%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC075+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:02:19 PM UTC 2026
% Result : Theorem 3.05s 1.36s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 118 ( 29 unt; 0 def)
% Number of atoms : 409 ( 118 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 523 ( 232 ~; 216 |; 44 &)
% ( 4 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 139 ( 123 !; 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(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(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(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox/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/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
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(X5,X6) != X3
| app(X6,X5) != X2 ) )
| ( nil = X1
& nil = X0 ) ) ) ) ),
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)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(X5,X6) != X3
| app(X6,X5) != X2 ) )
| ( nil = X1
& nil = X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ? [X5] :
( ? [X6] :
( ssList(X6)
& app(X5,X6) = X3
& app(X6,X5) = X2 )
& ssList(X5) )
& ( nil != X1
| nil != X0 ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f101,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(f103,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f121,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
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4) )
& ssList(sK5)
& sK3 = app(sK4,sK5)
& sK2 = app(sK5,sK4)
& ssList(sK4)
& ( nil != sK1
| nil != sK0 )
& 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(X5,sK4),skolemize(X6,sK5)],[f98]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f110]) ).
fof(f135,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,[],[f121]) ).
fof(f136,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,[],[f135]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK6(X0,X1))
& ssList(sK7(X0,X1))
& app(app(sK6(X0,X1),X1),sK7(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f136]) ).
fof(f142,plain,
ssList(sK2),
inference(cnf_transformation,[],[f129]) ).
fof(f143,plain,
( nil != sK1
| nil != sK0 ),
inference(cnf_transformation,[],[f129]) ).
fof(f144,plain,
ssList(sK4),
inference(cnf_transformation,[],[f129]) ).
fof(f145,plain,
sK2 = app(sK5,sK4),
inference(cnf_transformation,[],[f129]) ).
fof(f146,plain,
sK3 = app(sK4,sK5),
inference(cnf_transformation,[],[f129]) ).
fof(f147,plain,
ssList(sK5),
inference(cnf_transformation,[],[f129]) ).
fof(f148,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4) ),
inference(cnf_transformation,[],[f129]) ).
fof(f149,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f129]) ).
fof(f150,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f129]) ).
fof(f151,plain,
ssList(sK3),
inference(cnf_transformation,[],[f129]) ).
fof(f152,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f156,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f158,plain,
! [X2,X0,X1] :
( app(X1,X2) != app(X1,X0)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f159,plain,
! [X2,X0,X1] :
( app(X2,X1) != app(X0,X1)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f160,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f162,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f164,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f167,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f178,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,[],[f137]) ).
fof(f190,plain,
! [X4] :
( ~ segmentP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ segmentP(sK2,X4) ),
inference(definition_unfolding,[],[f148,f150,f149]) ).
fof(f191,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f143,f150,f149]) ).
fof(f199,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,[],[f178]) ).
fof(f294,plain,
! [X0] :
( sK3 != app(sK4,X0)
| sK5 = X0
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(sK5) ),
inference(superposition,[],[f158,f146]) ).
fof(f305,plain,
! [X0] :
( sK3 != app(sK4,X0)
| sK5 = X0
| ~ ssList(X0)
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f294,f144]) ).
fof(f313,plain,
! [X0] :
( sK3 != app(sK4,X0)
| sK5 = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f305,f147]) ).
fof(f331,plain,
! [X0] :
( sK2 != app(X0,sK4)
| sK5 = X0
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(sK5) ),
inference(superposition,[],[f159,f145]) ).
fof(f340,plain,
! [X0] :
( sK2 != app(X0,sK4)
| sK5 = X0
| ~ ssList(X0)
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f331,f144]) ).
fof(f348,plain,
! [X0] :
( sK2 != app(X0,sK4)
| sK5 = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f340,f147]) ).
fof(f355,plain,
! [X0,X1] :
( app(X0,X1) = app(nil,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f156,f160]) ).
fof(f357,plain,
! [X0] :
( app(sK5,app(sK4,X0)) = app(sK2,X0)
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(sK5) ),
inference(superposition,[],[f156,f145]) ).
fof(f374,plain,
! [X0,X1] :
( app(X0,X1) = app(nil,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f355]) ).
fof(f387,plain,
! [X0] :
( app(sK5,app(sK4,X0)) = app(sK2,X0)
| ~ ssList(X0)
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f357,f144]) ).
fof(f389,plain,
! [X0,X1] :
( app(X0,X1) = app(nil,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f374,f167]) ).
fof(f394,plain,
! [X0] :
( app(sK5,app(sK4,X0)) = app(sK2,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f387,f147]) ).
fof(f540,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(superposition,[],[f199,f160]) ).
fof(f541,plain,
! [X0] :
( segmentP(app(sK3,X0),sK5)
| ~ ssList(sK4)
| ~ ssList(X0)
| ~ ssList(sK5)
| ~ ssList(app(sK3,X0)) ),
inference(superposition,[],[f199,f146]) ).
fof(f542,plain,
! [X0] :
( segmentP(app(sK2,X0),sK4)
| ~ ssList(sK5)
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(app(sK2,X0)) ),
inference(superposition,[],[f199,f145]) ).
