%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC109+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 : n019.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 01:02:29 PM UTC 2026
% Result : Theorem 2.75s 1.32s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 140 ( 14 unt; 10 def)
% Number of atoms : 535 ( 88 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 677 ( 282 ~; 273 |; 89 &)
% ( 13 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 10 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 94 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
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(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X0,X1)
& segmentP(X1,X0) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ( neq(X0,nil)
& segmentP(X1,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
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) ) )
& ssList(X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f124,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X0)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X0)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f128]) ).
fof(f132,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(f148,definition,
! [X2,X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) ) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP0(X2,X3) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f149,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( sP0(X2,X3)
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f98,f148]) ).
fof(f150,plain,
! [X2,X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) ) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP0(X2,X3) ),
inference(nnf_transformation,[],[f148]) ).
fof(f151,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ssList(X4)
& cons(X2,nil) = X0
& app(app(X3,X0),X4) = X1
& ! [X5] :
( ~ ssItem(X5)
| ~ memberP(X3,X5)
| ~ lt(X2,X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ memberP(X4,X6)
| ~ lt(X6,X2) ) )
& ssList(X3) )
& ssItem(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f150]) ).
fof(f152,plain,
! [X0,X1] :
( ( ssList(sK3(X0,X1))
& cons(sK1(X0,X1),nil) = X0
& app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
& ! [X5] :
( ~ ssItem(X5)
| ~ memberP(sK2(X0,X1),X5)
| ~ lt(sK1(X0,X1),X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ memberP(sK3(X0,X1),X6)
| ~ lt(X6,sK1(X0,X1)) )
& ssList(sK2(X0,X1))
& ssItem(sK1(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1)),skolemize(X4,sK3(X0,X1))],[f151]) ).
fof(f153,plain,
( ssList(sK7)
& sK5 = sK7
& sK4 = sK6
& ( sP0(sK6,sK7)
| ( nil = sK7
& nil = sK6 ) )
& ( ( nil = sK5
& nil != sK4 )
| ( neq(sK5,nil)
& ( ~ neq(sK4,nil)
| ~ segmentP(sK5,sK4) ) ) )
& 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)],[f149]) ).
fof(f158,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f168,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,[],[f132]) ).
fof(f169,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,[],[f168]) ).
fof(f170,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK14(X0,X1))
& ssList(sK15(X0,X1))
& app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X4,sK14(X0,X1)),skolemize(X5,sK15(X0,X1))],[f169]) ).
fof(f173,plain,
! [X0,X1] :
( ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f174,plain,
! [X0,X1] :
( ssList(sK2(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f177,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f152]) ).
fof(f178,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| cons(sK1(X0,X1),nil) = X0 ),
inference(cnf_transformation,[],[f152]) ).
fof(f179,plain,
! [X0,X1] :
( ssList(sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f180,plain,
ssList(sK4),
inference(cnf_transformation,[],[f153]) ).
fof(f181,plain,
ssList(sK5),
inference(cnf_transformation,[],[f153]) ).
fof(f184,plain,
( nil != sK4
| neq(sK5,nil) ),
inference(cnf_transformation,[],[f153]) ).
fof(f185,plain,
( nil = sK5
| ~ neq(sK4,nil)
| ~ segmentP(sK5,sK4) ),
inference(cnf_transformation,[],[f153]) ).
fof(f187,plain,
( sP0(sK6,sK7)
| nil = sK6 ),
inference(cnf_transformation,[],[f153]) ).
fof(f188,plain,
( sP0(sK6,sK7)
| nil = sK7 ),
inference(cnf_transformation,[],[f153]) ).
fof(f189,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f153]) ).
fof(f190,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f153]) ).
fof(f201,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f214,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f215,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f218,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f232,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f235,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f240,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f253,plain,
( nil = sK7
| ~ neq(sK6,nil)
| ~ segmentP(sK7,sK6) ),
inference(definition_unfolding,[],[f185,f190,f189,f190,f189]) ).
fof(f254,plain,
( nil != sK6
| neq(sK7,nil) ),
inference(definition_unfolding,[],[f184,f189,f190]) ).
fof(f256,plain,
ssList(sK7),
inference(definition_unfolding,[],[f181,f190]) ).
fof(f257,plain,
ssList(sK6),
inference(definition_unfolding,[],[f180,f189]) ).
fof(f260,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f214]) ).
fof(f265,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f240]) ).
fof(f270,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f260]) ).
