%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC061+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 : n010.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 01:02:15 PM UTC 2026
% Result : Theorem 2.80s 1.32s
% Output : Refutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 16
% Syntax : Number of formulae : 161 ( 15 unt; 0 def)
% Number of atoms : 609 ( 129 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 816 ( 368 ~; 353 |; 54 &)
% ( 6 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 160 ( 144 !; 16 ?)
% 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(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
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(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
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(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
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 != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) != X2 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssList(X6)
& neq(X6,nil)
& segmentP(X1,X6)
& segmentP(X0,X6) ) ) ) ) ) ) ),
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 != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) != X2 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssList(X6)
& neq(X6,nil)
& segmentP(X1,X6)
& segmentP(X0,X6) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) = X2 )
& ssItem(X4) )
| ~ neq(X3,nil) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X6] :
( ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(X1,X6)
| ~ segmentP(X0,X6) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f106,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f114,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f120,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f123,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f126]) ).
fof(f128,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(f129,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ( nil = sK2
| nil != sK3 )
& ( ( ssList(sK5)
& sK3 = app(cons(sK4,nil),sK5)
& sK2 = app(sK5,cons(sK4,nil))
& ssItem(sK4) )
| ~ neq(sK3,nil) )
& ( ( nil = sK1
& nil != sK0 )
| ( neq(sK1,nil)
& ! [X6] :
( ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(sK1,X6)
| ~ segmentP(sK0,X6) ) ) )
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f98]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f136,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f137,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,[],[f128]) ).
fof(f138,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,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK10(X0,X1))
& ssList(sK11(X0,X1))
& app(app(sK10(X0,X1),X1),sK11(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f138]) ).
fof(f142,plain,
ssList(sK2),
inference(cnf_transformation,[],[f129]) ).
fof(f144,plain,
( nil != sK0
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f129]) ).
fof(f145,plain,
! [X6] :
( nil = sK1
| ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(sK1,X6)
| ~ segmentP(sK0,X6) ),
inference(cnf_transformation,[],[f129]) ).
fof(f146,plain,
( nil = sK1
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f129]) ).
fof(f147,plain,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(cnf_transformation,[],[f129]) ).
fof(f148,plain,
( sK2 = app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f129]) ).
fof(f149,plain,
( sK3 = app(cons(sK4,nil),sK5)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f129]) ).
fof(f150,plain,
( ~ neq(sK3,nil)
| ssList(sK5) ),
inference(cnf_transformation,[],[f129]) ).
fof(f151,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f129]) ).
fof(f152,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f129]) ).
fof(f153,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f129]) ).
fof(f154,plain,
ssList(sK3),
inference(cnf_transformation,[],[f129]) ).
fof(f158,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f165,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f166,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f170,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f171,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f174,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f175,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f176,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f178,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f181,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f182,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f184,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f186,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f188,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f192,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,[],[f139]) ).
fof(f193,plain,
( neq(sK3,nil)
| nil = sK3 ),
inference(definition_unfolding,[],[f146,f153,f153]) ).
fof(f194,plain,
! [X6] :
( ~ segmentP(sK3,X6)
| ~ ssList(X6)
| ~ neq(X6,nil)
| nil = sK3
| ~ segmentP(sK2,X6) ),
inference(definition_unfolding,[],[f145,f153,f153,f152]) ).
fof(f195,plain,
( nil != sK2
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f144,f152,f153]) ).
fof(f204,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,[],[f192]) ).
fof(f274,plain,
( ~ ssList(sK3)
| ~ ssList(sK3)
| ~ neq(sK3,nil)
| nil = sK3
| ~ segmentP(sK2,sK3) ),
inference(resolution,[],[f186,f194]) ).
fof(f275,plain,
( ~ ssList(sK3)
| ~ neq(sK3,nil)
| nil = sK3
| ~ segmentP(sK2,sK3) ),
inference(duplicate_literal_removal,[],[f274]) ).
fof(f276,plain,
( ~ ssList(sK3)
| nil = sK3
| ~ segmentP(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f275,f193]) ).
fof(f277,plain,
( ~ segmentP(sK2,sK3)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f276,f154]) ).
