# Entrants' Sample Solutions

## CVC4 1.5.2

Andrew Reynolds
University of Iowa, USA

### Sample solution for DAT013=1

```% SZS status Theorem for DAT013=1
% SZS output start Proof for DAT013=1
(skolem (let ((_let_0 (* (- 1) X))) (let ((_let_1 (* (- 1) BOUND_VARIABLE_358))) (forall ((U array) (V Int) (W Int) (BOUND_VARIABLE_358 Int)) (or (not (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_358) 1)) )))
( skv_1 skv_2 skv_3 skv_4 )
)
(instantiation (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 (forall ((A \$\$unsorted)) (not (empty A)) )
( skv_1 )
)
(skolem (forall ((A \$\$unsorted)) (empty A) )
( skv_2 )
)
(skolem (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 (forall ((C \$\$unsorted)) (or (not (in C skv_3)) (not (in C skv_5))) )
( skv_6 )
)
(skolem (forall ((C \$\$unsorted)) (not (in C (set_intersection2 skv_3 skv_5))) )
( skv_7 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (= A B) (and (subset A B) (subset B A))) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted) (C \$\$unsorted)) (= (= C (set_union2 A B)) (forall ((D \$\$unsorted)) (= (in D C) (or (in D A) (in D B))) )) )
( skv_3, skv_4, (set_union2 skv_3 skv_4) )
( skv_3, (set_difference skv_4 skv_3), (set_union2 skv_3 (set_difference skv_4 skv_3)) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted) (C \$\$unsorted)) (= (= C (set_intersection2 A B)) (forall ((D \$\$unsorted)) (= (in D C) (and (in D A) (in D B))) )) )
( skv_3, skv_4, (set_intersection2 skv_3 skv_4) )
( skv_3, skv_5, (set_intersection2 skv_3 skv_5) )
( skv_4, skv_5, (set_intersection2 skv_4 skv_5) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted) (C \$\$unsorted)) (= (= C (set_difference A B)) (forall ((D \$\$unsorted)) (= (in D C) (and (in D A) (not (in D B)))) )) )
( skv_3, skv_4, (set_difference skv_3 skv_4) )
( skv_4, skv_3, (set_difference skv_4 skv_3) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (proper_subset A B) (and (subset A B) (not (= A B)))) )
( skv_3, skv_4 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (subset (set_intersection2 A B) A) )
( skv_3, skv_4 )
( skv_3, skv_5 )
( skv_4, skv_5 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (subset (set_difference A B) A) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (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) )
)
(instantiation (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 )
)
(instantiation (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 )
)
(instantiation (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 )
)
(instantiation (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 )
)
(instantiation (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) )
)
(instantiation (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 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (= empty_set (set_difference A B)) (subset A B)) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (disjoint A B)) (disjoint B A)) )
( skv_4, skv_5 )
( skv_5, skv_3 )
)
(instantiation (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) )
)
(instantiation (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 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (forall ((C \$\$unsorted)) (= (in C A) (in C B)) )) (= A B)) )
( empty_set, (set_intersection2 skv_3 skv_5) )
( empty_set, (set_difference skv_4 skv_3) )
( skv_3, skv_4 )
)
(instantiation (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 )
)
(instantiation (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 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted) (BOUND_VARIABLE_802 \$\$unsorted)) (or (not (disjoint A B)) (not (in BOUND_VARIABLE_802 A)) (not (in BOUND_VARIABLE_802 B))) )
( skv_5, skv_4, skv_6 )
)
(instantiation (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 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (subset A B)) (= B (set_union2 A (set_difference B A)))) )
( skv_3, skv_4 )
)
(instantiation (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 )
)
(instantiation (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 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted) (BOUND_VARIABLE_844 \$\$unsorted)) (or (not (in BOUND_VARIABLE_844 (set_intersection2 A B))) (not (disjoint A B))) )
( skv_3, skv_4, skv_6 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (subset A B)) (not (proper_subset B A))) )
( skv_3, skv_4 )
)
(instantiation (forall ((A \$\$unsorted)) (or (not (empty A)) (= empty_set A)) )
( skv_1 )
)
(instantiation (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) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (empty A)) (= A B) (not (empty B))) )
( empty_set, skv_1 )
( skv_1, empty_set )
)
(instantiation (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) )
)
(instantiation (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 actual_world ((_ufmt_1 \$\$unsorted)) Bool true)
; cardinality of \$\$unsorted is 1
(declare-sort \$\$unsorted 0)
; rep: @uc___unsorted_0
; cardinality of it_2_\$\$unsorted is 4
(declare-sort it_2_\$\$unsorted 0)
; rep: @uc_it_2___unsorted_0
; rep: @uc_it_2___unsorted_1
; rep: @uc_it_2___unsorted_2
; rep: @uc_it_2___unsorted_3
(define-fun io_woman_1 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)))
(define-fun io_female_2 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)))
(define-fun io_human_person_3 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)))
(define-fun io_animate_4 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)))
(define-fun io_human_5 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)))
(define-fun io_organism_6 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)))
(define-fun io_living_7 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)))
(define-fun io_impartial_8 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool true)
(define-fun io_entity_9 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (ite (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)) true (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2))))
(define-fun io_mia_forename_10 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_1 \$x2)))
(define-fun io_forename_11 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_1 \$x2)))
(define-fun io_abstraction_12 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_1 \$x2)))
(define-fun io_unisex_13 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (ite (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2)) true (ite (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_1 \$x2)) true (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2)))))
(define-fun io_general_14 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_1 \$x2)))
(define-fun io_nonhuman_15 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_1 \$x2)))
(define-fun io_thing_16 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool true)
(define-fun io_relation_17 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_1 \$x2)))
(define-fun io_relname_18 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_1 \$x2)))
(define-fun io_object_19 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2)))
(define-fun io_nonliving_20 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2)))
(define-fun io_existent_21 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (ite (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)) true (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2))))
(define-fun io_specific_22 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (ite (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2)) true (ite (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_0 \$x2)) true (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2)))))
(define-fun io_substance_matter_23 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2)))
(define-fun io_food_24 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2)))
(define-fun io_beverage_25 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2)))
(define-fun io_shake_beverage_26 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_2 \$x2)))
(define-fun io_order_27 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2)))
(define-fun io_event_28 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2)))
(define-fun io_eventuality_29 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2)))
(define-fun io_nonexistent_30 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2)))
(define-fun io_singleton_31 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool true)
(define-fun io_act_32 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2)))
(define-fun io_of_33 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted) (\$x3 it_2_\$\$unsorted)) Bool true)
(define-fun io_nonreflexive_34 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted)) Bool (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2)))
(define-fun io_agent_35 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted) (\$x3 it_2_\$\$unsorted)) Bool (ite (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2) (= @uc_it_2___unsorted_2 \$x3)) false (ite (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2) (= @uc_it_2___unsorted_1 \$x3)) false (not (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2) (= @uc_it_2___unsorted_3 \$x3))))))
(define-fun io_patient_36 ((\$x1 \$\$unsorted) (\$x2 it_2_\$\$unsorted) (\$x3 it_2_\$\$unsorted)) Bool (not (and (= @uc___unsorted_0 \$x1) (= @uc_it_2___unsorted_3 \$x2) (= @uc_it_2___unsorted_0 \$x3))))
(define-fun io_past_37 ((_ufmt_1 \$\$unsorted) (_ufmt_2 it_2_\$\$unsorted)) Bool true)
% 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 a_holds ((\$x1 \$\$unsorted)) Bool true)
(define-fun a () \$\$unsorted @uc___unsorted_0)
(define-fun b () \$\$unsorted @uc___unsorted_0)
(define-fun an_a_nonce () \$\$unsorted @uc___unsorted_0)
(define-fun bt () \$\$unsorted @uc___unsorted_0)
(define-fun b_holds ((\$x1 \$\$unsorted)) Bool true)
(define-fun t_holds ((\$x1 \$\$unsorted)) Bool true)
(define-fun intruder_holds ((\$x1 \$\$unsorted)) Bool true)
(define-fun an_intruder_nonce () \$\$unsorted @uc___unsorted_0)
; cardinality of \$\$unsorted is 1
(declare-sort \$\$unsorted 0)
; rep: @uc___unsorted_0
; cardinality of it_4_\$\$unsorted is 2
(declare-sort it_4_\$\$unsorted 0)
; rep: @uc_it_4___unsorted_0
; rep: @uc_it_4___unsorted_1
(define-fun io_key_3 ((\$x1 it_4_\$\$unsorted) (\$x2 it_4_\$\$unsorted)) \$\$unsorted @uc___unsorted_0)
(define-fun io_party_of_protocol_5 ((\$x1 it_4_\$\$unsorted)) Bool true)
; cardinality of it_19_\$\$unsorted is 1
(declare-sort it_19_\$\$unsorted 0)
; rep: @uc_it_19___unsorted_0
(define-fun io_pair_8 ((\$x1 it_4_\$\$unsorted) (\$x2 it_4_\$\$unsorted)) it_4_\$\$unsorted @uc_it_4___unsorted_0)
(define-fun io_sent_9 ((\$x1 it_4_\$\$unsorted) (\$x2 it_4_\$\$unsorted) (\$x3 it_4_\$\$unsorted)) it_19_\$\$unsorted @uc_it_19___unsorted_0)
(define-fun io_message_10 ((\$x1 it_19_\$\$unsorted)) Bool true)
(define-fun io_a_stored_11 ((\$x1 it_4_\$\$unsorted)) Bool true)
(define-fun io_quadruple_12 ((\$x1 it_4_\$\$unsorted) (\$x2 it_4_\$\$unsorted) (\$x3 it_4_\$\$unsorted) (\$x4 it_4_\$\$unsorted)) it_4_\$\$unsorted @uc_it_4___unsorted_0)
(define-fun io_encrypt_13 ((\$x1 it_4_\$\$unsorted) (\$x2 it_4_\$\$unsorted)) it_4_\$\$unsorted @uc_it_4___unsorted_0)
(define-fun io_triple_14 ((\$x1 it_4_\$\$unsorted) (\$x2 it_4_\$\$unsorted) (\$x3 it_4_\$\$unsorted)) it_4_\$\$unsorted @uc_it_4___unsorted_0)
(define-fun io_fresh_to_b_16 ((\$x1 it_4_\$\$unsorted)) Bool true)
(define-fun io_generate_b_nonce_17 ((\$x1 it_4_\$\$unsorted)) it_4_\$\$unsorted @uc_it_4___unsorted_0)
(define-fun io_generate_expiration_time_18 ((\$x1 it_4_\$\$unsorted)) it_4_\$\$unsorted @uc_it_4___unsorted_0)
(define-fun io_b_stored_19 ((\$x1 it_4_\$\$unsorted)) Bool true)
(define-fun io_a_key_20 ((\$x1 it_4_\$\$unsorted)) Bool (= @uc_it_4___unsorted_1 \$x1))
(define-fun io_a_nonce_21 ((\$x1 it_4_\$\$unsorted)) Bool (= @uc_it_4___unsorted_0 \$x1))
(define-fun io_generate_key_22 ((\$x1 it_4_\$\$unsorted)) it_4_\$\$unsorted @uc_it_4___unsorted_1)
(define-fun io_intruder_message_23 ((\$x1 it_4_\$\$unsorted)) Bool true)
(define-fun io_fresh_intruder_nonce_25 ((\$x1 it_4_\$\$unsorted)) Bool true)
(define-fun io_generate_intruder_nonce_26 ((\$x1 it_4_\$\$unsorted)) it_4_\$\$unsorted @uc_it_4___unsorted_0)
% SZS output end FiniteModel for SWV017+1
```

## E 2.1

Stephan Schulz
DHBW Stuttgart, Germany

### Sample solution for SEU140+2

```# SZS status Theorem
# SZS output start CNFRefutation
fof(t63_xboole_1, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t63_xboole_1)).
fof(symmetry_r1_xboole_0, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', symmetry_r1_xboole_0)).
fof(t1_xboole_1, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X2,X3))=>subset(X1,X3))), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t1_xboole_1)).
fof(t40_xboole_1, lemma, (![X1]:![X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t40_xboole_1)).
fof(commutativity_k2_xboole_0, axiom, (![X1]:![X2]:set_union2(X1,X2)=set_union2(X2,X1)), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', commutativity_k2_xboole_0)).
fof(t2_boole, axiom, (![X1]:set_intersection2(X1,empty_set)=empty_set), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t2_boole)).
fof(t48_xboole_1, lemma, (![X1]:![X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t48_xboole_1)).
fof(t3_xboole_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/SystemOnTPTP10036/SEU140+2.tptp', t3_xboole_0)).
fof(d4_xboole_0, axiom, (![X1]:![X2]:![X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2)))))), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', d4_xboole_0)).
fof(l32_xboole_1, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', l32_xboole_1)).
fof(d7_xboole_0, axiom, (![X1]:![X2]:(disjoint(X1,X2)<=>set_intersection2(X1,X2)=empty_set)), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', d7_xboole_0)).
fof(t39_xboole_1, lemma, (![X1]:![X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t39_xboole_1)).
fof(t3_boole, axiom, (![X1]:set_difference(X1,empty_set)=X1), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t3_boole)).
fof(commutativity_k3_xboole_0, axiom, (![X1]:![X2]:set_intersection2(X1,X2)=set_intersection2(X2,X1)), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', commutativity_k3_xboole_0)).
fof(t36_xboole_1, lemma, (![X1]:![X2]:subset(set_difference(X1,X2),X1)), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t36_xboole_1)).
fof(t12_xboole_1, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_union2(X1,X2)=X2)), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t12_xboole_1)).
fof(t1_boole, axiom, (![X1]:set_union2(X1,empty_set)=X1), file('/tmp/SystemOnTPTP10036/SEU140+2.tptp', t1_boole)).
fof(c_0_17, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
fof(c_0_18, plain, (![X3]:![X4]:(~disjoint(X3,X4)|disjoint(X4,X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])).
fof(c_0_19, 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_17])])])).
fof(c_0_20, lemma, (![X4]:![X5]:![X6]:((~subset(X4,X5)|~subset(X5,X6))|subset(X4,X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])).
fof(c_0_21, lemma, (![X3]:![X4]:set_difference(set_union2(X3,X4),X4)=set_difference(X3,X4)), inference(variable_rename,[status(thm)],[t40_xboole_1])).
fof(c_0_22, plain, (![X3]:![X4]:set_union2(X3,X4)=set_union2(X4,X3)), inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0])).
fof(c_0_23, plain, (![X2]:set_intersection2(X2,empty_set)=empty_set), inference(variable_rename,[status(thm)],[t2_boole])).
fof(c_0_24, lemma, (![X3]:![X4]:set_difference(X3,set_difference(X3,X4))=set_intersection2(X3,X4)), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_25, lemma, (![X4]:![X5]:![X4]:![X5]:![X7]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X7,X4)|~in(X7,X5))|~disjoint(X4,X5)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])])).
cnf(c_0_26,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_27,negated_conjecture,(disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_28, plain, (![X5]:![X6]:![X7]:![X8]:![X8]:![X5]:![X6]:![X7]:(((((in(X8,X5)|~in(X8,X7))|X7!=set_difference(X5,X6))&((~in(X8,X6)|~in(X8,X7))|X7!=set_difference(X5,X6)))&(((~in(X8,X5)|in(X8,X6))|in(X8,X7))|X7!=set_difference(X5,X6)))&(((~in(esk5_3(X5,X6,X7),X7)|(~in(esk5_3(X5,X6,X7),X5)|in(esk5_3(X5,X6,X7),X6)))|X7=set_difference(X5,X6))&(((in(esk5_3(X5,X6,X7),X5)|in(esk5_3(X5,X6,X7),X7))|X7=set_difference(X5,X6))&((~in(esk5_3(X5,X6,X7),X6)|in(esk5_3(X5,X6,X7),X7))|X7=set_difference(X5,X6)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_xboole_0])])])])])])])])).
fof(c_0_29, lemma, (![X3]:![X4]:![X3]:![X4]:((set_difference(X3,X4)!=empty_set|subset(X3,X4))&(~subset(X3,X4)|set_difference(X3,X4)=empty_set))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])])])).
cnf(c_0_30,lemma,(subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_20])).
cnf(c_0_31,negated_conjecture,(subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_32, plain, (![X3]:![X4]:![X3]:![X4]:((~disjoint(X3,X4)|set_intersection2(X3,X4)=empty_set)&(set_intersection2(X3,X4)!=empty_set|disjoint(X3,X4)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])])])).
cnf(c_0_33,lemma,(set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_34,plain,(set_union2(X1,X2)=set_union2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_22])).
fof(c_0_35, lemma, (![X3]:![X4]:set_union2(X3,set_difference(X4,X3))=set_union2(X3,X4)), inference(variable_rename,[status(thm)],[t39_xboole_1])).
cnf(c_0_36,plain,(set_intersection2(X1,empty_set)=empty_set), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_37,lemma,(set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
fof(c_0_38, plain, (![X2]:set_difference(X2,empty_set)=X2), inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_39,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_40,negated_conjecture,(disjoint(esk13_0,esk12_0)), inference(spm,[status(thm)],[c_0_26, c_0_27])).
cnf(c_0_41,plain,(in(X4,X2)|X1!=set_difference(X2,X3)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_28])).
fof(c_0_42, plain, (![X3]:![X4]:set_intersection2(X3,X4)=set_intersection2(X4,X3)), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])).
cnf(c_0_43,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_44,negated_conjecture,(subset(X1,esk12_0)|~subset(X1,esk11_0)), inference(spm,[status(thm)],[c_0_30, c_0_31])).
fof(c_0_45, lemma, (![X3]:![X4]:subset(set_difference(X3,X4),X3)), inference(variable_rename,[status(thm)],[t36_xboole_1])).
fof(c_0_46, lemma, (![X3]:![X4]:(~subset(X3,X4)|set_union2(X3,X4)=X4)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])).
cnf(c_0_47,plain,(disjoint(X1,X2)|set_intersection2(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_48,lemma,(set_difference(set_union2(X1,X2),X1)=set_difference(X2,X1)), inference(spm,[status(thm)],[c_0_33, c_0_34])).
cnf(c_0_49,lemma,(set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_35])).
cnf(c_0_50,plain,(set_difference(X1,set_difference(X1,empty_set))=empty_set), inference(rw,[status(thm)],[c_0_36, c_0_37])).
cnf(c_0_51,plain,(set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_38])).
cnf(c_0_52,negated_conjecture,(~in(X1,esk12_0)|~in(X1,esk13_0)), inference(spm,[status(thm)],[c_0_39, c_0_40])).
cnf(c_0_53,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_54,plain,(in(X1,X2)|~in(X1,set_difference(X2,X3))), inference(er,[status(thm)],[c_0_41])).
cnf(c_0_55,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_56,plain,(set_intersection2(X1,X2)=set_intersection2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_57,lemma,(set_difference(X1,esk12_0)=empty_set|~subset(X1,esk11_0)), inference(spm,[status(thm)],[c_0_43, c_0_44])).
cnf(c_0_58,lemma,(subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_59,plain,(set_intersection2(X1,X2)=empty_set|~disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_32])).
fof(c_0_60, plain, (![X2]:set_union2(X2,empty_set)=X2), inference(variable_rename,[status(thm)],[t1_boole])).
cnf(c_0_61,lemma,(set_union2(X1,X2)=X2|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_62,plain,(disjoint(X1,X2)|set_difference(X1,set_difference(X1,X2))!=empty_set), inference(rw,[status(thm)],[c_0_47, c_0_37])).
cnf(c_0_63,lemma,(set_difference(set_difference(X1,X2),X2)=set_difference(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_48])).
cnf(c_0_64,plain,(set_difference(X1,X1)=empty_set), inference(rw,[status(thm)],[c_0_50, c_0_51])).
cnf(c_0_65,lemma,(disjoint(X1,esk13_0)|~in(esk9_2(X1,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_52, c_0_53])).
cnf(c_0_66,lemma,(disjoint(set_difference(X1,X2),X3)|in(esk9_2(set_difference(X1,X2),X3),X1)), inference(spm,[status(thm)],[c_0_54, c_0_55])).
cnf(c_0_67,plain,(set_difference(X1,set_difference(X1,X2))=set_difference(X2,set_difference(X2,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_37]), c_0_37])).
cnf(c_0_68,lemma,(set_difference(set_difference(esk11_0,X1),esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_57, c_0_58])).
cnf(c_0_69,plain,(set_difference(X1,set_difference(X1,X2))=empty_set|~disjoint(X1,X2)), inference(rw,[status(thm)],[c_0_59, c_0_37])).
cnf(c_0_70,plain,(set_union2(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_60])).
cnf(c_0_71,lemma,(set_union2(X1,set_difference(X1,X2))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_58]), c_0_34])).
cnf(c_0_72,lemma,(disjoint(set_difference(X1,X2),X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_64])])).
cnf(c_0_73,lemma,(disjoint(set_difference(esk12_0,X1),esk13_0)), inference(spm,[status(thm)],[c_0_65, c_0_66])).
cnf(c_0_74,lemma,(set_difference(esk12_0,set_difference(esk12_0,set_difference(esk11_0,X1)))=set_difference(esk11_0,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_51])).
cnf(c_0_75,lemma,(set_difference(X1,X2)=X1|~disjoint(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_69]), c_0_70]), c_0_34]), c_0_71])).
cnf(c_0_76,lemma,(disjoint(X1,set_difference(X2,X1))), inference(spm,[status(thm)],[c_0_26, c_0_72])).
cnf(c_0_77,lemma,(disjoint(set_difference(esk11_0,X1),esk13_0)), inference(spm,[status(thm)],[c_0_73, c_0_74])).
cnf(c_0_78,lemma,(set_difference(X1,set_difference(X2,X1))=X1), inference(spm,[status(thm)],[c_0_75, c_0_76])).
cnf(c_0_79,negated_conjecture,(~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_80,lemma,(\$false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for NLP042+1

```# SZS status CounterSatisfiable
# SZS output start Saturation
fof(ax26, axiom, (![X1]:![X2]:(beverage(X1,X2)=>food(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax26)).
fof(ax27, axiom, (![X1]:![X2]:(shake_beverage(X1,X2)=>beverage(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax27)).
fof(co1, 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_6.4.0_FLAT/NLP042+1.p', co1)).
fof(ax41, axiom, (![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax41)).
fof(ax11, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>general(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax11)).
fof(ax15, axiom, (![X1]:![X2]:(relname(X1,X2)=>relation(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax15)).
fof(ax16, axiom, (![X1]:![X2]:(forename(X1,X2)=>relname(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax16)).
fof(ax42, axiom, (![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax42)).
fof(ax1, axiom, (![X1]:![X2]:(woman(X1,X2)=>female(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax1)).
fof(ax25, axiom, (![X1]:![X2]:(food(X1,X2)=>substance_matter(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax25)).
fof(ax6, axiom, (![X1]:![X2]:(organism(X1,X2)=>entity(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax6)).
fof(ax7, axiom, (![X1]:![X2]:(human_person(X1,X2)=>organism(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax7)).
fof(ax8, axiom, (![X1]:![X2]:(woman(X1,X2)=>human_person(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax8)).
fof(ax38, axiom, (![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax38)).
fof(ax30, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>nonexistent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax30)).
fof(ax31, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>specific(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax31)).
fof(ax34, axiom, (![X1]:![X2]:(event(X1,X2)=>eventuality(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax34)).
fof(ax21, axiom, (![X1]:![X2]:(entity(X1,X2)=>specific(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax21)).
fof(ax14, axiom, (![X1]:![X2]:(relation(X1,X2)=>abstraction(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax14)).
fof(ax24, axiom, (![X1]:![X2]:(substance_matter(X1,X2)=>object(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax24)).
fof(ax40, axiom, (![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax40)).
fof(ax4, axiom, (![X1]:![X2]:(organism(X1,X2)=>living(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax4)).
fof(ax37, axiom, (![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax37)).
fof(ax2, axiom, (![X1]:![X2]:(human_person(X1,X2)=>animate(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax2)).
fof(ax39, axiom, (![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax39)).
fof(ax12, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>nonhuman(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax12)).
fof(ax44, axiom, (![X1]:![X2]:![X3]:![X4]:(((nonreflexive(X1,X2)&agent(X1,X2,X3))&patient(X1,X2,X4))=>X3!=X4)), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax44)).
fof(ax20, axiom, (![X1]:![X2]:(entity(X1,X2)=>existent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax20)).
fof(ax10, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax10)).
fof(ax43, 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_6.4.0_FLAT/NLP042+1.p', ax43)).
fof(ax19, axiom, (![X1]:![X2]:(object(X1,X2)=>nonliving(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax19)).
fof(ax3, axiom, (![X1]:![X2]:(human_person(X1,X2)=>human(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax3)).
fof(ax29, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax29)).
fof(ax17, axiom, (![X1]:![X2]:(object(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax17)).
fof(ax23, axiom, (![X1]:![X2]:(object(X1,X2)=>entity(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax23)).
fof(ax32, axiom, (![X1]:![X2]:(thing(X1,X2)=>singleton(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax32)).
fof(ax33, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax33)).
fof(ax13, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax13)).
fof(ax22, axiom, (![X1]:![X2]:(entity(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax22)).
fof(ax18, axiom, (![X1]:![X2]:(object(X1,X2)=>impartial(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax18)).
fof(ax5, axiom, (![X1]:![X2]:(organism(X1,X2)=>impartial(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax5)).
fof(ax36, axiom, (![X1]:![X2]:(order(X1,X2)=>act(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax36)).
fof(ax35, axiom, (![X1]:![X2]:(act(X1,X2)=>event(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax35)).
fof(ax28, axiom, (![X1]:![X2]:(order(X1,X2)=>event(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax28)).
fof(ax9, axiom, (![X1]:![X2]:(mia_forename(X1,X2)=>forename(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax9)).
fof(c_0_45, plain, (![X3]:![X4]:(~beverage(X3,X4)|food(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])).
fof(c_0_46, plain, (![X3]:![X4]:(~shake_beverage(X3,X4)|beverage(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])).
fof(c_0_47, 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)],[co1])).
fof(c_0_48, plain, (![X3]:![X4]:(~specific(X3,X4)|~general(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax41])])])).
fof(c_0_49, plain, (![X3]:![X4]:(~abstraction(X3,X4)|general(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])).
fof(c_0_50, plain, (![X3]:![X4]:(~relname(X3,X4)|relation(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])).
fof(c_0_51, plain, (![X3]:![X4]:(~forename(X3,X4)|relname(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])).
fof(c_0_52, plain, (![X3]:![X4]:(~unisex(X3,X4)|~female(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax42])])])).
fof(c_0_53, plain, (![X3]:![X4]:(~woman(X3,X4)|female(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])).
fof(c_0_54, plain, (![X3]:![X4]:(~food(X3,X4)|substance_matter(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])).
cnf(c_0_55,plain,(food(X1,X2)|~beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_45]), ['final']).
cnf(c_0_56,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46]), ['final']).
fof(c_0_57, plain, (![X3]:![X4]:(~organism(X3,X4)|entity(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])).
fof(c_0_58, plain, (![X3]:![X4]:(~human_person(X3,X4)|organism(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])).
fof(c_0_59, plain, (![X3]:![X4]:(~woman(X3,X4)|human_person(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])).
fof(c_0_60, 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])])])).
fof(c_0_61, plain, (![X3]:![X4]:(~existent(X3,X4)|~nonexistent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax38])])])).
fof(c_0_62, plain, (![X3]:![X4]:(~eventuality(X3,X4)|nonexistent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])])).
cnf(c_0_63,plain,(~general(X1,X2)|~specific(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
cnf(c_0_64,plain,(general(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_49]), ['final']).
fof(c_0_65, plain, (![X3]:![X4]:(~eventuality(X3,X4)|specific(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])])).
fof(c_0_66, plain, (![X3]:![X4]:(~event(X3,X4)|eventuality(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax34])])).
fof(c_0_67, plain, (![X3]:![X4]:(~entity(X3,X4)|specific(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])).
fof(c_0_68, plain, (![X3]:![X4]:(~relation(X3,X4)|abstraction(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax14])])).
cnf(c_0_69,plain,(relation(X1,X2)|~relname(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_50]), ['final']).
cnf(c_0_70,plain,(relname(X1,X2)|~forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_51]), ['final']).
cnf(c_0_71,plain,(~female(X1,X2)|~unisex(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_52]), ['final']).
cnf(c_0_72,plain,(female(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_53]), ['final']).
fof(c_0_73, plain, (![X3]:![X4]:(~substance_matter(X3,X4)|object(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])])).
cnf(c_0_74,plain,(substance_matter(X1,X2)|~food(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_54]), ['final']).
cnf(c_0_75,plain,(food(X1,X2)|~shake_beverage(X1,X2)), inference(spm,[status(thm)],[c_0_55, c_0_56]), ['final']).
cnf(c_0_76,plain,(entity(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_57]), ['final']).
cnf(c_0_77,plain,(organism(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_58]), ['final']).
cnf(c_0_78,plain,(human_person(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_59]), ['final']).
cnf(c_0_79,negated_conjecture,(woman(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
fof(c_0_80, plain, (![X3]:![X4]:(~nonliving(X3,X4)|~living(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax40])])])).
fof(c_0_81, plain, (![X3]:![X4]:(~organism(X3,X4)|living(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])).
fof(c_0_82, plain, (![X3]:![X4]:(~animate(X3,X4)|~nonliving(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax37])])])).
fof(c_0_83, plain, (![X3]:![X4]:(~human_person(X3,X4)|animate(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])).
fof(c_0_84, plain, (![X3]:![X4]:(~nonhuman(X3,X4)|~human(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax39])])])).
fof(c_0_85, plain, (![X3]:![X4]:(~abstraction(X3,X4)|nonhuman(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])).
fof(c_0_86, 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)],[ax44])])).
cnf(c_0_87,plain,(~nonexistent(X1,X2)|~existent(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_61]), ['final']).
cnf(c_0_88,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_62]), ['final']).
fof(c_0_89, plain, (![X3]:![X4]:(~entity(X3,X4)|existent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])).
cnf(c_0_90,plain,(~specific(X1,X2)|~abstraction(X1,X2)), inference(spm,[status(thm)],[c_0_63, c_0_64]), ['final']).
cnf(c_0_91,plain,(specific(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_65]), ['final']).
cnf(c_0_92,plain,(eventuality(X1,X2)|~event(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_66]), ['final']).
cnf(c_0_93,negated_conjecture,(event(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_94,plain,(specific(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_95,plain,(abstraction(X1,X2)|~relation(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_68]), ['final']).
cnf(c_0_96,plain,(relation(X1,X2)|~forename(X1,X2)), inference(spm,[status(thm)],[c_0_69, c_0_70]), ['final']).
cnf(c_0_97,plain,(~unisex(X1,X2)|~woman(X1,X2)), inference(spm,[status(thm)],[c_0_71, c_0_72]), ['final']).
fof(c_0_98, plain, (![X3]:![X4]:(~abstraction(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax10])])).
cnf(c_0_99,plain,(object(X1,X2)|~substance_matter(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_73]), ['final']).
cnf(c_0_100,plain,(substance_matter(X1,X2)|~shake_beverage(X1,X2)), inference(spm,[status(thm)],[c_0_74, c_0_75]), ['final']).
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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])])])])).
cnf(c_0_102,plain,(entity(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_76, c_0_77]), ['final']).
cnf(c_0_103,negated_conjecture,(human_person(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_78, c_0_79]), ['final']).
cnf(c_0_104,plain,(~living(X1,X2)|~nonliving(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_80]), ['final']).
cnf(c_0_105,plain,(living(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_81]), ['final']).
fof(c_0_106, plain, (![X3]:![X4]:(~object(X3,X4)|nonliving(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])).
cnf(c_0_107,plain,(~nonliving(X1,X2)|~animate(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_82]), ['final']).
cnf(c_0_108,plain,(animate(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_83]), ['final']).
cnf(c_0_109,plain,(~human(X1,X2)|~nonhuman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_84]), ['final']).
cnf(c_0_110,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_85]), ['final']).
fof(c_0_111, plain, (![X3]:![X4]:(~human_person(X3,X4)|human(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])).
cnf(c_0_112,plain,(X1!=X2|~patient(X3,X4,X2)|~agent(X3,X4,X1)|~nonreflexive(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_86])).
cnf(c_0_113,plain,(~eventuality(X1,X2)|~existent(X1,X2)), inference(spm,[status(thm)],[c_0_87, c_0_88]), ['final']).
cnf(c_0_114,plain,(existent(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_89]), ['final']).
cnf(c_0_115,plain,(~eventuality(X1,X2)|~abstraction(X1,X2)), inference(spm,[status(thm)],[c_0_90, c_0_91]), ['final']).
cnf(c_0_116,negated_conjecture,(eventuality(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_92, c_0_93]), ['final']).
cnf(c_0_117,plain,(~abstraction(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_90, c_0_94]), ['final']).
cnf(c_0_118,plain,(abstraction(X1,X2)|~forename(X1,X2)), inference(spm,[status(thm)],[c_0_95, c_0_96]), ['final']).
fof(c_0_119, plain, (![X3]:![X4]:(~eventuality(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])).
fof(c_0_120, plain, (![X3]:![X4]:(~object(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax17])])).
cnf(c_0_121,negated_conjecture,(~unisex(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_97, c_0_79]), ['final']).
cnf(c_0_122,plain,(unisex(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_98]), ['final']).
fof(c_0_123, plain, (![X3]:![X4]:(~object(X3,X4)|entity(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])).
cnf(c_0_124,plain,(object(X1,X2)|~shake_beverage(X1,X2)), inference(spm,[status(thm)],[c_0_99, c_0_100]), ['final']).
cnf(c_0_125,negated_conjecture,(shake_beverage(esk1_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_126,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]), ['final']).
cnf(c_0_127,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_128,negated_conjecture,(forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_129,negated_conjecture,(entity(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_102, c_0_103]), ['final']).
fof(c_0_130, plain, (![X3]:![X4]:(~thing(X3,X4)|singleton(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax32])])).
cnf(c_0_131,plain,(~nonliving(X1,X2)|~organism(X1,X2)), inference(spm,[status(thm)],[c_0_104, c_0_105]), ['final']).
cnf(c_0_132,plain,(nonliving(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_106]), ['final']).
cnf(c_0_133,plain,(~nonliving(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_107, c_0_108]), ['final']).
fof(c_0_134, plain, (![X3]:![X4]:(~eventuality(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax33])])).
fof(c_0_135, plain, (![X3]:![X4]:(~abstraction(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax13])])).
fof(c_0_136, plain, (![X3]:![X4]:(~entity(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])])).
cnf(c_0_137,plain,(~abstraction(X1,X2)|~human(X1,X2)), inference(spm,[status(thm)],[c_0_109, c_0_110]), ['final']).
cnf(c_0_138,plain,(human(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_111]), ['final']).
fof(c_0_139, plain, (![X3]:![X4]:(~object(X3,X4)|impartial(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])).
fof(c_0_140, plain, (![X3]:![X4]:(~organism(X3,X4)|impartial(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])).
fof(c_0_141, plain, (![X3]:![X4]:(~order(X3,X4)|act(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])).
fof(c_0_142, plain, (![X3]:![X4]:(~act(X3,X4)|event(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax35])])).
fof(c_0_143, plain, (![X3]:![X4]:(~order(X3,X4)|event(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])).
fof(c_0_144, plain, (![X3]:![X4]:(~mia_forename(X3,X4)|forename(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9])])).
cnf(c_0_145,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)), inference(er,[status(thm)],[c_0_112]), ['final']).
cnf(c_0_146,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_147,negated_conjecture,(nonreflexive(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_148,plain,(~eventuality(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_113, c_0_114]), ['final']).
cnf(c_0_149,negated_conjecture,(~abstraction(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_115, c_0_116]), ['final']).
cnf(c_0_150,plain,(~forename(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_117, c_0_118]), ['final']).
cnf(c_0_151,plain,(unisex(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_119]), ['final']).
cnf(c_0_152,plain,(unisex(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_120]), ['final']).
cnf(c_0_153,negated_conjecture,(~abstraction(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_121, c_0_122]), ['final']).
cnf(c_0_154,plain,(entity(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_123]), ['final']).
cnf(c_0_155,negated_conjecture,(object(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_124, c_0_125]), ['final']).
cnf(c_0_156,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_126, c_0_127]), c_0_128]), c_0_129])]), ['final']).
cnf(c_0_157,plain,(singleton(X1,X2)|~thing(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_130]), ['final']).
cnf(c_0_158,plain,(~object(X1,X2)|~organism(X1,X2)), inference(spm,[status(thm)],[c_0_131, c_0_132]), ['final']).
cnf(c_0_159,plain,(~object(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_133, c_0_132]), ['final']).
cnf(c_0_160,plain,(thing(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_134]), ['final']).
cnf(c_0_161,plain,(thing(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_135]), ['final']).
cnf(c_0_162,plain,(thing(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_136]), ['final']).
cnf(c_0_163,plain,(~abstraction(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_137, c_0_138]), ['final']).
cnf(c_0_164,plain,(impartial(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_139]), ['final']).
cnf(c_0_165,plain,(impartial(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_140]), ['final']).
cnf(c_0_166,plain,(act(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_141]), ['final']).
cnf(c_0_167,plain,(event(X1,X2)|~act(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_142]), ['final']).
cnf(c_0_168,plain,(event(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_143]), ['final']).
cnf(c_0_169,plain,(forename(X1,X2)|~mia_forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_144]), ['final']).
cnf(c_0_170,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_146]), c_0_147])]), ['final']).
cnf(c_0_171,negated_conjecture,(~entity(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_148, c_0_116]), ['final']).
cnf(c_0_172,negated_conjecture,(~forename(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_149, c_0_118]), ['final']).
cnf(c_0_173,negated_conjecture,(~entity(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_150, c_0_128]), ['final']).
cnf(c_0_174,negated_conjecture,(~eventuality(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_121, c_0_151]), ['final']).
cnf(c_0_175,negated_conjecture,(~object(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_121, c_0_152]), ['final']).
cnf(c_0_176,negated_conjecture,(~forename(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_153, c_0_118]), ['final']).
cnf(c_0_177,negated_conjecture,(entity(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_154, c_0_155]), ['final']).
cnf(c_0_178,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_179,negated_conjecture,(past(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_180,negated_conjecture,(order(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_181,negated_conjecture,(mia_forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_182,negated_conjecture,(actual_world(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
# SZS output end Saturation
```

### Sample solution for SWV017+1

