%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC165+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 : n005.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 03:08:08 PM UTC 2026
% Result : Theorem 47.51s 10.64s
% Output : CNFRefutation 47.51s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f555ERROR: Could not build tree for root c_141550ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax1) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
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(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(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax41) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
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(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
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(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X12] :
( lt(X12,X8)
& memberP(X10,X12)
& ssItem(X12) )
| ? [X11] :
( lt(X8,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,X2),X10) != X3
| cons(X8,nil) != X2 ) ) ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( neq(X4,X5)
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) ) ) ) )
| 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)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X12] :
( lt(X12,X8)
& memberP(X10,X12)
& ssItem(X12) )
| ? [X11] :
( lt(X8,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,X2),X10) != X3
| cons(X8,nil) != X2 ) ) ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( neq(X4,X5)
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) ) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f99,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(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f103,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(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) != X0 ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f146,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(f147,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(f148,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f151,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f152,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f151]) ).
fof(f154,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f155,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ) ) ),
inference(flattening,[],[f154]) ).
fof(f156,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f170,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f171,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f170]) ).
fof(f186,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f187,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f186]) ).
fof(f188,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f188]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f192]) ).
fof(f194,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X2 = X0 ) ) ),
inference(ennf_transformation,[],[f79]) ).
fof(f195,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X2 = X0 ) ) ),
inference(flattening,[],[f194]) ).
fof(f196,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != app(X1,X0)
| X2 = X0 ) ) ),
inference(ennf_transformation,[],[f80]) ).
fof(f197,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != app(X1,X0)
| X2 = X0 ) ) ),
inference(flattening,[],[f196]) ).
fof(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f199,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f200,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X12] :
( ~ lt(X12,X8)
| ~ memberP(X10,X12)
| ~ ssItem(X12) )
& ! [X11] :
( ~ lt(X8,X11)
| ~ memberP(X9,X11)
| ~ ssItem(X11) )
& app(app(X9,X2),X10) = X3
& cons(X8,nil) = X2 ) ) ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0 ) ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X12] :
( ~ lt(X12,X8)
| ~ memberP(X10,X12)
| ~ ssItem(X12) )
& ! [X11] :
( ~ lt(X8,X11)
| ~ memberP(X9,X11)
| ~ ssItem(X11) )
& app(app(X9,X2),X10) = X3
& cons(X8,nil) = X2 ) ) ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0 ) ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f236,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,[],[f99]) ).
fof(f237,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,[],[f236]) ).
fof(f238,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0
& ssList(sK10(X0,X1))
& ssList(sK9(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f237]) ).
fof(f242,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f243,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X3] :
( app(X1,X3) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f242]) ).
fof(f244,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK12(X0,X1)) = X0
& ssList(sK12(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X0,X1))],[f243]) ).
fof(f248,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,[],[f103]) ).
fof(f249,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,[],[f248]) ).
fof(f250,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
& ssList(sK15(X0,X1))
& ssList(sK14(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X4,sK14(X0,X1)),skolemize(X5,sK15(X0,X1))],[f249]) ).
fof(f279,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,[],[f146]) ).
fof(f280,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,[],[f279]) ).
fof(f281,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,[],[f147]) ).
fof(f282,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,[],[f281]) ).
fof(f283,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ( ( ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ( frontsegP(X2,X3)
& X0 = X1 ) )
& ( ~ frontsegP(X2,X3)
| X0 != X1
| frontsegP(cons(X0,X2),cons(X1,X3)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f156]) ).
fof(f284,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ( ( ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ( frontsegP(X2,X3)
& X0 = X1 ) )
& ( ~ frontsegP(X2,X3)
| X0 != X1
| frontsegP(cons(X0,X2),cons(X1,X3)) ) ) ) ) ) ),
inference(flattening,[],[f283]) ).
fof(f292,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK52(X0)
& ssItem(sK52(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X1,sK52(X0))],[f187]) ).
fof(f293,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK53(X0)
& ssList(sK53(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(X1,sK53(X0))],[f189]) ).
fof(f294,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f200]) ).
fof(f295,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(flattening,[],[f294]) ).
