%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU227+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:52:29 PM UTC 2026
% Result : Theorem 2.79s 0.92s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 79 ( 23 unt; 4 def)
% Number of atoms : 310 ( 40 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 382 ( 151 ~; 153 |; 55 &)
% ( 15 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 198 ( 0 sgn 168 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,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(f7,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(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,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(f10,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(f32,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(f33,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)],[f32]) ).
fof(f52,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,[],[f6]) ).
fof(f53,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,[],[f7]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f60,plain,
? [X0,X1] :
( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
& subset(X0,relation_dom(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f61,plain,
? [X0,X1] :
( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
& subset(X0,relation_dom(X1))
& relation(X1) ),
inference(flattening,[],[f60]) ).
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,[],[f52]) ).
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,[],[f53]) ).
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,[],[f54]) ).
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] :
( ( 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,[],[f55]) ).
fof(f81,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,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f81]) ).
fof(f94,plain,
( ~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))
& subset(sK21,relation_dom(sK22))
& relation(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X0,sK21),skolemize(X1,sK22)],[f61]) ).
fof(f101,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f104,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,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(f114,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f115,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f116,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f117,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f121,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f154,plain,
relation(sK22),
inference(cnf_transformation,[],[f94]) ).
fof(f155,plain,
subset(sK21,relation_dom(sK22)),
inference(cnf_transformation,[],[f94]) ).
fof(f156,plain,
~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),
inference(cnf_transformation,[],[f94]) ).
fof(f168,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,[],[f104,f121]) ).
fof(f172,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,[],[f110,f121]) ).
fof(f177,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f117,f121]) ).
fof(f179,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,[],[f168]) ).
fof(f182,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,[],[f172]) ).
fof(f186,plain,
! [X0,X5] :
( ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f177]) ).
fof(f187,definition,
sF23 = relation_image(sK22,sK21),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f188,plain,
relation_image(sK22,sK21) = sF23,
inference(reorient_equations,[],[f187]) ).
fof(f189,definition,
sF24 = relation_inverse_image(sK22,sF23),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f190,plain,
relation_inverse_image(sK22,sF23) = sF24,
inference(reorient_equations,[],[f189]) ).
fof(f191,plain,
~ subset(sK21,sF24),
inference(definition_folding,[],[f156,f190,f188]) ).
fof(f192,definition,
sF25 = relation_dom(sK22),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f193,plain,
relation_dom(sK22) = sF25,
inference(reorient_equations,[],[f192]) ).
fof(f194,plain,
subset(sK21,sF25),
inference(definition_folding,[],[f155,f193]) ).
fof(f278,plain,
in(sK6(sK21,sF24),sK21),
inference(resolution,[],[f115,f191]) ).
fof(f298,plain,
! [X0] :
( ~ in(X0,sK21)
| in(X0,sF25) ),
inference(resolution,[],[f114,f194]) ).
fof(f341,plain,
! [X0] :
( ~ in(X0,sF25)
| in(unordered_pair(unordered_pair(X0,sK9(sK22,X0)),singleton(X0)),sK22)
| ~ relation(sK22) ),
inference(superposition,[],[f186,f193]) ).
fof(f344,plain,
! [X0] :
( ~ in(X0,sF25)
| in(unordered_pair(unordered_pair(X0,sK9(sK22,X0)),singleton(X0)),sK22) ),
inference(forward_subsumption_resolution,[],[f341,f154]) ).
fof(f346,plain,
! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK22,X0))),sK22)
| ~ in(X0,sF25) ),
inference(forward_demodulation,[],[f344,f101]) ).
fof(f350,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| in(X1,relation_image(X2,X3))
| ~ in(X0,X3)
| ~ relation(X2) ),
inference(superposition,[],[f179,f101]) ).
fof(f357,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| in(X0,relation_inverse_image(X2,X3))
| ~ in(X1,X3)
| ~ relation(X2) ),
inference(superposition,[],[f182,f101]) ).
fof(f982,plain,
! [X0,X1] :
( in(sK9(sK22,X0),relation_image(sK22,X1))
| ~ in(X0,X1)
| ~ relation(sK22)
| ~ in(X0,sF25) ),
inference(resolution,[],[f350,f346]) ).
fof(f991,plain,
! [X0,X1] :
( in(sK9(sK22,X0),relation_image(sK22,X1))
| ~ in(X0,X1)
| ~ in(X0,sF25) ),
inference(forward_subsumption_resolution,[],[f982,f154]) ).
fof(f999,plain,
! [X0,X1] :
( in(X0,relation_inverse_image(sK22,X1))
| ~ in(sK9(sK22,X0),X1)
| ~ relation(sK22)
| ~ in(X0,sF25) ),
inference(resolution,[],[f357,f346]) ).
fof(f1008,plain,
! [X0,X1] :
( ~ in(sK9(sK22,X0),X1)
| in(X0,relation_inverse_image(sK22,X1))
| ~ in(X0,sF25) ),
inference(forward_subsumption_resolution,[],[f999,f154]) ).
