%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC073+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 : n017.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 03:07:46 PM UTC 2026
% Result : Theorem 134.94s 21.97s
% Output : CNFRefutation 134.94s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f549ERROR: Could not build tree for root c_364162ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax1) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
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(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f77,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( tl(X1) = tl(X0)
& hd(X1) = hd(X0)
& nil != X0
& nil != X1 )
=> X1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax77) ).
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(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 = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(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 = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| 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(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(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(f120,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) != X0 ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
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(f128,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ) ),
inference(ennf_transformation,[],[f23]) ).
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(f131,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ) ),
inference(ennf_transformation,[],[f25]) ).
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(f172,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f176,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f190,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| X1 = X0 ) ),
inference(ennf_transformation,[],[f77]) ).
fof(f191,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| X1 = X0 ) ),
inference(flattening,[],[f190]) ).
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(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 != X0
| nil != X1 )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(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 != X0
| nil != X1 )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f232,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f246,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(f247,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,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1))
& ssList(sK13(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f285,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f176]) ).
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 != sK53
| nil != sK54 )
& ( nil != sK56
| nil = sK55 )
& ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f298,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f318,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,[],[f248]) ).
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(f390,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f396,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f397,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f398,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f399,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f400,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f440,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f172]) ).
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(f473,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| X0 = X1 ),
inference(cnf_transformation,[],[f191]) ).
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(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(f501,plain,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( nil != sK53
| nil != sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
! [X4] :
( ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f504,f506,f505]) ).
fof(f508,plain,
( nil != sK55
| nil != sK56 ),
inference(definition_unfolding,[],[f502,f506,f505]) ).
fof(f509,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f506]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f505]) ).
fof(f516,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,[],[f318]) ).
fof(f530,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f444]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f298]) ).
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,[],[f516]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_139,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f544]) ).
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_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f390]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f396]) ).
tcf(c_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f398]) ).
tcf(c_151,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f399]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X0,X1)) = X1 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f400]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f403]) ).
tcf(c_192,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f440]) ).
tcf(c_195,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f530]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( X0 = nil )
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( tl(X0) != tl(X1) )
| ( hd(X0) != hd(X1) ) ),
inference(cnf_transformation,[],[f473]) ).
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_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_247,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_248,negated_conjecture,
( ( nil != sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_249,negated_conjecture,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_250,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,[],[f549]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f509]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f510]) ).
tcf(c_284,plain,
( ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(instantiation,[status(thm)],[c_139]) ).
tcf(c_304,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_367,negated_conjecture,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_247,c_247,c_248]) ).
tcf(c_371,negated_conjecture,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_248,c_367]) ).
tcf(c_809,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_250,c_153]) ).
tcf(c_8915,definition,
iPr_def_10 = hd(sK55),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8916,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8917,definition,
iPr_def_12 = tl(sK55),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8918,definition,
iPr_def_13 = app(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8919,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_809,c_8918,c_8917,c_8915,c_8916]) ).
tcf(c_8920,negated_conjecture,
nil != sK56,
inference(demodulation,[status(thm)],[c_371]) ).
tcf(c_8921,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8922,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_8923,negated_conjecture,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_8924,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_8927,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_8928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( neq(X0,X2)
| ~ neq(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_12467,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8916,c_140]) ).
tcf(c_12470,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12467,c_141]) ).
tcf(c_12486,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_8919,c_12470]) ).
tcf(c_12570,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8915,c_149]) ).
tcf(c_12571,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12570,c_8921]) ).
tcf(c_12585,plain,
( ssList(iPr_def_11)
| ( nil = sK55 ) ),
inference(superposition,[status(thm)],[c_12571,c_12470]) ).
tcf(c_12606,plain,
( ssList(iPr_def_12)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8917,c_151]) ).
tcf(c_12609,plain,
( ssList(iPr_def_12)
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12606,c_8921]) ).
tcf(c_13850,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(superposition,[status(thm)],[c_138,c_8924]) ).
tcf(c_13851,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_12486]) ).
tcf(c_13852,plain,
( neq(sK55,nil)
| ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_8923]) ).
tcf(c_13854,plain,
neq(sK55,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_13852,c_8920,c_8922,c_141]) ).
tcf(c_13855,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13850,c_141]) ).
tcf(c_13860,plain,
( ( sK56 = iPr_def_13 )
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10)
| ~ neq(nil,sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13851,c_8920,c_8922,c_141]) ).