fof(f301,plain,
( ssList(sK57)
& ssList(sK58)
& ssList(sK59)
& ssList(sK60)
& ( ( nil = sK59
& nil = sK60 )
| sP6(sK59,sK60) )
& ssItem(sK61)
& ssItem(sK62)
& ssList(sK63)
& ssList(sK64)
& ~ neq(sK61,sK62)
& sK57 = app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),sK64)
& sK57 = sK59
& sK58 = sK60 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60,sK61,sK62,sK63,sK64]),skolemize(X0,sK57),skolemize(X1,sK58),skolemize(X2,sK59),skolemize(X3,sK60),skolemize(X4,sK61),skolemize(X5,sK62),skolemize(X6,sK63),skolemize(X7,sK64)],[f233]) ).
fof(f303,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f234]) ).
fof(f310,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,[],[f238]) ).
fof(f316,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f323,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,[],[f250]) ).
fof(f393,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f394,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f395,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f406,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f408,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f420,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f421,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f282]) ).
fof(f424,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f427,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f152]) ).
fof(f429,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f430,plain,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| frontsegP(X2,X3) ),
inference(cnf_transformation,[],[f284]) ).
fof(f444,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f171]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK52(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f475,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK52(X0)) ),
inference(cnf_transformation,[],[f292]) ).
fof(f476,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK53(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f477,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK53(X0)) ),
inference(cnf_transformation,[],[f293]) ).
fof(f479,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f480,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f195]) ).
fof(f481,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f197]) ).
fof(f482,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f483,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f484,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f295]) ).
fof(f485,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f295]) ).
fof(f487,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f508,plain,
ssList(sK57),
inference(cnf_transformation,[],[f301]) ).
fof(f512,plain,
( nil = sK59
| sP6(sK59,sK60) ),
inference(cnf_transformation,[],[f301]) ).
fof(f514,plain,
ssItem(sK61),
inference(cnf_transformation,[],[f301]) ).
fof(f515,plain,
ssItem(sK62),
inference(cnf_transformation,[],[f301]) ).
fof(f516,plain,
ssList(sK63),
inference(cnf_transformation,[],[f301]) ).
fof(f517,plain,
ssList(sK64),
inference(cnf_transformation,[],[f301]) ).
fof(f518,plain,
~ neq(sK61,sK62),
inference(cnf_transformation,[],[f301]) ).
fof(f519,plain,
sK57 = app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),sK64),
inference(cnf_transformation,[],[f301]) ).
fof(f520,plain,
sK57 = sK59,
inference(cnf_transformation,[],[f301]) ).
fof(f522,plain,
sK59 = app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),sK64),
inference(definition_unfolding,[],[f519,f520]) ).
fof(f524,plain,
ssList(sK59),
inference(definition_unfolding,[],[f508,f520]) ).
fof(f526,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,[],[f310]) ).
fof(f528,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f316]) ).
fof(f530,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,[],[f323]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_54,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,[],[f526]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f528]) ).
tcf(c_67,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,[],[f530]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f394]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f395]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f406]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f408]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f420]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f555]) ).
tcf(c_170,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,[],[f421]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f424]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f427]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f429]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X1,X3)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(cnf_transformation,[],[f430]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f444]) ).
tcf(c_219,plain,
! [X0: $i] :
( ssItem(sK52(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f475]) ).
tcf(c_220,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK52(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_221,plain,
! [X0: $i] :
( ssList(sK53(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f477]) ).
tcf(c_222,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK53(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f476]) ).
tcf(c_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f479]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X2,X1) ) ),
inference(cnf_transformation,[],[f480]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X0,X2) ) ),
inference(cnf_transformation,[],[f481]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(X0,X1),X2) = app(X0,app(X1,X2)) )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f483]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f485]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f484]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f487]) ).
tcf(c_253,negated_conjecture,
app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),sK64) = sK59,
inference(cnf_transformation,[],[f522]) ).
tcf(c_254,negated_conjecture,
~ neq(sK61,sK62),
inference(cnf_transformation,[],[f518]) ).
tcf(c_255,negated_conjecture,
ssList(sK64),
inference(cnf_transformation,[],[f517]) ).
tcf(c_256,negated_conjecture,
ssList(sK63),
inference(cnf_transformation,[],[f516]) ).
tcf(c_257,negated_conjecture,
ssItem(sK62),
inference(cnf_transformation,[],[f515]) ).
tcf(c_258,negated_conjecture,
ssItem(sK61),
inference(cnf_transformation,[],[f514]) ).
