%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC396+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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:09:36 PM UTC 2026
% Result : Theorem 46.72s 8.33s
% Output : CNFRefutation 46.72s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f550ERROR: Could not build tree for root c_145356ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
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(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(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(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(flattening,[],[f129]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f133,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
inference(ennf_transformation,[],[f27]) ).
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(f176,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
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(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
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)
& ( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X2)
| ! [X8] :
( ~ neq(nil,X2)
| hd(X2) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(X2) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| X3 = X5
| ~ ssList(X5) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X4] :
( ssItem(X4)
& ~ memberP(X1,X4)
& memberP(X0,X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X2)
| ! [X8] :
( ~ neq(nil,X2)
| hd(X2) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(X2) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| X3 = X5
| ~ ssList(X5) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X4] :
( ssItem(X4)
& ~ memberP(X1,X4)
& memberP(X0,X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f240,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(f241,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,[],[f240]) ).
fof(f242,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))],[f241]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
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(nnf_transformation,[],[f146]) ).
fof(f278,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,[],[f277]) ).
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(nnf_transformation,[],[f147]) ).
fof(f280,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,[],[f279]) ).
fof(f285,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f176]) ).
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(nnf_transformation,[],[f200]) ).
fof(f293,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,[],[f292]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK55)
| ! [X8] :
( ~ neq(nil,sK55)
| hd(sK55) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(sK55) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| sK56 = X5
| ~ ssList(X5) )
& neq(sK55,nil) )
| ~ neq(sK56,nil) )
& ( nil != sK56
| nil = sK55 )
& ssItem(sK57)
& ~ memberP(sK54,sK57)
& memberP(sK53,sK57)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f309,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f242]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f242]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f397,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f399,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f402,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f413,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f416,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f280]) ).
fof(f417,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(cons(X1,X2),X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f419,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f443,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f444,plain,
! [X0] :
( ~ ssList(X0)
| nil != X0
| segmentP(nil,X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f480,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f293]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
~ memberP(sK54,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
memberP(sK53,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
memberP(sK55,sK57),
inference(definition_unfolding,[],[f505,f506]) ).
fof(f509,plain,
~ memberP(sK56,sK57),
inference(definition_unfolding,[],[f504,f507]) ).
fof(f510,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
fof(f511,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f515,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f311]) ).
fof(f531,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f444]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( app(X1,sK11(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_151,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f399]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cons(X0,app(X2,X1)) = app(cons(X0,X2),X1) )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(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,[],[f415]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f414]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| memberP(X0,X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ memberP(app(X0,X1),X2) ),
inference(cnf_transformation,[],[f413]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(cons(X2,X0),X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f417]) ).
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,[],[f416]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_195,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f531]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f477]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f480]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
memberP(sK55,sK57),
inference(cnf_transformation,[],[f508]) ).
tcf(c_247,negated_conjecture,
~ memberP(sK56,sK57),
inference(cnf_transformation,[],[f509]) ).
tcf(c_248,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f503]) ).
tcf(c_249,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_251,negated_conjecture,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(sK56,nil)
| ~ neq(nil,sK55)
| ~ ssList(cons(hd(sK55),nil))
| ~ ssList(app(tl(sK55),cons(hd(sK55),nil))) ),
inference(cnf_transformation,[],[f550]) ).
tcf(c_254,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f510]) ).
tcf(c_255,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f511]) ).
tcf(c_305,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_377,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_814,plain,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(sK56,nil)
| ~ neq(nil,sK55)
| ~ ssList(cons(hd(sK55),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_251,c_153]) ).
tcf(c_8904,definition,
iPr_def_10 = hd(sK55),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8905,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8906,definition,
iPr_def_12 = tl(sK55),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8907,definition,
iPr_def_13 = app(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8908,plain,
( ( iPr_def_13 = sK56 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssItem(iPr_def_10)
| ~ neq(sK56,nil)
| ~ neq(nil,sK55) ),
inference(demodulation,[status(thm)],[c_814,c_8907,c_8906,c_8904,c_8905]) ).
tcf(c_8909,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_255]) ).
tcf(c_8910,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8913,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_248]) ).
tcf(c_8914,negated_conjecture,
~ memberP(sK56,sK57),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_8915,negated_conjecture,
memberP(sK55,sK57),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_8916,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_8918,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_8923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X0,X2)
| ~ memberP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_12358,plain,
app(sK55,nil) = sK55,
inference(superposition,[status(thm)],[c_8909,c_232]) ).