fof(f385,plain,
( sK3 = cons(sK4,sK5)
| ~ neq(sK3,nil)
| ~ ssItem(sK4)
| ~ ssList(sK5) ),
inference(superposition,[],[f149,f171]) ).
fof(f392,plain,
( sK3 = cons(sK4,sK5)
| ~ neq(sK3,nil)
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f385,f147]) ).
fof(f394,plain,
( sK3 = cons(sK4,sK5)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f392,f150]) ).
fof(f397,plain,
( nil != sK3
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f158,f394]) ).
fof(f399,plain,
( nil != sK3
| ~ ssList(sK5)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f397,f147]) ).
fof(f401,plain,
( nil != sK3
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f399,f150]) ).
fof(f425,plain,
! [X0] :
( ~ segmentP(sK2,X0)
| ~ segmentP(X0,sK3)
| ~ ssList(sK3)
| ~ ssList(X0)
| ~ ssList(sK2)
| nil = sK3 ),
inference(resolution,[],[f188,f277]) ).
fof(f432,plain,
! [X0] :
( ~ segmentP(sK2,X0)
| ~ segmentP(X0,sK3)
| ~ ssList(X0)
| ~ ssList(sK2)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f425,f154]) ).
fof(f434,plain,
! [X0] :
( ~ segmentP(sK2,X0)
| ~ segmentP(X0,sK3)
| ~ ssList(X0)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f432,f142]) ).
fof(f524,plain,
! [X0] :
( app(sK5,app(cons(sK4,nil),X0)) = app(sK2,X0)
| ~ ssList(X0)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f170,f148]) ).
fof(f554,plain,
! [X0] :
( app(sK5,app(cons(sK4,nil),X0)) = app(sK2,X0)
| ~ ssList(X0)
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f524,f150]) ).
fof(f562,plain,
! [X0] :
( app(sK3,X0) = cons(sK4,app(sK5,X0))
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ ssList(X0)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f175,f394]) ).
fof(f566,plain,
( sK3 = cons(sK4,app(nil,sK5))
| ~ neq(sK3,nil)
| ~ ssItem(sK4)
| ~ ssList(nil)
| ~ ssList(sK5) ),
inference(superposition,[],[f149,f175]) ).
fof(f597,plain,
( sK3 = cons(sK4,app(nil,sK5))
| ~ neq(sK3,nil)
| ~ ssList(nil)
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f566,f147]) ).
fof(f601,plain,
! [X0] :
( app(sK3,X0) = cons(sK4,app(sK5,X0))
| ~ ssList(sK5)
| ~ ssList(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f562,f147]) ).
fof(f605,plain,
( sK3 = cons(sK4,app(nil,sK5))
| ~ neq(sK3,nil)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f597,f150]) ).
fof(f608,plain,
! [X0] :
( app(sK3,X0) = cons(sK4,app(sK5,X0))
| ~ ssList(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f601,f150]) ).
fof(f610,plain,
( sK3 = cons(sK4,app(nil,sK5))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f605,f181]) ).
fof(f687,plain,
( cons(sK4,sK5) = app(sK3,nil)
| ~ ssList(nil)
| ~ neq(sK3,nil)
| ~ ssList(sK5) ),
inference(superposition,[],[f608,f166]) ).
fof(f705,plain,
( cons(sK4,sK5) = app(sK3,nil)
| ~ ssList(nil)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f687,f150]) ).
fof(f706,plain,
( cons(sK4,sK5) = app(sK3,nil)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f705,f181]) ).
fof(f770,plain,
! [X0] :
( segmentP(app(sK3,X0),sK5)
| ~ ssList(cons(sK4,nil))
| ~ ssList(X0)
| ~ ssList(sK5)
| ~ ssList(app(sK3,X0))
| ~ neq(sK3,nil) ),
inference(superposition,[],[f204,f149]) ).
fof(f775,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(superposition,[],[f204,f174]) ).
fof(f777,plain,
! [X0] :
( segmentP(app(sK2,X0),cons(sK4,nil))
| ~ ssList(sK5)
| ~ ssList(X0)
| ~ ssList(cons(sK4,nil))
| ~ ssList(app(sK2,X0))
| ~ neq(sK3,nil) ),
inference(superposition,[],[f204,f148]) ).
fof(f784,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f775]) ).
