%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC152+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 : n001.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 03:08:06 PM UTC 2026
% Result : Theorem 79.88s 13.49s
% Output : CNFRefutation 79.88s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f552ERROR: Could not build tree for root c_193645ERROR: 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(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/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/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(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax41) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil != X2
| nil != X3 )
& ! [X10] :
( ? [X11] :
( leq(X10,X11)
& memberP(X3,X11)
& X10 != X11
& ssItem(X11) )
| ~ memberP(X3,X10)
| cons(X10,nil) != X2
| ~ ssItem(X10) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ( leq(X4,X5)
& ! [X9] :
( ( leq(X9,X5)
& leq(X4,X9) )
| ~ memberP(X7,X9)
| ~ ssItem(X9) ) )
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0
| ~ ssList(X8) ) ) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil != X2
| nil != X3 )
& ! [X10] :
( ? [X11] :
( leq(X10,X11)
& memberP(X3,X11)
& X10 != X11
& ssItem(X11) )
| ~ memberP(X3,X10)
| cons(X10,nil) != X2
| ~ ssItem(X10) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ( leq(X4,X5)
& ! [X9] :
( ( leq(X9,X5)
& leq(X4,X9) )
| ~ memberP(X7,X9)
| ~ ssItem(X9) ) )
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0
| ~ ssList(X8) ) ) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(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(f157,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(ennf_transformation,[],[f45]) ).
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(f200,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X10] :
( ! [X11] :
( ~ leq(X10,X11)
| ~ memberP(X3,X11)
| X10 = X11
| ~ ssItem(X11) )
& memberP(X3,X10)
& cons(X10,nil) = X2
& ssItem(X10) ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ( ~ leq(X4,X5)
| ? [X9] :
( ( ~ leq(X9,X5)
| ~ leq(X4,X9) )
& memberP(X7,X9)
& ssItem(X9) ) )
& leq(X5,X4)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X0
& ssList(X8) ) ) ) ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f233,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(f234,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,[],[f233]) ).
fof(f235,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))],[f234]) ).
fof(f239,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(f240,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,[],[f239]) ).
fof(f241,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f240]) ).
fof(f276,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(f277,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,[],[f276]) ).
fof(f278,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(f279,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,[],[f278]) ).
fof(f289,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(X1,sK51(X0))],[f187]) ).
fof(f290,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X1,sK52(X0))],[f189]) ).
fof(f291,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(f292,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,[],[f291]) ).
fof(f295,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ( ( nil = sK55
& nil = sK56 )
| ( ! [X11] :
( ~ leq(sK63,X11)
| ~ memberP(sK56,X11)
| sK63 = X11
| ~ ssItem(X11) )
& memberP(sK56,sK63)
& sK55 = cons(sK63,nil)
& ssItem(sK63) ) )
& ssItem(sK57)
& ssItem(sK58)
& ssList(sK59)
& ssList(sK60)
& ( ~ leq(sK57,sK58)
| ( ( ~ leq(sK62,sK58)
| ~ leq(sK57,sK62) )
& memberP(sK60,sK62)
& ssItem(sK62) ) )
& leq(sK58,sK57)
& sK53 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61)
& ssList(sK61)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61,sK62,sK63]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59),skolemize(X7,sK60),skolemize(X8,sK61),skolemize(X9,sK62),skolemize(X10,sK63)],[f221]) ).
fof(f304,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,[],[f235]) ).
fof(f310,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f241]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f389,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f400,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f402,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f279]) ).
fof(f418,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f421,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f152]) ).
fof(f427,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(cnf_transformation,[],[f157]) ).
fof(f468,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK51(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f469,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f289]) ).
fof(f470,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK52(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f290]) ).
fof(f473,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f474,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f195]) ).
fof(f478,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f292]) ).
fof(f479,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f292]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
( nil = sK55
| sK55 = cons(sK63,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
( nil = sK55
| ssItem(sK63) ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
ssList(sK59),
inference(cnf_transformation,[],[f295]) ).
fof(f509,plain,
ssList(sK60),
inference(cnf_transformation,[],[f295]) ).
fof(f514,plain,
sK53 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61),
inference(cnf_transformation,[],[f295]) ).
fof(f515,plain,
ssList(sK61),
inference(cnf_transformation,[],[f295]) ).
fof(f516,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f519,plain,
sK55 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61),
inference(definition_unfolding,[],[f514,f516]) ).
fof(f521,plain,
ssList(sK55),
inference(definition_unfolding,[],[f495,f516]) ).
fof(f523,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,[],[f304]) ).
fof(f525,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f310]) ).
