%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU262+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:03 PM UTC 2026
% Result : Theorem 10.95s 2.43s
% Output : Refutation 11.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 99 ( 19 unt; 5 def)
% Number of atoms : 295 ( 31 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 330 ( 134 ~; 140 |; 34 &)
% ( 15 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-2 aty)
% Number of variables : 200 ( 0 sgn 179 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f10,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f43,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f48,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f55,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f57,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f108,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f188,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f198,conjecture,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_dom(X2),X0)
& subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f199,negated_conjecture,
~ ! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_dom(X2),X0)
& subset(relation_rng(X2),X1) ) ),
inference(negated_conjecture,[status(cth)],[f198]) ).
fof(f266,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f305,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f347,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f378,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f382,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f388,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f422,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f108]) ).
fof(f495,plain,
? [X0,X1,X2] :
( ( ~ subset(relation_dom(X2),X0)
| ~ subset(relation_rng(X2),X1) )
& relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f199]) ).
fof(f744,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f378]) ).
fof(f745,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f744]) ).
fof(f746,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK47(X0,X1),X1)
& in(sK47(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(X2,sK47(X0,X1))],[f745]) ).
fof(f757,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f382]) ).
fof(f758,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f757]) ).
fof(f759,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK51(X0,X1),X3),X0)
| ~ in(sK51(X0,X1),X1) )
& ( in(ordered_pair(sK51(X0,X1),sK52(X0,X1)),X0)
| in(sK51(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK53(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51,sK52,sK53]),skolemize(X2,sK51(X0,X1)),skolemize(X4,sK52(X0,X1)),skolemize(X7,sK53(X0,X5))],[f758]) ).
fof(f775,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f388]) ).
fof(f776,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f775]) ).
fof(f777,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK63(X0,X1)),X0)
| ~ in(sK63(X0,X1),X1) )
& ( in(ordered_pair(sK64(X0,X1),sK63(X0,X1)),X0)
| in(sK63(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK65(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63,sK64,sK65]),skolemize(X2,sK63(X0,X1)),skolemize(X4,sK64(X0,X1)),skolemize(X7,sK65(X0,X5))],[f776]) ).
fof(f848,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f188]) ).
fof(f849,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f848]) ).
fof(f852,plain,
( ( ~ subset(relation_dom(sK110),sK108)
| ~ subset(relation_rng(sK110),sK109) )
& relation_of2_as_subset(sK110,sK108,sK109) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108,sK109,sK110]),skolemize(X0,sK108),skolemize(X1,sK109),skolemize(X2,sK110)],[f495]) ).
fof(f879,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f266]) ).
fof(f918,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f347]) ).
fof(f926,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f1067,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f746]) ).
fof(f1068,plain,
! [X0,X1] :
( in(sK47(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f746]) ).
fof(f1069,plain,
! [X0,X1] :
( ~ in(sK47(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f746]) ).
fof(f1088,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK53(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f759]) ).
fof(f1123,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK65(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f777]) ).
fof(f1128,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f57]) ).
fof(f1206,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f422]) ).
fof(f1359,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f849]) ).
fof(f1360,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f849]) ).
fof(f1374,plain,
relation_of2_as_subset(sK110,sK108,sK109),
inference(cnf_transformation,[],[f852]) ).
fof(f1375,plain,
( ~ subset(relation_dom(sK110),sK108)
| ~ subset(relation_rng(sK110),sK109) ),
inference(cnf_transformation,[],[f852]) ).
fof(f1475,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f879]) ).
fof(f1549,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f305]) ).
fof(f1588,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1128,f1549]) ).
fof(f1650,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK53(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1088,f1588]) ).
fof(f1657,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK65(X0,X5),X5),unordered_pair(sK65(X0,X5),sK65(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1123,f1588]) ).
fof(f1721,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f1360,f1588]) ).
fof(f1722,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f1359,f1588]) ).
fof(f1844,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK53(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1650]) ).
fof(f1856,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK65(X0,X5),X5),unordered_pair(sK65(X0,X5),sK65(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1657]) ).
fof(f1885,definition,
sF130 = relation_dom(sK110),
introduced(definition,[new_symbols(definition,[sF130])],[function_definition]) ).
