%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC388+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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:03:45 PM UTC 2026
% Result : Theorem 3.65s 1.19s
% Output : Refutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of formulae : 148 ( 22 unt; 10 def)
% Number of atoms : 551 ( 84 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 694 ( 291 ~; 285 |; 75 &)
% ( 22 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 137 ( 0 sgn 107 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ segmentP(X3,X2)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X0
& memberP(X1,X4) )
| ( ~ singletonP(X2)
& neq(X3,nil) )
| ( nil = X1
& nil = X0 ) ) ) ) ) ),
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
| ~ segmentP(X3,X2)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X0
& memberP(X1,X4) )
| ( ~ singletonP(X2)
& neq(X3,nil) )
| ( nil = X1
& nil = X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ( singletonP(X2)
| ~ neq(X3,nil) )
& ( nil != X1
| nil != X0 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ( singletonP(X2)
| ~ neq(X3,nil) )
& ( nil != X1
| nil != X0 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f113,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f114,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f135,plain,
( sK1 = sK3
& sK0 = sK2
& segmentP(sK3,sK2)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != sK0
| ~ memberP(sK1,X4) )
& ( singletonP(sK2)
| ~ neq(sK3,nil) )
& ( nil != sK1
| nil != sK0 )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f107]) ).
fof(f142,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f111]) ).
fof(f143,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f142]) ).
fof(f144,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f112]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,cons(X1,X5)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f144]) ).
fof(f146,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ( ssList(sK8(X0,X1))
& ssList(sK9(X0,X1))
& app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0 )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f145]) ).
fof(f147,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f113]) ).
fof(f148,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f147]) ).
fof(f149,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ( ssItem(sK10(X0))
& cons(sK10(X0),nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f148]) ).
fof(f150,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f114]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,X1),X5) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f151]) ).
fof(f153,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK11(X0,X1))
& ssList(sK12(X0,X1))
& app(app(sK11(X0,X1),X1),sK12(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X4,sK11(X0,X1)),skolemize(X5,sK12(X0,X1))],[f152]) ).
fof(f156,plain,
ssList(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f157,plain,
ssList(sK1),
inference(cnf_transformation,[],[f135]) ).
fof(f160,plain,
( nil != sK1
| nil != sK0 ),
inference(cnf_transformation,[],[f135]) ).
fof(f161,plain,
( singletonP(sK2)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f135]) ).
fof(f162,plain,
! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != sK0
| ~ memberP(sK1,X4) ),
inference(cnf_transformation,[],[f135]) ).
fof(f163,plain,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f135]) ).
fof(f164,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f135]) ).
fof(f165,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f135]) ).
fof(f178,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f181,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f188,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f192,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f194,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK10(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f195,plain,
! [X0] :
( ssItem(sK10(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f197,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f204,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| app(app(sK11(X0,X1),X1),sK12(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f205,plain,
! [X0,X1] :
( ssList(sK12(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f206,plain,
! [X0,X1] :
( ssList(sK11(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f218,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f219,plain,
! [X4] :
( cons(X4,nil) != sK2
| ~ ssItem(X4)
| ~ memberP(sK3,X4) ),
inference(definition_unfolding,[],[f162,f164,f165]) ).
fof(f220,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f160,f165,f164]) ).
fof(f221,plain,
ssList(sK3),
inference(definition_unfolding,[],[f157,f165]) ).
fof(f222,plain,
ssList(sK2),
inference(definition_unfolding,[],[f156,f164]) ).
fof(f226,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f192]) ).
fof(f237,definition,
( spl13_1
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f239,plain,
( nil != sK2
| spl13_1 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f241,definition,
( spl13_2
<=> nil = sK3 ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f242,plain,
( nil = sK3
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f244,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f220,f241,f237]) ).
fof(f246,definition,
( spl13_3
<=> neq(sK3,nil) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f248,plain,
( ~ neq(sK3,nil)
| spl13_3 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl13_4
<=> singletonP(sK2) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f252,plain,
( singletonP(sK2)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( ~ spl13_3
| spl13_4 ),
inference(avatar_split_clause,[],[f161,f250,f246]) ).
fof(f276,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3)
| spl13_3 ),
inference(resolution,[],[f178,f248]) ).
fof(f281,plain,
( nil = sK3
| ~ ssList(sK3)
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f276,f181]) ).
