%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC120+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 : 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 01:02:32 PM UTC 2026
% Result : Theorem 2.93s 1.32s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 12
% Syntax : Number of formulae : 115 ( 14 unt; 0 def)
% Number of atoms : 466 ( 112 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 620 ( 269 ~; 263 |; 56 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 130 ( 110 !; 20 ?)
% 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(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
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(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X0,X1)
& segmentP(X1,X2) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X3 != X4
& ? [X5] :
( ssList(X5)
& tl(X3) = X5
& app(X2,X5) = X4
& neq(nil,X3) ) )
| ( neq(X0,nil)
& segmentP(X1,X0) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X3 != X4
& ? [X5] :
( ssList(X5)
& tl(X3) = X5
& app(X2,X5) = X4
& neq(nil,X3) ) )
| ( neq(X0,nil)
& segmentP(X1,X0) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X3 = X4
| ! [X5] :
( ~ ssList(X5)
| tl(X3) != X5
| app(X2,X5) != X4
| ~ neq(nil,X3) ) )
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) )
| ( neq(X1,nil)
& ~ 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)
& ! [X4] :
( ~ ssList(X4)
| X3 = X4
| ! [X5] :
( ~ ssList(X5)
| tl(X3) != X5
| app(X2,X5) != X4
| ~ neq(nil,X3) ) )
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f108,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f115,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f116,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f115]) ).
fof(f122,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f123,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f122]) ).
fof(f125,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f131]) ).
fof(f133,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(f139,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f146,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f147,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f146]) ).
fof(f148,plain,
( sK1 = sK3
& sK0 = sK2
& ( ( neq(sK1,nil)
& ! [X4] :
( ~ ssList(X4)
| sK3 = X4
| ! [X5] :
( ~ ssList(X5)
| tl(sK3) != X5
| app(sK2,X5) != X4
| ~ neq(nil,sK3) ) )
& ( ~ neq(sK0,nil)
| ~ segmentP(sK1,sK0) ) )
| ( neq(sK1,nil)
& ~ neq(sK3,nil) ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f111]) ).
fof(f155,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,[],[f133]) ).
fof(f156,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,[],[f155]) ).
fof(f157,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK5(X0,X1))
& ssList(sK6(X0,X1))
& app(app(sK5(X0,X1),X1),sK6(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X4,sK5(X0,X1)),skolemize(X5,sK6(X0,X1))],[f156]) ).
fof(f163,plain,
ssList(sK2),
inference(cnf_transformation,[],[f148]) ).
fof(f164,plain,
ssList(sK3),
inference(cnf_transformation,[],[f148]) ).
fof(f165,plain,
( ~ neq(sK0,nil)
| ~ segmentP(sK1,sK0)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f148]) ).
fof(f167,plain,
! [X4,X5] :
( ~ ssList(X4)
| sK3 = X4
| ~ ssList(X5)
| tl(sK3) != X5
| app(sK2,X5) != X4
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f148]) ).
fof(f170,plain,
( neq(sK1,nil)
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f148]) ).
fof(f171,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f148]) ).
fof(f172,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f148]) ).
fof(f181,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f183,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f184,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f185,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f188,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f190,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f195,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f198,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f202,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f206,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,[],[f157]) ).
fof(f213,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f222,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f223,plain,
( neq(sK3,nil)
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f170,f172,f172]) ).
fof(f227,plain,
( ~ neq(sK2,nil)
| ~ segmentP(sK3,sK2)
| ~ neq(sK3,nil) ),
inference(definition_unfolding,[],[f165,f171,f172,f171]) ).
fof(f232,plain,
! [X4] :
( ~ ssList(X4)
| sK3 = X4
| ~ ssList(tl(sK3))
| app(sK2,tl(sK3)) != X4
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(equality_resolution,[],[f167]) ).
fof(f233,plain,
( ~ ssList(app(sK2,tl(sK3)))
| sK3 = app(sK2,tl(sK3))
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(equality_resolution,[],[f232]) ).
fof(f236,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f184]) ).
fof(f239,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,[],[f206]) ).
fof(f241,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f236]) ).
