%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC003+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 01:01:59 PM UTC 2026
% Result : Theorem 4.09s 1.64s
% Output : Refutation 5.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 106 ( 12 unt; 7 def)
% Number of atoms : 454 ( 77 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 587 ( 239 ~; 223 |; 93 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 183 ( 0 sgn 148 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0
& neq(X5,nil) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X3
| app(X8,X9) != X2
| ? [X10] :
( ssItem(X10)
& X7 != X10
& memberP(X3,X10)
& geq(X10,X7) ) ) ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0
& neq(X5,nil) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X3
| app(X8,X9) != X2
| ? [X10] :
( ssItem(X10)
& X7 != X10
& memberP(X3,X10)
& geq(X10,X7) ) ) ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ! [X10] :
( ~ ssItem(X10)
| X7 = X10
| ~ memberP(X3,X10)
| ~ geq(X10,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ! [X10] :
( ~ ssItem(X10)
| X7 = X10
| ~ memberP(X3,X10)
| ~ geq(X10,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f135,definition,
! [X1,X0,X3,X2] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ! [X10] :
( ~ ssItem(X10)
| X7 = X10
| ~ memberP(X3,X10)
| ~ geq(X10,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ~ sP0(X1,X0,X3,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f136,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( sP0(X1,X0,X3,X2)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f135]) ).
fof(f137,plain,
! [X1,X0,X3,X2] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ! [X10] :
( ~ ssItem(X10)
| X7 = X10
| ~ memberP(X3,X10)
| ~ geq(X10,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ~ sP0(X1,X0,X3,X2) ),
inference(nnf_transformation,[],[f135]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X0
| app(X4,X6) != X1
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X2
& app(X8,X9) = X3
& ! [X10] :
( ~ ssItem(X10)
| X7 = X10
| ~ memberP(X2,X10)
| ~ geq(X10,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ~ sP0(X0,X1,X2,X3) ),
inference(rectify,[],[f137]) ).
fof(f139,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X0
| app(X4,X6) != X1
| ~ neq(X5,nil) ) ) )
& app(app(sK2(X2,X3),cons(sK1(X2,X3),nil)),sK3(X2,X3)) = X2
& app(sK2(X2,X3),sK3(X2,X3)) = X3
& ! [X10] :
( ~ ssItem(X10)
| sK1(X2,X3) = X10
| ~ memberP(X2,X10)
| ~ geq(X10,sK1(X2,X3)) )
& ssList(sK3(X2,X3))
& ssList(sK2(X2,X3))
& ssItem(sK1(X2,X3)) )
| ~ sP0(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X7,sK1(X2,X3)),skolemize(X8,sK2(X2,X3)),skolemize(X9,sK3(X2,X3))],[f138]) ).
fof(f140,plain,
( sK5 = sK7
& sK4 = sK6
& ( sP0(sK5,sK4,sK7,sK6)
| ( neq(sK5,nil)
& ~ neq(sK7,nil) ) )
& ssList(sK7)
& ssList(sK6)
& ssList(sK5)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f136]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f121]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f147]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f156,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK2(X2,X3)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK3(X2,X3)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(sK2(X2,X3),sK3(X2,X3)) = X3 ),
inference(cnf_transformation,[],[f139]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(app(sK2(X2,X3),cons(sK1(X2,X3),nil)),sK3(X2,X3)) = X2 ),
inference(cnf_transformation,[],[f139]) ).
fof(f161,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != X0
| app(X4,X6) != X1
| ~ neq(X5,nil)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f139]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| neq(X0,nil) ),
inference(cnf_transformation,[],[f139]) ).
fof(f167,plain,
( sP0(sK5,sK4,sK7,sK6)
| ~ neq(sK7,nil) ),
inference(cnf_transformation,[],[f140]) ).
fof(f168,plain,
( sP0(sK5,sK4,sK7,sK6)
| neq(sK5,nil) ),
inference(cnf_transformation,[],[f140]) ).
fof(f169,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f140]) ).
fof(f170,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f140]) ).
fof(f181,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f194,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f197,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f198,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f201,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f217,plain,
( sP0(sK7,sK6,sK7,sK6)
| neq(sK7,nil) ),
inference(definition_unfolding,[],[f168,f170,f169,f170]) ).