tcf(c_13917,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( hd(cons(iPr_def_10,X0)) = iPr_def_10 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12571,c_150]) ).
tcf(c_14020,plain,
( ~ ssList(sK55)
| ~ segmentP(sK55,sK55)
| ~ segmentP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_13854,c_8924]) ).
tcf(c_14021,plain,
( ~ segmentP(sK55,sK55)
| ~ segmentP(sK56,sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14020,c_8921]) ).
tcf(c_14066,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK55 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_138,c_13860]) ).
tcf(c_14074,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK55 )
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14066,c_8921,c_141]) ).
tcf(c_14079,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_14074,c_12571,c_12609,c_14074]) ).
tcf(c_14085,plain,
( ( nil = sK55 )
| ~ segmentP(iPr_def_13,sK55)
| ~ segmentP(sK55,sK55) ),
inference(superposition,[status(thm)],[c_14079,c_14021]) ).
tcf(c_14131,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( sK56 != X0 )
| ( nil != X0 ) ),
inference(instantiation,[status(thm)],[c_8927]) ).
tcf(c_14132,plain,
( ( nil = sK56 )
| ( sK56 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_14131]) ).
tcf(c_14346,plain,
( ( nil = sK55 )
| ~ ssList(sK55)
| ~ segmentP(iPr_def_13,sK55) ),
inference(superposition,[status(thm)],[c_192,c_14085]) ).
tcf(c_14347,plain,
( ( nil = sK55 )
| ~ segmentP(iPr_def_13,sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14346,c_8921]) ).
tcf(c_14941,plain,
! [X0: $i] :
( neq(sK56,X0)
| ( sK56 = X0 )
| ~ ssList(sK56)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_14944,plain,
( neq(sK56,nil)
| ( sK56 = nil )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_14941]) ).
tcf(c_16312,plain,
( ( iPr_def_13 = sK56 )
| ~ ssList(iPr_def_12)
| ~ neq(nil,sK55)
| ~ ssItem(iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_8919,c_253,c_141,c_195,c_247,c_248,c_304,c_8919,c_12470,c_14132,c_14944]) ).
tcf(c_16313,plain,
( ( iPr_def_13 = sK56 )
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10)
| ~ neq(nil,sK55) ),
inference(renaming,[status(thm)],[c_16312]) ).
tcf(c_16585,plain,
( ( nil = sK55 )
| ( cons(hd(sK55),tl(sK55)) = sK55 ) ),
inference(superposition,[status(thm)],[c_8921,c_224]) ).
tcf(c_16591,plain,
( ( nil = sK55 )
| ( cons(iPr_def_10,iPr_def_12) = sK55 ) ),
inference(light_normalisation,[status(thm)],[c_16585,c_8915,c_8917]) ).
tcf(c_16762,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssItem(nil)
| ~ ssList(X0)
| ~ ssItem(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(superposition,[status(thm)],[c_49,c_8924]) ).
tcf(c_16763,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK55 )
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10)
| ~ ssItem(sK55)
| ~ ssItem(nil) ),
inference(superposition,[status(thm)],[c_49,c_16313]) ).
tcf(c_16814,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_16762,c_13855]) ).
tcf(c_16815,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(renaming,[status(thm)],[c_16814]) ).
tcf(c_16827,plain,
( ( sK56 = iPr_def_13 )
| ( nil = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_16763,c_14079]) ).
tcf(c_16834,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(iPr_def_13,X0)
| ~ segmentP(sK55,X0) ),
inference(superposition,[status(thm)],[c_16827,c_16815]) ).
tcf(c_20016,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8915,c_149]) ).
tcf(c_20018,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20016,c_8921]) ).
tcf(c_24961,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ~ neq(sK55,nil)
| ( X1 != nil )
| ( X0 != sK55 ) ),
inference(instantiation,[status(thm)],[c_8928]) ).
tcf(c_24962,plain,
( neq(nil,nil)
| ~ neq(sK55,nil)
| ( nil != sK55 )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_24961]) ).
tcf(c_29114,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( hd(cons(iPr_def_10,X0)) = iPr_def_10 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_20018,c_150]) ).
tcf(c_31333,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( hd(cons(iPr_def_10,X0)) = iPr_def_10 ) ),
inference(global_subsumption_just,[status(thm)],[c_29114,c_141,c_195,c_284,c_304,c_13854,c_13917,c_24962]) ).
