%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC090+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 : n012.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 01:02:23 PM UTC 2026
% Result : Theorem 0.52s 0.79s
% Output : Refutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 109 ( 29 unt; 0 def)
% Number of atoms : 380 ( 80 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 476 ( 205 ~; 186 |; 53 &)
% ( 4 <=>; 28 =>; 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 : 131 ( 109 !; 22 ?)
% 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(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
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
| ~ neq(X1,nil)
| ? [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 ) ) ) ) ) ) ) ),
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
| ~ neq(X1,nil)
| ? [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 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ? [X5] :
( ? [X6] :
( app(X5,X6) = X3
& app(X6,X5) = X2
& ssList(X6) )
& ssList(X5) )
& 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)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ? [X5] :
( ? [X6] :
( app(X5,X6) = X3
& app(X6,X5) = X2
& ssList(X6) )
& ssList(X5) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f102,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(f104,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f104]) ).
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(f114,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f122,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(f130,plain,
( sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4) )
& sK3 = app(sK4,sK5)
& sK2 = app(sK5,sK4)
& ssList(sK5)
& ssList(sK4)
& ssList(sK3)
& 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)],[f99]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f111]) ).
fof(f136,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,[],[f122]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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))],[f137]) ).
fof(f143,plain,
ssList(sK2),
inference(cnf_transformation,[],[f130]) ).
fof(f144,plain,
ssList(sK3),
inference(cnf_transformation,[],[f130]) ).
fof(f145,plain,
ssList(sK4),
inference(cnf_transformation,[],[f130]) ).
fof(f146,plain,
ssList(sK5),
inference(cnf_transformation,[],[f130]) ).
fof(f147,plain,
sK2 = app(sK5,sK4),
inference(cnf_transformation,[],[f130]) ).
fof(f148,plain,
sK3 = app(sK4,sK5),
inference(cnf_transformation,[],[f130]) ).
fof(f149,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4) ),
inference(cnf_transformation,[],[f130]) ).
fof(f150,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f130]) ).
fof(f151,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f130]) ).
fof(f152,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f130]) ).
fof(f153,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f157,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f159,plain,
! [X2,X0,X1] :
( app(X1,X2) != app(X1,X0)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f161,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f163,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f165,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f168,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f171,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f179,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,[],[f138]) ).
fof(f191,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f150,f152]) ).
fof(f192,plain,
! [X4] :
( ~ segmentP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ segmentP(sK2,X4) ),
inference(definition_unfolding,[],[f149,f152,f151]) ).
fof(f200,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,[],[f179]) ).
fof(f204,plain,
( ~ ssList(sK3)
| ~ neq(nil,nil)
| ~ ssList(nil)
| ~ segmentP(sK2,nil) ),
inference(resolution,[],[f171,f192]) ).
fof(f205,plain,
( ~ neq(nil,nil)
| ~ ssList(nil)
| ~ segmentP(sK2,nil) ),
inference(forward_subsumption_resolution,[],[f204,f144]) ).
fof(f206,plain,
( ~ segmentP(sK2,nil)
| ~ neq(nil,nil) ),
inference(forward_subsumption_resolution,[],[f205,f168]) ).
fof(f207,plain,
( ~ neq(nil,nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f206,f171]) ).
fof(f208,plain,
~ neq(nil,nil),
inference(forward_subsumption_resolution,[],[f207,f143]) ).
fof(f296,plain,
! [X0] :
( sK3 != app(sK4,X0)
| sK5 = X0
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(sK5) ),
inference(superposition,[],[f159,f148]) ).
fof(f307,plain,
! [X0] :
( sK3 != app(sK4,X0)
| sK5 = X0
| ~ ssList(X0)
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f296,f145]) ).
fof(f315,plain,
! [X0] :
( sK3 != app(sK4,X0)
| sK5 = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f307,f146]) ).
fof(f364,plain,
! [X0,X1] :
( app(X0,X1) = app(nil,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f157,f161]) ).
fof(f383,plain,
! [X0,X1] :
( app(X0,X1) = app(nil,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f364]) ).
fof(f398,plain,
! [X0,X1] :
( app(X0,X1) = app(nil,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f383,f168]) ).
fof(f549,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(superposition,[],[f200,f161]) ).
fof(f550,plain,
! [X0] :
( segmentP(app(sK3,X0),sK5)
| ~ ssList(sK4)
| ~ ssList(X0)
| ~ ssList(sK5)
| ~ ssList(app(sK3,X0)) ),
inference(superposition,[],[f200,f148]) ).
fof(f551,plain,
! [X0] :
( segmentP(app(sK2,X0),sK4)
| ~ ssList(sK5)
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(app(sK2,X0)) ),
inference(superposition,[],[f200,f147]) ).