fof(f218,plain,
( sP0(sK7,sK6,sK7,sK6)
| ~ neq(sK7,nil) ),
inference(definition_unfolding,[],[f167,f170,f169]) ).
fof(f221,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(X4,X6) != X1
| ~ neq(X5,nil)
| ~ sP0(app(app(X4,X5),X6),X1,X2,X3) ),
inference(equality_resolution,[],[f161]) ).
fof(f222,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP0(app(app(X4,X5),X6),app(X4,X6),X2,X3)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ neq(X5,nil)
| ~ ssList(X4) ),
inference(equality_resolution,[],[f221]) ).
fof(f227,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f201]) ).
fof(f229,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f227]) ).
fof(f234,definition,
( spl14_1
<=> neq(sK7,nil) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f238,definition,
( spl14_2
<=> sP0(sK7,sK6,sK7,sK6) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f240,plain,
( sP0(sK7,sK6,sK7,sK6)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f241,plain,
( ~ spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f218,f238,f234]) ).
fof(f242,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f217,f238,f234]) ).
fof(f249,plain,
( neq(sK7,nil)
| ~ spl14_2 ),
inference(resolution,[],[f162,f240]) ).
fof(f250,plain,
( spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f249,f238,f234]) ).
fof(f263,plain,
( ssItem(sK1(sK7,sK6))
| ~ spl14_2 ),
inference(resolution,[],[f155,f240]) ).
fof(f264,plain,
( ssList(sK2(sK7,sK6))
| ~ spl14_2 ),
inference(resolution,[],[f156,f240]) ).
fof(f267,plain,
( ssList(sK3(sK7,sK6))
| ~ spl14_2 ),
inference(resolution,[],[f157,f240]) ).
fof(f434,plain,
( sK6 = app(sK2(sK7,sK6),sK3(sK7,sK6))
| ~ spl14_2 ),
inference(resolution,[],[f159,f240]) ).
fof(f873,plain,
( sK7 = app(app(sK2(sK7,sK6),cons(sK1(sK7,sK6),nil)),sK3(sK7,sK6))
| ~ spl14_2 ),
inference(resolution,[],[f160,f240]) ).
fof(f2900,definition,
( spl14_110
<=> neq(cons(sK1(sK7,sK6),nil),nil) ),
introduced(definition,[new_symbols(definition,[spl14_110])],[avatar_definition]) ).
fof(f2901,plain,
( neq(cons(sK1(sK7,sK6),nil),nil)
| ~ spl14_110 ),
inference(avatar_component_clause,[],[f2900]) ).
fof(f2902,plain,
( ~ neq(cons(sK1(sK7,sK6),nil),nil)
| spl14_110 ),
inference(avatar_component_clause,[],[f2900]) ).
fof(f2904,definition,
( spl14_111
<=> ssList(cons(sK1(sK7,sK6),nil)) ),
introduced(definition,[new_symbols(definition,[spl14_111])],[avatar_definition]) ).
fof(f2905,plain,
( ssList(cons(sK1(sK7,sK6),nil))
| ~ spl14_111 ),
inference(avatar_component_clause,[],[f2904]) ).
fof(f2906,plain,
( ~ ssList(cons(sK1(sK7,sK6),nil))
| spl14_111 ),
inference(avatar_component_clause,[],[f2904]) ).
fof(f2908,definition,
( spl14_112
<=> ! [X0,X1] : ~ sP0(sK7,sK6,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl14_112])],[avatar_definition]) ).
fof(f2909,plain,
( ! [X0,X1] : ~ sP0(sK7,sK6,X0,X1)
| ~ spl14_112 ),
inference(avatar_component_clause,[],[f2908]) ).
fof(f3113,plain,
( ~ ssItem(sK1(sK7,sK6))
| ~ ssList(nil)
| spl14_111 ),
inference(resolution,[],[f2906,f181]) ).
fof(f3114,plain,
( ~ ssList(nil)
| ~ spl14_2
| spl14_111 ),
inference(forward_subsumption_resolution,[],[f3113,f263]) ).
fof(f3115,plain,
( $false
| ~ spl14_2
| spl14_111 ),
inference(forward_subsumption_resolution,[],[f3114,f197]) ).
