%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU070+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:47:11 PM UTC 2026
% Result : Theorem 6.20s 1.67s
% Output : Refutation 7.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 17 unt; 5 def)
% Number of atoms : 368 ( 47 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 477 ( 193 ~; 204 |; 63 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-3 aty)
% Number of variables : 230 ( 206 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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(f8,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(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f11,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(f33,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> subset(set_intersection2(X0,relation_inverse_image(X2,X1)),relation_inverse_image(X2,set_intersection2(relation_image(X2,X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> subset(set_intersection2(X0,relation_inverse_image(X2,X1)),relation_inverse_image(X2,set_intersection2(relation_image(X2,X0),X1))) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f55,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,[],[f7]) ).
fof(f56,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,[],[f8]) ).
fof(f57,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f61,plain,
? [X0,X1,X2] :
( ~ subset(set_intersection2(X0,relation_inverse_image(X2,X1)),relation_inverse_image(X2,set_intersection2(relation_image(X2,X0),X1)))
& relation(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f71,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,[],[f55]) ).
fof(f72,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,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| ~ in(X4,X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
& in(sK1(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
& in(sK2(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f72]) ).
fof(f74,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,[],[f56]) ).
fof(f75,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,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(sK3(X0,X1,X2),X4),X0)
| ~ in(X4,X1) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X0)
& in(sK4(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(X6,sK5(X0,X1,X6)),X0)
& in(sK5(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X5,sK4(X0,X1,X2)),skolemize(X8,sK5(X0,X1,X6))],[f75]) ).
fof(f77,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,[],[f57]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X2) )
& ( ( in(sK7(X0,X1,X2),X0)
& in(sK7(X0,X1,X2),X1) )
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f82]) ).
fof(f95,plain,
( ~ subset(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(relation_image(sK21,sK19),sK20)))
& relation(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X0,sK19),skolemize(X1,sK20),skolemize(X2,sK21)],[f61]) ).
fof(f106,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,[],[f73]) ).
fof(f110,plain,
! [X2,X0,X1,X6] :
( in(sK5(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f111,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK5(X0,X1,X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f112,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,[],[f76]) ).
fof(f117,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f119,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f120,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f121,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f125,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f157,plain,
relation(sK21),
inference(cnf_transformation,[],[f95]) ).
fof(f158,plain,
~ subset(set_intersection2(sK19,relation_inverse_image(sK21,sK20)),relation_inverse_image(sK21,set_intersection2(relation_image(sK21,sK19),sK20))),
inference(cnf_transformation,[],[f95]) ).
fof(f171,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f106,f125]) ).
fof(f175,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f112,f125]) ).
fof(f176,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f111,f125]) ).
fof(f178,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,relation_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f171]) ).
fof(f181,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,relation_inverse_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f175]) ).
fof(f182,plain,
! [X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f176]) ).
fof(f183,plain,
! [X0,X1,X6] :
( in(sK5(X0,X1,X6),X1)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f184,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f121]) ).
fof(f185,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f120]) ).
fof(f186,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f119]) ).
fof(f187,definition,
sF22 = relation_inverse_image(sK21,sK20),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f188,plain,
relation_inverse_image(sK21,sK20) = sF22,
inference(reorient_equations,[],[f187]) ).
fof(f189,definition,
sF23 = set_intersection2(sK19,sF22),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f190,plain,
set_intersection2(sK19,sF22) = sF23,
inference(reorient_equations,[],[f189]) ).
fof(f191,definition,
sF24 = relation_image(sK21,sK19),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f192,plain,
relation_image(sK21,sK19) = sF24,
inference(reorient_equations,[],[f191]) ).
fof(f193,definition,
sF25 = set_intersection2(sF24,sK20),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f194,plain,
set_intersection2(sF24,sK20) = sF25,
inference(reorient_equations,[],[f193]) ).