fof(f791,plain,
! [X0] :
( segmentP(app(sK2,X0),cons(sK4,nil))
| ~ ssList(X0)
| ~ ssList(cons(sK4,nil))
| ~ ssList(app(sK2,X0))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f777,f150]) ).
fof(f792,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f784,f181]) ).
fof(f796,plain,
! [X0] :
( segmentP(app(sK3,X0),sK5)
| ~ ssList(cons(sK4,nil))
| ~ ssList(X0)
| ~ ssList(app(sK3,X0))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f770,f150]) ).
fof(f798,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f792,f176]) ).
fof(f812,plain,
( segmentP(sK3,sK5)
| ~ ssList(cons(sK4,nil))
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ neq(sK3,nil)
| ~ ssList(sK3) ),
inference(superposition,[],[f796,f166]) ).
fof(f813,plain,
( segmentP(sK3,sK5)
| ~ ssList(cons(sK4,nil))
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ neq(sK3,nil) ),
inference(duplicate_literal_removal,[],[f812]) ).
fof(f816,plain,
( segmentP(sK3,sK5)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK3)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f813,f181]) ).
fof(f819,plain,
( ~ ssList(cons(sK4,nil))
| segmentP(sK3,sK5)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f816,f154]) ).
fof(f821,plain,
( segmentP(sK3,sK5)
| ~ neq(sK3,nil)
| ~ ssItem(sK4)
| ~ ssList(nil) ),
inference(resolution,[],[f819,f165]) ).
fof(f824,plain,
( segmentP(sK3,sK5)
| ~ neq(sK3,nil)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f821,f147]) ).
fof(f825,plain,
( segmentP(sK3,sK5)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f824,f181]) ).
fof(f826,plain,
( ~ neq(sK3,nil)
| ~ ssList(sK5)
| ~ neq(sK5,nil)
| nil = sK3
| ~ segmentP(sK2,sK5) ),
inference(resolution,[],[f825,f194]) ).
fof(f831,plain,
( ~ neq(sK3,nil)
| ~ neq(sK5,nil)
| nil = sK3
| ~ segmentP(sK2,sK5) ),
inference(forward_subsumption_resolution,[],[f826,f150]) ).
fof(f833,plain,
( ~ segmentP(sK2,sK5)
| ~ neq(sK5,nil)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f831,f401]) ).
fof(f1042,plain,
! [X0] :
( ssList(app(sK2,X0))
| ~ ssList(app(cons(sK4,nil),X0))
| ~ ssList(sK5)
| ~ ssList(X0)
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(superposition,[],[f176,f554]) ).
fof(f1053,plain,
! [X0] :
( ssList(app(sK2,X0))
| ~ ssList(app(cons(sK4,nil),X0))
| ~ ssList(X0)
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f1042,f150]) ).
fof(f1069,plain,
! [X0] :
( ssList(app(sK2,X0))
| ~ ssList(X0)
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f1053,f176]) ).
fof(f1159,plain,
! [X0] :
( segmentP(app(sK2,X0),cons(sK4,nil))
| ~ ssList(X0)
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f791,f1069]) ).
fof(f1162,plain,
( segmentP(sK2,cons(sK4,nil))
| ~ ssList(nil)
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil)
| ~ ssList(sK2) ),
inference(superposition,[],[f1159,f166]) ).
fof(f1167,plain,
( segmentP(sK2,cons(sK4,nil))
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f1162,f181]) ).
fof(f1170,plain,
( segmentP(sK2,cons(sK4,nil))
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f1167,f142]) ).
fof(f1173,plain,
( ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil)
| ~ segmentP(cons(sK4,nil),sK3)
| ~ ssList(cons(sK4,nil))
| nil = sK3 ),
inference(resolution,[],[f1170,f434]) ).
fof(f1178,plain,
( ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil)
| ~ segmentP(cons(sK4,nil),sK3)
| nil = sK3 ),
inference(duplicate_literal_removal,[],[f1173]) ).
fof(f1182,plain,
( ~ segmentP(cons(sK4,nil),sK3)
| ~ neq(sK3,nil)
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[],[f1178,f401]) ).
fof(f1274,plain,
( segmentP(cons(sK4,sK5),sK3)
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f798,f706]) ).
