%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC091+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 03:07:51 PM UTC 2026
% Result : Theorem 27.79s 6.81s
% Output : CNFRefutation 27.79s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f540ERROR: Could not build tree for root c_100550ERROR: 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(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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(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] :
( totalorderedP(X5)
& segmentP(X5,X2)
& frontsegP(X3,X5)
& neq(X2,X5)
& ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ totalorderedP(X2)
| ~ frontsegP(X3,X2)
| ~ 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)
=> ( ? [X5] :
( totalorderedP(X5)
& segmentP(X5,X2)
& frontsegP(X3,X5)
& neq(X2,X5)
& ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ totalorderedP(X2)
| ~ frontsegP(X3,X2)
| ~ neq(X1,nil)
| 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(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(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
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(f170,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f171,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f170]) ).
fof(f172,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f175,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(ennf_transformation,[],[f57]) ).
fof(f176,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f180,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f65]) ).
fof(f186,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f187,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f186]) ).
fof(f188,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f188]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f192]) ).
fof(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] :
( ~ totalorderedP(X5)
| ~ segmentP(X5,X2)
| ~ frontsegP(X3,X5)
| ~ neq(X2,X5)
| ~ ssList(X5) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& 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)
& ! [X5] :
( ~ totalorderedP(X5)
| ~ segmentP(X5,X2)
| ~ frontsegP(X3,X5)
| ~ neq(X2,X5)
| ~ ssList(X5) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& 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(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(f290,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(X1,sK51(X0))],[f187]) ).
fof(f291,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X1,sK52(X0))],[f189]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ! [X5] :
( ~ totalorderedP(X5)
| ~ segmentP(X5,sK55)
| ~ frontsegP(sK56,X5)
| ~ neq(sK55,X5)
| ~ ssList(X5) )
& ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& totalorderedP(sK55)
& frontsegP(sK56,sK55)
& 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(f309,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f242]) ).
fof(f310,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ssList(sK11(X0,X1)) ),
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(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(f396,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
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(f439,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f171]) ).
fof(f440,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f442,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(cnf_transformation,[],[f175]) ).
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(f451,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f469,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK51(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f470,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f290]) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK52(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f472,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f291]) ).
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(f500,plain,
! [X5] :
( ~ totalorderedP(X5)
| ~ segmentP(X5,sK55)
| ~ frontsegP(sK56,X5)
| ~ neq(sK55,X5)
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
neq(sK54,nil),
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,
neq(sK56,nil),
inference(definition_unfolding,[],[f504,f506]) ).
fof(f508,plain,
! [X4] :
( ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f501,f506,f505]) ).
fof(f509,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f506]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f505]) ).
fof(f514,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f311]) ).
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_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ssList(sK11(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f310]) ).
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_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,[],[f540]) ).
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_148,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f396]) ).
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_177,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f542]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f439]) ).
tcf(c_192,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f440]) ).
tcf(c_194,plain,
! [X0: $i] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f442]) ).
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_203,plain,
! [X0: $i] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f451]) ).
tcf(c_219,plain,
! [X0: $i] :
( ssItem(sK51(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f470]) ).
tcf(c_220,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK51(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f469]) ).
tcf(c_221,plain,
! [X0: $i] :
( ssList(sK52(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f472]) ).
tcf(c_222,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK52(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f471]) ).
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_229,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f543]) ).
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,[],[f507]) ).
tcf(c_247,negated_conjecture,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f503]) ).
tcf(c_249,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_250,negated_conjecture,
! [X0: $i] :
( ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0)
| ~ neq(sK55,X0) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f509]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f510]) ).
tcf(c_295,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_232]) ).
tcf(c_304,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_368,plain,
app(nil,nil) = nil,
inference(global_subsumption_just,[status(thm)],[c_229,c_141,c_295]) ).
