%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU227+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 : n009.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 12:47:52 PM UTC 2026
% Result : Theorem 5.01s 2.04s
% Output : Refutation 8.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 18 unt; 3 def)
% Number of atoms : 305 ( 41 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 385 ( 151 ~; 157 |; 55 &)
% ( 14 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 196 ( 166 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f16,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f28,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f31,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(f37,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(f151,conjecture,
! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
fof(f152,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
inference(negated_conjecture,[status(cth)],[f151]) ).
fof(f223,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f270,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f271,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f277,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f370,plain,
? [X0,X1] :
( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
& subset(X0,relation_dom(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f152]) ).
fof(f371,plain,
? [X0,X1] :
( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
& subset(X0,relation_dom(X1))
& relation(X1) ),
inference(flattening,[],[f370]) ).
fof(f498,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f270]) ).
fof(f499,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X3),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X8,X6),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f498]) ).
fof(f500,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(X4,sK11(X0,X1,X2)),X0)
| ~ in(X4,X1) )
| ~ in(sK11(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK12(X0,X1,X2),sK11(X0,X1,X2)),X0)
& in(sK12(X0,X1,X2),X1) )
| in(sK11(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(sK13(X0,X1,X6),X6),X0)
& in(sK13(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X3,sK11(X0,X1,X2)),skolemize(X5,sK12(X0,X1,X2)),skolemize(X8,sK13(X0,X1,X6))],[f499]) ).
fof(f501,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f271]) ).
fof(f502,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X6,X8),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f501]) ).
fof(f503,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(sK14(X0,X1,X2),X4),X0)
| ~ in(X4,X1) )
| ~ in(sK14(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X0)
& in(sK15(X0,X1,X2),X1) )
| in(sK14(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(X6,sK16(X0,X1,X6)),X0)
& in(sK16(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X3,sK14(X0,X1,X2)),skolemize(X5,sK15(X0,X1,X2)),skolemize(X8,sK16(X0,X1,X6))],[f502]) ).
fof(f537,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,[],[f277]) ).
fof(f538,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,[],[f537]) ).
fof(f539,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK37(X0,X1),X1)
& in(sK37(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(X2,sK37(X0,X1))],[f538]) ).
fof(f545,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,[],[f280]) ).
fof(f546,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,[],[f545]) ).
fof(f547,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK39(X0,X1),X3),X0)
| ~ in(sK39(X0,X1),X1) )
& ( in(ordered_pair(sK39(X0,X1),sK40(X0,X1)),X0)
| in(sK39(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK41(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39,sK40,sK41]),skolemize(X2,sK39(X0,X1)),skolemize(X4,sK40(X0,X1)),skolemize(X7,sK41(X0,X5))],[f546]) ).
fof(f600,plain,
( ~ subset(sK72,relation_inverse_image(sK73,relation_image(sK73,sK72)))
& subset(sK72,relation_dom(sK73))
& relation(sK73) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72,sK73]),skolemize(X0,sK72),skolemize(X1,sK73)],[f371]) ).
fof(f691,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f500]) ).
fof(f697,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f503]) ).
fof(f753,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f539]) ).
fof(f754,plain,
! [X0,X1] :
( in(sK37(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f539]) ).
fof(f755,plain,
! [X0,X1] :
( ~ in(sK37(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f539]) ).
fof(f766,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK41(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f547]) ).
fof(f788,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f944,plain,
relation(sK73),
inference(cnf_transformation,[],[f600]) ).
fof(f945,plain,
subset(sK72,relation_dom(sK73)),
inference(cnf_transformation,[],[f600]) ).
fof(f946,plain,
~ subset(sK72,relation_inverse_image(sK73,relation_image(sK73,sK72))),
inference(cnf_transformation,[],[f600]) ).
fof(f1062,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f223]) ).
fof(f1096,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f788,f1062]) ).
fof(f1118,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f691,f1096]) ).
fof(f1122,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f697,f1096]) ).
fof(f1152,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK41(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f766,f1096]) ).
fof(f1251,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| in(X6,relation_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1118]) ).
fof(f1254,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| in(X6,relation_inverse_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1122]) ).
fof(f1292,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK41(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1152]) ).
fof(f1328,definition,
sF86 = relation_image(sK73,sK72),
introduced(definition,[new_symbols(definition,[sF86])],[function_definition]) ).
