%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC079+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 03:07:48 PM UTC 2026
% Result : Theorem 16.04s 3.48s
% Output : CNFRefutation 16.04s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f240ERROR: Could not build tree for root c_59743ERROR: 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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/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) )
& ( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& hd(X3) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X2 != X5
& ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/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) )
& ( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& hd(X3) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X2 != X5
& ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& 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) )
| ( ! [X5] :
( ! [X6] :
( ~ neq(nil,X3)
| hd(X3) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6) )
| X2 = X5
| ~ ssList(X5) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ 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) )
| ( ! [X5] :
( ! [X6] :
( ~ neq(nil,X3)
| hd(X3) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6) )
| X2 = X5
| ~ ssList(X5) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ 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(f102,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f109,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f113,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f114,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f113]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f117]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f121,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f120]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f131,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)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f143,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f144,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f143]) ).
fof(f148,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( ~ neq(sK3,nil)
& neq(sK1,nil) )
| ( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK3)
| hd(sK3) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6) )
| sK2 = X5
| ~ ssList(X5) )
& ! [X4] :
( ~ segmentP(sK0,X4)
| ~ segmentP(sK1,X4)
| ~ neq(X4,nil)
| ~ 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(f151,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f109]) ).
fof(f153,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK8(X0)
& ssItem(sK8(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f118]) ).
fof(f155,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,[],[f131]) ).
fof(f156,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,[],[f155]) ).
fof(f157,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))],[f156]) ).
fof(f160,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK11(X0)
& ssList(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,
! [X6,X5] :
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| sK2 = X5
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f148]) ).
fof(f166,plain,
! [X6,X5] :
( neq(sK1,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| sK2 = X5
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f148]) ).
fof(f167,plain,
! [X4] :
( ~ neq(sK3,nil)
| ~ segmentP(sK0,X4)
| ~ segmentP(sK1,X4)
| ~ neq(X4,nil)
| ~ 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(f176,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f178,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f185,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f187,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f190,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f114]) ).
fof(f194,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK8(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f195,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK8(X0)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f197,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f202,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f208,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,[],[f157]) ).
fof(f216,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f139]) ).
fof(f219,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK11(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f220,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK11(X0)) ),
inference(cnf_transformation,[],[f160]) ).
fof(f226,plain,
! [X4] :
( ~ neq(sK3,nil)
| ~ segmentP(sK2,X4)
| ~ segmentP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f167,f172,f171]) ).
fof(f227,plain,
! [X6,X5] :
( neq(sK3,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| sK2 = X5
| ~ ssList(X5) ),
inference(definition_unfolding,[],[f166,f172]) ).
fof(f228,plain,
ssList(sK3),
inference(definition_unfolding,[],[f162,f172]) ).
fof(f229,plain,
ssList(sK2),
inference(definition_unfolding,[],[f161,f171]) ).
fof(f230,plain,
! [X6] :
( neq(sK3,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X6
| ~ ssItem(X6)
| cons(X6,nil) = sK2
| ~ ssList(cons(X6,nil)) ),
inference(equality_resolution,[],[f227]) ).
fof(f231,plain,
( neq(sK3,nil)
| ~ neq(nil,sK3)
| ~ ssItem(hd(sK3))
| sK2 = cons(hd(sK3),nil)
| ~ ssList(cons(hd(sK3),nil)) ),
inference(equality_resolution,[],[f230]) ).
fof(f232,plain,
! [X6] :
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X6
| ~ ssItem(X6)
| cons(X6,nil) = sK2
| ~ ssList(cons(X6,nil)) ),
inference(equality_resolution,[],[f165]) ).
fof(f233,plain,
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| ~ ssItem(hd(sK3))
| sK2 = cons(hd(sK3),nil)
| ~ ssList(cons(hd(sK3),nil)) ),
inference(equality_resolution,[],[f232]) ).
fof(f237,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,[],[f208]) ).
tcf(c_49,negated_conjecture,
neq(sK3,nil),
inference(cnf_transformation,[],[f240]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(sK3,nil)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_52,negated_conjecture,
( neq(sK3,nil)
| ( cons(hd(sK3),nil) = sK2 )
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3)
| ~ ssList(cons(hd(sK3),nil)) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_53,negated_conjecture,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3)
| ~ neq(sK3,nil)
| ~ ssList(cons(hd(sK3),nil)) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_56,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f228]) ).
