp13_{F}(V0,V1,V2,V2) | pppp5_{T}(V0,V1,V2) (used 0 times, uses = {}) #520: exists( #121, #55 ), references = 2, size of lhs = 2: P_empty_set_{F}(V0), disjoint_{F}(V1,V2) | P_set_intersection2_{T}(V1,V2,V0) (used 0 times, uses = {}) #587: mergings( V0 == V3, V3 == V4; #582 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3), V3 == V1 | pppp25_{T}(V1,V2) (used 0 times, uses = {}) #590: mergings( V0 == V3, V3 == V4; #583 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), in_{F}(V1,V2), in_{F}(V1,V3), disjoint_{F}(V3,V4) | pppp25_{T}(V2,V4) (used 0 times, uses = {}) #593: mergings( V0 == V3, V3 == V4; #584 ), references = 1, size of lhs = 4: P_empty_set_{F}(V0), in_{F}(V1,V2), in_{F}(V1,V3), disjoint_{F}(V4,V3) | pppp25_{T}(V2,V4) (used 0 times, uses = {}) #663: mergings( V4 == V5; #659 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), pppp1_{F}(V1), pppp14_{F}(V1,V2,V3,V4) | in_{T}(V4,V3) (used 0 times, uses = {}) #665: mergings( V4 == V5; #660 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), empty_{F}(V1), pppp14_{F}(V1,V2,V3,V4) | in_{T}(V4,V3) (used 0 times, uses = {}) #667: mergings( V4 == V5; #661 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), disjoint_{F}(V1,V1), pppp14_{F}(V1,V2,V3,V4) | in_{T}(V4,V3) (used 0 times, uses = {}) #720: disj( #86, input ), references = 1, size of lhs = 2: in_{F}(V0,V1), pppp17_{F}(V0,V2,V1) | in_{T}(V1,V2) (used 0 times, uses = {}) #786: disj( #51, input ), references = 1, size of lhs = 1: pppp14_{F}(V0,V1,V2,V2) | pppp7_{T}(V0,V1,V2) (used 0 times, uses = {}) #957: exists( #123, #102 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V3), P_set_intersection2_{F}(V1,V2,V4) | P_set_difference_{T}(V1,V3,V4) (used 0 times, uses = {}) #1117: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #1112 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_intersection2_{F}(V3,V2,V0) | P_set_intersection2_{T}(V3,V1,V0) (used 0 times, uses = {}) #1127: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #1122 ), references = 1, size of lhs = 3: P_empty_set_{F}(V0), pppp21_{F}(V1,V2), P_set_intersection2_{F}(V2,V1,V0) | FALSE (used 0 times, uses = {}) #1136: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #1131 ), references = 1, size of lhs = 2: pppp22_{F}(V0), P_empty_set_{F}(V1) | FALSE (used 0 times, uses = {}) #1143: mergings( V0 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #1137 ), references = 1, size of lhs = 1: P_empty_set_{F}(V0) | FALSE (used 0 times, uses = {}) #1145: #122+#1137, references = 1, size of lhs = 0: TRUE | FALSE (used 0 times, uses = {}) number of learnt formulas = 50 % SZS output end Refutation for /home/nivelle/TPTP-v6.1.0/Problems/SEU/SEU140+2.p  ### Sample solution for NLP042+1 % SZS status CounterSatisfiable for /home/nivelle/TPTP-v6.1.0/Problems/NLP/NLP042+1.p % SZS output start Model for /home/nivelle/TPTP-v6.1.0/Problems/NLP/NLP042+1.p Interpretation 4: Guesses: 0 : guesser 1, 0, ( | 1, 0 ), 0, 0s old, 0 lemmas 1 : guesser 4, 2, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 2 : guesser 17, 15, ( 0 | 2, 1 ), 0, 0s old, 1 lemmas 3 : guesser 29, 26, ( 2 | 1, 3, 0 ), 1, 0s old, 1 lemmas 4 : guesser 44, 41, ( 1, 0 | 3, 2 ), 2, 0s old, 2 lemmas Elements: { E0, E1, E2, E3 } Atoms: 0 : #_{T} E0 { } 1 : #_{T} E1 { 0 } 2 : pppp5_{T}(E1) { 0 } 3 : actual_world_{T}(E1) { 0 } 4 : pppp4_{T}(E1,E0) { 0, 1 } 5 : pppp3_{T}(E1,E0) { 0, 1 } 6 : order_{T}(E1,E0) { 0, 1 } 7 : nonreflexive_{T}(E1,E0) { 0, 1 } 8 : past_{T}(E1,E0) { 0, 1 } 9 : event_{T}(E1,E0) { 0, 1 } 10 : act_{T}(E1,E0) { 0, 1 } 11 : eventuality_{T}(E1,E0) { 0, 1 } 12 : unisex_{T}(E1,E0) { 0, 1 } 13 : nonexistent_{T}(E1,E0) { 0, 1 } 14 : specific_{T}(E1,E0) { 0, 1 } 15 : thing_{T}(E1,E0) { 0, 1 } 16 : singleton_{T}(E1,E0) { 0, 1 } 17 : #_{T} E2 { 0, 1, 2 } 18 : pppp2_{T}(E1,E2,E0) { 0, 1, 2 } 19 : forename_{T}(E1,E2) { 0, 1, 2 } 20 : mia_forename_{T}(E1,E2) { 0, 1, 2 } 21 : relname_{T}(E1,E2) { 0, 1, 2 } 22 : relation_{T}(E1,E2) { 0, 1, 2 } 23 : abstraction_{T}(E1,E2) { 0, 1, 2 } 24 : unisex_{T}(E1,E2) { 0, 1, 2 } 25 : general_{T}(E1,E2) { 0, 1, 2 } 26 : nonhuman_{T}(E1,E2) { 0, 1, 2 } 27 : thing_{T}(E1,E2) { 0, 1, 2 } 28 : singleton_{T}(E1,E2) { 0, 1, 2 } 29 : pppp0_{T}(E1,E1,E0) { 0, 1, 3 } 30 : patient_{T}(E1,E0,E1) { 0, 1, 3 } 31 : shake_beverage_{T}(E1,E1) { 0, 1, 3 } 32 : beverage_{T}(E1,E1) { 0, 1, 3 } 33 : food_{T}(E1,E1) { 0, 1, 3 } 34 : substance_matter_{T}(E1,E1) { 0, 1, 3 } 35 : object_{T}(E1,E1) { 0, 1, 3 } 36 : unisex_{T}(E1,E1) { 0, 1, 3 } 37 : impartial_{T}(E1,E1) { 0, 1, 3 } 38 : nonliving_{T}(E1,E1) { 0, 1, 3 } 39 : entity_{T}(E1,E1) { 0, 1, 3 } 40 : existent_{T}(E1,E1) { 0, 1, 3 } 41 : specific_{T}(E1,E1) { 0, 1, 3 } 42 : thing_{T}(E1,E1) { 0, 1, 3 } 43 : singleton_{T}(E1,E1) { 0, 1, 3 } 44 : #_{T} E3 { 0, 1, 2, 4 } 45 : pppp1_{T}(E1,E3,E2,E0) { 0, 1, 2, 4 } 46 : agent_{T}(E1,E0,E3) { 0, 1, 2, 4 } 47 : woman_{T}(E1,E3) { 0, 1, 2, 4 } 48 : of_{T}(E1,E2,E3) { 0, 1, 2, 4 } 49 : female_{T}(E1,E3) { 0, 1, 2, 4 } 50 : human_person_{T}(E1,E3) { 0, 1, 2, 4 } 51 : animate_{T}(E1,E3) { 0, 1, 2, 4 } 52 : human_{T}(E1,E3) { 0, 1, 2, 4 } 53 : organism_{T}(E1,E3) { 0, 1, 2, 4 } 54 : living_{T}(E1,E3) { 0, 1, 2, 4 } 55 : impartial_{T}(E1,E3) { 0, 1, 2, 4 } 56 : entity_{T}(E1,E3) { 0, 1, 2, 4 } 57 : existent_{T}(E1,E3) { 0, 1, 2, 4 } 58 : specific_{T}(E1,E3) { 0, 1, 2, 4 } 59 : thing_{T}(E1,E3) { 0, 1, 2, 4 } 60 : singleton_{T}(E1,E3) { 0, 1, 2, 4 } % SZS output end Model for /home/nivelle/TPTP-v6.1.0/Problems/NLP/NLP042+1.p  ### Sample solution for SWV017+1 % SZS status Satisfiable for /home/nivelle/TPTP-v6.1.0/Problems/SWV/SWV017+1.p % SZS output start Model for /home/nivelle/TPTP-v6.1.0/Problems/SWV/SWV017+1.p Interpretation 0: Guesses: 0 : guesser 1, 0, ( | 1, 0 ), 0, 0s old, 0 lemmas 1 : guesser 3, 1, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 2 : guesser 4, 2, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 3 : guesser 5, 3, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 4 : guesser 6, 4, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 5 : guesser 7, 5, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 6 : guesser 8, 6, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 7 : guesser 9, 7, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 8 : guesser 10, 8, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 9 : guesser 11, 9, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 10 : guesser 12, 10, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 11 : guesser 13, 11, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 12 : guesser 14, 12, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 13 : guesser 15, 13, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 14 : guesser 16, 14, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 15 : guesser 17, 15, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 16 : guesser 18, 16, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 17 : guesser 19, 17, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 18 : guesser 20, 18, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 19 : guesser 21, 19, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 20 : guesser 22, 20, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 21 : guesser 23, 21, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 22 : guesser 24, 22, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 23 : guesser 25, 23, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 24 : guesser 28, 26, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 25 : guesser 44, 42, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 26 : guesser 45, 43, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 27 : guesser 46, 44, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 28 : guesser 47, 45, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 29 : guesser 48, 46, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 30 : guesser 49, 47, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 31 : guesser 50, 48, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 32 : guesser 52, 50, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 33 : guesser 53, 51, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 34 : guesser 54, 52, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 35 : guesser 55, 53, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 36 : guesser 56, 54, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 37 : guesser 57, 55, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 38 : guesser 58, 56, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 39 : guesser 59, 57, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 40 : guesser 63, 61, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 41 : guesser 64, 62, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 42 : guesser 65, 63, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 43 : guesser 66, 64, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 44 : guesser 67, 65, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 45 : guesser 68, 66, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 46 : guesser 69, 67, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 47 : guesser 70, 68, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 48 : guesser 72, 70, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 49 : guesser 73, 71, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 50 : guesser 74, 72, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 51 : guesser 75, 73, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 52 : guesser 76, 74, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 53 : guesser 77, 75, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 54 : guesser 78, 76, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 55 : guesser 79, 77, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 56 : guesser 80, 78, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas 57 : guesser 81, 79, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas 58 : guesser 82, 80, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas Elements: { E0, E1 } Atoms: 0 : #_{T} E0 { } 1 : #_{T} E1 { 0 } 2 : P_at_{T}(E1) { 0 } 3 : P_t_{T}(E1) { 1 } 4 : P_a_{T}(E0) { 2 } 5 : P_b_{T}(E0) { 3 } 6 : P_an_a_nonce_{T}(E1) { 4 } 7 : P_bt_{T}(E1) { 5 } 8 : P_an_intruder_nonce_{T}(E1) { 6 } 9 : P_generate_b_nonce_{T}(E0,E1) { 7 } 10 : P_generate_expiration_time_{T}(E0,E1) { 8 } 11 : P_generate_key_{T}(E0,E0) { 9 } 12 : P_generate_intruder_nonce_{T}(E0,E1) { 10 } 13 : P_key_{T}(E0,E0,E1) { 11 } 14 : P_pair_{T}(E0,E0,E1) { 12 } 15 : P_encrypt_{T}(E0,E0,E0) { 13 } 16 : P_sent_{T}(E0,E0,E0,E0) { 14 } 17 : P_triple_{T}(E0,E0,E0,E1) { 15 } 18 : P_quadruple_{T}(E0,E0,E0,E0,E0) { 16 } 19 : P_generate_b_nonce_{T}(E1,E1) { 0, 17 } 20 : P_generate_expiration_time_{T}(E1,E1) { 0, 18 } 21 : P_generate_key_{T}(E1,E0) { 0, 19 } 22 : P_generate_intruder_nonce_{T}(E1,E0) { 0, 20 } 23 : P_key_{T}(E0,E1,E1) { 0, 21 } 24 : P_key_{T}(E1,E0,E0) { 0, 22 } 25 : P_key_{T}(E1,E1,E0) { 0, 23 } 26 : a_holds_{T}(E0) { 0, 1, 23 } 27 : party_of_protocol_{T}(E0) { 0, 1, 2, 23 } 28 : P_pair_{T}(E0,E1,E0) { 0, 24 } 29 : message_{T}(E0) { 0, 1, 2, 3, 4, 14, 23, 24 } 30 : a_stored_{T}(E0) { 0, 1, 2, 3, 4, 14, 23, 24 } 31 : b_holds_{T}(E0) { 0, 1, 2, 3, 4, 5, 14, 23, 24 } 32 : fresh_to_b_{T}(E1) { 0, 1, 2, 3, 4, 5, 14, 23, 24 } 33 : t_holds_{T}(E0) { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 } 34 : party_of_protocol_{T}(E1) { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 } 35 : a_nonce_{T}(E1) { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 } 36 : intruder_message_{T}(E0) { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 } 37 : intruder_message_{T}(E1) { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 } 38 : fresh_intruder_nonce_{T}(E1) { 0, 1, 2, 3, 4, 5, 6, 14, 22, 23, 24 } 39 : a_key_{T}(E0) { 0, 1, 2, 3, 4, 5, 9, 14, 22, 23, 24 } 40 : intruder_holds_{T}(E0) { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 } 41 : intruder_holds_{T}(E1) { 0, 1, 2, 3, 4, 5, 11, 14, 22, 23, 24 } 42 : fresh_intruder_nonce_{T}(E0) { 0, 1, 2, 3, 4, 5, 6, 14, 20, 22, 23, 24 } 43 : fresh_to_b_{T}(E0) { 0, 1, 2, 3, 4, 5, 6, 14, 20, 22, 23, 24 } 44 : P_pair_{T}(E1,E0,E1) { 0, 25 } 45 : P_pair_{T}(E1,E1,E1) { 0, 26 } 46 : P_encrypt_{T}(E0,E1,E0) { 0, 27 } 47 : P_encrypt_{T}(E1,E0,E0) { 0, 28 } 48 : P_encrypt_{T}(E1,E1,E1) { 0, 29 } 49 : P_sent_{T}(E0,E0,E1,E0) { 0, 30 } 50 : P_sent_{T}(E0,E1,E0,E1) { 0, 31 } 51 : message_{T}(E1) { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24, 31 } 52 : P_sent_{T}(E0,E1,E1,E0) { 0, 32 } 53 : P_sent_{T}(E1,E0,E0,E0) { 0, 33 } 54 : P_sent_{T}(E1,E0,E1,E1) { 0, 34 } 55 : P_sent_{T}(E1,E1,E0,E0) { 0, 35 } 56 : P_sent_{T}(E1,E1,E1,E1) { 0, 36 } 57 : P_triple_{T}(E0,E0,E1,E1) { 0, 37 } 58 : P_triple_{T}(E0,E1,E0,E0) { 0, 38 } 59 : P_triple_{T}(E0,E1,E1,E1) { 0, 39 } 60 : b_stored_{T}(E0) { 0, 1, 2, 3, 4, 5, 14, 17, 18, 23, 24, 29, 32, 39 } 61 : b_stored_{T}(E1) { 0, 1, 2, 3, 4, 5, 6, 7, 8, 12, 14, 20, 22, 23, 24, 29, 30, 32, 37, 39 } 62 : b_holds_{T}(E1) { 0, 1, 2, 3, 4, 5, 9, 11, 14, 17, 18, 22, 23, 24, 25, 28, 29, 30, 32, 37, 39 } 63 : P_triple_{T}(E1,E0,E0,E0) { 0, 40 } 64 : P_triple_{T}(E1,E0,E1,E0) { 0, 41 } 65 : P_triple_{T}(E1,E1,E0,E0) { 0, 42 } 66 : P_triple_{T}(E1,E1,E1,E0) { 0, 43 } 67 : P_quadruple_{T}(E0,E0,E0,E1,E0) { 0, 44 } 68 : P_quadruple_{T}(E0,E0,E1,E0,E0) { 0, 45 } 69 : P_quadruple_{T}(E0,E0,E1,E1,E1) { 0, 46 } 70 : P_quadruple_{T}(E0,E1,E0,E0,E0) { 0, 47 } 71 : a_holds_{T}(E1) { 0, 1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 22, 23, 24, 27, 30, 31, 34, 47 } 72 : P_quadruple_{T}(E0,E1,E0,E1,E0) { 0, 48 } 73 : P_quadruple_{T}(E0,E1,E1,E0,E1) { 0, 49 } 74 : P_quadruple_{T}(E0,E1,E1,E1,E1) { 0, 50 } 75 : P_quadruple_{T}(E1,E0,E0,E0,E1) { 0, 51 } 76 : P_quadruple_{T}(E1,E0,E0,E1,E1) { 0, 52 } 77 : P_quadruple_{T}(E1,E0,E1,E0,E0) { 0, 53 } 78 : P_quadruple_{T}(E1,E0,E1,E1,E0) { 0, 54 } 79 : P_quadruple_{T}(E1,E1,E0,E0,E0) { 0, 55 } 80 : P_quadruple_{T}(E1,E1,E0,E1,E0) { 0, 56 } 81 : P_quadruple_{T}(E1,E1,E1,E0,E1) { 0, 57 } 82 : P_quadruple_{T}(E1,E1,E1,E1,E0) { 0, 58 } % SZS output end Model for /home/nivelle/TPTP-v6.1.0/Problems/SWV/SWV017+1.p  ## iProver 1.0 Konstantin Korovin, Christoph Sticksel University of Manchester, United Kingdom ### Sample solution for NLP042+1 % SZS output start Saturation fof(f236,plain,( ( ! [Xxs0,X1] : (~general(X0,X1) | ~specific(X0,X1)) )), inference(cnf_transformation,[],[f194])). fof(f194,plain,( ! [X0,X1] : (~specific(X0,X1) | ~general(X0,X1))), inference(ennf_transformation,[],[f51])). fof(f51,plain,( ! [X0,X1] : (specific(X0,X1) => ~general(X0,X1))), inference(flattening,[],[f41])). fof(f41,axiom,( ! [X0,X1] : (specific(X0,X1) => ~general(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f219,plain,( ( ! [X0,X1] : (specific(X0,X1) | ~entity(X0,X1)) )), inference(cnf_transformation,[],[f177])). fof(f177,plain,( ! [X0,X1] : (~entity(X0,X1) | specific(X0,X1))), inference(ennf_transformation,[],[f21])). fof(f21,axiom,( ! [X0,X1] : (entity(X0,X1) => specific(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f211,plain,( ( ! [X0,X1] : (general(X0,X1) | ~abstraction(X0,X1)) )), inference(cnf_transformation,[],[f169])). fof(f169,plain,( ! [X0,X1] : (~abstraction(X0,X1) | general(X0,X1))), inference(ennf_transformation,[],[f11])). fof(f11,axiom,( ! [X0,X1] : (abstraction(X0,X1) => general(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f213,plain,( ( ! [X0,X1] : (abstraction(X0,X1) | ~relation(X0,X1)) )), inference(cnf_transformation,[],[f171])). fof(f171,plain,( ! [X0,X1] : (~relation(X0,X1) | abstraction(X0,X1))), inference(ennf_transformation,[],[f14])). fof(f14,axiom,( ! [X0,X1] : (relation(X0,X1) => abstraction(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f214,plain,( ( ! [X0,X1] : (relation(X0,X1) | ~relname(X0,X1)) )), inference(cnf_transformation,[],[f172])). fof(f172,plain,( ! [X0,X1] : (~relname(X0,X1) | relation(X0,X1))), inference(ennf_transformation,[],[f15])). fof(f15,axiom,( ! [X0,X1] : (relname(X0,X1) => relation(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f215,plain,( ( ! [X0,X1] : (relname(X0,X1) | ~forename(X0,X1)) )), inference(cnf_transformation,[],[f173])). fof(f173,plain,( ! [X0,X1] : (~forename(X0,X1) | relname(X0,X1))), inference(ennf_transformation,[],[f16])). fof(f16,axiom,( ! [X0,X1] : (forename(X0,X1) => relname(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f243,plain,( forename(sK5,sK7)), inference(cnf_transformation,[],[f201])). fof(f201,plain,( of(sK5,sK7,sK6) & woman(sK5,sK6) & mia_forename(sK5,sK7) & forename(sK5,sK7) & shake_beverage(sK5,sK8) & event(sK5,sK9) & agent(sK5,sK9,sK6) & patient(sK5,sK9,sK8) & nonreflexive(sK5,sK9) & order(sK5,sK9)), inference(skolemisation,[status(esa)],[f153])). fof(f153,plain,( ? [X0,X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & nonreflexive(X0,X4) & order(X0,X4))), inference(pure_predicate_removal,[],[f152])). fof(f152,plain,( ? [X0] : (actual_world(X0) & ? [X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & nonreflexive(X0,X4) & order(X0,X4)))), inference(pure_predicate_removal,[],[f53])). fof(f53,plain,( ? [X0] : (actual_world(X0) & ? [X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & past(X0,X4) & nonreflexive(X0,X4) & order(X0,X4)))), inference(flattening,[],[f46])). fof(f46,negated_conjecture,( ~~? [X0] : (actual_world(X0) & ? [X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & past(X0,X4) & nonreflexive(X0,X4) & order(X0,X4)))), inference(negated_conjecture,[],[f45])). fof(f45,conjecture,( ~? [X0] : (actual_world(X0) & ? [X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & past(X0,X4) & nonreflexive(X0,X4) & order(X0,X4)))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f206,plain,( ( ! [X0,X1] : (entity(X0,X1) | ~organism(X0,X1)) )), inference(cnf_transformation,[],[f164])). fof(f164,plain,( ! [X0,X1] : (~organism(X0,X1) | entity(X0,X1))), inference(ennf_transformation,[],[f6])). fof(f6,axiom,( ! [X0,X1] : (organism(X0,X1) => entity(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f235,plain,( ( ! [X0,X1] : (~living(X0,X1) | ~nonliving(X0,X1)) )), inference(cnf_transformation,[],[f193])). fof(f193,plain,( ! [X0,X1] : (~nonliving(X0,X1) | ~living(X0,X1))), inference(ennf_transformation,[],[f50])). fof(f50,plain,( ! [X0,X1] : (nonliving(X0,X1) => ~living(X0,X1))), inference(flattening,[],[f40])). fof(f40,axiom,( ! [X0,X1] : (nonliving(X0,X1) => ~living(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f217,plain,( ( ! [X0,X1] : (nonliving(X0,X1) | ~object(X0,X1)) )), inference(cnf_transformation,[],[f175])). fof(f175,plain,( ! [X0,X1] : (~object(X0,X1) | nonliving(X0,X1))), inference(ennf_transformation,[],[f19])). fof(f19,axiom,( ! [X0,X1] : (object(X0,X1) => nonliving(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f221,plain,( ( ! [X0,X1] : (object(X0,X1) | ~substance_matter(X0,X1)) )), inference(cnf_transformation,[],[f179])). fof(f179,plain,( ! [X0,X1] : (~substance_matter(X0,X1) | object(X0,X1))), inference(ennf_transformation,[],[f24])). fof(f24,axiom,( ! [X0,X1] : (substance_matter(X0,X1) => object(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f222,plain,( ( ! [X0,X1] : (substance_matter(X0,X1) | ~food(X0,X1)) )), inference(cnf_transformation,[],[f180])). fof(f180,plain,( ! [X0,X1] : (~food(X0,X1) | substance_matter(X0,X1))), inference(ennf_transformation,[],[f25])). fof(f25,axiom,( ! [X0,X1] : (food(X0,X1) => substance_matter(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f223,plain,( ( ! [X0,X1] : (food(X0,X1) | ~beverage(X0,X1)) )), inference(cnf_transformation,[],[f181])). fof(f181,plain,( ! [X0,X1] : (~beverage(X0,X1) | food(X0,X1))), inference(ennf_transformation,[],[f26])). fof(f26,axiom,( ! [X0,X1] : (beverage(X0,X1) => food(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f224,plain,( ( ! [X0,X1] : (beverage(X0,X1) | ~shake_beverage(X0,X1)) )), inference(cnf_transformation,[],[f182])). fof(f182,plain,( ! [X0,X1] : (~shake_beverage(X0,X1) | beverage(X0,X1))), inference(ennf_transformation,[],[f27])). fof(f27,axiom,( ! [X0,X1] : (shake_beverage(X0,X1) => beverage(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f244,plain,( shake_beverage(sK5,sK8)), inference(cnf_transformation,[],[f201])). fof(f205,plain,( ( ! [X0,X1] : (living(X0,X1) | ~organism(X0,X1)) )), inference(cnf_transformation,[],[f163])). fof(f163,plain,( ! [X0,X1] : (~organism(X0,X1) | living(X0,X1))), inference(ennf_transformation,[],[f4])). fof(f4,axiom,( ! [X0,X1] : (organism(X0,X1) => living(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f207,plain,( ( ! [X0,X1] : (organism(X0,X1) | ~human_person(X0,X1)) )), inference(cnf_transformation,[],[f165])). fof(f165,plain,( ! [X0,X1] : (~human_person(X0,X1) | organism(X0,X1))), inference(ennf_transformation,[],[f7])). fof(f7,axiom,( ! [X0,X1] : (human_person(X0,X1) => organism(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f234,plain,( ( ! [X0,X1] : (~human(X0,X1) | ~nonhuman(X0,X1)) )), inference(cnf_transformation,[],[f192])). fof(f192,plain,( ! [X0,X1] : (~nonhuman(X0,X1) | ~human(X0,X1))), inference(ennf_transformation,[],[f49])). fof(f49,plain,( ! [X0,X1] : (nonhuman(X0,X1) => ~human(X0,X1))), inference(flattening,[],[f39])). fof(f39,axiom,( ! [X0,X1] : (nonhuman(X0,X1) => ~human(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f212,plain,( ( ! [X0,X1] : (nonhuman(X0,X1) | ~abstraction(X0,X1)) )), inference(cnf_transformation,[],[f170])). fof(f170,plain,( ! [X0,X1] : (~abstraction(X0,X1) | nonhuman(X0,X1))), inference(ennf_transformation,[],[f12])). fof(f12,axiom,( ! [X0,X1] : (abstraction(X0,X1) => nonhuman(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f204,plain,( ( ! [X0,X1] : (human(X0,X1) | ~human_person(X0,X1)) )), inference(cnf_transformation,[],[f162])). fof(f162,plain,( ! [X0,X1] : (~human_person(X0,X1) | human(X0,X1))), inference(ennf_transformation,[],[f3])). fof(f3,axiom,( ! [X0,X1] : (human_person(X0,X1) => human(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f208,plain,( ( ! [X0,X1] : (human_person(X0,X1) | ~woman(X0,X1)) )), inference(cnf_transformation,[],[f166])). fof(f166,plain,( ! [X0,X1] : (~woman(X0,X1) | human_person(X0,X1))), inference(ennf_transformation,[],[f8])). fof(f8,axiom,( ! [X0,X1] : (woman(X0,X1) => human_person(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f233,plain,( ( ! [X0,X1] : (~nonexistent(X0,X1) | ~existent(X0,X1)) )), inference(cnf_transformation,[],[f191])). fof(f191,plain,( ! [X0,X1] : (~existent(X0,X1) | ~nonexistent(X0,X1))), inference(ennf_transformation,[],[f48])). fof(f48,plain,( ! [X0,X1] : (existent(X0,X1) => ~nonexistent(X0,X1))), inference(flattening,[],[f38])). fof(f38,axiom,( ! [X0,X1] : (existent(X0,X1) => ~nonexistent(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f227,plain,( ( ! [X0,X1] : (nonexistent(X0,X1) | ~eventuality(X0,X1)) )), inference(cnf_transformation,[],[f185])). fof(f185,plain,( ! [X0,X1] : (~eventuality(X0,X1) | nonexistent(X0,X1))), inference(ennf_transformation,[],[f30])). fof(f30,axiom,( ! [X0,X1] : (eventuality(X0,X1) => nonexistent(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f229,plain,( ( ! [X0,X1] : (eventuality(X0,X1) | ~event(X0,X1)) )), inference(cnf_transformation,[],[f187])). fof(f187,plain,( ! [X0,X1] : (~event(X0,X1) | eventuality(X0,X1))), inference(ennf_transformation,[],[f34])). fof(f34,axiom,( ! [X0,X1] : (event(X0,X1) => eventuality(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f245,plain,( event(sK5,sK9)), inference(cnf_transformation,[],[f201])). fof(f218,plain,( ( ! [X0,X1] : (existent(X0,X1) | ~entity(X0,X1)) )), inference(cnf_transformation,[],[f176])). fof(f176,plain,( ! [X0,X1] : (~entity(X0,X1) | existent(X0,X1))), inference(ennf_transformation,[],[f20])). fof(f20,axiom,( ! [X0,X1] : (entity(X0,X1) => existent(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f232,plain,( ( ! [X0,X1] : (~nonliving(X0,X1) | ~animate(X0,X1)) )), inference(cnf_transformation,[],[f190])). fof(f190,plain,( ! [X0,X1] : (~animate(X0,X1) | ~nonliving(X0,X1))), inference(ennf_transformation,[],[f47])). fof(f47,plain,( ! [X0,X1] : (animate(X0,X1) => ~nonliving(X0,X1))), inference(flattening,[],[f37])). fof(f37,axiom,( ! [X0,X1] : (animate(X0,X1) => ~nonliving(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f203,plain,( ( ! [X0,X1] : (animate(X0,X1) | ~human_person(X0,X1)) )), inference(cnf_transformation,[],[f161])). fof(f161,plain,( ! [X0,X1] : (~human_person(X0,X1) | animate(X0,X1))), inference(ennf_transformation,[],[f2])). fof(f2,axiom,( ! [X0,X1] : (human_person(X0,X1) => animate(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f228,plain,( ( ! [X0,X1] : (specific(X0,X1) | ~eventuality(X0,X1)) )), inference(cnf_transformation,[],[f186])). fof(f186,plain,( ! [X0,X1] : (~eventuality(X0,X1) | specific(X0,X1))), inference(ennf_transformation,[],[f31])). fof(f31,axiom,( ! [X0,X1] : (eventuality(X0,X1) => specific(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f237,plain,( ( ! [X0,X1] : (~female(X0,X1) | ~unisex(X0,X1)) )), inference(cnf_transformation,[],[f195])). fof(f195,plain,( ! [X0,X1] : (~unisex(X0,X1) | ~female(X0,X1))), inference(ennf_transformation,[],[f52])). fof(f52,plain,( ! [X0,X1] : (unisex(X0,X1) => ~female(X0,X1))), inference(flattening,[],[f42])). fof(f42,axiom,( ! [X0,X1] : (unisex(X0,X1) => ~female(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f210,plain,( ( ! [X0,X1] : (unisex(X0,X1) | ~abstraction(X0,X1)) )), inference(cnf_transformation,[],[f168])). fof(f168,plain,( ! [X0,X1] : (~abstraction(X0,X1) | unisex(X0,X1))), inference(ennf_transformation,[],[f10])). fof(f10,axiom,( ! [X0,X1] : (abstraction(X0,X1) => unisex(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f226,plain,( ( ! [X0,X1] : (unisex(X0,X1) | ~eventuality(X0,X1)) )), inference(cnf_transformation,[],[f184])). fof(f184,plain,( ! [X0,X1] : (~eventuality(X0,X1) | unisex(X0,X1))), inference(ennf_transformation,[],[f29])). fof(f29,axiom,( ! [X0,X1] : (eventuality(X0,X1) => unisex(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f216,plain,( ( ! [X0,X1] : (unisex(X0,X1) | ~object(X0,X1)) )), inference(cnf_transformation,[],[f174])). fof(f174,plain,( ! [X0,X1] : (~object(X0,X1) | unisex(X0,X1))), inference(ennf_transformation,[],[f17])). fof(f17,axiom,( ! [X0,X1] : (object(X0,X1) => unisex(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f238,plain,( ( ! [X2,X0,X3,X1] : (~of(X0,X3,X1) | X2 = X3 | ~forename(X0,X3) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1)) )), inference(cnf_transformation,[],[f197])). fof(f197,plain,( ! [X0,X1,X2] : (~entity(X0,X1) | ~forename(X0,X2) | ~of(X0,X2,X1) | ! [X3] : (~forename(X0,X3) | X2 = X3 | ~of(X0,X3,X1)))), inference(flattening,[],[f196])). fof(f196,plain,( ! [X0,X1,X2] : ((~entity(X0,X1) | ~forename(X0,X2) | ~of(X0,X2,X1)) | ! [X3] : (~forename(X0,X3) | X2 = X3 | ~of(X0,X3,X1)))), inference(ennf_transformation,[],[f43])). fof(f43,axiom,( ! [X0,X1,X2] : ((entity(X0,X1) & forename(X0,X2) & of(X0,X2,X1)) => ~? [X3] : (forename(X0,X3) & X2 != X3 & of(X0,X3,X1)))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f240,plain,( of(sK5,sK7,sK6)), inference(cnf_transformation,[],[f201])). fof(f220,plain,( ( ! [X0,X1] : (entity(X0,X1) | ~object(X0,X1)) )), inference(cnf_transformation,[],[f178])). fof(f178,plain,( ! [X0,X1] : (~object(X0,X1) | entity(X0,X1))), inference(ennf_transformation,[],[f23])). fof(f23,axiom,( ! [X0,X1] : (object(X0,X1) => entity(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f239,plain,( ( ! [X2,X0,X1] : (~nonreflexive(X0,X1) | ~agent(X0,X1,X2) | ~patient(X0,X1,X2)) )), inference(cnf_transformation,[],[f200])). fof(f200,plain,( ! [X0,X1,X2] : (~patient(X0,X1,X2) | ~agent(X0,X1,X2) | ~nonreflexive(X0,X1))), inference(equality_propagation,[],[f199])). fof(f199,plain,( ! [X0,X1,X2,X3] : (~nonreflexive(X0,X1) | ~agent(X0,X1,X2) | ~patient(X0,X1,X3) | X2 != X3)), inference(flattening,[],[f198])). fof(f198,plain,( ! [X0,X1,X2,X3] : ((~nonreflexive(X0,X1) | ~agent(X0,X1,X2) | ~patient(X0,X1,X3)) | X2 != X3)), inference(ennf_transformation,[],[f44])). fof(f44,axiom,( ! [X0,X1,X2,X3] : ((nonreflexive(X0,X1) & agent(X0,X1,X2) & patient(X0,X1,X3)) => X2 != X3)), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f247,plain,( patient(sK5,sK9,sK8)), inference(cnf_transformation,[],[f201])). fof(f248,plain,( nonreflexive(sK5,sK9)), inference(cnf_transformation,[],[f201])). fof(f202,plain,( ( ! [X0,X1] : (female(X0,X1) | ~woman(X0,X1)) )), inference(cnf_transformation,[],[f160])). fof(f160,plain,( ! [X0,X1] : (~woman(X0,X1) | female(X0,X1))), inference(ennf_transformation,[],[f1])). fof(f1,axiom,( ! [X0,X1] : (woman(X0,X1) => female(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f241,plain,( woman(sK5,sK6)), inference(cnf_transformation,[],[f201])). fof(f242,plain,( mia_forename(sK5,sK7)), inference(cnf_transformation,[],[f201])). fof(f246,plain,( agent(sK5,sK9,sK6)), inference(cnf_transformation,[],[f201])). fof(f249,plain,( order(sK5,sK9)), inference(cnf_transformation,[],[f201])). fof(f231,plain,( ( ! [X0,X1] : (act(X0,X1) | ~order(X0,X1)) )), inference(cnf_transformation,[],[f189])). fof(f189,plain,( ! [X0,X1] : (~order(X0,X1) | act(X0,X1))), inference(ennf_transformation,[],[f36])). fof(f36,axiom,( ! [X0,X1] : (order(X0,X1) => act(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f230,plain,( ( ! [X0,X1] : (event(X0,X1) | ~act(X0,X1)) )), inference(cnf_transformation,[],[f188])). fof(f188,plain,( ! [X0,X1] : (~act(X0,X1) | event(X0,X1))), inference(ennf_transformation,[],[f35])). fof(f35,axiom,( ! [X0,X1] : (act(X0,X1) => event(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f225,plain,( ( ! [X0,X1] : (event(X0,X1) | ~order(X0,X1)) )), inference(cnf_transformation,[],[f183])). fof(f183,plain,( ! [X0,X1] : (~order(X0,X1) | event(X0,X1))), inference(ennf_transformation,[],[f28])). fof(f28,axiom,( ! [X0,X1] : (order(X0,X1) => event(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). fof(f209,plain,( ( ! [X0,X1] : (forename(X0,X1) | ~mia_forename(X0,X1)) )), inference(cnf_transformation,[],[f167])). fof(f167,plain,( ! [X0,X1] : (~mia_forename(X0,X1) | forename(X0,X1))), inference(ennf_transformation,[],[f9])). fof(f9,axiom,( ! [X0,X1] : (mia_forename(X0,X1) => forename(X0,X1))), file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)). cnf(c_573,plain, ( specific(X0_i,X1_i) | ~ specific(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_500,plain,( X0_i = X0_i ),theory(equality) ). cnf(c_1761,plain, ( specific(X0_i,X1_i) | ~ specific(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_573,c_500]) ). cnf(c_564,plain, ( organism(X0_i,X1_i) | ~ organism(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1748,plain, ( organism(X0_i,X1_i) | ~ organism(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_564,c_500]) ). cnf(c_562,plain, ( human_person(X0_i,X1_i) | ~ human_person(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1736,plain, ( human_person(X0_i,X1_i) | ~ human_person(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_562,c_500]) ). cnf(c_557,plain, ( general(X0_i,X1_i) | ~ general(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1724,plain, ( general(X0_i,X1_i) | ~ general(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_557,c_500]) ). cnf(c_555,plain, ( abstraction(X0_i,X1_i) | ~ abstraction(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1703,plain, ( abstraction(X0_i,X1_i) | ~ abstraction(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_555,c_500]) ). cnf(c_553,plain, ( relation(X0_i,X1_i) | ~ relation(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1682,plain, ( relation(X0_i,X1_i) | ~ relation(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_553,c_500]) ). cnf(c_551,plain, ( relname(X0_i,X1_i) | ~ relname(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1661,plain, ( relname(X0_i,X1_i) | ~ relname(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_551,c_500]) ). cnf(c_548,plain, ( unisex(X0_i,X1_i) | ~ unisex(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1638,plain, ( unisex(X0_i,X1_i) | ~ unisex(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_548,c_500]) ). cnf(c_546,plain, ( female(X0_i,X1_i) | ~ female(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1569,plain, ( female(X0_i,X1_i) | ~ female(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_546,c_500]) ). cnf(c_543,plain, ( nonhuman(X0_i,X1_i) | ~ nonhuman(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1557,plain, ( nonhuman(X0_i,X1_i) | ~ nonhuman(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_543,c_500]) ). cnf(c_541,plain, ( human(X0_i,X1_i) | ~ human(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1545,plain, ( human(X0_i,X1_i) | ~ human(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_541,c_500]) ). cnf(c_538,plain, ( entity(X0_i,X1_i) | ~ entity(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1533,plain, ( entity(X0_i,X1_i) | ~ entity(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_538,c_500]) ). cnf(c_536,plain, ( eventuality(X0_i,X1_i) | ~ eventuality(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1520,plain, ( eventuality(X0_i,X1_i) | ~ eventuality(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_536,c_500]) ). cnf(c_528,plain, ( act(X0_i,X1_i) | ~ act(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1508,plain, ( act(X0_i,X1_i) | ~ act(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_528,c_500]) ). cnf(c_34,plain, ( ~ general(X0_i,X1_i) | ~ specific(X0_i,X1_i) ), inference(cnf_transformation,[],[f236]) ). cnf(c_574,plain, ( ~ general(X0_i,X1_i) | ~ specific(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_34]) ). cnf(c_17,plain, ( ~ entity(X0_i,X1_i) | specific(X0_i,X1_i) ), inference(cnf_transformation,[],[f219]) ). cnf(c_558,plain, ( ~ entity(X0_i,X1_i) | specific(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_17]) ). cnf(c_1166,plain, ( ~ entity(X0_i,X1_i) | ~ general(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_574,c_558]) ). cnf(c_9,plain, ( ~ abstraction(X0_i,X1_i) | general(X0_i,X1_i) ), inference(cnf_transformation,[],[f211]) ). cnf(c_556,plain, ( ~ abstraction(X0_i,X1_i) | general(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_9]) ). cnf(c_1325,plain, ( ~ entity(X0_i,X1_i) | ~ abstraction(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_1166,c_556]) ). cnf(c_11,plain, ( abstraction(X0_i,X1_i) | ~ relation(X0_i,X1_i) ), inference(cnf_transformation,[],[f213]) ). cnf(c_554,plain, ( abstraction(X0_i,X1_i) | ~ relation(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_11]) ). cnf(c_12,plain, ( relation(X0_i,X1_i) | ~ relname(X0_i,X1_i) ), inference(cnf_transformation,[],[f214]) ). cnf(c_552,plain, ( relation(X0_i,X1_i) | ~ relname(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_12]) ). cnf(c_13,plain, ( ~ forename(X0_i,X1_i) | relname(X0_i,X1_i) ), inference(cnf_transformation,[],[f215]) ). cnf(c_550,plain, ( ~ forename(X0_i,X1_i) | relname(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_13]) ). cnf(c_1054,plain, ( ~ forename(X0_i,X1_i) | relation(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_552,c_550]) ). cnf(c_1065,plain, ( ~ forename(X0_i,X1_i) | abstraction(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_554,c_1054]) ). cnf(c_1393,plain, ( ~ entity(X0_i,X1_i) | ~ forename(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_1325,c_1065]) ). cnf(c_44,plain, ( forename(sK5,sK7) ), inference(cnf_transformation,[],[f243]) ). cnf(c_539,plain, ( forename(sK5,sK7) ), inference(subtyping,[status(esa)],[c_44]) ). cnf(c_1401,plain, ( ~ entity(sK5,sK7) ), inference(resolution,[status(thm)],[c_1393,c_539]) ). cnf(c_4,plain, ( ~ organism(X0_i,X1_i) | entity(X0_i,X1_i) ), inference(cnf_transformation,[],[f206]) ). cnf(c_565,plain, ( ~ organism(X0_i,X1_i) | entity(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_4]) ). cnf(c_1405,plain, ( ~ organism(sK5,sK7) ), inference(resolution,[status(thm)],[c_1401,c_565]) ). cnf(c_524,plain, ( nonexistent(X0_i,X1_i) | ~ nonexistent(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1385,plain, ( nonexistent(X0_i,X1_i) | ~ nonexistent(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_524,c_500]) ). cnf(c_522,plain, ( existent(X0_i,X1_i) | ~ existent(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1373,plain, ( existent(X0_i,X1_i) | ~ existent(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_522,c_500]) ). cnf(c_519,plain, ( substance_matter(X0_i,X1_i) | ~ substance_matter(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1361,plain, ( substance_matter(X0_i,X1_i) | ~ substance_matter(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_519,c_500]) ). cnf(c_517,plain, ( food(X0_i,X1_i) | ~ food(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1349,plain, ( food(X0_i,X1_i) | ~ food(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_517,c_500]) ). cnf(c_515,plain, ( beverage(X0_i,X1_i) | ~ beverage(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1337,plain, ( beverage(X0_i,X1_i) | ~ beverage(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_515,c_500]) ). cnf(c_33,plain, ( ~ living(X0_i,X1_i) | ~ nonliving(X0_i,X1_i) ), inference(cnf_transformation,[],[f235]) ). cnf(c_509,plain, ( ~ living(X0_i,X1_i) | ~ nonliving(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_33]) ). cnf(c_15,plain, ( ~ object(X0_i,X1_i) | nonliving(X0_i,X1_i) ), inference(cnf_transformation,[],[f217]) ). cnf(c_510,plain, ( ~ object(X0_i,X1_i) | nonliving(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_15]) ). cnf(c_1157,plain, ( ~ living(X0_i,X1_i) | ~ object(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_509,c_510]) ). cnf(c_19,plain, ( object(X0_i,X1_i) | ~ substance_matter(X0_i,X1_i) ), inference(cnf_transformation,[],[f221]) ). cnf(c_520,plain, ( object(X0_i,X1_i) | ~ substance_matter(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_19]) ). cnf(c_20,plain, ( substance_matter(X0_i,X1_i) | ~ food(X0_i,X1_i) ), inference(cnf_transformation,[],[f222]) ). cnf(c_518,plain, ( substance_matter(X0_i,X1_i) | ~ food(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_20]) ). cnf(c_21,plain, ( food(X0_i,X1_i) | ~ beverage(X0_i,X1_i) ), inference(cnf_transformation,[],[f223]) ). cnf(c_516,plain, ( food(X0_i,X1_i) | ~ beverage(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_21]) ). cnf(c_22,plain, ( beverage(X0_i,X1_i) | ~ shake_beverage(X0_i,X1_i) ), inference(cnf_transformation,[],[f224]) ). cnf(c_514,plain, ( beverage(X0_i,X1_i) | ~ shake_beverage(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_22]) ). cnf(c_43,plain, ( shake_beverage(sK5,sK8) ), inference(cnf_transformation,[],[f244]) ). cnf(c_512,plain, ( shake_beverage(sK5,sK8) ), inference(subtyping,[status(esa)],[c_43]) ). cnf(c_600,plain, ( beverage(sK5,sK8) ), inference(resolution,[status(thm)],[c_514,c_512]) ). cnf(c_765,plain, ( food(sK5,sK8) ), inference(resolution,[status(thm)],[c_516,c_600]) ). cnf(c_925,plain, ( substance_matter(sK5,sK8) ), inference(resolution,[status(thm)],[c_518,c_765]) ). cnf(c_1013,plain, ( object(sK5,sK8) ), inference(resolution,[status(thm)],[c_520,c_925]) ). cnf(c_1309,plain, ( ~ living(sK5,sK8) ), inference(resolution,[status(thm)],[c_1157,c_1013]) ). cnf(c_3,plain, ( living(X0_i,X1_i) | ~ organism(X0_i,X1_i) ), inference(cnf_transformation,[],[f205]) ). cnf(c_507,plain, ( living(X0_i,X1_i) | ~ organism(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_3]) ). cnf(c_5,plain, ( ~ human_person(X0_i,X1_i) | organism(X0_i,X1_i) ), inference(cnf_transformation,[],[f207]) ). cnf(c_563,plain, ( ~ human_person(X0_i,X1_i) | organism(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_5]) ). cnf(c_1092,plain, ( ~ human_person(X0_i,X1_i) | living(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_507,c_563]) ). cnf(c_1313,plain, ( ~ human_person(sK5,sK8) ), inference(resolution,[status(thm)],[c_1309,c_1092]) ). cnf(c_32,plain, ( ~ human(X0_i,X1_i) | ~ nonhuman(X0_i,X1_i) ), inference(cnf_transformation,[],[f234]) ). cnf(c_542,plain, ( ~ human(X0_i,X1_i) | ~ nonhuman(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_32]) ). cnf(c_10,plain, ( ~ abstraction(X0_i,X1_i) | nonhuman(X0_i,X1_i) ), inference(cnf_transformation,[],[f212]) ). cnf(c_544,plain, ( ~ abstraction(X0_i,X1_i) | nonhuman(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_10]) ). cnf(c_1125,plain, ( ~ human(X0_i,X1_i) | ~ abstraction(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_542,c_544]) ). cnf(c_1285,plain, ( ~ human(X0_i,X1_i) | ~ forename(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_1125,c_1065]) ). cnf(c_1292,plain, ( ~ human(sK5,sK7) ), inference(resolution,[status(thm)],[c_1285,c_539]) ). cnf(c_2,plain, ( ~ human_person(X0_i,X1_i) | human(X0_i,X1_i) ), inference(cnf_transformation,[],[f204]) ). cnf(c_540,plain, ( ~ human_person(X0_i,X1_i) | human(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_2]) ). cnf(c_1296,plain, ( ~ human_person(sK5,sK7) ), inference(resolution,[status(thm)],[c_1292,c_540]) ). cnf(c_6,plain, ( ~ woman(X0_i,X1_i) | human_person(X0_i,X1_i) ), inference(cnf_transformation,[],[f208]) ). cnf(c_561,plain, ( ~ woman(X0_i,X1_i) | human_person(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_6]) ). cnf(c_1300,plain, ( ~ woman(sK5,sK7) ), inference(resolution,[status(thm)],[c_1296,c_561]) ). cnf(c_31,plain, ( ~ existent(X0_i,X1_i) | ~ nonexistent(X0_i,X1_i) ), inference(cnf_transformation,[],[f233]) ). cnf(c_525,plain, ( ~ existent(X0_i,X1_i) | ~ nonexistent(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_31]) ). cnf(c_25,plain, ( ~ eventuality(X0_i,X1_i) | nonexistent(X0_i,X1_i) ), inference(cnf_transformation,[],[f227]) ). cnf(c_523,plain, ( ~ eventuality(X0_i,X1_i) | nonexistent(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_25]) ). cnf(c_1118,plain, ( ~ existent(X0_i,X1_i) | ~ eventuality(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_525,c_523]) ). cnf(c_27,plain, ( ~ event(X0_i,X1_i) | eventuality(X0_i,X1_i) ), inference(cnf_transformation,[],[f229]) ). cnf(c_535,plain, ( ~ event(X0_i,X1_i) | eventuality(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_27]) ). cnf(c_1196,plain, ( ~ existent(X0_i,X1_i) | ~ event(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_1118,c_535]) ). cnf(c_42,plain,( event(sK5,sK9) ),inference(cnf_transformation,[],[f245]) ). cnf(c_534,plain, ( event(sK5,sK9) ), inference(subtyping,[status(esa)],[c_42]) ). cnf(c_1260,plain, ( ~ existent(sK5,sK9) ), inference(resolution,[status(thm)],[c_1196,c_534]) ). cnf(c_16,plain, ( ~ entity(X0_i,X1_i) | existent(X0_i,X1_i) ), inference(cnf_transformation,[],[f218]) ). cnf(c_521,plain, ( ~ entity(X0_i,X1_i) | existent(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_16]) ). cnf(c_1264,plain, ( ~ entity(sK5,sK9) ), inference(resolution,[status(thm)],[c_1260,c_521]) ). cnf(c_1268,plain, ( ~ organism(sK5,sK9) ), inference(resolution,[status(thm)],[c_1264,c_565]) ). cnf(c_1272,plain, ( ~ human_person(sK5,sK9) ), inference(resolution,[status(thm)],[c_1268,c_563]) ). cnf(c_1276,plain, ( ~ woman(sK5,sK9) ), inference(resolution,[status(thm)],[c_1272,c_561]) ). cnf(c_511,plain, ( object(X0_i,X1_i) | ~ object(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1253,plain, ( object(X0_i,X1_i) | ~ object(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_511,c_500]) ). cnf(c_508,plain, ( living(X0_i,X1_i) | ~ living(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1241,plain, ( living(X0_i,X1_i) | ~ living(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_508,c_500]) ). cnf(c_506,plain, ( nonliving(X0_i,X1_i) | ~ nonliving(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1229,plain, ( nonliving(X0_i,X1_i) | ~ nonliving(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_506,c_500]) ). cnf(c_504,plain, ( animate(X0_i,X1_i) | ~ animate(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_1217,plain, ( animate(X0_i,X1_i) | ~ animate(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_504,c_500]) ). cnf(c_499,plain, ( X0_i != X1_i | X2_i != X1_i | X2_i = X0_i ), theory(equality) ). cnf(c_1205,plain, ( X0_i != X1_i | X1_i = X0_i ), inference(resolution,[status(thm)],[c_499,c_500]) ). cnf(c_30,plain, ( ~ animate(X0_i,X1_i) | ~ nonliving(X0_i,X1_i) ), inference(cnf_transformation,[],[f232]) ). cnf(c_505,plain, ( ~ animate(X0_i,X1_i) | ~ nonliving(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_30]) ). cnf(c_1107,plain, ( ~ animate(X0_i,X1_i) | ~ object(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_505,c_510]) ). cnf(c_1183,plain, ( ~ animate(sK5,sK8) ), inference(resolution,[status(thm)],[c_1107,c_1013]) ). cnf(c_1,plain, ( animate(X0_i,X1_i) | ~ human_person(X0_i,X1_i) ), inference(cnf_transformation,[],[f203]) ). cnf(c_503,plain, ( animate(X0_i,X1_i) | ~ human_person(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_1]) ). cnf(c_755,plain, ( ~ woman(X0_i,X1_i) | animate(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_503,c_561]) ). cnf(c_1187,plain, ( ~ woman(sK5,sK8) ), inference(resolution,[status(thm)],[c_1183,c_755]) ). cnf(c_26,plain, ( specific(X0_i,X1_i) | ~ eventuality(X0_i,X1_i) ), inference(cnf_transformation,[],[f228]) ). cnf(c_537,plain, ( specific(X0_i,X1_i) | ~ eventuality(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_26]) ). cnf(c_946,plain, ( specific(X0_i,X1_i) | ~ event(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_537,c_535]) ). cnf(c_962,plain, ( specific(sK5,sK9) ), inference(resolution,[status(thm)],[c_946,c_534]) ). cnf(c_1165,plain, ( ~ general(sK5,sK9) ), inference(resolution,[status(thm)],[c_574,c_962]) ). cnf(c_1170,plain, ( ~ abstraction(sK5,sK9) ), inference(resolution,[status(thm)],[c_1165,c_556]) ). cnf(c_1174,plain, ( ~ forename(sK5,sK9) ), inference(resolution,[status(thm)],[c_1170,c_1065]) ). cnf(c_35,plain, ( ~ female(X0_i,X1_i) | ~ unisex(X0_i,X1_i) ), inference(cnf_transformation,[],[f237]) ). cnf(c_547,plain, ( ~ female(X0_i,X1_i) | ~ unisex(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_35]) ). cnf(c_8,plain, ( unisex(X0_i,X1_i) | ~ abstraction(X0_i,X1_i) ), inference(cnf_transformation,[],[f210]) ). cnf(c_549,plain, ( unisex(X0_i,X1_i) | ~ abstraction(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_8]) ). cnf(c_1071,plain, ( ~ forename(X0_i,X1_i) | unisex(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_549,c_1065]) ). cnf(c_1136,plain, ( ~ female(X0_i,X1_i) | ~ forename(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_547,c_1071]) ). cnf(c_1148,plain, ( ~ female(sK5,sK7) ), inference(resolution,[status(thm)],[c_1136,c_539]) ). cnf(c_24,plain, ( unisex(X0_i,X1_i) | ~ eventuality(X0_i,X1_i) ), inference(cnf_transformation,[],[f226]) ). cnf(c_526,plain, ( unisex(X0_i,X1_i) | ~ eventuality(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_24]) ). cnf(c_940,plain, ( unisex(X0_i,X1_i) | ~ event(X0_i,X1_i) ), inference(resolution,[status(thm)],[c_526,c_535]) ). cnf(c_954,plain, ( unisex(sK5,sK9) ), inference(resolution,[status(thm)],[c_940,c_534]) ). cnf(c_1135,plain, ( ~ female(sK5,sK9) ), inference(resolution,[status(thm)],[c_547,c_954]) ). cnf(c_14,plain, ( unisex(X0_i,X1_i) | ~ object(X0_i,X1_i) ), inference(cnf_transformation,[],[f216]) ). cnf(c_501,plain, ( unisex(X0_i,X1_i) | ~ object(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_14]) ). cnf(c_1016,plain, ( unisex(sK5,sK8) ), inference(resolution,[status(thm)],[c_501,c_1013]) ). cnf(c_1134,plain, ( ~ female(sK5,sK8) ), inference(resolution,[status(thm)],[c_547,c_1016]) ). cnf(c_36,plain, ( ~ entity(X0_i,X1_i) | ~ forename(X0_i,X2_i) | ~ forename(X0_i,X3_i) | ~ of(X0_i,X2_i,X1_i) | ~ of(X0_i,X3_i,X1_i) | X2_i = X3_i ), inference(cnf_transformation,[],[f238]) ). cnf(c_572,plain, ( ~ entity(X0_i,X1_i) | ~ forename(X0_i,X2_i) | ~ forename(X0_i,X3_i) | ~ of(X0_i,X2_i,X1_i) | ~ of(X0_i,X3_i,X1_i) | X2_i = X3_i ), inference(subtyping,[status(esa)],[c_36]) ). cnf(c_47,plain,( of(sK5,sK7,sK6) ),inference(cnf_transformation,[],[f240]) ). cnf(c_570,plain, ( of(sK5,sK7,sK6) ), inference(subtyping,[status(esa)],[c_47]) ). cnf(c_1039,plain, ( ~ entity(sK5,sK6) | ~ forename(sK5,sK7) | ~ forename(sK5,X0_i) | ~ of(sK5,X0_i,sK6) | X0_i = sK7 ), inference(resolution,[status(thm)],[c_572,c_570]) ). cnf(c_51,plain, ( forename(sK5,sK7) ), inference(subtyping,[status(esa)],[c_44]) ). cnf(c_1040,plain, ( ~ entity(sK5,sK6) | ~ forename(sK5,X0_i) | ~ of(sK5,X0_i,sK6) | X0_i = sK7 ), inference(global_propositional_subsumption,[status(thm)],[c_1039,c_51]) ). cnf(c_18,plain, ( entity(X0_i,X1_i) | ~ object(X0_i,X1_i) ), inference(cnf_transformation,[],[f220]) ). cnf(c_502,plain, ( entity(X0_i,X1_i) | ~ object(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_18]) ). cnf(c_1019,plain, ( entity(sK5,sK8) ), inference(resolution,[status(thm)],[c_502,c_1013]) ). cnf(c_571,plain, ( of(X0_i,X1_i,X2_i) | ~ of(X3_i,X4_i,X5_i) | X0_i != X3_i | X1_i != X4_i | X2_i != X5_i ), theory(equality) ). cnf(c_979,plain, ( of(X0_i,X1_i,X2_i) | ~ of(X3_i,X4_i,X2_i) | X0_i != X3_i | X1_i != X4_i ), inference(resolution,[status(thm)],[c_571,c_500]) ). cnf(c_991,plain, ( of(X0_i,X1_i,X2_i) | ~ of(X3_i,X1_i,X2_i) | X0_i != X3_i ), inference(resolution,[status(thm)],[c_979,c_500]) ). cnf(c_497,plain, ( patient(X0_i,X1_i,X2_i) | ~ patient(X3_i,X4_i,X5_i) | X0_i != X3_i | X1_i != X4_i | X2_i != X5_i ), theory(equality) ). cnf(c_903,plain, ( patient(X0_i,X1_i,X2_i) | ~ patient(X3_i,X4_i,X2_i) | X0_i != X3_i | X1_i != X4_i ), inference(resolution,[status(thm)],[c_497,c_500]) ). cnf(c_915,plain, ( patient(X0_i,X1_i,X2_i) | ~ patient(X3_i,X1_i,X2_i) | X0_i != X3_i ), inference(resolution,[status(thm)],[c_903,c_500]) ). cnf(c_495,plain, ( agent(X0_i,X1_i,X2_i) | ~ agent(X3_i,X4_i,X5_i) | X0_i != X3_i | X1_i != X4_i | X2_i != X5_i ), theory(equality) ). cnf(c_867,plain, ( agent(X0_i,X1_i,X2_i) | ~ agent(X3_i,X4_i,X2_i) | X0_i != X3_i | X1_i != X4_i ), inference(resolution,[status(thm)],[c_495,c_500]) ). cnf(c_879,plain, ( agent(X0_i,X1_i,X2_i) | ~ agent(X3_i,X1_i,X2_i) | X0_i != X3_i ), inference(resolution,[status(thm)],[c_867,c_500]) ). cnf(c_569,plain, ( forename(X0_i,X1_i) | ~ forename(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_843,plain, ( forename(X0_i,X1_i) | ~ forename(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_569,c_500]) ). cnf(c_567,plain, ( mia_forename(X0_i,X1_i) | ~ mia_forename(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_822,plain, ( mia_forename(X0_i,X1_i) | ~ mia_forename(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_567,c_500]) ). cnf(c_560,plain, ( woman(X0_i,X1_i) | ~ woman(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_801,plain, ( woman(X0_i,X1_i) | ~ woman(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_560,c_500]) ). cnf(c_532,plain, ( order(X0_i,X1_i) | ~ order(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_754,plain, ( order(X0_i,X1_i) | ~ order(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_532,c_500]) ). cnf(c_530,plain, ( event(X0_i,X1_i) | ~ event(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_733,plain, ( event(X0_i,X1_i) | ~ event(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_530,c_500]) ). cnf(c_513,plain, ( shake_beverage(X0_i,X1_i) | ~ shake_beverage(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_712,plain, ( shake_beverage(X0_i,X1_i) | ~ shake_beverage(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_513,c_500]) ). cnf(c_493,plain, ( nonreflexive(X0_i,X1_i) | ~ nonreflexive(X2_i,X3_i) | X0_i != X2_i | X1_i != X3_i ), theory(equality) ). cnf(c_691,plain, ( nonreflexive(X0_i,X1_i) | ~ nonreflexive(X2_i,X1_i) | X0_i != X2_i ), inference(resolution,[status(thm)],[c_493,c_500]) ). cnf(c_37,plain, ( ~ nonreflexive(X0_i,X1_i) | ~ agent(X0_i,X1_i,X2_i) | ~ patient(X0_i,X1_i,X2_i) ), inference(cnf_transformation,[],[f239]) ). cnf(c_498,plain, ( ~ nonreflexive(X0_i,X1_i) | ~ agent(X0_i,X1_i,X2_i) | ~ patient(X0_i,X1_i,X2_i) ), inference(subtyping,[status(esa)],[c_37]) ). cnf(c_40,plain, ( patient(sK5,sK9,sK8) ), inference(cnf_transformation,[],[f247]) ). cnf(c_496,plain, ( patient(sK5,sK9,sK8) ), inference(subtyping,[status(esa)],[c_40]) ). cnf(c_676,plain, ( ~ nonreflexive(sK5,sK9) | ~ agent(sK5,sK9,sK8) ), inference(resolution,[status(thm)],[c_498,c_496]) ). cnf(c_39,plain, ( nonreflexive(sK5,sK9) ), inference(cnf_transformation,[],[f248]) ). cnf(c_56,plain, ( nonreflexive(sK5,sK9) ), inference(subtyping,[status(esa)],[c_39]) ). cnf(c_677,plain, ( ~ agent(sK5,sK9,sK8) ), inference(global_propositional_subsumption,[status(thm)],[c_676,c_56]) ). cnf(c_0,plain, ( female(X0_i,X1_i) | ~ woman(X0_i,X1_i) ), inference(cnf_transformation,[],[f202]) ). cnf(c_545,plain, ( female(X0_i,X1_i) | ~ woman(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_0]) ). cnf(c_46,plain,( woman(sK5,sK6) ),inference(cnf_transformation,[],[f241]) ). cnf(c_559,plain, ( woman(sK5,sK6) ), inference(subtyping,[status(esa)],[c_46]) ). cnf(c_648,plain, ( female(sK5,sK6) ), inference(resolution,[status(thm)],[c_545,c_559]) ). cnf(c_45,plain, ( mia_forename(sK5,sK7) ), inference(cnf_transformation,[],[f242]) ). cnf(c_566,plain, ( mia_forename(sK5,sK7) ), inference(subtyping,[status(esa)],[c_45]) ). cnf(c_41,plain, ( agent(sK5,sK9,sK6) ), inference(cnf_transformation,[],[f246]) ). cnf(c_494,plain, ( agent(sK5,sK9,sK6) ), inference(subtyping,[status(esa)],[c_41]) ). cnf(c_492,plain, ( nonreflexive(sK5,sK9) ), inference(subtyping,[status(esa)],[c_39]) ). cnf(c_38,plain,( order(sK5,sK9) ),inference(cnf_transformation,[],[f249]) ). cnf(c_531,plain, ( order(sK5,sK9) ), inference(subtyping,[status(esa)],[c_38]) ). cnf(c_29,plain, ( ~ order(X0_i,X1_i) | act(X0_i,X1_i) ), inference(cnf_transformation,[],[f231]) ). cnf(c_527,plain, ( ~ order(X0_i,X1_i) | act(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_29]) ). cnf(c_28,plain, ( event(X0_i,X1_i) | ~ act(X0_i,X1_i) ), inference(cnf_transformation,[],[f230]) ). cnf(c_529,plain, ( event(X0_i,X1_i) | ~ act(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_28]) ). cnf(c_23,plain, ( event(X0_i,X1_i) | ~ order(X0_i,X1_i) ), inference(cnf_transformation,[],[f225]) ). cnf(c_533,plain, ( event(X0_i,X1_i) | ~ order(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_23]) ). cnf(c_7,plain, ( forename(X0_i,X1_i) | ~ mia_forename(X0_i,X1_i) ), inference(cnf_transformation,[],[f209]) ). cnf(c_568,plain, ( forename(X0_i,X1_i) | ~ mia_forename(X0_i,X1_i) ), inference(subtyping,[status(esa)],[c_7]) ). % SZS output end Saturation  ### Sample finite model for NLP042+1 %------ The model is defined over ground terms (initial term algebra). %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) %------ where \phi is a formula over the term algebra. %------ If we have equality in the problem then it is also defined as a predicate above, %------ with "=" on the right-hand-side of the definition interpreted over the term algebra$$term_algebra_type %------ See help for --sat_out_model for different model outputs. %------ equality_sorted(X0,X1,X2) can be used in the place of usual "=" %------ where the first argument stands for the sort ($i in the unsorted case)
% SZS output start Model