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_3237,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_249]) ).
tcf(c_3238,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3237]) ).
tcf(c_3240,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3238,c_141,c_3238]) ).
tcf(c_3241,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3240]) ).
tcf(c_3259,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ totalorderedP(X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X2,sK55)
| ~ frontsegP(sK56,X2)
| ( X1 != X2 )
| ( X0 != sK55 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_250]) ).
tcf(c_3260,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ ssList(sK55)
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3259]) ).
tcf(c_3262,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ totalorderedP(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3260,c_254,c_3260]) ).
tcf(c_3263,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3262]) ).
tcf(c_3285,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_246]) ).
tcf(c_3286,plain,
( ~ ssList(nil)
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3285]) ).
tcf(c_3287,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3286,c_141,c_3286]) ).
tcf(c_8971,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_3287]) ).
tcf(c_8972,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3263]) ).
tcf(c_8973,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3241]) ).
tcf(c_8974,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8975,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_8977,negated_conjecture,
frontsegP(sK56,sK55),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_8989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_12174,plain,
app(nil,sK55) = sK55,
inference(superposition,[status(thm)],[c_8974,c_155]) ).
tcf(c_12268,plain,
app(sK55,nil) = sK55,
inference(superposition,[status(thm)],[c_8974,c_232]) ).
tcf(c_13316,plain,
( segmentP(sK55,sK55)
| ~ ssList(sK55) ),
inference(instantiation,[status(thm)],[c_192]) ).
tcf(c_13459,plain,
( ( nil = sK56 )
| ( hd(sK56) = sK51(sK56) ) ),
inference(superposition,[status(thm)],[c_8975,c_220]) ).
tcf(c_13463,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_13459,c_8971]) ).
tcf(c_13630,plain,
( ( nil = sK56 )
| ( tl(sK56) = sK52(sK56) ) ),
inference(superposition,[status(thm)],[c_8975,c_222]) ).
tcf(c_13634,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_13630,c_8971]) ).
tcf(c_13753,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X0,sK55)
| ~ segmentP(X1,X2)
| ( sK55 != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_8989]) ).
tcf(c_13754,plain,
( segmentP(nil,sK55)
| ~ segmentP(nil,nil)
| ( sK55 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_13753]) ).
tcf(c_13781,plain,
( ssItem(hd(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_13463,c_219]) ).
tcf(c_13782,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_13781,c_8971,c_8975]) ).
tcf(c_13791,plain,
( ssList(tl(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_13634,c_221]) ).
tcf(c_13792,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_13791,c_8971,c_8975]) ).
tcf(c_13803,plain,
app(nil,tl(sK56)) = tl(sK56),
inference(superposition,[status(thm)],[c_13792,c_155]) ).
tcf(c_14149,plain,
( frontsegP(tl(sK56),nil)
| ~ ssList(nil)
| ~ ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_13803,c_377]) ).
tcf(c_14150,plain,
frontsegP(tl(sK56),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_14149,c_141,c_13792]) ).
tcf(c_14804,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_8975,c_224]) ).
tcf(c_14810,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_14804,c_8971]) ).
tcf(c_15188,plain,
( ( sK55 = nil )
| ~ ssList(sK55)
| ~ segmentP(sK55,sK55)
| ~ segmentP(sK56,sK55) ),
inference(instantiation,[status(thm)],[c_8973]) ).
tcf(c_15593,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_15706,plain,
( ( app(sK55,sK11(sK56,sK55)) = sK56 )
| ~ ssList(sK55)
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8977,c_63]) ).
tcf(c_15721,plain,
app(sK55,sK11(sK56,sK55)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_15706,c_8974,c_8975]) ).
tcf(c_18992,plain,
! [X0: $i] :
( frontsegP(sK56,cons(hd(sK56),X0))
| ~ ssList(X0)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ frontsegP(tl(sK56),X0) ),
inference(superposition,[status(thm)],[c_14810,c_177]) ).
