%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC065+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 : n026.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 01:02:16 PM UTC 2026
% Result : Theorem 2.65s 1.27s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 116 ( 18 unt; 0 def)
% Number of atoms : 492 ( 152 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 645 ( 269 ~; 262 |; 78 &)
% ( 6 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 161 ( 135 !; 26 ?)
% 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/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
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(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X0,X1)
& segmentP(X1,X2) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax79) ).
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
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X8] :
( ssList(X8)
& neq(X8,nil)
& segmentP(X1,X8)
& segmentP(X0,X8) ) ) ) ) ) ) ) ),
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
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X8] :
( ssList(X8)
& neq(X8,nil)
& segmentP(X1,X8)
& segmentP(X0,X8) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X8] :
( ~ ssList(X8)
| ~ neq(X8,nil)
| ~ segmentP(X1,X8)
| ~ segmentP(X0,X8) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X8] :
( ~ ssList(X8)
| ~ neq(X8,nil)
| ~ segmentP(X1,X8)
| ~ segmentP(X0,X8) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f107,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f121,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f124,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f127]) ).
fof(f129,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(f133,plain,
( sK1 = sK3
& sK0 = sK2
& sK3 = app(sK2,sK4)
& equalelemsP(sK2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != sK4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != sK2 ) ) )
& ssList(sK4)
& ( nil = sK3
| nil != sK2 )
& ( ( nil = sK1
& nil != sK0 )
| ( neq(sK1,nil)
& ! [X8] :
( ~ ssList(X8)
| ~ neq(X8,nil)
| ~ segmentP(sK1,X8)
| ~ segmentP(sK0,X8) ) ) )
& 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(f136,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,[],[f108]) ).
fof(f137,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,[],[f136]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f141,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,[],[f129]) ).
fof(f142,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,[],[f141]) ).
fof(f143,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK9(X0,X1))
& ssList(sK10(X0,X1))
& app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f142]) ).
fof(f149,plain,
ssList(sK2),
inference(cnf_transformation,[],[f133]) ).
fof(f150,plain,
ssList(sK3),
inference(cnf_transformation,[],[f133]) ).
fof(f152,plain,
( nil != sK0
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f133]) ).
fof(f153,plain,
! [X8] :
( nil = sK1
| ~ ssList(X8)
| ~ neq(X8,nil)
| ~ segmentP(sK1,X8)
| ~ segmentP(sK0,X8) ),
inference(cnf_transformation,[],[f133]) ).
fof(f154,plain,
( nil = sK1
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f133]) ).
fof(f155,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f133]) ).
fof(f156,plain,
ssList(sK4),
inference(cnf_transformation,[],[f133]) ).
fof(f159,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f133]) ).
fof(f160,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f133]) ).
fof(f161,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f133]) ).
fof(f173,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f175,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f180,plain,
! [X2,X0,X1] :
( app(X2,X1) != app(X0,X1)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f181,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f183,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f184,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f185,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f188,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f191,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f193,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f195,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f199,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,[],[f143]) ).
fof(f209,plain,
( neq(sK3,nil)
| nil = sK3 ),
inference(definition_unfolding,[],[f154,f161,f161]) ).
fof(f210,plain,
! [X8] :
( ~ segmentP(sK3,X8)
| ~ ssList(X8)
| ~ neq(X8,nil)
| nil = sK3
| ~ segmentP(sK2,X8) ),
inference(definition_unfolding,[],[f153,f161,f161,f160]) ).
fof(f211,plain,
( nil != sK2
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f152,f160,f161]) ).
fof(f217,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f184]) ).
fof(f220,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,[],[f199]) ).
fof(f223,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f217]) ).
fof(f230,plain,
( ~ ssList(sK3)
| ~ ssList(sK3)
| ~ neq(sK3,nil)
| nil = sK3
| ~ segmentP(sK2,sK3) ),
inference(resolution,[],[f193,f210]) ).
fof(f231,plain,
( ~ ssList(sK3)
| ~ neq(sK3,nil)
| nil = sK3
| ~ segmentP(sK2,sK3) ),
inference(duplicate_literal_removal,[],[f230]) ).
fof(f232,plain,
( ~ ssList(sK3)
| nil = sK3
| ~ segmentP(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f231,f209]) ).
fof(f233,plain,
( ~ segmentP(sK2,sK3)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f232,f150]) ).
fof(f270,plain,
( nil != sK3
| nil = sK4
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f175,f159]) ).
fof(f273,plain,
( nil != sK3
| nil = sK4
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f270,f156]) ).
