# Entrants' Sample Solutions

## CVC4---0.0

Andrew Reynolds1, Cesare Tinelli1, Clark Barrett2
1University of Iowa, USA
2New York University, USA

### Sample solution for NLP042+1

```---Current Model---
Representatives:
smt_individual :
0: e
eq_class( e ) : e, SKOLEM_941, SKOLEM_939
1: SKOLEM_940
eq_class( SKOLEM_940 ) : SKOLEM_940
2: SKOLEM_942
eq_class( SKOLEM_942 ) : SKOLEM_942
3: SKOLEM_943
eq_class( SKOLEM_943 ) : SKOLEM_943
Functions:
abstraction( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return false
if x_1 == SKOLEM_943
return false
if x_0 == SKOLEM_940
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
return true

act( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_943
return true
if x_0 == SKOLEM_940
if x_1 == SKOLEM_940
return false
return false

agent( x_0 : smt_individual, x_1 : smt_individual, x_2 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
if x_2 == e
return false
if x_2 == SKOLEM_940
return true
if x_1 == SKOLEM_940
if x_2 == e
return false
if x_1 == SKOLEM_943
if x_2 == e
return true
if x_2 == SKOLEM_940
return true
return false

animate( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
if x_1 == SKOLEM_942
return false
if x_0 == SKOLEM_940
if x_1 == e
return false
return false

beverage( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return true
if x_0 == SKOLEM_940
if x_1 == SKOLEM_940
return false
return false

entity( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
if x_1 == SKOLEM_942
return true
if x_0 == SKOLEM_940
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
return false

event( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_943
return true
if x_0 == SKOLEM_940
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
return false

eventuality( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return false
if x_1 == SKOLEM_943
return true
if x_0 == SKOLEM_940
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
return false

existent( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
if x_1 == SKOLEM_942
return true
if x_0 == SKOLEM_940
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
return false

female( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
if x_0 == SKOLEM_940
if x_1 == e
return false
return false

food( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return true
if x_0 == SKOLEM_940
if x_1 == SKOLEM_940
return false
return false

forename( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return false
if x_1 == SKOLEM_943
return false
if x_0 == SKOLEM_940
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return false
if x_1 == SKOLEM_943
return false
return true

general( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return false
if x_1 == SKOLEM_943
return false
if x_0 == SKOLEM_940
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
return true

human( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
if x_0 == SKOLEM_940
if x_1 == e
return false
return false

human_person( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
return false

impartial( x_0 : smt_individual, x_1 : smt_individual ) : Bool
return true

living( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
if x_1 == SKOLEM_942
return false
if x_0 == SKOLEM_940
if x_1 == e
return false
return false

mia_forename( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_0 == SKOLEM_940
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
return false

nonexistent( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return false
if x_0 == SKOLEM_940
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
return true

nonhuman( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_0 == SKOLEM_940
if x_1 == e
return true
return true

nonliving( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return true
if x_0 == SKOLEM_940
if x_1 == e
return true
return true

nonreflexive( x_0 : smt_individual, x_1 : smt_individual ) : Bool
return true

object( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return true
if x_0 == SKOLEM_940
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
return false

of( x_0 : smt_individual, x_1 : smt_individual, x_2 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
if x_2 == e
return false
if x_2 == SKOLEM_940
return true
if x_2 == SKOLEM_942
return false
if x_1 == SKOLEM_942
if x_2 == SKOLEM_940
return true
if x_1 == SKOLEM_943
if x_2 == SKOLEM_940
return false
if x_2 == SKOLEM_942
return false
if x_0 == SKOLEM_940
if x_1 == e
if x_2 == e
return false
if x_2 == SKOLEM_940
return true
if x_1 == SKOLEM_940
if x_2 == e
return true
if x_2 == SKOLEM_940
return true
if x_1 == SKOLEM_942
if x_2 == SKOLEM_940
return false
if x_1 == SKOLEM_943
if x_2 == SKOLEM_940
return true
return true

order( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_943
return true
if x_0 == SKOLEM_940
if x_1 == SKOLEM_940
return false
return false

organism( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
if x_0 == SKOLEM_940
if x_1 == e
return false
return false

patient( x_0 : smt_individual, x_1 : smt_individual, x_2 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
if x_2 == e
return true
if x_2 == SKOLEM_940
return false
if x_1 == SKOLEM_940
if x_2 == e
return true
if x_1 == SKOLEM_943
if x_2 == e
return false
if x_2 == SKOLEM_940
return false
if x_2 == SKOLEM_942
return true
return false

relation( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return false
if x_1 == SKOLEM_943
return false
if x_0 == SKOLEM_940
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
return true

relname( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return false
if x_1 == SKOLEM_943
return false
if x_0 == SKOLEM_940
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
return true

shake_beverage( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return true
return false

singleton( x_0 : smt_individual, x_1 : smt_individual ) : Bool
return true

specific( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
if x_1 == SKOLEM_942
return true
if x_1 == SKOLEM_943
return true
if x_0 == SKOLEM_940
if x_1 == e
return true
if x_1 == SKOLEM_940
return true
return false

substance_matter( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return false
if x_1 == SKOLEM_942
return true
if x_0 == SKOLEM_940
if x_1 == e
return false
return false

thing( x_0 : smt_individual, x_1 : smt_individual ) : Bool
return true

unisex( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return true
if x_1 == SKOLEM_940
return false
if x_0 == SKOLEM_940
if x_1 == e
return true
return true

woman( x_0 : smt_individual, x_1 : smt_individual ) : Bool
if x_0 == e
if x_1 == e
return false
if x_1 == SKOLEM_940
return true
return false
```

### Sample solution for SWV017+1

```---Current Model---
Representatives:
smt_individual :
0: t
eq_class( t ) : t, (generate_expiration_time (key bt b)), (generate_b_nonce (key bt b)), (key at t), an_intruder_nonce, (key at a), (sent t e (triple (encrypt (quadruple e e (generate_key e) e) e) (encrypt (triple e (generate_key e) e) e) e)), (triple (encrypt (quadruple e e (generate_key e) e) e) (encrypt (triple e (generate_key e) e) e) e), (encrypt (quadruple e e (generate_key e) e) e), (quadruple e e (generate_key e) e), (quadruple e e e e), bt, (sent t a (triple (encrypt (quadruple e e e e) at) e e)), (sent e b (pair (encrypt (triple e e (generate_expiration_time e)) bt) (encrypt (generate_b_nonce e) e))), (pair (encrypt (triple e e (generate_expiration_time e)) bt) (encrypt (generate_b_nonce e) e)), (sent e t (triple e e (encrypt (triple e e e) e))), (sent e e e), (sent e b (pair e e)), (triple b (generate_b_nonce e) (encrypt (triple e e (generate_expiration_time e)) bt)), (encrypt (triple e e (generate_expiration_time e)) bt), (encrypt (triple e (generate_key e) e) e), (triple e (generate_key e) e), (triple e e (encrypt (triple e e e) e)), (encrypt (triple e e e) e), (triple (encrypt (quadruple e e e e) at) e e), (triple e e e), (triple e e (generate_expiration_time e)), (encrypt (quadruple e e e e) at), (sent b t (triple b (generate_b_nonce e) (encrypt (triple e e (generate_expiration_time e)) bt))), (pair b an_a_nonce), (pair e e), (pair e (encrypt e e)), (pair a an_a_nonce), (sent a b (pair a an_a_nonce)), (sent a e (pair e (encrypt e e))), b, (generate_expiration_time t), (generate_expiration_time e), (encrypt (generate_b_nonce e) e), (generate_b_nonce t), (generate_b_nonce e), (encrypt e e), an_a_nonce, e
1: (generate_key e)
eq_class( (generate_key e) ) : (generate_key e), (generate_key (key bt b)), (key e e), (generate_intruder_nonce e), at, (key bt t), (key bt b), a, (generate_key t)
Functions:
a_holds( x_0 : smt_individual ) : Bool
return true

a_key( x_0 : smt_individual ) : Bool
if x_0 == (generate_key e)
return true
return false

a_nonce( x_0 : smt_individual ) : Bool
if x_0 == t
return true
if x_0 == (generate_key e)
return false
return false

a_stored( x_0 : smt_individual ) : Bool
return true

b_holds( x_0 : smt_individual ) : Bool
return true

b_stored( x_0 : smt_individual ) : Bool
return true

fresh_intruder_nonce( x_0 : smt_individual ) : Bool
return true

fresh_to_b( x_0 : smt_individual ) : Bool
return true

intruder_holds( x_0 : smt_individual ) : Bool
return true

intruder_message( x_0 : smt_individual ) : Bool
return true

message( x_0 : smt_individual ) : Bool
return true

party_of_protocol( x_0 : smt_individual ) : Bool
return true

t_holds( x_0 : smt_individual ) : Bool
return true

encrypt( x_0 : smt_individual, x_1 : smt_individual ) : smt_individual
return t

generate_b_nonce( x_0 : smt_individual ) : smt_individual
return t

generate_expiration_time( x_0 : smt_individual ) : smt_individual
return t

generate_intruder_nonce( x_0 : smt_individual ) : smt_individual
return (generate_key e)

generate_key( x_0 : smt_individual ) : smt_individual
return (generate_key e)

key( x_0 : smt_individual, x_1 : smt_individual ) : smt_individual
if x_0 == t
if x_1 == t
return (generate_key e)
if x_0 == (generate_key e)
if x_1 == t
return t
if x_1 == (generate_key e)
return t
return t

pair( x_0 : smt_individual, x_1 : smt_individual ) : smt_individual
return t

quadruple( x_0 : smt_individual, x_1 : smt_individual, x_2 : smt_individual, x_3 : smt_individual ) : smt_individual
return t

sent( x_0 : smt_individual, x_1 : smt_individual, x_2 : smt_individual ) : smt_individual
return t

triple( x_0 : smt_individual, x_1 : smt_individual, x_2 : smt_individual ) : smt_individual
return t
```

## E-KRHyper 1.3

Björn Pelzer
University Koblenz-Landau, Germany

### Sample solution for CSR082+1

```% SZS answers start Formulae
```

## E-MaLeS---1.1

Daniel Kuehlwein1, Josef Urban1, Stephan Schulz2 1Radboud University Nijmegen, The Netherlands
2Technische Universität München, Germany

## EP 1.4pre and EP 1.6pre

Stephan Schulz
Technische Universität München, Germany

### Sample solution for SEU140+2

```# Preprocessing time       : 0.012 s
# Problem is unsatisfiable (or provable), constructing proof object
# SZS status Theorem
# SZS output start CNFRefutation.
fof(8, axiom,![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', d3_tarski)).
fof(27, axiom,![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', symmetry_r1_xboole_0)).
fof(43, axiom,![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(51, conjecture,![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t63_xboole_1)).
fof(57, negated_conjecture,~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))),inference(assume_negation,[status(cth)],[51])).
fof(66, plain,![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)],[43,theory(equality)])).
fof(101, plain,![X1]:![X2]:((~(subset(X1,X2))|![X3]:(~(in(X3,X1))|in(X3,X2)))&(?[X3]:(in(X3,X1)&~(in(X3,X2)))|subset(X1,X2))),inference(fof_nnf,[status(thm)],[8])).
fof(102, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&(?[X7]:(in(X7,X4)&~(in(X7,X5)))|subset(X4,X5))),inference(variable_rename,[status(thm)],[101])).
fof(103, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(skolemize,[status(esa)],[102])).
fof(104, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(shift_quantors,[status(thm)],[103])).
fof(105, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)|subset(X4,X5))&(~(in(esk3_2(X4,X5),X5))|subset(X4,X5)))),inference(distribute,[status(thm)],[104])).
cnf(108,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)),inference(split_conjunct,[status(thm)],[105])).
fof(170, plain,![X1]:![X2]:(~(disjoint(X1,X2))|disjoint(X2,X1)),inference(fof_nnf,[status(thm)],[27])).
fof(171, plain,![X3]:![X4]:(~(disjoint(X3,X4))|disjoint(X4,X3)),inference(variable_rename,[status(thm)],[170])).
cnf(172,plain,(disjoint(X1,X2)|~disjoint(X2,X1)),inference(split_conjunct,[status(thm)],[171])).
fof(215, plain,![X1]:![X2]:((disjoint(X1,X2)|?[X3]:(in(X3,X1)&in(X3,X2)))&(![X3]:(~(in(X3,X1))|~(in(X3,X2)))|~(disjoint(X1,X2)))),inference(fof_nnf,[status(thm)],[66])).
fof(216, plain,![X4]:![X5]:((disjoint(X4,X5)|?[X6]:(in(X6,X4)&in(X6,X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(variable_rename,[status(thm)],[215])).
fof(217, plain,![X4]:![X5]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(skolemize,[status(esa)],[216])).
fof(218, plain,![X4]:![X5]:![X7]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&((~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(shift_quantors,[status(thm)],[217])).
fof(219, plain,![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)],[218])).
cnf(220,plain,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)),inference(split_conjunct,[status(thm)],[219])).
cnf(221,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)),inference(split_conjunct,[status(thm)],[219])).
cnf(222,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)),inference(split_conjunct,[status(thm)],[219])).
fof(244, negated_conjecture,?[X1]:?[X2]:?[X3]:((subset(X1,X2)&disjoint(X2,X3))&~(disjoint(X1,X3))),inference(fof_nnf,[status(thm)],[57])).
fof(245, negated_conjecture,?[X4]:?[X5]:?[X6]:((subset(X4,X5)&disjoint(X5,X6))&~(disjoint(X4,X6))),inference(variable_rename,[status(thm)],[244])).
fof(246, negated_conjecture,((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~(disjoint(esk11_0,esk13_0))),inference(skolemize,[status(esa)],[245])).
cnf(247,negated_conjecture,(~disjoint(esk11_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])).
cnf(248,negated_conjecture,(disjoint(esk12_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])).
cnf(249,negated_conjecture,(subset(esk11_0,esk12_0)),inference(split_conjunct,[status(thm)],[246])).
cnf(384,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X1)),inference(spm,[status(thm)],[172,221,theory(equality)])).
cnf(386,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X2)),inference(spm,[status(thm)],[172,222,theory(equality)])).
cnf(474,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)),inference(spm,[status(thm)],[108,249,theory(equality)])).
cnf(485,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)),inference(spm,[status(thm)],[220,248,theory(equality)])).
cnf(2151,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[247,384,theory(equality)])).
cnf(2160,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk13_0)),inference(spm,[status(thm)],[247,386,theory(equality)])).
cnf(2169,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk12_0)),inference(spm,[status(thm)],[485,2160,theory(equality)])).
cnf(2622,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[2169,474,theory(equality)])).
cnf(2640,negated_conjecture,(\$false),inference(rw,[status(thm)],[2622,2151,theory(equality)])).
cnf(2641,negated_conjecture,(\$false),inference(cn,[status(thm)],[2640,theory(equality)])).
cnf(2642,negated_conjecture,(\$false),2641,['proof']).
# SZS output end CNFRefutation
```

### Sample solution for NLP042+1

```# Preprocessing time       : 0.010 s
# Problem is satisfiable (or invalid), generating saturation derivation
# SZS status CounterSatisfiable
# SZS output start Saturation.
fof(1, axiom,![X1]:![X2]:(woman(X1,X2)=>female(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax1)).
fof(2, axiom,![X1]:![X2]:(human_person(X1,X2)=>animate(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax2)).
fof(3, axiom,![X1]:![X2]:(human_person(X1,X2)=>human(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax3)).
fof(4, axiom,![X1]:![X2]:(organism(X1,X2)=>living(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax4)).
fof(5, axiom,![X1]:![X2]:(organism(X1,X2)=>impartial(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax5)).
fof(6, axiom,![X1]:![X2]:(organism(X1,X2)=>entity(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax6)).
fof(7, axiom,![X1]:![X2]:(human_person(X1,X2)=>organism(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax7)).
fof(8, axiom,![X1]:![X2]:(woman(X1,X2)=>human_person(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax8)).
fof(9, axiom,![X1]:![X2]:(mia_forename(X1,X2)=>forename(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax9)).
fof(10, axiom,![X1]:![X2]:(abstraction(X1,X2)=>unisex(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax10)).
fof(11, axiom,![X1]:![X2]:(abstraction(X1,X2)=>general(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax11)).
fof(12, axiom,![X1]:![X2]:(abstraction(X1,X2)=>nonhuman(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax12)).
fof(13, axiom,![X1]:![X2]:(abstraction(X1,X2)=>thing(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax13)).
fof(14, axiom,![X1]:![X2]:(relation(X1,X2)=>abstraction(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax14)).
fof(15, axiom,![X1]:![X2]:(relname(X1,X2)=>relation(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax15)).
fof(16, axiom,![X1]:![X2]:(forename(X1,X2)=>relname(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax16)).
fof(17, axiom,![X1]:![X2]:(object(X1,X2)=>unisex(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax17)).
fof(18, axiom,![X1]:![X2]:(object(X1,X2)=>impartial(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax18)).
fof(19, axiom,![X1]:![X2]:(object(X1,X2)=>nonliving(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax19)).
fof(20, axiom,![X1]:![X2]:(entity(X1,X2)=>existent(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax20)).
fof(21, axiom,![X1]:![X2]:(entity(X1,X2)=>specific(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax21)).
fof(22, axiom,![X1]:![X2]:(entity(X1,X2)=>thing(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax22)).
fof(23, axiom,![X1]:![X2]:(object(X1,X2)=>entity(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax23)).
fof(24, axiom,![X1]:![X2]:(substance_matter(X1,X2)=>object(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax24)).
fof(25, axiom,![X1]:![X2]:(food(X1,X2)=>substance_matter(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax25)).
fof(26, axiom,![X1]:![X2]:(beverage(X1,X2)=>food(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax26)).
fof(27, axiom,![X1]:![X2]:(shake_beverage(X1,X2)=>beverage(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax27)).
fof(28, axiom,![X1]:![X2]:(order(X1,X2)=>event(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax28)).
fof(29, axiom,![X1]:![X2]:(eventuality(X1,X2)=>unisex(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax29)).
fof(30, axiom,![X1]:![X2]:(eventuality(X1,X2)=>nonexistent(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax30)).
fof(31, axiom,![X1]:![X2]:(eventuality(X1,X2)=>specific(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax31)).
fof(32, axiom,![X1]:![X2]:(thing(X1,X2)=>singleton(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax32)).
fof(33, axiom,![X1]:![X2]:(eventuality(X1,X2)=>thing(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax33)).
fof(34, axiom,![X1]:![X2]:(event(X1,X2)=>eventuality(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax34)).
fof(35, axiom,![X1]:![X2]:(act(X1,X2)=>event(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax35)).
fof(36, axiom,![X1]:![X2]:(order(X1,X2)=>act(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax36)).
fof(37, axiom,![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax37)).
fof(38, axiom,![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax38)).
fof(39, axiom,![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax39)).
fof(40, axiom,![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax40)).
fof(41, axiom,![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax41)).
fof(42, axiom,![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax42)).
fof(43, 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_4.1.0_FLAT/NLP042+1.p', ax43)).
fof(44, axiom,![X1]:![X2]:![X3]:![X4]:(((nonreflexive(X1,X2)&agent(X1,X2,X3))&patient(X1,X2,X4))=>~(X3=X4)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax44)).
fof(45, 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_4.1.0_FLAT/NLP042+1.p', co1)).
fof(46, 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)],[45])).
fof(47, plain,![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2))),inference(fof_simplification,[status(thm)],[37,theory(equality)])).
fof(48, plain,![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2))),inference(fof_simplification,[status(thm)],[38,theory(equality)])).
fof(49, plain,![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2))),inference(fof_simplification,[status(thm)],[39,theory(equality)])).
fof(50, plain,![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2))),inference(fof_simplification,[status(thm)],[40,theory(equality)])).
fof(51, plain,![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2))),inference(fof_simplification,[status(thm)],[41,theory(equality)])).
fof(52, plain,![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2))),inference(fof_simplification,[status(thm)],[42,theory(equality)])).
fof(53, plain,![X1]:![X2]:(~(woman(X1,X2))|female(X1,X2)),inference(fof_nnf,[status(thm)],[1])).
fof(54, plain,![X3]:![X4]:(~(woman(X3,X4))|female(X3,X4)),inference(variable_rename,[status(thm)],[53])).
cnf(55,plain,(female(X1,X2)|~woman(X1,X2)),inference(split_conjunct,[status(thm)],[54])).
fof(56, plain,![X1]:![X2]:(~(human_person(X1,X2))|animate(X1,X2)),inference(fof_nnf,[status(thm)],[2])).
fof(57, plain,![X3]:![X4]:(~(human_person(X3,X4))|animate(X3,X4)),inference(variable_rename,[status(thm)],[56])).
cnf(58,plain,(animate(X1,X2)|~human_person(X1,X2)),inference(split_conjunct,[status(thm)],[57])).
fof(59, plain,![X1]:![X2]:(~(human_person(X1,X2))|human(X1,X2)),inference(fof_nnf,[status(thm)],[3])).
fof(60, plain,![X3]:![X4]:(~(human_person(X3,X4))|human(X3,X4)),inference(variable_rename,[status(thm)],[59])).
cnf(61,plain,(human(X1,X2)|~human_person(X1,X2)),inference(split_conjunct,[status(thm)],[60])).
fof(62, plain,![X1]:![X2]:(~(organism(X1,X2))|living(X1,X2)),inference(fof_nnf,[status(thm)],[4])).
fof(63, plain,![X3]:![X4]:(~(organism(X3,X4))|living(X3,X4)),inference(variable_rename,[status(thm)],[62])).
cnf(64,plain,(living(X1,X2)|~organism(X1,X2)),inference(split_conjunct,[status(thm)],[63])).
fof(65, plain,![X1]:![X2]:(~(organism(X1,X2))|impartial(X1,X2)),inference(fof_nnf,[status(thm)],[5])).
fof(66, plain,![X3]:![X4]:(~(organism(X3,X4))|impartial(X3,X4)),inference(variable_rename,[status(thm)],[65])).
cnf(67,plain,(impartial(X1,X2)|~organism(X1,X2)),inference(split_conjunct,[status(thm)],[66])).
fof(68, plain,![X1]:![X2]:(~(organism(X1,X2))|entity(X1,X2)),inference(fof_nnf,[status(thm)],[6])).
fof(69, plain,![X3]:![X4]:(~(organism(X3,X4))|entity(X3,X4)),inference(variable_rename,[status(thm)],[68])).
cnf(70,plain,(entity(X1,X2)|~organism(X1,X2)),inference(split_conjunct,[status(thm)],[69])).
fof(71, plain,![X1]:![X2]:(~(human_person(X1,X2))|organism(X1,X2)),inference(fof_nnf,[status(thm)],[7])).
fof(72, plain,![X3]:![X4]:(~(human_person(X3,X4))|organism(X3,X4)),inference(variable_rename,[status(thm)],[71])).
cnf(73,plain,(organism(X1,X2)|~human_person(X1,X2)),inference(split_conjunct,[status(thm)],[72])).
fof(74, plain,![X1]:![X2]:(~(woman(X1,X2))|human_person(X1,X2)),inference(fof_nnf,[status(thm)],[8])).
fof(75, plain,![X3]:![X4]:(~(woman(X3,X4))|human_person(X3,X4)),inference(variable_rename,[status(thm)],[74])).
cnf(76,plain,(human_person(X1,X2)|~woman(X1,X2)),inference(split_conjunct,[status(thm)],[75])).
fof(77, plain,![X1]:![X2]:(~(mia_forename(X1,X2))|forename(X1,X2)),inference(fof_nnf,[status(thm)],[9])).
fof(78, plain,![X3]:![X4]:(~(mia_forename(X3,X4))|forename(X3,X4)),inference(variable_rename,[status(thm)],[77])).
cnf(79,plain,(forename(X1,X2)|~mia_forename(X1,X2)),inference(split_conjunct,[status(thm)],[78])).
fof(80, plain,![X1]:![X2]:(~(abstraction(X1,X2))|unisex(X1,X2)),inference(fof_nnf,[status(thm)],[10])).
fof(81, plain,![X3]:![X4]:(~(abstraction(X3,X4))|unisex(X3,X4)),inference(variable_rename,[status(thm)],[80])).
cnf(82,plain,(unisex(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[81])).
fof(83, plain,![X1]:![X2]:(~(abstraction(X1,X2))|general(X1,X2)),inference(fof_nnf,[status(thm)],[11])).
fof(84, plain,![X3]:![X4]:(~(abstraction(X3,X4))|general(X3,X4)),inference(variable_rename,[status(thm)],[83])).
cnf(85,plain,(general(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[84])).
fof(86, plain,![X1]:![X2]:(~(abstraction(X1,X2))|nonhuman(X1,X2)),inference(fof_nnf,[status(thm)],[12])).
fof(87, plain,![X3]:![X4]:(~(abstraction(X3,X4))|nonhuman(X3,X4)),inference(variable_rename,[status(thm)],[86])).
cnf(88,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[87])).
fof(89, plain,![X1]:![X2]:(~(abstraction(X1,X2))|thing(X1,X2)),inference(fof_nnf,[status(thm)],[13])).
fof(90, plain,![X3]:![X4]:(~(abstraction(X3,X4))|thing(X3,X4)),inference(variable_rename,[status(thm)],[89])).
cnf(91,plain,(thing(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[90])).
fof(92, plain,![X1]:![X2]:(~(relation(X1,X2))|abstraction(X1,X2)),inference(fof_nnf,[status(thm)],[14])).
fof(93, plain,![X3]:![X4]:(~(relation(X3,X4))|abstraction(X3,X4)),inference(variable_rename,[status(thm)],[92])).
cnf(94,plain,(abstraction(X1,X2)|~relation(X1,X2)),inference(split_conjunct,[status(thm)],[93])).
fof(95, plain,![X1]:![X2]:(~(relname(X1,X2))|relation(X1,X2)),inference(fof_nnf,[status(thm)],[15])).
fof(96, plain,![X3]:![X4]:(~(relname(X3,X4))|relation(X3,X4)),inference(variable_rename,[status(thm)],[95])).
cnf(97,plain,(relation(X1,X2)|~relname(X1,X2)),inference(split_conjunct,[status(thm)],[96])).
fof(98, plain,![X1]:![X2]:(~(forename(X1,X2))|relname(X1,X2)),inference(fof_nnf,[status(thm)],[16])).
fof(99, plain,![X3]:![X4]:(~(forename(X3,X4))|relname(X3,X4)),inference(variable_rename,[status(thm)],[98])).
cnf(100,plain,(relname(X1,X2)|~forename(X1,X2)),inference(split_conjunct,[status(thm)],[99])).
fof(101, plain,![X1]:![X2]:(~(object(X1,X2))|unisex(X1,X2)),inference(fof_nnf,[status(thm)],[17])).
fof(102, plain,![X3]:![X4]:(~(object(X3,X4))|unisex(X3,X4)),inference(variable_rename,[status(thm)],[101])).
cnf(103,plain,(unisex(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[102])).
fof(104, plain,![X1]:![X2]:(~(object(X1,X2))|impartial(X1,X2)),inference(fof_nnf,[status(thm)],[18])).
fof(105, plain,![X3]:![X4]:(~(object(X3,X4))|impartial(X3,X4)),inference(variable_rename,[status(thm)],[104])).
cnf(106,plain,(impartial(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[105])).
fof(107, plain,![X1]:![X2]:(~(object(X1,X2))|nonliving(X1,X2)),inference(fof_nnf,[status(thm)],[19])).
fof(108, plain,![X3]:![X4]:(~(object(X3,X4))|nonliving(X3,X4)),inference(variable_rename,[status(thm)],[107])).
cnf(109,plain,(nonliving(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[108])).
fof(110, plain,![X1]:![X2]:(~(entity(X1,X2))|existent(X1,X2)),inference(fof_nnf,[status(thm)],[20])).
fof(111, plain,![X3]:![X4]:(~(entity(X3,X4))|existent(X3,X4)),inference(variable_rename,[status(thm)],[110])).
cnf(112,plain,(existent(X1,X2)|~entity(X1,X2)),inference(split_conjunct,[status(thm)],[111])).
fof(113, plain,![X1]:![X2]:(~(entity(X1,X2))|specific(X1,X2)),inference(fof_nnf,[status(thm)],[21])).
fof(114, plain,![X3]:![X4]:(~(entity(X3,X4))|specific(X3,X4)),inference(variable_rename,[status(thm)],[113])).
cnf(115,plain,(specific(X1,X2)|~entity(X1,X2)),inference(split_conjunct,[status(thm)],[114])).
fof(116, plain,![X1]:![X2]:(~(entity(X1,X2))|thing(X1,X2)),inference(fof_nnf,[status(thm)],[22])).
fof(117, plain,![X3]:![X4]:(~(entity(X3,X4))|thing(X3,X4)),inference(variable_rename,[status(thm)],[116])).
cnf(118,plain,(thing(X1,X2)|~entity(X1,X2)),inference(split_conjunct,[status(thm)],[117])).
fof(119, plain,![X1]:![X2]:(~(object(X1,X2))|entity(X1,X2)),inference(fof_nnf,[status(thm)],[23])).
fof(120, plain,![X3]:![X4]:(~(object(X3,X4))|entity(X3,X4)),inference(variable_rename,[status(thm)],[119])).
cnf(121,plain,(entity(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[120])).
fof(122, plain,![X1]:![X2]:(~(substance_matter(X1,X2))|object(X1,X2)),inference(fof_nnf,[status(thm)],[24])).
fof(123, plain,![X3]:![X4]:(~(substance_matter(X3,X4))|object(X3,X4)),inference(variable_rename,[status(thm)],[122])).
cnf(124,plain,(object(X1,X2)|~substance_matter(X1,X2)),inference(split_conjunct,[status(thm)],[123])).
fof(125, plain,![X1]:![X2]:(~(food(X1,X2))|substance_matter(X1,X2)),inference(fof_nnf,[status(thm)],[25])).
fof(126, plain,![X3]:![X4]:(~(food(X3,X4))|substance_matter(X3,X4)),inference(variable_rename,[status(thm)],[125])).
cnf(127,plain,(substance_matter(X1,X2)|~food(X1,X2)),inference(split_conjunct,[status(thm)],[126])).
fof(128, plain,![X1]:![X2]:(~(beverage(X1,X2))|food(X1,X2)),inference(fof_nnf,[status(thm)],[26])).
fof(129, plain,![X3]:![X4]:(~(beverage(X3,X4))|food(X3,X4)),inference(variable_rename,[status(thm)],[128])).
cnf(130,plain,(food(X1,X2)|~beverage(X1,X2)),inference(split_conjunct,[status(thm)],[129])).
fof(131, plain,![X1]:![X2]:(~(shake_beverage(X1,X2))|beverage(X1,X2)),inference(fof_nnf,[status(thm)],[27])).
fof(132, plain,![X3]:![X4]:(~(shake_beverage(X3,X4))|beverage(X3,X4)),inference(variable_rename,[status(thm)],[131])).
cnf(133,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)),inference(split_conjunct,[status(thm)],[132])).
fof(134, plain,![X1]:![X2]:(~(order(X1,X2))|event(X1,X2)),inference(fof_nnf,[status(thm)],[28])).
fof(135, plain,![X3]:![X4]:(~(order(X3,X4))|event(X3,X4)),inference(variable_rename,[status(thm)],[134])).
cnf(136,plain,(event(X1,X2)|~order(X1,X2)),inference(split_conjunct,[status(thm)],[135])).
fof(137, plain,![X1]:![X2]:(~(eventuality(X1,X2))|unisex(X1,X2)),inference(fof_nnf,[status(thm)],[29])).
fof(138, plain,![X3]:![X4]:(~(eventuality(X3,X4))|unisex(X3,X4)),inference(variable_rename,[status(thm)],[137])).
cnf(139,plain,(unisex(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[138])).
fof(140, plain,![X1]:![X2]:(~(eventuality(X1,X2))|nonexistent(X1,X2)),inference(fof_nnf,[status(thm)],[30])).
fof(141, plain,![X3]:![X4]:(~(eventuality(X3,X4))|nonexistent(X3,X4)),inference(variable_rename,[status(thm)],[140])).
cnf(142,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[141])).
fof(143, plain,![X1]:![X2]:(~(eventuality(X1,X2))|specific(X1,X2)),inference(fof_nnf,[status(thm)],[31])).
fof(144, plain,![X3]:![X4]:(~(eventuality(X3,X4))|specific(X3,X4)),inference(variable_rename,[status(thm)],[143])).
cnf(145,plain,(specific(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[144])).
fof(146, plain,![X1]:![X2]:(~(thing(X1,X2))|singleton(X1,X2)),inference(fof_nnf,[status(thm)],[32])).
fof(147, plain,![X3]:![X4]:(~(thing(X3,X4))|singleton(X3,X4)),inference(variable_rename,[status(thm)],[146])).
cnf(148,plain,(singleton(X1,X2)|~thing(X1,X2)),inference(split_conjunct,[status(thm)],[147])).
fof(149, plain,![X1]:![X2]:(~(eventuality(X1,X2))|thing(X1,X2)),inference(fof_nnf,[status(thm)],[33])).
fof(150, plain,![X3]:![X4]:(~(eventuality(X3,X4))|thing(X3,X4)),inference(variable_rename,[status(thm)],[149])).
cnf(151,plain,(thing(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[150])).
fof(152, plain,![X1]:![X2]:(~(event(X1,X2))|eventuality(X1,X2)),inference(fof_nnf,[status(thm)],[34])).
fof(153, plain,![X3]:![X4]:(~(event(X3,X4))|eventuality(X3,X4)),inference(variable_rename,[status(thm)],[152])).
cnf(154,plain,(eventuality(X1,X2)|~event(X1,X2)),inference(split_conjunct,[status(thm)],[153])).
fof(155, plain,![X1]:![X2]:(~(act(X1,X2))|event(X1,X2)),inference(fof_nnf,[status(thm)],[35])).
fof(156, plain,![X3]:![X4]:(~(act(X3,X4))|event(X3,X4)),inference(variable_rename,[status(thm)],[155])).
cnf(157,plain,(event(X1,X2)|~act(X1,X2)),inference(split_conjunct,[status(thm)],[156])).
fof(158, plain,![X1]:![X2]:(~(order(X1,X2))|act(X1,X2)),inference(fof_nnf,[status(thm)],[36])).
fof(159, plain,![X3]:![X4]:(~(order(X3,X4))|act(X3,X4)),inference(variable_rename,[status(thm)],[158])).
cnf(160,plain,(act(X1,X2)|~order(X1,X2)),inference(split_conjunct,[status(thm)],[159])).
fof(161, plain,![X1]:![X2]:(~(animate(X1,X2))|~(nonliving(X1,X2))),inference(fof_nnf,[status(thm)],[47])).
fof(162, plain,![X3]:![X4]:(~(animate(X3,X4))|~(nonliving(X3,X4))),inference(variable_rename,[status(thm)],[161])).
cnf(163,plain,(~nonliving(X1,X2)|~animate(X1,X2)),inference(split_conjunct,[status(thm)],[162])).
fof(164, plain,![X1]:![X2]:(~(existent(X1,X2))|~(nonexistent(X1,X2))),inference(fof_nnf,[status(thm)],[48])).
fof(165, plain,![X3]:![X4]:(~(existent(X3,X4))|~(nonexistent(X3,X4))),inference(variable_rename,[status(thm)],[164])).
cnf(166,plain,(~nonexistent(X1,X2)|~existent(X1,X2)),inference(split_conjunct,[status(thm)],[165])).
fof(167, plain,![X1]:![X2]:(~(nonhuman(X1,X2))|~(human(X1,X2))),inference(fof_nnf,[status(thm)],[49])).
fof(168, plain,![X3]:![X4]:(~(nonhuman(X3,X4))|~(human(X3,X4))),inference(variable_rename,[status(thm)],[167])).
cnf(169,plain,(~human(X1,X2)|~nonhuman(X1,X2)),inference(split_conjunct,[status(thm)],[168])).
fof(170, plain,![X1]:![X2]:(~(nonliving(X1,X2))|~(living(X1,X2))),inference(fof_nnf,[status(thm)],[50])).
fof(171, plain,![X3]:![X4]:(~(nonliving(X3,X4))|~(living(X3,X4))),inference(variable_rename,[status(thm)],[170])).
cnf(172,plain,(~living(X1,X2)|~nonliving(X1,X2)),inference(split_conjunct,[status(thm)],[171])).
fof(173, plain,![X1]:![X2]:(~(specific(X1,X2))|~(general(X1,X2))),inference(fof_nnf,[status(thm)],[51])).
fof(174, plain,![X3]:![X4]:(~(specific(X3,X4))|~(general(X3,X4))),inference(variable_rename,[status(thm)],[173])).
cnf(175,plain,(~general(X1,X2)|~specific(X1,X2)),inference(split_conjunct,[status(thm)],[174])).
fof(176, plain,![X1]:![X2]:(~(unisex(X1,X2))|~(female(X1,X2))),inference(fof_nnf,[status(thm)],[52])).
fof(177, plain,![X3]:![X4]:(~(unisex(X3,X4))|~(female(X3,X4))),inference(variable_rename,[status(thm)],[176])).
cnf(178,plain,(~female(X1,X2)|~unisex(X1,X2)),inference(split_conjunct,[status(thm)],[177])).
fof(179, plain,![X1]:![X2]:![X3]:(((~(entity(X1,X2))|~(forename(X1,X3)))|~(of(X1,X3,X2)))|![X4]:((~(forename(X1,X4))|X4=X3)|~(of(X1,X4,X2)))),inference(fof_nnf,[status(thm)],[43])).
fof(180, plain,![X5]:![X6]:![X7]:(((~(entity(X5,X6))|~(forename(X5,X7)))|~(of(X5,X7,X6)))|![X8]:((~(forename(X5,X8))|X8=X7)|~(of(X5,X8,X6)))),inference(variable_rename,[status(thm)],[179])).
fof(181, 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)],[180])).
cnf(182,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)],[181])).
fof(183, plain,![X1]:![X2]:![X3]:![X4]:(((~(nonreflexive(X1,X2))|~(agent(X1,X2,X3)))|~(patient(X1,X2,X4)))|~(X3=X4)),inference(fof_nnf,[status(thm)],[44])).
fof(184, plain,![X5]:![X6]:![X7]:![X8]:(((~(nonreflexive(X5,X6))|~(agent(X5,X6,X7)))|~(patient(X5,X6,X8)))|~(X7=X8)),inference(variable_rename,[status(thm)],[183])).
cnf(185,plain,(X1!=X2|~patient(X3,X4,X2)|~agent(X3,X4,X1)|~nonreflexive(X3,X4)),inference(split_conjunct,[status(thm)],[184])).
fof(186, 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(fof_nnf,[status(thm)],[46])).
fof(187, negated_conjecture,?[X6]:(actual_world(X6)&?[X7]:?[X8]:?[X9]:?[X10]:((((((((((of(X6,X8,X7)&woman(X6,X7))&mia_forename(X6,X8))&forename(X6,X8))&shake_beverage(X6,X9))&event(X6,X10))&agent(X6,X10,X7))&patient(X6,X10,X9))&past(X6,X10))&nonreflexive(X6,X10))&order(X6,X10))),inference(variable_rename,[status(thm)],[186])).
fof(188, 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)],[187])).
cnf(189,negated_conjecture,(order(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(190,negated_conjecture,(nonreflexive(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(191,negated_conjecture,(past(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(192,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(193,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(194,negated_conjecture,(event(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(195,negated_conjecture,(shake_beverage(esk1_0,esk4_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(196,negated_conjecture,(forename(esk1_0,esk3_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(197,negated_conjecture,(mia_forename(esk1_0,esk3_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(198,negated_conjecture,(woman(esk1_0,esk2_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(199,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(200,negated_conjecture,(actual_world(esk1_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(201,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)),inference(er,[status(thm)],[185,theory(equality)])).
cnf(206,negated_conjecture,(human_person(esk1_0,esk2_0)),inference(spm,[status(thm)],[76,198,theory(equality)])).
cnf(207,negated_conjecture,(eventuality(esk1_0,esk5_0)),inference(spm,[status(thm)],[154,194,theory(equality)])).
cnf(209,plain,(relation(X1,X2)|~forename(X1,X2)),inference(spm,[status(thm)],[97,100,theory(equality)])).
cnf(210,plain,(food(X1,X2)|~shake_beverage(X1,X2)),inference(spm,[status(thm)],[130,133,theory(equality)])).
cnf(211,plain,(~unisex(X1,X2)|~woman(X1,X2)),inference(spm,[status(thm)],[178,55,theory(equality)])).
cnf(212,plain,(entity(X1,X2)|~human_person(X1,X2)),inference(spm,[status(thm)],[70,73,theory(equality)])).
cnf(213,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)|~nonreflexive(esk1_0,esk5_0)),inference(spm,[status(thm)],[201,192,theory(equality)])).
cnf(214,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)|\$false),inference(rw,[status(thm)],[213,190,theory(equality)])).
cnf(215,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)),inference(cn,[status(thm)],[214,theory(equality)])).
cnf(216,plain,(~existent(X1,X2)|~eventuality(X1,X2)),inference(spm,[status(thm)],[166,142,theory(equality)])).
cnf(217,plain,(~nonliving(X1,X2)|~human_person(X1,X2)),inference(spm,[status(thm)],[163,58,theory(equality)])).
cnf(218,plain,(~human(X1,X2)|~abstraction(X1,X2)),inference(spm,[status(thm)],[169,88,theory(equality)])).
cnf(219,plain,(~specific(X1,X2)|~abstraction(X1,X2)),inference(spm,[status(thm)],[175,85,theory(equality)])).
cnf(220,plain,(~nonliving(X1,X2)|~organism(X1,X2)),inference(spm,[status(thm)],[172,64,theory(equality)])).
cnf(221,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,esk3_0)|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)),inference(spm,[status(thm)],[182,199,theory(equality)])).
cnf(222,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|\$false|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)),inference(rw,[status(thm)],[221,196,theory(equality)])).
cnf(223,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)),inference(cn,[status(thm)],[222,theory(equality)])).
cnf(224,negated_conjecture,(~unisex(esk1_0,esk2_0)),inference(spm,[status(thm)],[211,198,theory(equality)])).
cnf(225,negated_conjecture,(~abstraction(esk1_0,esk2_0)),inference(spm,[status(thm)],[224,82,theory(equality)])).
cnf(226,negated_conjecture,(~object(esk1_0,esk2_0)),inference(spm,[status(thm)],[224,103,theory(equality)])).
cnf(227,negated_conjecture,(~eventuality(esk1_0,esk2_0)),inference(spm,[status(thm)],[224,139,theory(equality)])).
cnf(228,plain,(abstraction(X1,X2)|~forename(X1,X2)),inference(spm,[status(thm)],[94,209,theory(equality)])).
cnf(229,plain,(substance_matter(X1,X2)|~shake_beverage(X1,X2)),inference(spm,[status(thm)],[127,210,theory(equality)])).
cnf(230,negated_conjecture,(~forename(esk1_0,esk2_0)),inference(spm,[status(thm)],[225,228,theory(equality)])).
cnf(231,negated_conjecture,(entity(esk1_0,esk2_0)),inference(spm,[status(thm)],[212,206,theory(equality)])).
cnf(232,plain,(~eventuality(X1,X2)|~entity(X1,X2)),inference(spm,[status(thm)],[216,112,theory(equality)])).
cnf(233,negated_conjecture,(~entity(esk1_0,esk5_0)),inference(spm,[status(thm)],[232,207,theory(equality)])).
cnf(234,plain,(object(X1,X2)|~shake_beverage(X1,X2)),inference(spm,[status(thm)],[124,229,theory(equality)])).
cnf(235,negated_conjecture,(object(esk1_0,esk4_0)),inference(spm,[status(thm)],[234,195,theory(equality)])).
cnf(236,negated_conjecture,(entity(esk1_0,esk4_0)),inference(spm,[status(thm)],[121,235,theory(equality)])).
cnf(237,plain,(~human_person(X1,X2)|~object(X1,X2)),inference(spm,[status(thm)],[217,109,theory(equality)])).
cnf(239,plain,(~abstraction(X1,X2)|~human_person(X1,X2)),inference(spm,[status(thm)],[218,61,theory(equality)])).
cnf(241,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)|\$false),inference(rw,[status(thm)],[223,231,theory(equality)])).
cnf(242,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)),inference(cn,[status(thm)],[241,theory(equality)])).
cnf(243,plain,(~abstraction(X1,X2)|~entity(X1,X2)),inference(spm,[status(thm)],[219,115,theory(equality)])).
cnf(244,plain,(~abstraction(X1,X2)|~eventuality(X1,X2)),inference(spm,[status(thm)],[219,145,theory(equality)])).
cnf(245,plain,(~organism(X1,X2)|~object(X1,X2)),inference(spm,[status(thm)],[220,109,theory(equality)])).
cnf(246,negated_conjecture,(~abstraction(esk1_0,esk5_0)),inference(spm,[status(thm)],[244,207,theory(equality)])).
cnf(247,negated_conjecture,(~forename(esk1_0,esk5_0)),inference(spm,[status(thm)],[246,228,theory(equality)])).
cnf(249,plain,(~entity(X1,X2)|~forename(X1,X2)),inference(spm,[status(thm)],[243,228,theory(equality)])).
cnf(250,negated_conjecture,(~entity(esk1_0,esk3_0)),inference(spm,[status(thm)],[249,196,theory(equality)])).
cnf(251,negated_conjecture,(actual_world(esk1_0)),200,['final']).
cnf(252,negated_conjecture,(woman(esk1_0,esk2_0)),198,['final']).
cnf(253,negated_conjecture,(mia_forename(esk1_0,esk3_0)),197,['final']).
cnf(254,negated_conjecture,(forename(esk1_0,esk3_0)),196,['final']).
cnf(255,negated_conjecture,(shake_beverage(esk1_0,esk4_0)),195,['final']).
cnf(256,negated_conjecture,(order(esk1_0,esk5_0)),189,['final']).
cnf(257,negated_conjecture,(event(esk1_0,esk5_0)),194,['final']).
cnf(258,negated_conjecture,(nonreflexive(esk1_0,esk5_0)),190,['final']).
cnf(259,negated_conjecture,(past(esk1_0,esk5_0)),191,['final']).
cnf(260,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)),199,['final']).
cnf(261,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)),193,['final']).
cnf(262,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)),192,['final']).
cnf(263,negated_conjecture,(human_person(esk1_0,esk2_0)),206,['final']).
cnf(264,negated_conjecture,(eventuality(esk1_0,esk5_0)),207,['final']).
cnf(265,negated_conjecture,(entity(esk1_0,esk2_0)),231,['final']).
cnf(266,negated_conjecture,(object(esk1_0,esk4_0)),235,['final']).
cnf(267,negated_conjecture,(entity(esk1_0,esk4_0)),236,['final']).
cnf(268,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)),215,['final']).
cnf(269,negated_conjecture,(~unisex(esk1_0,esk2_0)),224,['final']).
cnf(270,negated_conjecture,(~eventuality(esk1_0,esk2_0)),227,['final']).
cnf(271,negated_conjecture,(~object(esk1_0,esk2_0)),226,['final']).
cnf(272,negated_conjecture,(~abstraction(esk1_0,esk2_0)),225,['final']).
cnf(273,negated_conjecture,(~forename(esk1_0,esk2_0)),230,['final']).
cnf(274,negated_conjecture,(~entity(esk1_0,esk5_0)),233,['final']).
cnf(275,negated_conjecture,(~abstraction(esk1_0,esk5_0)),246,['final']).
cnf(276,negated_conjecture,(~forename(esk1_0,esk5_0)),247,['final']).
cnf(277,negated_conjecture,(~entity(esk1_0,esk3_0)),250,['final']).
cnf(278,plain,(forename(X1,X2)|~mia_forename(X1,X2)),79,['final']).
cnf(279,plain,(event(X1,X2)|~order(X1,X2)),136,['final']).
cnf(280,plain,(human_person(X1,X2)|~woman(X1,X2)),76,['final']).
cnf(281,plain,(eventuality(X1,X2)|~event(X1,X2)),154,['final']).
cnf(282,plain,(female(X1,X2)|~woman(X1,X2)),55,['final']).
cnf(283,plain,(relname(X1,X2)|~forename(X1,X2)),100,['final']).
cnf(284,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)),133,['final']).
cnf(285,plain,(event(X1,X2)|~act(X1,X2)),157,['final']).
cnf(286,plain,(act(X1,X2)|~order(X1,X2)),160,['final']).
cnf(287,plain,(animate(X1,X2)|~human_person(X1,X2)),58,['final']).
cnf(288,plain,(human(X1,X2)|~human_person(X1,X2)),61,['final']).
cnf(289,plain,(organism(X1,X2)|~human_person(X1,X2)),73,['final']).
cnf(290,plain,(relation(X1,X2)|~relname(X1,X2)),97,['final']).
cnf(291,plain,(food(X1,X2)|~beverage(X1,X2)),130,['final']).
cnf(292,plain,(~unisex(X1,X2)|~female(X1,X2)),178,['final']).
cnf(293,plain,(entity(X1,X2)|~organism(X1,X2)),70,['final']).
cnf(294,plain,(living(X1,X2)|~organism(X1,X2)),64,['final']).
cnf(295,plain,(impartial(X1,X2)|~organism(X1,X2)),67,['final']).
cnf(296,plain,(impartial(X1,X2)|~object(X1,X2)),106,['final']).
cnf(297,plain,(entity(X1,X2)|~object(X1,X2)),121,['final']).
cnf(298,plain,(abstraction(X1,X2)|~relation(X1,X2)),94,['final']).
cnf(299,plain,(unisex(X1,X2)|~eventuality(X1,X2)),139,['final']).
cnf(300,plain,(thing(X1,X2)|~entity(X1,X2)),118,['final']).
cnf(301,plain,(thing(X1,X2)|~eventuality(X1,X2)),151,['final']).
cnf(302,plain,(existent(X1,X2)|~entity(X1,X2)),112,['final']).
cnf(303,plain,(unisex(X1,X2)|~abstraction(X1,X2)),82,['final']).
cnf(304,plain,(unisex(X1,X2)|~object(X1,X2)),103,['final']).
cnf(305,plain,(specific(X1,X2)|~entity(X1,X2)),115,['final']).
cnf(306,plain,(general(X1,X2)|~abstraction(X1,X2)),85,['final']).
cnf(307,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)),88,['final']).
cnf(308,plain,(specific(X1,X2)|~eventuality(X1,X2)),145,['final']).
cnf(309,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)),142,['final']).
cnf(310,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)),201,['final']).
cnf(311,plain,(~nonexistent(X1,X2)|~existent(X1,X2)),166,['final']).
cnf(312,plain,(thing(X1,X2)|~abstraction(X1,X2)),91,['final']).
cnf(313,plain,(object(X1,X2)|~substance_matter(X1,X2)),124,['final']).
cnf(314,plain,(nonliving(X1,X2)|~object(X1,X2)),109,['final']).
cnf(315,plain,(substance_matter(X1,X2)|~food(X1,X2)),127,['final']).
cnf(316,plain,(singleton(X1,X2)|~thing(X1,X2)),148,['final']).
cnf(317,plain,(~nonliving(X1,X2)|~animate(X1,X2)),163,['final']).
cnf(318,plain,(~nonhuman(X1,X2)|~human(X1,X2)),169,['final']).
cnf(319,plain,(~specific(X1,X2)|~general(X1,X2)),175,['final']).
cnf(320,plain,(~nonliving(X1,X2)|~living(X1,X2)),172,['final']).
cnf(321,plain,(X1=X2|~of(X3,X2,X4)|~of(X3,X1,X4)|~forename(X3,X2)|~forename(X3,X1)|~entity(X3,X4)),182,['final']).
cnf(322,plain,(~unisex(X1,X2)|~woman(X1,X2)),211,['final']).
cnf(323,plain,(relation(X1,X2)|~forename(X1,X2)),209,['final']).
cnf(324,plain,(food(X1,X2)|~shake_beverage(X1,X2)),210,['final']).
cnf(325,plain,(abstraction(X1,X2)|~forename(X1,X2)),228,['final']).
cnf(326,plain,(entity(X1,X2)|~human_person(X1,X2)),212,['final']).
cnf(327,plain,(~eventuality(X1,X2)|~existent(X1,X2)),216,['final']).
cnf(328,plain,(~eventuality(X1,X2)|~entity(X1,X2)),232,['final']).
cnf(329,plain,(substance_matter(X1,X2)|~shake_beverage(X1,X2)),229,['final']).
cnf(330,plain,(object(X1,X2)|~shake_beverage(X1,X2)),234,['final']).
cnf(331,plain,(~nonliving(X1,X2)|~human_person(X1,X2)),217,['final']).
cnf(332,plain,(~object(X1,X2)|~human_person(X1,X2)),237,['final']).
cnf(333,plain,(~abstraction(X1,X2)|~human(X1,X2)),218,['final']).
cnf(334,plain,(~abstraction(X1,X2)|~human_person(X1,X2)),239,['final']).
cnf(335,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)),242,['final']).
cnf(336,plain,(~specific(X1,X2)|~abstraction(X1,X2)),219,['final']).
cnf(337,plain,(~nonliving(X1,X2)|~organism(X1,X2)),220,['final']).
cnf(338,plain,(~eventuality(X1,X2)|~abstraction(X1,X2)),244,['final']).
cnf(339,plain,(~object(X1,X2)|~organism(X1,X2)),245,['final']).
cnf(340,plain,(~abstraction(X1,X2)|~entity(X1,X2)),243,['final']).
cnf(341,plain,(~forename(X1,X2)|~entity(X1,X2)),249,['final']).
# SZS output end Saturation.
```