tcf(c_12416,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8905,c_140]) ).
tcf(c_12419,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12416,c_141]) ).
tcf(c_12435,plain,
( ( sK56 = iPr_def_13 )
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10)
| ~ neq(sK56,nil)
| ~ neq(nil,sK55) ),
inference(backward_subsumption_resolution,[status(thm)],[c_8908,c_12419]) ).
tcf(c_12531,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8904,c_149]) ).
tcf(c_12532,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12531,c_8909]) ).
tcf(c_12546,plain,
( ssList(iPr_def_11)
| ( nil = sK55 ) ),
inference(superposition,[status(thm)],[c_12532,c_12419]) ).
tcf(c_12567,plain,
( ssList(iPr_def_12)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8906,c_151]) ).
tcf(c_12570,plain,
( ssList(iPr_def_12)
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12567,c_8909]) ).
tcf(c_12586,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11) ),
inference(superposition,[status(thm)],[c_8907,c_153]) ).
tcf(c_12886,plain,
( ssList(iPr_def_13)
| ( nil = sK55 )
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_12546,c_12586]) ).
tcf(c_12904,plain,
( ssList(iPr_def_13)
| ( nil = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_12886,c_12546,c_12570,c_12586]) ).
tcf(c_13249,plain,
( ~ ssItem(sK57)
| ~ memberP(nil,sK57) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_13298,plain,
( frontsegP(sK55,sK55)
| ~ ssList(sK55)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_12358,c_377]) ).
tcf(c_13308,plain,
frontsegP(sK55,sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_13298,c_8909,c_141]) ).
tcf(c_13634,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK56 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK56)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10)
| ~ neq(nil,sK55) ),
inference(superposition,[status(thm)],[c_138,c_12435]) ).
tcf(c_13640,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK56 )
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10)
| ~ neq(nil,sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13634,c_8910,c_141]) ).
tcf(c_13782,plain,
! [X0: $i] :
( ssList(cons(sK57,X0))
| ~ ssItem(sK57)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_13783,plain,
( ssList(cons(sK57,nil))
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(instantiation,[status(thm)],[c_13782]) ).
tcf(c_14017,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK56 )
| ( nil = sK55 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_138,c_13640]) ).
tcf(c_14026,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK56 )
| ( nil = sK55 )
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14017,c_8909,c_141]) ).
tcf(c_14032,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_14026,c_249,c_12532,c_12570,c_14026]) ).
tcf(c_14051,plain,
( ( nil = sK55 )
| ~ memberP(iPr_def_13,sK57) ),
inference(superposition,[status(thm)],[c_14032,c_8914]) ).
tcf(c_14402,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sK55,sK57)
| ( X1 != sK57 )
| ( X0 != sK55 ) ),
inference(instantiation,[status(thm)],[c_8923]) ).
tcf(c_15879,plain,
( ( nil = sK55 )
| ( cons(hd(sK55),tl(sK55)) = sK55 ) ),
inference(superposition,[status(thm)],[c_8909,c_224]) ).
tcf(c_15884,plain,
( ( nil = sK55 )
| ( cons(iPr_def_10,iPr_def_12) = sK55 ) ),
inference(light_normalisation,[status(thm)],[c_15879,c_8904,c_8906]) ).
tcf(c_16068,plain,
! [X0: $i] :
( ( app(cons(sK57,nil),X0) = cons(sK57,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8913,c_227]) ).
tcf(c_16212,plain,
! [X0: $i] :
( memberP(X0,sK57)
| ~ memberP(sK55,sK57)
| ( sK57 != sK57 )
| ( X0 != sK55 ) ),
inference(instantiation,[status(thm)],[c_14402]) ).
tcf(c_16213,plain,
sK57 = sK57,
inference(instantiation,[status(thm)],[c_8916]) ).
tcf(c_16214,plain,
( memberP(nil,sK57)
| ~ memberP(sK55,sK57)
| ( sK57 != sK57 )
| ( nil != sK55 ) ),
inference(instantiation,[status(thm)],[c_16212]) ).
tcf(c_16551,plain,
app(cons(sK57,nil),sK56) = cons(sK57,sK56),
inference(superposition,[status(thm)],[c_8910,c_16068]) ).