fof(f1369,plain,
! [X0] :
( in(sK9(sK22,X0),sF23)
| ~ in(X0,sK21)
| ~ in(X0,sF25) ),
inference(superposition,[],[f991,f188]) ).
fof(f1370,plain,
! [X0] :
( in(sK9(sK22,X0),sF23)
| ~ in(X0,sK21) ),
inference(forward_subsumption_resolution,[],[f1369,f298]) ).
fof(f1377,plain,
! [X0] :
( ~ in(X0,sK21)
| in(X0,relation_inverse_image(sK22,sF23))
| ~ in(X0,sF25) ),
inference(resolution,[],[f1370,f1008]) ).
fof(f1382,plain,
! [X0] :
( ~ in(X0,sK21)
| in(X0,relation_inverse_image(sK22,sF23)) ),
inference(forward_subsumption_resolution,[],[f1377,f298]) ).
fof(f1383,plain,
! [X0] :
( ~ in(X0,sK21)
| in(X0,sF24) ),
inference(forward_demodulation,[],[f1382,f190]) ).
fof(f1397,plain,
in(sK6(sK21,sF24),sF24),
inference(resolution,[],[f1383,f278]) ).
fof(f1421,definition,
( spl26_10
<=> in(sK6(sK21,sF24),sF24) ),
introduced(definition,[new_symbols(definition,[spl26_10])],[avatar_definition]) ).
fof(f1423,plain,
( in(sK6(sK21,sF24),sF24)
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f1425,plain,
spl26_10,
inference(avatar_split_clause,[],[f1397,f1421]) ).
fof(f1569,plain,
( subset(sK21,sF24)
| ~ spl26_10 ),
inference(resolution,[],[f1423,f116]) ).
fof(f1574,plain,
( $false
| ~ spl26_10 ),
inference(forward_subsumption_resolution,[],[f1569,f191]) ).
fof(f1575,plain,
~ spl26_10,
inference(avatar_contradiction_clause,[],[f1574]) ).
cnf(s10,plain,
spl26_10,
inference(sat_conversion,[],[f1425]) ).
cnf(s17,plain,
~ spl26_10,
inference(sat_conversion,[],[f1575]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s10,s17]) ).
fof(f1576,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU227+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:13:57 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.79/0.92 % (3451285)Will run a generic schedule for satisfiability detection.
% 2.79/0.92 % (3451290)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=874790836_2999 on theBenchmark for (2999ds/0Mi)
% 2.79/0.92 % (3451291)% WARNING: option uhcvi not known.
% 2.79/0.92 % TRYING [1]
% 2.79/0.92 % TRYING [2]
% 2.79/0.92 % TRYING [3]
% 2.79/0.92 % (3451291)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=845043603:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.79/0.92 % (3451293)dis+10_1_sil=32000:sp=arity:random_seed=2643260154:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.79/0.92 % (3451292)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2764058976:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.79/0.92 % (3451294)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2656407643:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.79/0.92 % (3451295)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=783118590:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.79/0.92 % (3451296)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2909616601:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.79/0.92 % TRYING [4]
% 2.79/0.92 % TRYING [5]
% 2.79/0.92 % (3451293)Instruction limit reached!
% 2.79/0.92 % (3451293)------------------------------
% 2.79/0.92 % (3451293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.92 % (3451293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.92 % (3451293)CaDiCaL version: 2.1.3
% 2.79/0.92 % (3451293)Termination reason: Instruction limit
% 2.79/0.92 % (3451293)Termination phase: Saturation
% 2.79/0.92 % (3451293)Time elapsed: 0.063 s
% 2.79/0.92 % (3451293)Peak memory usage: 12 MB
% 2.79/0.92 % (3451293)Instructions burned: 103 (million)
% 2.79/0.92 % (3451294)Instruction limit reached!
% 2.79/0.92 % (3451294)------------------------------
% 2.79/0.92 % (3451294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.92 % (3451294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.92 % (3451294)CaDiCaL version: 2.1.3
% 2.79/0.92 % (3451294)Termination reason: Instruction limit
% 2.79/0.92 % (3451294)Termination phase: Saturation
% 2.79/0.92 % (3451294)Time elapsed: 0.065 s
% 2.79/0.92 % (3451294)Peak memory usage: 12 MB
% 2.79/0.92 % (3451294)Instructions burned: 117 (million)
% 2.79/0.92 % (3451295)Instruction limit reached!
% 2.79/0.92 % (3451295)------------------------------
% 2.79/0.92 % (3451295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.92 % (3451295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.92 % (3451295)CaDiCaL version: 2.1.3
% 2.79/0.92 % (3451295)Termination reason: Instruction limit
% 2.79/0.92 % (3451295)Termination phase: Saturation
% 2.79/0.92 % (3451295)Time elapsed: 0.076 s
% 2.79/0.92 % (3451295)Peak memory usage: 13 MB
% 2.79/0.92 % (3451295)Instructions burned: 132 (million)
% 2.79/0.92 % (3451304)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2868235001:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.79/0.92 % (3451305)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1781256415:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.79/0.92 % TRYING [1]
% 2.79/0.92 % TRYING [2]
% 2.79/0.92 % TRYING [3]
% 2.79/0.92 % (3451306)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2397962700:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.79/0.92 % TRYING [4]
% 2.79/0.92 % (3451296)Instruction limit reached!
