%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC389+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 : n016.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 03:09:35 PM UTC 2026
% Result : Theorem 7.20s 1.89s
% Output : CNFRefutation 7.20s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f273ERROR: Could not build tree for root c_10773ERROR: 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(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(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
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] :
( ( ( singletonP(X0)
| ~ neq(X1,nil) )
& segmentP(X1,X0) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2
| ~ ssList(X6) ) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( singletonP(X0)
| ~ neq(X1,nil) )
& segmentP(X1,X0) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2
| ~ ssList(X6) ) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( ~ singletonP(X0)
& neq(X1,nil) )
| ~ segmentP(X1,X0) )
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) ) ) ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f106,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) != X0 ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f107,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f124,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f128,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f133,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(f154,plain,
( ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ( ( ~ singletonP(sK4)
& neq(sK5,nil) )
| ~ segmentP(sK5,sK4) )
& ( ( nil = sK6
& nil = sK7 )
| sP0(sK6,sK7) )
& sK4 = sK6
& sK5 = sK7
& ssList(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f150]) ).
fof(f168,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,[],[f123]) ).
fof(f169,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f168]) ).
fof(f170,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK14(X0),nil) = X0
& ssItem(sK14(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X2,sK14(X0))],[f169]) ).
fof(f171,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f124]) ).
fof(f172,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,[],[f133]) ).
fof(f173,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,[],[f172]) ).
fof(f174,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK15(X0,X1),X1),sK16(X0,X1)) = X0
& ssList(sK16(X0,X1))
& ssList(sK15(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X4,sK15(X0,X1)),skolemize(X5,sK16(X0,X1))],[f173]) ).
fof(f184,plain,
ssList(sK4),
inference(cnf_transformation,[],[f154]) ).
fof(f187,plain,
( ~ singletonP(sK4)
| ~ segmentP(sK5,sK4) ),
inference(cnf_transformation,[],[f154]) ).
fof(f188,plain,
( neq(sK5,nil)
| ~ segmentP(sK5,sK4) ),
inference(cnf_transformation,[],[f154]) ).
fof(f189,plain,
( nil = sK6
| sP0(sK6,sK7) ),
inference(cnf_transformation,[],[f154]) ).
fof(f190,plain,
( nil = sK7
| sP0(sK6,sK7) ),
inference(cnf_transformation,[],[f154]) ).
fof(f191,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f154]) ).
fof(f192,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f154]) ).
fof(f197,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f205,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f106]) ).
fof(f206,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f215,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f220,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f235,plain,
! [X0,X1] :
( ~ ssList(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f237,plain,
! [X0] :
( ~ ssList(X0)
| nil != X0
| segmentP(nil,X0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f240,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f246,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,[],[f174]) ).
fof(f258,plain,
( neq(sK7,nil)
| ~ segmentP(sK7,sK6) ),
inference(definition_unfolding,[],[f188,f192,f191,f192]) ).
fof(f259,plain,
( ~ singletonP(sK6)
| ~ segmentP(sK7,sK6) ),
inference(definition_unfolding,[],[f187,f192,f191,f191]) ).
fof(f261,plain,
ssList(sK6),
inference(definition_unfolding,[],[f184,f191]) ).
fof(f268,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f235]) ).
fof(f269,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f237]) ).
fof(f270,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,[],[f246]) ).
tcf(c_57,negated_conjecture,
( sP0(sK6,sK7)
| ( nil = sK7 ) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_58,negated_conjecture,
( sP0(sK6,sK7)
| ( nil = sK6 ) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_59,negated_conjecture,
( neq(sK7,nil)
| ~ segmentP(sK7,sK6) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_60,negated_conjecture,
( ~ singletonP(sK6)
| ~ segmentP(sK7,sK6) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_63,negated_conjecture,
ssList(sK6),
inference(cnf_transformation,[],[f261]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_87,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_90,plain,
ssList(nil),
inference(cnf_transformation,[],[f220]) ).
tcf(c_103,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_106,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_110,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_113,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,[],[f270]) ).
tcf(c_129,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_169,plain,
segmentP(nil,nil),
inference(global_subsumption_just,[status(thm)],[c_106,c_90,c_129]) ).
tcf(c_1247,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK7,sK6)
| ( X0 != sK7 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_87]) ).
tcf(c_1248,plain,
( ~ ssList(nil)
| ~ segmentP(sK7,sK6)
| ( nil != sK7 ) ),
inference(unflattening,[status(thm)],[c_1247]) ).
tcf(c_4003,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_76,c_103]) ).
tcf(c_4006,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4003,c_90]) ).
tcf(c_8207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(app(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_10153,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_113,c_85,c_113,c_8207]) ).
fof(f149,definition,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f150,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( ~ singletonP(X0)
& neq(X1,nil) )
| ~ segmentP(X1,X0) )
& ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(definition_folding,[],[f98,f149]) ).
fof(f151,plain,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) ) ) ) ),
inference(nnf_transformation,[],[f149]) ).
