%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC120+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 : n010.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 03:07:58 PM UTC 2026
% Result : Theorem 7.59s 6.88s
% Output : CNFRefutation 7.59s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f240ERROR: Could not build tree for root c_6802ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
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(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
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(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ? [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) )
& ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ? [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) )
| ( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ! [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) )
| ( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ! [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(f108,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f110,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f111,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f118]) ).
fof(f122,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f122]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(flattening,[],[f125]) ).
fof(f136,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f139,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) != X0 ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f143,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f144,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f143]) ).
fof(f148,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( ~ neq(sK3,nil)
& neq(sK1,nil) )
| ( ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) )
& ! [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(f152,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f111]) ).
fof(f155,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))],[f123]) ).
fof(f157,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f136]) ).
fof(f158,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(rectify,[],[f157]) ).
fof(f159,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0
& ssList(sK10(X0,X1))
& ssList(sK9(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f158]) ).
fof(f160,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK11(X0)
& ssItem(sK11(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X1,sK11(X0))],[f144]) ).
fof(f161,plain,
ssList(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f162,plain,
ssList(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f165,plain,
( ~ neq(sK3,nil)
| ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(cnf_transformation,[],[f148]) ).
fof(f167,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,[],[f148]) ).
fof(f168,plain,
! [X4,X5] :
( neq(sK1,nil)
| ~ neq(nil,sK3)
| app(sK2,X5) != X4
| tl(sK3) != X5
| ~ ssList(X5)
| sK3 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f148]) ).
fof(f171,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f148]) ).
fof(f172,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f148]) ).
fof(f184,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f108]) ).
fof(f186,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f188,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f195,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f197,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f119]) ).
fof(f199,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK8(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f200,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK8(X0)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f202,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f213,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
fof(f216,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f139]) ).
fof(f219,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK11(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f220,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK11(X0)) ),
inference(cnf_transformation,[],[f160]) ).
fof(f225,plain,
! [X4,X5] :
( neq(sK3,nil)
| ~ neq(nil,sK3)
| app(sK2,X5) != X4
| tl(sK3) != X5
| ~ ssList(X5)
| sK3 = X4
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f168,f172]) ).
fof(f227,plain,
( ~ neq(sK3,nil)
| ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(definition_unfolding,[],[f165,f171,f172,f171]) ).
fof(f228,plain,
ssList(sK3),
inference(definition_unfolding,[],[f162,f172]) ).
fof(f229,plain,
ssList(sK2),
inference(definition_unfolding,[],[f161,f171]) ).
fof(f230,plain,
! [X4] :
( neq(sK3,nil)
| ~ neq(nil,sK3)
| app(sK2,tl(sK3)) != X4
| ~ ssList(tl(sK3))
| sK3 = X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f225]) ).
fof(f231,plain,
( neq(sK3,nil)
| ~ neq(nil,sK3)
| ~ ssList(tl(sK3))
| sK3 = app(sK2,tl(sK3))
| ~ ssList(app(sK2,tl(sK3))) ),
inference(equality_resolution,[],[f230]) ).
fof(f232,plain,
! [X4] :
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| app(sK2,tl(sK3)) != X4
| ~ ssList(tl(sK3))
| sK3 = X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f167]) ).
fof(f233,plain,
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| ~ ssList(tl(sK3))
| sK3 = app(sK2,tl(sK3))
| ~ ssList(app(sK2,tl(sK3))) ),
inference(equality_resolution,[],[f232]) ).
fof(f239,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f213]) ).
tcf(c_49,negated_conjecture,
neq(sK3,nil),
inference(cnf_transformation,[],[f240]) ).
tcf(c_50,negated_conjecture,
( neq(sK3,nil)
| ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3)
| ~ ssList(app(sK2,tl(sK3))) ),
inference(cnf_transformation,[],[f231]) ).