fof(f282,plain,
( nil = sK3
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f281,f221]) ).
fof(f283,plain,
( spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f282,f246,f241]) ).
fof(f288,plain,
( sK2 = cons(sK10(sK2),nil)
| ~ ssList(sK2)
| ~ spl13_4 ),
inference(resolution,[],[f194,f252]) ).
fof(f289,plain,
( sK2 = cons(sK10(sK2),nil)
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f288,f222]) ).
fof(f294,plain,
( sK2 != sK2
| ~ ssItem(sK10(sK2))
| ~ memberP(sK3,sK10(sK2))
| ~ spl13_4 ),
inference(superposition,[],[f219,f289]) ).
fof(f299,plain,
( ~ ssItem(sK10(sK2))
| ~ memberP(sK3,sK10(sK2))
| ~ spl13_4 ),
inference(trivial_inequality_removal,[],[f294]) ).
fof(f302,definition,
( spl13_5
<=> memberP(sK3,sK10(sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f304,plain,
( ~ memberP(sK3,sK10(sK2))
| spl13_5 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f306,definition,
( spl13_6
<=> ssItem(sK10(sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f307,plain,
( ssItem(sK10(sK2))
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f308,plain,
( ~ ssItem(sK10(sK2))
| spl13_6 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f309,plain,
( ~ spl13_5
| ~ spl13_6
| ~ spl13_4 ),
inference(avatar_split_clause,[],[f299,f250,f306,f302]) ).
fof(f317,plain,
( ~ singletonP(sK2)
| ~ ssList(sK2)
| spl13_6 ),
inference(resolution,[],[f308,f195]) ).
fof(f318,plain,
( ~ ssList(sK2)
| ~ spl13_4
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f317,f252]) ).
fof(f319,plain,
( $false
| ~ spl13_4
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f318,f222]) ).
fof(f320,plain,
( ~ spl13_4
| spl13_6 ),
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f344,plain,
( segmentP(nil,sK2)
| ~ spl13_2 ),
inference(superposition,[],[f163,f242]) ).
fof(f352,plain,
( nil = sK2
| ~ ssList(sK2)
| ~ spl13_2 ),
inference(resolution,[],[f344,f197]) ).
fof(f353,plain,
( ~ ssList(sK2)
| spl13_1
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f352,f239]) ).
fof(f354,plain,
( $false
| spl13_1
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f353,f222]) ).
fof(f355,plain,
( spl13_1
| ~ spl13_2 ),
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f751,plain,
( sK3 = app(app(sK11(sK3,sK2),sK2),sK12(sK3,sK2))
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(resolution,[],[f204,f163]) ).
fof(f759,plain,
( sK3 = app(app(sK11(sK3,sK2),sK2),sK12(sK3,sK2))
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f751,f222]) ).
fof(f760,plain,
sK3 = app(app(sK11(sK3,sK2),sK2),sK12(sK3,sK2)),
inference(forward_subsumption_resolution,[],[f759,f221]) ).
fof(f767,plain,
( ! [X0] :
( memberP(app(X0,sK2),sK10(sK2))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK10(sK2))
| ~ ssList(app(X0,sK2)) )
| ~ spl13_4 ),
inference(superposition,[],[f226,f289]) ).
fof(f778,plain,
( ! [X0] :
( memberP(app(X0,sK2),sK10(sK2))
| ~ ssList(X0)
| ~ ssItem(sK10(sK2))
| ~ ssList(app(X0,sK2)) )
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f767,f181]) ).
fof(f783,plain,
( ! [X0] :
( memberP(app(X0,sK2),sK10(sK2))
| ~ ssList(X0)
| ~ ssList(app(X0,sK2)) )
| ~ spl13_4
| ~ spl13_6 ),
inference(forward_subsumption_resolution,[],[f778,f307]) ).
fof(f872,plain,
! [X0] :
( memberP(sK3,X0)
| ~ memberP(app(sK11(sK3,sK2),sK2),X0)
| ~ ssList(sK12(sK3,sK2))
| ~ ssList(app(sK11(sK3,sK2),sK2))
| ~ ssItem(X0) ),
inference(superposition,[],[f188,f760]) ).
fof(f886,definition,
( spl13_30
<=> ssList(sK12(sK3,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_30])],[avatar_definition]) ).
