%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC388+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 : n013.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 136.68s 36.04s
% Output : CNFRefutation 136.68s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f234ERROR: Could not build tree for root c_479702ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
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(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax39) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax53) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X0
& nil = X1 )
| ( neq(X3,nil)
& ~ singletonP(X2) )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& ssItem(X4) )
| ~ segmentP(X3,X2)
| 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)
=> ( ( nil = X0
& nil = X1 )
| ( neq(X3,nil)
& ~ singletonP(X2) )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& ssItem(X4) )
| ~ segmentP(X3,X2)
| 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)
& ( nil != X0
| nil != X1 )
& ( ~ neq(X3,nil)
| singletonP(X2) )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X0
| nil != X1 )
& ( ~ neq(X3,nil)
| singletonP(X2) )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f103,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(ennf_transformation,[],[f20]) ).
fof(f104,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(flattening,[],[f103]) ).
fof(f109,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f111,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f112,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f113,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f114,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f115,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f124,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ) ) ),
inference(flattening,[],[f123]) ).
fof(f125,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(f134,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f135,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( nil != sK0
| nil != sK1 )
& ( ~ neq(sK3,nil)
| singletonP(sK2) )
& ! [X4] :
( ~ memberP(sK1,X4)
| cons(X4,nil) != sK0
| ~ ssItem(X4) )
& segmentP(sK3,sK2)
& 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(f137,plain,
! [X0] :
( ~ ssList(X0)
| ( cons(sK7(X0),sK6(X0)) = X0
& ssItem(sK7(X0))
& ssList(sK6(X0)) )
| nil = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0))],[f104]) ).
fof(f138,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f109]) ).
fof(f140,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f112]) ).
fof(f141,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f140]) ).
fof(f142,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f113]) ).
fof(f143,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f142]) ).
fof(f144,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f145,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(rectify,[],[f144]) ).
fof(f146,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f145]) ).
fof(f147,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,[],[f115]) ).
fof(f148,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f147]) ).
fof(f149,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK10(X0),nil) = X0
& ssItem(sK10(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f148]) ).
fof(f150,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f116]) ).
fof(f151,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,[],[f125]) ).
fof(f152,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,[],[f151]) ).
fof(f153,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK11(X0,X1),X1),sK12(X0,X1)) = X0
& ssList(sK12(X0,X1))
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X4,sK11(X0,X1)),skolemize(X5,sK12(X0,X1))],[f152]) ).
fof(f156,plain,
ssList(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f157,plain,
ssList(sK1),
inference(cnf_transformation,[],[f135]) ).
fof(f160,plain,
( nil != sK0
| nil != sK1 ),
inference(cnf_transformation,[],[f135]) ).
fof(f161,plain,
( ~ neq(sK3,nil)
| singletonP(sK2) ),
inference(cnf_transformation,[],[f135]) ).
fof(f162,plain,
! [X4] :
( ~ memberP(sK1,X4)
| cons(X4,nil) != sK0
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f135]) ).
fof(f163,plain,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f135]) ).
fof(f164,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f135]) ).
fof(f165,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f135]) ).
fof(f172,plain,
! [X0] :
( ~ ssList(X0)
| cons(sK7(X0),sK6(X0)) = X0
| nil = X0 ),
inference(cnf_transformation,[],[f137]) ).
fof(f173,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK7(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f137]) ).
fof(f174,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK6(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f137]) ).
fof(f180,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f183,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f184,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f141]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f194,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
fof(f195,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f196,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| cons(sK10(X0),nil) = X0 ),
inference(cnf_transformation,[],[f149]) ).
fof(f197,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| ssItem(sK10(X0)) ),
inference(cnf_transformation,[],[f149]) ).
fof(f199,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f150]) ).
fof(f203,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ),
inference(cnf_transformation,[],[f124]) ).
fof(f206,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| app(app(sK11(X0,X1),X1),sK12(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f153]) ).
fof(f207,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ssList(sK12(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f208,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ssList(sK11(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f218,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f219,plain,
! [X4] :
( ~ memberP(sK3,X4)
| cons(X4,nil) != sK2
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f162,f164,f165]) ).
fof(f220,plain,
( nil != sK2
| nil != sK3 ),
inference(definition_unfolding,[],[f160,f165,f164]) ).
fof(f221,plain,
ssList(sK3),
inference(definition_unfolding,[],[f157,f165]) ).
fof(f222,plain,
ssList(sK2),
inference(definition_unfolding,[],[f156,f164]) ).
fof(f226,plain,
! [X2,X3,X1] :
( ~ ssList(app(X2,cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(app(X2,cons(X1,X3)),X1) ),
inference(equality_resolution,[],[f194]) ).