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,[],[f523]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f525]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f388]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f389]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f400]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f402]) ).
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,[],[f414]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f552]) ).
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,[],[f415]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f418]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f421]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f553]) ).
tcf(c_180,plain,
! [X0: $i] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f427]) ).
tcf(c_219,plain,
! [X0: $i] :
( ssItem(sK51(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f469]) ).
tcf(c_220,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK51(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f468]) ).
tcf(c_221,plain,
! [X0: $i] :
( ssList(sK52(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f471]) ).
tcf(c_222,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK52(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f470]) ).
tcf(c_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f473]) ).
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,[],[f474]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f479]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f478]) ).
tcf(c_247,negated_conjecture,
ssList(sK61),
inference(cnf_transformation,[],[f515]) ).
tcf(c_248,negated_conjecture,
app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61) = sK55,
inference(cnf_transformation,[],[f519]) ).
tcf(c_253,negated_conjecture,
ssList(sK60),
inference(cnf_transformation,[],[f509]) ).
tcf(c_254,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f508]) ).
tcf(c_255,negated_conjecture,
ssItem(sK58),
inference(cnf_transformation,[],[f507]) ).
tcf(c_256,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f506]) ).
tcf(c_258,negated_conjecture,
( ssItem(sK63)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_260,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK63,nil) = sK55 ) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_267,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f521]) ).
tcf(c_391,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_9043,definition,
iPr_def_10 = cons(sK63,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_9044,definition,
iPr_def_11 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_9045,definition,
iPr_def_12 = app(sK59,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_9046,definition,
iPr_def_13 = app(iPr_def_12,sK60),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_9047,definition,
iPr_def_14 = cons(sK58,nil),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_9048,definition,
iPr_def_15 = app(iPr_def_13,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_9049,definition,
iPr_def_16 = app(iPr_def_15,sK61),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_9050,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_267]) ).
tcf(c_9055,negated_conjecture,
( ( iPr_def_10 = sK55 )
| ( nil = sK55 ) ),
inference(demodulation,[status(thm)],[c_260,c_9043]) ).
tcf(c_9057,negated_conjecture,
( ssItem(sK63)
| ( nil = sK55 ) ),
inference(demodulation,[status(thm)],[c_258]) ).
tcf(c_9059,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_256]) ).
tcf(c_9060,negated_conjecture,
ssItem(sK58),
inference(demodulation,[status(thm)],[c_255]) ).
tcf(c_9061,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_9062,negated_conjecture,
ssList(sK60),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_9067,negated_conjecture,
iPr_def_16 = sK55,
inference(demodulation,[status(thm)],[c_248,c_9047,c_9044,c_9045,c_9046,c_9048,c_9049]) ).
tcf(c_9068,negated_conjecture,
ssList(sK61),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_12026,plain,
( ssItem(sK63)
| ( nil = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_9057,c_9067]) ).
tcf(c_12052,plain,
( ( iPr_def_10 = iPr_def_16 )
| ( nil = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_9055,c_9067]) ).
tcf(c_12405,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_14),sK58)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK58,nil))) ),
inference(superposition,[status(thm)],[c_9047,c_54]) ).
tcf(c_12416,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_14),sK58)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_14)) ),
inference(light_normalisation,[status(thm)],[c_12405,c_9047]) ).
tcf(c_12417,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_14),sK58)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12416,c_141,c_9060]) ).
tcf(c_12506,plain,
( memberP(iPr_def_15,sK58)
| ~ ssList(iPr_def_13)
| ~ ssList(app(iPr_def_13,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_9048,c_12417]) ).