fof(f243,plain,
neq(sK3,nil),
inference(duplicate_literal_removal,[],[f223]) ).
fof(f244,plain,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(forward_subsumption_resolution,[],[f227,f243]) ).
fof(f245,plain,
( sK3 = app(sK2,tl(sK3))
| ~ ssList(app(sK2,tl(sK3)))
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3) ),
inference(forward_subsumption_resolution,[],[f233,f243]) ).
fof(f305,plain,
! [X0] :
( tl(X0) != X0
| ~ ssItem(hd(X0))
| ~ ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f213,f190]) ).
fof(f311,plain,
! [X0] :
( tl(X0) != X0
| ~ ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f305,f222]) ).
fof(f314,plain,
! [X0] :
( tl(X0) != X0
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f311,f195]) ).
fof(f422,plain,
! [X0] :
( ~ segmentP(sK3,X0)
| ~ segmentP(X0,sK2)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(sK3)
| ~ neq(sK2,nil) ),
inference(resolution,[],[f202,f244]) ).
fof(f428,plain,
! [X0] :
( ~ segmentP(sK3,X0)
| ~ segmentP(X0,sK2)
| ~ ssList(X0)
| ~ ssList(sK3)
| ~ neq(sK2,nil) ),
inference(forward_subsumption_resolution,[],[f422,f163]) ).
fof(f429,plain,
! [X0] :
( ~ segmentP(sK3,X0)
| ~ segmentP(X0,sK2)
| ~ ssList(X0)
| ~ neq(sK2,nil) ),
inference(forward_subsumption_resolution,[],[f428,f164]) ).
fof(f430,plain,
( ~ segmentP(nil,sK2)
| ~ ssList(nil)
| ~ neq(sK2,nil)
| ~ ssList(sK3) ),
inference(resolution,[],[f429,f198]) ).
fof(f436,plain,
( ~ segmentP(nil,sK2)
| ~ neq(sK2,nil)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f430,f188]) ).
fof(f437,plain,
( ~ segmentP(nil,sK2)
| ~ neq(sK2,nil) ),
inference(forward_subsumption_resolution,[],[f436,f164]) ).
fof(f815,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(superposition,[],[f239,f181]) ).
fof(f828,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f815]) ).
fof(f839,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f828,f188]) ).
fof(f844,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f839,f183]) ).
fof(f1041,plain,
( segmentP(sK3,sK2)
| ~ ssList(tl(sK3))
| ~ ssList(sK2)
| ~ ssList(app(sK2,tl(sK3)))
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3) ),
inference(superposition,[],[f844,f245]) ).
fof(f1044,plain,
( segmentP(sK3,sK2)
| ~ ssList(tl(sK3))
| ~ ssList(sK2)
| ~ ssList(app(sK2,tl(sK3)))
| ~ neq(nil,sK3) ),
inference(duplicate_literal_removal,[],[f1041]) ).
fof(f1054,plain,
( ~ ssList(app(sK2,tl(sK3)))
| ~ ssList(tl(sK3))
| segmentP(sK3,sK2)
| ~ neq(nil,sK3) ),
inference(forward_subsumption_resolution,[],[f1044,f163]) ).
fof(f1062,plain,
( ~ ssList(tl(sK3))
| segmentP(sK3,sK2)
| ~ neq(nil,sK3)
| ~ ssList(tl(sK3))
| ~ ssList(sK2) ),
inference(resolution,[],[f1054,f183]) ).
fof(f1067,plain,
( ~ ssList(tl(sK3))
| segmentP(sK3,sK2)
| ~ neq(nil,sK3)
| ~ ssList(sK2) ),
inference(duplicate_literal_removal,[],[f1062]) ).
fof(f1070,plain,
( segmentP(sK3,sK2)
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3) ),
inference(forward_subsumption_resolution,[],[f1067,f163]) ).
fof(f1115,plain,
( ~ ssList(tl(sK3))
| ~ neq(nil,sK3)
| ~ neq(sK2,nil) ),
inference(resolution,[],[f1070,f244]) ).