### Sample solution for SWV017+1

```# Preprocessing time       : 0.010 s
# Problem is satisfiable (or invalid), generating saturation derivation
# SZS status Satisfiable
# SZS output start Saturation.
fof(1, axiom,a_holds(key(at,t)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_holds_key_at_for_t)).
fof(2, axiom,party_of_protocol(a),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_is_party_of_protocol)).
fof(3, axiom,message(sent(a,b,pair(a,an_a_nonce))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_sent_message_i_to_b)).
fof(4, axiom,a_stored(pair(b,an_a_nonce)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_stored_message_i)).
fof(6, axiom,b_holds(key(bt,t)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_hold_key_bt_for_t)).
fof(7, axiom,party_of_protocol(b),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_is_party_of_protocol)).
fof(8, axiom,fresh_to_b(an_a_nonce),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', nonce_a_is_fresh_to_b)).
fof(9, 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_4.1.0_FLAT/SWV017+1.p', b_creates_freash_nonces_in_time)).
fof(10, 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_4.1.0_FLAT/SWV017+1.p', b_accepts_secure_session_key)).
fof(11, axiom,t_holds(key(at,a)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', t_holds_key_at_for_a)).
fof(12, axiom,t_holds(key(bt,b)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', t_holds_key_bt_for_b)).
fof(13, axiom,party_of_protocol(t),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', t_is_party_of_protocol)).
fof(15, axiom,![X1]:![X2]:![X3]:(message(sent(X1,X2,X3))=>intruder_message(X3)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_can_record)).
fof(16, axiom,![X1]:![X2]:(intruder_message(pair(X1,X2))=>(intruder_message(X1)&intruder_message(X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_decomposes_pairs)).
fof(17, axiom,![X1]:![X2]:![X3]:(intruder_message(triple(X1,X2,X3))=>((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_decomposes_triples)).
fof(19, axiom,![X1]:![X2]:((intruder_message(X1)&intruder_message(X2))=>intruder_message(pair(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_composes_pairs)).
fof(20, axiom,![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))=>intruder_message(triple(X1,X2,X3))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_composes_triples)).
fof(22, 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_4.1.0_FLAT/SWV017+1.p', intruder_interception)).
fof(23, 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_4.1.0_FLAT/SWV017+1.p', intruder_message_sent)).
fof(24, axiom,![X2]:![X3]:((intruder_message(X2)&party_of_protocol(X3))=>intruder_holds(key(X2,X3))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_holds_key)).
fof(25, 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_4.1.0_FLAT/SWV017+1.p', intruder_key_encrypts)).
fof(26, axiom,a_nonce(an_a_nonce),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', an_a_nonce_is_a_nonce)).
fof(27, axiom,![X1]:~(a_nonce(generate_key(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', generated_keys_are_not_nonces)).
fof(28, axiom,![X1]:(a_nonce(generate_expiration_time(X1))&a_nonce(generate_b_nonce(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', generated_times_and_nonces_are_nonces)).
fof(29, axiom,![X1]:~((a_key(X1)&a_nonce(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', nothing_is_a_nonce_and_a_key)).
fof(30, axiom,![X1]:a_key(generate_key(X1)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', generated_keys_are_keys)).
fof(31, axiom,fresh_intruder_nonce(an_intruder_nonce),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', an_intruder_nonce_is_a_fresh_intruder_nonce)).
fof(32, axiom,![X1]:(fresh_intruder_nonce(X1)=>fresh_intruder_nonce(generate_intruder_nonce(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', can_generate_more_fresh_intruder_nonces)).
fof(33, axiom,![X1]:(fresh_intruder_nonce(X1)=>(fresh_to_b(X1)&intruder_message(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', fresh_intruder_nonces_are_fresh_to_b)).
fof(34, plain,![X1]:~(a_nonce(generate_key(X1))),inference(fof_simplification,[status(thm)],[27,theory(equality)])).
cnf(35,plain,(a_holds(key(at,t))),inference(split_conjunct,[status(thm)],[1])).
cnf(36,plain,(party_of_protocol(a)),inference(split_conjunct,[status(thm)],[2])).
cnf(37,plain,(message(sent(a,b,pair(a,an_a_nonce)))),inference(split_conjunct,[status(thm)],[3])).
cnf(38,plain,(a_stored(pair(b,an_a_nonce))),inference(split_conjunct,[status(thm)],[4])).
cnf(44,plain,(b_holds(key(bt,t))),inference(split_conjunct,[status(thm)],[6])).
cnf(45,plain,(party_of_protocol(b)),inference(split_conjunct,[status(thm)],[7])).
cnf(46,plain,(fresh_to_b(an_a_nonce)),inference(split_conjunct,[status(thm)],[8])).
fof(47, plain,![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)))),inference(fof_nnf,[status(thm)],[9])).
fof(48, plain,![X3]:![X4]:((~(message(sent(X3,b,pair(X3,X4))))|~(fresh_to_b(X4)))|(message(sent(b,t,triple(b,generate_b_nonce(X4),encrypt(triple(X3,X4,generate_expiration_time(X4)),bt))))&b_stored(pair(X3,X4)))),inference(variable_rename,[status(thm)],[47])).
fof(49, 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)],[48])).
cnf(50,plain,(b_stored(pair(X2,X1))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))),inference(split_conjunct,[status(thm)],[49])).
cnf(51,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)],[49])).
fof(52, plain,![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))),inference(fof_nnf,[status(thm)],[10])).
fof(53, 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(variable_rename,[status(thm)],[52])).
cnf(54,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)],[53])).
cnf(55,plain,(t_holds(key(at,a))),inference(split_conjunct,[status(thm)],[11])).
cnf(56,plain,(t_holds(key(bt,b))),inference(split_conjunct,[status(thm)],[12])).
cnf(57,plain,(party_of_protocol(t)),inference(split_conjunct,[status(thm)],[13])).
fof(61, plain,![X1]:![X2]:![X3]:(~(message(sent(X1,X2,X3)))|intruder_message(X3)),inference(fof_nnf,[status(thm)],[15])).
fof(62, plain,![X4]:![X5]:![X6]:(~(message(sent(X4,X5,X6)))|intruder_message(X6)),inference(variable_rename,[status(thm)],[61])).
cnf(63,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))),inference(split_conjunct,[status(thm)],[62])).
fof(64, plain,![X1]:![X2]:(~(intruder_message(pair(X1,X2)))|(intruder_message(X1)&intruder_message(X2))),inference(fof_nnf,[status(thm)],[16])).
fof(65, plain,![X3]:![X4]:(~(intruder_message(pair(X3,X4)))|(intruder_message(X3)&intruder_message(X4))),inference(variable_rename,[status(thm)],[64])).
fof(66, plain,![X3]:![X4]:((intruder_message(X3)|~(intruder_message(pair(X3,X4))))&(intruder_message(X4)|~(intruder_message(pair(X3,X4))))),inference(distribute,[status(thm)],[65])).
cnf(67,plain,(intruder_message(X2)|~intruder_message(pair(X1,X2))),inference(split_conjunct,[status(thm)],[66])).
cnf(68,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))),inference(split_conjunct,[status(thm)],[66])).
fof(69, plain,![X1]:![X2]:![X3]:(~(intruder_message(triple(X1,X2,X3)))|((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))),inference(fof_nnf,[status(thm)],[17])).
fof(70, plain,![X4]:![X5]:![X6]:(~(intruder_message(triple(X4,X5,X6)))|((intruder_message(X4)&intruder_message(X5))&intruder_message(X6))),inference(variable_rename,[status(thm)],[69])).
fof(71, 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)],[70])).
cnf(72,plain,(intruder_message(X3)|~intruder_message(triple(X1,X2,X3))),inference(split_conjunct,[status(thm)],[71])).
cnf(73,plain,(intruder_message(X2)|~intruder_message(triple(X1,X2,X3))),inference(split_conjunct,[status(thm)],[71])).
cnf(74,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))),inference(split_conjunct,[status(thm)],[71])).
fof(82, plain,![X1]:![X2]:((~(intruder_message(X1))|~(intruder_message(X2)))|intruder_message(pair(X1,X2))),inference(fof_nnf,[status(thm)],[19])).
fof(83, plain,![X3]:![X4]:((~(intruder_message(X3))|~(intruder_message(X4)))|intruder_message(pair(X3,X4))),inference(variable_rename,[status(thm)],[82])).
cnf(84,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[83])).
fof(85, plain,![X1]:![X2]:![X3]:(((~(intruder_message(X1))|~(intruder_message(X2)))|~(intruder_message(X3)))|intruder_message(triple(X1,X2,X3))),inference(fof_nnf,[status(thm)],[20])).
fof(86, plain,![X4]:![X5]:![X6]:(((~(intruder_message(X4))|~(intruder_message(X5)))|~(intruder_message(X6)))|intruder_message(triple(X4,X5,X6))),inference(variable_rename,[status(thm)],[85])).
cnf(87,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[86])).
fof(91, plain,![X1]:![X2]:![X3]:(((~(intruder_message(encrypt(X1,X2)))|~(intruder_holds(key(X2,X3))))|~(party_of_protocol(X3)))|intruder_message(X2)),inference(fof_nnf,[status(thm)],[22])).
fof(92, plain,![X4]:![X5]:![X6]:(((~(intruder_message(encrypt(X4,X5)))|~(intruder_holds(key(X5,X6))))|~(party_of_protocol(X6)))|intruder_message(X5)),inference(variable_rename,[status(thm)],[91])).
cnf(93,plain,(intruder_message(X1)|~party_of_protocol(X2)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))),inference(split_conjunct,[status(thm)],[92])).
fof(94, plain,![X1]:![X2]:![X3]:(((~(intruder_message(X1))|~(party_of_protocol(X2)))|~(party_of_protocol(X3)))|message(sent(X2,X3,X1))),inference(fof_nnf,[status(thm)],[23])).
fof(95, 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)],[94])).
cnf(96,plain,(message(sent(X1,X2,X3))|~party_of_protocol(X2)|~party_of_protocol(X1)|~intruder_message(X3)),inference(split_conjunct,[status(thm)],[95])).
fof(97, plain,![X2]:![X3]:((~(intruder_message(X2))|~(party_of_protocol(X3)))|intruder_holds(key(X2,X3))),inference(fof_nnf,[status(thm)],[24])).
fof(98, plain,![X4]:![X5]:((~(intruder_message(X4))|~(party_of_protocol(X5)))|intruder_holds(key(X4,X5))),inference(variable_rename,[status(thm)],[97])).
cnf(99,plain,(intruder_holds(key(X1,X2))|~party_of_protocol(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[98])).
fof(100, plain,![X1]:![X2]:![X3]:(((~(intruder_message(X1))|~(intruder_holds(key(X2,X3))))|~(party_of_protocol(X3)))|intruder_message(encrypt(X1,X2))),inference(fof_nnf,[status(thm)],[25])).
fof(101, plain,![X4]:![X5]:![X6]:(((~(intruder_message(X4))|~(intruder_holds(key(X5,X6))))|~(party_of_protocol(X6)))|intruder_message(encrypt(X4,X5))),inference(variable_rename,[status(thm)],[100])).
cnf(102,plain,(intruder_message(encrypt(X1,X2))|~party_of_protocol(X3)|~intruder_holds(key(X2,X3))|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[101])).
cnf(103,plain,(a_nonce(an_a_nonce)),inference(split_conjunct,[status(thm)],[26])).
fof(104, plain,![X2]:~(a_nonce(generate_key(X2))),inference(variable_rename,[status(thm)],[34])).
cnf(105,plain,(~a_nonce(generate_key(X1))),inference(split_conjunct,[status(thm)],[104])).
fof(106, plain,![X2]:(a_nonce(generate_expiration_time(X2))&a_nonce(generate_b_nonce(X2))),inference(variable_rename,[status(thm)],[28])).
cnf(107,plain,(a_nonce(generate_b_nonce(X1))),inference(split_conjunct,[status(thm)],[106])).
cnf(108,plain,(a_nonce(generate_expiration_time(X1))),inference(split_conjunct,[status(thm)],[106])).
fof(109, plain,![X1]:(~(a_key(X1))|~(a_nonce(X1))),inference(fof_nnf,[status(thm)],[29])).
fof(110, plain,![X2]:(~(a_key(X2))|~(a_nonce(X2))),inference(variable_rename,[status(thm)],[109])).
cnf(111,plain,(~a_nonce(X1)|~a_key(X1)),inference(split_conjunct,[status(thm)],[110])).
fof(112, plain,![X2]:a_key(generate_key(X2)),inference(variable_rename,[status(thm)],[30])).
cnf(113,plain,(a_key(generate_key(X1))),inference(split_conjunct,[status(thm)],[112])).
cnf(114,plain,(fresh_intruder_nonce(an_intruder_nonce)),inference(split_conjunct,[status(thm)],[31])).
fof(115, plain,![X1]:(~(fresh_intruder_nonce(X1))|fresh_intruder_nonce(generate_intruder_nonce(X1))),inference(fof_nnf,[status(thm)],[32])).
fof(116, plain,![X2]:(~(fresh_intruder_nonce(X2))|fresh_intruder_nonce(generate_intruder_nonce(X2))),inference(variable_rename,[status(thm)],[115])).
cnf(117,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),inference(split_conjunct,[status(thm)],[116])).
fof(118, plain,![X1]:(~(fresh_intruder_nonce(X1))|(fresh_to_b(X1)&intruder_message(X1))),inference(fof_nnf,[status(thm)],[33])).
fof(119, plain,![X2]:(~(fresh_intruder_nonce(X2))|(fresh_to_b(X2)&intruder_message(X2))),inference(variable_rename,[status(thm)],[118])).
fof(120, plain,![X2]:((fresh_to_b(X2)|~(fresh_intruder_nonce(X2)))&(intruder_message(X2)|~(fresh_intruder_nonce(X2)))),inference(distribute,[status(thm)],[119])).
cnf(121,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)),inference(split_conjunct,[status(thm)],[120])).
cnf(122,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)),inference(split_conjunct,[status(thm)],[120])).
cnf(123,plain,(intruder_message(an_intruder_nonce)),inference(spm,[status(thm)],[121,114,theory(equality)])).
cnf(125,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),inference(spm,[status(thm)],[121,117,theory(equality)])).
cnf(126,plain,(intruder_message(pair(a,an_a_nonce))),inference(spm,[status(thm)],[63,37,theory(equality)])).
cnf(133,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~party_of_protocol(X3)|~intruder_message(X2)),inference(spm,[status(thm)],[102,99,theory(equality)])).
cnf(135,plain,(b_stored(pair(a,an_a_nonce))|~fresh_to_b(an_a_nonce)),inference(spm,[status(thm)],[50,37,theory(equality)])).
cnf(136,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~intruder_message(pair(X1,X2))|~party_of_protocol(b)|~party_of_protocol(X1)),inference(spm,[status(thm)],[50,96,theory(equality)])).
cnf(137,plain,(b_stored(pair(a,an_a_nonce))|\$false),inference(rw,[status(thm)],[135,46,theory(equality)])).
cnf(138,plain,(b_stored(pair(a,an_a_nonce))),inference(cn,[status(thm)],[137,theory(equality)])).
cnf(139,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~intruder_message(pair(X1,X2))|\$false|~party_of_protocol(X1)),inference(rw,[status(thm)],[136,45,theory(equality)])).
cnf(140,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~intruder_message(pair(X1,X2))|~party_of_protocol(X1)),inference(cn,[status(thm)],[139,theory(equality)])).
cnf(147,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))))|~fresh_to_b(an_a_nonce)),inference(spm,[status(thm)],[51,37,theory(equality)])).
cnf(148,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~intruder_message(pair(X2,X1))|~party_of_protocol(b)|~party_of_protocol(X2)),inference(spm,[status(thm)],[51,96,theory(equality)])).
cnf(149,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))))|\$false),inference(rw,[status(thm)],[147,46,theory(equality)])).
cnf(150,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)],[149,theory(equality)])).
cnf(151,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~intruder_message(pair(X2,X1))|\$false|~party_of_protocol(X2)),inference(rw,[status(thm)],[148,45,theory(equality)])).
cnf(152,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~intruder_message(pair(X2,X1))|~party_of_protocol(X2)),inference(cn,[status(thm)],[151,theory(equality)])).
cnf(155,plain,(intruder_message(a)),inference(spm,[status(thm)],[68,126,theory(equality)])).
cnf(156,plain,(intruder_message(an_a_nonce)),inference(spm,[status(thm)],[67,126,theory(equality)])).
cnf(157,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)],[54,138,theory(equality)])).
cnf(158,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[133,45,theory(equality)])).
cnf(162,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[140,84,theory(equality)])).
cnf(167,plain,(b_holds(key(X1,X2))|~a_key(X1)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))|~intruder_message(X3)|~intruder_message(X2)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(spm,[status(thm)],[54,162,theory(equality)])).
cnf(168,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)],[63,150,theory(equality)])).
cnf(175,plain,(intruder_message(b)),inference(spm,[status(thm)],[74,168,theory(equality)])).
cnf(176,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[72,168,theory(equality)])).
cnf(177,plain,(intruder_message(generate_b_nonce(an_a_nonce))),inference(spm,[status(thm)],[73,168,theory(equality)])).
cnf(178,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|~party_of_protocol(b)|~party_of_protocol(a)),inference(spm,[status(thm)],[157,96,theory(equality)])).
cnf(179,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|\$false|~party_of_protocol(a)),inference(rw,[status(thm)],[178,45,theory(equality)])).
cnf(180,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|\$false|\$false),inference(rw,[status(thm)],[179,36,theory(equality)])).
cnf(181,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))),inference(cn,[status(thm)],[180,theory(equality)])).
cnf(187,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~party_of_protocol(X2)|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[152,84,theory(equality)])).
cnf(194,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[181,84,theory(equality)])).
cnf(195,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~a_key(X1)|~intruder_message(generate_b_nonce(an_a_nonce))|~intruder_message(X1)),inference(spm,[status(thm)],[194,158,theory(equality)])).
cnf(196,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~a_key(X1)|\$false|~intruder_message(X1)),inference(rw,[status(thm)],[195,177,theory(equality)])).
cnf(197,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~a_key(X1)|~intruder_message(X1)),inference(cn,[status(thm)],[196,theory(equality)])).
cnf(198,plain,(b_holds(key(X1,a))|~intruder_message(X1)|~a_key(X1)|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)),inference(spm,[status(thm)],[197,158,theory(equality)])).
cnf(199,plain,(b_holds(key(an_a_nonce,a))|~intruder_message(an_a_nonce)|~a_key(an_a_nonce)),inference(spm,[status(thm)],[197,176,theory(equality)])).
cnf(200,plain,(b_holds(key(an_a_nonce,a))|\$false|~a_key(an_a_nonce)),inference(rw,[status(thm)],[199,156,theory(equality)])).
cnf(201,plain,(b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)),inference(cn,[status(thm)],[200,theory(equality)])).
cnf(204,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)],[198,73])).
cnf(205,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)],[63,187,theory(equality)])).
cnf(207,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)],[72,205,theory(equality)])).
cnf(208,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)],[73,205,theory(equality)])).
cnf(224,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|~party_of_protocol(b)),inference(spm,[status(thm)],[167,96,theory(equality)])).
cnf(225,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|\$false),inference(rw,[status(thm)],[224,45,theory(equality)])).
cnf(226,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))),inference(cn,[status(thm)],[225,theory(equality)])).
cnf(229,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(encrypt(generate_b_nonce(X3),X1))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))),inference(spm,[status(thm)],[226,84,theory(equality)])).
cnf(230,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(generate_b_nonce(X3))|~intruder_message(X1)),inference(spm,[status(thm)],[229,158,theory(equality)])).
cnf(231,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X1)|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(csr,[status(thm)],[230,208])).
cnf(232,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)),inference(spm,[status(thm)],[231,158,theory(equality)])).
cnf(234,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)),inference(spm,[status(thm)],[231,207,theory(equality)])).
cnf(240,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(csr,[status(thm)],[232,73])).
cnf(241,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(csr,[status(thm)],[240,74])).
cnf(267,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[72,249,theory(equality)])).
cnf(268,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)],[73,249,theory(equality)])).
cnf(269,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|~intruder_message(b)|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(b)|~a_nonce(X1)),inference(spm,[status(thm)],[231,268,theory(equality)])).
cnf(271,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(b)|~a_nonce(X1)),inference(rw,[status(thm)],[269,175,theory(equality)])).
cnf(272,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|\$false|~fresh_to_b(X1)|~party_of_protocol(b)|~a_nonce(X1)),inference(rw,[status(thm)],[271,113,theory(equality)])).
cnf(273,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|\$false|~fresh_to_b(X1)|\$false|~a_nonce(X1)),inference(rw,[status(thm)],[272,45,theory(equality)])).
cnf(274,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|~intruder_message(generate_key(X1))|~fresh_to_b(X1)|~a_nonce(X1)),inference(cn,[status(thm)],[273,theory(equality)])).
cnf(276,plain,(a_holds(key(generate_key(an_a_nonce),b))),inference(spm,[status(thm)],[145,260,theory(equality)])).
cnf(277,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)],[146,260,theory(equality)])).
cnf(282,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)],[63,277,theory(equality)])).
cnf(283,plain,(b_holds(key(generate_key(an_a_nonce),a))|~intruder_message(an_a_nonce)|~intruder_message(a)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(spm,[status(thm)],[167,277,theory(equality)])).
cnf(285,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|~intruder_message(a)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(rw,[status(thm)],[283,156,theory(equality)])).
cnf(286,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|\$false|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(rw,[status(thm)],[285,155,theory(equality)])).
cnf(287,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|\$false|\$false|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(rw,[status(thm)],[286,113,theory(equality)])).
cnf(288,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|\$false|\$false|\$false|~party_of_protocol(a)),inference(rw,[status(thm)],[287,46,theory(equality)])).
cnf(289,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|\$false|\$false|\$false|\$false),inference(rw,[status(thm)],[288,36,theory(equality)])).
cnf(290,plain,(b_holds(key(generate_key(an_a_nonce),a))),inference(cn,[status(thm)],[289,theory(equality)])).
cnf(294,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[68,282,theory(equality)])).
cnf(295,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)],[140,282,theory(equality)])).
cnf(296,plain,(intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),inference(spm,[status(thm)],[67,282,theory(equality)])).
cnf(297,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)],[152,282,theory(equality)])).
cnf(311,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(an_a_nonce)|~intruder_message(X1)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(X1)),inference(spm,[status(thm)],[229,296,theory(equality)])).
cnf(315,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))|\$false|~intruder_message(X1)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(X1)),inference(rw,[status(thm)],[311,156,theory(equality)])).
cnf(316,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))|\$false|~intruder_message(X1)|\$false|~fresh_to_b(an_a_nonce)|~party_of_protocol(X1)),inference(rw,[status(thm)],[315,113,theory(equality)])).
cnf(317,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))|\$false|~intruder_message(X1)|\$false|\$false|~party_of_protocol(X1)),inference(rw,[status(thm)],[316,46,theory(equality)])).
cnf(318,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)],[317,theory(equality)])).
cnf(331,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X1)|~party_of_protocol(X1)|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)),inference(spm,[status(thm)],[318,158,theory(equality)])).
cnf(332,plain,(b_holds(key(generate_key(an_a_nonce),b))|~intruder_message(b)|~party_of_protocol(b)|~intruder_message(an_a_nonce)|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(spm,[status(thm)],[318,268,theory(equality)])).
cnf(334,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|~party_of_protocol(b)|~intruder_message(an_a_nonce)|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[332,175,theory(equality)])).
cnf(335,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|\$false|~intruder_message(an_a_nonce)|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[334,45,theory(equality)])).
cnf(336,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|\$false|\$false|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[335,156,theory(equality)])).
cnf(337,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|\$false|\$false|\$false|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[336,103,theory(equality)])).
cnf(338,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|\$false|\$false|\$false|\$false),inference(rw,[status(thm)],[337,46,theory(equality)])).
cnf(339,plain,(b_holds(key(generate_key(an_a_nonce),b))),inference(cn,[status(thm)],[338,theory(equality)])).
cnf(348,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)],[331,74])).
cnf(379,plain,(message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[192,369,theory(equality)])).
cnf(381,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[63,379,theory(equality)])).
cnf(382,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_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(a)),inference(spm,[status(thm)],[51,379,theory(equality)])).
cnf(384,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(a)),inference(spm,[status(thm)],[50,379,theory(equality)])).
cnf(386,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_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|\$false),inference(rw,[status(thm)],[382,155,theory(equality)])).
cnf(387,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_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),inference(cn,[status(thm)],[386,theory(equality)])).
cnf(393,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|\$false),inference(rw,[status(thm)],[384,155,theory(equality)])).
cnf(394,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),inference(cn,[status(thm)],[393,theory(equality)])).
cnf(401,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(generate_b_nonce(X2))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))),inference(spm,[status(thm)],[226,381,theory(equality)])).
cnf(403,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X2,generate_key(an_a_nonce)))|~party_of_protocol(X1)|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[140,381,theory(equality)])).
cnf(404,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[67,381,theory(equality)])).
cnf(405,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_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(X2)|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[152,381,theory(equality)])).
cnf(411,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|\$false|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(generate_b_nonce(X2))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))),inference(rw,[status(thm)],[401,113,theory(equality)])).
cnf(412,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(generate_b_nonce(X2))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))),inference(cn,[status(thm)],[411,theory(equality)])).
cnf(420,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),inference(spm,[status(thm)],[404,275,theory(equality)])).
cnf(452,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[394,122,theory(equality)])).
cnf(453,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)|~party_of_protocol(X1)|~fresh_intruder_nonce(encrypt(X2,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[403,122,theory(equality)])).
cnf(454,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)],[412,208])).
cnf(455,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)),inference(spm,[status(thm)],[454,158,theory(equality)])).
cnf(456,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)],[454,207,theory(equality)])).
cnf(485,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)],[455,74])).
cnf(489,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)],[73,472,theory(equality)])).
cnf(503,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|~intruder_message(a)|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(a)|~a_nonce(X1)),inference(spm,[status(thm)],[231,489,theory(equality)])).
cnf(513,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(a)|~a_nonce(X1)),inference(rw,[status(thm)],[503,155,theory(equality)])).
cnf(514,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|\$false|~fresh_to_b(X1)|~party_of_protocol(a)|~a_nonce(X1)),inference(rw,[status(thm)],[513,113,theory(equality)])).
cnf(515,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|\$false|~fresh_to_b(X1)|\$false|~a_nonce(X1)),inference(rw,[status(thm)],[514,36,theory(equality)])).
cnf(516,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|~intruder_message(generate_key(X1))|~fresh_to_b(X1)|~a_nonce(X1)),inference(cn,[status(thm)],[515,theory(equality)])).
cnf(548,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_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[387,122,theory(equality)])).
cnf(551,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)],[146,365,theory(equality)])).
cnf(553,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)],[63,551,theory(equality)])).
cnf(569,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_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))|~intruder_message(X1)),inference(spm,[status(thm)],[140,553,theory(equality)])).
cnf(571,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_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))|~intruder_message(X1)),inference(spm,[status(thm)],[152,553,theory(equality)])).
cnf(599,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))))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),inference(spm,[status(thm)],[295,122,theory(equality)])).
cnf(600,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))))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),inference(spm,[status(thm)],[297,122,theory(equality)])).
cnf(605,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)|~party_of_protocol(X2)|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[405,122,theory(equality)])).
cnf(634,plain,(party_of_protocol(t)),57,['final']).
cnf(635,plain,(party_of_protocol(a)),36,['final']).
cnf(636,plain,(party_of_protocol(b)),45,['final']).
cnf(637,plain,(fresh_to_b(an_a_nonce)),46,['final']).
cnf(638,plain,(a_nonce(an_a_nonce)),103,['final']).
cnf(639,plain,(fresh_intruder_nonce(an_intruder_nonce)),114,['final']).
cnf(640,plain,(a_key(generate_key(X1))),113,['final']).
cnf(641,plain,(a_nonce(generate_b_nonce(X1))),107,['final']).
cnf(642,plain,(a_nonce(generate_expiration_time(X1))),108,['final']).
cnf(643,plain,(a_holds(key(at,t))),35,['final']).
cnf(644,plain,(a_stored(pair(b,an_a_nonce))),38,['final']).
cnf(645,plain,(b_holds(key(bt,t))),44,['final']).
cnf(646,plain,(t_holds(key(at,a))),55,['final']).
cnf(647,plain,(t_holds(key(bt,b))),56,['final']).
cnf(648,plain,(message(sent(a,b,pair(a,an_a_nonce)))),37,['final']).
cnf(649,plain,(intruder_message(an_intruder_nonce)),123,['final']).
cnf(650,plain,(intruder_message(pair(a,an_a_nonce))),126,['final']).
cnf(651,plain,(intruder_message(a)),155,['final']).
cnf(652,plain,(intruder_message(an_a_nonce)),156,['final']).
cnf(653,plain,(b_stored(pair(a,an_a_nonce))),138,['final']).
cnf(654,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))))),150,['final']).
cnf(655,plain,(intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))),168,['final']).
cnf(656,plain,(intruder_message(b)),175,['final']).
cnf(657,plain,(intruder_message(generate_b_nonce(an_a_nonce))),177,['final']).
cnf(658,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),176,['final']).
cnf(660,plain,(a_holds(key(generate_key(an_a_nonce),b))),276,['final']).
cnf(661,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)))))),277,['final']).
cnf(662,plain,(b_holds(key(generate_key(an_a_nonce),a))),290,['final']).
cnf(663,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))))),282,['final']).
cnf(664,plain,(intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),296,['final']).
cnf(665,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),294,['final']).
cnf(666,plain,(b_holds(key(generate_key(an_a_nonce),b))),339,['final']).
cnf(669,plain,(~a_nonce(generate_key(X1))),105,['final']).
cnf(670,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)),122,['final']).
cnf(671,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)),121,['final']).
cnf(672,plain,(~a_nonce(X1)|~a_key(X1)),111,['final']).
cnf(673,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),117,['final']).
cnf(674,plain,(intruder_message(X1)|~intruder_message(pair(X2,X1))),67,['final']).
cnf(675,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))),68,['final']).
cnf(676,plain,(intruder_message(X1)|~intruder_message(triple(X2,X3,X1))),72,['final']).
cnf(677,plain,(intruder_message(X1)|~intruder_message(triple(X2,X1,X3))),73,['final']).
cnf(678,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))),63,['final']).
cnf(679,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))),74,['final']).
cnf(681,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)),84,['final']).
cnf(685,plain,(intruder_holds(key(X1,X2))|~intruder_message(X1)|~party_of_protocol(X2)),99,['final']).
cnf(686,plain,(message(sent(X1,X2,X3))|~intruder_message(X3)|~party_of_protocol(X2)|~party_of_protocol(X1)),96,['final']).
cnf(687,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)),87,['final']).
cnf(688,plain,(intruder_message(encrypt(X1,X2))|~intruder_holds(key(X2,X3))|~intruder_message(X1)|~party_of_protocol(X3)),102,['final']).
cnf(689,plain,(intruder_message(X1)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))|~party_of_protocol(X2)),93,['final']).
cnf(690,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~message(sent(X1,b,pair(X1,X2)))),50,['final']).
cnf(694,plain,(b_holds(key(X1,X2))|~a_key(X1)|~b_stored(pair(X2,X3))|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))),54,['final']).
cnf(695,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)))),51,['final']).
cnf(697,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),125,['final']).
cnf(698,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)),158,['final']).
cnf(699,plain,(b_stored(pair(X1,X2))|~intruder_message(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)),140,['final']).
cnf(700,plain,(b_stored(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),162,['final']).
cnf(705,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))))),157,['final']).
cnf(707,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)),152,['final']).
cnf(711,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)),181,['final']).
cnf(712,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)),194,['final']).
cnf(713,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)),197,['final']).
cnf(714,plain,(b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)),201,['final']).
cnf(716,plain,(b_holds(key(X1,a))|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)),204,['final']).
cnf(717,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)),187,['final']).
cnf(718,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)),205,['final']).
cnf(719,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),208,['final']).
cnf(720,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)),207,['final']).
cnf(722,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)),167,['final']).
cnf(724,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)),226,['final']).
cnf(725,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)),229,['final']).
cnf(726,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),231,['final']).
cnf(727,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)),234,['final']).
cnf(728,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),241,['final']).
cnf(735,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),267,['final']).
cnf(736,plain,(intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),268,['final']).
cnf(737,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),274,['final']).
cnf(740,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)),318,['final']).
cnf(742,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)),348,['final']).
cnf(745,plain,(message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)),379,['final']).
cnf(746,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)),381,['final']).
cnf(747,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),420,['final']).
cnf(748,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)))),394,['final']).
cnf(749,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)),452,['final']).
cnf(750,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)),403,['final']).
cnf(751,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)),453,['final']).
cnf(752,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)),454,['final']).
cnf(753,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)),456,['final']).
cnf(755,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)),485,['final']).
cnf(758,plain,(intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),489,['final']).
cnf(759,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),516,['final']).
cnf(763,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)))),387,['final']).
cnf(764,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)),548,['final']).
cnf(766,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)),551,['final']).
cnf(767,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)),553,['final']).
cnf(771,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))),295,['final']).
cnf(772,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))),297,['final']).
cnf(777,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))),599,['final']).
cnf(778,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))),569,['final']).
cnf(779,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)),405,['final']).
cnf(782,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)),605,['final']).
cnf(783,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))),571,['final']).
cnf(784,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))),600,['final']).
# SZS output end Saturation.
```

```# SZS status Theorem
# SZS answers Tuple [[s__agent__m, s__experiencer__m]|_]

# Proof found!
```

