%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC363+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 : n006.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 01:03:38 PM UTC 2026
% Result : Theorem 5.97s 1.65s
% Output : Refutation 7.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 111 ( 24 unt; 6 def)
% Number of atoms : 418 ( 66 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 525 ( 218 ~; 209 |; 63 &)
% ( 10 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 139 ( 0 sgn 113 !; 26 ?)
% 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/sandbox/benchmark/theBenchmark.p',ax3) ).
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(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
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
| ~ neq(X1,nil)
| segmentP(X1,X0)
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4) ) )
& neq(X3,nil) ) ) ) ) ) ),
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
| ~ neq(X1,nil)
| segmentP(X1,X0)
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4) ) )
& neq(X3,nil) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ segmentP(X1,X0)
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ssItem(X4) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ segmentP(X1,X0)
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ssItem(X4) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
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(f115,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f115]) ).
fof(f122,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(f123,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f131,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
( sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& ~ segmentP(sK1,sK0)
& ( nil = sK2
| nil != sK3 )
& ( ( sK2 = cons(sK4,nil)
& memberP(sK3,sK4)
& ssItem(sK4) )
| ~ neq(sK3,nil) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f143,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(f144,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,[],[f143]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ( ssList(sK9(X0,X1))
& ssList(sK10(X0,X1))
& app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0 )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f144]) ).
fof(f147,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,[],[f122]) ).
fof(f148,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,[],[f147]) ).
fof(f149,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))],[f148]) ).
fof(f152,plain,
ssList(sK0),
inference(cnf_transformation,[],[f134]) ).
fof(f153,plain,
ssList(sK1),
inference(cnf_transformation,[],[f134]) ).
fof(f156,plain,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f134]) ).
fof(f157,plain,
( memberP(sK3,sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f134]) ).
fof(f158,plain,
( sK2 = cons(sK4,nil)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f134]) ).
fof(f160,plain,
~ segmentP(sK1,sK0),
inference(cnf_transformation,[],[f134]) ).
fof(f161,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f134]) ).
fof(f162,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f134]) ).
fof(f163,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f134]) ).
fof(f179,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f187,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ memberP(X0,X1)
| app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f188,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ memberP(X0,X1)
| ssList(sK10(X0,X1))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f189,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ memberP(X0,X1)
| ssList(sK9(X0,X1))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f194,plain,
! [X2,X3,X0,X1] :
( ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f201,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,[],[f149]) ).
fof(f202,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f123]) ).
fof(f207,plain,
! [X0,X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f210,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f212,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f213,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f161,f163]) ).
fof(f214,plain,
~ segmentP(sK3,sK2),
inference(definition_unfolding,[],[f160,f163,f162]) ).
fof(f215,plain,
ssList(sK3),
inference(definition_unfolding,[],[f153,f163]) ).
fof(f216,plain,
ssList(sK2),
inference(definition_unfolding,[],[f152,f162]) ).
fof(f222,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,[],[f201]) ).
fof(f230,definition,
( spl13_1
<=> neq(sK3,nil) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f231,plain,
( ~ neq(sK3,nil)
| spl13_1 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f233,definition,
( spl13_2
<=> ssItem(sK4) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f234,plain,
( ssItem(sK4)
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f235,plain,
( ~ spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f156,f233,f230]) ).
fof(f237,definition,
( spl13_3
<=> memberP(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f238,plain,
( memberP(sK3,sK4)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f239,plain,
( ~ spl13_1
| spl13_3 ),
inference(avatar_split_clause,[],[f157,f237,f230]) ).
fof(f241,definition,
( spl13_4
<=> sK2 = cons(sK4,nil) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f242,plain,
( sK2 = cons(sK4,nil)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f243,plain,
( ~ spl13_1
| spl13_4 ),
inference(avatar_split_clause,[],[f158,f241,f230]) ).
fof(f251,plain,
( $false
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f231,f213]) ).
fof(f252,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f251]) ).
fof(f256,plain,
sK3 = app(sK3,nil),
inference(resolution,[],[f202,f215]) ).
fof(f260,plain,
sK2 = app(nil,sK2),
inference(resolution,[],[f210,f216]) ).