tcf(c_12507,plain,
( memberP(iPr_def_15,sK58)
| ~ ssList(iPr_def_15)
| ~ ssList(iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_12506,c_9048]) ).
tcf(c_13022,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_9044,c_140]) ).
tcf(c_13023,plain,
( ssList(iPr_def_14)
| ~ ssList(nil)
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_9047,c_140]) ).
tcf(c_13024,plain,
( ssList(iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK63) ),
inference(superposition,[status(thm)],[c_9043,c_140]) ).
tcf(c_13030,plain,
( ssList(iPr_def_10)
| ~ ssItem(sK63) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13024,c_141]) ).
tcf(c_13033,plain,
ssList(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_13023,c_141,c_9060]) ).
tcf(c_13034,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_13022,c_141,c_9059]) ).
tcf(c_13075,plain,
( ssList(iPr_def_10)
| ( nil = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_12026,c_13030]) ).
tcf(c_13147,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(sK59) ),
inference(superposition,[status(thm)],[c_9045,c_153]) ).
tcf(c_13148,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sK60) ),
inference(superposition,[status(thm)],[c_9046,c_153]) ).
tcf(c_13149,plain,
( ssList(iPr_def_15)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_9048,c_153]) ).
tcf(c_13170,plain,
( ssList(iPr_def_15)
| ~ ssList(iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13149,c_13033]) ).
tcf(c_13173,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13148,c_9062]) ).
tcf(c_13176,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_13147,c_13034,c_9061]) ).
tcf(c_13177,plain,
ssList(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_13173,c_13176]) ).
tcf(c_13178,plain,
ssList(iPr_def_15),
inference(backward_subsumption_resolution,[status(thm)],[c_13170,c_13177]) ).
tcf(c_13234,plain,
( ( nil = iPr_def_16 )
| ( app(nil,iPr_def_10) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13075,c_155]) ).
tcf(c_13759,plain,
( frontsegP(iPr_def_16,iPr_def_15)
| ~ ssList(iPr_def_15)
| ~ ssList(sK61) ),
inference(superposition,[status(thm)],[c_9049,c_391]) ).
tcf(c_13815,plain,
frontsegP(iPr_def_16,iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_13759,c_13178,c_9068]) ).
tcf(c_13949,plain,
( ~ ssList(nil)
| ~ ssItem(sK57)
| ( nil != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_9044,c_142]) ).
tcf(c_13950,plain,
( ~ ssList(nil)
| ~ ssItem(sK58)
| ( nil != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9047,c_142]) ).
tcf(c_13958,plain,
nil != iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_13950,c_141,c_9060]) ).
tcf(c_13959,plain,
nil != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_13949,c_141,c_9059]) ).
tcf(c_14408,plain,
( ( nil = iPr_def_15 )
| ( hd(iPr_def_15) = sK51(iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_13178,c_220]) ).
tcf(c_14612,plain,
( ( nil = iPr_def_15 )
| ( tl(iPr_def_15) = sK52(iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_13178,c_222]) ).
tcf(c_16083,plain,
( ( nil = iPr_def_15 )
| ( cons(hd(iPr_def_15),tl(iPr_def_15)) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_13178,c_224]) ).
tcf(c_16285,plain,
ssList(iPr_def_16),
inference(light_normalisation,[status(thm)],[c_9050,c_9067]) ).
tcf(c_16312,plain,
( ( iPr_def_10 = iPr_def_16 )
| ( nil = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_9055,c_9067]) ).
tcf(c_16968,plain,
( ( iPr_def_10 = iPr_def_16 )
| ( cons(sK58,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_16312,c_9047]) ).
tcf(c_17079,plain,
( ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ~ ssList(sK59)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_9045,c_230]) ).
tcf(c_17081,plain,
( ( nil = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ( nil != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_9048,c_230]) ).
tcf(c_17082,plain,
( ( nil = sK61 )
| ~ ssList(iPr_def_15)
| ~ ssList(sK61)
| ( nil != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_9049,c_230]) ).