fof(f3116,plain,
( ~ spl14_2
| spl14_111 ),
inference(avatar_contradiction_clause,[],[f3115]) ).
fof(f3155,definition,
( spl14_124
<=> nil = cons(sK1(sK7,sK6),nil) ),
introduced(definition,[new_symbols(definition,[spl14_124])],[avatar_definition]) ).
fof(f3156,plain,
( nil != cons(sK1(sK7,sK6),nil)
| spl14_124 ),
inference(avatar_component_clause,[],[f3155]) ).
fof(f3157,plain,
( nil = cons(sK1(sK7,sK6),nil)
| ~ spl14_124 ),
inference(avatar_component_clause,[],[f3155]) ).
fof(f3342,plain,
( nil = cons(sK1(sK7,sK6),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK1(sK7,sK6),nil))
| spl14_110 ),
inference(resolution,[],[f2902,f194]) ).
fof(f3728,plain,
( memberP(nil,sK1(sK7,sK6))
| ~ ssList(nil)
| ~ ssItem(sK1(sK7,sK6))
| ~ spl14_124 ),
inference(superposition,[],[f229,f3157]) ).
fof(f3733,plain,
( ~ ssList(nil)
| ~ ssItem(sK1(sK7,sK6))
| ~ spl14_124 ),
inference(forward_subsumption_resolution,[],[f3728,f198]) ).
fof(f3739,plain,
( ~ ssItem(sK1(sK7,sK6))
| ~ spl14_124 ),
inference(forward_subsumption_resolution,[],[f3733,f197]) ).
fof(f3746,plain,
( $false
| ~ spl14_2
| ~ spl14_124 ),
inference(forward_subsumption_resolution,[],[f3739,f263]) ).
fof(f3747,plain,
( ~ spl14_2
| ~ spl14_124 ),
inference(avatar_contradiction_clause,[],[f3746]) ).
fof(f3748,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK1(sK7,sK6),nil))
| spl14_110
| spl14_124 ),
inference(forward_subsumption_resolution,[],[f3342,f3156]) ).
fof(f3751,plain,
( ~ ssList(cons(sK1(sK7,sK6),nil))
| spl14_110
| spl14_124 ),
inference(forward_subsumption_resolution,[],[f3748,f197]) ).
fof(f3758,plain,
( $false
| spl14_110
| ~ spl14_111
| spl14_124 ),
inference(forward_subsumption_resolution,[],[f3751,f2905]) ).
fof(f3759,plain,
( spl14_110
| ~ spl14_111
| spl14_124 ),
inference(avatar_contradiction_clause,[],[f3758]) ).
fof(f3760,plain,
( $false
| ~ spl14_2
| ~ spl14_112 ),
inference(resolution,[],[f2909,f240]) ).
fof(f3761,plain,
( ~ spl14_2
| ~ spl14_112 ),
inference(avatar_contradiction_clause,[],[f3760]) ).
fof(f3806,plain,
( ! [X0,X1] :
( ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ ssList(cons(sK1(sK7,sK6),nil))
| ~ ssList(sK3(sK7,sK6))
| ~ neq(cons(sK1(sK7,sK6),nil),nil)
| ~ ssList(sK2(sK7,sK6)) )
| ~ spl14_2 ),
inference(superposition,[],[f222,f873]) ).
fof(f3807,plain,
( ! [X0,X1] :
( ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ ssList(sK3(sK7,sK6))
| ~ neq(cons(sK1(sK7,sK6),nil),nil)
| ~ ssList(sK2(sK7,sK6)) )
| ~ spl14_2
| ~ spl14_111 ),
inference(forward_subsumption_resolution,[],[f3806,f2905]) ).
fof(f3816,plain,
( ! [X0,X1] :
( ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ neq(cons(sK1(sK7,sK6),nil),nil)
| ~ ssList(sK2(sK7,sK6)) )
| ~ spl14_2
| ~ spl14_111 ),
inference(forward_subsumption_resolution,[],[f3807,f267]) ).
fof(f3847,plain,
( ! [X0,X1] :
( ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ ssList(sK2(sK7,sK6)) )
| ~ spl14_2
| ~ spl14_110
| ~ spl14_111 ),
inference(forward_subsumption_resolution,[],[f3816,f2901]) ).