```# SZS status Satisfiable
# SZS output start Saturation
fof(b_creates_freash_nonces_in_time, 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_6.4.0_FLAT/SWV017+1.p', b_creates_freash_nonces_in_time)).
fof(intruder_message_sent, 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_6.4.0_FLAT/SWV017+1.p', intruder_message_sent)).
fof(t_holds_key_bt_for_b, axiom, (t_holds(key(bt,b))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', t_holds_key_bt_for_b)).
fof(intruder_can_record, axiom, (![X1]:![X2]:![X3]:(message(sent(X1,X2,X3))=>intruder_message(X3))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', intruder_can_record)).
fof(a_sent_message_i_to_b, axiom, (message(sent(a,b,pair(a,an_a_nonce)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', a_sent_message_i_to_b)).
fof(nonce_a_is_fresh_to_b, axiom, (fresh_to_b(an_a_nonce)), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', nonce_a_is_fresh_to_b)).
fof(b_is_party_of_protocol, axiom, (party_of_protocol(b)), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', b_is_party_of_protocol)).
fof(intruder_composes_pairs, axiom, (![X1]:![X2]:((intruder_message(X1)&intruder_message(X2))=>intruder_message(pair(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', intruder_composes_pairs)).
fof(t_holds_key_at_for_a, axiom, (t_holds(key(at,a))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', t_holds_key_at_for_a)).
fof(intruder_decomposes_triples, axiom, (![X1]:![X2]:![X3]:(intruder_message(triple(X1,X2,X3))=>((intruder_message(X1)&intruder_message(X2))&intruder_message(X3)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', intruder_decomposes_triples)).
fof(a_stored_message_i, axiom, (a_stored(pair(b,an_a_nonce))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', a_stored_message_i)).
fof(an_a_nonce_is_a_nonce, axiom, (a_nonce(an_a_nonce)), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', an_a_nonce_is_a_nonce)).
fof(t_is_party_of_protocol, axiom, (party_of_protocol(t)), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', t_is_party_of_protocol)).
fof(intruder_composes_triples, axiom, (![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))=>intruder_message(triple(X1,X2,X3)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', intruder_composes_triples)).
fof(b_accepts_secure_session_key, 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_6.4.0_FLAT/SWV017+1.p', b_accepts_secure_session_key)).
fof(a_is_party_of_protocol, axiom, (party_of_protocol(a)), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', a_is_party_of_protocol)).
fof(intruder_key_encrypts, 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_6.4.0_FLAT/SWV017+1.p', intruder_key_encrypts)).
fof(intruder_holds_key, axiom, (![X2]:![X3]:((intruder_message(X2)&party_of_protocol(X3))=>intruder_holds(key(X2,X3)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', intruder_holds_key)).
fof(intruder_decomposes_pairs, axiom, (![X1]:![X2]:(intruder_message(pair(X1,X2))=>(intruder_message(X1)&intruder_message(X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', intruder_decomposes_pairs)).
fof(generated_keys_are_keys, axiom, (![X1]:a_key(generate_key(X1))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', generated_keys_are_keys)).
fof(fresh_intruder_nonces_are_fresh_to_b, axiom, (![X1]:(fresh_intruder_nonce(X1)=>(fresh_to_b(X1)&intruder_message(X1)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', fresh_intruder_nonces_are_fresh_to_b)).
fof(can_generate_more_fresh_intruder_nonces, axiom, (![X1]:(fresh_intruder_nonce(X1)=>fresh_intruder_nonce(generate_intruder_nonce(X1)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', can_generate_more_fresh_intruder_nonces)).
fof(intruder_interception, 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_6.4.0_FLAT/SWV017+1.p', intruder_interception)).
fof(nothing_is_a_nonce_and_a_key, axiom, (![X1]:~((a_key(X1)&a_nonce(X1)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', nothing_is_a_nonce_and_a_key)).
fof(generated_keys_are_not_nonces, axiom, (![X1]:~(a_nonce(generate_key(X1)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', generated_keys_are_not_nonces)).
fof(generated_times_and_nonces_are_nonces, axiom, (![X1]:(a_nonce(generate_expiration_time(X1))&a_nonce(generate_b_nonce(X1)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', generated_times_and_nonces_are_nonces)).
fof(an_intruder_nonce_is_a_fresh_intruder_nonce, axiom, (fresh_intruder_nonce(an_intruder_nonce)), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', an_intruder_nonce_is_a_fresh_intruder_nonce)).
fof(b_hold_key_bt_for_t, axiom, (b_holds(key(bt,t))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', b_hold_key_bt_for_t)).
fof(a_holds_key_at_for_t, axiom, (a_holds(key(at,t))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', a_holds_key_at_for_t)).
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)],[b_creates_freash_nonces_in_time])])])).
fof(c_0_35, 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)],[intruder_message_sent])])).
cnf(c_0_37,plain,(t_holds(key(bt,b))), inference(split_conjunct,[status(thm)],[t_holds_key_bt_for_b]), ['final']).
fof(c_0_38, plain, (![X4]:![X5]:![X6]:(~message(sent(X4,X5,X6))|intruder_message(X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_can_record])])).
cnf(c_0_39,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]), ['final']).
cnf(c_0_40,plain,(message(sent(a,b,pair(a,an_a_nonce)))), inference(split_conjunct,[status(thm)],[a_sent_message_i_to_b]), ['final']).
cnf(c_0_41,plain,(fresh_to_b(an_a_nonce)), inference(split_conjunct,[status(thm)],[nonce_a_is_fresh_to_b]), ['final']).
cnf(c_0_42,plain,(message(sent(X1,X2,X3))|~party_of_protocol(X2)|~party_of_protocol(X1)|~intruder_message(X3)), inference(split_conjunct,[status(thm)],[c_0_35]), ['final']).
cnf(c_0_43,plain,(party_of_protocol(b)), inference(split_conjunct,[status(thm)],[b_is_party_of_protocol]), ['final']).
fof(c_0_44, plain, (![X3]:![X4]:((~intruder_message(X3)|~intruder_message(X4))|intruder_message(pair(X3,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_composes_pairs])])).
cnf(c_0_47,plain,(t_holds(key(at,a))), inference(split_conjunct,[status(thm)],[t_holds_key_at_for_a]), ['final']).
fof(c_0_48, 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)],[intruder_decomposes_triples])])])).
cnf(c_0_49,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_38]), ['final']).
cnf(c_0_50,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_39, c_0_40]), c_0_41])]), ['final']).
cnf(c_0_51,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]), ['final']).
cnf(c_0_52,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_39, c_0_42]), c_0_43])]), ['final']).
cnf(c_0_53,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_44]), ['final']).
cnf(c_0_55,plain,(a_stored(pair(b,an_a_nonce))), inference(split_conjunct,[status(thm)],[a_stored_message_i]), ['final']).
cnf(c_0_57,plain,(a_nonce(an_a_nonce)), inference(split_conjunct,[status(thm)],[an_a_nonce_is_a_nonce]), ['final']).
cnf(c_0_58,plain,(party_of_protocol(t)), inference(split_conjunct,[status(thm)],[t_is_party_of_protocol]), ['final']).
fof(c_0_59, 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)],[intruder_composes_triples])])).
cnf(c_0_60,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
cnf(c_0_61,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_49, c_0_50]), ['final']).
fof(c_0_62, 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(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[b_accepts_secure_session_key])])])])).
cnf(c_0_63,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_51, c_0_42]), c_0_43])]), ['final']).
cnf(c_0_65,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_52, c_0_53]), ['final']).
cnf(c_0_67,plain,(party_of_protocol(a)), inference(split_conjunct,[status(thm)],[a_is_party_of_protocol]), ['final']).
cnf(c_0_69,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_56, c_0_42]), c_0_58]), c_0_43])]), ['final']).
cnf(c_0_70,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_59]), ['final']).
cnf(c_0_71,plain,(intruder_message(b)), inference(spm,[status(thm)],[c_0_60, c_0_61]), ['final']).
cnf(c_0_72,plain,(intruder_message(X3)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
cnf(c_0_73,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_62]), ['final']).
cnf(c_0_74,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_63, c_0_53]), ['final']).
fof(c_0_75, 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(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_key_encrypts])])])])).
fof(c_0_76, 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)],[intruder_holds_key])])).
fof(c_0_77, 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)],[intruder_decomposes_pairs])])])).
cnf(c_0_78,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_64, c_0_42]), c_0_58]), c_0_43])]), ['final']).
cnf(c_0_79,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_49, c_0_65]), ['final']).
cnf(c_0_80,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_66, c_0_42]), c_0_67]), c_0_58])]), ['final']).
cnf(c_0_82,plain,(b_stored(pair(a,an_a_nonce))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_40]), c_0_41])]), ['final']).
cnf(c_0_84,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_72, c_0_61]), ['final']).
cnf(c_0_85,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_73, c_0_74]), ['final']).
cnf(c_0_86,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_75]), ['final']).
cnf(c_0_87,plain,(intruder_holds(key(X1,X2))|~party_of_protocol(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_76]), ['final']).
cnf(c_0_88,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_77]), ['final']).
cnf(c_0_89,plain,(intruder_message(pair(a,an_a_nonce))), inference(spm,[status(thm)],[c_0_49, c_0_40]), ['final']).
cnf(c_0_91,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_72, c_0_79]), ['final']).
cnf(c_0_94,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_73, c_0_82]), ['final']).
cnf(c_0_95,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_66, c_0_68]), ['final']).
cnf(c_0_97,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_85, c_0_42]), c_0_43])]), ['final']).
cnf(c_0_98,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X3)), inference(spm,[status(thm)],[c_0_86, c_0_87])).
cnf(c_0_99,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_64, c_0_65]), c_0_71]), c_0_43])]), ['final']).
cnf(c_0_100,plain,(intruder_message(a)), inference(spm,[status(thm)],[c_0_88, c_0_89]), ['final']).
cnf(c_0_101,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_90, c_0_91]), c_0_71]), c_0_43])]), ['final']).
cnf(c_0_103,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_92, c_0_93]), ['final']).
fof(c_0_104, plain, (![X2]:a_key(generate_key(X2))), inference(variable_rename,[status(thm)],[generated_keys_are_keys])).
cnf(c_0_105,plain,(intruder_message(X2)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
cnf(c_0_106,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_94, c_0_42]), c_0_43]), c_0_67])]), ['final']).
cnf(c_0_108,plain,(intruder_message(X2)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_77]), ['final']).
cnf(c_0_109,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_49, c_0_95]), ['final']).
cnf(c_0_110,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_66, c_0_96]), ['final']).
cnf(c_0_111,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_97, c_0_53]), ['final']).
cnf(c_0_112,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_98, c_0_43]), ['final']).
cnf(c_0_114,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_56, c_0_65]), c_0_100]), c_0_67])]), ['final']).
cnf(c_0_118,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_49, c_0_103]), ['final']).
cnf(c_0_119,plain,(a_key(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_104]), ['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_105, c_0_79]), ['final']).
cnf(c_0_121,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_106, c_0_53]), ['final']).
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_108, c_0_109]), ['final']).
cnf(c_0_124,plain,(intruder_message(an_a_nonce)), inference(spm,[status(thm)],[c_0_108, c_0_89]), ['final']).
fof(c_0_125, 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)],[fresh_intruder_nonces_are_fresh_to_b])])])).
cnf(c_0_126,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_49, c_0_110]), ['final']).
cnf(c_0_127,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(generate_b_nonce(X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_111, c_0_112]), ['final']).
cnf(c_0_128,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_72, c_0_113]), ['final']).
cnf(c_0_130,plain,(intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_105, c_0_115])).
cnf(c_0_131,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_116, c_0_42]), c_0_58]), c_0_67])]), ['final']).
cnf(c_0_132,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_117, c_0_42]), c_0_58]), c_0_67])]), ['final']).
cnf(c_0_133,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_97, c_0_118]), c_0_119])]), c_0_120]), ['final']).
cnf(c_0_134,plain,(intruder_message(generate_b_nonce(an_a_nonce))), inference(spm,[status(thm)],[c_0_105, c_0_61]), ['final']).
cnf(c_0_135,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(generate_b_nonce(an_a_nonce))|~intruder_message(X1)|~a_key(X1)), inference(spm,[status(thm)],[c_0_121, c_0_112])).
cnf(c_0_136,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_122, c_0_42]), c_0_67]), c_0_58])]), ['final']).
fof(c_0_137, plain, (![X2]:(~fresh_intruder_nonce(X2)|fresh_intruder_nonce(generate_intruder_nonce(X2)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[can_generate_more_fresh_intruder_nonces])])).
cnf(c_0_138,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_111, c_0_123]), c_0_124]), c_0_119]), c_0_41])]), ['final']).
cnf(c_0_139,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_52, c_0_109]), ['final']).
cnf(c_0_140,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_125]), ['final']).
cnf(c_0_141,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_52, c_0_126]), ['final']).
cnf(c_0_142,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_83, c_0_91]), c_0_100]), c_0_67])]), ['final']).
cnf(c_0_143,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_nonce(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_127, c_0_128]), ['final']).
cnf(c_0_144,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_105, c_0_129]), ['final']).
cnf(c_0_145,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_130, c_0_81]), ['final']).
cnf(c_0_147,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_52, c_0_118]), ['final']).
cnf(c_0_148,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_63, c_0_126]), ['final']).
cnf(c_0_151,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_39, c_0_103]), c_0_100])]), ['final']).
cnf(c_0_152,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_63, c_0_109]), ['final']).
cnf(c_0_153,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_133, c_0_91]), ['final']).
cnf(c_0_154,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_125]), ['final']).
cnf(c_0_155,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_63, c_0_118]), ['final']).
cnf(c_0_156,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_51, c_0_103]), c_0_100])]), ['final']).
cnf(c_0_157,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_108, c_0_118])).
cnf(c_0_158,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)|~intruder_message(X4)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~party_of_protocol(X4)), inference(spm,[status(thm)],[c_0_127, c_0_120]), ['final']).
cnf(c_0_159,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_134]), c_0_124]), c_0_41])]), ['final']).
cnf(c_0_160,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)],[c_0_135, c_0_134])]), ['final']).
fof(c_0_163, 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(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_interception])])])])).
cnf(c_0_165,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_137]), ['final']).
fof(c_0_166, plain, (![X2]:(~a_key(X2)|~a_nonce(X2))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[nothing_is_a_nonce_and_a_key])])).
fof(c_0_167, plain, (![X2]:~a_nonce(generate_key(X2))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[generated_keys_are_not_nonces])])).
cnf(c_0_168,plain,(b_holds(key(generate_key(an_a_nonce),b))|~intruder_message(X1)), 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_138, c_0_130]), c_0_71]), c_0_43]), c_0_124]), c_0_57]), c_0_41])])).
fof(c_0_169, plain, (![X2]:![X2]:(a_nonce(generate_expiration_time(X2))&a_nonce(generate_b_nonce(X2)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[generated_times_and_nonces_are_nonces])])])).
cnf(c_0_170,plain,(fresh_intruder_nonce(an_intruder_nonce)), inference(split_conjunct,[status(thm)],[an_intruder_nonce_is_a_fresh_intruder_nonce]), ['final']).
cnf(c_0_171,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_139, c_0_140]), ['final']).
cnf(c_0_172,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))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_141, c_0_140]), ['final']).
cnf(c_0_175,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_143, c_0_144]), c_0_100]), c_0_119]), c_0_67])]), ['final']).
cnf(c_0_176,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(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_143, c_0_112]), c_0_105]), c_0_60]), ['final']).
cnf(c_0_177,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_143, c_0_145]), c_0_71]), c_0_119]), c_0_43])]), ['final']).
cnf(c_0_179,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_147, c_0_140]), ['final']).
cnf(c_0_180,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))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_148, c_0_140]), ['final']).
cnf(c_0_184,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_151, c_0_140]), ['final']).
cnf(c_0_186,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_152, c_0_140]), ['final']).
cnf(c_0_187,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_133, c_0_112]), c_0_60]), ['final']).
cnf(c_0_188,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~fresh_intruder_nonce(generate_key(an_a_nonce))|~intruder_message(X1)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153, c_0_140]), c_0_154]), ['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_155, c_0_140]), ['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_156, c_0_140]), ['final']).
cnf(c_0_191,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_157, c_0_81]), ['final']).
cnf(c_0_192,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_138, c_0_112]), c_0_60]), ['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)|~intruder_message(X4)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~party_of_protocol(X4)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158, c_0_112]), c_0_105]), c_0_60]), ['final']).
cnf(c_0_195,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)|~party_of_protocol(X3)), inference(spm,[status(thm)],[c_0_158, c_0_91]), ['final']).
cnf(c_0_196,plain,(b_holds(key(an_a_nonce,X1))|~intruder_message(X1)|~a_key(an_a_nonce)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_91]), c_0_124]), c_0_41])]), ['final']).
cnf(c_0_197,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_112]), c_0_105]), c_0_60]), ['final']).
cnf(c_0_198,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_160, c_0_112]), c_0_105]), ['final']).
cnf(c_0_199,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_160, c_0_84]), c_0_124])]), ['final']).
cnf(c_0_203,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_163]), ['final']).
cnf(c_0_208,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(spm,[status(thm)],[c_0_154, c_0_165]), ['final']).
cnf(c_0_209,plain,(~a_nonce(X1)|~a_key(X1)), inference(split_conjunct,[status(thm)],[c_0_166]), ['final']).
cnf(c_0_210,plain,(~a_nonce(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_167]), ['final']).
cnf(c_0_211,plain,(b_holds(key(generate_key(an_a_nonce),b))), inference(spm,[status(thm)],[c_0_168, c_0_81]), ['final']).
cnf(c_0_212,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_88, c_0_109]), ['final']).
cnf(c_0_213,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_85, c_0_95]), c_0_124]), c_0_100]), c_0_119]), c_0_41]), c_0_67])]), ['final']).
cnf(c_0_214,plain,(a_holds(key(generate_key(an_a_nonce),b))), inference(spm,[status(thm)],[c_0_122, c_0_68]), ['final']).
cnf(c_0_215,plain,(b_holds(key(bt,t))), inference(split_conjunct,[status(thm)],[b_hold_key_bt_for_t]), ['final']).
cnf(c_0_216,plain,(a_holds(key(at,t))), inference(split_conjunct,[status(thm)],[a_holds_key_at_for_t]), ['final']).
cnf(c_0_217,plain,(a_nonce(generate_expiration_time(X1))), inference(split_conjunct,[status(thm)],[c_0_169]), ['final']).
cnf(c_0_218,plain,(intruder_message(an_intruder_nonce)), inference(spm,[status(thm)],[c_0_154, c_0_170]), ['final']).
cnf(c_0_219,plain,(a_nonce(generate_b_nonce(X1))), inference(split_conjunct,[status(thm)],[c_0_169]), ['final']).
# SZS output end Saturation
```

## iProver 2.6

Konstantin Korovin
University of Manchester, United Kingdom

### Sample solution for SEU140+2

```% SZS status Theorem

% SZS output start CNFRefutation

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(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(f196,plain,(
( ! [X0,X1] : (in(sK8(X1,X0),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f131])).

fof(f197,plain,(
( ! [X0,X1] : (in(sK8(X1,X0),X1) | 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_17,plain,
( ~ in(X0_\$i,X1_\$i) | in(X0_\$i,X2_\$i) | ~ subset(X1_\$i,X2_\$i) ),
inference(cnf_transformation,[],[f149]) ).

cnf(c_262,plain,
( ~ in(sK8(sK12,sK10),sK10)
| in(sK8(sK12,sK10),X0_\$i)
| ~ subset(sK10,X0_\$i) ),
inference(instantiation,[status(thm)],[c_17]) ).

cnf(c_835,plain,
( ~ in(sK8(sK12,sK10),sK10)
| in(sK8(sK12,sK10),sK11)
| ~ subset(sK10,sK11) ),
inference(instantiation,[status(thm)],[c_262]) ).

cnf(c_62,plain,
( ~ in(X0_\$i,X1_\$i) | ~ in(X0_\$i,X2_\$i) | ~ disjoint(X2_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f198]) ).

cnf(c_243,plain,
( ~ in(sK8(sK12,sK10),sK12)
| ~ in(sK8(sK12,sK10),X0_\$i)
| ~ disjoint(X0_\$i,sK12) ),
inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_760,plain,
( ~ in(sK8(sK12,sK10),sK12)
| ~ in(sK8(sK12,sK10),sK11)
| ~ disjoint(sK11,sK12) ),
inference(instantiation,[status(thm)],[c_243]) ).

cnf(c_64,plain,
( in(sK8(X0_\$i,X1_\$i),X1_\$i) | disjoint(X1_\$i,X0_\$i) ),
inference(cnf_transformation,[],[f196]) ).

cnf(c_210,plain,
( in(sK8(sK12,sK10),sK10) | disjoint(sK10,sK12) ),
inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_63,plain,
( in(sK8(X0_\$i,X1_\$i),X0_\$i) | disjoint(X1_\$i,X0_\$i) ),
inference(cnf_transformation,[],[f197]) ).

cnf(c_209,plain,
( in(sK8(sK12,sK10),sK12) | disjoint(sK10,sK12) ),
inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_72,negated_conjecture,
( ~ disjoint(sK10,sK12) ),
inference(cnf_transformation,[],[f209]) ).

cnf(c_73,negated_conjecture,
( disjoint(sK11,sK12) ),
inference(cnf_transformation,[],[f208]) ).

cnf(c_74,negated_conjecture,
( subset(sK10,sK11) ),
inference(cnf_transformation,[],[f207]) ).

( \$false ),
inference(minisat,
[status(thm)],
[c_835,c_760,c_210,c_209,c_72,c_73,c_74]) ).

% SZS output end CNFRefutation
```

### Sample solution for NLP042+1

```% SZS status CounterSatisfiable

% SZS output start Saturation

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-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f98,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(f99,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,[],[f98])).

fof(f139,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,[],[f99])).

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-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

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(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(f54,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(f102,plain,(
of(sK0,sK2,sK1) & woman(sK0,sK1) & mia_forename(sK0,sK2) & forename(sK0,sK2) & shake_beverage(sK0,sK3) & event(sK0,sK4) & agent(sK0,sK4,sK1) & patient(sK0,sK4,sK3) & nonreflexive(sK0,sK4) & order(sK0,sK4)),
inference(skolemisation,[status(esa)],[f55])).
fof(f55,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,[],[f54])).

fof(f141,plain,(
of(sK0,sK2,sK1)),
inference(cnf_transformation,[],[f102])).

fof(f144,plain,(
forename(sK0,sK2)),
inference(cnf_transformation,[],[f102])).

fof(f44,axiom,(
! [X0,X1,X2,X3] : ((nonreflexive(X0,X1) & agent(X0,X1,X2) & patient(X0,X1,X3)) => X2 != X3)),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f100,plain,(
! [X0,X1,X2,X3] : ((~nonreflexive(X0,X1) | ~agent(X0,X1,X2) | ~patient(X0,X1,X3)) | X2 != X3)),
inference(ennf_transformation,[],[f44])).

fof(f101,plain,(
! [X0,X1,X2,X3] : (~nonreflexive(X0,X1) | ~agent(X0,X1,X2) | ~patient(X0,X1,X3) | X2 != X3)),
inference(flattening,[],[f100])).

fof(f140,plain,(
( ! [X2,X0,X3,X1] : (X2 != X3 | ~patient(X0,X1,X3) | ~agent(X0,X1,X2) | ~nonreflexive(X0,X1)) )),
inference(cnf_transformation,[],[f101])).

fof(f151,plain,(
( ! [X0,X3,X1] : (~patient(X0,X1,X3) | ~agent(X0,X1,X3) | ~nonreflexive(X0,X1)) )),
inference(equality_resolution,[],[f140])).

fof(f147,plain,(
agent(sK0,sK4,sK1)),
inference(cnf_transformation,[],[f102])).

fof(f149,plain,(
nonreflexive(sK0,sK4)),
inference(cnf_transformation,[],[f102])).

fof(f27,axiom,(
! [X0,X1] : (shake_beverage(X0,X1) => beverage(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f84,plain,(
! [X0,X1] : (~shake_beverage(X0,X1) | beverage(X0,X1))),
inference(ennf_transformation,[],[f27])).

fof(f125,plain,(
( ! [X0,X1] : (beverage(X0,X1) | ~shake_beverage(X0,X1)) )),
inference(cnf_transformation,[],[f84])).

fof(f26,axiom,(
! [X0,X1] : (beverage(X0,X1) => food(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f83,plain,(
! [X0,X1] : (~beverage(X0,X1) | food(X0,X1))),
inference(ennf_transformation,[],[f26])).

fof(f124,plain,(
( ! [X0,X1] : (food(X0,X1) | ~beverage(X0,X1)) )),
inference(cnf_transformation,[],[f83])).

fof(f25,axiom,(
! [X0,X1] : (food(X0,X1) => substance_matter(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f82,plain,(
! [X0,X1] : (~food(X0,X1) | substance_matter(X0,X1))),
inference(ennf_transformation,[],[f25])).

fof(f123,plain,(
( ! [X0,X1] : (substance_matter(X0,X1) | ~food(X0,X1)) )),
inference(cnf_transformation,[],[f82])).

fof(f24,axiom,(
! [X0,X1] : (substance_matter(X0,X1) => object(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f81,plain,(
! [X0,X1] : (~substance_matter(X0,X1) | object(X0,X1))),
inference(ennf_transformation,[],[f24])).

fof(f122,plain,(
( ! [X0,X1] : (object(X0,X1) | ~substance_matter(X0,X1)) )),
inference(cnf_transformation,[],[f81])).

fof(f8,axiom,(
! [X0,X1] : (woman(X0,X1) => human_person(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f68,plain,(
! [X0,X1] : (~woman(X0,X1) | human_person(X0,X1))),
inference(ennf_transformation,[],[f8])).

fof(f109,plain,(
( ! [X0,X1] : (human_person(X0,X1) | ~woman(X0,X1)) )),
inference(cnf_transformation,[],[f68])).

fof(f19,axiom,(
! [X0,X1] : (object(X0,X1) => nonliving(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f77,plain,(
! [X0,X1] : (~object(X0,X1) | nonliving(X0,X1))),
inference(ennf_transformation,[],[f19])).

fof(f118,plain,(
( ! [X0,X1] : (nonliving(X0,X1) | ~object(X0,X1)) )),
inference(cnf_transformation,[],[f77])).

fof(f2,axiom,(
! [X0,X1] : (human_person(X0,X1) => animate(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f63,plain,(
! [X0,X1] : (~human_person(X0,X1) | animate(X0,X1))),
inference(ennf_transformation,[],[f2])).

fof(f104,plain,(
( ! [X0,X1] : (animate(X0,X1) | ~human_person(X0,X1)) )),
inference(cnf_transformation,[],[f63])).

fof(f37,axiom,(
! [X0,X1] : (animate(X0,X1) => ~nonliving(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f47,plain,(
! [X0,X1] : (animate(X0,X1) => ~nonliving(X0,X1))),
inference(flattening,[],[f37])).

fof(f92,plain,(
! [X0,X1] : (~animate(X0,X1) | ~nonliving(X0,X1))),
inference(ennf_transformation,[],[f47])).

fof(f133,plain,(
( ! [X0,X1] : (~nonliving(X0,X1) | ~animate(X0,X1)) )),
inference(cnf_transformation,[],[f92])).

fof(f145,plain,(
shake_beverage(sK0,sK3)),
inference(cnf_transformation,[],[f102])).

fof(f16,axiom,(
! [X0,X1] : (forename(X0,X1) => relname(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f75,plain,(
! [X0,X1] : (~forename(X0,X1) | relname(X0,X1))),
inference(ennf_transformation,[],[f16])).