% 2.79/0.92 % (3451296)------------------------------
% 2.79/0.92 % (3451296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.92 % (3451296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.92 % (3451296)CaDiCaL version: 2.1.3
% 2.79/0.92 % (3451296)Termination reason: Instruction limit
% 2.79/0.92 % (3451296)Termination phase: Saturation
% 2.79/0.92 % (3451296)Time elapsed: 0.101 s
% 2.79/0.92 % (3451296)Peak memory usage: 13 MB
% 2.79/0.92 % (3451296)Instructions burned: 160 (million)
% 2.79/0.92 % TRYING [6]
% 2.79/0.92 % (3451310)ott-21_1_sil=16000:fs=off:random_seed=3409027033:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.79/0.92 % TRYING [5]
% 2.79/0.92 % (3451305)Instruction limit reached!
% 2.79/0.92 % (3451305)------------------------------
% 2.79/0.92 % (3451305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.92 % (3451305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.92 % (3451305)CaDiCaL version: 2.1.3
% 2.79/0.92 % (3451305)Termination reason: Instruction limit
% 2.79/0.92 % (3451305)Termination phase: Saturation
% 2.79/0.92 % (3451305)Time elapsed: 0.085 s
% 2.79/0.92 % (3451305)Peak memory usage: 13 MB
% 2.79/0.92 % (3451305)Instructions burned: 131 (million)
% 2.79/0.92 % (3451312)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4276634274:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 2.79/0.92 % TRYING [6]
% 2.79/0.92 % (3451310)Instruction limit reached!
% 2.79/0.92 % (3451310)------------------------------
% 2.79/0.92 % (3451310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.92 % (3451310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.92 % (3451310)CaDiCaL version: 2.1.3
% 2.79/0.92 % (3451310)Termination reason: Instruction limit
% 2.79/0.92 % (3451310)Termination phase: Saturation
% 2.79/0.92 % (3451310)Time elapsed: 0.095 s
% 2.79/0.92 % (3451310)Peak memory usage: 13 MB
% 2.79/0.92 % (3451310)Instructions burned: 183 (million)
% 2.79/0.92 % (3451314)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2125118712:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.79/0.92 % TRYING [1]
% 2.79/0.92 % TRYING [2]
% 2.79/0.92 % TRYING [3]
% 2.79/0.92 % TRYING [4]
% 2.79/0.92 % TRYING [7]
% 2.79/0.92 % (3451304)Instruction limit reached!
% 2.79/0.92 % (3451304)------------------------------
% 2.79/0.92 % (3451304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.92 % (3451304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.92 % (3451304)CaDiCaL version: 2.1.3
% 2.79/0.92 % (3451304)Termination reason: Instruction limit
% 2.79/0.92 % (3451304)Termination phase: Finite model building SAT solving
% 2.79/0.92 % (3451304)Time elapsed: 0.296 s
% 2.79/0.92 % (3451304)Peak memory usage: 34 MB
% 2.79/0.92 % (3451304)Instructions burned: 715 (million)
% 2.79/0.92 % (3451316)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=805953731:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 2.79/0.92 % (3451316) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3451285-3451316"...
% 2.79/0.92 % (3451306)Instruction limit reached!
% 2.79/0.92 % (3451306)------------------------------
% 2.79/0.92 % (3451306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.92 % (3451306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.92 % (3451306)CaDiCaL version: 2.1.3
% 2.79/0.92 % (3451306)Termination reason: Instruction limit
% 2.79/0.92 % (3451306)Termination phase: Saturation
% 2.79/0.92 % (3451306)Time elapsed: 0.349 s
% 2.79/0.92 % (3451306)Peak memory usage: 19 MB
% 2.79/0.92 % (3451306)Instructions burned: 684 (million)
% 2.79/0.92 % (3451316)...printing done.
% 2.79/0.92 % (3451316)Refutation found. Thanks to Tanya!
% 2.79/0.92 % SZS status Theorem for theBenchmark
% 2.79/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/0.92 % (3451316)------------------------------
% 2.79/0.92 % (3451316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.79/0.92 % (3451316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/0.92 % (3451316)CaDiCaL version: 2.1.3
% 2.79/0.92 % (3451316)Termination reason: Refutation
% 2.79/0.92 % (3451316)Time elapsed: 0.046 s
% 2.79/0.92 % (3451316)Peak memory usage: 13 MB
% 2.79/0.92 % (3451316)Instructions burned: 72 (million)
% 2.79/0.92 % (3451285)Success in time 0.486 s
% 2.79/0.92 % Vampire exiting
%------------------------------------------------------------------------------