tcf(c_17125,plain,
( ( nil = sK61 )
| ( nil != iPr_def_16 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17082,c_13178,c_9068]) ).
tcf(c_17128,plain,
nil != iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_17081,c_13958,c_13033,c_13177]) ).
tcf(c_17132,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_17079,c_13959,c_13034,c_9061]) ).
tcf(c_17150,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_14),sK58)
| ( iPr_def_10 = iPr_def_16 )
| ~ ssList(iPr_def_16)
| ~ ssItem(sK58)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK58,iPr_def_16))) ),
inference(superposition,[status(thm)],[c_16968,c_54]) ).
tcf(c_17167,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_14),sK58)
| ( iPr_def_10 = iPr_def_16 )
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK58,iPr_def_16))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17150,c_16285,c_9060]) ).
tcf(c_17193,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK60)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_9046,c_231]) ).
tcf(c_17195,plain,
( ( nil = iPr_def_15 )
| ~ ssList(iPr_def_15)
| ~ ssList(sK61)
| ( nil != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_9049,c_231]) ).
tcf(c_17238,plain,
( ( nil = iPr_def_15 )
| ( nil != iPr_def_16 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17195,c_13178,c_9068]) ).
tcf(c_17241,plain,
( ( nil = iPr_def_12 )
| ( nil != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17193,c_13176,c_9062]) ).
tcf(c_17371,plain,
nil != iPr_def_16,
inference(global_subsumption_just,[status(thm)],[c_17125,c_17128,c_17238]) ).
tcf(c_17375,plain,
ssList(iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_13075,c_17371]) ).
tcf(c_17381,plain,
iPr_def_10 = iPr_def_16,
inference(backward_subsumption_resolution,[status(thm)],[c_12052,c_17371]) ).
tcf(c_17383,plain,
ssItem(sK63),
inference(backward_subsumption_resolution,[status(thm)],[c_12026,c_17371]) ).
tcf(c_17391,plain,
frontsegP(iPr_def_10,iPr_def_15),
inference(demodulation,[status(thm)],[c_13815,c_17381]) ).
tcf(c_18609,plain,
iPr_def_10 = iPr_def_16,
inference(global_subsumption_just,[status(thm)],[c_17167,c_17381]) ).
tcf(c_19343,plain,
( ( iPr_def_10 = iPr_def_15 )
| ~ ssList(iPr_def_15)
| ~ ssList(iPr_def_10)
| ~ frontsegP(iPr_def_15,iPr_def_10) ),
inference(superposition,[status(thm)],[c_17391,c_174]) ).
tcf(c_19346,plain,
( ( iPr_def_10 = iPr_def_15 )
| ~ frontsegP(iPr_def_15,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19343,c_13178,c_17375]) ).
tcf(c_20204,plain,
! [X0: $i] :
( frontsegP(cons(sK63,X0),iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK63)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(superposition,[status(thm)],[c_9043,c_177]) ).
tcf(c_20208,plain,
! [X0: $i] :
( frontsegP(cons(sK63,X0),iPr_def_10)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20204,c_141,c_17383]) ).
tcf(c_23581,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK63 )
| ~ ssList(nil)
| ~ ssItem(sK63)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_9043,c_170]) ).
tcf(c_23582,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK63 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23581,c_141,c_17383]) ).
tcf(c_164430,plain,
ssList(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_9050,c_9067,c_18609]) ).
tcf(c_164432,negated_conjecture,
ssItem(sK63),
inference(global_subsumption_just,[status(thm)],[c_9057,c_17383]) ).
tcf(c_164559,plain,
app(iPr_def_15,sK61) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_9049,c_18609]) ).
tcf(c_164603,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_14),sK58)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK58,nil))) ),
inference(superposition,[status(thm)],[c_9047,c_54]) ).
tcf(c_164610,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_14),sK58)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_14)) ),
inference(light_normalisation,[status(thm)],[c_164603,c_9047]) ).
tcf(c_164611,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_14),sK58)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_164610,c_141,c_9060]) ).