fof(f558,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f549]) ).
fof(f565,plain,
! [X0] :
( segmentP(app(sK2,X0),sK4)
| ~ ssList(X0)
| ~ ssList(sK4)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f551,f146]) ).
fof(f566,plain,
! [X0] :
( segmentP(app(sK3,X0),sK5)
| ~ ssList(X0)
| ~ ssList(sK5)
| ~ ssList(app(sK3,X0)) ),
inference(forward_subsumption_resolution,[],[f550,f145]) ).
fof(f567,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f558,f168]) ).
fof(f572,plain,
! [X0] :
( segmentP(app(sK2,X0),sK4)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f565,f145]) ).
fof(f573,plain,
! [X0] :
( segmentP(app(sK3,X0),sK5)
| ~ ssList(X0)
| ~ ssList(app(sK3,X0)) ),
inference(forward_subsumption_resolution,[],[f566,f146]) ).
fof(f574,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f567,f163]) ).
fof(f709,plain,
( segmentP(sK2,sK4)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(sK2) ),
inference(superposition,[],[f572,f153]) ).
fof(f710,plain,
( segmentP(sK2,sK4)
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(duplicate_literal_removal,[],[f709]) ).
fof(f712,plain,
( segmentP(sK2,sK4)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f710,f168]) ).
fof(f716,plain,
segmentP(sK2,sK4),
inference(forward_subsumption_resolution,[],[f712,f143]) ).
fof(f725,plain,
( segmentP(sK3,sK5)
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ ssList(sK3) ),
inference(superposition,[],[f573,f153]) ).
fof(f726,plain,
( segmentP(sK3,sK5)
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(duplicate_literal_removal,[],[f725]) ).
fof(f728,plain,
( segmentP(sK3,sK5)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f726,f168]) ).
fof(f731,plain,
segmentP(sK3,sK5),
inference(forward_subsumption_resolution,[],[f728,f144]) ).
fof(f733,plain,
( ~ neq(sK5,nil)
| ~ ssList(sK5)
| ~ segmentP(sK2,sK5) ),
inference(resolution,[],[f731,f192]) ).
fof(f736,plain,
( ~ segmentP(sK2,sK5)
| ~ neq(sK5,nil) ),
inference(forward_subsumption_resolution,[],[f733,f146]) ).
fof(f816,plain,
( segmentP(sK3,sK4)
| ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(superposition,[],[f574,f148]) ).
fof(f818,plain,
( segmentP(sK2,sK5)
| ~ ssList(sK4)
| ~ ssList(sK5) ),
inference(superposition,[],[f574,f147]) ).
fof(f827,plain,
( segmentP(sK2,sK5)
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f818,f145]) ).
fof(f829,plain,
( segmentP(sK3,sK4)
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f816,f146]) ).
fof(f835,plain,
segmentP(sK2,sK5),
inference(forward_subsumption_resolution,[],[f827,f146]) ).
fof(f836,plain,
segmentP(sK3,sK4),
inference(forward_subsumption_resolution,[],[f829,f145]) ).
fof(f838,plain,
~ neq(sK5,nil),
inference(resolution,[],[f835,f736]) ).
fof(f850,plain,
( ~ neq(sK4,nil)
| ~ ssList(sK4)
| ~ segmentP(sK2,sK4) ),
inference(resolution,[],[f836,f192]) ).
fof(f852,plain,
( ~ neq(sK4,nil)
| ~ segmentP(sK2,sK4) ),
inference(forward_subsumption_resolution,[],[f850,f145]) ).
fof(f854,plain,
~ neq(sK4,nil),
inference(forward_subsumption_resolution,[],[f852,f716]) ).
fof(f880,plain,
( nil = sK4
| ~ ssList(nil)
| ~ ssList(sK4) ),
inference(resolution,[],[f854,f165]) ).
fof(f881,plain,
( nil = sK4
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f880,f168]) ).
fof(f882,plain,
nil = sK4,
inference(forward_subsumption_resolution,[],[f881,f145]) ).
fof(f884,plain,
( nil = sK5
| ~ ssList(nil)
| ~ ssList(sK5) ),
inference(resolution,[],[f838,f165]) ).
fof(f885,plain,
( nil = sK5
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f884,f168]) ).
fof(f886,plain,
nil = sK5,
inference(forward_subsumption_resolution,[],[f885,f146]) ).
fof(f893,plain,
neq(sK3,sK4),
inference(superposition,[],[f191,f882]) ).
fof(f895,plain,
~ neq(sK4,sK4),
inference(superposition,[],[f208,f882]) ).
