%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC382+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 : n015.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 03:09:33 PM UTC 2026
% Result : Theorem 15.91s 4.42s
% Output : CNFRefutation 15.91s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f249ERROR: Could not build tree for root c_44390ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
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(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(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(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) )
& ( ( segmentP(X1,X0)
& singletonP(X0) )
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& hd(X3) = X5
& cons(X5,nil) = X4
& ssItem(X5) )
& X2 != 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)
& singletonP(X0) )
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& hd(X3) = X5
& cons(X5,nil) = X4
& ssItem(X5) )
& X2 != 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)
| ~ singletonP(X0) )
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = 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)
| ~ singletonP(X0) )
& ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = 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(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(f122,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f132,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(f140,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f144,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f145,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f144]) ).
fof(f149,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( ~ neq(sK3,nil)
& neq(sK1,nil) )
| ( ( ~ segmentP(sK1,sK0)
| ~ singletonP(sK0) )
& ! [X4] :
( ! [X5] :
( ~ neq(nil,sK3)
| hd(sK3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| sK2 = 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,[],[f109]) ).
fof(f154,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)
| ( ( ~ singletonP(X0)
| ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(nnf_transformation,[],[f122]) ).
fof(f156,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f155]) ).
fof(f157,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK9(X0),nil) = X0
& ssItem(sK9(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0))],[f156]) ).
fof(f159,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,[],[f132]) ).
fof(f160,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,[],[f159]) ).
fof(f161,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK10(X0,X1),X1),sK11(X0,X1)) = X0
& ssList(sK11(X0,X1))
& ssList(sK10(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f160]) ).
fof(f164,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK12(X0)
& ssList(sK12(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X1,sK12(X0))],[f145]) ).
fof(f165,plain,
ssList(sK0),
inference(cnf_transformation,[],[f149]) ).
fof(f166,plain,
ssList(sK1),
inference(cnf_transformation,[],[f149]) ).
fof(f169,plain,
( ~ neq(sK3,nil)
| ~ segmentP(sK1,sK0)
| ~ singletonP(sK0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f171,plain,
! [X4,X5] :
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK2 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f149]) ).
fof(f172,plain,
! [X4,X5] :
( neq(sK1,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK2 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f149]) ).
fof(f175,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f149]) ).
fof(f176,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f149]) ).
fof(f180,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f189,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f191,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f194,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f196,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f114]) ).
fof(f198,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK8(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f199,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK8(X0)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f205,plain,
! [X0,X1] :
( ~ ssList(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f216,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,[],[f161]) ).
fof(f224,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f140]) ).
fof(f227,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK12(X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f228,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK12(X0)) ),
inference(cnf_transformation,[],[f164]) ).
fof(f233,plain,
! [X4,X5] :
( neq(sK3,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK2 = X4
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f172,f176]) ).
fof(f235,plain,
( ~ neq(sK3,nil)
| ~ segmentP(sK3,sK2)
| ~ singletonP(sK2) ),
inference(definition_unfolding,[],[f169,f175,f176,f175]) ).
fof(f236,plain,
ssList(sK3),
inference(definition_unfolding,[],[f166,f176]) ).
fof(f237,plain,
ssList(sK2),
inference(definition_unfolding,[],[f165,f175]) ).
fof(f238,plain,
! [X5] :
( neq(sK3,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X5
| ~ ssItem(X5)
| cons(X5,nil) = sK2
| ~ ssList(cons(X5,nil)) ),
inference(equality_resolution,[],[f233]) ).
fof(f239,plain,
( neq(sK3,nil)
| ~ neq(nil,sK3)
| ~ ssItem(hd(sK3))
| sK2 = cons(hd(sK3),nil)
| ~ ssList(cons(hd(sK3),nil)) ),
inference(equality_resolution,[],[f238]) ).
fof(f240,plain,
! [X5] :
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| hd(sK3) != X5
| ~ ssItem(X5)
| cons(X5,nil) = sK2
| ~ ssList(cons(X5,nil)) ),
inference(equality_resolution,[],[f171]) ).
fof(f241,plain,
( ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| ~ ssItem(hd(sK3))
| sK2 = cons(hd(sK3),nil)
| ~ ssList(cons(hd(sK3),nil)) ),
inference(equality_resolution,[],[f240]) ).