fof(f1275,plain,
( segmentP(sK2,sK5)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f798,f148]) ).
fof(f1285,plain,
( ~ ssList(cons(sK4,nil))
| segmentP(sK2,sK5)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f1275,f150]) ).
fof(f1286,plain,
( segmentP(cons(sK4,sK5),sK3)
| ~ ssList(sK3)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f1274,f181]) ).
fof(f1294,plain,
( segmentP(cons(sK4,sK5),sK3)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f1286,f154]) ).
fof(f1307,plain,
( segmentP(sK3,sK3)
| ~ neq(sK3,nil)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f1294,f394]) ).
fof(f1310,plain,
( segmentP(sK3,sK3)
| ~ neq(sK3,nil) ),
inference(duplicate_literal_removal,[],[f1307]) ).
fof(f1356,plain,
( segmentP(sK2,sK5)
| ~ neq(sK3,nil)
| ~ ssItem(sK4)
| ~ ssList(nil) ),
inference(resolution,[],[f1285,f165]) ).
fof(f1359,plain,
( segmentP(sK2,sK5)
| ~ neq(sK3,nil)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f1356,f147]) ).
fof(f1360,plain,
( segmentP(sK2,sK5)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f1359,f181]) ).
fof(f1362,plain,
( ~ neq(sK3,nil)
| ~ neq(sK5,nil)
| ~ neq(sK3,nil) ),
inference(resolution,[],[f1360,f833]) ).
fof(f1370,plain,
( ~ neq(sK5,nil)
| ~ neq(sK3,nil) ),
inference(duplicate_literal_removal,[],[f1362]) ).
fof(f1376,plain,
( ~ neq(sK3,nil)
| nil = sK5
| ~ ssList(nil)
| ~ ssList(sK5) ),
inference(resolution,[],[f1370,f178]) ).
fof(f1379,plain,
( ~ neq(sK3,nil)
| nil = sK5
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f1376,f150]) ).
fof(f1380,plain,
( ~ neq(sK3,nil)
| nil = sK5 ),
inference(forward_subsumption_resolution,[],[f1379,f181]) ).
fof(f1406,plain,
( nil = sK5
| nil = sK3 ),
inference(resolution,[],[f1380,f193]) ).
fof(f1436,plain,
! [X0] :
( app(X0,sK5) = X0
| ~ ssList(X0)
| nil = sK3 ),
inference(superposition,[],[f166,f1406]) ).
fof(f2389,plain,
( sK3 = cons(sK4,nil)
| ~ neq(sK3,nil)
| ~ ssList(nil)
| nil = sK3 ),
inference(superposition,[],[f610,f1436]) ).
fof(f2450,plain,
( sK3 = cons(sK4,nil)
| ~ neq(sK3,nil)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f2389,f401]) ).
fof(f2488,plain,
( sK3 = cons(sK4,nil)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f2450,f181]) ).
fof(f2546,plain,
( ~ segmentP(sK3,sK3)
| ~ neq(sK3,nil)
| ~ ssList(sK3)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f1182,f2488]) ).
fof(f2558,plain,
( ~ segmentP(sK3,sK3)
| ~ neq(sK3,nil)
| ~ ssList(sK3) ),
inference(duplicate_literal_removal,[],[f2546]) ).
fof(f2575,plain,
( ~ neq(sK3,nil)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f2558,f1310]) ).
fof(f2589,plain,
~ neq(sK3,nil),
inference(forward_subsumption_resolution,[],[f2575,f154]) ).
fof(f2613,plain,
nil = sK3,
inference(resolution,[],[f2589,f193]) ).
fof(f2629,plain,
( sK3 != sK3
| sK2 = sK3 ),
inference(superposition,[],[f151,f2613]) ).
fof(f2635,plain,
! [X0] :
( segmentP(X0,sK3)
| ~ ssList(X0) ),
inference(superposition,[],[f184,f2613]) ).
fof(f2674,plain,
~ neq(sK3,sK3),
inference(superposition,[],[f2589,f2613]) ).
fof(f2677,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f2629]) ).
fof(f2741,plain,
~ neq(sK2,sK2),
inference(superposition,[],[f2674,f2677]) ).
