%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC087+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 03:07:50 PM UTC 2026
% Result : Theorem 31.60s 11.88s
% Output : CNFRefutation 31.60s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f558ERROR: Could not build tree for root c_93157ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(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(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)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X3)
& ? [X8] :
( neq(nil,X3)
& hd(X3) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X3) = X6
& ssList(X7) )
& ssList(X6) )
& X2 != X5
& ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) ) )
| 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)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X3)
& ? [X8] :
( neq(nil,X3)
& hd(X3) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X3) = X6
& ssList(X7) )
& ssList(X6) )
& X2 != X5
& ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(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(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)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| ! [X8] :
( ~ neq(nil,X3)
| hd(X3) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(X3) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| X2 = X5
| ~ ssList(X5) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| ! [X8] :
( ~ neq(nil,X3)
| hd(X3) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(X3) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| X2 = X5
| ~ ssList(X5) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
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(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK56)
| ! [X8] :
( ~ neq(nil,sK56)
| hd(sK56) != X8
| cons(X8,nil) != X7
| ~ ssItem(X8) )
| app(X6,X7) != X5
| tl(sK56) != X6
| ~ ssList(X7) )
| ~ ssList(X6) )
| sK55 = X5
| ~ ssList(X5) )
& ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) ) )
& 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(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(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(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(f502,plain,
! [X4] :
( ~ neq(sK56,nil)
| ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
! [X4] :
( ~ neq(sK56,nil)
| ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f502,f507,f506]) ).
fof(f513,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
fof(f514,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f520,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]) ).
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,[],[f520]) ).
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,[],[f552]) ).
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_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_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,
neq(sK56,nil),
inference(cnf_transformation,[],[f557]) ).
tcf(c_248,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(sK56,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_249,negated_conjecture,
( neq(sK56,nil)
| ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil))) ),
inference(cnf_transformation,[],[f558]) ).
tcf(c_250,negated_conjecture,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil))) ),
inference(cnf_transformation,[],[f559]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f513]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f514]) ).
tcf(c_382,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0) ),
inference(global_subsumption_just,[status(thm)],[c_248,c_246,c_248]) ).
tcf(c_383,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(renaming,[status(thm)],[c_382]) ).
tcf(c_384,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_249,c_246]) ).
tcf(c_386,plain,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_250,c_246,c_250]) ).
tcf(c_387,negated_conjecture,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil))) ),
inference(renaming,[status(thm)],[c_386]) ).
tcf(c_810,plain,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_387,c_153]) ).
tcf(c_3242,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK55,X1)
| ~ segmentP(sK56,X1)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_383]) ).
tcf(c_3243,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3242]) ).
tcf(c_3245,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3243,c_141,c_3243]) ).
tcf(c_3246,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3245]) ).
tcf(c_3264,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ( X1 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_810]) ).
tcf(c_3265,plain,
( ( nil = sK56 )
| ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(unflattening,[status(thm)],[c_3264]) ).
tcf(c_3266,plain,
( ( nil = sK56 )
| ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_3265,c_253,c_141,c_3265]) ).
tcf(c_3287,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_384]) ).
tcf(c_3288,plain,
( ~ ssList(nil)
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3287]) ).
tcf(c_3289,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3288,c_141,c_3288]) ).
tcf(c_3294,plain,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3266,c_3289]) ).
tcf(c_3297,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ( nil != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_384,c_383]) ).
tcf(c_3298,plain,
( ~ ssList(sK56)
| ~ segmentP(sK55,sK56)
| ~ segmentP(sK56,sK56) ),
inference(unflattening,[status(thm)],[c_3297]) ).
tcf(c_3299,plain,
( ~ segmentP(sK56,sK56)
| ~ segmentP(sK55,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_3298,c_253,c_3298]) ).
tcf(c_3300,plain,
( ~ segmentP(sK55,sK56)
| ~ segmentP(sK56,sK56) ),
inference(renaming,[status(thm)],[c_3299]) ).