tcf(c_16997,plain,
( ssList(cons(sK57,sK56))
| ~ ssList(sK56)
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_16551,c_153]) ).
tcf(c_16998,plain,
( ssList(cons(sK57,sK56))
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16997,c_8910]) ).
tcf(c_17007,plain,
ssList(cons(sK57,sK56)),
inference(global_subsumption_just,[status(thm)],[c_16998,c_248,c_141,c_13783,c_16998]) ).
tcf(c_17009,plain,
( ssList(cons(sK57,iPr_def_13))
| ( nil = sK55 ) ),
inference(superposition,[status(thm)],[c_14032,c_17007]) ).
tcf(c_17314,plain,
ssList(cons(sK57,iPr_def_13)),
inference(global_subsumption_just,[status(thm)],[c_17009,c_248,c_246,c_13249,c_16214,c_16213,c_17009]) ).
tcf(c_17316,plain,
app(cons(sK57,nil),cons(sK57,iPr_def_13)) = cons(sK57,cons(sK57,iPr_def_13)),
inference(superposition,[status(thm)],[c_17314,c_16068]) ).
tcf(c_17390,plain,
( ( app(sK55,sK11(sK55,sK55)) = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_13308,c_63]) ).
tcf(c_17395,plain,
app(sK55,sK11(sK55,sK55)) = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_17390,c_8909]) ).
tcf(c_17584,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_8907,c_165]) ).
tcf(c_17626,plain,
( ( sK11(sK55,sK55) = nil )
| ~ ssList(sK55)
| ~ ssList(sK11(sK55,sK55))
| ( nil != sK55 ) ),
inference(superposition,[status(thm)],[c_17395,c_230]) ).
tcf(c_17634,plain,
( ( sK11(sK55,sK55) = nil )
| ~ ssList(sK11(sK55,sK55))
| ( nil != sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17626,c_8909]) ).
tcf(c_18392,plain,
nil != sK55,
inference(global_subsumption_just,[status(thm)],[c_17634,c_248,c_246,c_13249,c_16214,c_16213]) ).
tcf(c_18399,plain,
~ memberP(iPr_def_13,sK57),
inference(backward_subsumption_resolution,[status(thm)],[c_14051,c_18392]) ).
tcf(c_18405,plain,
sK56 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_14032,c_18392]) ).
tcf(c_18422,plain,
ssList(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_12904,c_18392]) ).
tcf(c_18428,plain,
ssList(iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_12570,c_18392]) ).
tcf(c_18433,plain,
ssList(iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_12546,c_18392]) ).
tcf(c_18434,plain,
ssItem(iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_12532,c_18392]) ).
tcf(c_18456,plain,
app(cons(sK57,nil),iPr_def_13) = cons(sK57,iPr_def_13),
inference(demodulation,[status(thm)],[c_16551,c_18405]) ).
tcf(c_18993,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8905,c_140]) ).
tcf(c_18996,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18993,c_141]) ).
tcf(c_19341,plain,
ssList(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_18996,c_248,c_246,c_12546,c_13249,c_16214,c_16213]) ).
tcf(c_19509,plain,
! [X0: $i] :
( ( app(cons(iPr_def_10,nil),X0) = cons(iPr_def_10,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_18434,c_227]) ).
tcf(c_19517,plain,
! [X0: $i] :
( ( cons(iPr_def_10,X0) = app(iPr_def_11,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_19509,c_8905]) ).
tcf(c_20344,plain,
( ssList(iPr_def_12)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8906,c_151]) ).
tcf(c_20347,plain,
( ssList(iPr_def_12)
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20344,c_8909]) ).
tcf(c_20609,plain,
! [X0: $i,X1: $i] :
( ( cons(sK57,app(X1,X0)) = app(cons(sK57,X1),X0) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8913,c_154]) ).
tcf(c_20716,plain,
ssList(iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_20347,c_248,c_246,c_12570,c_13249,c_16214,c_16213]) ).
tcf(c_21230,plain,
! [X0: $i] :
( ( cons(sK57,app(X0,sK55)) = app(cons(sK57,X0),sK55) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8909,c_20609]) ).
tcf(c_21483,plain,
cons(sK57,app(iPr_def_13,sK55)) = app(cons(sK57,iPr_def_13),sK55),
inference(superposition,[status(thm)],[c_18422,c_21230]) ).