tcf(c_164660,plain,
( memberP(iPr_def_15,sK58)
| ~ ssList(iPr_def_13)
| ~ ssList(app(iPr_def_13,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_9048,c_164611]) ).
tcf(c_164661,plain,
( memberP(iPr_def_15,sK58)
| ~ ssList(iPr_def_15)
| ~ ssList(iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_164660,c_9048]) ).
tcf(c_164678,plain,
memberP(iPr_def_15,sK58),
inference(global_subsumption_just,[status(thm)],[c_164661,c_12507,c_13178,c_13177]) ).
tcf(c_165001,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_9044,c_140]) ).
tcf(c_165002,plain,
( ssList(iPr_def_14)
| ~ ssList(nil)
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_9047,c_140]) ).
tcf(c_165006,plain,
ssList(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_165002,c_141,c_9060]) ).
tcf(c_165007,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_165001,c_141,c_9059]) ).
tcf(c_165116,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(sK59) ),
inference(superposition,[status(thm)],[c_9045,c_153]) ).
tcf(c_165117,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sK60) ),
inference(superposition,[status(thm)],[c_9046,c_153]) ).
tcf(c_165118,plain,
( ssList(iPr_def_15)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_9048,c_153]) ).
tcf(c_165136,plain,
( ssList(iPr_def_15)
| ~ ssList(iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165118,c_165006]) ).
tcf(c_165139,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165117,c_9062]) ).
tcf(c_165142,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_165116,c_165007,c_9061]) ).
tcf(c_165143,plain,
ssList(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_165139,c_165142]) ).
tcf(c_165144,plain,
ssList(iPr_def_15),
inference(backward_subsumption_resolution,[status(thm)],[c_165136,c_165143]) ).
tcf(c_165659,plain,
( frontsegP(iPr_def_10,iPr_def_15)
| ~ ssList(iPr_def_15)
| ~ ssList(sK61) ),
inference(superposition,[status(thm)],[c_164559,c_391]) ).
tcf(c_165711,plain,
frontsegP(iPr_def_10,iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_165659,c_165144,c_9068]) ).
tcf(c_165814,plain,
( ~ ssList(nil)
| ~ ssItem(sK58)
| ( nil != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9047,c_142]) ).
tcf(c_165817,plain,
nil != iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_165814,c_141,c_9060]) ).
tcf(c_166188,plain,
( ( nil = iPr_def_15 )
| ( hd(iPr_def_15) = sK51(iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_165144,c_220]) ).
tcf(c_166692,plain,
( ( nil = iPr_def_15 )
| ( tl(iPr_def_15) = sK52(iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_165144,c_222]) ).
tcf(c_167939,plain,
( ( nil = iPr_def_15 )
| ( cons(hd(iPr_def_15),tl(iPr_def_15)) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_165144,c_224]) ).
tcf(c_168738,plain,
( ( nil = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ( nil != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_9048,c_230]) ).
tcf(c_168775,plain,
nil != iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_168738,c_165817,c_165006,c_165143]) ).
tcf(c_169609,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssList(iPr_def_15)
| ~ ssList(sK61)
| ~ ssItem(X0)
| ~ memberP(iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_164559,c_165]) ).
tcf(c_169650,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_15,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_169609,c_165144,c_9068]) ).
tcf(c_169844,plain,
( ( iPr_def_10 = iPr_def_15 )
| ~ ssList(iPr_def_15)
| ~ ssList(iPr_def_10)
| ~ frontsegP(iPr_def_15,iPr_def_10) ),
inference(superposition,[status(thm)],[c_165711,c_174]) ).
tcf(c_169845,plain,
( ( iPr_def_10 = iPr_def_15 )
| ~ frontsegP(iPr_def_15,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_169844,c_165144,c_164430]) ).
tcf(c_170162,plain,
hd(iPr_def_15) = sK51(iPr_def_15),
inference(global_subsumption_just,[status(thm)],[c_166188,c_14408,c_17128]) ).
tcf(c_170164,plain,
( ssItem(hd(iPr_def_15))
| ( nil = iPr_def_15 )
| ~ ssList(iPr_def_15) ),
inference(superposition,[status(thm)],[c_170162,c_219]) ).