tcf(c_8936,definition,
iPr_def_10 = hd(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8937,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8938,definition,
iPr_def_12 = tl(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8939,definition,
iPr_def_13 = app(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8940,plain,
( ~ segmentP(sK55,sK56)
| ~ segmentP(sK56,sK56) ),
inference(demodulation,[status(thm)],[c_3300]) ).
tcf(c_8941,plain,
( ( iPr_def_13 = sK55 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_3294,c_8939,c_8938,c_8936,c_8937]) ).
tcf(c_8942,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_3289]) ).
tcf(c_8943,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3246]) ).
tcf(c_8944,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8945,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_11888,plain,
( ~ ssList(sK56)
| ~ segmentP(sK55,sK56) ),
inference(superposition,[status(thm)],[c_192,c_8940]) ).
tcf(c_11889,plain,
~ segmentP(sK55,sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_11888,c_8945]) ).
tcf(c_12237,plain,
app(sK56,nil) = sK56,
inference(superposition,[status(thm)],[c_8945,c_232]) ).
tcf(c_12238,plain,
app(sK55,nil) = sK55,
inference(superposition,[status(thm)],[c_8944,c_232]) ).
tcf(c_12300,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8937,c_140]) ).
tcf(c_12303,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12300,c_141]) ).
tcf(c_12339,plain,
( ssItem(iPr_def_10)
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8936,c_149]) ).
tcf(c_12340,plain,
ssItem(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12339,c_8942,c_8945]) ).
tcf(c_12345,plain,
( ( sK55 = iPr_def_13 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_8941,c_12340]) ).
tcf(c_12349,plain,
( ( sK55 = iPr_def_13 )
| ~ ssList(iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_12345,c_12303,c_12340,c_12345]) ).
tcf(c_12355,plain,
ssList(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_12303,c_12303,c_12340]) ).
tcf(c_12365,plain,
( ssList(iPr_def_12)
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8938,c_151]) ).
tcf(c_12368,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_12365,c_8942,c_8945]) ).
tcf(c_12375,plain,
sK55 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_12349,c_12368]) ).
tcf(c_12376,plain,
app(iPr_def_13,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_12238,c_12375]) ).
tcf(c_12379,plain,
~ segmentP(iPr_def_13,sK56),
inference(demodulation,[status(thm)],[c_11889,c_12375]) ).
tcf(c_12380,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(iPr_def_13,X0)
| ~ segmentP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_8943,c_12375]) ).
tcf(c_12381,plain,
ssList(iPr_def_13),
inference(demodulation,[status(thm)],[c_8944,c_12375]) ).
tcf(c_12389,plain,
app(nil,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_12368,c_155]) ).
tcf(c_13299,plain,
( ~ ssList(nil)
| ~ ssItem(iPr_def_10)
| ( nil != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_8937,c_142]) ).
tcf(c_13300,plain,
nil != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_13299,c_141,c_12340]) ).
tcf(c_13562,plain,
! [X0: $i] :
( ( hd(cons(iPr_def_10,X0)) = iPr_def_10 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12340,c_150]) ).
tcf(c_13680,plain,
! [X0: $i] :
( ( tl(cons(iPr_def_10,X0)) = X0 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12340,c_152]) ).
tcf(c_13899,plain,
hd(cons(iPr_def_10,nil)) = iPr_def_10,
inference(superposition,[status(thm)],[c_141,c_13562]) ).
tcf(c_13905,plain,
hd(cons(iPr_def_10,iPr_def_12)) = iPr_def_10,
inference(superposition,[status(thm)],[c_12368,c_13562]) ).
tcf(c_13907,plain,
hd(iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_13899,c_8937]) ).
tcf(c_14050,plain,
tl(cons(iPr_def_10,nil)) = nil,
inference(superposition,[status(thm)],[c_141,c_13680]) ).
tcf(c_14056,plain,
tl(cons(iPr_def_10,iPr_def_12)) = iPr_def_12,
inference(superposition,[status(thm)],[c_12368,c_13680]) ).
