%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET155+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:40:19 PM UTC 2026
% Result : Theorem 1.66s 1.13s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 118 ( 10 unt; 11 def)
% Number of atoms : 301 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 292 ( 109 ~; 132 |; 30 &)
% ( 17 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 89 !; 8 ?)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X1)
| member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( member(X0,X2)
& ~ member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X1,X2) )
=> equal_set(difference(X2,union(X0,X1)),intersection(difference(X2,X0),difference(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI26) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X1,X2) )
=> equal_set(difference(X2,union(X0,X1)),intersection(difference(X2,X0),difference(X2,X1))) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ~ equal_set(difference(X2,union(X0,X1)),intersection(difference(X2,X0),difference(X2,X1)))
& subset(X0,X2)
& subset(X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ~ equal_set(difference(X2,union(X0,X1)),intersection(difference(X2,X0),difference(X2,X1)))
& subset(X0,X2)
& subset(X1,X2) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f20,plain,
( ~ equal_set(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1)))
& subset(sK0,sK2)
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f22,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,[],[f19]) ).
fof(f23,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,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
~ equal_set(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f44,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f45,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
( ~ subset(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1)))
| ~ subset(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))) ),
inference(resolution,[],[f36,f33]) ).
fof(f56,definition,
( spl4_1
<=> subset(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f57,plain,
( ~ subset(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1)))
| spl4_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,definition,
( spl4_2
<=> subset(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f60,plain,
( ~ subset(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1)))
| spl4_2 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f54,f59,f56]) ).
fof(f63,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),intersection(difference(sK2,sK0),difference(sK2,sK1)))
| spl4_1 ),
inference(resolution,[],[f57,f38]) ).
fof(f70,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),difference(sK2,sK0))
| spl4_1 ),
inference(resolution,[],[f63,f41]) ).
fof(f72,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK2)
| spl4_1 ),
inference(resolution,[],[f70,f47]) ).
fof(f84,definition,
( spl4_3
<=> member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),union(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f85,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),union(sK0,sK1))
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,definition,
( spl4_4
<=> member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f88,plain,
( ~ member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK2)
| spl4_4 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( $false
| spl4_1
| spl4_4 ),
inference(resolution,[],[f88,f72]) ).
fof(f91,plain,
( spl4_1
| spl4_4 ),
inference(avatar_contradiction_clause,[],[f90]) ).
fof(f94,definition,
( spl4_5
<=> member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK0) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f95,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK0)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,definition,
( spl4_6
<=> member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK1) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f98,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK1)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f107,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),intersection(difference(sK2,sK0),difference(sK2,sK1)))
| spl4_2 ),
inference(resolution,[],[f60,f39]) ).
fof(f108,plain,
( member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,union(sK0,sK1)))
| spl4_2 ),
inference(resolution,[],[f60,f38]) ).
fof(f110,plain,
( member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK2)
| spl4_2 ),
inference(resolution,[],[f108,f47]) ).
fof(f111,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),union(sK0,sK1))
| spl4_2 ),
inference(resolution,[],[f108,f46]) ).
fof(f112,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK0))
| ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK1))
| spl4_2 ),
inference(resolution,[],[f107,f42]) ).
fof(f114,definition,
( spl4_7
<=> member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f115,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK1))
| spl4_7 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl4_8
<=> member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f118,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK0))
| spl4_8 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( ~ spl4_7
| ~ spl4_8
| spl4_2 ),
inference(avatar_split_clause,[],[f112,f59,f117,f114]) ).
fof(f120,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK0)
| spl4_2 ),
inference(resolution,[],[f111,f45]) ).
fof(f121,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK1)
| spl4_2 ),
inference(resolution,[],[f111,f44]) ).
fof(f124,definition,
( spl4_9
<=> member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK1) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f125,plain,
( member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK1)
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,definition,
( spl4_10
<=> member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
fof(f128,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK2)
| spl4_10 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f130,plain,
( $false
| spl4_2
| spl4_10 ),
inference(resolution,[],[f128,f110]) ).
