%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC108+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 0.74s 0.87s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 147 ( 20 unt; 11 def)
% Number of atoms : 492 ( 101 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 583 ( 238 ~; 244 |; 66 &)
% ( 17 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 98 ( 0 sgn 78 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X2,X1) = X0 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/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)
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ rearsegP(X3,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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)
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) )
| ( ( 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(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f175,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
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] :
( X1 = X3
& X0 = X2
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) ) )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& rearsegP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) ) )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& rearsegP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f243,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(f244,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,[],[f243]) ).
fof(f245,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))],[f244]) ).
fof(f246,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(f247,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,[],[f246]) ).
fof(f248,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))],[f247]) ).
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(nnf_transformation,[],[f200]) ).
fof(f293,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,[],[f292]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ( ( nil = sK54
& nil != sK53 )
| ( neq(sK54,nil)
& ( ~ neq(sK53,nil)
| ~ segmentP(sK54,sK53) ) ) )
& ( ( nil = sK56
& nil = sK55 )
| ( neq(sK55,nil)
& rearsegP(sK56,sK55) ) )
& ssList(sK56)
& 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)],[f222]) ).
fof(f312,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| app(sK12(X0,X1),X1) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f245]) ).
fof(f313,plain,
! [X0,X1] :
( ssList(sK12(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f245]) ).
fof(f318,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,[],[f248]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f401,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f442,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f480,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f482,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil = sK55
| rearsegP(sK56,sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil = sK55
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( nil = sK56
| rearsegP(sK56,sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK56
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil != sK53
| ~ neq(sK53,nil)
| ~ segmentP(sK54,sK53) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( nil != sK53
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( nil = sK54
| ~ neq(sK53,nil)
| ~ segmentP(sK54,sK53) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f515,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,[],[f318]) ).
fof(f545,definition,
( spl57_1
<=> rearsegP(sK56,sK55) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f547,plain,
( rearsegP(sK56,sK55)
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f549,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,[],[f549]) ).
fof(f551,plain,
( nil = sK55
| ~ spl57_2 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f552,plain,
( spl57_1
| spl57_2 ),
inference(avatar_split_clause,[],[f500,f549,f545]) ).
fof(f554,definition,
( spl57_3
<=> neq(sK55,nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f556,plain,
( neq(sK55,nil)
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f557,plain,
( spl57_3
| spl57_2 ),
inference(avatar_split_clause,[],[f501,f549,f554]) ).
fof(f559,definition,
( spl57_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f561,plain,
( nil = sK56
| ~ spl57_4 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f562,plain,
( spl57_1
| spl57_4 ),
inference(avatar_split_clause,[],[f502,f559,f545]) ).
fof(f563,plain,
( spl57_3
| spl57_4 ),
inference(avatar_split_clause,[],[f503,f559,f554]) ).
fof(f565,definition,
( spl57_5
<=> segmentP(sK54,sK53) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f567,plain,
( ~ segmentP(sK54,sK53)
| spl57_5 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f569,definition,
( spl57_6
<=> neq(sK53,nil) ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f571,plain,
( ~ neq(sK53,nil)
| spl57_6 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f573,definition,
( spl57_7
<=> nil = sK53 ),
introduced(definition,[new_symbols(definition,[spl57_7])],[avatar_definition]) ).
fof(f574,plain,
( nil = sK53
| ~ spl57_7 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f575,plain,
( nil != sK53
| spl57_7 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f576,plain,
( ~ spl57_5
| ~ spl57_6
| ~ spl57_7 ),
inference(avatar_split_clause,[],[f504,f573,f569,f565]) ).
fof(f578,definition,
( spl57_8
<=> neq(sK54,nil) ),
introduced(definition,[new_symbols(definition,[spl57_8])],[avatar_definition]) ).
fof(f580,plain,
( neq(sK54,nil)
| ~ spl57_8 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f581,plain,
( spl57_8
| ~ spl57_7 ),
inference(avatar_split_clause,[],[f505,f573,f578]) ).
fof(f583,definition,
( spl57_9
<=> nil = sK54 ),
introduced(definition,[new_symbols(definition,[spl57_9])],[avatar_definition]) ).
fof(f585,plain,
( nil = sK54
| ~ spl57_9 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f586,plain,
( ~ spl57_5
| ~ spl57_6
| spl57_9 ),
inference(avatar_split_clause,[],[f506,f583,f569,f565]) ).
fof(f589,definition,
( spl57_10
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_10])],[avatar_definition]) ).
fof(f590,plain,
( ssList(nil)
| ~ spl57_10 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f622,plain,
spl57_10,
inference(avatar_split_clause,[],[f389,f589]) ).
fof(f626,plain,
( nil = sK53
| ~ spl57_2 ),
inference(superposition,[],[f508,f551]) ).