## FIMO 0.3

Orkunt Sabuncu
University of Potsdam, Germany

### Sample solution for NLP042+1

```% SZS output start Model
finite domain: {1,2,3,4}
esk2_0 = 1
esk3_0 = 2
esk4_0 = 3
esk5_0 = 4
esk1_0 = 1
abstraction/2:
(1,2) <=> True
(X1,X2) <=> abstraction(1,X2) : X1>1
impartial/2:
(X0,X1) <=> True *p*
woman/2:
(1,1) <=> True
(X1,X2) <=> woman(1,X2) : X1>1
act/2:
(1,4) <=> True
(X1,X2) <=> act(1,X2) : X1>1
animate/2:
(1,1) <=> True
(X1,X2) <=> animate(1,X2) : X1>1
thing/2:
(X0,X1) <=> True *p*
organism/2:
(1,1) <=> True
(X1,X2) <=> organism(1,X2) : X1>1
relname/2:
(1,2) <=> True
(X1,X2) <=> relname(1,X2) : X1>1
nonexistent/2:
(1,4) <=> True
(X1,X2) <=> nonexistent(1,X2) : X1>1
general/2:
(1,2) <=> True
(X1,X2) <=> general(1,X2) : X1>1
food/2:
(1,3) <=> True
(X1,X2) <=> food(1,X2) : X1>1
female/2:
(1,1) <=> True
(X1,X2) <=> female(1,X2) : X1>1
shake_beverage/2:
(1,3) <=> True
(X1,X2) <=> shake_beverage(1,X2) : X1>1
of/3:
(1,2,1) <=> True
(X1,X2,X3) <=> of(1,X2,X3) : X1>1
forename/2:
(1,2) <=> True
(X1,X2) <=> forename(1,X2) : X1>1
beverage/2:
(1,3) <=> True
(X1,X2) <=> beverage(1,X2) : X1>1
order/2:
(1,4) <=> True
(X1,X2) <=> order(1,X2) : X1>1
existent/2:
(1,1) <=> True
(1,2) <=> True
(1,3) <=> True
(X1,X2) <=> existent(1,X2) : X1>1
nonreflexive/2:
(1,4) <=> True
(X1,X2) <=> nonreflexive(1,X2) : X1>1
singleton/2:
(X0,X1) <=> True *p*
living/2:
(1,1) <=> True
(X1,X2) <=> living(1,X2) : X1>1
specific/2:
(1,1) <=> True
(1,3) <=> True
(1,4) <=> True
(X1,X2) <=> specific(1,X2) : X1>1
patient/3:
(1,4,3) <=> True
(X1,X2,X3) <=> patient(1,X2,X3) : X1>1
actual_world/1:
(X0) <=> True *p*
object/2:
(1,3) <=> True
(X1,X2) <=> object(1,X2) : X1>1
past/2:
(X0,X1) <=> True *p*
agent/3:
(1,4,1) <=> True
(X1,X2,X3) <=> agent(1,X2,X3) : X1>1
human/2:
(1,1) <=> True
(X1,X2) <=> human(1,X2) : X1>1
event/2:
(1,4) <=> True
(X1,X2) <=> event(1,X2) : X1>1
nonliving/2:
(1,2) <=> True
(1,3) <=> True
(1,4) <=> True
(X1,X2) <=> nonliving(1,X2) : X1>1
human_person/2:
(1,1) <=> True
(X1,X2) <=> human_person(1,X2) : X1>1
eventuality/2:
(1,4) <=> True
(X1,X2) <=> eventuality(1,X2) : X1>1
unisex/2:
(1,2) <=> True
(1,3) <=> True
(1,4) <=> True
(X1,X2) <=> unisex(1,X2) : X1>1
entity/2:
(1,1) <=> True
(1,3) <=> True
(X1,X2) <=> entity(1,X2) : X1>1
relation/2:
(1,2) <=> True
(X1,X2) <=> relation(1,X2) : X1>1
nonhuman/2:
(1,2) <=> True
(1,3) <=> True
(1,4) <=> True
(X1,X2) <=> nonhuman(1,X2) : X1>1
mia_forename/2:
(1,2) <=> True
(X1,X2) <=> mia_forename(1,X2) : X1>1
substance_matter/2:
(1,3) <=> True
(X1,X2) <=> substance_matter(1,X2) : X1>1
% SZS output end Model
```

### Sample solution for SWV017+1

```% SZS output start Model
finite domain: {1,2}
a = 1
b = 1
bt = 1
an_intruder_nonce = 2
t = 1
an_a_nonce = 2
at = 2
triple/3:
(1,1,1) = 1
(1,1,2) = 2
(1,2,2) = 2
(2,1,1) = 2
(2,1,2) = 2
(2,2,1) = 2
(1,2,1) = 1
(2,2,2) = 1
generate_expiration_time/1:
(2) = 2
(1) = 2
key/2:
(2,1) = 2
(1,1) = 2
(1,2) = 1
(2,2) = 1
generate_intruder_nonce/1:
(1) = 1
(2) = 2
sent/3:
(1,1,2) = 2
(1,2,1) = 2
(1,2,2) = 2
(2,1,1) = 2
(2,1,2) = 2
(2,2,1) = 2
(1,1,1) = 2
(2,2,2) = 1
(1,1,1,2) = 2
(1,2,1,1) = 2
(1,2,1,2) = 2
(2,1,1,1) = 2
(2,1,1,2) = 2
(2,2,1,1) = 2
(2,2,1,2) = 2
(1,1,2,1) = 2
(1,1,2,2) = 2
(1,2,2,1) = 2
(1,2,2,2) = 2
(2,2,2,1) = 2
(2,2,2,2) = 2
(1,1,1,1) = 2
(2,1,2,1) = 1
(2,1,2,2) = 1
generate_b_nonce/1:
(2) = 2
(1) = 2
generate_key/1:
(1) = 1
(2) = 1
encrypt/2:
(1,1) = 1
(2,2) = 2
(2,1) = 1
(1,2) = 1
pair/2:
(2,1) = 2
(1,2) = 2
(2,2) = 2
(1,1) = 2
t_holds/1:
(2) <=> True
a_holds/1:
(X0) <=> True *p*
message/1:
(2) <=> True
b_stored/1:
(X0) <=> True *p*
intruder_message/1:
(1) <=> True
(2) <=> True
fresh_intruder_nonce/1:
(2) <=> True
a_key/1:
(1) <=> True
b_holds/1:
(X0) <=> True *p*
a_nonce/1:
(2) <=> True
a_stored/1:
(2) <=> True
intruder_holds/1:
(2) <=> True
fresh_to_b/1:
(2) <=> True
party_of_protocol/1:
(1) <=> True
% SZS output end Model
```

## iProver 0.99

Konstantin Korovin, Christoph Sticksel
University of Manchester, United Kingdom

### Sample solution for SEU140+2

```% SZS output start CNFRefutation

fof(f208,plain,(
subset(sK10,sK11)),
inference(cnf_transformation,[],[f134])).

fof(f134,plain,(
subset(sK10,sK11) & disjoint(sK11,sK12) & ~disjoint(sK10,sK12)),
inference(skolemisation,[status(esa)],[f99])).
fof(f99,plain,(
? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
inference(flattening,[],[f98])).

fof(f98,plain,(
? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
inference(ennf_transformation,[],[f52])).

fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).

fof(f51,conjecture,(
! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
file('/M/TPTP-v5.2.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f209,plain,(
disjoint(sK11,sK12)),
inference(cnf_transformation,[],[f134])).

fof(f210,plain,(
~disjoint(sK10,sK12)),
inference(cnf_transformation,[],[f134])).

fof(f179,plain,(
( ! [X0,X1] : (disjoint(X1,X0) | ~disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f83])).

fof(f83,plain,(
! [X0,X1] : (~disjoint(X0,X1) | disjoint(X1,X0))),
inference(ennf_transformation,[],[f27])).

fof(f27,axiom,(
! [X0,X1] : (disjoint(X0,X1) => disjoint(X1,X0))),
file('/M/TPTP-v5.2.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f197,plain,(
( ! [X0,X1] : (in(sK8(X1,X0),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f132])).

fof(f132,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)],[f93])).
fof(f93,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(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(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(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('/M/TPTP-v5.2.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f150,plain,(
( ! [X0,X3,X1] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )),
inference(cnf_transformation,[],[f116])).

fof(f116,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)],[f115])).
fof(f115,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,[],[f114])).

fof(f114,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,[],[f78])).

fof(f78,plain,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (~in(X2,X0) | in(X2,X1)))),
inference(ennf_transformation,[],[f8])).

fof(f8,axiom,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
file('/M/TPTP-v5.2.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f199,plain,(
( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
inference(cnf_transformation,[],[f132])).

fof(f198,plain,(
( ! [X0,X1] : (in(sK8(X1,X0),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f132])).

cnf(c_x_1,plain,
( subset(sK10,sK11) ),
inference(cnf_transformation,[],[f208]) ).

cnf(c_x_2,plain,
( disjoint(sK11,sK12) ),
inference(cnf_transformation,[],[f209]) ).

cnf(c_x_3,plain,
( ~ disjoint(sK10,sK12) ),
inference(cnf_transformation,[],[f210]) ).

cnf(c_x_4,plain,
( ~ disjoint(X0,X1) | disjoint(X1,X0) ),
inference(cnf_transformation,[],[f179]) ).

cnf(c_1_85,plain,
( ~ disjoint(X0,X1) | disjoint(X1,X0) ),
inference(subtyping,[status(esa)],[c_x_4]) ).

cnf(c_1_93,plain,
( ~ disjoint(sK11,sK12) | disjoint(sK12,sK11) ),
inference(instantiation,[status(thm)],[c_1_85]) ).

cnf(c_x_5,plain,
( in(sK8(X0,X1),X1) | disjoint(X1,X0) ),
inference(cnf_transformation,[],[f197]) ).

cnf(c_1_88,plain,
( in(sK8(X0,X1),X1) | disjoint(X1,X0) ),
inference(subtyping,[status(esa)],[c_x_5]) ).

cnf(c_1_998,plain,
( in(sK8(sK12,sK10),sK10) | disjoint(sK10,sK12) ),
inference(instantiation,[status(thm)],[c_1_88]) ).

cnf(c_x_6,plain,
( ~ in(X0,X1) | ~ subset(X1,X2) | in(X0,X2) ),
inference(cnf_transformation,[],[f150]) ).

cnf(c_1_27,plain,
( ~ in(X0,X1) | ~ subset(X1,X2) | in(X0,X2) ),
inference(subtyping,[status(esa)],[c_x_6]) ).

cnf(c_1_99,plain,
( ~ in(sK8(X0,X1),X1) | ~ subset(X1,X2) | in(sK8(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_1_27]) ).

cnf(c_1_3533,plain,
( ~ in(sK8(X0,X1),X1) | ~ subset(X1,sK11) | in(sK8(X0,X1),sK11) ),
inference(instantiation,[status(thm)],[c_1_99]) ).

cnf(c_1_8636,plain,
( ~ in(sK8(X0,sK10),sK10)
| ~ subset(sK10,sK11)
| in(sK8(X0,sK10),sK11) ),
inference(instantiation,[status(thm)],[c_1_3533]) ).

cnf(c_1_8768,plain,
( ~ in(sK8(sK12,sK10),sK10)
| ~ subset(sK10,sK11)
| in(sK8(sK12,sK10),sK11) ),
inference(instantiation,[status(thm)],[c_1_8636]) ).

cnf(c_x_7,plain,
( ~ in(X0,X1) | ~ in(X0,X2) | ~ disjoint(X1,X2) ),
inference(cnf_transformation,[],[f199]) ).

cnf(c_1_86,plain,
( ~ in(X0,X1) | ~ in(X0,X2) | ~ disjoint(X1,X2) ),
inference(subtyping,[status(esa)],[c_x_7]) ).

cnf(c_1_101,plain,
( ~ in(sK8(X0,X1),X0) | ~ in(sK8(X0,X1),X2) | ~ disjoint(X0,X2) ),
inference(instantiation,[status(thm)],[c_1_86]) ).

cnf(c_1_3083,plain,
( ~ in(sK8(X0,X1),X0)
| ~ in(sK8(X0,X1),sK11)
| ~ disjoint(X0,sK11) ),
inference(instantiation,[status(thm)],[c_1_101]) ).

cnf(c_1_9305,plain,
( ~ in(sK8(sK12,sK10),sK12)
| ~ in(sK8(sK12,sK10),sK11)
| ~ disjoint(sK12,sK11) ),
inference(instantiation,[status(thm)],[c_1_3083]) ).

cnf(c_x_8,plain,
( in(sK8(X0,X1),X0) | disjoint(X1,X0) ),
inference(cnf_transformation,[],[f198]) ).

cnf(c_1_87,plain,
( in(sK8(X0,X1),X0) | disjoint(X1,X0) ),
inference(subtyping,[status(esa)],[c_x_8]) ).

cnf(c_1_658,plain,
( in(sK8(sK12,X0),sK12) | disjoint(X0,sK12) ),
inference(instantiation,[status(thm)],[c_1_87]) ).

cnf(c_1_9713,plain,
( in(sK8(sK12,sK10),sK12) | disjoint(sK10,sK12) ),
inference(instantiation,[status(thm)],[c_1_658]) ).

( \$false ),
inference(minisat,
[status(thm)],
[c_x_1,c_x_2,c_x_3,c_1_93,c_1_998,c_1_8768,c_1_9305,
c_1_9713]) ).

% SZS output end CNFRefutation
```

### Sample solution for NLP042+1

```% SZS output start Model

%------ Negative definition of \$\$equality_sorted
fof(lit_def,axiom,
(! [X0,X1,X2] :
( ~(\$\$equality_sorted(X0,X1,X2)) <=>
(
(
( X0=\$i & X1=sK9 )
&
( X2!=sK9 )
)

|
(
( X0=\$i & X1=sK8 )
&
( X2!=sK8 )
)

|
(
( X0=\$i & X1=sK6 )
&
( X2!=sK6 )
)

|
(
( X0=\$i & X1=sK7 )
&
( X2!=sK7 )
)

|
(
( X0=\$i & X2=sK9 )
&
( X1!=sK9 )
)

|
(
( X0=\$i & X2=sK8 )
&
( X1!=sK8 )
)

|
(
( X0=\$i & X2=sK6 )
&
( X1!=sK6 )
)

|
(
( X0=\$i & X2=sK7 )
&
( X1!=sK7 )
)

)
)
)
).

%------ Positive definition of female
fof(lit_def,axiom,
(! [X0,X1] :
( female(X0,X1) <=>
(
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of woman
fof(lit_def,axiom,
(! [X0,X1] :
( woman(X0,X1) <=>
(
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of animate
fof(lit_def,axiom,
(! [X0,X1] :
( animate(X0,X1) <=>
(
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of human_person
fof(lit_def,axiom,
(! [X0,X1] :
( human_person(X0,X1) <=>
(
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of human
fof(lit_def,axiom,
(! [X0,X1] :
( human(X0,X1) <=>
(
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of living
fof(lit_def,axiom,
(! [X0,X1] :
( living(X0,X1) <=>
(
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of organism
fof(lit_def,axiom,
(! [X0,X1] :
( organism(X0,X1) <=>
(
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of entity
fof(lit_def,axiom,
(! [X0,X1] :
( entity(X0,X1) <=>
(
(
( X0=sK5 & X1=sK8 )
)

|
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK8 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of forename
fof(lit_def,axiom,
(! [X0,X1] :
( forename(X0,X1) <=>
(
(
( X0=sK5 & X1=sK7 )
)

|
(
( X1=sK7 )
&
( X0!=sK5 )
)

)
)
)
).

%------ Positive definition of mia_forename
fof(lit_def,axiom,
(! [X0,X1] :
( mia_forename(X0,X1) <=>
(
(
( X0=sK5 & X1=sK7 )
)

|
(
( X1=sK7 )
)

)
)
)
).

%------ Positive definition of unisex
fof(lit_def,axiom,
(! [X0,X1] :
( unisex(X0,X1) <=>
(
(
( X0=sK5 & X1=sK9 )
)

|
(
( X0=sK5 & X1=sK8 )
)

|
(
( X0=sK5 & X1=sK7 )
)

|
(
( X1=sK9 )
)

|
(
( X1=sK8 )
)

|
(
( X1=sK7 )
)

)
)
)
).

%------ Positive definition of abstraction
fof(lit_def,axiom,
(! [X0,X1] :
( abstraction(X0,X1) <=>
(
(
( X0=sK5 & X1=sK7 )
)

|
(
( X1=sK7 )
)

)
)
)
).

%------ Positive definition of general
fof(lit_def,axiom,
(! [X0,X1] :
( general(X0,X1) <=>
(
(
( X0=sK5 & X1=sK7 )
)

|
(
( X1=sK7 )
)

)
)
)
).

%------ Positive definition of nonhuman
fof(lit_def,axiom,
(! [X0,X1] :
( nonhuman(X0,X1) <=>
(
(
( X0=sK5 & X1=sK7 )
)

|
(
( X1=sK7 )
)

)
)
)
).

%------ Positive definition of relation
fof(lit_def,axiom,
(! [X0,X1] :
( relation(X0,X1) <=>
(
(
( X0=sK5 & X1=sK7 )
)

|
(
( X1=sK7 )
)

)
)
)
).

%------ Positive definition of relname
fof(lit_def,axiom,
(! [X0,X1] :
( relname(X0,X1) <=>
(
(
( X0=sK5 & X1=sK7 )
)

|
(
( X1=sK7 )
)

)
)
)
).

%------ Positive definition of object
fof(lit_def,axiom,
(! [X0,X1] :
( object(X0,X1) <=>
(
(
( X0=sK5 & X1=sK8 )
)

|
(
( X1=sK8 )
)

)
)
)
).

%------ Positive definition of nonliving
fof(lit_def,axiom,
(! [X0,X1] :
( nonliving(X0,X1) <=>
(
(
( X0=sK5 & X1=sK8 )
)

|
(
( X1=sK8 )
)

)
)
)
).

%------ Positive definition of existent
fof(lit_def,axiom,
(! [X0,X1] :
( existent(X0,X1) <=>
(
(
( X0=sK5 & X1=sK8 )
)

|
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK8 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of specific
fof(lit_def,axiom,
(! [X0,X1] :
( specific(X0,X1) <=>
(
(
( X0=sK5 & X1=sK9 )
)

|
(
( X0=sK5 & X1=sK8 )
)

|
(
( X0=sK5 & X1=sK6 )
)

|
(
( X1=sK9 )
)

|
(
( X1=sK8 )
)

|
(
( X1=sK6 )
)

)
)
)
).

%------ Positive definition of substance_matter
fof(lit_def,axiom,
(! [X0,X1] :
( substance_matter(X0,X1) <=>
(
(
( X0=sK5 & X1=sK8 )
)

|
(
( X1=sK8 )
)

)
)
)
).

%------ Positive definition of food
fof(lit_def,axiom,
(! [X0,X1] :
( food(X0,X1) <=>
(
(
( X0=sK5 & X1=sK8 )
)

|
(
( X1=sK8 )
)

)
)
)
).

%------ Positive definition of beverage
fof(lit_def,axiom,
(! [X0,X1] :
( beverage(X0,X1) <=>
(
(
( X0=sK5 & X1=sK8 )
)

|
(
( X1=sK8 )
)

)
)
)
).

%------ Positive definition of shake_beverage
fof(lit_def,axiom,
(! [X0,X1] :
( shake_beverage(X0,X1) <=>
(
(
( X0=sK5 & X1=sK8 )
)

|
(
( X1=sK8 )
)

)
)
)
).

%------ Positive definition of event
fof(lit_def,axiom,
(! [X0,X1] :
( event(X0,X1) <=>
(
(
( X0=sK5 & X1=sK9 )
)

|
(
( X1=sK9 )
)

)
)
)
).

%------ Positive definition of order
fof(lit_def,axiom,
(! [X0,X1] :
( order(X0,X1) <=>
(
(
( X0=sK5 & X1=sK9 )
)

|
(
( X1=sK9 )
)

)
)
)
).

%------ Positive definition of eventuality
fof(lit_def,axiom,
(! [X0,X1] :
( eventuality(X0,X1) <=>
(
(
( X0=sK5 & X1=sK9 )
)

|
(
( X1=sK9 )
)

)
)
)
).

%------ Positive definition of nonexistent
fof(lit_def,axiom,
(! [X0,X1] :
( nonexistent(X0,X1) <=>
(
(
( X0=sK5 & X1=sK9 )
)

|
(
( X1=sK9 )
)

)
)
)
).

%------ Positive definition of act
fof(lit_def,axiom,
(! [X0,X1] :
( act(X0,X1) <=>
(
(
( X0=sK5 & X1=sK9 )
)

|
(
( X1=sK9 )
)

)
)
)
).

%------ Positive definition of of
fof(lit_def,axiom,
(! [X0,X1,X2] :
( of(X0,X1,X2) <=>
(
(
( X0=sK5 & X1=sK7 & X2=sK6 )
)

|
(
( X1=sK7 & X2=sK6 )
)

)
)
)
).

%------ Positive definition of nonreflexive
fof(lit_def,axiom,
(! [X0,X1] :
( nonreflexive(X0,X1) <=>
(
(
( X0=sK5 & X1=sK9 )
)

|
(
( X1=sK9 )
)

)
)
)
).

%------ Positive definition of agent
fof(lit_def,axiom,
(! [X0,X1,X2] :
( agent(X0,X1,X2) <=>
(
(
( X0=sK5 & X1=sK9 & X2=sK6 )
)

|
(
( X1=sK9 & X2=sK6 )
)

)
)
)
).

%------ Positive definition of patient
fof(lit_def,axiom,
(! [X0,X1,X2] :
( patient(X0,X1,X2) <=>
(
(
( X0=sK5 & X1=sK9 & X2=sK8 )
)

|
(
( X1=sK9 & X2=sK8 )
)

)
)
)
).

% SZS output end Model
```

