%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC192+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 : n016.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 03:08:49 PM UTC 2026
% Result : Theorem 46.78s 8.48s
% Output : CNFRefutation 46.78s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f547ERROR: Could not build tree for root c_152101ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( X4 = X5
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) ) ) ) )
| 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)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( X4 = X5
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) ) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f99,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
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(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f146,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f147,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f148,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f200,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X8] :
( ssItem(X8)
& memberP(X3,X8)
& cons(X8,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0 ) ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X8] :
( ssItem(X8)
& memberP(X3,X8)
& cons(X8,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& X4 != X5
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0 ) ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f235,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f235]) ).
fof(f277,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f146]) ).
fof(f278,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f277]) ).
fof(f279,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f147]) ).
fof(f280,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f279]) ).
fof(f292,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f200]) ).
fof(f293,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(flattening,[],[f292]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( nil = sK55
& nil = sK56 )
| ( ssItem(sK61)
& memberP(sK56,sK61)
& sK55 = cons(sK61,nil) ) )
& ssItem(sK57)
& ssItem(sK58)
& ssList(sK59)
& ssList(sK60)
& sK57 != sK58
& sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59),skolemize(X7,sK60),skolemize(X8,sK61)],[f222]) ).
fof(f305,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
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(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f416,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f280]) ).
fof(f419,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f479,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f293]) ).
fof(f480,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f293]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil = sK55
| ssItem(sK61) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil = sK55
| sK55 = cons(sK61,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
ssList(sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK57 != sK58,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f514,plain,
sK55 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(definition_unfolding,[],[f511,f512]) ).
fof(f516,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f512]) ).
fof(f518,plain,
! [X2,X3,X1] :
( ~ ssList(app(X2,cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(app(X2,cons(X1,X3)),X1) ),
inference(equality_resolution,[],[f305]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f518]) ).
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_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f415]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f414]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f547]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[],[f416]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f480]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f479]) ).
tcf(c_246,negated_conjecture,
app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60) = sK55,
inference(cnf_transformation,[],[f514]) ).
tcf(c_247,negated_conjecture,
sK57 != sK58,
inference(cnf_transformation,[],[f510]) ).
tcf(c_248,negated_conjecture,
ssList(sK60),
inference(cnf_transformation,[],[f509]) ).
tcf(c_249,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f508]) ).
tcf(c_250,negated_conjecture,
ssItem(sK58),
inference(cnf_transformation,[],[f507]) ).
tcf(c_251,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f506]) ).
tcf(c_253,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK61,nil) = sK55 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_257,negated_conjecture,
( ssItem(sK61)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_261,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f516]) ).
tcf(c_8895,definition,
iPr_def_10 = cons(sK61,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8896,definition,
iPr_def_11 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8897,definition,
iPr_def_12 = app(sK59,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8898,definition,
iPr_def_13 = cons(sK58,nil),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8899,definition,
iPr_def_14 = app(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_8900,definition,
iPr_def_15 = app(iPr_def_14,sK60),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_8901,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_261]) ).
tcf(c_8903,negated_conjecture,
( ssItem(sK61)
| ( nil = sK55 ) ),
inference(demodulation,[status(thm)],[c_257]) ).
tcf(c_8907,negated_conjecture,
( ( iPr_def_10 = sK55 )
| ( nil = sK55 ) ),
inference(demodulation,[status(thm)],[c_253,c_8895]) ).
tcf(c_8909,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_251]) ).
tcf(c_8910,negated_conjecture,
ssItem(sK58),
inference(demodulation,[status(thm)],[c_250]) ).
tcf(c_8911,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_8912,negated_conjecture,
ssList(sK60),
inference(demodulation,[status(thm)],[c_248]) ).
tcf(c_8913,negated_conjecture,
sK57 != sK58,
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_8914,negated_conjecture,
iPr_def_15 = sK55,
inference(demodulation,[status(thm)],[c_246,c_8898,c_8896,c_8897,c_8899,c_8900]) ).
tcf(c_11795,plain,
( ssItem(sK61)
| ( nil = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_8903,c_8914]) ).
tcf(c_11813,plain,
( ( iPr_def_10 = iPr_def_15 )
| ( nil = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_8907,c_8914]) ).
tcf(c_12783,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8896,c_140]) ).
tcf(c_12784,plain,
( ssList(iPr_def_13)
| ~ ssList(nil)
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_8898,c_140]) ).
tcf(c_12794,plain,
ssList(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_12784,c_141,c_8910]) ).
tcf(c_12795,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_12783,c_141,c_8909]) ).