fof(f549,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f540]) ).
fof(f556,plain,
! [X0] :
( segmentP(app(sK2,X0),sK4)
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f542,f147]) ).
fof(f557,plain,
! [X0] :
( segmentP(app(sK3,X0),sK5)
| ~ ssList(X0)
| ~ ssList(sK5)
| ~ ssList(app(sK3,X0)) ),
inference(forward_subsumption_resolution,[],[f541,f144]) ).
fof(f558,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f549,f167]) ).
fof(f563,plain,
! [X0] :
( segmentP(app(sK2,X0),sK4)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f556,f144]) ).
fof(f564,plain,
! [X0] :
( segmentP(app(sK3,X0),sK5)
| ~ ssList(X0)
| ~ ssList(app(sK3,X0)) ),
inference(forward_subsumption_resolution,[],[f557,f147]) ).
fof(f565,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f558,f162]) ).
fof(f568,plain,
( app(sK5,sK4) = app(sK2,nil)
| ~ ssList(nil)
| ~ ssList(sK4) ),
inference(superposition,[],[f394,f152]) ).
fof(f590,plain,
( app(sK5,sK4) = app(sK2,nil)
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f568,f167]) ).
fof(f592,plain,
app(sK5,sK4) = app(sK2,nil),
inference(forward_subsumption_resolution,[],[f590,f144]) ).
fof(f593,plain,
sK2 = app(sK2,nil),
inference(forward_demodulation,[],[f592,f145]) ).
fof(f646,plain,
( segmentP(sK2,sK4)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(sK2) ),
inference(superposition,[],[f563,f152]) ).
fof(f647,plain,
( segmentP(sK2,sK4)
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(duplicate_literal_removal,[],[f646]) ).
fof(f649,plain,
( segmentP(sK2,sK4)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f647,f167]) ).
fof(f652,plain,
segmentP(sK2,sK4),
inference(forward_subsumption_resolution,[],[f649,f142]) ).
fof(f660,plain,
( segmentP(sK3,sK5)
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ ssList(sK3) ),
inference(superposition,[],[f564,f152]) ).
fof(f661,plain,
( segmentP(sK3,sK5)
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(duplicate_literal_removal,[],[f660]) ).
fof(f663,plain,
( segmentP(sK3,sK5)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f661,f167]) ).
fof(f665,plain,
segmentP(sK3,sK5),
inference(forward_subsumption_resolution,[],[f663,f151]) ).
fof(f666,plain,
( ~ neq(sK5,nil)
| ~ ssList(sK5)
| ~ segmentP(sK2,sK5) ),
inference(resolution,[],[f665,f190]) ).
fof(f669,plain,
( ~ segmentP(sK2,sK5)
| ~ neq(sK5,nil) ),
inference(forward_subsumption_resolution,[],[f666,f147]) ).
fof(f805,plain,
( segmentP(sK3,sK4)
| ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(superposition,[],[f565,f146]) ).
fof(f807,plain,
( segmentP(sK2,sK5)
| ~ ssList(sK4)
| ~ ssList(sK5) ),
inference(superposition,[],[f565,f145]) ).
fof(f816,plain,
( segmentP(sK2,sK5)
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f807,f144]) ).
fof(f818,plain,
( segmentP(sK3,sK4)
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f805,f147]) ).
fof(f824,plain,
segmentP(sK2,sK5),
inference(forward_subsumption_resolution,[],[f816,f147]) ).
fof(f825,plain,
segmentP(sK3,sK4),
inference(forward_subsumption_resolution,[],[f818,f144]) ).
fof(f827,plain,
~ neq(sK5,nil),
inference(resolution,[],[f824,f669]) ).
fof(f834,plain,
( ~ neq(sK4,nil)
| ~ ssList(sK4)
| ~ segmentP(sK2,sK4) ),
inference(resolution,[],[f825,f190]) ).
fof(f837,plain,
( ~ neq(sK4,nil)
| ~ segmentP(sK2,sK4) ),
inference(forward_subsumption_resolution,[],[f834,f144]) ).
fof(f840,plain,
~ neq(sK4,nil),
inference(forward_subsumption_resolution,[],[f837,f652]) ).
fof(f847,plain,
( nil = sK4
| ~ ssList(nil)
| ~ ssList(sK4) ),
inference(resolution,[],[f840,f164]) ).
fof(f848,plain,
( nil = sK4
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f847,f167]) ).
fof(f849,plain,
nil = sK4,
inference(forward_subsumption_resolution,[],[f848,f144]) ).
fof(f872,plain,
( nil = sK5
| ~ ssList(nil)
| ~ ssList(sK5) ),
inference(resolution,[],[f827,f164]) ).
fof(f873,plain,
( nil = sK5
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f872,f167]) ).
fof(f874,plain,
nil = sK5,
inference(forward_subsumption_resolution,[],[f873,f147]) ).
fof(f881,plain,
( sK3 != sK4
| sK2 != sK4 ),
inference(superposition,[],[f191,f849]) ).