tcf(c_31334,plain,
! [X0: $i] :
( ( hd(cons(iPr_def_10,X0)) = iPr_def_10 )
| ~ ssList(X0) ),
inference(renaming,[status(thm)],[c_31333]) ).
tcf(c_31367,plain,
hd(cons(iPr_def_10,sK56)) = iPr_def_10,
inference(superposition,[status(thm)],[c_8922,c_31334]) ).
tcf(c_33185,plain,
( ssItem(iPr_def_10)
| ( cons(iPr_def_10,sK56) = nil )
| ~ ssList(cons(iPr_def_10,sK56)) ),
inference(superposition,[status(thm)],[c_31367,c_149]) ).
tcf(c_33205,plain,
ssItem(iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_33185,c_141,c_195,c_284,c_304,c_12571,c_13854,c_24962]) ).
tcf(c_42890,plain,
( ( nil = sK55 )
| ( cons(hd(sK55),tl(sK55)) = sK55 ) ),
inference(superposition,[status(thm)],[c_8921,c_224]) ).
tcf(c_42900,plain,
( ( nil = sK55 )
| ( cons(iPr_def_10,iPr_def_12) = sK55 ) ),
inference(light_normalisation,[status(thm)],[c_42890,c_8915,c_8917]) ).
tcf(c_45605,plain,
cons(iPr_def_10,iPr_def_12) = sK55,
inference(global_subsumption_just,[status(thm)],[c_42900,c_141,c_195,c_284,c_304,c_13854,c_16591,c_24962]) ).
tcf(c_45611,plain,
( ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10)
| ( nil != sK55 ) ),
inference(superposition,[status(thm)],[c_45605,c_148]) ).
tcf(c_45621,plain,
( ~ ssList(iPr_def_12)
| ( nil != sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45611,c_33205]) ).
tcf(c_73825,plain,
nil != sK55,
inference(global_subsumption_just,[status(thm)],[c_45621,c_141,c_195,c_284,c_304,c_13854,c_24962]) ).
tcf(c_73834,plain,
sK56 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_16827,c_73825]) ).
tcf(c_113815,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8915,c_149]) ).
tcf(c_113816,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_113815,c_8921]) ).
tcf(c_113942,plain,
( ssList(iPr_def_12)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8917,c_151]) ).
tcf(c_113947,plain,
( ssList(iPr_def_12)
| ( nil = sK55 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_113942,c_8921]) ).
tcf(c_114042,plain,
ssItem(iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_113816,c_141,c_195,c_284,c_304,c_12571,c_13854,c_24962]) ).
tcf(c_114044,plain,
ssList(iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_113947,c_141,c_195,c_284,c_304,c_12609,c_13854,c_24962]) ).
tcf(c_117298,plain,
( ( nil = sK55 )
| ( cons(hd(sK55),tl(sK55)) = sK55 ) ),
inference(superposition,[status(thm)],[c_8921,c_224]) ).
tcf(c_117307,plain,
( ( nil = sK55 )
| ( cons(iPr_def_10,iPr_def_12) = sK55 ) ),
inference(light_normalisation,[status(thm)],[c_117298,c_8915,c_8917]) ).
tcf(c_117929,plain,
cons(iPr_def_10,iPr_def_12) = sK55,
inference(global_subsumption_just,[status(thm)],[c_117307,c_141,c_195,c_284,c_304,c_13854,c_16591,c_24962]) ).
tcf(c_117935,plain,
( ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10)
| ( nil != sK55 ) ),
inference(superposition,[status(thm)],[c_117929,c_148]) ).
tcf(c_117941,plain,
nil != sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_117935,c_114044,c_114042]) ).
tcf(c_201889,plain,
ssList(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_8922,c_73834]) ).
tcf(c_201891,negated_conjecture,
neq(sK55,nil),
inference(global_subsumption_just,[status(thm)],[c_8923,c_13854]) ).
tcf(c_201893,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(iPr_def_13,X0)
| ~ segmentP(sK55,X0)
| ~ neq(X0,nil) ),
inference(light_normalisation,[status(thm)],[c_8924,c_73834]) ).
tcf(c_201898,plain,
( ~ ssList(sK55)
| ~ segmentP(iPr_def_13,sK55)
| ~ segmentP(sK55,sK55) ),
inference(superposition,[status(thm)],[c_201891,c_201893]) ).