tcf(c_49,negated_conjecture,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f163]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sK3,X0)
| ( cons(X0,nil) != sK2 ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_51,negated_conjecture,
( singletonP(sK2)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_52,negated_conjecture,
( ( sK2 != nil )
| ( sK3 != nil ) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_55,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f221]) ).
tcf(c_56,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f222]) ).
tcf(c_63,plain,
! [X0: $i] :
( ssList(sK6(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_64,plain,
! [X0: $i] :
( ssItem(sK7(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_65,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(sK7(X0),sK6(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_74,plain,
ssList(nil),
inference(cnf_transformation,[],[f183]) ).
tcf(c_75,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_86,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f195]) ).
tcf(c_88,plain,
! [X0: $i] :
( ssItem(sK10(X0))
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_89,plain,
! [X0: $i] :
( ( cons(sK10(X0),nil) = X0 )
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_91,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_94,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X2,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ssList(sK11(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( ssList(sK12(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ( app(app(sK11(X0,X1),X1),sK12(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_110,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_119,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1001,plain,
! [X0: $i,X1: $i] :
( singletonP(sK2)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_70]) ).
tcf(c_1002,plain,
( singletonP(sK2)
| ( sK3 = nil )
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(unflattening,[status(thm)],[c_1001]) ).
tcf(c_1003,plain,
( singletonP(sK2)
| ( sK3 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_1002,c_55,c_74,c_1002]) ).
tcf(c_1021,plain,
( ( sK3 = nil )
| ( sK2 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_1003,c_86]) ).
tcf(c_1022,plain,
sK2 != nil,
inference(global_subsumption_just,[status(thm)],[c_1021,c_52,c_1021]) ).
tcf(c_1037,plain,
! [X0: $i] :
( ssItem(sK10(X0))
| ( sK3 = nil )
| ~ ssList(X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_1003,c_88]) ).
tcf(c_1038,plain,
( ssItem(sK10(sK2))
| ( sK3 = nil )
| ~ ssList(sK2) ),
inference(unflattening,[status(thm)],[c_1037]) ).
tcf(c_1872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2892,plain,
( ( sK3 = nil )
| ( cons(sK10(sK2),nil) = sK2 )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_1003,c_89]) ).
tcf(c_2894,plain,
( ( sK3 = nil )
| ( cons(sK10(sK2),nil) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2892,c_56]) ).
tcf(c_2905,plain,
( ( sK3 = nil )
| ~ ssItem(sK10(sK2))
| ~ memberP(sK3,sK10(sK2)) ),
inference(superposition,[status(thm)],[c_2894,c_50]) ).
tcf(c_2908,plain,
( memberP(sK2,sK10(sK2))
| ( sK3 = nil )
| ~ ssList(nil)
| ~ ssItem(sK10(sK2)) ),
inference(superposition,[status(thm)],[c_2894,c_76]) ).
tcf(c_2913,plain,
( memberP(sK2,sK10(sK2))
| ( sK3 = nil )
| ~ ssItem(sK10(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2908,c_74]) ).
tcf(c_2917,plain,
( ( sK3 = nil )
| ~ memberP(sK3,sK10(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_2905,c_56,c_1038,c_2905]) ).
tcf(c_2923,plain,
( memberP(sK2,sK10(sK2))
| ( sK3 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_2913,c_56,c_1038,c_2913]) ).
tcf(c_3092,plain,
( ( sK2 = nil )
| ( cons(sK7(sK2),sK6(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_56,c_65]) ).
tcf(c_3101,plain,
cons(sK7(sK2),sK6(sK2)) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_3092,c_1022]) ).
tcf(c_3166,plain,
( memberP(sK2,sK7(sK2))
| ~ ssList(sK6(sK2))
| ~ ssItem(sK7(sK2)) ),
inference(superposition,[status(thm)],[c_3101,c_76]) ).
tcf(c_3270,plain,
( ssList(sK6(sK2))
| ( sK2 = nil )
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_3271,plain,
( ssItem(sK7(sK2))
| ( sK2 = nil )
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3274,plain,
( ( sK2 = nil )
| ~ ssList(sK2)
| ~ segmentP(nil,sK2) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_3650,plain,
! [X0: $i] :
( segmentP(X0,sK2)
| ~ ssList(sK2)
| ~ ssList(sK3)
| ~ ssList(X0)
| ~ segmentP(X0,sK3) ),
inference(superposition,[status(thm)],[c_49,c_96]) ).
