%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC015+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 : Fri Sep 25 03:07:31 PM UTC 2026
% Result : Theorem 10.23s 2.79s
% Output : CNFRefutation 10.23s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f213ERROR: Could not build tree for root c_24502ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X1
& cons(X6,nil) = X0
& ssList(X7) )
& ssItem(X6) )
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& app(X2,X5) = X4
& tl(X3) = X5
& ssList(X5) )
& X3 != X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X1
& cons(X6,nil) = X0
& ssList(X7) )
& ssItem(X6) )
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& app(X2,X5) = X4
& tl(X3) = X5
& ssList(X5) )
& X3 != X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X1
| cons(X6,nil) != X0
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| app(X2,X5) != X4
| tl(X3) != X5
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X1
| cons(X6,nil) != X0
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| app(X2,X5) != X4
| tl(X3) != X5
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f114,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X2 = X0 ) ) ),
inference(ennf_transformation,[],[f79]) ).
fof(f115,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X2 = X0 ) ) ),
inference(flattening,[],[f114]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f122,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f122]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(flattening,[],[f129]) ).
fof(f133,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f133]) ).
fof(f136,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f137,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f136]) ).
fof(f138,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( ~ neq(sK3,nil)
& neq(sK1,nil) )
| ( ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != sK1
| cons(X6,nil) != sK0
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X4] :
( ! [X5] :
( ~ neq(nil,sK3)
| app(sK2,X5) != X4
| tl(sK3) != X5
| ~ ssList(X5) )
| sK3 = X4
| ~ ssList(X4) )
& neq(sK1,nil) ) )
& sK0 = sK2
& sK1 = sK3 ),
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(f143,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f145,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK8(X0)
& ssList(sK8(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f127]) ).
fof(f146,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK9(X0)
& ssItem(sK9(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f134]) ).
fof(f147,plain,
ssList(sK0),
inference(cnf_transformation,[],[f138]) ).
fof(f148,plain,
ssList(sK1),
inference(cnf_transformation,[],[f138]) ).
fof(f151,plain,
! [X6,X7] :
( ~ neq(sK3,nil)
| app(cons(X6,nil),X7) != sK1
| cons(X6,nil) != sK0
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f138]) ).
fof(f152,plain,
! [X6,X7] :
( neq(sK1,nil)
| app(cons(X6,nil),X7) != sK1
| cons(X6,nil) != sK0
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f138]) ).
fof(f153,plain,
! [X4,X5] :
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| app(sK2,X5) != X4
| tl(sK3) != X5
| ~ ssList(X5)
| sK3 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f138]) ).
fof(f157,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f138]) ).
fof(f158,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f138]) ).
fof(f162,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f171,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f178,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f115]) ).
fof(f180,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f182,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f185,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f187,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f123]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK8(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f190,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK8(X0)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f194,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK9(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f195,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK9(X0)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f197,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f201,plain,
! [X6,X7] :
( neq(sK3,nil)
| app(cons(X6,nil),X7) != sK3
| cons(X6,nil) != sK2
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(definition_unfolding,[],[f152,f157,f158,f158]) ).
fof(f202,plain,
! [X6,X7] :
( ~ neq(sK3,nil)
| app(cons(X6,nil),X7) != sK3
| cons(X6,nil) != sK2
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(definition_unfolding,[],[f151,f157,f158]) ).
fof(f203,plain,
ssList(sK3),
inference(definition_unfolding,[],[f148,f158]) ).
fof(f204,plain,
ssList(sK2),
inference(definition_unfolding,[],[f147,f157]) ).
fof(f207,plain,
! [X4] :
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| app(sK2,tl(sK3)) != X4
| ~ ssList(tl(sK3))
| sK3 = X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f153]) ).
fof(f208,plain,
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| ~ ssList(tl(sK3))
| sK3 = app(sK2,tl(sK3))
| ~ ssList(app(sK2,tl(sK3))) ),
inference(equality_resolution,[],[f207]) ).
tcf(c_49,negated_conjecture,
neq(sK3,nil),
inference(cnf_transformation,[],[f213]) ).