fof(f1122,plain,
( ~ neq(nil,sK3)
| ~ neq(sK2,nil)
| nil = sK3
| ~ ssList(sK3) ),
inference(resolution,[],[f1115,f195]) ).
fof(f1127,plain,
( ~ neq(sK2,nil)
| ~ neq(nil,sK3)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f1122,f164]) ).
fof(f1181,plain,
( ~ neq(nil,sK3)
| nil = sK3
| nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f1127,f185]) ).
fof(f1182,plain,
( ~ neq(nil,sK3)
| nil = sK3
| nil = sK2
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f1181,f188]) ).
fof(f1183,plain,
( ~ neq(nil,sK3)
| nil = sK3
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f1182,f163]) ).
fof(f1209,plain,
( nil = sK3
| nil = sK2
| nil = sK3
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(resolution,[],[f1183,f185]) ).
fof(f1210,plain,
( nil = sK3
| nil = sK2
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f1209]) ).
fof(f1212,plain,
( nil = sK3
| nil = sK2
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f1210,f164]) ).
fof(f1213,plain,
( nil = sK3
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f1212,f188]) ).
fof(f1220,plain,
( neq(sK3,sK3)
| nil = sK2 ),
inference(superposition,[],[f243,f1213]) ).
fof(f1229,plain,
( nil = sK2
| ~ ssList(sK3) ),
inference(resolution,[],[f1220,f241]) ).
fof(f1231,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f1229,f164]) ).
fof(f1259,plain,
! [X0] :
( app(sK2,X0) = X0
| ~ ssList(X0) ),
inference(superposition,[],[f181,f1231]) ).
fof(f1262,plain,
! [X0] :
( segmentP(X0,sK2)
| ~ ssList(X0) ),
inference(superposition,[],[f198,f1231]) ).
fof(f1263,plain,
neq(sK3,sK2),
inference(superposition,[],[f243,f1231]) ).
fof(f1290,plain,
( ~ ssList(nil)
| ~ neq(sK2,nil) ),
inference(resolution,[],[f1262,f437]) ).
fof(f1297,plain,
~ neq(sK2,nil),
inference(forward_subsumption_resolution,[],[f1290,f188]) ).
fof(f1301,plain,
~ neq(sK2,sK2),
inference(forward_demodulation,[],[f1297,f1231]) ).
fof(f1443,plain,
( sK3 = tl(sK3)
| ~ ssList(tl(sK3))
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3)
| ~ ssList(tl(sK3)) ),
inference(superposition,[],[f245,f1259]) ).
fof(f1482,plain,
( sK3 = tl(sK3)
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3) ),
inference(duplicate_literal_removal,[],[f1443]) ).
fof(f1496,plain,
( sK3 = tl(sK3)
| ~ neq(sK2,sK3)
| ~ ssList(tl(sK3)) ),
inference(forward_demodulation,[],[f1482,f1231]) ).
fof(f1778,plain,
( sK3 != sK3
| nil = sK3
| ~ ssList(sK3)
| ~ neq(sK2,sK3)
| ~ ssList(tl(sK3)) ),
inference(superposition,[],[f314,f1496]) ).
fof(f1781,plain,
( nil = sK3
| ~ ssList(sK3)
| ~ neq(sK2,sK3)
| ~ ssList(tl(sK3)) ),
inference(trivial_inequality_removal,[],[f1778]) ).
fof(f1783,plain,
( nil = sK3
| ~ ssList(sK3)
| ~ neq(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f1781,f195]) ).
fof(f1794,plain,
( nil = sK3
| ~ neq(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f1783,f164]) ).
fof(f1806,plain,
( ~ neq(sK2,sK3)
| sK2 = sK3 ),
inference(forward_demodulation,[],[f1794,f1231]) ).
fof(f1823,plain,
( sK2 = sK3
| sK2 = sK3
| ~ ssList(sK3)
| ~ ssList(sK2) ),
inference(resolution,[],[f1806,f185]) ).
fof(f1824,plain,
( sK2 = sK3
| ~ ssList(sK3)
| ~ ssList(sK2) ),
inference(duplicate_literal_removal,[],[f1823]) ).
fof(f1826,plain,
( sK2 = sK3
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f1824,f164]) ).
fof(f1827,plain,
sK2 = sK3,
inference(forward_subsumption_resolution,[],[f1826,f163]) ).
fof(f1850,plain,
neq(sK2,sK2),
inference(superposition,[],[f1263,f1827]) ).
fof(f1858,plain,
$false,
inference(forward_subsumption_resolution,[],[f1850,f1301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC120+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n006.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 07:59:10 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 2.93/1.32 % (3811586)Detected formulas, will run a generic FOF schedule.
