%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC058+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 : n002.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 01:02:14 PM UTC 2026
% Result : Theorem 4.23s 1.58s
% Output : Refutation 6.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of formulae : 144 ( 19 unt; 11 def)
% Number of atoms : 507 ( 97 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 639 ( 276 ~; 266 |; 60 &)
% ( 19 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 94 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X2,X1) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
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(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) ) ) )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ rearsegP(X3,X2) ) ) ) ) ) ),
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
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) ) ) )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ rearsegP(X3,X2) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X2,X1) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f103,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(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f172,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) ) ) )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& rearsegP(X3,X2) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f242,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != X0 ) )
& ( ? [X2] :
( ssList(X2)
& app(X2,X1) = X0 )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f243,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != X0 ) )
& ( ? [X3] :
( ssList(X3)
& app(X3,X1) = X0 )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f242]) ).
fof(f244,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != X0 ) )
& ( ( ssList(sK12(X0,X1))
& app(sK12(X0,X1),X1) = X0 )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X0,X1))],[f243]) ).
fof(f245,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,[],[f103]) ).
fof(f246,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,[],[f245]) ).
fof(f247,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK13(X0,X1))
& ssList(sK14(X0,X1))
& app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f246]) ).
fof(f272,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f291,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f291]) ).
fof(f295,plain,
( ssList(sK56)
& sK54 = sK56
& sK53 = sK55
& ( ( nil = sK54
& nil != sK53 )
| ( neq(sK54,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) ) ) )
& ( ( nil = sK56
& nil = sK55 )
| ( neq(sK55,nil)
& rearsegP(sK56,sK55) ) )
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f221]) ).
fof(f311,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| app(sK12(X0,X1),X1) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f244]) ).
fof(f312,plain,
! [X0,X1] :
( ssList(sK12(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f244]) ).
fof(f317,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,[],[f247]) ).
fof(f385,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f400,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f439,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f479,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f481,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK54),
inference(cnf_transformation,[],[f295]) ).
fof(f497,plain,
ssList(sK55),
inference(cnf_transformation,[],[f295]) ).
fof(f498,plain,
( nil = sK55
| rearsegP(sK56,sK55) ),
inference(cnf_transformation,[],[f295]) ).
fof(f499,plain,
( nil = sK55
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f500,plain,
( nil = sK56
| rearsegP(sK56,sK55) ),
inference(cnf_transformation,[],[f295]) ).
fof(f501,plain,
( nil = sK56
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f503,plain,
( nil != sK53
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
! [X4] :
( nil = sK54
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f295]) ).
fof(f514,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f317]) ).
fof(f523,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f385]) ).
fof(f540,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f523]) ).
fof(f544,definition,
( spl57_1
<=> rearsegP(sK56,sK55) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f546,plain,
( rearsegP(sK56,sK55)
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f548,definition,
( spl57_2
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f550,plain,
( nil = sK55
| ~ spl57_2 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f551,plain,
( spl57_1
| spl57_2 ),
inference(avatar_split_clause,[],[f498,f548,f544]) ).
fof(f553,definition,
( spl57_3
<=> neq(sK55,nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f555,plain,
( neq(sK55,nil)
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f556,plain,
( spl57_3
| spl57_2 ),
inference(avatar_split_clause,[],[f499,f548,f553]) ).
fof(f558,definition,
( spl57_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f560,plain,
( nil = sK56
| ~ spl57_4 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f561,plain,
( spl57_1
| spl57_4 ),
inference(avatar_split_clause,[],[f500,f558,f544]) ).
fof(f562,plain,
( spl57_3
| spl57_4 ),
inference(avatar_split_clause,[],[f501,f558,f553]) ).