fof(f116,plain,(
( ! [X0,X1] : (relname(X0,X1) | ~forename(X0,X1)) )),
inference(cnf_transformation,[],[f75])).

fof(f15,axiom,(
! [X0,X1] : (relname(X0,X1) => relation(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f74,plain,(
! [X0,X1] : (~relname(X0,X1) | relation(X0,X1))),
inference(ennf_transformation,[],[f15])).

fof(f115,plain,(
( ! [X0,X1] : (relation(X0,X1) | ~relname(X0,X1)) )),
inference(cnf_transformation,[],[f74])).

fof(f14,axiom,(
! [X0,X1] : (relation(X0,X1) => abstraction(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f73,plain,(
! [X0,X1] : (~relation(X0,X1) | abstraction(X0,X1))),
inference(ennf_transformation,[],[f14])).

fof(f114,plain,(
( ! [X0,X1] : (abstraction(X0,X1) | ~relation(X0,X1)) )),
inference(cnf_transformation,[],[f73])).

fof(f21,axiom,(
! [X0,X1] : (entity(X0,X1) => specific(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f79,plain,(
! [X0,X1] : (~entity(X0,X1) | specific(X0,X1))),
inference(ennf_transformation,[],[f21])).

fof(f120,plain,(
( ! [X0,X1] : (specific(X0,X1) | ~entity(X0,X1)) )),
inference(cnf_transformation,[],[f79])).

fof(f11,axiom,(
! [X0,X1] : (abstraction(X0,X1) => general(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f71,plain,(
! [X0,X1] : (~abstraction(X0,X1) | general(X0,X1))),
inference(ennf_transformation,[],[f11])).

fof(f112,plain,(
( ! [X0,X1] : (general(X0,X1) | ~abstraction(X0,X1)) )),
inference(cnf_transformation,[],[f71])).

fof(f41,axiom,(
! [X0,X1] : (specific(X0,X1) => ~general(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f51,plain,(
! [X0,X1] : (specific(X0,X1) => ~general(X0,X1))),
inference(flattening,[],[f41])).

fof(f96,plain,(
! [X0,X1] : (~specific(X0,X1) | ~general(X0,X1))),
inference(ennf_transformation,[],[f51])).

fof(f137,plain,(
( ! [X0,X1] : (~general(X0,X1) | ~specific(X0,X1)) )),
inference(cnf_transformation,[],[f96])).

fof(f7,axiom,(
! [X0,X1] : (human_person(X0,X1) => organism(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f67,plain,(
! [X0,X1] : (~human_person(X0,X1) | organism(X0,X1))),
inference(ennf_transformation,[],[f7])).

fof(f108,plain,(
( ! [X0,X1] : (organism(X0,X1) | ~human_person(X0,X1)) )),
inference(cnf_transformation,[],[f67])).

fof(f6,axiom,(
! [X0,X1] : (organism(X0,X1) => entity(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f66,plain,(
! [X0,X1] : (~organism(X0,X1) | entity(X0,X1))),
inference(ennf_transformation,[],[f6])).

fof(f107,plain,(
( ! [X0,X1] : (entity(X0,X1) | ~organism(X0,X1)) )),
inference(cnf_transformation,[],[f66])).

fof(f34,axiom,(
! [X0,X1] : (event(X0,X1) => eventuality(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f89,plain,(
! [X0,X1] : (~event(X0,X1) | eventuality(X0,X1))),
inference(ennf_transformation,[],[f34])).

fof(f130,plain,(
( ! [X0,X1] : (eventuality(X0,X1) | ~event(X0,X1)) )),
inference(cnf_transformation,[],[f89])).

fof(f31,axiom,(
! [X0,X1] : (eventuality(X0,X1) => specific(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f88,plain,(
! [X0,X1] : (~eventuality(X0,X1) | specific(X0,X1))),
inference(ennf_transformation,[],[f31])).

fof(f129,plain,(
( ! [X0,X1] : (specific(X0,X1) | ~eventuality(X0,X1)) )),
inference(cnf_transformation,[],[f88])).

fof(f146,plain,(
event(sK0,sK4)),
inference(cnf_transformation,[],[f102])).

fof(f30,axiom,(
! [X0,X1] : (eventuality(X0,X1) => nonexistent(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f87,plain,(
! [X0,X1] : (~eventuality(X0,X1) | nonexistent(X0,X1))),
inference(ennf_transformation,[],[f30])).

fof(f128,plain,(
( ! [X0,X1] : (nonexistent(X0,X1) | ~eventuality(X0,X1)) )),
inference(cnf_transformation,[],[f87])).

fof(f20,axiom,(
! [X0,X1] : (entity(X0,X1) => existent(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f78,plain,(
! [X0,X1] : (~entity(X0,X1) | existent(X0,X1))),
inference(ennf_transformation,[],[f20])).

fof(f119,plain,(
( ! [X0,X1] : (existent(X0,X1) | ~entity(X0,X1)) )),
inference(cnf_transformation,[],[f78])).

fof(f38,axiom,(
! [X0,X1] : (existent(X0,X1) => ~nonexistent(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f48,plain,(
! [X0,X1] : (existent(X0,X1) => ~nonexistent(X0,X1))),
inference(flattening,[],[f38])).

fof(f93,plain,(
! [X0,X1] : (~existent(X0,X1) | ~nonexistent(X0,X1))),
inference(ennf_transformation,[],[f48])).

fof(f134,plain,(
( ! [X0,X1] : (~nonexistent(X0,X1) | ~existent(X0,X1)) )),
inference(cnf_transformation,[],[f93])).

fof(f23,axiom,(
! [X0,X1] : (object(X0,X1) => entity(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f80,plain,(
! [X0,X1] : (~object(X0,X1) | entity(X0,X1))),
inference(ennf_transformation,[],[f23])).

fof(f121,plain,(
( ! [X0,X1] : (entity(X0,X1) | ~object(X0,X1)) )),
inference(cnf_transformation,[],[f80])).

fof(f9,axiom,(
! [X0,X1] : (mia_forename(X0,X1) => forename(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f69,plain,(
! [X0,X1] : (~mia_forename(X0,X1) | forename(X0,X1))),
inference(ennf_transformation,[],[f9])).

fof(f110,plain,(
( ! [X0,X1] : (forename(X0,X1) | ~mia_forename(X0,X1)) )),
inference(cnf_transformation,[],[f69])).

fof(f28,axiom,(
! [X0,X1] : (order(X0,X1) => event(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f85,plain,(
! [X0,X1] : (~order(X0,X1) | event(X0,X1))),
inference(ennf_transformation,[],[f28])).

fof(f126,plain,(
( ! [X0,X1] : (event(X0,X1) | ~order(X0,X1)) )),
inference(cnf_transformation,[],[f85])).

fof(f12,axiom,(
! [X0,X1] : (abstraction(X0,X1) => nonhuman(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f72,plain,(
! [X0,X1] : (~abstraction(X0,X1) | nonhuman(X0,X1))),
inference(ennf_transformation,[],[f12])).

fof(f113,plain,(
( ! [X0,X1] : (nonhuman(X0,X1) | ~abstraction(X0,X1)) )),
inference(cnf_transformation,[],[f72])).

fof(f3,axiom,(
! [X0,X1] : (human_person(X0,X1) => human(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f64,plain,(
! [X0,X1] : (~human_person(X0,X1) | human(X0,X1))),
inference(ennf_transformation,[],[f3])).

fof(f105,plain,(
( ! [X0,X1] : (human(X0,X1) | ~human_person(X0,X1)) )),
inference(cnf_transformation,[],[f64])).

fof(f39,axiom,(
! [X0,X1] : (nonhuman(X0,X1) => ~human(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f49,plain,(
! [X0,X1] : (nonhuman(X0,X1) => ~human(X0,X1))),
inference(flattening,[],[f39])).

fof(f94,plain,(
! [X0,X1] : (~nonhuman(X0,X1) | ~human(X0,X1))),
inference(ennf_transformation,[],[f49])).

fof(f135,plain,(
( ! [X0,X1] : (~human(X0,X1) | ~nonhuman(X0,X1)) )),
inference(cnf_transformation,[],[f94])).

fof(f29,axiom,(
! [X0,X1] : (eventuality(X0,X1) => unisex(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f86,plain,(
! [X0,X1] : (~eventuality(X0,X1) | unisex(X0,X1))),
inference(ennf_transformation,[],[f29])).

fof(f127,plain,(
( ! [X0,X1] : (unisex(X0,X1) | ~eventuality(X0,X1)) )),
inference(cnf_transformation,[],[f86])).

fof(f1,axiom,(
! [X0,X1] : (woman(X0,X1) => female(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f62,plain,(
! [X0,X1] : (~woman(X0,X1) | female(X0,X1))),
inference(ennf_transformation,[],[f1])).

fof(f103,plain,(
( ! [X0,X1] : (female(X0,X1) | ~woman(X0,X1)) )),
inference(cnf_transformation,[],[f62])).

fof(f42,axiom,(
! [X0,X1] : (unisex(X0,X1) => ~female(X0,X1))),
file('/Users/korovin/TPTP-v6.1.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f52,plain,(
! [X0,X1] : (unisex(X0,X1) => ~female(X0,X1))),
inference(flattening,[],[f42])).

fof(f97,plain,(
! [X0,X1] : (~unisex(X0,X1) | ~female(X0,X1))),
inference(ennf_transformation,[],[f52])).

fof(f138,plain,(
( ! [X0,X1] : (~female(X0,X1) | ~unisex(X0,X1)) )),
inference(cnf_transformation,[],[f97])).

fof(f142,plain,(
woman(sK0,sK1)),
inference(cnf_transformation,[],[f102])).

fof(f143,plain,(
mia_forename(sK0,sK2)),
inference(cnf_transformation,[],[f102])).

fof(f148,plain,(
patient(sK0,sK4,sK3)),
inference(cnf_transformation,[],[f102])).

fof(f150,plain,(
order(sK0,sK4)),
inference(cnf_transformation,[],[f102])).

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)
| X3_\$i = X2_\$i ),
inference(cnf_transformation,[],[f139]) ).

cnf(c_495,plain,
( ~ entity(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ forename(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i)
| ~ forename(X0_\$\$iProver_event_1_\$i,X2_\$\$iProver_event_2_\$i)
| ~ of(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i,X0_\$\$iProver_event_2_\$i)
| ~ of(X0_\$\$iProver_event_1_\$i,X2_\$\$iProver_event_2_\$i,X0_\$\$iProver_event_2_\$i)
| X2_\$\$iProver_event_2_\$i = X1_\$\$iProver_event_2_\$i ),
inference(subtyping,[status(esa)],[c_36]) ).

cnf(c_47,negated_conjecture,
( of(sK0,sK2,sK1) ),
inference(cnf_transformation,[],[f141]) ).

cnf(c_484,negated_conjecture,
( of(sK0,sK2,sK1) ),
inference(subtyping,[status(esa)],[c_47]) ).

cnf(c_649,plain,
( ~ entity(sK0,sK1)
| ~ forename(sK0,sK2)
| ~ forename(sK0,X0_\$\$iProver_event_2_\$i)
| ~ of(sK0,X0_\$\$iProver_event_2_\$i,sK1)
| sK2 = X0_\$\$iProver_event_2_\$i ),
inference(resolution,[status(thm)],[c_495,c_484]) ).

cnf(c_44,negated_conjecture,
( forename(sK0,sK2) ),
inference(cnf_transformation,[],[f144]) ).

cnf(c_650,plain,
( ~ entity(sK0,sK1)
| ~ forename(sK0,X0_\$\$iProver_event_2_\$i)
| ~ of(sK0,X0_\$\$iProver_event_2_\$i,sK1)
| sK2 = X0_\$\$iProver_event_2_\$i ),
inference(global_propositional_subsumption,[status(thm)],[c_649,c_44]) ).

cnf(c_663,plain,
( ~ entity(sK0,sK1) | ~ forename(sK0,sK2) | sK2 = sK2 ),
inference(resolution,[status(thm)],[c_650,c_484]) ).

cnf(c_664,plain,
( ~ entity(sK0,sK1) | sK2 = sK2 ),
inference(global_propositional_subsumption,[status(thm)],[c_663,c_44]) ).

cnf(c_498,plain,
( X0_\$\$iProver_event_2_\$i = X0_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_667,plain,
( sK2 = sK2 ),
inference(forward_subsumption_resolution,[status(thm)],[c_664,c_498]) ).

cnf(c_508,plain,
( agent(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| ~ agent(X0_\$\$iProver_event_1_\$i,X2_\$\$iProver_event_2_\$i,X3_\$\$iProver_event_2_\$i)
| X0_\$\$iProver_event_2_\$i != X2_\$\$iProver_event_2_\$i
| X1_\$\$iProver_event_2_\$i != X3_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_684,plain,
( agent(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,sK2)
| ~ agent(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i,sK2)
| X0_\$\$iProver_event_2_\$i != X1_\$\$iProver_event_2_\$i ),
inference(resolution,[status(thm)],[c_667,c_508]) ).

cnf(c_507,plain,
( patient(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| ~ patient(X0_\$\$iProver_event_1_\$i,X2_\$\$iProver_event_2_\$i,X3_\$\$iProver_event_2_\$i)
| X0_\$\$iProver_event_2_\$i != X2_\$\$iProver_event_2_\$i
| X1_\$\$iProver_event_2_\$i != X3_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_683,plain,
( patient(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,sK2)
| ~ patient(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i,sK2)
| X0_\$\$iProver_event_2_\$i != X1_\$\$iProver_event_2_\$i ),
inference(resolution,[status(thm)],[c_667,c_507]) ).

cnf(c_506,plain,
( of(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| ~ of(X0_\$\$iProver_event_1_\$i,X2_\$\$iProver_event_2_\$i,X3_\$\$iProver_event_2_\$i)
| X0_\$\$iProver_event_2_\$i != X2_\$\$iProver_event_2_\$i
| X1_\$\$iProver_event_2_\$i != X3_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_682,plain,
( of(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,sK2)
| ~ of(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i,sK2)
| X0_\$\$iProver_event_2_\$i != X1_\$\$iProver_event_2_\$i ),
inference(resolution,[status(thm)],[c_667,c_506]) ).

cnf(c_499,plain,
( X0_\$\$iProver_event_2_\$i != X1_\$\$iProver_event_2_\$i
| X2_\$\$iProver_event_2_\$i != X1_\$\$iProver_event_2_\$i
| X2_\$\$iProver_event_2_\$i = X0_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_671,plain,
( sK2 = X0_\$\$iProver_event_2_\$i | X0_\$\$iProver_event_2_\$i != sK2 ),
inference(resolution,[status(thm)],[c_667,c_499]) ).

cnf(c_638,plain,
( agent(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| ~ agent(X0_\$\$iProver_event_1_\$i,X2_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| X0_\$\$iProver_event_2_\$i != X2_\$\$iProver_event_2_\$i ),
inference(resolution,[status(thm)],[c_508,c_498]) ).

cnf(c_629,plain,
( patient(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| ~ patient(X0_\$\$iProver_event_1_\$i,X2_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| X0_\$\$iProver_event_2_\$i != X2_\$\$iProver_event_2_\$i ),
inference(resolution,[status(thm)],[c_507,c_498]) ).

cnf(c_620,plain,
( ~ of(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| of(X0_\$\$iProver_event_1_\$i,X2_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| X2_\$\$iProver_event_2_\$i != X0_\$\$iProver_event_2_\$i ),
inference(resolution,[status(thm)],[c_506,c_498]) ).

cnf(c_612,plain,
( X0_\$\$iProver_event_2_\$i != X1_\$\$iProver_event_2_\$i
| X1_\$\$iProver_event_2_\$i = X0_\$\$iProver_event_2_\$i ),
inference(resolution,[status(thm)],[c_499,c_498]) ).

cnf(c_37,plain,
( ~ patient(X0_\$i,X1_\$i,X2_\$i)
| ~ agent(X0_\$i,X1_\$i,X2_\$i)
| ~ nonreflexive(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f151]) ).

cnf(c_494,plain,
( ~ patient(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| ~ agent(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i,X1_\$\$iProver_event_2_\$i)
| ~ nonreflexive(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_37]) ).

cnf(c_41,negated_conjecture,
( agent(sK0,sK4,sK1) ),
inference(cnf_transformation,[],[f147]) ).

cnf(c_490,negated_conjecture,
( agent(sK0,sK4,sK1) ),
inference(subtyping,[status(esa)],[c_41]) ).

cnf(c_604,plain,
( ~ patient(sK0,sK4,sK1) | ~ nonreflexive(sK0,sK4) ),
inference(resolution,[status(thm)],[c_494,c_490]) ).

cnf(c_39,negated_conjecture,
( nonreflexive(sK0,sK4) ),
inference(cnf_transformation,[],[f149]) ).

cnf(c_605,plain,
( ~ patient(sK0,sK4,sK1) ),
inference(global_propositional_subsumption,[status(thm)],[c_604,c_39]) ).

cnf(c_22,plain,
( beverage(X0_\$i,X1_\$i) | ~ shake_beverage(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f125]) ).

cnf(c_21,plain,
( food(X0_\$i,X1_\$i) | ~ beverage(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f124]) ).

cnf(c_20,plain,
( substance_matter(X0_\$i,X1_\$i) | ~ food(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f123]) ).

cnf(c_19,plain,
( object(X0_\$i,X1_\$i) | ~ substance_matter(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f122]) ).

cnf(c_176,plain,
( object(X0_\$i,X1_\$i) | ~ food(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_20,c_19]) ).

cnf(c_186,plain,
( object(X0_\$i,X1_\$i) | ~ beverage(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_21,c_176]) ).

cnf(c_196,plain,
( object(X0_\$i,X1_\$i) | ~ shake_beverage(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_22,c_186]) ).

cnf(c_6,plain,
( ~ woman(X0_\$i,X1_\$i) | human_person(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f109]) ).

cnf(c_15,plain,
( ~ object(X0_\$i,X1_\$i) | nonliving(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f118]) ).

cnf(c_1,plain,
( animate(X0_\$i,X1_\$i) | ~ human_person(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f104]) ).

cnf(c_30,plain,
( ~ animate(X0_\$i,X1_\$i) | ~ nonliving(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f133]) ).

cnf(c_96,plain,
( ~ human_person(X0_\$i,X1_\$i) | ~ nonliving(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_1,c_30]) ).

cnf(c_228,plain,
( ~ human_person(X0_\$i,X1_\$i) | ~ object(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_15,c_96]) ).

cnf(c_258,plain,
( ~ woman(X0_\$i,X1_\$i) | ~ object(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_6,c_228]) ).

cnf(c_300,plain,
( ~ woman(X0_\$i,X1_\$i) | ~ shake_beverage(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_196,c_258]) ).

cnf(c_482,plain,
( ~ woman(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ shake_beverage(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_300]) ).

cnf(c_43,negated_conjecture,
( shake_beverage(sK0,sK3) ),
inference(cnf_transformation,[],[f145]) ).

cnf(c_488,negated_conjecture,
( shake_beverage(sK0,sK3) ),
inference(subtyping,[status(esa)],[c_43]) ).

cnf(c_575,plain,
( ~ woman(sK0,sK3) ),
inference(resolution,[status(thm)],[c_482,c_488]) ).

cnf(c_13,plain,
( ~ forename(X0_\$i,X1_\$i) | relname(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f116]) ).

cnf(c_12,plain,
( relation(X0_\$i,X1_\$i) | ~ relname(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f115]) ).

cnf(c_11,plain,
( abstraction(X0_\$i,X1_\$i) | ~ relation(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f114]) ).

cnf(c_146,plain,
( abstraction(X0_\$i,X1_\$i) | ~ relname(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_12,c_11]) ).

cnf(c_156,plain,
( ~ forename(X0_\$i,X1_\$i) | abstraction(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_13,c_146]) ).

cnf(c_17,plain,
( ~ entity(X0_\$i,X1_\$i) | specific(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f120]) ).

cnf(c_9,plain,
( ~ abstraction(X0_\$i,X1_\$i) | general(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f112]) ).

cnf(c_34,plain,
( ~ general(X0_\$i,X1_\$i) | ~ specific(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f137]) ).

cnf(c_126,plain,
( ~ abstraction(X0_\$i,X1_\$i) | ~ specific(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_9,c_34]) ).

cnf(c_246,plain,
( ~ entity(X0_\$i,X1_\$i) | ~ abstraction(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_17,c_126]) ).

cnf(c_328,plain,
( ~ entity(X0_\$i,X1_\$i) | ~ forename(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_156,c_246]) ).

cnf(c_479,plain,
( ~ entity(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ forename(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_328]) ).

cnf(c_487,negated_conjecture,
( forename(sK0,sK2) ),
inference(subtyping,[status(esa)],[c_44]) ).

cnf(c_566,plain,
( ~ entity(sK0,sK2) ),
inference(resolution,[status(thm)],[c_479,c_487]) ).

cnf(c_5,plain,
( ~ human_person(X0_\$i,X1_\$i) | organism(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f108]) ).

cnf(c_4,plain,
( ~ organism(X0_\$i,X1_\$i) | entity(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f107]) ).

cnf(c_218,plain,
( ~ human_person(X0_\$i,X1_\$i) | entity(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_5,c_4]) ).

cnf(c_266,plain,
( ~ woman(X0_\$i,X1_\$i) | entity(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_6,c_218]) ).

cnf(c_483,plain,
( ~ woman(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| entity(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_266]) ).

cnf(c_568,plain,
( ~ woman(sK0,sK2) ),
inference(resolution,[status(thm)],[c_566,c_483]) ).

cnf(c_27,plain,
( ~ event(X0_\$i,X1_\$i) | eventuality(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f130]) ).

cnf(c_26,plain,
( specific(X0_\$i,X1_\$i) | ~ eventuality(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f129]) ).

cnf(c_238,plain,
( ~ abstraction(X0_\$i,X1_\$i) | ~ eventuality(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_26,c_126]) ).

cnf(c_336,plain,
( ~ forename(X0_\$i,X1_\$i) | ~ eventuality(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_156,c_238]) ).

cnf(c_350,plain,
( ~ forename(X0_\$i,X1_\$i) | ~ event(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_27,c_336]) ).

cnf(c_478,plain,
( ~ forename(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ event(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_350]) ).

cnf(c_42,negated_conjecture,
( event(sK0,sK4) ),
inference(cnf_transformation,[],[f146]) ).

cnf(c_489,negated_conjecture,
( event(sK0,sK4) ),
inference(subtyping,[status(esa)],[c_42]) ).

cnf(c_562,plain,
( ~ forename(sK0,sK4) ),
inference(resolution,[status(thm)],[c_478,c_489]) ).

cnf(c_25,plain,
( ~ eventuality(X0_\$i,X1_\$i) | nonexistent(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f128]) ).

cnf(c_16,plain,
( ~ entity(X0_\$i,X1_\$i) | existent(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f119]) ).

cnf(c_31,plain,
( ~ existent(X0_\$i,X1_\$i) | ~ nonexistent(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f134]) ).

cnf(c_166,plain,
( ~ entity(X0_\$i,X1_\$i) | ~ nonexistent(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_16,c_31]) ).

cnf(c_206,plain,
( ~ entity(X0_\$i,X1_\$i) | ~ eventuality(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_25,c_166]) ).

cnf(c_366,plain,
( ~ entity(X0_\$i,X1_\$i) | ~ event(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_27,c_206]) ).

cnf(c_476,plain,
( ~ entity(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ event(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_366]) ).

cnf(c_549,plain,
( ~ entity(sK0,sK4) ),
inference(resolution,[status(thm)],[c_476,c_489]) ).

cnf(c_551,plain,
( ~ woman(sK0,sK4) ),
inference(resolution,[status(thm)],[c_549,c_483]) ).

cnf(c_18,plain,
( entity(X0_\$i,X1_\$i) | ~ object(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f121]) ).

cnf(c_308,plain,
( entity(X0_\$i,X1_\$i) | ~ shake_beverage(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_196,c_18]) ).

cnf(c_481,plain,
( entity(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ shake_beverage(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_308]) ).

cnf(c_537,plain,
( entity(sK0,sK3) ),
inference(resolution,[status(thm)],[c_481,c_488]) ).

cnf(c_509,plain,
( ~ nonreflexive(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| nonreflexive(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i)
| X1_\$\$iProver_event_2_\$i != X0_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_505,plain,
( ~ order(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| order(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i)
| X1_\$\$iProver_event_2_\$i != X0_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_504,plain,
( ~ event(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| event(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i)
| X1_\$\$iProver_event_2_\$i != X0_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_503,plain,
( ~ shake_beverage(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| shake_beverage(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i)
| X1_\$\$iProver_event_2_\$i != X0_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_502,plain,
( ~ mia_forename(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| mia_forename(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i)
| X1_\$\$iProver_event_2_\$i != X0_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_501,plain,
( ~ forename(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| forename(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i)
| X1_\$\$iProver_event_2_\$i != X0_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_500,plain,
( ~ woman(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| woman(X0_\$\$iProver_event_1_\$i,X1_\$\$iProver_event_2_\$i)
| X1_\$\$iProver_event_2_\$i != X0_\$\$iProver_event_2_\$i ),
theory(equality) ).

cnf(c_7,plain,
( forename(X0_\$i,X1_\$i) | ~ mia_forename(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f110]) ).

cnf(c_497,plain,
( forename(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ mia_forename(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_7]) ).

cnf(c_23,plain,
( event(X0_\$i,X1_\$i) | ~ order(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f126]) ).

cnf(c_496,plain,
( event(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ order(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_23]) ).

cnf(c_10,plain,
( ~ abstraction(X0_\$i,X1_\$i) | nonhuman(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f113]) ).

cnf(c_2,plain,
( ~ human_person(X0_\$i,X1_\$i) | human(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f105]) ).

cnf(c_32,plain,
( ~ human(X0_\$i,X1_\$i) | ~ nonhuman(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f135]) ).

cnf(c_106,plain,
( ~ human_person(X0_\$i,X1_\$i) | ~ nonhuman(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_2,c_32]) ).

cnf(c_136,plain,
( ~ human_person(X0_\$i,X1_\$i) | ~ abstraction(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_10,c_106]) ).

cnf(c_274,plain,
( ~ woman(X0_\$i,X1_\$i) | ~ abstraction(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_6,c_136]) ).

cnf(c_320,plain,
( ~ woman(X0_\$i,X1_\$i) | ~ forename(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_156,c_274]) ).

cnf(c_480,plain,
( ~ woman(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ forename(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_320]) ).

cnf(c_24,plain,
( unisex(X0_\$i,X1_\$i) | ~ eventuality(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f127]) ).

cnf(c_0,plain,
( female(X0_\$i,X1_\$i) | ~ woman(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f103]) ).

cnf(c_35,plain,
( ~ female(X0_\$i,X1_\$i) | ~ unisex(X0_\$i,X1_\$i) ),
inference(cnf_transformation,[],[f138]) ).

cnf(c_86,plain,
( ~ woman(X0_\$i,X1_\$i) | ~ unisex(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_0,c_35]) ).

cnf(c_288,plain,
( ~ woman(X0_\$i,X1_\$i) | ~ eventuality(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_24,c_86]) ).

cnf(c_358,plain,
( ~ woman(X0_\$i,X1_\$i) | ~ event(X0_\$i,X1_\$i) ),
inference(resolution,[status(thm)],[c_27,c_288]) ).

cnf(c_477,plain,
( ~ woman(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i)
| ~ event(X0_\$\$iProver_event_1_\$i,X0_\$\$iProver_event_2_\$i) ),
inference(subtyping,[status(esa)],[c_358]) ).

cnf(c_46,negated_conjecture,
( woman(sK0,sK1) ),
inference(cnf_transformation,[],[f142]) ).

cnf(c_485,negated_conjecture,
( woman(sK0,sK1) ),
inference(subtyping,[status(esa)],[c_46]) ).

cnf(c_45,negated_conjecture,
( mia_forename(sK0,sK2) ),
inference(cnf_transformation,[],[f143]) ).

cnf(c_486,negated_conjecture,
( mia_forename(sK0,sK2) ),
inference(subtyping,[status(esa)],[c_45]) ).

cnf(c_40,negated_conjecture,
( patient(sK0,sK4,sK3) ),
inference(cnf_transformation,[],[f148]) ).

cnf(c_491,negated_conjecture,
( patient(sK0,sK4,sK3) ),
inference(subtyping,[status(esa)],[c_40]) ).

cnf(c_492,negated_conjecture,
( nonreflexive(sK0,sK4) ),
inference(subtyping,[status(esa)],[c_39]) ).

cnf(c_38,negated_conjecture,
( order(sK0,sK4) ),
inference(cnf_transformation,[],[f150]) ).

cnf(c_493,negated_conjecture,
( order(sK0,sK4) ),
inference(subtyping,[status(esa)],[c_38]) ).

% SZS output end Saturation
```

### Sample solution for SWV017+1

```% SZS status Satisfiable

% SZS output start Saturation

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-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f39,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(f44,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,[],[f39])).

fof(f45,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,[],[f44])).

fof(f75,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,[],[f45])).

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-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f46,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(f47,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,[],[f46])).

fof(f79,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,[],[f47])).

fof(f15,axiom,(
! [X0,X1,X2] : (message(sent(X0,X1,X2)) => intruder_message(X2))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f48,plain,(
! [X0,X1,X2] : (~message(sent(X0,X1,X2)) | intruder_message(X2))),
inference(ennf_transformation,[],[f15])).

fof(f80,plain,(
( ! [X2,X0,X1] : (intruder_message(X2) | ~message(sent(X0,X1,X2))) )),
inference(cnf_transformation,[],[f48])).

fof(f16,axiom,(
! [X0,X1] : (intruder_message(pair(X0,X1)) => (intruder_message(X0) & intruder_message(X1)))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f49,plain,(
! [X0,X1] : (~intruder_message(pair(X0,X1)) | (intruder_message(X0) & intruder_message(X1)))),
inference(ennf_transformation,[],[f16])).

fof(f82,plain,(
( ! [X0,X1] : (intruder_message(X1) | ~intruder_message(pair(X0,X1))) )),
inference(cnf_transformation,[],[f49])).

fof(f81,plain,(
( ! [X0,X1] : (intruder_message(X0) | ~intruder_message(pair(X0,X1))) )),
inference(cnf_transformation,[],[f49])).

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-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f50,plain,(
! [X0,X1,X2] : (~intruder_message(triple(X0,X1,X2)) | (intruder_message(X0) & intruder_message(X1) & intruder_message(X2)))),
inference(ennf_transformation,[],[f17])).

fof(f85,plain,(
( ! [X2,X0,X1] : (intruder_message(X2) | ~intruder_message(triple(X0,X1,X2))) )),
inference(cnf_transformation,[],[f50])).

fof(f84,plain,(
( ! [X2,X0,X1] : (intruder_message(X1) | ~intruder_message(triple(X0,X1,X2))) )),
inference(cnf_transformation,[],[f50])).

fof(f83,plain,(
( ! [X2,X0,X1] : (intruder_message(X0) | ~intruder_message(triple(X0,X1,X2))) )),
inference(cnf_transformation,[],[f50])).

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-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f51,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(f89,plain,(
( ! [X2,X0,X3,X1] : (intruder_message(X3) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
inference(cnf_transformation,[],[f51])).

fof(f88,plain,(
( ! [X2,X0,X3,X1] : (intruder_message(X2) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
inference(cnf_transformation,[],[f51])).

fof(f87,plain,(
( ! [X2,X0,X3,X1] : (intruder_message(X1) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
inference(cnf_transformation,[],[f51])).

fof(f86,plain,(
( ! [X2,X0,X3,X1] : (intruder_message(X0) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
inference(cnf_transformation,[],[f51])).

fof(f19,axiom,(
! [X0,X1] : ((intruder_message(X0) & intruder_message(X1)) => intruder_message(pair(X0,X1)))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f52,plain,(
! [X0,X1] : ((~intruder_message(X0) | ~intruder_message(X1)) | intruder_message(pair(X0,X1)))),
inference(ennf_transformation,[],[f19])).

fof(f53,plain,(
! [X0,X1] : (~intruder_message(X0) | ~intruder_message(X1) | intruder_message(pair(X0,X1)))),
inference(flattening,[],[f52])).

fof(f90,plain,(
( ! [X0,X1] : (intruder_message(pair(X0,X1)) | ~intruder_message(X1) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f53])).

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-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f54,plain,(
! [X0,X1,X2] : ((~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2)) | intruder_message(triple(X0,X1,X2)))),
inference(ennf_transformation,[],[f20])).

fof(f55,plain,(
! [X0,X1,X2] : (~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2) | intruder_message(triple(X0,X1,X2)))),
inference(flattening,[],[f54])).

fof(f91,plain,(
( ! [X2,X0,X1] : (intruder_message(triple(X0,X1,X2)) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f55])).

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-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f56,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(f57,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,[],[f56])).

fof(f92,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,[],[f57])).