% 2.93/1.32 % (3811594)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=404518381:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.93/1.32 % (3811594)Instruction limit reached!
% 2.93/1.32 % (3811594)------------------------------
% 2.93/1.32 % (3811594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.32 % (3811594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.32 % (3811594)CaDiCaL version: 2.1.3
% 2.93/1.32 % (3811594)Termination reason: Instruction limit
% 2.93/1.32 % (3811594)Termination phase: Saturation
% 2.93/1.32 % (3811594)Time elapsed: 0.037 s
% 2.93/1.32 % (3811594)Peak memory usage: 89 MB
% 2.93/1.32 % (3811594)Instructions burned: 109 (million)
% 2.93/1.32 % (3811597)dis-21_1_sil=8000:lcm=predicate:random_seed=1894828020: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)
% 2.93/1.32 % (3811593)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=393209835:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.93/1.32 % (3811591)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=564800208:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.93/1.32 % (3811596)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3164562918:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.93/1.32 % (3811592)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=1935631929:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.93/1.32 % (3811595)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2311475774:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.93/1.32 % (3811595)First to succeed.
% 2.93/1.32 % (3811595)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3811586"
% 2.93/1.32 % (3811596)Also succeeded, but the first one will report.
% 2.93/1.32 % (3811597)Instruction limit reached!
% 2.93/1.32 % (3811597)------------------------------
% 2.93/1.32 % (3811597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.32 % (3811597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.32 % (3811597)CaDiCaL version: 2.1.3
% 2.93/1.32 % (3811597)Termination reason: Instruction limit
% 2.93/1.32 % (3811597)Termination phase: Saturation
% 2.93/1.32 % (3811597)Time elapsed: 0.076 s
% 2.93/1.32 % (3811597)Peak memory usage: 90 MB
% 2.93/1.32 % (3811597)Instructions burned: 130 (million)
% 2.93/1.32 % (3811603)lrs+10_1_sil=8000:sp=occurrence:random_seed=58003888:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.93/1.32 % (3811603)Instruction limit reached!
% 2.93/1.32 % (3811603)------------------------------
% 2.93/1.32 % (3811603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.32 % (3811603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.32 % (3811603)CaDiCaL version: 2.1.3
% 2.93/1.32 % (3811603)Termination reason: Instruction limit
% 2.93/1.32 % (3811603)Termination phase: Saturation
% 2.93/1.32 % (3811603)Time elapsed: 0.091 s
% 2.93/1.32 % (3811603)Peak memory usage: 93 MB
% 2.93/1.32 % (3811603)Instructions burned: 287 (million)
% 2.93/1.32 % (3811606)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4177399717:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.93/1.32 % (3811595)Refutation found. Thanks to Tanya!
% 2.93/1.32 % SZS status Theorem for theBenchmark
% 2.93/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.95/1.54 % (3811595)------------------------------
% 3.95/1.54 % (3811595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.54 % (3811595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.54 % (3811595)CaDiCaL version: 2.1.3
% 3.95/1.54 % (3811595)Termination reason: Refutation
% 3.95/1.54 % (3811595)Time elapsed: 0.035 s
% 3.95/1.54 % (3811595)Peak memory usage: 89 MB
% 3.95/1.54 % (3811595)Instructions burned: 59 (million)
% 3.95/1.54 % (3811595)------------------------------
% 3.95/1.54 % (3811595)------------------------------
% 3.95/1.54 % (3811586)Success in time 0.47 s
% 3.95/1.54 % Vampire exiting
%------------------------------------------------------------------------------