tcf(c_51,negated_conjecture,
( ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3)
| ~ neq(sK3,nil)
| ~ ssList(app(sK2,tl(sK3))) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( neq(sK3,nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,nil) != sK2 )
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ neq(sK3,nil)
| ( cons(X0,nil) != sK2 )
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_56,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f203]) ).
tcf(c_57,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f204]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X2,X1) ) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_81,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_84,plain,
ssList(nil),
inference(cnf_transformation,[],[f185]) ).
tcf(c_86,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_88,plain,
! [X0: $i] :
( ssList(sK8(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_89,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK8(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_91,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_93,plain,
! [X0: $i] :
( ssItem(sK9(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_94,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK9(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_96,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_131,negated_conjecture,
neq(sK3,nil),
inference(global_subsumption_just,[status(thm)],[c_52,c_49]) ).
tcf(c_133,negated_conjecture,
( ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3)
| ~ ssList(app(sK2,tl(sK3))) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_49,c_51]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( app(cons(X0,nil),X1) != sK3 )
| ( cons(X0,nil) != sK2 ) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_49,c_53]) ).
tcf(c_136,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,nil) != sK2 )
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(renaming,[status(thm)],[c_135]) ).
tcf(c_695,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_131,c_81]) ).
tcf(c_696,plain,
( ~ ssList(sK3)
| ( sK3 != nil ) ),
inference(unflattening,[status(thm)],[c_695]) ).
tcf(c_697,plain,
sK3 != nil,
inference(global_subsumption_just,[status(thm)],[c_696,c_56,c_696]) ).
tcf(c_721,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(tl(sK3))
| ~ ssList(app(sK2,tl(sK3)))
| ( X1 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_133,c_80]) ).
tcf(c_722,plain,
( ( sK3 = nil )
| ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ ssList(tl(sK3))
| ~ ssList(app(sK2,tl(sK3))) ),
inference(unflattening,[status(thm)],[c_721]) ).
tcf(c_723,plain,
( ~ ssList(app(sK2,tl(sK3)))
| ~ ssList(tl(sK3))
| ( app(sK2,tl(sK3)) = sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_722,c_56,c_84,c_696,c_722]) ).
tcf(c_724,plain,
( ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(tl(sK3))
| ~ ssList(app(sK2,tl(sK3))) ),
inference(renaming,[status(thm)],[c_723]) ).
tcf(c_1888,plain,
( ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(sK2)
| ~ ssList(tl(sK3)) ),
inference(superposition,[status(thm)],[c_79,c_724]) ).
tcf(c_1891,plain,
( ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(tl(sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1888,c_57]) ).
tcf(c_1926,plain,
( ( sK3 = nil )
| ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_91,c_1891]) ).
tcf(c_1929,plain,
app(sK2,tl(sK3)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_1926,c_697,c_56]) ).
tcf(c_2005,plain,
( ( sK3 = nil )
| ( tl(sK3) = sK8(sK3) ) ),
inference(superposition,[status(thm)],[c_56,c_89]) ).
tcf(c_2015,plain,
tl(sK3) = sK8(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2005,c_697]) ).
tcf(c_2037,plain,
( ssList(tl(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_2015,c_88]) ).
tcf(c_2038,plain,
ssList(tl(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2037,c_697,c_56]) ).
tcf(c_2190,plain,
( ssItem(hd(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_2198,plain,
( ( sK3 = nil )
| ( hd(sK3) = sK9(sK3) ) ),
inference(superposition,[status(thm)],[c_56,c_94]) ).
tcf(c_2210,plain,
hd(sK3) = sK9(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2198,c_697]) ).
tcf(c_2384,plain,
( ssItem(hd(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_2210,c_93]) ).
tcf(c_2385,plain,
ssItem(hd(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2384,c_697,c_56]) ).
tcf(c_2569,plain,
( ( sK3 = nil )
| ( cons(hd(sK3),tl(sK3)) = sK3 ) ),
inference(superposition,[status(thm)],[c_56,c_86]) ).
tcf(c_2581,plain,
cons(hd(sK3),tl(sK3)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_2569,c_697]) ).
