%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC063+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 : n018.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 03:07:44 PM UTC 2026
% Result : Theorem 4.86s 2.21s
% Output : CNFRefutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 130 ( 46 unt; 3 def)
% Number of atoms : 502 ( 111 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 520 ( 230 ~; 216 |; 52 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 100 !; 16 ?; 33 :)
% 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(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
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] :
( ( ( ? [X6] :
( segmentP(X0,X6)
& segmentP(X1,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( segmentP(X0,X6)
& segmentP(X1,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(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(f134,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
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] :
( ( ( ! [X6] :
( ~ segmentP(X0,X6)
| ~ segmentP(X1,X6)
| ~ neq(X6,nil)
| ~ ssList(X6) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( app(X5,cons(X4,nil)) = X3
& app(cons(X4,nil),X5) = X2
& ssList(X5) ) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f245,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(f246,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,[],[f245]) ).
fof(f247,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))],[f246]) ).
fof(f272,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f295,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ( ( ! [X6] :
( ~ segmentP(sK53,X6)
| ~ segmentP(sK54,X6)
| ~ neq(X6,nil)
| ~ ssList(X6) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(sK56,nil)
| ( ssItem(sK57)
& sK56 = app(sK58,cons(sK57,nil))
& sK55 = app(cons(sK57,nil),sK58)
& ssList(sK58) ) )
& ( nil != sK56
| nil = sK55 )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58)],[f221]) ).
fof(f317,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,[],[f247]) ).
fof(f386,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f389,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f402,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f481,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f496,plain,
ssList(sK54),
inference(cnf_transformation,[],[f295]) ).
fof(f498,plain,
! [X6] :
( ~ segmentP(sK53,X6)
| ~ segmentP(sK54,X6)
| ~ neq(X6,nil)
| ~ ssList(X6)
| nil != sK53 ),
inference(cnf_transformation,[],[f295]) ).
fof(f499,plain,
( neq(sK54,nil)
| nil != sK53 ),
inference(cnf_transformation,[],[f295]) ).
fof(f500,plain,
! [X6] :
( ~ segmentP(sK53,X6)
| ~ segmentP(sK54,X6)
| ~ neq(X6,nil)
| ~ ssList(X6)
| nil = sK54 ),
inference(cnf_transformation,[],[f295]) ).
fof(f501,plain,
( neq(sK54,nil)
| nil = sK54 ),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f295]) ).
fof(f503,plain,
( ~ neq(sK56,nil)
| sK56 = app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
( ~ neq(sK56,nil)
| sK55 = app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f295]) ).
fof(f505,plain,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
( neq(sK56,nil)
| nil = sK56 ),
inference(definition_unfolding,[],[f501,f508,f508]) ).
fof(f511,plain,
! [X6] :
( ~ segmentP(sK55,X6)
| ~ segmentP(sK56,X6)
| ~ neq(X6,nil)
| ~ ssList(X6)
| nil = sK56 ),
inference(definition_unfolding,[],[f500,f508,f508,f507]) ).
fof(f512,plain,
( neq(sK56,nil)
| nil != sK55 ),
inference(definition_unfolding,[],[f499,f507,f508]) ).
fof(f513,plain,
! [X6] :
( ~ segmentP(sK55,X6)
| ~ segmentP(sK56,X6)
| ~ neq(X6,nil)
| ~ ssList(X6)
| nil != sK55 ),
inference(definition_unfolding,[],[f498,f507,f508,f507]) ).
fof(f514,plain,
ssList(sK56),
inference(definition_unfolding,[],[f496,f508]) ).
fof(f515,plain,
ssList(sK55),
inference(definition_unfolding,[],[f495,f507]) ).
fof(f521,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,[],[f317]) ).
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,[],[f521]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f386]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f388]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f389]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f402]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f481]) ).
tcf(c_247,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_248,negated_conjecture,
( ssList(sK58)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_249,negated_conjecture,
( ( app(cons(sK57,nil),sK58) = sK55 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_250,negated_conjecture,
( ( app(sK58,cons(sK57,nil)) = sK56 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_251,negated_conjecture,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_252,negated_conjecture,
( neq(sK56,nil)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f510]) ).
tcf(c_253,negated_conjecture,
! [X0: $i] :
( ( nil = sK56 )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_254,negated_conjecture,
( neq(sK56,nil)
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_255,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil)
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f513]) ).
tcf(c_257,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f514]) ).
tcf(c_258,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f515]) ).
tcf(c_367,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_251,c_251,c_252,c_254,c_247]) ).
tcf(c_369,negated_conjecture,
ssList(sK58),
inference(global_subsumption_just,[status(thm)],[c_248,c_248,c_252,c_254,c_247]) ).
tcf(c_377,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_254,c_247]) ).
tcf(c_387,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK56,
inference(global_subsumption_just,[status(thm)],[c_250,c_250,c_377]) ).