fof(f629,plain,
( spl57_7
| ~ spl57_2 ),
inference(avatar_split_clause,[],[f626,f549,f573]) ).
fof(f631,plain,
( nil = sK54
| ~ spl57_4 ),
inference(superposition,[],[f509,f561]) ).
fof(f634,plain,
( spl57_9
| ~ spl57_4 ),
inference(avatar_split_clause,[],[f631,f559,f583]) ).
fof(f635,plain,
( ~ neq(nil,nil)
| spl57_6
| ~ spl57_7 ),
inference(superposition,[],[f571,f574]) ).
fof(f638,plain,
( neq(nil,nil)
| ~ spl57_8
| ~ spl57_9 ),
inference(superposition,[],[f580,f585]) ).
fof(f641,plain,
( $false
| spl57_6
| ~ spl57_7
| ~ spl57_8
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f638,f635]) ).
fof(f642,plain,
( spl57_6
| ~ spl57_7
| ~ spl57_8
| ~ spl57_9 ),
inference(avatar_contradiction_clause,[],[f641]) ).
fof(f643,plain,
( ~ segmentP(sK54,nil)
| spl57_5
| ~ spl57_7 ),
inference(forward_demodulation,[],[f567,f574]) ).
fof(f647,plain,
( rearsegP(sK56,sK53)
| ~ spl57_1 ),
inference(forward_demodulation,[],[f547,f508]) ).
fof(f648,plain,
( neq(sK53,nil)
| ~ spl57_3 ),
inference(forward_demodulation,[],[f556,f508]) ).
fof(f659,plain,
( ~ ssList(sK54)
| spl57_5
| ~ spl57_7 ),
inference(resolution,[],[f442,f643]) ).
fof(f660,plain,
( $false
| spl57_5
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f659,f497]) ).
fof(f661,plain,
( spl57_5
| ~ spl57_7 ),
inference(avatar_contradiction_clause,[],[f660]) ).
fof(f662,plain,
( nil != sK53
| spl57_2 ),
inference(forward_demodulation,[],[f550,f508]) ).
fof(f663,plain,
( rearsegP(sK54,sK53)
| ~ spl57_1 ),
inference(forward_demodulation,[],[f647,f509]) ).
fof(f664,plain,
( spl57_6
| ~ spl57_3 ),
inference(avatar_split_clause,[],[f648,f554,f569]) ).
fof(f665,plain,
( ~ spl57_7
| spl57_2 ),
inference(avatar_split_clause,[],[f662,f549,f573]) ).
fof(f911,plain,
( sK54 = app(sK12(sK54,sK53),sK53)
| ~ ssList(sK53)
| ~ ssList(sK54)
| ~ spl57_1 ),
inference(resolution,[],[f312,f663]) ).
fof(f916,plain,
( sK54 = app(sK12(sK54,sK53),sK53)
| ~ ssList(sK54)
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f911,f496]) ).
fof(f920,plain,
( sK54 = app(sK12(sK54,sK53),sK53)
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f916,f497]) ).
fof(f923,plain,
( nil != sK54
| nil = sK53
| ~ ssList(sK53)
| ~ ssList(sK12(sK54,sK53))
| ~ spl57_1 ),
inference(superposition,[],[f480,f920]) ).
fof(f928,definition,
( spl57_22
<=> ssList(sK12(sK54,sK53)) ),
introduced(definition,[new_symbols(definition,[spl57_22])],[avatar_definition]) ).
fof(f929,plain,
( ssList(sK12(sK54,sK53))
| ~ spl57_22 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f930,plain,
( ~ ssList(sK12(sK54,sK53))
| spl57_22 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f945,plain,
( ~ rearsegP(sK54,sK53)
| ~ ssList(sK53)
| ~ ssList(sK54)
| spl57_22 ),
inference(resolution,[],[f930,f313]) ).
fof(f946,plain,
( ~ ssList(sK53)
| ~ ssList(sK54)
| ~ spl57_1
| spl57_22 ),
inference(forward_subsumption_resolution,[],[f945,f663]) ).
fof(f947,plain,
( ~ ssList(sK54)
| ~ spl57_1
| spl57_22 ),
inference(forward_subsumption_resolution,[],[f946,f496]) ).
fof(f948,plain,
( $false
| ~ spl57_1
| spl57_22 ),
inference(forward_subsumption_resolution,[],[f947,f497]) ).
fof(f949,plain,
( ~ spl57_1
| spl57_22 ),
inference(avatar_contradiction_clause,[],[f948]) ).
fof(f1783,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| segmentP(app(X0,X1),X1)
| ~ ssList(app(X0,X1)) ),
inference(superposition,[],[f515,f482]) ).