%------ Negative definition of $$equality_sorted fof(lit_def,axiom, (! [X0_tType,X0_i,X1_i] : ( ~($$equality_sorted(X0_$tType,X0_$i,X1_$i)) <=> ( ( ( X0_$tType=$i & X0_$i=sK9 )
&
( X1_$i!=sK9 ) ) | ( ( X0_$tType=$i & X0_$i=sK8 )
&
( X1_$i!=sK8 ) ) | ( ( X0_$tType=$i & X0_$i=sK6 )
&
( X1_$i!=sK6 ) ) | ( ( X0_$tType=$i & X0_$i=sK7 )
&
( X1_$i!=sK7 ) ) | ( ( X0_$tType=$i & X1_$i=sK9 )
&
( X0_$i!=sK9 ) ) | ( ( X0_$tType=$i & X1_$i=sK8 )
&
( X0_$i!=sK8 ) ) | ( ( X0_$tType=$i & X1_$i=sK6 )
&
( X0_$i!=sK6 ) ) | ( ( X0_$tType=$i & X1_$i=sK7 )
&
( X0_$i!=sK7 ) ) ) ) ) ). %------ Positive definition of female fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( female(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK6 ) ) | ( ( X1_$i=sK6 )
)

)
)
)
).

%------ Positive definition of woman
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( woman(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK6 )
)

|
(
( X1_$i=sK6 ) ) ) ) ) ). %------ Positive definition of animate fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( animate(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK6 ) ) | ( ( X1_$i=sK6 )
)

)
)
)
).

%------ Positive definition of human_person
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( human_person(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK6 )
)

|
(
( X1_$i=sK6 ) ) ) ) ) ). %------ Positive definition of human fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( human(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK6 ) ) | ( ( X1_$i=sK6 )
)

)
)
)
).

%------ Positive definition of living
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( living(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK6 )
)

|
(
( X1_$i=sK6 ) ) ) ) ) ). %------ Positive definition of organism fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( organism(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK6 ) ) | ( ( X1_$i=sK6 )
)

)
)
)
).

%------ Positive definition of entity
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( entity(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK8 )
)

|
(
( X0_$i=sK5 & X1_$i=sK6 )
)

|
(
( X1_$i=sK8 ) ) | ( ( X1_$i=sK6 )
)

)
)
)
).

%------ Positive definition of forename
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( forename(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK7 )
)

|
(
( X1_$i=sK7 ) ) ) ) ) ). %------ Positive definition of mia_forename fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( mia_forename(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK7 ) ) | ( ( X1_$i=sK7 )
)

)
)
)
).

%------ Positive definition of unisex
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( unisex(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK9 )
)

|
(
( X0_$i=sK5 & X1_$i=sK8 )
)

|
(
( X0_$i=sK5 & X1_$i=sK7 )
)

|
(
( X1_$i=sK9 ) ) | ( ( X1_$i=sK8 )
)

|
(
( X1_$i=sK7 ) ) ) ) ) ). %------ Positive definition of abstraction fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( abstraction(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK7 ) ) | ( ( X1_$i=sK7 )
)

)
)
)
).

%------ Positive definition of general
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( general(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK7 )
)

|
(
( X1_$i=sK7 ) ) ) ) ) ). %------ Positive definition of nonhuman fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( nonhuman(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK7 ) ) | ( ( X1_$i=sK7 )
)

)
)
)
).

%------ Positive definition of relation
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( relation(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK7 )
)

|
(
( X1_$i=sK7 ) ) ) ) ) ). %------ Positive definition of relname fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( relname(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK7 ) ) | ( ( X1_$i=sK7 )
)

)
)
)
).

%------ Positive definition of object
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( object(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK8 )
)

|
(
( X1_$i=sK8 ) ) ) ) ) ). %------ Positive definition of nonliving fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( nonliving(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK8 ) ) | ( ( X1_$i=sK8 )
)

)
)
)
).

%------ Positive definition of existent
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( existent(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK8 )
)

|
(
( X0_$i=sK5 & X1_$i=sK6 )
)

|
(
( X1_$i=sK8 ) ) | ( ( X1_$i=sK6 )
)

)
)
)
).

%------ Positive definition of specific
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( specific(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK9 )
)

|
(
( X0_$i=sK5 & X1_$i=sK8 )
)

|
(
( X0_$i=sK5 & X1_$i=sK6 )
)

|
(
( X1_$i=sK9 ) ) | ( ( X1_$i=sK8 )
)

|
(
( X1_$i=sK6 ) ) ) ) ) ). %------ Positive definition of substance_matter fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( substance_matter(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK8 ) ) | ( ( X1_$i=sK8 )
)

)
)
)
).

%------ Positive definition of food
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( food(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK8 )
)

|
(
( X1_$i=sK8 ) ) ) ) ) ). %------ Positive definition of beverage fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( beverage(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK8 ) ) | ( ( X1_$i=sK8 )
)

)
)
)
).

%------ Positive definition of shake_beverage
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( shake_beverage(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK8 )
)

|
(
( X1_$i=sK8 ) ) ) ) ) ). %------ Positive definition of event fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( event(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK9 ) ) | ( ( X1_$i=sK9 )
)

)
)
)
).

%------ Positive definition of order
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( order(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK9 )
)

|
(
( X1_$i=sK9 ) ) ) ) ) ). %------ Positive definition of eventuality fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( eventuality(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK9 ) ) | ( ( X1_$i=sK9 )
)

)
)
)
).

%------ Positive definition of nonexistent
fof(lit_def,axiom,
(! [X0_$i,X1_$i] :
( nonexistent(X0_$i,X1_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK9 )
)

|
(
( X1_$i=sK9 ) ) ) ) ) ). %------ Positive definition of act fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( act(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK9 ) ) | ( ( X1_$i=sK9 )
)

)
)
)
).

%------ Positive definition of of
fof(lit_def,axiom,
(! [X0_$i,X1_$i,X2_$i] : ( of(X0_$i,X1_$i,X2_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK7 & X2_$i=sK6 ) ) | ( ( X1_$i=sK7 & X2_$i=sK6 ) ) ) ) ) ). %------ Positive definition of nonreflexive fof(lit_def,axiom, (! [X0_$i,X1_$i] : ( nonreflexive(X0_$i,X1_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK9 ) ) | ( ( X1_$i=sK9 )
)

)
)
)
).

%------ Positive definition of agent
fof(lit_def,axiom,
(! [X0_$i,X1_$i,X2_$i] : ( agent(X0_$i,X1_$i,X2_$i) <=>
(
(
( X0_$i=sK5 & X1_$i=sK9 & X2_$i=sK6 ) ) | ( ( X1_$i=sK9 & X2_$i=sK6 ) ) ) ) ) ). %------ Positive definition of patient fof(lit_def,axiom, (! [X0_$i,X1_$i,X2_$i] :
( patient(X0_$i,X1_$i,X2_$i) <=> ( ( ( X0_$i=sK5 & X1_$i=sK9 & X2_$i=sK8 )
)

|
(
( X1_$i=sK9 & X2_$i=sK8 )
)

)
)
)
).

% SZS output end Model


### Sample solution for SWV017+1

% SZS output start Saturation

fof(f168,plain,(
( ! [X0] : (~a_nonce(generate_key(X0))) )),
inference(cnf_transformation,[],[f36])).

fof(f36,plain,(
! [X0] : ~a_nonce(generate_key(X0))),
inference(flattening,[],[f27])).

fof(f27,axiom,(
! [X0] : ~a_nonce(generate_key(X0))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f160,plain,(
( ! [X0,X1] : (intruder_message(pair(X0,X1)) | ~intruder_message(X1) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f123])).

fof(f123,plain,(
! [X0,X1] : (~intruder_message(X0) | ~intruder_message(X1) | intruder_message(pair(X0,X1)))),
inference(flattening,[],[f122])).

fof(f122,plain,(
! [X0,X1] : ((~intruder_message(X0) | ~intruder_message(X1)) | intruder_message(pair(X0,X1)))),
inference(ennf_transformation,[],[f19])).

fof(f19,axiom,(
! [X0,X1] : ((intruder_message(X0) & intruder_message(X1)) => intruder_message(pair(X0,X1)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f176,plain,(
( ! [X0] : (intruder_message(X0) | ~fresh_intruder_nonce(X0)) )),
inference(cnf_transformation,[],[f138])).

fof(f138,plain,(
! [X0] : (~fresh_intruder_nonce(X0) | (fresh_to_b(X0) & intruder_message(X0)))),
inference(ennf_transformation,[],[f33])).

fof(f33,axiom,(
! [X0] : (fresh_intruder_nonce(X0) => (fresh_to_b(X0) & intruder_message(X0)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f163,plain,(
( ! [X2,X0,X1] : (intruder_message(X1) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(encrypt(X0,X1))) )),
inference(cnf_transformation,[],[f129])).

fof(f129,plain,(
! [X0,X1,X2] : (~intruder_message(encrypt(X0,X1)) | ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2) | intruder_message(X1))),
inference(flattening,[],[f128])).

fof(f128,plain,(
! [X0,X1,X2] : ((~intruder_message(encrypt(X0,X1)) | ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2)) | intruder_message(X1))),
inference(ennf_transformation,[],[f22])).

fof(f22,axiom,(
! [X0,X1,X2] : ((intruder_message(encrypt(X0,X1)) & intruder_holds(key(X1,X2)) & party_of_protocol(X2)) => intruder_message(X1))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f156,plain,(
( ! [X2,X0,X3,X1] : (intruder_message(X0) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
inference(cnf_transformation,[],[f121])).

fof(f121,plain,(
! [X0,X1,X2,X3] : (~intruder_message(quadruple(X0,X1,X2,X3)) | (intruder_message(X0) & intruder_message(X1) & intruder_message(X2) & intruder_message(X3)))),
inference(ennf_transformation,[],[f18])).

fof(f18,axiom,(
! [X0,X1,X2,X3] : (intruder_message(quadruple(X0,X1,X2,X3)) => (intruder_message(X0) & intruder_message(X1) & intruder_message(X2) & intruder_message(X3)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f157,plain,(
( ! [X2,X0,X3,X1] : (intruder_message(X1) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
inference(cnf_transformation,[],[f121])).

fof(f158,plain,(
( ! [X2,X0,X3,X1] : (intruder_message(X2) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
inference(cnf_transformation,[],[f121])).

fof(f159,plain,(
( ! [X2,X0,X3,X1] : (intruder_message(X3) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
inference(cnf_transformation,[],[f121])).

fof(f153,plain,(
( ! [X2,X0,X1] : (intruder_message(X0) | ~intruder_message(triple(X0,X1,X2))) )),
inference(cnf_transformation,[],[f120])).

fof(f120,plain,(
! [X0,X1,X2] : (~intruder_message(triple(X0,X1,X2)) | (intruder_message(X0) & intruder_message(X1) & intruder_message(X2)))),
inference(ennf_transformation,[],[f17])).

fof(f17,axiom,(
! [X0,X1,X2] : (intruder_message(triple(X0,X1,X2)) => (intruder_message(X0) & intruder_message(X1) & intruder_message(X2)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f154,plain,(
( ! [X2,X0,X1] : (intruder_message(X1) | ~intruder_message(triple(X0,X1,X2))) )),
inference(cnf_transformation,[],[f120])).

fof(f155,plain,(
( ! [X2,X0,X1] : (intruder_message(X2) | ~intruder_message(triple(X0,X1,X2))) )),
inference(cnf_transformation,[],[f120])).

fof(f151,plain,(
( ! [X0,X1] : (intruder_message(X0) | ~intruder_message(pair(X0,X1))) )),
inference(cnf_transformation,[],[f119])).

fof(f119,plain,(
! [X0,X1] : (~intruder_message(pair(X0,X1)) | (intruder_message(X0) & intruder_message(X1)))),
inference(ennf_transformation,[],[f16])).

fof(f16,axiom,(
! [X0,X1] : (intruder_message(pair(X0,X1)) => (intruder_message(X0) & intruder_message(X1)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f152,plain,(
( ! [X0,X1] : (intruder_message(X1) | ~intruder_message(pair(X0,X1))) )),
inference(cnf_transformation,[],[f119])).

fof(f150,plain,(
( ! [X2,X0,X1] : (intruder_message(X2) | ~message(sent(X0,X1,X2))) )),
inference(cnf_transformation,[],[f118])).

fof(f118,plain,(
! [X0,X1,X2] : (~message(sent(X0,X1,X2)) | intruder_message(X2))),
inference(ennf_transformation,[],[f15])).

fof(f15,axiom,(
! [X0,X1,X2] : (message(sent(X0,X1,X2)) => intruder_message(X2))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f161,plain,(
( ! [X2,X0,X1] : (intruder_message(triple(X0,X1,X2)) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f125])).

fof(f125,plain,(
! [X0,X1,X2] : (~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2) | intruder_message(triple(X0,X1,X2)))),
inference(flattening,[],[f124])).

fof(f124,plain,(
! [X0,X1,X2] : ((~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2)) | intruder_message(triple(X0,X1,X2)))),
inference(ennf_transformation,[],[f20])).

fof(f20,axiom,(
! [X0,X1,X2] : ((intruder_message(X0) & intruder_message(X1) & intruder_message(X2)) => intruder_message(triple(X0,X1,X2)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f162,plain,(
( ! [X2,X0,X3,X1] : (intruder_message(quadruple(X0,X1,X2,X3)) | ~intruder_message(X3) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f127])).

fof(f127,plain,(
! [X0,X1,X2,X3] : (~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2) | ~intruder_message(X3) | intruder_message(quadruple(X0,X1,X2,X3)))),
inference(flattening,[],[f126])).

fof(f126,plain,(
! [X0,X1,X2,X3] : ((~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2) | ~intruder_message(X3)) | intruder_message(quadruple(X0,X1,X2,X3)))),
inference(ennf_transformation,[],[f21])).

fof(f21,axiom,(
! [X0,X1,X2,X3] : ((intruder_message(X0) & intruder_message(X1) & intruder_message(X2) & intruder_message(X3)) => intruder_message(quadruple(X0,X1,X2,X3)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f166,plain,(
( ! [X2,X0,X1] : (intruder_message(encrypt(X0,X1)) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f135])).

fof(f135,plain,(
! [X0,X1,X2] : (~intruder_message(X0) | ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2) | intruder_message(encrypt(X0,X1)))),
inference(flattening,[],[f134])).

fof(f134,plain,(
! [X0,X1,X2] : ((~intruder_message(X0) | ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2)) | intruder_message(encrypt(X0,X1)))),
inference(ennf_transformation,[],[f25])).

fof(f25,axiom,(
! [X0,X1,X2] : ((intruder_message(X0) & intruder_holds(key(X1,X2)) & party_of_protocol(X2)) => intruder_message(encrypt(X0,X1)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f147,plain,(
t_holds(key(bt,b))),
inference(cnf_transformation,[],[f12])).

fof(f12,axiom,(
t_holds(key(bt,b))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f146,plain,(
t_holds(key(at,a))),
inference(cnf_transformation,[],[f11])).

fof(f11,axiom,(
t_holds(key(at,a))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f143,plain,(
party_of_protocol(b)),
inference(cnf_transformation,[],[f7])).

fof(f7,axiom,(
party_of_protocol(b)),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f139,plain,(
party_of_protocol(a)),
inference(cnf_transformation,[],[f2])).