fof(f265,plain,
! [X0] :
( ~ ssList(app(sK2,X0))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK2)
| segmentP(app(sK2,X0),sK2) ),
inference(superposition,[],[f222,f260]) ).
fof(f266,plain,
! [X0] :
( ~ ssList(app(sK2,X0))
| ~ ssList(X0)
| ~ ssList(sK2)
| segmentP(app(sK2,X0),sK2) ),
inference(forward_subsumption_resolution,[],[f265,f179]) ).
fof(f267,plain,
! [X0] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f266,f216]) ).
fof(f277,plain,
( ! [X0] :
( cons(sK4,X0) = app(cons(sK4,nil),X0)
| ~ ssList(X0) )
| ~ spl13_2 ),
inference(resolution,[],[f207,f234]) ).
fof(f278,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(sK4,X0) = app(sK2,X0) )
| ~ spl13_2
| ~ spl13_4 ),
inference(forward_demodulation,[],[f277,f242]) ).
fof(f284,plain,
( ! [X0] :
( ~ memberP(X0,sK4)
| app(sK9(X0,sK4),cons(sK4,sK10(X0,sK4))) = X0
| ~ ssList(X0) )
| ~ spl13_2 ),
inference(resolution,[],[f187,f234]) ).
fof(f285,plain,
( sK3 = app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4)))
| ~ ssList(sK3)
| ~ spl13_2
| ~ spl13_3 ),
inference(resolution,[],[f284,f238]) ).
fof(f286,plain,
( sK3 = app(sK9(sK3,sK4),cons(sK4,sK10(sK3,sK4)))
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f285,f215]) ).
fof(f292,definition,
( spl13_8
<=> ssList(sK9(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f293,plain,
( ~ ssList(sK9(sK3,sK4))
| spl13_8 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f300,plain,
! [X0] :
( ~ ssList(X0)
| ssList(app(sK2,X0)) ),
inference(resolution,[],[f212,f216]) ).
fof(f303,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,app(sK2,X1)),X2),sK2)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(sK2)
| ~ ssList(app(sK2,X1))
| ~ ssList(X1)
| ~ ssList(app(sK2,X1)) ),
inference(resolution,[],[f194,f267]) ).
fof(f306,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,app(sK2,X1)),X2),sK2)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(sK2)
| ~ ssList(app(sK2,X1))
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f303]) ).
fof(f308,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,app(sK2,X1)),X2),sK2)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X1))
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f306,f216]) ).
fof(f310,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,app(sK2,X1)),X2),sK2)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f308,f300]) ).
fof(f320,plain,
( ! [X0] :
( ~ memberP(X0,sK4)
| ssList(sK10(X0,sK4))
| ~ ssList(X0) )
| ~ spl13_2 ),
inference(resolution,[],[f188,f234]) ).
fof(f321,plain,
( ssList(sK10(sK3,sK4))
| ~ ssList(sK3)
| ~ spl13_2
| ~ spl13_3 ),
inference(resolution,[],[f320,f238]) ).
fof(f322,plain,
( ssList(sK10(sK3,sK4))
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f321,f215]) ).
fof(f324,plain,
( cons(sK4,sK10(sK3,sK4)) = app(sK2,sK10(sK3,sK4))
| ~ spl13_2
| ~ spl13_3
| ~ spl13_4 ),
inference(resolution,[],[f322,f278]) ).
fof(f327,plain,
( sK3 = app(sK9(sK3,sK4),app(sK2,sK10(sK3,sK4)))
| ~ spl13_2
| ~ spl13_3
| ~ spl13_4 ),
inference(superposition,[],[f286,f324]) ).
fof(f373,plain,
( ! [X0] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(X0)
| ~ ssList(sK9(sK3,sK4))
| ~ ssList(sK10(sK3,sK4)) )
| ~ spl13_2
| ~ spl13_3
| ~ spl13_4 ),
inference(superposition,[],[f310,f327]) ).
fof(f400,plain,
( $false
| ~ spl13_2
| ~ spl13_3
| spl13_8 ),
inference(unit_resulting_resolution,[],[f189,f215,f234,f238,f293]) ).
