%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET758+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:41:51 PM UTC 2026
% Result : Theorem 2.60s 1.25s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 78 ( 18 unt; 4 def)
% Number of atoms : 284 ( 17 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 337 ( 131 ~; 120 |; 63 &)
% ( 10 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 192 ( 0 sgn 169 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X2)
& member(X6,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X6) )
=> X5 = X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( member(X3,image3(X0,X1,X2))
<=> ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image3) ).
fof(f25,axiom,
! [X0,X1,X2,X3] :
( member(X3,inverse_image3(X0,X1,X2))
<=> ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X3,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image3) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( ( maps(X0,X1,X2)
& subset(X3,X2) )
=> subset(image3(X0,inverse_image3(X0,X3,X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa08) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( maps(X0,X1,X2)
& subset(X3,X2) )
=> subset(image3(X0,inverse_image3(X0,X3,X1),X2),X3) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f41,plain,
? [X0,X1,X2,X3] :
( ~ subset(image3(X0,inverse_image3(X0,X3,X1),X2),X3)
& maps(X0,X1,X2)
& subset(X3,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f42,plain,
? [X0,X1,X2,X3] :
( ~ subset(image3(X0,inverse_image3(X0,X3,X1),X2),X3)
& maps(X0,X1,X2)
& subset(X3,X2) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f44,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f44]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK3(X0,X2,X3),X2)
& apply(X0,X3,sK3(X0,X2,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X2,X3))],[f36]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& ? [X5] :
( member(X5,X1)
& apply(X0,X5,X3) ) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& member(sK6(X0,X1,X3),X1)
& apply(X0,sK6(X0,X1,X3),X3) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X5,sK6(X0,X1,X3))],[f72]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ( member(X3,inverse_image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X3,X4) ) )
& ( ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X3,X4) ) )
| ~ member(X3,inverse_image3(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ( member(X3,inverse_image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X3,X4) ) )
& ( ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X3,X4) ) )
| ~ member(X3,inverse_image3(X0,X1,X2)) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ( member(X3,inverse_image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X3,X4) ) )
& ( ( member(X3,X2)
& ? [X5] :
( member(X5,X1)
& apply(X0,X3,X5) ) )
| ~ member(X3,inverse_image3(X0,X1,X2)) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( ( member(X3,inverse_image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X3,X4) ) )
& ( ( member(X3,X2)
& member(sK8(X0,X1,X3),X1)
& apply(X0,X3,sK8(X0,X1,X3)) )
| ~ member(X3,inverse_image3(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X5,sK8(X0,X1,X3))],[f79]) ).
fof(f81,plain,
( ~ subset(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)
& maps(sK9,sK10,sK11)
& subset(sK12,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f42]) ).
fof(f82,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f84,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f108,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ maps(X0,X1,X2)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| X6 = X7 ),
inference(cnf_transformation,[],[f62]) ).
fof(f120,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK6(X0,X1,X3),X3)
| ~ member(X3,image3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f121,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| member(sK6(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f122,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| member(X3,X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f127,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3,sK8(X0,X1,X3))
| ~ member(X3,inverse_image3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,inverse_image3(X0,X1,X2))
| member(sK8(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,inverse_image3(X0,X1,X2))
| member(X3,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f131,plain,
subset(sK12,sK11),
inference(cnf_transformation,[],[f81]) ).
fof(f132,plain,
maps(sK9,sK10,sK11),
inference(cnf_transformation,[],[f81]) ).
fof(f133,plain,
~ subset(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12),
inference(cnf_transformation,[],[f81]) ).
fof(f138,plain,
member(sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12),image3(sK9,inverse_image3(sK9,sK12,sK10),sK11)),
inference(resolution,[],[f83,f133]) ).
fof(f140,plain,
! [X0] :
( ~ member(X0,sK12)
| member(X0,sK11) ),
inference(resolution,[],[f82,f131]) ).
fof(f142,plain,
member(sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12),sK11),
inference(resolution,[],[f122,f138]) ).
fof(f143,plain,
member(sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),inverse_image3(sK9,sK12,sK10)),
inference(resolution,[],[f121,f138]) ).
fof(f144,plain,
member(sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),sK10),
inference(resolution,[],[f143,f129]) ).