fof(f273,definition,
( spl16_1
<=> segmentP(sK7,sK6) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f274,plain,
( segmentP(sK7,sK6)
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( ~ segmentP(sK7,sK6)
| spl16_1 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f277,definition,
( spl16_2
<=> neq(sK6,nil) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f279,plain,
( ~ neq(sK6,nil)
| spl16_2 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f281,definition,
( spl16_3
<=> nil = sK6 ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f282,plain,
( nil = sK6
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f283,plain,
( nil != sK6
| spl16_3 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f286,definition,
( spl16_4
<=> neq(sK7,nil) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f288,plain,
( neq(sK7,nil)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f289,plain,
( spl16_4
| ~ spl16_3 ),
inference(avatar_split_clause,[],[f254,f281,f286]) ).
fof(f291,definition,
( spl16_5
<=> nil = sK7 ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
fof(f293,plain,
( nil = sK7
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f294,plain,
( ~ spl16_1
| ~ spl16_2
| spl16_5 ),
inference(avatar_split_clause,[],[f253,f291,f277,f273]) ).
fof(f297,definition,
( spl16_6
<=> sP0(sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
fof(f299,plain,
( sP0(sK6,sK7)
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f300,plain,
( spl16_3
| spl16_6 ),
inference(avatar_split_clause,[],[f187,f297,f281]) ).
fof(f301,plain,
( spl16_5
| spl16_6 ),
inference(avatar_split_clause,[],[f188,f297,f291]) ).
fof(f302,plain,
( ~ segmentP(sK7,nil)
| spl16_1
| ~ spl16_3 ),
inference(superposition,[],[f275,f282]) ).
fof(f304,plain,
( ~ segmentP(nil,nil)
| spl16_1
| ~ spl16_3
| ~ spl16_5 ),
inference(forward_demodulation,[],[f302,f293]) ).
fof(f305,plain,
( neq(nil,nil)
| ~ spl16_4
| ~ spl16_5 ),
inference(superposition,[],[f288,f293]) ).
fof(f309,plain,
( ~ ssList(nil)
| spl16_1
| ~ spl16_3
| ~ spl16_5 ),
inference(resolution,[],[f232,f304]) ).
fof(f310,plain,
( $false
| spl16_1
| ~ spl16_3
| ~ spl16_5 ),
inference(forward_subsumption_resolution,[],[f309,f218]) ).
fof(f311,plain,
( spl16_1
| ~ spl16_3
| ~ spl16_5 ),
inference(avatar_contradiction_clause,[],[f310]) ).
fof(f314,plain,
( ~ ssList(nil)
| ~ spl16_4
| ~ spl16_5 ),
inference(resolution,[],[f270,f305]) ).
fof(f315,plain,
( $false
| ~ spl16_4
| ~ spl16_5 ),
inference(forward_subsumption_resolution,[],[f314,f218]) ).
fof(f316,plain,
( ~ spl16_4
| ~ spl16_5 ),
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f1165,plain,
( segmentP(nil,sK6)
| ~ spl16_1
| ~ spl16_5 ),
inference(forward_demodulation,[],[f274,f293]) ).
fof(f1169,plain,
( ~ segmentP(sK6,nil)
| nil = sK6
| ~ ssList(nil)
| ~ ssList(sK6)
| ~ spl16_1
| ~ spl16_5 ),
inference(resolution,[],[f1165,f235]) ).
fof(f1172,plain,
( nil = sK6
| ~ ssList(nil)
| ~ ssList(sK6)
| ~ spl16_1
| ~ spl16_5 ),
inference(forward_subsumption_resolution,[],[f1169,f232]) ).
fof(f1177,plain,
( ~ ssList(nil)
| ~ ssList(sK6)
| ~ spl16_1
| spl16_3
| ~ spl16_5 ),
inference(forward_subsumption_resolution,[],[f1172,f283]) ).
fof(f1180,plain,
( ~ ssList(sK6)
| ~ spl16_1
| spl16_3
| ~ spl16_5 ),
inference(forward_subsumption_resolution,[],[f1177,f218]) ).
fof(f1182,plain,
( $false
| ~ spl16_1
| spl16_3
| ~ spl16_5 ),
inference(forward_subsumption_resolution,[],[f1180,f257]) ).
fof(f1183,plain,
( ~ spl16_1
| spl16_3
| ~ spl16_5 ),
inference(avatar_contradiction_clause,[],[f1182]) ).
fof(f1210,plain,
( nil = sK6
| ~ ssList(nil)
| ~ ssList(sK6)
| spl16_2 ),
inference(resolution,[],[f279,f215]) ).