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-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f60,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(f61,plain,(
! [X0,X1,X2] : (~intruder_message(X0) | ~party_of_protocol(X1) | ~party_of_protocol(X2) | message(sent(X1,X2,X0)))),
inference(flattening,[],[f60])).

fof(f94,plain,(
( ! [X2,X0,X1] : (message(sent(X1,X2,X0)) | ~party_of_protocol(X2) | ~party_of_protocol(X1) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f61])).

fof(f27,axiom,(
! [X0] : ~a_nonce(generate_key(X0))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f98,plain,(
( ! [X0] : (~a_nonce(generate_key(X0))) )),
inference(cnf_transformation,[],[f36])).

fof(f28,axiom,(
! [X0] : (a_nonce(generate_expiration_time(X0)) & a_nonce(generate_b_nonce(X0)))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f100,plain,(
( ! [X0] : (a_nonce(generate_b_nonce(X0))) )),
inference(cnf_transformation,[],[f28])).

fof(f99,plain,(
( ! [X0] : (a_nonce(generate_expiration_time(X0))) )),
inference(cnf_transformation,[],[f28])).

fof(f32,axiom,(
! [X0] : (fresh_intruder_nonce(X0) => fresh_intruder_nonce(generate_intruder_nonce(X0)))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f67,plain,(
! [X0] : (~fresh_intruder_nonce(X0) | fresh_intruder_nonce(generate_intruder_nonce(X0)))),
inference(ennf_transformation,[],[f32])).

fof(f104,plain,(
( ! [X0] : (fresh_intruder_nonce(generate_intruder_nonce(X0)) | ~fresh_intruder_nonce(X0)) )),
inference(cnf_transformation,[],[f67])).

fof(f33,axiom,(
! [X0] : (fresh_intruder_nonce(X0) => (fresh_to_b(X0) & intruder_message(X0)))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f68,plain,(
! [X0] : (~fresh_intruder_nonce(X0) | (fresh_to_b(X0) & intruder_message(X0)))),
inference(ennf_transformation,[],[f33])).

fof(f106,plain,(
( ! [X0] : (intruder_message(X0) | ~fresh_intruder_nonce(X0)) )),
inference(cnf_transformation,[],[f68])).

fof(f105,plain,(
( ! [X0] : (fresh_to_b(X0) | ~fresh_intruder_nonce(X0)) )),
inference(cnf_transformation,[],[f68])).

fof(f4,axiom,(
a_stored(pair(b,an_a_nonce))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f71,plain,(
a_stored(pair(b,an_a_nonce))),
inference(cnf_transformation,[],[f4])).

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-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f40,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(f42,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,[],[f40])).

fof(f43,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,[],[f42])).

fof(f72,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,[],[f43])).

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-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f64,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(f65,plain,(
! [X0,X1,X2] : (~intruder_message(X0) | ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2) | intruder_message(encrypt(X0,X1)))),
inference(flattening,[],[f64])).

fof(f96,plain,(
( ! [X2,X0,X1] : (intruder_message(encrypt(X0,X1)) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f65])).

fof(f24,axiom,(
! [X1,X2] : ((intruder_message(X1) & party_of_protocol(X2)) => intruder_holds(key(X1,X2)))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f62,plain,(
! [X0,X1] : ((~intruder_message(X0) | ~party_of_protocol(X1)) | intruder_holds(key(X0,X1)))),
inference(ennf_transformation,[],[f35])).

fof(f63,plain,(
! [X0,X1] : (~intruder_message(X0) | ~party_of_protocol(X1) | intruder_holds(key(X0,X1)))),
inference(flattening,[],[f62])).

fof(f95,plain,(
( ! [X0,X1] : (intruder_holds(key(X0,X1)) | ~party_of_protocol(X1) | ~intruder_message(X0)) )),
inference(cnf_transformation,[],[f63])).

fof(f31,axiom,(
fresh_intruder_nonce(an_intruder_nonce)),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f103,plain,(
fresh_intruder_nonce(an_intruder_nonce)),
inference(cnf_transformation,[],[f31])).

fof(f26,axiom,(
a_nonce(an_a_nonce)),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f97,plain,(
a_nonce(an_a_nonce)),
inference(cnf_transformation,[],[f26])).

fof(f13,axiom,(
party_of_protocol(t)),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f78,plain,(
party_of_protocol(t)),
inference(cnf_transformation,[],[f13])).

fof(f12,axiom,(
t_holds(key(bt,b))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f77,plain,(
t_holds(key(bt,b))),
inference(cnf_transformation,[],[f12])).

fof(f11,axiom,(
t_holds(key(at,a))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f76,plain,(
t_holds(key(at,a))),
inference(cnf_transformation,[],[f11])).

fof(f8,axiom,(
fresh_to_b(an_a_nonce)),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f74,plain,(
fresh_to_b(an_a_nonce)),
inference(cnf_transformation,[],[f8])).

fof(f7,axiom,(
party_of_protocol(b)),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f73,plain,(
party_of_protocol(b)),
inference(cnf_transformation,[],[f7])).

fof(f3,axiom,(
message(sent(a,b,pair(a,an_a_nonce)))),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f70,plain,(
message(sent(a,b,pair(a,an_a_nonce)))),
inference(cnf_transformation,[],[f3])).

fof(f2,axiom,(
party_of_protocol(a)),
file('/Users/korovin/TPTP-v6.1.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f69,plain,(
party_of_protocol(a)),
inference(cnf_transformation,[],[f2])).

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,[],[f75]) ).

cnf(c_233,plain,
( message(sent(b,t,triple(b,generate_b_nonce(X0_\$\$iProver_fresh_intruder_nonce_1_\$i),encrypt(triple(X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X0_\$\$iProver_fresh_intruder_nonce_1_\$i,generate_expiration_time(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)),bt))))
| ~ message(sent(X1_\$\$iProver_fresh_intruder_nonce_1_\$i,b,pair(X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X0_\$\$iProver_fresh_intruder_nonce_1_\$i)))
| ~ fresh_to_b(X0_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_6]) ).

cnf(c_10,plain,
| ~ message(sent(X1_\$i,t,triple(X1_\$i,X6_\$i,encrypt(triple(X0_\$i,X2_\$i,X3_\$i),X5_\$i))))
| ~ t_holds(key(X4_\$i,X0_\$i))
| ~ t_holds(key(X5_\$i,X1_\$i))
| ~ a_nonce(X2_\$i) ),
inference(cnf_transformation,[],[f79]) ).

cnf(c_229,plain,
| ~ message(sent(X1_\$\$iProver_fresh_intruder_nonce_1_\$i,t,triple(X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X6_\$\$iProver_fresh_intruder_nonce_1_\$i,encrypt(triple(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X2_\$\$iProver_fresh_intruder_nonce_1_\$i,X3_\$\$iProver_fresh_intruder_nonce_1_\$i),X5_\$\$iProver_fresh_intruder_nonce_1_\$i))))
| ~ t_holds(key(X4_\$\$iProver_fresh_intruder_nonce_1_\$i,X0_\$\$iProver_fresh_intruder_nonce_1_\$i))
| ~ t_holds(key(X5_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i))
| ~ a_nonce(X2_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_10]) ).

cnf(c_11,plain,
( ~ message(sent(X0_\$i,X1_\$i,X2_\$i)) | intruder_message(X2_\$i) ),
inference(cnf_transformation,[],[f80]) ).

cnf(c_228,plain,
( ~ message(sent(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X2_\$\$iProver_fresh_intruder_nonce_1_\$i))
| intruder_message(X2_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_11]) ).

cnf(c_12,plain,
( ~ intruder_message(pair(X0_\$i,X1_\$i)) | intruder_message(X1_\$i) ),
inference(cnf_transformation,[],[f82]) ).

cnf(c_227,plain,
( ~ intruder_message(pair(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i))
| intruder_message(X1_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_12]) ).

cnf(c_13,plain,
( ~ intruder_message(pair(X0_\$i,X1_\$i)) | intruder_message(X0_\$i) ),
inference(cnf_transformation,[],[f81]) ).

cnf(c_226,plain,
( ~ intruder_message(pair(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i))
| intruder_message(X0_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_13]) ).

cnf(c_14,plain,
( ~ intruder_message(triple(X0_\$i,X1_\$i,X2_\$i))
| intruder_message(X2_\$i) ),
inference(cnf_transformation,[],[f85]) ).

cnf(c_225,plain,
( ~ intruder_message(triple(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X2_\$\$iProver_fresh_intruder_nonce_1_\$i))
| intruder_message(X2_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_14]) ).

cnf(c_15,plain,
( ~ intruder_message(triple(X0_\$i,X1_\$i,X2_\$i))
| intruder_message(X1_\$i) ),
inference(cnf_transformation,[],[f84]) ).

cnf(c_224,plain,
( ~ intruder_message(triple(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X2_\$\$iProver_fresh_intruder_nonce_1_\$i))
| intruder_message(X1_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_15]) ).

cnf(c_16,plain,
( ~ intruder_message(triple(X0_\$i,X1_\$i,X2_\$i))
| intruder_message(X0_\$i) ),
inference(cnf_transformation,[],[f83]) ).

cnf(c_223,plain,
( ~ intruder_message(triple(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X2_\$\$iProver_fresh_intruder_nonce_1_\$i))
| intruder_message(X0_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_16]) ).

cnf(c_17,plain,
| intruder_message(X3_\$i) ),
inference(cnf_transformation,[],[f89]) ).

cnf(c_222,plain,
| intruder_message(X3_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_17]) ).

cnf(c_18,plain,
| intruder_message(X2_\$i) ),
inference(cnf_transformation,[],[f88]) ).

cnf(c_221,plain,
| intruder_message(X2_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_18]) ).

cnf(c_19,plain,
| intruder_message(X1_\$i) ),
inference(cnf_transformation,[],[f87]) ).

cnf(c_220,plain,
| intruder_message(X1_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_19]) ).

cnf(c_20,plain,
| intruder_message(X0_\$i) ),
inference(cnf_transformation,[],[f86]) ).

cnf(c_219,plain,
| intruder_message(X0_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_20]) ).

cnf(c_21,plain,
( intruder_message(pair(X0_\$i,X1_\$i))
| ~ intruder_message(X1_\$i)
| ~ intruder_message(X0_\$i) ),
inference(cnf_transformation,[],[f90]) ).

cnf(c_218,plain,
( intruder_message(pair(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i))
| ~ intruder_message(X1_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ intruder_message(X0_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_21]) ).

cnf(c_22,plain,
( intruder_message(triple(X0_\$i,X1_\$i,X2_\$i))
| ~ intruder_message(X1_\$i)
| ~ intruder_message(X0_\$i)
| ~ intruder_message(X2_\$i) ),
inference(cnf_transformation,[],[f91]) ).

cnf(c_217,plain,
( intruder_message(triple(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X2_\$\$iProver_fresh_intruder_nonce_1_\$i))
| ~ intruder_message(X1_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ intruder_message(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ intruder_message(X2_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_22]) ).

cnf(c_23,plain,
| ~ intruder_message(X1_\$i)
| ~ intruder_message(X0_\$i)
| ~ intruder_message(X3_\$i)
| ~ intruder_message(X2_\$i) ),
inference(cnf_transformation,[],[f92]) ).

cnf(c_216,plain,
| ~ intruder_message(X1_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ intruder_message(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ intruder_message(X2_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ intruder_message(X3_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_23]) ).

cnf(c_25,plain,
( ~ party_of_protocol(X0_\$i)
| ~ party_of_protocol(X1_\$i)
| message(sent(X1_\$i,X0_\$i,X2_\$i))
| ~ intruder_message(X2_\$i) ),
inference(cnf_transformation,[],[f94]) ).

cnf(c_215,plain,
( ~ party_of_protocol(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ party_of_protocol(X1_\$\$iProver_fresh_intruder_nonce_1_\$i)
| message(sent(X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X2_\$\$iProver_fresh_intruder_nonce_1_\$i))
| ~ intruder_message(X2_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_25]) ).

cnf(c_29,plain,
( ~ a_nonce(generate_key(X0_\$i)) ),
inference(cnf_transformation,[],[f98]) ).

cnf(c_213,plain,
( ~ a_nonce(generate_key(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)) ),
inference(subtyping,[status(esa)],[c_29]) ).

cnf(c_30,plain,
( a_nonce(generate_b_nonce(X0_\$i)) ),
inference(cnf_transformation,[],[f100]) ).

cnf(c_212,plain,
( a_nonce(generate_b_nonce(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)) ),
inference(subtyping,[status(esa)],[c_30]) ).

cnf(c_31,plain,
( a_nonce(generate_expiration_time(X0_\$i)) ),
inference(cnf_transformation,[],[f99]) ).

cnf(c_211,plain,
( a_nonce(generate_expiration_time(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)) ),
inference(subtyping,[status(esa)],[c_31]) ).

cnf(c_35,plain,
( fresh_intruder_nonce(generate_intruder_nonce(X0_\$i))
| ~ fresh_intruder_nonce(X0_\$i) ),
inference(cnf_transformation,[],[f104]) ).

cnf(c_209,plain,
( fresh_intruder_nonce(generate_intruder_nonce(X0_\$\$iProver_fresh_intruder_nonce_1_\$i))
| ~ fresh_intruder_nonce(X0_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_35]) ).

cnf(c_36,plain,
( intruder_message(X0_\$i) | ~ fresh_intruder_nonce(X0_\$i) ),
inference(cnf_transformation,[],[f106]) ).

cnf(c_208,plain,
( intruder_message(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ fresh_intruder_nonce(X0_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_36]) ).

cnf(c_37,plain,
( fresh_to_b(X0_\$i) | ~ fresh_intruder_nonce(X0_\$i) ),
inference(cnf_transformation,[],[f105]) ).

cnf(c_207,plain,
( fresh_to_b(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ fresh_intruder_nonce(X0_\$\$iProver_fresh_intruder_nonce_1_\$i) ),
inference(subtyping,[status(esa)],[c_37]) ).

cnf(c_2,plain,
( a_stored(pair(b,an_a_nonce)) ),
inference(cnf_transformation,[],[f71]) ).

cnf(c_3,plain,
( message(sent(a,X0_\$i,pair(X1_\$i,encrypt(X2_\$i,X3_\$i))))
| ~ a_stored(pair(X0_\$i,X4_\$i)) ),
inference(cnf_transformation,[],[f72]) ).

cnf(c_61,plain,
( message(sent(a,b,pair(X0_\$i,encrypt(X1_\$i,X2_\$i))))
inference(resolution,[status(thm)],[c_2,c_3]) ).

cnf(c_206,plain,
( message(sent(a,b,pair(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,encrypt(X1_\$\$iProver_fresh_intruder_nonce_1_\$i,X2_\$\$iProver_fresh_intruder_nonce_1_\$i))))
inference(subtyping,[status(esa)],[c_61]) ).

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,[],[f96]) ).

cnf(c_26,plain,
( ~ party_of_protocol(X0_\$i)
| ~ intruder_message(X1_\$i)
| intruder_holds(key(X1_\$i,X0_\$i)) ),
inference(cnf_transformation,[],[f95]) ).

cnf(c_95,plain,
( ~ party_of_protocol(X0_\$i)
| intruder_message(encrypt(X1_\$i,X2_\$i))
| ~ intruder_message(X2_\$i)
| ~ intruder_message(X1_\$i) ),
inference(resolution,[status(thm)],[c_27,c_26]) ).

cnf(c_168,plain,
( ~ party_of_protocol(X0_\$i) | ~ sP0_iProver_split ),
inference(splitting,
[splitting(split),new_symbols(definition,[~ sP0_iProver_split])],
[c_95]) ).

cnf(c_205,plain,
( ~ party_of_protocol(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ sP0_iProver_split ),
inference(subtyping,[status(esa)],[c_168]) ).

cnf(c_169,plain,
( intruder_message(encrypt(X0_\$i,X1_\$i))
| ~ intruder_message(X1_\$i)
| ~ intruder_message(X0_\$i)
| sP0_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_95]) ).

cnf(c_204,plain,
( intruder_message(encrypt(X0_\$\$iProver_fresh_intruder_nonce_1_\$i,X1_\$\$iProver_fresh_intruder_nonce_1_\$i))
| ~ intruder_message(X1_\$\$iProver_fresh_intruder_nonce_1_\$i)
| ~ intruder_message(X0_\$\$iProver_fresh_intruder_nonce_1_\$i)
| sP0_iProver_split ),
inference(subtyping,[status(esa)],[c_169]) ).

cnf(c_34,plain,
( fresh_intruder_nonce(an_intruder_nonce) ),
inference(cnf_transformation,[],[f103]) ).

cnf(c_210,plain,
( fresh_intruder_nonce(an_intruder_nonce) ),
inference(subtyping,[status(esa)],[c_34]) ).

cnf(c_28,plain,
( a_nonce(an_a_nonce) ),
inference(cnf_transformation,[],[f97]) ).

cnf(c_214,plain,
( a_nonce(an_a_nonce) ),
inference(subtyping,[status(esa)],[c_28]) ).

cnf(c_9,plain,
( party_of_protocol(t) ),
inference(cnf_transformation,[],[f78]) ).

cnf(c_230,plain,
( party_of_protocol(t) ),
inference(subtyping,[status(esa)],[c_9]) ).

cnf(c_8,plain,
( t_holds(key(bt,b)) ),
inference(cnf_transformation,[],[f77]) ).

cnf(c_231,plain,
( t_holds(key(bt,b)) ),
inference(subtyping,[status(esa)],[c_8]) ).

cnf(c_7,plain,
( t_holds(key(at,a)) ),
inference(cnf_transformation,[],[f76]) ).

cnf(c_232,plain,
( t_holds(key(at,a)) ),
inference(subtyping,[status(esa)],[c_7]) ).

cnf(c_5,plain,
( fresh_to_b(an_a_nonce) ),
inference(cnf_transformation,[],[f74]) ).

cnf(c_234,plain,
( fresh_to_b(an_a_nonce) ),
inference(subtyping,[status(esa)],[c_5]) ).

cnf(c_4,plain,
( party_of_protocol(b) ),
inference(cnf_transformation,[],[f73]) ).

cnf(c_235,plain,
( party_of_protocol(b) ),
inference(subtyping,[status(esa)],[c_4]) ).

cnf(c_1,plain,
( message(sent(a,b,pair(a,an_a_nonce))) ),
inference(cnf_transformation,[],[f70]) ).

cnf(c_236,plain,
( message(sent(a,b,pair(a,an_a_nonce))) ),
inference(subtyping,[status(esa)],[c_1]) ).

cnf(c_0,plain,
( party_of_protocol(a) ),
inference(cnf_transformation,[],[f69]) ).

cnf(c_237,plain,
( party_of_protocol(a) ),
inference(subtyping,[status(esa)],[c_0]) ).

% SZS output end Saturation
```

## iProverModulo 2.5-0.1

Guillaume Burel
ENSIIE, University Parisâ€‘Saclay, 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

%-------------------------------------------------------------
% Proof by iprover

cnf(c_67,plain,
( ~ in(X0,X1) | ~ in(X0,X2) | ~ disjoint(X1,X2) ),
file('/tmp/iprover_modulo_6ea52b.p', c_0_101) ).

cnf(c_143,plain,
( ~ in(X0,X1) | ~ in(X0,X2) | ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_67]) ).

cnf(c_201,plain,
( ~ in(X0,X1) | ~ in(X0,X2) | ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_143]) ).

cnf(c_242,plain,
( ~ in(X0,X1) | ~ in(X0,X2) | ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_201]) ).

cnf(c_273,plain,
( ~ in(X0,X1) | ~ in(X0,X2) | ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_242]) ).

cnf(c_526,plain,
( ~ in(X0,X1) | ~ in(X0,X2) | ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_273]) ).

cnf(c_89,negated_conjecture,
( disjoint(sk3_esk4_0,sk3_esk5_0) ),
file('/tmp/iprover_modulo_6ea52b.p', c_0_123) ).

cnf(c_187,negated_conjecture,
( disjoint(sk3_esk4_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_89]) ).

cnf(c_221,negated_conjecture,
( disjoint(sk3_esk4_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_187]) ).

cnf(c_222,negated_conjecture,
( disjoint(sk3_esk4_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_221]) ).

cnf(c_266,negated_conjecture,
( disjoint(sk3_esk4_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_222]) ).

cnf(c_512,negated_conjecture,
( disjoint(sk3_esk4_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_266]) ).

cnf(c_1166,plain,
( ~ in(X0,sk3_esk4_0) | ~ in(X0,sk3_esk5_0) ),
inference(resolution,[status(thm)],[c_526,c_512]) ).

cnf(c_1167,plain,
( ~ in(X0,sk3_esk4_0) | ~ in(X0,sk3_esk5_0) ),
inference(rewriting,[status(thm)],[c_1166]) ).

cnf(c_88,negated_conjecture,
( subset(sk3_esk3_0,sk3_esk4_0) ),
file('/tmp/iprover_modulo_6ea52b.p', c_0_122) ).

cnf(c_185,negated_conjecture,
( subset(sk3_esk3_0,sk3_esk4_0) ),
inference(copy,[status(esa)],[c_88]) ).

cnf(c_220,negated_conjecture,
( subset(sk3_esk3_0,sk3_esk4_0) ),
inference(copy,[status(esa)],[c_185]) ).

cnf(c_223,negated_conjecture,
( subset(sk3_esk3_0,sk3_esk4_0) ),
inference(copy,[status(esa)],[c_220]) ).

cnf(c_265,negated_conjecture,
( subset(sk3_esk3_0,sk3_esk4_0) ),
inference(copy,[status(esa)],[c_223]) ).

cnf(c_510,plain,
( subset(sk3_esk3_0,sk3_esk4_0) ),
inference(copy,[status(esa)],[c_265]) ).

cnf(c_35,plain,
( ~ in(X0,X1) | in(X0,X2) | ~ subset(X1,X2) ),
file('/tmp/iprover_modulo_6ea52b.p', c_0_193_0) ).

cnf(c_426,plain,
( ~ in(X0,X1) | in(X0,X2) | ~ subset(X1,X2) ),
inference(copy,[status(esa)],[c_35]) ).

cnf(c_534,plain,
( ~ in(X0,sk3_esk3_0) | in(X0,sk3_esk4_0) ),
inference(resolution,[status(thm)],[c_510,c_426]) ).

cnf(c_535,plain,
( ~ in(X0,sk3_esk3_0) | in(X0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_534]) ).

cnf(c_1234,plain,
( ~ in(X0,sk3_esk3_0) | ~ in(X0,sk3_esk5_0) ),
inference(resolution,[status(thm)],[c_1167,c_535]) ).

cnf(c_1235,plain,
( ~ in(X0,sk3_esk3_0) | ~ in(X0,sk3_esk5_0) ),
inference(rewriting,[status(thm)],[c_1234]) ).

cnf(c_71,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X1) ),
file('/tmp/iprover_modulo_6ea52b.p', c_0_105) ).

cnf(c_151,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X1) ),
inference(copy,[status(esa)],[c_71]) ).

cnf(c_205,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X1) ),
inference(copy,[status(esa)],[c_151]) ).

cnf(c_238,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X1) ),
inference(copy,[status(esa)],[c_205]) ).

cnf(c_251,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X1) ),
inference(copy,[status(esa)],[c_238]) ).

cnf(c_482,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X1) ),
inference(copy,[status(esa)],[c_251]) ).

cnf(c_1258,plain,
( ~ in(sk3_esk1_2(X0,sk3_esk5_0),sk3_esk3_0) | disjoint(X0,sk3_esk5_0) ),
inference(resolution,[status(thm)],[c_1235,c_482]) ).

cnf(c_1259,plain,
( ~ in(sk3_esk1_2(X0,sk3_esk5_0),sk3_esk3_0) | disjoint(X0,sk3_esk5_0) ),
inference(rewriting,[status(thm)],[c_1258]) ).

cnf(c_70,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X0) ),
file('/tmp/iprover_modulo_6ea52b.p', c_0_104) ).

cnf(c_149,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X0) ),
inference(copy,[status(esa)],[c_70]) ).

cnf(c_204,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X0) ),
inference(copy,[status(esa)],[c_149]) ).

cnf(c_239,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X0) ),
inference(copy,[status(esa)],[c_204]) ).

cnf(c_250,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X0) ),
inference(copy,[status(esa)],[c_239]) ).

cnf(c_480,plain,
( disjoint(X0,X1) | in(sk3_esk1_2(X0,X1),X0) ),
inference(copy,[status(esa)],[c_250]) ).

cnf(c_1510,plain,
( disjoint(sk3_esk3_0,sk3_esk5_0) ),
inference(resolution,[status(thm)],[c_1259,c_480]) ).

cnf(c_1511,plain,
( disjoint(sk3_esk3_0,sk3_esk5_0) ),
inference(rewriting,[status(thm)],[c_1510]) ).

cnf(c_80,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk5_0) ),
file('/tmp/iprover_modulo_6ea52b.p', c_0_120) ).

cnf(c_183,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_80]) ).

cnf(c_212,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_183]) ).

cnf(c_231,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_212]) ).

cnf(c_257,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_231]) ).

cnf(c_494,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk5_0) ),
inference(copy,[status(esa)],[c_257]) ).

cnf(c_2721,plain,
( \$false ),
inference(forward_subsumption_resolution,[status(thm)],[c_1511,c_494]) ).

% SZS output end CNFRefutation
```