fof(f1329,plain,
relation_image(sK73,sK72) = sF86,
inference(reorient_equations,[],[f1328]) ).
fof(f1330,definition,
sF87 = relation_inverse_image(sK73,sF86),
introduced(definition,[new_symbols(definition,[sF87])],[function_definition]) ).
fof(f1331,plain,
relation_inverse_image(sK73,sF86) = sF87,
inference(reorient_equations,[],[f1330]) ).
fof(f1332,plain,
~ subset(sK72,sF87),
inference(definition_folding,[],[f946,f1331,f1329]) ).
fof(f1333,definition,
sF88 = relation_dom(sK73),
introduced(definition,[new_symbols(definition,[sF88])],[function_definition]) ).
fof(f1334,plain,
relation_dom(sK73) = sF88,
inference(reorient_equations,[],[f1333]) ).
fof(f1335,plain,
subset(sK72,sF88),
inference(definition_folding,[],[f945,f1334]) ).
fof(f1390,plain,
! [X0] :
( ~ in(X0,sK72)
| in(X0,sF88) ),
inference(resolution,[],[f753,f1335]) ).
fof(f1450,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(sK41(X1,X0),relation_image(X1,X2))
| ~ in(X0,X2)
| ~ relation(X1) ),
inference(resolution,[],[f1292,f1251]) ).
fof(f1455,plain,
! [X2,X0,X1] :
( in(sK41(X1,X0),relation_image(X1,X2))
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| ~ in(X0,X2) ),
inference(duplicate_literal_removal,[],[f1450]) ).
fof(f1467,plain,
! [X2,X0,X1] :
( in(X0,relation_inverse_image(X1,X2))
| ~ in(sK41(X1,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(resolution,[],[f1254,f1292]) ).
fof(f1476,plain,
! [X2,X0,X1] :
( ~ in(sK41(X1,X0),X2)
| in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(duplicate_literal_removal,[],[f1467]) ).
fof(f1522,plain,
! [X0] :
( in(sK41(sK73,X0),sF86)
| ~ relation(sK73)
| ~ in(X0,relation_dom(sK73))
| ~ in(X0,sK72) ),
inference(superposition,[],[f1455,f1329]) ).
fof(f1526,plain,
! [X0] :
( in(sK41(sK73,X0),sF86)
| ~ in(X0,relation_dom(sK73))
| ~ in(X0,sK72) ),
inference(forward_subsumption_resolution,[],[f1522,f944]) ).
fof(f1529,plain,
! [X0] :
( ~ in(X0,sF88)
| in(sK41(sK73,X0),sF86)
| ~ in(X0,sK72) ),
inference(forward_demodulation,[],[f1526,f1334]) ).
fof(f1530,plain,
! [X0] :
( in(sK41(sK73,X0),sF86)
| ~ in(X0,sK72) ),
inference(forward_subsumption_resolution,[],[f1529,f1390]) ).
fof(f1531,plain,
! [X0] :
( ~ in(X0,sK72)
| in(X0,relation_inverse_image(sK73,sF86))
| ~ relation(sK73)
| ~ in(X0,relation_dom(sK73)) ),
inference(resolution,[],[f1530,f1476]) ).
fof(f1532,plain,
! [X0] :
( ~ in(X0,sK72)
| in(X0,relation_inverse_image(sK73,sF86))
| ~ in(X0,relation_dom(sK73)) ),
inference(forward_subsumption_resolution,[],[f1531,f944]) ).
fof(f1533,plain,
! [X0] :
( in(X0,sF87)
| ~ in(X0,sK72)
| ~ in(X0,relation_dom(sK73)) ),
inference(forward_demodulation,[],[f1532,f1331]) ).
fof(f1534,plain,
! [X0] :
( ~ in(X0,sF88)
| in(X0,sF87)
| ~ in(X0,sK72) ),
inference(forward_demodulation,[],[f1533,f1334]) ).
fof(f1535,plain,
! [X0] :
( ~ in(X0,sK72)
| in(X0,sF87) ),
inference(forward_subsumption_resolution,[],[f1534,f1390]) ).
fof(f1541,plain,
! [X0] :
( in(sK37(sK72,X0),sF87)
| subset(sK72,X0) ),
inference(resolution,[],[f1535,f754]) ).
fof(f1543,plain,
( subset(sK72,sF87)
| subset(sK72,sF87) ),
inference(resolution,[],[f1541,f755]) ).
fof(f1544,plain,
subset(sK72,sF87),
inference(duplicate_literal_removal,[],[f1543]) ).
fof(f1545,plain,
$false,
inference(forward_subsumption_resolution,[],[f1544,f1332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU227+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n009.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 04:10:30 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 5.01/2.04 % (2653078)Detected formulas, will run a generic FOF schedule.