fof(f564,definition,
( spl57_5
<=> ! [X4] :
( ~ ssList(X4)
| ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil) ) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f565,plain,
( ! [X4] :
( ~ ssList(X4)
| ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil) )
| ~ spl57_5 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f567,definition,
( spl57_6
<=> nil = sK53 ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f569,plain,
( nil != sK53
| spl57_6 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f572,definition,
( spl57_7
<=> neq(sK54,nil) ),
introduced(definition,[new_symbols(definition,[spl57_7])],[avatar_definition]) ).
fof(f574,plain,
( neq(sK54,nil)
| ~ spl57_7 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f575,plain,
( spl57_7
| ~ spl57_6 ),
inference(avatar_split_clause,[],[f503,f567,f572]) ).
fof(f577,definition,
( spl57_8
<=> nil = sK54 ),
introduced(definition,[new_symbols(definition,[spl57_8])],[avatar_definition]) ).
fof(f579,plain,
( nil = sK54
| ~ spl57_8 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f580,plain,
( spl57_5
| spl57_8 ),
inference(avatar_split_clause,[],[f504,f577,f564]) ).
fof(f583,definition,
( spl57_9
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_9])],[avatar_definition]) ).
fof(f584,plain,
( ssList(nil)
| ~ spl57_9 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f616,plain,
spl57_9,
inference(avatar_split_clause,[],[f388,f583]) ).
fof(f622,plain,
( nil = sK54
| ~ spl57_4 ),
inference(superposition,[],[f507,f560]) ).
fof(f625,plain,
( spl57_8
| ~ spl57_4 ),
inference(avatar_split_clause,[],[f622,f558,f577]) ).
fof(f626,plain,
( neq(nil,nil)
| ~ spl57_7
| ~ spl57_8 ),
inference(superposition,[],[f574,f579]) ).
fof(f629,plain,
( ! [X4] :
( ~ segmentP(sK55,X4)
| ~ ssList(X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil) )
| ~ spl57_5 ),
inference(forward_demodulation,[],[f565,f506]) ).
fof(f638,plain,
( neq(nil,nil)
| ~ spl57_2
| ~ spl57_3 ),
inference(forward_demodulation,[],[f555,f550]) ).
fof(f652,plain,
( rearsegP(sK54,sK55)
| ~ spl57_1 ),
inference(forward_demodulation,[],[f546,f507]) ).
fof(f653,plain,
( ~ ssList(sK55)
| ~ segmentP(sK54,sK55)
| ~ neq(sK55,nil)
| ~ ssList(sK55)
| ~ spl57_5 ),
inference(resolution,[],[f629,f439]) ).
fof(f655,plain,
( ~ ssList(sK55)
| ~ segmentP(sK54,sK55)
| ~ neq(sK55,nil)
| ~ spl57_5 ),
inference(duplicate_literal_removal,[],[f653]) ).
fof(f657,plain,
( ~ segmentP(sK54,sK55)
| ~ neq(sK55,nil)
| ~ spl57_5 ),
inference(forward_subsumption_resolution,[],[f655,f497]) ).
fof(f659,plain,
( ~ segmentP(sK54,sK55)
| ~ spl57_3
| ~ spl57_5 ),
inference(forward_subsumption_resolution,[],[f657,f555]) ).
fof(f661,definition,
( spl57_16
<=> neq(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl57_16])],[avatar_definition]) ).
fof(f662,plain,
( neq(nil,nil)
| ~ spl57_16 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f918,plain,
( sK54 = app(sK12(sK54,sK55),sK55)
| ~ ssList(sK55)
| ~ ssList(sK54)
| ~ spl57_1 ),
inference(resolution,[],[f311,f652]) ).
fof(f923,plain,
( sK54 = app(sK12(sK54,sK55),sK55)
| ~ ssList(sK54)
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f918,f497]) ).
fof(f927,plain,
( sK54 = app(sK12(sK54,sK55),sK55)
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f923,f496]) ).
fof(f930,plain,
( nil != sK54
| nil = sK55
| ~ ssList(sK55)
| ~ ssList(sK12(sK54,sK55))
| ~ spl57_1 ),
inference(superposition,[],[f479,f927]) ).