fof(f1228,plain,
( sK7 = app(app(sK2(sK6,sK7),sK6),sK3(sK6,sK7))
| ~ spl16_6 ),
inference(resolution,[],[f299,f177]) ).
fof(f1229,plain,
( sK6 = cons(sK1(sK6,sK7),nil)
| ~ spl16_6 ),
inference(resolution,[],[f299,f178]) ).
fof(f1230,plain,
( sP0(nil,sK7)
| ~ spl16_3
| ~ spl16_6 ),
inference(superposition,[],[f299,f282]) ).
fof(f1231,plain,
( nil = cons(sK1(nil,sK7),nil)
| ~ spl16_3
| ~ spl16_6 ),
inference(forward_demodulation,[],[f1229,f282]) ).
fof(f1378,plain,
( nil != nil
| ~ ssItem(sK1(nil,sK7))
| ~ ssList(nil)
| ~ spl16_3
| ~ spl16_6 ),
inference(superposition,[],[f201,f1231]) ).
fof(f1384,plain,
( ~ ssItem(sK1(nil,sK7))
| ~ ssList(nil)
| ~ spl16_3
| ~ spl16_6 ),
inference(trivial_inequality_removal,[],[f1378]) ).
fof(f1388,plain,
( ~ ssItem(sK1(nil,sK7))
| ~ spl16_3
| ~ spl16_6 ),
inference(forward_subsumption_resolution,[],[f1384,f218]) ).
fof(f1392,definition,
( spl16_58
<=> ssItem(sK1(nil,sK7)) ),
introduced(definition,[new_symbols(definition,[spl16_58])],[avatar_definition]) ).
fof(f1394,plain,
( ~ ssItem(sK1(nil,sK7))
| spl16_58 ),
inference(avatar_component_clause,[],[f1392]) ).
fof(f1399,plain,
( ~ spl16_58
| ~ spl16_3
| ~ spl16_6 ),
inference(avatar_split_clause,[],[f1388,f297,f281,f1392]) ).
fof(f1629,plain,
( ~ sP0(nil,sK7)
| spl16_58 ),
inference(resolution,[],[f1394,f173]) ).
fof(f1630,plain,
( $false
| ~ spl16_3
| ~ spl16_6
| spl16_58 ),
inference(forward_subsumption_resolution,[],[f1629,f1230]) ).
fof(f1631,plain,
( ~ spl16_3
| ~ spl16_6
| spl16_58 ),
inference(avatar_contradiction_clause,[],[f1630]) ).
fof(f1642,plain,
( ~ ssList(nil)
| ~ ssList(sK6)
| spl16_2
| spl16_3 ),
inference(forward_subsumption_resolution,[],[f1210,f283]) ).
fof(f1646,plain,
( ~ ssList(sK6)
| spl16_2
| spl16_3 ),
inference(forward_subsumption_resolution,[],[f1642,f218]) ).
fof(f1658,plain,
( $false
| spl16_2
| spl16_3 ),
inference(forward_subsumption_resolution,[],[f1646,f257]) ).
fof(f1659,plain,
( spl16_2
| spl16_3 ),
inference(avatar_contradiction_clause,[],[f1658]) ).
fof(f1741,plain,
( segmentP(sK7,sK6)
| ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7))
| ~ ssList(sK6)
| ~ ssList(sK7)
| ~ spl16_6 ),
inference(superposition,[],[f265,f1228]) ).
fof(f1756,definition,
( spl16_93
<=> ssList(sK3(sK6,sK7)) ),
introduced(definition,[new_symbols(definition,[spl16_93])],[avatar_definition]) ).
fof(f1758,plain,
( ~ ssList(sK3(sK6,sK7))
| spl16_93 ),
inference(avatar_component_clause,[],[f1756]) ).
fof(f1794,plain,
( ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7))
| ~ ssList(sK6)
| ~ ssList(sK7)
| spl16_1
| ~ spl16_6 ),
inference(forward_subsumption_resolution,[],[f1741,f275]) ).
fof(f1796,definition,
( spl16_102
<=> ssList(sK2(sK6,sK7)) ),
introduced(definition,[new_symbols(definition,[spl16_102])],[avatar_definition]) ).
fof(f1798,plain,
( ~ ssList(sK2(sK6,sK7))
| spl16_102 ),
inference(avatar_component_clause,[],[f1796]) ).
fof(f1803,plain,
( ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7))
| ~ ssList(sK7)
| spl16_1
| ~ spl16_6 ),
inference(forward_subsumption_resolution,[],[f1794,f257]) ).