% 5.01/2.04 % (2653084)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=3969652899:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.01/2.04 % (2653088)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2435493499:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.01/2.04 % (2653086)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1320116093:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.01/2.04 % (2653087)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3180812355:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.01/2.04 % (2653089)dis-21_1_sil=8000:lcm=predicate:random_seed=1822004163: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)
% 5.01/2.04 % (2653083)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=325140279:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.01/2.04 % (2653085)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=263081701:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.01/2.04 % (2653086)Instruction limit reached!
% 5.01/2.04 % (2653086)------------------------------
% 5.01/2.04 % (2653086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653086)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653086)Termination reason: Instruction limit
% 5.01/2.04 % (2653086)Termination phase: Saturation
% 5.01/2.04 % (2653086)Time elapsed: 0.070 s
% 5.01/2.04 % (2653086)Peak memory usage: 90 MB
% 5.01/2.04 % (2653086)Instructions burned: 110 (million)
% 5.01/2.04 % (2653087)Instruction limit reached!
% 5.01/2.04 % (2653087)------------------------------
% 5.01/2.04 % (2653087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653087)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653087)Termination reason: Instruction limit
% 5.01/2.04 % (2653087)Termination phase: Saturation
% 5.01/2.04 % (2653087)Time elapsed: 0.080 s
% 5.01/2.04 % (2653087)Peak memory usage: 89 MB
% 5.01/2.04 % (2653087)Instructions burned: 119 (million)
% 5.01/2.04 % (2653089)Instruction limit reached!
% 5.01/2.04 % (2653089)------------------------------
% 5.01/2.04 % (2653089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653089)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653089)Termination reason: Instruction limit
% 5.01/2.04 % (2653089)Termination phase: Saturation
% 5.01/2.04 % (2653089)Time elapsed: 0.081 s
% 5.01/2.04 % (2653089)Peak memory usage: 90 MB
% 5.01/2.04 % (2653089)Instructions burned: 130 (million)
% 5.01/2.04 % (2653088)Instruction limit reached!
% 5.01/2.04 % (2653088)------------------------------
% 5.01/2.04 % (2653088)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653088)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653088)Termination reason: Instruction limit
% 5.01/2.04 % (2653088)Termination phase: Saturation
% 5.01/2.04 % (2653088)Time elapsed: 0.101 s
% 5.01/2.04 % (2653088)Peak memory usage: 90 MB
% 5.01/2.04 % (2653088)Instructions burned: 139 (million)
% 5.01/2.04 % (2653097)lrs+10_1_sil=8000:sp=occurrence:random_seed=3660446109:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.01/2.04 % (2653099)lrs+1011_1_sil=32000:sp=occurrence:random_seed=499692118:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.01/2.04 % (2653098)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3635586057:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.01/2.04 % (2653100)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=1016625875:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.01/2.04 % (2653098)Instruction limit reached!
% 5.01/2.04 % (2653098)------------------------------
% 5.01/2.04 % (2653098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653098)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653098)Termination reason: Instruction limit
% 5.01/2.04 % (2653098)Termination phase: Saturation
% 5.01/2.04 % (2653098)Time elapsed: 0.077 s
% 5.01/2.04 % (2653098)Peak memory usage: 89 MB
% 5.01/2.04 % (2653098)Instructions burned: 159 (million)
% 5.01/2.04 % (2653100)Instruction limit reached!
% 5.01/2.04 % (2653100)------------------------------
% 5.01/2.04 % (2653100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653100)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653100)Termination reason: Instruction limit
% 5.01/2.04 % (2653100)Termination phase: Saturation
% 5.01/2.04 % (2653100)Time elapsed: 0.140 s
% 5.01/2.04 % (2653100)Peak memory usage: 93 MB
% 5.01/2.04 % (2653100)Instructions burned: 248 (million)
% 5.01/2.04 % (2653097)Instruction limit reached!