## lean-nanoCoP 1.0

Jens Otten
University of Oslo, Norway

### Sample solution for SET014^4

If leanCoP proves it ...
```% SZS status Theorem for SEU140+2.p
% SZS output start Proof for SEU140+2.p

%-----------------------------------------------------
fof(t63_xboole_1, conjecture, ! [_62808, _62811, _62814] : (subset(_62808, _62811) & disjoint(_62811, _62814) => disjoint(_62808, _62814)), file('SEU140+2.p', t63_xboole_1)).
fof(d3_tarski, axiom, ! [_63043, _63046] : (subset(_63043, _63046) <=> ! [_63064] : (in(_63064, _63043) => in(_63064, _63046))), file('SEU140+2.p', d3_tarski)).
fof(t3_xboole_0, lemma, ! [_63293, _63296] : (~ (~ disjoint(_63293, _63296) & ! [_63318] : ~ (in(_63318, _63293) & in(_63318, _63296))) & ~ (? [_63318] : (in(_63318, _63293) & in(_63318, _63296)) & disjoint(_63293, _63296))), 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(_28677, _28733), in(_28847, _28677), -(in(_28847, _28733))], clausify(d3_tarski)).
cnf(5, plain, [-(disjoint(_39765, _39852)), -(in(9 ^ [_39852, _39765], _39765))], clausify(t3_xboole_0)).
cnf(6, plain, [-(disjoint(_39765, _39852)), -(in(9 ^ [_39852, _39765], _39852))], clausify(t3_xboole_0)).
cnf(7, plain, [disjoint(_39765, _39852), in(_40269, _39765), in(_40269, _39852)], clausify(t3_xboole_0)).

cnf('1',plain,[disjoint(12 ^ [], 13 ^ []), in(9 ^ [13 ^ [], 11 ^ []], 12 ^ []), in(9 ^ [13 ^ [], 11 ^ []], 13 ^ [])],start(7,bind([[_39765, _40269, _39852], [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([[_28733, _28847, _28677], [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([[_39765, _39852], [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([[_39765, _39852], [11 ^ [], 13 ^ []]]))).
cnf('1.3.1',plain,[disjoint(11 ^ [], 13 ^ [])],extension(3)).
%-----------------------------------------------------

% SZS output end Proof for SEU140+2.p
```
If nanoCoP proves it ...
```% SZS status Theorem for SEU140+2.p
% SZS output start Proof for SEU140+2.p

- I^V is skolem term f_I(V) for variable list V
- (I^K)^V:C is clause C with index (I^K)^V

Non-clausal matrix:
[(589 ^ _84387) ^ [] : [-(subset(585 ^ [], 586 ^ []))], (591 ^ _84387) ^ [] : [-(disjoint(586 ^ [], 587 ^ []))], (593 ^ _84387) ^ [] : [disjoint(585 ^ [], 587 ^ [])], (86 ^ _84387) ^ [_87252, _87254, _87256, _87258] : [-(set_difference(_87258, _87254) = set_difference(_87256, _87252)), _87258 = _87256, _87254 = _87252], (96 ^ _84387) ^ [_87611, _87613, _87615, _87617] : [-(set_intersection2(_87617, _87613) = set_intersection2(_87615, _87611)), _87617 = _87615, _87613 = _87611], (106 ^ _84387) ^ [_87950, _87952, _87954, _87956] : [-(set_union2(_87956, _87952) = set_union2(_87954, _87950)), _87956 = _87954, _87952 = _87950], (2 ^ _84387) ^ [_84535] : [-(_84535 = _84535)], (4 ^ _84387) ^ [_84642, _84644] : [_84644 = _84642, -(_84642 = _84644)], (10 ^ _84387) ^ [_84846, _84848, _84850] : [-(_84850 = _84846), _84850 = _84848, _84848 = _84846], (20 ^ _84387) ^ [_85187, _85189, _85191, _85193] : [-(proper_subset(_85191, _85187)), proper_subset(_85193, _85189), _85193 = _85191, _85189 = _85187], (34 ^ _84387) ^ [_85631, _85633, _85635, _85637] : [-(in(_85635, _85631)), in(_85637, _85633), _85637 = _85635, _85633 = _85631], (48 ^ _84387) ^ [_86047, _86049] : [-(empty(_86047)), _86049 = _86047, empty(_86049)], (58 ^ _84387) ^ [_86370, _86372, _86374, _86376] : [-(subset(_86374, _86370)), subset(_86376, _86372), _86376 = _86374, _86372 = _86370], (72 ^ _84387) ^ [_86794, _86796, _86798, _86800] : [-(disjoint(_86798, _86794)), disjoint(_86800, _86796), _86800 = _86798, _86796 = _86794], (116 ^ _84387) ^ [_88291, _88293] : [in(_88293, _88291), in(_88291, _88293)], (122 ^ _84387) ^ [_88502, _88504] : [proper_subset(_88504, _88502), proper_subset(_88502, _88504)], (128 ^ _84387) ^ [_88698, _88700] : [-(set_union2(_88700, _88698) = set_union2(_88698, _88700))], (130 ^ _84387) ^ [_88798, _88800] : [-(set_intersection2(_88800, _88798) = set_intersection2(_88798, _88800))], (132 ^ _84387) ^ [_88942, _88944] : [_88944 = _88942, 135 ^ _84387 : [(136 ^ _84387) ^ [] : [-(subset(_88944, _88942))], (138 ^ _84387) ^ [] : [-(subset(_88942, _88944))]]], (140 ^ _84387) ^ [_89179, _89181] : [-(_89181 = _89179), subset(_89181, _89179), subset(_89179, _89181)], (150 ^ _84387) ^ [_89495] : [_89495 = empty_set, 153 ^ _84387 : [(154 ^ _84387) ^ [_89608] : [in(_89608, _89495)]]], (156 ^ _84387) ^ [_89674] : [-(in(157 ^ [_89674], _89674)), -(_89674 = empty_set)], (185 ^ _84387) ^ [_90704, _90706, _90708] : [-(_90704 = set_union2(_90708, _90706)), 189 ^ _84387 : [(190 ^ _84387) ^ [] : [-(in(186 ^ [_90704, _90706, _90708], _90704))], (192 ^ _84387) ^ [] : [in(186 ^ [_90704, _90706, _90708], _90708)], (194 ^ _84387) ^ [] : [in(186 ^ [_90704, _90706, _90708], _90706)]], 195 ^ _84387 : [(202 ^ _84387) ^ [] : [in(186 ^ [_90704, _90706, _90708], _90704)], (196 ^ _84387) ^ [] : [-(in(186 ^ [_90704, _90706, _90708], _90708)), -(in(186 ^ [_90704, _90706, _90708], _90706))]]], (163 ^ _84387) ^ [_89979, _89981, _89983] : [_89979 = set_union2(_89983, _89981), 166 ^ _84387 : [(177 ^ _84387) ^ [_90439] : [178 ^ _84387 : [(179 ^ _84387) ^ [] : [in(_90439, _89983)], (181 ^ _84387) ^ [] : [in(_90439, _89981)]], -(in(_90439, _89979))], (167 ^ _84387) ^ [_90161] : [in(_90161, _89979), -(in(_90161, _89983)), -(in(_90161, _89981))]]], (216 ^ _84387) ^ [_91798, _91800] : [218 ^ _84387 : [(219 ^ _84387) ^ [] : [-(in(217 ^ [_91798, _91800], _91800))], (221 ^ _84387) ^ [] : [in(217 ^ [_91798, _91800], _91798)]], -(subset(_91800, _91798))], (206 ^ _84387) ^ [_91484, _91486] : [subset(_91486, _91484), 209 ^ _84387 : [(210 ^ _84387) ^ [_91621] : [in(_91621, _91486), -(in(_91621, _91484))]]], (247 ^ _84387) ^ [_92923, _92925, _92927] : [-(_92923 = set_intersection2(_92927, _92925)), 259 ^ _84387 : [(260 ^ _84387) ^ [] : [-(in(248 ^ [_92923, _92925, _92927], _92927))], (262 ^ _84387) ^ [] : [-(in(248 ^ [_92923, _92925, _92927], _92925))], (264 ^ _84387) ^ [] : [in(248 ^ [_92923, _92925, _92927], _92923)]], 251 ^ _84387 : [(252 ^ _84387) ^ [] : [-(in(248 ^ [_92923, _92925, _92927], _92923))], (254 ^ _84387) ^ [] : [in(248 ^ [_92923, _92925, _92927], _92927), in(248 ^ [_92923, _92925, _92927], _92925)]]], (225 ^ _84387) ^ [_92198, _92200, _92202] : [_92198 = set_intersection2(_92202, _92200), 228 ^ _84387 : [(229 ^ _84387) ^ [_92380] : [in(_92380, _92198), 232 ^ _84387 : [(233 ^ _84387) ^ [] : [-(in(_92380, _92202))], (235 ^ _84387) ^ [] : [-(in(_92380, _92200))]]], (237 ^ _84387) ^ [_92639] : [-(in(_92639, _92198)), in(_92639, _92202), in(_92639, _92200)]]], (290 ^ _84387) ^ [_94450, _94452, _94454] : [-(_94450 = set_difference(_94454, _94452)), 302 ^ _84387 : [(303 ^ _84387) ^ [] : [-(in(291 ^ [_94450, _94452, _94454], _94454))], (305 ^ _84387) ^ [] : [in(291 ^ [_94450, _94452, _94454], _94452)], (307 ^ _84387) ^ [] : [in(291 ^ [_94450, _94452, _94454], _94450)]], 294 ^ _84387 : [(295 ^ _84387) ^ [] : [-(in(291 ^ [_94450, _94452, _94454], _94450))], (297 ^ _84387) ^ [] : [in(291 ^ [_94450, _94452, _94454], _94454), -(in(291 ^ [_94450, _94452, _94454], _94452))]]], (268 ^ _84387) ^ [_93719, _93721, _93723] : [_93719 = set_difference(_93723, _93721), 271 ^ _84387 : [(272 ^ _84387) ^ [_93903] : [in(_93903, _93719), 275 ^ _84387 : [(276 ^ _84387) ^ [] : [-(in(_93903, _93723))], (278 ^ _84387) ^ [] : [in(_93903, _93721)]]], (280 ^ _84387) ^ [_94163] : [-(in(_94163, _93719)), in(_94163, _93723), -(in(_94163, _93721))]]], (311 ^ _84387) ^ [_95236, _95238] : [disjoint(_95238, _95236), -(set_intersection2(_95238, _95236) = empty_set)], (317 ^ _84387) ^ [_95404, _95406] : [set_intersection2(_95406, _95404) = empty_set, -(disjoint(_95406, _95404))], (323 ^ _84387) ^ [_95651, _95653] : [proper_subset(_95653, _95651), 326 ^ _84387 : [(327 ^ _84387) ^ [] : [-(subset(_95653, _95651))], (329 ^ _84387) ^ [] : [_95653 = _95651]]], (331 ^ _84387) ^ [_95889, _95891] : [-(proper_subset(_95891, _95889)), subset(_95891, _95889), -(_95891 = _95889)], (341 ^ _84387) ^ [] : [true___, -(true___)], (347 ^ _84387) ^ [] : [true___, -(true___)], (353 ^ _84387) ^ [] : [true___, -(true___)], (359 ^ _84387) ^ [] : [true___, -(true___)], (365 ^ _84387) ^ [] : [-(empty(empty_set))], (367 ^ _84387) ^ [_96722, _96724] : [-(empty(_96724)), empty(set_union2(_96724, _96722))], (373 ^ _84387) ^ [_96938, _96940] : [-(empty(_96940)), empty(set_union2(_96938, _96940))], (379 ^ _84387) ^ [_97139, _97141] : [-(set_union2(_97141, _97141) = _97141)], (381 ^ _84387) ^ [_97236, _97238] : [-(set_intersection2(_97238, _97238) = _97238)], (383 ^ _84387) ^ [_97332, _97334] : [proper_subset(_97334, _97334)], (385 ^ _84387) ^ [_97470, _97472] : [set_difference(_97472, _97470) = empty_set, -(subset(_97472, _97470))], (391 ^ _84387) ^ [_97638, _97640] : [subset(_97640, _97638), -(set_difference(_97640, _97638) = empty_set)], (398 ^ _84387) ^ [] : [-(empty(396 ^ []))], (401 ^ _84387) ^ [] : [empty(399 ^ [])], (403 ^ _84387) ^ [_98020, _98022] : [-(subset(_98022, _98022))], (405 ^ _84387) ^ [_98129, _98131] : [disjoint(_98131, _98129), -(disjoint(_98129, _98131))], (411 ^ _84387) ^ [_98339, _98341] : [subset(_98341, _98339), -(set_union2(_98341, _98339) = _98339)], (417 ^ _84387) ^ [_98540, _98542] : [-(subset(set_intersection2(_98542, _98540), _98542))], (419 ^ _84387) ^ [_98666, _98668, _98670] : [-(subset(_98670, set_intersection2(_98668, _98666))), subset(_98670, _98668), subset(_98670, _98666)], (429 ^ _84387) ^ [_98952] : [-(set_union2(_98952, empty_set) = _98952)], (431 ^ _84387) ^ [_99076, _99078, _99080] : [-(subset(_99080, _99076)), subset(_99080, _99078), subset(_99078, _99076)], (441 ^ _84387) ^ [_99399, _99401, _99403] : [subset(_99403, _99401), -(subset(set_intersection2(_99403, _99399), set_intersection2(_99401, _99399)))], (447 ^ _84387) ^ [_99627, _99629] : [subset(_99629, _99627), -(set_intersection2(_99629, _99627) = _99629)], (453 ^ _84387) ^ [_99814] : [-(set_intersection2(_99814, empty_set) = empty_set)], (455 ^ _84387) ^ [_99924, _99926] : [-(_99926 = _99924), 459 ^ _84387 : [(460 ^ _84387) ^ [] : [-(in(456 ^ [_99924, _99926], _99926))], (462 ^ _84387) ^ [] : [in(456 ^ [_99924, _99926], _99924)]], 463 ^ _84387 : [(464 ^ _84387) ^ [] : [-(in(456 ^ [_99924, _99926], _99924))], (466 ^ _84387) ^ [] : [in(456 ^ [_99924, _99926], _99926)]]], (470 ^ _84387) ^ [_100425] : [-(subset(empty_set, _100425))], (472 ^ _84387) ^ [_100546, _100548, _100550] : [subset(_100550, _100548), -(subset(set_difference(_100550, _100546), set_difference(_100548, _100546)))], (478 ^ _84387) ^ [_100759, _100761] : [-(subset(set_difference(_100761, _100759), _100761))], (480 ^ _84387) ^ [_100900, _100902] : [set_difference(_100902, _100900) = empty_set, -(subset(_100902, _100900))], (486 ^ _84387) ^ [_101068, _101070] : [subset(_101070, _101068), -(set_difference(_101070, _101068) = empty_set)], (492 ^ _84387) ^ [_101271, _101273] : [-(set_union2(_101273, set_difference(_101271, _101273)) = set_union2(_101273, _101271))], (494 ^ _84387) ^ [_101360] : [-(set_difference(_101360, empty_set) = _101360)], (496 ^ _84387) ^ [_101490, _101492] : [-(disjoint(_101492, _101490)), 500 ^ _84387 : [(501 ^ _84387) ^ [] : [-(in(499 ^ [_101490, _101492], _101492))], (503 ^ _84387) ^ [] : [-(in(499 ^ [_101490, _101492], _101490))]]], (505 ^ _84387) ^ [_101804, _101806] : [disjoint(_101806, _101804), 506 ^ _84387 : [(507 ^ _84387) ^ [_101896] : [in(_101896, _101806), in(_101896, _101804)]]], (515 ^ _84387) ^ [_102153] : [subset(_102153, empty_set), -(_102153 = empty_set)], (521 ^ _84387) ^ [_102342, _102344] : [-(set_difference(set_union2(_102344, _102342), _102342) = set_difference(_102344, _102342))], (523 ^ _84387) ^ [_102460, _102462] : [subset(_102462, _102460), -(_102460 = set_union2(_102462, set_difference(_102460, _102462)))], (529 ^ _84387) ^ [_102667, _102669] : [-(set_difference(_102669, set_difference(_102669, _102667)) = set_intersection2(_102669, _102667))], (531 ^ _84387) ^ [_102756] : [-(set_difference(empty_set, _102756) = empty_set)], (533 ^ _84387) ^ [_102886, _102888] : [-(disjoint(_102888, _102886)), -(in(536 ^ [_102886, _102888], set_intersection2(_102888, _102886)))], (540 ^ _84387) ^ [_103121, _103123] : [541 ^ _84387 : [(542 ^ _84387) ^ [_103194] : [in(_103194, set_intersection2(_103123, _103121))]], disjoint(_103123, _103121)], (546 ^ _84387) ^ [_103360, _103362] : [subset(_103362, _103360), proper_subset(_103360, _103362)], (552 ^ _84387) ^ [_103555] : [empty(_103555), -(_103555 = empty_set)], (558 ^ _84387) ^ [_103757, _103759] : [in(_103759, _103757), empty(_103757)], (564 ^ _84387) ^ [_103949, _103951] : [-(subset(_103951, set_union2(_103951, _103949)))], (566 ^ _84387) ^ [_104061, _104063] : [empty(_104063), -(_104063 = _104061), empty(_104061)], (576 ^ _84387) ^ [_104352, _104354, _104356] : [-(subset(set_union2(_104356, _104352), _104354)), subset(_104356, _104354), subset(_104352, _104354)]]
Connection proof:
[(505 ^ 0) ^ [587 ^ [], 586 ^ []] : [disjoint(586 ^ [], 587 ^ []), 506 ^ 0 : [(507 ^ 0) ^ [499 ^ [587 ^ [], 585 ^ []]] : [in(499 ^ [587 ^ [], 585 ^ []], 586 ^ []), in(499 ^ [587 ^ [], 585 ^ []], 587 ^ [])]]], [(591 ^ 1) ^ [] : [-(disjoint(586 ^ [], 587 ^ []))]], [(163 ^ 3) ^ [586 ^ [], set_difference(586 ^ [], 585 ^ []), 585 ^ []] : [-(in(499 ^ [587 ^ [], 585 ^ []], 586 ^ [])), 166 ^ 3 : [(177 ^ 3) ^ [499 ^ [587 ^ [], 585 ^ []]] : [178 ^ 3 : [(179 ^ 3) ^ [] : [in(499 ^ [587 ^ [], 585 ^ []], 585 ^ [])], (181 ^ 3) ^ [] : [in(499 ^ [587 ^ [], 585 ^ []], set_difference(586 ^ [], 585 ^ []))]]]], 586 ^ [] = set_union2(585 ^ [], set_difference(586 ^ [], 585 ^ []))], [(496 ^ 8) ^ [587 ^ [], 585 ^ []] : [-(in(499 ^ [587 ^ [], 585 ^ []], 585 ^ [])), 500 ^ 8 : [(501 ^ 8) ^ [] : []], -(disjoint(585 ^ [], 587 ^ []))], [(593 ^ 9) ^ [] : [disjoint(585 ^ [], 587 ^ [])]]], [(523 ^ 4) ^ [586 ^ [], 585 ^ []] : [-(586 ^ [] = set_union2(585 ^ [], set_difference(586 ^ [], 585 ^ []))), subset(585 ^ [], 586 ^ [])], [(589 ^ 5) ^ [] : [-(subset(585 ^ [], 586 ^ []))]]]], [(496 ^ 3) ^ [587 ^ [], 585 ^ []] : [-(in(499 ^ [587 ^ [], 585 ^ []], 587 ^ [])), 500 ^ 3 : [(503 ^ 3) ^ [] : []], -(disjoint(585 ^ [], 587 ^ []))], [(593 ^ 4) ^ [] : [disjoint(585 ^ [], 587 ^ [])]]]]

% SZS output end Proof for SEU140+2.p
```

## LEO-II 1.7.0

Alexander Steen
Freie Universität Berlin, Germany

### Sample solution for SET014^4

```% SZS status Theorem for /opt/TPTP/Problems/SET/SET014^4.p : (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:7,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('/opt/TPTP/Problems/SET/SET014^4.p',complement)).
thf(disjoint,definition,(disjoint = (^[X:(\$i>\$o),Y:(\$i>\$o)]: (((intersection@X)@Y) = emptyset))),file('/opt/TPTP/Problems/SET/SET014^4.p',disjoint)).
thf(emptyset,definition,(emptyset = (^[X:\$i]: \$false)),file('/opt/TPTP/Problems/SET/SET014^4.p',emptyset)).
thf(excl_union,definition,(excl_union = (^[X:(\$i>\$o),Y:(\$i>\$o),U:\$i]: (((X@U) & (~ (Y@U))) | ((~ (X@U)) & (Y@U))))),file('/opt/TPTP/Problems/SET/SET014^4.p',excl_union)).
thf(in,definition,(in = (^[X:\$i,M:(\$i>\$o)]: (M@X))),file('/opt/TPTP/Problems/SET/SET014^4.p',in)).
thf(intersection,definition,(intersection = (^[X:(\$i>\$o),Y:(\$i>\$o),U:\$i]: ((X@U) & (Y@U)))),file('/opt/TPTP/Problems/SET/SET014^4.p',intersection)).
thf(is_a,definition,(is_a = (^[X:\$i,M:(\$i>\$o)]: (M@X))),file('/opt/TPTP/Problems/SET/SET014^4.p',is_a)).
thf(meets,definition,(meets = (^[X:(\$i>\$o),Y:(\$i>\$o)]: (?[U:\$i]: ((X@U) & (Y@U))))),file('/opt/TPTP/Problems/SET/SET014^4.p',meets)).
thf(misses,definition,(misses = (^[X:(\$i>\$o),Y:(\$i>\$o)]: (~ (?[U:\$i]: ((X@U) & (Y@U)))))),file('/opt/TPTP/Problems/SET/SET014^4.p',misses)).
thf(setminus,definition,(setminus = (^[X:(\$i>\$o),Y:(\$i>\$o),U:\$i]: ((X@U) & (~ (Y@U))))),file('/opt/TPTP/Problems/SET/SET014^4.p',setminus)).
thf(singleton,definition,(singleton = (^[X:\$i,U:\$i]: (U = X))),file('/opt/TPTP/Problems/SET/SET014^4.p',singleton)).
thf(subset,definition,(subset = (^[X:(\$i>\$o),Y:(\$i>\$o)]: (![U:\$i]: ((X@U) => (Y@U))))),file('/opt/TPTP/Problems/SET/SET014^4.p',subset)).
thf(union,definition,(union = (^[X:(\$i>\$o),Y:(\$i>\$o),U:\$i]: ((X@U) | (Y@U)))),file('/opt/TPTP/Problems/SET/SET014^4.p',union)).
thf(unord_pair,definition,(unord_pair = (^[X:\$i,Y:\$i,U:\$i]: ((U = X) | (U = Y)))),file('/opt/TPTP/Problems/SET/SET014^4.p',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('/opt/TPTP/Problems/SET/SET014^4.p',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 /opt/TPTP/Problems/SET/SET014^4.p : (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:7,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)
```

## Leo-III 1.1

Alexander Steen
Freie Universität Berlin, Germany

### Sample solution for SET014^4

```% SZS status Theorem for /opt/TPTP/Problems/SET/SET014^4.p : 3651 ms resp. 1253 ms w/o parsing
% SZS output start CNFRefutation for /opt/TPTP/Problems/SET/SET014^4.p
thf(union_type, type, union: ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(union_def, definition, (union = (^ [A:(\$i > \$o),B:(\$i > \$o),C:\$i]: ((A @ C) | (B @ C))))).
thf(subset_type, type, subset: ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(subset_def, definition, (subset = (^ [A:(\$i > \$o),B:(\$i > \$o)]: ! [C:\$i]: ((A @ C) => (B @ C))))).
thf(sk1_type, type, sk1: (\$i > \$o)).
thf(sk2_type, type, sk2: (\$i > \$o)).
thf(sk3_type, type, sk3: (\$i > \$o)).
thf(sk4_type, type, sk4: \$i).
thf(1,conjecture,((! [A:(\$i > \$o),B:(\$i > \$o),C:(\$i > \$o)]: (((subset @ A @ C) & (subset @ B @ C)) => (subset @ (union @ A @ B) @ C)))),file('/opt/TPTP/Problems/SET/SET014^4.p',thm)).
thf(2,negated_conjecture,((~ (! [A:(\$i > \$o),B:(\$i > \$o),C:(\$i > \$o)]: (((subset @ A @ C) & (subset @ B @ C)) => (subset @ (union @ A @ B) @ C))))),inference(neg_conjecture,[status(cth)],[1])).
thf(3,plain,((~ (! [A:(\$i > \$o),B:(\$i > \$o),C:(\$i > \$o)]: ((! [D:\$i]: ((A @ D) => (C @ D)) & ! [D:\$i]: ((B @ D) => (C @ D))) => (! [D:\$i]: (((A @ D) | (B @ D)) => (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(5,plain,((sk1 @ sk4) | (sk2 @ sk4)),inference(cnf,[status(esa)],[3])).
thf(6,plain,(! [A:\$i] : ((~ (sk2 @ A)) | (sk3 @ A))),inference(cnf,[status(esa)],[3])).
thf(8,plain,(! [A:\$i] : ((~ (sk2 @ A)) | (sk3 @ A))),inference(simp,[status(thm)],[6])).
thf(4,plain,((~ (sk3 @ sk4))),inference(cnf,[status(esa)],[3])).
thf(11,plain,(! [A:\$i] : ((~ (sk2 @ A)) | ((sk3 @ sk4) != (sk3 @ A)))),inference(paramod_ordered,[status(thm)],[8,4])).
thf(12,plain,((~ (sk2 @ sk4))),inference(pattern_uni,[status(thm)],[11:[bind(A, \$thf(sk4))]])).
thf(13,plain,((sk1 @ sk4) | ((sk2 @ sk4) != (sk2 @ sk4))),inference(paramod_ordered,[status(thm)],[5,12])).
thf(14,plain,((sk1 @ sk4)),inference(pattern_uni,[status(thm)],[13:[]])).
thf(7,plain,(! [A:\$i] : ((~ (sk1 @ A)) | (sk3 @ A))),inference(cnf,[status(esa)],[3])).
thf(9,plain,(! [A:\$i] : ((~ (sk1 @ A)) | ((sk3 @ sk4) != (sk3 @ A)))),inference(paramod_ordered,[status(thm)],[7,4])).
thf(10,plain,((~ (sk1 @ sk4))),inference(pattern_uni,[status(thm)],[9:[bind(A, \$thf(sk4))]])).
thf(15,plain,(((sk1 @ sk4) != (sk1 @ sk4))),inference(paramod_ordered,[status(thm)],[14,10])).
thf(16,plain,(\$false),inference(pattern_uni,[status(thm)],[15:[]])).
% SZS output end CNFRefutation for /opt/TPTP/Problems/SET/SET014^4.p
```

## MaLARea 0.6

Josef Urban
Czech Technical University in Prague, Czech Republic

### Sample solution for SEU140+2

```# SZS status Theorem
# SZS output start CNFRefutation
fof(t63_xboole_1, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t63_xboole_1)).
fof(symmetry_r1_xboole_0, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', symmetry_r1_xboole_0)).
fof(t1_xboole_1, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X2,X3))=>subset(X1,X3))), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t1_xboole_1)).
fof(t40_xboole_1, lemma, (![X1]:![X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t40_xboole_1)).
fof(commutativity_k2_xboole_0, axiom, (![X1]:![X2]:set_union2(X1,X2)=set_union2(X2,X1)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', commutativity_k2_xboole_0)).
fof(t2_boole, axiom, (![X1]:set_intersection2(X1,empty_set)=empty_set), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t2_boole)).
fof(t48_xboole_1, lemma, (![X1]:![X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t48_xboole_1)).
fof(t3_xboole_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/SystemOnTPTP4890/SEU140+2.tptp', t3_xboole_0)).
fof(d4_xboole_0, axiom, (![X1]:![X2]:![X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2)))))), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', d4_xboole_0)).
fof(l32_xboole_1, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', l32_xboole_1)).
fof(d7_xboole_0, axiom, (![X1]:![X2]:(disjoint(X1,X2)<=>set_intersection2(X1,X2)=empty_set)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', d7_xboole_0)).
fof(t39_xboole_1, lemma, (![X1]:![X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t39_xboole_1)).
fof(t3_boole, axiom, (![X1]:set_difference(X1,empty_set)=X1), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t3_boole)).
fof(commutativity_k3_xboole_0, axiom, (![X1]:![X2]:set_intersection2(X1,X2)=set_intersection2(X2,X1)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', commutativity_k3_xboole_0)).
fof(t36_xboole_1, lemma, (![X1]:![X2]:subset(set_difference(X1,X2),X1)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t36_xboole_1)).
fof(t12_xboole_1, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_union2(X1,X2)=X2)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t12_xboole_1)).
fof(t1_boole, axiom, (![X1]:set_union2(X1,empty_set)=X1), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t1_boole)).
fof(c_0_17, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
fof(c_0_18, plain, (![X3]:![X4]:(~disjoint(X3,X4)|disjoint(X4,X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])).
fof(c_0_19, 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_17])])])).
fof(c_0_20, lemma, (![X4]:![X5]:![X6]:((~subset(X4,X5)|~subset(X5,X6))|subset(X4,X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])).
fof(c_0_21, lemma, (![X3]:![X4]:set_difference(set_union2(X3,X4),X4)=set_difference(X3,X4)), inference(variable_rename,[status(thm)],[t40_xboole_1])).
fof(c_0_22, plain, (![X3]:![X4]:set_union2(X3,X4)=set_union2(X4,X3)), inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0])).
fof(c_0_23, plain, (![X2]:set_intersection2(X2,empty_set)=empty_set), inference(variable_rename,[status(thm)],[t2_boole])).
fof(c_0_24, lemma, (![X3]:![X4]:set_difference(X3,set_difference(X3,X4))=set_intersection2(X3,X4)), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_25, lemma, (![X4]:![X5]:![X4]:![X5]:![X7]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X7,X4)|~in(X7,X5))|~disjoint(X4,X5)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])])).
cnf(c_0_26,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_27,negated_conjecture,(disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_28, plain, (![X5]:![X6]:![X7]:![X8]:![X8]:![X5]:![X6]:![X7]:(((((in(X8,X5)|~in(X8,X7))|X7!=set_difference(X5,X6))&((~in(X8,X6)|~in(X8,X7))|X7!=set_difference(X5,X6)))&(((~in(X8,X5)|in(X8,X6))|in(X8,X7))|X7!=set_difference(X5,X6)))&(((~in(esk5_3(X5,X6,X7),X7)|(~in(esk5_3(X5,X6,X7),X5)|in(esk5_3(X5,X6,X7),X6)))|X7=set_difference(X5,X6))&(((in(esk5_3(X5,X6,X7),X5)|in(esk5_3(X5,X6,X7),X7))|X7=set_difference(X5,X6))&((~in(esk5_3(X5,X6,X7),X6)|in(esk5_3(X5,X6,X7),X7))|X7=set_difference(X5,X6)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_xboole_0])])])])])])])])).
fof(c_0_29, lemma, (![X3]:![X4]:![X3]:![X4]:((set_difference(X3,X4)!=empty_set|subset(X3,X4))&(~subset(X3,X4)|set_difference(X3,X4)=empty_set))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])])])).
cnf(c_0_30,lemma,(subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_20])).
cnf(c_0_31,negated_conjecture,(subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_32, plain, (![X3]:![X4]:![X3]:![X4]:((~disjoint(X3,X4)|set_intersection2(X3,X4)=empty_set)&(set_intersection2(X3,X4)!=empty_set|disjoint(X3,X4)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])])])).
cnf(c_0_33,lemma,(set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_34,plain,(set_union2(X1,X2)=set_union2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_22])).
fof(c_0_35, lemma, (![X3]:![X4]:set_union2(X3,set_difference(X4,X3))=set_union2(X3,X4)), inference(variable_rename,[status(thm)],[t39_xboole_1])).
cnf(c_0_36,plain,(set_intersection2(X1,empty_set)=empty_set), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_37,lemma,(set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
fof(c_0_38, plain, (![X2]:set_difference(X2,empty_set)=X2), inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_39,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_40,negated_conjecture,(disjoint(esk13_0,esk12_0)), inference(spm,[status(thm)],[c_0_26, c_0_27])).
cnf(c_0_41,plain,(in(X4,X2)|X1!=set_difference(X2,X3)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_28])).
fof(c_0_42, plain, (![X3]:![X4]:set_intersection2(X3,X4)=set_intersection2(X4,X3)), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])).
cnf(c_0_43,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_44,negated_conjecture,(subset(X1,esk12_0)|~subset(X1,esk11_0)), inference(spm,[status(thm)],[c_0_30, c_0_31])).
fof(c_0_45, lemma, (![X3]:![X4]:subset(set_difference(X3,X4),X3)), inference(variable_rename,[status(thm)],[t36_xboole_1])).
fof(c_0_46, lemma, (![X3]:![X4]:(~subset(X3,X4)|set_union2(X3,X4)=X4)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])).
cnf(c_0_47,plain,(disjoint(X1,X2)|set_intersection2(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_48,lemma,(set_difference(set_union2(X1,X2),X1)=set_difference(X2,X1)), inference(spm,[status(thm)],[c_0_33, c_0_34])).
cnf(c_0_49,lemma,(set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_35])).
cnf(c_0_50,plain,(set_difference(X1,set_difference(X1,empty_set))=empty_set), inference(rw,[status(thm)],[c_0_36, c_0_37])).
cnf(c_0_51,plain,(set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_38])).
cnf(c_0_52,negated_conjecture,(~in(X1,esk12_0)|~in(X1,esk13_0)), inference(spm,[status(thm)],[c_0_39, c_0_40])).
cnf(c_0_53,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_54,plain,(in(X1,X2)|~in(X1,set_difference(X2,X3))), inference(er,[status(thm)],[c_0_41])).
cnf(c_0_55,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_56,plain,(set_intersection2(X1,X2)=set_intersection2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_57,lemma,(set_difference(X1,esk12_0)=empty_set|~subset(X1,esk11_0)), inference(spm,[status(thm)],[c_0_43, c_0_44])).
cnf(c_0_58,lemma,(subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_59,plain,(set_intersection2(X1,X2)=empty_set|~disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_32])).
fof(c_0_60, plain, (![X2]:set_union2(X2,empty_set)=X2), inference(variable_rename,[status(thm)],[t1_boole])).
cnf(c_0_61,lemma,(set_union2(X1,X2)=X2|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_62,plain,(disjoint(X1,X2)|set_difference(X1,set_difference(X1,X2))!=empty_set), inference(rw,[status(thm)],[c_0_47, c_0_37])).
cnf(c_0_63,lemma,(set_difference(set_difference(X1,X2),X2)=set_difference(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_48])).
cnf(c_0_64,plain,(set_difference(X1,X1)=empty_set), inference(rw,[status(thm)],[c_0_50, c_0_51])).
cnf(c_0_65,lemma,(disjoint(X1,esk13_0)|~in(esk9_2(X1,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_52, c_0_53])).
cnf(c_0_66,lemma,(disjoint(set_difference(X1,X2),X3)|in(esk9_2(set_difference(X1,X2),X3),X1)), inference(spm,[status(thm)],[c_0_54, c_0_55])).
cnf(c_0_67,plain,(set_difference(X1,set_difference(X1,X2))=set_difference(X2,set_difference(X2,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_37]), c_0_37])).
cnf(c_0_68,lemma,(set_difference(set_difference(esk11_0,X1),esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_57, c_0_58])).
cnf(c_0_69,plain,(set_difference(X1,set_difference(X1,X2))=empty_set|~disjoint(X1,X2)), inference(rw,[status(thm)],[c_0_59, c_0_37])).
cnf(c_0_70,plain,(set_union2(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_60])).
cnf(c_0_71,lemma,(set_union2(X1,set_difference(X1,X2))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_58]), c_0_34])).
cnf(c_0_72,lemma,(disjoint(set_difference(X1,X2),X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_64])])).
cnf(c_0_73,lemma,(disjoint(set_difference(esk12_0,X1),esk13_0)), inference(spm,[status(thm)],[c_0_65, c_0_66])).
cnf(c_0_74,lemma,(set_difference(esk12_0,set_difference(esk12_0,set_difference(esk11_0,X1)))=set_difference(esk11_0,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_51])).
cnf(c_0_75,lemma,(set_difference(X1,X2)=X1|~disjoint(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_69]), c_0_70]), c_0_34]), c_0_71])).
cnf(c_0_76,lemma,(disjoint(X1,set_difference(X2,X1))), inference(spm,[status(thm)],[c_0_26, c_0_72])).
cnf(c_0_77,lemma,(disjoint(set_difference(esk11_0,X1),esk13_0)), inference(spm,[status(thm)],[c_0_73, c_0_74])).
cnf(c_0_78,lemma,(set_difference(X1,set_difference(X2,X1))=X1), inference(spm,[status(thm)],[c_0_75, c_0_76])).
cnf(c_0_79,negated_conjecture,(~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_80,lemma,(\$false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79]), ['proof']).
# SZS output end CNFRefutation
```

## Princess 170717

Philipp Rümmer
Uppsala University, Sweden

### Sample solution for DAT013=1

```% SZS status Theorem for DAT013=1
% SZS output start Proof for DAT013=1
Assumptions after simplification:
---------------------------------

(co1)
? [v0: \$int] :  ? [v1: \$int] :  ? [v2: \$int] : (in_array(v0) &  ! [v3: \$int] :
! [v4: \$int] : ( ~ (\$lesseq(v4, 0) |  ~ (\$lesseq(v3, v2)) |  ~ (\$lesseq(v1,
v3)) |  ~ (read(v0, v3) = v4)) &  ? [v3: \$int] :  ? [v4: \$int] :
(\$lesseq(v4, 0)\$lesseq(v3, v2) & \$lesseq(3, \$difference(v3, v1)) & read(v0,
v3) = v4))

Further assumptions not needed in the proof:
--------------------------------------------
ax1, ax2

Those formulas are unsatisfiable:
---------------------------------

Begin of proof
|
| DELTA: instantiating (co1) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
|   (1)  in_array(all_4_2) &  ! [v0: \$int] :  ! [v1: \$int] : ( ~ (\$lesseq(v1, 0)
|            |  ~ (\$lesseq(v0, all_4_0)) |  ~ (\$lesseq(all_4_1, v0)) |  ~
|            (read(all_4_2, v0) = v1)) &  ? [v0: \$int] :  ? [v1: \$int] :
|          (\$lesseq(v1, 0)\$lesseq(v0, all_4_0) & \$lesseq(3, \$difference(v0,
|                all_4_1)) & read(all_4_2, v0) = v1)
|
| ALPHA: (1) implies:
|   (2)   ! [v0: \$int] :  ! [v1: \$int] : ( ~ (\$lesseq(v1, 0) |  ~ (\$lesseq(v0,
|                all_4_0)) |  ~ (\$lesseq(all_4_1, v0)) |  ~ (read(all_4_2, v0) =
|              v1))
|   (3)   ? [v0: \$int] :  ? [v1: \$int] : (\$lesseq(v1, 0)\$lesseq(v0, all_4_0) &
|          \$lesseq(3, \$difference(v0, all_4_1)) & read(all_4_2, v0) = v1)
|
| DELTA: instantiating (3) with fresh symbols all_9_0, all_9_1 gives:
|   (4)  \$lesseq(all_9_0, 0)\$lesseq(all_9_1, all_4_0) & \$lesseq(3,
|          \$difference(all_9_1, all_4_1)) & read(all_4_2, all_9_1) = all_9_0
|
| ALPHA: (4) implies:
|   (5)  \$lesseq(3, \$difference(all_9_1, all_4_1))
|   (6)  \$lesseq(all_9_1, all_4_0)
|   (7)  \$lesseq(all_9_0, 0)
|   (8)  read(all_4_2, all_9_1) = all_9_0
|
| GROUND_INST: instantiating (2) with all_9_0, all_9_1, simplifying with (8)
|              gives:
|   (9)   ~ (\$lesseq(all_9_0, 0) |  ~ (\$lesseq(all_9_1, all_4_0)) |  ~
|          (\$lesseq(all_4_1, all_9_1))
|
| BETA: splitting (9) gives:
|
| Case 1:
| |
| |   (10)  \$lesseq(1, all_9_0)
| |
| | COMBINE_INEQS: (7), (10) imply:
| |   (11)  \$lesseq(0, -1)
| |
| | CLOSE: (11) is inconsistent.
| |
| Case 2:
| |
| |   (12)   ~ (\$lesseq(all_9_1, all_4_0)) |  ~ (\$lesseq(all_4_1, all_9_1))
| |
| | BETA: splitting (12) gives:
| |
| | Case 1:
| | |
| | |   (13)  \$lesseq(1, \$difference(all_9_1, all_4_0))
| | |
| | | COMBINE_INEQS: (6), (13) imply:
| | |   (14)  \$lesseq(0, -1)
| | |
| | | CLOSE: (14) is inconsistent.
| | |
| | Case 2:
| | |
| | |   (15)  \$lesseq(1, \$difference(all_4_1, all_9_1))
| | |
| | | COMBINE_INEQS: (5), (15) imply:
| | |   (16)  \$lesseq(0, -1)
| | |
| | | CLOSE: (16) is inconsistent.
| | |
| | End of split
| |
| End of split
|
End of proof
% SZS output end Proof for DAT013=1
```