tcf(c_19017,plain,
! [X0: $i] :
( frontsegP(sK56,cons(hd(sK56),X0))
| ~ ssList(X0)
| ~ frontsegP(tl(sK56),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18992,c_13792,c_13782]) ).
tcf(c_19069,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(nil)
| ~ frontsegP(tl(sK56),nil) ),
inference(instantiation,[status(thm)],[c_19017]) ).
tcf(c_22524,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(hd(sK56))
| ( cons(hd(sK56),X0) != nil ) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_22525,plain,
! [X0: $i] :
( ssList(cons(hd(sK56),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_22533,plain,
( totalorderedP(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_203]) ).
tcf(c_22535,plain,
( ssList(cons(hd(sK56),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_22525]) ).
tcf(c_22536,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK56))
| ( cons(hd(sK56),nil) != nil ) ),
inference(instantiation,[status(thm)],[c_22524]) ).
tcf(c_23898,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_15593]) ).
tcf(c_23909,plain,
! [X0: $i] :
( segmentP(app(nil,X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_368,c_23898]) ).
tcf(c_23913,plain,
! [X0: $i] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12174,c_23898]) ).
tcf(c_23945,plain,
! [X0: $i] :
( segmentP(app(nil,X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23909,c_141]) ).
tcf(c_23954,plain,
! [X0: $i] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23913,c_8974,c_141]) ).
tcf(c_24587,plain,
( segmentP(sK55,nil)
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_12174,c_23945]) ).
tcf(c_24595,plain,
segmentP(sK55,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_24587,c_8974]) ).
tcf(c_24617,plain,
( ( nil = sK55 )
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ segmentP(nil,sK55) ),
inference(superposition,[status(thm)],[c_24595,c_191]) ).
tcf(c_24618,plain,
( ( nil = sK55 )
| ~ segmentP(nil,sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24617,c_8974,c_141]) ).
tcf(c_24779,plain,
( segmentP(sK55,sK55)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_12268,c_23954]) ).
tcf(c_24780,plain,
( segmentP(sK56,sK55)
| ~ ssList(sK11(sK56,sK55)) ),
inference(superposition,[status(thm)],[c_15721,c_23954]) ).
tcf(c_24786,plain,
segmentP(sK55,sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_24779,c_141]) ).
tcf(c_25602,plain,
( ( nil = sK56 )
| ( hd(sK56) = sK51(sK56) ) ),
inference(superposition,[status(thm)],[c_8975,c_220]) ).
tcf(c_25603,plain,
( ( nil = sK55 )
| ( hd(sK55) = sK51(sK55) ) ),
inference(superposition,[status(thm)],[c_8974,c_220]) ).
tcf(c_25606,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_25602,c_8971]) ).
tcf(c_25722,plain,
( segmentP(sK56,sK55)
| ~ ssList(sK55)
| ~ ssList(sK56)
| ~ frontsegP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_62,c_24780]) ).
tcf(c_25723,plain,
segmentP(sK56,sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_25722,c_8974,c_8975,c_8977]) ).
tcf(c_25727,plain,
( ( nil = sK55 )
| ~ ssList(sK55)
| ~ segmentP(sK55,sK55) ),
inference(superposition,[status(thm)],[c_25723,c_8973]) ).
tcf(c_25729,plain,
nil = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_25727,c_8974,c_24786]) ).
tcf(c_25809,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,nil)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_8972,c_25729]) ).
tcf(c_28028,plain,
( ( nil = sK56 )
| ( tl(sK56) = sK52(sK56) ) ),
inference(superposition,[status(thm)],[c_8975,c_222]) ).
tcf(c_28032,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_28028,c_8971]) ).
tcf(c_29821,plain,
( ssItem(hd(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_25606,c_219]) ).
tcf(c_29822,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_29821,c_8971,c_8975]) ).
tcf(c_29975,plain,
( ssList(tl(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_28032,c_221]) ).