fof(f888,plain,
( ~ ssList(sK12(sK3,sK2))
| spl13_30 ),
inference(avatar_component_clause,[],[f886]) ).
fof(f890,definition,
( spl13_31
<=> ssList(app(sK11(sK3,sK2),sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_31])],[avatar_definition]) ).
fof(f891,plain,
( ssList(app(sK11(sK3,sK2),sK2))
| ~ spl13_31 ),
inference(avatar_component_clause,[],[f890]) ).
fof(f892,plain,
( ~ ssList(app(sK11(sK3,sK2),sK2))
| spl13_31 ),
inference(avatar_component_clause,[],[f890]) ).
fof(f912,definition,
( spl13_36
<=> ! [X0] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(app(sK11(sK3,sK2),sK2),X0) ) ),
introduced(definition,[new_symbols(definition,[spl13_36])],[avatar_definition]) ).
fof(f913,plain,
( ! [X0] :
( ~ memberP(app(sK11(sK3,sK2),sK2),X0)
| ~ ssItem(X0)
| memberP(sK3,X0) )
| ~ spl13_36 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f914,plain,
( ~ spl13_31
| ~ spl13_30
| spl13_36 ),
inference(avatar_split_clause,[],[f872,f912,f886,f890]) ).
fof(f924,definition,
( spl13_39
<=> ssList(sK11(sK3,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_39])],[avatar_definition]) ).
fof(f925,plain,
( ssList(sK11(sK3,sK2))
| ~ spl13_39 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f926,plain,
( ~ ssList(sK11(sK3,sK2))
| spl13_39 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f931,plain,
( ~ segmentP(sK3,sK2)
| ~ ssList(sK2)
| ~ ssList(sK3)
| spl13_30 ),
inference(resolution,[],[f888,f205]) ).
fof(f932,plain,
( ~ ssList(sK2)
| ~ ssList(sK3)
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f931,f163]) ).
fof(f933,plain,
( ~ ssList(sK3)
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f932,f222]) ).
fof(f934,plain,
( $false
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f933,f221]) ).
fof(f935,plain,
spl13_30,
inference(avatar_contradiction_clause,[],[f934]) ).
fof(f989,plain,
( ~ segmentP(sK3,sK2)
| ~ ssList(sK2)
| ~ ssList(sK3)
| spl13_39 ),
inference(resolution,[],[f926,f206]) ).
fof(f990,plain,
( ~ ssList(sK2)
| ~ ssList(sK3)
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f989,f163]) ).
fof(f991,plain,
( ~ ssList(sK3)
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f990,f222]) ).
fof(f992,plain,
( $false
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f991,f221]) ).
fof(f993,plain,
spl13_39,
inference(avatar_contradiction_clause,[],[f992]) ).
fof(f1234,plain,
( ~ ssList(sK2)
| ~ ssList(sK11(sK3,sK2))
| spl13_31 ),
inference(resolution,[],[f892,f218]) ).
fof(f1237,plain,
( ~ ssList(sK11(sK3,sK2))
| spl13_31 ),
inference(forward_subsumption_resolution,[],[f1234,f222]) ).
fof(f1240,plain,
( $false
| spl13_31
| ~ spl13_39 ),
inference(forward_subsumption_resolution,[],[f1237,f925]) ).
fof(f1241,plain,
( spl13_31
| ~ spl13_39 ),
inference(avatar_contradiction_clause,[],[f1240]) ).
fof(f5989,plain,
( ~ ssItem(sK10(sK2))
| memberP(sK3,sK10(sK2))
| ~ ssList(sK11(sK3,sK2))
| ~ ssList(app(sK11(sK3,sK2),sK2))
| ~ spl13_4
| ~ spl13_6
| ~ spl13_36 ),
inference(resolution,[],[f913,f783]) ).
fof(f5992,plain,
( memberP(sK3,sK10(sK2))
| ~ ssList(sK11(sK3,sK2))
| ~ ssList(app(sK11(sK3,sK2),sK2))
| ~ spl13_4
| ~ spl13_6
| ~ spl13_36 ),
inference(forward_subsumption_resolution,[],[f5989,f307]) ).
fof(f5996,plain,
( ~ ssList(sK11(sK3,sK2))
| ~ ssList(app(sK11(sK3,sK2),sK2))
| ~ spl13_4
| spl13_5
| ~ spl13_6
| ~ spl13_36 ),
inference(forward_subsumption_resolution,[],[f5992,f304]) ).