fof(f1784,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| segmentP(app(X0,X1),X1) ),
inference(duplicate_literal_removal,[],[f1783]) ).
fof(f1793,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| segmentP(app(X0,X1),X1) ),
inference(forward_subsumption_resolution,[],[f1784,f401]) ).
fof(f1802,plain,
( ! [X0,X1] :
( segmentP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl57_10 ),
inference(forward_subsumption_resolution,[],[f1793,f590]) ).
fof(f2429,plain,
( segmentP(sK54,sK53)
| ~ ssList(sK53)
| ~ ssList(sK12(sK54,sK53))
| ~ spl57_1
| ~ spl57_10 ),
inference(superposition,[],[f1802,f920]) ).
fof(f2465,plain,
( nil != sK54
| ~ ssList(sK53)
| ~ ssList(sK12(sK54,sK53))
| ~ spl57_1
| spl57_7 ),
inference(forward_subsumption_resolution,[],[f923,f575]) ).
fof(f2467,plain,
( segmentP(sK54,sK53)
| ~ ssList(sK12(sK54,sK53))
| ~ spl57_1
| ~ spl57_10 ),
inference(forward_subsumption_resolution,[],[f2429,f496]) ).
fof(f2469,plain,
( nil != sK54
| ~ ssList(sK12(sK54,sK53))
| ~ spl57_1
| spl57_7 ),
inference(forward_subsumption_resolution,[],[f2465,f496]) ).
fof(f2474,plain,
( segmentP(sK54,sK53)
| ~ spl57_1
| ~ spl57_10
| ~ spl57_22 ),
inference(forward_subsumption_resolution,[],[f2467,f929]) ).
fof(f2476,plain,
( nil != sK54
| ~ spl57_1
| spl57_7
| ~ spl57_22 ),
inference(forward_subsumption_resolution,[],[f2469,f929]) ).
fof(f2477,plain,
( spl57_5
| ~ spl57_1
| ~ spl57_10
| ~ spl57_22 ),
inference(avatar_split_clause,[],[f2474,f928,f589,f545,f565]) ).
fof(f2479,plain,
( ~ spl57_9
| ~ spl57_1
| spl57_7
| ~ spl57_22 ),
inference(avatar_split_clause,[],[f2476,f928,f573,f545,f583]) ).
cnf(s1,plain,
( spl57_1
| spl57_2 ),
inference(sat_conversion,[],[f552]) ).
cnf(s2,plain,
( spl57_2
| spl57_3 ),
inference(sat_conversion,[],[f557]) ).
cnf(s3,plain,
( spl57_1
| spl57_4 ),
inference(sat_conversion,[],[f562]) ).
cnf(s4,plain,
( spl57_3
| spl57_4 ),
inference(sat_conversion,[],[f563]) ).
cnf(s5,plain,
( ~ spl57_5
| ~ spl57_6
| ~ spl57_7 ),
inference(sat_conversion,[],[f576]) ).
cnf(s6,plain,
( ~ spl57_7
| spl57_8 ),
inference(sat_conversion,[],[f581]) ).
cnf(s7,plain,
( ~ spl57_5
| ~ spl57_6
| spl57_9 ),
inference(sat_conversion,[],[f586]) ).
cnf(s17,plain,
spl57_10,
inference(sat_conversion,[],[f622]) ).
cnf(s19,plain,
( ~ spl57_2
| spl57_7 ),
inference(sat_conversion,[],[f629]) ).
cnf(s22,plain,
( ~ spl57_4
| spl57_9 ),
inference(sat_conversion,[],[f634]) ).
cnf(s26,plain,
( spl57_6
| ~ spl57_7
| ~ spl57_8
| ~ spl57_9 ),
inference(sat_conversion,[],[f642]) ).
cnf(s30,plain,
( spl57_5
| ~ spl57_7 ),
inference(sat_conversion,[],[f661]) ).
cnf(s31,plain,
( ~ spl57_3
| spl57_6 ),
inference(sat_conversion,[],[f664]) ).
cnf(s32,plain,
( spl57_2
| ~ spl57_7 ),
inference(sat_conversion,[],[f665]) ).
cnf(s39,plain,
( ~ spl57_1
| spl57_22 ),
inference(sat_conversion,[],[f949]) ).
cnf(s100,plain,
( ~ spl57_1
| spl57_5
| ~ spl57_10
| ~ spl57_22 ),
inference(sat_conversion,[],[f2477]) ).
cnf(s102,plain,
( ~ spl57_1
| spl57_7
| ~ spl57_9
| ~ spl57_22 ),
inference(sat_conversion,[],[f2479]) ).
cnf(s107,plain,
spl57_1,
inference(rat,[],[s26,s5,s6,s30,s19,s22,s1,s3]) ).