tcf(c_260,negated_conjecture,
( sP6(sK59,sK60)
| ( nil = sK59 ) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_264,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f524]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
tcf(c_3323,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0)
| ( X1 != sK62 )
| ( X0 != sK61 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_254]) ).
tcf(c_3324,plain,
( ( sK61 = sK62 )
| ~ ssItem(sK62)
| ~ ssItem(sK61) ),
inference(unflattening,[status(thm)],[c_3323]) ).
tcf(c_3325,plain,
sK61 = sK62,
inference(global_subsumption_just,[status(thm)],[c_3324,c_258,c_257,c_3324]) ).
tcf(c_6897,plain,
app(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),sK64) = sK59,
inference(light_normalisation,[status(thm)],[c_253,c_3325]) ).
tcf(c_13422,definition,
iPr_def_10 = cons(sK61,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_13423,definition,
iPr_def_11 = app(sK63,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_13424,definition,
iPr_def_12 = app(iPr_def_11,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_13425,definition,
iPr_def_13 = app(iPr_def_12,sK64),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_13427,definition,
iPr_def_15 = cons(iPr_def_14,nil),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_13432,plain,
iPr_def_13 = sK59,
inference(demodulation,[status(thm)],[c_6897,c_13422,c_13423,c_13424,c_13425]) ).
tcf(c_13448,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_264]) ).
tcf(c_13450,negated_conjecture,
ssItem(sK61),
inference(demodulation,[status(thm)],[c_258]) ).
tcf(c_13451,negated_conjecture,
ssList(sK63),
inference(demodulation,[status(thm)],[c_256]) ).
tcf(c_13452,negated_conjecture,
ssList(sK64),
inference(demodulation,[status(thm)],[c_255]) ).
tcf(c_16482,plain,
ssList(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_13448,c_13432]) ).
tcf(c_17178,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK61)
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK61,nil))) ),
inference(superposition,[status(thm)],[c_13422,c_54]) ).
tcf(c_17188,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK61)
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_17178,c_13422]) ).
tcf(c_17189,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK61)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17188,c_141,c_13450]) ).
tcf(c_17263,plain,
( memberP(iPr_def_12,sK61)
| ~ ssList(iPr_def_11)
| ~ ssList(app(iPr_def_11,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_13424,c_17189]) ).
tcf(c_17264,plain,
( memberP(iPr_def_12,sK61)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_17263,c_13424]) ).
tcf(c_17539,plain,
app(sK63,nil) = sK63,
inference(superposition,[status(thm)],[c_13451,c_232]) ).
tcf(c_17618,plain,
( ssList(iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK61) ),
inference(superposition,[status(thm)],[c_13422,c_140]) ).
tcf(c_17627,plain,
ssList(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_17618,c_141,c_13450]) ).
tcf(c_17740,plain,
( ssList(iPr_def_11)
| ~ ssList(iPr_def_10)
| ~ ssList(sK63) ),
inference(superposition,[status(thm)],[c_13423,c_153]) ).
tcf(c_17741,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_13424,c_153]) ).
tcf(c_17772,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17741,c_17627]) ).
tcf(c_17775,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_17740,c_17627,c_13451]) ).
tcf(c_17776,plain,
ssList(iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_17772,c_17775]) ).
tcf(c_17793,plain,
( memberP(iPr_def_12,sK61)
| ~ ssList(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_17264,c_17775]) ).
tcf(c_17794,plain,
memberP(iPr_def_12,sK61),
inference(forward_subsumption_resolution,[status(thm)],[c_17793,c_17776]) ).
tcf(c_18482,plain,
( frontsegP(iPr_def_12,iPr_def_11)
| ~ ssList(iPr_def_11)
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_13424,c_393]) ).
tcf(c_18541,plain,
frontsegP(iPr_def_12,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_18482,c_17775,c_17627]) ).
tcf(c_18719,plain,
( ~ ssList(nil)
| ~ ssItem(sK61)
| ( nil != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13422,c_142]) ).
tcf(c_18726,plain,
nil != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_18719,c_141,c_13450]) ).
tcf(c_19211,plain,
( ( nil = iPr_def_11 )
| ( hd(iPr_def_11) = sK52(iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_17775,c_220]) ).