fof(f195,definition,
sF26 = relation_inverse_image(sK21,sF25),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f196,plain,
relation_inverse_image(sK21,sF25) = sF26,
inference(reorient_equations,[],[f195]) ).
fof(f197,plain,
~ subset(sF23,sF26),
inference(definition_folding,[],[f158,f196,f194,f192,f190,f188]) ).
fof(f209,plain,
! [X0] :
( ~ in(X0,sF23)
| in(X0,sK19) ),
inference(superposition,[],[f185,f190]) ).
fof(f211,plain,
! [X0] :
( in(sK6(sF23,X0),sK19)
| subset(sF23,X0) ),
inference(resolution,[],[f209,f117]) ).
fof(f215,plain,
! [X0] :
( ~ in(X0,sF23)
| in(X0,sF22) ),
inference(superposition,[],[f186,f190]) ).
fof(f217,plain,
! [X0] :
( in(sK6(sF23,X0),sF22)
| subset(sF23,X0) ),
inference(resolution,[],[f215,f117]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(sK5(X1,X2,X0),relation_image(X1,X3))
| ~ in(X0,X3)
| ~ relation(X1) ),
inference(resolution,[],[f182,f178]) ).
fof(f222,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(X0,relation_inverse_image(X1,X3))
| ~ in(sK5(X1,X2,X0),X3)
| ~ relation(X1) ),
inference(resolution,[],[f182,f181]) ).
fof(f230,plain,
! [X2,X3,X0,X1] :
( ~ in(sK5(X1,X2,X0),X3)
| ~ relation(X1)
| in(X0,relation_inverse_image(X1,X3))
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(duplicate_literal_removal,[],[f222]) ).
fof(f231,plain,
! [X2,X3,X0,X1] :
( in(sK5(X1,X2,X0),relation_image(X1,X3))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2))
| ~ in(X0,X3) ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f280,plain,
! [X0] :
( ~ in(X0,sF24)
| in(X0,sF25)
| ~ in(X0,sK20) ),
inference(superposition,[],[f184,f194]) ).
fof(f358,plain,
! [X0,X1] :
( in(sK5(sK21,X0,X1),sF24)
| ~ relation(sK21)
| ~ in(X1,relation_inverse_image(sK21,X0))
| ~ in(X1,sK19) ),
inference(superposition,[],[f231,f192]) ).
fof(f360,plain,
! [X0,X1] :
( in(sK5(sK21,X0,X1),sF24)
| ~ in(X1,relation_inverse_image(sK21,X0))
| ~ in(X1,sK19) ),
inference(forward_subsumption_resolution,[],[f358,f157]) ).
fof(f362,plain,
! [X0,X1] :
( ~ in(sK5(sK21,X1,X0),sK20)
| ~ in(X0,sK19)
| in(sK5(sK21,X1,X0),sF25)
| ~ in(X0,relation_inverse_image(sK21,X1)) ),
inference(resolution,[],[f360,f280]) ).
fof(f374,plain,
! [X0] :
( ~ in(X0,relation_inverse_image(sK21,sK20))
| ~ relation(sK21)
| ~ in(X0,sK19)
| in(sK5(sK21,sK20,X0),sF25)
| ~ in(X0,relation_inverse_image(sK21,sK20)) ),
inference(resolution,[],[f183,f362]) ).
fof(f383,plain,
! [X0] :
( ~ in(X0,relation_inverse_image(sK21,sK20))
| ~ relation(sK21)
| ~ in(X0,sK19)
| in(sK5(sK21,sK20,X0),sF25) ),
inference(duplicate_literal_removal,[],[f374]) ).
fof(f385,plain,
! [X0] :
( ~ in(X0,relation_inverse_image(sK21,sK20))
| ~ in(X0,sK19)
| in(sK5(sK21,sK20,X0),sF25) ),
inference(forward_subsumption_resolution,[],[f383,f157]) ).