### Sample solution for SWV017+1

```% SZS output start Saturation

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

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

fof(f27,axiom,(
! [X0] : ~a_nonce(generate_key(X0))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f12,axiom,(
t_holds(key(bt,b))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f11,axiom,(
t_holds(key(at,a))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f4,axiom,(
a_stored(pair(b,an_a_nonce))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

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

fof(f9,axiom,(
! [X0,X1] : ((message(sent(X0,b,pair(X0,X1))) & fresh_to_b(X1)) => (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) & b_stored(pair(X0,X1))))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

fof(f23,axiom,(
! [X0,X1,X2] : ((intruder_message(X0) & party_of_protocol(X1) & party_of_protocol(X2)) => message(sent(X1,X2,X0)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f3,axiom,(
message(sent(a,b,pair(a,an_a_nonce)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

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

fof(f5,axiom,(
! [X0,X1,X2,X3,X4,X5] : ((message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))) & a_stored(pair(X4,X5))) => (message(sent(a,X4,pair(X3,encrypt(X0,X2)))) & a_holds(key(X2,X4))))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

fof(f14,axiom,(
! [X0,X1,X2,X3,X4,X5,X6] : ((message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5)))) & t_holds(key(X5,X0)) & t_holds(key(X6,X2)) & a_nonce(X3)) => message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

fof(f32,axiom,(
! [X0] : (fresh_intruder_nonce(X0) => fresh_intruder_nonce(generate_intruder_nonce(X0)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f31,axiom,(
fresh_intruder_nonce(an_intruder_nonce)),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f8,axiom,(
fresh_to_b(an_a_nonce)),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

fof(f33,axiom,(
! [X0] : (fresh_intruder_nonce(X0) => (fresh_to_b(X0) & intruder_message(X0)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f7,axiom,(
party_of_protocol(b)),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f2,axiom,(
party_of_protocol(a)),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f13,axiom,(
party_of_protocol(t)),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

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

fof(f24,axiom,(
! [X1,X2] : ((intruder_message(X1) & party_of_protocol(X2)) => intruder_holds(key(X1,X2)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

fof(f19,axiom,(
! [X0,X1] : ((intruder_message(X0) & intruder_message(X1)) => intruder_message(pair(X0,X1)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

fof(f18,axiom,(
! [X0,X1,X2,X3] : (intruder_message(quadruple(X0,X1,X2,X3)) => (intruder_message(X0) & intruder_message(X1) & intruder_message(X2) & intruder_message(X3)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

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

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

fof(f17,axiom,(
! [X0,X1,X2] : (intruder_message(triple(X0,X1,X2)) => (intruder_message(X0) & intruder_message(X1) & intruder_message(X2)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

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

fof(f16,axiom,(
! [X0,X1] : (intruder_message(pair(X0,X1)) => (intruder_message(X0) & intruder_message(X1)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

fof(f15,axiom,(
! [X0,X1,X2] : (message(sent(X0,X1,X2)) => intruder_message(X2))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

fof(f22,axiom,(
! [X0,X1,X2] : ((intruder_message(encrypt(X0,X1)) & intruder_holds(key(X1,X2)) & party_of_protocol(X2)) => intruder_message(X1))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

fof(f20,axiom,(
! [X0,X1,X2] : ((intruder_message(X0) & intruder_message(X1) & intruder_message(X2)) => intruder_message(triple(X0,X1,X2)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

fof(f21,axiom,(
! [X0,X1,X2,X3] : ((intruder_message(X0) & intruder_message(X1) & intruder_message(X2) & intruder_message(X3)) => intruder_message(quadruple(X0,X1,X2,X3)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

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

fof(f25,axiom,(
! [X0,X1,X2] : ((intruder_message(X0) & intruder_holds(key(X1,X2)) & party_of_protocol(X2)) => intruder_message(encrypt(X0,X1)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f30,axiom,(
! [X0] : a_key(generate_key(X0))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

fof(f29,axiom,(
! [X0] : ~(a_key(X0) & a_nonce(X0))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

fof(f28,axiom,(
! [X0] : (a_nonce(generate_expiration_time(X0)) & a_nonce(generate_b_nonce(X0)))),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

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

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

fof(f26,axiom,(
a_nonce(an_a_nonce)),
file('/M/TPTP-v5.2.0/Problems/SWV/SWV017+1.p',unknown)).

cnf(c_x_1,plain,
( ~ a_nonce(generate_key(X0)) ),
inference(cnf_transformation,[],[f168]) ).

cnf(c_x_2,plain,
( t_holds(key(bt,b)) ),
inference(cnf_transformation,[],[f147]) ).

cnf(c_x_3,plain,
( t_holds(key(at,a)) ),
inference(cnf_transformation,[],[f146]) ).

cnf(c_x_4,plain,
( a_stored(pair(b,an_a_nonce)) ),
inference(cnf_transformation,[],[f141]) ).

cnf(c_x_5,plain,
( ~ 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(cnf_transformation,[],[f145]) ).

cnf(c_x_6,plain,
( ~ party_of_protocol(X0)
| ~ party_of_protocol(X1)
| ~ intruder_message(X2)
| message(sent(X0,X1,X2)) ),
inference(cnf_transformation,[],[f164]) ).

cnf(c_x_7,plain,
( message(sent(a,b,pair(a,an_a_nonce))) ),
inference(cnf_transformation,[],[f140]) ).

cnf(c_x_8,plain,
| ~ a_stored(pair(X0,X1))
| message(sent(a,X0,pair(X4,encrypt(X5,X2)))) ),
inference(cnf_transformation,[],[f142]) ).

cnf(c_x_9,plain,
( ~ 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)
inference(cnf_transformation,[],[f149]) ).

cnf(c_x_10,plain,
( ~ fresh_intruder_nonce(X0)
| fresh_intruder_nonce(generate_intruder_nonce(X0)) ),
inference(cnf_transformation,[],[f174]) ).

cnf(c_x_11,plain,
( fresh_intruder_nonce(an_intruder_nonce) ),
inference(cnf_transformation,[],[f173]) ).

cnf(c_x_12,plain,
( fresh_to_b(an_a_nonce) ),
inference(cnf_transformation,[],[f144]) ).

cnf(c_x_13,plain,
( ~ fresh_intruder_nonce(X0) | fresh_to_b(X0) ),
inference(cnf_transformation,[],[f175]) ).

cnf(c_x_14,plain,
( party_of_protocol(b) ),
inference(cnf_transformation,[],[f143]) ).

cnf(c_x_15,plain,
( party_of_protocol(a) ),
inference(cnf_transformation,[],[f139]) ).

cnf(c_x_16,plain,
( party_of_protocol(t) ),
inference(cnf_transformation,[],[f148]) ).

cnf(c_x_17,plain,
( ~ party_of_protocol(X0)
| ~ intruder_message(X1)
| intruder_holds(key(X1,X0)) ),
inference(cnf_transformation,[],[f165]) ).

cnf(c_x_18,plain,
( ~ intruder_message(X0)
| ~ intruder_message(X1)
| intruder_message(pair(X0,X1)) ),
inference(cnf_transformation,[],[f160]) ).

cnf(c_x_19,plain,
( ~ fresh_intruder_nonce(X0) | intruder_message(X0) ),
inference(cnf_transformation,[],[f176]) ).

cnf(c_x_20,plain,
( ~ intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X0) ),
inference(cnf_transformation,[],[f156]) ).

cnf(c_x_21,plain,
( ~ intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X1) ),
inference(cnf_transformation,[],[f157]) ).

cnf(c_x_22,plain,
( ~ intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X2) ),
inference(cnf_transformation,[],[f158]) ).

cnf(c_x_23,plain,
( ~ intruder_message(quadruple(X0,X1,X2,X3)) | intruder_message(X3) ),
inference(cnf_transformation,[],[f159]) ).

cnf(c_x_24,plain,
( ~ intruder_message(triple(X0,X1,X2)) | intruder_message(X0) ),
inference(cnf_transformation,[],[f153]) ).

cnf(c_x_25,plain,
( ~ intruder_message(triple(X0,X1,X2)) | intruder_message(X1) ),
inference(cnf_transformation,[],[f154]) ).

cnf(c_x_26,plain,
( ~ intruder_message(triple(X0,X1,X2)) | intruder_message(X2) ),
inference(cnf_transformation,[],[f155]) ).

cnf(c_x_27,plain,
( ~ intruder_message(pair(X0,X1)) | intruder_message(X0) ),
inference(cnf_transformation,[],[f151]) ).

cnf(c_x_28,plain,
( ~ intruder_message(pair(X0,X1)) | intruder_message(X1) ),
inference(cnf_transformation,[],[f152]) ).

cnf(c_x_29,plain,
( ~ message(sent(X0,X1,X2)) | intruder_message(X2) ),
inference(cnf_transformation,[],[f150]) ).

cnf(c_x_30,plain,
( ~ party_of_protocol(X0)
| ~ intruder_message(encrypt(X1,X2))
| ~ intruder_holds(key(X2,X0))
| intruder_message(X2) ),
inference(cnf_transformation,[],[f163]) ).

cnf(c_x_31,plain,
( ~ intruder_message(X0)
| ~ intruder_message(X1)
| ~ intruder_message(X2)
| intruder_message(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f161]) ).

cnf(c_x_32,plain,
( ~ intruder_message(X0)
| ~ intruder_message(X1)
| ~ intruder_message(X2)
| ~ intruder_message(X3)
inference(cnf_transformation,[],[f162]) ).

cnf(c_x_33,plain,
( ~ party_of_protocol(X0)
| ~ intruder_message(X1)
| ~ intruder_holds(key(X2,X0))
| intruder_message(encrypt(X1,X2)) ),
inference(cnf_transformation,[],[f166]) ).

cnf(c_2_3,plain,
( a_key(generate_key(X0)) ),
inference(cnf_transformation,[],[f172]) ).

cnf(c_2_4,plain,
( ~ a_nonce(X0) | ~ a_key(X0) ),
inference(cnf_transformation,[],[f171]) ).

cnf(c_2_0,plain,
( a_nonce(generate_expiration_time(X0)) ),
inference(cnf_transformation,[],[f169]) ).

cnf(c_2_2,plain,
( a_nonce(generate_b_nonce(X0)) ),
inference(cnf_transformation,[],[f170]) ).

cnf(c_2_5,plain,
( ~ a_nonce(generate_key(X0)) ),
inference(resolution,[status(thm)],[c_2_4,c_2_3]) ).

cnf(c_2_1,plain,
( a_nonce(an_a_nonce) ),
inference(cnf_transformation,[],[f167]) ).

% SZS output end Saturation
```

### Sample solution for CSR082+1

```% SZS answers Tuple [[s__agent__m,s__experiencer__m]] for /home/korovin/iprover/LTB/CSR082+1.p
```

## leanCoP---2.2

Jens Otten
University of Potsdam, Germany

### Sample solution for SEU140+2

```Start of proof for SEU140+2.p
%-----------------------------------------------------
fof(t63_xboole_1,conjecture,![_G25211, _G25214, _G25217]: (subset(_G25211, _G25214)&disjoint(_G25214, _G25217)=>disjoint(_G25211, _G25217)),file('SEU140+2.p',t63_xboole_1)).
fof(d3_tarski,axiom,![_G25288, _G25291]: (subset(_G25288, _G25291)<=>![_G25297]: (in(_G25297, _G25288)=>in(_G25297, _G25291))),file('SEU140+2.p',d3_tarski)).
fof(t3_xboole_0,lemma,![_G25352, _G25355]: (~ (~disjoint(_G25352, _G25355)&![_G25363]: ~ (in(_G25363, _G25352)&in(_G25363, _G25355)))& ~ (?[_G25363]: (in(_G25363, _G25352)&in(_G25363, _G25355))&disjoint(_G25352, _G25355))),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(_G2579, _G2580), in(_G2584, _G2579), -in(_G2584, _G2580)], clausify(d3_tarski)).
cnf(5, plain, [-disjoint(_G2973, _G2974), -in(9^[_G2974, _G2973], _G2973)], clausify(t3_xboole_0)).
cnf(6, plain, [-disjoint(_G2973, _G2974), -in(9^[_G2974, _G2973], _G2974)], clausify(t3_xboole_0)).
cnf(7, plain, [disjoint(_G2973, _G2974), in(_G2980, _G2973), in(_G2980, _G2974)], clausify(t3_xboole_0)).

cnf('1',plain,[disjoint(12^[], 13^[]), in(9^[13^[], 11^[]], 12^[]), in(9^[13^[], 11^[]], 13^[])],start(7,bind([[_G2973, _G2980, _G2974], [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([[_G2580, _G2584, _G2579], [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([[_G2973, _G2974], [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([[_G2973, _G2974], [11^[], 13^[]]]))).
cnf('1.3.1',plain,[disjoint(11^[], 13^[])],extension(3)).
%-----------------------------------------------------
End of proof for SEU140+2.p
```

## leanCoP-ARDE---2.2

Mario Frank, Jens Otten, Thomas Raths
University of Potsdam, Germany

### Sample solution for SEU140+2

```Start of proof for SEU140+2.p
%-----------------------------------------------------
fof(t63_xboole_1,conjecture,![_G25211, _G25214, _G25217]: (subset(_G25211, _G25214)&disjoint(_G25214, _G25217)=>disjoint(_G25211, _G25217)),file('SEU140+2.p',t63_xboole_1)).
fof(d3_tarski,axiom,![_G25288, _G25291]: (subset(_G25288, _G25291)<=>![_G25297]: (in(_G25297, _G25288)=>in(_G25297, _G25291))),file('SEU140+2.p',d3_tarski)).
fof(t3_xboole_0,lemma,![_G25352, _G25355]: (~ (~disjoint(_G25352, _G25355)&![_G25363]: ~ (in(_G25363, _G25352)&in(_G25363, _G25355)))& ~ (?[_G25363]: (in(_G25363, _G25352)&in(_G25363, _G25355))&disjoint(_G25352, _G25355))),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(_G2579, _G2580), in(_G2584, _G2579), -in(_G2584, _G2580)], clausify(d3_tarski)).
cnf(5, plain, [-disjoint(_G2973, _G2974), -in(9^[_G2974, _G2973], _G2973)], clausify(t3_xboole_0)).
cnf(6, plain, [-disjoint(_G2973, _G2974), -in(9^[_G2974, _G2973], _G2974)], clausify(t3_xboole_0)).
cnf(7, plain, [disjoint(_G2973, _G2974), in(_G2980, _G2973), in(_G2980, _G2974)], clausify(t3_xboole_0)).

cnf('1',plain,[disjoint(12^[], 13^[]), in(9^[13^[], 11^[]], 12^[]), in(9^[13^[], 11^[]], 13^[])],start(7,bind([[_G2973, _G2980, _G2974], [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([[_G2580, _G2584, _G2579], [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([[_G2973, _G2974], [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([[_G2973, _G2974], [11^[], 13^[]]]))).
cnf('1.3.1',plain,[disjoint(11^[], 13^[])],extension(3)).
%-----------------------------------------------------
End of proof for SEU140+2.p
```

