%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC021+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 03:07:33 PM UTC 2026
% Result : Theorem 6.38s 11.76s
% Output : CNFRefutation 6.38s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f542ERROR: Could not build tree for root c_21556ERROR: 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/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax68) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X0
& nil = X1 )
| ? [X5] :
( strictorderedP(X5)
& segmentP(X5,X2)
& frontsegP(X3,X5)
& neq(X2,X5)
& ssList(X5) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ strictorderedP(X2)
| ~ frontsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X0
& nil = X1 )
| ? [X5] :
( strictorderedP(X5)
& segmentP(X5,X2)
& frontsegP(X3,X5)
& neq(X2,X5)
& ssList(X5) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ strictorderedP(X2)
| ~ frontsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(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(f153,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f175,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(ennf_transformation,[],[f57]) ).
fof(f182,plain,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f68]) ).
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(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X0
| nil != X1 )
& ! [X5] :
( ~ strictorderedP(X5)
| ~ segmentP(X5,X2)
| ~ frontsegP(X3,X5)
| ~ neq(X2,X5)
| ~ ssList(X5) )
& ! [X4] :
( ~ frontsegP(X0,X4)
| ~ frontsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& strictorderedP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X0
| nil != X1 )
& ! [X5] :
( ~ strictorderedP(X5)
| ~ segmentP(X5,X2)
| ~ frontsegP(X3,X5)
| ~ neq(X2,X5)
| ~ ssList(X5) )
& ! [X4] :
( ~ frontsegP(X0,X4)
| ~ frontsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& strictorderedP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f240,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f241,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X3] :
( app(X1,X3) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f240]) ).
fof(f242,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f241]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(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)
& ( nil != sK53
| nil != sK54 )
& ! [X5] :
( ~ strictorderedP(X5)
| ~ segmentP(X5,sK55)
| ~ frontsegP(sK56,X5)
| ~ neq(sK55,X5)
| ~ ssList(X5) )
& ! [X4] :
( ~ frontsegP(sK53,X4)
| ~ frontsegP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& strictorderedP(sK55)
& frontsegP(sK56,sK55)
& 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(f311,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f242]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(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(f423,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f442,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(cnf_transformation,[],[f175]) ).
fof(f458,plain,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f182]) ).
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(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil != sK53
| nil != sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
! [X5] :
( ~ strictorderedP(X5)
| ~ segmentP(X5,sK55)
| ~ frontsegP(sK56,X5)
| ~ neq(sK55,X5)
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4] :
( ~ frontsegP(sK53,X4)
| ~ frontsegP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
frontsegP(sK56,sK55),
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] :
( ~ frontsegP(sK55,X4)
| ~ frontsegP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f502,f506,f505]) ).
fof(f508,plain,
( nil != sK55
| nil != sK56 ),
inference(definition_unfolding,[],[f500,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]) ).
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_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_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_175,plain,
! [X0: $i] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f423]) ).
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_194,plain,
! [X0: $i] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f442]) ).
tcf(c_209,plain,
! [X0: $i] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f458]) ).
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_246,negated_conjecture,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f504]) ).
tcf(c_248,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_249,negated_conjecture,
! [X0: $i] :
( ~ strictorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0)
| ~ neq(sK55,X0) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_250,negated_conjecture,
( ( nil != sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f509]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f510]) ).
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_3243,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK55,X1)
| ~ frontsegP(sK56,X1)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_248]) ).
tcf(c_3244,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3243]) ).
tcf(c_3246,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ frontsegP(sK56,X0)
| ~ frontsegP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3244,c_141,c_3244]) ).
tcf(c_3247,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3246]) ).
tcf(c_3265,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ strictorderedP(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_249]) ).
tcf(c_3266,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ ssList(sK55)
| ~ strictorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3265]) ).
tcf(c_3268,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ strictorderedP(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3266,c_254,c_3266]) ).
tcf(c_3269,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ strictorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3268]) ).
tcf(c_8923,plain,
! [X0: $i] :
( ( sK55 = X0 )
| ~ strictorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3269]) ).
tcf(c_8924,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3247]) ).
tcf(c_8925,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8926,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_8927,negated_conjecture,
( ( nil != sK55 )
| ( nil != sK56 ) ),
inference(demodulation,[status(thm)],[c_250]) ).
tcf(c_8929,negated_conjecture,
frontsegP(sK56,sK55),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_11771,plain,
( ( nil = sK55 )
| ~ ssList(sK55)
| ~ frontsegP(sK55,sK55) ),
inference(superposition,[status(thm)],[c_8929,c_8924]) ).
tcf(c_11772,plain,
( ( nil = sK55 )
| ~ frontsegP(sK55,sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11771,c_8925]) ).
tcf(c_11865,plain,
( ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_175,c_11772]) ).
tcf(c_11866,plain,
nil = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_11865,c_8925]) ).
tcf(c_11870,plain,
nil != sK56,
inference(backward_subsumption_resolution,[status(thm)],[c_8927,c_11866]) ).
tcf(c_11871,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ strictorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,nil)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_8923,c_11866]) ).
tcf(c_11909,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ strictorderedP(X0)
| ~ ssList(X0)
| ~ frontsegP(sK56,X0) ),
inference(global_subsumption_just,[status(thm)],[c_11871,c_194,c_11871]) ).
tcf(c_14027,plain,
( ( nil = sK56 )
| ( hd(sK56) = sK51(sK56) ) ),
inference(superposition,[status(thm)],[c_8926,c_220]) ).
tcf(c_14028,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14027,c_11870]) ).
tcf(c_14187,plain,
( ( nil = sK56 )
| ( tl(sK56) = sK52(sK56) ) ),
inference(superposition,[status(thm)],[c_8926,c_222]) ).