fof(f386,plain,
! [X0] :
( in(sK5(sK21,sK20,X0),sF25)
| ~ in(X0,sK19)
| ~ in(X0,sF22) ),
inference(forward_demodulation,[],[f385,f188]) ).
fof(f387,plain,
! [X0] :
( ~ in(X0,sK19)
| ~ in(X0,sF22)
| ~ relation(sK21)
| in(X0,relation_inverse_image(sK21,sF25))
| ~ in(X0,relation_inverse_image(sK21,sK20)) ),
inference(resolution,[],[f386,f230]) ).
fof(f390,plain,
! [X0] :
( ~ in(X0,sK19)
| ~ in(X0,sF22)
| in(X0,relation_inverse_image(sK21,sF25))
| ~ in(X0,relation_inverse_image(sK21,sK20)) ),
inference(forward_subsumption_resolution,[],[f387,f157]) ).
fof(f391,plain,
! [X0] :
( in(X0,sF26)
| ~ in(X0,sK19)
| ~ in(X0,sF22)
| ~ in(X0,relation_inverse_image(sK21,sK20)) ),
inference(forward_demodulation,[],[f390,f196]) ).
fof(f392,plain,
! [X0] :
( ~ in(X0,sF22)
| in(X0,sF26)
| ~ in(X0,sK19)
| ~ in(X0,sF22) ),
inference(forward_demodulation,[],[f391,f188]) ).
fof(f393,plain,
! [X0] :
( ~ in(X0,sF22)
| in(X0,sF26)
| ~ in(X0,sK19) ),
inference(duplicate_literal_removal,[],[f392]) ).
fof(f400,plain,
! [X0] :
( in(sK6(sF23,X0),sF26)
| ~ in(sK6(sF23,X0),sK19)
| subset(sF23,X0) ),
inference(resolution,[],[f393,f217]) ).
fof(f402,plain,
! [X0] :
( in(sK6(sF23,X0),sF26)
| subset(sF23,X0) ),
inference(forward_subsumption_resolution,[],[f400,f211]) ).
fof(f403,plain,
( subset(sF23,sF26)
| subset(sF23,sF26) ),
inference(resolution,[],[f402,f118]) ).
fof(f404,plain,
subset(sF23,sF26),
inference(duplicate_literal_removal,[],[f403]) ).
fof(f405,plain,
$false,
inference(forward_subsumption_resolution,[],[f404,f197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU070+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:32:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 6.20/1.67 % (2968918)Detected formulas, will run a generic FOF schedule.
% 6.20/1.67 % (2968928)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1030530106:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.20/1.67 % (2968929)dis-21_1_sil=8000:lcm=predicate:random_seed=2934364464: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)
% 6.20/1.67 % (2968927)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=885942310:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.20/1.67 % (2968926)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2314757547:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.20/1.67 % (2968923)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=371107477:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.20/1.67 % (2968925)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=2642889458:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.20/1.67 % (2968924)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=2664651605:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.20/1.67 % (2968926)Refutation not found, incomplete strategy
% 6.20/1.67 % (2968926)------------------------------
% 6.20/1.67 % (2968926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968926)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968926)Termination reason: Refutation not found, incomplete strategy
% 6.20/1.67 % (2968926)Time elapsed: 0.002 s
% 6.20/1.67 % (2968926)Peak memory usage: 88 MB
% 6.20/1.67 % (2968926)Instructions burned: 2 (million)
% 6.20/1.67 % (2968929)Instruction limit reached!
% 6.20/1.67 % (2968929)------------------------------
% 6.20/1.67 % (2968929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968929)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968929)Termination reason: Instruction limit
% 6.20/1.67 % (2968929)Termination phase: Saturation
% 6.20/1.67 % (2968929)Time elapsed: 0.068 s
% 6.20/1.67 % (2968929)Peak memory usage: 89 MB
% 6.20/1.67 % (2968929)Instructions burned: 131 (million)
% 6.20/1.67 % (2968927)Instruction limit reached!