tcf(c_201899,plain,
( ~ segmentP(iPr_def_13,sK55)
| ~ segmentP(sK55,sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201898,c_8921]) ).
tcf(c_201902,plain,
~ segmentP(iPr_def_13,sK55),
inference(global_subsumption_just,[status(thm)],[c_201899,c_141,c_195,c_284,c_304,c_13854,c_14347,c_24962]) ).
tcf(c_202035,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssItem(nil)
| ~ ssList(X0)
| ~ ssItem(X0)
| ~ segmentP(iPr_def_13,X0)
| ~ segmentP(sK55,X0) ),
inference(superposition,[status(thm)],[c_49,c_201893]) ).
tcf(c_202075,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(iPr_def_13,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_202035,c_141,c_195,c_284,c_304,c_13854,c_16834,c_24962]) ).
tcf(c_202076,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(iPr_def_13,X0)
| ~ segmentP(sK55,X0) ),
inference(renaming,[status(thm)],[c_202075]) ).
tcf(c_202357,plain,
app(sK55,nil) = sK55,
inference(superposition,[status(thm)],[c_8921,c_232]) ).
tcf(c_202358,plain,
app(iPr_def_13,nil) = iPr_def_13,
inference(superposition,[status(thm)],[c_201889,c_232]) ).
tcf(c_202420,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8916,c_140]) ).
tcf(c_202423,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_202420,c_141]) ).
tcf(c_202432,plain,
ssList(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_202423,c_141,c_195,c_284,c_304,c_12585,c_13854,c_24962]) ).
tcf(c_202462,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8915,c_149]) ).
tcf(c_202463,plain,
ssItem(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_202462,c_117941,c_8921]) ).
tcf(c_202470,plain,
( ssList(iPr_def_12)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8917,c_151]) ).
tcf(c_202473,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_202470,c_117941,c_8921]) ).
tcf(c_202628,plain,
app(nil,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_202473,c_155]) ).
tcf(c_203607,plain,
( ~ ssList(nil)
| ~ ssItem(iPr_def_10)
| ( nil != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_8916,c_142]) ).
tcf(c_203609,plain,
nil != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_203607,c_141,c_202463]) ).
tcf(c_203646,plain,
! [X0: $i] :
( ( hd(cons(iPr_def_10,X0)) = iPr_def_10 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_202463,c_150]) ).
tcf(c_203763,plain,
! [X0: $i] :
( ( tl(cons(iPr_def_10,X0)) = X0 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_202463,c_152]) ).
tcf(c_203904,plain,
hd(cons(iPr_def_10,nil)) = iPr_def_10,
inference(superposition,[status(thm)],[c_141,c_203646]) ).
tcf(c_203910,plain,
hd(cons(iPr_def_10,iPr_def_12)) = iPr_def_10,
inference(superposition,[status(thm)],[c_202473,c_203646]) ).
tcf(c_203912,plain,
hd(iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_203904,c_8916]) ).
tcf(c_204013,plain,
tl(cons(iPr_def_10,nil)) = nil,
inference(superposition,[status(thm)],[c_141,c_203763]) ).
tcf(c_204019,plain,
tl(cons(iPr_def_10,iPr_def_12)) = iPr_def_12,
inference(superposition,[status(thm)],[c_202473,c_203763]) ).
tcf(c_204021,plain,
tl(iPr_def_11) = nil,
inference(light_normalisation,[status(thm)],[c_204013,c_8916]) ).
tcf(c_205569,plain,
( ( nil = sK55 )
| ( cons(hd(sK55),tl(sK55)) = sK55 ) ),
inference(superposition,[status(thm)],[c_8921,c_224]) ).
tcf(c_205579,plain,
( ( nil = sK55 )
| ( cons(iPr_def_10,iPr_def_12) = sK55 ) ),
inference(light_normalisation,[status(thm)],[c_205569,c_8915,c_8917]) ).
tcf(c_205580,plain,
cons(iPr_def_10,iPr_def_12) = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_205579,c_117941]) ).
tcf(c_205707,plain,
tl(sK55) = iPr_def_12,
inference(demodulation,[status(thm)],[c_204019,c_205580]) ).
tcf(c_205708,plain,
hd(sK55) = iPr_def_10,
inference(demodulation,[status(thm)],[c_203910,c_205580]) ).