fof(f1886,plain,
relation_dom(sK110) = sF130,
inference(reorient_equations,[],[f1885]) ).
fof(f1887,definition,
sF131 = relation_rng(sK110),
introduced(definition,[new_symbols(definition,[sF131])],[function_definition]) ).
fof(f1888,plain,
relation_rng(sK110) = sF131,
inference(reorient_equations,[],[f1887]) ).
fof(f1889,plain,
( ~ subset(sF130,sK108)
| ~ subset(sF131,sK109) ),
inference(definition_folding,[],[f1375,f1888,f1886]) ).
fof(f1896,definition,
( spl132_1
<=> subset(sF131,sK109) ),
introduced(definition,[new_symbols(definition,[spl132_1])],[avatar_definition]) ).
fof(f1898,plain,
( ~ subset(sF131,sK109)
| spl132_1 ),
inference(avatar_component_clause,[],[f1896]) ).
fof(f1900,definition,
( spl132_2
<=> subset(sF130,sK108) ),
introduced(definition,[new_symbols(definition,[spl132_2])],[avatar_definition]) ).
fof(f1902,plain,
( ~ subset(sF130,sK108)
| spl132_2 ),
inference(avatar_component_clause,[],[f1900]) ).
fof(f1903,plain,
( ~ spl132_1
| ~ spl132_2 ),
inference(avatar_split_clause,[],[f1889,f1900,f1896]) ).
fof(f1975,definition,
( spl132_6
<=> relation(sK110) ),
introduced(definition,[new_symbols(definition,[spl132_6])],[avatar_definition]) ).
fof(f1976,plain,
( relation(sK110)
| ~ spl132_6 ),
inference(avatar_component_clause,[],[f1975]) ).
fof(f1985,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f918,f1206]) ).
fof(f1986,plain,
relation(sK110),
inference(resolution,[],[f1985,f1374]) ).
fof(f1987,plain,
spl132_6,
inference(avatar_split_clause,[],[f1986,f1975]) ).
fof(f1995,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK65(X1,X0)),unordered_pair(sK65(X1,X0),sK65(X1,X0))),X1)
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) ),
inference(superposition,[],[f1856,f926]) ).
fof(f2351,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),cartesian_product2(X2,X3))
| in(X0,X3) ),
inference(superposition,[],[f1722,f926]) ).
fof(f2480,plain,
! [X2,X0,X1] :
( subset(X0,cartesian_product2(X1,X2))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(resolution,[],[f1475,f1206]) ).
fof(f2483,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ in(X3,X0)
| in(X3,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f2480,f1067]) ).
fof(f4483,plain,
! [X0] :
( in(X0,cartesian_product2(sK108,sK109))
| ~ in(X0,sK110) ),
inference(resolution,[],[f2483,f1374]) ).
fof(f4488,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK110)
| in(X0,sK108) ),
inference(resolution,[],[f4483,f1721]) ).
fof(f4491,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),sK110)
| in(X0,sK109) ),
inference(resolution,[],[f4483,f2351]) ).
fof(f4557,plain,
! [X0] :
( in(X0,sK109)
| ~ in(X0,relation_rng(sK110))
| ~ relation(sK110) ),
inference(resolution,[],[f4491,f1995]) ).
fof(f4562,plain,
( ! [X0] :
( in(X0,sK109)
| ~ in(X0,relation_rng(sK110)) )
| ~ spl132_6 ),
inference(forward_subsumption_resolution,[],[f4557,f1976]) ).
fof(f4563,plain,
( ! [X0] :
( ~ in(X0,sF131)
| in(X0,sK109) )
| ~ spl132_6 ),
inference(forward_demodulation,[],[f4562,f1888]) ).
fof(f4574,plain,
! [X0] :
( in(X0,sK108)
| ~ in(X0,relation_dom(sK110))
| ~ relation(sK110) ),
inference(resolution,[],[f4488,f1844]) ).
fof(f4581,plain,
( ! [X0] :
( in(X0,sK108)
| ~ in(X0,relation_dom(sK110)) )
| ~ spl132_6 ),
inference(forward_subsumption_resolution,[],[f4574,f1976]) ).
fof(f4583,plain,
( ! [X0] :
( ~ in(X0,sF130)
| in(X0,sK108) )
| ~ spl132_6 ),
inference(forward_demodulation,[],[f4581,f1886]) ).