tcf(c_3659,plain,
! [X0: $i] :
( segmentP(X0,sK2)
| ~ ssList(X0)
| ~ segmentP(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3650,c_56,c_55]) ).
tcf(c_3663,plain,
( segmentP(nil,sK2)
| ~ ssList(nil)
| ~ segmentP(nil,sK3) ),
inference(instantiation,[status(thm)],[c_3659]) ).
tcf(c_4022,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK3 = nil )
| ( sK10(sK2) = X0 )
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK10(sK2))
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_2894,c_78]) ).
tcf(c_4033,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK3 = nil )
| ( sK10(sK2) = X0 )
| ~ ssItem(X0)
| ~ ssItem(sK10(sK2))
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4022,c_74]) ).
tcf(c_4770,plain,
( ( app(app(sK11(sK3,sK2),sK2),sK12(sK3,sK2)) = sK3 )
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_49,c_100]) ).
tcf(c_4780,plain,
app(app(sK11(sK3,sK2),sK2),sK12(sK3,sK2)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_4770,c_56,c_55]) ).
tcf(c_5783,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ ssList(sK12(sK3,sK2))
| ~ ssList(app(sK11(sK3,sK2),sK2))
| ~ memberP(app(sK11(sK3,sK2),sK2),X0) ),
inference(superposition,[status(thm)],[c_4780,c_79]) ).
tcf(c_17853,plain,
! [X0: $i,X1: $i] :
( segmentP(nil,sK3)
| ~ segmentP(X1,X0)
| ( nil != X1 )
| ( sK3 != X0 ) ),
inference(instantiation,[status(thm)],[c_1872]) ).
tcf(c_17854,plain,
( segmentP(nil,sK3)
| ~ segmentP(nil,nil)
| ( nil != nil )
| ( sK3 != nil ) ),
inference(instantiation,[status(thm)],[c_17853]) ).
tcf(c_92810,plain,
! [X0: $i] :
( memberP(app(X0,sK2),sK10(sK2))
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssItem(sK10(sK2))
| ~ memberP(sK2,sK10(sK2)) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_176077,plain,
singletonP(sK2),
inference(global_subsumption_just,[status(thm)],[c_1003,c_56,c_55,c_74,c_110,c_52,c_119,c_1002,c_1021,c_3274,c_3663,c_17854]) ).
tcf(c_176105,plain,
( ( cons(sK10(sK2),nil) = sK2 )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_176077,c_89]) ).
tcf(c_176106,plain,
cons(sK10(sK2),nil) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_176105,c_56]) ).
tcf(c_176767,plain,
( ( sK2 = nil )
| ( cons(sK7(sK2),sK6(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_56,c_65]) ).
tcf(c_176776,plain,
cons(sK7(sK2),sK6(sK2)) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_176767,c_1022]) ).
tcf(c_176948,plain,
( memberP(sK2,sK7(sK2))
| ~ ssList(sK6(sK2))
| ~ ssItem(sK7(sK2)) ),
inference(superposition,[status(thm)],[c_176776,c_76]) ).
tcf(c_177216,plain,
memberP(sK2,sK7(sK2)),
inference(global_subsumption_just,[status(thm)],[c_176948,c_56,c_52,c_1021,c_3166,c_3270,c_3271]) ).
tcf(c_177892,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK10(sK2) = X0 )
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK10(sK2))
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_176106,c_78]) ).
tcf(c_177898,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK10(sK2) = X0 )
| ~ ssItem(X0)
| ~ ssItem(sK10(sK2))
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_177892,c_74]) ).
tcf(c_178431,plain,
! [X0: $i] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0)
| ( sK10(sK2) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_177898,c_56,c_74,c_110,c_75,c_52,c_119,c_1021,c_1038,c_3274,c_3663,c_4033,c_17854]) ).
tcf(c_178432,plain,
! [X0: $i] :
( ( sK10(sK2) = X0 )
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(renaming,[status(thm)],[c_178431]) ).
tcf(c_178441,plain,
( ( sK7(sK2) = sK10(sK2) )
| ~ ssItem(sK7(sK2)) ),
inference(superposition,[status(thm)],[c_177216,c_178432]) ).
tcf(c_341147,plain,
( ( sK2 = nil )
| ( cons(sK7(sK2),sK6(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_56,c_65]) ).
tcf(c_341229,plain,
singletonP(sK2),
inference(global_subsumption_just,[status(thm)],[c_1003,c_56,c_74,c_110,c_119,c_1003,c_1022,c_3274,c_3663,c_17854]) ).
tcf(c_341453,plain,
( ( cons(sK10(sK2),nil) = sK2 )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_341229,c_89]) ).