tcf(c_19444,plain,
( ( nil = iPr_def_11 )
| ( tl(iPr_def_11) = sK53(iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_17775,c_222]) ).
tcf(c_21264,plain,
( ( nil = iPr_def_11 )
| ( cons(hd(iPr_def_11),tl(iPr_def_11)) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_17775,c_224]) ).
tcf(c_22299,plain,
( ( nil = iPr_def_10 )
| ~ ssList(iPr_def_10)
| ~ ssList(sK63)
| ( nil != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_13423,c_230]) ).
tcf(c_22300,plain,
( ( nil = iPr_def_10 )
| ~ ssList(iPr_def_11)
| ~ ssList(iPr_def_10)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_13424,c_230]) ).
tcf(c_22301,plain,
( ( nil = sK64 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK64)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_13425,c_230]) ).
tcf(c_22353,plain,
( ( nil = sK64 )
| ( nil != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22301,c_17776,c_13452]) ).
tcf(c_22356,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_22300,c_18726,c_17775,c_17627]) ).
tcf(c_22357,plain,
nil != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_22299,c_18726,c_17627,c_13451]) ).
tcf(c_22398,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK64)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_13425,c_231]) ).
tcf(c_22450,plain,
( ( nil = iPr_def_12 )
| ( nil != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22398,c_17776,c_13452]) ).
tcf(c_22829,plain,
nil != iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_22353,c_22356,c_22450]) ).
tcf(c_23024,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ ssList(iPr_def_11)
| ~ ssList(iPr_def_10)
| ~ ssItem(X0)
| ~ memberP(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_13424,c_165]) ).
tcf(c_23025,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sK64)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_13425,c_165]) ).
tcf(c_23056,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23025,c_17776,c_13452]) ).
tcf(c_23060,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_11,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23024,c_17775,c_17627]) ).
tcf(c_23413,plain,
! [X0: $i] :
( frontsegP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sK64)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_13425,c_176]) ).
tcf(c_23475,plain,
! [X0: $i] :
( frontsegP(iPr_def_13,X0)
| ~ ssList(X0)
| ~ frontsegP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23413,c_17776,c_13452]) ).
tcf(c_24546,plain,
( memberP(iPr_def_13,sK61)
| ~ ssItem(sK61) ),
inference(superposition,[status(thm)],[c_17794,c_23056]) ).
tcf(c_24547,plain,
memberP(iPr_def_13,sK61),
inference(forward_subsumption_resolution,[status(thm)],[c_24546,c_13450]) ).
tcf(c_25037,plain,
( frontsegP(iPr_def_13,iPr_def_11)
| ~ ssList(iPr_def_11) ),
inference(superposition,[status(thm)],[c_18541,c_23475]) ).
tcf(c_25040,plain,
frontsegP(iPr_def_13,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_25037,c_17775]) ).
tcf(c_27316,plain,
! [X0: $i,X1: $i] :
( ( app(app(X0,X1),sK64) = app(X0,app(X1,sK64)) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_13452,c_228]) ).
tcf(c_29498,plain,
! [X0: $i] :
( ( X0 = sK63 )
| ~ ssList(iPr_def_10)
| ~ ssList(sK63)
| ~ ssList(X0)
| ( app(X0,iPr_def_10) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_13423,c_225]) ).
tcf(c_29615,plain,
! [X0: $i] :
( ( X0 = sK63 )
| ~ ssList(X0)
| ( app(X0,iPr_def_10) != iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29498,c_17627,c_13451]) ).
tcf(c_30017,plain,
( ( sK63 = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ( iPr_def_11 != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_13424,c_29615]) ).
tcf(c_30022,plain,
( ( sK63 = iPr_def_11 )
| ( iPr_def_11 != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30017,c_17775]) ).
tcf(c_30100,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(sK63)
| ~ ssList(nil)
| ~ ssList(X0)
| ( app(sK63,X0) != sK63 ) ),
inference(superposition,[status(thm)],[c_17539,c_226]) ).
tcf(c_30172,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ( app(sK63,X0) != sK63 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30100,c_13451,c_141]) ).
tcf(c_30534,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(sK63)
| ~ ssList(X0)
| ~ ssList(app(app(sK63,iPr_def_10),X0)) ),
inference(superposition,[status(thm)],[c_13423,c_67]) ).