tcf(c_389,negated_conjecture,
app(cons(sK57,nil),sK58) = sK55,
inference(global_subsumption_just,[status(thm)],[c_249,c_252,c_254,c_247,c_249]) ).
tcf(c_397,plain,
! [X0: $i] :
( ~ neq(X0,nil)
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_253,c_247,c_253,c_255]) ).
tcf(c_398,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(renaming,[status(thm)],[c_397]) ).
tcf(c_399,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ neq(X0,nil) ),
inference(global_subsumption_just,[status(thm)],[c_255,c_398]) ).
tcf(c_3250,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_399]) ).
tcf(c_3251,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3250]) ).
tcf(c_3253,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3251,c_141,c_3251]) ).
tcf(c_3254,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3253]) ).
tcf(c_8907,definition,
iPr_def_10 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8908,definition,
iPr_def_11 = app(iPr_def_10,sK58),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8909,definition,
iPr_def_12 = app(sK58,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8912,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3254]) ).
tcf(c_8913,negated_conjecture,
iPr_def_11 = sK55,
inference(demodulation,[status(thm)],[c_389,c_8907,c_8908]) ).
tcf(c_8914,negated_conjecture,
iPr_def_12 = sK56,
inference(demodulation,[status(thm)],[c_387,c_8909]) ).
tcf(c_8915,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_369]) ).
tcf(c_8916,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_367]) ).
tcf(c_8917,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_258]) ).
tcf(c_8918,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_257]) ).
tcf(c_11754,plain,
ssList(iPr_def_11),
inference(light_normalisation,[status(thm)],[c_8917,c_8913]) ).
tcf(c_11755,plain,
ssList(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_8918,c_8914]) ).
tcf(c_11760,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(iPr_def_12,X0)
| ~ segmentP(iPr_def_11,X0) ),
inference(light_normalisation,[status(thm)],[c_8912,c_8913,c_8914]) ).
tcf(c_12105,plain,
app(nil,sK58) = sK58,
inference(superposition,[status(thm)],[c_8915,c_155]) ).
tcf(c_12190,plain,
app(iPr_def_11,nil) = iPr_def_11,
inference(superposition,[status(thm)],[c_11754,c_232]) ).
tcf(c_12191,plain,
app(iPr_def_12,nil) = iPr_def_12,
inference(superposition,[status(thm)],[c_11755,c_232]) ).
tcf(c_12253,plain,
( ssList(iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8907,c_140]) ).
tcf(c_12256,plain,
ssList(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12253,c_141,c_8916]) ).
tcf(c_12284,plain,
app(iPr_def_10,nil) = iPr_def_10,
inference(superposition,[status(thm)],[c_12256,c_232]) ).
tcf(c_12285,plain,
app(nil,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_12256,c_155]) ).
tcf(c_13444,plain,
( ~ ssList(nil)
| ~ ssItem(sK57)
| ( nil != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_8907,c_142]) ).
tcf(c_13445,plain,
nil != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_13444,c_141,c_8916]) ).
tcf(c_26859,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),sK58)
| ~ ssList(iPr_def_10)
| ~ ssList(sK58)
| ~ ssList(X0)
| ~ ssList(app(app(iPr_def_10,sK58),X0)) ),
inference(superposition,[status(thm)],[c_8908,c_67]) ).
tcf(c_26860,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(sK58)
| ~ ssList(X0)
| ~ ssList(app(app(sK58,iPr_def_10),X0)) ),
inference(superposition,[status(thm)],[c_8909,c_67]) ).
tcf(c_26862,plain,
! [X0: $i] :
( segmentP(app(sK58,X0),sK58)
| ~ ssList(sK58)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK58),X0)) ),
inference(superposition,[status(thm)],[c_12105,c_67]) ).
tcf(c_26958,plain,
! [X0: $i] :
( segmentP(app(sK58,X0),sK58)
| ~ ssList(sK58)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(sK58,X0)) ),
inference(light_normalisation,[status(thm)],[c_26862,c_12105]) ).
tcf(c_26959,plain,
! [X0: $i] :
( segmentP(app(sK58,X0),sK58)
| ~ ssList(X0)
| ~ ssList(app(sK58,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26958,c_8915,c_141]) ).
tcf(c_26968,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(sK58)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_12,X0)) ),
inference(light_normalisation,[status(thm)],[c_26860,c_8909]) ).
tcf(c_26969,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_10)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_12,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26968,c_12256,c_8915]) ).
tcf(c_26973,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),sK58)
| ~ ssList(iPr_def_10)
| ~ ssList(sK58)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_11,X0)) ),
inference(light_normalisation,[status(thm)],[c_26859,c_8908]) ).
tcf(c_26974,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),sK58)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_11,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26973,c_12256,c_8915]) ).
tcf(c_27887,plain,
( segmentP(iPr_def_12,sK58)
| ~ ssList(iPr_def_10)
| ~ ssList(app(sK58,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_8909,c_26959]) ).