fof(f3848,plain,
( ! [X0,X1] : ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ spl14_2
| ~ spl14_110
| ~ spl14_111 ),
inference(forward_subsumption_resolution,[],[f3847,f264]) ).
fof(f3849,plain,
( ! [X0,X1] : ~ sP0(sK7,sK6,X0,X1)
| ~ spl14_2
| ~ spl14_110
| ~ spl14_111 ),
inference(forward_demodulation,[],[f3848,f434]) ).
fof(f3850,plain,
( spl14_112
| ~ spl14_2
| ~ spl14_110
| ~ spl14_111 ),
inference(avatar_split_clause,[],[f3849,f2904,f2900,f238,f2908]) ).
cnf(s1,plain,
( ~ spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f241]) ).
cnf(s2,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f242]) ).
cnf(s3,plain,
( spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f250]) ).
cnf(s124,plain,
( ~ spl14_2
| spl14_111 ),
inference(sat_conversion,[],[f3116]) ).
cnf(s147,plain,
( ~ spl14_2
| ~ spl14_124 ),
inference(sat_conversion,[],[f3747]) ).
cnf(s149,plain,
( spl14_110
| ~ spl14_111
| spl14_124 ),
inference(sat_conversion,[],[f3759]) ).
cnf(s150,plain,
( ~ spl14_2
| ~ spl14_112 ),
inference(sat_conversion,[],[f3761]) ).
cnf(s159,plain,
( ~ spl14_2
| ~ spl14_110
| ~ spl14_111
| spl14_112 ),
inference(sat_conversion,[],[f3850]) ).
cnf(s196,plain,
spl14_1,
inference(rat,[],[s2,s3]) ).
cnf(s200,plain,
spl14_2,
inference(rat,[],[s1,s196]) ).
cnf(s204,plain,
~ spl14_112,
inference(rat,[],[s150,s200]) ).
cnf(s205,plain,
~ spl14_124,
inference(rat,[],[s147,s200]) ).
cnf(s206,plain,
spl14_111,
inference(rat,[],[s124,s200]) ).
cnf(s211,plain,
spl14_110,
inference(rat,[],[s149,s205,s206]) ).
cnf(s217,plain,
$false,
inference(rat,[],[s159,s204,s200,s206,s211]) ).
fof(f3851,plain,
$false,
inference(avatar_sat_refutation,[],[s217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC003+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n014.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 07:24:16 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 4.09/1.64 % (1606197)Detected formulas, will run a generic FOF schedule.
% 4.09/1.64 % (1606204)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=3284612216:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.09/1.64 % (1606202)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=3278887500:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.09/1.64 % (1606203)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=1611128495:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.09/1.64 % (1606206)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1510408859:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.09/1.64 % (1606208)dis-21_1_sil=8000:lcm=predicate:random_seed=1327386459: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)
% 4.09/1.64 % (1606205)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2625648612:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.09/1.64 % (1606207)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=970208806:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.09/1.64 % (1606205)Instruction limit reached!
% 4.09/1.64 % (1606205)------------------------------
% 4.09/1.64 % (1606205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.64 % (1606205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.64 % (1606205)CaDiCaL version: 2.1.3
% 4.09/1.64 % (1606205)Termination reason: Instruction limit
% 4.09/1.64 % (1606205)Termination phase: Saturation
% 4.09/1.64 % (1606205)Time elapsed: 0.069 s
% 4.09/1.64 % (1606205)Peak memory usage: 89 MB
% 4.09/1.64 % (1606205)Instructions burned: 110 (million)
% 4.09/1.64 % (1606206)Instruction limit reached!
% 4.09/1.64 % (1606206)------------------------------
% 4.09/1.64 % (1606206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.64 % (1606206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.64 % (1606206)CaDiCaL version: 2.1.3
% 4.09/1.64 % (1606206)Termination reason: Instruction limit
% 4.09/1.64 % (1606206)Termination phase: Saturation
% 4.09/1.64 % (1606206)Time elapsed: 0.071 s
% 4.09/1.64 % (1606206)Peak memory usage: 88 MB
% 4.09/1.64 % (1606206)Instructions burned: 119 (million)
% 4.09/1.64 % (1606208)Instruction limit reached!