tcf(c_30685,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(sK63)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_11,X0)) ),
inference(light_normalisation,[status(thm)],[c_30534,c_13423]) ).
tcf(c_30686,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_10)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_11,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30685,c_17627,c_13451]) ).
tcf(c_30847,plain,
! [X0: $i,X1: $i] :
( frontsegP(nil,X1)
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ frontsegP(iPr_def_10,cons(X0,X1)) ),
inference(superposition,[status(thm)],[c_13422,c_179]) ).
tcf(c_30866,plain,
! [X0: $i,X1: $i] :
( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ frontsegP(iPr_def_10,cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30847,c_141,c_13450]) ).
tcf(c_32517,plain,
( segmentP(iPr_def_12,iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(app(iPr_def_11,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_13424,c_30686]) ).
tcf(c_32524,plain,
( segmentP(iPr_def_12,iPr_def_10)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_32517,c_13424]) ).
tcf(c_32525,plain,
segmentP(iPr_def_12,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_32524,c_17776,c_17627]) ).
tcf(c_32549,plain,
( ( nil = iPr_def_10 )
| ~ ssList(iPr_def_10)
| ( sK63 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_13423,c_30172]) ).
tcf(c_32555,plain,
sK63 != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_32549,c_18726,c_17627]) ).
tcf(c_33405,plain,
hd(iPr_def_11) = sK52(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_19211,c_19211,c_22357]) ).
tcf(c_33407,plain,
( ssItem(hd(iPr_def_11))
| ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11) ),
inference(superposition,[status(thm)],[c_33405,c_219]) ).
tcf(c_33408,plain,
ssItem(hd(iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_33407,c_22357,c_17775]) ).
tcf(c_40658,plain,
! [X0: $i] :
( ( app(app(sK63,X0),sK64) = app(sK63,app(X0,sK64)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_13451,c_27316]) ).
tcf(c_42688,plain,
app(app(sK63,iPr_def_12),sK64) = app(sK63,app(iPr_def_12,sK64)),
inference(superposition,[status(thm)],[c_17776,c_40658]) ).
tcf(c_42701,plain,
app(app(sK63,iPr_def_12),sK64) = app(sK63,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_42688,c_13425]) ).
tcf(c_48951,plain,
tl(iPr_def_11) = sK53(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_19444,c_19444,c_22357]) ).
tcf(c_48953,plain,
( ssList(tl(iPr_def_11))
| ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11) ),
inference(superposition,[status(thm)],[c_48951,c_221]) ).
tcf(c_48954,plain,
ssList(tl(iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_48953,c_22357,c_17775]) ).
tcf(c_48983,plain,
app(nil,tl(iPr_def_11)) = tl(iPr_def_11),
inference(superposition,[status(thm)],[c_48954,c_155]) ).
tcf(c_53432,plain,
( frontsegP(tl(iPr_def_11),nil)
| ~ ssList(nil)
| ~ ssList(tl(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_48983,c_393]) ).
tcf(c_53444,plain,
frontsegP(tl(iPr_def_11),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_53432,c_141,c_48954]) ).
tcf(c_53498,plain,
( ( tl(iPr_def_11) = nil )
| ~ ssList(nil)
| ~ ssList(tl(iPr_def_11))
| ~ frontsegP(nil,tl(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53444,c_174]) ).
tcf(c_53501,plain,
( ( tl(iPr_def_11) = nil )
| ~ frontsegP(nil,tl(iPr_def_11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53498,c_141,c_48954]) ).
tcf(c_54751,plain,
iPr_def_11 != iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_30022,c_30022,c_32555]) ).
tcf(c_87675,plain,
( ssList(app(sK63,iPr_def_13))
| ~ ssList(sK64)
| ~ ssList(app(sK63,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_42701,c_153]) ).
tcf(c_87677,plain,
( segmentP(app(sK63,iPr_def_13),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(sK64)
| ~ ssList(sK63)
| ~ ssList(app(app(sK63,iPr_def_12),sK64)) ),
inference(superposition,[status(thm)],[c_42701,c_67]) ).
tcf(c_87695,plain,
( ssList(app(sK63,iPr_def_13))
| ~ ssList(app(sK63,iPr_def_12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87675,c_13452]) ).