fof(f403,plain,
( ~ spl13_2
| ~ spl13_3
| spl13_8 ),
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f407,plain,
( ! [X0] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(X0)
| ~ ssList(sK9(sK3,sK4)) )
| ~ spl13_2
| ~ spl13_3
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f373,f322]) ).
fof(f417,definition,
( spl13_15
<=> ! [X0] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[spl13_15])],[avatar_definition]) ).
fof(f418,plain,
( ! [X0] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(X0) )
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f419,plain,
( ~ spl13_8
| spl13_15
| ~ spl13_2
| ~ spl13_3
| ~ spl13_4 ),
inference(avatar_split_clause,[],[f407,f241,f237,f233,f417,f292]) ).
fof(f422,plain,
( segmentP(sK3,sK2)
| ~ ssList(nil)
| ~ spl13_15 ),
inference(superposition,[],[f418,f256]) ).
fof(f423,plain,
( ~ ssList(nil)
| ~ spl13_15 ),
inference(forward_subsumption_resolution,[],[f422,f214]) ).
fof(f425,plain,
( $false
| ~ spl13_15 ),
inference(forward_subsumption_resolution,[],[f423,f179]) ).
fof(f426,plain,
~ spl13_15,
inference(avatar_contradiction_clause,[],[f425]) ).
cnf(s1,plain,
( ~ spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f235]) ).
cnf(s2,plain,
( ~ spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f239]) ).
cnf(s3,plain,
( ~ spl13_1
| spl13_4 ),
inference(sat_conversion,[],[f243]) ).
cnf(s5,plain,
spl13_1,
inference(sat_conversion,[],[f252]) ).
cnf(s11,plain,
( ~ spl13_2
| ~ spl13_3
| spl13_8 ),
inference(sat_conversion,[],[f403]) ).
cnf(s14,plain,
( ~ spl13_2
| ~ spl13_3
| ~ spl13_4
| ~ spl13_8
| spl13_15 ),
inference(sat_conversion,[],[f419]) ).
cnf(s16,plain,
~ spl13_15,
inference(sat_conversion,[],[f426]) ).
cnf(s17,plain,
( ~ spl13_2
| ~ spl13_3
| ~ spl13_4
| ~ spl13_8 ),
inference(rat,[],[s14,s16]) ).
cnf(s18,plain,
spl13_4,
inference(rat,[],[s3,s5]) ).
cnf(s19,plain,
spl13_3,
inference(rat,[],[s2,s5]) ).
cnf(s20,plain,
spl13_2,
inference(rat,[],[s1,s5]) ).
cnf(s21,plain,
~ spl13_8,
inference(rat,[],[s17,s19,s18,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s11,s19,s21,s20]) ).
fof(f428,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC363+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n006.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 09:17:33 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 5.97/1.64 % (3833941)Detected formulas, will run a generic FOF schedule.
% 5.97/1.64 % (3833950)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3783246427:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.97/1.64 % (3833951)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3895706379:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.97/1.64 % (3833950)Instruction limit reached!
% 5.97/1.64 % (3833950)------------------------------
% 5.97/1.64 % (3833950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.64 % (3833950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.64 % (3833950)CaDiCaL version: 2.1.3
% 5.97/1.64 % (3833950)Termination reason: Instruction limit
% 5.97/1.64 % (3833950)Termination phase: Saturation
% 5.97/1.64 % (3833950)Time elapsed: 0.040 s
% 5.97/1.64 % (3833950)Peak memory usage: 89 MB
% 5.97/1.64 % (3833950)Instructions burned: 120 (million)
% 5.97/1.64 % (3833948)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=993521800:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.97/1.64 % (3833947)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=2213202825:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.97/1.64 % (3833949)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1656939386:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.97/1.64 % (3833946)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=3900955978:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.97/1.64 % (3833949)Refutation not found, incomplete strategy
% 5.97/1.64 % (3833949)------------------------------
% 5.97/1.64 % (3833949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.64 % (3833949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.64 % (3833949)CaDiCaL version: 2.1.3
% 5.97/1.64 % (3833949)Termination reason: Refutation not found, incomplete strategy
% 5.97/1.64 % (3833949)Time elapsed: 0.003 s
% 5.97/1.64 % (3833949)Peak memory usage: 88 MB
% 5.97/1.64 % (3833949)Instructions burned: 4 (million)
% 5.97/1.64 % (3833952)dis-21_1_sil=8000:lcm=predicate:random_seed=3878807179: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)
% 5.97/1.64 % (3833952)Instruction limit reached!