tcf(c_27896,plain,
( segmentP(iPr_def_12,sK58)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_27887,c_8909]) ).
tcf(c_27897,plain,
segmentP(iPr_def_12,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_27896,c_11755,c_12256]) ).
tcf(c_28020,plain,
( segmentP(iPr_def_12,iPr_def_10)
| ~ ssList(nil)
| ~ ssList(app(iPr_def_12,nil)) ),
inference(superposition,[status(thm)],[c_12191,c_26969]) ).
tcf(c_28025,plain,
( segmentP(iPr_def_12,iPr_def_10)
| ~ ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(light_normalisation,[status(thm)],[c_28020,c_12191]) ).
tcf(c_28026,plain,
segmentP(iPr_def_12,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_28025,c_11755,c_141]) ).
tcf(c_28050,plain,
( segmentP(iPr_def_11,sK58)
| ~ ssList(nil)
| ~ ssList(app(iPr_def_11,nil)) ),
inference(superposition,[status(thm)],[c_12190,c_26974]) ).
tcf(c_28055,plain,
( segmentP(iPr_def_11,sK58)
| ~ ssList(iPr_def_11)
| ~ ssList(nil) ),
inference(light_normalisation,[status(thm)],[c_28050,c_12190]) ).
tcf(c_28056,plain,
segmentP(iPr_def_11,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_28055,c_11754,c_141]) ).
tcf(c_29233,plain,
( ( nil = sK58 )
| ~ ssList(sK58)
| ~ segmentP(iPr_def_11,sK58) ),
inference(superposition,[status(thm)],[c_27897,c_11760]) ).
tcf(c_29234,plain,
( ( nil = sK58 )
| ~ segmentP(iPr_def_11,sK58) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29233,c_8915]) ).
tcf(c_29339,plain,
( ( nil = iPr_def_10 )
| ~ ssList(iPr_def_10)
| ~ segmentP(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_28026,c_11760]) ).
tcf(c_29340,plain,
~ segmentP(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_29339,c_13445,c_12256]) ).
tcf(c_29360,plain,
nil = sK58,
inference(global_subsumption_just,[status(thm)],[c_29234,c_28056,c_29234]) ).
tcf(c_29460,plain,
app(nil,iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_8909,c_29360]) ).
tcf(c_29461,plain,
app(iPr_def_10,nil) = iPr_def_11,
inference(demodulation,[status(thm)],[c_8908,c_29360]) ).
tcf(c_29463,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_29461,c_12284]) ).
tcf(c_29464,plain,
iPr_def_10 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_29460,c_12285]) ).
tcf(c_29515,plain,
~ segmentP(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_29340,c_29463]) ).
tcf(c_29558,plain,
segmentP(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_28026,c_29464]) ).
tcf(c_29632,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_29558,c_29515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC063+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 16:13:18 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 4.86/2.21 % SZS status Started for theBenchmark.p
% 4.86/2.21 % SZS status Theorem for theBenchmark.p
% 4.86/2.21
% 4.86/2.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.86/2.21
% 4.86/2.21 % ------ iProver source info
% 4.86/2.21
% 4.86/2.21 % git: date: 2026-07-19 20:42:38 +0200
% 4.86/2.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.86/2.21 % git: non_committed_changes: false
% 4.86/2.21
% 4.86/2.21 % ------ Parsing...
% 4.86/2.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.86/2.21
% 4.86/2.21 % ------ 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 %
% 4.86/2.21
% 4.86/2.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.86/2.21
% 4.86/2.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.86/2.21 % ------ Proving...
% 4.86/2.21 % ------ Problem Properties
% 4.86/2.21
% 4.86/2.21 %
% 4.86/2.21 % clauses 192
% 4.86/2.21 % conjectures 6
% 4.86/2.21 % EPR 58
% 4.86/2.21 % Horn 124
% 4.86/2.21 % unary 26
% 4.86/2.21 % binary 41
% 4.86/2.21 % lits 634
% 4.86/2.21 % lits eq 85
% 4.86/2.21 % fd_pure 0
% 4.86/2.21 % fd_pseudo 0
% 4.86/2.21 % fd_cond 22
% 4.86/2.21 % fd_pseudo_cond 14
% 4.86/2.21 % AC symbols 0
% 4.86/2.21
% 4.86/2.21 % ------ Schedule dynamic 5 is on
% 4.86/2.21
% 4.86/2.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.86/2.21
% 4.86/2.21
% 4.86/2.21 % ------
% 4.86/2.21 % Current options:
% 4.86/2.21 % ------
% 4.86/2.21
% 4.86/2.21
% 4.86/2.21 %
% 4.86/2.21
% 4.86/2.21 % ------ Proving...
% 4.86/2.21 %
% 4.86/2.21
% 4.86/2.21 % SZS status Theorem for theBenchmark.p
% 4.86/2.21
% 4.86/2.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.86/2.21
% 4.86/2.21
%------------------------------------------------------------------------------