fof(f888,plain,
sK2 = app(sK2,sK4),
inference(superposition,[],[f593,f849]) ).
fof(f893,plain,
sK4 = sK5,
inference(forward_demodulation,[],[f874,f849]) ).
fof(f1071,plain,
( sK2 != sK2
| sK2 = sK5
| ~ ssList(sK2) ),
inference(superposition,[],[f348,f888]) ).
fof(f1089,plain,
( sK2 = sK5
| ~ ssList(sK2) ),
inference(trivial_inequality_removal,[],[f1071]) ).
fof(f1093,plain,
sK2 = sK5,
inference(forward_subsumption_resolution,[],[f1089,f142]) ).
fof(f1098,plain,
sK2 = sK4,
inference(forward_demodulation,[],[f1093,f893]) ).
fof(f1141,plain,
! [X0,X1] :
( app(X0,X1) = app(sK4,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f389,f849]) ).
fof(f1187,plain,
( sK3 = app(sK4,sK3)
| ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(superposition,[],[f1141,f146]) ).
fof(f1231,plain,
( sK3 = app(sK4,sK3)
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f1187,f147]) ).
fof(f1254,plain,
sK3 = app(sK4,sK3),
inference(forward_subsumption_resolution,[],[f1231,f144]) ).
fof(f1269,plain,
( sK3 != sK3
| sK3 = sK5
| ~ ssList(sK3) ),
inference(superposition,[],[f313,f1254]) ).
fof(f1286,plain,
( sK3 = sK5
| ~ ssList(sK3) ),
inference(trivial_inequality_removal,[],[f1269]) ).
fof(f1291,plain,
sK3 = sK5,
inference(forward_subsumption_resolution,[],[f1286,f151]) ).
fof(f1298,plain,
sK3 = sK4,
inference(forward_demodulation,[],[f1291,f893]) ).
fof(f2098,plain,
sK2 != sK4,
inference(forward_subsumption_resolution,[],[f881,f1298]) ).
fof(f2099,plain,
$false,
inference(forward_subsumption_resolution,[],[f2098,f1098]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC075+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n006.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 07:43:55 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 3.05/1.36 % (3806612)Detected formulas, will run a generic FOF schedule.
% 3.05/1.36 % (3806617)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=3063016431:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.05/1.36 % (3806620)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3983388728:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.05/1.36 % (3806622)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4273825174:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.05/1.36 % (3806623)dis-21_1_sil=8000:lcm=predicate:random_seed=2913081740: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)
% 3.05/1.36 % (3806621)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3832862730:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.05/1.36 % (3806618)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=3702470293:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.05/1.36 % (3806619)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=3704126917:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.05/1.36 % (3806621)First to succeed.
% 3.05/1.36 % (3806621)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3806612"
% 3.05/1.36 % (3806622)Also succeeded, but the first one will report.
% 3.05/1.36 % (3806620)Instruction limit reached!
% 3.05/1.36 % (3806620)------------------------------
% 3.05/1.36 % (3806620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.36 % (3806620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.36 % (3806620)CaDiCaL version: 2.1.3
% 3.05/1.36 % (3806620)Termination reason: Instruction limit
% 3.05/1.36 % (3806620)Termination phase: Saturation
% 3.05/1.36 % (3806620)Time elapsed: 0.069 s
% 3.05/1.36 % (3806620)Peak memory usage: 89 MB
% 3.05/1.36 % (3806620)Instructions burned: 109 (million)
% 3.05/1.36 % (3806623)Instruction limit reached!
% 3.05/1.36 % (3806623)------------------------------
% 3.05/1.36 % (3806623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.36 % (3806623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.36 % (3806623)CaDiCaL version: 2.1.3
% 3.05/1.36 % (3806623)Termination reason: Instruction limit
% 3.05/1.36 % (3806623)Termination phase: Saturation
% 3.05/1.36 % (3806623)Time elapsed: 0.079 s
% 3.05/1.36 % (3806623)Peak memory usage: 90 MB
% 3.05/1.36 % (3806623)Instructions burned: 134 (million)
% 3.05/1.36 % (3806631)lrs+10_1_sil=8000:sp=occurrence:random_seed=1387418143:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.05/1.36 % (3806632)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3030045522:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.05/1.36 % (3806621)Refutation found. Thanks to Tanya!
% 3.05/1.36 % SZS status Theorem for theBenchmark
% 3.05/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.46 % (3806621)------------------------------
% 3.84/1.46 % (3806621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.46 % (3806621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.46 % (3806621)CaDiCaL version: 2.1.3
% 3.84/1.46 % (3806621)Termination reason: Refutation
% 3.84/1.46 % (3806621)Time elapsed: 0.033 s
% 3.84/1.46 % (3806621)Peak memory usage: 88 MB
% 3.84/1.46 % (3806621)Instructions burned: 54 (million)
% 3.84/1.46 % (3806621)------------------------------
% 3.84/1.46 % (3806621)------------------------------
% 3.84/1.46 % (3806612)Success in time 0.481 s
% 3.84/1.46 % Vampire exiting
%------------------------------------------------------------------------------