## 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)].
```

## Satallax 3.0

Michael Färber
Universität Innsbruck, Austria

### Sample solution for SET014^4

```% SZS output start Proof
thf(ty\$i, type, \$i : \$tType).
thf(tyeigen__3, type, eigen__3 : \$i).
thf(tyeigen__2, type, eigen__2 : (\$i>\$o)).
thf(tyeigen__1, type, eigen__1 : (\$i>\$o)).
thf(tyeigen__0, type, eigen__0 : (\$i>\$o)).
thf(thm,conjecture,(![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:(((![X4:\$i]:((X1 @ X4) => (X3 @ X4))) & (![X4:\$i]:((X2 @ X4) => (X3 @ X4)))) => (![X4:\$i]:(((X1 @ X4) | (X2 @ X4)) => (X3 @ X4)))))))).
thf(h0,negated_conjecture,(~((![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:(((![X4:\$i]:((X1 @ X4) => (X3 @ X4))) & (![X4:\$i]:((X2 @ X4) => (X3 @ X4)))) => (![X4:\$i]:(((X1 @ X4) | (X2 @ X4)) => (X3 @ X4))))))))),inference(assume_negation,[status(cth)],[thm])).
thf(h1,assumption,(~((![X1:\$i>\$o]:(![X2:\$i>\$o]:(((![X3:\$i]:((eigen__0 @ X3) => (X2 @ X3))) & (![X3:\$i]:((X1 @ X3) => (X2 @ X3)))) => (![X3:\$i]:(((eigen__0 @ X3) | (X1 @ X3)) => (X2 @ X3)))))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:\$i>\$o]:(((![X2:\$i]:((eigen__0 @ X2) => (X1 @ X2))) & (![X2:\$i]:((eigen__1 @ X2) => (X1 @ X2)))) => (![X2:\$i]:(((eigen__0 @ X2) | (eigen__1 @ X2)) => (X1 @ X2))))))),introduced(assumption,[])).
thf(h3,assumption,(~((((![X1:\$i]:((eigen__0 @ X1) => (eigen__2 @ X1))) & (![X1:\$i]:((eigen__1 @ X1) => (eigen__2 @ X1)))) => (![X1:\$i]:(((eigen__0 @ X1) | (eigen__1 @ X1)) => (eigen__2 @ X1)))))),introduced(assumption,[])).
thf(h4,assumption,((![X1:\$i]:((eigen__0 @ X1) => (eigen__2 @ X1))) & (![X1:\$i]:((eigen__1 @ X1) => (eigen__2 @ X1)))),introduced(assumption,[])).
thf(h5,assumption,(~((![X1:\$i]:(((eigen__0 @ X1) | (eigen__1 @ X1)) => (eigen__2 @ X1))))),introduced(assumption,[])).
thf(h6,assumption,(![X1:\$i]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(assumption,[])).
thf(h7,assumption,(![X1:\$i]:((eigen__1 @ X1) => (eigen__2 @ X1))),introduced(assumption,[])).
thf(h8,assumption,(~((((eigen__0 @ eigen__3) | (eigen__1 @ eigen__3)) => (eigen__2 @ eigen__3)))),introduced(assumption,[])).
thf(h9,assumption,((eigen__0 @ eigen__3) | (eigen__1 @ eigen__3)),introduced(assumption,[])).
thf(h10,assumption,(~((eigen__2 @ eigen__3))),introduced(assumption,[])).
thf(h11,assumption,(eigen__0 @ eigen__3),introduced(assumption,[])).
thf(h12,assumption,(eigen__1 @ eigen__3),introduced(assumption,[])).
thf(h13,assumption,((eigen__0 @ eigen__3) => (eigen__2 @ eigen__3)),introduced(assumption,[])).
thf(h14,assumption,(~((eigen__0 @ eigen__3))),introduced(assumption,[])).
thf(h15,assumption,(eigen__2 @ eigen__3),introduced(assumption,[])).
thf(11,plain,\$false,inference(tab_conflict,[status(thm),assumptions([h14,h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[h11,h14])).
thf(12,plain,\$false,inference(tab_conflict,[status(thm),assumptions([h15,h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[h15,h10])).
thf(10,plain,\$false,inference(tab_imp,[status(thm),assumptions([h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h13,11,12,h14,h15])).
thf(9,plain,\$false,inference(tab_all,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_all(discharge,[h13])],[h6:[bind(X1,\$thf(eigen__3))],10,h13])).
thf(h16,assumption,((eigen__1 @ eigen__3) => (eigen__2 @ eigen__3)),introduced(assumption,[])).
thf(h17,assumption,(~((eigen__1 @ eigen__3))),introduced(assumption,[])).
thf(15,plain,\$false,inference(tab_conflict,[status(thm),assumptions([h17,h16,h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[h12,h17])).
thf(16,plain,\$false,inference(tab_conflict,[status(thm),assumptions([h15,h16,h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[h15,h10])).
thf(14,plain,\$false,inference(tab_imp,[status(thm),assumptions([h16,h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h17]),tab_imp(discharge,[h15])],[h16,15,16,h17,h15])).
thf(13,plain,\$false,inference(tab_all,[status(thm),assumptions([h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_all(discharge,[h16])],[h7:[bind(X1,\$thf(eigen__3))],14,h16])).
thf(8,plain,\$false,inference(tab_or,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_or(discharge,[h11]),tab_or(discharge,[h12])],[h9,9,13,h11,h12])).
thf(7,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,8,h9,h10])).
thf(6,plain,\$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,7,h8])).
thf(5,plain,\$false,inference(tab_and,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_and(discharge,[h6,h7])],[h4,6,h6,h7])).
thf(4,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,5,h4,h5])).
thf(3,plain,\$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,4,h3])).
thf(2,plain,\$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,3,h2])).
thf(1,plain,\$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,2,h1])).
thf(0,theorem,(![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:(((![X4:\$i]:((X1 @ X4) => (X3 @ X4))) & (![X4:\$i]:((X2 @ X4) => (X3 @ X4)))) => (![X4:\$i]:(((X1 @ X4) | (X2 @ X4)) => (X3 @ X4))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% SZS output end Proof
```

### Sample solution for SYO553^1

```% SZS output start Proof
thf(ty\$i, type, \$i : \$tType).
thf(tyeigen__2, type, eigen__2 : \$i).
thf(claim,conjecture,(?[X1:\$i>\$i>\$i]:(![X2:\$i]:(![X3:\$i]:(((X1 @ X2) @ X3) = X3))))).
thf(h0,negated_conjecture,(~(?[X1:\$i>\$i>\$i]:(![X2:\$i]:(![X3:\$i]:(((X1 @ X2) @ X3) = X3))))),inference(assume_negation,[status(cth)],[claim])).
thf(h1,assumption,(~((![X1:\$i]:(![X2:\$i]:(X2 = X2))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:\$i]:(X1 = X1)))),introduced(assumption,[])).
thf(h3,assumption,(~((eigen__2 = eigen__2))),introduced(assumption,[])).
thf(4,plain,\$false,inference(tab_refl,[status(thm),assumptions([h3,h2,h1,h0])],[h3])).
thf(3,plain,\$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,4,h3])).
thf(2,plain,\$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,3,h2])).
thf(1,plain,\$false,inference(tab_negex,[status(thm),assumptions([h0]),tab_negex(discharge,[h1])],[h0:[bind(X1,\$thf((^[X1:\$i]:(^[X2:\$i]:X2))))],2,h1])).
thf(0,theorem,(?[X1:\$i>\$i>\$i]:(![X2:\$i]:(![X3:\$i]:(((X1 @ X2) @ X3) = X3)))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% SZS output end Proof
```

## Satallax 3.2

Michael Färber
Universität Innsbruck, Austria

### Sample solution for SET014^4

```% SZS output start Proof
thf(ty_\$i, type, \$i : \$tType).
thf(ty_eigen__2, type, eigen__2 : (\$i>\$o)).
thf(ty_eigen__1, type, eigen__1 : (\$i>\$o)).
thf(ty_eigen__0, type, eigen__0 : (\$i>\$o)).
thf(ty_eigen__3, type, eigen__3 : \$i).
thf(sP1,plain,(sP1 <=> (eigen__0 @ eigen__3),introduced(definition,[new_symbols(
definition,[sP1])]))).
thf(sP2,plain,(sP2 <=> (sP1 => (eigen__2 @ eigen__3)),introduced(definition,[new
_symbols(definition,[sP2])]))).
thf(sP3,plain,(sP3 <=> (eigen__1 @ eigen__3),introduced(definition,[new_symbols(
definition,[sP3])]))).
thf(sP4,plain,(sP4 <=> (sP3 => (eigen__2 @ eigen__3)),introduced(definition,[new
_symbols(definition,[sP4])]))).
thf(sP5,plain,(sP5 <=> (![X1:\$i]:((eigen__1 @ X1) => (eigen__2 @ X1))),introduce
d(definition,[new_symbols(definition,[sP5])]))).
thf(sP6,plain,(sP6 <=> (eigen__2 @ eigen__3),introduced(definition,[new_symbols(
definition,[sP6])]))).
thf(sP7,plain,(sP7 <=> (![X1:\$i]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduce
d(definition,[new_symbols(definition,[sP7])]))).
thf(def_in,definition,(in = (^[X1:\$i]:(^[X2:\$i>\$o]:(X2 @ X1))))).
thf(def_is_a,definition,(is_a = (^[X1:\$i]:(^[X2:\$i>\$o]:(X2 @ X1))))).
thf(def_emptyset,definition,(emptyset = (^[X1:\$i]:\$false))).
thf(def_unord_pair,definition,(unord_pair = (^[X1:\$i]:(^[X2:\$i]:(^[X3:\$i]:((~((X
3 = X1))) => (X3 = X2))))))).
thf(def_singleton,definition,(singleton = (^[X1:\$i]:(^[X2:\$i]:(X2 = X1))))).
thf(def_union,definition,(union = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:((~((X1 @
X3))) => (X2 @ X3))))))).
thf(def_excl_union,definition,(excl_union = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:
(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))).
thf(def_intersection,definition,(intersection = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:
\$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
thf(def_setminus,definition,(setminus = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:(~((
(X1 @ X3) => (X2 @ X3))))))))).
thf(def_complement,definition,(complement = (^[X1:\$i>\$o]:(^[X2:\$i]:(~((X1 @ X2))
))))).
thf(def_disjoint,definition,(disjoint = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(((intersectio
n @ X1) @ X2) = emptyset))))).
thf(def_subset,definition,(subset = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(![X3:\$i]:((X1 @ X
3) => (X2 @ X3))))))).
thf(def_meets,definition,(meets = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(~((![X3:\$i]:((X1 @
X3) => (~((X2 @ X3))))))))))).
thf(def_misses,definition,(misses = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(![X3:\$i]:((X1 @ X
3) => (~((X2 @ X3))))))))).
thf(thm,conjecture,(![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:((~(((![X4:\$i]:((X1 @
X4) => (X3 @ X4))) => (~((![X4:\$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:\$i]:(
((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4)))))))).
thf(h0,negated_conjecture,(~((![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:((~(((![X4:\$
i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:\$i]:((X2 @ X4) => (X3 @ X4)))))))) => (
![X4:\$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4))))))))),inference(assume_ne
gation,[status(cth)],[thm])).
thf(h1,assumption,(~((![X1:\$i>\$o]:(![X2:\$i>\$o]:((~(((![X3:\$i]:((eigen__0 @ X3) =
> (X2 @ X3))) => (~((![X3:\$i]:((X1 @ X3) => (X2 @ X3)))))))) => (![X3:\$i]:(((~((
eigen__0 @ X3))) => (X1 @ X3)) => (X2 @ X3)))))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:\$i>\$o]:((~(((![X2:\$i]:((eigen__0 @ X2) => (X1 @ X2)))
=> (~((![X2:\$i]:((eigen__1 @ X2) => (X1 @ X2)))))))) => (![X2:\$i]:(((~((eigen__
0 @ X2))) => (eigen__1 @ X2)) => (X1 @ X2))))))),introduced(assumption,[])).
thf(h3,assumption,(~(((~((sP7 => (~(sP5))))) => (![X1:\$i]:(((~((eigen__0 @ X1)))
=> (eigen__1 @ X1)) => (eigen__2 @ X1)))))),introduced(assumption,[])).
thf(h4,assumption,(~((sP7 => (~(sP5))))),introduced(assumption,[])).
thf(h5,assumption,(~((![X1:\$i]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (ei
gen__2 @ X1))))),introduced(assumption,[])).
thf(h6,assumption,sP7,introduced(assumption,[])).
thf(h7,assumption,sP5,introduced(assumption,[])).
thf(h8,assumption,(~((((~(sP1)) => sP3) => sP6))),introduced(assumption,[])).
thf(h9,assumption,((~(sP1)) => sP3),introduced(assumption,[])).
thf(h10,assumption,(~(sP6)),introduced(assumption,[])).
thf(h11,assumption,sP1,introduced(assumption,[])).
thf(h12,assumption,sP3,introduced(assumption,[])).
thf(1,plain,((~(sP2) | ~(sP1)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(2,plain,(~(sP7) | sP2),inference(all_rule,[status(thm)],[])).
thf(3,plain,\$false,inference(prop_unsat,[status(thm),assumptions([h11,h9,h10,h8,
h6,h7,h4,h5,h3,h2,h1,h0])],[h10,h11,h6,1,2])).
thf(4,plain,((~(sP4) | ~(sP3)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(5,plain,(~(sP5) | sP4),inference(all_rule,[status(thm)],[])).
thf(6,plain,\$false,inference(prop_unsat,[status(thm),assumptions([h12,h9,h10,h8,
h6,h7,h4,h5,h3,h2,h1,h0])],[h10,h12,h7,4,5])).
thf(7,plain,\$false,inference(tab_imp,[status(thm),assumptions([h9,h10,h8,h6,h7,h
4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,3,6,h1
1,h12])).
thf(8,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5
,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,7,h9,h10])).
thf(9,plain,\$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3
,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,8,h8])
).
thf(10,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h
1,h0]),tab_negimp(discharge,[h6,h7])],[h4,9,h6,h7])).
thf(11,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0])
,tab_negimp(discharge,[h4,h5])],[h3,10,h4,h5])).
thf(12,plain,\$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),ta
b_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,11,h3])).
thf(13,plain,\$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_n
egall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2])).
thf(14,plain,\$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_nega
ll(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1])).
% SZS output end Proof
```

### Sample solution for SYO553^1

```% SZS output start Proof
thf(ty_\$i, type, \$i : \$tType).
thf(ty_eigen__2, type, eigen__2 : \$i).
thf(h0, assumption, (![X1:\$i>\$o]:(![X2:\$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1)))))
,introduced(assumption,[])).
thf(eigendef_eigen__1, definition, (eigen__1 = (eps__0 @ (^[X1:\$i]:(~((![X2:\$i]:
(X2 = X2))))))), introduced(definition,[new_symbols(definition,[eigen__1]))).
thf(eigendef_eigen__2, definition, (eigen__2 = (eps__0 @ (^[X1:\$i]:(~((X1 = X1))
)))), introduced(definition,[new_symbols(definition,[eigen__2]))).
thf(sP1,plain,(sP1 <=> (![X1:\$i]:(![X2:\$i]:(X2 = X2))),introduced(definition,[ne
w_symbols(definition,[sP1])]))).
thf(sP2,plain,(sP2 <=> (![X1:\$i]:(X1 = X1)),introduced(definition,[new_symbols(d
efinition,[sP2])]))).
thf(sP3,plain,(sP3 <=> (![X1:\$i>\$i>\$i]:(~((![X2:\$i]:(![X3:\$i]:(((X1 @ X2) @ X3)
= X3)))))),introduced(definition,[new_symbols(definition,[sP3])]))).
thf(sP4,plain,(sP4 <=> (eigen__2 = eigen__2),introduced(definition,[new_symbols(
definition,[sP4])]))).
thf(claim,conjecture,(~(sP3))).
thf(h1,negated_conjecture,sP3,inference(assume_negation,[status(cth)],[claim])).
thf(1,plain,(~(sP3) | ~(sP1)),inference(all_rule,[status(thm)],[])).
thf(2,plain,(sP1 | ~(sP2)),inference(eigen_choice_rule,[status(thm),assumptions(
[h0])],[h0,eigendef_eigen__1])).
thf(3,plain,(sP2 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions(
[h0])],[h0,eigendef_eigen__2])).
thf(4,plain,sP4,inference(prop_rule,[status(thm)],[])).
thf(5,plain,\$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[h1,1
,2,3,4])).
thf(6,plain,\$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eige
nvar_choice(discharge,[h0])],[5,h0])).
% SZS output end Proof
```

## Scavenger EP-0.2

Bruno Woltzenlogel Paleo
Australian National University, Australia

### Sample solution for SEU140+2

Can't solve it :-(. So ...

### Sample solution for SYN054+1

```% SZS status Theorem for SYN054+1.p
% SZS output start CNFRefutation for SYN054+1.p
cnf(1,plain,
~((big_p MYOWNX3)),
inference(decision,[],[]).
cnf(2,axiom,
predicate3 | (big_p skolemize0),
inference(axiom,[status(thm)],[]).
cnf(3,plain,
predicate3,
inference(unit-propagation-resolution,[],[1,2]).
cnf(4,axiom,
~(predicate3) | (big_q skolemize1),
inference(axiom,[status(thm)],[]).
cnf(5,plain,
(big_q skolemize1),
inference(unit-propagation-resolution,[],[3,4]).
cnf(6,axiom,
~((big_q MYOWNX2)) | (predicate4 MYOWNX2 MYOWNX2),
inference(axiom,[status(thm)],[]).
cnf(7,plain,
(predicate4 skolemize1 skolemize1),
inference(unit-propagation-resolution,[],[5,6]).
cnf(8,axiom,
~((predicate4 MYOWNX2 MYOWNX2)) | (big_s MYOWNX2),
inference(axiom,[status(thm)],[]).
cnf(9,plain,
(big_s skolemize1),
inference(unit-propagation-resolution,[],[7,8]).
cnf(10,axiom,
~((big_q MYOWNX0)) | ~((predicate0 MYOWNX0 MYOWNX0)),
inference(axiom,[status(thm)],[]).
cnf(11,plain,
~((predicate0 skolemize1 skolemize1)),
inference(unit-propagation-resolution,[],[5,10]).
cnf(12,axiom,
~((big_s MYOWNX0)) | (predicate0 MYOWNX0 MYOWNX0),
inference(axiom,[status(thm)],[]).
cnf(13,plain,
~((big_s skolemize1)),
inference(unit-propagation-resolution,[],[11,12]).
cnf(14,plain,
\$false,
inference(conflict,[],[9,13]).
cnf(15,plain,
(big_p skolemize0),
inference(conflict-driven-clause-learning,[],[14]).
cnf(16,axiom,
~((big_p MYOWNX1)) | (predicate1 MYOWNX1 MYOWNX1),
inference(axiom,[status(thm)],[]).
cnf(17,plain,
(predicate1 skolemize0 skolemize0),
inference(unit-propagation-resolution,[],[15,16]).
cnf(18,axiom,
~((big_p MYOWNX3)) | (predicate5 MYOWNX3 MYOWNX3),
inference(axiom,[status(thm)],[]).
cnf(19,plain,
(predicate5 skolemize0 skolemize0),
inference(unit-propagation-resolution,[],[15,18]).
cnf(20,axiom,
~((big_r MYOWNX3)) | ~((predicate5 MYOWNX3 MYOWNX3)),
inference(axiom,[status(thm)],[]).
cnf(21,plain,
~((big_r skolemize0)),
inference(unit-propagation-resolution,[],[19,20]).
cnf(22,axiom,
~((predicate2 MYOWNX1 MYOWNX1)) | ~((predicate1 MYOWNX1 MYOWNX1)) | (big_r
MYOWNX1),
inference(axiom,[status(thm)],[]).
cnf(23,plain,
~((predicate2 skolemize0 skolemize0)),
inference(unit-propagation-resolution,[],[17,21,22]).
cnf(24,axiom,
~((predicate1 MYOWNX1 MYOWNX1)) | (predicate2 MYOWNX1 MYOWNX1) | (big_q
MYOWNX1),
inference(axiom,[status(thm)],[]).
cnf(25,plain,
(big_q skolemize0),
inference(unit-propagation-resolution,[],[17,23,24]).
cnf(26,plain,
(predicate4 skolemize0 skolemize0),
inference(unit-propagation-resolution,[],[25,6]).
cnf(27,plain,
(big_s skolemize0),
inference(unit-propagation-resolution,[],[26,8]).
cnf(28,plain,
~((predicate0 skolemize0 skolemize0)),
inference(unit-propagation-resolution,[],[25,10]).
cnf(29,plain,
~((big_s skolemize0)),
inference(unit-propagation-resolution,[],[28,12]).
cnf(30,plain,
\$false,
inference(conflict,[],[27,29]).
% SZS output end CNFRefutation for SYN054+1.p
```

## Vampire 4.0

Giles Reger
University of Manchester, United Kingdom

### Sample solution for SEU140+2

```% SZS status Theorem for SEU140+2
% SZS output start Proof for SEU140+2
fof(f6,axiom,(
! [X0] : (empty_set = X0 <=> ! [X1] : ~in(X1,X0))),
file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',d1_xboole_0)).
fof(f8,axiom,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',d3_tarski)).
fof(f9,axiom,(
! [X0,X1,X2] : (set_intersection2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (in(X3,X0) & in(X3,X1))))),
file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',d3_xboole_0)).
fof(f11,axiom,(
! [X0,X1] : (disjoint(X0,X1) <=> set_intersection2(X0,X1) = empty_set)),
file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',d7_xboole_0)).
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('/tmp/SystemOnTPTP11775/SEU140+2.tptp',t3_xboole_0)).
fof(f51,conjecture,(
! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',t63_xboole_1)).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).
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(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(f63,plain,(
! [X0] : (empty_set = X0 <=> ! [X1] : ~in(X1,X0))),
inference(flattening,[],[f6])).
fof(f74,plain,(
? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
inference(ennf_transformation,[],[f52])).
fof(f75,plain,(
? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
inference(flattening,[],[f74])).
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(f96,plain,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (~in(X2,X0) | in(X2,X1)))),
inference(ennf_transformation,[],[f8])).
fof(f101,plain,(
subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f75])).
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(f106,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | set_intersection2(X0,X1) = empty_set) & (set_intersection2(X0,X1) != empty_set | disjoint(X0,X1)))),
inference(nnf_transformation,[],[f11])).
fof(f109,plain,(
! [X0] : ((empty_set != X0 | ! [X1] : ~in(X1,X0)) & (? [X1] : in(X1,X0) | empty_set = X0))),
inference(nnf_transformation,[],[f63])).
fof(f110,plain,(
! [X0] : ((empty_set != X0 | ! [X2] : ~in(X2,X0)) & (? [X1] : in(X1,X0) | empty_set = X0))),
inference(rectify,[],[f109])).
fof(f111,plain,(
! [X0] : ((empty_set != X0 | ! [X2] : ~in(X2,X0)) & (in(sK5(X0),X0) | empty_set = X0))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f110])).
fof(f116,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(f117,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,[],[f116])).
fof(f118,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,[],[f117])).
fof(f119,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(sK7(X2,X1,X0),X2) | (in(sK7(X2,X1,X0),X0) & in(sK7(X2,X1,X0),X1))) & (~in(sK7(X2,X1,X0),X2) | ~in(sK7(X2,X1,X0),X0) | ~in(sK7(X2,X1,X0),X1))) | set_intersection2(X0,X1) = X2))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f118])).
fof(f124,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,[],[f96])).
fof(f125,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,[],[f124])).
fof(f126,plain,(
! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & ((in(sK9(X1,X0),X0) & ~in(sK9(X1,X0),X1)) | subset(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f125])).
fof(f133,plain,(
subset(sK0,sK1)),
inference(cnf_transformation,[],[f101])).
fof(f134,plain,(
disjoint(sK1,sK2)),
inference(cnf_transformation,[],[f101])).
fof(f135,plain,(
~disjoint(sK0,sK2)),
inference(cnf_transformation,[],[f101])).
fof(f146,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f103])).
fof(f147,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f103])).
fof(f162,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f106])).
fof(f169,plain,(
( ! [X2,X0] : (~in(X2,X0) | empty_set != X0) )),
inference(cnf_transformation,[],[f111])).
fof(f189,plain,(
( ! [X4,X2,X0,X1] : (in(X4,X2) | ~in(X4,X1) | ~in(X4,X0) | set_intersection2(X0,X1) != X2) )),
inference(cnf_transformation,[],[f119])).
fof(f202,plain,(
( ! [X0,X3,X1] : (~subset(X0,X1) | ~in(X3,X0) | in(X3,X1)) )),
inference(cnf_transformation,[],[f126])).
fof(f218,plain,(
( ! [X2] : (~in(X2,empty_set)) )),
inference(equality_resolution,[],[f169])).
fof(f222,plain,(
( ! [X4,X0,X1] : (in(X4,set_intersection2(X0,X1)) | ~in(X4,X1) | ~in(X4,X0)) )),
inference(equality_resolution,[],[f189])).
fof(f234,plain,(
set_intersection2(sK1,sK2) = empty_set),
inference(unit_resulting_resolution,[],[f134,f162])).
fof(f467,plain,(
in(sK4(sK2,sK0),sK0)),
inference(unit_resulting_resolution,[],[f135,f146])).
fof(f480,plain,(
in(sK4(sK2,sK0),sK1)),
inference(unit_resulting_resolution,[],[f133,f467,f202])).
fof(f513,plain,(
in(sK4(sK2,sK0),sK2)),
inference(unit_resulting_resolution,[],[f135,f147])).
fof(f857,plain,(
in(sK4(sK2,sK0),set_intersection2(sK1,sK2))),
inference(unit_resulting_resolution,[],[f513,f480,f222])).
fof(f865,plain,(
in(sK4(sK2,sK0),empty_set)),
inference(forward_demodulation,[],[f857,f234])).
fof(f866,plain,(
\$false),
inference(subsumption_resolution,[],[f865,f218])).
% SZS output end Proof for SEU140+2
```

## Vampire 4.1

Giles Reger
University of Manchester, United Kingdom

### Sample solution for DAT013=1

```tff(type_def_6, type, array: \$tType).
tff(func_def_0, type, read: (array * \$int) > \$int).
tff(func_def_1, type, write: (array * \$int * \$int) > array).
tff(func_def_7, type, sK0: array).
tff(func_def_8, type, sK1: \$int).
tff(func_def_9, type, sK2: \$int).
tff(func_def_10, type, sK3: \$int).
tff(f3,conjecture,(
! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((\$lesseq(X3,X2) & \$lesseq(X1,X3)) => \$greater(read(X0,X3),0)) => ! [X4 : \$int] : ((\$lesseq(X4,X2) & \$lesseq(\$sum(X1,3),X4)) => \$greater(read(X0,X4),0)))),
file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/DAT/DAT013=1.p',unknown)).
tff(f4,negated_conjecture,(
~! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((\$lesseq(X3,X2) & \$lesseq(X1,X3)) => \$greater(read(X0,X3),0)) => ! [X4 : \$int] : ((\$lesseq(X4,X2) & \$lesseq(\$sum(X1,3),X4)) => \$greater(read(X0,X4),0)))),
inference(negated_conjecture,[],[f3])).
tff(f6,plain,(
~! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((~\$less(X2,X3) & ~\$less(X3,X1)) => \$less(0,read(X0,X3))) => ! [X4 : \$int] : ((~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3))) => \$less(0,read(X0,X4))))),
inference(evaluation,[],[f4])).
tff(f7,plain,(
( ! [X0:\$int,X1:\$int] : (\$sum(X0,X1) = \$sum(X1,X0)) )),
introduced(theory_axiom,[])).
tff(f9,plain,(
( ! [X0:\$int] : (\$sum(X0,0) = X0) )),
introduced(theory_axiom,[])).
tff(f12,plain,(
( ! [X0:\$int] : (~\$less(X0,X0)) )),
introduced(theory_axiom,[])).
tff(f13,plain,(
( ! [X2:\$int,X0:\$int,X1:\$int] : (~\$less(X1,X2) | ~\$less(X0,X1) | \$less(X0,X2)) )),
introduced(theory_axiom,[])).
tff(f14,plain,(
( ! [X0:\$int,X1:\$int] : (\$less(X1,X0) | \$less(X0,X1) | X0 = X1) )),
introduced(theory_axiom,[])).
tff(f15,plain,(
( ! [X2:\$int,X0:\$int,X1:\$int] : (\$less(\$sum(X0,X2),\$sum(X1,X2)) | ~\$less(X0,X1)) )),
introduced(theory_axiom,[])).
tff(f20,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X4 : \$int] : (~\$less(0,read(X0,X4)) & (~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3)))) & ! [X3 : \$int] : (\$less(0,read(X0,X3)) | (\$less(X2,X3) | \$less(X3,X1))))),
inference(ennf_transformation,[],[f6])).
tff(f21,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X4 : \$int] : (~\$less(0,read(X0,X4)) & ~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3))) & ! [X3 : \$int] : (\$less(0,read(X0,X3)) | \$less(X2,X3) | \$less(X3,X1)))),
inference(flattening,[],[f20])).
tff(f22,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X3 : \$int] : (~\$less(0,read(X0,X3)) & ~\$less(X2,X3) & ~\$less(X3,\$sum(X1,3))) & ! [X4 : \$int] : (\$less(0,read(X0,X4)) | \$less(X2,X4) | \$less(X4,X1)))),
inference(rectify,[],[f21])).
tff(f23,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X3 : \$int] : (~\$less(0,read(X0,X3)) & ~\$less(X2,X3) & ~\$less(X3,\$sum(X1,3))) & ! [X4 : \$int] : (\$less(0,read(X0,X4)) | \$less(X2,X4) | \$less(X4,X1))) => (? [X3 : \$int] : (~\$less(0,read(sK0,X3)) & ~\$less(sK2,X3) & ~\$less(X3,\$sum(sK1,3))) & ! [X4 : \$int] : (\$less(0,read(sK0,X4)) | \$less(sK2,X4) | \$less(X4,sK1)))),
introduced(choice_axiom,[])).
tff(f24,plain,(
( ! [X2:\$int,X0:array,X1:\$int] : (? [X3 : \$int] : (~\$less(0,read(X0,X3)) & ~\$less(X2,X3) & ~\$less(X3,\$sum(X1,3))) => (~\$less(0,read(X0,sK3)) & ~\$less(X2,sK3) & ~\$less(sK3,\$sum(X1,3)))) )),
introduced(choice_axiom,[])).
tff(f25,plain,(
(~\$less(0,read(sK0,sK3)) & ~\$less(sK2,sK3) & ~\$less(sK3,\$sum(sK1,3))) & ! [X4 : \$int] : (\$less(0,read(sK0,X4)) | \$less(sK2,X4) | \$less(X4,sK1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f22,f24,f23])).
tff(f29,plain,(
( ! [X4:\$int] : (\$less(0,read(sK0,X4)) | \$less(sK2,X4) | \$less(X4,sK1)) )),
inference(cnf_transformation,[],[f25])).
tff(f30,plain,(
~\$less(sK3,\$sum(sK1,3))),
inference(cnf_transformation,[],[f25])).
tff(f31,plain,(
~\$less(sK2,sK3)),
inference(cnf_transformation,[],[f25])).
tff(f32,plain,(
inference(cnf_transformation,[],[f25])).
tff(f33,plain,(
~\$less(sK3,\$sum(3,sK1))),
inference(forward_demodulation,[],[f30,f7])).
tff(f98,plain,(
\$less(\$sum(3,sK1),sK3) | \$sum(3,sK1) = sK3),
inference(resolution,[],[f14,f33])).
tff(f131,plain,(
spl4_8 <=> \$sum(3,sK1) = sK3),
introduced(AVATAR_definition,[new_symbols(naming,[spl4_8])])).
tff(f132,plain,(
\$sum(3,sK1) = sK3 | ~spl4_8),
inference(AVATAR_component_clause,[],[f131])).
tff(f137,plain,(
spl4_10 <=> \$less(\$sum(3,sK1),sK3)),
introduced(AVATAR_definition,[new_symbols(naming,[spl4_10])])).
tff(f138,plain,(
\$less(\$sum(3,sK1),sK3) | ~spl4_10),
inference(AVATAR_component_clause,[],[f137])).
tff(f142,plain,(
spl4_8 | spl4_10),
inference(AVATAR_split_clause,[],[f98,f137,f131])).
tff(f172,plain,(
( ! [X6:\$int,X4:\$int,X5:\$int] : (\$less(\$sum(X5,X4),\$sum(X6,X5)) | ~\$less(X4,X6)) )),
inference(superposition,[],[f15,f7])).
tff(f489,plain,(
( ! [X6:\$int,X7:\$int] : (\$less(X6,\$sum(X7,X6)) | ~\$less(0,X7)) )),
inference(superposition,[],[f172,f9])).
tff(f659,plain,(
\$less(sK2,sK3) | \$less(sK3,sK1)),
inference(resolution,[],[f29,f32])).
tff(f662,plain,(
\$less(sK3,sK1)),
inference(subsumption_resolution,[],[f659,f31])).
tff(f664,plain,(
( ! [X0:\$int] : (~\$less(X0,sK3) | \$less(X0,sK1)) )),
inference(resolution,[],[f662,f13])).
tff(f673,plain,(
( ! [X4:\$int] : (\$less(\$sum(sK1,X4),sK3) | ~\$less(X4,3)) ) | ~spl4_8),
inference(superposition,[],[f172,f132])).
tff(f2473,plain,(
\$less(sK1,sK3) | ~\$less(0,3) | ~spl4_8),
inference(superposition,[],[f673,f9])).
tff(f2478,plain,(
\$less(sK1,sK3) | ~spl4_8),
inference(evaluation,[],[f2473])).
tff(f2480,plain,(
\$less(sK1,sK1) | ~spl4_8),
inference(resolution,[],[f2478,f664])).
tff(f2484,plain,(
\$false | ~spl4_8),
inference(subsumption_resolution,[],[f2480,f12])).
tff(f2485,plain,(
~spl4_8),
tff(f2513,plain,(
( ! [X2:\$int] : (~\$less(X2,\$sum(3,sK1)) | \$less(X2,sK3)) ) | ~spl4_10),
inference(resolution,[],[f138,f13])).
tff(f2962,plain,(
~\$less(0,3) | \$less(sK1,sK3) | ~spl4_10),
inference(resolution,[],[f489,f2513])).
tff(f2989,plain,(
\$less(sK1,sK3) | ~spl4_10),
inference(evaluation,[],[f2962])).
tff(f2991,plain,(
\$less(sK1,sK1) | ~spl4_10),
inference(resolution,[],[f2989,f664])).
tff(f2995,plain,(
\$false | ~spl4_10),
inference(subsumption_resolution,[],[f2991,f12])).
tff(f2996,plain,(
~spl4_10),
tff(f2997,plain,(
\$false),
inference(AVATAR_sat_refutation,[],[f142,f2485,f2996])).
```

### Sample solution for NLP042+1