fof(f906,plain,
sK4 = sK5,
inference(forward_demodulation,[],[f886,f882]) ).
fof(f1150,plain,
! [X0,X1] :
( app(X0,X1) = app(sK4,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f398,f882]) ).
fof(f1197,plain,
( sK3 = app(sK4,sK3)
| ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(superposition,[],[f1150,f148]) ).
fof(f1241,plain,
( sK3 = app(sK4,sK3)
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f1197,f146]) ).
fof(f1264,plain,
sK3 = app(sK4,sK3),
inference(forward_subsumption_resolution,[],[f1241,f145]) ).
fof(f1278,plain,
( sK3 != sK3
| sK3 = sK5
| ~ ssList(sK3) ),
inference(superposition,[],[f315,f1264]) ).
fof(f1295,plain,
( sK3 = sK5
| ~ ssList(sK3) ),
inference(trivial_inequality_removal,[],[f1278]) ).
fof(f1300,plain,
sK3 = sK5,
inference(forward_subsumption_resolution,[],[f1295,f144]) ).
fof(f1307,plain,
sK3 = sK4,
inference(forward_demodulation,[],[f1300,f906]) ).
fof(f1330,plain,
neq(sK4,sK4),
inference(superposition,[],[f893,f1307]) ).
fof(f1337,plain,
$false,
inference(forward_subsumption_resolution,[],[f1330,f895]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC090+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Mon Sep 28 07:48:34 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.32 Running first-order theorem proving
% 0.05/0.32 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
% 0.52/0.79 % (3222532)Detected formulas, will run a generic FOF schedule.
% 0.52/0.79 % (3222541)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2752719073:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.52/0.79 % (3222537)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=2427434310:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.52/0.79 % (3222540)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1163336541:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.52/0.79 % (3222543)dis-21_1_sil=8000:lcm=predicate:random_seed=3978274512: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)
% 0.52/0.79 % (3222539)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=501539483:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.52/0.79 % (3222538)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=1493582229:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.52/0.79 % (3222542)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3115580314:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.52/0.79 % (3222541)First to succeed.
% 0.52/0.79 % (3222541)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3222532"
% 0.52/0.79 % (3222540)Instruction limit reached!
% 0.52/0.79 % (3222540)------------------------------
% 0.52/0.79 % (3222540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.52/0.79 % (3222540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.79 % (3222540)CaDiCaL version: 2.1.3
% 0.52/0.79 % (3222540)Termination reason: Instruction limit
% 0.52/0.79 % (3222540)Termination phase: Saturation
% 0.52/0.79 % (3222540)Time elapsed: 0.039 s
% 0.52/0.79 % (3222540)Peak memory usage: 89 MB
% 0.52/0.79 % (3222540)Instructions burned: 111 (million)
% 0.52/0.79 % (3222543)Instruction limit reached!
% 0.52/0.79 % (3222543)------------------------------
% 0.52/0.79 % (3222543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.52/0.79 % (3222543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.79 % (3222543)CaDiCaL version: 2.1.3
% 0.52/0.79 % (3222543)Termination reason: Instruction limit
% 0.52/0.79 % (3222543)Termination phase: Saturation
% 0.52/0.79 % (3222543)Time elapsed: 0.041 s
% 0.52/0.79 % (3222543)Peak memory usage: 90 MB
% 0.52/0.79 % (3222543)Instructions burned: 131 (million)
% 0.52/0.79 % (3222542)Also succeeded, but the first one will report.
% 0.52/0.79 % (3222552)lrs+10_1_sil=32000:urr=on:br=off:random_seed=652028799:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.52/0.79 % (3222551)lrs+10_1_sil=8000:sp=occurrence:random_seed=4217989096:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.52/0.79 % (3222541)Refutation found. Thanks to Tanya!
% 0.52/0.79 % SZS status Theorem for theBenchmark
% 0.52/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 2.10/0.89 % (3222541)------------------------------
% 2.10/0.89 % (3222541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.10/0.89 % (3222541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.89 % (3222541)CaDiCaL version: 2.1.3
% 2.10/0.89 % (3222541)Termination reason: Refutation
% 2.10/0.89 % (3222541)Time elapsed: 0.012 s
% 2.10/0.89 % (3222541)Peak memory usage: 88 MB
% 2.10/0.89 % (3222541)Instructions burned: 34 (million)
% 2.10/0.89 % (3222541)------------------------------
% 2.10/0.89 % (3222541)------------------------------
% 2.10/0.89 % (3222532)Success in time 0.275 s
% 2.10/0.89 % Vampire exiting
%------------------------------------------------------------------------------