fof(f6000,plain,
( ~ ssList(app(sK11(sK3,sK2),sK2))
| ~ spl13_4
| spl13_5
| ~ spl13_6
| ~ spl13_36
| ~ spl13_39 ),
inference(forward_subsumption_resolution,[],[f5996,f925]) ).
fof(f6002,plain,
( $false
| ~ spl13_4
| spl13_5
| ~ spl13_6
| ~ spl13_31
| ~ spl13_36
| ~ spl13_39 ),
inference(forward_subsumption_resolution,[],[f6000,f891]) ).
fof(f6003,plain,
( ~ spl13_4
| spl13_5
| ~ spl13_6
| ~ spl13_31
| ~ spl13_36
| ~ spl13_39 ),
inference(avatar_contradiction_clause,[],[f6002]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f244]) ).
cnf(s2,plain,
( ~ spl13_3
| spl13_4 ),
inference(sat_conversion,[],[f253]) ).
cnf(s3,plain,
( spl13_2
| spl13_3 ),
inference(sat_conversion,[],[f283]) ).
cnf(s4,plain,
( ~ spl13_4
| ~ spl13_5
| ~ spl13_6 ),
inference(sat_conversion,[],[f309]) ).
cnf(s6,plain,
( ~ spl13_4
| spl13_6 ),
inference(sat_conversion,[],[f320]) ).
cnf(s8,plain,
( spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f355]) ).
cnf(s36,plain,
( ~ spl13_30
| ~ spl13_31
| spl13_36 ),
inference(sat_conversion,[],[f914]) ).
cnf(s40,plain,
spl13_30,
inference(sat_conversion,[],[f935]) ).
cnf(s42,plain,
spl13_39,
inference(sat_conversion,[],[f993]) ).
cnf(s49,plain,
( spl13_31
| ~ spl13_39 ),
inference(sat_conversion,[],[f1241]) ).
cnf(s264,plain,
( ~ spl13_4
| spl13_5
| ~ spl13_6
| ~ spl13_31
| ~ spl13_36
| ~ spl13_39 ),
inference(sat_conversion,[],[f6003]) ).
cnf(s367,plain,
spl13_31,
inference(rat,[],[s49,s42]) ).
cnf(s371,plain,
spl13_36,
inference(rat,[],[s36,s367,s40]) ).
cnf(s376,plain,
( ~ spl13_4
| ~ spl13_6 ),
inference(rat,[],[s264,s4,s42,s371,s367]) ).
cnf(s377,plain,
~ spl13_4,
inference(rat,[],[s376,s6]) ).
cnf(s378,plain,
~ spl13_3,
inference(rat,[],[s2,s377]) ).
cnf(s379,plain,
spl13_2,
inference(rat,[],[s3,s378]) ).
cnf(s380,plain,
spl13_1,
inference(rat,[],[s8,s379]) ).
cnf(s381,plain,
$false,
inference(rat,[],[s1,s379,s380]) ).
fof(f6006,plain,
$false,
inference(avatar_sat_refutation,[],[s381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC388+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 % Computer : n018.cluster.edu
% 0.06/0.20 % Model : x86_64 x86_64
% 0.06/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.20 % Memory : 8046.5625MB
% 0.06/0.20 % OS : Linux 6.8.0-71-generic
% 0.06/0.20 % CPULimit : 300
% 0.06/0.20 % WCLimit : 300
% 0.06/0.20 % DateTime : Mon Sep 28 09:27:55 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running first-order theorem proving
% 0.06/0.23 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
% 3.65/1.19 % (3248877)Detected formulas, will run a generic FOF schedule.
% 3.65/1.19 % (3248885)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3383765264:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.65/1.19 % (3248885)Instruction limit reached!