```# SZS output start Saturation.
tff(u283,axiom,
(![X1, X0] : ((~woman(X0,X1) | human_person(X0,X1))))).

tff(u282,axiom,
(![X1, X0] : ((~woman(X0,X1) | female(X0,X1))))).

tff(u281,negated_conjecture,
woman(sK0,sK1)).

tff(u280,negated_conjecture,
~female(sK0,sK4)).

tff(u279,negated_conjecture,
~female(sK0,sK2)).

tff(u278,negated_conjecture,
~female(sK0,sK3)).

tff(u277,negated_conjecture,
female(sK0,sK1)).

tff(u276,axiom,
(![X1, X0] : ((~human_person(X0,X1) | organism(X0,X1))))).

tff(u275,axiom,
(![X1, X0] : ((~human_person(X0,X1) | human(X0,X1))))).

tff(u274,axiom,
(![X1, X0] : ((~human_person(X0,X1) | animate(X0,X1))))).

tff(u273,negated_conjecture,
human_person(sK0,sK1)).

tff(u272,negated_conjecture,
~animate(sK0,sK3)).

tff(u271,negated_conjecture,
animate(sK0,sK1)).

tff(u270,negated_conjecture,
~human(sK0,sK2)).

tff(u269,negated_conjecture,
human(sK0,sK1)).

tff(u268,axiom,
(![X1, X0] : ((~organism(X0,X1) | entity(X0,X1))))).

tff(u267,axiom,
(![X1, X0] : ((~organism(X0,X1) | living(X0,X1))))).

tff(u266,negated_conjecture,
organism(sK0,sK1)).

tff(u265,negated_conjecture,
~living(sK0,sK3)).

tff(u264,negated_conjecture,
living(sK0,sK1)).

tff(u263,axiom,
(![X1, X0] : ((~entity(X0,X1) | specific(X0,X1))))).

tff(u262,axiom,
(![X1, X0] : ((~entity(X0,X1) | existent(X0,X1))))).

tff(u261,negated_conjecture,
entity(sK0,sK1)).

tff(u260,negated_conjecture,
entity(sK0,sK3)).

tff(u259,axiom,
(![X1, X0] : ((~mia_forename(X0,X1) | forename(X0,X1))))).

tff(u258,negated_conjecture,
mia_forename(sK0,sK2)).

tff(u257,axiom,
(![X1, X0] : ((~forename(X0,X1) | relname(X0,X1))))).

tff(u256,negated_conjecture,
forename(sK0,sK2)).

tff(u255,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | nonhuman(X0,X1))))).

tff(u254,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | general(X0,X1))))).

tff(u253,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | unisex(X0,X1))))).

tff(u252,negated_conjecture,
abstraction(sK0,sK2)).

tff(u251,axiom,
(![X1, X0] : ((~unisex(X0,X1) | ~female(X0,X1))))).

tff(u250,negated_conjecture,
unisex(sK0,sK2)).

tff(u249,negated_conjecture,
unisex(sK0,sK4)).

tff(u248,negated_conjecture,
unisex(sK0,sK3)).

tff(u247,negated_conjecture,
~general(sK0,sK4)).

tff(u246,negated_conjecture,
~general(sK0,sK1)).

tff(u245,negated_conjecture,
~general(sK0,sK3)).

tff(u244,negated_conjecture,
general(sK0,sK2)).

tff(u243,axiom,
(![X1, X0] : ((~nonhuman(X0,X1) | ~human(X0,X1))))).

tff(u242,negated_conjecture,
nonhuman(sK0,sK2)).

tff(u241,axiom,
(![X1, X0] : ((~relation(X0,X1) | abstraction(X0,X1))))).

tff(u240,negated_conjecture,
relation(sK0,sK2)).

tff(u239,axiom,
(![X1, X0] : ((~relname(X0,X1) | relation(X0,X1))))).

tff(u238,negated_conjecture,
relname(sK0,sK2)).

tff(u237,axiom,
(![X1, X0] : ((~object(X0,X1) | entity(X0,X1))))).

tff(u236,axiom,
(![X1, X0] : ((~object(X0,X1) | nonliving(X0,X1))))).

tff(u235,axiom,
(![X1, X0] : ((~object(X0,X1) | unisex(X0,X1))))).

tff(u234,negated_conjecture,
object(sK0,sK3)).

tff(u233,axiom,
(![X1, X0] : ((~nonliving(X0,X1) | ~living(X0,X1))))).

tff(u232,axiom,
(![X1, X0] : ((~nonliving(X0,X1) | ~animate(X0,X1))))).

tff(u231,negated_conjecture,
nonliving(sK0,sK3)).

tff(u230,negated_conjecture,
~existent(sK0,sK4)).

tff(u229,negated_conjecture,
existent(sK0,sK1)).

tff(u228,negated_conjecture,
existent(sK0,sK3)).

tff(u227,axiom,
(![X1, X0] : ((~specific(X0,X1) | ~general(X0,X1))))).

tff(u226,negated_conjecture,
specific(sK0,sK1)).

tff(u225,negated_conjecture,
specific(sK0,sK4)).

tff(u224,negated_conjecture,
specific(sK0,sK3)).

tff(u223,axiom,
(![X1, X0] : ((~substance_matter(X0,X1) | object(X0,X1))))).

tff(u222,negated_conjecture,
substance_matter(sK0,sK3)).

tff(u221,axiom,
(![X1, X0] : ((~food(X0,X1) | substance_matter(X0,X1))))).

tff(u220,negated_conjecture,
food(sK0,sK3)).

tff(u219,axiom,
(![X1, X0] : ((~beverage(X0,X1) | food(X0,X1))))).

tff(u218,negated_conjecture,
beverage(sK0,sK3)).

tff(u217,axiom,
(![X1, X0] : ((~shake_beverage(X0,X1) | beverage(X0,X1))))).

tff(u216,negated_conjecture,
shake_beverage(sK0,sK3)).

tff(u215,axiom,
(![X1, X0] : ((~order(X0,X1) | act(X0,X1))))).

tff(u214,axiom,
(![X1, X0] : ((~order(X0,X1) | event(X0,X1))))).

tff(u213,negated_conjecture,
order(sK0,sK4)).

tff(u212,axiom,
(![X1, X0] : ((~event(X0,X1) | eventuality(X0,X1))))).

tff(u211,negated_conjecture,
event(sK0,sK4)).

tff(u210,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | specific(X0,X1))))).

tff(u209,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | nonexistent(X0,X1))))).

tff(u208,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | unisex(X0,X1))))).

tff(u207,negated_conjecture,
eventuality(sK0,sK4)).

tff(u206,axiom,
(![X1, X0] : ((~nonexistent(X0,X1) | ~existent(X0,X1))))).

tff(u205,negated_conjecture,
nonexistent(sK0,sK4)).

tff(u204,axiom,
(![X1, X0] : ((~act(X0,X1) | event(X0,X1))))).

tff(u203,negated_conjecture,
act(sK0,sK4)).

tff(u202,axiom,
(![X1, X3, X0, X2] : ((~of(X0,X3,X1) | (X2 = X3) | ~forename(X0,X3) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1))))).

tff(u201,negated_conjecture,
(![X0] : ((~of(sK0,X0,sK1) | (sK2 = X0) | ~forename(sK0,X0))))).

tff(u200,negated_conjecture,
of(sK0,sK2,sK1)).

tff(u199,negated_conjecture,
nonreflexive(sK0,sK4)).

tff(u198,negated_conjecture,
~agent(sK0,sK4,sK3)).

tff(u197,negated_conjecture,
agent(sK0,sK4,sK1)).

tff(u196,axiom,
(![X1, X3, X0] : ((~patient(X0,X1,X3) | ~agent(X0,X1,X3) | ~nonreflexive(X0,X1))))).

tff(u195,negated_conjecture,
patient(sK0,sK4,sK3)).

# SZS output end Saturation.
```

### Sample solution for SWV017+1

```tff(declare\$i,type,\$i:\$tType).
tff(declare_\$i1,type,at:\$i).
tff(declare_\$i2,type,an_a_nonce:\$i).
tff(finite_domain,axiom,
! [X:\$i] : (
X = at | X = an_a_nonce
) ).

tff(distinct_domain,axiom,
at != an_a_nonce
).

tff(declare_t,type,t:\$i).
tff(t_definition,axiom,t = at).
tff(declare_a,type,a:\$i).
tff(a_definition,axiom,a = at).
tff(declare_b,type,b:\$i).
tff(b_definition,axiom,b = at).
tff(declare_bt,type,bt:\$i).
tff(bt_definition,axiom,bt = an_a_nonce).
tff(declare_an_intruder_nonce,type,an_intruder_nonce:\$i).
tff(an_intruder_nonce_definition,axiom,an_intruder_nonce = an_a_nonce).
tff(declare_key,type,key: \$i * \$i > \$i).
tff(function_key,axiom,
key(at,at) = at
& key(at,an_a_nonce) = at
& key(an_a_nonce,at) = at
& key(an_a_nonce,an_a_nonce) = an_a_nonce

).

tff(declare_pair,type,pair: \$i * \$i > \$i).
tff(function_pair,axiom,
pair(at,at) = at
& pair(at,an_a_nonce) = an_a_nonce
& pair(an_a_nonce,at) = at
& pair(an_a_nonce,an_a_nonce) = at

).

tff(declare_sent,type,sent: \$i * \$i * \$i > \$i).
tff(function_sent,axiom,
sent(at,at,at) = at
& sent(at,at,an_a_nonce) = at
& sent(at,an_a_nonce,at) = at
& sent(at,an_a_nonce,an_a_nonce) = an_a_nonce
& sent(an_a_nonce,at,at) = at
& sent(an_a_nonce,at,an_a_nonce) = at
& sent(an_a_nonce,an_a_nonce,at) = at
& sent(an_a_nonce,an_a_nonce,an_a_nonce) = at

).

).

tff(declare_encrypt,type,encrypt: \$i * \$i > \$i).
tff(function_encrypt,axiom,
encrypt(at,at) = an_a_nonce
& encrypt(at,an_a_nonce) = an_a_nonce
& encrypt(an_a_nonce,at) = at
& encrypt(an_a_nonce,an_a_nonce) = at

).

tff(declare_triple,type,triple: \$i * \$i * \$i > \$i).
tff(function_triple,axiom,
triple(at,at,at) = at
& triple(at,at,an_a_nonce) = an_a_nonce
& triple(at,an_a_nonce,at) = at
& triple(at,an_a_nonce,an_a_nonce) = at
& triple(an_a_nonce,at,at) = at
& triple(an_a_nonce,at,an_a_nonce) = an_a_nonce
& triple(an_a_nonce,an_a_nonce,at) = at
& triple(an_a_nonce,an_a_nonce,an_a_nonce) = an_a_nonce

).

tff(declare_generate_b_nonce,type,generate_b_nonce: \$i > \$i).
tff(function_generate_b_nonce,axiom,
generate_b_nonce(at) = an_a_nonce
& generate_b_nonce(an_a_nonce) = an_a_nonce

).

tff(declare_generate_expiration_time,type,generate_expiration_time: \$i > \$i).
tff(function_generate_expiration_time,axiom,
generate_expiration_time(at) = an_a_nonce
& generate_expiration_time(an_a_nonce) = an_a_nonce

).

tff(declare_generate_key,type,generate_key: \$i > \$i).
tff(function_generate_key,axiom,
generate_key(at) = at
& generate_key(an_a_nonce) = at

).

tff(declare_generate_intruder_nonce,type,generate_intruder_nonce: \$i > \$i).
tff(function_generate_intruder_nonce,axiom,
generate_intruder_nonce(at) = at
& generate_intruder_nonce(an_a_nonce) = an_a_nonce

).

tff(declare_a_holds,type,a_holds: \$i > \$o ).
fof(predicate_a_holds,axiom,
a_holds(at)
& a_holds(an_a_nonce)

).

tff(declare_party_of_protocol,type,party_of_protocol: \$i > \$o ).
fof(predicate_party_of_protocol,axiom,
party_of_protocol(at)
& party_of_protocol(an_a_nonce)

).

tff(declare_message,type,message: \$i > \$o ).
fof(predicate_message,axiom,
message(at)
& message(an_a_nonce)

).

tff(declare_a_stored,type,a_stored: \$i > \$o ).
fof(predicate_a_stored,axiom,
~a_stored(at)
& a_stored(an_a_nonce)

).

tff(declare_b_holds,type,b_holds: \$i > \$o ).
fof(predicate_b_holds,axiom,
b_holds(at)
& b_holds(an_a_nonce)

).

tff(declare_fresh_to_b,type,fresh_to_b: \$i > \$o ).
fof(predicate_fresh_to_b,axiom,
fresh_to_b(at)
& fresh_to_b(an_a_nonce)

).

tff(declare_b_stored,type,b_stored: \$i > \$o ).
fof(predicate_b_stored,axiom,
b_stored(at)
& b_stored(an_a_nonce)

).

tff(declare_a_key,type,a_key: \$i > \$o ).
fof(predicate_a_key,axiom,
a_key(at)
& ~a_key(an_a_nonce)

).

tff(declare_t_holds,type,t_holds: \$i > \$o ).
fof(predicate_t_holds,axiom,
t_holds(at)
& ~t_holds(an_a_nonce)

).

tff(declare_a_nonce,type,a_nonce: \$i > \$o ).
fof(predicate_a_nonce,axiom,
~a_nonce(at)
& a_nonce(an_a_nonce)

).

tff(declare_intruder_message,type,intruder_message: \$i > \$o ).
fof(predicate_intruder_message,axiom,
intruder_message(at)
& intruder_message(an_a_nonce)

).

tff(declare_intruder_holds,type,intruder_holds: \$i > \$o ).
fof(predicate_intruder_holds,axiom,
intruder_holds(at)
& intruder_holds(an_a_nonce)

).

tff(declare_fresh_intruder_nonce,type,fresh_intruder_nonce: \$i > \$o ).
fof(predicate_fresh_intruder_nonce,axiom,
~fresh_intruder_nonce(at)
& fresh_intruder_nonce(an_a_nonce)

).
```

## Vampire 4.2

Giles Reger
University of Manchester, United Kingdom

### Sample solution for DAT013=1

```tff(type_def_5, type, array: \$tType).
tff(func_def_0, type, read: (array * \$int) > \$int).
tff(func_def_1, type, write: (array * \$int * \$int) > array).
tff(func_def_7, type, sK0: array).
tff(func_def_8, type, sK1: \$int).
tff(func_def_9, type, sK2: \$int).
tff(func_def_10, type, sK3: \$int).
tff(f3,conjecture,(
! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((\$lesseq(X3,X2) & \$lesseq(X1,X3)) => \$greater(read(X0,X3),0)) => ! [X4 : \$int] : ((\$lesseq(X4,X2) & \$lesseq(\$sum(X1,3),X4)) => \$greater(read(X0,X4),0)))),
file('TPTP/TPTP-v6.4.0/Problems/DAT/DAT013=1.p',unknown)).
tff(f4,negated_conjecture,(
~! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((\$lesseq(X3,X2) & \$lesseq(X1,X3)) => \$greater(read(X0,X3),0)) => ! [X4 : \$int] : ((\$lesseq(X4,X2) & \$lesseq(\$sum(X1,3),X4)) => \$greater(read(X0,X4),0)))),
inference(negated_conjecture,[],[f3])).
tff(f6,plain,(
~! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((~\$less(X2,X3) & ~\$less(X3,X1)) => \$less(0,read(X0,X3))) => ! [X4 : \$int] : ((~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3))) => \$less(0,read(X0,X4))))),
inference(evaluation,[],[f4])).
tff(f7,plain,(
( ! [X0:\$int,X1:\$int] : (\$sum(X0,X1) = \$sum(X1,X0)) )),
introduced(theory_axiom,[])).
tff(f9,plain,(
( ! [X0:\$int] : (\$sum(X0,0) = X0) )),
introduced(theory_axiom,[])).
tff(f12,plain,(
( ! [X0:\$int] : (~\$less(X0,X0)) )),
introduced(theory_axiom,[])).
tff(f13,plain,(
( ! [X2:\$int,X0:\$int,X1:\$int] : (~\$less(X1,X2) | ~\$less(X0,X1) | \$less(X0,X2)) )),
introduced(theory_axiom,[])).
tff(f14,plain,(
( ! [X0:\$int,X1:\$int] : (\$less(X1,X0) | \$less(X0,X1) | X0 = X1) )),
introduced(theory_axiom,[])).
tff(f15,plain,(
( ! [X2:\$int,X0:\$int,X1:\$int] : (\$less(\$sum(X0,X2),\$sum(X1,X2)) | ~\$less(X0,X1)) )),
introduced(theory_axiom,[])).
tff(f20,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X4 : \$int] : (~\$less(0,read(X0,X4)) & (~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3)))) & ! [X3 : \$int] : (\$less(0,read(X0,X3)) | (\$less(X2,X3) | \$less(X3,X1))))),
inference(ennf_transformation,[],[f6])).
tff(f21,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X4 : \$int] : (~\$less(0,read(X0,X4)) & ~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3))) & ! [X3 : \$int] : (\$less(0,read(X0,X3)) | \$less(X2,X3) | \$less(X3,X1)))),
inference(flattening,[],[f20])).
tff(f22,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X3 : \$int] : (~\$less(0,read(X0,X3)) & ~\$less(X2,X3) & ~\$less(X3,\$sum(X1,3))) & ! [X4 : \$int] : (\$less(0,read(X0,X4)) | \$less(X2,X4) | \$less(X4,X1)))),
inference(rectify,[],[f21])).
tff(f23,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X3 : \$int] : (~\$less(0,read(X0,X3)) & ~\$less(X2,X3) & ~\$less(X3,\$sum(X1,3))) & ! [X4 : \$int] : (\$less(0,read(X0,X4)) | \$less(X2,X4) | \$less(X4,X1))) => (? [X3 : \$int] : (~\$less(0,read(sK0,X3)) & ~\$less(sK2,X3) & ~\$less(X3,\$sum(sK1,3))) & ! [X4 : \$int] : (\$less(0,read(sK0,X4)) | \$less(sK2,X4) | \$less(X4,sK1)))),
introduced(choice_axiom,[])).
tff(f24,plain,(
( ! [X2:\$int,X0:array,X1:\$int] : (? [X3 : \$int] : (~\$less(0,read(X0,X3)) & ~\$less(X2,X3) & ~\$less(X3,\$sum(X1,3))) => (~\$less(0,read(X0,sK3)) & ~\$less(X2,sK3) & ~\$less(sK3,\$sum(X1,3)))) )),
introduced(choice_axiom,[])).
tff(f25,plain,(
(~\$less(0,read(sK0,sK3)) & ~\$less(sK2,sK3) & ~\$less(sK3,\$sum(sK1,3))) & ! [X4 : \$int] : (\$less(0,read(sK0,X4)) | \$less(sK2,X4) | \$less(X4,sK1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f22,f24,f23])).
tff(f29,plain,(
( ! [X4:\$int] : (\$less(0,read(sK0,X4)) | \$less(sK2,X4) | \$less(X4,sK1)) )),
inference(cnf_transformation,[],[f25])).
tff(f30,plain,(
~\$less(sK3,\$sum(sK1,3))),
inference(cnf_transformation,[],[f25])).
tff(f31,plain,(
~\$less(sK2,sK3)),
inference(cnf_transformation,[],[f25])).
tff(f32,plain,(
inference(cnf_transformation,[],[f25])).
tff(f33,plain,(
~\$less(sK3,\$sum(3,sK1))),
inference(forward_demodulation,[],[f30,f7])).
tff(f98,plain,(
\$less(\$sum(3,sK1),sK3) | \$sum(3,sK1) = sK3),
inference(resolution,[],[f14,f33])).
tff(f131,plain,(
spl4_8 <=> \$sum(3,sK1) = sK3),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])])).
tff(f132,plain,(
\$sum(3,sK1) = sK3 | ~spl4_8),
inference(avatar_component_clause,[],[f131])).
tff(f137,plain,(
spl4_10 <=> \$less(\$sum(3,sK1),sK3)),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])])).
tff(f138,plain,(
\$less(\$sum(3,sK1),sK3) | ~spl4_10),
inference(avatar_component_clause,[],[f137])).
tff(f142,plain,(
spl4_8 | spl4_10),
inference(avatar_split_clause,[],[f98,f137,f131])).
tff(f172,plain,(
( ! [X6:\$int,X4:\$int,X5:\$int] : (\$less(\$sum(X5,X4),\$sum(X6,X5)) | ~\$less(X4,X6)) )),
inference(superposition,[],[f15,f7])).
tff(f489,plain,(
( ! [X6:\$int,X7:\$int] : (\$less(X6,\$sum(X7,X6)) | ~\$less(0,X7)) )),
inference(superposition,[],[f172,f9])).
tff(f659,plain,(
\$less(sK2,sK3) | \$less(sK3,sK1)),
inference(resolution,[],[f29,f32])).
tff(f662,plain,(
\$less(sK3,sK1)),
inference(subsumption_resolution,[],[f659,f31])).
tff(f664,plain,(
( ! [X0:\$int] : (~\$less(X0,sK3) | \$less(X0,sK1)) )),
inference(resolution,[],[f662,f13])).
tff(f673,plain,(
( ! [X4:\$int] : (\$less(\$sum(sK1,X4),sK3) | ~\$less(X4,3)) ) | ~spl4_8),
inference(superposition,[],[f172,f132])).
tff(f2468,plain,(
\$less(sK1,sK3) | ~\$less(0,3) | ~spl4_8),
inference(superposition,[],[f673,f9])).
tff(f2473,plain,(
\$less(sK1,sK3) | ~spl4_8),
inference(evaluation,[],[f2468])).
tff(f2475,plain,(
\$less(sK1,sK1) | ~spl4_8),
inference(resolution,[],[f2473,f664])).
tff(f2479,plain,(
\$false | ~spl4_8),
inference(subsumption_resolution,[],[f2475,f12])).
tff(f2480,plain,(
~spl4_8),
tff(f2508,plain,(
( ! [X2:\$int] : (~\$less(X2,\$sum(3,sK1)) | \$less(X2,sK3)) ) | ~spl4_10),
inference(resolution,[],[f138,f13])).
tff(f2961,plain,(
~\$less(0,3) | \$less(sK1,sK3) | ~spl4_10),
inference(resolution,[],[f489,f2508])).
tff(f2988,plain,(
\$less(sK1,sK3) | ~spl4_10),
inference(evaluation,[],[f2961])).
tff(f2990,plain,(
\$less(sK1,sK1) | ~spl4_10),
inference(resolution,[],[f2988,f664])).
tff(f2994,plain,(
\$false | ~spl4_10),
inference(subsumption_resolution,[],[f2990,f12])).
tff(f2995,plain,(
~spl4_10),
tff(f2996,plain,(
\$false),
inference(avatar_sat_refutation,[],[f142,f2480,f2995])).
```

### Sample solution for SEU140+2

```fof(f3,axiom,(
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f4,axiom,(
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f10,axiom,(
! [X0,X1,X2] : (set_difference(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (~in(X3,X1) & in(X3,X0))))),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f11,axiom,(
! [X0,X1] : (disjoint(X0,X1) <=> set_intersection2(X0,X1) = empty_set)),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f20,axiom,(
! [X0,X1] : set_union2(X0,X0) = X0),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f23,axiom,(
! [X0,X1] : (empty_set = set_difference(X0,X1) <=> subset(X0,X1))),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f28,axiom,(
! [X0,X1] : (subset(X0,X1) => set_union2(X0,X1) = X1)),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f31,axiom,(
! [X0] : set_union2(X0,empty_set) = X0),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f39,axiom,(
! [X0,X1] : subset(set_difference(X0,X1),X0)),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f41,axiom,(
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f42,axiom,(
! [X0] : set_difference(X0,empty_set) = X0),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f43,axiom,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f45,axiom,(
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f47,axiom,(
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f51,conjecture,(
! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).
fof(f55,axiom,(
! [X0,X1] : subset(X0,set_union2(X0,X1))),
file('TPTP/TPTP-v6.4.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f58,plain,(
! [X0] : set_union2(X0,X0) = X0),
inference(rectify,[],[f20])).
fof(f62,plain,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f73,plain,(
! [X0,X1] : (set_union2(X0,X1) = X1 | ~subset(X0,X1))),
inference(ennf_transformation,[],[f28])).
fof(f82,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
inference(ennf_transformation,[],[f62])).
fof(f87,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
inference(ennf_transformation,[],[f52])).
fof(f88,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
inference(flattening,[],[f87])).
fof(f114,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : (((in(X3,X1) | ~in(X3,X0)) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | (in(X3,X1) | ~in(X3,X0))) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
inference(nnf_transformation,[],[f10])).
fof(f115,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | in(X3,X1) | ~in(X3,X0)) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
inference(flattening,[],[f114])).
fof(f116,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
inference(rectify,[],[f115])).
fof(f117,plain,(
! [X2,X1,X0] : (? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2))) => ((in(sK4(X0,X1,X2),X1) | ~in(sK4(X0,X1,X2),X0) | ~in(sK4(X0,X1,X2),X2)) & ((~in(sK4(X0,X1,X2),X1) & in(sK4(X0,X1,X2),X0)) | in(sK4(X0,X1,X2),X2))))),
introduced(choice_axiom,[])).
fof(f118,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ((in(sK4(X0,X1,X2),X1) | ~in(sK4(X0,X1,X2),X0) | ~in(sK4(X0,X1,X2),X2)) & ((~in(sK4(X0,X1,X2),X1) & in(sK4(X0,X1,X2),X0)) | in(sK4(X0,X1,X2),X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f116,f117])).
fof(f119,plain,(
! [X0,X1] : ((disjoint(X0,X1) | set_intersection2(X0,X1) != empty_set) & (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)))),
inference(nnf_transformation,[],[f11])).
fof(f120,plain,(
! [X0,X1] : ((empty_set = set_difference(X0,X1) | ~subset(X0,X1)) & (subset(X0,X1) | empty_set != set_difference(X0,X1)))),
inference(nnf_transformation,[],[f23])).
fof(f129,plain,(
! [X1,X0] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
introduced(choice_axiom,[])).
fof(f130,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)) | disjoint(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f82,f129])).
fof(f133,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11))),
introduced(choice_axiom,[])).
fof(f134,plain,(
~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f88,f133])).
fof(f137,plain,(
( ! [X0,X1] : (set_union2(X0,X1) = set_union2(X1,X0)) )),
inference(cnf_transformation,[],[f3])).
fof(f138,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = set_intersection2(X1,X0)) )),
inference(cnf_transformation,[],[f4])).
fof(f159,plain,(
( ! [X4,X2,X0,X1] : (in(X4,X0) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
inference(cnf_transformation,[],[f118])).
fof(f160,plain,(
( ! [X4,X2,X0,X1] : (~in(X4,X1) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
inference(cnf_transformation,[],[f118])).
fof(f165,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f119])).
fof(f171,plain,(
( ! [X0] : (set_union2(X0,X0) = X0) )),
inference(cnf_transformation,[],[f58])).
fof(f175,plain,(
( ! [X0,X1] : (~subset(X0,X1) | empty_set = set_difference(X0,X1)) )),
inference(cnf_transformation,[],[f120])).
fof(f180,plain,(
( ! [X0,X1] : (~subset(X0,X1) | set_union2(X0,X1) = X1) )),
inference(cnf_transformation,[],[f73])).
fof(f183,plain,(
( ! [X0] : (set_union2(X0,empty_set) = X0) )),
inference(cnf_transformation,[],[f31])).
fof(f192,plain,(
( ! [X0,X1] : (subset(set_difference(X0,X1),X0)) )),
inference(cnf_transformation,[],[f39])).
fof(f195,plain,(
( ! [X0,X1] : (set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))) )),
inference(cnf_transformation,[],[f41])).
fof(f196,plain,(
( ! [X0] : (set_difference(X0,empty_set) = X0) )),
inference(cnf_transformation,[],[f42])).
fof(f197,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).
fof(f198,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).
fof(f201,plain,(
( ! [X0,X1] : (set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)) )),
inference(cnf_transformation,[],[f45])).
fof(f203,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))) )),
inference(cnf_transformation,[],[f47])).
fof(f208,plain,(
subset(sK10,sK11)),
inference(cnf_transformation,[],[f134])).
fof(f209,plain,(
disjoint(sK11,sK12)),
inference(cnf_transformation,[],[f134])).
fof(f210,plain,(
~disjoint(sK10,sK12)),
inference(cnf_transformation,[],[f134])).
fof(f213,plain,(
( ! [X0,X1] : (subset(X0,set_union2(X0,X1))) )),
inference(cnf_transformation,[],[f55])).
fof(f216,plain,(
( ! [X0,X1] : (set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0))) )),
inference(definition_unfolding,[],[f138,f203,f203])).
fof(f224,plain,(
( ! [X0,X1] : (~disjoint(X0,X1) | empty_set = set_difference(X0,set_difference(X0,X1))) )),
inference(definition_unfolding,[],[f165,f203])).
fof(f243,plain,(
( ! [X4,X0,X1] : (~in(X4,set_difference(X0,X1)) | ~in(X4,X1)) )),
inference(equality_resolution,[],[f160])).
fof(f244,plain,(
( ! [X4,X0,X1] : (~in(X4,set_difference(X0,X1)) | in(X4,X0)) )),
inference(equality_resolution,[],[f159])).
fof(f281,plain,(
( ! [X1] : (set_union2(empty_set,X1) = X1) )),
inference(superposition,[],[f137,f183])).
fof(f286,plain,(
( ! [X6,X7] : (subset(X6,set_union2(X7,X6))) )),
inference(superposition,[],[f213,f137])).
fof(f324,plain,(
( ! [X4,X3] : (empty_set = set_difference(X3,set_union2(X4,X3))) )),
inference(resolution,[],[f175,f286])).
fof(f326,plain,(
( ! [X6,X7] : (empty_set = set_difference(set_difference(X6,X7),X6)) )),
inference(resolution,[],[f175,f192])).
fof(f340,plain,(
set_union2(sK10,sK11) = sK11),
inference(resolution,[],[f180,f208])).
fof(f399,plain,(
( ! [X10,X8,X9] : (~in(sK8(X8,set_difference(X9,X10)),X10) | disjoint(X8,set_difference(X9,X10))) )),
inference(resolution,[],[f243,f198])).
fof(f405,plain,(
( ! [X4,X2,X3] : (in(sK8(set_difference(X2,X3),X4),X2) | disjoint(set_difference(X2,X3),X4)) )),
inference(resolution,[],[f244,f197])).
fof(f468,plain,(
( ! [X4,X5] : (set_union2(X5,set_union2(X4,X5)) = set_union2(X5,set_difference(X4,X5))) )),
inference(superposition,[],[f195,f201])).
fof(f477,plain,(
( ! [X4,X5] : (set_union2(X5,X4) = set_union2(X5,set_union2(X4,X5))) )),
inference(forward_demodulation,[],[f468,f195])).
fof(f615,plain,(
empty_set = set_difference(sK11,set_difference(sK11,sK12))),
inference(resolution,[],[f224,f209])).
fof(f726,plain,(
( ! [X6,X7] : (set_difference(X7,set_difference(X7,set_union2(X6,X7))) = set_difference(set_union2(X6,X7),set_difference(X6,X7))) )),
inference(superposition,[],[f216,f201])).
fof(f772,plain,(
( ! [X6,X7] : (set_difference(X7,empty_set) = set_difference(set_union2(X6,X7),set_difference(X6,X7))) )),
inference(forward_demodulation,[],[f726,f324])).
fof(f773,plain,(
( ! [X6,X7] : (set_difference(set_union2(X6,X7),set_difference(X6,X7)) = X7) )),
inference(forward_demodulation,[],[f772,f196])).
fof(f1209,plain,(
set_union2(set_difference(sK11,sK12),empty_set) = set_union2(set_difference(sK11,sK12),sK11)),
inference(superposition,[],[f195,f615])).
fof(f1226,plain,(
set_union2(set_difference(sK11,sK12),empty_set) = set_union2(sK11,set_difference(sK11,sK12))),
inference(forward_demodulation,[],[f1209,f137])).
fof(f1227,plain,(
set_union2(empty_set,set_difference(sK11,sK12)) = set_union2(sK11,set_difference(sK11,sK12))),
inference(forward_demodulation,[],[f1226,f137])).
fof(f1228,plain,(
set_union2(sK11,set_difference(sK11,sK12)) = set_difference(sK11,sK12)),
inference(forward_demodulation,[],[f1227,f281])).
fof(f1312,plain,(
( ! [X10,X11] : (set_union2(X10,empty_set) = set_union2(X10,set_difference(X10,X11))) )),
inference(superposition,[],[f195,f326])).
fof(f1331,plain,(
( ! [X10,X11] : (set_union2(X10,set_difference(X10,X11)) = X10) )),
inference(forward_demodulation,[],[f1312,f183])).
fof(f1333,plain,(
set_difference(sK11,sK12) = sK11),
inference(backward_demodulation,[],[f1331,f1228])).
fof(f2114,plain,(
set_union2(sK11,sK10) = set_union2(sK11,sK11)),
inference(superposition,[],[f477,f340])).
fof(f2148,plain,(
set_union2(sK11,sK10) = sK11),
inference(forward_demodulation,[],[f2114,f171])).
fof(f2201,plain,(
set_difference(sK11,set_difference(sK11,sK10)) = sK10),
inference(superposition,[],[f773,f2148])).
fof(f2214,plain,(
set_difference(set_union2(sK11,sK12),sK11) = sK12),
inference(superposition,[],[f773,f1333])).
fof(f4504,plain,(
( ! [X4,X2,X3] : (disjoint(set_difference(X2,X3),set_difference(X4,X2)) | disjoint(set_difference(X2,X3),set_difference(X4,X2))) )),
inference(resolution,[],[f405,f399])).
fof(f4539,plain,(
( ! [X4,X2,X3] : (disjoint(set_difference(X2,X3),set_difference(X4,X2))) )),
inference(duplicate_literal_removal,[],[f4504])).
fof(f4747,plain,(
( ! [X41] : (disjoint(sK10,set_difference(X41,sK11))) )),
inference(superposition,[],[f4539,f2201])).
fof(f4918,plain,(
disjoint(sK10,sK12)),
inference(superposition,[],[f4747,f2214])).
fof(f4925,plain,(
\$false),
inference(subsumption_resolution,[],[f4918,f210])).
```

### Sample solution for NLP042+1