fof(f2,axiom,(
party_of_protocol(a)),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f148,plain,(
party_of_protocol(t)),
inference(cnf_transformation,[],[f13])).

fof(f13,axiom,(
party_of_protocol(t)),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f144,plain,(
fresh_to_b(an_a_nonce)),
inference(cnf_transformation,[],[f8])).

fof(f8,axiom,(
fresh_to_b(an_a_nonce)),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f175,plain,(
( ! [X0] : (fresh_to_b(X0) | ~fresh_intruder_nonce(X0)) )),
inference(cnf_transformation,[],[f138])).

fof(f174,plain,(
( ! [X0] : (fresh_intruder_nonce(generate_intruder_nonce(X0)) | ~fresh_intruder_nonce(X0)) )),
inference(cnf_transformation,[],[f137])).

fof(f137,plain,(
! [X0] : (~fresh_intruder_nonce(X0) | fresh_intruder_nonce(generate_intruder_nonce(X0)))),
inference(ennf_transformation,[],[f32])).

fof(f32,axiom,(
! [X0] : (fresh_intruder_nonce(X0) => fresh_intruder_nonce(generate_intruder_nonce(X0)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f173,plain,(
fresh_intruder_nonce(an_intruder_nonce)),
inference(cnf_transformation,[],[f31])).

fof(f31,axiom,(
fresh_intruder_nonce(an_intruder_nonce)),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f141,plain,(
a_stored(pair(b,an_a_nonce))),
inference(cnf_transformation,[],[f4])).

fof(f4,axiom,(
a_stored(pair(b,an_a_nonce))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f145,plain,(
( ! [X0,X1] : (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) | ~fresh_to_b(X1) | ~message(sent(X0,b,pair(X0,X1)))) )),
inference(cnf_transformation,[],[f115])).

fof(f115,plain,(
! [X0,X1] : (~message(sent(X0,b,pair(X0,X1))) | ~fresh_to_b(X1) | message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))))),
inference(flattening,[],[f114])).

fof(f114,plain,(
! [X0,X1] : ((~message(sent(X0,b,pair(X0,X1))) | ~fresh_to_b(X1)) | message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))))),
inference(ennf_transformation,[],[f109])).

fof(f109,plain,(
! [X0,X1] : ((message(sent(X0,b,pair(X0,X1))) & fresh_to_b(X1)) => message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))))),
inference(pure_predicate_removal,[],[f9])).

fof(f9,axiom,(
! [X0,X1] : ((message(sent(X0,b,pair(X0,X1))) & fresh_to_b(X1)) => (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) & b_stored(pair(X0,X1))))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f164,plain,(
( ! [X2,X0,X1] : (message(sent(X1,X2,X0)) | ~party_of_protocol(X2) | ~party_of_protocol(X1) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f131])).

fof(f131,plain,(
! [X0,X1,X2] : (~intruder_message(X0) | ~party_of_protocol(X1) | ~party_of_protocol(X2) | message(sent(X1,X2,X0)))),
inference(flattening,[],[f130])).

fof(f130,plain,(
! [X0,X1,X2] : ((~intruder_message(X0) | ~party_of_protocol(X1) | ~party_of_protocol(X2)) | message(sent(X1,X2,X0)))),
inference(ennf_transformation,[],[f23])).

fof(f23,axiom,(
! [X0,X1,X2] : ((intruder_message(X0) & party_of_protocol(X1) & party_of_protocol(X2)) => message(sent(X1,X2,X0)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f140,plain,(
message(sent(a,b,pair(a,an_a_nonce)))),
inference(cnf_transformation,[],[f3])).

fof(f3,axiom,(
message(sent(a,b,pair(a,an_a_nonce)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f142,plain,(
( ! [X4,X2,X0,X5,X3,X1] : (message(sent(a,X4,pair(X3,encrypt(X0,X2)))) | ~a_stored(pair(X4,X5)) | ~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0)))) )),
inference(cnf_transformation,[],[f113])).

fof(f113,plain,(
! [X0,X1,X2,X3,X4,X5] : (~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))) | ~a_stored(pair(X4,X5)) | message(sent(a,X4,pair(X3,encrypt(X0,X2)))))),
inference(flattening,[],[f112])).

fof(f112,plain,(
! [X0,X1,X2,X3,X4,X5] : ((~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))) | ~a_stored(pair(X4,X5))) | message(sent(a,X4,pair(X3,encrypt(X0,X2)))))),
inference(ennf_transformation,[],[f110])).

fof(f110,plain,(
! [X0,X1,X2,X3,X4,X5] : ((message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))) & a_stored(pair(X4,X5))) => message(sent(a,X4,pair(X3,encrypt(X0,X2)))))),
inference(pure_predicate_removal,[],[f5])).

fof(f5,axiom,(
! [X0,X1,X2,X3,X4,X5] : ((message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))) & a_stored(pair(X4,X5))) => (message(sent(a,X4,pair(X3,encrypt(X0,X2)))) & a_holds(key(X2,X4))))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f149,plain,(
( ! [X6,X4,X2,X0,X5,X3,X1] : (message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))) | ~a_nonce(X3) | ~t_holds(key(X6,X2)) | ~t_holds(key(X5,X0)) | ~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5))))) )),
inference(cnf_transformation,[],[f117])).

fof(f117,plain,(
! [X0,X1,X2,X3,X4,X5,X6] : (~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5)))) | ~t_holds(key(X5,X0)) | ~t_holds(key(X6,X2)) | ~a_nonce(X3) | message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))))),
inference(flattening,[],[f116])).

fof(f116,plain,(
! [X0,X1,X2,X3,X4,X5,X6] : ((~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5)))) | ~t_holds(key(X5,X0)) | ~t_holds(key(X6,X2)) | ~a_nonce(X3)) | message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))))),
inference(ennf_transformation,[],[f14])).

fof(f14,axiom,(
! [X0,X1,X2,X3,X4,X5,X6] : ((message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5)))) & t_holds(key(X5,X0)) & t_holds(key(X6,X2)) & a_nonce(X3)) => message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f165,plain,(
( ! [X0,X1] : (intruder_holds(key(X0,X1)) | ~party_of_protocol(X1) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f133])).

fof(f133,plain,(
! [X0,X1] : (~intruder_message(X0) | ~party_of_protocol(X1) | intruder_holds(key(X0,X1)))),
inference(flattening,[],[f132])).

fof(f132,plain,(
! [X0,X1] : ((~intruder_message(X0) | ~party_of_protocol(X1)) | intruder_holds(key(X0,X1)))),
inference(ennf_transformation,[],[f35])).

fof(f35,plain,(
! [X0,X1] : ((intruder_message(X0) & party_of_protocol(X1)) => intruder_holds(key(X0,X1)))),
inference(rectify,[],[f24])).

fof(f24,axiom,(
! [X1,X2] : ((intruder_message(X1) & party_of_protocol(X2)) => intruder_holds(key(X1,X2)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f171,plain,(
( ! [X0] : (~a_nonce(X0) | ~a_key(X0)) )),
inference(cnf_transformation,[],[f136])).

fof(f136,plain,(
! [X0] : (~a_key(X0) | ~a_nonce(X0))),
inference(ennf_transformation,[],[f29])).

fof(f29,axiom,(
! [X0] : ~(a_key(X0) & a_nonce(X0))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f172,plain,(
( ! [X0] : (a_key(generate_key(X0))) )),
inference(cnf_transformation,[],[f30])).

fof(f30,axiom,(
! [X0] : a_key(generate_key(X0))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f170,plain,(
( ! [X0] : (a_nonce(generate_b_nonce(X0))) )),
inference(cnf_transformation,[],[f28])).

fof(f28,axiom,(
! [X0] : (a_nonce(generate_expiration_time(X0)) & a_nonce(generate_b_nonce(X0)))),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f169,plain,(
( ! [X0] : (a_nonce(generate_expiration_time(X0))) )),
inference(cnf_transformation,[],[f28])).

fof(f167,plain,(
a_nonce(an_a_nonce)),
inference(cnf_transformation,[],[f26])).

fof(f26,axiom,(
a_nonce(an_a_nonce)),
file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

cnf(c_29,plain,
( ~ a_nonce(generate_key(X0_$i)) ), inference(cnf_transformation,[],[f168]) ). cnf(c_291,plain, ( ~ a_nonce(generate_key(X0_$$iProver_key_i_1)) ), inference(subtyping,[status(esa)],[c_29]) ). cnf(c_21,plain, ( intruder_message(pair(X0_i,X1_i)) | ~ intruder_message(X0_i) | ~ intruder_message(X1_i) ), inference(cnf_transformation,[],[f160]) ). cnf(c_298,plain, ( intruder_message(pair(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1)) | ~ intruder_message(X0_$$iProver_key_$i_1) | ~ intruder_message(X1_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_21]) ). cnf(c_36,plain, ( intruder_message(X0_i) | ~ fresh_intruder_nonce(X0_i) ), inference(cnf_transformation,[],[f176]) ). cnf(c_285,plain, ( intruder_message(X0_$$iProver_key_$i_1)
| ~ fresh_intruder_nonce(X0_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_36]) ). cnf(c_24,plain, ( ~ party_of_protocol(X0_i) | ~ intruder_message(encrypt(X1_i,X2_i)) | intruder_message(X2_i) | ~ intruder_holds(key(X2_i,X0_i)) ), inference(cnf_transformation,[],[f163]) ). cnf(c_295,plain, ( ~ party_of_protocol(X0_$$iProver_key_$i_1) | ~ intruder_message(encrypt(X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1))
| intruder_message(X2_$$iProver_key_i_1) | ~ intruder_holds(key(X2_$$iProver_key_$i_1,X0_$$iProver_key_i_1)) ), inference(subtyping,[status(esa)],[c_24]) ). cnf(c_20,plain, ( ~ intruder_message(quadruple(X0_i,X1_i,X2_i,X3_i)) | intruder_message(X0_i) ), inference(cnf_transformation,[],[f156]) ). cnf(c_299,plain, ( ~ intruder_message(quadruple(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1,X3_$$iProver_key_i_1)) | intruder_message(X0_$$iProver_key_$i_1) ),
inference(subtyping,[status(esa)],[c_20]) ).

cnf(c_19,plain,
( ~ intruder_message(quadruple(X0_$i,X1_$i,X2_$i,X3_$i))
| intruder_message(X1_$i) ), inference(cnf_transformation,[],[f157]) ). cnf(c_300,plain, ( ~ intruder_message(quadruple(X0_$$iProver_key_i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_i_1,X3_$$iProver_key_$i_1)) | intruder_message(X1_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_19]) ). cnf(c_18,plain, ( ~ intruder_message(quadruple(X0_i,X1_i,X2_i,X3_i)) | intruder_message(X2_i) ), inference(cnf_transformation,[],[f158]) ). cnf(c_301,plain, ( ~ intruder_message(quadruple(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1,X3_$$iProver_key_i_1)) | intruder_message(X2_$$iProver_key_$i_1) ),
inference(subtyping,[status(esa)],[c_18]) ).

cnf(c_17,plain,
( ~ intruder_message(quadruple(X0_$i,X1_$i,X2_$i,X3_$i))
| intruder_message(X3_$i) ), inference(cnf_transformation,[],[f159]) ). cnf(c_302,plain, ( ~ intruder_message(quadruple(X0_$$iProver_key_i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_i_1,X3_$$iProver_key_$i_1)) | intruder_message(X3_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_17]) ). cnf(c_16,plain, ( ~ intruder_message(triple(X0_i,X1_i,X2_i)) | intruder_message(X0_i) ), inference(cnf_transformation,[],[f153]) ). cnf(c_303,plain, ( ~ intruder_message(triple(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1)) | intruder_message(X0_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_16]) ). cnf(c_15,plain, ( ~ intruder_message(triple(X0_i,X1_i,X2_i)) | intruder_message(X1_i) ), inference(cnf_transformation,[],[f154]) ). cnf(c_304,plain, ( ~ intruder_message(triple(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1)) | intruder_message(X1_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_15]) ). cnf(c_14,plain, ( ~ intruder_message(triple(X0_i,X1_i,X2_i)) | intruder_message(X2_i) ), inference(cnf_transformation,[],[f155]) ). cnf(c_305,plain, ( ~ intruder_message(triple(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1)) | intruder_message(X2_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_14]) ). cnf(c_13,plain, ( ~ intruder_message(pair(X0_i,X1_i)) | intruder_message(X0_i) ), inference(cnf_transformation,[],[f151]) ). cnf(c_306,plain, ( ~ intruder_message(pair(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1)) | intruder_message(X0_$$iProver_key_$i_1) ), inference(subtyping,[status(esa)],[c_13]) ). cnf(c_12,plain, ( ~ intruder_message(pair(X0_$i,X1_$i)) | intruder_message(X1_$i) ),
inference(cnf_transformation,[],[f152]) ).

cnf(c_307,plain,
( ~ intruder_message(pair(X0_$$iProver_key_i_1,X1_$$iProver_key_$i_1)) | intruder_message(X1_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_12]) ). cnf(c_11,plain, ( ~ message(sent(X0_i,X1_i,X2_i)) | intruder_message(X2_i) ), inference(cnf_transformation,[],[f150]) ). cnf(c_308,plain, ( ~ message(sent(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1)) | intruder_message(X2_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_11]) ). cnf(c_22,plain, ( intruder_message(triple(X0_i,X1_i,X2_i)) | ~ intruder_message(X0_i) | ~ intruder_message(X1_i) | ~ intruder_message(X2_i) ), inference(cnf_transformation,[],[f161]) ). cnf(c_297,plain, ( intruder_message(triple(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1)) | ~ intruder_message(X0_$$iProver_key_i_1) | ~ intruder_message(X1_$$iProver_key_$i_1)
| ~ intruder_message(X2_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_22]) ). cnf(c_23,plain, ( intruder_message(quadruple(X0_i,X1_i,X2_i,X3_i)) | ~ intruder_message(X0_i) | ~ intruder_message(X1_i) | ~ intruder_message(X2_i) | ~ intruder_message(X3_i) ), inference(cnf_transformation,[],[f162]) ). cnf(c_296,plain, ( intruder_message(quadruple(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1,X3_$$iProver_key_i_1)) | ~ intruder_message(X0_$$iProver_key_$i_1) | ~ intruder_message(X1_$$iProver_key_i_1) | ~ intruder_message(X2_$$iProver_key_$i_1)
| ~ intruder_message(X3_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_23]) ). cnf(c_27,plain, ( ~ party_of_protocol(X0_i) | intruder_message(encrypt(X1_i,X2_i)) | ~ intruder_message(X1_i) | ~ intruder_holds(key(X2_i,X0_i)) ), inference(cnf_transformation,[],[f166]) ). cnf(c_292,plain, ( ~ party_of_protocol(X0_$$iProver_key_$i_1) | intruder_message(encrypt(X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1))
| ~ intruder_message(X1_$$iProver_key_i_1) | ~ intruder_holds(key(X2_$$iProver_key_$i_1,X0_$$iProver_key_i_1)) ), inference(subtyping,[status(esa)],[c_27]) ). cnf(c_8,plain, ( t_holds(key(bt,b)) ), inference(cnf_transformation,[],[f147]) ). cnf(c_280,plain, ( t_holds(key(bt,b)) ), inference(subtyping,[status(esa)],[c_8]) ). cnf(c_7,plain, ( t_holds(key(at,a)) ), inference(cnf_transformation,[],[f146]) ). cnf(c_279,plain, ( t_holds(key(at,a)) ), inference(subtyping,[status(esa)],[c_7]) ). cnf(c_4,plain, ( party_of_protocol(b) ), inference(cnf_transformation,[],[f143]) ). cnf(c_277,plain, ( party_of_protocol(b) ), inference(subtyping,[status(esa)],[c_4]) ). cnf(c_0,plain, ( party_of_protocol(a) ), inference(cnf_transformation,[],[f139]) ). cnf(c_274,plain, ( party_of_protocol(a) ), inference(subtyping,[status(esa)],[c_0]) ). cnf(c_9,plain, ( party_of_protocol(t) ), inference(cnf_transformation,[],[f148]) ). cnf(c_281,plain, ( party_of_protocol(t) ), inference(subtyping,[status(esa)],[c_9]) ). cnf(c_5,plain, ( fresh_to_b(an_a_nonce) ), inference(cnf_transformation,[],[f144]) ). cnf(c_278,plain, ( fresh_to_b(an_a_nonce) ), inference(subtyping,[status(esa)],[c_5]) ). cnf(c_37,plain, ( fresh_to_b(X0_i) | ~ fresh_intruder_nonce(X0_i) ), inference(cnf_transformation,[],[f175]) ). cnf(c_284,plain, ( fresh_to_b(X0_$$iProver_key_$i_1)
| ~ fresh_intruder_nonce(X0_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_37]) ). cnf(c_35,plain, ( fresh_intruder_nonce(generate_intruder_nonce(X0_i)) | ~ fresh_intruder_nonce(X0_i) ), inference(cnf_transformation,[],[f174]) ). cnf(c_286,plain, ( fresh_intruder_nonce(generate_intruder_nonce(X0_$$iProver_key_$i_1)) | ~ fresh_intruder_nonce(X0_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_35]) ). cnf(c_34,plain, ( fresh_intruder_nonce(an_intruder_nonce) ), inference(cnf_transformation,[],[f173]) ). cnf(c_283,plain, ( fresh_intruder_nonce(an_intruder_nonce) ), inference(subtyping,[status(esa)],[c_34]) ). cnf(c_2,plain, ( a_stored(pair(b,an_a_nonce)) ), inference(cnf_transformation,[],[f141]) ). cnf(c_276,plain, ( a_stored(pair(b,an_a_nonce)) ), inference(subtyping,[status(esa)],[c_2]) ). cnf(c_6,plain, ( message(sent(b,t,triple(b,generate_b_nonce(X0_i),encrypt(triple(X1_i,X0_i,generate_expiration_time(X0_i)),bt)))) | ~ message(sent(X1_i,b,pair(X1_i,X0_i))) | ~ fresh_to_b(X0_i) ), inference(cnf_transformation,[],[f145]) ). cnf(c_310,plain, ( message(sent(b,t,triple(b,generate_b_nonce(X0_$$iProver_key_$i_1),encrypt(triple(X1_$$iProver_key_i_1,X0_$$iProver_key_$i_1,generate_expiration_time(X0_$$iProver_key_i_1)),bt)))) | ~ message(sent(X1_$$iProver_key_$i_1,b,pair(X1_$$iProver_key_i_1,X0_$$iProver_key_$i_1))) | ~ fresh_to_b(X0_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_6]) ). cnf(c_25,plain, ( ~ party_of_protocol(X0_i) | ~ party_of_protocol(X1_i) | message(sent(X0_i,X1_i,X2_i)) | ~ intruder_message(X2_i) ), inference(cnf_transformation,[],[f164]) ). cnf(c_294,plain, ( ~ party_of_protocol(X0_$$iProver_key_$i_1)
| ~ party_of_protocol(X1_$$iProver_key_i_1) | message(sent(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1))
| ~ intruder_message(X2_$$iProver_key_i_1) ), inference(subtyping,[status(esa)],[c_25]) ). cnf(c_1,plain, ( message(sent(a,b,pair(a,an_a_nonce))) ), inference(cnf_transformation,[],[f140]) ). cnf(c_275,plain, ( message(sent(a,b,pair(a,an_a_nonce))) ), inference(subtyping,[status(esa)],[c_1]) ). cnf(c_3,plain, ( message(sent(a,X0_i,pair(X1_i,encrypt(X2_i,X3_i)))) | ~ message(sent(t,a,triple(encrypt(quadruple(X0_i,X4_i,X3_i,X5_i),at),X1_i,X2_i))) | ~ a_stored(pair(X0_i,X4_i)) ), inference(cnf_transformation,[],[f142]) ). cnf(c_311,plain, ( message(sent(a,X0_$$iProver_key_$i_1,pair(X1_$$iProver_key_i_1,encrypt(X2_$$iProver_key_$i_1,X3_$$iProver_key_i_1)))) | ~ message(sent(t,a,triple(encrypt(quadruple(X0_$$iProver_key_$i_1,X4_$$iProver_key_i_1,X3_$$iProver_key_$i_1,X5_$$iProver_key_i_1),at),X1_$$iProver_key_$i_1,X2_$$iProver_key_i_1))) | ~ a_stored(pair(X0_$$iProver_key_$i_1,X4_$$iProver_key_i_1)) ), inference(subtyping,[status(esa)],[c_3]) ). cnf(c_10,plain, ( message(sent(t,X0_i,triple(encrypt(quadruple(X1_i,X2_i,generate_key(X2_i),X3_i),X4_i),encrypt(triple(X0_i,generate_key(X2_i),X3_i),X5_i),X6_i))) | ~ message(sent(X1_i,t,triple(X1_i,X6_i,encrypt(triple(X0_i,X2_i,X3_i),X5_i)))) | ~ t_holds(key(X5_i,X1_i)) | ~ t_holds(key(X4_i,X0_i)) | ~ a_nonce(X2_i) ), inference(cnf_transformation,[],[f149]) ). cnf(c_309,plain, ( message(sent(t,X0_$$iProver_key_$i_1,triple(encrypt(quadruple(X1_$$iProver_key_i_1,X2_$$iProver_key_$i_1,generate_key(X2_$$iProver_key_i_1),X3_$$iProver_key_$i_1),X4_$$iProver_key_i_1),encrypt(triple(X0_$$iProver_key_$i_1,generate_key(X2_$$iProver_key_i_1),X3_$$iProver_key_$i_1),X5_$$iProver_key_i_1),X6_$$iProver_key_$i_1)))
| ~ message(sent(X1_$$iProver_key_i_1,t,triple(X1_$$iProver_key_$i_1,X6_$$iProver_key_i_1,encrypt(triple(X0_$$iProver_key_$i_1,X2_$$iProver_key_i_1,X3_$$iProver_key_$i_1),X5_$$iProver_key_i_1)))) | ~ t_holds(key(X5_$$iProver_key_$i_1,X1_$$iProver_key_i_1)) | ~ t_holds(key(X4_$$iProver_key_$i_1,X0_$$iProver_key_i_1)) | ~ a_nonce(X2_$$iProver_key_$i_1) ),
inference(subtyping,[status(esa)],[c_10]) ).

cnf(c_26,plain,
( ~ party_of_protocol(X0_$i) | ~ intruder_message(X1_$i)
| intruder_holds(key(X1_$i,X0_$i)) ),
inference(cnf_transformation,[],[f165]) ).

cnf(c_293,plain,
( ~ party_of_protocol(X0_$$iProver_key_i_1) | ~ intruder_message(X1_$$iProver_key_$i_1) | intruder_holds(key(X1_$$iProver_key_i_1,X0_$$iProver_key_$i_1)) ),
inference(subtyping,[status(esa)],[c_26]) ).

cnf(c_32,plain,
( ~ a_nonce(X0_$i) | ~ a_key(X0_$i) ),
inference(cnf_transformation,[],[f171]) ).

cnf(c_321,plain,
( ~ a_nonce(X0_$$iProver_key_i_1) | ~ a_key(X0_$$iProver_key_$i_1) ), inference(subtyping,[status(esa)],[c_32]) ). cnf(c_33,plain, ( a_key(generate_key(X0_$i)) ),
inference(cnf_transformation,[],[f172]) ).

cnf(c_320,plain,
( a_key(generate_key(X0_$$iProver_key_i_1)) ), inference(subtyping,[status(esa)],[c_33]) ). cnf(c_338,plain, ( ~ a_nonce(generate_key(X0_$$iProver_key_$i_1)) ), inference(resolution,[status(thm)],[c_321,c_320]) ). cnf(c_30,plain, ( a_nonce(generate_b_nonce(X0_$i)) ),
inference(cnf_transformation,[],[f170]) ).

cnf(c_319,plain,
( a_nonce(generate_b_nonce(X0_$$iProver_key_i_1)) ), inference(subtyping,[status(esa)],[c_30]) ). cnf(c_31,plain, ( a_nonce(generate_expiration_time(X0_i)) ), inference(cnf_transformation,[],[f169]) ). cnf(c_318,plain, ( a_nonce(generate_expiration_time(X0_$$iProver_key_$i_1)) ), inference(subtyping,[status(esa)],[c_31]) ). cnf(c_28,plain, ( a_nonce(an_a_nonce) ), inference(cnf_transformation,[],[f167]) ). cnf(c_317,plain, ( a_nonce(an_a_nonce) ), inference(subtyping,[status(esa)],[c_28]) ). % SZS output end Saturation  ### Sample finite model for SWV017+1 %------ The model is defined over ground terms (initial term algebra). %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) %------ where \phi is a formula over the term algebra. %------ If we have equality in the problem then it is also defined as a predicate above, %------ with "=" on the right-hand-side of the definition interpreted over the term algebra $$term_algebra_type %------ See help for --sat_out_model for different model outputs. %------ equality_sorted(X0,X1,X2) can be used in the place of usual "=" %------ where the first argument stands for the sort (i in the unsorted case) % SZS output start Model %------ Negative definition of party_of_protocol fof(lit_def,axiom, (! [X0_$$iProver_key_$i_1] :
( ~(party_of_protocol(X0_$$iProver_key_i_1)) <=> false ) ) ). %------ Negative definition of message fof(lit_def,axiom, (! [X0_$$iProver_message_$i_1] : ( ~(message(X0_$$iProver_message_i_1)) <=> false ) ) ). %------ Negative definition of a_stored fof(lit_def,axiom, (! [X0_$$iProver_key_$i_1] :
( ~(a_stored(X0_$$iProver_key_i_1)) <=> false ) ) ). %------ Positive definition of fresh_to_b fof(lit_def,axiom, (! [X0_$$iProver_key_$i_1] : ( fresh_to_b(X0_$$iProver_key_i_1) <=> true ) ) ). %------ Negative definition of t_holds fof(lit_def,axiom, (! [X0_$$iProver_intruder_holds_$i_1] :
( ~(t_holds(X0_$$iProver_intruder_holds_i_1)) <=> false ) ) ). %------ Positive definition of a_nonce fof(lit_def,axiom, (! [X0_$$iProver_key_$i_1] : ( a_nonce(X0_$$iProver_key_i_1) <=> ( ( ( X0_$$iProver_key_$i_1=$$iProver_Domain_$$iProver_key_$i_1_1 ) ) ) ) ) ). %------ Positive definition of intruder_message fof(lit_def,axiom, (! [X0_$$iProver_key_i_1] : ( intruder_message(X0_$$iProver_key_$i_1) <=>
$true ) ) ). %------ Negative definition of intruder_holds fof(lit_def,axiom, (! [X0_$$iProver_intruder_holds_i_1] : ( ~(intruder_holds(X0_$$iProver_intruder_holds_$i_1)) <=>
$false ) ) ). %------ Positive definition of a_key fof(lit_def,axiom, (! [X0_$$iProver_key_i_1] : ( a_key(X0_$$iProver_key_$i_1) <=>
(
(
( X0_$$iProver_key_i_1=$$iProver_Domain_$$iProver_key_i_1_2 ) ) ) ) ) ). %------ Negative definition of fresh_intruder_nonce fof(lit_def,axiom, (! [X0_$$iProver_key_$i_1] : ( ~(fresh_intruder_nonce(X0_$$iProver_key_i_1)) <=> false ) ) ). %------ Positive definition of$$iProver_Flat_an_a_nonce fof(lit_def,axiom, (! [X0_$$iProver_key_i_1] : ($$iProver_Flat_an_a_nonce(X0_$$iProver_key_i_1) <=> ( ( ( X0_$$iProver_key_$i_1=$$iProver_Domain_$$iProver_key_$i_1_1 ) ) ) ) ) ). %------ Positive definition of $$iProver_Flat_generate_b_nonce fof(lit_def,axiom, (! [X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1] : ($$iProver_Flat_generate_b_nonce(X0_$$iProver_key_i_1,X1_$$iProver_key_$i_1) <=> ( ( ( X0_$$iProver_key_i_1=$$iProver_Domain_$$iProver_key_i_1_1 ) ) ) ) ) ). %------ Positive definition of$$iProver_Flat_generate_expiration_time fof(lit_def,axiom, (! [X0_$$iProver_key_i_1,X1_$$iProver_key_$i_1] :
( $$iProver_Flat_generate_expiration_time(X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1) <=> ( ( ( X0_$$iProver_key_$i_1=$$iProver_Domain_$$iProver_key_$i_1_1 ) ) ) ) ) ). %------ Positive definition of $$iProver_Flat_generate_key fof(lit_def,axiom, (! [X0_$$iProver_key_$i_1,X1_$$iProver_key_i_1] : ($$iProver_Flat_generate_key(X0_$$iProver_key_i_1,X1_$$iProver_key_$i_1) <=> ( ( ( X0_$$iProver_key_i_1=$$iProver_Domain_$$iProver_key_i_1_2 ) ) ) ) ) ). % SZS output end Model  ## iProver 2.0 Konstantin Korovin University of Manchester, United Kingdom ### Sample proof for SEU140+2 % SZS status Theorem % SZS output start CNFRefutation fof(f43,axiom,( ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))), file('/Users/korovin/TPTP-v6.1.0/Problems/SEU/SEU140+2.p',unknown)). fof(f70,plain,( ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))), inference(rectify,[],[f43])). fof(f71,plain,( ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))), inference(flattening,[],[f70])). fof(f131,plain,( ! [X0,X1] : ((disjoint(X0,X1) | (in(sK8(X1,X0),X0) & in(sK8(X1,X0),X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))), inference(skolemisation,[status(esa)],[f92])). fof(f92,plain,( ! [X0,X1] : ((disjoint(X0,X1) | ? [X3] : (in(X3,X0) & in(X3,X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))), inference(ennf_transformation,[],[f71])). fof(f198,plain,( ( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )), inference(cnf_transformation,[],[f131])). fof(f8,axiom,( ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))), file('/Users/korovin/TPTP-v6.1.0/Problems/SEU/SEU140+2.p',unknown)). fof(f77,plain,( ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (~in(X2,X0) | in(X2,X1)))), inference(ennf_transformation,[],[f8])). fof(f113,plain,( ! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))), inference(nnf_transformation,[],[f77])). fof(f115,plain,( ! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & ((in(sK2(X1,X0),X0) & ~in(sK2(X1,X0),X1)) | subset(X0,X1)))), inference(skolemisation,[status(esa)],[f114])). fof(f114,plain,( ! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))), inference(rectify,[],[f113])). fof(f149,plain,( ( ! [X0,X3,X1] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )), inference(cnf_transformation,[],[f115])). fof(f197,plain,( ( ! [X0,X1] : (in(sK8(X1,X0),X1) | disjoint(X0,X1)) )), inference(cnf_transformation,[],[f131])). fof(f196,plain,( ( ! [X0,X1] : (in(sK8(X1,X0),X0) | disjoint(X0,X1)) )), inference(cnf_transformation,[],[f131])). fof(f51,conjecture,( ! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))), file('/Users/korovin/TPTP-v6.1.0/Problems/SEU/SEU140+2.p',unknown)). fof(f52,negated_conjecture,( ~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))), inference(negated_conjecture,[],[f51])). fof(f97,plain,( ? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))), inference(ennf_transformation,[],[f52])). fof(f133,plain,( subset(sK10,sK11) & disjoint(sK11,sK12) & ~disjoint(sK10,sK12)), inference(skolemisation,[status(esa)],[f98])). fof(f98,plain,( ? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))), inference(flattening,[],[f97])). fof(f209,plain,( ~disjoint(sK10,sK12)), inference(cnf_transformation,[],[f133])). fof(f208,plain,( disjoint(sK11,sK12)), inference(cnf_transformation,[],[f133])). fof(f207,plain,( subset(sK10,sK11)), inference(cnf_transformation,[],[f133])). cnf(c_414,plain, ( ~ in(X0_i,X1_i) | ~ in(X0_i,X2_i) | ~ disjoint(X1_i,X2_i) ), inference(cnf_transformation,[],[f198]) ). cnf(c_563,plain, ( ~ in(X0_i,X1_i) | ~ in(X0_i,X2_i) | ~ disjoint(X1_i,X2_i) ), inference(subtyping,[status(esa)],[c_414]) ). cnf(c_1466,plain, ( ~ in(sK8(sK12,sK10),sK11) | ~ in(sK8(sK12,sK10),X0_i) | ~ disjoint(sK11,X0_i) ), inference(instantiation,[status(thm)],[c_563]) ). cnf(c_2229,plain, ( ~ in(sK8(sK12,sK10),sK12) | ~ in(sK8(sK12,sK10),sK11) | ~ disjoint(sK11,sK12) ), inference(instantiation,[status(thm)],[c_1466]) ). cnf(c_372,plain, ( ~ in(X0_i,X1_i) | in(X0_i,X2_i) | ~ subset(X1_i,X2_i) ), inference(cnf_transformation,[],[f149]) ). cnf(c_614,plain, ( ~ in(X0_i,X1_i) | in(X0_i,X2_i) | ~ subset(X1_i,X2_i) ), inference(subtyping,[status(esa)],[c_372]) ). cnf(c_653,plain, ( ~ in(sK8(sK12,sK10),sK10) | in(sK8(sK12,sK10),X0_i) | ~ subset(sK10,X0_i) ), inference(instantiation,[status(thm)],[c_614]) ). cnf(c_1127,plain, ( ~ in(sK8(sK12,sK10),sK10) | in(sK8(sK12,sK10),sK11) | ~ subset(sK10,sK11) ), inference(instantiation,[status(thm)],[c_653]) ). cnf(c_415,plain, ( in(sK8(X0_i,X1_i),X0_i) | disjoint(X1_i,X0_i) ), inference(cnf_transformation,[],[f197]) ). cnf(c_562,plain, ( in(sK8(X0_i,X1_i),X0_i) | disjoint(X1_i,X0_i) ), inference(subtyping,[status(esa)],[c_415]) ). cnf(c_630,plain, ( in(sK8(sK12,sK10),sK12) | disjoint(sK10,sK12) ), inference(instantiation,[status(thm)],[c_562]) ). cnf(c_416,plain, ( in(sK8(X0_i,X1_i),X1_i) | disjoint(X1_i,X0_i) ), inference(cnf_transformation,[],[f196]) ). cnf(c_561,plain, ( in(sK8(X0_i,X1_i),X1_i) | disjoint(X1_i,X0_i) ), inference(subtyping,[status(esa)],[c_416]) ). cnf(c_629,plain, ( in(sK8(sK12,sK10),sK10) | disjoint(sK10,sK12) ), inference(instantiation,[status(thm)],[c_561]) ). cnf(c_72,plain, ( ~ disjoint(sK10,sK12) ), inference(cnf_transformation,[],[f209]) ). cnf(c_73,plain, ( disjoint(sK11,sK12) ), inference(cnf_transformation,[],[f208]) ). cnf(c_74,plain, ( subset(sK10,sK11) ), inference(cnf_transformation,[],[f207]) ). cnf(contradiction,plain, ( false ), inference(minisat, [status(thm)], [c_2229,c_1127,c_630,c_629,c_72,c_73,c_74]) ). % SZS output end CNFRefutation  ### Sample model for NLP042+1 % SZS status CounterSatisfiable ------ Building Model...Done %------ The model is defined over ground terms (initial term algebra). %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) %------ where \phi is a formula over the term algebra. %------ If we have equality in the problem then it is also defined as a predicate above, %------ with "=" on the right-hand-side of the definition interpreted over the term algebra$$term_algebra_type %------ See help for --sat_out_model for different model outputs. %------ equality_sorted(X0,X1,X2) can be used in the place of usual "=" %------ where the first argument stands for the sort ($i in the unsorted case)

% SZS output start Model

%------ Positive definition of $$equality_sorted fof(lit_def,axiom, (! [X0_tType,X0_$$iProver_of_2_$i,X1_$$iProver_of_2_i] : ($$equality_sorted(X0_$tType,X0_$$iProver_of_2_i,X1_$$iProver_of_2_$i) <=> ( ( ( X0_$tType=$$iProver_of_2_i ) & ( X0_$$iProver_of_2_$i!=esk5_0 | X1_$$iProver_of_2_i!=esk4_0 ) & ( X0_$$iProver_of_2_$i!=esk4_0 )
&
( X0_$$iProver_of_2_i!=esk4_0 | X1_$$iProver_of_2_$i!=esk2_0 ) & ( X0_$$iProver_of_2_i!=esk2_0 ) & ( X0_$$iProver_of_2_$i!=esk2_0 | X1_$$iProver_of_2_i!=esk5_0 ) & ( X0_$$iProver_of_2_$i!=esk3_0 ) & ( X1_$$iProver_of_2_i!=esk4_0 ) & ( X1_$$iProver_of_2_$i!=esk2_0 )
&
( X1_$$iProver_of_2_i!=esk3_0 ) ) | ( ( X0_tType=$$iProver_of_2_$i & X0_$$iProver_of_2_i=esk4_0 & X1_$$iProver_of_2_$i=esk4_0 )
)

|
(
( X0_$tType=$$iProver_of_2_i & X0_$$iProver_of_2_$i=esk2_0 & X1_$$iProver_of_2_i=esk2_0 ) ) | ( ( X0_tType=$$iProver_of_2_$i & X0_$$iProver_of_2_i=esk3_0 & X1_$$iProver_of_2_$i=esk3_0 )
)

|
(
( X0_$tType=$$iProver_of_2_i & X1_$$iProver_of_2_$i=X0_$$iProver_of_2_i ) & ( X0_$$iProver_of_2_$i!=esk4_0 ) & ( X0_$$iProver_of_2_i!=esk2_0 ) & ( X0_$$iProver_of_2_$i!=esk3_0 )
)

)
)
)
).

%------ Positive definition of forename
fof(lit_def,axiom,
(! [X0_$$iProver_of_1_i,X0_$$iProver_of_2_$i] : ( forename(X0_$$iProver_of_1_i,X0_$$iProver_of_2_$i) <=>
(
(
( X0_$$iProver_of_1_i=esk1_0 & X0_$$iProver_of_2_$i=esk3_0 ) ) ) ) ) ). %------ Positive definition of of fof(lit_def,axiom, (! [X0_$$iProver_of_1_i,X0_$$iProver_of_2_$i,X1_$$iProver_of_2_i] : ( of(X0_$$iProver_of_1_$i,X0_$$iProver_of_2_i,X1_$$iProver_of_2_$i) <=>
(
(
( X0_$$iProver_of_1_i=esk1_0 & X0_$$iProver_of_2_$i=esk3_0 & X1_$$iProver_of_2_i=esk2_0 ) ) ) ) ) ). % SZS output end Model  ### Sample model for SWV017+1 % SZS status Satisfiable ------ Building Model...Done %------ The model is defined over ground terms (initial term algebra). %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) %------ where \phi is a formula over the term algebra. %------ If we have equality in the problem then it is also defined as a predicate above, %------ with "=" on the right-hand-side of the definition interpreted over the term algebra$$term_algebra_type %------ See help for --sat_out_model for different model outputs. %------ equality_sorted(X0,X1,X2) can be used in the place of usual "=" %------ where the first argument stands for the sort ($i in the unsorted case)

% SZS output start Model

%------ Negative definition of message
fof(lit_def,axiom,
(! [X0_$$iProver_message_1_i] : ( ~(message(X0_$$iProver_message_1_$i)) <=>$false
)
)
).

%------ Negative definition of t_holds
fof(lit_def,axiom,
(! [X0_$$iProver_t_holds_1_i] : ( ~(t_holds(X0_$$iProver_t_holds_1_$i)) <=>$false
)
)
).

%------ Positive definition of intruder_message
fof(lit_def,axiom,
(! [X0_$$iProver_sent_2_i] : ( intruder_message(X0_$$iProver_sent_2_$i) <=>$true
)
)
).

%------ Negative definition of party_of_protocol
fof(lit_def,axiom,
(! [X0_$$iProver_sent_2_i] : ( ~(party_of_protocol(X0_$$iProver_sent_2_$i)) <=>$false
)
)
).

%------ Negative definition of fresh_intruder_nonce
fof(lit_def,axiom,
(! [X0_$$iProver_sent_2_i] : ( ~(fresh_intruder_nonce(X0_$$iProver_sent_2_$i)) <=>$false
)
)
).

%------ Positive definition of sP0_iProver_split
fof(lit_def,axiom,
( sP0_iProver_split <=>
$false ) ). %------ Positive definition of sP1_iProver_split fof(lit_def,axiom, ( sP1_iProver_split <=>$true
)
).