tcf(c_205902,plain,
! [X0: $i] :
( ( app(cons(iPr_def_10,nil),X0) = cons(iPr_def_10,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_202463,c_227]) ).
tcf(c_205905,plain,
! [X0: $i] :
( ( cons(iPr_def_10,X0) = app(iPr_def_11,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_205902,c_8916]) ).
tcf(c_216461,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(X0)
| ~ ssList(app(app(iPr_def_12,iPr_def_11),X0)) ),
inference(superposition,[status(thm)],[c_8918,c_67]) ).
tcf(c_216467,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(app(nil,iPr_def_12),X0)) ),
inference(superposition,[status(thm)],[c_202628,c_67]) ).
tcf(c_216539,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_12,X0)) ),
inference(light_normalisation,[status(thm)],[c_216467,c_202628]) ).
tcf(c_216540,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_12)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_12,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_216539,c_202473,c_141]) ).
tcf(c_216569,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_13,X0)) ),
inference(light_normalisation,[status(thm)],[c_216461,c_8918]) ).
tcf(c_216570,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_13,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_216569,c_202473,c_202432]) ).
tcf(c_219790,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( X0 = sK55 )
| ( X0 = nil )
| ~ ssList(sK55)
| ~ ssList(X0)
| ( tl(X0) != tl(sK55) )
| ( hd(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_205708,c_223]) ).
tcf(c_219812,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( X0 = sK55 )
| ( X0 = nil )
| ~ ssList(sK55)
| ~ ssList(X0)
| ( tl(X0) != iPr_def_12 )
| ( hd(X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_219790,c_205707]) ).
tcf(c_219813,plain,
! [X0: $i] :
( ( X0 = sK55 )
| ( X0 = nil )
| ~ ssList(X0)
| ( tl(X0) != iPr_def_12 )
| ( hd(X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_219812,c_117941,c_8921]) ).
tcf(c_223228,plain,
( ( sK55 = iPr_def_11 )
| ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ( tl(iPr_def_11) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_203912,c_219813]) ).
tcf(c_223242,plain,
( ( sK55 = iPr_def_11 )
| ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ( nil != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_223228,c_204021]) ).
tcf(c_223243,plain,
( ( sK55 = iPr_def_11 )
| ( nil != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_223242,c_203609,c_202432]) ).
tcf(c_236893,plain,
cons(iPr_def_10,iPr_def_12) = app(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_202473,c_205905]) ).
tcf(c_236901,plain,
app(iPr_def_11,iPr_def_12) = sK55,
inference(light_normalisation,[status(thm)],[c_236893,c_205580]) ).
tcf(c_237826,plain,
! [X0: $i] :
( segmentP(app(sK55,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(X0)
| ~ ssList(app(app(iPr_def_11,iPr_def_12),X0)) ),
inference(superposition,[status(thm)],[c_236901,c_67]) ).
tcf(c_237868,plain,
! [X0: $i] :
( segmentP(app(sK55,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(X0)
| ~ ssList(app(sK55,X0)) ),
inference(light_normalisation,[status(thm)],[c_237826,c_236901]) ).
tcf(c_237869,plain,
! [X0: $i] :
( segmentP(app(sK55,X0),iPr_def_12)
| ~ ssList(X0)
| ~ ssList(app(sK55,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_237868,c_202473,c_202432]) ).
tcf(c_280946,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(app(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_292975,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8916,c_140]) ).
tcf(c_292979,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_292975,c_141]) ).
tcf(c_293017,plain,
ssList(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_292979,c_141,c_195,c_284,c_304,c_12585,c_13854,c_24962]) ).
tcf(c_293516,plain,
( ssList(iPr_def_12)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8917,c_151]) ).
tcf(c_293524,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_293516,c_117941,c_8921]) ).
tcf(c_293608,plain,
app(nil,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_293524,c_155]) ).
tcf(c_336657,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_153,c_67,c_280946]) ).
tcf(c_339059,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_336657]) ).
tcf(c_339077,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8918,c_339059]) ).
tcf(c_339081,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_293608,c_339059]) ).
tcf(c_339130,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_12)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_339081,c_293524,c_141]) ).
tcf(c_339142,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_339077,c_293524,c_293017]) ).
tcf(c_359282,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_12)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_216540,c_339130]) ).
