%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC110+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 3.07s 1.60s
% Output : Refutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 10
% Syntax : Number of formulae : 99 ( 19 unt; 0 def)
% Number of atoms : 411 ( 160 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 530 ( 218 ~; 206 |; 73 &)
% ( 6 <=>; 27 =>; 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 : 140 ( 116 !; 24 ?)
% 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/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).
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/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [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)
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [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)
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) ) ) ) ) ) ),
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)
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) ) )
& 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)
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) ) )
& 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(f109,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(f111,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f111]) ).
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(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)
& ( ~ neq(sK0,nil)
| ~ segmentP(sK1,sK0) ) ) )
& 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(f151,plain,
( nil != sK0
| ~ neq(sK0,nil)
| ~ segmentP(sK1,sK0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f152,plain,
( nil != sK0
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f133]) ).
fof(f153,plain,
( nil = sK1
| ~ neq(sK0,nil)
| ~ segmentP(sK1,sK0) ),
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(f174,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f175,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f177,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f179,plain,
! [X2,X0,X1] :
( app(X1,X2) != app(X1,X0)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f112]) ).
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(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(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(f210,plain,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil)
| nil = sK3 ),
inference(definition_unfolding,[],[f153,f161,f160,f161,f160]) ).
fof(f211,plain,
( nil != sK2
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f152,f160,f161]) ).
fof(f212,plain,
( nil != sK2
| ~ neq(sK2,nil)
| ~ segmentP(sK3,sK2) ),
inference(definition_unfolding,[],[f151,f160,f160,f161,f160]) ).
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(f252,plain,
( nil != sK3
| nil = sK2
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f174,f159]) ).
fof(f255,plain,
( nil != sK3
| nil = sK2
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f252,f156]) ).
fof(f256,plain,
( nil != sK3
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f255,f149]) ).
fof(f257,plain,
( nil != sK3
| nil = sK4
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f175,f159]) ).
fof(f260,plain,
( nil != sK3
| nil = sK4
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f257,f156]) ).
fof(f261,plain,
( nil != sK3
| nil = sK4 ),
inference(forward_subsumption_resolution,[],[f260,f149]) ).
fof(f301,plain,
! [X0,X1] :
( app(X0,X1) != X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f179,f173]) ).
fof(f309,plain,
! [X0,X1] :
( app(X0,X1) != X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f301]) ).
fof(f315,plain,
! [X0,X1] :
( app(X0,X1) != X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f309,f188]) ).
fof(f355,plain,
! [X0] :
( app(sK2,app(sK4,X0)) = app(sK3,X0)
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f177,f159]) ).
fof(f390,plain,
! [X0] :
( app(sK2,app(sK4,X0)) = app(sK3,X0)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f355,f156]) ).
fof(f396,plain,
! [X0] :
( app(sK2,app(sK4,X0)) = app(sK3,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f390,f149]) ).
fof(f471,plain,
( app(sK2,sK4) = app(sK3,nil)
| ~ ssList(nil)
| ~ ssList(sK4) ),
inference(superposition,[],[f396,f173]) ).
fof(f489,plain,
( app(sK2,sK4) = app(sK3,nil)
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f471,f188]) ).
fof(f490,plain,
app(sK2,sK4) = app(sK3,nil),
inference(forward_subsumption_resolution,[],[f489,f156]) ).
fof(f491,plain,
sK3 = app(sK3,nil),
inference(forward_demodulation,[],[f490,f159]) ).
fof(f605,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(f616,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f605]) ).
fof(f626,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f616,f188]) ).
fof(f633,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f626,f183]) ).
fof(f718,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f633,f159]) ).
fof(f730,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f718,f156]) ).
fof(f735,plain,
segmentP(sK3,sK2),
inference(forward_subsumption_resolution,[],[f730,f149]) ).
fof(f736,plain,
( ~ neq(sK2,nil)
| nil = sK3 ),
inference(resolution,[],[f735,f210]) ).
fof(f744,plain,
( nil = sK3
| nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f736,f185]) ).
fof(f745,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f744,f155]) ).
fof(f747,plain,
( nil = sK3
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f745,f188]) ).
fof(f748,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f747,f149]) ).
fof(f768,plain,
( sK3 != sK3
| sK3 = sK4 ),
inference(superposition,[],[f261,f748]) ).
fof(f776,plain,
sK3 = sK4,
inference(trivial_inequality_removal,[],[f768]) ).
fof(f779,plain,
! [X0,X1] :
( sK3 = X1
| app(X0,X1) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f315,f748]) ).
fof(f810,plain,
! [X0,X1] :
( app(X0,X1) != X0
| sK4 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f779,f776]) ).