% 5.01/2.04 % (2653097)------------------------------
% 5.01/2.04 % (2653097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653097)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653097)Termination reason: Instruction limit
% 5.01/2.04 % (2653097)Termination phase: Saturation
% 5.01/2.04 % (2653097)Time elapsed: 0.185 s
% 5.01/2.04 % (2653097)Peak memory usage: 93 MB
% 5.01/2.04 % (2653097)Instructions burned: 285 (million)
% 5.01/2.04 % (2653099)Instruction limit reached!
% 5.01/2.04 % (2653099)------------------------------
% 5.01/2.04 % (2653099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653099)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653099)Termination reason: Instruction limit
% 5.01/2.04 % (2653099)Termination phase: Saturation
% 5.01/2.04 % (2653099)Time elapsed: 0.219 s
% 5.01/2.04 % (2653099)Peak memory usage: 92 MB
% 5.01/2.04 % (2653099)Instructions burned: 326 (million)
% 5.01/2.04 % (2653105)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=855118214:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.01/2.04 % (2653107)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3677992847:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.01/2.04 % (2653106)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=931984251:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.01/2.04 % (2653107)Instruction limit reached!
% 5.01/2.04 % (2653107)------------------------------
% 5.01/2.04 % (2653107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653107)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653107)Termination reason: Instruction limit
% 5.01/2.04 % (2653107)Termination phase: Saturation
% 5.01/2.04 % (2653107)Time elapsed: 0.069 s
% 5.01/2.04 % (2653107)Peak memory usage: 90 MB
% 5.01/2.04 % (2653107)Instructions burned: 113 (million)
% 5.01/2.04 % (2653108)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=10427727:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.01/2.04 % (2653105)Instruction limit reached!
% 5.01/2.04 % (2653105)------------------------------
% 5.01/2.04 % (2653105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653105)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653105)Termination reason: Instruction limit
% 5.01/2.04 % (2653105)Termination phase: Saturation
% 5.01/2.04 % (2653105)Time elapsed: 0.186 s
% 5.01/2.04 % (2653105)Peak memory usage: 91 MB
% 5.01/2.04 % (2653105)Instructions burned: 294 (million)
% 5.01/2.04 % (2653108)Instruction limit reached!
% 5.01/2.04 % (2653108)------------------------------
% 5.01/2.04 % (2653108)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653108)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653108)Termination reason: Instruction limit
% 5.01/2.04 % (2653108)Termination phase: Saturation
% 5.01/2.04 % (2653108)Time elapsed: 0.066 s
% 5.01/2.04 % (2653108)Peak memory usage: 89 MB
% 5.01/2.04 % (2653108)Instructions burned: 128 (million)
% 5.01/2.04 % (2653083)First to succeed.
% 5.01/2.04 % (2653083)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2653078"
% 5.01/2.04 % (2653112)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1053075450:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.01/2.04 % (2653114)lrs+10_1_sil=8000:sp=occurrence:random_seed=3690919208:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 5.01/2.04 % (2653112)Instruction limit reached!
% 5.01/2.04 % (2653112)------------------------------
% 5.01/2.04 % (2653112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/2.04 % (2653112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/2.04 % (2653112)CaDiCaL version: 2.1.3
% 5.01/2.04 % (2653112)Termination reason: Instruction limit
% 5.01/2.04 % (2653112)Termination phase: Saturation
% 5.01/2.04 % (2653112)Time elapsed: 0.073 s
% 5.01/2.04 % (2653112)Peak memory usage: 89 MB
% 5.01/2.04 % (2653112)Instructions burned: 116 (million)
% 5.01/2.04 % (2653115)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3080665815:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 5.01/2.04 % (2653083)Refutation found. Thanks to Tanya!
% 5.01/2.04 % SZS status Theorem for theBenchmark
% 5.01/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 8.90/2.23 % (2653083)------------------------------
% 8.90/2.23 % (2653083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.23 % (2653083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.23 % (2653083)CaDiCaL version: 2.1.3
% 8.90/2.23 % (2653083)Termination reason: Refutation
% 8.90/2.23 % (2653083)Time elapsed: 0.735 s
% 8.90/2.23 % (2653083)Peak memory usage: 131 MB
% 8.90/2.23 % (2653083)Instructions burned: 1134 (million)
% 8.90/2.23 % (2653083)------------------------------
% 8.90/2.23 % (2653083)------------------------------
% 8.90/2.23 % (2653078)Success in time 1.175 s
% 8.90/2.23 % Vampire exiting
%------------------------------------------------------------------------------