% 6.20/1.67 % (2968927)------------------------------
% 6.20/1.67 % (2968927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968927)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968927)Termination reason: Instruction limit
% 6.20/1.67 % (2968927)Termination phase: Saturation
% 6.20/1.67 % (2968927)Time elapsed: 0.071 s
% 6.20/1.67 % (2968927)Peak memory usage: 89 MB
% 6.20/1.67 % (2968927)Instructions burned: 120 (million)
% 6.20/1.67 % (2968928)Instruction limit reached!
% 6.20/1.67 % (2968928)------------------------------
% 6.20/1.67 % (2968928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968928)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968928)Termination reason: Instruction limit
% 6.20/1.67 % (2968928)Termination phase: Saturation
% 6.20/1.67 % (2968928)Time elapsed: 0.111 s
% 6.20/1.67 % (2968928)Peak memory usage: 89 MB
% 6.20/1.67 % (2968928)Instructions burned: 139 (million)
% 6.20/1.67 % (2968938)lrs+10_1_sil=32000:urr=on:br=off:random_seed=660063808:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.20/1.67 % (2968937)lrs+10_1_sil=8000:sp=occurrence:random_seed=1915139742:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.20/1.67 % (2968938)Instruction limit reached!
% 6.20/1.67 % (2968938)------------------------------
% 6.20/1.67 % (2968938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968938)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968938)Termination reason: Instruction limit
% 6.20/1.67 % (2968938)Termination phase: Saturation
% 6.20/1.67 % (2968938)Time elapsed: 0.043 s
% 6.20/1.67 % (2968938)Peak memory usage: 90 MB
% 6.20/1.67 % (2968938)Instructions burned: 160 (million)
% 6.20/1.67 % (2968939)lrs+1011_1_sil=32000:sp=occurrence:random_seed=513109603:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.20/1.67 % (2968926)------------------------------
% 6.20/1.67 % (2968926)------------------------------
% 6.20/1.67 % (2968942)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=1803666418:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.20/1.67 % (2968942)Instruction limit reached!
% 6.20/1.67 % (2968942)------------------------------
% 6.20/1.67 % (2968942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968942)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968942)Termination reason: Instruction limit
% 6.20/1.67 % (2968942)Termination phase: Saturation
% 6.20/1.67 % (2968942)Time elapsed: 0.075 s
% 6.20/1.67 % (2968942)Peak memory usage: 95 MB
% 6.20/1.67 % (2968942)Instructions burned: 250 (million)
% 6.20/1.67 % (2968937)Instruction limit reached!
% 6.20/1.67 % (2968937)------------------------------
% 6.20/1.67 % (2968937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968937)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968937)Termination reason: Instruction limit
% 6.20/1.67 % (2968937)Termination phase: Saturation
% 6.20/1.67 % (2968937)Time elapsed: 0.170 s
% 6.20/1.67 % (2968937)Peak memory usage: 91 MB
% 6.20/1.67 % (2968937)Instructions burned: 285 (million)
% 6.20/1.67 % (2968944)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2627632615:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.20/1.67 % (2968944)Refutation not found, incomplete strategy
% 6.20/1.67 % (2968944)------------------------------
% 6.20/1.67 % (2968944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968944)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968944)Termination reason: Refutation not found, incomplete strategy
% 6.20/1.67 % (2968944)Time elapsed: 0.003 s
% 6.20/1.67 % (2968944)Peak memory usage: 89 MB
% 6.20/1.67 % (2968944)Instructions burned: 3 (million)
% 6.20/1.67 % (2968939)Instruction limit reached!
% 6.20/1.67 % (2968939)------------------------------
% 6.20/1.67 % (2968939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968939)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968939)Termination reason: Instruction limit
% 6.20/1.67 % (2968939)Termination phase: Saturation
% 6.20/1.67 % (2968939)Time elapsed: 0.213 s
% 6.20/1.67 % (2968939)Peak memory usage: 91 MB
% 6.20/1.67 % (2968939)Instructions burned: 326 (million)
% 6.20/1.67 % (2968946)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=960358739:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.20/1.67 % (2968947)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=818469533:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 6.20/1.67 % (2968947)Instruction limit reached!