tcf(c_14058,plain,
tl(iPr_def_11) = nil,
inference(light_normalisation,[status(thm)],[c_14050,c_8937]) ).
tcf(c_15593,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_8945,c_224]) ).
tcf(c_15604,plain,
( ( nil = sK56 )
| ( cons(iPr_def_10,iPr_def_12) = sK56 ) ),
inference(light_normalisation,[status(thm)],[c_15593,c_8936,c_8938]) ).
tcf(c_15605,plain,
cons(iPr_def_10,iPr_def_12) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_15604,c_8942]) ).
tcf(c_15734,plain,
tl(sK56) = iPr_def_12,
inference(demodulation,[status(thm)],[c_14056,c_15605]) ).
tcf(c_15735,plain,
hd(sK56) = iPr_def_10,
inference(demodulation,[status(thm)],[c_13905,c_15605]) ).
tcf(c_15958,plain,
! [X0: $i] :
( ( app(cons(iPr_def_10,nil),X0) = cons(iPr_def_10,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12340,c_227]) ).
tcf(c_15961,plain,
! [X0: $i] :
( ( cons(iPr_def_10,X0) = app(iPr_def_11,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_15958,c_8937]) ).
tcf(c_18041,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8937,c_140]) ).
tcf(c_18044,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18041,c_141]) ).
tcf(c_18513,plain,
ssList(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_18044,c_12303,c_12340]) ).
tcf(c_18531,plain,
( ssList(iPr_def_12)
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8938,c_151]) ).
tcf(c_18534,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_18531,c_8942,c_8945]) ).
tcf(c_25604,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_8939,c_67]) ).
tcf(c_25612,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_12389,c_67]) ).
tcf(c_25665,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_25612,c_12389]) ).
tcf(c_25666,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_25665,c_12368,c_141]) ).
tcf(c_25705,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_25604,c_8939]) ).
tcf(c_25706,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_25705,c_12368,c_12355]) ).
tcf(c_26517,plain,
! [X0: $i] :
( ssList(app(sK56,X0))
| ~ ssList(sK56)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_28912,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( X0 = sK56 )
| ( X0 = nil )
| ~ ssList(sK56)
| ~ ssList(X0)
| ( tl(X0) != tl(sK56) )
| ( hd(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_15735,c_223]) ).
tcf(c_28930,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( X0 = sK56 )
| ( X0 = nil )
| ~ ssList(sK56)
| ~ ssList(X0)
| ( tl(X0) != iPr_def_12 )
| ( hd(X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_28912,c_15734]) ).
tcf(c_28931,plain,
! [X0: $i] :
( ( X0 = sK56 )
| ( X0 = nil )
| ~ ssList(X0)
| ( tl(X0) != iPr_def_12 )
| ( hd(X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28930,c_8942,c_8945]) ).
tcf(c_31437,plain,
( ( sK56 = iPr_def_11 )
| ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ( tl(iPr_def_11) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_13907,c_28931]) ).
tcf(c_31447,plain,
( ( sK56 = iPr_def_11 )
| ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ( nil != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_31437,c_14058]) ).
tcf(c_31448,plain,
( ( sK56 = iPr_def_11 )
| ( nil != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31447,c_13300,c_12355]) ).
tcf(c_39191,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_43579,plain,
cons(iPr_def_10,iPr_def_12) = app(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_12368,c_15961]) ).
tcf(c_43586,plain,
app(iPr_def_11,iPr_def_12) = sK56,
inference(light_normalisation,[status(thm)],[c_43579,c_15605]) ).
tcf(c_44008,plain,
! [X0: $i] :
( segmentP(app(sK56,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_43586,c_67]) ).
tcf(c_44053,plain,
! [X0: $i] :
( segmentP(app(sK56,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(X0)
| ~ ssList(app(sK56,X0)) ),
inference(light_normalisation,[status(thm)],[c_44008,c_43586]) ).
tcf(c_44054,plain,
! [X0: $i] :
( segmentP(app(sK56,X0),iPr_def_12)
| ~ ssList(X0)
| ~ ssList(app(sK56,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44053,c_12368,c_12355]) ).