tcf(c_21485,plain,
cons(sK57,app(cons(sK57,iPr_def_13),sK55)) = app(cons(sK57,cons(sK57,iPr_def_13)),sK55),
inference(superposition,[status(thm)],[c_17314,c_21230]) ).
tcf(c_27253,plain,
! [X0: $i] :
( neq(X0,sK55)
| ( X0 = sK55 )
| ~ ssList(sK55)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_27256,plain,
( neq(nil,sK55)
| ( nil = sK55 )
| ~ ssList(sK55)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_27253]) ).
tcf(c_27611,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( sK56 != X0 )
| ( nil != X0 ) ),
inference(instantiation,[status(thm)],[c_8918]) ).
tcf(c_27612,plain,
( ( nil = sK56 )
| ( sK56 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_27611]) ).
tcf(c_34514,plain,
cons(iPr_def_10,iPr_def_12) = sK55,
inference(global_subsumption_just,[status(thm)],[c_15884,c_248,c_246,c_13249,c_15884,c_16214,c_16213]) ).
tcf(c_39124,plain,
! [X0: $i] :
( neq(sK56,X0)
| ( sK56 = X0 )
| ~ ssList(sK56)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_39127,plain,
( neq(sK56,nil)
| ( sK56 = nil )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_39124]) ).
tcf(c_41160,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ~ ssList(iPr_def_13)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK57,nil),X0) ),
inference(superposition,[status(thm)],[c_18456,c_165]) ).
tcf(c_41170,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK57,nil),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41160,c_18422]) ).
tcf(c_50629,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| memberP(cons(sK57,nil),X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,iPr_def_13))
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK57,cons(sK57,iPr_def_13)),X0) ),
inference(superposition,[status(thm)],[c_17316,c_167]) ).
tcf(c_50634,plain,
( ssList(cons(sK57,cons(sK57,iPr_def_13)))
| ~ ssList(cons(sK57,iPr_def_13))
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_17316,c_153]) ).
tcf(c_50641,plain,
! [X0: $i] :
( memberP(cons(sK57,cons(sK57,iPr_def_13)),X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,iPr_def_13))
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK57,iPr_def_13),X0) ),
inference(superposition,[status(thm)],[c_17316,c_166]) ).
tcf(c_50643,plain,
( ssList(cons(sK57,cons(sK57,iPr_def_13)))
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50634,c_17314]) ).
tcf(c_50658,plain,
! [X0: $i] :
( memberP(cons(sK57,cons(sK57,iPr_def_13)),X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK57,iPr_def_13),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50641,c_17314]) ).
tcf(c_50689,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| memberP(cons(sK57,nil),X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,nil))
| ~ memberP(cons(sK57,cons(sK57,iPr_def_13)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50629,c_17314]) ).
tcf(c_55092,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssItem(X0)
| ~ memberP(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_8907,c_166]) ).
tcf(c_55130,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_11,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55092,c_20716,c_19341]) ).
tcf(c_64531,plain,
cons(iPr_def_10,iPr_def_12) = app(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_18428,c_19517]) ).
tcf(c_64546,plain,
app(iPr_def_11,iPr_def_12) = sK55,
inference(light_normalisation,[status(thm)],[c_64531,c_34514]) ).
tcf(c_65346,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| memberP(iPr_def_11,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_64546,c_167]) ).
tcf(c_65374,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| memberP(iPr_def_11,X0)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65346,c_18428,c_18433]) ).
tcf(c_73569,plain,
( ssList(cons(sK57,app(iPr_def_13,sK55)))
| ~ ssList(sK55)
| ~ ssList(cons(sK57,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_21483,c_153]) ).
tcf(c_73587,plain,
ssList(cons(sK57,app(iPr_def_13,sK55))),
inference(forward_subsumption_resolution,[status(thm)],[c_73569,c_8909,c_17314]) ).
tcf(c_75569,plain,
cons(sK57,cons(sK57,app(iPr_def_13,sK55))) = app(cons(sK57,cons(sK57,iPr_def_13)),sK55),
inference(light_normalisation,[status(thm)],[c_21485,c_21483]) ).