fof(f4592,plain,
( ! [X0] :
( in(sK47(sF130,X0),sK108)
| subset(sF130,X0) )
| ~ spl132_6 ),
inference(resolution,[],[f4583,f1068]) ).
fof(f4596,plain,
( subset(sF130,sK108)
| subset(sF130,sK108)
| ~ spl132_6 ),
inference(resolution,[],[f4592,f1069]) ).
fof(f4601,plain,
( subset(sF130,sK108)
| ~ spl132_6 ),
inference(duplicate_literal_removal,[],[f4596]) ).
fof(f4618,plain,
( $false
| spl132_2
| ~ spl132_6 ),
inference(forward_subsumption_resolution,[],[f4601,f1902]) ).
fof(f4619,plain,
( spl132_2
| ~ spl132_6 ),
inference(avatar_contradiction_clause,[],[f4618]) ).
fof(f4628,plain,
( ! [X0] :
( in(sK47(sF131,X0),sK109)
| subset(sF131,X0) )
| ~ spl132_6 ),
inference(resolution,[],[f4563,f1068]) ).
fof(f4632,plain,
( subset(sF131,sK109)
| subset(sF131,sK109)
| ~ spl132_6 ),
inference(resolution,[],[f4628,f1069]) ).
fof(f4637,plain,
( subset(sF131,sK109)
| ~ spl132_6 ),
inference(duplicate_literal_removal,[],[f4632]) ).
fof(f4638,plain,
( $false
| spl132_1
| ~ spl132_6 ),
inference(forward_subsumption_resolution,[],[f4637,f1898]) ).
fof(f4639,plain,
( spl132_1
| ~ spl132_6 ),
inference(avatar_contradiction_clause,[],[f4638]) ).
cnf(s1,plain,
( ~ spl132_1
| ~ spl132_2 ),
inference(sat_conversion,[],[f1903]) ).
cnf(s4,plain,
spl132_6,
inference(sat_conversion,[],[f1987]) ).
cnf(s113,plain,
( spl132_2
| ~ spl132_6 ),
inference(sat_conversion,[],[f4619]) ).
cnf(s114,plain,
( spl132_1
| ~ spl132_6 ),
inference(sat_conversion,[],[f4639]) ).
cnf(s115,plain,
spl132_1,
inference(rat,[],[s114,s4]) ).
cnf(s116,plain,
spl132_2,
inference(rat,[],[s113,s4]) ).
cnf(s118,plain,
$false,
inference(rat,[],[s1,s116,s115]) ).
fof(f4640,plain,
$false,
inference(avatar_sat_refutation,[],[s118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU262+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 04:22:06 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.95/2.43 % (798079)Detected formulas, will run a generic FOF schedule.
% 10.95/2.43 % (798088)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=331520253:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.95/2.43 % (798084)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4156003111:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.95/2.43 % (798086)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=402994506:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.95/2.43 % (798085)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4220164588:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.95/2.43 % (798088)Instruction limit reached!
% 10.95/2.43 % (798088)------------------------------
% 10.95/2.43 % (798088)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798088)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798088)Termination reason: Instruction limit
% 10.95/2.43 % (798088)Termination phase: Saturation
% 10.95/2.43 % (798088)Time elapsed: 0.044 s
% 10.95/2.43 % (798088)Peak memory usage: 90 MB
% 10.95/2.43 % (798088)Instructions burned: 120 (million)
% 10.95/2.43 % (798087)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=81479753:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.95/2.43 % (798089)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3928014970:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.95/2.43 % (798090)dis-21_1_sil=8000:lcm=predicate:random_seed=2119422755:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 10.95/2.43 % (798087)Instruction limit reached!
% 10.95/2.43 % (798087)------------------------------
% 10.95/2.43 % (798087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798087)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798087)Termination reason: Instruction limit
% 10.95/2.43 % (798087)Termination phase: Saturation
% 10.95/2.43 % (798087)Time elapsed: 0.070 s
% 10.95/2.43 % (798087)Peak memory usage: 90 MB
% 10.95/2.43 % (798087)Instructions burned: 110 (million)
% 10.95/2.43 % (798090)Instruction limit reached!
