%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC343+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 03:09:22 PM UTC 2026
% Result : Theorem 3.81s 1.28s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 115 ( 21 unt; 2 def)
% Number of atoms : 538 ( 180 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 712 ( 298 ~; 290 |; 106 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 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 : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 207 ( 0 sgn 162 !; 45 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ? [X9] :
( strictorderedP(X0)
& ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> ( ! [X12] :
( ssItem(X12)
=> ! [X13] :
( ssList(X13)
=> ( ~ lt(X12,X10)
| app(X13,cons(X12,nil)) != X0 ) ) )
| app(cons(X10,nil),X11) != X9 ) ) )
& app(X0,X9) = X1
& ssList(X9) ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ strictorderedP(X2)
| app(X2,X4) != X3 ) )
| 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 = X1
| nil != X0 )
& ? [X9] :
( strictorderedP(X0)
& ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> ( ! [X12] :
( ssItem(X12)
=> ! [X13] :
( ssList(X13)
=> ( ~ lt(X12,X10)
| app(X13,cons(X12,nil)) != X0 ) ) )
| app(cons(X10,nil),X11) != X9 ) ) )
& app(X0,X9) = X1
& ssList(X9) ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ strictorderedP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ! [X9] :
( ~ strictorderedP(X0)
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& lt(X12,X10)
& app(X13,cons(X12,nil)) = X0 ) )
& app(cons(X10,nil),X11) = X9 ) )
| app(X0,X9) != X1
| ~ ssList(X9) ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != X2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ! [X9] :
( ~ strictorderedP(X0)
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& lt(X12,X10)
& app(X13,cons(X12,nil)) = X0 ) )
& app(cons(X10,nil),X11) = X9 ) )
| app(X0,X9) != X1
| ~ ssList(X9) ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != X2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f301,plain,
( ssList(sK58)
& ssList(sK59)
& ssList(sK60)
& ssList(sK61)
& ( ( nil != sK59
& nil = sK58 )
| sP6(sK59,sK58) )
& ( nil != sK60
| nil = sK61 )
& ssList(sK62)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != sK60
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != sK62
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(sK60)
& sK61 = app(sK60,sK62)
& sK58 = sK60
& sK59 = sK61 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58,sK59,sK60,sK61,sK62]),skolemize(X0,sK58),skolemize(X1,sK59),skolemize(X2,sK60),skolemize(X3,sK61),skolemize(X4,sK62)],[f233]) ).
fof(f512,plain,
( nil != sK59
| sP6(sK59,sK58) ),
inference(cnf_transformation,[],[f301]) ).
fof(f513,plain,
( nil = sK58
| sP6(sK59,sK58) ),
inference(cnf_transformation,[],[f301]) ).
fof(f514,plain,
( nil != sK60
| nil = sK61 ),
inference(cnf_transformation,[],[f301]) ).
fof(f515,plain,
ssList(sK62),
inference(cnf_transformation,[],[f301]) ).
fof(f516,plain,
! [X8,X6,X7,X5] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != sK60
| ~ ssList(X8)
| ~ ssItem(X7)
| app(cons(X5,nil),X6) != sK62
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f301]) ).
fof(f517,plain,
strictorderedP(sK60),
inference(cnf_transformation,[],[f301]) ).
fof(f518,plain,
sK61 = app(sK60,sK62),
inference(cnf_transformation,[],[f301]) ).
fof(f519,plain,
sK58 = sK60,
inference(cnf_transformation,[],[f301]) ).
fof(f520,plain,
sK59 = sK61,
inference(cnf_transformation,[],[f301]) ).
fof(f521,plain,
( nil = sK60
| sP6(sK61,sK60) ),
inference(definition_unfolding,[],[f513,f520,f519,f519]) ).
fof(f522,plain,
( nil != sK61
| sP6(sK61,sK60) ),
inference(definition_unfolding,[],[f512,f520,f519,f520]) ).
tcf(c_253,negated_conjecture,
app(sK60,sK62) = sK61,
inference(cnf_transformation,[],[f518]) ).
tcf(c_254,negated_conjecture,
strictorderedP(sK60),
inference(cnf_transformation,[],[f517]) ).