fof(f152,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X6] :
( ~ lt(X6,X2)
| ~ memberP(X4,X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(X2,X5)
| ~ memberP(X3,X5)
| ~ ssItem(X5) )
& app(app(X3,X0),X4) = X1
& cons(X2,nil) = X0
& ssList(X4) ) ) ) ),
inference(rectify,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( ssItem(sK1(X0,X1))
& ssList(sK2(X0,X1))
& ! [X6] :
( ~ lt(X6,sK1(X0,X1))
| ~ memberP(sK3(X0,X1),X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(sK1(X0,X1),X5)
| ~ memberP(sK2(X0,X1),X5)
| ~ ssItem(X5) )
& app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
& cons(sK1(X0,X1),nil) = X0
& ssList(sK3(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1)),skolemize(X4,sK3(X0,X1))],[f152]) ).
fof(f177,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssItem(sK1(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f178,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK2(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f181,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f153]) ).
fof(f182,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| cons(sK1(X0,X1),nil) = X0 ),
inference(cnf_transformation,[],[f153]) ).
fof(f183,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK3(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ssList(sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( cons(sK1(X0,X1),nil) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ssList(sK2(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_1275,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ( nil = sK7 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_57]) ).
tcf(c_1276,plain,
( ssItem(sK1(sK6,sK7))
| ( nil = sK7 ) ),
inference(unflattening,[status(thm)],[c_1275]) ).
tcf(c_1283,plain,
! [X0: $i,X1: $i] :
( ssList(sK2(X0,X1))
| ( nil = sK6 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_58]) ).
tcf(c_1284,plain,
( ssList(sK2(sK6,sK7))
| ( nil = sK6 ) ),
inference(unflattening,[status(thm)],[c_1283]) ).
tcf(c_1291,plain,
! [X0: $i,X1: $i] :
( ssList(sK2(X0,X1))
| ( nil = sK7 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_57]) ).
tcf(c_1292,plain,
( ssList(sK2(sK6,sK7))
| ( nil = sK7 ) ),
inference(unflattening,[status(thm)],[c_1291]) ).
tcf(c_1359,plain,
! [X0: $i,X1: $i] :
( ( nil = sK6 )
| ( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_58]) ).
tcf(c_1360,plain,
( ( nil = sK6 )
| ( app(app(sK2(sK6,sK7),sK6),sK3(sK6,sK7)) = sK7 ) ),
inference(unflattening,[status(thm)],[c_1359]) ).
tcf(c_1367,plain,
! [X0: $i,X1: $i] :
( ( nil = sK7 )
| ( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_57]) ).
tcf(c_1368,plain,
( ( nil = sK7 )
| ( app(app(sK2(sK6,sK7),sK6),sK3(sK6,sK7)) = sK7 ) ),
inference(unflattening,[status(thm)],[c_1367]) ).
tcf(c_1383,plain,
! [X0: $i,X1: $i] :
( ( nil = sK7 )
| ( cons(sK1(X0,X1),nil) = X0 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_57]) ).
tcf(c_1384,plain,
( ( nil = sK7 )
| ( cons(sK1(sK6,sK7),nil) = sK6 ) ),
inference(unflattening,[status(thm)],[c_1383]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i] :
( ssList(sK3(X0,X1))
| ( nil = sK6 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_1392,plain,
( ssList(sK3(sK6,sK7))
| ( nil = sK6 ) ),
inference(unflattening,[status(thm)],[c_1391]) ).
tcf(c_1399,plain,
! [X0: $i,X1: $i] :
( ssList(sK3(X0,X1))
| ( nil = sK7 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_57]) ).
tcf(c_1400,plain,
( ssList(sK3(sK6,sK7))
| ( nil = sK7 ) ),
inference(unflattening,[status(thm)],[c_1399]) ).
tcf(c_4174,plain,
( singletonP(sK6)
| ( nil = sK7 )
| ~ ssItem(sK1(sK6,sK7)) ),
inference(superposition,[status(thm)],[c_1384,c_4006]) ).
tcf(c_4199,plain,
( singletonP(sK6)
| ( nil = sK7 ) ),
inference(global_subsumption_just,[status(thm)],[c_4174,c_1276,c_4174]) ).
tcf(c_5704,negated_conjecture,
~ segmentP(sK7,sK6),
inference(global_subsumption_just,[status(thm)],[c_60,c_90,c_60,c_1248,c_4199]) ).
tcf(c_5778,plain,
! [X0: $i] :
( ( nil = sK7 )
| ( app(cons(sK1(sK6,sK7),nil),X0) = cons(sK1(sK6,sK7),X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_1276,c_67]) ).
tcf(c_6803,plain,
( ( nil = sK7 )
| ( app(cons(sK1(sK6,sK7),nil),sK6) = cons(sK1(sK6,sK7),sK6) ) ),
inference(superposition,[status(thm)],[c_63,c_5778]) ).
tcf(c_7509,plain,
( ( nil = sK7 )
| ( cons(sK1(sK6,sK7),sK6) = app(sK6,sK6) ) ),
inference(superposition,[status(thm)],[c_1384,c_6803]) ).