% SZS output end Model


## iProverModulo 0.7-0.3

Guillaume Burel
ENSIIE/Cedric, France

### Sample solution for SEU140+2

% SZS output start CNFRefutation
% Axioms transformation by autotheo
# Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
# Orienting axioms whose shape is orientable
fof(t6_boole,axiom,![A]:(empty(A)=>A=empty_set),input).
fof(t6_boole_0,plain,![A]:(~empty(A)
|A=empty_set),inference(orientation, [status(thm)], [t6_boole]))
fof(t4_boole,axiom,![A]:set_difference(empty_set,A)=empty_set,input).
fof(t4_boole_0,plain,![A]:(set_difference(empty_set,A)=empty_set
|$false),inference(orientation, [status(thm)], [t4_boole])) fof(t3_boole,axiom,![A]:set_difference(A,empty_set)=A,input). fof(t3_boole_0,plain,![A]:(set_difference(A,empty_set)=A |$false),inference(orientation, [status(thm)], [t3_boole]))
fof(t2_tarski,axiom,![A,B]:(![C]:(in(C,A)<=>in(C,B))=>A=B),input).
fof(t2_tarski_0,plain,![A,B]:(A=B
|~![C]:(in(C,A)
<=>in(C,B))),inference(orientation, [status(thm)], [t2_tarski]))
fof(t2_boole,axiom,![A]:set_intersection2(A,empty_set)=empty_set,input).
fof(t2_boole_0,plain,![A]:(set_intersection2(A,empty_set)=empty_set
|$false),inference(orientation, [status(thm)], [t2_boole])) fof(t1_boole,axiom,![A]:set_union2(A,empty_set)=A,input). fof(t1_boole_0,plain,![A]:(set_union2(A,empty_set)=A |$false),inference(orientation, [status(thm)], [t1_boole]))
fof(symmetry_r1_xboole_0,axiom,![A,B]:(disjoint(A,B)=>disjoint(B,A)),input).
fof(symmetry_r1_xboole_0_0,plain,![A,B]:(~disjoint(A,B)
|disjoint(B,A)),inference(orientation, [status(thm)], [symmetry_r1_xboole_0]))
fof(reflexivity_r1_tarski,axiom,![A,B]:subset(A,A),input).
fof(reflexivity_r1_tarski_0,plain,![A]:(subset(A,A)
|$false),inference(orientation, [status(thm)], [reflexivity_r1_tarski])) fof(irreflexivity_r2_xboole_0,axiom,![A,B]:~proper_subset(A,A),input). fof(irreflexivity_r2_xboole_0_0,plain,![A]:(~proper_subset(A,A) |$false),inference(orientation, [status(thm)], [irreflexivity_r2_xboole_0]))
fof(idempotence_k3_xboole_0,axiom,![A,B]:set_intersection2(A,A)=A,input).
fof(idempotence_k3_xboole_0_0,plain,![A]:(set_intersection2(A,A)=A
|$false),inference(orientation, [status(thm)], [idempotence_k3_xboole_0])) fof(idempotence_k2_xboole_0,axiom,![A,B]:set_union2(A,A)=A,input). fof(idempotence_k2_xboole_0_0,plain,![A]:(set_union2(A,A)=A |$false),inference(orientation, [status(thm)], [idempotence_k2_xboole_0]))
fof(fc3_xboole_0,axiom,![A,B]:(~empty(A)=>~empty(set_union2(B,A))),input).
fof(fc3_xboole_0_0,plain,![A,B]:(empty(A)
|~empty(set_union2(B,A))),inference(orientation, [status(thm)], [fc3_xboole_0]))
fof(fc2_xboole_0,axiom,![A,B]:(~empty(A)=>~empty(set_union2(A,B))),input).
fof(fc2_xboole_0_0,plain,![A,B]:(empty(A)
|~empty(set_union2(A,B))),inference(orientation, [status(thm)], [fc2_xboole_0]))
fof(fc1_xboole_0,axiom,empty(empty_set),input).
fof(fc1_xboole_0_0,plain,![]:(empty(empty_set)
|$false),inference(orientation, [status(thm)], [fc1_xboole_0])) fof(dt_k4_xboole_0,axiom,$true,input).
fof(dt_k4_xboole_0_0,plain,![]:($true |$false),inference(orientation, [status(thm)], [dt_k4_xboole_0]))
fof(dt_k3_xboole_0,axiom,$true,input). fof(dt_k3_xboole_0_0,plain,![]:($true
|$false),inference(orientation, [status(thm)], [dt_k3_xboole_0])) fof(dt_k2_xboole_0,axiom,$true,input).
fof(dt_k2_xboole_0_0,plain,![]:($true |$false),inference(orientation, [status(thm)], [dt_k2_xboole_0]))
fof(dt_k1_xboole_0,axiom,$true,input). fof(dt_k1_xboole_0_0,plain,![]:($true
|$false),inference(orientation, [status(thm)], [dt_k1_xboole_0])) fof(d8_xboole_0,axiom,![A,B]:(proper_subset(A,B)<=>(subset(A,B)&A!=B)),input). fof(d8_xboole_0_0,plain,![A,B]:(proper_subset(A,B) |~(subset(A,B) &A!=B)),inference(orientation, [status(thm)], [d8_xboole_0])) fof(d8_xboole_0_1,plain,![A,B]:(~proper_subset(A,B) |(subset(A,B) &A!=B)),inference(orientation, [status(thm)], [d8_xboole_0])) fof(d7_xboole_0,axiom,![A,B]:(disjoint(A,B)<=>set_intersection2(A,B)=empty_set),input). fof(d7_xboole_0_0,plain,![A,B]:(disjoint(A,B) |~set_intersection2(A,B)=empty_set),inference(orientation, [status(thm)], [d7_xboole_0])) fof(d7_xboole_0_1,plain,![A,B]:(~disjoint(A,B) |set_intersection2(A,B)=empty_set),inference(orientation, [status(thm)], [d7_xboole_0])) fof(d4_xboole_0,axiom,![A,B,C]:(C=set_difference(A,B)<=>![D]:(in(D,C)<=>(in(D,A)&~in(D,B)))),input). fof(d4_xboole_0_0,plain,![A,B,C]:(C=set_difference(A,B) |~![D]:(in(D,C) <=>(in(D,A) &~in(D,B)))),inference(orientation, [status(thm)], [d4_xboole_0])) fof(d4_xboole_0_1,plain,![A,B,C]:(~C=set_difference(A,B) |![D]:(in(D,C) <=>(in(D,A) &~in(D,B)))),inference(orientation, [status(thm)], [d4_xboole_0])) fof(d3_xboole_0,axiom,![A,B,C]:(C=set_intersection2(A,B)<=>![D]:(in(D,C)<=>(in(D,A)&in(D,B)))),input). fof(d3_xboole_0_0,plain,![A,B,C]:(C=set_intersection2(A,B) |~![D]:(in(D,C) <=>(in(D,A) &in(D,B)))),inference(orientation, [status(thm)], [d3_xboole_0])) fof(d3_xboole_0_1,plain,![A,B,C]:(~C=set_intersection2(A,B) |![D]:(in(D,C) <=>(in(D,A) &in(D,B)))),inference(orientation, [status(thm)], [d3_xboole_0])) fof(d3_tarski,axiom,![A,B]:(subset(A,B)<=>![C]:(in(C,A)=>in(C,B))),input). fof(d3_tarski_0,plain,![A,B]:(subset(A,B) |~![C]:(in(C,A) =>in(C,B))),inference(orientation, [status(thm)], [d3_tarski])) fof(d3_tarski_1,plain,![A,B]:(~subset(A,B) |![C]:(in(C,A) =>in(C,B))),inference(orientation, [status(thm)], [d3_tarski])) fof(d2_xboole_0,axiom,![A,B,C]:(C=set_union2(A,B)<=>![D]:(in(D,C)<=>(in(D,A)|in(D,B)))),input). fof(d2_xboole_0_0,plain,![A,B,C]:(C=set_union2(A,B) |~![D]:(in(D,C) <=>(in(D,A) |in(D,B)))),inference(orientation, [status(thm)], [d2_xboole_0])) fof(d2_xboole_0_1,plain,![A,B,C]:(~C=set_union2(A,B) |![D]:(in(D,C) <=>(in(D,A) |in(D,B)))),inference(orientation, [status(thm)], [d2_xboole_0])) fof(d1_xboole_0,axiom,![A]:(A=empty_set<=>![B]:~in(B,A)),input). fof(d1_xboole_0_0,plain,![A]:(A=empty_set |~![B]:~in(B,A)),inference(orientation, [status(thm)], [d1_xboole_0])) fof(d1_xboole_0_1,plain,![A]:(~A=empty_set |![B]:~in(B,A)),inference(orientation, [status(thm)], [d1_xboole_0])) fof(d10_xboole_0,axiom,![A,B]:(A=B<=>(subset(A,B)&subset(B,A))),input). fof(d10_xboole_0_0,plain,![A,B]:(A=B |~(subset(A,B) &subset(B,A))),inference(orientation, [status(thm)], [d10_xboole_0])) fof(d10_xboole_0_1,plain,![A,B]:(~A=B |(subset(A,B) &subset(B,A))),inference(orientation, [status(thm)], [d10_xboole_0])) fof(commutativity_k3_xboole_0,axiom,![A,B]:set_intersection2(A,B)=set_intersection2(B,A),input). fof(commutativity_k3_xboole_0_0,plain,![A,B]:(set_intersection2(A,B)=set_intersection2(B,A) |$false),inference(orientation, [status(thm)], [commutativity_k3_xboole_0]))
fof(commutativity_k2_xboole_0,axiom,![A,B]:set_union2(A,B)=set_union2(B,A),input).
fof(commutativity_k2_xboole_0_0,plain,![A,B]:(set_union2(A,B)=set_union2(B,A)
|$false),inference(orientation, [status(thm)], [commutativity_k2_xboole_0])) fof(antisymmetry_r2_xboole_0,axiom,![A,B]:(proper_subset(A,B)=>~proper_subset(B,A)),input). fof(antisymmetry_r2_xboole_0_0,plain,![A,B]:(~proper_subset(A,B) |~proper_subset(B,A)),inference(orientation, [status(thm)], [antisymmetry_r2_xboole_0])) fof(antisymmetry_r2_hidden,axiom,![A,B]:(in(A,B)=>~in(B,A)),input). fof(antisymmetry_r2_hidden_0,plain,![A,B]:(~in(A,B) |~in(B,A)),inference(orientation, [status(thm)], [antisymmetry_r2_hidden])) fof(def_lhs_atom1, axiom, ![B,A]: lhs_atom1(B,A) <=> ~in(A,B), inference(definition,[],[])) fof(to_be_clausified_0, plain, ![A,B]: (lhs_atom1(B,A) |~in(B,A)), inference(fold_definition,[status(thm)],[antisymmetry_r2_hidden_0, def_lhs_atom1])) fof(def_lhs_atom2, axiom, ![B,A]: lhs_atom2(B,A) <=> ~proper_subset(A,B), inference(definition,[],[])) fof(to_be_clausified_1, plain, ![A,B]: (lhs_atom2(B,A) |~proper_subset(B,A)), inference(fold_definition,[status(thm)],[antisymmetry_r2_xboole_0_0, def_lhs_atom2])) fof(def_lhs_atom3, axiom, ![B,A]: lhs_atom3(B,A) <=> set_union2(A,B)=set_union2(B,A), inference(definition,[],[])) fof(to_be_clausified_2, plain, ![A,B]: (lhs_atom3(B,A) |$false), inference(fold_definition,[status(thm)],[commutativity_k2_xboole_0_0, def_lhs_atom3]))
fof(def_lhs_atom4, axiom, ![B,A]: lhs_atom4(B,A) <=> set_intersection2(A,B)=set_intersection2(B,A), inference(definition,[],[]))
fof(to_be_clausified_3, plain, ![A,B]: (lhs_atom4(B,A)
|$false), inference(fold_definition,[status(thm)],[commutativity_k3_xboole_0_0, def_lhs_atom4])) fof(def_lhs_atom5, axiom, ![B,A]: lhs_atom5(B,A) <=> ~A=B, inference(definition,[],[])) fof(to_be_clausified_4, plain, ![A,B]: (lhs_atom5(B,A) |(subset(A,B) &subset(B,A))), inference(fold_definition,[status(thm)],[d10_xboole_0_1, def_lhs_atom5])) fof(def_lhs_atom6, axiom, ![B,A]: lhs_atom6(B,A) <=> A=B, inference(definition,[],[])) fof(to_be_clausified_5, plain, ![A,B]: (lhs_atom6(B,A) |~(subset(A,B) &subset(B,A))), inference(fold_definition,[status(thm)],[d10_xboole_0_0, def_lhs_atom6])) fof(def_lhs_atom7, axiom, ![A]: lhs_atom7(A) <=> ~A=empty_set, inference(definition,[],[])) fof(to_be_clausified_6, plain, ![A]: (lhs_atom7(A) |![B]:~in(B,A)), inference(fold_definition,[status(thm)],[d1_xboole_0_1, def_lhs_atom7])) fof(def_lhs_atom8, axiom, ![A]: lhs_atom8(A) <=> A=empty_set, inference(definition,[],[])) fof(to_be_clausified_7, plain, ![A]: (lhs_atom8(A) |~![B]:~in(B,A)), inference(fold_definition,[status(thm)],[d1_xboole_0_0, def_lhs_atom8])) fof(def_lhs_atom9, axiom, ![C,B,A]: lhs_atom9(C,B,A) <=> ~C=set_union2(A,B), inference(definition,[],[])) fof(to_be_clausified_8, plain, ![A,B,C]: (lhs_atom9(C,B,A) |![D]:(in(D,C) <=>(in(D,A) |in(D,B)))), inference(fold_definition,[status(thm)],[d2_xboole_0_1, def_lhs_atom9])) fof(def_lhs_atom10, axiom, ![C,B,A]: lhs_atom10(C,B,A) <=> C=set_union2(A,B), inference(definition,[],[])) fof(to_be_clausified_9, plain, ![A,B,C]: (lhs_atom10(C,B,A) |~![D]:(in(D,C) <=>(in(D,A) |in(D,B)))), inference(fold_definition,[status(thm)],[d2_xboole_0_0, def_lhs_atom10])) fof(def_lhs_atom11, axiom, ![B,A]: lhs_atom11(B,A) <=> ~subset(A,B), inference(definition,[],[])) fof(to_be_clausified_10, plain, ![A,B]: (lhs_atom11(B,A) |![C]:(in(C,A) =>in(C,B))), inference(fold_definition,[status(thm)],[d3_tarski_1, def_lhs_atom11])) fof(def_lhs_atom12, axiom, ![B,A]: lhs_atom12(B,A) <=> subset(A,B), inference(definition,[],[])) fof(to_be_clausified_11, plain, ![A,B]: (lhs_atom12(B,A) |~![C]:(in(C,A) =>in(C,B))), inference(fold_definition,[status(thm)],[d3_tarski_0, def_lhs_atom12])) fof(def_lhs_atom13, axiom, ![C,B,A]: lhs_atom13(C,B,A) <=> ~C=set_intersection2(A,B), inference(definition,[],[])) fof(to_be_clausified_12, plain, ![A,B,C]: (lhs_atom13(C,B,A) |![D]:(in(D,C) <=>(in(D,A) &in(D,B)))), inference(fold_definition,[status(thm)],[d3_xboole_0_1, def_lhs_atom13])) fof(def_lhs_atom14, axiom, ![C,B,A]: lhs_atom14(C,B,A) <=> C=set_intersection2(A,B), inference(definition,[],[])) fof(to_be_clausified_13, plain, ![A,B,C]: (lhs_atom14(C,B,A) |~![D]:(in(D,C) <=>(in(D,A) &in(D,B)))), inference(fold_definition,[status(thm)],[d3_xboole_0_0, def_lhs_atom14])) fof(def_lhs_atom15, axiom, ![C,B,A]: lhs_atom15(C,B,A) <=> ~C=set_difference(A,B), inference(definition,[],[])) fof(to_be_clausified_14, plain, ![A,B,C]: (lhs_atom15(C,B,A) |![D]:(in(D,C) <=>(in(D,A) &~in(D,B)))), inference(fold_definition,[status(thm)],[d4_xboole_0_1, def_lhs_atom15])) fof(def_lhs_atom16, axiom, ![C,B,A]: lhs_atom16(C,B,A) <=> C=set_difference(A,B), inference(definition,[],[])) fof(to_be_clausified_15, plain, ![A,B,C]: (lhs_atom16(C,B,A) |~![D]:(in(D,C) <=>(in(D,A) &~in(D,B)))), inference(fold_definition,[status(thm)],[d4_xboole_0_0, def_lhs_atom16])) fof(def_lhs_atom17, axiom, ![B,A]: lhs_atom17(B,A) <=> ~disjoint(A,B), inference(definition,[],[])) fof(to_be_clausified_16, plain, ![A,B]: (lhs_atom17(B,A) |set_intersection2(A,B)=empty_set), inference(fold_definition,[status(thm)],[d7_xboole_0_1, def_lhs_atom17])) fof(def_lhs_atom18, axiom, ![B,A]: lhs_atom18(B,A) <=> disjoint(A,B), inference(definition,[],[])) fof(to_be_clausified_17, plain, ![A,B]: (lhs_atom18(B,A) |~set_intersection2(A,B)=empty_set), inference(fold_definition,[status(thm)],[d7_xboole_0_0, def_lhs_atom18])) fof(to_be_clausified_18, plain, ![A,B]: (lhs_atom2(B,A) |(subset(A,B) &A!=B)), inference(fold_definition,[status(thm)],[d8_xboole_0_1, def_lhs_atom2])) fof(def_lhs_atom19, axiom, ![B,A]: lhs_atom19(B,A) <=> proper_subset(A,B), inference(definition,[],[])) fof(to_be_clausified_19, plain, ![A,B]: (lhs_atom19(B,A) |~(subset(A,B) &A!=B)), inference(fold_definition,[status(thm)],[d8_xboole_0_0, def_lhs_atom19])) fof(def_lhs_atom20, axiom, ![]: lhs_atom20() <=>$true, inference(definition,[],[]))
fof(to_be_clausified_20, plain, ![]: (lhs_atom20
|$false), inference(fold_definition,[status(thm)],[dt_k1_xboole_0_0, def_lhs_atom20])) fof(to_be_clausified_21, plain, ![]: (lhs_atom20 |$false), inference(fold_definition,[status(thm)],[dt_k2_xboole_0_0, def_lhs_atom20]))
fof(to_be_clausified_22, plain, ![]: (lhs_atom20
|$false), inference(fold_definition,[status(thm)],[dt_k3_xboole_0_0, def_lhs_atom20])) fof(to_be_clausified_23, plain, ![]: (lhs_atom20 |$false), inference(fold_definition,[status(thm)],[dt_k4_xboole_0_0, def_lhs_atom20]))
fof(def_lhs_atom21, axiom, ![]: lhs_atom21() <=> empty(empty_set), inference(definition,[],[]))
fof(to_be_clausified_24, plain, ![]: (lhs_atom21
|$false), inference(fold_definition,[status(thm)],[fc1_xboole_0_0, def_lhs_atom21])) fof(def_lhs_atom22, axiom, ![A]: lhs_atom22(A) <=> empty(A), inference(definition,[],[])) fof(to_be_clausified_25, plain, ![A,B]: (lhs_atom22(A) |~empty(set_union2(A,B))), inference(fold_definition,[status(thm)],[fc2_xboole_0_0, def_lhs_atom22])) fof(to_be_clausified_26, plain, ![A,B]: (lhs_atom22(A) |~empty(set_union2(B,A))), inference(fold_definition,[status(thm)],[fc3_xboole_0_0, def_lhs_atom22])) fof(def_lhs_atom23, axiom, ![A]: lhs_atom23(A) <=> set_union2(A,A)=A, inference(definition,[],[])) fof(to_be_clausified_27, plain, ![A]: (lhs_atom23(A) |$false), inference(fold_definition,[status(thm)],[idempotence_k2_xboole_0_0, def_lhs_atom23]))
fof(def_lhs_atom24, axiom, ![A]: lhs_atom24(A) <=> set_intersection2(A,A)=A, inference(definition,[],[]))
fof(to_be_clausified_28, plain, ![A]: (lhs_atom24(A)
|$false), inference(fold_definition,[status(thm)],[idempotence_k3_xboole_0_0, def_lhs_atom24])) fof(def_lhs_atom25, axiom, ![A]: lhs_atom25(A) <=> ~proper_subset(A,A), inference(definition,[],[])) fof(to_be_clausified_29, plain, ![A]: (lhs_atom25(A) |$false), inference(fold_definition,[status(thm)],[irreflexivity_r2_xboole_0_0, def_lhs_atom25]))
fof(def_lhs_atom26, axiom, ![A]: lhs_atom26(A) <=> subset(A,A), inference(definition,[],[]))
fof(to_be_clausified_30, plain, ![A]: (lhs_atom26(A)
|$false), inference(fold_definition,[status(thm)],[reflexivity_r1_tarski_0, def_lhs_atom26])) fof(to_be_clausified_31, plain, ![A,B]: (lhs_atom17(B,A) |disjoint(B,A)), inference(fold_definition,[status(thm)],[symmetry_r1_xboole_0_0, def_lhs_atom17])) fof(def_lhs_atom27, axiom, ![A]: lhs_atom27(A) <=> set_union2(A,empty_set)=A, inference(definition,[],[])) fof(to_be_clausified_32, plain, ![A]: (lhs_atom27(A) |$false), inference(fold_definition,[status(thm)],[t1_boole_0, def_lhs_atom27]))
fof(def_lhs_atom28, axiom, ![A]: lhs_atom28(A) <=> set_intersection2(A,empty_set)=empty_set, inference(definition,[],[]))
fof(to_be_clausified_33, plain, ![A]: (lhs_atom28(A)
|$false), inference(fold_definition,[status(thm)],[t2_boole_0, def_lhs_atom28])) fof(to_be_clausified_34, plain, ![A,B]: (lhs_atom6(B,A) |~![C]:(in(C,A) <=>in(C,B))), inference(fold_definition,[status(thm)],[t2_tarski_0, def_lhs_atom6])) fof(def_lhs_atom29, axiom, ![A]: lhs_atom29(A) <=> set_difference(A,empty_set)=A, inference(definition,[],[])) fof(to_be_clausified_35, plain, ![A]: (lhs_atom29(A) |$false), inference(fold_definition,[status(thm)],[t3_boole_0, def_lhs_atom29]))
fof(def_lhs_atom30, axiom, ![A]: lhs_atom30(A) <=> set_difference(empty_set,A)=empty_set, inference(definition,[],[]))
fof(to_be_clausified_36, plain, ![A]: (lhs_atom30(A)
|$false), inference(fold_definition,[status(thm)],[t4_boole_0, def_lhs_atom30])) fof(def_lhs_atom31, axiom, ![A]: lhs_atom31(A) <=> ~empty(A), inference(definition,[],[])) fof(to_be_clausified_37, plain, ![A]: (lhs_atom31(A) |A=empty_set), inference(fold_definition,[status(thm)],[t6_boole_0, def_lhs_atom31])) # Start CNF derivation fof(c_0_0, axiom, (![X3]:![X1]:![X2]:(lhs_atom14(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)&in(X4,X1)))))), file('', to_be_clausified_13)). fof(c_0_1, axiom, (![X3]:![X1]:![X2]:(lhs_atom16(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)&~(in(X4,X1))))))), file('', to_be_clausified_15)). fof(c_0_2, axiom, (![X3]:![X1]:![X2]:(lhs_atom10(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)|in(X4,X1)))))), file('', to_be_clausified_9)). fof(c_0_3, axiom, (![X1]:![X2]:(lhs_atom6(X1,X2)|~(![X3]:(in(X3,X2)<=>in(X3,X1))))), file('', to_be_clausified_34)). fof(c_0_4, axiom, (![X3]:![X1]:![X2]:(lhs_atom13(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)&in(X4,X1))))), file('', to_be_clausified_12)). fof(c_0_5, axiom, (![X3]:![X1]:![X2]:(lhs_atom15(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)&~(in(X4,X1)))))), file('', to_be_clausified_14)). fof(c_0_6, axiom, (![X3]:![X1]:![X2]:(lhs_atom9(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)|in(X4,X1))))), file('', to_be_clausified_8)). fof(c_0_7, axiom, (![X1]:![X2]:(lhs_atom12(X1,X2)|~(![X3]:(in(X3,X2)=>in(X3,X1))))), file('', to_be_clausified_11)). fof(c_0_8, axiom, (![X1]:![X2]:(lhs_atom6(X1,X2)|~((subset(X2,X1)&subset(X1,X2))))), file('', to_be_clausified_5)). fof(c_0_9, axiom, (![X1]:![X2]:(lhs_atom22(X2)|~(empty(set_union2(X1,X2))))), file('', to_be_clausified_26)). fof(c_0_10, axiom, (![X1]:![X2]:(lhs_atom22(X2)|~(empty(set_union2(X2,X1))))), file('', to_be_clausified_25)). fof(c_0_11, axiom, (![X1]:![X2]:(lhs_atom11(X1,X2)|![X3]:(in(X3,X2)=>in(X3,X1)))), file('', to_be_clausified_10)). fof(c_0_12, axiom, (![X1]:![X2]:(lhs_atom19(X1,X2)|~((subset(X2,X1)&X2!=X1)))), file('', to_be_clausified_19)). fof(c_0_13, axiom, (![X1]:![X2]:(lhs_atom18(X1,X2)|~(set_intersection2(X2,X1)=empty_set))), file('', to_be_clausified_17)). fof(c_0_14, axiom, (![X1]:![X2]:(lhs_atom2(X1,X2)|~(proper_subset(X1,X2)))), file('', to_be_clausified_1)). fof(c_0_15, axiom, (![X1]:![X2]:(lhs_atom1(X1,X2)|~(in(X1,X2)))), file('', to_be_clausified_0)). fof(c_0_16, axiom, (![X1]:![X2]:(lhs_atom17(X1,X2)|disjoint(X1,X2))), file('', to_be_clausified_31)). fof(c_0_17, axiom, (![X1]:![X2]:(lhs_atom2(X1,X2)|(subset(X2,X1)&X2!=X1))), file('', to_be_clausified_18)). fof(c_0_18, axiom, (![X1]:![X2]:(lhs_atom17(X1,X2)|set_intersection2(X2,X1)=empty_set)), file('', to_be_clausified_16)). fof(c_0_19, axiom, (![X1]:![X2]:(lhs_atom5(X1,X2)|(subset(X2,X1)&subset(X1,X2)))), file('', to_be_clausified_4)). fof(c_0_20, axiom, (![X2]:(lhs_atom7(X2)|![X1]:~(in(X1,X2)))), file('', to_be_clausified_6)). fof(c_0_21, axiom, (![X2]:(lhs_atom8(X2)|~(![X1]:~(in(X1,X2))))), file('', to_be_clausified_7)). fof(c_0_22, axiom, (![X1]:![X2]:(lhs_atom4(X1,X2)|~$true)), file('', to_be_clausified_3)).
fof(c_0_23, axiom, (![X1]:![X2]:(lhs_atom3(X1,X2)|~$true)), file('', to_be_clausified_2)). fof(c_0_24, axiom, (![X2]:(lhs_atom31(X2)|X2=empty_set)), file('', to_be_clausified_37)). fof(c_0_25, axiom, (![X2]:(lhs_atom30(X2)|~$true)), file('', to_be_clausified_36)).
fof(c_0_26, axiom, (![X2]:(lhs_atom29(X2)|~$true)), file('', to_be_clausified_35)). fof(c_0_27, axiom, (![X2]:(lhs_atom28(X2)|~$true)), file('', to_be_clausified_33)).
fof(c_0_28, axiom, (![X2]:(lhs_atom27(X2)|~$true)), file('', to_be_clausified_32)). fof(c_0_29, axiom, (![X2]:(lhs_atom26(X2)|~$true)), file('', to_be_clausified_30)).
fof(c_0_30, axiom, (![X2]:(lhs_atom25(X2)|~$true)), file('', to_be_clausified_29)). fof(c_0_31, axiom, (![X2]:(lhs_atom24(X2)|~$true)), file('', to_be_clausified_28)).
fof(c_0_32, axiom, (![X2]:(lhs_atom23(X2)|~$true)), file('', to_be_clausified_27)). fof(c_0_33, axiom, ((lhs_atom21|~$true)), file('', to_be_clausified_24)).
fof(c_0_34, axiom, ((lhs_atom20|~$true)), file('', to_be_clausified_23)). fof(c_0_35, axiom, ((lhs_atom20|~$true)), file('', to_be_clausified_22)).
fof(c_0_36, axiom, ((lhs_atom20|~$true)), file('', to_be_clausified_21)). fof(c_0_37, axiom, ((lhs_atom20|~$true)), file('', to_be_clausified_20)).
fof(c_0_38, axiom, (![X3]:![X1]:![X2]:(lhs_atom14(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)&in(X4,X1)))))), c_0_0).
fof(c_0_39, plain, (![X3]:![X1]:![X2]:(lhs_atom16(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)&~in(X4,X1)))))), inference(fof_simplification,[status(thm)],[c_0_1])).
fof(c_0_40, axiom, (![X3]:![X1]:![X2]:(lhs_atom10(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)|in(X4,X1)))))), c_0_2).
fof(c_0_41, axiom, (![X1]:![X2]:(lhs_atom6(X1,X2)|~(![X3]:(in(X3,X2)<=>in(X3,X1))))), c_0_3).
fof(c_0_42, axiom, (![X3]:![X1]:![X2]:(lhs_atom13(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)&in(X4,X1))))), c_0_4).
fof(c_0_43, plain, (![X3]:![X1]:![X2]:(lhs_atom15(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)&~in(X4,X1))))), inference(fof_simplification,[status(thm)],[c_0_5])).
fof(c_0_44, axiom, (![X3]:![X1]:![X2]:(lhs_atom9(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)|in(X4,X1))))), c_0_6).
fof(c_0_45, axiom, (![X1]:![X2]:(lhs_atom12(X1,X2)|~(![X3]:(in(X3,X2)=>in(X3,X1))))), c_0_7).
fof(c_0_46, axiom, (![X1]:![X2]:(lhs_atom6(X1,X2)|~((subset(X2,X1)&subset(X1,X2))))), c_0_8).
fof(c_0_47, plain, (![X1]:![X2]:(lhs_atom22(X2)|~empty(set_union2(X1,X2)))), inference(fof_simplification,[status(thm)],[c_0_9])).
fof(c_0_48, plain, (![X1]:![X2]:(lhs_atom22(X2)|~empty(set_union2(X2,X1)))), inference(fof_simplification,[status(thm)],[c_0_10])).
fof(c_0_49, axiom, (![X1]:![X2]:(lhs_atom11(X1,X2)|![X3]:(in(X3,X2)=>in(X3,X1)))), c_0_11).
fof(c_0_50, axiom, (![X1]:![X2]:(lhs_atom19(X1,X2)|~((subset(X2,X1)&X2!=X1)))), c_0_12).
fof(c_0_51, plain, (![X1]:![X2]:(lhs_atom18(X1,X2)|set_intersection2(X2,X1)!=empty_set)), inference(fof_simplification,[status(thm)],[c_0_13])).
fof(c_0_52, plain, (![X1]:![X2]:(lhs_atom2(X1,X2)|~proper_subset(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_14])).
fof(c_0_53, plain, (![X1]:![X2]:(lhs_atom1(X1,X2)|~in(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_15])).
fof(c_0_54, axiom, (![X1]:![X2]:(lhs_atom17(X1,X2)|disjoint(X1,X2))), c_0_16).
fof(c_0_55, axiom, (![X1]:![X2]:(lhs_atom2(X1,X2)|(subset(X2,X1)&X2!=X1))), c_0_17).
fof(c_0_56, axiom, (![X1]:![X2]:(lhs_atom17(X1,X2)|set_intersection2(X2,X1)=empty_set)), c_0_18).
fof(c_0_57, axiom, (![X1]:![X2]:(lhs_atom5(X1,X2)|(subset(X2,X1)&subset(X1,X2)))), c_0_19).
fof(c_0_58, plain, (![X2]:(lhs_atom7(X2)|![X1]:~in(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_20])).
fof(c_0_59, plain, (![X2]:(lhs_atom8(X2)|~(![X1]:~in(X1,X2)))), inference(fof_simplification,[status(thm)],[c_0_21])).
fof(c_0_60, plain, (![X1]:![X2]:lhs_atom4(X1,X2)), inference(fof_simplification,[status(thm)],[c_0_22])).
fof(c_0_61, plain, (![X1]:![X2]:lhs_atom3(X1,X2)), inference(fof_simplification,[status(thm)],[c_0_23])).
fof(c_0_62, axiom, (![X2]:(lhs_atom31(X2)|X2=empty_set)), c_0_24).
fof(c_0_63, plain, (![X2]:lhs_atom30(X2)), inference(fof_simplification,[status(thm)],[c_0_25])).
fof(c_0_64, plain, (![X2]:lhs_atom29(X2)), inference(fof_simplification,[status(thm)],[c_0_26])).
fof(c_0_65, plain, (![X2]:lhs_atom28(X2)), inference(fof_simplification,[status(thm)],[c_0_27])).
fof(c_0_66, plain, (![X2]:lhs_atom27(X2)), inference(fof_simplification,[status(thm)],[c_0_28])).
fof(c_0_67, plain, (![X2]:lhs_atom26(X2)), inference(fof_simplification,[status(thm)],[c_0_29])).
fof(c_0_68, plain, (![X2]:lhs_atom25(X2)), inference(fof_simplification,[status(thm)],[c_0_30])).
fof(c_0_69, plain, (![X2]:lhs_atom24(X2)), inference(fof_simplification,[status(thm)],[c_0_31])).
fof(c_0_70, plain, (![X2]:lhs_atom23(X2)), inference(fof_simplification,[status(thm)],[c_0_32])).
fof(c_0_71, plain, (lhs_atom21), inference(fof_simplification,[status(thm)],[c_0_33])).
fof(c_0_72, plain, (lhs_atom20), inference(fof_simplification,[status(thm)],[c_0_34])).
fof(c_0_73, plain, (lhs_atom20), inference(fof_simplification,[status(thm)],[c_0_35])).
fof(c_0_74, plain, (lhs_atom20), inference(fof_simplification,[status(thm)],[c_0_36])).
fof(c_0_75, plain, (lhs_atom20), inference(fof_simplification,[status(thm)],[c_0_37])).
fof(c_0_76, plain, (![X5]:![X6]:![X7]:(((~in(esk4_3(X5,X6,X7),X5)|(~in(esk4_3(X5,X6,X7),X7)|~in(esk4_3(X5,X6,X7),X6)))|lhs_atom14(X5,X6,X7))&(((in(esk4_3(X5,X6,X7),X7)|in(esk4_3(X5,X6,X7),X5))|lhs_atom14(X5,X6,X7))&((in(esk4_3(X5,X6,X7),X6)|in(esk4_3(X5,X6,X7),X5))|lhs_atom14(X5,X6,X7))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])).
fof(c_0_77, plain, (![X5]:![X6]:![X7]:(((~in(esk5_3(X5,X6,X7),X5)|(~in(esk5_3(X5,X6,X7),X7)|in(esk5_3(X5,X6,X7),X6)))|lhs_atom16(X5,X6,X7))&(((in(esk5_3(X5,X6,X7),X7)|in(esk5_3(X5,X6,X7),X5))|lhs_atom16(X5,X6,X7))&((~in(esk5_3(X5,X6,X7),X6)|in(esk5_3(X5,X6,X7),X5))|lhs_atom16(X5,X6,X7))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])])).
fof(c_0_78, plain, (![X5]:![X6]:![X7]:((((~in(esk2_3(X5,X6,X7),X7)|~in(esk2_3(X5,X6,X7),X5))|lhs_atom10(X5,X6,X7))&((~in(esk2_3(X5,X6,X7),X6)|~in(esk2_3(X5,X6,X7),X5))|lhs_atom10(X5,X6,X7)))&((in(esk2_3(X5,X6,X7),X5)|(in(esk2_3(X5,X6,X7),X7)|in(esk2_3(X5,X6,X7),X6)))|lhs_atom10(X5,X6,X7)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])).
fof(c_0_79, plain, (![X4]:![X5]:(((~in(esk6_2(X4,X5),X5)|~in(esk6_2(X4,X5),X4))|lhs_atom6(X4,X5))&((in(esk6_2(X4,X5),X5)|in(esk6_2(X4,X5),X4))|lhs_atom6(X4,X5)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])])).
fof(c_0_80, plain, (![X5]:![X6]:![X7]:![X8]:![X9]:((((in(X8,X7)|~in(X8,X5))|lhs_atom13(X5,X6,X7))&((in(X8,X6)|~in(X8,X5))|lhs_atom13(X5,X6,X7)))&(((~in(X9,X7)|~in(X9,X6))|in(X9,X5))|lhs_atom13(X5,X6,X7)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])])])).
fof(c_0_81, plain, (![X5]:![X6]:![X7]:![X8]:![X9]:((((in(X8,X7)|~in(X8,X5))|lhs_atom15(X5,X6,X7))&((~in(X8,X6)|~in(X8,X5))|lhs_atom15(X5,X6,X7)))&(((~in(X9,X7)|in(X9,X6))|in(X9,X5))|lhs_atom15(X5,X6,X7)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])])).
fof(c_0_82, plain, (![X5]:![X6]:![X7]:![X8]:![X9]:(((~in(X8,X5)|(in(X8,X7)|in(X8,X6)))|lhs_atom9(X5,X6,X7))&(((~in(X9,X7)|in(X9,X5))|lhs_atom9(X5,X6,X7))&((~in(X9,X6)|in(X9,X5))|lhs_atom9(X5,X6,X7))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])])).
fof(c_0_83, plain, (![X4]:![X5]:((in(esk3_2(X4,X5),X5)|lhs_atom12(X4,X5))&(~in(esk3_2(X4,X5),X4)|lhs_atom12(X4,X5)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])).
fof(c_0_84, plain, (![X3]:![X4]:(lhs_atom6(X3,X4)|(~subset(X4,X3)|~subset(X3,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])).
fof(c_0_85, plain, (![X3]:![X4]:(lhs_atom22(X4)|~empty(set_union2(X3,X4)))), inference(variable_rename,[status(thm)],[c_0_47])).
fof(c_0_86, plain, (![X3]:![X4]:(lhs_atom22(X4)|~empty(set_union2(X4,X3)))), inference(variable_rename,[status(thm)],[c_0_48])).
fof(c_0_87, plain, (![X4]:![X5]:![X6]:(lhs_atom11(X4,X5)|(~in(X6,X5)|in(X6,X4)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])).
fof(c_0_88, plain, (![X3]:![X4]:(lhs_atom19(X3,X4)|(~subset(X4,X3)|X4=X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])).
fof(c_0_89, plain, (![X3]:![X4]:(lhs_atom18(X3,X4)|set_intersection2(X4,X3)!=empty_set)), inference(variable_rename,[status(thm)],[c_0_51])).
fof(c_0_90, plain, (![X3]:![X4]:(lhs_atom2(X3,X4)|~proper_subset(X3,X4))), inference(variable_rename,[status(thm)],[c_0_52])).
fof(c_0_91, plain, (![X3]:![X4]:(lhs_atom1(X3,X4)|~in(X3,X4))), inference(variable_rename,[status(thm)],[c_0_53])).
fof(c_0_92, plain, (![X3]:![X4]:(lhs_atom17(X3,X4)|disjoint(X3,X4))), inference(variable_rename,[status(thm)],[c_0_54])).
fof(c_0_93, plain, (![X3]:![X4]:((subset(X4,X3)|lhs_atom2(X3,X4))&(X4!=X3|lhs_atom2(X3,X4)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_55])])).
fof(c_0_94, plain, (![X3]:![X4]:(lhs_atom17(X3,X4)|set_intersection2(X4,X3)=empty_set)), inference(variable_rename,[status(thm)],[c_0_56])).
fof(c_0_95, plain, (![X3]:![X4]:((subset(X4,X3)|lhs_atom5(X3,X4))&(subset(X3,X4)|lhs_atom5(X3,X4)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_57])])).
fof(c_0_96, plain, (![X3]:![X4]:(lhs_atom7(X3)|~in(X4,X3))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_58])])).
fof(c_0_97, plain, (![X3]:(lhs_atom8(X3)|in(esk1_1(X3),X3))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])).
fof(c_0_98, plain, (![X3]:![X4]:lhs_atom4(X3,X4)), inference(variable_rename,[status(thm)],[c_0_60])).
fof(c_0_99, plain, (![X3]:![X4]:lhs_atom3(X3,X4)), inference(variable_rename,[status(thm)],[c_0_61])).
fof(c_0_100, plain, (![X3]:(lhs_atom31(X3)|X3=empty_set)), inference(variable_rename,[status(thm)],[c_0_62])).
fof(c_0_101, plain, (![X3]:lhs_atom30(X3)), inference(variable_rename,[status(thm)],[c_0_63])).
fof(c_0_102, plain, (![X3]:lhs_atom29(X3)), inference(variable_rename,[status(thm)],[c_0_64])).
fof(c_0_103, plain, (![X3]:lhs_atom28(X3)), inference(variable_rename,[status(thm)],[c_0_65])).
fof(c_0_104, plain, (![X3]:lhs_atom27(X3)), inference(variable_rename,[status(thm)],[c_0_66])).
fof(c_0_105, plain, (![X3]:lhs_atom26(X3)), inference(variable_rename,[status(thm)],[c_0_67])).
fof(c_0_106, plain, (![X3]:lhs_atom25(X3)), inference(variable_rename,[status(thm)],[c_0_68])).
fof(c_0_107, plain, (![X3]:lhs_atom24(X3)), inference(variable_rename,[status(thm)],[c_0_69])).
fof(c_0_108, plain, (![X3]:lhs_atom23(X3)), inference(variable_rename,[status(thm)],[c_0_70])).
fof(c_0_109, plain, (lhs_atom21), c_0_71).
fof(c_0_110, plain, (lhs_atom20), c_0_72).
fof(c_0_111, plain, (lhs_atom20), c_0_73).
fof(c_0_112, plain, (lhs_atom20), c_0_74).
fof(c_0_113, plain, (lhs_atom20), c_0_75).
cnf(c_0_114,plain,(lhs_atom14(X1,X2,X3)|~in(esk4_3(X1,X2,X3),X2)|~in(esk4_3(X1,X2,X3),X3)|~in(esk4_3(X1,X2,X3),X1)), inference(split_conjunct,[status(thm)],[c_0_76])).
cnf(c_0_115,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X2)|~in(esk5_3(X1,X2,X3),X3)|~in(esk5_3(X1,X2,X3),X1)), inference(split_conjunct,[status(thm)],[c_0_77])).
cnf(c_0_116,plain,(lhs_atom10(X1,X2,X3)|~in(esk2_3(X1,X2,X3),X1)|~in(esk2_3(X1,X2,X3),X3)), inference(split_conjunct,[status(thm)],[c_0_78])).
cnf(c_0_117,plain,(lhs_atom10(X1,X2,X3)|~in(esk2_3(X1,X2,X3),X1)|~in(esk2_3(X1,X2,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_78])).
cnf(c_0_118,plain,(lhs_atom10(X1,X2,X3)|in(esk2_3(X1,X2,X3),X2)|in(esk2_3(X1,X2,X3),X3)|in(esk2_3(X1,X2,X3),X1)), inference(split_conjunct,[status(thm)],[c_0_78])).
cnf(c_0_119,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X1)|~in(esk5_3(X1,X2,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_77])).
cnf(c_0_120,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X1)|in(esk5_3(X1,X2,X3),X3)), inference(split_conjunct,[status(thm)],[c_0_77])).
cnf(c_0_121,plain,(lhs_atom14(X1,X2,X3)|in(esk4_3(X1,X2,X3),X1)|in(esk4_3(X1,X2,X3),X3)), inference(split_conjunct,[status(thm)],[c_0_76])).
cnf(c_0_122,plain,(lhs_atom14(X1,X2,X3)|in(esk4_3(X1,X2,X3),X1)|in(esk4_3(X1,X2,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_76])).
cnf(c_0_123,plain,(lhs_atom6(X1,X2)|~in(esk6_2(X1,X2),X1)|~in(esk6_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_79])).
cnf(c_0_124,plain,(lhs_atom13(X1,X2,X3)|in(X4,X1)|~in(X4,X2)|~in(X4,X3)), inference(split_conjunct,[status(thm)],[c_0_80])).
cnf(c_0_125,plain,(lhs_atom15(X1,X2,X3)|in(X4,X1)|in(X4,X2)|~in(X4,X3)), inference(split_conjunct,[status(thm)],[c_0_81])).
cnf(c_0_126,plain,(lhs_atom9(X1,X2,X3)|in(X4,X2)|in(X4,X3)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_82])).