fof(f1804,plain,
( ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7))
| spl16_1
| ~ spl16_6 ),
inference(forward_subsumption_resolution,[],[f1803,f256]) ).
fof(f1805,plain,
( ~ spl16_93
| ~ spl16_102
| spl16_1
| ~ spl16_6 ),
inference(avatar_split_clause,[],[f1804,f297,f273,f1796,f1756]) ).
fof(f1970,plain,
( ~ sP0(sK6,sK7)
| spl16_93 ),
inference(resolution,[],[f1758,f179]) ).
fof(f1971,plain,
( $false
| ~ spl16_6
| spl16_93 ),
inference(forward_subsumption_resolution,[],[f1970,f299]) ).
fof(f1972,plain,
( ~ spl16_6
| spl16_93 ),
inference(avatar_contradiction_clause,[],[f1971]) ).
fof(f2052,plain,
( ~ sP0(sK6,sK7)
| spl16_102 ),
inference(resolution,[],[f1798,f174]) ).
fof(f2053,plain,
( $false
| ~ spl16_6
| spl16_102 ),
inference(forward_subsumption_resolution,[],[f2052,f299]) ).
fof(f2054,plain,
( ~ spl16_6
| spl16_102 ),
inference(avatar_contradiction_clause,[],[f2053]) ).
cnf(s2,plain,
( ~ spl16_3
| spl16_4 ),
inference(sat_conversion,[],[f289]) ).
cnf(s3,plain,
( ~ spl16_1
| ~ spl16_2
| spl16_5 ),
inference(sat_conversion,[],[f294]) ).
cnf(s5,plain,
( spl16_3
| spl16_6 ),
inference(sat_conversion,[],[f300]) ).
cnf(s6,plain,
( spl16_5
| spl16_6 ),
inference(sat_conversion,[],[f301]) ).
cnf(s7,plain,
( spl16_1
| ~ spl16_3
| ~ spl16_5 ),
inference(sat_conversion,[],[f311]) ).
cnf(s8,plain,
( ~ spl16_4
| ~ spl16_5 ),
inference(sat_conversion,[],[f316]) ).
cnf(s56,plain,
( ~ spl16_1
| spl16_3
| ~ spl16_5 ),
inference(sat_conversion,[],[f1183]) ).
cnf(s72,plain,
( ~ spl16_3
| ~ spl16_6
| ~ spl16_58 ),
inference(sat_conversion,[],[f1399]) ).
cnf(s97,plain,
( ~ spl16_3
| ~ spl16_6
| spl16_58 ),
inference(sat_conversion,[],[f1631]) ).
cnf(s100,plain,
( spl16_2
| spl16_3 ),
inference(sat_conversion,[],[f1659]) ).
cnf(s118,plain,
( spl16_1
| ~ spl16_6
| ~ spl16_93
| ~ spl16_102 ),
inference(sat_conversion,[],[f1805]) ).
cnf(s124,plain,
( ~ spl16_6
| spl16_93 ),
inference(sat_conversion,[],[f1972]) ).
cnf(s128,plain,
( ~ spl16_6
| spl16_102 ),
inference(sat_conversion,[],[f2054]) ).
cnf(s155,plain,
( ~ spl16_6
| spl16_1 ),
inference(rat,[],[s118,s124,s128]) ).
cnf(s156,plain,
spl16_1,
inference(rat,[],[s7,s5,s6,s155]) ).
cnf(s157,plain,
( ~ spl16_6
| ~ spl16_3 ),
inference(rat,[],[s72,s97]) ).
cnf(s158,plain,
~ spl16_3,
inference(rat,[],[s157,s6,s8,s2]) ).
cnf(s159,plain,
spl16_2,
inference(rat,[],[s100,s158]) ).
cnf(s160,plain,
~ spl16_5,
inference(rat,[],[s56,s156,s158]) ).
cnf(s165,plain,
$false,
inference(rat,[],[s3,s156,s160,s159]) ).
fof(f2055,plain,
$false,
inference(avatar_sat_refutation,[],[s165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC109+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 07:54:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.75/1.32 % (3842501)Detected formulas, will run a generic FOF schedule.
% 2.75/1.32 % (3842509)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3426162418:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.32 % (3842509)Instruction limit reached!