tcf(c_12908,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(sK59) ),
inference(superposition,[status(thm)],[c_8897,c_153]) ).
tcf(c_12909,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_8899,c_153]) ).
tcf(c_12933,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12909,c_12794]) ).
tcf(c_12936,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_12908,c_12795,c_8911]) ).
tcf(c_12937,plain,
ssList(iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_12933,c_12936]) ).
tcf(c_13642,plain,
( ~ ssList(nil)
| ~ ssItem(sK58)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8898,c_142]) ).
tcf(c_13650,plain,
nil != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_13642,c_141,c_8910]) ).
tcf(c_15889,plain,
ssList(iPr_def_15),
inference(light_normalisation,[status(thm)],[c_8901,c_8914]) ).
tcf(c_15908,plain,
( ( iPr_def_10 = iPr_def_15 )
| ( nil = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_8907,c_8914]) ).
tcf(c_16249,plain,
( ( iPr_def_10 = iPr_def_15 )
| ( cons(sK57,iPr_def_15) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_15908,c_8896]) ).
tcf(c_16993,plain,
( ( nil = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ( nil != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8899,c_230]) ).
tcf(c_17033,plain,
nil != iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_16993,c_13650,c_12794,c_12936]) ).
tcf(c_17156,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_11),sK57)
| ( iPr_def_10 = iPr_def_15 )
| ~ ssList(iPr_def_15)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK57,iPr_def_15))) ),
inference(superposition,[status(thm)],[c_16249,c_54]) ).
tcf(c_17179,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_11),sK57)
| ( iPr_def_10 = iPr_def_15 )
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK57,iPr_def_15))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17156,c_15889,c_8909]) ).
tcf(c_17656,plain,
( ( nil = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(sK60)
| ( nil != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_8900,c_231]) ).
tcf(c_17692,plain,
nil != iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_17656,c_17033,c_12937,c_8912]) ).
tcf(c_17700,plain,
iPr_def_10 = iPr_def_15,
inference(backward_subsumption_resolution,[status(thm)],[c_11813,c_17692]) ).
tcf(c_17702,plain,
ssItem(sK61),
inference(backward_subsumption_resolution,[status(thm)],[c_11795,c_17692]) ).
tcf(c_18287,plain,
iPr_def_10 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_17179,c_17700]) ).
tcf(c_24524,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK61 )
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_8895,c_170]) ).
tcf(c_24531,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK61 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24524,c_141,c_17702]) ).
tcf(c_101649,negated_conjecture,
ssItem(sK61),
inference(global_subsumption_just,[status(thm)],[c_8903,c_17702]) ).
tcf(c_101658,plain,
app(iPr_def_14,sK60) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_8900,c_18287]) ).
tcf(c_102358,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8896,c_140]) ).
tcf(c_102359,plain,
( ssList(iPr_def_13)
| ~ ssList(nil)
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_8898,c_140]) ).
tcf(c_102364,plain,
ssList(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_102359,c_141,c_8910]) ).
tcf(c_102365,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_102358,c_141,c_8909]) ).
tcf(c_102562,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(sK59) ),
inference(superposition,[status(thm)],[c_8897,c_153]) ).
tcf(c_102563,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_8899,c_153]) ).
tcf(c_102576,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102563,c_102364]) ).
tcf(c_102579,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_102562,c_102365,c_8911]) ).
tcf(c_102580,plain,
ssList(iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_102576,c_102579]) ).
tcf(c_103117,plain,
( memberP(iPr_def_11,sK57)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8896,c_168]) ).
tcf(c_103118,plain,
( memberP(iPr_def_13,sK58)
| ~ ssList(nil)
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_8898,c_168]) ).
tcf(c_103121,plain,
memberP(iPr_def_13,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_103118,c_141,c_8910]) ).
tcf(c_103122,plain,
memberP(iPr_def_11,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_103117,c_141,c_8909]) ).
tcf(c_106980,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_8899,c_165]) ).
tcf(c_106981,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssList(iPr_def_14)
| ~ ssList(sK60)
| ~ ssItem(X0)
| ~ memberP(iPr_def_14,X0) ),
inference(superposition,[status(thm)],[c_101658,c_165]) ).
tcf(c_107015,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_14,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106981,c_102580,c_8912]) ).
tcf(c_107019,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106980,c_102364,c_102579]) ).
tcf(c_107057,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ ssList(iPr_def_11)
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_8897,c_166]) ).
tcf(c_107058,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_8899,c_166]) ).
tcf(c_107097,plain,
! [X0: $i] :
( memberP(iPr_def_14,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107058,c_102364,c_102579]) ).