cnf(c_0_127,plain,(lhs_atom15(X1,X2,X3)|~in(X4,X1)|~in(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_81])).
cnf(c_0_128,plain,(lhs_atom6(X1,X2)|in(esk6_2(X1,X2),X1)|in(esk6_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_79])).
cnf(c_0_129,plain,(lhs_atom15(X1,X2,X3)|in(X4,X3)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_81])).
cnf(c_0_130,plain,(lhs_atom13(X1,X2,X3)|in(X4,X3)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_80])).
cnf(c_0_131,plain,(lhs_atom13(X1,X2,X3)|in(X4,X2)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_80])).
cnf(c_0_132,plain,(lhs_atom9(X1,X2,X3)|in(X4,X1)|~in(X4,X3)), inference(split_conjunct,[status(thm)],[c_0_82])).
cnf(c_0_133,plain,(lhs_atom9(X1,X2,X3)|in(X4,X1)|~in(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_82])).
cnf(c_0_134,plain,(lhs_atom12(X1,X2)|~in(esk3_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_83])).
cnf(c_0_135,plain,(lhs_atom6(X1,X2)|~subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_84])).
cnf(c_0_136,plain,(lhs_atom12(X1,X2)|in(esk3_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_83])).
cnf(c_0_137,plain,(lhs_atom22(X2)|~empty(set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_85])).
cnf(c_0_138,plain,(lhs_atom22(X1)|~empty(set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_86])).
cnf(c_0_139,plain,(in(X1,X2)|lhs_atom11(X2,X3)|~in(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_87])).
cnf(c_0_140,plain,(X1=X2|lhs_atom19(X2,X1)|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_88])).
cnf(c_0_141,plain,(lhs_atom18(X2,X1)|set_intersection2(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_89])).
cnf(c_0_142,plain,(lhs_atom2(X1,X2)|~proper_subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_90])).
cnf(c_0_143,plain,(lhs_atom1(X1,X2)|~in(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_91])).
cnf(c_0_144,plain,(disjoint(X1,X2)|lhs_atom17(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_92])).
cnf(c_0_145,plain,(lhs_atom2(X1,X2)|subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_93])).
cnf(c_0_146,plain,(set_intersection2(X1,X2)=empty_set|lhs_atom17(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_94])).
cnf(c_0_147,plain,(lhs_atom5(X1,X2)|subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_95])).
cnf(c_0_148,plain,(lhs_atom5(X1,X2)|subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_95])).
cnf(c_0_149,plain,(lhs_atom7(X2)|~in(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_96])).
cnf(c_0_150,plain,(in(esk1_1(X1),X1)|lhs_atom8(X1)), inference(split_conjunct,[status(thm)],[c_0_97])).
cnf(c_0_151,plain,(lhs_atom2(X1,X2)|X2!=X1), inference(split_conjunct,[status(thm)],[c_0_93])).
cnf(c_0_152,plain,(lhs_atom4(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_98])).
cnf(c_0_153,plain,(lhs_atom3(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_99])).
cnf(c_0_154,plain,(X1=empty_set|lhs_atom31(X1)), inference(split_conjunct,[status(thm)],[c_0_100])).
cnf(c_0_155,plain,(lhs_atom30(X1)), inference(split_conjunct,[status(thm)],[c_0_101])).
cnf(c_0_156,plain,(lhs_atom29(X1)), inference(split_conjunct,[status(thm)],[c_0_102])).
cnf(c_0_157,plain,(lhs_atom28(X1)), inference(split_conjunct,[status(thm)],[c_0_103])).
cnf(c_0_158,plain,(lhs_atom27(X1)), inference(split_conjunct,[status(thm)],[c_0_104])).
cnf(c_0_159,plain,(lhs_atom26(X1)), inference(split_conjunct,[status(thm)],[c_0_105])).
cnf(c_0_160,plain,(lhs_atom25(X1)), inference(split_conjunct,[status(thm)],[c_0_106])).
cnf(c_0_161,plain,(lhs_atom24(X1)), inference(split_conjunct,[status(thm)],[c_0_107])).
cnf(c_0_162,plain,(lhs_atom23(X1)), inference(split_conjunct,[status(thm)],[c_0_108])).
cnf(c_0_163,plain,(lhs_atom21), inference(split_conjunct,[status(thm)],[c_0_109])).
cnf(c_0_164,plain,(lhs_atom20), inference(split_conjunct,[status(thm)],[c_0_110])).
cnf(c_0_165,plain,(lhs_atom20), inference(split_conjunct,[status(thm)],[c_0_111])).
cnf(c_0_166,plain,(lhs_atom20), inference(split_conjunct,[status(thm)],[c_0_112])).
cnf(c_0_167,plain,(lhs_atom20), inference(split_conjunct,[status(thm)],[c_0_113])).
cnf(c_0_168,plain,(lhs_atom14(X1,X2,X3)|~in(esk4_3(X1,X2,X3),X2)|~in(esk4_3(X1,X2,X3),X3)|~in(esk4_3(X1,X2,X3),X1)), c_0_114, ['final']).
cnf(c_0_169,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X2)|~in(esk5_3(X1,X2,X3),X3)|~in(esk5_3(X1,X2,X3),X1)), c_0_115, ['final']).
cnf(c_0_170,plain,(lhs_atom10(X1,X2,X3)|~in(esk2_3(X1,X2,X3),X1)|~in(esk2_3(X1,X2,X3),X3)), c_0_116, ['final']).
cnf(c_0_171,plain,(lhs_atom10(X1,X2,X3)|~in(esk2_3(X1,X2,X3),X1)|~in(esk2_3(X1,X2,X3),X2)), c_0_117, ['final']).
cnf(c_0_172,plain,(lhs_atom10(X1,X2,X3)|in(esk2_3(X1,X2,X3),X2)|in(esk2_3(X1,X2,X3),X3)|in(esk2_3(X1,X2,X3),X1)), c_0_118, ['final']).
cnf(c_0_173,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X1)|~in(esk5_3(X1,X2,X3),X2)), c_0_119, ['final']).
cnf(c_0_174,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X1)|in(esk5_3(X1,X2,X3),X3)), c_0_120, ['final']).
cnf(c_0_175,plain,(lhs_atom14(X1,X2,X3)|in(esk4_3(X1,X2,X3),X1)|in(esk4_3(X1,X2,X3),X3)), c_0_121, ['final']).
cnf(c_0_176,plain,(lhs_atom14(X1,X2,X3)|in(esk4_3(X1,X2,X3),X1)|in(esk4_3(X1,X2,X3),X2)), c_0_122, ['final']).
cnf(c_0_177,plain,(lhs_atom6(X1,X2)|~in(esk6_2(X1,X2),X1)|~in(esk6_2(X1,X2),X2)), c_0_123, ['final']).
cnf(c_0_178,plain,(lhs_atom13(X1,X2,X3)|in(X4,X1)|~in(X4,X2)|~in(X4,X3)), c_0_124, ['final']).
cnf(c_0_179,plain,(lhs_atom15(X1,X2,X3)|in(X4,X1)|in(X4,X2)|~in(X4,X3)), c_0_125, ['final']).
cnf(c_0_180,plain,(lhs_atom9(X1,X2,X3)|in(X4,X2)|in(X4,X3)|~in(X4,X1)), c_0_126, ['final']).
cnf(c_0_181,plain,(lhs_atom15(X1,X2,X3)|~in(X4,X1)|~in(X4,X2)), c_0_127, ['final']).
cnf(c_0_182,plain,(lhs_atom6(X1,X2)|in(esk6_2(X1,X2),X1)|in(esk6_2(X1,X2),X2)), c_0_128, ['final']).
cnf(c_0_183,plain,(lhs_atom15(X1,X2,X3)|in(X4,X3)|~in(X4,X1)), c_0_129, ['final']).
cnf(c_0_184,plain,(lhs_atom13(X1,X2,X3)|in(X4,X3)|~in(X4,X1)), c_0_130, ['final']).
cnf(c_0_185,plain,(lhs_atom13(X1,X2,X3)|in(X4,X2)|~in(X4,X1)), c_0_131, ['final']).
cnf(c_0_186,plain,(lhs_atom9(X1,X2,X3)|in(X4,X1)|~in(X4,X3)), c_0_132, ['final']).
cnf(c_0_187,plain,(lhs_atom9(X1,X2,X3)|in(X4,X1)|~in(X4,X2)), c_0_133, ['final']).
cnf(c_0_188,plain,(lhs_atom12(X1,X2)|~in(esk3_2(X1,X2),X1)), c_0_134, ['final']).
cnf(c_0_189,plain,(lhs_atom6(X1,X2)|~subset(X1,X2)|~subset(X2,X1)), c_0_135, ['final']).
cnf(c_0_190,plain,(lhs_atom12(X1,X2)|in(esk3_2(X1,X2),X2)), c_0_136, ['final']).
cnf(c_0_191,plain,(lhs_atom22(X2)|~empty(set_union2(X1,X2))), c_0_137, ['final']).
cnf(c_0_192,plain,(lhs_atom22(X1)|~empty(set_union2(X1,X2))), c_0_138, ['final']).
cnf(c_0_193,plain,(in(X1,X2)|lhs_atom11(X2,X3)|~in(X1,X3)), c_0_139, ['final']).
cnf(c_0_194,plain,(X1=X2|lhs_atom19(X2,X1)|~subset(X1,X2)), c_0_140, ['final']).
cnf(c_0_195,plain,(lhs_atom18(X2,X1)|set_intersection2(X1,X2)!=empty_set), c_0_141, ['final']).
cnf(c_0_196,plain,(lhs_atom2(X1,X2)|~proper_subset(X1,X2)), c_0_142, ['final']).
cnf(c_0_197,plain,(lhs_atom1(X1,X2)|~in(X1,X2)), c_0_143, ['final']).
cnf(c_0_198,plain,(disjoint(X1,X2)|lhs_atom17(X1,X2)), c_0_144, ['final']).
cnf(c_0_199,plain,(lhs_atom2(X1,X2)|subset(X2,X1)), c_0_145, ['final']).
cnf(c_0_200,plain,(set_intersection2(X1,X2)=empty_set|lhs_atom17(X2,X1)), c_0_146, ['final']).
cnf(c_0_201,plain,(lhs_atom5(X1,X2)|subset(X2,X1)), c_0_147, ['final']).
cnf(c_0_202,plain,(lhs_atom5(X1,X2)|subset(X1,X2)), c_0_148, ['final']).
cnf(c_0_203,plain,(lhs_atom7(X2)|~in(X1,X2)), c_0_149, ['final']).
cnf(c_0_204,plain,(in(esk1_1(X1),X1)|lhs_atom8(X1)), c_0_150, ['final']).
cnf(c_0_205,plain,(lhs_atom2(X1,X2)|X2!=X1), c_0_151, ['final']).
cnf(c_0_206,plain,(lhs_atom4(X1,X2)), c_0_152, ['final']).
cnf(c_0_207,plain,(lhs_atom3(X1,X2)), c_0_153, ['final']).
cnf(c_0_208,plain,(X1=empty_set|lhs_atom31(X1)), c_0_154, ['final']).
cnf(c_0_209,plain,(lhs_atom30(X1)), c_0_155, ['final']).
cnf(c_0_210,plain,(lhs_atom29(X1)), c_0_156, ['final']).
cnf(c_0_211,plain,(lhs_atom28(X1)), c_0_157, ['final']).
cnf(c_0_212,plain,(lhs_atom27(X1)), c_0_158, ['final']).
cnf(c_0_213,plain,(lhs_atom26(X1)), c_0_159, ['final']).
cnf(c_0_214,plain,(lhs_atom25(X1)), c_0_160, ['final']).
cnf(c_0_215,plain,(lhs_atom24(X1)), c_0_161, ['final']).
cnf(c_0_216,plain,(lhs_atom23(X1)), c_0_162, ['final']).
cnf(c_0_217,plain,(lhs_atom21), c_0_163, ['final']).
cnf(c_0_218,plain,(lhs_atom20), c_0_164, ['final']).
cnf(c_0_219,plain,(lhs_atom20), c_0_165, ['final']).
cnf(c_0_220,plain,(lhs_atom20), c_0_166, ['final']).
cnf(c_0_221,plain,(lhs_atom20), c_0_167, ['final']).
# End CNF derivation
cnf(c_0_168_0,axiom,X1=set_intersection2(X3,X2)|~in(sk1_esk4_3(X1,X2,X3),X2)|~in(sk1_esk4_3(X1,X2,X3),X3)|~in(sk1_esk4_3(X1,X2,X3),X1),inference(unfold_definition, [status(thm)], [c_0_168, def_lhs_atom14])).
cnf(c_0_169_0,axiom,X1=set_difference(X3,X2)|in(sk1_esk5_3(X1,X2,X3),X2)|~in(sk1_esk5_3(X1,X2,X3),X3)|~in(sk1_esk5_3(X1,X2,X3),X1),inference(unfold_definition, [status(thm)], [c_0_169, def_lhs_atom16])).
cnf(c_0_170_0,axiom,X1=set_union2(X3,X2)|~in(sk1_esk2_3(X1,X2,X3),X1)|~in(sk1_esk2_3(X1,X2,X3),X3),inference(unfold_definition, [status(thm)], [c_0_170, def_lhs_atom10])).
cnf(c_0_171_0,axiom,X1=set_union2(X3,X2)|~in(sk1_esk2_3(X1,X2,X3),X1)|~in(sk1_esk2_3(X1,X2,X3),X2),inference(unfold_definition, [status(thm)], [c_0_171, def_lhs_atom10])).
cnf(c_0_172_0,axiom,X1=set_union2(X3,X2)|in(sk1_esk2_3(X1,X2,X3),X2)|in(sk1_esk2_3(X1,X2,X3),X3)|in(sk1_esk2_3(X1,X2,X3),X1),inference(unfold_definition, [status(thm)], [c_0_172, def_lhs_atom10])).
cnf(c_0_173_0,axiom,X1=set_difference(X3,X2)|in(sk1_esk5_3(X1,X2,X3),X1)|~in(sk1_esk5_3(X1,X2,X3),X2),inference(unfold_definition, [status(thm)], [c_0_173, def_lhs_atom16])).
cnf(c_0_174_0,axiom,X1=set_difference(X3,X2)|in(sk1_esk5_3(X1,X2,X3),X1)|in(sk1_esk5_3(X1,X2,X3),X3),inference(unfold_definition, [status(thm)], [c_0_174, def_lhs_atom16])).
cnf(c_0_175_0,axiom,X1=set_intersection2(X3,X2)|in(sk1_esk4_3(X1,X2,X3),X1)|in(sk1_esk4_3(X1,X2,X3),X3),inference(unfold_definition, [status(thm)], [c_0_175, def_lhs_atom14])).
cnf(c_0_176_0,axiom,X1=set_intersection2(X3,X2)|in(sk1_esk4_3(X1,X2,X3),X1)|in(sk1_esk4_3(X1,X2,X3),X2),inference(unfold_definition, [status(thm)], [c_0_176, def_lhs_atom14])).
cnf(c_0_177_0,axiom,X2=X1|~in(sk1_esk6_2(X1,X2),X1)|~in(sk1_esk6_2(X1,X2),X2),inference(unfold_definition, [status(thm)], [c_0_177, def_lhs_atom6])).
cnf(c_0_178_0,axiom,~X1=set_intersection2(X3,X2)|in(X4,X1)|~in(X4,X2)|~in(X4,X3),inference(unfold_definition, [status(thm)], [c_0_178, def_lhs_atom13])).
cnf(c_0_179_0,axiom,~X1=set_difference(X3,X2)|in(X4,X1)|in(X4,X2)|~in(X4,X3),inference(unfold_definition, [status(thm)], [c_0_179, def_lhs_atom15])).
cnf(c_0_180_0,axiom,~X1=set_union2(X3,X2)|in(X4,X2)|in(X4,X3)|~in(X4,X1),inference(unfold_definition, [status(thm)], [c_0_180, def_lhs_atom9])).
cnf(c_0_181_0,axiom,~X1=set_difference(X3,X2)|~in(X4,X1)|~in(X4,X2),inference(unfold_definition, [status(thm)], [c_0_181, def_lhs_atom15])).
cnf(c_0_182_0,axiom,X2=X1|in(sk1_esk6_2(X1,X2),X1)|in(sk1_esk6_2(X1,X2),X2),inference(unfold_definition, [status(thm)], [c_0_182, def_lhs_atom6])).
cnf(c_0_183_0,axiom,~X1=set_difference(X3,X2)|in(X4,X3)|~in(X4,X1),inference(unfold_definition, [status(thm)], [c_0_183, def_lhs_atom15])).
cnf(c_0_184_0,axiom,~X1=set_intersection2(X3,X2)|in(X4,X3)|~in(X4,X1),inference(unfold_definition, [status(thm)], [c_0_184, def_lhs_atom13])).
cnf(c_0_185_0,axiom,~X1=set_intersection2(X3,X2)|in(X4,X2)|~in(X4,X1),inference(unfold_definition, [status(thm)], [c_0_185, def_lhs_atom13])).
cnf(c_0_186_0,axiom,~X1=set_union2(X3,X2)|in(X4,X1)|~in(X4,X3),inference(unfold_definition, [status(thm)], [c_0_186, def_lhs_atom9])).
cnf(c_0_187_0,axiom,~X1=set_union2(X3,X2)|in(X4,X1)|~in(X4,X2),inference(unfold_definition, [status(thm)], [c_0_187, def_lhs_atom9])).
cnf(c_0_188_0,axiom,subset(X2,X1)|~in(sk1_esk3_2(X1,X2),X1),inference(unfold_definition, [status(thm)], [c_0_188, def_lhs_atom12])).
cnf(c_0_189_0,axiom,X2=X1|~subset(X1,X2)|~subset(X2,X1),inference(unfold_definition, [status(thm)], [c_0_189, def_lhs_atom6])).
cnf(c_0_190_0,axiom,subset(X2,X1)|in(sk1_esk3_2(X1,X2),X2),inference(unfold_definition, [status(thm)], [c_0_190, def_lhs_atom12])).
cnf(c_0_191_0,axiom,empty(X2)|~empty(set_union2(X1,X2)),inference(unfold_definition, [status(thm)], [c_0_191, def_lhs_atom22])).
cnf(c_0_192_0,axiom,empty(X1)|~empty(set_union2(X1,X2)),inference(unfold_definition, [status(thm)], [c_0_192, def_lhs_atom22])).
cnf(c_0_193_0,axiom,~subset(X3,X2)|in(X1,X2)|~in(X1,X3),inference(unfold_definition, [status(thm)], [c_0_193, def_lhs_atom11])).
cnf(c_0_194_0,axiom,proper_subset(X1,X2)|X1=X2|~subset(X1,X2),inference(unfold_definition, [status(thm)], [c_0_194, def_lhs_atom19])).
cnf(c_0_195_0,axiom,disjoint(X1,X2)|set_intersection2(X1,X2)!=empty_set,inference(unfold_definition, [status(thm)], [c_0_195, def_lhs_atom18])).
cnf(c_0_196_0,axiom,~proper_subset(X2,X1)|~proper_subset(X1,X2),inference(unfold_definition, [status(thm)], [c_0_196, def_lhs_atom2])).
cnf(c_0_197_0,axiom,~in(X2,X1)|~in(X1,X2),inference(unfold_definition, [status(thm)], [c_0_197, def_lhs_atom1])).
cnf(c_0_198_0,axiom,~disjoint(X2,X1)|disjoint(X1,X2),inference(unfold_definition, [status(thm)], [c_0_198, def_lhs_atom17])).
cnf(c_0_199_0,axiom,~proper_subset(X2,X1)|subset(X2,X1),inference(unfold_definition, [status(thm)], [c_0_199, def_lhs_atom2])).
cnf(c_0_200_0,axiom,~disjoint(X1,X2)|set_intersection2(X1,X2)=empty_set,inference(unfold_definition, [status(thm)], [c_0_200, def_lhs_atom17])).
cnf(c_0_201_0,axiom,~X2=X1|subset(X2,X1),inference(unfold_definition, [status(thm)], [c_0_201, def_lhs_atom5])).
cnf(c_0_202_0,axiom,~X2=X1|subset(X1,X2),inference(unfold_definition, [status(thm)], [c_0_202, def_lhs_atom5])).
cnf(c_0_203_0,axiom,~X2=empty_set|~in(X1,X2),inference(unfold_definition, [status(thm)], [c_0_203, def_lhs_atom7])).
cnf(c_0_204_0,axiom,X1=empty_set|in(sk1_esk1_1(X1),X1),inference(unfold_definition, [status(thm)], [c_0_204, def_lhs_atom8])).
cnf(c_0_205_0,axiom,~proper_subset(X2,X1)|X2!=X1,inference(unfold_definition, [status(thm)], [c_0_205, def_lhs_atom2])).
cnf(c_0_208_0,axiom,~empty(X1)|X1=empty_set,inference(unfold_definition, [status(thm)], [c_0_208, def_lhs_atom31])).
cnf(c_0_206_0,axiom,set_intersection2(X2,X1)=set_intersection2(X1,X2),inference(unfold_definition, [status(thm)], [c_0_206, def_lhs_atom4])).
cnf(c_0_207_0,axiom,set_union2(X2,X1)=set_union2(X1,X2),inference(unfold_definition, [status(thm)], [c_0_207, def_lhs_atom3])).
cnf(c_0_209_0,axiom,set_difference(empty_set,X1)=empty_set,inference(unfold_definition, [status(thm)], [c_0_209, def_lhs_atom30])).
cnf(c_0_210_0,axiom,set_difference(X1,empty_set)=X1,inference(unfold_definition, [status(thm)], [c_0_210, def_lhs_atom29])).
cnf(c_0_211_0,axiom,set_intersection2(X1,empty_set)=empty_set,inference(unfold_definition, [status(thm)], [c_0_211, def_lhs_atom28])).
cnf(c_0_212_0,axiom,set_union2(X1,empty_set)=X1,inference(unfold_definition, [status(thm)], [c_0_212, def_lhs_atom27])).
cnf(c_0_213_0,axiom,subset(X1,X1),inference(unfold_definition, [status(thm)], [c_0_213, def_lhs_atom26])).
cnf(c_0_214_0,axiom,~proper_subset(X1,X1),inference(unfold_definition, [status(thm)], [c_0_214, def_lhs_atom25])).
cnf(c_0_215_0,axiom,set_intersection2(X1,X1)=X1,inference(unfold_definition, [status(thm)], [c_0_215, def_lhs_atom24])).
cnf(c_0_216_0,axiom,set_union2(X1,X1)=X1,inference(unfold_definition, [status(thm)], [c_0_216, def_lhs_atom23])).
cnf(c_0_217_0,axiom,empty(empty_set),inference(unfold_definition, [status(thm)], [c_0_217, def_lhs_atom21])).
cnf(c_0_218_0,axiom,$true,inference(unfold_definition, [status(thm)], [c_0_218, def_lhs_atom20])). cnf(c_0_219_0,axiom,$true,inference(unfold_definition, [status(thm)], [c_0_219, def_lhs_atom20])).
cnf(c_0_220_0,axiom,$true,inference(unfold_definition, [status(thm)], [c_0_220, def_lhs_atom20])). cnf(c_0_221_0,axiom,$true,inference(unfold_definition, [status(thm)], [c_0_221, def_lhs_atom20])).
# Orienting (remaining) axiom formulas using strategy ClausalAll
# CNF of (remaining) axioms:
# Start CNF derivation
fof(c_0_0, axiom, (![X1]:![X2]:~((in(X1,X2)&empty(X2)))), file('', t7_boole)).
fof(c_0_1, axiom, (![X1]:![X2]:~((empty(X1)&(X1!=X2&empty(X2))))), file('', t8_boole)).
fof(c_0_2, axiom, (?[X1]:~(empty(X1))), file('', rc2_xboole_0)).
fof(c_0_3, axiom, (?[X1]:empty(X1)), file('', rc1_xboole_0)).
fof(c_0_4, axiom, (![X1]:![X2]:~((in(X1,X2)&empty(X2)))), c_0_0).
fof(c_0_5, axiom, (![X1]:![X2]:~((empty(X1)&(X1!=X2&empty(X2))))), c_0_1).
fof(c_0_6, plain, (?[X1]:~empty(X1)), inference(fof_simplification,[status(thm)],[c_0_2])).
fof(c_0_7, axiom, (?[X1]:empty(X1)), c_0_3).
fof(c_0_8, plain, (![X3]:![X4]:(~in(X3,X4)|~empty(X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])).
fof(c_0_9, plain, (![X3]:![X4]:(~empty(X3)|(X3=X4|~empty(X4)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])).
fof(c_0_10, plain, (~empty(esk1_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])])).
fof(c_0_11, plain, (empty(esk2_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])).
cnf(c_0_12,plain,(~empty(X1)|~in(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8])).
cnf(c_0_13,plain,(X2=X1|~empty(X1)|~empty(X2)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_14,plain,(~empty(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_15,plain,(empty(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])).
cnf(c_0_16,plain,(~empty(X1)|~in(X2,X1)), c_0_12, ['final']).
cnf(c_0_17,plain,(X2=X1|~empty(X1)|~empty(X2)), c_0_13, ['final']).
cnf(c_0_18,plain,(~empty(esk1_0)), c_0_14, ['final']).
cnf(c_0_19,plain,(empty(esk2_0)), c_0_15, ['final']).
# End CNF derivation
# Generating one_way clauses for all literals in the CNF.
cnf(c_0_16_0, axiom, (~empty(X1)
|~in(X2,X1)), inference(literals_permutation, [status(thm)], [c_0_16]))
cnf(c_0_16_1, axiom, (~in(X2,X1)
|~empty(X1)), inference(literals_permutation, [status(thm)], [c_0_16]))
cnf(c_0_17_0, axiom, (X2=X1
|(~empty(X1)
|~empty(X2))), inference(literals_permutation, [status(thm)], [c_0_17]))
cnf(c_0_17_1, axiom, ((~empty(X1)
|X2=X1)
|~empty(X2)), inference(literals_permutation, [status(thm)], [c_0_17]))
cnf(c_0_17_2, axiom, (~empty(X2)
|(~empty(X1)
|X2=X1)), inference(literals_permutation, [status(thm)], [c_0_17]))
cnf(c_0_18_0, axiom, ~empty(sk2_esk1_0), inference(literals_permutation, [status(thm)], [c_0_18]))
cnf(c_0_19_0, axiom, empty(sk2_esk2_0), inference(literals_permutation, [status(thm)], [c_0_19]))
# CNF of non-axioms
# Start CNF derivation
fof(c_0_0, lemma, (![X1]:![X2]:![X3]:(subset(X1,X2)=>subset(set_difference(X1,X3),set_difference(X2,X3)))), file('', t33_xboole_1)).
fof(c_0_1, lemma, (![X1]:![X2]:![X3]:(subset(X1,X2)=>subset(set_intersection2(X1,X3),set_intersection2(X2,X3)))), file('', t26_xboole_1)).
fof(c_0_2, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~(in(X3,set_intersection2(X1,X2)))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2))))), file('', t4_xboole_0)).
fof(c_0_3, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X3,X2))=>subset(set_union2(X1,X3),X2))), file('', t8_xboole_1)).
fof(c_0_4, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X1,X3))=>subset(X1,set_intersection2(X2,X3)))), file('', t19_xboole_1)).
fof(c_0_5, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), file('', t3_xboole_0)).
fof(c_0_6, lemma, (![X1]:![X2]:(subset(X1,X2)=>X2=set_union2(X1,set_difference(X2,X1)))), file('', t45_xboole_1)).
fof(c_0_7, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X2,X3))=>subset(X1,X3))), file('', t1_xboole_1)).
fof(c_0_8, lemma, (![X1]:![X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), file('', t48_xboole_1)).
fof(c_0_9, lemma, (![X1]:![X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), file('', t40_xboole_1)).
fof(c_0_10, lemma, (![X1]:![X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), file('', t39_xboole_1)).
fof(c_0_11, lemma, (![X1]:![X2]:~((subset(X1,X2)&proper_subset(X2,X1)))), file('', t60_xboole_1)).
fof(c_0_12, lemma, (![X1]:![X2]:subset(X1,set_union2(X1,X2))), file('', t7_xboole_1)).
fof(c_0_13, lemma, (![X1]:![X2]:subset(set_difference(X1,X2),X1)), file('', t36_xboole_1)).
fof(c_0_14, lemma, (![X1]:![X2]:subset(set_intersection2(X1,X2),X1)), file('', t17_xboole_1)).
fof(c_0_15, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_intersection2(X1,X2)=X1)), file('', t28_xboole_1)).
fof(c_0_16, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_union2(X1,X2)=X2)), file('', t12_xboole_1)).
fof(c_0_17, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), file('', t37_xboole_1)).
fof(c_0_18, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), file('', l32_xboole_1)).
fof(c_0_19, lemma, (![X1]:(subset(X1,empty_set)=>X1=empty_set)), file('', t3_xboole_1)).
fof(c_0_20, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('', t63_xboole_1)).
fof(c_0_21, lemma, (![X1]:subset(empty_set,X1)), file('', t2_xboole_1)).
fof(c_0_22, lemma, (![X1]:![X2]:![X3]:(subset(X1,X2)=>subset(set_difference(X1,X3),set_difference(X2,X3)))), c_0_0).
fof(c_0_23, lemma, (![X1]:![X2]:![X3]:(subset(X1,X2)=>subset(set_intersection2(X1,X3),set_intersection2(X2,X3)))), c_0_1).
fof(c_0_24, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~in(X3,set_intersection2(X1,X2))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_2])).
fof(c_0_25, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X3,X2))=>subset(set_union2(X1,X3),X2))), c_0_3).
fof(c_0_26, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X1,X3))=>subset(X1,set_intersection2(X2,X3)))), c_0_4).
fof(c_0_27, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_5])).
fof(c_0_28, lemma, (![X1]:![X2]:(subset(X1,X2)=>X2=set_union2(X1,set_difference(X2,X1)))), c_0_6).
fof(c_0_29, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X2,X3))=>subset(X1,X3))), c_0_7).
fof(c_0_30, lemma, (![X1]:![X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), c_0_8).
fof(c_0_31, lemma, (![X1]:![X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), c_0_9).
fof(c_0_32, lemma, (![X1]:![X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), c_0_10).
fof(c_0_33, lemma, (![X1]:![X2]:~((subset(X1,X2)&proper_subset(X2,X1)))), c_0_11).
fof(c_0_34, lemma, (![X1]:![X2]:subset(X1,set_union2(X1,X2))), c_0_12).
fof(c_0_35, lemma, (![X1]:![X2]:subset(set_difference(X1,X2),X1)), c_0_13).
fof(c_0_36, lemma, (![X1]:![X2]:subset(set_intersection2(X1,X2),X1)), c_0_14).
fof(c_0_37, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_intersection2(X1,X2)=X1)), c_0_15).
fof(c_0_38, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_union2(X1,X2)=X2)), c_0_16).
fof(c_0_39, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), c_0_17).
fof(c_0_40, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), c_0_18).
fof(c_0_41, lemma, (![X1]:(subset(X1,empty_set)=>X1=empty_set)), c_0_19).
fof(c_0_42, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[c_0_20])).
fof(c_0_43, lemma, (![X1]:subset(empty_set,X1)), c_0_21).
fof(c_0_44, lemma, (![X4]:![X5]:![X6]:(~subset(X4,X5)|subset(set_difference(X4,X6),set_difference(X5,X6)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])])).
fof(c_0_45, lemma, (![X4]:![X5]:![X6]:(~subset(X4,X5)|subset(set_intersection2(X4,X6),set_intersection2(X5,X6)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])).
fof(c_0_46, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:((disjoint(X4,X5)|in(esk2_2(X4,X5),set_intersection2(X4,X5)))&(~in(X9,set_intersection2(X7,X8))|~disjoint(X7,X8)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])])).
fof(c_0_47, lemma, (![X4]:![X5]:![X6]:((~subset(X4,X5)|~subset(X6,X5))|subset(set_union2(X4,X6),X5))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])).
fof(c_0_48, lemma, (![X4]:![X5]:![X6]:((~subset(X4,X5)|~subset(X4,X6))|subset(X4,set_intersection2(X5,X6)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])).
fof(c_0_49, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:(((in(esk1_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk1_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X9,X7)|~in(X9,X8))|~disjoint(X7,X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])])])])).
fof(c_0_50, lemma, (![X3]:![X4]:(~subset(X3,X4)|X4=set_union2(X3,set_difference(X4,X3)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])).
fof(c_0_51, lemma, (![X4]:![X5]:![X6]:((~subset(X4,X5)|~subset(X5,X6))|subset(X4,X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])).
fof(c_0_52, lemma, (![X3]:![X4]:set_difference(X3,set_difference(X3,X4))=set_intersection2(X3,X4)), inference(variable_rename,[status(thm)],[c_0_30])).
fof(c_0_53, lemma, (![X3]:![X4]:set_difference(set_union2(X3,X4),X4)=set_difference(X3,X4)), inference(variable_rename,[status(thm)],[c_0_31])).
fof(c_0_54, lemma, (![X3]:![X4]:set_union2(X3,set_difference(X4,X3))=set_union2(X3,X4)), inference(variable_rename,[status(thm)],[c_0_32])).
fof(c_0_55, lemma, (![X3]:![X4]:(~subset(X3,X4)|~proper_subset(X4,X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])).
fof(c_0_56, lemma, (![X3]:![X4]:subset(X3,set_union2(X3,X4))), inference(variable_rename,[status(thm)],[c_0_34])).
fof(c_0_57, lemma, (![X3]:![X4]:subset(set_difference(X3,X4),X3)), inference(variable_rename,[status(thm)],[c_0_35])).
fof(c_0_58, lemma, (![X3]:![X4]:subset(set_intersection2(X3,X4),X3)), inference(variable_rename,[status(thm)],[c_0_36])).
fof(c_0_59, lemma, (![X3]:![X4]:(~subset(X3,X4)|set_intersection2(X3,X4)=X3)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])).
fof(c_0_60, lemma, (![X3]:![X4]:(~subset(X3,X4)|set_union2(X3,X4)=X4)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])).
fof(c_0_61, lemma, (![X3]:![X4]:![X5]:![X6]:((set_difference(X3,X4)!=empty_set|subset(X3,X4))&(~subset(X5,X6)|set_difference(X5,X6)=empty_set))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])])).
fof(c_0_62, lemma, (![X3]:![X4]:![X5]:![X6]:((set_difference(X3,X4)!=empty_set|subset(X3,X4))&(~subset(X5,X6)|set_difference(X5,X6)=empty_set))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])).
fof(c_0_63, lemma, (![X2]:(~subset(X2,empty_set)|X2=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])).
fof(c_0_64, negated_conjecture, (((subset(esk3_0,esk4_0)&disjoint(esk4_0,esk5_0))&~disjoint(esk3_0,esk5_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])).
fof(c_0_65, lemma, (![X2]:subset(empty_set,X2)), inference(variable_rename,[status(thm)],[c_0_43])).
cnf(c_0_66,lemma,(subset(set_difference(X1,X2),set_difference(X3,X2))|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_44])).
cnf(c_0_67,lemma,(subset(set_intersection2(X1,X2),set_intersection2(X3,X2))|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_68,lemma,(~disjoint(X1,X2)|~in(X3,set_intersection2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_69,lemma,(subset(set_union2(X1,X2),X3)|~subset(X2,X3)|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_70,lemma,(subset(X1,set_intersection2(X2,X3))|~subset(X1,X3)|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48])).
cnf(c_0_71,lemma,(in(esk2_2(X1,X2),set_intersection2(X1,X2))|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_72,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_49])).
cnf(c_0_73,lemma,(X1=set_union2(X2,set_difference(X1,X2))|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_74,lemma,(subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_51])).
cnf(c_0_75,lemma,(disjoint(X1,X2)|in(esk1_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_49])).
cnf(c_0_76,lemma,(disjoint(X1,X2)|in(esk1_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_49])).
cnf(c_0_77,lemma,(set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_52])).
cnf(c_0_78,lemma,(set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_53])).
cnf(c_0_79,lemma,(set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_54])).
cnf(c_0_80,lemma,(~proper_subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_55])).
cnf(c_0_81,lemma,(subset(X1,set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_56])).
cnf(c_0_82,lemma,(subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_57])).
cnf(c_0_83,lemma,(subset(set_intersection2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_58])).
cnf(c_0_84,lemma,(set_intersection2(X1,X2)=X1|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_59])).
cnf(c_0_85,lemma,(set_union2(X1,X2)=X2|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_60])).
cnf(c_0_86,lemma,(subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_61])).
cnf(c_0_87,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_61])).
cnf(c_0_88,lemma,(subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_62])).
cnf(c_0_89,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_62])).
cnf(c_0_90,lemma,(X1=empty_set|~subset(X1,empty_set)), inference(split_conjunct,[status(thm)],[c_0_63])).
cnf(c_0_91,negated_conjecture,(~disjoint(esk3_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
cnf(c_0_92,lemma,(subset(empty_set,X1)), inference(split_conjunct,[status(thm)],[c_0_65])).
cnf(c_0_93,negated_conjecture,(subset(esk3_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
cnf(c_0_94,negated_conjecture,(disjoint(esk4_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
cnf(c_0_95,lemma,(subset(set_difference(X1,X2),set_difference(X3,X2))|~subset(X1,X3)), c_0_66, ['final']).
cnf(c_0_96,lemma,(subset(set_intersection2(X1,X2),set_intersection2(X3,X2))|~subset(X1,X3)), c_0_67, ['final']).
cnf(c_0_97,lemma,(~disjoint(X1,X2)|~in(X3,set_intersection2(X1,X2))), c_0_68, ['final']).
cnf(c_0_98,lemma,(subset(set_union2(X1,X2),X3)|~subset(X2,X3)|~subset(X1,X3)), c_0_69, ['final']).
cnf(c_0_99,lemma,(subset(X1,set_intersection2(X2,X3))|~subset(X1,X3)|~subset(X1,X2)), c_0_70, ['final']).
cnf(c_0_100,lemma,(in(esk2_2(X1,X2),set_intersection2(X1,X2))|disjoint(X1,X2)), c_0_71, ['final']).
cnf(c_0_101,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_72, ['final']).
cnf(c_0_102,lemma,(set_union2(X2,set_difference(X1,X2))=X1|~subset(X2,X1)), c_0_73, ['final']).
cnf(c_0_103,lemma,(subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3)), c_0_74, ['final']).
cnf(c_0_104,lemma,(disjoint(X1,X2)|in(esk1_2(X1,X2),X1)), c_0_75, ['final']).
cnf(c_0_105,lemma,(disjoint(X1,X2)|in(esk1_2(X1,X2),X2)), c_0_76, ['final']).
cnf(c_0_106,lemma,(set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), c_0_77, ['final']).
cnf(c_0_107,lemma,(set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), c_0_78, ['final']).
cnf(c_0_108,lemma,(set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), c_0_79, ['final']).
cnf(c_0_109,lemma,(~proper_subset(X1,X2)|~subset(X2,X1)), c_0_80, ['final']).
cnf(c_0_110,lemma,(subset(X1,set_union2(X1,X2))), c_0_81, ['final']).
cnf(c_0_111,lemma,(subset(set_difference(X1,X2),X1)), c_0_82, ['final']).
cnf(c_0_112,lemma,(subset(set_intersection2(X1,X2),X1)), c_0_83, ['final']).
cnf(c_0_113,lemma,(set_intersection2(X1,X2)=X1|~subset(X1,X2)), c_0_84, ['final']).
cnf(c_0_114,lemma,(set_union2(X1,X2)=X2|~subset(X1,X2)), c_0_85, ['final']).
cnf(c_0_115,lemma,(subset(X1,X2)|set_difference(X1,X2)!=empty_set), c_0_86, ['final']).
cnf(c_0_116,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), c_0_87, ['final']).
cnf(c_0_117,lemma,(subset(X1,X2)|set_difference(X1,X2)!=empty_set), c_0_88, ['final']).
cnf(c_0_118,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), c_0_89, ['final']).
cnf(c_0_119,lemma,(X1=empty_set|~subset(X1,empty_set)), c_0_90, ['final']).
cnf(c_0_120,negated_conjecture,(~disjoint(esk3_0,esk5_0)), c_0_91, ['final']).
cnf(c_0_121,lemma,(subset(empty_set,X1)), c_0_92, ['final']).
cnf(c_0_122,negated_conjecture,(subset(esk3_0,esk4_0)), c_0_93, ['final']).
cnf(c_0_123,negated_conjecture,(disjoint(esk4_0,esk5_0)), c_0_94, ['final']).
# End CNF derivation