tcf(c_14188,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14187,c_11870]) ).
tcf(c_14319,plain,
( ssItem(hd(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_14028,c_219]) ).
tcf(c_14320,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14319,c_11870,c_8926]) ).
tcf(c_14329,plain,
( ssList(tl(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_14188,c_221]) ).
tcf(c_14330,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14329,c_11870,c_8926]) ).
tcf(c_14344,plain,
app(nil,tl(sK56)) = tl(sK56),
inference(superposition,[status(thm)],[c_14330,c_155]) ).
tcf(c_14394,plain,
( frontsegP(tl(sK56),nil)
| ~ ssList(nil)
| ~ ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_14344,c_377]) ).
tcf(c_14395,plain,
frontsegP(tl(sK56),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_14394,c_141,c_14330]) ).
tcf(c_16345,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_8926,c_224]) ).
tcf(c_16348,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_16345,c_11870]) ).
tcf(c_16580,plain,
! [X0: $i] :
( ( app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_14320,c_227]) ).
tcf(c_16890,plain,
app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
inference(superposition,[status(thm)],[c_14330,c_16580]) ).
tcf(c_16892,plain,
app(cons(hd(sK56),nil),tl(sK56)) = sK56,
inference(light_normalisation,[status(thm)],[c_16890,c_16348]) ).
tcf(c_17522,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(superposition,[status(thm)],[c_16892,c_377]) ).
tcf(c_17526,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17522,c_14330]) ).
tcf(c_20044,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_16348,c_177]) ).
tcf(c_20070,plain,
! [X0: $i] :
( frontsegP(sK56,cons(hd(sK56),X0))
| ~ ssList(X0)
| ~ frontsegP(tl(sK56),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20044,c_14330,c_14320]) ).
tcf(c_20128,plain,
( frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(nil)
| ~ frontsegP(tl(sK56),nil) ),
inference(instantiation,[status(thm)],[c_20070]) ).
tcf(c_21240,plain,
frontsegP(sK56,cons(hd(sK56),nil)),
inference(global_subsumption_just,[status(thm)],[c_17526,c_141,c_14395,c_20128]) ).
tcf(c_21245,plain,
( ( cons(hd(sK56),nil) = nil )
| ~ strictorderedP(cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(superposition,[status(thm)],[c_21240,c_11909]) ).
tcf(c_21543,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(hd(sK56))
| ( cons(hd(sK56),X0) != nil ) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_21544,plain,
! [X0: $i] :
( ssList(cons(hd(sK56),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_21551,plain,
( strictorderedP(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_209]) ).
tcf(c_21554,plain,
( ssList(cons(hd(sK56),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_21544]) ).
tcf(c_21555,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sK56))
| ( cons(hd(sK56),nil) != nil ) ),
inference(instantiation,[status(thm)],[c_21543]) ).
tcf(c_21556,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_21555,c_21554,c_21551,c_21245,c_14320,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC021+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.37 % Computer : n011.cluster.edu
% 0.11/10.37 % Model : x86_64 x86_64
% 0.11/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.37 % Memory : 8046.5625MB
% 0.11/10.37 % OS : Linux 6.8.0-71-generic
% 0.11/10.37 % CPULimit : 300
% 0.11/10.37 % WCLimit : 300
% 0.11/10.37 % DateTime : Thu Sep 24 15:57:24 UTC 2026
% 0.11/10.37 % CPUTime :
% 0.11/10.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/10.40 Running first-order theorem proving
% 0.16/10.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.41
% 0.16/10.41 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.41
% 0.16/10.41 % Detected problem language: tptp
% 0.16/10.43 % Proving...
% 6.38/11.76 % SZS status Started for theBenchmark.p
% 6.38/11.76 % SZS status Theorem for theBenchmark.p
% 6.38/11.76
% 6.38/11.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.38/11.76
% 6.38/11.76 % ------ iProver source info
% 6.38/11.76
% 6.38/11.76 % git: date: 2026-07-19 20:42:38 +0200
% 6.38/11.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.38/11.76 % git: non_committed_changes: false
% 6.38/11.76
% 6.38/11.76 % ------ Parsing...
% 6.38/11.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.38/11.76
% 6.38/11.76 % ------ 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 %
% 6.38/11.76
% 6.38/11.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.38/11.76
% 6.38/11.76 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.38/11.76 % ------ Proving...
% 6.38/11.76 % ------ Problem Properties
% 6.38/11.76
% 6.38/11.76 %
% 6.38/11.76 % clauses 187
% 6.38/11.76 % conjectures 5
% 6.38/11.76 % EPR 56
% 6.38/11.76 % Horn 119
% 6.38/11.76 % unary 20
% 6.38/11.76 % binary 41
% 6.38/11.76 % lits 633
% 6.38/11.76 % lits eq 82
% 6.38/11.76 % fd_pure 0
% 6.38/11.76 % fd_pseudo 0
% 6.38/11.76 % fd_cond 23
% 6.38/11.76 % fd_pseudo_cond 14
% 6.38/11.76 % AC symbols 0
% 6.38/11.76
% 6.38/11.76 % ------ Schedule dynamic 5 is on
% 6.38/11.76
% 6.38/11.76 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.38/11.76
% 6.38/11.76
% 6.38/11.76 % ------
% 6.38/11.76 % Current options:
% 6.38/11.76 % ------
% 6.38/11.76
% 6.38/11.76
% 6.38/11.76 %
% 6.38/11.76
% 6.38/11.76 % ------ Proving...
% 6.38/11.76 %
% 6.38/11.76
% 6.38/11.76 % SZS status Theorem for theBenchmark.p
% 6.38/11.76
% 6.38/11.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.38/11.76
% 6.38/11.76
%------------------------------------------------------------------------------