tcf(c_82956,plain,
( segmentP(iPr_def_13,iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(app(iPr_def_12,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8939,c_25666]) ).
tcf(c_82965,plain,
( segmentP(iPr_def_13,iPr_def_12)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_82956,c_8939]) ).
tcf(c_82966,plain,
segmentP(iPr_def_13,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_82965,c_12381,c_12355]) ).
tcf(c_85035,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_39191]) ).
tcf(c_85050,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_8939,c_85035]) ).
tcf(c_85134,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85050,c_18534,c_18513]) ).
tcf(c_90903,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_25706,c_85134]) ).
tcf(c_90909,plain,
( segmentP(iPr_def_13,iPr_def_11)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_12376,c_90903]) ).
tcf(c_90914,plain,
segmentP(iPr_def_13,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_90909,c_141]) ).
tcf(c_91029,plain,
! [X0: $i] :
( segmentP(app(sK56,X0),iPr_def_12)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_44054,c_253,c_26517,c_44054]) ).
tcf(c_91036,plain,
( segmentP(sK56,iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_12237,c_91029]) ).
tcf(c_91040,plain,
segmentP(sK56,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_91036,c_141]) ).
tcf(c_92269,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ segmentP(iPr_def_13,iPr_def_12) ),
inference(superposition,[status(thm)],[c_91040,c_12380]) ).
tcf(c_92270,plain,
nil = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_92269,c_12368,c_82966]) ).
tcf(c_92277,plain,
sK56 = iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_31448,c_92270]) ).
tcf(c_93153,plain,
~ segmentP(iPr_def_13,iPr_def_11),
inference(demodulation,[status(thm)],[c_12379,c_92277]) ).
tcf(c_93157,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_93153,c_90914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC087+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n001.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 16:24:45 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 31.60/11.88 % SZS status Started for theBenchmark.p
% 31.60/11.88 % SZS status Theorem for theBenchmark.p
% 31.60/11.88
% 31.60/11.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.60/11.88
% 31.60/11.88 % ------ iProver source info
% 31.60/11.88
% 31.60/11.88 % git: date: 2026-07-19 20:42:38 +0200
% 31.60/11.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.60/11.88 % git: non_committed_changes: false
% 31.60/11.88
% 31.60/11.88 % ------ Parsing...
% 31.60/11.88 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.60/11.88
% 31.60/11.88 % ------ 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: 5 0s sf_e pe_s pe_e %
% 31.60/11.88
% 31.60/11.88 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.60/11.88
% 31.60/11.88 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.60/11.88 % ------ Proving...
% 31.60/11.88 % ------ Problem Properties
% 31.60/11.88
% 31.60/11.88 %
% 31.60/11.88 % clauses 190
% 31.60/11.88 % conjectures 2
% 31.60/11.88 % EPR 55
% 31.60/11.88 % Horn 122
% 31.60/11.88 % unary 23
% 31.60/11.88 % binary 41
% 31.60/11.88 % lits 635
% 31.60/11.88 % lits eq 85
% 31.60/11.88 % fd_pure 0
% 31.60/11.88 % fd_pseudo 0
% 31.60/11.88 % fd_cond 22
% 31.60/11.88 % fd_pseudo_cond 14
% 31.60/11.88 % AC symbols 0
% 31.60/11.88
% 31.60/11.88 % ------ Schedule dynamic 5 is on
% 31.60/11.88
% 31.60/11.88 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 31.60/11.88
% 31.60/11.88
% 31.60/11.88 % ------
% 31.60/11.88 % Current options:
% 31.60/11.88 % ------
% 31.60/11.88
% 31.60/11.88
% 31.60/11.88 %
% 31.60/11.88
% 31.60/11.88 % ------ Proving...
% 31.60/11.88 %
% 31.60/11.88
% 31.60/11.88 % SZS status Theorem for theBenchmark.p
% 31.60/11.88
% 31.60/11.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.60/11.88
% 31.60/11.88
%------------------------------------------------------------------------------