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,[],[f233]) ).
tcf(c_53,negated_conjecture,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_56,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f228]) ).
tcf(c_57,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f229]) ).
tcf(c_69,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_73,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_80,plain,
ssList(nil),
inference(cnf_transformation,[],[f195]) ).
tcf(c_82,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_84,plain,
! [X0: $i] :
( ssList(sK8(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_85,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK8(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_87,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_104,plain,
! [X0: $i] :
( ssItem(sK11(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_105,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK11(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_150,negated_conjecture,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_49,c_53]) ).
tcf(c_152,negated_conjecture,
neq(sK3,nil),
inference(global_subsumption_just,[status(thm)],[c_50,c_49]) ).
tcf(c_154,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_881,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_152,c_73]) ).
tcf(c_882,plain,
( ~ ssList(sK3)
| ( sK3 != nil ) ),
inference(unflattening,[status(thm)],[c_881]) ).
tcf(c_883,plain,
sK3 != nil,
inference(global_subsumption_just,[status(thm)],[c_882,c_56,c_882]) ).
tcf(c_907,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_154,c_72]) ).
tcf(c_908,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_907]) ).
tcf(c_909,plain,
( ~ ssList(app(sK2,tl(sK3)))
| ~ ssList(tl(sK3))
| ( app(sK2,tl(sK3)) = sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_908,c_56,c_80,c_882,c_908]) ).
tcf(c_910,plain,
( ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(tl(sK3))
| ~ ssList(app(sK2,tl(sK3))) ),
inference(renaming,[status(thm)],[c_909]) ).
tcf(c_934,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK3,sK2)
| ( X1 != sK2 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_150,c_72]) ).
tcf(c_935,plain,
( ( nil = sK2 )
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ segmentP(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_934]) ).
tcf(c_936,plain,
( ( nil = sK2 )
| ~ segmentP(sK3,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_935,c_57,c_80,c_935]) ).
tcf(c_2416,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_57,c_69]) ).
tcf(c_2429,plain,
( ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(sK2)
| ~ ssList(tl(sK3)) ),
inference(superposition,[status(thm)],[c_71,c_910]) ).
tcf(c_2432,plain,
( ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(tl(sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2429,c_57]) ).
tcf(c_2520,plain,
( ( sK3 = nil )
| ( app(sK2,tl(sK3)) = sK3 )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_87,c_2432]) ).
tcf(c_2524,plain,
app(sK2,tl(sK3)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_2520,c_883,c_56]) ).
tcf(c_2590,plain,
( ( sK3 = nil )
| ( tl(sK3) = sK8(sK3) ) ),
inference(superposition,[status(thm)],[c_56,c_85]) ).
tcf(c_2600,plain,
tl(sK3) = sK8(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2590,c_883]) ).
tcf(c_2719,plain,
( ssList(tl(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_2600,c_84]) ).
tcf(c_2720,plain,
ssList(tl(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2719,c_883,c_56]) ).
tcf(c_2788,plain,
( ( sK3 = nil )
| ( hd(sK3) = sK11(sK3) ) ),
inference(superposition,[status(thm)],[c_56,c_105]) ).
tcf(c_2799,plain,
hd(sK3) = sK11(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2788,c_883]) ).
tcf(c_2901,plain,
app(nil,tl(sK3)) = tl(sK3),
inference(superposition,[status(thm)],[c_2720,c_69]) ).
tcf(c_2925,plain,
( ssItem(hd(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_2799,c_104]) ).
tcf(c_2926,plain,
ssItem(hd(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2925,c_883,c_56]) ).
tcf(c_3314,plain,
( ( sK3 = nil )
| ( cons(hd(sK3),tl(sK3)) = sK3 ) ),
inference(superposition,[status(thm)],[c_56,c_82]) ).
tcf(c_3327,plain,
cons(hd(sK3),tl(sK3)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_3314,c_883]) ).
tcf(c_3600,plain,
( ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ( tl(sK3) != sK3 ) ),
inference(superposition,[status(thm)],[c_3327,c_101]) ).
tcf(c_3602,plain,
tl(sK3) != sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_3600,c_2926,c_2720]) ).
tcf(c_6045,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK2),X0)) ),
inference(superposition,[status(thm)],[c_2416,c_95]) ).