tcf(c_57,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f229]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_72,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_75,plain,
ssList(nil),
inference(cnf_transformation,[],[f190]) ).
tcf(c_77,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_79,plain,
! [X0: $i] :
( ssItem(sK8(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_80,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK8(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_82,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_87,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_90,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,[],[f237]) ).
tcf(c_101,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_104,plain,
! [X0: $i] :
( ssList(sK11(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_105,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK11(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_150,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sK3,X0)
| ~ segmentP(sK2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_49,c_51]) ).
tcf(c_151,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ~ neq(X0,nil) ),
inference(renaming,[status(thm)],[c_150]) ).
tcf(c_152,negated_conjecture,
neq(sK3,nil),
inference(global_subsumption_just,[status(thm)],[c_52,c_49]) ).
tcf(c_154,negated_conjecture,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3)
| ~ ssList(cons(hd(sK3),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_49,c_53]) ).
tcf(c_890,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_152,c_72]) ).
tcf(c_891,plain,
( ~ ssList(sK3)
| ( sK3 != nil ) ),
inference(unflattening,[status(thm)],[c_890]) ).
tcf(c_892,plain,
sK3 != nil,
inference(global_subsumption_just,[status(thm)],[c_891,c_56,c_891]) ).
tcf(c_918,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_151,c_71]) ).
tcf(c_919,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0) ),
inference(unflattening,[status(thm)],[c_918]) ).
tcf(c_921,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_919,c_75,c_919]) ).
tcf(c_922,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0) ),
inference(renaming,[status(thm)],[c_921]) ).
tcf(c_954,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( cons(hd(sK3),nil) = sK2 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sK3))
| ~ ssList(cons(hd(sK3),nil))
| ( X1 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_154,c_71]) ).
tcf(c_955,plain,
( ( sK3 = nil )
| ( cons(hd(sK3),nil) = sK2 )
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ ssItem(hd(sK3))
| ~ ssList(cons(hd(sK3),nil)) ),
inference(unflattening,[status(thm)],[c_954]) ).
tcf(c_956,plain,
( ~ ssList(cons(hd(sK3),nil))
| ~ ssItem(hd(sK3))
| ( cons(hd(sK3),nil) = sK2 ) ),
inference(global_subsumption_just,[status(thm)],[c_955,c_56,c_75,c_891,c_955]) ).
tcf(c_957,plain,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssItem(hd(sK3))
| ~ ssList(cons(hd(sK3),nil)) ),
inference(renaming,[status(thm)],[c_956]) ).
tcf(c_2450,plain,
( ( nil = sK2 )
| ~ ssList(sK2)
| ~ segmentP(sK3,sK2) ),
inference(superposition,[status(thm)],[c_87,c_922]) ).
tcf(c_2453,plain,
( ( nil = sK2 )
| ~ segmentP(sK3,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2450,c_57]) ).
tcf(c_2472,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_57,c_101]) ).
tcf(c_2502,plain,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssList(nil)
| ~ ssItem(hd(sK3)) ),
inference(superposition,[status(thm)],[c_70,c_957]) ).
tcf(c_2503,plain,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssItem(hd(sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2502,c_75]) ).
tcf(c_2626,plain,
( ( sK3 = nil )
| ( cons(hd(sK3),nil) = sK2 )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_82,c_2503]) ).
tcf(c_2627,plain,
cons(hd(sK3),nil) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_2626,c_892,c_56]) ).
tcf(c_2640,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK3))
| ( nil != sK2 ) ),
inference(superposition,[status(thm)],[c_2627,c_63]) ).
tcf(c_2641,plain,
( ~ ssItem(hd(sK3))
| ( nil != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2640,c_75]) ).
tcf(c_2661,plain,
( ( sK3 = nil )
| ( hd(sK3) = sK8(sK3) ) ),
inference(superposition,[status(thm)],[c_56,c_80]) ).
tcf(c_2671,plain,
hd(sK3) = sK8(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2661,c_892]) ).
tcf(c_2705,plain,
( ssItem(hd(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_2671,c_79]) ).
tcf(c_2706,plain,
ssItem(hd(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2705,c_892,c_56]) ).
tcf(c_2707,plain,
nil != sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_2641,c_2706]) ).
tcf(c_2711,plain,
~ segmentP(sK3,sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_2453,c_2707]) ).