%-------------------------------------------------------------
% Dedukti proof by iprover
#NAME iprover_sig.
builtin_eq : (FOL.i -> (FOL.i -> Type)).
True : Type.
disjoint : (FOL.i -> (FOL.i -> Type)).
empty : (FOL.i -> Type).
empty_set : FOL.i.
in : (FOL.i -> (FOL.i -> Type)).
proper_subset : (FOL.i -> (FOL.i -> Type)).
set_difference : (FOL.i -> (FOL.i -> FOL.i)).
set_intersection2 : (FOL.i -> (FOL.i -> FOL.i)).
set_union2 : (FOL.i -> (FOL.i -> FOL.i)).
sk1_esk1_1 : (FOL.i -> FOL.i).
sk1_esk2_3 : (FOL.i -> (FOL.i -> (FOL.i -> FOL.i))).
sk1_esk3_2 : (FOL.i -> (FOL.i -> FOL.i)).
sk1_esk4_3 : (FOL.i -> (FOL.i -> (FOL.i -> FOL.i))).
sk1_esk5_3 : (FOL.i -> (FOL.i -> (FOL.i -> FOL.i))).
sk1_esk6_2 : (FOL.i -> (FOL.i -> FOL.i)).
sk2_esk1_0 : FOL.i.
sk2_esk2_0 : FOL.i.
sk3_esk1_2 : (FOL.i -> (FOL.i -> FOL.i)).
sk3_esk2_2 : (FOL.i -> (FOL.i -> FOL.i)).
sk3_esk3_0 : FOL.i.
sk3_esk4_0 : FOL.i.
sk3_esk5_0 : FOL.i.
subset :
(FOL.i -> (FOL.i -> Type)).
[X0 : FOL.i] set_intersection2 X0 X0 -->  X0
[X0 : FOL.i] set_intersection2 X0 empty_set -->  empty_set.
[X0 : FOL.i] set_union2 X0 X0 -->  X0
[X0 : FOL.i] set_union2 X0 empty_set -->  X0.
[X0 : FOL.i] set_difference X0 empty_set -->  X0
[X0 : FOL.i] set_difference empty_set X0 -->
empty_set.
#NAME iprover_prf.
clause2 :
(((iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 ->
FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_).
clause5 :
((iprover_sig.disjoint iprover_sig.sk3_esk4_0 iprover_sig.sk3_esk5_0 ->
FOL.proof FOL.bot_) -> FOL.proof FOL.bot_).
clause6 :
(X0 : FOL.i ->
(X1 : FOL.i ->
(((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_)
->
((iprover_sig.disjoint X1 X0 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_)))).
{clause4} :
((iprover_sig.disjoint iprover_sig.sk3_esk5_0 iprover_sig.sk3_esk4_0 ->
FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) :=
(lit1 :
(iprover_sig.disjoint iprover_sig.sk3_esk5_0 iprover_sig.sk3_esk4_0 ->
FOL.proof FOL.bot_) => clause5
(tp : iprover_sig.disjoint iprover_sig.sk3_esk4_0 iprover_sig.sk3_esk5_0 =>
clause6 iprover_sig.sk3_esk4_0 iprover_sig.sk3_esk5_0
(tn :
(iprover_sig.disjoint iprover_sig.sk3_esk4_0 iprover_sig.sk3_esk5_0 ->
FOL.proof FOL.bot_) => tn tp) lit1)).
clause9 :
(X0 : FOL.i ->
(X1 : FOL.i ->
((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) ->
((iprover_sig.in (iprover_sig.sk3_esk1_2 X0 X1) X0 -> FOL.proof FOL.bot_)
-> FOL.proof FOL.bot_)))).
clause11 :
((iprover_sig.subset iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk4_0 ->
FOL.proof FOL.bot_) -> FOL.proof FOL.bot_).
clause12 :
(X1 : FOL.i ->
(X2 : FOL.i ->
(X0 : FOL.i ->
(((iprover_sig.subset X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_)
->
((iprover_sig.in X2 X1 -> FOL.proof FOL.bot_) ->
(((iprover_sig.in X2 X0 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) ->
FOL.proof FOL.bot_)))))).
{clause10} :
(X0 : FOL.i ->
(((iprover_sig.in X0 iprover_sig.sk3_esk3_0 -> FOL.proof FOL.bot_) ->
FOL.proof FOL.bot_) ->
((iprover_sig.in X0 iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) ->
FOL.proof FOL.bot_))) :=
(X0 : FOL.i =>
(lit3 :
((iprover_sig.in X0 iprover_sig.sk3_esk3_0 -> FOL.proof FOL.bot_) ->
FOL.proof FOL.bot_) =>
(lit2 : (iprover_sig.in X0 iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) =>
clause11
(tp : iprover_sig.subset iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk4_0 =>
clause12 iprover_sig.sk3_esk4_0 X0 iprover_sig.sk3_esk3_0
(tn :
(iprover_sig.subset iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk4_0 ->
FOL.proof FOL.bot_) => tn tp) lit2 lit3)))).
{clause8} :
(X0 : FOL.i ->
((iprover_sig.disjoint iprover_sig.sk3_esk3_0 X0 -> FOL.proof FOL.bot_) ->
((iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_))) :=
(X0 : FOL.i =>
(lit5 :
(iprover_sig.disjoint iprover_sig.sk3_esk3_0 X0 -> FOL.proof FOL.bot_) =>
(lit4 :
(iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) => clause9
iprover_sig.sk3_esk3_0 X0 lit5
(tp : iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
iprover_sig.sk3_esk3_0 => clause10
(iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
(tn :
(iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
iprover_sig.sk3_esk3_0 -> FOL.proof FOL.bot_) => tn tp) lit4)))).
clause14 :
(X1 : FOL.i ->
(X0 : FOL.i ->
((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) ->
((iprover_sig.in (iprover_sig.sk3_esk1_2 X0 X1) X1 -> FOL.proof FOL.bot_)
-> FOL.proof FOL.bot_)))).
clause15 :
(X1 : FOL.i ->
(X2 : FOL.i ->
(X0 : FOL.i ->
(((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof
FOL.bot_) ->
(((iprover_sig.in X2 X1 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) ->
(((iprover_sig.in X2 X0 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) ->
FOL.proof FOL.bot_)))))).
{clause13} :
(X1 : FOL.i ->
(X0 : FOL.i ->
(X2 : FOL.i ->
(((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof
FOL.bot_) ->
(((iprover_sig.in (iprover_sig.sk3_esk1_2 X2 X0) X1 -> FOL.proof
FOL.bot_) -> FOL.proof FOL.bot_) ->
((iprover_sig.disjoint X2 X0 -> FOL.proof FOL.bot_) -> FOL.proof
FOL.bot_)))))) :=
(X1 : FOL.i =>
(X0 : FOL.i =>
(X2 : FOL.i =>
(lit6 :
((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof
FOL.bot_) =>
(lit7 :
((iprover_sig.in (iprover_sig.sk3_esk1_2 X2 X0) X1 -> FOL.proof
FOL.bot_) -> FOL.proof FOL.bot_) =>
(lit8 : (iprover_sig.disjoint X2 X0 -> FOL.proof FOL.bot_) => clause14
X0 X2 lit8
(tp : iprover_sig.in (iprover_sig.sk3_esk1_2 X2 X0) X0 => clause15 X1
(iprover_sig.sk3_esk1_2 X2 X0) X0 lit6 lit7
(tn :
(iprover_sig.in (iprover_sig.sk3_esk1_2 X2 X0) X0 -> FOL.proof
FOL.bot_) => tn tp)))))))).
{clause7} :
(X0 : FOL.i ->
(((iprover_sig.disjoint X0 iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) ->
FOL.proof FOL.bot_) ->
((iprover_sig.disjoint iprover_sig.sk3_esk3_0 X0 -> FOL.proof FOL.bot_) ->
FOL.proof FOL.bot_))) :=
(X0 : FOL.i =>
(lit9 :
((iprover_sig.disjoint X0 iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) ->
FOL.proof FOL.bot_) =>
(lit5 :
(iprover_sig.disjoint iprover_sig.sk3_esk3_0 X0 -> FOL.proof FOL.bot_) =>
clause8 X0 lit5
(tp : iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
iprover_sig.sk3_esk4_0 => clause13 iprover_sig.sk3_esk4_0 X0
iprover_sig.sk3_esk3_0 lit9
(tn :
(iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) => tn tp) lit5)))).
{clause3} :
((iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 ->
FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) :=
(lit10 :
(iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 ->
FOL.proof FOL.bot_) => clause4
(tp : iprover_sig.disjoint iprover_sig.sk3_esk5_0 iprover_sig.sk3_esk4_0 =>
clause7 iprover_sig.sk3_esk5_0
(tn :
(iprover_sig.disjoint iprover_sig.sk3_esk5_0 iprover_sig.sk3_esk4_0 ->
FOL.proof FOL.bot_) => tn tp) lit10)).
{clause1} : FOL.proof FOL.bot_ := clause2
(tnl1 :
(iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 ->
FOL.proof FOL.bot_) => clause3
(tl1 : iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 =>
tnl1 tl1)).
{empty_clause} : FOL.proof FOL.bot_ :=
clause1.
% SZS output end CNFRefutation


## leanCoP 2.2

Jens Otten
University of Potsdam, Germany

### Sample solution for SEU140+2

% SZS status Theorem for SEU140+2.p
% SZS output start Proof for SEU140+2.p

%-----------------------------------------------------
fof(t63_xboole_1,conjecture,! [_63308,_63311,_63314] : (subset(_63308,_63311) & disjoint(_63311,_63314) => disjoint(_63308,_63314)),file('SEU140+2.p',t63_xboole_1)).
fof(d3_tarski,axiom,! [_63543,_63546] : (subset(_63543,_63546) <=> ! [_63564] : (in(_63564,_63543) => in(_63564,_63546))),file('SEU140+2.p',d3_tarski)).
fof(t3_xboole_0,lemma,! [_63793,_63796] : (~ (~ disjoint(_63793,_63796) & ! [_63818] : ~ (in(_63818,_63793) & in(_63818,_63796))) & ~ (? [_63818] : (in(_63818,_63793) & in(_63818,_63796)) & disjoint(_63793,_63796))),file('SEU140+2.p',t3_xboole_0)).

cnf(1,plain,[-(subset(11^[],12^[]))],clausify(t63_xboole_1)).
cnf(2,plain,[-(disjoint(12^[],13^[]))],clausify(t63_xboole_1)).
cnf(3,plain,[disjoint(11^[],13^[])],clausify(t63_xboole_1)).
cnf(4,plain,[subset(_29177,_29233),in(_29347,_29177),-(in(_29347,_29233))],clausify(d3_tarski)).
cnf(5,plain,[-(disjoint(_40265,_40352)),-(in(9^[_40352,_40265],_40265))],clausify(t3_xboole_0)).
cnf(6,plain,[-(disjoint(_40265,_40352)),-(in(9^[_40352,_40265],_40352))],clausify(t3_xboole_0)).
cnf(7,plain,[disjoint(_40265,_40352),in(_40769,_40265),in(_40769,_40352)],clausify(t3_xboole_0)).

cnf('1',plain,[disjoint(12^[],13^[]),in(9^[13^[],11^[]],12^[]),in(9^[13^[],11^[]],13^[])],start(7,bind([[_40265,_40769,_40352],[12^[],9^[13^[],11^[]],13^[]]]))).
cnf('1.1',plain,[-(disjoint(12^[],13^[]))],extension(2)).
cnf('1.2',plain,[-(in(9^[13^[],11^[]],12^[])),subset(11^[],12^[]),in(9^[13^[],11^[]],11^[])],extension(4,bind([[_29233,_29347,_29177],[12^[],9^[13^[],11^[]],11^[]]]))).
cnf('1.2.1',plain,[-(subset(11^[],12^[]))],extension(1)).
cnf('1.2.2',plain,[-(in(9^[13^[],11^[]],11^[])),-(disjoint(11^[],13^[]))],extension(5,bind([[_40265,_40352],[11^[],13^[]]]))).
cnf('1.2.2.1',plain,[disjoint(11^[],13^[])],extension(3)).
cnf('1.3',plain,[-(in(9^[13^[],11^[]],13^[])),-(disjoint(11^[],13^[]))],extension(6,bind([[_40265,_40352],[11^[],13^[]]]))).
cnf('1.3.1',plain,[disjoint(11^[],13^[])],extension(3)).
%-----------------------------------------------------

% SZS output end Proof for SEU140+2.p


## LEO-II 1.6.2

Christoph Benzmüller
Freie Universität Berlin, Germany

### Sample solution for SET014^4


No.of.Axioms: 0

Length.of.Defs: 1901

Contains.Choice.Funs: false
(rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:3,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)
********************************
*   All subproblems solved!    *
********************************
% SZS status Theorem for /tmp/SystemOnTPTP42612/SET014^4.tptp : (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:3,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)

%**** Beginning of derivation protocol ****
% SZS output start CNFRefutation
thf(tp_complement,type,(complement: (($i>$o)>($i>$o)))).
thf(tp_disjoint,type,(disjoint: (($i>$o)>(($i>$o)>$o)))). thf(tp_emptyset,type,(emptyset: ($i>$o))). thf(tp_excl_union,type,(excl_union: (($i>$o)>(($i>$o)>($i>$o))))). thf(tp_in,type,(in: ($i>(($i>$o)>$o)))). thf(tp_intersection,type,(intersection: (($i>$o)>(($i>$o)>($i>$o))))). thf(tp_is_a,type,(is_a: ($i>(($i>$o)>$o)))). thf(tp_meets,type,(meets: (($i>$o)>(($i>$o)>$o)))).
thf(tp_misses,type,(misses: (($i>$o)>(($i>$o)>$o)))). thf(tp_sK1_X,type,(sK1_X: ($i>$o))). thf(tp_sK2_SY0,type,(sK2_SY0: ($i>$o))). thf(tp_sK3_SY2,type,(sK3_SY2: ($i>$o))). thf(tp_sK4_SX0,type,(sK4_SX0:$i)).
thf(tp_setminus,type,(setminus: (($i>$o)>(($i>$o)>($i>$o))))).
thf(tp_singleton,type,(singleton: ($i>($i>$o)))). thf(tp_subset,type,(subset: (($i>$o)>(($i>$o)>$o)))).
thf(tp_union,type,(union: (($i>$o)>(($i>$o)>($i>$o))))).
thf(tp_unord_pair,type,(unord_pair: ($i>($i>($i>$o))))).
thf(complement,definition,(complement = (^[X:($i>$o),U:$i]: (~ (X@U)))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',complement)). thf(disjoint,definition,(disjoint = (^[X:($i>$o),Y:($i>$o)]: (((intersection@X)@Y) = emptyset))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',disjoint)). thf(emptyset,definition,(emptyset = (^[X:$i]: $false)),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',emptyset)). thf(excl_union,definition,(excl_union = (^[X:($i>$o),Y:($i>$o),U:$i]: (((X@U) & (~ (Y@U))) | ((~ (X@U)) & (Y@U))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',excl_union)).
thf(in,definition,(in = (^[X:$i,M:($i>$o)]: (M@X))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',in)). thf(intersection,definition,(intersection = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) & (Y@U)))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',intersection)).
thf(is_a,definition,(is_a = (^[X:$i,M:($i>$o)]: (M@X))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',is_a)). thf(meets,definition,(meets = (^[X:($i>$o),Y:($i>$o)]: (?[U:$i]: ((X@U) & (Y@U))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',meets)).
thf(misses,definition,(misses = (^[X:($i>$o),Y:($i>$o)]: (~ (?[U:$i]: ((X@U) & (Y@U)))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',misses)). thf(setminus,definition,(setminus = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) & (~ (Y@U))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',setminus)).
thf(singleton,definition,(singleton = (^[X:$i,U:$i]: (U = X))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',singleton)).
thf(subset,definition,(subset = (^[X:($i>$o),Y:($i>$o)]: (![U:$i]: ((X@U) => (Y@U))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',subset)). thf(union,definition,(union = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) | (Y@U)))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',union)).
thf(unord_pair,definition,(unord_pair = (^[X:$i,Y:$i,U:$i]: ((U = X) | (U = Y)))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',unord_pair)). thf(1,conjecture,(![X:($i>$o),Y:($i>$o),A:($i>$o)]: ((((subset@X)@A) & ((subset@Y)@A)) => ((subset@((union@X)@Y))@A))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',thm)). thf(2,negated_conjecture,(((![X:($i>$o),Y:($i>$o),A:($i>$o)]: ((((subset@X)@A) & ((subset@Y)@A)) => ((subset@((union@X)@Y))@A)))=$false)),inference(negate_conjecture,[status(cth)],[1])).
thf(3,plain,(((![SY0:($i>$o),SY1:($i>$o)]: ((((subset@sK1_X)@SY1) & ((subset@SY0)@SY1)) => ((subset@((union@sK1_X)@SY0))@SY1)))=$false)),inference(extcnf_forall_neg,[status(esa)],[2])). thf(4,plain,(((![SY2:($i>$o)]: ((((subset@sK1_X)@SY2) & ((subset@sK2_SY0)@SY2)) => ((subset@((union@sK1_X)@sK2_SY0))@SY2)))=$false)),inference(extcnf_forall_neg,[status(esa)],[3])).
thf(5,plain,((((((subset@sK1_X)@sK3_SY2) & ((subset@sK2_SY0)@sK3_SY2)) => ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=$false)),inference(extcnf_forall_neg,[status(esa)],[4])). thf(6,plain,((((subset@sK1_X)@sK3_SY2)=$true)),inference(standard_cnf,[status(thm)],[5])).
thf(7,plain,((((subset@sK2_SY0)@sK3_SY2)=$true)),inference(standard_cnf,[status(thm)],[5])). thf(8,plain,((((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2)=$false)),inference(standard_cnf,[status(thm)],[5])).
thf(9,plain,(((~ ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=$true)),inference(polarity_switch,[status(thm)],[8])). thf(10,plain,((((subset@sK2_SY0)@sK3_SY2)=$true)),inference(copy,[status(thm)],[7])).
thf(11,plain,((((subset@sK1_X)@sK3_SY2)=$true)),inference(copy,[status(thm)],[6])). thf(12,plain,(((~ ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=$true)),inference(copy,[status(thm)],[9])).
thf(13,plain,(((~ (![SX0:$i]: ((~ ((sK1_X@SX0) | (sK2_SY0@SX0))) | (sK3_SY2@SX0))))=$true)),inference(unfold_def,[status(thm)],[12,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
thf(14,plain,(((![SX0:$i]: ((~ (sK1_X@SX0)) | (sK3_SY2@SX0)))=$true)),inference(unfold_def,[status(thm)],[11,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
thf(15,plain,(((![SX0:$i]: ((~ (sK2_SY0@SX0)) | (sK3_SY2@SX0)))=$true)),inference(unfold_def,[status(thm)],[10,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
thf(16,plain,(((![SX0:$i]: ((~ ((sK1_X@SX0) | (sK2_SY0@SX0))) | (sK3_SY2@SX0)))=$false)),inference(extcnf_not_pos,[status(thm)],[13])).
thf(17,plain,(![SV1:$i]: ((((~ (sK1_X@SV1)) | (sK3_SY2@SV1))=$true))),inference(extcnf_forall_pos,[status(thm)],[14])).
thf(18,plain,(![SV2:$i]: ((((~ (sK2_SY0@SV2)) | (sK3_SY2@SV2))=$true))),inference(extcnf_forall_pos,[status(thm)],[15])).
thf(19,plain,((((~ ((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0))) | (sK3_SY2@sK4_SX0))=$false)),inference(extcnf_forall_neg,[status(esa)],[16])). thf(20,plain,(![SV1:$i]: (((~ (sK1_X@SV1))=$true) | ((sK3_SY2@SV1)=$true))),inference(extcnf_or_pos,[status(thm)],[17])).
thf(21,plain,(![SV2:$i]: (((~ (sK2_SY0@SV2))=$true) | ((sK3_SY2@SV2)=$true))),inference(extcnf_or_pos,[status(thm)],[18])). thf(22,plain,(((~ ((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0)))=$false)),inference(extcnf_or_neg,[status(thm)],[19])).
thf(23,plain,(((sK3_SY2@sK4_SX0)=$false)),inference(extcnf_or_neg,[status(thm)],[19])). thf(24,plain,(![SV1:$i]: (((sK1_X@SV1)=$false) | ((sK3_SY2@SV1)=$true))),inference(extcnf_not_pos,[status(thm)],[20])).
thf(25,plain,(![SV2:$i]: (((sK2_SY0@SV2)=$false) | ((sK3_SY2@SV2)=$true))),inference(extcnf_not_pos,[status(thm)],[21])). thf(26,plain,((((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0))=$true)),inference(extcnf_not_neg,[status(thm)],[22])).
thf(27,plain,(((sK1_X@sK4_SX0)=$true) | ((sK2_SY0@sK4_SX0)=$true)),inference(extcnf_or_pos,[status(thm)],[26])).
thf(28,plain,((($false)=$true)),inference(fo_atp_e,[status(thm)],[23,27,25,24])).
thf(29,plain,($false),inference(solved_all_splits,[solved_all_splits(join,[])],[28])). % SZS output end CNFRefutation %**** End of derivation protocol **** %**** no. of clauses in derivation: 29 **** %**** clause counter: 28 **** % SZS status Theorem for /tmp/SystemOnTPTP42612/SET014^4.tptp : (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:3,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)  ## MaLARea 0.5 Josef Urban Radboud University Nijmegen, The Netherlands ### Sample solution for SEU140+2 # SZS status Theorem # SZS output start CNFRefutation. fof(c_0_0, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), file('/Users/schulz/EPROVER/TPTP_5.4.0_FLAT/SEU140+2.p', symmetry_r1_xboole_0)). fof(c_0_1, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), file('/Users/schulz/EPROVER/TPTP_5.4.0_FLAT/SEU140+2.p', t3_xboole_0)). fof(c_0_2, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('/Users/schulz/EPROVER/TPTP_5.4.0_FLAT/SEU140+2.p', t63_xboole_1)). fof(c_0_3, axiom, (![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2)))), file('/Users/schulz/EPROVER/TPTP_5.4.0_FLAT/SEU140+2.p', d3_tarski)). fof(c_0_4, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), c_0_0). fof(c_0_5, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_1])). fof(c_0_6, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[c_0_2])). fof(c_0_7, plain, (![X3]:![X4]:(~disjoint(X3,X4)|disjoint(X4,X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])). fof(c_0_8, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X9,X7)|~in(X9,X8))|~disjoint(X7,X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])])). fof(c_0_9, negated_conjecture, (((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])). cnf(c_0_10,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), inference(split_conjunct,[status((null))],[c_0_7])). cnf(c_0_11,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), inference(split_conjunct,[status((null))],[c_0_8])). fof(c_0_12, axiom, (![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2)))), c_0_3). cnf(c_0_13,lemma,(~in(X3,X2)|~in(X3,X1)|~disjoint(X1,X2)), inference(split_conjunct,[status((null))],[c_0_8])). cnf(c_0_14,negated_conjecture,(disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status((null))],[c_0_9])). cnf(c_0_15,negated_conjecture,(~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status((null))],[c_0_9])). cnf(c_0_16,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_10). cnf(c_0_17,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_11). fof(c_0_18, plain, (![X4]:![X5]:![X6]:![X7]:![X8]:((~subset(X4,X5)|(~in(X6,X4)|in(X6,X5)))&((in(esk3_2(X7,X8),X7)|subset(X7,X8))&(~in(esk3_2(X7,X8),X8)|subset(X7,X8))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])])])). cnf(c_0_19,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), inference(split_conjunct,[status((null))],[c_0_8])). cnf(c_0_20,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_13). cnf(c_0_21,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_14). cnf(c_0_22,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_15). cnf(c_0_23,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_16). cnf(c_0_24,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_17). cnf(c_0_25,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)), inference(split_conjunct,[status((null))],[c_0_18])). cnf(c_0_26,negated_conjecture,(subset(esk11_0,esk12_0)), inference(split_conjunct,[status((null))],[c_0_9])). cnf(c_0_27,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_19). cnf(c_0_28,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_20). cnf(c_0_29,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_21). cnf(c_0_30,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_22). cnf(c_0_31,lemma,(disjoint(X1,X2)|in(esk9_2(X2,X1),X2)), inference(spm,[status(thm)],[c_0_23, c_0_24, theory(equality)]])). cnf(c_0_32,plain,(in(X1,X2)|~subset(X3,X2)|~in(X1,X3)), c_0_25). cnf(c_0_33,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_26). cnf(c_0_34,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_27). cnf(c_0_35,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)), inference(spm,[status(thm)],[c_0_28, c_0_29, theory(equality)]])). cnf(c_0_36,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk13_0)), inference(spm,[status(thm)],[c_0_30, c_0_31, theory(equality)]])). cnf(c_0_37,plain,(in(X1,X2)|~subset(X3,X2)|~in(X1,X3)), c_0_32). cnf(c_0_38,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_33). cnf(c_0_39,lemma,(disjoint(X1,X2)|in(esk9_2(X2,X1),X1)), inference(spm,[status(thm)],[c_0_23, c_0_34, theory(equality)]])). cnf(c_0_40,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk12_0)), inference(spm,[status(thm)],[c_0_35, c_0_36, theory(equality)]])). cnf(c_0_41,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)), inference(spm,[status(thm)],[c_0_37, c_0_38, theory(equality)]])). cnf(c_0_42,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk11_0)), inference(spm,[status(thm)],[c_0_30, c_0_39, theory(equality)]])). cnf(c_0_43,negated_conjecture,($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41, theory(equality)]]), c_0_42, theory(equality)]]), theory(equality,[symmetry])]]), ['proof']).
# SZS output end CNFRefutation.


Dominique Pastre
University Paris Descartes, France

### Sample solution for SEU140+2

SZS status Theorem for SEU140+2.p

SZS output start Proof for SEU140+2.p

* * * * * * * * * * * * * * * * * * * * * * * *
in the following, N is the number of a (sub)theorem
E is the current step
or the step when a hypothesis or conclusion has been added or modified
hyp(N,H,E) means that H is an hypothesis of (sub)theorem N
concl(N,C,E) means that C is the conclusion of (sub)theorem N
obj_ct(N,C) means that C is a created object or a given constant
newconcl(N,C,E) means that the new conclusion of N is C
(C replaces the precedent conclusion)
a subtheorem N-i or N+i is a subtheorem of the (sub)theorem N
N is proved if all N-i have been proved (&-node)
or if one N+i have been proved (|-node)
the initial theorem is numbered 0

* * * theorem to be proved
![A,B,C]: (subset(A,B)&disjoint(B,C)=>disjoint(A,C))

* * * proof :

* * * * * * theoreme 0 * * * * * *
*** newconcl(0,![A,B,C]: (subset(A,B)&disjoint(B,C)=>disjoint(A,C)),1)
*** explanation : initial theorem
------------------------------------------------------- action ini
create object(s) z3 z2 z1
*** newconcl(0,subset(z1,z2)&disjoint(z2,z3)=>disjoint(z1,z3),2)
*** because concl((0,![A,B,C]: (subset(A,B)&disjoint(B,C)=>disjoint(A,C))),1)
*** explanation : the universal variable(s) of the conclusion is(are) instantiated
------------------------------------------------------- rule !
*** newconcl(0,disjoint(z1,z3),3)
*** because concl(0,subset(z1,z2)&disjoint(z2,z3)=>disjoint(z1,z3),2)
*** explanation : to prove H=>C, assume H and prove C
------------------------------------------------------- rule =>
*** because hyp(0,disjoint(z2,z3),3)
*** explanation : rule if hyp(A,disjoint(B,C),_)then addhyp(A,set_intersection2(B,C)::empty_set,_)
built from the definition of disjoint (fof axiom:d7_xboole_0 )
------------------------------------------------------- rule disjoint
*** because hyp(0,subset(z1,z2),3),obj_ct(0,z1),obj_ct(0,z2)
*** explanation : rule if (hyp(A,subset(B,C),_),obj_ct(A,B),obj_ct(A,C))then addhyp(A,set_difference(B,C)::empty_set,_)
built from the axiom lemma:l32_xboole_1
------------------------------------------------------- rule lemma:l32_xboole_1_1
*** newconcl(0,set_intersection2(z1,z3)::empty_set,109)
*** because concl(0,disjoint(z1,z3),3)
*** explanation : the conclusion  disjoint(z1,z3) is replaced by its definition(fof axiom:d7_xboole_0 )
------------------------------------------------------- rule def_concl_pred
*** newconcl(0,seul(set_intersection2(z1,z3)::A,A=empty_set),110)
*** because concl(0,set_intersection2(z1,z3)::empty_set,109)
*** explanation :  FX::Y is rewriten only(FX::Z, Z=Y)
------------------------------------------------------- rule concl2pts
*** because concl(0,seul(set_intersection2(z1,z3)::A,A=empty_set),110)
*** explanation : creation of object z4 and of its definition
------------------------------------------------------- rule concl_only
*** because hyp(0,set_intersection2(z1,z3)::z4,111),obj_ct(0,z1),obj_ct(0,z3)
*** explanation : rule if (hyp(A,set_intersection2(B,C)::D,_),obj_ct(A,B),obj_ct(A,C))then addhyp(A,set_intersection2(C,B)::D,_)
built from the axiom axiom:commutativity_k3_xboole_0
------------------------------------------------------- rule axiom:commutativity_k3_xboole_0_1
*** newconcl(0,![A]: ~in(A,z4),114)
*** because concl(0,z4=empty_set,111)
*** explanation : sufficient condition (rule :  axiom:d1_xboole_0_1 (fof axiom:d1_xboole_0 )
------------------------------------------------------- rule axiom:d1_xboole_0_1_cs
create object(s) z5
*** newconcl(0,~in(z5,z4),115)
*** because concl((0,![A]: ~in(A,z4)),114)
*** explanation : the universal variable(s) of the conclusion is(are) instantiated
------------------------------------------------------- rule !
*** because concl(0,~in(z5,z4),115)
*** explanation : assume in(z5,z4) and search for a contradiction
------------------------------------------------------- rule concl_not
*** because hyp(0,set_intersection2(z1,z3)::z4,111),hyp(0,in(z5,z4),116),obj_ct(0,z5)
*** explanation : rule if (hyp(A,set_intersection2(D,_)::B,_),hyp(A,in(C,B),_),obj_ct(A,C))then addhyp(A,in(C,D),_)
built from the definition of set_intersection2 (fof axiom:d3_xboole_0 )
------------------------------------------------------- rule set_intersection2_
*** because hyp(0,subset(z1,z2),3),hyp(0,in(z5,z1),118),obj_ct(0,z5)
*** explanation : rule if (hyp(A,subset(B,D),_),hyp(A,in(C,B),_),obj_ct(A,C))then addhyp(A,in(C,D),_)
built from the definition of subset (fof axiom:d3_tarski )
------------------------------------------------------- rule subset
*** because hyp(0,set_intersection2(z3,z1)::z4,113),hyp(0,in(z5,z4),116),obj_ct(0,z5)
*** explanation : rule if (hyp(A,set_intersection2(D,_)::B,_),hyp(A,in(C,B),_),obj_ct(A,C))then addhyp(A,in(C,D),_)
built from the definition of set_intersection2 (fof axiom:d3_xboole_0 )
------------------------------------------------------- rule set_intersection2_
*** because hyp(0,set_intersection2(z2,z3)::empty_set,4),hyp(0,in(z5,z2),119),hyp(0,in(z5,z3),120),obj_ct(0,z5)
*** explanation : rule if (hyp(A,set_intersection2(B,D)::E,_),hyp(A,in(C,B),_),hyp(A,in(C,D),_),obj_ct(A,C))then addhyp(A,in(C,E),_)
built from the definition of set_intersection2 (fof axiom:d3_xboole_0 )
------------------------------------------------------- rule set_intersection2_2
*** because hyp(0,set_difference(z1,z2)::empty_set,21),hyp(0,in(z5,empty_set),121),hyp(0,in(z5,z2),119),obj_ct(0,z5)
*** explanation : rule if (hyp(A,set_difference(_,D)::B,_),hyp(A,in(C,B),_),hyp(A,in(C,D),_),obj_ct(A,C))then addhyp(A,false,_)
built from the definition of set_difference (fof axiom:d4_xboole_0 )
------------------------------------------------------- rule set_difference1
*** newconcl(0,true,124)
*** because hyp(0,false,123),concl(0,false,116)
*** explanation : the conclusion false to be proved is a hypothesis
------------------------------------------------------- rule stop_hyp_concl
then the initial theorem is proved
* * * * * * * * * * * * * * * * * * * * * * * *