% 5.97/1.64 % (3833952)------------------------------
% 5.97/1.64 % (3833952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.64 % (3833952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.64 % (3833952)CaDiCaL version: 2.1.3
% 5.97/1.64 % (3833952)Termination reason: Instruction limit
% 5.97/1.64 % (3833952)Termination phase: Saturation
% 5.97/1.64 % (3833952)Time elapsed: 0.075 s
% 5.97/1.64 % (3833952)Peak memory usage: 90 MB
% 5.97/1.64 % (3833952)Instructions burned: 130 (million)
% 5.97/1.64 % (3833959)lrs+10_1_sil=8000:sp=occurrence:random_seed=1234050894:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.97/1.64 % (3833951)Instruction limit reached!
% 5.97/1.64 % (3833951)------------------------------
% 5.97/1.64 % (3833951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.64 % (3833951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.64 % (3833951)CaDiCaL version: 2.1.3
% 5.97/1.64 % (3833951)Termination reason: Instruction limit
% 5.97/1.64 % (3833951)Termination phase: Saturation
% 5.97/1.64 % (3833951)Time elapsed: 0.094 s
% 5.97/1.64 % (3833951)Peak memory usage: 90 MB
% 5.97/1.64 % (3833951)Instructions burned: 140 (million)
% 5.97/1.64 % (3833959)Instruction limit reached!
% 5.97/1.64 % (3833959)------------------------------
% 5.97/1.64 % (3833959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.64 % (3833959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.64 % (3833959)CaDiCaL version: 2.1.3
% 5.97/1.64 % (3833959)Termination reason: Instruction limit
% 5.97/1.64 % (3833959)Termination phase: Saturation
% 5.97/1.64 % (3833959)Time elapsed: 0.094 s
% 5.97/1.64 % (3833959)Peak memory usage: 93 MB
% 5.97/1.64 % (3833959)Instructions burned: 285 (million)
% 5.97/1.65 % (3833962)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1287636271:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.97/1.65 % (3833963)lrs+1011_1_sil=32000:sp=occurrence:random_seed=968934965:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.97/1.65 % (3833949)------------------------------
% 5.97/1.65 % (3833949)------------------------------
% 5.97/1.65 % (3833964)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=77329551:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.97/1.65 % (3833962)Instruction limit reached!
% 5.97/1.65 % (3833962)------------------------------
% 5.97/1.65 % (3833962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.65 % (3833962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.65 % (3833962)CaDiCaL version: 2.1.3
% 5.97/1.65 % (3833962)Termination reason: Instruction limit
% 5.97/1.65 % (3833962)Termination phase: Saturation
% 5.97/1.65 % (3833962)Time elapsed: 0.077 s
% 5.97/1.65 % (3833962)Peak memory usage: 91 MB
% 5.97/1.65 % (3833962)Instructions burned: 157 (million)
% 5.97/1.65 % (3833964)Instruction limit reached!
% 5.97/1.65 % (3833964)------------------------------
% 5.97/1.65 % (3833964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.65 % (3833964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.65 % (3833964)CaDiCaL version: 2.1.3
% 5.97/1.65 % (3833964)Termination reason: Instruction limit
% 5.97/1.65 % (3833964)Termination phase: Saturation
% 5.97/1.65 % (3833964)Time elapsed: 0.063 s
% 5.97/1.65 % (3833964)Peak memory usage: 93 MB
% 5.97/1.65 % (3833964)Instructions burned: 249 (million)
% 5.97/1.65 % (3833967)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2770324232:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.97/1.65 % (3833969)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=382010065:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.97/1.65 % (3833970)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2519465325:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 5.97/1.65 % (3833963)Instruction limit reached!