tcf(c_29976,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_29975,c_8971,c_8975]) ).
tcf(c_30275,plain,
nil = sK55,
inference(global_subsumption_just,[status(thm)],[c_25603,c_254,c_141,c_195,c_304,c_13316,c_13754,c_15188,c_24618,c_25723]) ).
tcf(c_30287,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,nil)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_8972,c_30275]) ).
tcf(c_35891,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ frontsegP(sK56,X0) ),
inference(global_subsumption_just,[status(thm)],[c_30287,c_194,c_25809]) ).
tcf(c_35975,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_8975,c_224]) ).
tcf(c_35978,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_35975,c_8971]) ).
tcf(c_37027,plain,
! [X0: $i] :
( ( app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_29822,c_227]) ).
tcf(c_39743,plain,
app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
inference(superposition,[status(thm)],[c_29976,c_37027]) ).
tcf(c_39745,plain,
app(cons(hd(sK56),nil),tl(sK56)) = sK56,
inference(light_normalisation,[status(thm)],[c_39743,c_35978]) ).
tcf(c_56164,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(superposition,[status(thm)],[c_39745,c_377]) ).
tcf(c_56172,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56164,c_29976]) ).
tcf(c_100526,plain,
frontsegP(sK56,cons(hd(sK56),nil)),
inference(global_subsumption_just,[status(thm)],[c_56172,c_141,c_14150,c_19069]) ).
tcf(c_100532,plain,
( ( cons(hd(sK56),nil) = nil )
| ~ totalorderedP(cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(superposition,[status(thm)],[c_100526,c_35891]) ).
tcf(c_100550,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_100532,c_22536,c_22535,c_22533,c_13782,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC091+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 16:16:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 27.79/6.81 % SZS status Started for theBenchmark.p
% 27.79/6.81 % SZS status Theorem for theBenchmark.p
% 27.79/6.81
% 27.79/6.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 27.79/6.81
% 27.79/6.81 % ------ iProver source info
% 27.79/6.81
% 27.79/6.81 % git: date: 2026-07-19 20:42:38 +0200
% 27.79/6.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 27.79/6.81 % git: non_committed_changes: false
% 27.79/6.81
% 27.79/6.81 % ------ Parsing...
% 27.79/6.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 27.79/6.81
% 27.79/6.81 % ------ 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 %
% 27.79/6.81
% 27.79/6.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 27.79/6.81
% 27.79/6.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.79/6.81 % ------ Proving...
% 27.79/6.81 % ------ Problem Properties
% 27.79/6.81
% 27.79/6.81 %
% 27.79/6.81 % clauses 189
% 27.79/6.81 % conjectures 4
% 27.79/6.81 % EPR 58
% 27.79/6.81 % Horn 121
% 27.79/6.81 % unary 21
% 27.79/6.81 % binary 41
% 27.79/6.81 % lits 637
% 27.79/6.81 % lits eq 82
% 27.79/6.81 % fd_pure 0
% 27.79/6.81 % fd_pseudo 0
% 27.79/6.81 % fd_cond 23
% 27.79/6.81 % fd_pseudo_cond 14
% 27.79/6.81 % AC symbols 0
% 27.79/6.81
% 27.79/6.81 % ------ Schedule dynamic 5 is on
% 27.79/6.81
% 27.79/6.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 27.79/6.81
% 27.79/6.81
% 27.79/6.81 % ------
% 27.79/6.81 % Current options:
% 27.79/6.81 % ------
% 27.79/6.81
% 27.79/6.81
% 27.79/6.81 %
% 27.79/6.81
% 27.79/6.81 % ------ Proving...
% 27.79/6.81 %
% 27.79/6.81
% 27.79/6.81 % SZS status Theorem for theBenchmark.p
% 27.79/6.81
% 27.79/6.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.79/6.82
% 27.79/6.82
%------------------------------------------------------------------------------