fof(f131,plain,
( spl4_2
| spl4_10 ),
inference(avatar_contradiction_clause,[],[f130]) ).
fof(f134,definition,
( spl4_11
<=> member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK0) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f135,plain,
( member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK0)
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK2)
| member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK1)
| spl4_7 ),
inference(resolution,[],[f115,f48]) ).
fof(f138,plain,
( spl4_9
| ~ spl4_10
| spl4_7 ),
inference(avatar_split_clause,[],[f137,f114,f127,f124]) ).
fof(f139,plain,
( $false
| spl4_2
| ~ spl4_9 ),
inference(resolution,[],[f125,f121]) ).
fof(f141,plain,
( spl4_2
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f139]) ).
fof(f142,plain,
( ~ member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK2)
| member(sK3(difference(sK2,union(sK0,sK1)),intersection(difference(sK2,sK0),difference(sK2,sK1))),sK0)
| spl4_8 ),
inference(resolution,[],[f118,f48]) ).
fof(f143,plain,
( spl4_11
| ~ spl4_10
| spl4_8 ),
inference(avatar_split_clause,[],[f142,f117,f127,f134]) ).
fof(f144,plain,
( $false
| spl4_2
| ~ spl4_11 ),
inference(resolution,[],[f135,f120]) ).
fof(f146,plain,
( spl4_2
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f144]) ).
fof(f147,plain,
( ~ member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),difference(sK2,union(sK0,sK1)))
| spl4_1 ),
inference(resolution,[],[f57,f39]) ).
fof(f148,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),intersection(difference(sK2,sK0),difference(sK2,sK1)))
| spl4_1 ),
inference(resolution,[],[f57,f38]) ).
fof(f156,plain,
( ~ member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK2)
| member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),union(sK0,sK1))
| spl4_1 ),
inference(resolution,[],[f147,f48]) ).
fof(f157,plain,
( spl4_3
| ~ spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f156,f56,f87,f84]) ).
fof(f159,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),difference(sK2,sK0))
| spl4_1 ),
inference(resolution,[],[f148,f41]) ).
fof(f160,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),difference(sK2,sK1))
| spl4_1 ),
inference(resolution,[],[f148,f40]) ).
fof(f161,plain,
( member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK1)
| member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK0)
| ~ spl4_3 ),
inference(resolution,[],[f85,f43]) ).
fof(f163,plain,
( ~ member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK0)
| spl4_1 ),
inference(resolution,[],[f159,f46]) ).
fof(f165,plain,
( ~ member(sK3(intersection(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,union(sK0,sK1))),sK1)
| spl4_1 ),
inference(resolution,[],[f160,f46]) ).
fof(f166,plain,
( $false
| spl4_1
| ~ spl4_5 ),
inference(resolution,[],[f163,f95]) ).
fof(f167,plain,
( spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f166]) ).
fof(f168,plain,
( spl4_5
| spl4_6
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f161,f84,f97,f94]) ).
fof(f170,plain,
( $false
| spl4_1
| ~ spl4_6 ),
inference(resolution,[],[f165,f98]) ).
fof(f171,plain,
( spl4_1
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f170]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
( spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(sat_conversion,[],[f119]) ).
cnf(s7,plain,
( spl4_2
| spl4_10 ),
inference(sat_conversion,[],[f131]) ).
cnf(s9,plain,
( spl4_7
| spl4_9
| ~ spl4_10 ),
inference(sat_conversion,[],[f138]) ).
cnf(s10,plain,
( spl4_2
| ~ spl4_9 ),
inference(sat_conversion,[],[f141]) ).
cnf(s11,plain,
( spl4_8
| ~ spl4_10
| spl4_11 ),
inference(sat_conversion,[],[f143]) ).
cnf(s12,plain,
( spl4_2
| ~ spl4_11 ),
inference(sat_conversion,[],[f146]) ).