## LEO-II---1.4

Christoph Benzmüller
Free University Berlin, Germany

### Sample solution for SEU140+2

```% SZS output start CNFRefutation
thf(tp_disjoint,type,(disjoint: (\$i>(\$i>\$o)))).
thf(tp_empty,type,(empty: (\$i>\$o))).
thf(tp_empty_set,type,(empty_set: \$i)).
thf(tp_in,type,(in: (\$i>(\$i>\$o)))).
thf(tp_proper_subset,type,(proper_subset: (\$i>(\$i>\$o)))).
thf(tp_sK1,type,(sK1: \$i)).
thf(tp_sK2,type,(sK2: \$i)).
thf(tp_sK3,type,(sK3: \$i)).
thf(tp_sK4,type,(sK4: (\$i>(\$i>\$i)))).
thf(tp_sK5,type,(sK5: (\$i>(\$i>\$i)))).
thf(tp_sK6,type,(sK6: (\$i>(\$i>\$i)))).
thf(tp_set_difference,type,(set_difference: (\$i>(\$i>\$i)))).
thf(tp_set_intersection2,type,(set_intersection2: (\$i>(\$i>\$i)))).
thf(tp_set_union2,type,(set_union2: (\$i>(\$i>\$i)))).
thf(tp_subset,type,(subset: (\$i>(\$i>\$o)))).
thf(9,axiom,(![A:\$i,B:\$i]: (((disjoint@A)@B) =>
((disjoint@B)@A))),file('SEU140+2.p',symmetry_r1_xboole_0)).
thf(10,axiom,(![A:\$i,B:\$i]:
((subset@A)@A)),file('SEU140+2.p',reflexivity_r1_tarski)).
thf(23,axiom,(![A:\$i,B:\$i]: (((proper_subset@A)@B) <=>
(((subset@A)@B) & (A != B)))),file('SEU140+2.p',d8_xboole_0)).
thf(24,axiom,(![A:\$i,B:\$i]: (((disjoint@A)@B) <=>
(((set_intersection2@A)@B) =
empty_set))),file('SEU140+2.p',d7_xboole_0)).
thf(27,axiom,(![A:\$i,B:\$i]: (((subset@A)@B) <=> (![C:\$i]: (((in@C)@A)
=> ((in@C)@B))))),file('SEU140+2.p',d3_tarski)).
thf(30,axiom,(![A:\$i,B:\$i]: ((A = B) <=> (((subset@A)@B) &
((subset@B)@A)))),file('SEU140+2.p',d10_xboole_0)).
thf(35,axiom,(![A:\$i,B:\$i,C:\$i]: ((((subset@A)@B) & ((subset@C)@B))
=> ((subset@((set_union2@A)@C))@B))),file('SEU140+2.p',t8_xboole_1)).
thf(36,axiom,(![A:\$i,B:\$i]:
((subset@A)@((set_union2@A)@B))),file('SEU140+2.p',t7_xboole_1)).
thf(37,axiom,(![A:\$i,B:\$i]: (~ (((subset@A)@B) &
((proper_subset@B)@A)))),file('SEU140+2.p',t60_xboole_1)).
thf(38,axiom,(![A:\$i,B:\$i]: ((~ ((~ ((disjoint@A)@B)) & (![C:\$i]: (~
((in@C)@((set_intersection2@A)@B)))))) & (~ ((?[C:\$i]:
((in@C)@((set_intersection2@A)@B))) &
((disjoint@A)@B))))),file('SEU140+2.p',t4_xboole_0)).
thf(40,axiom,(![A:\$i,B:\$i]: (((subset@A)@B) => (B =
((set_union2@A)@((set_difference@B)@A))))),file('SEU140+2.p',t45_xboole_1)).
thf(42,axiom,(![A:\$i]: (((subset@A)@empty_set) => (A =
empty_set))),file('SEU140+2.p',t3_xboole_1)).
thf(43,axiom,(![A:\$i,B:\$i]: ((~ ((~ ((disjoint@A)@B)) & (![C:\$i]: (~
(((in@C)@A) & ((in@C)@B)))))) & (~ ((?[C:\$i]: (((in@C)@A) &
((in@C)@B))) & ((disjoint@A)@B))))),file('SEU140+2.p',t3_xboole_0)).
thf(45,axiom,(![A:\$i,B:\$i]: ((((set_difference@A)@B) = empty_set) <=>
((subset@A)@B))),file('SEU140+2.p',t37_xboole_1)).
thf(46,axiom,(![A:\$i,B:\$i]:
((subset@((set_difference@A)@B))@A)),file('SEU140+2.p',t36_xboole_1)).
thf(47,axiom,(![A:\$i,B:\$i,C:\$i]: (((subset@A)@B) =>
((subset@((set_difference@A)@C))@((set_difference@B)@C)))),file('SEU140+2.p',t33_xboole_1)).
thf(48,axiom,(![A:\$i]: ((subset@empty_set)@A)),file('SEU140+2.p',t2_xboole_1)).
thf(49,axiom,(![A:\$i,B:\$i]: (((subset@A)@B) =>
(((set_intersection2@A)@B) = A))),file('SEU140+2.p',t28_xboole_1)).
thf(50,axiom,(![A:\$i,B:\$i,C:\$i]: (((subset@A)@B) =>
((subset@((set_intersection2@A)@C))@((set_intersection2@B)@C)))),file('SEU140+2.p',t26_xboole_1)).
thf(51,axiom,(![A:\$i,B:\$i,C:\$i]: ((((subset@A)@B) & ((subset@B)@C))
=> ((subset@A)@C))),file('SEU140+2.p',t1_xboole_1)).
thf(52,axiom,(![A:\$i,B:\$i,C:\$i]: ((((subset@A)@B) & ((subset@A)@C))
=> ((subset@A)@((set_intersection2@B)@C)))),file('SEU140+2.p',t19_xboole_1)).
thf(53,axiom,(![A:\$i,B:\$i]:
((subset@((set_intersection2@A)@B))@A)),file('SEU140+2.p',t17_xboole_1)).
thf(54,axiom,(![A:\$i,B:\$i]: (((subset@A)@B) => (((set_union2@A)@B) =
B))),file('SEU140+2.p',t12_xboole_1)).
thf(55,axiom,(![A:\$i,B:\$i]: ((((set_difference@A)@B) = empty_set) <=>
((subset@A)@B))),file('SEU140+2.p',l32_xboole_1)).
thf(56,conjecture,(![A:\$i,B:\$i,C:\$i]: ((((subset@A)@B) &
((disjoint@B)@C)) =>
((disjoint@A)@C))),file('SEU140+2.p',t63_xboole_1)).
thf(57,negated_conjecture,(((![A:\$i,B:\$i,C:\$i]: ((((subset@A)@B) &
((disjoint@B)@C)) =>
((disjoint@A)@C)))=\$false)),inference(negate_conjecture,[status(cth)],[56])).
thf(58,plain,(((![A:\$i,B:\$i,C:\$i]: ((((subset@A)@B) &
((disjoint@B)@C)) =>
((disjoint@A)@C)))=\$false)),inference(unfold_def,[status(thm)],[57])).
thf(59,plain,(((![A:\$i,B:\$i]: (((disjoint@A)@B) =>
((disjoint@B)@A)))=\$true)),inference(unfold_def,[status(thm)],[9])).
thf(60,plain,(((![A:\$i,B:\$i]:
((subset@A)@A))=\$true)),inference(unfold_def,[status(thm)],[10])).
thf(61,plain,(((![A:\$i,B:\$i]: (((proper_subset@A)@B) <=>
(((subset@A)@B) & (A !=
B))))=\$true)),inference(unfold_def,[status(thm)],[23])).
thf(62,plain,(((![A:\$i,B:\$i]: (((disjoint@A)@B) <=>
(((set_intersection2@A)@B) =
empty_set)))=\$true)),inference(unfold_def,[status(thm)],[24])).
thf(63,plain,(((![A:\$i,B:\$i]: (((subset@A)@B) <=> (![C:\$i]:
(((in@C)@A) => ((in@C)@B)))))=\$true)),inference(unfold_def,[status(thm)],[27])).
thf(64,plain,(((![A:\$i,B:\$i]: ((A = B) <=> (((subset@A)@B) &
((subset@B)@A))))=\$true)),inference(unfold_def,[status(thm)],[30])).
thf(65,plain,(((![A:\$i,B:\$i,C:\$i]: ((((subset@A)@B) & ((subset@C)@B))
=> ((subset@((set_union2@A)@C))@B)))=\$true)),inference(unfold_def,[status(thm)],[35])).
thf(66,plain,(((![A:\$i,B:\$i]:
((subset@A)@((set_union2@A)@B)))=\$true)),inference(unfold_def,[status(thm)],[36])).
thf(67,plain,(((![A:\$i,B:\$i]: (~ (((subset@A)@B) &
((proper_subset@B)@A))))=\$true)),inference(unfold_def,[status(thm)],[37])).
thf(68,plain,(((![A:\$i,B:\$i]: ((~ ((~ ((disjoint@A)@B)) & (![C:\$i]:
(~ ((in@C)@((set_intersection2@A)@B)))))) & (~ ((?[C:\$i]:
((in@C)@((set_intersection2@A)@B))) &
((disjoint@A)@B)))))=\$true)),inference(unfold_def,[status(thm)],[38])).
thf(69,plain,(((![A:\$i,B:\$i]: (((subset@A)@B) => (B =
((set_union2@A)@((set_difference@B)@A)))))=\$true)),inference(unfold_def,[status(thm)],[40])).
thf(70,plain,(((![A:\$i]: (((subset@A)@empty_set) => (A =
empty_set)))=\$true)),inference(unfold_def,[status(thm)],[42])).
thf(71,plain,(((![A:\$i,B:\$i]: ((~ ((~ ((disjoint@A)@B)) & (![C:\$i]:
(~ (((in@C)@A) & ((in@C)@B)))))) & (~ ((?[C:\$i]: (((in@C)@A) &
((in@C)@B))) & ((disjoint@A)@B)))))=\$true)),inference(unfold_def,[status(thm)],[43])).
thf(72,plain,(((![A:\$i,B:\$i]: ((((set_difference@A)@B) = empty_set)
<=> ((subset@A)@B)))=\$true)),inference(unfold_def,[status(thm)],[45])).
thf(73,plain,(((![A:\$i,B:\$i]:
((subset@((set_difference@A)@B))@A))=\$true)),inference(unfold_def,[status(thm)],[46])).
thf(74,plain,(((![A:\$i,B:\$i,C:\$i]: (((subset@A)@B) =>
((subset@((set_difference@A)@C))@((set_difference@B)@C))))=\$true)),inference(unfold_def,[status(thm)],[47])).
thf(75,plain,(((![A:\$i]:
((subset@empty_set)@A))=\$true)),inference(unfold_def,[status(thm)],[48])).
thf(76,plain,(((![A:\$i,B:\$i]: (((subset@A)@B) =>
(((set_intersection2@A)@B) =
A)))=\$true)),inference(unfold_def,[status(thm)],[49])).
thf(77,plain,(((![A:\$i,B:\$i,C:\$i]: (((subset@A)@B) =>
((subset@((set_intersection2@A)@C))@((set_intersection2@B)@C))))=\$true)),inference(unfold_def,[status(thm)],[50])).
thf(78,plain,(((![A:\$i,B:\$i,C:\$i]: ((((subset@A)@B) & ((subset@B)@C))
=> ((subset@A)@C)))=\$true)),inference(unfold_def,[status(thm)],[51])).
thf(79,plain,(((![A:\$i,B:\$i,C:\$i]: ((((subset@A)@B) & ((subset@A)@C))
=> ((subset@A)@((set_intersection2@B)@C))))=\$true)),inference(unfold_def,[status(thm)],[52])).
thf(80,plain,(((![A:\$i,B:\$i]:
((subset@((set_intersection2@A)@B))@A))=\$true)),inference(unfold_def,[status(thm)],[53])).
thf(81,plain,(((![A:\$i,B:\$i]: (((subset@A)@B) => (((set_union2@A)@B)
= B)))=\$true)),inference(unfold_def,[status(thm)],[54])).
thf(82,plain,(((![A:\$i,B:\$i]: ((((set_difference@A)@B) = empty_set)
<=> ((subset@A)@B)))=\$true)),inference(unfold_def,[status(thm)],[55])).
thf(83,plain,((((((subset@sK1)@sK2) & ((disjoint@sK2)@sK3)) =>
((disjoint@sK1)@sK3))=\$false)),inference(extcnf_forall_neg,[status(esa)],[58])).
thf(84,plain,((((subset@sK1)@sK2)=\$true)),inference(standard_cnf,[status(thm)],[83])).
thf(85,plain,((((disjoint@sK2)@sK3)=\$true)),inference(standard_cnf,[status(thm)],[83])).
thf(86,plain,((((disjoint@sK1)@sK3)=\$false)),inference(standard_cnf,[status(thm)],[83])).
thf(87,plain,(((~
((disjoint@sK1)@sK3))=\$true)),inference(polarity_switch,[status(thm)],[86])).
thf(88,plain,(((![A:\$i,B:\$i]: ((~ ((disjoint@A)@B)) |
((disjoint@B)@A)))=\$true)),inference(extcnf_combined,[status(esa)],[59])).
thf(89,plain,(((![A:\$i]:
((subset@A)@A))=\$true)),inference(extcnf_combined,[status(esa)],[60])).
thf(90,plain,((((![A:\$i,B:\$i]: (((A = B) | (~ ((subset@A)@B))) |
((proper_subset@A)@B))) & ((![A:\$i,B:\$i]: ((~ ((proper_subset@A)@B)) |
(~ (A = B)))) & (![A:\$i,B:\$i]: ((~ ((proper_subset@A)@B)) |
((subset@A)@B)))))=\$true)),inference(extcnf_combined,[status(esa)],[61])).
thf(91,plain,((((![A:\$i,B:\$i]: ((~ (((set_intersection2@A)@B) =
empty_set)) | ((disjoint@A)@B))) & (![A:\$i,B:\$i]: ((~
((disjoint@A)@B)) | (((set_intersection2@A)@B) =
empty_set))))=\$true)),inference(extcnf_combined,[status(esa)],[62])).
thf(92,plain,((((![A:\$i,B:\$i]: ((((in@((sK4@B)@A))@A) & (~
((in@((sK4@B)@A))@B))) | ((subset@A)@B))) & (![A:\$i,B:\$i]: ((~
((subset@A)@B)) | (![C:\$i]: ((~ ((in@C)@A)) |
((in@C)@B))))))=\$true)),inference(extcnf_combined,[status(esa)],[63])).
thf(93,plain,((((![A:\$i,B:\$i]: (((~ ((subset@A)@B)) | (~
((subset@B)@A))) | (A = B))) & ((![A:\$i,B:\$i]: ((~ (A = B)) |
((subset@A)@B))) & (![A:\$i,B:\$i]: ((~ (A = B)) |
((subset@B)@A)))))=\$true)),inference(extcnf_combined,[status(esa)],[64])).
thf(94,plain,(((![A:\$i,B:\$i,C:\$i]: (((~ ((subset@A)@B)) | (~
((subset@C)@B))) |
((subset@((set_union2@A)@C))@B)))=\$true)),inference(extcnf_combined,[status(esa)],[65])).
thf(95,plain,(((![A:\$i,B:\$i]: ((~ ((proper_subset@B)@A)) | (~
((subset@A)@B))))=\$true)),inference(extcnf_combined,[status(esa)],[67])).
thf(96,plain,((((![A:\$i,B:\$i]: (((disjoint@A)@B) |
((in@((sK5@B)@A))@((set_intersection2@A)@B)))) & (![A:\$i,B:\$i]:
((![C:\$i]: (~ ((in@C)@((set_intersection2@A)@B)))) | (~
((disjoint@A)@B)))))=\$true)),inference(extcnf_combined,[status(esa)],[68])).
thf(97,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) | (B =
((set_union2@A)@((set_difference@B)@A)))))=\$true)),inference(extcnf_combined,[status(esa)],[69])).
thf(98,plain,(((![A:\$i]: ((~ ((subset@A)@empty_set)) | (A =
empty_set)))=\$true)),inference(extcnf_combined,[status(esa)],[70])).
thf(99,plain,((((![A:\$i,B:\$i]: (((disjoint@A)@B) |
(((in@((sK6@B)@A))@A) & ((in@((sK6@B)@A))@B)))) & (![A:\$i,B:\$i]:
((![C:\$i]: ((~ ((in@C)@A)) | (~ ((in@C)@B)))) | (~
((disjoint@A)@B)))))=\$true)),inference(extcnf_combined,[status(esa)],[71])).
thf(100,plain,((((![A:\$i,B:\$i]: ((~ (((set_difference@A)@B) =
empty_set)) | ((subset@A)@B))) & (![A:\$i,B:\$i]: ((~ ((subset@A)@B)) |
(((set_difference@A)@B) =
empty_set))))=\$true)),inference(extcnf_combined,[status(esa)],[72])).
thf(101,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) | (![C:\$i]:
((subset@((set_difference@A)@C))@((set_difference@B)@C)))))=\$true)),inference(extcnf_combined,[status(esa)],[74])).
thf(102,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) |
(((set_intersection2@A)@B) =
A)))=\$true)),inference(extcnf_combined,[status(esa)],[76])).
thf(103,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) | (![C:\$i]:
((subset@((set_intersection2@A)@C))@((set_intersection2@B)@C)))))=\$true)),inference(extcnf_combined,[status(esa)],[77])).
thf(104,plain,(((![A:\$i,B:\$i,C:\$i]: (((~ ((subset@A)@B)) | (~
((subset@B)@C))) |
((subset@A)@C)))=\$true)),inference(extcnf_combined,[status(esa)],[78])).
thf(105,plain,(((![A:\$i,B:\$i,C:\$i]: (((~ ((subset@A)@B)) | (~
((subset@A)@C))) |
((subset@A)@((set_intersection2@B)@C))))=\$true)),inference(extcnf_combined,[status(esa)],[79])).
thf(106,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) |
(((set_union2@A)@B) =
B)))=\$true)),inference(extcnf_combined,[status(esa)],[81])).
thf(107,plain,((((![A:\$i,B:\$i]: ((~ (((set_difference@A)@B) =
empty_set)) | ((subset@A)@B))) & (![A:\$i,B:\$i]: ((~ ((subset@A)@B)) |
(((set_difference@A)@B) =
empty_set))))=\$true)),inference(extcnf_combined,[status(esa)],[82])).
thf(108,plain,((((![A:\$i,B:\$i]: ((~ (((set_difference@A)@B) =
empty_set)) | ((subset@A)@B))) & (![A:\$i,B:\$i]: ((~ ((subset@A)@B)) |
(((set_difference@A)@B) =
empty_set))))=\$true)),inference(copy,[status(thm)],[107])).
thf(109,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) |
(((set_union2@A)@B) =
B)))=\$true)),inference(copy,[status(thm)],[106])).
thf(110,plain,(((![A:\$i,B:\$i]:
((subset@((set_intersection2@A)@B))@A))=\$true)),inference(copy,[status(thm)],[80])).
thf(111,plain,(((![A:\$i,B:\$i,C:\$i]: (((~ ((subset@A)@B)) | (~
((subset@A)@C))) |
((subset@A)@((set_intersection2@B)@C))))=\$true)),inference(copy,[status(thm)],[105])).
thf(112,plain,(((![A:\$i,B:\$i,C:\$i]: (((~ ((subset@A)@B)) | (~
((subset@B)@C))) |
((subset@A)@C)))=\$true)),inference(copy,[status(thm)],[104])).
thf(113,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) | (![C:\$i]:
((subset@((set_intersection2@A)@C))@((set_intersection2@B)@C)))))=\$true)),inference(copy,[status(thm)],[103])).
thf(114,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) |
(((set_intersection2@A)@B) =
A)))=\$true)),inference(copy,[status(thm)],[102])).
thf(115,plain,(((![A:\$i]:
((subset@empty_set)@A))=\$true)),inference(copy,[status(thm)],[75])).
thf(116,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) | (![C:\$i]:
((subset@((set_difference@A)@C))@((set_difference@B)@C)))))=\$true)),inference(copy,[status(thm)],[101])).
thf(117,plain,(((![A:\$i,B:\$i]:
((subset@((set_difference@A)@B))@A))=\$true)),inference(copy,[status(thm)],[73])).
thf(118,plain,((((![A:\$i,B:\$i]: ((~ (((set_difference@A)@B) =
empty_set)) | ((subset@A)@B))) & (![A:\$i,B:\$i]: ((~ ((subset@A)@B)) |
(((set_difference@A)@B) =
empty_set))))=\$true)),inference(copy,[status(thm)],[100])).
thf(119,plain,((((![A:\$i,B:\$i]: (((disjoint@A)@B) |
(((in@((sK6@B)@A))@A) & ((in@((sK6@B)@A))@B)))) & (![A:\$i,B:\$i]:
((![C:\$i]: ((~ ((in@C)@A)) | (~ ((in@C)@B)))) | (~
((disjoint@A)@B)))))=\$true)),inference(copy,[status(thm)],[99])).
thf(120,plain,(((![A:\$i]: ((~ ((subset@A)@empty_set)) | (A =
empty_set)))=\$true)),inference(copy,[status(thm)],[98])).
thf(121,plain,(((![A:\$i,B:\$i]: ((~ ((subset@A)@B)) | (B =
((set_union2@A)@((set_difference@B)@A)))))=\$true)),inference(copy,[status(thm)],[97])).
thf(122,plain,((((![A:\$i,B:\$i]: (((disjoint@A)@B) |
((in@((sK5@B)@A))@((set_intersection2@A)@B)))) & (![A:\$i,B:\$i]:
((![C:\$i]: (~ ((in@C)@((set_intersection2@A)@B)))) | (~
((disjoint@A)@B)))))=\$true)),inference(copy,[status(thm)],[96])).
thf(123,plain,(((![A:\$i,B:\$i]: ((~ ((proper_subset@B)@A)) | (~
((subset@A)@B))))=\$true)),inference(copy,[status(thm)],[95])).
thf(124,plain,(((![A:\$i,B:\$i]:
((subset@A)@((set_union2@A)@B)))=\$true)),inference(copy,[status(thm)],[66])).
thf(125,plain,(((![A:\$i,B:\$i,C:\$i]: (((~ ((subset@A)@B)) | (~
((subset@C)@B))) |
((subset@((set_union2@A)@C))@B)))=\$true)),inference(copy,[status(thm)],[94])).
thf(126,plain,((((![A:\$i,B:\$i]: (((~ ((subset@A)@B)) | (~
((subset@B)@A))) | (A = B))) & ((![A:\$i,B:\$i]: ((~ (A = B)) |
((subset@A)@B))) & (![A:\$i,B:\$i]: ((~ (A = B)) |
((subset@B)@A)))))=\$true)),inference(copy,[status(thm)],[93])).
thf(127,plain,((((![A:\$i,B:\$i]: ((((in@((sK4@B)@A))@A) & (~
((in@((sK4@B)@A))@B))) | ((subset@A)@B))) & (![A:\$i,B:\$i]: ((~
((subset@A)@B)) | (![C:\$i]: ((~ ((in@C)@A)) |
((in@C)@B))))))=\$true)),inference(copy,[status(thm)],[92])).
thf(128,plain,((((![A:\$i,B:\$i]: ((~ (((set_intersection2@A)@B) =
empty_set)) | ((disjoint@A)@B))) & (![A:\$i,B:\$i]: ((~
((disjoint@A)@B)) | (((set_intersection2@A)@B) =
empty_set))))=\$true)),inference(copy,[status(thm)],[91])).
thf(129,plain,((((![A:\$i,B:\$i]: (((A = B) | (~ ((subset@A)@B))) |
((proper_subset@A)@B))) & ((![A:\$i,B:\$i]: ((~ ((proper_subset@A)@B)) |
(~ (A = B)))) & (![A:\$i,B:\$i]: ((~ ((proper_subset@A)@B)) |
((subset@A)@B)))))=\$true)),inference(copy,[status(thm)],[90])).
thf(130,plain,(((![A:\$i]:
((subset@A)@A))=\$true)),inference(copy,[status(thm)],[89])).
thf(131,plain,(((![A:\$i,B:\$i]: ((~ ((disjoint@A)@B)) |
((disjoint@B)@A)))=\$true)),inference(copy,[status(thm)],[88])).
thf(132,plain,((((disjoint@sK2)@sK3)=\$true)),inference(copy,[status(thm)],[85])).
thf(133,plain,((((subset@sK1)@sK2)=\$true)),inference(copy,[status(thm)],[84])).
thf(134,plain,(((~
((disjoint@sK1)@sK3))=\$true)),inference(copy,[status(thm)],[87])).
thf(135,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: ((~
(((set_difference@SX0)@SX1) = empty_set)) | ((subset@SX0)@SX1)))) | (~
(![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(((set_difference@SX0)@SX1) =
empty_set))))))=\$true)),inference(unfold_def,[status(thm)],[108])).
thf(136,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: ((~
(((set_difference@SX0)@SX1) = empty_set)) | ((subset@SX0)@SX1)))) | (~
(![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(((set_difference@SX0)@SX1) =
empty_set))))))=\$true)),inference(unfold_def,[status(thm)],[118])).
thf(137,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: (((disjoint@SX0)@SX1) | (~
((~ ((in@((sK6@SX1)@SX0))@SX0)) | (~ ((in@((sK6@SX1)@SX0))@SX1)))))))
| (~ (![SX0:\$i,SX1:\$i]: ((![SX2:\$i]: ((~ ((in@SX2)@SX0)) | (~
((in@SX2)@SX1)))) | (~
((disjoint@SX0)@SX1)))))))=\$true)),inference(unfold_def,[status(thm)],[119])).
thf(138,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: (((disjoint@SX0)@SX1) |
((in@((sK5@SX1)@SX0))@((set_intersection2@SX0)@SX1))))) | (~
(![SX0:\$i,SX1:\$i]: ((![SX2:\$i]: (~
((in@SX2)@((set_intersection2@SX0)@SX1)))) | (~
((disjoint@SX0)@SX1)))))))=\$true)),inference(unfold_def,[status(thm)],[122])).
thf(139,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: (((~ ((subset@SX0)@SX1)) |
(~ ((subset@SX1)@SX0))) | (SX0 = SX1)))) | (~ (~ ((~
(![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) | ((subset@SX0)@SX1)))) | (~
(![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX1)@SX0)))))))))=\$true)),inference(unfold_def,[status(thm)],[126])).
thf(140,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: ((~ ((~
((in@((sK4@SX1)@SX0))@SX0)) | (~ (~ ((in@((sK4@SX1)@SX0))@SX1))))) |
((subset@SX0)@SX1)))) | (~ (![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1))
| (![SX2:\$i]: ((~ ((in@SX2)@SX0)) |
((in@SX2)@SX1))))))))=\$true)),inference(unfold_def,[status(thm)],[127])).
thf(141,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: ((~
(((set_intersection2@SX0)@SX1) = empty_set)) | ((disjoint@SX0)@SX1))))
| (~ (![SX0:\$i,SX1:\$i]: ((~ ((disjoint@SX0)@SX1)) |
(((set_intersection2@SX0)@SX1) =
empty_set))))))=\$true)),inference(unfold_def,[status(thm)],[128])).
thf(142,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: (((SX0 = SX1) | (~
((subset@SX0)@SX1))) | ((proper_subset@SX0)@SX1)))) | (~ (~ ((~
(![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1)) | (~ (SX0 = SX1)))))
| (~ (![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1)) |
((subset@SX0)@SX1)))))))))=\$true)),inference(unfold_def,[status(thm)],[129])).
thf(143,plain,(![SV1:\$i]: (((![SY702:\$i]: ((~ ((subset@SV1)@SY702)) |
(((set_union2@SV1)@SY702) =
SY702)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[109])).
thf(144,plain,(![SV2:\$i]: (((![SY703:\$i]:
((subset@((set_intersection2@SV2)@SY703))@SV2))=\$true))),inference(extcnf_forall_pos,[status(thm)],[110])).
thf(145,plain,(![SV3:\$i]: (((![SY704:\$i,SY705:\$i]: (((~
((subset@SV3)@SY704)) | (~ ((subset@SV3)@SY705))) |
((subset@SV3)@((set_intersection2@SY704)@SY705))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[111])).
thf(146,plain,(![SV4:\$i]: (((![SY706:\$i,SY707:\$i]: (((~
((subset@SV4)@SY706)) | (~ ((subset@SY706)@SY707))) |
((subset@SV4)@SY707)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[112])).
thf(147,plain,(![SV5:\$i]: (((![SY708:\$i]: ((~ ((subset@SV5)@SY708)) |
(![SY709:\$i]: ((subset@((set_intersection2@SV5)@SY709))@((set_intersection2@SY708)@SY709)))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[113])).
thf(148,plain,(![SV6:\$i]: (((![SY710:\$i]: ((~ ((subset@SV6)@SY710)) |
(((set_intersection2@SV6)@SY710) =
SV6)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[114])).
thf(149,plain,(![SV7:\$i]:
((((subset@empty_set)@SV7)=\$true))),inference(extcnf_forall_pos,[status(thm)],[115])).
thf(150,plain,(![SV8:\$i]: (((![SY711:\$i]: ((~ ((subset@SV8)@SY711)) |
(![SY712:\$i]: ((subset@((set_difference@SV8)@SY712))@((set_difference@SY711)@SY712)))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[116])).
thf(151,plain,(![SV9:\$i]: (((![SY713:\$i]:
((subset@((set_difference@SV9)@SY713))@SV9))=\$true))),inference(extcnf_forall_pos,[status(thm)],[117])).
thf(152,plain,(![SV10:\$i]: ((((~ ((subset@SV10)@empty_set)) | (SV10 =
empty_set))=\$true))),inference(extcnf_forall_pos,[status(thm)],[120])).
thf(153,plain,(![SV11:\$i]: (((![SY714:\$i]: ((~ ((subset@SV11)@SY714))
| (SY714 = ((set_union2@SV11)@((set_difference@SY714)@SV11)))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[121])).
thf(154,plain,(![SV12:\$i]: (((![SY715:\$i]: ((~
((proper_subset@SY715)@SV12)) | (~
((subset@SV12)@SY715))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[123])).
thf(155,plain,(![SV13:\$i]: (((![SY716:\$i]:
((subset@SV13)@((set_union2@SV13)@SY716)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[124])).
thf(156,plain,(![SV14:\$i]: (((![SY717:\$i,SY718:\$i]: (((~
((subset@SV14)@SY717)) | (~ ((subset@SY718)@SY717))) |
((subset@((set_union2@SV14)@SY718))@SY717)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[125])).
thf(157,plain,(![SV15:\$i]:
((((subset@SV15)@SV15)=\$true))),inference(extcnf_forall_pos,[status(thm)],[130])).
thf(158,plain,(![SV16:\$i]: (((![SY719:\$i]: ((~
((disjoint@SV16)@SY719)) |
((disjoint@SY719)@SV16)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[131])).
thf(159,plain,((((disjoint@sK1)@sK3)=\$false)),inference(extcnf_not_pos,[status(thm)],[134])).
thf(160,plain,((((~ (![SX0:\$i,SX1:\$i]: ((~
(((set_difference@SX0)@SX1) = empty_set)) | ((subset@SX0)@SX1)))) | (~
(![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(((set_difference@SX0)@SX1) =
empty_set)))))=\$false)),inference(extcnf_not_pos,[status(thm)],[135])).
thf(161,plain,((((~ (![SX0:\$i,SX1:\$i]: ((~
(((set_difference@SX0)@SX1) = empty_set)) | ((subset@SX0)@SX1)))) | (~
(![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(((set_difference@SX0)@SX1) =
empty_set)))))=\$false)),inference(extcnf_not_pos,[status(thm)],[136])).
thf(162,plain,((((~ (![SX0:\$i,SX1:\$i]: (((disjoint@SX0)@SX1) | (~ ((~
((in@((sK6@SX1)@SX0))@SX0)) | (~ ((in@((sK6@SX1)@SX0))@SX1))))))) | (~
(![SX0:\$i,SX1:\$i]: ((![SX2:\$i]: ((~ ((in@SX2)@SX0)) | (~
((in@SX2)@SX1)))) | (~
((disjoint@SX0)@SX1))))))=\$false)),inference(extcnf_not_pos,[status(thm)],[137])).
thf(163,plain,((((~ (![SX0:\$i,SX1:\$i]: (((disjoint@SX0)@SX1) |
((in@((sK5@SX1)@SX0))@((set_intersection2@SX0)@SX1))))) | (~
(![SX0:\$i,SX1:\$i]: ((![SX2:\$i]: (~
((in@SX2)@((set_intersection2@SX0)@SX1)))) | (~
((disjoint@SX0)@SX1))))))=\$false)),inference(extcnf_not_pos,[status(thm)],[138])).
thf(164,plain,((((~ (![SX0:\$i,SX1:\$i]: (((~ ((subset@SX0)@SX1)) | (~
((subset@SX1)@SX0))) | (SX0 = SX1)))) | (~ (~ ((~ (![SX0:\$i,SX1:\$i]:
((~ (SX0 = SX1)) | ((subset@SX0)@SX1)))) | (~ (![SX0:\$i,SX1:\$i]: ((~
(SX0 = SX1)) | ((subset@SX1)@SX0))))))))=\$false)),inference(extcnf_not_pos,[status(thm)],[139])).
thf(165,plain,((((~ (![SX0:\$i,SX1:\$i]: ((~ ((~
((in@((sK4@SX1)@SX0))@SX0)) | (~ (~ ((in@((sK4@SX1)@SX0))@SX1))))) |
((subset@SX0)@SX1)))) | (~ (![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1))
| (![SX2:\$i]: ((~ ((in@SX2)@SX0)) |
((in@SX2)@SX1)))))))=\$false)),inference(extcnf_not_pos,[status(thm)],[140])).
thf(166,plain,((((~ (![SX0:\$i,SX1:\$i]: ((~
(((set_intersection2@SX0)@SX1) = empty_set)) | ((disjoint@SX0)@SX1))))
| (~ (![SX0:\$i,SX1:\$i]: ((~ ((disjoint@SX0)@SX1)) |
(((set_intersection2@SX0)@SX1) =
empty_set)))))=\$false)),inference(extcnf_not_pos,[status(thm)],[141])).
thf(167,plain,((((~ (![SX0:\$i,SX1:\$i]: (((SX0 = SX1) | (~
((subset@SX0)@SX1))) | ((proper_subset@SX0)@SX1)))) | (~ (~ ((~
(![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1)) | (~ (SX0 = SX1)))))
| (~ (![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1)) |
((subset@SX0)@SX1))))))))=\$false)),inference(extcnf_not_pos,[status(thm)],[142])).
thf(168,plain,(![SV17:\$i,SV1:\$i]: ((((~ ((subset@SV1)@SV17)) |
(((set_union2@SV1)@SV17) =
SV17))=\$true))),inference(extcnf_forall_pos,[status(thm)],[143])).
thf(169,plain,(![SV18:\$i,SV2:\$i]:
((((subset@((set_intersection2@SV2)@SV18))@SV2)=\$true))),inference(extcnf_forall_pos,[status(thm)],[144])).
thf(170,plain,(![SV19:\$i,SV3:\$i]: (((![SY720:\$i]: (((~
((subset@SV3)@SV19)) | (~ ((subset@SV3)@SY720))) |
((subset@SV3)@((set_intersection2@SV19)@SY720))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[145])).
thf(171,plain,(![SV20:\$i,SV4:\$i]: (((![SY721:\$i]: (((~
((subset@SV4)@SV20)) | (~ ((subset@SV20)@SY721))) |
((subset@SV4)@SY721)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[146])).
thf(172,plain,(![SV21:\$i,SV5:\$i]: ((((~ ((subset@SV5)@SV21)) |
(![SY722:\$i]: ((subset@((set_intersection2@SV5)@SY722))@((set_intersection2@SV21)@SY722))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[147])).
thf(173,plain,(![SV22:\$i,SV6:\$i]: ((((~ ((subset@SV6)@SV22)) |
(((set_intersection2@SV6)@SV22) =
SV6))=\$true))),inference(extcnf_forall_pos,[status(thm)],[148])).
thf(174,plain,(![SV23:\$i,SV8:\$i]: ((((~ ((subset@SV8)@SV23)) |
(![SY723:\$i]: ((subset@((set_difference@SV8)@SY723))@((set_difference@SV23)@SY723))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[150])).
thf(175,plain,(![SV24:\$i,SV9:\$i]:
((((subset@((set_difference@SV9)@SV24))@SV9)=\$true))),inference(extcnf_forall_pos,[status(thm)],[151])).
thf(176,plain,(![SV10:\$i]: (((~ ((subset@SV10)@empty_set))=\$true) |
((SV10 = empty_set)=\$true))),inference(extcnf_or_pos,[status(thm)],[152])).
thf(177,plain,(![SV25:\$i,SV11:\$i]: ((((~ ((subset@SV11)@SV25)) |
(SV25 = ((set_union2@SV11)@((set_difference@SV25)@SV11))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[153])).
thf(178,plain,(![SV12:\$i,SV26:\$i]: ((((~ ((proper_subset@SV26)@SV12))
| (~ ((subset@SV12)@SV26)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[154])).
thf(179,plain,(![SV27:\$i,SV13:\$i]:
((((subset@SV13)@((set_union2@SV13)@SV27))=\$true))),inference(extcnf_forall_pos,[status(thm)],[155])).
thf(180,plain,(![SV28:\$i,SV14:\$i]: (((![SY724:\$i]: (((~
((subset@SV14)@SV28)) | (~ ((subset@SY724)@SV28))) |
((subset@((set_union2@SV14)@SY724))@SV28)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[156])).
thf(181,plain,(![SV29:\$i,SV16:\$i]: ((((~ ((disjoint@SV16)@SV29)) |
((disjoint@SV29)@SV16))=\$true))),inference(extcnf_forall_pos,[status(thm)],[158])).
thf(182,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ (((set_difference@SX0)@SX1)
= empty_set)) |
((subset@SX0)@SX1))))=\$false)),inference(extcnf_or_neg,[status(thm)],[160])).
thf(183,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(((set_difference@SX0)@SX1) =
empty_set))))=\$false)),inference(extcnf_or_neg,[status(thm)],[160])).
thf(184,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ (((set_difference@SX0)@SX1)
= empty_set)) |
((subset@SX0)@SX1))))=\$false)),inference(extcnf_or_neg,[status(thm)],[161])).
thf(185,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(((set_difference@SX0)@SX1) =
empty_set))))=\$false)),inference(extcnf_or_neg,[status(thm)],[161])).
thf(186,plain,(((~ (![SX0:\$i,SX1:\$i]: (((disjoint@SX0)@SX1) | (~ ((~
((in@((sK6@SX1)@SX0))@SX0)) | (~
((in@((sK6@SX1)@SX0))@SX1)))))))=\$false)),inference(extcnf_or_neg,[status(thm)],[162])).
thf(187,plain,(((~ (![SX0:\$i,SX1:\$i]: ((![SX2:\$i]: ((~
((in@SX2)@SX0)) | (~ ((in@SX2)@SX1)))) | (~
((disjoint@SX0)@SX1)))))=\$false)),inference(extcnf_or_neg,[status(thm)],[162])).
thf(188,plain,(((~ (![SX0:\$i,SX1:\$i]: (((disjoint@SX0)@SX1) |
((in@((sK5@SX1)@SX0))@((set_intersection2@SX0)@SX1)))))=\$false)),inference(extcnf_or_neg,[status(thm)],[163])).
thf(189,plain,(((~ (![SX0:\$i,SX1:\$i]: ((![SX2:\$i]: (~
((in@SX2)@((set_intersection2@SX0)@SX1)))) | (~
((disjoint@SX0)@SX1)))))=\$false)),inference(extcnf_or_neg,[status(thm)],[163])).
thf(190,plain,(((~ (![SX0:\$i,SX1:\$i]: (((~ ((subset@SX0)@SX1)) | (~
((subset@SX1)@SX0))) | (SX0 =
SX1))))=\$false)),inference(extcnf_or_neg,[status(thm)],[164])).
thf(191,plain,(((~ (~ ((~ (![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX0)@SX1)))) | (~ (![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX1)@SX0)))))))=\$false)),inference(extcnf_or_neg,[status(thm)],[164])).
thf(192,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ ((~
((in@((sK4@SX1)@SX0))@SX0)) | (~ (~ ((in@((sK4@SX1)@SX0))@SX1))))) |
((subset@SX0)@SX1))))=\$false)),inference(extcnf_or_neg,[status(thm)],[165])).
thf(193,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(![SX2:\$i]: ((~ ((in@SX2)@SX0)) |
((in@SX2)@SX1))))))=\$false)),inference(extcnf_or_neg,[status(thm)],[165])).
thf(194,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~
(((set_intersection2@SX0)@SX1) = empty_set)) |
((disjoint@SX0)@SX1))))=\$false)),inference(extcnf_or_neg,[status(thm)],[166])).
thf(195,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ ((disjoint@SX0)@SX1)) |
(((set_intersection2@SX0)@SX1) =
empty_set))))=\$false)),inference(extcnf_or_neg,[status(thm)],[166])).
thf(196,plain,(((~ (![SX0:\$i,SX1:\$i]: (((SX0 = SX1) | (~
((subset@SX0)@SX1))) |
((proper_subset@SX0)@SX1))))=\$false)),inference(extcnf_or_neg,[status(thm)],[167])).
thf(197,plain,(((~ (~ ((~ (![SX0:\$i,SX1:\$i]: ((~
((proper_subset@SX0)@SX1)) | (~ (SX0 = SX1))))) | (~
(![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1)) |
((subset@SX0)@SX1)))))))=\$false)),inference(extcnf_or_neg,[status(thm)],[167])).
thf(198,plain,(![SV17:\$i,SV1:\$i]: (((~ ((subset@SV1)@SV17))=\$true) |
((((set_union2@SV1)@SV17) =
SV17)=\$true))),inference(extcnf_or_pos,[status(thm)],[168])).
thf(199,plain,(![SV30:\$i,SV19:\$i,SV3:\$i]: (((((~ ((subset@SV3)@SV19))
| (~ ((subset@SV3)@SV30))) |
((subset@SV3)@((set_intersection2@SV19)@SV30)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[170])).
thf(200,plain,(![SV31:\$i,SV20:\$i,SV4:\$i]: (((((~ ((subset@SV4)@SV20))
| (~ ((subset@SV20)@SV31))) |
((subset@SV4)@SV31))=\$true))),inference(extcnf_forall_pos,[status(thm)],[171])).
thf(201,plain,(![SV21:\$i,SV5:\$i]: (((~ ((subset@SV5)@SV21))=\$true) |
((![SY722:\$i]: ((subset@((set_intersection2@SV5)@SY722))@((set_intersection2@SV21)@SY722)))=\$true))),inference(extcnf_or_pos,[status(thm)],[172])).
thf(202,plain,(![SV22:\$i,SV6:\$i]: (((~ ((subset@SV6)@SV22))=\$true) |
((((set_intersection2@SV6)@SV22) =
SV6)=\$true))),inference(extcnf_or_pos,[status(thm)],[173])).
thf(203,plain,(![SV23:\$i,SV8:\$i]: (((~ ((subset@SV8)@SV23))=\$true) |
((![SY723:\$i]: ((subset@((set_difference@SV8)@SY723))@((set_difference@SV23)@SY723)))=\$true))),inference(extcnf_or_pos,[status(thm)],[174])).
thf(204,plain,(![SV10:\$i]: ((((subset@SV10)@empty_set)=\$false) |
((SV10 = empty_set)=\$true))),inference(extcnf_not_pos,[status(thm)],[176])).
thf(205,plain,(![SV25:\$i,SV11:\$i]: (((~ ((subset@SV11)@SV25))=\$true)
| ((SV25 = ((set_union2@SV11)@((set_difference@SV25)@SV11)))=\$true))),inference(extcnf_or_pos,[status(thm)],[177])).
thf(206,plain,(![SV12:\$i,SV26:\$i]: (((~
((proper_subset@SV26)@SV12))=\$true) | ((~
((subset@SV12)@SV26))=\$true))),inference(extcnf_or_pos,[status(thm)],[178])).
thf(207,plain,(![SV32:\$i,SV28:\$i,SV14:\$i]: (((((~
((subset@SV14)@SV28)) | (~ ((subset@SV32)@SV28))) |
((subset@((set_union2@SV14)@SV32))@SV28))=\$true))),inference(extcnf_forall_pos,[status(thm)],[180])).
thf(208,plain,(![SV29:\$i,SV16:\$i]: (((~
((disjoint@SV16)@SV29))=\$true) |
(((disjoint@SV29)@SV16)=\$true))),inference(extcnf_or_pos,[status(thm)],[181])).
thf(209,plain,(((![SX0:\$i,SX1:\$i]: ((~ (((set_difference@SX0)@SX1) =
empty_set)) | ((subset@SX0)@SX1)))=\$true)),inference(extcnf_not_neg,[status(thm)],[182])).
thf(210,plain,(((![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(((set_difference@SX0)@SX1) =
empty_set)))=\$true)),inference(extcnf_not_neg,[status(thm)],[183])).
thf(211,plain,(((![SX0:\$i,SX1:\$i]: ((~ (((set_difference@SX0)@SX1) =
empty_set)) | ((subset@SX0)@SX1)))=\$true)),inference(extcnf_not_neg,[status(thm)],[184])).
thf(212,plain,(((![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(((set_difference@SX0)@SX1) =
empty_set)))=\$true)),inference(extcnf_not_neg,[status(thm)],[185])).
thf(213,plain,(((![SX0:\$i,SX1:\$i]: (((disjoint@SX0)@SX1) | (~ ((~
((in@((sK6@SX1)@SX0))@SX0)) | (~
((in@((sK6@SX1)@SX0))@SX1))))))=\$true)),inference(extcnf_not_neg,[status(thm)],[186])).
thf(214,plain,(((![SX0:\$i,SX1:\$i]: ((![SX2:\$i]: ((~ ((in@SX2)@SX0)) |
(~ ((in@SX2)@SX1)))) | (~
((disjoint@SX0)@SX1))))=\$true)),inference(extcnf_not_neg,[status(thm)],[187])).
thf(215,plain,(((![SX0:\$i,SX1:\$i]: (((disjoint@SX0)@SX1) |
((in@((sK5@SX1)@SX0))@((set_intersection2@SX0)@SX1))))=\$true)),inference(extcnf_not_neg,[status(thm)],[188])).
thf(216,plain,(((![SX0:\$i,SX1:\$i]: ((![SX2:\$i]: (~
((in@SX2)@((set_intersection2@SX0)@SX1)))) | (~
((disjoint@SX0)@SX1))))=\$true)),inference(extcnf_not_neg,[status(thm)],[189])).
thf(217,plain,(((![SX0:\$i,SX1:\$i]: (((~ ((subset@SX0)@SX1)) | (~
((subset@SX1)@SX0))) | (SX0 =
SX1)))=\$true)),inference(extcnf_not_neg,[status(thm)],[190])).
thf(218,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX0)@SX1)))) | (~ (![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX1)@SX0))))))=\$true)),inference(extcnf_not_neg,[status(thm)],[191])).
thf(219,plain,(((![SX0:\$i,SX1:\$i]: ((~ ((~
((in@((sK4@SX1)@SX0))@SX0)) | (~ (~ ((in@((sK4@SX1)@SX0))@SX1))))) |
((subset@SX0)@SX1)))=\$true)),inference(extcnf_not_neg,[status(thm)],[192])).
thf(220,plain,(((![SX0:\$i,SX1:\$i]: ((~ ((subset@SX0)@SX1)) |
(![SX2:\$i]: ((~ ((in@SX2)@SX0)) |
((in@SX2)@SX1)))))=\$true)),inference(extcnf_not_neg,[status(thm)],[193])).
thf(221,plain,(((![SX0:\$i,SX1:\$i]: ((~ (((set_intersection2@SX0)@SX1)
= empty_set)) |
((disjoint@SX0)@SX1)))=\$true)),inference(extcnf_not_neg,[status(thm)],[194])).
thf(222,plain,(((![SX0:\$i,SX1:\$i]: ((~ ((disjoint@SX0)@SX1)) |
(((set_intersection2@SX0)@SX1) =
empty_set)))=\$true)),inference(extcnf_not_neg,[status(thm)],[195])).
thf(223,plain,(((![SX0:\$i,SX1:\$i]: (((SX0 = SX1) | (~
((subset@SX0)@SX1))) |
((proper_subset@SX0)@SX1)))=\$true)),inference(extcnf_not_neg,[status(thm)],[196])).
thf(224,plain,(((~ ((~ (![SX0:\$i,SX1:\$i]: ((~
((proper_subset@SX0)@SX1)) | (~ (SX0 = SX1))))) | (~
(![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1)) |
((subset@SX0)@SX1))))))=\$true)),inference(extcnf_not_neg,[status(thm)],[197])).
thf(225,plain,(![SV17:\$i,SV1:\$i]: ((((subset@SV1)@SV17)=\$false) |
((((set_union2@SV1)@SV17) =
SV17)=\$true))),inference(extcnf_not_pos,[status(thm)],[198])).
thf(226,plain,(![SV30:\$i,SV19:\$i,SV3:\$i]: ((((~ ((subset@SV3)@SV19))
| (~ ((subset@SV3)@SV30)))=\$true) |
(((subset@SV3)@((set_intersection2@SV19)@SV30))=\$true))),inference(extcnf_or_pos,[status(thm)],[199])).
thf(227,plain,(![SV31:\$i,SV20:\$i,SV4:\$i]: ((((~ ((subset@SV4)@SV20))
| (~ ((subset@SV20)@SV31)))=\$true) |
(((subset@SV4)@SV31)=\$true))),inference(extcnf_or_pos,[status(thm)],[200])).
thf(228,plain,(![SV21:\$i,SV33:\$i,SV5:\$i]:
((((subset@((set_intersection2@SV5)@SV33))@((set_intersection2@SV21)@SV33))=\$true)
| ((~ ((subset@SV5)@SV21))=\$true))),inference(extcnf_forall_pos,[status(thm)],[201])).
thf(229,plain,(![SV22:\$i,SV6:\$i]: ((((subset@SV6)@SV22)=\$false) |
((((set_intersection2@SV6)@SV22) =
SV6)=\$true))),inference(extcnf_not_pos,[status(thm)],[202])).
thf(230,plain,(![SV23:\$i,SV34:\$i,SV8:\$i]:
((((subset@((set_difference@SV8)@SV34))@((set_difference@SV23)@SV34))=\$true)
| ((~ ((subset@SV8)@SV23))=\$true))),inference(extcnf_forall_pos,[status(thm)],[203])).
thf(231,plain,(![SV25:\$i,SV11:\$i]: ((((subset@SV11)@SV25)=\$false) |
((SV25 = ((set_union2@SV11)@((set_difference@SV25)@SV11)))=\$true))),inference(extcnf_not_pos,[status(thm)],[205])).
thf(232,plain,(![SV12:\$i,SV26:\$i]:
((((proper_subset@SV26)@SV12)=\$false) | ((~
((subset@SV12)@SV26))=\$true))),inference(extcnf_not_pos,[status(thm)],[206])).
thf(233,plain,(![SV32:\$i,SV28:\$i,SV14:\$i]: ((((~
((subset@SV14)@SV28)) | (~ ((subset@SV32)@SV28)))=\$true) |
(((subset@((set_union2@SV14)@SV32))@SV28)=\$true))),inference(extcnf_or_pos,[status(thm)],[207])).
thf(234,plain,(![SV29:\$i,SV16:\$i]: ((((disjoint@SV16)@SV29)=\$false) |
(((disjoint@SV29)@SV16)=\$true))),inference(extcnf_not_pos,[status(thm)],[208])).
thf(235,plain,(![SV35:\$i]: (((![SY725:\$i]: ((~
(((set_difference@SV35)@SY725) = empty_set)) |
((subset@SV35)@SY725)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[209])).
thf(236,plain,(![SV36:\$i]: (((![SY726:\$i]: ((~ ((subset@SV36)@SY726))
| (((set_difference@SV36)@SY726) =
empty_set)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[210])).
thf(237,plain,(![SV37:\$i]: (((![SY727:\$i]: ((~
(((set_difference@SV37)@SY727) = empty_set)) |
((subset@SV37)@SY727)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[211])).
thf(238,plain,(![SV38:\$i]: (((![SY728:\$i]: ((~ ((subset@SV38)@SY728))
| (((set_difference@SV38)@SY728) =
empty_set)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[212])).
thf(239,plain,(![SV39:\$i]: (((![SY729:\$i]: (((disjoint@SV39)@SY729) |
(~ ((~ ((in@((sK6@SY729)@SV39))@SV39)) | (~
((in@((sK6@SY729)@SV39))@SY729))))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[213])).
thf(240,plain,(![SV40:\$i]: (((![SY730:\$i]: ((![SY731:\$i]: ((~
((in@SY731)@SV40)) | (~ ((in@SY731)@SY730)))) | (~
((disjoint@SV40)@SY730))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[214])).
thf(241,plain,(![SV41:\$i]: (((![SY732:\$i]: (((disjoint@SV41)@SY732) |
((in@((sK5@SY732)@SV41))@((set_intersection2@SV41)@SY732))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[215])).
thf(242,plain,(![SV42:\$i]: (((![SY733:\$i]: ((![SY734:\$i]: (~
((in@SY734)@((set_intersection2@SV42)@SY733)))) | (~
((disjoint@SV42)@SY733))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[216])).
thf(243,plain,(![SV43:\$i]: (((![SY735:\$i]: (((~
((subset@SV43)@SY735)) | (~ ((subset@SY735)@SV43))) | (SV43 =
SY735)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[217])).
thf(244,plain,((((~ (![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX0)@SX1)))) | (~ (![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX1)@SX0)))))=\$false)),inference(extcnf_not_pos,[status(thm)],[218])).
thf(245,plain,(![SV44:\$i]: (((![SY736:\$i]: ((~ ((~
((in@((sK4@SY736)@SV44))@SV44)) | (~ (~
((in@((sK4@SY736)@SV44))@SY736))))) |
((subset@SV44)@SY736)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[219])).
thf(246,plain,(![SV45:\$i]: (((![SY737:\$i]: ((~ ((subset@SV45)@SY737))
| (![SY738:\$i]: ((~ ((in@SY738)@SV45)) |
((in@SY738)@SY737)))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[220])).
thf(247,plain,(![SV46:\$i]: (((![SY739:\$i]: ((~
(((set_intersection2@SV46)@SY739) = empty_set)) |
((disjoint@SV46)@SY739)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[221])).
thf(248,plain,(![SV47:\$i]: (((![SY740:\$i]: ((~
((disjoint@SV47)@SY740)) | (((set_intersection2@SV47)@SY740) =
empty_set)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[222])).
thf(249,plain,(![SV48:\$i]: (((![SY741:\$i]: (((SV48 = SY741) | (~
((subset@SV48)@SY741))) |
((proper_subset@SV48)@SY741)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[223])).
thf(250,plain,((((~ (![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1))
| (~ (SX0 = SX1))))) | (~ (![SX0:\$i,SX1:\$i]: ((~
((proper_subset@SX0)@SX1)) |
((subset@SX0)@SX1)))))=\$false)),inference(extcnf_not_pos,[status(thm)],[224])).
thf(251,plain,(![SV30:\$i,SV19:\$i,SV3:\$i]: (((~
((subset@SV3)@SV19))=\$true) | ((~ ((subset@SV3)@SV30))=\$true) |
(((subset@SV3)@((set_intersection2@SV19)@SV30))=\$true))),inference(extcnf_or_pos,[status(thm)],[226])).
thf(252,plain,(![SV31:\$i,SV20:\$i,SV4:\$i]: (((~
((subset@SV4)@SV20))=\$true) | ((~ ((subset@SV20)@SV31))=\$true) |
(((subset@SV4)@SV31)=\$true))),inference(extcnf_or_pos,[status(thm)],[227])).
thf(253,plain,(![SV33:\$i,SV21:\$i,SV5:\$i]:
((((subset@SV5)@SV21)=\$false) |
(((subset@((set_intersection2@SV5)@SV33))@((set_intersection2@SV21)@SV33))=\$true))),inference(extcnf_not_pos,[status(thm)],[228])).
thf(254,plain,(![SV34:\$i,SV23:\$i,SV8:\$i]:
((((subset@SV8)@SV23)=\$false) |
(((subset@((set_difference@SV8)@SV34))@((set_difference@SV23)@SV34))=\$true))),inference(extcnf_not_pos,[status(thm)],[230])).
thf(255,plain,(![SV26:\$i,SV12:\$i]: ((((subset@SV12)@SV26)=\$false) |
(((proper_subset@SV26)@SV12)=\$false))),inference(extcnf_not_pos,[status(thm)],[232])).
thf(256,plain,(![SV32:\$i,SV28:\$i,SV14:\$i]: (((~
((subset@SV14)@SV28))=\$true) | ((~ ((subset@SV32)@SV28))=\$true) |
(((subset@((set_union2@SV14)@SV32))@SV28)=\$true))),inference(extcnf_or_pos,[status(thm)],[233])).
thf(257,plain,(![SV49:\$i,SV35:\$i]: ((((~
(((set_difference@SV35)@SV49) = empty_set)) |
((subset@SV35)@SV49))=\$true))),inference(extcnf_forall_pos,[status(thm)],[235])).
thf(258,plain,(![SV50:\$i,SV36:\$i]: ((((~ ((subset@SV36)@SV50)) |
(((set_difference@SV36)@SV50) =
empty_set))=\$true))),inference(extcnf_forall_pos,[status(thm)],[236])).
thf(259,plain,(![SV51:\$i,SV37:\$i]: ((((~
(((set_difference@SV37)@SV51) = empty_set)) |
((subset@SV37)@SV51))=\$true))),inference(extcnf_forall_pos,[status(thm)],[237])).
thf(260,plain,(![SV52:\$i,SV38:\$i]: ((((~ ((subset@SV38)@SV52)) |
(((set_difference@SV38)@SV52) =
empty_set))=\$true))),inference(extcnf_forall_pos,[status(thm)],[238])).
thf(261,plain,(![SV53:\$i,SV39:\$i]: (((((disjoint@SV39)@SV53) | (~ ((~
((in@((sK6@SV53)@SV39))@SV39)) | (~
((in@((sK6@SV53)@SV39))@SV53)))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[239])).
thf(262,plain,(![SV54:\$i,SV40:\$i]: ((((![SY742:\$i]: ((~
((in@SY742)@SV40)) | (~ ((in@SY742)@SV54)))) | (~
((disjoint@SV40)@SV54)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[240])).
thf(263,plain,(![SV55:\$i,SV41:\$i]: (((((disjoint@SV41)@SV55) |
((in@((sK5@SV55)@SV41))@((set_intersection2@SV41)@SV55)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[241])).
thf(264,plain,(![SV56:\$i,SV42:\$i]: ((((![SY743:\$i]: (~
((in@SY743)@((set_intersection2@SV42)@SV56)))) | (~
((disjoint@SV42)@SV56)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[242])).
thf(265,plain,(![SV57:\$i,SV43:\$i]: (((((~ ((subset@SV43)@SV57)) | (~
((subset@SV57)@SV43))) | (SV43 =
SV57))=\$true))),inference(extcnf_forall_pos,[status(thm)],[243])).
thf(266,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX0)@SX1))))=\$false)),inference(extcnf_or_neg,[status(thm)],[244])).
thf(267,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX1)@SX0))))=\$false)),inference(extcnf_or_neg,[status(thm)],[244])).
thf(268,plain,(![SV44:\$i,SV58:\$i]: ((((~ ((~
((in@((sK4@SV58)@SV44))@SV44)) | (~ (~
((in@((sK4@SV58)@SV44))@SV58))))) |
((subset@SV44)@SV58))=\$true))),inference(extcnf_forall_pos,[status(thm)],[245])).
thf(269,plain,(![SV59:\$i,SV45:\$i]: ((((~ ((subset@SV45)@SV59)) |
(![SY744:\$i]: ((~ ((in@SY744)@SV45)) |
((in@SY744)@SV59))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[246])).
thf(270,plain,(![SV60:\$i,SV46:\$i]: ((((~
(((set_intersection2@SV46)@SV60) = empty_set)) |
((disjoint@SV46)@SV60))=\$true))),inference(extcnf_forall_pos,[status(thm)],[247])).
thf(271,plain,(![SV61:\$i,SV47:\$i]: ((((~ ((disjoint@SV47)@SV61)) |
(((set_intersection2@SV47)@SV61) =
empty_set))=\$true))),inference(extcnf_forall_pos,[status(thm)],[248])).
thf(272,plain,(![SV62:\$i,SV48:\$i]: (((((SV48 = SV62) | (~
((subset@SV48)@SV62))) |
((proper_subset@SV48)@SV62))=\$true))),inference(extcnf_forall_pos,[status(thm)],[249])).
thf(273,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1))
| (~ (SX0 = SX1)))))=\$false)),inference(extcnf_or_neg,[status(thm)],[250])).
thf(274,plain,(((~ (![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1))
| ((subset@SX0)@SX1))))=\$false)),inference(extcnf_or_neg,[status(thm)],[250])).
thf(275,plain,(![SV30:\$i,SV19:\$i,SV3:\$i]:
((((subset@SV3)@SV19)=\$false) | ((~ ((subset@SV3)@SV30))=\$true) |
(((subset@SV3)@((set_intersection2@SV19)@SV30))=\$true))),inference(extcnf_not_pos,[status(thm)],[251])).
thf(276,plain,(![SV4:\$i,SV31:\$i,SV20:\$i]:
((((subset@SV20)@SV31)=\$false) | ((~ ((subset@SV4)@SV20))=\$true) |
(((subset@SV4)@SV31)=\$true))),inference(extcnf_not_pos,[status(thm)],[252])).
thf(277,plain,(![SV32:\$i,SV28:\$i,SV14:\$i]:
((((subset@SV14)@SV28)=\$false) | ((~ ((subset@SV32)@SV28))=\$true) |
(((subset@((set_union2@SV14)@SV32))@SV28)=\$true))),inference(extcnf_not_pos,[status(thm)],[256])).
thf(278,plain,(![SV49:\$i,SV35:\$i]: (((~ (((set_difference@SV35)@SV49)
= empty_set))=\$true) |
(((subset@SV35)@SV49)=\$true))),inference(extcnf_or_pos,[status(thm)],[257])).
thf(279,plain,(![SV50:\$i,SV36:\$i]: (((~ ((subset@SV36)@SV50))=\$true)
| ((((set_difference@SV36)@SV50) =
empty_set)=\$true))),inference(extcnf_or_pos,[status(thm)],[258])).
thf(280,plain,(![SV51:\$i,SV37:\$i]: (((~ (((set_difference@SV37)@SV51)
= empty_set))=\$true) |
(((subset@SV37)@SV51)=\$true))),inference(extcnf_or_pos,[status(thm)],[259])).
thf(281,plain,(![SV52:\$i,SV38:\$i]: (((~ ((subset@SV38)@SV52))=\$true)
| ((((set_difference@SV38)@SV52) =
empty_set)=\$true))),inference(extcnf_or_pos,[status(thm)],[260])).
thf(282,plain,(![SV53:\$i,SV39:\$i]: ((((disjoint@SV39)@SV53)=\$true) |
((~ ((~ ((in@((sK6@SV53)@SV39))@SV39)) | (~
((in@((sK6@SV53)@SV39))@SV53))))=\$true))),inference(extcnf_or_pos,[status(thm)],[261])).
thf(283,plain,(![SV54:\$i,SV40:\$i]: (((![SY742:\$i]: ((~
((in@SY742)@SV40)) | (~ ((in@SY742)@SV54))))=\$true) | ((~
((disjoint@SV40)@SV54))=\$true))),inference(extcnf_or_pos,[status(thm)],[262])).
thf(284,plain,(![SV55:\$i,SV41:\$i]: ((((disjoint@SV41)@SV55)=\$true) |
(((in@((sK5@SV55)@SV41))@((set_intersection2@SV41)@SV55))=\$true))),inference(extcnf_or_pos,[status(thm)],[263])).
thf(285,plain,(![SV56:\$i,SV42:\$i]: (((![SY743:\$i]: (~
((in@SY743)@((set_intersection2@SV42)@SV56))))=\$true) | ((~
((disjoint@SV42)@SV56))=\$true))),inference(extcnf_or_pos,[status(thm)],[264])).
thf(286,plain,(![SV57:\$i,SV43:\$i]: ((((~ ((subset@SV43)@SV57)) | (~
((subset@SV57)@SV43)))=\$true) | ((SV43 =
SV57)=\$true))),inference(extcnf_or_pos,[status(thm)],[265])).
thf(287,plain,(((![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX0)@SX1)))=\$true)),inference(extcnf_not_neg,[status(thm)],[266])).
thf(288,plain,(((![SX0:\$i,SX1:\$i]: ((~ (SX0 = SX1)) |
((subset@SX1)@SX0)))=\$true)),inference(extcnf_not_neg,[status(thm)],[267])).
thf(289,plain,(![SV44:\$i,SV58:\$i]: (((~ ((~
((in@((sK4@SV58)@SV44))@SV44)) | (~ (~
((in@((sK4@SV58)@SV44))@SV58)))))=\$true) |
(((subset@SV44)@SV58)=\$true))),inference(extcnf_or_pos,[status(thm)],[268])).
thf(290,plain,(![SV59:\$i,SV45:\$i]: (((~ ((subset@SV45)@SV59))=\$true)
| ((![SY744:\$i]: ((~ ((in@SY744)@SV45)) |
((in@SY744)@SV59)))=\$true))),inference(extcnf_or_pos,[status(thm)],[269])).
thf(291,plain,(![SV60:\$i,SV46:\$i]: (((~
(((set_intersection2@SV46)@SV60) = empty_set))=\$true) |
(((disjoint@SV46)@SV60)=\$true))),inference(extcnf_or_pos,[status(thm)],[270])).
thf(292,plain,(![SV61:\$i,SV47:\$i]: (((~
((disjoint@SV47)@SV61))=\$true) | ((((set_intersection2@SV47)@SV61) =
empty_set)=\$true))),inference(extcnf_or_pos,[status(thm)],[271])).
thf(293,plain,(![SV62:\$i,SV48:\$i]: ((((SV48 = SV62) | (~
((subset@SV48)@SV62)))=\$true) |
(((proper_subset@SV48)@SV62)=\$true))),inference(extcnf_or_pos,[status(thm)],[272])).
thf(294,plain,(((![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1)) |
(~ (SX0 = SX1))))=\$true)),inference(extcnf_not_neg,[status(thm)],[273])).
thf(295,plain,(((![SX0:\$i,SX1:\$i]: ((~ ((proper_subset@SX0)@SX1)) |
((subset@SX0)@SX1)))=\$true)),inference(extcnf_not_neg,[status(thm)],[274])).
thf(296,plain,(![SV19:\$i,SV30:\$i,SV3:\$i]:
((((subset@SV3)@SV30)=\$false) | (((subset@SV3)@SV19)=\$false) |
(((subset@SV3)@((set_intersection2@SV19)@SV30))=\$true))),inference(extcnf_not_pos,[status(thm)],[275])).
thf(297,plain,(![SV31:\$i,SV20:\$i,SV4:\$i]:
((((subset@SV4)@SV20)=\$false) | (((subset@SV20)@SV31)=\$false) |
(((subset@SV4)@SV31)=\$true))),inference(extcnf_not_pos,[status(thm)],[276])).
thf(298,plain,(![SV14:\$i,SV28:\$i,SV32:\$i]:
((((subset@SV32)@SV28)=\$false) | (((subset@SV14)@SV28)=\$false) |
(((subset@((set_union2@SV14)@SV32))@SV28)=\$true))),inference(extcnf_not_pos,[status(thm)],[277])).
thf(299,plain,(![SV49:\$i,SV35:\$i]: (((((set_difference@SV35)@SV49) =
empty_set)=\$false) |
(((subset@SV35)@SV49)=\$true))),inference(extcnf_not_pos,[status(thm)],[278])).
thf(300,plain,(![SV50:\$i,SV36:\$i]: ((((subset@SV36)@SV50)=\$false) |
((((set_difference@SV36)@SV50) =
empty_set)=\$true))),inference(extcnf_not_pos,[status(thm)],[279])).
thf(301,plain,(![SV51:\$i,SV37:\$i]: (((((set_difference@SV37)@SV51) =
empty_set)=\$false) |
(((subset@SV37)@SV51)=\$true))),inference(extcnf_not_pos,[status(thm)],[280])).
thf(302,plain,(![SV52:\$i,SV38:\$i]: ((((subset@SV38)@SV52)=\$false) |
((((set_difference@SV38)@SV52) =
empty_set)=\$true))),inference(extcnf_not_pos,[status(thm)],[281])).
thf(303,plain,(![SV39:\$i,SV53:\$i]: ((((~
((in@((sK6@SV53)@SV39))@SV39)) | (~
((in@((sK6@SV53)@SV39))@SV53)))=\$false) |
(((disjoint@SV39)@SV53)=\$true))),inference(extcnf_not_pos,[status(thm)],[282])).
thf(304,plain,(![SV54:\$i,SV40:\$i,SV63:\$i]: ((((~ ((in@SV63)@SV40)) |
(~ ((in@SV63)@SV54)))=\$true) | ((~
((disjoint@SV40)@SV54))=\$true))),inference(extcnf_forall_pos,[status(thm)],[283])).
thf(305,plain,(![SV56:\$i,SV42:\$i,SV64:\$i]: (((~
((in@SV64)@((set_intersection2@SV42)@SV56)))=\$true) | ((~
((disjoint@SV42)@SV56))=\$true))),inference(extcnf_forall_pos,[status(thm)],[285])).
thf(306,plain,(![SV57:\$i,SV43:\$i]: (((~ ((subset@SV43)@SV57))=\$true)
| ((~ ((subset@SV57)@SV43))=\$true) | ((SV43 =
SV57)=\$true))),inference(extcnf_or_pos,[status(thm)],[286])).
thf(307,plain,(![SV65:\$i]: (((![SY745:\$i]: ((~ (SV65 = SY745)) |
((subset@SV65)@SY745)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[287])).
thf(308,plain,(![SV66:\$i]: (((![SY746:\$i]: ((~ (SV66 = SY746)) |
((subset@SY746)@SV66)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[288])).
thf(309,plain,(![SV44:\$i,SV58:\$i]: ((((~
((in@((sK4@SV58)@SV44))@SV44)) | (~ (~
((in@((sK4@SV58)@SV44))@SV58))))=\$false) |
(((subset@SV44)@SV58)=\$true))),inference(extcnf_not_pos,[status(thm)],[289])).
thf(310,plain,(![SV59:\$i,SV45:\$i,SV67:\$i]: ((((~ ((in@SV67)@SV45)) |
((in@SV67)@SV59))=\$true) | ((~
((subset@SV45)@SV59))=\$true))),inference(extcnf_forall_pos,[status(thm)],[290])).
thf(311,plain,(![SV60:\$i,SV46:\$i]: (((((set_intersection2@SV46)@SV60)
= empty_set)=\$false) |
(((disjoint@SV46)@SV60)=\$true))),inference(extcnf_not_pos,[status(thm)],[291])).
thf(312,plain,(![SV61:\$i,SV47:\$i]: ((((disjoint@SV47)@SV61)=\$false) |
((((set_intersection2@SV47)@SV61) =
empty_set)=\$true))),inference(extcnf_not_pos,[status(thm)],[292])).
thf(313,plain,(![SV62:\$i,SV48:\$i]: (((SV48 = SV62)=\$true) | ((~
((subset@SV48)@SV62))=\$true) |
(((proper_subset@SV48)@SV62)=\$true))),inference(extcnf_or_pos,[status(thm)],[293])).
thf(314,plain,(![SV68:\$i]: (((![SY747:\$i]: ((~
((proper_subset@SV68)@SY747)) | (~ (SV68 =
SY747))))=\$true))),inference(extcnf_forall_pos,[status(thm)],[294])).
thf(315,plain,(![SV69:\$i]: (((![SY748:\$i]: ((~
((proper_subset@SV69)@SY748)) |
((subset@SV69)@SY748)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[295])).
thf(316,plain,(![SV39:\$i,SV53:\$i]: (((~
((in@((sK6@SV53)@SV39))@SV39))=\$false) |
(((disjoint@SV39)@SV53)=\$true))),inference(extcnf_or_neg,[status(thm)],[303])).
thf(317,plain,(![SV39:\$i,SV53:\$i]: (((~
((in@((sK6@SV53)@SV39))@SV53))=\$false) |
(((disjoint@SV39)@SV53)=\$true))),inference(extcnf_or_neg,[status(thm)],[303])).
thf(318,plain,(![SV63:\$i,SV54:\$i,SV40:\$i]:
((((disjoint@SV40)@SV54)=\$false) | (((~ ((in@SV63)@SV40)) | (~
((in@SV63)@SV54)))=\$true))),inference(extcnf_not_pos,[status(thm)],[304])).
thf(319,plain,(![SV64:\$i,SV56:\$i,SV42:\$i]:
((((disjoint@SV42)@SV56)=\$false) | ((~
((in@SV64)@((set_intersection2@SV42)@SV56)))=\$true))),inference(extcnf_not_pos,[status(thm)],[305])).
thf(320,plain,(![SV57:\$i,SV43:\$i]: ((((subset@SV43)@SV57)=\$false) |
((~ ((subset@SV57)@SV43))=\$true) | ((SV43 =
SV57)=\$true))),inference(extcnf_not_pos,[status(thm)],[306])).
thf(321,plain,(![SV70:\$i,SV65:\$i]: ((((~ (SV65 = SV70)) |
((subset@SV65)@SV70))=\$true))),inference(extcnf_forall_pos,[status(thm)],[307])).
thf(322,plain,(![SV71:\$i,SV66:\$i]: ((((~ (SV66 = SV71)) |
((subset@SV71)@SV66))=\$true))),inference(extcnf_forall_pos,[status(thm)],[308])).
thf(323,plain,(![SV44:\$i,SV58:\$i]: (((~
((in@((sK4@SV58)@SV44))@SV44))=\$false) |
(((subset@SV44)@SV58)=\$true))),inference(extcnf_or_neg,[status(thm)],[309])).
thf(324,plain,(![SV44:\$i,SV58:\$i]: (((~ (~
((in@((sK4@SV58)@SV44))@SV58)))=\$false) |
(((subset@SV44)@SV58)=\$true))),inference(extcnf_or_neg,[status(thm)],[309])).
thf(325,plain,(![SV67:\$i,SV59:\$i,SV45:\$i]:
((((subset@SV45)@SV59)=\$false) | (((~ ((in@SV67)@SV45)) |
((in@SV67)@SV59))=\$true))),inference(extcnf_not_pos,[status(thm)],[310])).
thf(326,plain,(![SV62:\$i,SV48:\$i]: ((((subset@SV48)@SV62)=\$false) |
((SV48 = SV62)=\$true) |
(((proper_subset@SV48)@SV62)=\$true))),inference(extcnf_not_pos,[status(thm)],[313])).
thf(327,plain,(![SV72:\$i,SV68:\$i]: ((((~ ((proper_subset@SV68)@SV72))
| (~ (SV68 = SV72)))=\$true))),inference(extcnf_forall_pos,[status(thm)],[314])).
thf(328,plain,(![SV73:\$i,SV69:\$i]: ((((~ ((proper_subset@SV69)@SV73))
| ((subset@SV69)@SV73))=\$true))),inference(extcnf_forall_pos,[status(thm)],[315])).
thf(329,plain,(![SV39:\$i,SV53:\$i]:
((((in@((sK6@SV53)@SV39))@SV39)=\$true) |
(((disjoint@SV39)@SV53)=\$true))),inference(extcnf_not_neg,[status(thm)],[316])).
thf(330,plain,(![SV39:\$i,SV53:\$i]:
((((in@((sK6@SV53)@SV39))@SV53)=\$true) |
(((disjoint@SV39)@SV53)=\$true))),inference(extcnf_not_neg,[status(thm)],[317])).
thf(331,plain,(![SV54:\$i,SV40:\$i,SV63:\$i]: (((~
((in@SV63)@SV40))=\$true) | ((~ ((in@SV63)@SV54))=\$true) |
(((disjoint@SV40)@SV54)=\$false))),inference(extcnf_or_pos,[status(thm)],[318])).
thf(332,plain,(![SV56:\$i,SV42:\$i,SV64:\$i]:
((((in@SV64)@((set_intersection2@SV42)@SV56))=\$false) |
(((disjoint@SV42)@SV56)=\$false))),inference(extcnf_not_pos,[status(thm)],[319])).
thf(333,plain,(![SV43:\$i,SV57:\$i]: ((((subset@SV57)@SV43)=\$false) |
((SV43 = SV57)=\$true) |
(((subset@SV43)@SV57)=\$false))),inference(extcnf_not_pos,[status(thm)],[320])).
thf(334,plain,(![SV70:\$i,SV65:\$i]: (((~ (SV65 = SV70))=\$true) |
(((subset@SV65)@SV70)=\$true))),inference(extcnf_or_pos,[status(thm)],[321])).
thf(335,plain,(![SV71:\$i,SV66:\$i]: (((~ (SV66 = SV71))=\$true) |
(((subset@SV71)@SV66)=\$true))),inference(extcnf_or_pos,[status(thm)],[322])).
thf(336,plain,(![SV44:\$i,SV58:\$i]:
((((in@((sK4@SV58)@SV44))@SV44)=\$true) |
(((subset@SV44)@SV58)=\$true))),inference(extcnf_not_neg,[status(thm)],[323])).
thf(337,plain,(![SV44:\$i,SV58:\$i]: (((~
((in@((sK4@SV58)@SV44))@SV58))=\$true) |
(((subset@SV44)@SV58)=\$true))),inference(extcnf_not_neg,[status(thm)],[324])).
thf(338,plain,(![SV59:\$i,SV45:\$i,SV67:\$i]: (((~
((in@SV67)@SV45))=\$true) | (((in@SV67)@SV59)=\$true) |
(((subset@SV45)@SV59)=\$false))),inference(extcnf_or_pos,[status(thm)],[325])).
thf(339,plain,(![SV72:\$i,SV68:\$i]: (((~
((proper_subset@SV68)@SV72))=\$true) | ((~ (SV68 =
SV72))=\$true))),inference(extcnf_or_pos,[status(thm)],[327])).
thf(340,plain,(![SV73:\$i,SV69:\$i]: (((~
((proper_subset@SV69)@SV73))=\$true) |
(((subset@SV69)@SV73)=\$true))),inference(extcnf_or_pos,[status(thm)],[328])).
thf(341,plain,(![SV54:\$i,SV40:\$i,SV63:\$i]: ((((in@SV63)@SV40)=\$false)
| ((~ ((in@SV63)@SV54))=\$true) |
(((disjoint@SV40)@SV54)=\$false))),inference(extcnf_not_pos,[status(thm)],[331])).
thf(342,plain,(![SV70:\$i,SV65:\$i]: (((SV65 = SV70)=\$false) |
(((subset@SV65)@SV70)=\$true))),inference(extcnf_not_pos,[status(thm)],[334])).
thf(343,plain,(![SV71:\$i,SV66:\$i]: (((SV66 = SV71)=\$false) |
(((subset@SV71)@SV66)=\$true))),inference(extcnf_not_pos,[status(thm)],[335])).
thf(344,plain,(![SV44:\$i,SV58:\$i]:
((((in@((sK4@SV58)@SV44))@SV58)=\$false) |
(((subset@SV44)@SV58)=\$true))),inference(extcnf_not_pos,[status(thm)],[337])).
thf(345,plain,(![SV59:\$i,SV45:\$i,SV67:\$i]: ((((in@SV67)@SV45)=\$false)
| (((in@SV67)@SV59)=\$true) |
(((subset@SV45)@SV59)=\$false))),inference(extcnf_not_pos,[status(thm)],[338])).
thf(346,plain,(![SV72:\$i,SV68:\$i]: (((SV68 = SV72)=\$false) | ((~
((proper_subset@SV68)@SV72))=\$true))),inference(extcnf_not_pos,[status(thm)],[339])).
thf(347,plain,(![SV73:\$i,SV69:\$i]:
((((proper_subset@SV69)@SV73)=\$false) |
(((subset@SV69)@SV73)=\$true))),inference(extcnf_not_pos,[status(thm)],[340])).
thf(348,plain,(![SV40:\$i,SV54:\$i,SV63:\$i]: ((((in@SV63)@SV54)=\$false)
| (((disjoint@SV40)@SV54)=\$false) |
(((in@SV63)@SV40)=\$false))),inference(extcnf_not_pos,[status(thm)],[341])).
thf(349,plain,(![SV72:\$i,SV68:\$i]:
((((proper_subset@SV68)@SV72)=\$false) | ((SV68 =
SV72)=\$false))),inference(extcnf_not_pos,[status(thm)],[346])).
thf(350,plain,(((\$false)=\$true)),inference(fo_atp_e,[status(thm)],[132,348,345,333,326,298,297,296,349,347,344,343,342,336,332,330,329,312,311,302,301,300,299,284,255,254,253,234,231,229,225,204,179,175,169,159,157,149,133])).
thf(351,plain,(\$false),inference(solved_all_splits,[solved_all_splits(join,[])],[350])).
% SZS output end CNFRefutation
```