tcf(c_2763,plain,
( ( sK3 = nil )
| ( tl(sK3) = sK11(sK3) ) ),
inference(superposition,[status(thm)],[c_56,c_105]) ).
tcf(c_2773,plain,
tl(sK3) = sK11(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2763,c_892]) ).
tcf(c_3049,plain,
( ssList(tl(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_2773,c_104]) ).
tcf(c_3050,plain,
ssList(tl(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_3049,c_892,c_56]) ).
tcf(c_3187,plain,
( ( sK3 = nil )
| ( cons(hd(sK3),tl(sK3)) = sK3 ) ),
inference(superposition,[status(thm)],[c_56,c_77]) ).
tcf(c_3199,plain,
cons(hd(sK3),tl(sK3)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_3187,c_892]) ).
tcf(c_3333,plain,
! [X0: $i] :
( ( app(cons(X0,nil),tl(sK3)) = cons(X0,tl(sK3)) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_3050,c_61]) ).
tcf(c_5285,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_2472,c_90]) ).
tcf(c_5298,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_5285,c_2472]) ).
tcf(c_5299,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5298,c_57,c_75]) ).
tcf(c_59687,plain,
app(cons(hd(sK3),nil),tl(sK3)) = cons(hd(sK3),tl(sK3)),
inference(superposition,[status(thm)],[c_2706,c_3333]) ).
tcf(c_59694,plain,
app(sK2,tl(sK3)) = sK3,
inference(light_normalisation,[status(thm)],[c_59687,c_2627,c_3199]) ).
tcf(c_59737,plain,
( segmentP(sK3,sK2)
| ~ ssList(tl(sK3))
| ~ ssList(app(sK2,tl(sK3))) ),
inference(superposition,[status(thm)],[c_59694,c_5299]) ).
tcf(c_59742,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK3)
| ~ ssList(tl(sK3)) ),
inference(light_normalisation,[status(thm)],[c_59737,c_59694]) ).
tcf(c_59743,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_59742,c_2711,c_56,c_3050]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC079+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.56 % Computer : n017.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Thu Sep 24 16:12:02 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.60 Running first-order theorem proving
% 0.09/0.60 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.62
% 0.09/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.62
% 0.09/0.62 % Detected problem language: tptp
% 0.12/0.63 % Proving...
% 16.04/3.48 % SZS status Started for theBenchmark.p
% 16.04/3.48 % SZS status Theorem for theBenchmark.p
% 16.04/3.48
% 16.04/3.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.04/3.48
% 16.04/3.48 % ------ iProver source info
% 16.04/3.48
% 16.04/3.48 % git: date: 2026-07-19 20:42:38 +0200
% 16.04/3.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.04/3.48 % git: non_committed_changes: false
% 16.04/3.48
% 16.04/3.48 % ------ Parsing...
% 16.04/3.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.04/3.48
% 16.04/3.48 % ------ 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 %
% 16.04/3.48
% 16.04/3.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.04/3.48
% 16.04/3.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.04/3.48 % ------ Proving...
% 16.04/3.48 % ------ Problem Properties
% 16.04/3.48
% 16.04/3.48 %
% 16.04/3.48 % clauses 52
% 16.04/3.48 % conjectures 2
% 16.04/3.48 % EPR 15
% 16.04/3.48 % Horn 39
% 16.04/3.48 % unary 9
% 16.04/3.48 % binary 5
% 16.04/3.48 % lits 167
% 16.04/3.48 % lits eq 52
% 16.04/3.48 % fd_pure 0
% 16.04/3.48 % fd_pseudo 0
% 16.04/3.48 % fd_cond 14
% 16.04/3.48 % fd_pseudo_cond 6
% 16.04/3.48 % AC symbols 0
% 16.04/3.48
% 16.04/3.48 % ------ Schedule dynamic 5 is on
% 16.04/3.48
% 16.04/3.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 16.04/3.48
% 16.04/3.48
% 16.04/3.48 % ------
% 16.04/3.48 % Current options:
% 16.04/3.48 % ------
% 16.04/3.48
% 16.04/3.48
% 16.04/3.48 %
% 16.04/3.48
% 16.04/3.48 % ------ Proving...
% 16.04/3.48 %
% 16.04/3.48
% 16.04/3.48 % SZS status Theorem for theBenchmark.p
% 16.04/3.48
% 16.04/3.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.04/3.48
% 16.04/3.48
%------------------------------------------------------------------------------