tcf(c_87731,plain,
( segmentP(app(sK63,iPr_def_13),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(sK64)
| ~ ssList(sK63)
| ~ ssList(app(sK63,iPr_def_13)) ),
inference(light_normalisation,[status(thm)],[c_87677,c_42701]) ).
tcf(c_87732,plain,
( segmentP(app(sK63,iPr_def_13),iPr_def_12)
| ~ ssList(app(sK63,iPr_def_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87731,c_17776,c_13452,c_13451]) ).
tcf(c_88114,plain,
( ssList(app(sK63,iPr_def_13))
| ~ ssList(iPr_def_12)
| ~ ssList(sK63) ),
inference(superposition,[status(thm)],[c_153,c_87695]) ).
tcf(c_88115,plain,
ssList(app(sK63,iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_88114,c_17776,c_13451]) ).
tcf(c_88246,plain,
segmentP(app(sK63,iPr_def_13),iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_87732,c_87732,c_88115]) ).
tcf(c_96648,plain,
cons(hd(iPr_def_11),tl(iPr_def_11)) = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_21264,c_21264,c_22357]) ).
tcf(c_96681,plain,
( frontsegP(nil,tl(iPr_def_11))
| ~ frontsegP(iPr_def_10,iPr_def_11)
| ~ ssList(tl(iPr_def_11))
| ~ ssItem(hd(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_96648,c_30866]) ).
tcf(c_96693,plain,
( memberP(iPr_def_11,hd(iPr_def_11))
| ~ ssList(tl(iPr_def_11))
| ~ ssItem(hd(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_96648,c_168]) ).
tcf(c_96698,plain,
memberP(iPr_def_11,hd(iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_96693,c_48954,c_33408]) ).
tcf(c_96700,plain,
( frontsegP(nil,tl(iPr_def_11))
| ~ frontsegP(iPr_def_10,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_96681,c_48954,c_33408]) ).
tcf(c_97052,plain,
( memberP(iPr_def_12,hd(iPr_def_11))
| ~ ssItem(hd(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_96698,c_23060]) ).
tcf(c_97054,plain,
memberP(iPr_def_12,hd(iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_97052,c_33408]) ).
tcf(c_97258,plain,
( memberP(iPr_def_13,hd(iPr_def_11))
| ~ ssItem(hd(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_97054,c_23056]) ).
tcf(c_97259,plain,
memberP(iPr_def_13,hd(iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_97258,c_33408]) ).
fof(f232,definition,
! [X2,X3] :
( ~ sP6(X2,X3)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X12] :
( ~ lt(X12,X8)
| ~ memberP(X10,X12)
| ~ ssItem(X12) )
& ! [X11] :
( ~ lt(X8,X11)
| ~ memberP(X9,X11)
| ~ ssItem(X11) )
& app(app(X9,X2),X10) = X3
& cons(X8,nil) = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f233,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| sP6(X2,X3) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0 ) ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f222,f232]) ).
fof(f298,plain,
! [X2,X3] :
( ~ sP6(X2,X3)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X12] :
( ~ lt(X12,X8)
| ~ memberP(X10,X12)
| ~ ssItem(X12) )
& ! [X11] :
( ~ lt(X8,X11)
| ~ memberP(X9,X11)
| ~ ssItem(X11) )
& app(app(X9,X2),X10) = X3
& cons(X8,nil) = X2 ) ) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f299,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(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 ) ) ) ),
inference(rectify,[],[f298]) ).
fof(f300,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ( ssItem(sK54(X0,X1))
& ssList(sK55(X0,X1))
& ssList(sK56(X0,X1))
& ! [X6] :
( ~ lt(X6,sK54(X0,X1))
| ~ memberP(sK56(X0,X1),X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(sK54(X0,X1),X5)
| ~ memberP(sK55(X0,X1),X5)
| ~ ssItem(X5) )
& app(app(sK55(X0,X1),X0),sK56(X0,X1)) = X1
& cons(sK54(X0,X1),nil) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54,sK55,sK56]),skolemize(X2,sK54(X0,X1)),skolemize(X3,sK55(X0,X1)),skolemize(X4,sK56(X0,X1))],[f299]) ).