## MaLARea 0.4

Josef Urban1, Daniel Kuehlwein1, Stephan Schulz2, Jiri Vyskocil3
2Technische Universität München, Germany
3Czech Technical University, Czech Republic

Dominique Pastre
University Paris Descartes, France

### Sample solution for SEU140+2

```SZS output start proof for SEU140+2.p

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

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

* * * proof :

* * * * * * theoreme 0 * * * * * *
*** newconcl(0, ![A, B, C]: (subset(A, B)&disjoint(B, C)=>disjoint(A, C)), 1)
*** explanation : initial theorem
------------------------------------------------------- action ini
create object(s) z3 z2 z1
*** newconcl(0, subset(z1, z2)&disjoint(z2, z3)=>disjoint(z1, z3), 2)
*** because concl((0, ![A, B, C]: (subset(A, B)&disjoint(B, C)=>disjoint(A, C))), 1)
*** explanation : the universal variable(s) of the conclusion is(are) instantiated
------------------------------------------------------- rule !
*** newconcl(0, disjoint(z1, z3), 3)
*** because concl(0, subset(z1, z2)&disjoint(z2, z3)=>disjoint(z1, z3), 2)
*** explanation : to prove H=>C, assume H and prove C
------------------------------------------------------- rule =>
*** because hyp(0, disjoint(z2, z3), 3)
*** explanation : rule if hyp(A, disjoint(B, C), _)then addhyp(A, set_intersection2(B, C)::empty_set, _)
built from the definition of disjoint (fof d7_xboole_0 )
------------------------------------------------------- rule disjoint
*** because hyp(0, subset(z1, z2), 3), obj_ct(0, z1), obj_ct(0, z2)
*** explanation : rule if (hyp(A, subset(B, C), _), obj_ct(A, B), obj_ct(A, C))then addhyp(A, set_difference(B, C)::empty_set, _)
built from the axiom l32_xboole_1
------------------------------------------------------- rule l32_xboole_1_1
*** newconcl(0, set_intersection2(z1, z3)::empty_set, 109)
*** because concl(0, disjoint(z1, z3), 3)
*** explanation : the conclusion  disjoint(z1, z3) is replaced by its definition(fof d7_xboole_0 )
------------------------------------------------------- rule def_concl_pred
*** newconcl(0, seul(set_intersection2(z1, z3)::A, A=empty_set), 110)
*** because concl(0, set_intersection2(z1, z3)::empty_set, 109)
*** explanation :  FX::Y is rewriten only(FX::Z, Z=Y)
------------------------------------------------------- rule concl2pts
*** addhyp(0, set_intersection2(z1, z3)::z4, 111), newconcl(0, z4=empty_set, 111)
*** because concl(0, seul(set_intersection2(z1, z3)::A, A=empty_set), 110)
*** explanation : creation of object z4 and of its definition
------------------------------------------------------- rule concl_only
*** because hyp(0, set_intersection2(z1, z3)::z4, 111), obj_ct(0, z1), obj_ct(0, z3)
*** explanation : rule if (hyp(A, set_intersection2(B, C)::D, _), obj_ct(A, B), obj_ct(A, C))then addhyp(A, set_intersection2(C, B)::D, _)
built from the axiom commutativity_k3_xboole_0
------------------------------------------------------- rule commutativity_k3_xboole_0_1
*** newconcl(0, ![A]: ~in(A, z4), 114)
*** because concl(0, z4=empty_set, 111)
*** explanation : sufficient condition (rule :  d1_xboole_0_1 (fof d1_xboole_0 )
------------------------------------------------------- rule d1_xboole_0_1_cs
create object(s) z5
*** newconcl(0, ~in(z5, z4), 115)
*** because concl((0, ![A]: ~in(A, z4)), 114)
*** explanation : the universal variable(s) of the conclusion is(are) instantiated
------------------------------------------------------- rule !
*** addhyp(0, in(z5, z4), 116), newconcl(0, false, 116)
*** because concl(0, ~in(z5, z4), 115)
*** explanation : assume in(z5, z4) and search for a contradiction
------------------------------------------------------- rule concl_not
*** because hyp(0, set_intersection2(z1, z3)::z4, 111), hyp(0, in(z5, z4), 116), obj_ct(0, z5)
*** explanation : rule if (hyp(A, set_intersection2(D, _)::B, _), hyp(A, in(C, B), _), obj_ct(A, C))then addhyp(A, in(C, D), _)
built from the definition of set_intersection2 (fof d3_xboole_0 )
------------------------------------------------------- rule set_intersection2
*** because hyp(0, subset(z1, z2), 3), hyp(0, in(z5, z1), 118), obj_ct(0, z5)
*** explanation : rule if (hyp(A, subset(B, D), _), hyp(A, in(C, B), _), obj_ct(A, C))then addhyp(A, in(C, D), _)
built from the definition of subset (fof d3_tarski )
------------------------------------------------------- rule subset
*** because hyp(0, set_intersection2(z3, z1)::z4, 113), hyp(0, in(z5, z4), 116), obj_ct(0, z5)
*** explanation : rule if (hyp(A, set_intersection2(D, _)::B, _), hyp(A, in(C, B), _), obj_ct(A, C))then addhyp(A, in(C, D), _)
built from the definition of set_intersection2 (fof d3_xboole_0 )
------------------------------------------------------- rule set_intersection2
*** because hyp(0, set_intersection2(z2, z3)::empty_set, 4), hyp(0, in(z5, z2), 119), hyp(0, in(z5, z3), 120), obj_ct(0, z5)
*** explanation : rule if (hyp(A, set_intersection2(B, D)::E, _), hyp(A, in(C, B), _), hyp(A, in(C, D), _), obj_ct(A, C))then addhyp(A, in(C, E), _)
built from the definition of set_intersection2 (fof d3_xboole_0 )
------------------------------------------------------- rule set_intersection4
*** because hyp(0, set_difference(z1, z2)::empty_set, 21), hyp(0, in(z5, empty_set), 121), hyp(0, in(z5, z2), 119), obj_ct(0, z5)
*** explanation : rule if (hyp(A, set_difference(_, D)::B, _), hyp(A, in(C, B), _), hyp(A, in(C, D), _), obj_ct(A, C))then addhyp(A, false, _)
built from the definition of set_difference (fof d4_xboole_0 )
------------------------------------------------------- rule set_difference1
*** newconcl(0, true, 123)
*** because hyp(0, false, 122), concl(0, false, 116)
*** explanation : the conclusion false to be proved is a hypothesis
------------------------------------------------------- rule stop_hyp_concl
then the initial theorem is proved
* * * * * * * * * * * * * * * * * * * * * * * *

SZS output end proof for SEU140+2.p
```

## Nitrox 2012

Jasmin C. Blanchette1, Emina Torlak2
1Technische Universität München, Germany
2University of California, USA

### Sample solution for NLP042+1

```% SZS status Satisfiable
% SZS output start FiniteModel
Nitpick found a model for card TPTP_Interpret.ind = 2:

Constants:
bnd_a = i1
bnd_a_holds = (%x. _)(i1 := False, i2 := True)
bnd_a_key = (%x. _)(i1 := False, i2 := True)
bnd_a_nonce = (%x. _)(i1 := True, i2 := False)
bnd_a_stored = (%x. _)(i1 := True, i2 := False)
bnd_an_a_nonce = i1
bnd_an_intruder_nonce = i2
bnd_at = i1
bnd_b = i1
bnd_b_holds = (%x. _)(i1 := False, i2 := True)
bnd_b_stored = (%x. _)(i1 := True, i2 := False)
bnd_bt = i1
bnd_encrypt =
(%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1), i2 := (%x. _)(i1 := i2, i2 := i2))
bnd_fresh_intruder_nonce = (%x. _)(i1 := False, i2 := True)
bnd_fresh_to_b = (%x. _)(i1 := True, i2 := True)
bnd_generate_b_nonce = (%x. _)(i1 := i1, i2 := i1)
bnd_generate_expiration_time = (%x. _)(i1 := i1, i2 := i1)
bnd_generate_intruder_nonce = (%x. _)(i1 := i1, i2 := i2)
bnd_generate_key = (%x. _)(i1 := i2, i2 := i2)
bnd_intruder_holds = (%x. _)(i1 := False, i2 := True)
bnd_intruder_message = (%x. _)(i1 := True, i2 := True)
bnd_key =
(%x. _)
(i1 := (%x. _)(i1 := i2, i2 := i1), i2 := (%x. _)(i1 := i2, i2 := i1))
bnd_message = (%x. _)(i1 := False, i2 := True)
bnd_pair =
(%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1), i2 := (%x. _)(i1 := i2, i2 := i2))
bnd_party_of_protocol = (%x. _)(i1 := True, i2 := False)
(%x. _)
(i1 := (%x. _)
(i1 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1),
i2 := (%x. _)(i1 := i2, i2 := i1)),
i2 := (%x. _)
(i1 := (%x. _)(i1 := i2, i2 := i2),
i2 := (%x. _)(i1 := i2, i2 := i2))),
i2 := (%x. _)
(i1 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i2),
i2 := (%x. _)(i1 := i2, i2 := i2)),
i2 := (%x. _)
(i1 := (%x. _)(i1 := i2, i2 := i1),
i2 := (%x. _)(i1 := i2, i2 := i2))))
bnd_sent =
(%x. _)
(i1 := (%x. _)
(i1 := (%x. _)(i1 := i2, i2 := i2),
i2 := (%x. _)(i1 := i2, i2 := i1)),
i2 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1),
i2 := (%x. _)(i1 := i1, i2 := i1)))
bnd_t = i1
bnd_t_holds = (%x. _)(i1 := True, i2 := True)
bnd_triple =
(%x. _)
(i1 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1),
i2 := (%x. _)(i1 := i1, i2 := i1)),
i2 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1),
i2 := (%x. _)(i1 := i1, i2 := i2)))
% SZS output end FiniteModel
```

### Sample solution for SWV017+1

```% SZS status Satisfiable
% SZS output start FiniteModel
Nitpick found a model for card TPTP_Interpret.ind = 2:

Constants:
bnd_a = i1
bnd_a_holds = (%x. _)(i1 := False, i2 := True)
bnd_a_key = (%x. _)(i1 := False, i2 := True)
bnd_a_nonce = (%x. _)(i1 := True, i2 := False)
bnd_a_stored = (%x. _)(i1 := True, i2 := False)
bnd_an_a_nonce = i1
bnd_an_intruder_nonce = i2
bnd_at = i1
bnd_b = i1
bnd_b_holds = (%x. _)(i1 := False, i2 := True)
bnd_b_stored = (%x. _)(i1 := True, i2 := False)
bnd_bt = i1
bnd_encrypt =
(%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1), i2 := (%x. _)(i1 := i2, i2 := i2))
bnd_fresh_intruder_nonce = (%x. _)(i1 := False, i2 := True)
bnd_fresh_to_b = (%x. _)(i1 := True, i2 := True)
bnd_generate_b_nonce = (%x. _)(i1 := i1, i2 := i1)
bnd_generate_expiration_time = (%x. _)(i1 := i1, i2 := i1)
bnd_generate_intruder_nonce = (%x. _)(i1 := i1, i2 := i2)
bnd_generate_key = (%x. _)(i1 := i2, i2 := i2)
bnd_intruder_holds = (%x. _)(i1 := False, i2 := True)
bnd_intruder_message = (%x. _)(i1 := True, i2 := True)
bnd_key =
(%x. _)
(i1 := (%x. _)(i1 := i2, i2 := i1), i2 := (%x. _)(i1 := i2, i2 := i1))
bnd_message = (%x. _)(i1 := False, i2 := True)
bnd_pair =
(%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1), i2 := (%x. _)(i1 := i2, i2 := i2))
bnd_party_of_protocol = (%x. _)(i1 := True, i2 := False)
(%x. _)
(i1 := (%x. _)
(i1 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1),
i2 := (%x. _)(i1 := i2, i2 := i1)),
i2 := (%x. _)
(i1 := (%x. _)(i1 := i2, i2 := i2),
i2 := (%x. _)(i1 := i2, i2 := i2))),
i2 := (%x. _)
(i1 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i2),
i2 := (%x. _)(i1 := i2, i2 := i2)),
i2 := (%x. _)
(i1 := (%x. _)(i1 := i2, i2 := i1),
i2 := (%x. _)(i1 := i2, i2 := i2))))
bnd_sent =
(%x. _)
(i1 := (%x. _)
(i1 := (%x. _)(i1 := i2, i2 := i2),
i2 := (%x. _)(i1 := i2, i2 := i1)),
i2 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1),
i2 := (%x. _)(i1 := i1, i2 := i1)))
bnd_t = i1
bnd_t_holds = (%x. _)(i1 := True, i2 := True)
bnd_triple =
(%x. _)
(i1 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1),
i2 := (%x. _)(i1 := i1, i2 := i1)),
i2 := (%x. _)
(i1 := (%x. _)(i1 := i1, i2 := i1),
i2 := (%x. _)(i1 := i1, i2 := i2)))
% SZS output end FiniteModel
```

Koen Claessen
Chalmers University of Technology, Sweden

### Sample solution for MGT019+2

```% domain size is 1
disbanding_rate(!1,!1) = !1
efficient_producers = !1
environment(!1) <=> \$true
first_movers = !1
founding_rate(!1,!1) = !1
greater(!1,!1) <=> \$false
greater_or_equal(!1,!1) <=> \$true
growth_rate(!1,!1) = !1
in_environment(!1,!1) <=> \$true
stable(!1) <=> \$true
subpopulations(!1,!1,!1,!1) <=> \$true
```

### Sample solution for SWV010+1

```% domain size is 1
a_holds(X1)
a_stored(X1)
b_holds(X1)
b_stored(X1)
fresh_to_b(X1)
message(X1)
party_of_protocol(X1)
t_holds(X1)
```

## 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)].
```

## PS-E---1.0

Daniel Kuehlwein1, Josef Urban1, Stephan Schulz2 1Radboud University Nijmegen, The Netherlands
2Technische Universität München, Germany

## STP---1.0

1Articulate Software, USA
2Technische Universität München, Germany

### Sample solution for SEU140+2

```cnf(00001,plain,empty(empty_set)).
cnf(00002,plain,empty(skf54)).
cnf(00003,plain,~disjoint(X370, X369)|disjoint(X369,X370)).;{VAR59<-X369,VAR60<-X370}
cnf(00004,plain,~empty(skf56)).
cnf(00005,plain,~in(X318, X320)|~empty(X320)).;{VAR117<-X320,VAR118<-X318}
cnf(00006,plain,in(skf97, X480)|disjoint(X479,X480)).;{VAR96<-X479,VAR95<-X480}
cnf(00007,plain,~X333=X334|~proper_subset(X333,X334)).;{VAR39<-X334,VAR40<-X333}
cnf(00008,plain,~subset(X490, empty_set)|X490=empty_set).;{VAR98<-X490}
cnf(00009,plain,\$true).
cnf(00010,plain,subset(X72, X72)).;{VAR58<-X72}
cnf(00011,plain,~proper_subset(X47, X47)).;{VAR50<-X47}
cnf(00012,plain,~in(X4, X3)|~in(X3, X4)).;{VAR1<-X4,VAR0<-X3}
cnf(00013,plain,set_union2(X12, X11)=set_union2(X11,X12)).;{VAR5<-X12,VAR4<-X11}
cnf(00014,plain,X33!=empty_set|~in(X32,X33)).;{VAR12<-X33,VAR10<-X32}
cnf(00015,plain,in(skf13(X34), X36)|X36=empty_set).;{VAR12<-X36,VAR10<-X34}
cnf(00016,plain,set_intersection2(X16,X15)=set_intersection2(X15, X16)).;{VAR7<-X16,VAR6<-X15}
cnf(00017,plain,subset(X19, X20)|X19!=X20).;{VAR9<-X19,VAR8<-X20}
cnf(00018,plain,subset(X24, X23)|X23!=X24).;{VAR9<-X23,VAR8<-X24}
cnf(00019,plain,in(skf24(X124), X126)|subset(X126,X127)).;{VAR20<-X124,VAR22<-X127,VAR23<-X126}
cnf(00020,plain,in(skf97, X475)|disjoint(X475,X476)).;{VAR96<-X475,VAR95<-X476}
cnf(00021,plain,~in(X215, empty_set)). : resolution[00005,00001];{X205<-empty_set,X203<-X215}
cnf(00022,plain,~in(X225, skf54)). : resolution[00005,00002];{X205<-skf54,X203<-X225}
cnf(00023,plain,~proper_subset(\$true, X335)). : resolution[00007,00009];{X333<-\$true,X334<-X335}
cnf(00024,plain,X523=empty_set). : resolution[00008,00010];{X490<-X72,X72<-X523}
cnf(00025,plain,~in(X123, X123)). : factoring[00012];{X3<-X123}
cnf(00026,plain,~proper_subset(set_union2(X466, X467), X468)). : resolution[00007,00013];{X12<-X466,X333<-set_union2(X12,X11),X11<-X467,X334<-X468}
cnf(00027,plain,~in(X390, empty(skf56))). : resolution[00004,00014];{X32<-X390,X33<-empty(skf56)}
cnf(00028,plain,~in(X371, proper_subset(X373, X373))). : resolution[00011,00014];{X32<-X371,X47<-X373,X33<-proper_subset(X47,X47)}
cnf(00029,plain,~proper_subset(set_intersection2(X471, X472),X473)). : resolution[00007,00016];{X333<-set_intersection2(X16,X15),X334<-X473,X16<-X471,X15<-X472}
cnf(00030,plain,subset(empty(skf56), X379)). : resolution[00004,00017];{X20<-X379,X19<-empty(skf56)}
cnf(00031,plain,subset(proper_subset(X358, X358), X359)). : resolution[00011,00017];{X20<-X359,X47<-X358,X19<-proper_subset(X47,X47)}
cnf(00032,plain,subset(X387, empty(skf56))). : resolution[00004,00018];{X23<-empty(skf56),X24<-X387}
cnf(00033,plain,subset(X364, proper_subset(X366, X366))). : resolution[00011,00018];{X47<-X366,X23<-proper_subset(X47,X47),X24<-X364}
cnf(00034,plain,~empty(X430)|subset(X430, X431)). : resolution[00005,00019];{X126<-X430,X127<-X431,X205<-X126,X203<-skf24(X124)}
cnf(00035,plain,~empty(X449)|subset(X449, X450)). : resolution[00005,00019];{X318<-skf24(X124),X126<-X449,X127<-X450,X320<-X126}
cnf(00036,plain,disjoint(X504, empty_set)). : resolution[00006,00021];{X479<-X504,X215<-skf97,X480<-empty_set}
cnf(00037,plain,empty_set=empty_set). : resolution[00021,00015];{X36<-empty_set,X215<-skf13(X34)}
cnf(00038,plain,disjoint(empty_set, X481)). : resolution[00020,00021];{X215<-skf97,X476<-X481,X475<-empty_set}
cnf(00039,plain,disjoint(X510, skf54)). : resolution[00006,00022];{X225<-skf97,X479<-X510,X480<-skf54}
cnf(00040,plain,skf54=empty_set). : resolution[00022,00015];{X225<-skf13(X34),X36<-skf54}
cnf(00041,plain,subset(skf54, X241)). : resolution[00022,00019];{X126<-skf54,X225<-skf24(X124),X127<-X241}
cnf(00042,plain,disjoint(skf54, X488)). : resolution[00020,00022];{X225<-skf97,X476<-X488,X475<-skf54}
cnf(00043,plain,\$false). : resolution[00024,00011];{X523<-proper_subset(X47, X47)}
cnf(00044,plain,subset(X406, in(X408, X408))). : resolution[00025,00018];{X23<-in(X123, X123),X123<-X408,X24<-X406}
cnf(00045,plain,skf13(X418)=empty_set). : resolution[00025,00015];{X36<-skf13(X34),X123<-skf13(X34),X34<-X418}
cnf(00046,plain,~in(X414, in(X416, X416))). : resolution[00025,00014];{X32<-X414,X33<-in(X123, X123),X123<-X416}
cnf(00047,plain,subset(in(X398, X398), X399)). : resolution[00025,00017];{X20<-X399,X19<-in(X123, X123),X123<-X398}
cnf(00048,plain,subset(skf24(X150), X151)). : resolution[00019,00025];{X126<-skf24(X124),X127<-X151,X123<-skf24(X124),X124<-X150}
cnf(00049,plain,disjoint(skf97, X477)). : resolution[00020,00025];{X476<-X477,X123<-skf97,X475<-skf97}
cnf(00050,plain,~proper_subset(empty_set, X342)). : resolution[00007,00037];{X333<-empty_set,X334<-X342}
cnf(00051,plain,~proper_subset(skf54, X346)). : resolution[00007,00040];{X333<-skf54,X334<-X346}
cnf(00052,plain,~proper_subset(skf13(X423), X424)). : resolution[00045,00007];{X333<-skf13(X418),X334<-X424,X418<-X423}
cnf(00053,plain,disjoint(X491, skf97)). : resolution[00049,00003];{X477<-X369,X369<-X491,X370<-skf97}
```

## SuperZenon 0.0.1

David Delahaye1, Melanie Jacquel2
1CEDRIC/CNAM, 2Siemens IC-MOL

### Sample solution for SEU140+2