tcf(c_2640,plain,
! [X0: $i] :
( ( app(cons(X0,nil),tl(sK3)) = cons(X0,tl(sK3)) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_2038,c_61]) ).
tcf(c_2850,plain,
! [X0: $i] :
( ssList(cons(hd(sK3),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sK3)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_2851,plain,
( ssList(cons(hd(sK3),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sK3)) ),
inference(instantiation,[status(thm)],[c_2850]) ).
tcf(c_3858,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(tl(sK3))
| ( app(X0,tl(sK3)) != sK3 ) ),
inference(superposition,[status(thm)],[c_1929,c_77]) ).
tcf(c_3893,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ ssList(X0)
| ( app(X0,tl(sK3)) != sK3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3858,c_57,c_2038]) ).
tcf(c_23400,plain,
app(cons(hd(sK3),nil),tl(sK3)) = cons(hd(sK3),tl(sK3)),
inference(superposition,[status(thm)],[c_2385,c_2640]) ).
tcf(c_23403,plain,
app(cons(hd(sK3),nil),tl(sK3)) = sK3,
inference(light_normalisation,[status(thm)],[c_23400,c_2581]) ).
tcf(c_24484,plain,
( ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ( cons(hd(sK3),nil) != sK2 ) ),
inference(superposition,[status(thm)],[c_23403,c_136]) ).
tcf(c_24494,plain,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssList(cons(hd(sK3),nil)) ),
inference(superposition,[status(thm)],[c_23403,c_3893]) ).
tcf(c_24497,plain,
cons(hd(sK3),nil) != sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_24484,c_2385,c_2038]) ).
tcf(c_24498,plain,
~ ssList(cons(hd(sK3),nil)),
inference(backward_subsumption_resolution,[status(thm)],[c_24494,c_24497]) ).
tcf(c_24502,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_24498,c_2851,c_2190,c_696,c_84,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC015+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 15:55:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 10.23/2.79 % SZS status Started for theBenchmark.p
% 10.23/2.79 % SZS status Theorem for theBenchmark.p
% 10.23/2.79
% 10.23/2.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.23/2.79
% 10.23/2.79 % ------ iProver source info
% 10.23/2.79
% 10.23/2.79 % git: date: 2026-07-19 20:42:38 +0200
% 10.23/2.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.23/2.79 % git: non_committed_changes: false
% 10.23/2.79
% 10.23/2.79 % ------ Parsing...
% 10.23/2.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.23/2.79
% 10.23/2.79 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 10.23/2.79
% 10.23/2.79 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.23/2.79
% 10.23/2.79 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.23/2.79 % ------ Proving...
% 10.23/2.79 % ------ Problem Properties
% 10.23/2.79
% 10.23/2.79 %
% 10.23/2.79 % clauses 40
% 10.23/2.79 % conjectures 3
% 10.23/2.79 % EPR 7
% 10.23/2.79 % Horn 27
% 10.23/2.79 % unary 8
% 10.23/2.79 % binary 2
% 10.23/2.79 % lits 123
% 10.23/2.79 % lits eq 50
% 10.23/2.79 % fd_pure 0
% 10.23/2.79 % fd_pseudo 0
% 10.23/2.79 % fd_cond 12
% 10.23/2.79 % fd_pseudo_cond 5
% 10.23/2.79 % AC symbols 0
% 10.23/2.79
% 10.23/2.79 % ------ Schedule dynamic 5 is on
% 10.23/2.79
% 10.23/2.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.23/2.79
% 10.23/2.79
% 10.23/2.79 % ------
% 10.23/2.79 % Current options:
% 10.23/2.79 % ------
% 10.23/2.79
% 10.23/2.79
% 10.23/2.79 %
% 10.23/2.79
% 10.23/2.79 % ------ Proving...
% 10.23/2.79 %
% 10.23/2.79
% 10.23/2.79 % SZS status Theorem for theBenchmark.p
% 10.23/2.79
% 10.23/2.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.23/2.79
% 10.23/2.79
%------------------------------------------------------------------------------