% 10.95/2.43 % (798090)------------------------------
% 10.95/2.43 % (798090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798090)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798090)Termination reason: Instruction limit
% 10.95/2.43 % (798090)Termination phase: Saturation
% 10.95/2.43 % (798090)Time elapsed: 0.079 s
% 10.95/2.43 % (798090)Peak memory usage: 91 MB
% 10.95/2.43 % (798090)Instructions burned: 130 (million)
% 10.95/2.43 % (798089)Instruction limit reached!
% 10.95/2.43 % (798089)------------------------------
% 10.95/2.43 % (798089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798089)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798089)Termination reason: Instruction limit
% 10.95/2.43 % (798089)Termination phase: Saturation
% 10.95/2.43 % (798089)Time elapsed: 0.100 s
% 10.95/2.43 % (798089)Peak memory usage: 91 MB
% 10.95/2.43 % (798089)Instructions burned: 140 (million)
% 10.95/2.43 % (798095)lrs+10_1_sil=8000:sp=occurrence:random_seed=1230045573:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.95/2.43 % (798095)Instruction limit reached!
% 10.95/2.43 % (798095)------------------------------
% 10.95/2.43 % (798095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798095)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798095)Termination reason: Instruction limit
% 10.95/2.43 % (798095)Termination phase: Saturation
% 10.95/2.43 % (798095)Time elapsed: 0.102 s
% 10.95/2.43 % (798095)Peak memory usage: 94 MB
% 10.95/2.43 % (798095)Instructions burned: 286 (million)
% 10.95/2.43 % (798099)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2699443480:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.95/2.43 % (798100)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1996795338:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.95/2.43 % (798099)Refutation not found, incomplete strategy
% 10.95/2.43 % (798099)------------------------------
% 10.95/2.43 % (798099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798099)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798099)Termination reason: Refutation not found, incomplete strategy
% 10.95/2.43 % (798099)Time elapsed: 0.005 s
% 10.95/2.43 % (798099)Peak memory usage: 89 MB
% 10.95/2.43 % (798099)Instructions burned: 5 (million)
% 10.95/2.43 % (798101)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1049898716:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 10.95/2.43 % (798103)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1163191976:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 10.95/2.43 % (798101)Instruction limit reached!
% 10.95/2.43 % (798101)------------------------------
% 10.95/2.43 % (798101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798101)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798101)Termination reason: Instruction limit
% 10.95/2.43 % (798101)Termination phase: Saturation
% 10.95/2.43 % (798101)Time elapsed: 0.148 s
% 10.95/2.43 % (798101)Peak memory usage: 93 MB
% 10.95/2.43 % (798101)Instructions burned: 250 (million)
% 10.95/2.43 % (798103)Instruction limit reached!
% 10.95/2.43 % (798103)------------------------------
% 10.95/2.43 % (798103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798103)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798103)Termination reason: Instruction limit
% 10.95/2.43 % (798103)Termination phase: Saturation
% 10.95/2.43 % (798103)Time elapsed: 0.102 s
% 10.95/2.43 % (798103)Peak memory usage: 91 MB
% 10.95/2.43 % (798103)Instructions burned: 296 (million)
% 10.95/2.43 % (798100)Instruction limit reached!
% 10.95/2.43 % (798100)------------------------------
% 10.95/2.43 % (798100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798100)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798100)Termination reason: Instruction limit
% 10.95/2.43 % (798100)Termination phase: Saturation
% 10.95/2.43 % (798100)Time elapsed: 0.227 s
% 10.95/2.43 % (798100)Peak memory usage: 93 MB
% 10.95/2.43 % (798100)Instructions burned: 326 (million)
% 10.95/2.43 % (798099)------------------------------
% 10.95/2.43 % (798099)------------------------------
% 10.95/2.43 % (798108)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3751057469:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.95/2.43 % (798109)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3984667771:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 10.95/2.43 % (798109)Instruction limit reached!
% 10.95/2.43 % (798109)------------------------------
% 10.95/2.43 % (798109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798109)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798109)Termination reason: Instruction limit
% 10.95/2.43 % (798109)Termination phase: Saturation
% 10.95/2.43 % (798109)Time elapsed: 0.039 s
% 10.95/2.43 % (798109)Peak memory usage: 90 MB
% 10.95/2.43 % (798109)Instructions burned: 115 (million)
% 10.95/2.43 % (798110)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2955874930:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 10.95/2.43 % (798111)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4164043145:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 10.95/2.43 % (798110)Instruction limit reached!