```tff(u283,axiom,
(![X1, X0] : ((~woman(X0,X1) | human_person(X0,X1))))).

tff(u282,axiom,
(![X1, X0] : ((~woman(X0,X1) | female(X0,X1))))).

tff(u281,negated_conjecture,
woman(sK0,sK1)).

tff(u280,negated_conjecture,
~female(sK0,sK4)).

tff(u279,negated_conjecture,
~female(sK0,sK2)).

tff(u278,negated_conjecture,
~female(sK0,sK3)).

tff(u277,negated_conjecture,
female(sK0,sK1)).

tff(u276,axiom,
(![X1, X0] : ((~human_person(X0,X1) | organism(X0,X1))))).

tff(u275,axiom,
(![X1, X0] : ((~human_person(X0,X1) | human(X0,X1))))).

tff(u274,axiom,
(![X1, X0] : ((~human_person(X0,X1) | animate(X0,X1))))).

tff(u273,negated_conjecture,
human_person(sK0,sK1)).

tff(u272,negated_conjecture,
~animate(sK0,sK3)).

tff(u271,negated_conjecture,
animate(sK0,sK1)).

tff(u270,negated_conjecture,
~human(sK0,sK2)).

tff(u269,negated_conjecture,
human(sK0,sK1)).

tff(u268,axiom,
(![X1, X0] : ((~organism(X0,X1) | entity(X0,X1))))).

tff(u267,axiom,
(![X1, X0] : ((~organism(X0,X1) | living(X0,X1))))).

tff(u266,negated_conjecture,
organism(sK0,sK1)).

tff(u265,negated_conjecture,
~living(sK0,sK3)).

tff(u264,negated_conjecture,
living(sK0,sK1)).

tff(u263,axiom,
(![X1, X0] : ((~entity(X0,X1) | specific(X0,X1))))).

tff(u262,axiom,
(![X1, X0] : ((~entity(X0,X1) | existent(X0,X1))))).

tff(u261,negated_conjecture,
entity(sK0,sK1)).

tff(u260,negated_conjecture,
entity(sK0,sK3)).

tff(u259,axiom,
(![X1, X0] : ((~mia_forename(X0,X1) | forename(X0,X1))))).

tff(u258,negated_conjecture,
mia_forename(sK0,sK2)).

tff(u257,axiom,
(![X1, X0] : ((~forename(X0,X1) | relname(X0,X1))))).

tff(u256,negated_conjecture,
forename(sK0,sK2)).

tff(u255,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | nonhuman(X0,X1))))).

tff(u254,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | general(X0,X1))))).

tff(u253,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | unisex(X0,X1))))).

tff(u252,negated_conjecture,
abstraction(sK0,sK2)).

tff(u251,axiom,
(![X1, X0] : ((~unisex(X0,X1) | ~female(X0,X1))))).

tff(u250,negated_conjecture,
unisex(sK0,sK2)).

tff(u249,negated_conjecture,
unisex(sK0,sK4)).

tff(u248,negated_conjecture,
unisex(sK0,sK3)).

tff(u247,negated_conjecture,
~general(sK0,sK4)).

tff(u246,negated_conjecture,
~general(sK0,sK1)).

tff(u245,negated_conjecture,
~general(sK0,sK3)).

tff(u244,negated_conjecture,
general(sK0,sK2)).

tff(u243,axiom,
(![X1, X0] : ((~nonhuman(X0,X1) | ~human(X0,X1))))).

tff(u242,negated_conjecture,
nonhuman(sK0,sK2)).

tff(u241,axiom,
(![X1, X0] : ((~relation(X0,X1) | abstraction(X0,X1))))).

tff(u240,negated_conjecture,
relation(sK0,sK2)).

tff(u239,axiom,
(![X1, X0] : ((~relname(X0,X1) | relation(X0,X1))))).

tff(u238,negated_conjecture,
relname(sK0,sK2)).

tff(u237,axiom,
(![X1, X0] : ((~object(X0,X1) | entity(X0,X1))))).

tff(u236,axiom,
(![X1, X0] : ((~object(X0,X1) | nonliving(X0,X1))))).

tff(u235,axiom,
(![X1, X0] : ((~object(X0,X1) | unisex(X0,X1))))).

tff(u234,negated_conjecture,
object(sK0,sK3)).

tff(u233,axiom,
(![X1, X0] : ((~nonliving(X0,X1) | ~living(X0,X1))))).

tff(u232,axiom,
(![X1, X0] : ((~nonliving(X0,X1) | ~animate(X0,X1))))).

tff(u231,negated_conjecture,
nonliving(sK0,sK3)).

tff(u230,negated_conjecture,
~existent(sK0,sK4)).

tff(u229,negated_conjecture,
existent(sK0,sK1)).

tff(u228,negated_conjecture,
existent(sK0,sK3)).

tff(u227,axiom,
(![X1, X0] : ((~specific(X0,X1) | ~general(X0,X1))))).

tff(u226,negated_conjecture,
specific(sK0,sK1)).

tff(u225,negated_conjecture,
specific(sK0,sK4)).

tff(u224,negated_conjecture,
specific(sK0,sK3)).

tff(u223,axiom,
(![X1, X0] : ((~substance_matter(X0,X1) | object(X0,X1))))).

tff(u222,negated_conjecture,
substance_matter(sK0,sK3)).

tff(u221,axiom,
(![X1, X0] : ((~food(X0,X1) | substance_matter(X0,X1))))).

tff(u220,negated_conjecture,
food(sK0,sK3)).

tff(u219,axiom,
(![X1, X0] : ((~beverage(X0,X1) | food(X0,X1))))).

tff(u218,negated_conjecture,
beverage(sK0,sK3)).

tff(u217,axiom,
(![X1, X0] : ((~shake_beverage(X0,X1) | beverage(X0,X1))))).

tff(u216,negated_conjecture,
shake_beverage(sK0,sK3)).

tff(u215,axiom,
(![X1, X0] : ((~order(X0,X1) | act(X0,X1))))).

tff(u214,axiom,
(![X1, X0] : ((~order(X0,X1) | event(X0,X1))))).

tff(u213,negated_conjecture,
order(sK0,sK4)).

tff(u212,axiom,
(![X1, X0] : ((~event(X0,X1) | eventuality(X0,X1))))).

tff(u211,negated_conjecture,
event(sK0,sK4)).

tff(u210,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | specific(X0,X1))))).

tff(u209,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | nonexistent(X0,X1))))).

tff(u208,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | unisex(X0,X1))))).

tff(u207,negated_conjecture,
eventuality(sK0,sK4)).

tff(u206,axiom,
(![X1, X0] : ((~nonexistent(X0,X1) | ~existent(X0,X1))))).

tff(u205,negated_conjecture,
nonexistent(sK0,sK4)).

tff(u204,axiom,
(![X1, X0] : ((~act(X0,X1) | event(X0,X1))))).

tff(u203,negated_conjecture,
act(sK0,sK4)).

tff(u202,axiom,
(![X1, X3, X0, X2] : ((~of(X0,X3,X1) | (X2 = X3) | ~forename(X0,X3) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1))))).

tff(u201,negated_conjecture,
(![X0] : ((~of(sK0,X0,sK1) | (sK2 = X0) | ~forename(sK0,X0))))).

tff(u200,negated_conjecture,
of(sK0,sK2,sK1)).

tff(u199,negated_conjecture,
nonreflexive(sK0,sK4)).

tff(u198,negated_conjecture,
~agent(sK0,sK4,sK3)).

tff(u197,negated_conjecture,
agent(sK0,sK4,sK1)).

tff(u196,axiom,
(![X1, X3, X0] : ((~patient(X0,X1,X3) | ~agent(X0,X1,X3) | ~nonreflexive(X0,X1))))).

tff(u195,negated_conjecture,
patient(sK0,sK4,sK3)).

```

### Sample solution for SWV017+1

```tff(declare_\$i,type,\$i:\$tType).
tff(declare_\$i1,type,at:\$i).
tff(declare_\$i2,type,t:\$i).
tff(finite_domain,axiom,
! [X:\$i] : (
X = at | X = t
) ).

tff(distinct_domain,axiom,
at != t
).

tff(declare_a,type,a:\$i).
tff(a_definition,axiom,a = at).
tff(declare_b,type,b:\$i).
tff(b_definition,axiom,b = at).
tff(declare_an_a_nonce,type,an_a_nonce:\$i).
tff(an_a_nonce_definition,axiom,an_a_nonce = t).
tff(declare_bt,type,bt:\$i).
tff(bt_definition,axiom,bt = at).
tff(declare_an_intruder_nonce,type,an_intruder_nonce:\$i).
tff(an_intruder_nonce_definition,axiom,an_intruder_nonce = at).
tff(declare_key,type,key: \$i * \$i > \$i).
tff(function_key,axiom,
key(at,at) = at
& key(at,t) = t
& key(t,at) = t
& key(t,t) = t

).

tff(declare_pair,type,pair: \$i * \$i > \$i).
tff(function_pair,axiom,
pair(at,at) = at
& pair(at,t) = t
& pair(t,at) = at
& pair(t,t) = at

).

tff(declare_sent,type,sent: \$i * \$i * \$i > \$i).
tff(function_sent,axiom,
sent(at,at,at) = at
& sent(at,at,t) = at
& sent(at,t,at) = at
& sent(at,t,t) = at
& sent(t,at,at) = at
& sent(t,at,t) = at
& sent(t,t,at) = at
& sent(t,t,t) = at

).

).

tff(declare_encrypt,type,encrypt: \$i * \$i > \$i).
tff(function_encrypt,axiom,
encrypt(at,at) = at
& encrypt(at,t) = at
& encrypt(t,at) = at
& encrypt(t,t) = t

).

tff(declare_triple,type,triple: \$i * \$i * \$i > \$i).
tff(function_triple,axiom,
triple(at,at,at) = t
& triple(at,at,t) = at
& triple(at,t,at) = at
& triple(at,t,t) = at
& triple(t,at,at) = t
& triple(t,at,t) = t
& triple(t,t,at) = at
& triple(t,t,t) = at

).

tff(declare_generate_b_nonce,type,generate_b_nonce: \$i > \$i).
tff(function_generate_b_nonce,axiom,
generate_b_nonce(at) = t
& generate_b_nonce(t) = t

).

tff(declare_generate_expiration_time,type,generate_expiration_time: \$i > \$i).
tff(function_generate_expiration_time,axiom,
generate_expiration_time(at) = t
& generate_expiration_time(t) = t

).

tff(declare_generate_key,type,generate_key: \$i > \$i).
tff(function_generate_key,axiom,
generate_key(at) = at
& generate_key(t) = at

).

tff(declare_generate_intruder_nonce,type,generate_intruder_nonce: \$i > \$i).
tff(function_generate_intruder_nonce,axiom,
generate_intruder_nonce(at) = at
& generate_intruder_nonce(t) = t

).

tff(declare_a_holds,type,a_holds: \$i > \$o ).
tff(predicate_a_holds,axiom,
%         a_holds(at) undefined in model
%         a_holds(t) undefined in model

).

tff(declare_party_of_protocol,type,party_of_protocol: \$i > \$o ).
tff(predicate_party_of_protocol,axiom,
party_of_protocol(at)
& party_of_protocol(t)

).

tff(declare_message,type,message: \$i > \$o ).
tff(predicate_message,axiom,
message(at)
& ~message(t)

).

tff(declare_a_stored,type,a_stored: \$i > \$o ).
tff(predicate_a_stored,axiom,
~a_stored(at)
& a_stored(t)

).

tff(declare_b_holds,type,b_holds: \$i > \$o ).
tff(predicate_b_holds,axiom,
%         b_holds(at) undefined in model
%         b_holds(t) undefined in model

).

tff(declare_fresh_to_b,type,fresh_to_b: \$i > \$o ).
tff(predicate_fresh_to_b,axiom,
fresh_to_b(at)
& fresh_to_b(t)

).

tff(declare_b_stored,type,b_stored: \$i > \$o ).
tff(predicate_b_stored,axiom,
%         b_stored(at) undefined in model
%         b_stored(t) undefined in model

).

tff(declare_a_key,type,a_key: \$i > \$o ).
tff(predicate_a_key,axiom,
a_key(at)
& ~a_key(t)

).

tff(declare_t_holds,type,t_holds: \$i > \$o ).
tff(predicate_t_holds,axiom,
t_holds(at)
& ~t_holds(t)

).

tff(declare_a_nonce,type,a_nonce: \$i > \$o ).
tff(predicate_a_nonce,axiom,
~a_nonce(at)
& a_nonce(t)

).

tff(declare_intruder_message,type,intruder_message: \$i > \$o ).
tff(predicate_intruder_message,axiom,
intruder_message(at)
& intruder_message(t)

).

tff(declare_intruder_holds,type,intruder_holds: \$i > \$o ).
tff(predicate_intruder_holds,axiom,
intruder_holds(at)
& intruder_holds(t)

).

tff(declare_fresh_intruder_nonce,type,fresh_intruder_nonce: \$i > \$o ).
tff(predicate_fresh_intruder_nonce,axiom,
fresh_intruder_nonce(at)
& ~fresh_intruder_nonce(t)

).

```

## Zipperposition 1.1

Simon Cruanes
Inria Nancy, France

### Sample solution for PUZ081^1

(Zipperposition can't prove SET014^4)
```% SZS status Theorem for 'examples/ho/PUZ081^1.p'
% SZS output start Refutation
tff(0, plain, is_a(mel,islander) & is_a(zoey,islander),
file('examples/ho/PUZ081^1.p', 'kk_6_4')).
tff(1, plain, is_a(zoey, islander), inference('cnf', [status(esa)], [0])).
tff(2, plain, ![X]: (is_a(X,islander) => (is_a(X,knave) | is_a(X,knight))),
file('examples/ho/PUZ081^1.p', 'kk_6_1')).
tff(3, plain,
![X0]: (is_a(X0, knight) | is_a(X0, knave) | ~ is_a(X0, islander)),
inference('cnf', [status(esa)], [2])).
tff(4, plain, (is_a(zoey, knight) | is_a(zoey, knave)),
inference('s_sup-', [status(thm)], [1, 3])).
tff(5, plain, (is_a(zoey, knave)) | (is_a(zoey, knight)),
inference('split', [status(esa)], [4])).
tff(6, plain, says(zoey,is_a(mel,knave)),
file('examples/ho/PUZ081^1.p', 'kk_6_5')).
tff(7, plain, says(zoey, is_a(mel, knave)),
inference('cnf', [status(esa)], [6])).
tff(8, plain, ![X]: (is_a(X,knight) => (![A:\$o]: (says(X,A) => A))),
file('examples/ho/PUZ081^1.p', 'kk_6_2')).
tff(9, plain, ![X1, X2 : \$o]: (~ says(X1, X2) | X2 | ~ is_a(X1, knight)),
inference('cnf', [status(esa)], [8])).
tff(10, plain, (is_a(mel, knave) | ~ is_a(zoey, knight)),
inference('s_sup-', [status(thm)], [7, 9])).
tff(11, plain, (is_a(mel, knave)) | ~ (is_a(zoey, knight)),
inference('split', [status(esa)], [10])).
tff(12, plain,
?[Y,Z]:
(is_a(zoey,Z) & is_a(mel,Y) & ((Z = knight) <~> (Z = knave)) &
((Y = knight) <~> (Y = knave))),
file('examples/ho/PUZ081^1.p', 'query')).
tff(13, plain,
~
(?[Y,Z]:
(is_a(zoey,Z) & is_a(mel,Y) & ((Z = knight) <~> (Z = knave)) &
((Y = knight) <~> (Y = knave)))),
inference('neg_goal', [status(esa)], [12])).
tff(14, plain,
![X5, X6]:
(~ is_a(mel, X5)
| X5 != knave
| X5 = knight
| X6 != knight
| X6 = knave
| ~ is_a(zoey, X6)),
inference('cnf', [status(esa)], [13])).
tff(15, plain, (~ is_a(zoey, knight) | knave = knight | ~ is_a(mel, knave)),
inference('simplify', [status(thm)], [14])).
tff(16, plain,
~ (is_a(mel, knave)) | ~ (is_a(zoey, knight)) | (knight = knave),
inference('split', [status(esa)], [15])).
tff(17, plain, (is_a(zoey, knave)) <= ((is_a(zoey, knave))),
inference('split', [status(esa)], [4])).
tff(18, plain,
![X5, X6]:
(~ is_a(mel, X5)
| X5 != knight
| X5 = knave
| X6 != knave
| X6 = knight
| ~ is_a(zoey, X6)),
inference('cnf', [status(esa)], [13])).
tff(19, plain, (~ is_a(zoey, knave) | knight = knave | ~ is_a(mel, knight)),
inference('simplify', [status(thm)], [18])).
tff(20, plain, (knight = knave) <= ((knight = knave)),
inference('split', [status(esa)], [19])).
tff(21, plain, (is_a(mel, knave) | says(zoey, \$false)),
inference('fool_param', [status(thm)], [7])).
tff(22, plain, (says(zoey, \$false)) <= ((says(zoey, \$false))),
inference('split', [status(esa)], [21])).
tff(23, plain, (~ is_a(zoey, knight)) <= ((says(zoey, \$false))),
inference('s_sup-', [status(thm)], [22, 9])).
tff(24, plain,
(~ is_a(zoey, knave)) <= ((says(zoey, \$false)) & (knight = knave)),
inference('s_sup-', [status(thm)], [20, 23])).
tff(25, plain,
~ (is_a(zoey, knave)) | ~ (says(zoey, \$false)) | ~ (knight = knave),
inference('s_sup-', [status(thm)], [17, 24])).
tff(26, plain,
~ (says(zoey, \$false)) | (is_a(zoey, knight)) | ~ (knight = knave),
inference('sat_resolution', [status(thm)], [5, 25])).
tff(27, plain,
(is_a(mel, knave)) | ~ (says(zoey, \$false)) | ~ (knight = knave),
inference('sat_resolution', [status(thm)], [26, 11])).
tff(28, plain, (is_a(mel, knave)) | (says(zoey, \$false)),
inference('split', [status(esa)], [21])).
tff(29, plain, (is_a(mel, knave)) | ~ (knight = knave),
inference('sat_resolution', [status(thm)], [27, 28])).
tff(kk_6_6, axiom, (says(mel,~(is_a(mel,knave) | is_a(zoey,knave))))).
tff(31, plain, zip_tseitin = (~(is_a(zoey,knave) | is_a(mel,knave))),
by_def([status(thm)])).
tff(no_name, axiom,
(zip_tseitin <=> (~(is_a(zoey,knave) | is_a(mel,knave))))).
tff(33, plain, says(mel,zip_tseitin),
inference('preprocess(flatten)', [status(esa)], [30, 32])).
tff(34, plain, says(mel, zip_tseitin),
inference('cnf', [status(esa)], [33])).
tff(35, plain, (zip_tseitin | says(mel, \$false)),
inference('fool_param', [status(thm)], [34])).
tff(36, plain, (zip_tseitin) | (says(mel, \$false)),
inference('split', [status(esa)], [35])).
tff(37, plain, (is_a(mel, knave)) <= ((is_a(mel, knave))),
inference('split', [status(esa)], [21])).
tff(38, plain, (says(mel, \$false)) <= ((says(mel, \$false))),
inference('split', [status(esa)], [35])).
tff(39, plain, (~ is_a(mel, knight)) <= ((says(mel, \$false))),
inference('s_sup-', [status(thm)], [38, 9])).
tff(40, plain,
(~ is_a(mel, knave)) <= ((says(mel, \$false)) & (knight = knave)),
inference('s_sup-', [status(thm)], [20, 39])).
tff(41, plain,
~ (is_a(mel, knave)) | ~ (says(mel, \$false)) | ~ (knight = knave),
inference('s_sup-', [status(thm)], [37, 40])).
tff(42, plain, (zip_tseitin) | ~ (is_a(mel, knave)) | ~ (knight = knave),
inference('sat_resolution', [status(thm)], [36, 41])).
tff(43, plain, zip_tseitin <=> (~(is_a(mel,knave) | is_a(zoey,knave))),
inference('renaming', [status(esa)], [30, 31])).
tff(44, plain, (~ is_a(mel, knave) | ~ zip_tseitin),
inference('cnf', [status(esa)], [43])).
tff(45, plain, ~ (zip_tseitin) | ~ (is_a(mel, knave)),
inference('split', [status(esa)], [44])).
tff(46, plain, ~ (is_a(mel, knave)) | ~ (knight = knave),
inference('sat_resolution', [status(thm)], [42, 45])).
tff(47, plain, ~ (knight = knave),
inference('sat_resolution', [status(thm)], [29, 46])).
tff(48, plain, ~ (is_a(mel, knave)) | ~ (is_a(zoey, knight)),
inference('sat_resolution', [status(thm)], [16, 47])).
tff(49, plain, ~ (is_a(mel, knave)) | (is_a(zoey, knave)),
inference('sat_resolution', [status(thm)], [5, 48])).
tff(50, plain, ![X]: (is_a(X,knave) => (![A:\$o]: (says(X,A) => (~A)))),
file('examples/ho/PUZ081^1.p', 'kk_6_3')).
tff(51, plain, ![X3, X4 : \$o]: (~ says(X3, X4) | ~ X4 | ~ is_a(X3, knave)),
inference('cnf', [status(esa)], [50])).
tff(52, plain, (~ is_a(mel, knave) | ~ is_a(zoey, knave)),
inference('s_sup-', [status(thm)], [7, 51])).
tff(53, plain, ~ (is_a(mel, knave)) | ~ (is_a(zoey, knave)),
inference('split', [status(esa)], [52])).
tff(54, plain, ~ (is_a(mel, knave)),
inference('sat_resolution', [status(thm)], [49, 53])).
tff(55, plain, ~ (is_a(zoey, knight)),
inference('sat_resolution', [status(thm)], [11, 54])).
tff(56, plain, (is_a(zoey, knave)),
inference('sat_resolution', [status(thm)], [5, 55])).
tff(57, plain,
~ (is_a(zoey, knave)) | ~ (is_a(mel, knight)) | (knight = knave),
inference('split', [status(esa)], [19])).
tff(58, plain, ~ (is_a(zoey, knave)) | ~ (is_a(mel, knight)),
inference('sat_resolution', [status(thm)], [57, 47])).
tff(59, plain, is_a(mel, islander), inference('cnf', [status(esa)], [0])).
tff(60, plain, (is_a(mel, knight) | is_a(mel, knave)),
inference('s_sup-', [status(thm)], [59, 3])).
tff(61, plain, (is_a(mel, knave)) | (is_a(mel, knight)),
inference('split', [status(esa)], [60])).
tff(62, plain, (is_a(mel, knight)),
inference('sat_resolution', [status(thm)], [61, 54])).
tff(63, plain, ~ (is_a(zoey, knave)),
inference('sat_resolution', [status(thm)], [58, 62])).
tff(64, plain, \$false, inference('sat_resolution', [status(thm)], [56, 63])).

% SZS output end Refutation
```

### Sample solution for DAT013=1

```% SZS output start Refutation
tff(0, plain,
![U:array,V:\$int,W:\$int]:
((![X:\$int]:
(((\$lesseq(\$int, X, W)) & (\$lesseq(\$int, V, X))) =>
(![Y:\$int]:
(((\$lesseq(\$int, Y, W)) & (\$lesseq(\$int, (\$sum(\$int, V, 3)), Y))) =>
file('DAT013=1.p', 'co1')).
tff(1, plain,
~
(![U:array,V:\$int,W:\$int]:
((![X:\$int]:
(((\$lesseq(\$int, X, W)) & (\$lesseq(\$int, V, X))) =>
(![Y:\$int]:
(((\$lesseq(\$int, Y, W)) & (\$lesseq(\$int, (\$sum(\$int, V, 3)), Y))) =>
inference('neg_goal', [status(esa)], [0])).
inference('cnf', [status(esa)], [1])).
tff(3, plain,
![X7 : \$int]:
(\$less(0, read(sk_U, X7)) | \$less(X7, sk_V) | \$less(sk_W, X7)),
inference('cnf', [status(esa)], [1])).
tff(4, plain,
![X7 : \$int]:
| \$lesseq(\$sum(1, X7), sk_V)
| \$lesseq(\$sum(1, sk_W), X7)),
inference('rw_lit', [status(thm)], [3])).
tff(5, plain, (\$lesseq(\$sum(1, sk_W), sk_Y) | \$lesseq(\$sum(1, sk_Y), sk_V)),
inference('canc_ineq_chaining', [status(thm)], [2, 4])).
tff(6, plain, \$lesseq(sk_Y, sk_W), inference('cnf', [status(esa)], [1])).
tff(7, plain, \$lesseq(\$sum(1, sk_Y), sk_V),
inference('clc', [status(thm)], [5, 6])).
tff(8, plain, \$lesseq(\$sum(3, sk_V), sk_Y),
inference('cnf', [status(esa)], [1])).
tff(9, plain, \$false,
inference('canc_ineq_chaining', [status(thm)], [7, 8])).

% SZS output end Refutation

```

### Sample solution for SEU140+1

```% SZS status Theorem for 'SEU140+2.p'
% SZS output start Refutation
tff(0, plain, \$false, inference('simplify', [status(thm)], [1])).
tff(1, plain, (\$false | empty_set != empty_set),
inference('demod', [status(thm)], [2, 3])).
tff(3, plain, subset(sk_A2, sk_B1), inference('cnf', [status(esa)], [4])).
tff(2, plain, (~ subset(sk_A2, sk_B1) | empty_set != empty_set),
inference('s_sup-', [status(thm)], [5, 6])).
tff(6, plain, set_intersection2(sk_A2, sk_C4) != empty_set,
inference('simplify', [status(thm)], [7])).
tff(5, plain,
![X0]: (~ subset(X0, sk_B1) | set_intersection2(X0, sk_C4) = empty_set),
inference('simplify', [status(thm)], [8])).
tff(4, plain, ~(![A,B,C]: ((disjoint(B,C) & subset(A,B)) => disjoint(A,C))),
inference('neg_goal', [status(esa)], [9])).
tff(9, plain, ![A,B,C]: ((disjoint(B,C) & subset(A,B)) => disjoint(A,C)),
file('SEU140+2.p', 't63_xboole_1')).
tff(8, plain,
![X0]:
(\$false | set_intersection2(X0, sk_C4) = empty_set | ~ subset(X0, sk_B1)),
inference('demod', [status(thm)], [10, 11])).
tff(7, plain, (set_intersection2(sk_A2, sk_C4) != empty_set | \$false),
inference('s_sup-', [status(thm)], [12, 13])).
tff(13, plain, ~ disjoint(sk_A2, sk_C4),
inference('cnf', [status(esa)], [4])).
tff(12, plain,
![X36, X38]:
(disjoint(X36, X38) | set_intersection2(X36, X38) != empty_set),
inference('cnf', [status(esa)], [14])).
tff(11, plain, ![X74]: subset(empty_set, X74),
inference('cnf', [status(esa)], [15])).
tff(10, plain,
![X0]:
(~ subset(empty_set, set_intersection2(X0, sk_C4))
| set_intersection2(X0, sk_C4) = empty_set | ~ subset(X0, sk_B1)),
inference('s_sup-', [status(thm)], [16, 17])).
tff(17, plain,
![X0, X1, X2]:
(~ subset(set_intersection2(X1, X0), set_intersection2(X2, X0))
| set_intersection2(X2, X0) = set_intersection2(X1, X0)
| ~ subset(X2, X1)),
inference('simplify', [status(thm)], [18])).
tff(16, plain, set_intersection2(sk_B1, sk_C4) = empty_set,
inference('simplify', [status(thm)], [19])).
tff(15, plain, ![A]: subset(empty_set,A),
file('SEU140+2.p', 't2_xboole_1')).
tff(14, plain,
![A,B]: (disjoint(A,B) <=> (set_intersection2(A,B) = empty_set)),
file('SEU140+2.p', 'd7_xboole_0')).
tff(19, plain, (set_intersection2(sk_B1, sk_C4) = empty_set | \$false),
inference('s_sup-', [status(thm)], [20, 21])).
tff(18, plain,
![X0, X1, X2]:
(~ subset(X2, X1) | set_intersection2(X2, X0) = set_intersection2(X1, X0)
| \$false
| ~ subset(set_intersection2(X1, X0), set_intersection2(X2, X0))),
inference('s_sup-', [status(thm)], [22, 23])).
tff(23, plain,
![X9, X10]: (X9 = X10 | ~ subset(X9, X10) | ~ subset(X10, X9)),
inference('cnf', [status(esa)], [24])).
tff(22, plain,
![X66, X67, X68]:
(~ subset(X66, X67)
| subset(set_intersection2(X66, X68), set_intersection2(X67, X68))),
inference('cnf', [status(esa)], [25])).
tff(21, plain,
![X36, X37]:
(set_intersection2(X36, X37) = empty_set | ~ disjoint(X36, X37)),
inference('cnf', [status(esa)], [14])).
tff(20, plain, disjoint(sk_B1, sk_C4), inference('cnf', [status(esa)], [4])).
tff(25, plain,
![A,B,C]:
(subset(A,B) => subset(set_intersection2(A,C),set_intersection2(B,C))),
file('SEU140+2.p', 't26_xboole_1')).
tff(24, plain, ![A,B]: ((A = B) <=> (subset(B,A) & subset(A,B))),
file('SEU140+2.p', 'd10_xboole_0')).

% SZS output end Refutation

```