fof(f935,definition,
( spl57_23
<=> ssList(sK12(sK54,sK55)) ),
introduced(definition,[new_symbols(definition,[spl57_23])],[avatar_definition]) ).
fof(f936,plain,
( ssList(sK12(sK54,sK55))
| ~ spl57_23 ),
inference(avatar_component_clause,[],[f935]) ).
fof(f937,plain,
( ~ ssList(sK12(sK54,sK55))
| spl57_23 ),
inference(avatar_component_clause,[],[f935]) ).
fof(f952,plain,
( ~ rearsegP(sK54,sK55)
| ~ ssList(sK55)
| ~ ssList(sK54)
| spl57_23 ),
inference(resolution,[],[f937,f312]) ).
fof(f953,plain,
( ~ ssList(sK55)
| ~ ssList(sK54)
| ~ spl57_1
| spl57_23 ),
inference(forward_subsumption_resolution,[],[f952,f652]) ).
fof(f954,plain,
( ~ ssList(sK54)
| ~ spl57_1
| spl57_23 ),
inference(forward_subsumption_resolution,[],[f953,f497]) ).
fof(f955,plain,
( $false
| ~ spl57_1
| spl57_23 ),
inference(forward_subsumption_resolution,[],[f954,f496]) ).
fof(f956,plain,
( ~ spl57_1
| spl57_23 ),
inference(avatar_contradiction_clause,[],[f955]) ).
fof(f1594,plain,
( nil != sK55
| spl57_6 ),
inference(forward_demodulation,[],[f569,f506]) ).
fof(f1610,plain,
( spl57_16
| ~ spl57_2
| ~ spl57_3 ),
inference(avatar_split_clause,[],[f638,f553,f548,f661]) ).
fof(f1611,plain,
( spl57_16
| ~ spl57_7
| ~ spl57_8 ),
inference(avatar_split_clause,[],[f626,f577,f572,f661]) ).
fof(f1612,plain,
( nil != sK54
| nil = sK55
| ~ ssList(sK12(sK54,sK55))
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f930,f497]) ).
fof(f1614,plain,
( nil != sK54
| nil = sK55
| ~ spl57_1
| ~ spl57_23 ),
inference(forward_subsumption_resolution,[],[f1612,f936]) ).
fof(f1621,plain,
( ~ spl57_2
| spl57_6 ),
inference(avatar_split_clause,[],[f1594,f567,f548]) ).
fof(f1622,plain,
( spl57_2
| ~ spl57_8
| ~ spl57_1
| ~ spl57_23 ),
inference(avatar_split_clause,[],[f1614,f935,f544,f577,f548]) ).
fof(f1636,plain,
( ~ ssList(nil)
| ~ spl57_16 ),
inference(resolution,[],[f662,f540]) ).
fof(f1637,plain,
( $false
| ~ spl57_9
| ~ spl57_16 ),
inference(forward_subsumption_resolution,[],[f1636,f584]) ).
fof(f1638,plain,
( ~ spl57_9
| ~ spl57_16 ),
inference(avatar_contradiction_clause,[],[f1637]) ).
fof(f1822,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| segmentP(app(X0,X1),X1)
| ~ ssList(app(X0,X1)) ),
inference(superposition,[],[f514,f481]) ).
fof(f1823,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| segmentP(app(X0,X1),X1) ),
inference(duplicate_literal_removal,[],[f1822]) ).
fof(f1832,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| segmentP(app(X0,X1),X1) ),
inference(forward_subsumption_resolution,[],[f1823,f400]) ).
fof(f1839,plain,
( ! [X0,X1] :
( segmentP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f1832,f584]) ).
fof(f2378,plain,
( segmentP(sK54,sK55)
| ~ ssList(sK55)
| ~ ssList(sK12(sK54,sK55))
| ~ spl57_1
| ~ spl57_9 ),
inference(superposition,[],[f1839,f927]) ).