fof(f274,plain,
( nil != sK3
| nil = sK4 ),
inference(forward_subsumption_resolution,[],[f273,f149]) ).
fof(f297,plain,
! [X0] :
( ~ segmentP(sK2,X0)
| ~ segmentP(X0,sK3)
| ~ ssList(sK3)
| ~ ssList(X0)
| ~ ssList(sK2)
| nil = sK3 ),
inference(resolution,[],[f195,f233]) ).
fof(f303,plain,
! [X0] :
( ~ segmentP(sK2,X0)
| ~ segmentP(X0,sK3)
| ~ ssList(X0)
| ~ ssList(sK2)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f297,f150]) ).
fof(f305,plain,
! [X0] :
( ~ segmentP(sK2,X0)
| ~ segmentP(X0,sK3)
| ~ ssList(X0)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f303,f149]) ).
fof(f306,plain,
( ~ segmentP(nil,sK3)
| ~ ssList(nil)
| nil = sK3
| ~ ssList(sK2) ),
inference(resolution,[],[f305,f191]) ).
fof(f312,plain,
( ~ segmentP(nil,sK3)
| nil = sK3
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f306,f188]) ).
fof(f313,plain,
( ~ segmentP(nil,sK3)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f312,f149]) ).
fof(f350,plain,
! [X0,X1] :
( app(X1,X0) != X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f180,f181]) ).
fof(f354,plain,
! [X0,X1] :
( app(X1,X0) != X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f350]) ).
fof(f361,plain,
! [X0,X1] :
( app(X1,X0) != X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f354,f188]) ).
fof(f622,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(superposition,[],[f220,f181]) ).
fof(f623,plain,
! [X0] :
( segmentP(app(sK3,X0),sK4)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(app(sK3,X0)) ),
inference(superposition,[],[f220,f159]) ).
fof(f633,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f622]) ).
fof(f642,plain,
! [X0] :
( segmentP(app(sK3,X0),sK4)
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(app(sK3,X0)) ),
inference(forward_subsumption_resolution,[],[f623,f149]) ).
fof(f643,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f633,f188]) ).
fof(f649,plain,
! [X0] :
( segmentP(app(sK3,X0),sK4)
| ~ ssList(X0)
| ~ ssList(app(sK3,X0)) ),
inference(forward_subsumption_resolution,[],[f642,f156]) ).
fof(f650,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f643,f183]) ).
fof(f654,plain,
( segmentP(sK3,sK4)
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ ssList(sK3) ),
inference(superposition,[],[f649,f173]) ).
fof(f655,plain,
( segmentP(sK3,sK4)
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(duplicate_literal_removal,[],[f654]) ).
fof(f657,plain,
( segmentP(sK3,sK4)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f655,f188]) ).
fof(f660,plain,
segmentP(sK3,sK4),
inference(forward_subsumption_resolution,[],[f657,f150]) ).
fof(f777,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f650,f159]) ).
fof(f790,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f777,f156]) ).
fof(f795,plain,
segmentP(sK3,sK2),
inference(forward_subsumption_resolution,[],[f790,f149]) ).
fof(f797,plain,
( ~ ssList(sK2)
| ~ neq(sK2,nil)
| nil = sK3
| ~ segmentP(sK2,sK2) ),
inference(resolution,[],[f795,f210]) ).
fof(f801,plain,
( ~ segmentP(sK2,sK2)
| nil = sK3
| ~ neq(sK2,nil) ),
inference(forward_subsumption_resolution,[],[f797,f149]) ).
fof(f812,plain,
( nil = sK3
| ~ neq(sK2,nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f801,f193]) ).
fof(f816,plain,
( ~ neq(sK2,nil)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f812,f149]) ).
fof(f837,plain,
( nil = sK3
| nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f816,f185]) ).
fof(f838,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f837,f155]) ).
fof(f840,plain,
( nil = sK3
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f838,f188]) ).
fof(f841,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f840,f149]) ).
fof(f856,plain,
( sK3 != sK3
| sK3 = sK4 ),
inference(superposition,[],[f274,f841]) ).
fof(f864,plain,
sK3 = sK4,
inference(trivial_inequality_removal,[],[f856]) ).
fof(f871,plain,
( ~ segmentP(nil,sK4)
| nil = sK4 ),
inference(superposition,[],[f313,f864]) ).
fof(f890,plain,
( ~ segmentP(sK3,sK4)
| nil = sK4 ),
inference(forward_demodulation,[],[f871,f841]) ).