% 10.95/2.43 % (798110)------------------------------
% 10.95/2.43 % (798110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798110)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798110)Termination reason: Instruction limit
% 10.95/2.43 % (798110)Termination phase: Saturation
% 10.95/2.43 % (798110)Time elapsed: 0.067 s
% 10.95/2.43 % (798110)Peak memory usage: 90 MB
% 10.95/2.43 % (798110)Instructions burned: 129 (million)
% 10.95/2.43 % (798115)lrs+10_1_sil=8000:sp=occurrence:random_seed=2857782925:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 10.95/2.43 % (798111)Instruction limit reached!
% 10.95/2.43 % (798111)------------------------------
% 10.95/2.43 % (798111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798111)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798111)Termination reason: Instruction limit
% 10.95/2.43 % (798111)Termination phase: Saturation
% 10.95/2.43 % (798111)Time elapsed: 0.075 s
% 10.95/2.43 % (798111)Peak memory usage: 89 MB
% 10.95/2.43 % (798111)Instructions burned: 115 (million)
% 10.95/2.43 % (798117)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3547396182:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 10.95/2.43 % (798119)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1432401410:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 10.95/2.43 % (798115)Instruction limit reached!
% 10.95/2.43 % (798115)------------------------------
% 10.95/2.43 % (798115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798115)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798115)Termination reason: Instruction limit
% 10.95/2.43 % (798115)Termination phase: Saturation
% 10.95/2.43 % (798115)Time elapsed: 0.309 s
% 10.95/2.43 % (798115)Peak memory usage: 102 MB
% 10.95/2.43 % (798115)Instructions burned: 909 (million)
% 10.95/2.43 % (798117)Instruction limit reached!
% 10.95/2.43 % (798117)------------------------------
% 10.95/2.43 % (798117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798117)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798117)Termination reason: Instruction limit
% 10.95/2.43 % (798117)Termination phase: Saturation
% 10.95/2.43 % (798117)Time elapsed: 0.267 s
% 10.95/2.43 % (798117)Peak memory usage: 93 MB
% 10.95/2.43 % (798117)Instructions burned: 437 (million)
% 10.95/2.43 % (798084)First to succeed.
% 10.95/2.43 % (798084)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-798079"
% 10.95/2.43 % (798122)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4182823584:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 10.95/2.43 % (798122)Instruction limit reached!
% 10.95/2.43 % (798122)------------------------------
% 10.95/2.43 % (798122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.95/2.43 % (798122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.95/2.43 % (798122)CaDiCaL version: 2.1.3
% 10.95/2.43 % (798122)Termination reason: Instruction limit
% 10.95/2.43 % (798122)Termination phase: Saturation
% 10.95/2.43 % (798122)Time elapsed: 0.044 s
% 10.95/2.43 % (798122)Peak memory usage: 92 MB
% 10.95/2.43 % (798122)Instructions burned: 135 (million)
% 10.95/2.43 % (798123)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=518952061:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 10.95/2.43 % (798125)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1843158149:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 10.95/2.43 % (798084)Refutation found. Thanks to Tanya!
% 10.95/2.43 % SZS status Theorem for theBenchmark
% 10.95/2.43 % SZS output start Proof for theBenchmark
% See solution above
% 11.72/2.53 % (798084)------------------------------
% 11.72/2.53 % (798084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.72/2.53 % (798084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.72/2.53 % (798084)CaDiCaL version: 2.1.3
% 11.72/2.53 % (798084)Termination reason: Refutation
% 11.72/2.53 % (798084)Time elapsed: 1.152 s
% 11.72/2.53 % (798084)Peak memory usage: 138 MB
% 11.72/2.53 % (798084)Instructions burned: 1704 (million)
% 11.72/2.53 % (798084)------------------------------
% 11.72/2.53 % (798084)------------------------------
% 11.72/2.53 % (798079)Success in time 1.59 s
% 11.72/2.53 % Vampire exiting
%------------------------------------------------------------------------------