tcf(c_170165,plain,
ssItem(hd(iPr_def_15)),
inference(forward_subsumption_resolution,[status(thm)],[c_170164,c_168775,c_165144]) ).
tcf(c_172107,plain,
! [X0: $i] :
( frontsegP(cons(sK63,X0),iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK63)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(superposition,[status(thm)],[c_9043,c_177]) ).
tcf(c_172114,plain,
! [X0: $i] :
( frontsegP(cons(sK63,X0),iPr_def_10)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[c_172107,c_141,c_164432]) ).
tcf(c_173068,plain,
( memberP(iPr_def_10,sK58)
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_164678,c_169650]) ).
tcf(c_173069,plain,
memberP(iPr_def_10,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_173068,c_9060]) ).
tcf(c_175148,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK63 )
| ~ ssList(nil)
| ~ ssItem(sK63)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_9043,c_170]) ).
tcf(c_175152,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK63 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_175148,c_141,c_164432]) ).
tcf(c_175722,plain,
tl(iPr_def_15) = sK52(iPr_def_15),
inference(global_subsumption_just,[status(thm)],[c_166692,c_14612,c_17128]) ).
tcf(c_175724,plain,
( ssList(tl(iPr_def_15))
| ( nil = iPr_def_15 )
| ~ ssList(iPr_def_15) ),
inference(superposition,[status(thm)],[c_175722,c_221]) ).
tcf(c_175725,plain,
ssList(tl(iPr_def_15)),
inference(forward_subsumption_resolution,[status(thm)],[c_175724,c_168775,c_165144]) ).
tcf(c_181915,plain,
! [X0: $i] :
( frontsegP(cons(sK63,X0),iPr_def_10)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_172114,c_180,c_20208]) ).
tcf(c_189248,plain,
cons(hd(iPr_def_15),tl(iPr_def_15)) = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_167939,c_16083,c_17128]) ).
tcf(c_189279,plain,
( memberP(iPr_def_15,hd(iPr_def_15))
| ~ ssList(tl(iPr_def_15))
| ~ ssItem(hd(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_189248,c_168]) ).
tcf(c_189284,plain,
memberP(iPr_def_15,hd(iPr_def_15)),
inference(forward_subsumption_resolution,[status(thm)],[c_189279,c_175725,c_170165]) ).
tcf(c_189560,plain,
( memberP(iPr_def_10,hd(iPr_def_15))
| ~ ssItem(hd(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_189284,c_169650]) ).
tcf(c_189561,plain,
memberP(iPr_def_10,hd(iPr_def_15)),
inference(forward_subsumption_resolution,[status(thm)],[c_189560,c_170165]) ).
tcf(c_190648,plain,
! [X0: $i] :
( ~ memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ( X0 = sK63 ) ),
inference(global_subsumption_just,[status(thm)],[c_175152,c_171,c_23582]) ).
tcf(c_190649,plain,
! [X0: $i] :
( ( X0 = sK63 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(renaming,[status(thm)],[c_190648]) ).
tcf(c_190658,plain,
( ( sK58 = sK63 )
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_173069,c_190649]) ).
tcf(c_190660,plain,
( ( hd(iPr_def_15) = sK63 )
| ~ ssItem(hd(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_189561,c_190649]) ).
tcf(c_190661,plain,
sK58 = sK63,
inference(forward_subsumption_resolution,[status(thm)],[c_190658,c_9060]) ).
tcf(c_190662,plain,
hd(iPr_def_15) = sK63,
inference(forward_subsumption_resolution,[status(thm)],[c_190660,c_170165]) ).
tcf(c_190722,plain,
cons(sK63,nil) = iPr_def_14,
inference(demodulation,[status(thm)],[c_9047,c_190661]) ).
tcf(c_190735,plain,
iPr_def_10 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_190722,c_9043]) ).
tcf(c_190762,plain,
app(iPr_def_13,iPr_def_10) = iPr_def_15,
inference(demodulation,[status(thm)],[c_9048,c_190735]) ).