% 4.09/1.64 % (1606208)------------------------------
% 4.09/1.64 % (1606208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.64 % (1606208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.64 % (1606208)CaDiCaL version: 2.1.3
% 4.09/1.64 % (1606208)Termination reason: Instruction limit
% 4.09/1.64 % (1606208)Termination phase: Saturation
% 4.09/1.64 % (1606208)Time elapsed: 0.072 s
% 4.09/1.64 % (1606208)Peak memory usage: 90 MB
% 4.09/1.64 % (1606208)Instructions burned: 130 (million)
% 4.09/1.64 % (1606207)Instruction limit reached!
% 4.09/1.64 % (1606207)------------------------------
% 4.09/1.64 % (1606207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.64 % (1606207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.64 % (1606207)CaDiCaL version: 2.1.3
% 4.09/1.64 % (1606207)Termination reason: Instruction limit
% 4.09/1.64 % (1606207)Termination phase: Saturation
% 4.09/1.64 % (1606207)Time elapsed: 0.088 s
% 4.09/1.64 % (1606207)Peak memory usage: 89 MB
% 4.09/1.64 % (1606207)Instructions burned: 140 (million)
% 4.09/1.64 % (1606217)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3093768906:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.09/1.64 % (1606219)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=3663446421:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.09/1.64 % (1606218)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2771875322:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.09/1.64 % (1606216)lrs+10_1_sil=8000:sp=occurrence:random_seed=581463016:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.09/1.64 % (1606217)Instruction limit reached!
% 4.09/1.64 % (1606217)------------------------------
% 4.09/1.64 % (1606217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.64 % (1606217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.64 % (1606217)CaDiCaL version: 2.1.3
% 4.09/1.64 % (1606217)Termination reason: Instruction limit
% 4.09/1.64 % (1606217)Termination phase: Saturation
% 4.09/1.64 % (1606217)Time elapsed: 0.075 s
% 4.09/1.64 % (1606217)Peak memory usage: 92 MB
% 4.09/1.64 % (1606217)Instructions burned: 159 (million)
% 4.09/1.64 % (1606216)First to succeed.
% 4.09/1.64 % (1606216)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1606197"
% 4.09/1.64 % (1606204)Also succeeded, but the first one will report.
% 4.09/1.64 % (1606219)Instruction limit reached!
% 4.09/1.64 % (1606219)------------------------------
% 4.09/1.64 % (1606219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.64 % (1606219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.64 % (1606219)CaDiCaL version: 2.1.3
% 4.09/1.64 % (1606219)Termination reason: Instruction limit
% 4.09/1.64 % (1606219)Termination phase: Saturation
% 4.09/1.64 % (1606219)Time elapsed: 0.115 s
% 4.09/1.64 % (1606219)Peak memory usage: 94 MB
% 4.09/1.64 % (1606219)Instructions burned: 248 (million)
% 4.09/1.64 % (1606218)Also succeeded, but the first one will report.
% 4.09/1.64 % (1606224)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2611849570:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 4.09/1.64 % (1606225)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1889819694:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.09/1.64 % (1606216)Refutation found. Thanks to Tanya!
% 4.09/1.64 % SZS status Theorem for theBenchmark
% 4.09/1.64 % SZS output start Proof for theBenchmark
% See solution above
% 5.88/1.84 % (1606216)------------------------------
% 5.88/1.84 % (1606216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.88/1.84 % (1606216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.88/1.84 % (1606216)CaDiCaL version: 2.1.3
% 5.88/1.84 % (1606216)Termination reason: Refutation
% 5.88/1.84 % (1606216)Time elapsed: 0.083 s
% 5.88/1.84 % (1606216)Peak memory usage: 91 MB
% 5.88/1.84 % (1606216)Instructions burned: 134 (million)
% 5.88/1.84 % (1606216)------------------------------
% 5.88/1.84 % (1606216)------------------------------
% 5.88/1.84 % (1606197)Success in time 0.784 s
% 5.88/1.84 % Vampire exiting
%------------------------------------------------------------------------------