% 6.20/1.67 % (2968947)------------------------------
% 6.20/1.67 % (2968947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968947)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968947)Termination reason: Instruction limit
% 6.20/1.67 % (2968947)Termination phase: Saturation
% 6.20/1.67 % (2968947)Time elapsed: 0.079 s
% 6.20/1.67 % (2968947)Peak memory usage: 90 MB
% 6.20/1.67 % (2968947)Instructions burned: 114 (million)
% 6.20/1.67 % (2968950)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=411442721:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.20/1.67 % (2968944)------------------------------
% 6.20/1.67 % (2968944)------------------------------
% 6.20/1.67 % (2968923)First to succeed.
% 6.20/1.67 % (2968950)Instruction limit reached!
% 6.20/1.67 % (2968950)------------------------------
% 6.20/1.67 % (2968950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968950)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968950)Termination reason: Instruction limit
% 6.20/1.67 % (2968950)Termination phase: Saturation
% 6.20/1.67 % (2968950)Time elapsed: 0.066 s
% 6.20/1.67 % (2968950)Peak memory usage: 89 MB
% 6.20/1.67 % (2968950)Instructions burned: 127 (million)
% 6.20/1.67 % (2968923)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2968918"
% 6.20/1.67 % (2968952)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1383279593:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.20/1.67 % (2968952)Instruction limit reached!
% 6.20/1.67 % (2968952)------------------------------
% 6.20/1.67 % (2968952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968952)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968952)Termination reason: Instruction limit
% 6.20/1.67 % (2968952)Termination phase: Saturation
% 6.20/1.67 % (2968952)Time elapsed: 0.067 s
% 6.20/1.67 % (2968952)Peak memory usage: 89 MB
% 6.20/1.67 % (2968952)Instructions burned: 114 (million)
% 6.20/1.67 % (2968955)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3384352168:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.20/1.67 % (2968954)lrs+10_1_sil=8000:sp=occurrence:random_seed=930493251:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.20/1.67 % (2968955)Refutation not found, incomplete strategy
% 6.20/1.67 % (2968955)------------------------------
% 6.20/1.67 % (2968955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (2968955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (2968955)CaDiCaL version: 2.1.3
% 6.20/1.67 % (2968955)Termination reason: Refutation not found, incomplete strategy
% 6.20/1.67 % (2968955)Time elapsed: 0.003 s
% 6.20/1.67 % (2968955)Peak memory usage: 89 MB
% 6.20/1.67 % (2968955)Instructions burned: 3 (million)
% 6.20/1.67 % (2968925)Also succeeded, but the first one will report.
% 6.20/1.67 % (2968946)Also succeeded, but the first one will report.
% 6.20/1.67 % (2968957)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1680866312:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.20/1.67 % (2968923)Refutation found. Thanks to Tanya!
% 6.20/1.67 % SZS status Theorem for theBenchmark
% 6.20/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 7.82/1.86 % (2968923)------------------------------
% 7.82/1.86 % (2968923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.82/1.86 % (2968923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.82/1.86 % (2968923)CaDiCaL version: 2.1.3
% 7.82/1.86 % (2968923)Termination reason: Refutation
% 7.82/1.86 % (2968923)Time elapsed: 0.652 s
% 7.82/1.86 % (2968923)Peak memory usage: 129 MB
% 7.82/1.86 % (2968923)Instructions burned: 974 (million)
% 7.82/1.86 % (2968923)------------------------------
% 7.82/1.86 % (2968923)------------------------------
% 7.82/1.86 % (2968918)Success in time 1.057 s
% 7.82/1.86 % Vampire exiting
%------------------------------------------------------------------------------