fof(f501,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ssItem(sK54(X0,X1)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f507,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| cons(sK54(X0,X1),nil) = X0 ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( ( cons(sK54(X0,X1),nil) = X0 )
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] :
( ssItem(sK54(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_3331,plain,
! [X0: $i,X1: $i] :
( ssItem(sK54(X0,X1))
| ( nil = sK59 )
| ( X1 != sK60 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_252,c_260]) ).
tcf(c_3332,plain,
( ssItem(sK54(sK59,sK60))
| ( nil = sK59 ) ),
inference(unflattening,[status(thm)],[c_3331]) ).
tcf(c_3455,plain,
! [X0: $i,X1: $i] :
( ( nil = sK59 )
| ( cons(sK54(X0,X1),nil) = X0 )
| ( X1 != sK60 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_246,c_260]) ).
tcf(c_3456,plain,
( ( nil = sK59 )
| ( cons(sK54(sK59,sK60),nil) = sK59 ) ),
inference(unflattening,[status(thm)],[c_3455]) ).
tcf(c_13434,plain,
( ( iPr_def_15 = sK59 )
| ( nil = sK59 ) ),
inference(demodulation,[status(thm)],[c_3456]) ).
tcf(c_13446,plain,
( ssItem(iPr_def_14)
| ( nil = sK59 ) ),
inference(demodulation,[status(thm)],[c_3332]) ).
tcf(c_16507,plain,
( ssItem(iPr_def_14)
| ( nil = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_13446,c_13432]) ).
tcf(c_16522,plain,
( ( iPr_def_13 = iPr_def_15 )
| ( nil = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_13434,c_13432]) ).
tcf(c_22858,plain,
iPr_def_13 = iPr_def_15,
inference(backward_subsumption_resolution,[status(thm)],[c_16522,c_22829]) ).
tcf(c_22859,plain,
ssItem(iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_16507,c_22829]) ).
tcf(c_22917,plain,
cons(iPr_def_14,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_13427,c_22858]) ).
tcf(c_23605,plain,
! [X0: $i] :
( ( app(cons(iPr_def_14,nil),X0) = cons(iPr_def_14,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_22859,c_227]) ).
tcf(c_23612,plain,
! [X0: $i] :
( ( cons(iPr_def_14,X0) = app(iPr_def_13,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_23605,c_22917]) ).
tcf(c_34420,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = iPr_def_14 )
| ~ ssList(nil)
| ~ ssItem(iPr_def_14)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_22917,c_170]) ).
tcf(c_34440,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = iPr_def_14 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34420,c_141,c_22859]) ).
tcf(c_113157,plain,
cons(iPr_def_14,sK64) = app(iPr_def_13,sK64),
inference(superposition,[status(thm)],[c_13452,c_23612]) ).
tcf(c_113859,plain,
! [X0: $i] :
( memberP(cons(iPr_def_14,sK64),X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sK64)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_113157,c_165]) ).
tcf(c_113904,plain,
! [X0: $i] :
( memberP(cons(iPr_def_14,sK64),X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_113859,c_16482,c_13452]) ).
tcf(c_114948,plain,
! [X0: $i] :
( memberP(sK64,X0)
| ( X0 = iPr_def_14 )
| ~ ssList(sK64)
| ~ ssItem(iPr_def_14)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_113904,c_170]) ).
tcf(c_114949,plain,
! [X0: $i] :
( memberP(sK64,X0)
| ( X0 = iPr_def_14 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_114948,c_13452,c_22859]) ).
tcf(c_116579,plain,
! [X0: $i] :
( ~ memberP(iPr_def_13,X0)
| ~ ssItem(X0)
| ( X0 = iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_114949,c_171,c_34440]) ).
tcf(c_116580,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(renaming,[status(thm)],[c_116579]) ).
tcf(c_116589,plain,
( ( sK61 = iPr_def_14 )
| ~ ssItem(sK61) ),
inference(superposition,[status(thm)],[c_24547,c_116580]) ).
tcf(c_116591,plain,
( ( hd(iPr_def_11) = iPr_def_14 )
| ~ ssItem(hd(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_97259,c_116580]) ).
tcf(c_116593,plain,
sK61 = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_116589,c_13450]) ).
tcf(c_116595,plain,
hd(iPr_def_11) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_116591,c_33408]) ).
tcf(c_116970,plain,
cons(iPr_def_14,nil) = iPr_def_10,
inference(demodulation,[status(thm)],[c_13422,c_116593]) ).