tcf(c_107101,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_11,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107057,c_102365,c_8911]) ).
tcf(c_108536,plain,
( memberP(iPr_def_12,sK57)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_103122,c_107101]) ).
tcf(c_108537,plain,
memberP(iPr_def_12,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_108536,c_8909]) ).
tcf(c_111126,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK61 )
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_8895,c_170]) ).
tcf(c_111129,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK61 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111126,c_141,c_101649]) ).
tcf(c_139600,plain,
( memberP(iPr_def_14,sK57)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_108537,c_107019]) ).
tcf(c_139601,plain,
memberP(iPr_def_14,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_139600,c_8909]) ).
tcf(c_139608,plain,
( memberP(iPr_def_14,sK58)
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_103121,c_107097]) ).
tcf(c_139609,plain,
memberP(iPr_def_14,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_139608,c_8910]) ).
tcf(c_139611,plain,
( memberP(iPr_def_10,sK57)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_139601,c_107015]) ).
tcf(c_139612,plain,
memberP(iPr_def_10,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_139611,c_8909]) ).
tcf(c_139626,plain,
( memberP(iPr_def_10,sK58)
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_139609,c_107015]) ).
tcf(c_139627,plain,
memberP(iPr_def_10,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_139626,c_8910]) ).
tcf(c_152042,plain,
! [X0: $i] :
( ~ memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ( X0 = sK61 ) ),
inference(global_subsumption_just,[status(thm)],[c_111129,c_171,c_24531]) ).
tcf(c_152043,plain,
! [X0: $i] :
( ( X0 = sK61 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(renaming,[status(thm)],[c_152042]) ).
tcf(c_152052,plain,
( ( sK58 = sK61 )
| ~ ssItem(sK58) ),
inference(superposition,[status(thm)],[c_139627,c_152043]) ).
tcf(c_152053,plain,
( ( sK57 = sK61 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_139612,c_152043]) ).
tcf(c_152054,plain,
sK57 = sK61,
inference(forward_subsumption_resolution,[status(thm)],[c_152053,c_8909]) ).
tcf(c_152055,plain,
sK58 = sK61,
inference(forward_subsumption_resolution,[status(thm)],[c_152052,c_8910]) ).
tcf(c_152099,plain,
sK58 != sK61,
inference(demodulation,[status(thm)],[c_8913,c_152054]) ).
tcf(c_152101,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_152099,c_152055]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC192+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 16:58:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 46.78/8.48 % SZS status Started for theBenchmark.p
% 46.78/8.48 % SZS status Theorem for theBenchmark.p
% 46.78/8.48
% 46.78/8.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 46.78/8.48
% 46.78/8.48 % ------ iProver source info
% 46.78/8.48
% 46.78/8.48 % git: date: 2026-07-19 20:42:38 +0200
% 46.78/8.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 46.78/8.48 % git: non_committed_changes: false
% 46.78/8.48
% 46.78/8.48 % ------ Parsing...
% 46.78/8.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 46.78/8.48
% 46.78/8.48 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 46.78/8.48
% 46.78/8.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 46.78/8.48
% 46.78/8.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 46.78/8.48 % ------ Proving...
% 46.78/8.48 % ------ Problem Properties
% 46.78/8.48
% 46.78/8.48 %
% 46.78/8.48 % clauses 200
% 46.78/8.48 % conjectures 14
% 46.78/8.48 % EPR 63
% 46.78/8.48 % Horn 126
% 46.78/8.48 % unary 30
% 46.78/8.48 % binary 46
% 46.78/8.48 % lits 644
% 46.78/8.48 % lits eq 94
% 46.78/8.48 % fd_pure 0
% 46.78/8.48 % fd_pseudo 0
% 46.78/8.48 % fd_cond 21
% 46.78/8.48 % fd_pseudo_cond 14
% 46.78/8.48 % AC symbols 0
% 46.78/8.48
% 46.78/8.48 % ------ Schedule dynamic 5 is on
% 46.78/8.48
% 46.78/8.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 46.78/8.48
% 46.78/8.48
% 46.78/8.48 % ------
% 46.78/8.48 % Current options:
% 46.78/8.48 % ------
% 46.78/8.48
% 46.78/8.48
% 46.78/8.48 %
% 46.78/8.48
% 46.78/8.48 % ------ Proving...
% 46.78/8.48 %
% 46.78/8.48
% 46.78/8.48 % SZS status Theorem for theBenchmark.p
% 46.78/8.48
% 46.78/8.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 46.78/8.48
% 46.78/8.48
%------------------------------------------------------------------------------