tcf(c_341455,plain,
cons(sK10(sK2),nil) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_341453,c_56]) ).
tcf(c_341634,plain,
( ~ ssItem(sK10(sK2))
| ~ memberP(sK3,sK10(sK2)) ),
inference(superposition,[status(thm)],[c_341455,c_50]) ).
tcf(c_341635,plain,
! [X0: $i] :
( memberP(app(X0,sK2),sK10(sK2))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK10(sK2))
| ~ ssList(app(X0,cons(sK10(sK2),nil))) ),
inference(superposition,[status(thm)],[c_341455,c_82]) ).
tcf(c_341636,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK10(sK2) = X0 )
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK10(sK2))
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_341455,c_78]) ).
tcf(c_341656,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK10(sK2) = X0 )
| ~ ssItem(X0)
| ~ ssItem(sK10(sK2))
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_341636,c_74]) ).
tcf(c_341668,plain,
! [X0: $i] :
( memberP(app(X0,sK2),sK10(sK2))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK10(sK2))
| ~ ssList(app(X0,sK2)) ),
inference(light_normalisation,[status(thm)],[c_341635,c_341455]) ).
tcf(c_341669,plain,
! [X0: $i] :
( memberP(app(X0,sK2),sK10(sK2))
| ~ ssList(X0)
| ~ ssItem(sK10(sK2))
| ~ ssList(app(X0,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_341668,c_74]) ).
tcf(c_341740,plain,
( ( app(app(sK11(sK3,sK2),sK2),sK12(sK3,sK2)) = sK3 )
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_49,c_100]) ).
tcf(c_341752,plain,
app(app(sK11(sK3,sK2),sK2),sK12(sK3,sK2)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_341740,c_56,c_55]) ).
tcf(c_341775,plain,
~ memberP(sK3,sK10(sK2)),
inference(global_subsumption_just,[status(thm)],[c_341634,c_56,c_74,c_110,c_52,c_119,c_1021,c_2917,c_3274,c_3663,c_17854]) ).
tcf(c_342760,plain,
cons(sK7(sK2),sK6(sK2)) = sK2,
inference(global_subsumption_just,[status(thm)],[c_341147,c_3101]) ).
tcf(c_342764,plain,
( memberP(sK2,sK7(sK2))
| ~ ssList(sK6(sK2))
| ~ ssItem(sK7(sK2)) ),
inference(superposition,[status(thm)],[c_342760,c_76]) ).
tcf(c_347171,plain,
! [X0: $i] :
( ssList(app(X0,sK2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c_109,c_56]) ).
tcf(c_347303,plain,
! [X0: $i] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0)
| ( sK10(sK2) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_341656,c_178432]) ).
tcf(c_347304,plain,
! [X0: $i] :
( ( sK10(sK2) = X0 )
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(renaming,[status(thm)],[c_347303]) ).
tcf(c_347348,plain,
! [X0: $i] :
( memberP(app(X0,sK2),sK10(sK2))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_341669,c_56,c_74,c_110,c_119,c_1022,c_1038,c_2923,c_3274,c_3663,c_17854,c_92810]) ).
tcf(c_349935,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ ssList(sK12(sK3,sK2))
| ~ ssList(app(sK11(sK3,sK2),sK2))
| ~ memberP(app(sK11(sK3,sK2),sK2),X0) ),
inference(superposition,[status(thm)],[c_341752,c_79]) ).
tcf(c_364232,plain,
memberP(sK2,sK7(sK2)),
inference(global_subsumption_just,[status(thm)],[c_342764,c_56,c_52,c_1021,c_3166,c_3270,c_3271]) ).
tcf(c_364254,plain,
( ( sK7(sK2) = sK10(sK2) )
| ~ ssItem(sK7(sK2)) ),
inference(superposition,[status(thm)],[c_364232,c_347304]) ).
tcf(c_364337,plain,
sK7(sK2) = sK10(sK2),
inference(global_subsumption_just,[status(thm)],[c_364254,c_56,c_52,c_1021,c_3271,c_178441]) ).
tcf(c_364343,plain,
! [X0: $i] :
( memberP(app(X0,sK2),sK7(sK2))
| ~ ssList(X0) ),
inference(demodulation,[status(thm)],[c_347348,c_364337]) ).
tcf(c_364345,plain,
~ memberP(sK3,sK7(sK2)),
inference(demodulation,[status(thm)],[c_341775,c_364337]) ).
tcf(c_364357,plain,
( ssItem(sK7(sK2))
| ~ ssList(sK2)
| ~ singletonP(sK2) ),
inference(superposition,[status(thm)],[c_364337,c_88]) ).