fof(f244,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f205]) ).
fof(f246,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,[],[f216]) ).
tcf(c_49,negated_conjecture,
neq(sK3,nil),
inference(cnf_transformation,[],[f249]) ).
tcf(c_50,negated_conjecture,
( neq(sK3,nil)
| ( cons(hd(sK3),nil) = sK2 )
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3)
| ~ ssList(cons(hd(sK3),nil)) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_51,negated_conjecture,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3)
| ~ neq(sK3,nil)
| ~ ssList(cons(hd(sK3),nil)) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_53,negated_conjecture,
( ~ singletonP(sK2)
| ~ segmentP(sK3,sK2)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_56,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f236]) ).
tcf(c_57,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f237]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_72,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_75,plain,
ssList(nil),
inference(cnf_transformation,[],[f194]) ).
tcf(c_77,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_79,plain,
! [X0: $i] :
( ssItem(sK8(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_80,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK8(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_82,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_84,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_94,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,[],[f246]) ).
tcf(c_105,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_108,plain,
! [X0: $i] :
( ssList(sK12(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_109,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK12(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_155,negated_conjecture,
( ~ singletonP(sK2)
| ~ segmentP(sK3,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_49,c_53]) ).
tcf(c_157,negated_conjecture,
neq(sK3,nil),
inference(global_subsumption_just,[status(thm)],[c_50,c_49]) ).
tcf(c_159,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_51,c_49,c_51]) ).
tcf(c_978,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_157,c_72]) ).
tcf(c_979,plain,
( ~ ssList(sK3)
| ( sK3 != nil ) ),
inference(unflattening,[status(thm)],[c_978]) ).
tcf(c_980,plain,
sK3 != nil,
inference(global_subsumption_just,[status(thm)],[c_979,c_56,c_979]) ).
tcf(c_1004,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_159,c_71]) ).
tcf(c_1005,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_1004]) ).
tcf(c_1006,plain,
( ~ ssList(cons(hd(sK3),nil))
| ~ ssItem(hd(sK3))
| ( cons(hd(sK3),nil) = sK2 ) ),
inference(global_subsumption_just,[status(thm)],[c_1005,c_56,c_75,c_979,c_1005]) ).
tcf(c_1007,plain,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssItem(hd(sK3))
| ~ ssList(cons(hd(sK3),nil)) ),
inference(renaming,[status(thm)],[c_1006]) ).
tcf(c_2621,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_57,c_105]) ).
tcf(c_2649,plain,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssList(nil)
| ~ ssItem(hd(sK3)) ),
inference(superposition,[status(thm)],[c_70,c_1007]) ).
tcf(c_2652,plain,
( ( cons(hd(sK3),nil) = sK2 )
| ~ ssItem(hd(sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2649,c_75]) ).
tcf(c_2701,plain,
( ( sK3 = nil )
| ( cons(hd(sK3),nil) = sK2 )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_82,c_2652]) ).
tcf(c_2702,plain,
cons(hd(sK3),nil) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_2701,c_980,c_56]) ).
tcf(c_2789,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_70,c_84]) ).
tcf(c_2791,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2789,c_75]) ).
tcf(c_2801,plain,
( singletonP(sK2)
| ~ ssItem(hd(sK3)) ),
inference(superposition,[status(thm)],[c_2702,c_2791]) ).
tcf(c_2808,plain,
( singletonP(sK2)
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_82,c_2801]) ).
tcf(c_2809,plain,
singletonP(sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_2808,c_980,c_56]) ).
tcf(c_2810,plain,
~ segmentP(sK3,sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_155,c_2809]) ).
tcf(c_2876,plain,
( ( sK3 = nil )
| ( hd(sK3) = sK8(sK3) ) ),
inference(superposition,[status(thm)],[c_56,c_80]) ).
tcf(c_2886,plain,
hd(sK3) = sK8(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2876,c_980]) ).
tcf(c_2965,plain,
( ssItem(hd(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_2886,c_79]) ).
tcf(c_2966,plain,
ssItem(hd(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2965,c_980,c_56]) ).
tcf(c_3045,plain,
( ( sK3 = nil )
| ( tl(sK3) = sK12(sK3) ) ),
inference(superposition,[status(thm)],[c_56,c_109]) ).