fof(f2394,plain,
( ~ ssList(sK55)
| ~ ssList(sK12(sK54,sK55))
| ~ spl57_1
| ~ spl57_3
| ~ spl57_5
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f2378,f659]) ).
fof(f2404,plain,
( ~ ssList(sK12(sK54,sK55))
| ~ spl57_1
| ~ spl57_3
| ~ spl57_5
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f2394,f497]) ).
fof(f2411,plain,
( $false
| ~ spl57_1
| ~ spl57_3
| ~ spl57_5
| ~ spl57_9
| ~ spl57_23 ),
inference(forward_subsumption_resolution,[],[f2404,f936]) ).
fof(f2412,plain,
( ~ spl57_1
| ~ spl57_3
| ~ spl57_5
| ~ spl57_9
| ~ spl57_23 ),
inference(avatar_contradiction_clause,[],[f2411]) ).
cnf(s1,plain,
( spl57_1
| spl57_2 ),
inference(sat_conversion,[],[f551]) ).
cnf(s2,plain,
( spl57_2
| spl57_3 ),
inference(sat_conversion,[],[f556]) ).
cnf(s3,plain,
( spl57_1
| spl57_4 ),
inference(sat_conversion,[],[f561]) ).
cnf(s4,plain,
( spl57_3
| spl57_4 ),
inference(sat_conversion,[],[f562]) ).
cnf(s6,plain,
( ~ spl57_6
| spl57_7 ),
inference(sat_conversion,[],[f575]) ).
cnf(s7,plain,
( spl57_5
| spl57_8 ),
inference(sat_conversion,[],[f580]) ).
cnf(s17,plain,
spl57_9,
inference(sat_conversion,[],[f616]) ).
cnf(s20,plain,
( ~ spl57_4
| spl57_8 ),
inference(sat_conversion,[],[f625]) ).
cnf(s33,plain,
( ~ spl57_1
| spl57_23 ),
inference(sat_conversion,[],[f956]) ).
cnf(s69,plain,
( ~ spl57_2
| ~ spl57_3
| spl57_16 ),
inference(sat_conversion,[],[f1610]) ).
cnf(s70,plain,
( ~ spl57_7
| ~ spl57_8
| spl57_16 ),
inference(sat_conversion,[],[f1611]) ).
cnf(s75,plain,
( ~ spl57_2
| spl57_6 ),
inference(sat_conversion,[],[f1621]) ).
cnf(s76,plain,
( ~ spl57_1
| spl57_2
| ~ spl57_8
| ~ spl57_23 ),
inference(sat_conversion,[],[f1622]) ).
cnf(s82,plain,
( ~ spl57_9
| ~ spl57_16 ),
inference(sat_conversion,[],[f1638]) ).
cnf(s107,plain,
( ~ spl57_1
| ~ spl57_3
| ~ spl57_5
| ~ spl57_9
| ~ spl57_23 ),
inference(sat_conversion,[],[f2412]) ).
cnf(s110,plain,
~ spl57_16,
inference(rat,[],[s82,s17]) ).
cnf(s115,plain,
spl57_1,
inference(rat,[],[s6,s70,s75,s20,s1,s3,s110]) ).
cnf(s116,plain,
spl57_23,
inference(rat,[],[s33,s115]) ).
cnf(s118,plain,
spl57_2,
inference(rat,[],[s107,s7,s2,s76,s115,s17,s116]) ).
cnf(s119,plain,
spl57_6,
inference(rat,[],[s75,s118]) ).
cnf(s120,plain,
~ spl57_3,
inference(rat,[],[s69,s110,s118]) ).
cnf(s121,plain,
spl57_7,
inference(rat,[],[s6,s119]) ).
cnf(s123,plain,
spl57_4,
inference(rat,[],[s4,s120]) ).
cnf(s124,plain,
~ spl57_8,
inference(rat,[],[s70,s110,s121]) ).
cnf(s125,plain,
$false,
inference(rat,[],[s20,s124,s123]) ).
fof(f2413,plain,
$false,
inference(avatar_sat_refutation,[],[s125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC058+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 28 07:41:22 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 4.23/1.58 % (190219)Detected formulas, will run a generic FOF schedule.