fof(f145,plain,
member(sK8(sK9,sK12,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12))),sK12),
inference(resolution,[],[f128,f143]) ).
fof(f147,plain,
member(sK8(sK9,sK12,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12))),sK11),
inference(resolution,[],[f145,f140]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ member(X0,sK10)
| ~ apply(sK9,X0,X2)
| ~ apply(sK9,X0,X1)
| ~ member(X1,sK11)
| ~ member(X2,sK11)
| X1 = X2 ),
inference(resolution,[],[f108,f132]) ).
fof(f156,plain,
! [X0,X1] :
( ~ apply(sK9,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),X0)
| ~ apply(sK9,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),X1)
| ~ member(X1,sK11)
| ~ member(X0,sK11)
| X0 = X1 ),
inference(resolution,[],[f155,f144]) ).
fof(f158,plain,
! [X0,X1] :
( ~ apply(sK9,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),X0)
| ~ member(X0,sK11)
| ~ member(sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12),sK11)
| sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12) = X0
| ~ member(sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12),image3(sK9,inverse_image3(sK9,sK12,sK10),X1)) ),
inference(resolution,[],[f156,f120]) ).
fof(f163,plain,
! [X0,X1] :
( ~ apply(sK9,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),X0)
| ~ member(X0,sK11)
| sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12) = X0
| ~ member(sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12),image3(sK9,inverse_image3(sK9,sK12,sK10),X1)) ),
inference(forward_subsumption_resolution,[],[f158,f142]) ).
fof(f165,definition,
( spl13_1
<=> ! [X1] : ~ member(sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12),image3(sK9,inverse_image3(sK9,sK12,sK10),X1)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f166,plain,
( ! [X1] : ~ member(sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12),image3(sK9,inverse_image3(sK9,sK12,sK10),X1))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,definition,
( spl13_2
<=> ! [X0] :
( ~ apply(sK9,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),X0)
| sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12) = X0
| ~ member(X0,sK11) ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f169,plain,
( ! [X0] :
( ~ apply(sK9,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),X0)
| sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12) = X0
| ~ member(X0,sK11) )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f170,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f163,f168,f165]) ).
fof(f173,plain,
( ! [X0,X1] :
( ~ member(sK8(sK9,X0,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12))),sK11)
| sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12) = sK8(sK9,X0,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)))
| ~ member(sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),inverse_image3(sK9,X0,X1)) )
| ~ spl13_2 ),
inference(resolution,[],[f169,f127]) ).
fof(f175,plain,
( ! [X0] :
( sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12) = sK8(sK9,sK12,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)))
| ~ member(sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),inverse_image3(sK9,sK12,X0)) )
| ~ spl13_2 ),
inference(resolution,[],[f173,f147]) ).
fof(f177,definition,
( spl13_3
<=> ! [X0] : ~ member(sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),inverse_image3(sK9,sK12,X0)) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f178,plain,
( ! [X0] : ~ member(sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)),inverse_image3(sK9,sK12,X0))
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f180,definition,
( spl13_4
<=> sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12) = sK8(sK9,sK12,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12))) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f182,plain,
( sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12) = sK8(sK9,sK12,sK6(sK9,inverse_image3(sK9,sK12,sK10),sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)))
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f183,plain,
( spl13_3
| spl13_4
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f175,f168,f180,f177]) ).
fof(f184,plain,
( $false
| ~ spl13_3 ),
inference(resolution,[],[f178,f143]) ).
fof(f186,plain,
~ spl13_3,
inference(avatar_contradiction_clause,[],[f184]) ).
fof(f195,plain,
( member(sK0(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12),sK12)
| ~ spl13_4 ),
inference(superposition,[],[f145,f182]) ).
fof(f202,plain,
( $false
| ~ spl13_1 ),
inference(resolution,[],[f166,f138]) ).
fof(f204,plain,
~ spl13_1,
inference(avatar_contradiction_clause,[],[f202]) ).
fof(f213,plain,
( subset(image3(sK9,inverse_image3(sK9,sK12,sK10),sK11),sK12)
| ~ spl13_4 ),
inference(resolution,[],[f195,f84]) ).
fof(f215,plain,
( $false
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f213,f133]) ).