tcf(c_75573,plain,
! [X0: $i] :
( memberP(sK55,X0)
| memberP(cons(sK57,cons(sK57,iPr_def_13)),X0)
| ~ ssList(sK55)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,cons(sK57,iPr_def_13)))
| ~ memberP(cons(sK57,cons(sK57,app(iPr_def_13,sK55))),X0) ),
inference(superposition,[status(thm)],[c_75569,c_167]) ).
tcf(c_75649,plain,
! [X0: $i] :
( memberP(sK55,X0)
| memberP(cons(sK57,cons(sK57,iPr_def_13)),X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,cons(sK57,iPr_def_13)))
| ~ memberP(cons(sK57,cons(sK57,app(iPr_def_13,sK55))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75573,c_8909]) ).
tcf(c_104373,plain,
iPr_def_13 = sK56,
inference(global_subsumption_just,[status(thm)],[c_8908,c_255,c_254,c_248,c_141,c_246,c_195,c_249,c_305,c_8908,c_12532,c_12546,c_12570,c_13249,c_16214,c_16213,c_27256,c_27612,c_39127]) ).
tcf(c_104377,plain,
ssList(iPr_def_13),
inference(demodulation,[status(thm)],[c_8910,c_104373]) ).
tcf(c_108523,plain,
! [X0: $i] :
( ( app(cons(sK57,nil),X0) = cons(sK57,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8913,c_227]) ).
tcf(c_108691,plain,
app(cons(sK57,nil),iPr_def_13) = cons(sK57,iPr_def_13),
inference(superposition,[status(thm)],[c_104377,c_108523]) ).
tcf(c_111281,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ~ ssList(iPr_def_13)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0)
| ~ ssList(cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_108691,c_166]) ).
tcf(c_111294,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0)
| ~ ssList(cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111281,c_104377]) ).
tcf(c_143587,plain,
! [X0: $i] :
( ~ memberP(cons(sK57,cons(sK57,app(iPr_def_13,sK55))),X0)
| ~ ssItem(X0)
| memberP(cons(sK57,cons(sK57,iPr_def_13)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_75649,c_248,c_141,c_246,c_12546,c_12570,c_13249,c_13783,c_16214,c_16213,c_17584,c_50643,c_50658,c_55130,c_65374,c_75649,c_111294]) ).
tcf(c_143588,plain,
! [X0: $i] :
( memberP(cons(sK57,cons(sK57,iPr_def_13)),X0)
| ~ ssItem(X0)
| ~ memberP(cons(sK57,cons(sK57,app(iPr_def_13,sK55))),X0) ),
inference(renaming,[status(thm)],[c_143587]) ).
tcf(c_143597,plain,
! [X0: $i] :
( memberP(cons(sK57,cons(sK57,iPr_def_13)),X0)
| ~ ssItem(sK57)
| ~ ssItem(X0)
| ~ ssList(cons(sK57,app(iPr_def_13,sK55)))
| ~ memberP(cons(sK57,app(iPr_def_13,sK55)),X0) ),
inference(superposition,[status(thm)],[c_169,c_143588]) ).
tcf(c_143603,plain,
! [X0: $i] :
( memberP(cons(sK57,cons(sK57,iPr_def_13)),X0)
| ~ ssItem(X0)
| ~ memberP(cons(sK57,app(iPr_def_13,sK55)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_143597,c_8913,c_73587]) ).
tcf(c_143616,plain,
! [X0: $i] :
( memberP(cons(sK57,cons(sK57,iPr_def_13)),X0)
| ~ ssItem(sK57)
| ~ ssItem(X0)
| ~ ssList(app(iPr_def_13,sK55))
| ~ memberP(app(iPr_def_13,sK55),X0) ),
inference(superposition,[status(thm)],[c_169,c_143603]) ).
tcf(c_143623,plain,
! [X0: $i] :
( memberP(cons(sK57,cons(sK57,iPr_def_13)),X0)
| ~ ssItem(X0)
| ~ ssList(app(iPr_def_13,sK55))
| ~ memberP(app(iPr_def_13,sK55),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_143616,c_8913]) ).
tcf(c_145240,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ( X0 = sK57 )
| ~ ssItem(sK57)
| ~ ssItem(X0)
| ~ ssList(app(iPr_def_13,sK55))
| ~ ssList(cons(sK57,iPr_def_13))
| ~ memberP(app(iPr_def_13,sK55),X0) ),
inference(superposition,[status(thm)],[c_143623,c_170]) ).