tcf(c_8500,plain,
( ( nil = sK7 )
| ~ ssList(sK6)
| ~ ssItem(sK1(sK6,sK7))
| ( app(sK6,sK6) != sK6 ) ),
inference(superposition,[status(thm)],[c_7509,c_75]) ).
tcf(c_8509,plain,
( ( nil = sK7 )
| ~ ssItem(sK1(sK6,sK7))
| ( app(sK6,sK6) != sK6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8500,c_63]) ).
tcf(c_10165,plain,
( segmentP(sK7,sK6)
| ( nil = sK7 )
| ~ ssList(sK6)
| ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7)) ),
inference(superposition,[status(thm)],[c_1368,c_10153]) ).
tcf(c_10166,plain,
( segmentP(sK7,sK6)
| ( nil = sK6 )
| ~ ssList(sK6)
| ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7)) ),
inference(superposition,[status(thm)],[c_1360,c_10153]) ).
tcf(c_10316,plain,
( segmentP(sK7,sK6)
| ( nil = sK6 )
| ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10166,c_63]) ).
tcf(c_10321,plain,
( segmentP(sK7,sK6)
| ( nil = sK7 )
| ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10165,c_63]) ).
tcf(c_10691,plain,
nil = sK7,
inference(global_subsumption_just,[status(thm)],[c_8509,c_90,c_60,c_1248,c_1292,c_1400,c_4199,c_10321]) ).
tcf(c_10725,plain,
( ssList(sK3(sK6,nil))
| ( nil = sK6 ) ),
inference(demodulation,[status(thm)],[c_1392,c_10691]) ).
tcf(c_10728,plain,
~ segmentP(nil,sK6),
inference(demodulation,[status(thm)],[c_5704,c_10691]) ).
tcf(c_10763,plain,
nil = sK6,
inference(global_subsumption_just,[status(thm)],[c_10725,c_90,c_60,c_1248,c_1284,c_1392,c_4199,c_10316]) ).
tcf(c_10765,plain,
~ segmentP(nil,nil),
inference(demodulation,[status(thm)],[c_10728,c_10763]) ).
tcf(c_10773,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10765,c_169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC389+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43 % Computer : n016.cluster.edu
% 0.13/0.43 % Model : x86_64 x86_64
% 0.13/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.43 % Memory : 8046.5625MB
% 0.13/0.43 % OS : Linux 6.8.0-71-generic
% 0.13/0.43 % CPULimit : 300
% 0.13/0.43 % WCLimit : 300
% 0.13/0.43 % DateTime : Thu Sep 24 18:03:58 UTC 2026
% 0.13/0.43 % CPUTime :
% 0.13/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.49 Running first-order theorem proving
% 0.13/0.49 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
% 0.22/0.50
% 0.22/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.50
% 0.22/0.50 % Detected problem language: tptp
% 0.22/0.52 % Proving...
% 7.20/1.89 % SZS status Started for theBenchmark.p
% 7.20/1.89 % SZS status Theorem for theBenchmark.p
% 7.20/1.89
% 7.20/1.89 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.20/1.89
% 7.20/1.89 % ------ iProver source info
% 7.20/1.89
% 7.20/1.89 % git: date: 2026-07-19 20:42:38 +0200
% 7.20/1.89 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.20/1.89 % git: non_committed_changes: false
% 7.20/1.89
% 7.20/1.89 % ------ Parsing...
% 7.20/1.89 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.20/1.89
% 7.20/1.89 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 7.20/1.89
% 7.20/1.89 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.20/1.89
% 7.20/1.89 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.20/1.89 % ------ Proving...
% 7.20/1.89 % ------ Problem Properties
% 7.20/1.89
% 7.20/1.89 %
% 7.20/1.89 % clauses 76
% 7.20/1.89 % conjectures 3
% 7.20/1.89 % EPR 25
% 7.20/1.89 % Horn 60
% 7.20/1.89 % unary 9
% 7.20/1.89 % binary 19
% 7.20/1.89 % lits 254
% 7.20/1.89 % lits eq 52
% 7.20/1.89 % fd_pure 0
% 7.20/1.89 % fd_pseudo 0
% 7.20/1.89 % fd_cond 5
% 7.20/1.89 % fd_pseudo_cond 8
% 7.20/1.89 % AC symbols 0
% 7.20/1.89
% 7.20/1.89 % ------ Schedule dynamic 5 is on
% 7.20/1.89
% 7.20/1.89 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.20/1.89
% 7.20/1.89
% 7.20/1.89 % ------
% 7.20/1.89 % Current options:
% 7.20/1.89 % ------
% 7.20/1.89
% 7.20/1.89
% 7.20/1.89 %
% 7.20/1.89
% 7.20/1.89 % ------ Proving...
% 7.20/1.89 %
% 7.20/1.89
% 7.20/1.89 % SZS status Theorem for theBenchmark.p
% 7.20/1.89
% 7.20/1.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.20/1.90
% 7.20/1.90
%------------------------------------------------------------------------------