fof(f898,plain,
nil = sK4,
inference(forward_subsumption_resolution,[],[f890,f660]) ).
fof(f905,plain,
! [X0,X1] :
( sK3 = X1
| app(X1,X0) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f361,f841]) ).
fof(f906,plain,
! [X0,X1] :
( app(X1,X0) != X0
| sK4 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f905,f864]) ).
fof(f914,plain,
( sK3 != sK4
| sK2 = sK4
| ~ ssList(sK2)
| ~ ssList(sK4) ),
inference(superposition,[],[f906,f159]) ).
fof(f927,plain,
( sK2 = sK4
| ~ ssList(sK2)
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f914,f864]) ).
fof(f935,plain,
( sK2 = sK4
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f927,f149]) ).
fof(f938,plain,
sK2 = sK4,
inference(forward_subsumption_resolution,[],[f935,f156]) ).
fof(f997,plain,
( sK2 != sK4
| neq(sK3,sK4) ),
inference(superposition,[],[f211,f898]) ).
fof(f1024,plain,
neq(sK3,sK4),
inference(forward_subsumption_resolution,[],[f997,f938]) ).
fof(f1028,plain,
neq(sK4,sK4),
inference(forward_demodulation,[],[f1024,f864]) ).
fof(f1033,plain,
~ ssList(sK4),
inference(resolution,[],[f1028,f223]) ).
fof(f1035,plain,
$false,
inference(forward_subsumption_resolution,[],[f1033,f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC065+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 07:44:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.65/1.27 % (3679446)Detected formulas, will run a generic FOF schedule.
% 2.65/1.27 % (3679454)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=604063456:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.27 % (3679453)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=2162322224:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.27 % (3679456)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1257002605:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.27 % (3679451)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=1196150568:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.27 % (3679452)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=2234291139:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.27 % (3679455)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1262961541:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.27 % (3679457)dis-21_1_sil=8000:lcm=predicate:random_seed=83696097: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)
% 2.65/1.27 % (3679454)Instruction limit reached!
% 2.65/1.27 % (3679454)------------------------------
% 2.65/1.27 % (3679454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (3679454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (3679454)CaDiCaL version: 2.1.3
% 2.65/1.27 % (3679454)Termination reason: Instruction limit
% 2.65/1.27 % (3679454)Termination phase: Saturation
% 2.65/1.27 % (3679454)Time elapsed: 0.042 s
% 2.65/1.27 % (3679454)Peak memory usage: 89 MB
% 2.65/1.27 % (3679454)Instructions burned: 112 (million)
% 2.65/1.27 % (3679455)First to succeed.
% 2.65/1.27 % (3679455)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3679446"
% 2.65/1.27 % (3679456)Also succeeded, but the first one will report.
% 2.65/1.27 % (3679457)Instruction limit reached!
% 2.65/1.27 % (3679457)------------------------------
% 2.65/1.27 % (3679457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (3679457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (3679457)CaDiCaL version: 2.1.3
% 2.65/1.27 % (3679457)Termination reason: Instruction limit
% 2.65/1.27 % (3679457)Termination phase: Saturation
% 2.65/1.27 % (3679457)Time elapsed: 0.075 s
% 2.65/1.27 % (3679457)Peak memory usage: 90 MB
% 2.65/1.27 % (3679457)Instructions burned: 130 (million)
% 2.65/1.27 % (3679465)lrs+10_1_sil=8000:sp=occurrence:random_seed=2188942017:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.65/1.27 % (3679466)lrs+10_1_sil=32000:urr=on:br=off:random_seed=893705239:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.65/1.27 % (3679465)Also succeeded, but the first one will report.
% 2.65/1.27 % (3679455)Refutation found. Thanks to Tanya!
% 2.65/1.27 % SZS status Theorem for theBenchmark
% 2.65/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.47 % (3679455)------------------------------
% 3.64/1.47 % (3679455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.47 % (3679455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.47 % (3679455)CaDiCaL version: 2.1.3
% 3.64/1.47 % (3679455)Termination reason: Refutation
% 3.64/1.47 % (3679455)Time elapsed: 0.020 s
% 3.64/1.47 % (3679455)Peak memory usage: 89 MB
% 3.64/1.47 % (3679455)Instructions burned: 31 (million)
% 3.64/1.47 % (3679455)------------------------------
% 3.64/1.47 % (3679455)------------------------------
% 3.64/1.47 % (3679446)Success in time 0.435 s
% 3.64/1.47 % Vampire exiting
%------------------------------------------------------------------------------