cnf(s108,plain,
spl57_22,
inference(rat,[],[s39,s107]) ).
cnf(s109,plain,
spl57_5,
inference(rat,[],[s100,s108,s17,s107]) ).
cnf(s111,plain,
spl57_2,
inference(rat,[],[s7,s31,s102,s2,s32,s109,s107,s108]) ).
cnf(s112,plain,
spl57_7,
inference(rat,[],[s19,s111]) ).
cnf(s113,plain,
spl57_8,
inference(rat,[],[s6,s112]) ).
cnf(s114,plain,
~ spl57_6,
inference(rat,[],[s5,s109,s112]) ).
cnf(s115,plain,
~ spl57_3,
inference(rat,[],[s31,s114]) ).
cnf(s116,plain,
~ spl57_9,
inference(rat,[],[s26,s112,s113,s114]) ).
cnf(s117,plain,
spl57_4,
inference(rat,[],[s4,s115]) ).
cnf(s119,plain,
$false,
inference(rat,[],[s22,s116,s117]) ).
fof(f2480,plain,
$false,
inference(avatar_sat_refutation,[],[s119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC108+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Mon Sep 28 07:54:04 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.74/0.87 % (3224198)Detected formulas, will run a generic FOF schedule.
% 0.74/0.87 % (3224209)dis-21_1_sil=8000:lcm=predicate:random_seed=1048555768: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)
% 0.74/0.87 % (3224207)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=513028940:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.74/0.87 % (3224206)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3015643044:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.74/0.87 % (3224205)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=1805894055:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.74/0.87 % (3224203)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=285153358:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.74/0.87 % (3224204)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=3798010094:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.74/0.87 % (3224208)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3267037833:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.74/0.87 % (3224207)Instruction limit reached!
% 0.74/0.87 % (3224207)------------------------------
% 0.74/0.87 % (3224207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.74/0.87 % (3224207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.87 % (3224207)CaDiCaL version: 2.1.3
% 0.74/0.87 % (3224207)Termination reason: Instruction limit
% 0.74/0.87 % (3224207)Termination phase: Saturation
% 0.74/0.87 % (3224207)Time elapsed: 0.031 s
% 0.74/0.87 % (3224207)Peak memory usage: 88 MB
% 0.74/0.87 % (3224207)Instructions burned: 121 (million)
% 0.74/0.87 % (3224206)Instruction limit reached!
% 0.74/0.87 % (3224206)------------------------------
% 0.74/0.87 % (3224206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.74/0.87 % (3224206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.87 % (3224206)CaDiCaL version: 2.1.3
% 0.74/0.87 % (3224206)Termination reason: Instruction limit
% 0.74/0.87 % (3224206)Termination phase: Saturation
% 0.74/0.87 % (3224206)Time elapsed: 0.037 s
% 0.74/0.87 % (3224206)Peak memory usage: 89 MB
% 0.74/0.87 % (3224206)Instructions burned: 111 (million)
% 0.74/0.87 % (3224208)First to succeed.
% 0.74/0.87 % (3224208)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3224198"
% 0.74/0.87 % (3224209)Instruction limit reached!
% 0.74/0.87 % (3224209)------------------------------
% 0.74/0.87 % (3224209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.74/0.87 % (3224209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.87 % (3224209)CaDiCaL version: 2.1.3
% 0.74/0.87 % (3224209)Termination reason: Instruction limit
% 0.74/0.87 % (3224209)Termination phase: Saturation
% 0.74/0.87 % (3224209)Time elapsed: 0.041 s
% 0.74/0.87 % (3224209)Peak memory usage: 90 MB
% 0.74/0.87 % (3224209)Instructions burned: 132 (million)
% 0.74/0.87 % (3224217)lrs+10_1_sil=8000:sp=occurrence:random_seed=3270201247:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.74/0.87 % (3224218)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2661926784:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.74/0.87 % (3224219)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3215160358:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 0.74/0.87 % (3224208)Refutation found. Thanks to Tanya!
% 0.74/0.87 % SZS status Theorem for theBenchmark
% 0.74/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/0.97 % (3224208)------------------------------
% 2.52/0.97 % (3224208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/0.97 % (3224208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.97 % (3224208)CaDiCaL version: 2.1.3
% 2.52/0.97 % (3224208)Termination reason: Refutation
% 2.52/0.97 % (3224208)Time elapsed: 0.029 s
% 2.52/0.97 % (3224208)Peak memory usage: 91 MB
% 2.52/0.97 % (3224208)Instructions burned: 77 (million)
% 2.52/0.97 % (3224208)------------------------------
% 2.52/0.97 % (3224208)------------------------------
% 2.52/0.97 % (3224198)Success in time 0.33 s
% 2.52/0.97 % Vampire exiting
%------------------------------------------------------------------------------