SZS output end Proof for SEU140+2.p


## Prover9 2009-11A

William McCune, Bob Veroff
University of New Mexico, USA

### Sample solution for SEU140+2

8 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
26 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
42 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -((exists C (in(C,A) & in(C,B))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
55 -(all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(negated_conjecture) # label(non_clause).  [assumption].
60 subset(c3,c4) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
61 disjoint(c4,c5) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
75 disjoint(A,B) | in(f7(A,B),A) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
76 disjoint(A,B) | in(f7(A,B),B) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
92 -disjoint(c3,c5) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
101 -in(A,B) | -in(A,C) | -disjoint(B,C) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
109 -disjoint(A,B) | disjoint(B,A) # label(symmetry_r1_xboole_0) # label(axiom).  [clausify(26)].
123 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom).  [clausify(8)].
273 -disjoint(c5,c3).  [ur(109,b,92,a)].
300 -in(A,c3) | in(A,c4).  [resolve(123,a,60,a)].
959 in(f7(c5,c3),c3).  [resolve(273,a,76,a)].
960 in(f7(c5,c3),c5).  [resolve(273,a,75,a)].
1084 -in(f7(c5,c3),c4).  [ur(101,b,960,a,c,61,a)].
1292 $F. [resolve(300,a,959,a),unit_del(a,1084)].  ## SPASS+T 2.2.22 Uwe Waldmann Max-Planck-Institut für Informatik, Germany ### Sample solution for DAT013=1 SPASS V 2.2.22 in combination with yices. SPASS beiseite: Proof found by SPASS. Problem: DAT013=1+tff2fof.dfgt SPASS derived 36 clauses, backtracked 5 clauses and kept 67 clauses. SPASS backtracked 2 times (0 times due to theory inconsistency). SPASS allocated 6259 KBytes. SPASS spent 0:00:00.01 on the problem. 0:00:00.00 for the input. 0:00:00.00 for the FLOTTER CNF translation. 0:00:00.00 for inferences. 0:00:00.00 for the backtracking. 0:00:00.00 for the reduction. 0:00:00.00 for interacting with the SMT procedure. % SZS output start CNFRefutation for DAT013=1+tff2fof.dfgt % Here is a proof with depth 3, length 19 : 4[0:Inp] || -> lesseq(skc8,skc6)*. 5[0:Inp] || -> lesseq(plus(skc7,3),skc8)*. 6[0:Inp] || greater(read(skc5,skc8),0)* -> . 9[0:Inp] || lesseq(U,skc6) lesseq(skc7,U) -> greater(read(skc5,U),0)*. 18[0:ThA] || -> equal(plus(U,0),U)**. 25[0:ThA] || -> lesseq(U,V) less(plus(W,V),plus(W,U))*. 42[0:ArS:6.0] || less(0,read(skc5,skc8))* -> . 43[0:TOC:42.0] || -> lesseq(read(skc5,skc8),0)*. 44[0:ArS:9.2] || lesseq(U,skc6) lesseq(skc7,U) -> less(0,read(skc5,U))*. 45[0:TOC:44.1] || -> less(U,skc7) less(skc6,U) less(0,read(skc5,U))*. 49[0:OCh:5.0,25.1] || -> lesseq(3,U) less(plus(skc7,U),skc8)*. 51[0:SpR:18.0,49.1] || -> lesseq(3,0) less(skc7,skc8)*. 57[0:ArS:51.0] || -> less(skc7,skc8)*. 77(e)[0:OCE:45.2,43.0] || -> less(skc8,skc7)* less(skc6,skc8). 80[1:Spt:77.0] || -> less(skc8,skc7)*. 81(e)[1:OCE:80.0,57.0] || -> . 84[1:Spt:81.0,77.0,80.0] || less(skc8,skc7)* -> . 85[1:Spt:81.0,77.1] || -> less(skc6,skc8)*. 89(e)[1:OCE:85.0,4.0] || -> . % SZS output end CNFRefutation for DAT013=1+tff2fof.dfgt Formulae used in the proof : fof_co1 fof_ax1  ## Vampire 2.6 Krystof Hoder, Andrei Voronkov University of Manchester, England ### Sample solution for SEU140+2 % SZS output start Proof for SEU140+2 fof(f1738,plain,($false),
inference(subsumption_resolution,[],[f1737,f136])).
fof(f136,plain,(
~disjoint(sK0,sK2)),
inference(cnf_transformation,[],[f104])).
fof(f104,plain,(
subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)),
inference(skolemisation,[status(esa)],[f76])).
fof(f76,plain,(
? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
inference(flattening,[],[f75])).
fof(f75,plain,(
? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
file('Problems/SEU/SEU140+2.p',t63_xboole_1)).
fof(f1737,plain,(
disjoint(sK0,sK2)),
inference(duplicate_literal_removal,[],[f1736])).
fof(f1736,plain,(
disjoint(sK0,sK2) | disjoint(sK0,sK2)),
inference(resolution,[],[f1707,f378])).
fof(f378,plain,(
( ! [X1] : (~in(sK4(sK2,X1),sK1) | disjoint(X1,sK2)) )),
inference(resolution,[],[f372,f148])).
fof(f148,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f106])).
fof(f106,plain,(
! [X0,X1] : ((disjoint(X0,X1) | (in(sK4(X1,X0),X0) & in(sK4(X1,X0),X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
inference(skolemisation,[status(esa)],[f79])).
fof(f79,plain,(
! [X0,X1] : ((disjoint(X0,X1) | ? [X3] : (in(X3,X0) & in(X3,X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
inference(ennf_transformation,[],[f61])).
fof(f61,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
inference(flattening,[],[f60])).
fof(f60,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f43,axiom,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
file('Problems/SEU/SEU140+2.p',t3_xboole_0)).
fof(f372,plain,(
( ! [X0] : (~in(X0,sK2) | ~in(X0,sK1)) )),
inference(resolution,[],[f149,f135])).
fof(f135,plain,(
disjoint(sK1,sK2)),
inference(cnf_transformation,[],[f104])).
fof(f149,plain,(
( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
inference(cnf_transformation,[],[f106])).
fof(f1707,plain,(
( ! [X0] : (in(sK4(X0,sK0),sK1) | disjoint(sK0,X0)) )),
inference(resolution,[],[f1706,f147])).
fof(f147,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f106])).
fof(f1706,plain,(
( ! [X78] : (~in(X78,sK0) | in(X78,sK1)) )),
inference(resolution,[],[f1661,f134])).
fof(f134,plain,(
subset(sK0,sK1)),
inference(cnf_transformation,[],[f104])).
fof(f1661,plain,(
( ! [X6,X7,X5] : (~subset(X5,X6) | in(X7,X6) | ~in(X7,X5)) )),
inference(superposition,[],[f236,f218])).
fof(f218,plain,(
( ! [X0,X1] : (set_difference(X0,set_difference(X0,X1)) = X0 | ~subset(X0,X1)) )),
inference(definition_unfolding,[],[f150,f144])).
fof(f144,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))) )),
inference(cnf_transformation,[],[f47])).
fof(f47,axiom,(
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))),
file('Problems/SEU/SEU140+2.p',t48_xboole_1)).
fof(f150,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = X0 | ~subset(X0,X1)) )),
inference(cnf_transformation,[],[f80])).
fof(f80,plain,(
! [X0,X1] : (~subset(X0,X1) | set_intersection2(X0,X1) = X0)),
inference(ennf_transformation,[],[f34])).
fof(f34,axiom,(
! [X0,X1] : (subset(X0,X1) => set_intersection2(X0,X1) = X0)),
file('Problems/SEU/SEU140+2.p',t28_xboole_1)).
fof(f236,plain,(
( ! [X4,X0,X1] : (~in(X4,set_difference(X0,set_difference(X0,X1))) | in(X4,X1)) )),
inference(equality_resolution,[],[f230])).
fof(f230,plain,(
( ! [X4,X2,X0,X1] : (in(X4,X1) | ~in(X4,X2) | set_difference(X0,set_difference(X0,X1)) != X2) )),
inference(definition_unfolding,[],[f196,f144])).
fof(f196,plain,(
( ! [X4,X2,X0,X1] : (in(X4,X1) | ~in(X4,X2) | set_intersection2(X0,X1) != X2) )),
inference(cnf_transformation,[],[f123])).
fof(f123,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X4] : ((~in(X4,X2) | (in(X4,X0) & in(X4,X1))) & (~in(X4,X0) | ~in(X4,X1) | in(X4,X2)))) & (((in(sK8(X2,X1,X0),X2) | (in(sK8(X2,X1,X0),X0) & in(sK8(X2,X1,X0),X1))) & (~in(sK8(X2,X1,X0),X2) | ~in(sK8(X2,X1,X0),X0) | ~in(sK8(X2,X1,X0),X1))) | set_intersection2(X0,X1) = X2))),
inference(skolemisation,[status(esa)],[f122])).
fof(f122,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X4] : ((~in(X4,X2) | (in(X4,X0) & in(X4,X1))) & (~in(X4,X0) | ~in(X4,X1) | in(X4,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | ~in(X3,X0) | ~in(X3,X1))) | set_intersection2(X0,X1) = X2))),
inference(rectify,[],[f121])).
fof(f121,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X0) | ~in(X3,X1) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | ~in(X3,X0) | ~in(X3,X1))) | set_intersection2(X0,X1) = X2))),
inference(flattening,[],[f120])).
fof(f120,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & ((~in(X3,X0) | ~in(X3,X1)) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | (~in(X3,X0) | ~in(X3,X1)))) | set_intersection2(X0,X1) = X2))),
inference(nnf_transformation,[],[f9])).
fof(f9,axiom,(
! [X0,X1,X2] : (set_intersection2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (in(X3,X0) & in(X3,X1))))),
file('Problems/SEU/SEU140+2.p',d3_xboole_0)).
% SZS output end Proof for SEU140+2


## ZenonArith 0.1.0

Guillaume Bury
Inria, France

### Sample solution for DAT013=1

Add LoadPath "/usr/local/lib".
Require Import zenon.
Require Import zenon_arith.
Parameter zenon_U : Set.
Parameter zenon_E : zenon_U.
Parameter array : Type.
Parameter read : ((array) -> (Z) -> (Z)).
Parameter write : ((array) -> (Z) -> (Z) -> (array)).
Axiom write_proper : Proper ( eq ==>eq ==>eq ==>eq) write.
Parameter ax1 : (forall v_U:(array),(forall v_V:(Z),(forall v_W:(Z),(((
read (write v_U (v_V)%Z (v_W)%Z) (v_V)%Z))%Z = (v_W)%Z)))).
Parameter ax2 : (forall v_X:(array),(forall v_Y:(Z),(forall v_Z:(Z),(
forall v_X1:(Z),(((v_Y)%Z = (v_Z)%Z)\/(((read (write v_X (v_Y)%Z (v_X1)
%Z) (v_Z)%Z))%Z = ((read v_X (v_Z)%Z))%Z)))))).
Theorem co1 : (forall v_U : (array), (forall v_V : (Z), (forall v_W : (Z), ((forall v_X : (Z), ((((((v_V)%Z # (1)) <= ((v_X)%Z # (1))))%Q/\((((v_X)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read v_U (v_X)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))->(forall v_Y : (Z), ((((((((v_V)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read v_U (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q)))))).
Proof.
apply NNPP. intro zenon_G.
apply (zenon_notallex_s (fun v_U : (array) => (forall v_V : (Z), (forall v_W : (Z), ((forall v_X : (Z), ((((((v_V)%Z # (1)) <= ((v_X)%Z # (1))))%Q/\((((v_X)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read v_U (v_X)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))->(forall v_Y : (Z), ((((((((v_V)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read v_U (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q)))))) zenon_G); [ zenon_intro zenon_Hd; idtac ].
elim zenon_Hd. zenon_intro zenon_Tv_U_a. zenon_intro zenon_He.
apply (zenon_notallex_s (fun v_V : (Z) => (forall v_W : (Z), ((forall v_X : (Z), ((((((v_V)%Z # (1)) <= ((v_X)%Z # (1))))%Q/\((((v_X)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_X)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))->(forall v_Y : (Z), ((((((((v_V)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))))) zenon_He); [ zenon_intro zenon_Hf; idtac ].
elim zenon_Hf. zenon_intro zenon_Tv_V_b. zenon_intro zenon_H10.
apply (zenon_notallex_s (fun v_W : (Z) => ((forall v_X : (Z), ((((((zenon_Tv_V_b)%Z # (1)) <= ((v_X)%Z # (1))))%Q/\((((v_X)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_X)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))->(forall v_Y : (Z), ((((((((zenon_Tv_V_b)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q)))) zenon_H10); [ zenon_intro zenon_H11; idtac ].
elim zenon_H11. zenon_intro zenon_Tv_W_c. zenon_intro zenon_H12.
apply (zenon_notimply_s _ _ zenon_H12). zenon_intro zenon_H4. zenon_intro zenon_H13.
apply (zenon_notallex_s (fun v_Y : (Z) => ((((((((zenon_Tv_V_b)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((zenon_Tv_W_c)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q)) zenon_H13); [ zenon_intro zenon_H14; idtac ].
elim zenon_H14. zenon_intro zenon_Tv_Y_d. zenon_intro zenon_H15.
apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H19. zenon_intro zenon_H18.
(* ARITH -- 'var' : ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q : '(Prop)', ((zenon_Vi)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z) : '(Prop)',
* ->((((((zenon_Tv_V_b)%Z + (3)%Z))%Z # (1)) <= ((zenon_Tv_Y_d)%Z # (1))))%Q,
* |- ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q, ((zenon_Vi)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z), *)
pose (zenon_Vi := (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z).
pose proof (Z.eq_refl zenon_Vi) as zenon_H1a; change zenon_Vi with (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z in zenon_H1a at 2.
cut ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q; [zenon_intro zenon_H1b | subst zenon_Vi; arith_omega zenon_H19 ].
generalize (zenon_H4 (zenon_Tv_Y_d)%Z). zenon_intro zenon_H1c.
apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
apply (zenon_notand_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ].
(* ARITH -- 'neg2_$lesseq' : (zenon_Tv_V_b)%Z : '(Z)', (zenon_Tv_Y_d)%Z : '(Z)', * ->(~((((zenon_Tv_V_b)%Z # (1)) <= ((zenon_Tv_Y_d)%Z # (1))))%Q), * |- ((((zenon_Tv_V_b)%Z # (1)) > ((zenon_Tv_Y_d)%Z # (1))))%Q, *) apply (arith_refut _ _ (arith_neg_leq ((zenon_Tv_V_b)%Z # (1)) ((zenon_Tv_Y_d)%Z # (1)))); [zenon_intro zenon_H21 | exact zenon_H20]. (* ARITH -- 'int_gt' : (zenon_Tv_V_b)%Z : '(Z)', (zenon_Tv_Y_d)%Z : '(Z)', * ->((((zenon_Tv_V_b)%Z # (1)) > ((zenon_Tv_Y_d)%Z # (1))))%Q, * |- ((((((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z # (1)) >= ((1)%Z # (1))))%Q, *) cut ((((((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z # (1)) >= ((1)%Z # (1))))%Q; [ zenon_intro zenon_H22 | arith_omega zenon_H21 ]. (* ARITH -- 'var' : ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q : '(Prop)', ((zenon_Vw)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z) : '(Prop)', * ->((((((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z # (1)) >= ((1)%Z # (1))))%Q, * |- ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q, ((zenon_Vw)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z), *) pose (zenon_Vw := (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z). pose proof (Z.eq_refl zenon_Vw) as zenon_H23; change zenon_Vw with (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z in zenon_H23 at 2. cut ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q; [zenon_intro zenon_H24 | subst zenon_Vw; arith_omega zenon_H22 ]. (* ARITH -- 'simplex_lin' : ((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z) : '(Prop)', ((zenon_Vw)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z) : '(Prop)', ((zenon_Vi)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z) : '(Prop)', * ->((zenon_Vw)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z), ((zenon_Vi)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z), * |- ((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z), *) cut ((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z); [ zenon_intro zenon_H25 | subst zenon_Vw; subst zenon_Vi; arith_norm; apply eq_refl ]. (* ARITH -- 'simplex_bound' : (zenon_Vw)%Z : '(Z)', ((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z) : '(Prop)', ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q : '(Prop)', * ->((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z), ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q, * |- ((((zenon_Vw)%Z # (1)) <= ((-3)%Z # (1))))%Q, *) cut (((zenon_Vw)%Z = (zenon_Vi)%Z)); [ zenon_intro zenon_H26 | arith_simpl ((-1)%Z # (1)) zenon_H25 ]. Qle_mult ((1)%Z # (1)) zenon_H1b zenon_H1b_zenon_H25. pose proof (zenon_H1b_zenon_H25) as zenon_H27_pre. cut ((((zenon_Vw)%Z # (1)) <= ((-3)%Z # (1))))%Q; [ zenon_intro zenon_H27 | rewrite -> zenon_H26; arith_simpl 1 zenon_H27_pre ]. (* ARITH -- 'conflict' : ((((zenon_Vw)%Z # (1)) <= ((-3)%Z # (1))))%Q : '(Prop)', ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q : '(Prop)', * ->((((zenon_Vw)%Z # (1)) <= ((-3)%Z # (1))))%Q, ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q, * |- *) arith_trans_simpl zenon_H27 zenon_H24. exact (zenon_H1f zenon_H18). exact (zenon_H16 zenon_H1d). Qed.  ## Vampire 4.0 Giles Reger University of Manchester, United Kingdom ### Sample solution for DAT013=1 % SZS output start Proof for DAT013=1 fof(f2288,plain,($false),
inference(subsumption_resolution,[],[f2287,f2273])).
fof(f2273,plain,(
$lesseq(sK1,sK3)), inference(evaluation,[],[f2269])). fof(f2269,plain,($lesseq(sK1,sK3) | ~$lesseq(0,3)), inference(superposition,[],[f2092,f36])). fof(f36,plain,( ( ! [X0:$int] : ($sum(0,X0) = X0) )), inference(superposition,[],[f8,f10])). fof(f10,plain,( ( ! [X0:$int] : ($sum(X0,0) = X0) )), introduced(theory_axiom,[])). fof(f8,plain,( ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) )), introduced(theory_axiom,[])). fof(f2092,plain,( ( ! [X2:$int] : ($lesseq($sum(X2,sK1),sK3) | ~$lesseq(X2,3)) )), inference(resolution,[],[f79,f16])). fof(f16,plain,( ( ! [X2:$int,X0:$int,X1:$int] : ($lesseq($sum(X0,X2),$sum(X1,X2)) | ~$lesseq(X0,X1)) )),
introduced(theory_axiom,[])).
fof(f79,plain,(
( ! [X11:$int] : (~$lesseq(X11,$sum(3,sK1)) |$lesseq(X11,sK3)) )),
inference(resolution,[],[f14,f34])).
fof(f34,plain,(
$lesseq($sum(3,sK1),sK3)),
inference(forward_demodulation,[],[f31,f8])).
fof(f31,plain,(
$lesseq($sum(sK1,3),sK3)),
inference(cnf_transformation,[],[f25])).
fof(f25,plain,(
! [X4 : $int] : (~$lesseq(sK1,X4) | ~$lesseq(X4,sK2) | ~$lesseq(read(sK0,X4),0)) & ($lesseq($sum(sK1,3),sK3) & $lesseq(sK3,sK2) &$lesseq(read(sK0,sK3),0))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f24])).
fof(f24,plain,(
? [X0 : array,X1 : $int,X2 :$int] : (! [X4 : $int] : (~$lesseq(X1,X4) | ~$lesseq(X4,X2) | ~$lesseq(read(X0,X4),0)) & ? [X3 : $int] : ($lesseq($sum(X1,3),X3) &$lesseq(X3,X2) & $lesseq(read(X0,X3),0)))), inference(rectify,[],[f23])). fof(f23,plain,( ? [X0 : array,X1 :$int,X2 : $int] : (! [X3 :$int] : (~$lesseq(X1,X3) | ~$lesseq(X3,X2) | ~$lesseq(read(X0,X3),0)) & ? [X4 :$int] : ($lesseq($sum(X1,3),X4) & $lesseq(X4,X2) &$lesseq(read(X0,X4),0)))),
inference(flattening,[],[f22])).
fof(f22,plain,(
? [X0 : array,X1 : $int,X2 :$int] : (! [X3 : $int] : ((~$lesseq(X1,X3) | ~$lesseq(X3,X2)) | ~$lesseq(read(X0,X3),0)) & ? [X4 : $int] : (($lesseq($sum(X1,3),X4) &$lesseq(X4,X2)) & $lesseq(read(X0,X4),0)))), inference(ennf_transformation,[],[f7])). fof(f7,plain,( ~! [X0 : array,X1 :$int,X2 : $int] : (! [X3 :$int] : (($lesseq(X1,X3) &$lesseq(X3,X2)) => ~$lesseq(read(X0,X3),0)) => ! [X4 :$int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) => ~$lesseq(read(X0,X4),0)))),
inference(evaluation,[],[f4])).
fof(f4,negated_conjecture,(
~! [X0 : array,X1 : $int,X2 :$int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) =>$greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq($sum(X1,3),X4) &$lesseq(X4,X2)) => $greater(read(X0,X4),0)))), inference(negated_conjecture,[],[f3])). fof(f3,conjecture,( ! [X0 : array,X1 :$int,X2 : $int] : (! [X3 :$int] : (($lesseq(X1,X3) &$lesseq(X3,X2)) => $greater(read(X0,X3),0)) => ! [X4 :$int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) =>$greater(read(X0,X4),0)))),
file('Problems/DAT/DAT013=1.p',unknown)).
fof(f14,plain,(
( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X1,X2) | ~$lesseq(X0,X1) |$lesseq(X0,X2)) )),
introduced(theory_axiom,[])).
fof(f2287,plain,(
~$lesseq(sK1,sK3)), inference(subsumption_resolution,[],[f2282,f32])). fof(f32,plain,($lesseq(sK3,sK2)),
inference(cnf_transformation,[],[f25])).
fof(f2282,plain,(
~$lesseq(sK3,sK2) | ~$lesseq(sK1,sK3)),
inference(resolution,[],[f33,f30])).
fof(f30,plain,(
( ! [X4:$int] : (~$lesseq(read(sK0,X4),0) | ~$lesseq(X4,sK2) | ~$lesseq(sK1,X4)) )),
inference(cnf_transformation,[],[f25])).
fof(f33,plain,(
$lesseq(read(sK0,sK3),0)), inference(cnf_transformation,[],[f25])). % SZS output end Proof for DAT013=1  ### Sample solution for SEU140+2 % SZS output start Proof for SEU140+2 fof(f926,plain,($false),
inference(subsumption_resolution,[],[f901,f501])).
fof(f501,plain,(
in(sK4(sK2,sK0),sK1)),
inference(unit_resulting_resolution,[],[f133,f323,f190])).
fof(f190,plain,(
( ! [X0,X3,X1] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )),
inference(cnf_transformation,[],[f118])).
fof(f118,plain,(
! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & ((in(sK7(X1,X0),X0) & ~in(sK7(X1,X0),X1)) | subset(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f117])).
fof(f117,plain,(
! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))),
inference(rectify,[],[f116])).
fof(f116,plain,(
! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))),
inference(nnf_transformation,[],[f98])).
fof(f98,plain,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (~in(X2,X0) | in(X2,X1)))),
inference(ennf_transformation,[],[f8])).
fof(f8,axiom,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
file('Problems/SEU/SEU140+2.p',d3_tarski)).
fof(f323,plain,(
in(sK4(sK2,sK0),sK0)),
inference(unit_resulting_resolution,[],[f135,f146])).
fof(f146,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f103])).
fof(f103,plain,(
! [X0,X1] : ((disjoint(X0,X1) | (in(sK4(X1,X0),X0) & in(sK4(X1,X0),X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f78])).
fof(f78,plain,(
! [X0,X1] : ((disjoint(X0,X1) | ? [X3] : (in(X3,X0) & in(X3,X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
inference(ennf_transformation,[],[f61])).
fof(f61,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
inference(flattening,[],[f60])).
fof(f60,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f43,axiom,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
file('Problems/SEU/SEU140+2.p',t3_xboole_0)).
fof(f135,plain,(
~disjoint(sK0,sK2)),
inference(cnf_transformation,[],[f101])).
fof(f101,plain,(
subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f75])).
fof(f75,plain,(
? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
inference(flattening,[],[f74])).
fof(f74,plain,(
? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
file('Problems/SEU/SEU140+2.p',t63_xboole_1)).
fof(f133,plain,(
subset(sK0,sK1)),
inference(cnf_transformation,[],[f101])).
fof(f901,plain,(
~in(sK4(sK2,sK0),sK1)),
inference(unit_resulting_resolution,[],[f134,f326,f148])).
fof(f148,plain,(
( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
inference(cnf_transformation,[],[f103])).
fof(f326,plain,(
in(sK4(sK2,sK0),sK2)),
inference(unit_resulting_resolution,[],[f135,f147])).
fof(f147,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f103])).
fof(f134,plain,(
disjoint(sK1,sK2)),
inference(cnf_transformation,[],[f101])).
% SZS output end Proof for SEU140+2


### Sample solution for NLP042+1

% # SZS output start Saturation.
cnf(u110,negated_conjecture,
past(sK0,sK4)).

cnf(u101,negated_conjecture,
actual_world(sK0)).

cnf(u109,negated_conjecture,
patient(sK0,sK4,sK3)).

cnf(u184,negated_conjecture,
~patient(sK0,sK4,X0) | ~agent(sK0,sK4,X0)).

cnf(u108,negated_conjecture,
agent(sK0,sK4,sK1)).

cnf(u203,negated_conjecture,
~agent(sK0,sK4,sK3)).

cnf(u111,negated_conjecture,
nonreflexive(sK0,sK4)).

cnf(u157,axiom,
~nonreflexive(X0,X1) | ~agent(X0,X1,X3) | ~patient(X0,X1,X3)).

cnf(u102,negated_conjecture,
of(sK0,sK2,sK1)).

cnf(u193,negated_conjecture,
~of(sK0,X0,sK1) | sK2 = X0 | ~forename(sK0,X0)).

cnf(u155,axiom,
~of(X0,X2,X1) | X2 = X3 | ~forename(X0,X3) | ~of(X0,X3,X1) | ~forename(X0,X2) | ~entity(X0,X1)).

cnf(u125,axiom,
act(X0,X1) | ~order(X0,X1)).

cnf(u120,axiom,
~act(X0,X1) | event(X0,X1)).

cnf(u152,axiom,
singleton(X0,X1) | ~thing(X0,X1)).

cnf(u181,negated_conjecture,
nonexistent(sK0,sK4)).

cnf(u122,axiom,
~nonexistent(X0,X1) | ~existent(X0,X1)).

cnf(u175,negated_conjecture,
eventuality(sK0,sK4)).

cnf(u135,axiom,
~eventuality(X0,X1) | nonexistent(X0,X1)).

cnf(u140,axiom,
~eventuality(X0,X1) | specific(X0,X1)).

cnf(u142,axiom,
~eventuality(X0,X1) | unisex(X0,X1)).

cnf(u144,axiom,
~eventuality(X0,X1) | thing(X0,X1)).

cnf(u127,axiom,
event(X0,X1) | ~order(X0,X1)).

cnf(u107,negated_conjecture,
event(sK0,sK4)).

cnf(u153,axiom,
~event(X0,X1) | eventuality(X0,X1)).

cnf(u112,negated_conjecture,
order(sK0,sK4)).

cnf(u176,axiom,
~order(X0,X1) | eventuality(X0,X1)).

cnf(u106,negated_conjecture,
shake_beverage(sK0,sK3)).

cnf(u113,axiom,
~shake_beverage(X0,X1) | beverage(X0,X1)).

cnf(u158,negated_conjecture,
beverage(sK0,sK3)).

cnf(u114,axiom,
~beverage(X0,X1) | food(X0,X1)).

cnf(u159,negated_conjecture,
food(sK0,sK3)).

cnf(u115,axiom,
~food(X0,X1) | substance_matter(X0,X1)).

cnf(u160,negated_conjecture,
substance_matter(sK0,sK3)).

cnf(u117,axiom,
~substance_matter(X0,X1) | object(X0,X1)).

cnf(u180,negated_conjecture,
specific(sK0,sK4)).

cnf(u150,axiom,
specific(X0,X1) | ~entity(X0,X1)).

cnf(u147,axiom,
~specific(X0,X1) | ~general(X0,X1)).

cnf(u149,axiom,
existent(X0,X1) | ~entity(X0,X1)).

cnf(u183,negated_conjecture,
~existent(sK0,sK4)).

cnf(u163,negated_conjecture,
nonliving(sK0,sK3)).

cnf(u123,axiom,
~nonliving(X0,X1) | ~animate(X0,X1)).

cnf(u128,axiom,
~nonliving(X0,X1) | ~living(X0,X1)).

cnf(u161,negated_conjecture,
object(sK0,sK3)).

cnf(u138,axiom,
~object(X0,X1) | nonliving(X0,X1)).

cnf(u139,axiom,
~object(X0,X1) | impartial(X0,X1)).

cnf(u141,axiom,
~object(X0,X1) | entity(X0,X1)).

cnf(u146,axiom,
~object(X0,X1) | unisex(X0,X1)).

cnf(u148,axiom,
relname(X0,X1) | ~forename(X0,X1)).

cnf(u116,axiom,
~relname(X0,X1) | relation(X0,X1)).

cnf(u173,axiom,
relation(X0,X1) | ~forename(X0,X1)).

cnf(u118,axiom,
~relation(X0,X1) | abstraction(X0,X1)).

cnf(u178,negated_conjecture,
thing(sK0,sK4)).

cnf(u145,axiom,
thing(X0,X1) | ~abstraction(X0,X1)).

cnf(u151,axiom,
thing(X0,X1) | ~entity(X0,X1)).

cnf(u207,negated_conjecture,
nonhuman(sK0,sK2)).

cnf(u121,axiom,
~nonhuman(X0,X1) | ~human(X0,X1)).

cnf(u136,axiom,
general(X0,X1) | ~abstraction(X0,X1)).

cnf(u174,axiom,
~general(X0,X1) | ~entity(X0,X1)).

cnf(u182,negated_conjecture,
~general(sK0,sK4)).

cnf(u179,negated_conjecture,
unisex(sK0,sK4)).

cnf(u172,negated_conjecture,
unisex(sK0,sK3)).

cnf(u143,axiom,
unisex(X0,X1) | ~abstraction(X0,X1)).

cnf(u202,negated_conjecture,
~unisex(sK0,sK1)).

cnf(u205,negated_conjecture,
abstraction(sK0,sK2)).

cnf(u204,negated_conjecture,
~abstraction(sK0,sK1)).

cnf(u185,negated_conjecture,
~abstraction(sK0,sK4)).

cnf(u137,axiom,
~abstraction(X0,X1) | nonhuman(X0,X1)).

cnf(u200,axiom,
~abstraction(X0,X1) | ~entity(X0,X1)).

cnf(u119,axiom,
forename(X0,X1) | ~mia_forename(X0,X1)).

cnf(u105,negated_conjecture,
forename(sK0,sK2)).

cnf(u199,axiom,
~forename(X0,X1) | abstraction(X0,X1)).

cnf(u104,negated_conjecture,
mia_forename(sK0,sK2)).

cnf(u206,axiom,
~mia_forename(X0,X1) | abstraction(X0,X1)).

cnf(u191,negated_conjecture,
entity(sK0,sK1)).

cnf(u171,negated_conjecture,
entity(sK0,sK3)).

cnf(u134,axiom,
entity(X0,X1) | ~organism(X0,X1)).

cnf(u212,negated_conjecture,
~entity(sK0,sK2)).

cnf(u186,negated_conjecture,
~entity(sK0,sK4)).

cnf(u166,negated_conjecture,
impartial(sK0,sK3)).

cnf(u133,axiom,
impartial(X0,X1) | ~organism(X0,X1)).

cnf(u131,axiom,
living(X0,X1) | ~organism(X0,X1)).

cnf(u164,negated_conjecture,
~living(sK0,sK3)).

cnf(u132,axiom,
organism(X0,X1) | ~human_person(X0,X1)).

cnf(u214,negated_conjecture,
~organism(sK0,sK2)).

cnf(u187,negated_conjecture,
~organism(sK0,sK4)).

cnf(u167,negated_conjecture,
~organism(sK0,sK3)).

cnf(u130,axiom,
human(X0,X1) | ~human_person(X0,X1)).

cnf(u209,negated_conjecture,
~human(sK0,sK2)).

cnf(u129,axiom,
animate(X0,X1) | ~human_person(X0,X1)).

cnf(u165,negated_conjecture,
~animate(sK0,sK3)).

cnf(u126,axiom,
human_person(X0,X1) | ~woman(X0,X1)).

cnf(u210,negated_conjecture,
~human_person(sK0,sK2)).

cnf(u188,negated_conjecture,
~human_person(sK0,sK4)).

cnf(u168,negated_conjecture,
~human_person(sK0,sK3)).

cnf(u124,axiom,
female(X0,X1) | ~woman(X0,X1)).

cnf(u154,axiom,
~female(X0,X1) | ~unisex(X0,X1)).

cnf(u103,negated_conjecture,
woman(sK0,sK1)).

cnf(u177,axiom,
~woman(X0,X1) | ~unisex(X0,X1)).

cnf(u211,negated_conjecture,
~woman(sK0,sK2)).

cnf(u198,negated_conjecture,
~woman(sK0,sK4)).

cnf(u170,negated_conjecture,
~woman(sK0,sK3)).

% # SZS output end Saturation.


### Sample solution for SWV017+1

% SZS output start FiniteModel for SWV017+1
fof(domain,interpretation_domain,
! [X] : (
X = fmb1 | X = fmb2
) ).

fof(distinct_domain,interpreted_domain,
fmb1 != fmb2
).

fof(constant_at,functors,at = fmb1).
fof(constant_t,functors,t = fmb2).
fof(constant_a,functors,a = fmb1).
fof(constant_b,functors,b = fmb1).
fof(constant_an_a_nonce,functors,an_a_nonce = fmb1).
fof(constant_bt,functors,bt = fmb1).
fof(constant_an_intruder_nonce,functors,an_intruder_nonce = fmb1).

fof(function_key,functors,
key(fmb1,fmb1) = fmb1 &
key(fmb1,fmb2) = fmb2 &
key(fmb2,fmb1) = fmb2 &
key(fmb2,fmb2) = fmb2
).

fof(function_pair,functors,
pair(fmb1,fmb1) = fmb2 &
pair(fmb1,fmb2) = fmb1 &
pair(fmb2,fmb1) = fmb1 &
pair(fmb2,fmb2) = fmb1
).

fof(function_sent,functors,
sent(fmb1,fmb1,fmb1) = fmb1 &
sent(fmb1,fmb1,fmb2) = fmb1 &
sent(fmb1,fmb2,fmb1) = fmb1 &
sent(fmb1,fmb2,fmb2) = fmb1 &
sent(fmb2,fmb1,fmb1) = fmb1 &
sent(fmb2,fmb1,fmb2) = fmb1 &
sent(fmb2,fmb2,fmb1) = fmb1 &
sent(fmb2,fmb2,fmb2) = fmb1
).

).

fof(function_encrypt,functors,
encrypt(fmb1,fmb1) = fmb2 &
encrypt(fmb1,fmb2) = fmb2 &
encrypt(fmb2,fmb1) = fmb1 &
encrypt(fmb2,fmb2) = fmb1
).

fof(function_triple,functors,
triple(fmb1,fmb1,fmb1) = fmb2 &
triple(fmb1,fmb1,fmb2) = fmb2 &
triple(fmb1,fmb2,fmb1) = fmb2 &
triple(fmb1,fmb2,fmb2) = fmb1 &
triple(fmb2,fmb1,fmb1) = fmb2 &
triple(fmb2,fmb1,fmb2) = fmb1 &
triple(fmb2,fmb2,fmb1) = fmb1 &
triple(fmb2,fmb2,fmb2) = fmb1
).

fof(function_generate_b_nonce,functors,
generate_b_nonce(fmb1) = fmb1 &
generate_b_nonce(fmb2) = fmb1
).

fof(function_generate_expiration_time,functors,
generate_expiration_time(fmb1) = fmb1 &
generate_expiration_time(fmb2) = fmb1
).

fof(function_generate_key,functors,
generate_key(fmb1) = fmb2 &
generate_key(fmb2) = fmb2
).

fof(function_generate_intruder_nonce,functors,
generate_intruder_nonce(fmb1) = fmb1 &
generate_intruder_nonce(fmb2) = fmb1
).

fof(predicate_a_holds,predicates,
~a_holds(fmb1)  &
~a_holds(fmb2)
).

fof(predicate_party_of_protocol,predicates,
party_of_protocol(fmb1)  &
party_of_protocol(fmb2)
).

fof(predicate_message,predicates,
message(fmb1)  &
~message(fmb2)
).

fof(predicate_a_stored,predicates,
a_stored(fmb1)  &
a_stored(fmb2)
).

fof(predicate_b_holds,predicates,
~b_holds(fmb1)  &
~b_holds(fmb2)
).

fof(predicate_fresh_to_b,predicates,
fresh_to_b(fmb1)  &
~fresh_to_b(fmb2)
).

fof(predicate_b_stored,predicates,
~b_stored(fmb1)  &
~b_stored(fmb2)
).

fof(predicate_a_key,predicates,
~a_key(fmb1)  &
a_key(fmb2)
).

fof(predicate_t_holds,predicates,
t_holds(fmb1)  &
~t_holds(fmb2)
).

fof(predicate_a_nonce,predicates,
a_nonce(fmb1)  &
~a_nonce(fmb2)
).

fof(predicate_intruder_message,predicates,
intruder_message(fmb1)  &
intruder_message(fmb2)
).

fof(predicate_intruder_holds,predicates,
intruder_holds(fmb1)  &
intruder_holds(fmb2)
).

fof(predicate_fresh_intruder_nonce,predicates,
fresh_intruder_nonce(fmb1)  &
~fresh_intruder_nonce(fmb2)
).
% SZS output end FiniteModel for SWV017+1