% 2.75/1.32 % (3842509)------------------------------
% 2.75/1.32 % (3842509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.32 % (3842509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.32 % (3842509)CaDiCaL version: 2.1.3
% 2.75/1.32 % (3842509)Termination reason: Instruction limit
% 2.75/1.32 % (3842509)Termination phase: Saturation
% 2.75/1.32 % (3842509)Time elapsed: 0.040 s
% 2.75/1.32 % (3842509)Peak memory usage: 89 MB
% 2.75/1.32 % (3842509)Instructions burned: 111 (million)
% 2.75/1.32 % (3842510)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1657553118:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.32 % (3842507)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=2826901277:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.32 % (3842512)dis-21_1_sil=8000:lcm=predicate:random_seed=3110405690: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)
% 2.75/1.32 % (3842508)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=1020514183:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.32 % (3842506)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=2105470008:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.32 % (3842511)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1400505825:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.32 % (3842510)Instruction limit reached!
% 2.75/1.32 % (3842510)------------------------------
% 2.75/1.32 % (3842510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.32 % (3842510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.32 % (3842510)CaDiCaL version: 2.1.3
% 2.75/1.32 % (3842510)Termination reason: Instruction limit
% 2.75/1.32 % (3842510)Termination phase: Saturation
% 2.75/1.32 % (3842510)Time elapsed: 0.054 s
% 2.75/1.32 % (3842510)Peak memory usage: 88 MB
% 2.75/1.32 % (3842510)Instructions burned: 121 (million)
% 2.75/1.32 % (3842512)Instruction limit reached!
% 2.75/1.32 % (3842512)------------------------------
% 2.75/1.32 % (3842512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.32 % (3842512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.32 % (3842512)CaDiCaL version: 2.1.3
% 2.75/1.32 % (3842512)Termination reason: Instruction limit
% 2.75/1.32 % (3842512)Termination phase: Saturation
% 2.75/1.32 % (3842512)Time elapsed: 0.073 s
% 2.75/1.32 % (3842512)Peak memory usage: 90 MB
% 2.75/1.32 % (3842512)Instructions burned: 130 (million)
% 2.75/1.32 % (3842511)Instruction limit reached!
% 2.75/1.32 % (3842511)------------------------------
% 2.75/1.32 % (3842511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.32 % (3842511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.32 % (3842511)CaDiCaL version: 2.1.3
% 2.75/1.32 % (3842511)Termination reason: Instruction limit
% 2.75/1.32 % (3842511)Termination phase: Saturation
% 2.75/1.32 % (3842511)Time elapsed: 0.094 s
% 2.75/1.32 % (3842511)Peak memory usage: 90 MB
% 2.75/1.32 % (3842511)Instructions burned: 140 (million)
% 2.75/1.32 % (3842520)lrs+10_1_sil=8000:sp=occurrence:random_seed=3115104055:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.75/1.32 % (3842520)First to succeed.
% 2.75/1.32 % (3842520)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3842501"
% 2.75/1.32 % (3842521)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3248864156:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.75/1.32 % (3842522)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2816620124:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.75/1.32 % (3842523)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=761522762:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 2.75/1.32 % (3842522)Also succeeded, but the first one will report.
% 2.75/1.32 % (3842521)Instruction limit reached!
% 2.75/1.32 % (3842521)------------------------------
% 2.75/1.32 % (3842521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.32 % (3842521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.32 % (3842521)CaDiCaL version: 2.1.3
% 2.75/1.32 % (3842521)Termination reason: Instruction limit
% 2.75/1.32 % (3842521)Termination phase: Saturation
% 2.75/1.32 % (3842521)Time elapsed: 0.082 s
% 2.75/1.32 % (3842521)Peak memory usage: 93 MB
% 2.75/1.32 % (3842521)Instructions burned: 157 (million)
% 2.75/1.32 % (3842520)Refutation found. Thanks to Tanya!
% 2.75/1.32 % SZS status Theorem for theBenchmark
% 2.75/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.52 % (3842520)------------------------------
% 3.98/1.52 % (3842520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.52 % (3842520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.52 % (3842520)CaDiCaL version: 2.1.3
% 3.98/1.52 % (3842520)Termination reason: Refutation
% 3.98/1.52 % (3842520)Time elapsed: 0.023 s
% 3.98/1.52 % (3842520)Peak memory usage: 91 MB
% 3.98/1.52 % (3842520)Instructions burned: 63 (million)
% 3.98/1.52 % (3842520)------------------------------
% 3.98/1.52 % (3842520)------------------------------
% 3.98/1.52 % (3842501)Success in time 0.473 s
% 3.98/1.52 % Vampire exiting
%------------------------------------------------------------------------------