tcf(c_145246,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ( X0 = sK57 )
| ~ ssItem(X0)
| ~ ssList(app(iPr_def_13,sK55))
| ~ memberP(app(iPr_def_13,sK55),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_145240,c_8913,c_17314]) ).
tcf(c_145260,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ~ memberP(app(iPr_def_13,sK55),X0)
| ~ ssList(app(iPr_def_13,sK55))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_145246,c_248,c_141,c_13783,c_41170,c_50689,c_143623]) ).
tcf(c_145261,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ~ ssItem(X0)
| ~ ssList(app(iPr_def_13,sK55))
| ~ memberP(app(iPr_def_13,sK55),X0) ),
inference(renaming,[status(thm)],[c_145260]) ).
tcf(c_145272,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ~ ssList(iPr_def_13)
| ~ ssList(sK55)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(app(iPr_def_13,sK55)) ),
inference(superposition,[status(thm)],[c_166,c_145261]) ).
tcf(c_145279,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(app(iPr_def_13,sK55)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_145272,c_18422,c_8909]) ).
tcf(c_145286,plain,
! [X0: $i] :
( memberP(cons(sK57,iPr_def_13),X0)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(global_subsumption_just,[status(thm)],[c_145279,c_248,c_141,c_246,c_12546,c_12570,c_13249,c_13783,c_16214,c_16213,c_17584,c_55130,c_65374,c_111294]) ).
tcf(c_145301,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ( X0 = sK57 )
| ~ ssList(iPr_def_13)
| ~ ssItem(sK57)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_145286,c_170]) ).
tcf(c_145303,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ( X0 = sK57 )
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_145301,c_18422,c_8913]) ).
tcf(c_145341,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ memberP(sK55,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_145303,c_248,c_246,c_12546,c_12570,c_13249,c_16214,c_16213,c_17584,c_55130,c_65374]) ).
tcf(c_145342,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(renaming,[status(thm)],[c_145341]) ).
tcf(c_145350,plain,
( memberP(iPr_def_13,sK57)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8915,c_145342]) ).
tcf(c_145356,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_145350,c_18399,c_8913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC396+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 18:01:49 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.38 Running first-order theorem proving
% 0.08/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 46.72/8.33 % SZS status Started for theBenchmark.p
% 46.72/8.33 % SZS status Theorem for theBenchmark.p
% 46.72/8.33
% 46.72/8.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 46.72/8.33
% 46.72/8.33 % ------ iProver source info
% 46.72/8.33
% 46.72/8.33 % git: date: 2026-07-19 20:42:38 +0200
% 46.72/8.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 46.72/8.33 % git: non_committed_changes: false
% 46.72/8.33
% 46.72/8.33 % ------ Parsing...
% 46.72/8.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 46.72/8.33
% 46.72/8.33 % ------ 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 %
% 46.72/8.33
% 46.72/8.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 46.72/8.33
% 46.72/8.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 46.72/8.33 % ------ Proving...
% 46.72/8.33 % ------ Problem Properties
% 46.72/8.33
% 46.72/8.33 %
% 46.72/8.33 % clauses 196
% 46.72/8.33 % conjectures 7
% 46.72/8.33 % EPR 61
% 46.72/8.33 % Horn 126
% 46.72/8.33 % unary 25
% 46.72/8.33 % binary 44
% 46.72/8.33 % lits 649
% 46.72/8.33 % lits eq 87
% 46.72/8.33 % fd_pure 0
% 46.72/8.33 % fd_pseudo 0
% 46.72/8.33 % fd_cond 21
% 46.72/8.33 % fd_pseudo_cond 16
% 46.72/8.33 % AC symbols 0
% 46.72/8.33
% 46.72/8.33 % ------ Schedule dynamic 5 is on
% 46.72/8.33
% 46.72/8.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 46.72/8.33
% 46.72/8.33
% 46.72/8.33 % ------
% 46.72/8.33 % Current options:
% 46.72/8.33 % ------
% 46.72/8.33
% 46.72/8.33
% 46.72/8.33 %
% 46.72/8.33
% 46.72/8.33 % ------ Proving...
% 46.72/8.33 %
% 46.72/8.33
% 46.72/8.33 % SZS status Theorem for theBenchmark.p
% 46.72/8.33
% 46.72/8.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 46.72/8.34
%------------------------------------------------------------------------------