```(* PROOF-FOUND *)
1. H13: (-. (All A, (All B, (All C, (((subset A B) /\ (disjoint B C)) => (disjoint A C))))))
H14: (All A, (All B, ((-. ((-. (disjoint A B)) /\ (All C, (-. ((in C A) /\ (in C B)))))) /\ (-. ((Ex C, ((in C A) /\ (in C B))) /\ (disjoint A B))))))
### [NotAllEx H13] --> 2
2. H15: (-. (All B, (All C, (((subset T_2 B) /\ (disjoint B C)) => (disjoint T_2 C)))))
### [NotAllEx H15] --> 3
3. H16: (-. (All C, (((subset T_2 T_3) /\ (disjoint T_3 C)) => (disjoint T_2 C))))
### [NotAllEx H16] --> 4
4. H17: (-. (disjoint T_2 T_18))
H19: (subset T_2 T_3)
H20: (disjoint T_3 T_18)
### [All H14] --> 5
5. H21: (All B, ((-. ((-. (disjoint T_3 B)) /\ (All C, (-. ((in C T_3) /\ (in C B)))))) /\ (-. ((Ex C, ((in C T_3) /\ (in C B))) /\ (disjoint T_3 B)))))
### [All H21] --> 6
6. H22: (-. ((Ex C, ((in C T_3) /\ (in C T_18))) /\ (disjoint T_3 T_18)))
### [NotAnd H22] --> 7 8
7. H23: (-. (Ex C, ((in C T_3) /\ (in C T_18))))
### [All H14] --> 9
9. H24: (All B, ((-. ((-. (disjoint T_2 B)) /\ (All C, (-. ((in C T_2) /\ (in C B)))))) /\ (-. ((Ex C, ((in C T_2) /\ (in C B))) /\ (disjoint T_2 B)))))
### [All H24] --> 10
10. H25: (-. ((-. (disjoint T_2 T_18)) /\ (All C, (-. ((in C T_2) /\ (in C T_18))))))
### [NotAnd H25] --> 11 12
11. H26: (-. (-. (disjoint T_2 T_18)))
### [NotNot H26] --> 13
13. H27: (disjoint T_2 T_18)
### [Axiom H27 H17]

12. H28: (-. (All C, (-. ((in C T_2) /\ (in C T_18)))))
### [NotAllEx H28] --> 14
14. H29: (-. (-. ((in T_8 T_2) /\ (in T_8 T_18))))
### [NotNot H29] --> 15
15. H30: (in T_8 T_2)
H31: (in T_8 T_18)
### [NotExists H23] --> 16
16. H32: (-. ((in T_8 T_3) /\ (in T_8 T_18)))
### [NotAnd H32] --> 17 18
17. H33: (-. (in T_8 T_3))
### [Extension/test/d3_tarskiinst H19 H34 H35 H2 H3 H8] --> 19 20
19. H34: (-. (in T_8 T_2))
### [Axiom H30 H34]

20. H35: (in T_8 T_3)
### [Axiom H35 H33]

18. H36: (-. (in T_8 T_18))
### [Axiom H31 H36]

8. H37: (-. (disjoint T_3 T_18))
### [Axiom H20 H37]
```

## Vampire 0.6

Andrei Voronkov, Kryštof Hoder
University of Manchester, United Kingdom

### Sample solution for SYN075+1

```% SZS status Theorem for SYN075+1
% SZS output start Proof for SYN075+1
fof(f509,plain,(
\$false),
inference(subsumption_resolution,[],[f508,f145])).
fof(f145,plain,(
big_f(\$sk3,\$sk4)),
inference(backtracking_split_refutation,[],[f69,f70_D,f124])).
fof(f124,plain,(
\$false | \$spl1),
inference(subsumption_resolution,[],[f123,f110])).
fof(f110,plain,(
( ! [X0] : (~big_f(\$sk3,X0)) ) | \$spl1),
inference(forward_demodulation,[],[f106,f92])).
fof(f92,plain,(
( ! [X0] : (\$sk2(\$sk3,X0) = \$sk3) ) | \$spl1),
inference(factoring,[],[f85])).
fof(f85,plain,(
( ! [X2,X3] : (\$sk2(X2,X3) = X2 | \$sk2(X2,X3) = \$sk3) ) | \$spl1),
inference(resolution,[],[f82,f15])).
fof(f15,plain,(
( ! [X2,X3] : (~big_f(X2,X3) | \$sk3 = X2) )),
inference(cnf_transformation,[],[f10])).
fof(f10,plain,(
! [X2,X3] : ((~big_f(X2,X3) | (\$sk3 = X2 & \$sk4 = X3)) & (\$sk3 != X2 | \$sk4 != X3 | big_f(X2,X3)))),
inference(skolemisation,[status(esa)],[f9])).
fof(f9,plain,(
? [X0,X1] : ! [X2,X3] : ((~big_f(X2,X3) | (X0 = X2 & X1 = X3)) & (X0 != X2 | X1 != X3 | big_f(X2,X3)))),
inference(flattening,[],[f8])).
fof(f8,plain,(
? [X0,X1] : ! [X2,X3] : ((~big_f(X2,X3) | (X0 = X2 & X1 = X3)) & ((X0 != X2 | X1 != X3) | big_f(X2,X3)))),
inference(nnf_transformation,[],[f1])).
fof(f1,axiom,(
? [X0,X1] : ! [X2,X3] : (big_f(X2,X3) <=> (X0 = X2 & X1 = X3))),
file('/tmp/SystemOnTPTP10164/SYN075+1.tptp',pel52_1)).
fof(f82,plain,(
( ! [X4,X0] : (big_f(\$sk2(X4,X0),X0) | \$sk2(X4,X0) = X4) ) | \$spl1),
inference(subsumption_resolution,[],[f73,f70])).
fof(f73,plain,(
( ! [X4,X0] : (big_f(\$sk2(X4,X0),X0) | \$sk0(X0) != X0 | \$sk2(X4,X0) = X4) ) | \$spl1),
inference(backward_demodulation,[],[f70,f13])).
fof(f13,plain,(
( ! [X4,X0] : (\$sk0(X0) != X0 | \$sk2(X4,X0) = X4 | big_f(\$sk2(X4,X0),\$sk0(X0))) )),
inference(cnf_transformation,[],[f7])).
fof(f7,plain,(
! [X0] : ((! [X3] : ((~big_f(X3,\$sk0(X0)) | \$sk1(X0) = X3) & (\$sk1(X0) != X3 | big_f(X3,\$sk0(X0)))) | \$sk0(X0) = X0) & (! [X4] : ((big_f(\$sk2(X4,X0),\$sk0(X0)) | \$sk2(X4,X0) = X4) & (~big_f(\$sk2(X4,X0),\$sk0(X0)) | \$sk2(X4,X0) != X4)) | \$sk0(X0) != X0))),
inference(skolemisation,[status(esa)],[f6])).
fof(f6,plain,(
! [X0] : ? [X1] : ((? [X2] : ! [X3] : ((~big_f(X3,X1) | X2 = X3) & (X2 != X3 | big_f(X3,X1))) | X0 = X1) & (! [X4] : ? [X5] : ((big_f(X5,X1) | X4 = X5) & (~big_f(X5,X1) | X4 != X5)) | X0 != X1))),
inference(rectify,[],[f5])).
fof(f5,plain,(
! [X0] : ? [X1] : ((? [X2] : ! [X3] : ((~big_f(X3,X1) | X2 = X3) & (X2 != X3 | big_f(X3,X1))) | X0 = X1) & (! [X2] : ? [X3] : ((big_f(X3,X1) | X2 = X3) & (~big_f(X3,X1) | X2 != X3)) | X0 != X1))),
inference(nnf_transformation,[],[f4])).
fof(f4,plain,(
! [X0] : ? [X1] : (? [X2] : ! [X3] : (big_f(X3,X1) <=> X2 = X3) <~> X0 = X1)),
inference(ennf_transformation,[],[f3])).
fof(f3,plain,(
~? [X0] : ! [X1] : (? [X2] : ! [X3] : (big_f(X3,X1) <=> X2 = X3) <=> X0 = X1)),
inference(rectify,[],[f2])).
fof(f2,negated_conjecture,(
~? [X1] : ! [X3] : (? [X0] : ! [X2] : (big_f(X2,X3) <=> X0 = X2) <=> X1 = X3)),
file('/tmp/SystemOnTPTP10164/SYN075+1.tptp',pel52)).
fof(f106,plain,(
( ! [X0] : (~big_f(\$sk2(\$sk3,X0),X0)) ) | \$spl1),
inference(resolution,[],[f92,f83])).
fof(f83,plain,(
( ! [X4,X0] : (\$sk2(X4,X0) != X4 | ~big_f(\$sk2(X4,X0),X0)) ) | \$spl1),
inference(subsumption_resolution,[],[f74,f70])).
fof(f74,plain,(
( ! [X4,X0] : (~big_f(\$sk2(X4,X0),X0) | \$sk0(X0) != X0 | \$sk2(X4,X0) != X4) ) | \$spl1),
inference(backward_demodulation,[],[f70,f14])).
fof(f14,plain,(
( ! [X4,X0] : (\$sk2(X4,X0) != X4 | \$sk0(X0) != X0 | ~big_f(\$sk2(X4,X0),\$sk0(X0))) )),
inference(cnf_transformation,[],[f7])).
fof(f123,plain,(
big_f(\$sk3,\$sk4) | \$spl1),
inference(forward_demodulation,[],[f118,f92])).
fof(f118,plain,(
( ! [X2] : (big_f(\$sk2(\$sk3,X2),\$sk4)) ) | \$spl1),
inference(resolution,[],[f116,f92])).
fof(f116,plain,(
( ! [X0] : (\$sk3 != X0 | big_f(X0,\$sk4)) ) | \$spl1),
inference(forward_demodulation,[],[f112,f70])).
fof(f112,plain,(
( ! [X0] : (big_f(X0,\$sk0(\$sk4)) | \$sk3 != X0) ) | \$spl1),
inference(resolution,[],[f17,f70])).
fof(f17,plain,(
( ! [X2,X3] : (\$sk4 != X3 | big_f(X2,X3) | \$sk3 != X2) )),
inference(cnf_transformation,[],[f10])).
fof(f70,plain,(
( ! [X0] : (\$sk0(X0) = X0) ) | \$spl1),
inference(cnf_transformation,[],[f70_D])).
fof(f70_D,plain,(
( ! [X0] : (\$sk0(X0) = X0) ) <=> ~\$spl1),
introduced(backtracking_splitting_component,[])).
fof(f69,plain,(
( ! [X0] : (big_f(\$sk3,\$sk4) | \$sk0(X0) = X0) )),
inference(duplicate_literal_removal,[],[f68])).
fof(f68,plain,(
( ! [X0] : (big_f(\$sk3,\$sk4) | \$sk0(X0) = X0 | \$sk0(X0) = X0) )),
inference(superposition,[],[f34,f21])).
fof(f21,plain,(
( ! [X2] : (\$sk1(X2) = \$sk3 | \$sk0(X2) = X2) )),
inference(resolution,[],[f18,f15])).
fof(f18,plain,(
( ! [X0] : (big_f(\$sk1(X0),\$sk0(X0)) | \$sk0(X0) = X0) )),
inference(equality_resolution,[],[f12])).
fof(f12,plain,(
( ! [X0,X3] : (\$sk1(X0) != X3 | big_f(X3,\$sk0(X0)) | \$sk0(X0) = X0) )),
inference(cnf_transformation,[],[f7])).
fof(f34,plain,(
( ! [X0] : (big_f(\$sk1(X0),\$sk4) | \$sk0(X0) = X0) )),
inference(duplicate_literal_removal,[],[f29])).
fof(f29,plain,(
( ! [X0] : (big_f(\$sk1(X0),\$sk4) | \$sk0(X0) = X0 | \$sk0(X0) = X0) )),
inference(superposition,[],[f18,f20])).
fof(f20,plain,(
( ! [X1] : (\$sk0(X1) = X1 | \$sk0(X1) = \$sk4) )),
inference(resolution,[],[f18,f16])).
fof(f16,plain,(
( ! [X2,X3] : (~big_f(X2,X3) | \$sk4 = X3) )),
inference(cnf_transformation,[],[f10])).
fof(f508,plain,(
~big_f(\$sk3,\$sk4)),
inference(forward_demodulation,[],[f507,f24])).
fof(f24,plain,(
\$sk0(\$sk4) = \$sk4),
inference(factoring,[],[f20])).
fof(f507,plain,(
~big_f(\$sk3,\$sk0(\$sk4))),
inference(forward_demodulation,[],[f506,f293])).
fof(f293,plain,(
\$sk2(\$sk3,\$sk4) = \$sk3),
inference(factoring,[],[f234])).
fof(f234,plain,(
( ! [X1] : (\$sk2(X1,\$sk4) = X1 | \$sk2(X1,\$sk4) = \$sk3) )),
inference(resolution,[],[f64,f15])).
fof(f64,plain,(
( ! [X3] : (big_f(\$sk2(X3,\$sk4),\$sk4) | \$sk2(X3,\$sk4) = X3) )),
inference(forward_demodulation,[],[f57,f24])).
fof(f57,plain,(
( ! [X3] : (\$sk2(X3,\$sk4) = X3 | big_f(\$sk2(X3,\$sk4),\$sk0(\$sk4))) )),
inference(resolution,[],[f13,f24])).
fof(f506,plain,(
~big_f(\$sk2(\$sk3,\$sk4),\$sk0(\$sk4))),
inference(subsumption_resolution,[],[f496,f16])).
fof(f496,plain,(
\$sk0(\$sk4) != \$sk4 | ~big_f(\$sk2(\$sk3,\$sk4),\$sk0(\$sk4))),
inference(resolution,[],[f14,f293])).
% SZS output end Proof for SYN075+1
```

## Vampire 2.6

Krystof Hoder, Andrei Voronkov
University of Manchester, England

### Sample solution for SEU140+2

```% SZS output start Proof for SEU140+2
fof(f1738,plain,(
\$false),
inference(subsumption_resolution,[],[f1737,f136])).
fof(f136,plain,(
~disjoint(sK0,sK2)),
inference(cnf_transformation,[],[f104])).
fof(f104,plain,(
subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)),
inference(skolemisation,[status(esa)],[f76])).
fof(f76,plain,(
? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
inference(flattening,[],[f75])).
fof(f75,plain,(
? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
file('Problems/SEU/SEU140+2.p',t63_xboole_1)).
fof(f1737,plain,(
disjoint(sK0,sK2)),
inference(duplicate_literal_removal,[],[f1736])).
fof(f1736,plain,(
disjoint(sK0,sK2) | disjoint(sK0,sK2)),
inference(resolution,[],[f1707,f378])).
fof(f378,plain,(
( ! [X1] : (~in(sK4(sK2,X1),sK1) | disjoint(X1,sK2)) )),
inference(resolution,[],[f372,f148])).
fof(f148,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f106])).
fof(f106,plain,(
! [X0,X1] : ((disjoint(X0,X1) | (in(sK4(X1,X0),X0) & in(sK4(X1,X0),X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
inference(skolemisation,[status(esa)],[f79])).
fof(f79,plain,(
! [X0,X1] : ((disjoint(X0,X1) | ? [X3] : (in(X3,X0) & in(X3,X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
inference(ennf_transformation,[],[f61])).
fof(f61,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
inference(flattening,[],[f60])).
fof(f60,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f43,axiom,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
file('Problems/SEU/SEU140+2.p',t3_xboole_0)).
fof(f372,plain,(
( ! [X0] : (~in(X0,sK2) | ~in(X0,sK1)) )),
inference(resolution,[],[f149,f135])).
fof(f135,plain,(
disjoint(sK1,sK2)),
inference(cnf_transformation,[],[f104])).
fof(f149,plain,(
( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
inference(cnf_transformation,[],[f106])).
fof(f1707,plain,(
( ! [X0] : (in(sK4(X0,sK0),sK1) | disjoint(sK0,X0)) )),
inference(resolution,[],[f1706,f147])).
fof(f147,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f106])).
fof(f1706,plain,(
( ! [X78] : (~in(X78,sK0) | in(X78,sK1)) )),
inference(resolution,[],[f1661,f134])).
fof(f134,plain,(
subset(sK0,sK1)),
inference(cnf_transformation,[],[f104])).
fof(f1661,plain,(
( ! [X6,X7,X5] : (~subset(X5,X6) | in(X7,X6) | ~in(X7,X5)) )),
inference(superposition,[],[f236,f218])).
fof(f218,plain,(
( ! [X0,X1] : (set_difference(X0,set_difference(X0,X1)) = X0 | ~subset(X0,X1)) )),
inference(definition_unfolding,[],[f150,f144])).
fof(f144,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))) )),
inference(cnf_transformation,[],[f47])).
fof(f47,axiom,(
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))),
file('Problems/SEU/SEU140+2.p',t48_xboole_1)).
fof(f150,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = X0 | ~subset(X0,X1)) )),
inference(cnf_transformation,[],[f80])).
fof(f80,plain,(
! [X0,X1] : (~subset(X0,X1) | set_intersection2(X0,X1) = X0)),
inference(ennf_transformation,[],[f34])).
fof(f34,axiom,(
! [X0,X1] : (subset(X0,X1) => set_intersection2(X0,X1) = X0)),
file('Problems/SEU/SEU140+2.p',t28_xboole_1)).
fof(f236,plain,(
( ! [X4,X0,X1] : (~in(X4,set_difference(X0,set_difference(X0,X1))) | in(X4,X1)) )),
inference(equality_resolution,[],[f230])).
fof(f230,plain,(
( ! [X4,X2,X0,X1] : (in(X4,X1) | ~in(X4,X2) | set_difference(X0,set_difference(X0,X1)) != X2) )),
inference(definition_unfolding,[],[f196,f144])).
fof(f196,plain,(
( ! [X4,X2,X0,X1] : (in(X4,X1) | ~in(X4,X2) | set_intersection2(X0,X1) != X2) )),
inference(cnf_transformation,[],[f123])).
fof(f123,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X4] : ((~in(X4,X2) | (in(X4,X0) & in(X4,X1))) & (~in(X4,X0) | ~in(X4,X1) | in(X4,X2)))) & (((in(sK8(X2,X1,X0),X2) | (in(sK8(X2,X1,X0),X0) & in(sK8(X2,X1,X0),X1))) & (~in(sK8(X2,X1,X0),X2) | ~in(sK8(X2,X1,X0),X0) | ~in(sK8(X2,X1,X0),X1))) | set_intersection2(X0,X1) = X2))),
inference(skolemisation,[status(esa)],[f122])).
fof(f122,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X4] : ((~in(X4,X2) | (in(X4,X0) & in(X4,X1))) & (~in(X4,X0) | ~in(X4,X1) | in(X4,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | ~in(X3,X0) | ~in(X3,X1))) | set_intersection2(X0,X1) = X2))),
inference(rectify,[],[f121])).
fof(f121,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X0) | ~in(X3,X1) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | ~in(X3,X0) | ~in(X3,X1))) | set_intersection2(X0,X1) = X2))),
inference(flattening,[],[f120])).
fof(f120,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & ((~in(X3,X0) | ~in(X3,X1)) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | (~in(X3,X0) | ~in(X3,X1)))) | set_intersection2(X0,X1) = X2))),
inference(nnf_transformation,[],[f9])).
fof(f9,axiom,(
! [X0,X1,X2] : (set_intersection2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (in(X3,X0) & in(X3,X1))))),
file('Problems/SEU/SEU140+2.p',d3_xboole_0)).
% SZS output end Proof for SEU140+2
```

### Sample solution for NLP042+1