cnf(s13,plain,
( spl4_1
| spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f157]) ).
cnf(s14,plain,
( spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f167]) ).
cnf(s15,plain,
( ~ spl4_3
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f168]) ).
cnf(s16,plain,
( spl4_1
| ~ spl4_6 ),
inference(sat_conversion,[],[f171]) ).
cnf(s17,plain,
spl4_1,
inference(rat,[],[s13,s15,s3,s14,s16]) ).
cnf(s18,plain,
~ spl4_2,
inference(rat,[],[s1,s17]) ).
cnf(s19,plain,
~ spl4_11,
inference(rat,[],[s12,s18]) ).
cnf(s20,plain,
~ spl4_9,
inference(rat,[],[s10,s18]) ).
cnf(s21,plain,
spl4_10,
inference(rat,[],[s7,s18]) ).
cnf(s22,plain,
spl4_7,
inference(rat,[],[s9,s21,s20]) ).
cnf(s23,plain,
spl4_8,
inference(rat,[],[s11,s19,s21]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s5,s18,s23,s22]) ).
fof(f172,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET155+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.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 00:53:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 1.66/1.13 % (1931826)Detected formulas, will run a generic FOF schedule.
% 1.66/1.13 % (1931837)dis-21_1_sil=8000:lcm=predicate:random_seed=3141528829: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)
% 1.66/1.13 % (1931837)First to succeed.
% 1.66/1.13 % (1931837)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1931826"
% 1.66/1.13 % (1931831)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=2532439788:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.66/1.13 % (1931833)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=184756614:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.66/1.13 % (1931834)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=630600019:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.66/1.13 % (1931836)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1586852882:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.66/1.13 % (1931832)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=1418997599:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.66/1.13 % (1931834)Refutation not found, incomplete strategy
% 1.66/1.13 % (1931834)------------------------------
% 1.66/1.13 % (1931834)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.66/1.13 % (1931834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/1.13 % (1931834)CaDiCaL version: 2.1.3
% 1.66/1.13 % (1931834)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.13 % (1931834)Time elapsed: 0.001 s
% 1.66/1.13 % (1931834)Peak memory usage: 88 MB
% 1.66/1.13 % (1931834)Instructions burned: 1 (million)
% 1.66/1.13 % (1931836)Also succeeded, but the first one will report.
% 1.66/1.13 % (1931835)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2986246175:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.66/1.13 % (1931835)Instruction limit reached!
% 1.66/1.13 % (1931835)------------------------------
% 1.66/1.13 % (1931835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.66/1.13 % (1931835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/1.13 % (1931835)CaDiCaL version: 2.1.3
% 1.66/1.13 % (1931835)Termination reason: Instruction limit
% 1.66/1.13 % (1931835)Termination phase: Saturation
% 1.66/1.13 % (1931835)Time elapsed: 0.073 s
% 1.66/1.13 % (1931835)Peak memory usage: 89 MB
% 1.66/1.13 % (1931835)Instructions burned: 119 (million)
% 1.66/1.13 % (1931837)Refutation found. Thanks to Tanya!
% 1.66/1.13 % SZS status Theorem for theBenchmark
% 1.66/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.32 % (1931837)------------------------------
% 2.55/1.32 % (1931837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.32 % (1931837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.32 % (1931837)CaDiCaL version: 2.1.3
% 2.55/1.32 % (1931837)Termination reason: Refutation
% 2.55/1.32 % (1931837)Time elapsed: 0.003 s
% 2.55/1.32 % (1931837)Peak memory usage: 89 MB
% 2.55/1.32 % (1931837)Instructions burned: 6 (million)
% 2.55/1.32 % (1931837)------------------------------
% 2.55/1.32 % (1931837)------------------------------
% 2.55/1.32 % (1931826)Success in time 0.271 s
% 2.55/1.32 % Vampire exiting
%------------------------------------------------------------------------------