fof(f818,plain,
( sK3 != sK3
| nil = sK4
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(superposition,[],[f810,f491]) ).
fof(f820,plain,
( nil = sK4
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(trivial_inequality_removal,[],[f818]) ).
fof(f828,plain,
( nil = sK4
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f820,f188]) ).
fof(f836,plain,
nil = sK4,
inference(forward_subsumption_resolution,[],[f828,f150]) ).
fof(f856,plain,
( sK2 != sK4
| neq(sK3,sK4) ),
inference(superposition,[],[f211,f836]) ).
fof(f857,plain,
( sK2 != sK4
| ~ neq(sK2,sK4)
| ~ segmentP(sK3,sK2) ),
inference(superposition,[],[f212,f836]) ).
fof(f860,plain,
( sK3 != sK4
| sK2 = sK4 ),
inference(superposition,[],[f256,f836]) ).
fof(f873,plain,
sK2 = sK4,
inference(forward_subsumption_resolution,[],[f860,f776]) ).
fof(f874,plain,
( sK2 != sK4
| ~ neq(sK2,sK4) ),
inference(forward_subsumption_resolution,[],[f857,f735]) ).
fof(f875,plain,
( neq(sK4,sK4)
| sK2 != sK4 ),
inference(forward_demodulation,[],[f856,f776]) ).
fof(f1090,plain,
~ neq(sK2,sK4),
inference(forward_subsumption_resolution,[],[f874,f873]) ).
fof(f1091,plain,
~ neq(sK4,sK4),
inference(forward_demodulation,[],[f1090,f873]) ).
fof(f1098,plain,
sK2 != sK4,
inference(forward_subsumption_resolution,[],[f875,f1091]) ).
fof(f1099,plain,
$false,
inference(forward_subsumption_resolution,[],[f1098,f873]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC110+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 28 08:00:18 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.07/1.60 % (198405)Detected formulas, will run a generic FOF schedule.
% 3.07/1.60 % (198414)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1911880923:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.07/1.60 % (198410)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=3824393594:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.07/1.60 % (198414)First to succeed.
% 3.07/1.60 % (198414)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-198405"
% 3.07/1.60 % (198412)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=1829260945:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.07/1.60 % (198411)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=2101747840:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.07/1.60 % (198413)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=91757950:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.07/1.60 % (198416)dis-21_1_sil=8000:lcm=predicate:random_seed=781888587: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)
% 3.07/1.60 % (198415)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3261986900:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.07/1.60 % (198415)Also succeeded, but the first one will report.
% 3.07/1.60 % (198413)Instruction limit reached!
% 3.07/1.60 % (198413)------------------------------
% 3.07/1.60 % (198413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.60 % (198413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.60 % (198413)CaDiCaL version: 2.1.3
% 3.07/1.60 % (198413)Termination reason: Instruction limit
% 3.07/1.60 % (198413)Termination phase: Saturation
% 3.07/1.60 % (198413)Time elapsed: 0.111 s
% 3.07/1.60 % (198413)Peak memory usage: 89 MB
% 3.07/1.60 % (198413)Instructions burned: 110 (million)
% 3.07/1.60 % (198416)Instruction limit reached!
% 3.07/1.60 % (198416)------------------------------
% 3.07/1.60 % (198416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.60 % (198416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.60 % (198416)CaDiCaL version: 2.1.3
% 3.07/1.60 % (198416)Termination reason: Instruction limit
% 3.07/1.60 % (198416)Termination phase: Saturation
% 3.07/1.60 % (198416)Time elapsed: 0.120 s
% 3.07/1.60 % (198416)Peak memory usage: 90 MB
% 3.07/1.60 % (198416)Instructions burned: 129 (million)
% 3.07/1.60 % (198414)Refutation found. Thanks to Tanya!
% 3.07/1.60 % SZS status Theorem for theBenchmark
% 3.07/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 4.17/1.83 % (198414)------------------------------
% 4.17/1.83 % (198414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.83 % (198414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.83 % (198414)CaDiCaL version: 2.1.3
% 4.17/1.83 % (198414)Termination reason: Refutation
% 4.17/1.83 % (198414)Time elapsed: 0.017 s
% 4.17/1.83 % (198414)Peak memory usage: 88 MB
% 4.17/1.83 % (198414)Instructions burned: 31 (million)
% 4.17/1.83 % (198414)------------------------------
% 4.17/1.83 % (198414)------------------------------
% 4.17/1.83 % (198405)Success in time 0.46 s
% 4.17/1.83 % Vampire exiting
%------------------------------------------------------------------------------