## VampireZ3 1.0

Giles Reger
University of Manchester, United Kingdom

### Sample solution for DAT013=1

% SZS output start Proof for DAT013=1
fof(f208,plain,(
$false), inference(sat_splitting_refutation,[],[f20,f34,f19,f35,f18,f36,f16,f37,f15,f38,f14,f39,f13,f40,f12,f41,f11,f42,f10,f43,f9,f44,f8,f45,f28,f46,f29,f47,f33,f49,f32,f51,f31,f53,f30,f54,f55,f57,f59,f60,f61,f62,f63,f70,f71,f73,f72,f74,f76,f83,f77,f78,f84,f79,f85,f80,f81,f86,f82,f87,f89,f90,f95,f92,f93,f96,f101,f102,f98,f99,f103,f107,f114,f109,f118,f116,f110,f122,f120,f111,f123,f112,f124,f113,f128,f126,f132,f133,f141,f134,f142,f136,f143,f137,f144,f138,f145,f139,f146,f140,f147,f152,f164,f153,f165,f155,f167,f156,f157,f168,f158,f169,f160,f171,f161,f162,f172,f163,f173,f177,f178,f180,f189,f181,f190,f182,f183,f186,f203,f205,f200,f206,f201,f202,f207])). fof(f207,plain,( ( ! [X1:$int] : (~$lesseq(X1,sK2) | ~$lesseq(sK1,X1) | $lesseq(0,read(sK0,X1))) ) |$spl120),
inference(cnf_transformation,[],[f207_D])).
fof(f207_D,plain,(
( ! [X1:$int] : (~$lesseq(X1,sK2) | ~$lesseq(sK1,X1) |$lesseq(0,read(sK0,X1))) ) <=> ~$spl120), introduced(sat_splitting_component,[new_symbols(naming,[$spl120])])).
fof(f202,plain,(
( ! [X2:$int] : (~$lesseq(X2,sK2) | ~$lesseq(sK1,X2) |$lesseq(0,read(sK0,X2))) ) | ($spl8 |$spl34)),
inference(resolution,[],[f54,f38])).
fof(f201,plain,(
( ! [X1:$int] : (~$lesseq(X1,sK2) | ~$lesseq(sK1,X1) |$lesseq(0,read(sK0,X1))) ) | ($spl8 |$spl34)),
inference(resolution,[],[f54,f38])).
fof(f206,plain,(
( ! [X0:$int] : (~$lesseq(X0,sK2) | ~$lesseq(sK1,X0) |$lesseq(1,read(sK0,X0))) ) | $spl118), inference(cnf_transformation,[],[f206_D])). fof(f206_D,plain,( ( ! [X0:$int] : (~$lesseq(X0,sK2) | ~$lesseq(sK1,X0) | $lesseq(1,read(sK0,X0))) ) <=> ~$spl118),
introduced(sat_splitting_component,[new_symbols(naming,[$spl118])])). fof(f200,plain,( ( ! [X0:$int] : (~$lesseq(X0,sK2) | ~$lesseq(sK1,X0) | $lesseq(1,read(sK0,X0))) ) | ($spl34 | $spl42)), inference(resolution,[],[f54,f74])). fof(f205,plain,( ~$lesseq(sK1,sK3) | $spl117), inference(cnf_transformation,[],[f205_D])). fof(f205_D,plain,( ~$lesseq(sK1,sK3) <=> ~$spl117), introduced(sat_splitting_component,[new_symbols(naming,[$spl117])])).
fof(f203,plain,(
~$lesseq(sK1,sK3) | ($spl28 | $spl30 |$spl34)),
inference(subsumption_resolution,[],[f199,f51])).
fof(f199,plain,(
~$lesseq(sK3,sK2) | ~$lesseq(sK1,sK3) | ($spl28 |$spl34)),
inference(resolution,[],[f54,f49])).
fof(f186,plain,(
( ! [X4:$int,X3:$int] : ($sum($uminus(X4),$uminus(X3)) =$uminus($sum(X4,X3))) ) |$spl110),
inference(cnf_transformation,[],[f186_D])).
fof(f186_D,plain,(
( ! [X4:$int,X3:$int] : ($sum($uminus(X4),$uminus(X3)) =$uminus($sum(X4,X3))) ) <=> ~$spl110),
introduced(sat_splitting_component,[new_symbols(naming,[$spl110])])). fof(f183,plain,( ( ! [X10:$int,X9:$int] : ($sum($uminus(X10),$uminus(X9)) = $uminus($sum(X10,X9))) ) | ($spl16 |$spl22)),
inference(superposition,[],[f45,f42])).
fof(f182,plain,(
( ! [X8:$int,X7:$int] : ($sum($uminus(X8),$uminus(X7)) =$uminus($sum(X8,X7))) ) | ($spl16 | $spl22)), inference(superposition,[],[f45,f42])). fof(f190,plain,( ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($uminus($sum(X5,X4)),$sum(X6,$uminus(X5))) | ~$lesseq($uminus(X4),X6)) ) |$spl114),
inference(cnf_transformation,[],[f190_D])).
fof(f190_D,plain,(
( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($uminus($sum(X5,X4)),$sum(X6,$uminus(X5))) | ~$lesseq($uminus(X4),X6)) ) <=> ~$spl114), introduced(sat_splitting_component,[new_symbols(naming,[$spl114])])).
fof(f181,plain,(
( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($uminus($sum(X5,X4)),$sum(X6,$uminus(X5))) | ~$lesseq($uminus(X4),X6)) ) | ($spl6 |$spl16)),
inference(superposition,[],[f37,f42])).
fof(f189,plain,(
( ! [X2:$int,X3:$int,X1:$int] : ($lesseq($sum(X3,$uminus(X2)),$uminus($sum(X2,X1))) | ~$lesseq(X3,$uminus(X1))) ) | $spl112), inference(cnf_transformation,[],[f189_D])). fof(f189_D,plain,( ( ! [X2:$int,X3:$int,X1:$int] : ($lesseq($sum(X3,$uminus(X2)),$uminus($sum(X2,X1))) | ~$lesseq(X3,$uminus(X1))) ) <=> ~$spl112),
introduced(sat_splitting_component,[new_symbols(naming,[$spl112])])). fof(f180,plain,( ( ! [X2:$int,X3:$int,X1:$int] : ($lesseq($sum(X3,$uminus(X2)),$uminus($sum(X2,X1))) | ~$lesseq(X3,$uminus(X1))) ) | ($spl6 | $spl16)), inference(superposition,[],[f37,f42])). fof(f178,plain,( ( ! [X6:$int,X5:$int] : ($sum($uminus(X6),$uminus(X5)) = $uminus($sum(X6,X5))) ) | ($spl16 |$spl22)),
inference(superposition,[],[f42,f45])).
fof(f177,plain,(
( ! [X4:$int,X3:$int] : ($sum($uminus(X4),$uminus(X3)) =$uminus($sum(X4,X3))) ) | ($spl16 | $spl22)), inference(superposition,[],[f42,f45])). fof(f173,plain,( ( ! [X10:$int,X11:$int] : ($lesseq($sum(X11,X10),X10) | ~$lesseq(X11,0)) ) | $spl108), inference(cnf_transformation,[],[f173_D])). fof(f173_D,plain,( ( ! [X10:$int,X11:$int] : ($lesseq($sum(X11,X10),X10) | ~$lesseq(X11,0)) ) <=> ~$spl108), introduced(sat_splitting_component,[new_symbols(naming,[$spl108])])).
fof(f163,plain,(
( ! [X10:$int,X11:$int] : ($lesseq($sum(X11,X10),X10) | ~$lesseq(X11,0)) ) | ($spl6 | $spl38)), inference(superposition,[],[f37,f63])). fof(f172,plain,( ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X6,X5),$sum(X5,X4)) | ~$lesseq(X6,X4)) ) | $spl106), inference(cnf_transformation,[],[f172_D])). fof(f172_D,plain,( ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X6,X5),$sum(X5,X4)) | ~$lesseq(X6,X4)) ) <=> ~$spl106), introduced(sat_splitting_component,[new_symbols(naming,[$spl106])])).
fof(f162,plain,(
( ! [X8:$int,X7:$int,X9:$int] : ($lesseq($sum(X9,X8),$sum(X8,X7)) | ~$lesseq(X9,X7)) ) | ($spl6 | $spl22)), inference(superposition,[],[f37,f45])). fof(f161,plain,( ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X6,X5),$sum(X5,X4)) | ~$lesseq(X6,X4)) ) | ($spl6 |$spl22)),
inference(superposition,[],[f37,f45])).
fof(f171,plain,(
( ! [X2:$int,X3:$int] : ($lesseq($sum(X3,$uminus(X2)),0) | ~$lesseq(X3,X2)) ) | $spl104), inference(cnf_transformation,[],[f171_D])). fof(f171_D,plain,( ( ! [X2:$int,X3:$int] : ($lesseq($sum(X3,$uminus(X2)),0) | ~$lesseq(X3,X2)) ) <=> ~$spl104),
introduced(sat_splitting_component,[new_symbols(naming,[$spl104])])). fof(f160,plain,( ( ! [X2:$int,X3:$int] : ($lesseq($sum(X3,$uminus(X2)),0) | ~$lesseq(X3,X2)) ) | ($spl6 | $spl14)), inference(superposition,[],[f37,f41])). fof(f169,plain,( ( ! [X10:$int,X11:$int] : ($lesseq(X10,$sum(X11,X10)) | ~$lesseq(0,X11)) ) | $spl102), inference(cnf_transformation,[],[f169_D])). fof(f169_D,plain,( ( ! [X10:$int,X11:$int] : ($lesseq(X10,$sum(X11,X10)) | ~$lesseq(0,X11)) ) <=> ~$spl102), introduced(sat_splitting_component,[new_symbols(naming,[$spl102])])).
fof(f158,plain,(
( ! [X10:$int,X11:$int] : ($lesseq(X10,$sum(X11,X10)) | ~$lesseq(0,X11)) ) | ($spl6 | $spl38)), inference(superposition,[],[f37,f63])). fof(f168,plain,( ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X5,X4),$sum(X6,X5)) | ~$lesseq(X4,X6)) ) | $spl100), inference(cnf_transformation,[],[f168_D])). fof(f168_D,plain,( ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X5,X4),$sum(X6,X5)) | ~$lesseq(X4,X6)) ) <=> ~$spl100), introduced(sat_splitting_component,[new_symbols(naming,[$spl100])])).
fof(f157,plain,(
( ! [X8:$int,X7:$int,X9:$int] : ($lesseq($sum(X8,X7),$sum(X9,X8)) | ~$lesseq(X7,X9)) ) | ($spl6 | $spl22)), inference(superposition,[],[f37,f45])). fof(f156,plain,( ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X5,X4),$sum(X6,X5)) | ~$lesseq(X4,X6)) ) | ($spl6 |$spl22)),
inference(superposition,[],[f37,f45])).
fof(f167,plain,(
( ! [X2:$int,X3:$int] : ($lesseq(0,$sum(X3,$uminus(X2))) | ~$lesseq(X2,X3)) ) | $spl98), inference(cnf_transformation,[],[f167_D])). fof(f167_D,plain,( ( ! [X2:$int,X3:$int] : ($lesseq(0,$sum(X3,$uminus(X2))) | ~$lesseq(X2,X3)) ) <=> ~$spl98),
introduced(sat_splitting_component,[new_symbols(naming,[$spl98])])). fof(f155,plain,( ( ! [X2:$int,X3:$int] : ($lesseq(0,$sum(X3,$uminus(X2))) | ~$lesseq(X2,X3)) ) | ($spl6 | $spl14)), inference(superposition,[],[f37,f41])). fof(f165,plain,( ( ! [X8:$int,X7:$int,X9:$int] : (~$lesseq(X7,X8) | ~$lesseq($sum(X8,X9),$sum(X7,X9)) | $sum(X7,X9) =$sum(X8,X9)) ) | $spl96), inference(cnf_transformation,[],[f165_D])). fof(f165_D,plain,( ( ! [X8:$int,X7:$int,X9:$int] : (~$lesseq(X7,X8) | ~$lesseq($sum(X8,X9),$sum(X7,X9)) | $sum(X7,X9) =$sum(X8,X9)) ) <=> ~$spl96), introduced(sat_splitting_component,[new_symbols(naming,[$spl96])])).
fof(f153,plain,(
( ! [X8:$int,X7:$int,X9:$int] : (~$lesseq(X7,X8) | ~$lesseq($sum(X8,X9),$sum(X7,X9)) |$sum(X7,X9) = $sum(X8,X9)) ) | ($spl2 | $spl6)), inference(resolution,[],[f37,f35])). fof(f164,plain,( ( ! [X6:$int,X4:$int,X5:$int,X3:$int] : (~$lesseq(X3,X4) | ~$lesseq(X5,$sum(X3,X6)) | $lesseq(X5,$sum(X4,X6))) ) | $spl94), inference(cnf_transformation,[],[f164_D])). fof(f164_D,plain,( ( ! [X6:$int,X4:$int,X5:$int,X3:$int] : (~$lesseq(X3,X4) | ~$lesseq(X5,$sum(X3,X6)) | $lesseq(X5,$sum(X4,X6))) ) <=> ~$spl94), introduced(sat_splitting_component,[new_symbols(naming,[$spl94])])).
fof(f152,plain,(
( ! [X6:$int,X4:$int,X5:$int,X3:$int] : (~$lesseq(X3,X4) | ~$lesseq(X5,$sum(X3,X6)) |$lesseq(X5,$sum(X4,X6))) ) | ($spl6 | $spl10)), inference(resolution,[],[f37,f39])). fof(f147,plain,( ( ! [X19:$int] : (~$lesseq(X19,sK3) |$lesseq(X19,sK2)) ) | $spl92), inference(cnf_transformation,[],[f147_D])). fof(f147_D,plain,( ( ! [X19:$int] : (~$lesseq(X19,sK3) |$lesseq(X19,sK2)) ) <=> ~$spl92), introduced(sat_splitting_component,[new_symbols(naming,[$spl92])])).
fof(f140,plain,(
( ! [X19:$int] : (~$lesseq(X19,sK3) | $lesseq(X19,sK2)) ) | ($spl10 | $spl30)), inference(resolution,[],[f39,f51])). fof(f146,plain,( ( ! [X17:$int,X18:$int] : (~$lesseq(X17,1) | $lesseq(X17,X18) |$lesseq(X18,0)) ) | $spl90), inference(cnf_transformation,[],[f146_D])). fof(f146_D,plain,( ( ! [X17:$int,X18:$int] : (~$lesseq(X17,1) | $lesseq(X17,X18) |$lesseq(X18,0)) ) <=> ~$spl90), introduced(sat_splitting_component,[new_symbols(naming,[$spl90])])).
fof(f139,plain,(
( ! [X17:$int,X18:$int] : (~$lesseq(X17,1) |$lesseq(X17,X18) | $lesseq(X18,0)) ) | ($spl10 | $spl42)), inference(resolution,[],[f39,f74])). fof(f145,plain,( ( ! [X14:$int,X15:$int,X16:$int] : (~$lesseq(X14,$sum(X15,1)) | $lesseq(X14,X16) |$lesseq(X16,X15)) ) | $spl88), inference(cnf_transformation,[],[f145_D])). fof(f145_D,plain,( ( ! [X14:$int,X15:$int,X16:$int] : (~$lesseq(X14,$sum(X15,1)) | $lesseq(X14,X16) |$lesseq(X16,X15)) ) <=> ~$spl88), introduced(sat_splitting_component,[new_symbols(naming,[$spl88])])).
fof(f138,plain,(
( ! [X14:$int,X15:$int,X16:$int] : (~$lesseq(X14,$sum(X15,1)) |$lesseq(X14,X16) | $lesseq(X16,X15)) ) | ($spl0 | $spl10)), inference(resolution,[],[f39,f34])). fof(f144,plain,( ( ! [X13:$int] : (~$lesseq(X13,$sum(3,sK1)) | $lesseq(X13,sK3)) ) |$spl86),
inference(cnf_transformation,[],[f144_D])).
fof(f144_D,plain,(
( ! [X13:$int] : (~$lesseq(X13,$sum(3,sK1)) |$lesseq(X13,sK3)) ) <=> ~$spl86), introduced(sat_splitting_component,[new_symbols(naming,[$spl86])])).
fof(f137,plain,(
( ! [X13:$int] : (~$lesseq(X13,$sum(3,sK1)) |$lesseq(X13,sK3)) ) | ($spl10 |$spl36)),
inference(resolution,[],[f39,f57])).
fof(f143,plain,(
( ! [X12:$int] : (~$lesseq(X12,read(sK0,sK3)) | $lesseq(X12,0)) ) |$spl84),
inference(cnf_transformation,[],[f143_D])).
fof(f143_D,plain,(
( ! [X12:$int] : (~$lesseq(X12,read(sK0,sK3)) | $lesseq(X12,0)) ) <=> ~$spl84),
introduced(sat_splitting_component,[new_symbols(naming,[$spl84])])). fof(f136,plain,( ( ! [X12:$int] : (~$lesseq(X12,read(sK0,sK3)) |$lesseq(X12,0)) ) | ($spl10 |$spl28)),
inference(resolution,[],[f39,f49])).
fof(f142,plain,(
( ! [X8:$int,X9:$int] : (~$lesseq(X8,X9) |$lesseq(X8,0) | $lesseq(1,X9)) ) |$spl82),
inference(cnf_transformation,[],[f142_D])).
fof(f142_D,plain,(
( ! [X8:$int,X9:$int] : (~$lesseq(X8,X9) |$lesseq(X8,0) | $lesseq(1,X9)) ) <=> ~$spl82),
introduced(sat_splitting_component,[new_symbols(naming,[$spl82])])). fof(f134,plain,( ( ! [X8:$int,X9:$int] : (~$lesseq(X8,X9) | $lesseq(X8,0) |$lesseq(1,X9)) ) | ($spl10 |$spl42)),
inference(resolution,[],[f39,f74])).
fof(f141,plain,(
( ! [X4:$int,X2:$int,X3:$int] : (~$lesseq(X2,X3) | $lesseq(X2,X4) |$lesseq(X4,X3)) ) | $spl80), inference(cnf_transformation,[],[f141_D])). fof(f141_D,plain,( ( ! [X4:$int,X2:$int,X3:$int] : (~$lesseq(X2,X3) |$lesseq(X2,X4) | $lesseq(X4,X3)) ) <=> ~$spl80),
introduced(sat_splitting_component,[new_symbols(naming,[$spl80])])). fof(f133,plain,( ( ! [X6:$int,X7:$int,X5:$int] : (~$lesseq(X5,X6) |$lesseq(X5,X7) | $lesseq(X7,X6)) ) | ($spl8 | $spl10)), inference(resolution,[],[f39,f38])). fof(f132,plain,( ( ! [X4:$int,X2:$int,X3:$int] : (~$lesseq(X2,X3) |$lesseq(X2,X4) | $lesseq(X4,X3)) ) | ($spl8 | $spl10)), inference(resolution,[],[f39,f38])). fof(f126,plain,( sK2 = sK3 |$spl76),
inference(cnf_transformation,[],[f126_D])).
fof(f126_D,plain,(
sK2 = sK3 <=> ~$spl76), introduced(sat_splitting_component,[new_symbols(naming,[$spl76])])).
fof(f128,plain,(
~$lesseq(sK2,sK3) |$spl79),
inference(cnf_transformation,[],[f128_D])).
fof(f128_D,plain,(
~$lesseq(sK2,sK3) <=> ~$spl79),
introduced(sat_splitting_component,[new_symbols(naming,[$spl79])])). fof(f113,plain,( ~$lesseq(sK2,sK3) | sK2 = sK3 | ($spl2 |$spl30)),
inference(resolution,[],[f35,f51])).
fof(f124,plain,(
( ! [X9:$int] : (~$lesseq(X9,1) | 1 = X9 | $lesseq(X9,0)) ) |$spl74),
inference(cnf_transformation,[],[f124_D])).
fof(f124_D,plain,(
( ! [X9:$int] : (~$lesseq(X9,1) | 1 = X9 | $lesseq(X9,0)) ) <=> ~$spl74),
introduced(sat_splitting_component,[new_symbols(naming,[$spl74])])). fof(f112,plain,( ( ! [X9:$int] : (~$lesseq(X9,1) | 1 = X9 |$lesseq(X9,0)) ) | ($spl2 |$spl42)),
inference(resolution,[],[f35,f74])).
fof(f123,plain,(
( ! [X8:$int,X7:$int] : (~$lesseq(X7,$sum(X8,1)) | $sum(X8,1) = X7 |$lesseq(X7,X8)) ) | $spl72), inference(cnf_transformation,[],[f123_D])). fof(f123_D,plain,( ( ! [X8:$int,X7:$int] : (~$lesseq(X7,$sum(X8,1)) |$sum(X8,1) = X7 | $lesseq(X7,X8)) ) <=> ~$spl72),
introduced(sat_splitting_component,[new_symbols(naming,[$spl72])])). fof(f111,plain,( ( ! [X8:$int,X7:$int] : (~$lesseq(X7,$sum(X8,1)) |$sum(X8,1) = X7 | $lesseq(X7,X8)) ) | ($spl0 | $spl2)), inference(resolution,[],[f35,f34])). fof(f120,plain,($sum(3,sK1) = sK3 | $spl68), inference(cnf_transformation,[],[f120_D])). fof(f120_D,plain,($sum(3,sK1) = sK3 <=> ~$spl68), introduced(sat_splitting_component,[new_symbols(naming,[$spl68])])).
fof(f122,plain,(
~$lesseq(sK3,$sum(3,sK1)) | $spl71), inference(cnf_transformation,[],[f122_D])). fof(f122_D,plain,( ~$lesseq(sK3,$sum(3,sK1)) <=> ~$spl71),
introduced(sat_splitting_component,[new_symbols(naming,[$spl71])])). fof(f110,plain,( ~$lesseq(sK3,$sum(3,sK1)) |$sum(3,sK1) = sK3 | ($spl2 |$spl36)),
inference(resolution,[],[f35,f57])).
fof(f116,plain,(
read(sK0,sK3) = 0 | $spl64), inference(cnf_transformation,[],[f116_D])). fof(f116_D,plain,( read(sK0,sK3) = 0 <=> ~$spl64),
introduced(sat_splitting_component,[new_symbols(naming,[$spl64])])). fof(f118,plain,( ~$lesseq(0,read(sK0,sK3)) | $spl67), inference(cnf_transformation,[],[f118_D])). fof(f118_D,plain,( ~$lesseq(0,read(sK0,sK3)) <=> ~$spl67), introduced(sat_splitting_component,[new_symbols(naming,[$spl67])])).
fof(f109,plain,(
~$lesseq(0,read(sK0,sK3)) | read(sK0,sK3) = 0 | ($spl2 | $spl28)), inference(resolution,[],[f35,f49])). fof(f114,plain,( ( ! [X5:$int] : (~$lesseq(0,X5) | 0 = X5 |$lesseq(1,X5)) ) | $spl62), inference(cnf_transformation,[],[f114_D])). fof(f114_D,plain,( ( ! [X5:$int] : (~$lesseq(0,X5) | 0 = X5 |$lesseq(1,X5)) ) <=> ~$spl62), introduced(sat_splitting_component,[new_symbols(naming,[$spl62])])).
fof(f107,plain,(
( ! [X5:$int] : (~$lesseq(0,X5) | 0 = X5 | $lesseq(1,X5)) ) | ($spl2 | $spl42)), inference(resolution,[],[f35,f74])). fof(f103,plain,( ( ! [X0:$int] : ($lesseq(X0,$sum(1,X0))) ) | $spl60), inference(cnf_transformation,[],[f103_D])). fof(f103_D,plain,( ( ! [X0:$int] : ($lesseq(X0,$sum(1,X0))) ) <=> ~$spl60), introduced(sat_splitting_component,[new_symbols(naming,[$spl60])])).
fof(f99,plain,(
( ! [X1:$int] : ($lesseq(X1,$sum(1,X1))) ) | ($spl22 | $spl54)), inference(superposition,[],[f95,f45])). fof(f98,plain,( ( ! [X0:$int] : ($lesseq(X0,$sum(1,X0))) ) | ($spl22 |$spl54)),
inference(superposition,[],[f95,f45])).
fof(f102,plain,(
( ! [X0:$int] : (~$lesseq($sum(1,$sum(X0,1)),X0)) ) | $spl58), inference(cnf_transformation,[],[f102_D])). fof(f102_D,plain,( ( ! [X0:$int] : (~$lesseq($sum(1,$sum(X0,1)),X0)) ) <=> ~$spl58),
introduced(sat_splitting_component,[new_symbols(naming,[$spl58])])). fof(f101,plain,( ( ! [X0:$int] : (~$lesseq($sum(1,$sum(X0,1)),X0)) ) | ($spl4 | $spl22 |$spl54)),
inference(forward_demodulation,[],[f97,f45])).
fof(f97,plain,(
( ! [X0:$int] : (~$lesseq($sum($sum(X0,1),1),X0)) ) | ($spl4 |$spl54)),
inference(resolution,[],[f95,f36])).
fof(f96,plain,(
( ! [X0:$int] : (~$lesseq($sum(1,X0),X0)) ) |$spl56),
inference(cnf_transformation,[],[f96_D])).
fof(f96_D,plain,(
( ! [X0:$int] : (~$lesseq($sum(1,X0),X0)) ) <=> ~$spl56),
introduced(sat_splitting_component,[new_symbols(naming,[$spl56])])). fof(f93,plain,( ( ! [X1:$int] : (~$lesseq($sum(1,X1),X1)) ) | ($spl22 |$spl44)),
inference(superposition,[],[f83,f45])).
fof(f92,plain,(
( ! [X0:$int] : (~$lesseq($sum(1,X0),X0)) ) | ($spl22 | $spl44)), inference(superposition,[],[f83,f45])). fof(f95,plain,( ( ! [X1:$int] : ($lesseq(X1,$sum(X1,1))) ) | $spl54), inference(cnf_transformation,[],[f95_D])). fof(f95_D,plain,( ( ! [X1:$int] : ($lesseq(X1,$sum(X1,1))) ) <=> ~$spl54), introduced(sat_splitting_component,[new_symbols(naming,[$spl54])])).
fof(f90,plain,(
( ! [X2:$int] : ($lesseq(X2,$sum(X2,1))) ) | ($spl8 | $spl44)), inference(resolution,[],[f83,f38])). fof(f89,plain,( ( ! [X1:$int] : ($lesseq(X1,$sum(X1,1))) ) | ($spl8 |$spl44)),
inference(resolution,[],[f83,f38])).
fof(f87,plain,(
( ! [X4:$int] : (~$lesseq(1,X4) | ~$lesseq(X4,0)) ) |$spl52),
inference(cnf_transformation,[],[f87_D])).
fof(f87_D,plain,(
( ! [X4:$int] : (~$lesseq(1,X4) | ~$lesseq(X4,0)) ) <=> ~$spl52),
introduced(sat_splitting_component,[new_symbols(naming,[$spl52])])). fof(f82,plain,( ( ! [X4:$int] : (~$lesseq(1,X4) | ~$lesseq(X4,0)) ) | ($spl4 |$spl38)),
inference(superposition,[],[f36,f63])).
fof(f86,plain,(
( ! [X0:$int,X1:$int] : (~$lesseq($sum(1,X0),X1) | ~$lesseq(X1,X0)) ) |$spl50),
inference(cnf_transformation,[],[f86_D])).
fof(f86_D,plain,(
( ! [X0:$int,X1:$int] : (~$lesseq($sum(1,X0),X1) | ~$lesseq(X1,X0)) ) <=> ~$spl50),
introduced(sat_splitting_component,[new_symbols(naming,[$spl50])])). fof(f81,plain,( ( ! [X2:$int,X3:$int] : (~$lesseq($sum(1,X2),X3) | ~$lesseq(X3,X2)) ) | ($spl4 |$spl22)),
inference(superposition,[],[f36,f45])).
fof(f80,plain,(
( ! [X0:$int,X1:$int] : (~$lesseq($sum(1,X0),X1) | ~$lesseq(X1,X0)) ) | ($spl4 | $spl22)), inference(superposition,[],[f36,f45])). fof(f85,plain,( ( ! [X7:$int] : (~$lesseq(0,X7) |$lesseq(1,$sum(X7,1))) ) |$spl48),
inference(cnf_transformation,[],[f85_D])).
fof(f85_D,plain,(
( ! [X7:$int] : (~$lesseq(0,X7) | $lesseq(1,$sum(X7,1))) ) <=> ~$spl48), introduced(sat_splitting_component,[new_symbols(naming,[$spl48])])).
fof(f79,plain,(
( ! [X7:$int] : (~$lesseq(0,X7) | $lesseq(1,$sum(X7,1))) ) | ($spl4 |$spl42)),
inference(resolution,[],[f36,f74])).
fof(f84,plain,(
( ! [X4:$int,X3:$int] : (~$lesseq(X3,X4) |$lesseq(X3,$sum(X4,1))) ) |$spl46),
inference(cnf_transformation,[],[f84_D])).
fof(f84_D,plain,(
( ! [X4:$int,X3:$int] : (~$lesseq(X3,X4) |$lesseq(X3,$sum(X4,1))) ) <=> ~$spl46),
introduced(sat_splitting_component,[new_symbols(naming,[$spl46])])). fof(f78,plain,( ( ! [X6:$int,X5:$int] : (~$lesseq(X5,X6) | $lesseq(X5,$sum(X6,1))) ) | ($spl4 |$spl8)),
inference(resolution,[],[f36,f38])).
fof(f77,plain,(
( ! [X4:$int,X3:$int] : (~$lesseq(X3,X4) |$lesseq(X3,$sum(X4,1))) ) | ($spl4 | $spl8)), inference(resolution,[],[f36,f38])). fof(f83,plain,( ( ! [X2:$int] : (~$lesseq($sum(X2,1),X2)) ) | $spl44), inference(cnf_transformation,[],[f83_D])). fof(f83_D,plain,( ( ! [X2:$int] : (~$lesseq($sum(X2,1),X2)) ) <=> ~$spl44), introduced(sat_splitting_component,[new_symbols(naming,[$spl44])])).
fof(f76,plain,(
( ! [X2:$int] : (~$lesseq($sum(X2,1),X2)) ) | ($spl4 | $spl12)), inference(resolution,[],[f36,f40])). fof(f74,plain,( ( ! [X4:$int] : ($lesseq(1,X4) |$lesseq(X4,0)) ) | $spl42), inference(cnf_transformation,[],[f74_D])). fof(f74_D,plain,( ( ! [X4:$int] : ($lesseq(1,X4) |$lesseq(X4,0)) ) <=> ~$spl42), introduced(sat_splitting_component,[new_symbols(naming,[$spl42])])).
fof(f72,plain,(
( ! [X4:$int] : ($lesseq(1,X4) | $lesseq(X4,0)) ) | ($spl0 | $spl38)), inference(superposition,[],[f34,f63])). fof(f73,plain,( ( ! [X0:$int,X1:$int] : ($lesseq($sum(1,X0),X1) |$lesseq(X1,X0)) ) | $spl40), inference(cnf_transformation,[],[f73_D])). fof(f73_D,plain,( ( ! [X0:$int,X1:$int] : ($lesseq($sum(1,X0),X1) |$lesseq(X1,X0)) ) <=> ~$spl40), introduced(sat_splitting_component,[new_symbols(naming,[$spl40])])).
fof(f71,plain,(
( ! [X2:$int,X3:$int] : ($lesseq($sum(1,X2),X3) | $lesseq(X3,X2)) ) | ($spl0 | $spl22)), inference(superposition,[],[f34,f45])). fof(f70,plain,( ( ! [X0:$int,X1:$int] : ($lesseq($sum(1,X0),X1) |$lesseq(X1,X0)) ) | ($spl0 |$spl22)),
inference(superposition,[],[f34,f45])).
fof(f63,plain,(
( ! [X0:$int] : ($sum(0,X0) = X0) ) | $spl38), inference(cnf_transformation,[],[f63_D])). fof(f63_D,plain,( ( ! [X0:$int] : ($sum(0,X0) = X0) ) <=> ~$spl38),
introduced(sat_splitting_component,[new_symbols(naming,[$spl38])])). fof(f62,plain,( ( ! [X0:$int] : ($sum(0,X0) = X0) ) | ($spl18 | $spl22)), inference(superposition,[],[f43,f45])). fof(f61,plain,( ( ! [X0:$int] : ($sum(0,X0) = X0) ) | ($spl18 | $spl22)), inference(superposition,[],[f43,f45])). fof(f60,plain,( ( ! [X0:$int] : ($sum(0,X0) = X0) ) | ($spl18 | $spl22)), inference(superposition,[],[f45,f43])). fof(f59,plain,( ( ! [X0:$int] : ($sum(0,X0) = X0) ) | ($spl18 | $spl22)), inference(superposition,[],[f45,f43])). fof(f57,plain,($lesseq($sum(3,sK1),sK3) |$spl36),
inference(cnf_transformation,[],[f57_D])).
fof(f57_D,plain,(
$lesseq($sum(3,sK1),sK3) <=> ~$spl36), introduced(sat_splitting_component,[new_symbols(naming,[$spl36])])).
fof(f55,plain,(
$lesseq($sum(3,sK1),sK3) | ($spl22 |$spl32)),
inference(backward_demodulation,[],[f45,f53])).
fof(f54,plain,(
( ! [X4:$int] : (~$lesseq(read(sK0,X4),0) | ~$lesseq(X4,sK2) | ~$lesseq(sK1,X4)) ) | $spl34), inference(cnf_transformation,[],[f54_D])). fof(f54_D,plain,( ( ! [X4:$int] : (~$lesseq(read(sK0,X4),0) | ~$lesseq(X4,sK2) | ~$lesseq(sK1,X4)) ) <=> ~$spl34),
introduced(sat_splitting_component,[new_symbols(naming,[$spl34])])). fof(f30,plain,( ( ! [X4:$int] : (~$lesseq(read(sK0,X4),0) | ~$lesseq(X4,sK2) | ~$lesseq(sK1,X4)) )), inference(cnf_transformation,[],[f25])). fof(f25,plain,( ! [X4 :$int] : (~$lesseq(sK1,X4) | ~$lesseq(X4,sK2) | ~$lesseq(read(sK0,X4),0)) & ($lesseq($sum(sK1,3),sK3) &$lesseq(sK3,sK2) & $lesseq(read(sK0,sK3),0))), inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f24])). fof(f24,plain,( ? [X0 : array,X1 :$int,X2 : $int] : (! [X4 :$int] : (~$lesseq(X1,X4) | ~$lesseq(X4,X2) | ~$lesseq(read(X0,X4),0)) & ? [X3 :$int] : ($lesseq($sum(X1,3),X3) & $lesseq(X3,X2) &$lesseq(read(X0,X3),0)))),
inference(rectify,[],[f23])).
fof(f23,plain,(
? [X0 : array,X1 : $int,X2 :$int] : (! [X3 : $int] : (~$lesseq(X1,X3) | ~$lesseq(X3,X2) | ~$lesseq(read(X0,X3),0)) & ? [X4 : $int] : ($lesseq($sum(X1,3),X4) &$lesseq(X4,X2) & $lesseq(read(X0,X4),0)))), inference(flattening,[],[f22])). fof(f22,plain,( ? [X0 : array,X1 :$int,X2 : $int] : (! [X3 :$int] : ((~$lesseq(X1,X3) | ~$lesseq(X3,X2)) | ~$lesseq(read(X0,X3),0)) & ? [X4 :$int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) &$lesseq(read(X0,X4),0)))),
inference(ennf_transformation,[],[f7])).
fof(f7,plain,(
~! [X0 : array,X1 : $int,X2 :$int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) => ~$lesseq(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq($sum(X1,3),X4) &$lesseq(X4,X2)) => ~$lesseq(read(X0,X4),0)))), inference(evaluation,[],[f4])). fof(f4,negated_conjecture,( ~! [X0 : array,X1 :$int,X2 : $int] : (! [X3 :$int] : (($lesseq(X1,X3) &$lesseq(X3,X2)) => $greater(read(X0,X3),0)) => ! [X4 :$int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) =>$greater(read(X0,X4),0)))),
inference(negated_conjecture,[],[f3])).
fof(f3,conjecture,(
! [X0 : array,X1 : $int,X2 :$int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) =>$greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq($sum(X1,3),X4) &$lesseq(X4,X2)) => $greater(read(X0,X4),0)))), file('Problems/DAT/DAT013=1.p',unknown)). fof(f53,plain,($lesseq($sum(sK1,3),sK3) |$spl32),
inference(cnf_transformation,[],[f53_D])).
fof(f53_D,plain,(
$lesseq($sum(sK1,3),sK3) <=> ~$spl32), introduced(sat_splitting_component,[new_symbols(naming,[$spl32])])).
fof(f31,plain,(
$lesseq($sum(sK1,3),sK3)),
inference(cnf_transformation,[],[f25])).
fof(f51,plain,(
$lesseq(sK3,sK2) |$spl30),
inference(cnf_transformation,[],[f51_D])).
fof(f51_D,plain,(
$lesseq(sK3,sK2) <=> ~$spl30),
introduced(sat_splitting_component,[new_symbols(naming,[$spl30])])). fof(f32,plain,($lesseq(sK3,sK2)),
inference(cnf_transformation,[],[f25])).
fof(f49,plain,(
$lesseq(read(sK0,sK3),0) |$spl28),
inference(cnf_transformation,[],[f49_D])).
fof(f49_D,plain,(
$lesseq(read(sK0,sK3),0) <=> ~$spl28),
introduced(sat_splitting_component,[new_symbols(naming,[$spl28])])). fof(f33,plain,($lesseq(read(sK0,sK3),0)),
inference(cnf_transformation,[],[f25])).
fof(f47,plain,(
( ! [X2:$int,X0,X3:$int,X1:$int] : (read(X0,X2) = read(write(X0,X1,X3),X2) | X1 = X2) ) |$spl26),
inference(cnf_transformation,[],[f47_D])).
fof(f47_D,plain,(
( ! [X2:$int,X0,X3:$int,X1:$int] : (read(X0,X2) = read(write(X0,X1,X3),X2) | X1 = X2) ) <=> ~$spl26),
introduced(sat_splitting_component,[new_symbols(naming,[$spl26])])). fof(f29,plain,( ( ! [X2:$int,X0,X3:$int,X1:$int] : (read(X0,X2) = read(write(X0,X1,X3),X2) | X1 = X2) )),
inference(cnf_transformation,[],[f21])).
fof(f21,plain,(
! [X0 : array,X1 : $int,X2 :$int,X3 : $int] : (X1 = X2 | read(X0,X2) = read(write(X0,X1,X3),X2))), inference(rectify,[],[f2])). fof(f2,axiom,( ! [X3 : array,X4 :$int,X5 : $int,X6 :$int] : (X4 = X5 | read(X3,X5) = read(write(X3,X4,X6),X5))),
file('Problems/DAT/DAT013=1.p',unknown)).
fof(f46,plain,(
( ! [X2:$int,X0,X1:$int] : (read(write(X0,X1,X2),X1) = X2) ) | $spl24), inference(cnf_transformation,[],[f46_D])). fof(f46_D,plain,( ( ! [X2:$int,X0,X1:$int] : (read(write(X0,X1,X2),X1) = X2) ) <=> ~$spl24),
introduced(sat_splitting_component,[new_symbols(naming,[$spl24])])). fof(f28,plain,( ( ! [X2:$int,X0,X1:$int] : (read(write(X0,X1,X2),X1) = X2) )), inference(cnf_transformation,[],[f1])). fof(f1,axiom,( ! [X0 : array,X1 :$int,X2 : $int] : read(write(X0,X1,X2),X1) = X2), file('Problems/DAT/DAT013=1.p',unknown)). fof(f45,plain,( ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) ) |$spl22),
inference(cnf_transformation,[],[f45_D])).
fof(f45_D,plain,(
( ! [X0:$int,X1:$int] : ($sum(X0,X1) =$sum(X1,X0)) ) <=> ~$spl22), introduced(sat_splitting_component,[new_symbols(naming,[$spl22])])).
fof(f8,plain,(
( ! [X0:$int,X1:$int] : ($sum(X0,X1) =$sum(X1,X0)) )),
introduced(theory_axiom,[])).
fof(f44,plain,(
( ! [X2:$int,X0:$int,X1:$int] : ($sum(X0,$sum(X1,X2)) =$sum($sum(X0,X1),X2)) ) |$spl20),
inference(cnf_transformation,[],[f44_D])).
fof(f44_D,plain,(
( ! [X2:$int,X0:$int,X1:$int] : ($sum(X0,$sum(X1,X2)) =$sum($sum(X0,X1),X2)) ) <=> ~$spl20),
introduced(sat_splitting_component,[new_symbols(naming,[$spl20])])). fof(f9,plain,( ( ! [X2:$int,X0:$int,X1:$int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
introduced(theory_axiom,[])).
fof(f43,plain,(
( ! [X0:$int] : ($sum(X0,0) = X0) ) | $spl18), inference(cnf_transformation,[],[f43_D])). fof(f43_D,plain,( ( ! [X0:$int] : ($sum(X0,0) = X0) ) <=> ~$spl18),
introduced(sat_splitting_component,[new_symbols(naming,[$spl18])])). fof(f10,plain,( ( ! [X0:$int] : ($sum(X0,0) = X0) )), introduced(theory_axiom,[])). fof(f42,plain,( ( ! [X0:$int,X1:$int] : ($sum($uminus(X1),$uminus(X0)) = $uminus($sum(X0,X1))) ) | $spl16), inference(cnf_transformation,[],[f42_D])). fof(f42_D,plain,( ( ! [X0:$int,X1:$int] : ($sum($uminus(X1),$uminus(X0)) = $uminus($sum(X0,X1))) ) <=> ~$spl16), introduced(sat_splitting_component,[new_symbols(naming,[$spl16])])).
fof(f11,plain,(
( ! [X0:$int,X1:$int] : ($sum($uminus(X1),$uminus(X0)) =$uminus($sum(X0,X1))) )), introduced(theory_axiom,[])). fof(f41,plain,( ( ! [X0:$int] : (0 = $sum(X0,$uminus(X0))) ) | $spl14), inference(cnf_transformation,[],[f41_D])). fof(f41_D,plain,( ( ! [X0:$int] : (0 = $sum(X0,$uminus(X0))) ) <=> ~$spl14), introduced(sat_splitting_component,[new_symbols(naming,[$spl14])])).
fof(f12,plain,(
( ! [X0:$int] : (0 =$sum(X0,$uminus(X0))) )), introduced(theory_axiom,[])). fof(f40,plain,( ( ! [X0:$int] : ($lesseq(X0,X0)) ) |$spl12),
inference(cnf_transformation,[],[f40_D])).
fof(f40_D,plain,(
( ! [X0:$int] : ($lesseq(X0,X0)) ) <=> ~$spl12), introduced(sat_splitting_component,[new_symbols(naming,[$spl12])])).
fof(f13,plain,(
( ! [X0:$int] : ($lesseq(X0,X0)) )),
introduced(theory_axiom,[])).
fof(f39,plain,(
( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X1,X2) | ~$lesseq(X0,X1) |$lesseq(X0,X2)) ) | $spl10), inference(cnf_transformation,[],[f39_D])). fof(f39_D,plain,( ( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X1,X2) | ~$lesseq(X0,X1) | $lesseq(X0,X2)) ) <=> ~$spl10),
introduced(sat_splitting_component,[new_symbols(naming,[$spl10])])). fof(f14,plain,( ( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X0,X1) | ~$lesseq(X1,X2) | $lesseq(X0,X2)) )), introduced(theory_axiom,[])). fof(f38,plain,( ( ! [X0:$int,X1:$int] : ($lesseq(X0,X1) | $lesseq(X1,X0)) ) |$spl8),
inference(cnf_transformation,[],[f38_D])).
fof(f38_D,plain,(
( ! [X0:$int,X1:$int] : ($lesseq(X0,X1) |$lesseq(X1,X0)) ) <=> ~$spl8), introduced(sat_splitting_component,[new_symbols(naming,[$spl8])])).
fof(f15,plain,(
( ! [X0:$int,X1:$int] : ($lesseq(X0,X1) |$lesseq(X1,X0)) )),
introduced(theory_axiom,[])).
fof(f37,plain,(
( ! [X2:$int,X0:$int,X1:$int] : ($lesseq($sum(X0,X2),$sum(X1,X2)) | ~$lesseq(X0,X1)) ) |$spl6),
inference(cnf_transformation,[],[f37_D])).
fof(f37_D,plain,(
( ! [X2:$int,X0:$int,X1:$int] : ($lesseq($sum(X0,X2),$sum(X1,X2)) | ~$lesseq(X0,X1)) ) <=> ~$spl6),
introduced(sat_splitting_component,[new_symbols(naming,[$spl6])])). fof(f16,plain,( ( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X0,X1) |$lesseq($sum(X0,X2),$sum(X1,X2))) )),
introduced(theory_axiom,[])).
fof(f36,plain,(
( ! [X0:$int,X1:$int] : (~$lesseq($sum(X0,1),X1) | ~$lesseq(X1,X0)) ) |$spl4),
inference(cnf_transformation,[],[f36_D])).
fof(f36_D,plain,(
( ! [X0:$int,X1:$int] : (~$lesseq($sum(X0,1),X1) | ~$lesseq(X1,X0)) ) <=> ~$spl4),
introduced(sat_splitting_component,[new_symbols(naming,[$spl4])])). fof(f18,plain,( ( ! [X0:$int,X1:$int] : (~$lesseq(X1,X0) | ~$lesseq($sum(X0,1),X1)) )),
introduced(theory_axiom,[])).
fof(f35,plain,(
( ! [X0:$int,X1:$int] : (~$lesseq(X1,X0) | ~$lesseq(X0,X1) | X0 = X1) ) | $spl2), inference(cnf_transformation,[],[f35_D])). fof(f35_D,plain,( ( ! [X0:$int,X1:$int] : (~$lesseq(X1,X0) | ~$lesseq(X0,X1) | X0 = X1) ) <=> ~$spl2),
introduced(sat_splitting_component,[new_symbols(naming,[$spl2])])). fof(f19,plain,( ( ! [X0:$int,X1:$int] : (~$lesseq(X1,X0) | ~$lesseq(X0,X1) | X0 = X1) )), introduced(theory_axiom,[])). fof(f34,plain,( ( ! [X0:$int,X1:$int] : ($lesseq($sum(X0,1),X1) |$lesseq(X1,X0)) ) | $spl0), inference(cnf_transformation,[],[f34_D])). fof(f34_D,plain,( ( ! [X0:$int,X1:$int] : ($lesseq($sum(X0,1),X1) |$lesseq(X1,X0)) ) <=> ~$spl0), introduced(sat_splitting_component,[new_symbols(naming,[$spl0])])).
fof(f20,plain,(
( ! [X0:$int,X1:$int] : ($lesseq(X1,X0) |$lesseq(\$sum(X0,1),X1)) )),
introduced(theory_axiom,[])).
% SZS output end Proof for DAT013=1