tcf(c_6076,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_6045,c_2416]) ).
tcf(c_6077,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6076,c_57,c_80]) ).
tcf(c_6749,plain,
( segmentP(sK3,sK2)
| ~ ssList(tl(sK3))
| ~ ssList(app(sK2,tl(sK3))) ),
inference(superposition,[status(thm)],[c_2524,c_6077]) ).
tcf(c_6756,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK3)
| ~ ssList(tl(sK3)) ),
inference(light_normalisation,[status(thm)],[c_6749,c_2524]) ).
tcf(c_6757,plain,
segmentP(sK3,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_6756,c_56,c_2720]) ).
tcf(c_6773,plain,
nil = sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_936,c_6757]) ).
tcf(c_6797,plain,
app(nil,tl(sK3)) = sK3,
inference(demodulation,[status(thm)],[c_2524,c_6773]) ).
tcf(c_6801,plain,
tl(sK3) = sK3,
inference(demodulation,[status(thm)],[c_2901,c_6797]) ).
tcf(c_6802,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6801,c_3602]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC120+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.60 % Computer : n010.cluster.edu
% 0.11/5.60 % Model : x86_64 x86_64
% 0.11/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.60 % Memory : 8046.5625MB
% 0.11/5.60 % OS : Linux 6.8.0-71-generic
% 0.11/5.61 % CPULimit : 300
% 0.11/5.61 % WCLimit : 300
% 0.11/5.61 % DateTime : Thu Sep 24 16:30:05 UTC 2026
% 0.11/5.61 % CPUTime :
% 0.11/5.61 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.64 Running first-order theorem proving
% 0.11/5.64 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
% 0.11/5.66
% 0.11/5.66 % ======== iProver multi-core TPTP/SMT =========
% 0.11/5.66
% 0.11/5.66 % Detected problem language: tptp
% 0.11/5.67 % Proving...
% 7.59/6.88 % SZS status Started for theBenchmark.p
% 7.59/6.88 % SZS status Theorem for theBenchmark.p
% 7.59/6.88
% 7.59/6.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.59/6.88
% 7.59/6.88 % ------ iProver source info
% 7.59/6.88
% 7.59/6.88 % git: date: 2026-07-19 20:42:38 +0200
% 7.59/6.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.59/6.88 % git: non_committed_changes: false
% 7.59/6.88
% 7.59/6.88 % ------ Parsing...
% 7.59/6.88 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.59/6.88
% 7.59/6.88 % ------ 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 %
% 7.59/6.88
% 7.59/6.88 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.59/6.88
% 7.59/6.88 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.59/6.88 % ------ Proving...
% 7.59/6.88 % ------ Problem Properties
% 7.59/6.88
% 7.59/6.88 %
% 7.59/6.88 % clauses 52
% 7.59/6.88 % conjectures 2
% 7.59/6.88 % EPR 15
% 7.59/6.88 % Horn 39
% 7.59/6.88 % unary 9
% 7.59/6.88 % binary 6
% 7.59/6.88 % lits 165
% 7.59/6.88 % lits eq 53
% 7.59/6.88 % fd_pure 0
% 7.59/6.88 % fd_pseudo 0
% 7.59/6.88 % fd_cond 13
% 7.59/6.88 % fd_pseudo_cond 6
% 7.59/6.88 % AC symbols 0
% 7.59/6.88
% 7.59/6.88 % ------ Schedule dynamic 5 is on
% 7.59/6.88
% 7.59/6.88 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.59/6.88
% 7.59/6.88
% 7.59/6.88 % ------
% 7.59/6.88 % Current options:
% 7.59/6.88 % ------
% 7.59/6.88
% 7.59/6.88
% 7.59/6.88 %
% 7.59/6.88
% 7.59/6.88 % ------ Proving...
% 7.59/6.88 %
% 7.59/6.88
% 7.59/6.88 % SZS status Theorem for theBenchmark.p
% 7.59/6.88
% 7.59/6.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.59/6.89
% 7.59/6.89
%------------------------------------------------------------------------------