fof(f3004,plain,
! [X0] :
( segmentP(X0,sK2)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f2635,f2677]) ).
fof(f3012,plain,
( ~ ssList(nil)
| nil = sK2
| ~ ssList(sK2) ),
inference(resolution,[],[f3004,f182]) ).
fof(f3032,plain,
( nil = sK2
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f3012,f181]) ).
fof(f3036,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f3032,f142]) ).
fof(f3056,plain,
( sK2 != sK2
| neq(sK3,sK2) ),
inference(superposition,[],[f195,f3036]) ).
fof(f3109,plain,
neq(sK3,sK2),
inference(trivial_inequality_removal,[],[f3056]) ).
fof(f3136,plain,
neq(sK2,sK2),
inference(forward_demodulation,[],[f3109,f2677]) ).
fof(f3152,plain,
$false,
inference(forward_subsumption_resolution,[],[f3136,f2741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC061+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.34 % Computer : n010.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8046.5625MB
% 0.11/0.34 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 28 07:40:17 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.38 Running first-order theorem proving
% 0.15/0.38 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
% 2.80/1.32 % (1746080)Detected formulas, will run a generic FOF schedule.
% 2.80/1.32 % (1746091)dis-21_1_sil=8000:lcm=predicate:random_seed=1089376750: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)
% 2.80/1.32 % (1746085)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=2929344005:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.80/1.32 % (1746088)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3999330294:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.80/1.32 % (1746090)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=637784275:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.80/1.32 % (1746089)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2669062616:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.80/1.32 % (1746086)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=2567936777:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.80/1.32 % (1746087)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=2119464041:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.80/1.32 % (1746091)Instruction limit reached!
% 2.80/1.32 % (1746091)------------------------------
% 2.80/1.32 % (1746091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.32 % (1746091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.32 % (1746091)CaDiCaL version: 2.1.3
% 2.80/1.32 % (1746091)Termination reason: Instruction limit
% 2.80/1.32 % (1746091)Termination phase: Saturation
% 2.80/1.32 % (1746091)Time elapsed: 0.042 s
% 2.80/1.32 % (1746091)Peak memory usage: 90 MB
% 2.80/1.32 % (1746091)Instructions burned: 130 (million)
% 2.80/1.32 % (1746089)First to succeed.
% 2.80/1.32 % (1746089)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1746080"
% 2.80/1.32 % (1746090)Also succeeded, but the first one will report.
% 2.80/1.32 % (1746088)Instruction limit reached!
% 2.80/1.32 % (1746088)------------------------------
% 2.80/1.32 % (1746088)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.32 % (1746088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.32 % (1746088)CaDiCaL version: 2.1.3
% 2.80/1.32 % (1746088)Termination reason: Instruction limit
% 2.80/1.32 % (1746088)Termination phase: Saturation
% 2.80/1.32 % (1746088)Time elapsed: 0.067 s
% 2.80/1.32 % (1746088)Peak memory usage: 89 MB
% 2.80/1.32 % (1746088)Instructions burned: 110 (million)
% 2.80/1.32 % (1746099)lrs+10_1_sil=8000:sp=occurrence:random_seed=3774639004:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.80/1.32 % (1746099)Also succeeded, but the first one will report.
% 2.80/1.32 % (1746100)lrs+10_1_sil=32000:urr=on:br=off:random_seed=220347857:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.80/1.32 % (1746089)Refutation found. Thanks to Tanya!
% 2.80/1.32 % SZS status Theorem for theBenchmark
% 2.80/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 4.10/1.52 % (1746089)------------------------------
% 4.10/1.52 % (1746089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.52 % (1746089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.52 % (1746089)CaDiCaL version: 2.1.3
% 4.10/1.52 % (1746089)Termination reason: Refutation
% 4.10/1.52 % (1746089)Time elapsed: 0.054 s
% 4.10/1.52 % (1746089)Peak memory usage: 89 MB
% 4.10/1.52 % (1746089)Instructions burned: 90 (million)
% 4.10/1.52 % (1746089)------------------------------
% 4.10/1.52 % (1746089)------------------------------
% 4.10/1.52 % (1746080)Success in time 0.488 s
% 4.10/1.52 % Vampire exiting
%------------------------------------------------------------------------------