tcf(c_364358,plain,
ssItem(sK7(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_364357,c_56,c_341229]) ).
tcf(c_371686,plain,
( ssList(sK11(sK3,sK2))
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(resolution,[status(thm)],[c_98,c_49]) ).
tcf(c_372892,plain,
( ssList(sK12(sK3,sK2))
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(resolution,[status(thm)],[c_99,c_49]) ).
tcf(c_375846,plain,
ssList(sK11(sK3,sK2)),
inference(global_subsumption_just,[status(thm)],[c_371686,c_56,c_55,c_371686]) ).
tcf(c_375862,plain,
ssList(app(sK11(sK3,sK2),sK2)),
inference(resolution,[status(thm)],[c_375846,c_347171]) ).
tcf(c_479689,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(app(sK11(sK3,sK2),sK2),X0) ),
inference(global_subsumption_just,[status(thm)],[c_349935,c_56,c_55,c_5783,c_372892,c_375862]) ).
tcf(c_479700,plain,
( memberP(sK3,sK7(sK2))
| ~ ssItem(sK7(sK2))
| ~ ssList(sK11(sK3,sK2)) ),
inference(superposition,[status(thm)],[c_364343,c_479689]) ).
tcf(c_479701,plain,
~ ssList(sK11(sK3,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_479700,c_364345,c_364358]) ).
tcf(c_479702,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_479701,c_371686,c_55,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC388+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 17:58:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 136.68/36.04 % SZS status Started for theBenchmark.p
% 136.68/36.04 % SZS status Theorem for theBenchmark.p
% 136.68/36.04
% 136.68/36.04 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 136.68/36.04
% 136.68/36.04 % ------ iProver source info
% 136.68/36.04
% 136.68/36.04 % git: date: 2026-07-19 20:42:38 +0200
% 136.68/36.04 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 136.68/36.04 % git: non_committed_changes: false
% 136.68/36.04
% 136.68/36.04 % ------ Parsing...
% 136.68/36.04 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 136.68/36.04
% 136.68/36.04 % ------ 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 %
% 136.68/36.04
% 136.68/36.04 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 136.68/36.04
% 136.68/36.04 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 136.68/36.04 % ------ Proving...
% 136.68/36.04 % ------ Problem Properties
% 136.68/36.04
% 136.68/36.04 %
% 136.68/36.04 % clauses 55
% 136.68/36.04 % conjectures 4
% 136.68/36.04 % EPR 17
% 136.68/36.04 % Horn 49
% 136.68/36.04 % unary 11
% 136.68/36.04 % binary 6
% 136.68/36.04 % lits 181
% 136.68/36.04 % lits eq 34
% 136.68/36.04 % fd_pure 0
% 136.68/36.04 % fd_pseudo 0
% 136.68/36.04 % fd_cond 5
% 136.68/36.04 % fd_pseudo_cond 6
% 136.68/36.04 % AC symbols 0
% 136.68/36.04
% 136.68/36.04 % ------ Schedule dynamic 5 is on
% 136.68/36.04
% 136.68/36.04 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 136.68/36.04
% 136.68/36.04
% 136.68/36.04 % ------
% 136.68/36.04 % Current options:
% 136.68/36.04 % ------
% 136.68/36.04
% 136.68/36.04
% 136.68/36.04 %
% 136.68/36.04
% 136.68/36.04 % ------ Proving...
% 136.68/36.04 % Proof_search_loop: time out after: 4630 full_loop iterations
% 136.68/36.04
% 136.68/36.04 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 136.68/36.04
% 136.68/36.04
% 136.68/36.04 % ------
% 136.68/36.04 % Current options:
% 136.68/36.04 % ------
% 136.68/36.04
% 136.68/36.04
% 136.68/36.04 %
% 136.68/36.04
% 136.68/36.04 % ------ Proving...
% 136.68/36.04 % Proof_search_loop: time out after: 5405 full_loop iterations
% 136.68/36.04
% 136.68/36.04 % ------ Option_1: Negative Selections Time Limit: 35.
% 136.68/36.04
% 136.68/36.04
% 136.68/36.04 % ------
% 136.68/36.04 % Current options:
% 136.68/36.04 % ------
% 136.68/36.04
% 136.68/36.04
% 136.68/36.04 %
% 136.68/36.04
% 136.68/36.04 % ------ Proving...
% 136.68/36.04 %
% 136.68/36.04
% 136.68/36.04 % SZS status Theorem for theBenchmark.p
% 136.68/36.04
% 136.68/36.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 136.68/36.05
% 136.68/36.05
%------------------------------------------------------------------------------