tcf(c_116973,plain,
iPr_def_10 = iPr_def_13,
inference(demodulation,[status(thm)],[c_22917,c_116970]) ).
tcf(c_117066,plain,
segmentP(app(sK63,iPr_def_10),iPr_def_12),
inference(demodulation,[status(thm)],[c_88246,c_116973]) ).
tcf(c_117168,plain,
frontsegP(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_25040,c_116973]) ).
tcf(c_117271,plain,
frontsegP(nil,tl(iPr_def_11)),
inference(backward_subsumption_resolution,[status(thm)],[c_96700,c_117168]) ).
tcf(c_117282,plain,
tl(iPr_def_11) = nil,
inference(backward_subsumption_resolution,[status(thm)],[c_53501,c_117271]) ).
tcf(c_117284,plain,
cons(hd(iPr_def_11),nil) = iPr_def_11,
inference(demodulation,[status(thm)],[c_96648,c_117282]) ).
tcf(c_117446,plain,
segmentP(iPr_def_11,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_117066,c_13423]) ).
tcf(c_119761,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ segmentP(iPr_def_12,iPr_def_11) ),
inference(superposition,[status(thm)],[c_117446,c_191]) ).
tcf(c_119762,plain,
~ segmentP(iPr_def_12,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_119761,c_54751,c_17776,c_17775]) ).
tcf(c_141550,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_119762,c_117284,c_116970,c_116595,c_32525]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC165+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.59 % Computer : n005.cluster.edu
% 0.10/0.59 % Model : x86_64 x86_64
% 0.10/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.59 % Memory : 8046.5625MB
% 0.10/0.59 % OS : Linux 6.8.0-71-generic
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Thu Sep 24 16:45:03 UTC 2026
% 0.10/0.60 % CPUTime :
% 0.10/0.60 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.63 Running first-order theorem proving
% 0.14/0.63 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
% 0.14/0.65
% 0.14/0.65 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.65
% 0.14/0.65 % Detected problem language: tptp
% 0.14/0.66 % Proving...
% 47.51/10.64 % SZS status Started for theBenchmark.p
% 47.51/10.64 % SZS status Theorem for theBenchmark.p
% 47.51/10.64
% 47.51/10.64 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 47.51/10.64
% 47.51/10.64 % ------ iProver source info
% 47.51/10.64
% 47.51/10.64 % git: date: 2026-07-19 20:42:38 +0200
% 47.51/10.64 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 47.51/10.64 % git: non_committed_changes: false
% 47.51/10.64
% 47.51/10.64 % ------ Parsing...
% 47.51/10.64 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 47.51/10.64
% 47.51/10.64 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 3 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 47.51/10.64
% 47.51/10.64 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 47.51/10.64
% 47.51/10.64 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 47.51/10.64 % ------ Proving...
% 47.51/10.64 % ------ Problem Properties
% 47.51/10.64
% 47.51/10.64 %
% 47.51/10.64 % clauses 211
% 47.51/10.64 % conjectures 5
% 47.51/10.64 % EPR 70
% 47.51/10.64 % Horn 133
% 47.51/10.64 % unary 33
% 47.51/10.64 % binary 50
% 47.51/10.64 % lits 671
% 47.51/10.64 % lits eq 108
% 47.51/10.64 % fd_pure 0
% 47.51/10.64 % fd_pseudo 0
% 47.51/10.64 % fd_cond 21
% 47.51/10.64 % fd_pseudo_cond 14
% 47.51/10.64 % AC symbols 0
% 47.51/10.64
% 47.51/10.64 % ------ Schedule dynamic 5 is on
% 47.51/10.64
% 47.51/10.64 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 47.51/10.64
% 47.51/10.64
% 47.51/10.64 % ------
% 47.51/10.64 % Current options:
% 47.51/10.64 % ------
% 47.51/10.64
% 47.51/10.64
% 47.51/10.64 %
% 47.51/10.64
% 47.51/10.64 % ------ Proving...
% 47.51/10.64 %
% 47.51/10.64
% 47.51/10.64 % SZS status Theorem for theBenchmark.p
% 47.51/10.64
% 47.51/10.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 47.51/10.65
% 47.51/10.65
%------------------------------------------------------------------------------