tcf(c_359288,plain,
( segmentP(iPr_def_13,iPr_def_12)
| ~ ssList(iPr_def_11) ),
inference(superposition,[status(thm)],[c_8918,c_359282]) ).
tcf(c_359296,plain,
segmentP(iPr_def_13,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_359288,c_202432]) ).
tcf(c_359819,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_216570,c_339142]) ).
tcf(c_359825,plain,
( segmentP(iPr_def_13,iPr_def_11)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_202358,c_359819]) ).
tcf(c_359830,plain,
segmentP(iPr_def_13,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_359825,c_141]) ).
tcf(c_359924,plain,
( segmentP(sK55,iPr_def_12)
| ~ ssList(nil)
| ~ ssList(app(sK55,nil)) ),
inference(superposition,[status(thm)],[c_202357,c_237869]) ).
tcf(c_359929,plain,
( segmentP(sK55,iPr_def_12)
| ~ ssList(sK55)
| ~ ssList(nil) ),
inference(light_normalisation,[status(thm)],[c_359924,c_202357]) ).
tcf(c_359930,plain,
segmentP(sK55,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_359929,c_8921,c_141]) ).
tcf(c_359955,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ segmentP(iPr_def_13,iPr_def_12) ),
inference(superposition,[status(thm)],[c_359930,c_202076]) ).
tcf(c_359956,plain,
nil = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_359955,c_202473,c_359296]) ).
tcf(c_359963,plain,
sK55 = iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_223243,c_359956]) ).
tcf(c_361429,plain,
~ segmentP(iPr_def_13,iPr_def_11),
inference(demodulation,[status(thm)],[c_201902,c_359963]) ).
tcf(c_364162,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_361429,c_359830]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC073+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 16:10:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 134.94/21.97 % SZS status Started for theBenchmark.p
% 134.94/21.97 % SZS status Theorem for theBenchmark.p
% 134.94/21.97
% 134.94/21.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 134.94/21.97
% 134.94/21.97 % ------ iProver source info
% 134.94/21.97
% 134.94/21.97 % git: date: 2026-07-19 20:42:38 +0200
% 134.94/21.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 134.94/21.97 % git: non_committed_changes: false
% 134.94/21.97
% 134.94/21.97 % ------ Parsing...
% 134.94/21.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 134.94/21.97
% 134.94/21.97 % ------ 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 %
% 134.94/21.97
% 134.94/21.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 134.94/21.97
% 134.94/21.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 134.94/21.97 % ------ Proving...
% 134.94/21.97 % ------ Problem Properties
% 134.94/21.97
% 134.94/21.97 %
% 134.94/21.97 % clauses 194
% 134.94/21.97 % conjectures 5
% 134.94/21.97 % EPR 59
% 134.94/21.97 % Horn 124
% 134.94/21.97 % unary 23
% 134.94/21.97 % binary 43
% 134.94/21.97 % lits 649
% 134.94/21.97 % lits eq 86
% 134.94/21.97 % fd_pure 0
% 134.94/21.97 % fd_pseudo 0
% 134.94/21.97 % fd_cond 21
% 134.94/21.97 % fd_pseudo_cond 16
% 134.94/21.97 % AC symbols 0
% 134.94/21.97
% 134.94/21.97 % ------ Schedule dynamic 5 is on
% 134.94/21.97
% 134.94/21.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 134.94/21.97
% 134.94/21.97
% 134.94/21.97 % ------
% 134.94/21.97 % Current options:
% 134.94/21.97 % ------
% 134.94/21.97
% 134.94/21.97
% 134.94/21.97 %
% 134.94/21.97
% 134.94/21.97 % ------ Proving...
% 134.94/21.97 % Proof_search_loop: time out after: 6279 full_loop iterations
% 134.94/21.97
% 134.94/21.97 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 134.94/21.97
% 134.94/21.97
% 134.94/21.97 % ------
% 134.94/21.97 % Current options:
% 134.94/21.97 % ------
% 134.94/21.97
% 134.94/21.97
% 134.94/21.97 %
% 134.94/21.97
% 134.94/21.97 % ------ Proving...
% 134.94/21.97 %
% 134.94/21.97
% 134.94/21.97 % SZS status Theorem for theBenchmark.p
% 134.94/21.97
% 134.94/21.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 134.94/21.98
% 134.94/21.98
%------------------------------------------------------------------------------