tcf(c_3054,plain,
tl(sK3) = sK12(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_3045,c_980]) ).
tcf(c_3312,plain,
( ssList(tl(sK3))
| ( sK3 = nil )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_3054,c_108]) ).
tcf(c_3313,plain,
ssList(tl(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_3312,c_980,c_56]) ).
tcf(c_3500,plain,
( ( sK3 = nil )
| ( cons(hd(sK3),tl(sK3)) = sK3 ) ),
inference(superposition,[status(thm)],[c_56,c_77]) ).
tcf(c_3513,plain,
cons(hd(sK3),tl(sK3)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_3500,c_980]) ).
tcf(c_3583,plain,
! [X0: $i] :
( ( app(cons(X0,nil),tl(sK3)) = cons(X0,tl(sK3)) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_3313,c_61]) ).
tcf(c_5779,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_2621,c_94]) ).
tcf(c_5796,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_5779,c_2621]) ).
tcf(c_5797,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5796,c_57,c_75]) ).
tcf(c_44283,plain,
app(cons(hd(sK3),nil),tl(sK3)) = cons(hd(sK3),tl(sK3)),
inference(superposition,[status(thm)],[c_2966,c_3583]) ).
tcf(c_44291,plain,
app(sK2,tl(sK3)) = sK3,
inference(light_normalisation,[status(thm)],[c_44283,c_2702,c_3513]) ).
tcf(c_44385,plain,
( segmentP(sK3,sK2)
| ~ ssList(tl(sK3))
| ~ ssList(app(sK2,tl(sK3))) ),
inference(superposition,[status(thm)],[c_44291,c_5797]) ).
tcf(c_44389,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK3)
| ~ ssList(tl(sK3)) ),
inference(light_normalisation,[status(thm)],[c_44385,c_44291]) ).
tcf(c_44390,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_44389,c_2810,c_56,c_3313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC382+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 % Computer : n015.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Thu Sep 24 17:59:56 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 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
% 0.14/0.48
% 0.14/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.48
% 0.14/0.49 % Detected problem language: tptp
% 0.23/0.50 % Proving...
% 15.91/4.42 % SZS status Started for theBenchmark.p
% 15.91/4.42 % SZS status Theorem for theBenchmark.p
% 15.91/4.42
% 15.91/4.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.91/4.42
% 15.91/4.42 % ------ iProver source info
% 15.91/4.42
% 15.91/4.42 % git: date: 2026-07-19 20:42:38 +0200
% 15.91/4.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.91/4.42 % git: non_committed_changes: false
% 15.91/4.42
% 15.91/4.42 % ------ Parsing...
% 15.91/4.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.91/4.42
% 15.91/4.42 % ------ 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 %
% 15.91/4.42
% 15.91/4.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.91/4.42
% 15.91/4.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.91/4.42 % ------ Proving...
% 15.91/4.42 % ------ Problem Properties
% 15.91/4.42
% 15.91/4.42 %
% 15.91/4.42 % clauses 55
% 15.91/4.42 % conjectures 3
% 15.91/4.42 % EPR 15
% 15.91/4.42 % Horn 42
% 15.91/4.42 % unary 10
% 15.91/4.42 % binary 5
% 15.91/4.42 % lits 173
% 15.91/4.42 % lits eq 52
% 15.91/4.42 % fd_pure 0
% 15.91/4.42 % fd_pseudo 0
% 15.91/4.42 % fd_cond 13
% 15.91/4.42 % fd_pseudo_cond 6
% 15.91/4.42 % AC symbols 0
% 15.91/4.42
% 15.91/4.42 % ------ Schedule dynamic 5 is on
% 15.91/4.42
% 15.91/4.42 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.91/4.42
% 15.91/4.42
% 15.91/4.42 % ------
% 15.91/4.42 % Current options:
% 15.91/4.42 % ------
% 15.91/4.42
% 15.91/4.42
% 15.91/4.42 %
% 15.91/4.42
% 15.91/4.42 % ------ Proving...
% 15.91/4.42 %
% 15.91/4.42
% 15.91/4.42 % SZS status Theorem for theBenchmark.p
% 15.91/4.42
% 15.91/4.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.91/4.42
% 15.91/4.42
%------------------------------------------------------------------------------