% 3.65/1.19 % (3248885)------------------------------
% 3.65/1.19 % (3248885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.19 % (3248885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.19 % (3248885)CaDiCaL version: 2.1.3
% 3.65/1.19 % (3248885)Termination reason: Instruction limit
% 3.65/1.19 % (3248885)Termination phase: Saturation
% 3.65/1.19 % (3248885)Time elapsed: 0.038 s
% 3.65/1.19 % (3248885)Peak memory usage: 89 MB
% 3.65/1.19 % (3248885)Instructions burned: 111 (million)
% 3.65/1.19 % (3248884)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=1405187911:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.65/1.19 % (3248886)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=988337179:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.65/1.19 % (3248883)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=1910053665:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.65/1.19 % (3248887)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=170604626:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.65/1.19 % (3248882)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=411154537:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.65/1.19 % (3248888)dis-21_1_sil=8000:lcm=predicate:random_seed=1596160817: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)
% 3.65/1.19 % (3248886)Instruction limit reached!
% 3.65/1.19 % (3248886)------------------------------
% 3.65/1.19 % (3248886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.19 % (3248886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.19 % (3248886)CaDiCaL version: 2.1.3
% 3.65/1.19 % (3248886)Termination reason: Instruction limit
% 3.65/1.19 % (3248886)Termination phase: Saturation
% 3.65/1.19 % (3248886)Time elapsed: 0.053 s
% 3.65/1.19 % (3248886)Peak memory usage: 88 MB
% 3.65/1.19 % (3248886)Instructions burned: 120 (million)
% 3.65/1.19 % (3248888)Instruction limit reached!
% 3.65/1.19 % (3248888)------------------------------
% 3.65/1.19 % (3248888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.19 % (3248888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.19 % (3248888)CaDiCaL version: 2.1.3
% 3.65/1.19 % (3248888)Termination reason: Instruction limit
% 3.65/1.19 % (3248888)Termination phase: Saturation
% 3.65/1.19 % (3248888)Time elapsed: 0.073 s
% 3.65/1.19 % (3248888)Peak memory usage: 90 MB
% 3.65/1.19 % (3248888)Instructions burned: 129 (million)
% 3.65/1.19 % (3248887)Instruction limit reached!
% 3.65/1.19 % (3248887)------------------------------
% 3.65/1.19 % (3248887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.19 % (3248887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.19 % (3248887)CaDiCaL version: 2.1.3
% 3.65/1.19 % (3248887)Termination reason: Instruction limit
% 3.65/1.19 % (3248887)Termination phase: Saturation
% 3.65/1.19 % (3248887)Time elapsed: 0.095 s
% 3.65/1.19 % (3248887)Peak memory usage: 90 MB
% 3.65/1.19 % (3248887)Instructions burned: 139 (million)
% 3.65/1.19 % (3248890)lrs+10_1_sil=8000:sp=occurrence:random_seed=810596547:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.65/1.19 % (3248890)First to succeed.
% 3.65/1.19 % (3248890)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3248877"
% 3.65/1.19 % (3248897)lrs+10_1_sil=32000:urr=on:br=off:random_seed=957652616:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.65/1.19 % (3248898)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2071973822:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.65/1.19 % (3248899)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=2467913602:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 3.65/1.19 % (3248897)Instruction limit reached!
% 3.65/1.19 % (3248897)------------------------------
% 3.65/1.19 % (3248897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.19 % (3248897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.19 % (3248897)CaDiCaL version: 2.1.3
% 3.65/1.19 % (3248897)Termination reason: Instruction limit
% 3.65/1.19 % (3248897)Termination phase: Saturation
% 3.65/1.19 % (3248897)Time elapsed: 0.077 s
% 3.65/1.19 % (3248897)Peak memory usage: 91 MB
% 3.65/1.19 % (3248897)Instructions burned: 157 (million)
% 3.65/1.19 % (3248890)Refutation found. Thanks to Tanya!
% 3.65/1.19 % SZS status Theorem for theBenchmark
% 3.65/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 4.22/1.38 % (3248890)------------------------------
% 4.22/1.38 % (3248890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.38 % (3248890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.38 % (3248890)CaDiCaL version: 2.1.3
% 4.22/1.38 % (3248890)Termination reason: Refutation
% 4.22/1.38 % (3248890)Time elapsed: 0.072 s
% 4.22/1.38 % (3248890)Peak memory usage: 93 MB
% 4.22/1.38 % (3248890)Instructions burned: 212 (million)
% 4.22/1.38 % (3248890)------------------------------
% 4.22/1.38 % (3248890)------------------------------
% 4.22/1.38 % (3248877)Success in time 0.515 s
% 4.22/1.38 % Vampire exiting
%------------------------------------------------------------------------------