```fof(model1,interpretation_domain,
! [X] : ( X = "sK4" | X = "sK3" | X = "sK2" | X = "sK1" | X = "sK0" ) ).
fof(model2,interpretation_terms,
( sK3 = "sK3" & sK4 = "sK4" & sK1 = "sK1" & sK0 = "sK0" & sK2 = "sK2") ).
fof(model3,interpretation_atoms,
( ~woman("sK1","sK0") &
~woman("sK1","sK1") &
~woman("sK1","sK2") &
~woman("sK1","sK3") &
~woman("sK1","sK4") &
~woman("sK2","sK0") &
~woman("sK2","sK1") &
~woman("sK2","sK2") &
~woman("sK2","sK3") &
~woman("sK2","sK4") &
~woman("sK3","sK0") &
~woman("sK3","sK1") &
~woman("sK0","sK2") &
~woman("sK0","sK4") &
~woman("sK0","sK3") &
woman("sK0","sK1") &
woman("sK0","sK0") &
~woman("sK4","sK4") &
~woman("sK4","sK3") &
~woman("sK4","sK2") &
~woman("sK4","sK1") &
~woman("sK4","sK0") &
~woman("sK3","sK4") &
~woman("sK3","sK3") &
~woman("sK3","sK2") &
~female("sK3","sK1") &
~female("sK3","sK0") &
~female("sK2","sK4") &
~female("sK2","sK3") &
~female("sK2","sK2") &
~female("sK2","sK1") &
~female("sK2","sK0") &
~female("sK1","sK4") &
~female("sK1","sK3") &
~female("sK1","sK2") &
~female("sK1","sK1") &
~female("sK1","sK0") &
female("sK0","sK1") &
~female("sK0","sK4") &
~female("sK0","sK2") &
~female("sK0","sK3") &
female("sK0","sK0") &
~female("sK4","sK4") &
~female("sK4","sK3") &
~female("sK4","sK2") &
~female("sK4","sK1") &
~female("sK4","sK0") &
~female("sK3","sK4") &
~female("sK3","sK3") &
~female("sK3","sK2") &
~human_person("sK3","sK1") &
~human_person("sK3","sK0") &
~human_person("sK2","sK4") &
~human_person("sK2","sK3") &
~human_person("sK2","sK2") &
~human_person("sK2","sK1") &
~human_person("sK2","sK0") &
~human_person("sK1","sK4") &
~human_person("sK1","sK3") &
~human_person("sK1","sK2") &
~human_person("sK1","sK1") &
~human_person("sK1","sK0") &
~human_person("sK0","sK2") &
~human_person("sK0","sK4") &
~human_person("sK0","sK3") &
human_person("sK0","sK1") &
human_person("sK0","sK0") &
~human_person("sK4","sK4") &
~human_person("sK4","sK3") &
~human_person("sK4","sK2") &
~human_person("sK4","sK1") &
~human_person("sK4","sK0") &
~human_person("sK3","sK4") &
~human_person("sK3","sK3") &
~human_person("sK3","sK2") &
~animate("sK3","sK1") &
~animate("sK3","sK0") &
~animate("sK2","sK4") &
~animate("sK2","sK3") &
~animate("sK2","sK2") &
~animate("sK2","sK1") &
~animate("sK2","sK0") &
~animate("sK1","sK4") &
~animate("sK1","sK3") &
~animate("sK1","sK2") &
~animate("sK1","sK1") &
~animate("sK1","sK0") &
~animate("sK0","sK3") &
animate("sK0","sK1") &
animate("sK0","sK4") &
animate("sK0","sK2") &
animate("sK0","sK0") &
~animate("sK4","sK4") &
~animate("sK4","sK3") &
~animate("sK4","sK2") &
~animate("sK4","sK1") &
~animate("sK4","sK0") &
~animate("sK3","sK4") &
~animate("sK3","sK3") &
~animate("sK3","sK2") &
~human("sK3","sK1") &
~human("sK3","sK0") &
~human("sK2","sK4") &
~human("sK2","sK3") &
~human("sK2","sK2") &
~human("sK2","sK1") &
~human("sK2","sK0") &
~human("sK1","sK4") &
~human("sK1","sK3") &
~human("sK1","sK2") &
~human("sK1","sK1") &
~human("sK1","sK0") &
human("sK0","sK1") &
~human("sK0","sK2") &
human("sK0","sK4") &
human("sK0","sK3") &
human("sK0","sK0") &
~human("sK4","sK4") &
~human("sK4","sK3") &
~human("sK4","sK2") &
~human("sK4","sK1") &
~human("sK4","sK0") &
~human("sK3","sK4") &
~human("sK3","sK3") &
~human("sK3","sK2") &
~organism("sK3","sK1") &
~organism("sK3","sK0") &
~organism("sK2","sK4") &
~organism("sK2","sK3") &
~organism("sK2","sK2") &
~organism("sK2","sK1") &
~organism("sK2","sK0") &
~organism("sK1","sK4") &
~organism("sK1","sK3") &
~organism("sK1","sK2") &
~organism("sK1","sK1") &
~organism("sK1","sK0") &
organism("sK0","sK1") &
~organism("sK0","sK4") &
~organism("sK0","sK3") &
~organism("sK0","sK2") &
organism("sK0","sK0") &
~organism("sK4","sK4") &
~organism("sK4","sK3") &
~organism("sK4","sK2") &
~organism("sK4","sK1") &
~organism("sK4","sK0") &
~organism("sK3","sK4") &
~organism("sK3","sK3") &
~organism("sK3","sK2") &
~living("sK3","sK1") &
~living("sK3","sK0") &
~living("sK2","sK4") &
~living("sK2","sK3") &
~living("sK2","sK2") &
~living("sK2","sK1") &
~living("sK2","sK0") &
~living("sK1","sK4") &
~living("sK1","sK3") &
~living("sK1","sK2") &
~living("sK1","sK1") &
~living("sK1","sK0") &
living("sK0","sK1") &
~living("sK0","sK3") &
living("sK0","sK4") &
living("sK0","sK2") &
living("sK0","sK0") &
~living("sK4","sK4") &
~living("sK4","sK3") &
~living("sK4","sK2") &
~living("sK4","sK1") &
~living("sK4","sK0") &
~living("sK3","sK4") &
~living("sK3","sK3") &
~living("sK3","sK2") &
impartial("sK2","sK1") &
impartial("sK2","sK0") &
impartial("sK1","sK4") &
impartial("sK1","sK3") &
impartial("sK1","sK2") &
impartial("sK1","sK1") &
impartial("sK1","sK0") &
impartial("sK0","sK4") &
impartial("sK0","sK3") &
impartial("sK0","sK2") &
impartial("sK0","sK1") &
impartial("sK0","sK0") &
impartial("sK4","sK4") &
impartial("sK4","sK3") &
impartial("sK4","sK2") &
impartial("sK4","sK1") &
impartial("sK4","sK0") &
impartial("sK3","sK4") &
impartial("sK3","sK3") &
impartial("sK3","sK2") &
impartial("sK3","sK1") &
impartial("sK3","sK0") &
impartial("sK2","sK4") &
impartial("sK2","sK3") &
impartial("sK2","sK2") &
entity("sK3","sK1") &
entity("sK3","sK0") &
entity("sK2","sK4") &
entity("sK2","sK3") &
entity("sK2","sK2") &
entity("sK2","sK1") &
entity("sK2","sK0") &
entity("sK1","sK4") &
entity("sK1","sK3") &
entity("sK1","sK2") &
entity("sK1","sK1") &
entity("sK1","sK0") &
~entity("sK0","sK4") &
entity("sK0","sK1") &
~entity("sK0","sK2") &
entity("sK0","sK3") &
entity("sK0","sK0") &
entity("sK4","sK4") &
entity("sK4","sK3") &
entity("sK4","sK2") &
entity("sK4","sK1") &
entity("sK4","sK0") &
entity("sK3","sK4") &
entity("sK3","sK3") &
entity("sK3","sK2") &
~mia_forename("sK3","sK1") &
~mia_forename("sK3","sK0") &
~mia_forename("sK2","sK4") &
~mia_forename("sK2","sK3") &
~mia_forename("sK2","sK2") &
~mia_forename("sK2","sK1") &
~mia_forename("sK2","sK0") &
~mia_forename("sK1","sK4") &
~mia_forename("sK1","sK3") &
~mia_forename("sK1","sK2") &
~mia_forename("sK1","sK1") &
~mia_forename("sK1","sK0") &
mia_forename("sK0","sK2") &
~mia_forename("sK0","sK0") &
~mia_forename("sK0","sK4") &
~mia_forename("sK0","sK3") &
~mia_forename("sK0","sK1") &
~mia_forename("sK4","sK4") &
~mia_forename("sK4","sK3") &
~mia_forename("sK4","sK2") &
~mia_forename("sK4","sK1") &
~mia_forename("sK4","sK0") &
~mia_forename("sK3","sK4") &
~mia_forename("sK3","sK3") &
~mia_forename("sK3","sK2") &
~forename("sK4","sK4") &
~forename("sK3","sK4") &
~forename("sK2","sK4") &
~forename("sK1","sK4") &
~forename("sK4","sK3") &
~forename("sK4","sK0") &
~forename("sK3","sK3") &
~forename("sK3","sK0") &
~forename("sK2","sK3") &
~forename("sK2","sK0") &
~forename("sK1","sK3") &
~forename("sK1","sK0") &
~forename("sK0","sK1") &
~forename("sK0","sK0") &
forename("sK0","sK2") &
~forename("sK4","sK1") &
~forename("sK3","sK1") &
~forename("sK2","sK1") &
~forename("sK1","sK1") &
~forename("sK0","sK4") &
~forename("sK0","sK3") &
~forename("sK4","sK2") &
~forename("sK3","sK2") &
~forename("sK2","sK2") &
~forename("sK1","sK2") &
~abstraction("sK3","sK1") &
~abstraction("sK3","sK0") &
~abstraction("sK2","sK4") &
~abstraction("sK2","sK3") &
~abstraction("sK2","sK2") &
~abstraction("sK2","sK1") &
~abstraction("sK2","sK0") &
~abstraction("sK1","sK4") &
~abstraction("sK1","sK3") &
~abstraction("sK1","sK2") &
~abstraction("sK1","sK1") &
~abstraction("sK1","sK0") &
abstraction("sK0","sK2") &
~abstraction("sK0","sK1") &
~abstraction("sK0","sK4") &
~abstraction("sK0","sK3") &
~abstraction("sK0","sK0") &
~abstraction("sK4","sK4") &
~abstraction("sK4","sK3") &
~abstraction("sK4","sK2") &
~abstraction("sK4","sK1") &
~abstraction("sK4","sK0") &
~abstraction("sK3","sK4") &
~abstraction("sK3","sK3") &
~abstraction("sK3","sK2") &
unisex("sK3","sK1") &
unisex("sK3","sK0") &
unisex("sK2","sK4") &
unisex("sK2","sK3") &
unisex("sK2","sK2") &
unisex("sK2","sK1") &
unisex("sK2","sK0") &
unisex("sK1","sK4") &
unisex("sK1","sK3") &
unisex("sK1","sK2") &
unisex("sK1","sK1") &
unisex("sK1","sK0") &
unisex("sK0","sK4") &
~unisex("sK0","sK1") &
unisex("sK0","sK3") &
unisex("sK0","sK2") &
~unisex("sK0","sK0") &
unisex("sK4","sK4") &
unisex("sK4","sK3") &
unisex("sK4","sK2") &
unisex("sK4","sK1") &
unisex("sK4","sK0") &
unisex("sK3","sK4") &
unisex("sK3","sK3") &
unisex("sK3","sK2") &
~general("sK2","sK2") &
~general("sK2","sK1") &
~general("sK2","sK0") &
~general("sK1","sK4") &
~general("sK1","sK3") &
~general("sK1","sK2") &
~general("sK1","sK1") &
~general("sK1","sK0") &
~general("sK0","sK4") &
~general("sK0","sK3") &
~general("sK0","sK1") &
~general("sK0","sK0") &
general("sK0","sK2") &
~general("sK4","sK4") &
~general("sK4","sK3") &
~general("sK4","sK2") &
~general("sK4","sK1") &
~general("sK4","sK0") &
~general("sK3","sK4") &
~general("sK3","sK3") &
~general("sK3","sK2") &
~general("sK3","sK1") &
~general("sK3","sK0") &
~general("sK2","sK4") &
~general("sK2","sK3") &
~nonhuman("sK3","sK1") &
~nonhuman("sK3","sK0") &
~nonhuman("sK2","sK4") &
~nonhuman("sK2","sK3") &
~nonhuman("sK2","sK2") &
~nonhuman("sK2","sK1") &
~nonhuman("sK2","sK0") &
~nonhuman("sK1","sK4") &
~nonhuman("sK1","sK3") &
~nonhuman("sK1","sK2") &
~nonhuman("sK1","sK1") &
~nonhuman("sK1","sK0") &
nonhuman("sK0","sK2") &
~nonhuman("sK0","sK1") &
~nonhuman("sK0","sK4") &
~nonhuman("sK0","sK3") &
~nonhuman("sK0","sK0") &
~nonhuman("sK4","sK4") &
~nonhuman("sK4","sK3") &
~nonhuman("sK4","sK2") &
~nonhuman("sK4","sK1") &
~nonhuman("sK4","sK0") &
~nonhuman("sK3","sK4") &
~nonhuman("sK3","sK3") &
~nonhuman("sK3","sK2") &
thing("sK2","sK1") &
thing("sK2","sK0") &
thing("sK1","sK4") &
thing("sK1","sK3") &
thing("sK1","sK2") &
thing("sK1","sK1") &
thing("sK1","sK0") &
thing("sK0","sK4") &
thing("sK0","sK3") &
thing("sK0","sK2") &
thing("sK0","sK1") &
thing("sK0","sK0") &
thing("sK4","sK4") &
thing("sK4","sK3") &
thing("sK4","sK2") &
thing("sK4","sK1") &
thing("sK4","sK0") &
thing("sK3","sK4") &
thing("sK3","sK3") &
thing("sK3","sK2") &
thing("sK3","sK1") &
thing("sK3","sK0") &
thing("sK2","sK4") &
thing("sK2","sK3") &
thing("sK2","sK2") &
~relation("sK3","sK1") &
~relation("sK3","sK0") &
~relation("sK2","sK4") &
~relation("sK2","sK3") &
~relation("sK2","sK2") &
~relation("sK2","sK1") &
~relation("sK2","sK0") &
~relation("sK1","sK4") &
~relation("sK1","sK3") &
~relation("sK1","sK2") &
~relation("sK1","sK1") &
~relation("sK1","sK0") &
relation("sK0","sK2") &
~relation("sK0","sK4") &
~relation("sK0","sK3") &
~relation("sK0","sK1") &
~relation("sK0","sK0") &
~relation("sK4","sK4") &
~relation("sK4","sK3") &
~relation("sK4","sK2") &
~relation("sK4","sK1") &
~relation("sK4","sK0") &
~relation("sK3","sK4") &
~relation("sK3","sK3") &
~relation("sK3","sK2") &
~relname("sK3","sK1") &
~relname("sK3","sK0") &
~relname("sK2","sK4") &
~relname("sK2","sK3") &
~relname("sK2","sK2") &
~relname("sK2","sK1") &
~relname("sK2","sK0") &
~relname("sK1","sK4") &
~relname("sK1","sK3") &
~relname("sK1","sK2") &
~relname("sK1","sK1") &
~relname("sK1","sK0") &
relname("sK0","sK2") &
~relname("sK0","sK4") &
~relname("sK0","sK3") &
~relname("sK0","sK1") &
~relname("sK0","sK0") &
~relname("sK4","sK4") &
~relname("sK4","sK3") &
~relname("sK4","sK2") &
~relname("sK4","sK1") &
~relname("sK4","sK0") &
~relname("sK3","sK4") &
~relname("sK3","sK3") &
~relname("sK3","sK2") &
object("sK3","sK1") &
object("sK3","sK0") &
object("sK2","sK4") &
object("sK2","sK3") &
object("sK2","sK2") &
object("sK2","sK1") &
object("sK2","sK0") &
object("sK1","sK4") &
object("sK1","sK3") &
object("sK1","sK2") &
object("sK1","sK1") &
object("sK1","sK0") &
~object("sK0","sK1") &
object("sK0","sK3") &
~object("sK0","sK2") &
~object("sK0","sK4") &
~object("sK0","sK0") &
object("sK4","sK4") &
object("sK4","sK3") &
object("sK4","sK2") &
object("sK4","sK1") &
object("sK4","sK0") &
object("sK3","sK4") &
object("sK3","sK3") &
object("sK3","sK2") &
nonliving("sK3","sK1") &
nonliving("sK3","sK0") &
nonliving("sK2","sK4") &
nonliving("sK2","sK3") &
nonliving("sK2","sK2") &
nonliving("sK2","sK1") &
nonliving("sK2","sK0") &
nonliving("sK1","sK4") &
nonliving("sK1","sK3") &
nonliving("sK1","sK2") &
nonliving("sK1","sK1") &
nonliving("sK1","sK0") &
~nonliving("sK0","sK1") &
nonliving("sK0","sK3") &
~nonliving("sK0","sK4") &
~nonliving("sK0","sK2") &
~nonliving("sK0","sK0") &
nonliving("sK4","sK4") &
nonliving("sK4","sK3") &
nonliving("sK4","sK2") &
nonliving("sK4","sK1") &
nonliving("sK4","sK0") &
nonliving("sK3","sK4") &
nonliving("sK3","sK3") &
nonliving("sK3","sK2") &
existent("sK2","sK2") &
existent("sK2","sK1") &
existent("sK2","sK0") &
existent("sK1","sK4") &
existent("sK1","sK3") &
existent("sK1","sK2") &
existent("sK1","sK1") &
existent("sK1","sK0") &
existent("sK0","sK3") &
existent("sK0","sK2") &
existent("sK0","sK1") &
existent("sK0","sK0") &
~existent("sK0","sK4") &
existent("sK4","sK4") &
existent("sK4","sK3") &
existent("sK4","sK2") &
existent("sK4","sK1") &
existent("sK4","sK0") &
existent("sK3","sK4") &
existent("sK3","sK3") &
existent("sK3","sK2") &
existent("sK3","sK1") &
existent("sK3","sK0") &
existent("sK2","sK4") &
existent("sK2","sK3") &
specific("sK2","sK3") &
specific("sK2","sK2") &
specific("sK2","sK1") &
specific("sK2","sK0") &
specific("sK1","sK4") &
specific("sK1","sK3") &
specific("sK1","sK2") &
specific("sK1","sK1") &
specific("sK1","sK0") &
specific("sK0","sK3") &
specific("sK0","sK1") &
specific("sK0","sK0") &
~specific("sK0","sK2") &
specific("sK0","sK4") &
specific("sK4","sK4") &
specific("sK4","sK3") &
specific("sK4","sK2") &
specific("sK4","sK1") &
specific("sK4","sK0") &
specific("sK3","sK4") &
specific("sK3","sK3") &
specific("sK3","sK2") &
specific("sK3","sK1") &
specific("sK3","sK0") &
specific("sK2","sK4") &
~substance_matter("sK3","sK1") &
~substance_matter("sK3","sK0") &
~substance_matter("sK2","sK4") &
~substance_matter("sK2","sK3") &
~substance_matter("sK2","sK2") &
~substance_matter("sK2","sK1") &
~substance_matter("sK2","sK0") &
~substance_matter("sK1","sK4") &
~substance_matter("sK1","sK3") &
~substance_matter("sK1","sK2") &
~substance_matter("sK1","sK1") &
~substance_matter("sK1","sK0") &
~substance_matter("sK0","sK4") &
~substance_matter("sK0","sK1") &
~substance_matter("sK0","sK2") &
substance_matter("sK0","sK3") &
~substance_matter("sK0","sK0") &
~substance_matter("sK4","sK4") &
~substance_matter("sK4","sK3") &
~substance_matter("sK4","sK2") &
~substance_matter("sK4","sK1") &
~substance_matter("sK4","sK0") &
~substance_matter("sK3","sK4") &
~substance_matter("sK3","sK3") &
~substance_matter("sK3","sK2") &
~food("sK3","sK1") &
~food("sK3","sK0") &
~food("sK2","sK4") &
~food("sK2","sK3") &
~food("sK2","sK2") &
~food("sK2","sK1") &
~food("sK2","sK0") &
~food("sK1","sK4") &
~food("sK1","sK3") &
~food("sK1","sK2") &
~food("sK1","sK1") &
~food("sK1","sK0") &
~food("sK0","sK2") &
food("sK0","sK3") &
~food("sK0","sK4") &
~food("sK0","sK1") &
~food("sK0","sK0") &
~food("sK4","sK4") &
~food("sK4","sK3") &
~food("sK4","sK2") &
~food("sK4","sK1") &
~food("sK4","sK0") &
~food("sK3","sK4") &
~food("sK3","sK3") &
~food("sK3","sK2") &
~beverage("sK3","sK1") &
~beverage("sK3","sK0") &
~beverage("sK2","sK4") &
~beverage("sK2","sK3") &
~beverage("sK2","sK2") &
~beverage("sK2","sK1") &
~beverage("sK2","sK0") &
~beverage("sK1","sK4") &
~beverage("sK1","sK3") &
~beverage("sK1","sK2") &
~beverage("sK1","sK1") &
~beverage("sK1","sK0") &
~beverage("sK0","sK2") &
beverage("sK0","sK3") &
~beverage("sK0","sK4") &
~beverage("sK0","sK1") &
~beverage("sK0","sK0") &
~beverage("sK4","sK4") &
~beverage("sK4","sK3") &
~beverage("sK4","sK2") &
~beverage("sK4","sK1") &
~beverage("sK4","sK0") &
~beverage("sK3","sK4") &
~beverage("sK3","sK3") &
~beverage("sK3","sK2") &
~shake_beverage("sK3","sK1") &
~shake_beverage("sK3","sK0") &
~shake_beverage("sK2","sK4") &
~shake_beverage("sK2","sK3") &
~shake_beverage("sK2","sK2") &
~shake_beverage("sK2","sK1") &
~shake_beverage("sK2","sK0") &
~shake_beverage("sK1","sK4") &
~shake_beverage("sK1","sK3") &
~shake_beverage("sK1","sK2") &
~shake_beverage("sK1","sK1") &
~shake_beverage("sK1","sK0") &
shake_beverage("sK0","sK3") &
~shake_beverage("sK0","sK4") &
~shake_beverage("sK0","sK2") &
~shake_beverage("sK0","sK1") &
~shake_beverage("sK0","sK0") &
~shake_beverage("sK4","sK4") &
~shake_beverage("sK4","sK3") &
~shake_beverage("sK4","sK2") &
~shake_beverage("sK4","sK1") &
~shake_beverage("sK4","sK0") &
~shake_beverage("sK3","sK4") &
~shake_beverage("sK3","sK3") &
~shake_beverage("sK3","sK2") &
~order("sK3","sK1") &
~order("sK3","sK0") &
~order("sK2","sK4") &
~order("sK2","sK3") &
~order("sK2","sK2") &
~order("sK2","sK1") &
~order("sK2","sK0") &
~order("sK1","sK4") &
~order("sK1","sK3") &
~order("sK1","sK2") &
~order("sK1","sK1") &
~order("sK1","sK0") &
~order("sK0","sK2") &
order("sK0","sK4") &
~order("sK0","sK3") &
~order("sK0","sK1") &
~order("sK0","sK0") &
~order("sK4","sK4") &
~order("sK4","sK3") &
~order("sK4","sK2") &
~order("sK4","sK1") &
~order("sK4","sK0") &
~order("sK3","sK4") &
~order("sK3","sK3") &
~order("sK3","sK2") &
~event("sK3","sK1") &
~event("sK3","sK0") &
~event("sK2","sK4") &
~event("sK2","sK3") &
~event("sK2","sK2") &
~event("sK2","sK1") &
~event("sK2","sK0") &
~event("sK1","sK4") &
~event("sK1","sK3") &
~event("sK1","sK2") &
~event("sK1","sK1") &
~event("sK1","sK0") &
~event("sK0","sK2") &
event("sK0","sK4") &
~event("sK0","sK3") &
~event("sK0","sK1") &
~event("sK0","sK0") &
~event("sK4","sK4") &
~event("sK4","sK3") &
~event("sK4","sK2") &
~event("sK4","sK1") &
~event("sK4","sK0") &
~event("sK3","sK4") &
~event("sK3","sK3") &
~event("sK3","sK2") &
~eventuality("sK3","sK1") &
~eventuality("sK3","sK0") &
~eventuality("sK2","sK4") &
~eventuality("sK2","sK3") &
~eventuality("sK2","sK2") &
~eventuality("sK2","sK1") &
~eventuality("sK2","sK0") &
~eventuality("sK1","sK4") &
~eventuality("sK1","sK3") &
~eventuality("sK1","sK2") &
~eventuality("sK1","sK1") &
~eventuality("sK1","sK0") &
eventuality("sK0","sK4") &
~eventuality("sK0","sK1") &
~eventuality("sK0","sK2") &
~eventuality("sK0","sK3") &
~eventuality("sK0","sK0") &
~eventuality("sK4","sK4") &
~eventuality("sK4","sK3") &
~eventuality("sK4","sK2") &
~eventuality("sK4","sK1") &
~eventuality("sK4","sK0") &
~eventuality("sK3","sK4") &
~eventuality("sK3","sK3") &
~eventuality("sK3","sK2") &
~nonexistent("sK2","sK2") &
~nonexistent("sK2","sK1") &
~nonexistent("sK2","sK0") &
~nonexistent("sK1","sK4") &
~nonexistent("sK1","sK3") &
~nonexistent("sK1","sK2") &
~nonexistent("sK1","sK1") &
~nonexistent("sK1","sK0") &
~nonexistent("sK0","sK3") &
~nonexistent("sK0","sK2") &
~nonexistent("sK0","sK1") &
~nonexistent("sK0","sK0") &
nonexistent("sK0","sK4") &
~nonexistent("sK4","sK4") &
~nonexistent("sK4","sK3") &
~nonexistent("sK4","sK2") &
~nonexistent("sK4","sK1") &
~nonexistent("sK4","sK0") &
~nonexistent("sK3","sK4") &
~nonexistent("sK3","sK3") &
~nonexistent("sK3","sK2") &
~nonexistent("sK3","sK1") &
~nonexistent("sK3","sK0") &
~nonexistent("sK2","sK4") &
~nonexistent("sK2","sK3") &
singleton("sK2","sK1") &
singleton("sK2","sK0") &
singleton("sK1","sK4") &
singleton("sK1","sK3") &
singleton("sK1","sK2") &
singleton("sK1","sK1") &
singleton("sK1","sK0") &
singleton("sK0","sK4") &
singleton("sK0","sK3") &
singleton("sK0","sK2") &
singleton("sK0","sK1") &
singleton("sK0","sK0") &
singleton("sK4","sK4") &
singleton("sK4","sK3") &
singleton("sK4","sK2") &
singleton("sK4","sK1") &
singleton("sK4","sK0") &
singleton("sK3","sK4") &
singleton("sK3","sK3") &
singleton("sK3","sK2") &
singleton("sK3","sK1") &
singleton("sK3","sK0") &
singleton("sK2","sK4") &
singleton("sK2","sK3") &
singleton("sK2","sK2") &
~act("sK3","sK1") &
~act("sK3","sK0") &
~act("sK2","sK4") &
~act("sK2","sK3") &
~act("sK2","sK2") &
~act("sK2","sK1") &
~act("sK2","sK0") &
~act("sK1","sK4") &
~act("sK1","sK3") &
~act("sK1","sK2") &
~act("sK1","sK1") &
~act("sK1","sK0") &
act("sK0","sK4") &
~act("sK0","sK2") &
~act("sK0","sK3") &
~act("sK0","sK1") &
~act("sK0","sK0") &
~act("sK4","sK4") &
~act("sK4","sK3") &
~act("sK4","sK2") &
~act("sK4","sK1") &
~act("sK4","sK0") &
~act("sK3","sK4") &
~act("sK3","sK3") &
~act("sK3","sK2") &
~of("sK4","sK0","sK0") &
~of("sK3","sK4","sK4") &
~of("sK3","sK4","sK3") &
~of("sK3","sK4","sK2") &
~of("sK3","sK4","sK1") &
~of("sK3","sK4","sK0") &
~of("sK3","sK3","sK4") &
~of("sK3","sK3","sK3") &
~of("sK3","sK3","sK2") &
~of("sK3","sK3","sK1") &
~of("sK3","sK3","sK0") &
~of("sK3","sK0","sK4") &
~of("sK3","sK0","sK3") &
~of("sK3","sK0","sK2") &
~of("sK3","sK0","sK1") &
~of("sK4","sK0","sK1") &
~of("sK4","sK0","sK2") &
~of("sK4","sK0","sK3") &
~of("sK4","sK0","sK4") &
~of("sK4","sK3","sK0") &
~of("sK4","sK3","sK1") &
~of("sK4","sK3","sK2") &
~of("sK4","sK3","sK3") &
~of("sK4","sK3","sK4") &
~of("sK4","sK4","sK0") &
~of("sK4","sK4","sK1") &
~of("sK4","sK4","sK2") &
~of("sK4","sK4","sK3") &
~of("sK4","sK4","sK4") &
of("sK1","sK2","sK0") &
of("sK1","sK2","sK1") &
~of("sK1","sK0","sK0") &
~of("sK1","sK0","sK1") &
~of("sK1","sK0","sK2") &
~of("sK1","sK0","sK3") &
~of("sK1","sK0","sK4") &
~of("sK1","sK3","sK0") &
~of("sK1","sK3","sK1") &
~of("sK1","sK3","sK2") &
~of("sK1","sK3","sK3") &
~of("sK1","sK3","sK4") &
~of("sK1","sK4","sK0") &
~of("sK1","sK4","sK1") &
~of("sK1","sK4","sK2") &
~of("sK1","sK4","sK3") &
~of("sK1","sK4","sK4") &
~of("sK2","sK0","sK0") &
~of("sK2","sK0","sK1") &
~of("sK2","sK0","sK2") &
~of("sK2","sK0","sK3") &
~of("sK2","sK0","sK4") &
~of("sK2","sK3","sK0") &
~of("sK2","sK3","sK1") &
~of("sK2","sK3","sK2") &
~of("sK2","sK3","sK3") &
~of("sK2","sK3","sK4") &
~of("sK2","sK4","sK0") &
~of("sK2","sK4","sK1") &
~of("sK2","sK4","sK2") &
~of("sK2","sK4","sK3") &
~of("sK2","sK4","sK4") &
~of("sK3","sK0","sK0") &
~of("sK2","sK1","sK4") &
~of("sK3","sK1","sK0") &
~of("sK3","sK1","sK1") &
~of("sK3","sK1","sK2") &
~of("sK3","sK1","sK3") &
~of("sK3","sK1","sK4") &
~of("sK4","sK1","sK0") &
~of("sK4","sK1","sK1") &
~of("sK4","sK1","sK2") &
~of("sK4","sK1","sK3") &
~of("sK4","sK1","sK4") &
of("sK0","sK2","sK0") &
of("sK0","sK2","sK2") &
of("sK0","sK2","sK3") &
of("sK0","sK2","sK4") &
~of("sK0","sK4","sK0") &
~of("sK0","sK4","sK2") &
~of("sK0","sK4","sK3") &
~of("sK0","sK4","sK4") &
~of("sK0","sK3","sK0") &
~of("sK0","sK3","sK2") &
~of("sK0","sK3","sK3") &
~of("sK0","sK3","sK4") &
of("sK0","sK1","sK0") &
of("sK0","sK1","sK1") &
of("sK0","sK1","sK2") &
of("sK0","sK1","sK3") &
of("sK0","sK1","sK4") &
~of("sK0","sK3","sK1") &
~of("sK0","sK4","sK1") &
of("sK0","sK2","sK1") &
of("sK1","sK2","sK2") &
of("sK1","sK2","sK3") &
of("sK1","sK2","sK4") &
of("sK2","sK2","sK0") &
of("sK2","sK2","sK1") &
of("sK2","sK2","sK2") &
of("sK2","sK2","sK3") &
of("sK2","sK2","sK4") &
of("sK3","sK2","sK0") &
of("sK3","sK2","sK1") &
of("sK3","sK2","sK2") &
of("sK3","sK2","sK3") &
of("sK3","sK2","sK4") &
of("sK4","sK2","sK0") &
of("sK4","sK2","sK1") &
of("sK4","sK2","sK2") &
~of("sK2","sK1","sK3") &
~of("sK2","sK1","sK2") &
~of("sK2","sK1","sK1") &
~of("sK2","sK1","sK0") &
~of("sK1","sK1","sK4") &
~of("sK1","sK1","sK3") &
~of("sK1","sK1","sK2") &
~of("sK1","sK1","sK1") &
~of("sK1","sK1","sK0") &
of("sK0","sK0","sK4") &
of("sK0","sK0","sK3") &
of("sK0","sK0","sK2") &
of("sK0","sK0","sK1") &
of("sK0","sK0","sK0") &
of("sK4","sK2","sK4") &
of("sK4","sK2","sK3") &
~nonreflexive("sK3","sK1") &
~nonreflexive("sK3","sK0") &
~nonreflexive("sK2","sK4") &
~nonreflexive("sK2","sK3") &
~nonreflexive("sK2","sK2") &
~nonreflexive("sK2","sK1") &
~nonreflexive("sK2","sK0") &
~nonreflexive("sK1","sK4") &
~nonreflexive("sK1","sK3") &
~nonreflexive("sK1","sK2") &
~nonreflexive("sK1","sK1") &
~nonreflexive("sK1","sK0") &
nonreflexive("sK0","sK4") &
nonreflexive("sK0","sK1") &
nonreflexive("sK0","sK3") &
nonreflexive("sK0","sK2") &
nonreflexive("sK0","sK0") &
~nonreflexive("sK4","sK4") &
~nonreflexive("sK4","sK3") &
~nonreflexive("sK4","sK2") &
~nonreflexive("sK4","sK1") &
~nonreflexive("sK4","sK0") &
~nonreflexive("sK3","sK4") &
~nonreflexive("sK3","sK3") &
~nonreflexive("sK3","sK2") &
agent("sK2","sK0","sK0") &
agent("sK1","sK4","sK4") &
agent("sK1","sK4","sK3") &
agent("sK1","sK4","sK2") &
agent("sK1","sK4","sK1") &
agent("sK1","sK4","sK0") &
agent("sK1","sK3","sK4") &
agent("sK1","sK3","sK3") &
agent("sK1","sK3","sK2") &
agent("sK1","sK3","sK1") &
agent("sK1","sK3","sK0") &
agent("sK1","sK2","sK4") &
agent("sK1","sK2","sK3") &
agent("sK1","sK2","sK2") &
agent("sK1","sK2","sK1") &
agent("sK2","sK0","sK1") &
agent("sK2","sK0","sK2") &
agent("sK2","sK0","sK3") &
agent("sK2","sK0","sK4") &
agent("sK2","sK1","sK0") &
agent("sK2","sK1","sK1") &
agent("sK2","sK1","sK2") &
agent("sK2","sK1","sK3") &
agent("sK2","sK1","sK4") &
agent("sK2","sK2","sK0") &
agent("sK2","sK2","sK1") &
agent("sK2","sK2","sK2") &
agent("sK2","sK2","sK3") &
agent("sK2","sK2","sK4") &
agent("sK2","sK3","sK0") &
agent("sK2","sK3","sK1") &
agent("sK0","sK0","sK0") &
agent("sK0","sK0","sK1") &
agent("sK0","sK0","sK2") &
agent("sK0","sK0","sK3") &
agent("sK0","sK0","sK4") &
agent("sK0","sK1","sK0") &
agent("sK0","sK1","sK1") &
agent("sK0","sK1","sK2") &
agent("sK0","sK1","sK3") &
agent("sK0","sK1","sK4") &
agent("sK0","sK2","sK0") &
agent("sK0","sK2","sK1") &
agent("sK0","sK2","sK2") &
agent("sK0","sK2","sK3") &
agent("sK0","sK2","sK4") &
agent("sK0","sK3","sK0") &
agent("sK0","sK3","sK1") &
agent("sK0","sK3","sK2") &
agent("sK0","sK3","sK3") &
agent("sK0","sK3","sK4") &
agent("sK1","sK0","sK0") &
agent("sK1","sK0","sK1") &
agent("sK1","sK0","sK2") &
agent("sK1","sK0","sK3") &
agent("sK1","sK0","sK4") &
agent("sK1","sK1","sK0") &
agent("sK1","sK1","sK1") &
agent("sK1","sK1","sK2") &
agent("sK1","sK1","sK3") &
agent("sK1","sK1","sK4") &
agent("sK1","sK2","sK0") &
agent("sK3","sK4","sK4") &
agent("sK4","sK0","sK0") &
agent("sK4","sK0","sK1") &
agent("sK4","sK0","sK2") &
agent("sK4","sK0","sK3") &
agent("sK4","sK0","sK4") &
agent("sK4","sK1","sK0") &
agent("sK4","sK1","sK1") &
agent("sK4","sK1","sK2") &
agent("sK4","sK1","sK3") &
agent("sK4","sK1","sK4") &
agent("sK4","sK2","sK0") &
agent("sK4","sK2","sK1") &
agent("sK4","sK2","sK2") &
agent("sK4","sK2","sK3") &
agent("sK4","sK2","sK4") &
agent("sK4","sK3","sK0") &
agent("sK4","sK3","sK1") &
agent("sK4","sK3","sK2") &
agent("sK4","sK3","sK3") &
agent("sK4","sK3","sK4") &
agent("sK4","sK4","sK0") &
agent("sK4","sK4","sK1") &
agent("sK4","sK4","sK2") &
agent("sK4","sK4","sK3") &
agent("sK4","sK4","sK4") &
agent("sK0","sK4","sK0") &
agent("sK0","sK4","sK2") &
agent("sK0","sK4","sK4") &
agent("sK0","sK4","sK1") &
~agent("sK0","sK4","sK3") &
agent("sK2","sK3","sK2") &
agent("sK2","sK3","sK3") &
agent("sK2","sK3","sK4") &
agent("sK2","sK4","sK0") &
agent("sK2","sK4","sK1") &
agent("sK2","sK4","sK2") &
agent("sK2","sK4","sK3") &
agent("sK2","sK4","sK4") &
agent("sK3","sK0","sK0") &
agent("sK3","sK0","sK1") &
agent("sK3","sK0","sK2") &
agent("sK3","sK0","sK3") &
agent("sK3","sK0","sK4") &
agent("sK3","sK1","sK0") &
agent("sK3","sK1","sK1") &
agent("sK3","sK1","sK2") &
agent("sK3","sK4","sK3") &
agent("sK3","sK4","sK2") &
agent("sK3","sK4","sK1") &
agent("sK3","sK4","sK0") &
agent("sK3","sK3","sK4") &
agent("sK3","sK3","sK3") &
agent("sK3","sK3","sK2") &
agent("sK3","sK3","sK1") &
agent("sK3","sK3","sK0") &
agent("sK3","sK2","sK4") &
agent("sK3","sK2","sK3") &
agent("sK3","sK2","sK2") &
agent("sK3","sK2","sK1") &
agent("sK3","sK2","sK0") &
agent("sK3","sK1","sK4") &
agent("sK3","sK1","sK3") &
patient("sK2","sK4","sK0") &
patient("sK2","sK3","sK4") &
patient("sK2","sK3","sK3") &
patient("sK2","sK3","sK2") &
patient("sK2","sK3","sK1") &
patient("sK2","sK3","sK0") &
patient("sK2","sK2","sK4") &
patient("sK2","sK2","sK3") &
patient("sK2","sK2","sK2") &
patient("sK2","sK2","sK1") &
patient("sK2","sK2","sK0") &
patient("sK2","sK1","sK4") &
patient("sK2","sK1","sK3") &
patient("sK2","sK1","sK2") &
patient("sK2","sK1","sK1") &
patient("sK2","sK4","sK1") &
patient("sK2","sK4","sK2") &
patient("sK2","sK4","sK3") &
patient("sK2","sK4","sK4") &
patient("sK3","sK0","sK0") &
patient("sK3","sK0","sK1") &
patient("sK3","sK0","sK2") &
patient("sK3","sK0","sK3") &
patient("sK3","sK0","sK4") &
patient("sK3","sK1","sK0") &
patient("sK3","sK1","sK1") &
patient("sK3","sK1","sK2") &
patient("sK3","sK1","sK3") &
patient("sK3","sK1","sK4") &
patient("sK3","sK2","sK0") &
patient("sK3","sK2","sK1") &
patient("sK1","sK0","sK0") &
patient("sK1","sK0","sK1") &
patient("sK1","sK0","sK2") &
patient("sK1","sK0","sK3") &
patient("sK1","sK0","sK4") &
patient("sK1","sK1","sK0") &
patient("sK1","sK1","sK1") &
patient("sK1","sK1","sK2") &
patient("sK1","sK1","sK3") &
patient("sK1","sK1","sK4") &
patient("sK1","sK2","sK0") &
patient("sK1","sK2","sK1") &
patient("sK1","sK2","sK2") &
patient("sK1","sK2","sK3") &
patient("sK1","sK2","sK4") &
patient("sK1","sK3","sK0") &
patient("sK1","sK3","sK1") &
patient("sK1","sK3","sK2") &
patient("sK1","sK3","sK3") &
patient("sK1","sK3","sK4") &
patient("sK1","sK4","sK0") &
patient("sK1","sK4","sK1") &
patient("sK1","sK4","sK2") &
patient("sK1","sK4","sK3") &
patient("sK1","sK4","sK4") &
patient("sK2","sK0","sK0") &
patient("sK2","sK0","sK1") &
patient("sK2","sK0","sK2") &
patient("sK2","sK0","sK3") &
patient("sK2","sK0","sK4") &
patient("sK2","sK1","sK0") &
patient("sK4","sK3","sK4") &
patient("sK4","sK4","sK0") &
patient("sK4","sK4","sK1") &
patient("sK4","sK4","sK2") &
patient("sK4","sK4","sK3") &
patient("sK4","sK4","sK4") &
~patient("sK0","sK0","sK0") &
~patient("sK0","sK0","sK1") &
~patient("sK0","sK0","sK2") &
~patient("sK0","sK0","sK3") &
~patient("sK0","sK0","sK4") &
~patient("sK0","sK2","sK0") &
~patient("sK0","sK2","sK1") &
~patient("sK0","sK2","sK2") &
~patient("sK0","sK2","sK3") &
~patient("sK0","sK2","sK4") &
~patient("sK0","sK3","sK0") &
~patient("sK0","sK3","sK1") &
~patient("sK0","sK3","sK2") &
~patient("sK0","sK3","sK3") &
~patient("sK0","sK3","sK4") &
~patient("sK0","sK1","sK0") &
~patient("sK0","sK1","sK1") &
~patient("sK0","sK1","sK2") &
~patient("sK0","sK1","sK3") &
~patient("sK0","sK1","sK4") &
~patient("sK0","sK4","sK0") &
~patient("sK0","sK4","sK2") &
~patient("sK0","sK4","sK4") &
patient("sK0","sK4","sK3") &
~patient("sK0","sK4","sK1") &
patient("sK3","sK2","sK2") &
patient("sK3","sK2","sK3") &
patient("sK3","sK2","sK4") &
patient("sK3","sK3","sK0") &
patient("sK3","sK3","sK1") &
patient("sK3","sK3","sK2") &
patient("sK3","sK3","sK3") &
patient("sK3","sK3","sK4") &
patient("sK3","sK4","sK0") &
patient("sK3","sK4","sK1") &
patient("sK3","sK4","sK2") &
patient("sK3","sK4","sK3") &
patient("sK3","sK4","sK4") &
patient("sK4","sK0","sK0") &
patient("sK4","sK0","sK1") &
patient("sK4","sK0","sK2") &
patient("sK4","sK3","sK3") &
patient("sK4","sK3","sK2") &
patient("sK4","sK3","sK1") &
patient("sK4","sK3","sK0") &
patient("sK4","sK2","sK4") &
patient("sK4","sK2","sK3") &
patient("sK4","sK2","sK2") &
patient("sK4","sK2","sK1") &
patient("sK4","sK2","sK0") &
patient("sK4","sK1","sK4") &
patient("sK4","sK1","sK3") &
patient("sK4","sK1","sK2") &
patient("sK4","sK1","sK1") &
patient("sK4","sK1","sK0") &
patient("sK4","sK0","sK4") &
patient("sK4","sK0","sK3") &
actual_world("sK0") &
actual_world("sK1") &
actual_world("sK2") &
actual_world("sK3") &
actual_world("sK4") &
past("sK0","sK0") &
past("sK0","sK1") &
past("sK0","sK2") &
past("sK0","sK3") &
past("sK0","sK4") &
past("sK1","sK0") &
past("sK1","sK1") &
past("sK1","sK2") &
past("sK1","sK3") &
past("sK1","sK4") &
past("sK2","sK0") &
past("sK2","sK1") &
past("sK2","sK2") &
past("sK2","sK3") &
past("sK2","sK4") &
past("sK3","sK0") &
past("sK3","sK1") &
past("sK3","sK2") &
past("sK3","sK3") &
past("sK3","sK4") &
past("sK4","sK0") &
past("sK4","sK1") &
past("sK4","sK2") &
past("sK4","sK3") &
past("sK4","sK4") ) ).
```

### Sample solution for SWV017+1

```# SZS output start Saturation.
cnf(u82,axiom,
fresh_intruder_nonce(generate_intruder_nonce(X0)) | ~fresh_intruder_nonce(X0)).

cnf(u70,axiom,
fresh_intruder_nonce(an_intruder_nonce)).

cnf(u89,axiom,
intruder_holds(key(X0,X1)) | ~party_of_protocol(X1) | ~intruder_message(X0)).

cnf(u97,axiom,
intruder_message(triple(X0,X1,X2)) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)).

cnf(u98,axiom,
intruder_message(encrypt(X0,X1)) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(X0)).

cnf(u104,axiom,
intruder_message(quadruple(X0,X1,X2,X3)) | ~intruder_message(X3) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)).

cnf(u90,axiom,
intruder_message(pair(X0,X1)) | ~intruder_message(X1) | ~intruder_message(X0)).

cnf(u103,axiom,

cnf(u102,axiom,

cnf(u101,axiom,

cnf(u100,axiom,

cnf(u99,axiom,
intruder_message(X1) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(encrypt(X0,X1))).

cnf(u95,axiom,
intruder_message(X2) | ~intruder_message(triple(X0,X1,X2))).

cnf(u94,axiom,
intruder_message(X1) | ~intruder_message(triple(X0,X1,X2))).

cnf(u93,axiom,
intruder_message(X0) | ~intruder_message(triple(X0,X1,X2))).

cnf(u92,axiom,
intruder_message(X2) | ~message(sent(X0,X1,X2))).

cnf(u88,axiom,
intruder_message(X1) | ~intruder_message(pair(X0,X1))).

cnf(u87,axiom,
intruder_message(X0) | ~intruder_message(pair(X0,X1))).

cnf(u84,axiom,
intruder_message(X0) | ~fresh_intruder_nonce(X0)).

cnf(u81,axiom,
a_nonce(generate_b_nonce(X0))).

cnf(u80,axiom,
a_nonce(generate_expiration_time(X0))).

cnf(u71,axiom,
a_nonce(an_a_nonce)).

cnf(u86,axiom,
~a_nonce(X0) | ~a_key(X0)).

cnf(u85,axiom,
~a_nonce(generate_key(X0))).

cnf(u77,axiom,
t_holds(key(bt,b))).

cnf(u76,axiom,
t_holds(key(at,a))).

cnf(u79,axiom,
a_key(generate_key(X0))).

cnf(u109,axiom,
~a_key(generate_b_nonce(X1))).

cnf(u108,axiom,
~a_key(generate_expiration_time(X0))).

cnf(u107,axiom,
~a_key(an_a_nonce)).

cnf(u83,axiom,
fresh_to_b(X0) | ~fresh_intruder_nonce(X0)).

cnf(u69,axiom,
fresh_to_b(an_a_nonce)).

cnf(u75,axiom,
a_stored(pair(b,an_a_nonce))).

cnf(u91,axiom,
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)))).

cnf(u105,axiom,

cnf(u78,axiom,
message(sent(a,b,pair(a,an_a_nonce)))).

cnf(u106,axiom,
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))))).

cnf(u96,axiom,
message(sent(X1,X2,X0)) | ~party_of_protocol(X2) | ~party_of_protocol(X1) | ~intruder_message(X0)).

cnf(u74,axiom,
party_of_protocol(b)).

cnf(u73,axiom,
party_of_protocol(a)).

cnf(u72,axiom,
party_of_protocol(t)).

# SZS output end Saturation.
```

### Sample solution for CSR082+1

```% SZS answers Tuple [[s__agent__m,s__experiencer__m]|_] for CSR082+1
```

## Zenon 0.7.1

Damien Doligez
INRIA, France

### Sample solution for SEU140+2

```(* PROOF-FOUND *)
(* BEGIN-PROOF *)
Theorem t63_xboole_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zen
on_U, (((subset A B)/\(disjoint B C))->(disjoint A C))))).
Proof.
apply NNPP. intro zenon_G.
apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zen
on_U, (((subset A B)/\(disjoint B C))->(disjoint A C))))) zenon_G); [ zenon_intr
o zenon_H3; idtac ].
elim zenon_H3. zenon_intro zenon_TA_e. zenon_intro zenon_H5.
apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((subset zenon
_TA_e B)/\(disjoint B C))->(disjoint zenon_TA_e C)))) zenon_H5); [ zenon_intro z
enon_H6; idtac ].
elim zenon_H6. zenon_intro zenon_TB_h. zenon_intro zenon_H8.
apply (zenon_notallex_s (fun C : zenon_U => (((subset zenon_TA_e zenon_TB_h)/\(d
isjoint zenon_TB_h C))->(disjoint zenon_TA_e C))) zenon_H8); [ zenon_intro zenon
_H9; idtac ].
elim zenon_H9. zenon_intro zenon_TC_k. zenon_intro zenon_Hb.
apply (zenon_notimply_s _ _ zenon_Hb). zenon_intro zenon_Hd. zenon_intro zenon_H
c.
apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_Hf. zenon_intro zenon_He.
generalize (d3_tarski zenon_TA_e). zenon_intro zenon_H10.
generalize (zenon_H10 zenon_TB_h). zenon_intro zenon_H11.
apply (zenon_equiv_s _ _ zenon_H11); [ zenon_intro zenon_H14; zenon_intro zenon_
H13 | zenon_intro zenon_Hf; zenon_intro zenon_H12 ].
exact (zenon_H14 zenon_Hf).
generalize (t3_xboole_0 zenon_TB_h). zenon_intro zenon_H15.
generalize (zenon_H15 zenon_TC_k). zenon_intro zenon_H16.
apply (zenon_and_s _ _ zenon_H16). zenon_intro zenon_H18. zenon_intro zenon_H17.
apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H1a | zenon_intro zeno
n_H19 ].
generalize (t3_xboole_0 zenon_TC_k). zenon_intro zenon_H1b.
generalize (zenon_H1b zenon_TB_h). zenon_intro zenon_H1c.
apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H1d.
apply (zenon_notand_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zeno
n_H1f ].
apply zenon_H20. zenon_intro zenon_H21.
apply (zenon_notand_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zeno
n_H22 ].
generalize (t3_xboole_0 zenon_TA_e). zenon_intro zenon_H24.
generalize (zenon_H24 zenon_TC_k). zenon_intro zenon_H25.
apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26.
apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zeno
n_H28 ].
exact (zenon_H29 zenon_Hc).
apply (zenon_notallex_s (fun C : zenon_U => (~((in C zenon_TA_e)/\(in C zenon_TC
_k)))) zenon_H28); [ zenon_intro zenon_H2a; idtac ].
elim zenon_H2a. zenon_intro zenon_TC_br. zenon_intro zenon_H2c.
apply zenon_H2c. zenon_intro zenon_H2d.
apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H2f. zenon_intro zenon_H2e.
apply zenon_H23. exists zenon_TC_br. apply NNPP. zenon_intro zenon_H30.
apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zeno
n_H31 ].
exact (zenon_H32 zenon_H2e).
generalize (zenon_H12 zenon_TC_br). zenon_intro zenon_H33.
apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon
_H34 ].
exact (zenon_H35 zenon_H2f).
exact (zenon_H31 zenon_H34).
exact (zenon_H22 zenon_H21).
apply (zenon_notallex_s (fun C : zenon_U => (~((in C zenon_TC_k)/\(in C zenon_TB
_h)))) zenon_H1f); [ zenon_intro zenon_H36; idtac ].
elim zenon_H36. zenon_intro zenon_TC_cd. zenon_intro zenon_H38.
apply zenon_H38. zenon_intro zenon_H39.
apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
apply zenon_H1a. exists zenon_TC_cd. apply NNPP. zenon_intro zenon_H3c.
apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zeno
n_H3d ].
exact (zenon_H3e zenon_H3a).
exact (zenon_H3d zenon_H3b).
exact (zenon_H19 zenon_He).
Qed.
(* END-PROOF *)
```