tcf(c_190796,plain,
cons(sK63,tl(iPr_def_15)) = iPr_def_15,
inference(demodulation,[status(thm)],[c_189248,c_190662]) ).
tcf(c_192793,plain,
( frontsegP(iPr_def_15,iPr_def_10)
| ~ ssList(tl(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_190796,c_181915]) ).
tcf(c_192794,plain,
frontsegP(iPr_def_15,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_192793,c_175725]) ).
tcf(c_193506,plain,
iPr_def_10 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_169845,c_19346,c_192794]) ).
tcf(c_193514,plain,
app(iPr_def_13,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_190762,c_193506]) ).
tcf(c_193619,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_10)
| ~ ssList(X0)
| ( app(X0,iPr_def_10) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_193514,c_225]) ).
tcf(c_193636,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ~ ssList(X0)
| ( app(X0,iPr_def_10) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_193619,c_165143,c_164430]) ).
tcf(c_193644,plain,
( ( nil = iPr_def_13 )
| ~ ssList(nil)
| ( app(nil,iPr_def_10) != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_193636]) ).
tcf(c_193645,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_193644,c_17238,c_17241,c_17128,c_17132,c_13234,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC152+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n001.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Thu Sep 24 16:46:23 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.49 Running first-order theorem proving
% 0.19/0.49 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.50
% 0.25/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.50
% 0.25/0.51 % Detected problem language: tptp
% 0.25/0.52 % Proving...
% 79.88/13.49 % SZS status Started for theBenchmark.p
% 79.88/13.49 % SZS status Theorem for theBenchmark.p
% 79.88/13.49
% 79.88/13.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 79.88/13.49
% 79.88/13.49 % ------ iProver source info
% 79.88/13.49
% 79.88/13.49 % git: date: 2026-07-19 20:42:38 +0200
% 79.88/13.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 79.88/13.49 % git: non_committed_changes: false
% 79.88/13.49
% 79.88/13.49 % ------ Parsing...
% 79.88/13.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 79.88/13.49
% 79.88/13.49 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 79.88/13.49
% 79.88/13.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 79.88/13.49
% 79.88/13.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 79.88/13.49 % ------ Proving...
% 79.88/13.49 % ------ Problem Properties
% 79.88/13.49
% 79.88/13.49 %
% 79.88/13.49 % clauses 207
% 79.88/13.49 % conjectures 20
% 79.88/13.49 % EPR 69
% 79.88/13.49 % Horn 131
% 79.88/13.49 % unary 32
% 79.88/13.49 % binary 48
% 79.88/13.49 % lits 663
% 79.88/13.49 % lits eq 98
% 79.88/13.49 % fd_pure 0
% 79.88/13.49 % fd_pseudo 0
% 79.88/13.49 % fd_cond 23
% 79.88/13.49 % fd_pseudo_cond 14
% 79.88/13.49 % AC symbols 0
% 79.88/13.49
% 79.88/13.49 % ------ Schedule dynamic 5 is on
% 79.88/13.49
% 79.88/13.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 79.88/13.49
% 79.88/13.49
% 79.88/13.49 % ------
% 79.88/13.49 % Current options:
% 79.88/13.49 % ------
% 79.88/13.49
% 79.88/13.49
% 79.88/13.49 %
% 79.88/13.49
% 79.88/13.49 % ------ Proving...
% 79.88/13.49 % Proof_search_loop: time out after: 8053 full_loop iterations
% 79.88/13.49
% 79.88/13.49 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 79.88/13.49
% 79.88/13.49
% 79.88/13.49 % ------
% 79.88/13.49 % Current options:
% 79.88/13.49 % ------
% 79.88/13.49
% 79.88/13.49
% 79.88/13.49 %
% 79.88/13.49
% 79.88/13.49 % ------ Proving...
% 79.88/13.49 %
% 79.88/13.49
% 79.88/13.49 % SZS status Theorem for theBenchmark.p
% 79.88/13.49
% 79.88/13.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 79.88/13.49
% 79.88/13.49
%------------------------------------------------------------------------------