fof(f216,plain,
~ spl13_4,
inference(avatar_contradiction_clause,[],[f215]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f170]) ).
cnf(s2,plain,
( ~ spl13_2
| spl13_3
| spl13_4 ),
inference(sat_conversion,[],[f183]) ).
cnf(s3,plain,
~ spl13_3,
inference(sat_conversion,[],[f186]) ).
cnf(s6,plain,
~ spl13_1,
inference(sat_conversion,[],[f204]) ).
cnf(s8,plain,
~ spl13_4,
inference(sat_conversion,[],[f216]) ).
cnf(s9,plain,
~ spl13_2,
inference(rat,[],[s2,s8,s3]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s6]) ).
fof(f217,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET758+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 02:45:25 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/1.25 % (1817603)Detected formulas, will run a generic FOF schedule.
% 2.60/1.25 % (1817608)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=325942507:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.25 % (1817609)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=1000486960:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.25 % (1817613)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3824659734:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.25 % (1817612)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2770823258:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.25 % (1817610)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=1523447094:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.25 % (1817611)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1314181446:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.25 % (1817613)First to succeed.
% 2.60/1.25 % (1817611)Refutation not found, incomplete strategy
% 2.60/1.25 % (1817611)------------------------------
% 2.60/1.25 % (1817611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.25 % (1817611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.25 % (1817611)CaDiCaL version: 2.1.3
% 2.60/1.25 % (1817611)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.25 % (1817611)Time elapsed: 0.003 s
% 2.60/1.25 % (1817611)Peak memory usage: 88 MB
% 2.60/1.25 % (1817611)Instructions burned: 3 (million)
% 2.60/1.25 % (1817613)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1817603"
% 2.60/1.25 % (1817614)dis-21_1_sil=8000:lcm=predicate:random_seed=1749081583: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)
% 2.60/1.25 % (1817612)Instruction limit reached!
% 2.60/1.25 % (1817612)------------------------------
% 2.60/1.25 % (1817612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.25 % (1817612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.25 % (1817612)CaDiCaL version: 2.1.3
% 2.60/1.25 % (1817612)Termination reason: Instruction limit
% 2.60/1.25 % (1817612)Termination phase: Saturation
% 2.60/1.25 % (1817612)Time elapsed: 0.049 s
% 2.60/1.25 % (1817612)Peak memory usage: 87 MB
% 2.60/1.25 % (1817612)Instructions burned: 121 (million)
% 2.60/1.25 % (1817614)Instruction limit reached!
% 2.60/1.25 % (1817614)------------------------------
% 2.60/1.25 % (1817614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.25 % (1817614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.25 % (1817614)CaDiCaL version: 2.1.3
% 2.60/1.25 % (1817614)Termination reason: Instruction limit
% 2.60/1.25 % (1817614)Termination phase: Saturation
% 2.60/1.25 % (1817614)Time elapsed: 0.084 s
% 2.60/1.25 % (1817614)Peak memory usage: 89 MB
% 2.60/1.25 % (1817614)Instructions burned: 129 (million)
% 2.60/1.25 % (1817622)lrs+10_1_sil=8000:sp=occurrence:random_seed=3465635929:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.60/1.25 % (1817623)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2924843047:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.60/1.25 % (1817611)------------------------------
% 2.60/1.25 % (1817611)------------------------------
% 2.60/1.25 % (1817613)Refutation found. Thanks to Tanya!
% 2.60/1.25 % SZS status Theorem for theBenchmark
% 2.60/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.32/1.35 % (1817613)------------------------------
% 3.32/1.35 % (1817613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.35 % (1817613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.35 % (1817613)CaDiCaL version: 2.1.3
% 3.32/1.35 % (1817613)Termination reason: Refutation
% 3.32/1.35 % (1817613)Time elapsed: 0.009 s
% 3.32/1.35 % (1817613)Peak memory usage: 90 MB
% 3.32/1.35 % (1817613)Instructions burned: 10 (million)
% 3.32/1.35 % (1817613)------------------------------
% 3.32/1.35 % (1817613)------------------------------
% 3.32/1.35 % (1817603)Success in time 0.402 s
% 3.32/1.35 % Vampire exiting
%------------------------------------------------------------------------------