% 5.97/1.65 % (3833963)------------------------------
% 5.97/1.65 % (3833963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.65 % (3833963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.65 % (3833963)CaDiCaL version: 2.1.3
% 5.97/1.65 % (3833963)Termination reason: Instruction limit
% 5.97/1.65 % (3833963)Termination phase: Saturation
% 5.97/1.65 % (3833963)Time elapsed: 0.203 s
% 5.97/1.65 % (3833963)Peak memory usage: 92 MB
% 5.97/1.65 % (3833963)Instructions burned: 326 (million)
% 5.97/1.65 % (3833970)Instruction limit reached!
% 5.97/1.65 % (3833970)------------------------------
% 5.97/1.65 % (3833970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.65 % (3833970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.65 % (3833970)CaDiCaL version: 2.1.3
% 5.97/1.65 % (3833970)Termination reason: Instruction limit
% 5.97/1.65 % (3833970)Termination phase: Saturation
% 5.97/1.65 % (3833970)Time elapsed: 0.042 s
% 5.97/1.65 % (3833970)Peak memory usage: 90 MB
% 5.97/1.65 % (3833970)Instructions burned: 115 (million)
% 5.97/1.65 % (3833975)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=93915500:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 5.97/1.65 % (3833974)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2961541436:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.97/1.65 % (3833967)Instruction limit reached!
% 5.97/1.65 % (3833967)------------------------------
% 5.97/1.65 % (3833967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.65 % (3833967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.65 % (3833967)CaDiCaL version: 2.1.3
% 5.97/1.65 % (3833967)Termination reason: Instruction limit
% 5.97/1.65 % (3833967)Termination phase: Saturation
% 5.97/1.65 % (3833967)Time elapsed: 0.185 s
% 5.97/1.65 % (3833967)Peak memory usage: 90 MB
% 5.97/1.65 % (3833967)Instructions burned: 296 (million)
% 5.97/1.65 % (3833975)Instruction limit reached!
% 5.97/1.65 % (3833975)------------------------------
% 5.97/1.65 % (3833975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.65 % (3833975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.65 % (3833975)CaDiCaL version: 2.1.3
% 5.97/1.65 % (3833975)Termination reason: Instruction limit
% 5.97/1.65 % (3833975)Termination phase: Saturation
% 5.97/1.65 % (3833975)Time elapsed: 0.037 s
% 5.97/1.65 % (3833975)Peak memory usage: 89 MB
% 5.97/1.65 % (3833975)Instructions burned: 116 (million)
% 5.97/1.65 % (3833974)Instruction limit reached!
% 5.97/1.65 % (3833974)------------------------------
% 5.97/1.65 % (3833974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.65 % (3833974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.65 % (3833974)CaDiCaL version: 2.1.3
% 5.97/1.65 % (3833974)Termination reason: Instruction limit
% 5.97/1.65 % (3833974)Termination phase: Saturation
% 5.97/1.65 % (3833974)Time elapsed: 0.064 s
% 5.97/1.65 % (3833974)Peak memory usage: 89 MB
% 5.97/1.65 % (3833974)Instructions burned: 128 (million)
% 5.97/1.65 % (3833947)First to succeed.
% 5.97/1.65 % (3833947)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3833941"
% 5.97/1.65 % (3833946)Also succeeded, but the first one will report.
% 5.97/1.65 % (3833978)lrs+10_1_sil=8000:sp=occurrence:random_seed=2101424500:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 5.97/1.65 % (3833979)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=885046676:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.97/1.65 % (3833980)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3360269818:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 5.97/1.65 % (3833947)Refutation found. Thanks to Tanya!
% 5.97/1.65 % SZS status Theorem for theBenchmark
% 5.97/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 7.60/1.82 % (3833947)------------------------------
% 7.60/1.82 % (3833947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.60/1.82 % (3833947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.60/1.82 % (3833947)CaDiCaL version: 2.1.3
% 7.60/1.82 % (3833947)Termination reason: Refutation
% 7.60/1.82 % (3833947)Time elapsed: 0.654 s
% 7.60/1.82 % (3833947)Peak memory usage: 129 MB
% 7.60/1.82 % (3833947)Instructions burned: 968 (million)
% 7.60/1.82 % (3833947)------------------------------
% 7.60/1.82 % (3833947)------------------------------
% 7.60/1.82 % (3833941)Success in time 0.993 s
% 7.60/1.82 % Vampire exiting
%------------------------------------------------------------------------------