% 4.23/1.58 % (190227)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1863055559:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.23/1.58 % (190227)Instruction limit reached!
% 4.23/1.58 % (190227)------------------------------
% 4.23/1.58 % (190227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.58 % (190227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.58 % (190227)CaDiCaL version: 2.1.3
% 4.23/1.58 % (190227)Termination reason: Instruction limit
% 4.23/1.58 % (190227)Termination phase: Saturation
% 4.23/1.58 % (190227)Time elapsed: 0.056 s
% 4.23/1.58 % (190227)Peak memory usage: 89 MB
% 4.23/1.58 % (190227)Instructions burned: 110 (million)
% 4.23/1.58 % (190228)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1435763065:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.23/1.58 % (190226)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=4265257777:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.23/1.58 % (190225)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=4075632962:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.23/1.58 % (190229)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4084791864:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.23/1.58 % (190230)dis-21_1_sil=8000:lcm=predicate:random_seed=314855066: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)
% 4.23/1.58 % (190224)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=2364471063:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.23/1.58 % (190229)First to succeed.
% 4.23/1.58 % (190229)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-190219"
% 4.23/1.58 % (190228)Instruction limit reached!
% 4.23/1.58 % (190228)------------------------------
% 4.23/1.58 % (190228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.58 % (190228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.58 % (190228)CaDiCaL version: 2.1.3
% 4.23/1.58 % (190228)Termination reason: Instruction limit
% 4.23/1.58 % (190228)Termination phase: Saturation
% 4.23/1.58 % (190228)Time elapsed: 0.102 s
% 4.23/1.58 % (190228)Peak memory usage: 88 MB
% 4.23/1.58 % (190228)Instructions burned: 120 (million)
% 4.23/1.58 % (190230)Instruction limit reached!
% 4.23/1.58 % (190230)------------------------------
% 4.23/1.58 % (190230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.58 % (190230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.58 % (190230)CaDiCaL version: 2.1.3
% 4.23/1.58 % (190230)Termination reason: Instruction limit
% 4.23/1.58 % (190230)Termination phase: Saturation
% 4.23/1.58 % (190230)Time elapsed: 0.121 s
% 4.23/1.58 % (190230)Peak memory usage: 90 MB
% 4.23/1.58 % (190230)Instructions burned: 129 (million)
% 4.23/1.58 % (190232)lrs+10_1_sil=8000:sp=occurrence:random_seed=1352942166:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.23/1.58 % (190232)Also succeeded, but the first one will report.
% 4.23/1.58 % (190239)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1551998283:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.23/1.58 % (190240)lrs+1011_1_sil=32000:sp=occurrence:random_seed=842376930:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 4.23/1.58 % (190229)Refutation found. Thanks to Tanya!
% 4.23/1.58 % SZS status Theorem for theBenchmark
% 4.23/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 6.09/1.88 % (190229)------------------------------
% 6.09/1.88 % (190229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.09/1.88 % (190229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.09/1.88 % (190229)CaDiCaL version: 2.1.3
% 6.09/1.88 % (190229)Termination reason: Refutation
% 6.09/1.88 % (190229)Time elapsed: 0.084 s
% 6.09/1.88 % (190229)Peak memory usage: 90 MB
% 6.09/1.88 % (190229)Instructions burned: 76 (million)
% 6.09/1.88 % (190229)------------------------------
% 6.09/1.88 % (190229)------------------------------
% 6.09/1.88 % (190219)Success in time 0.765 s
% 6.09/1.88 % Vampire exiting
%------------------------------------------------------------------------------