tcf(c_255,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X0)
| ~ lt(X3,X0)
| ( app(X2,cons(X3,nil)) != sK60 )
| ( app(cons(X0,nil),X1) != sK62 ) ),
inference(cnf_transformation,[],[f516]) ).
tcf(c_256,negated_conjecture,
ssList(sK62),
inference(cnf_transformation,[],[f515]) ).
tcf(c_257,negated_conjecture,
( ( nil = sK61 )
| ( nil != sK60 ) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_258,negated_conjecture,
( sP6(sK61,sK60)
| ( nil = sK60 ) ),
inference(cnf_transformation,[],[f521]) ).
tcf(c_259,negated_conjecture,
( sP6(sK61,sK60)
| ( nil != sK61 ) ),
inference(cnf_transformation,[],[f522]) ).
tcf(c_383,negated_conjecture,
sP6(sK61,sK60),
inference(global_subsumption_just,[status(thm)],[c_258,c_258,c_259,c_257]) ).
tcf(c_385,negated_conjecture,
sP6(sK61,sK60),
inference(global_subsumption_just,[status(thm)],[c_259,c_383]) ).
tcf(c_9201,definition,
iPr_def_10 = app(sK60,sK62),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_9212,negated_conjecture,
ssList(sK62),
inference(demodulation,[status(thm)],[c_256]) ).
tcf(c_9213,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X0)
| ~ lt(X3,X0)
| ( app(X2,cons(X3,nil)) != sK60 )
| ( app(cons(X0,nil),X1) != sK62 ) ),
inference(demodulation,[status(thm)],[c_255]) ).
tcf(c_9215,negated_conjecture,
iPr_def_10 = sK61,
inference(demodulation,[status(thm)],[c_253,c_9201]) ).
fof(f232,definition,
! [X1,X0] :
( ~ sP6(X1,X0)
| ! [X9] :
( ~ strictorderedP(X0)
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& lt(X12,X10)
& app(X13,cons(X12,nil)) = X0 ) )
& app(cons(X10,nil),X11) = X9 ) )
| app(X0,X9) != X1
| ~ ssList(X9) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f233,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| sP6(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != X2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f222,f232]) ).
fof(f298,plain,
! [X1,X0] :
( ~ sP6(X1,X0)
| ! [X9] :
( ~ strictorderedP(X0)
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& lt(X12,X10)
& app(X13,cons(X12,nil)) = X0 ) )
& app(cons(X10,nil),X11) = X9 ) )
| app(X0,X9) != X1
| ~ ssList(X9) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f299,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ! [X2] :
( ~ strictorderedP(X1)
| ? [X3] :
( ssItem(X3)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& lt(X5,X3)
& app(X6,cons(X5,nil)) = X1 ) )
& app(cons(X3,nil),X4) = X2 ) )
| app(X1,X2) != X0
| ~ ssList(X2) ) ),
inference(rectify,[],[f298]) ).
fof(f300,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ! [X2] :
( ~ strictorderedP(X1)
| ( ssItem(sK54(X1,X2))
& ssList(sK55(X1,X2))
& ssItem(sK56(X1,X2))
& ssList(sK57(X1,X2))
& lt(sK56(X1,X2),sK54(X1,X2))
& app(sK57(X1,X2),cons(sK56(X1,X2),nil)) = X1
& app(cons(sK54(X1,X2),nil),sK55(X1,X2)) = X2 )
| app(X1,X2) != X0
| ~ ssList(X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54,sK55,sK56,sK57]),skolemize(X3,sK54(X1,X2)),skolemize(X4,sK55(X1,X2)),skolemize(X5,sK56(X1,X2)),skolemize(X6,sK57(X1,X2))],[f299]) ).
fof(f501,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1)
| ~ strictorderedP(X1)
| ssItem(sK54(X1,X2))
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f300]) ).
fof(f502,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1)
| ~ strictorderedP(X1)
| ssList(sK55(X1,X2))
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f300]) ).
fof(f503,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1)
| ~ strictorderedP(X1)
| ssItem(sK56(X1,X2))
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f300]) ).
fof(f504,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1)
| ~ strictorderedP(X1)
| ssList(sK57(X1,X2))
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f300]) ).
fof(f505,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1)
| ~ strictorderedP(X1)
| lt(sK56(X1,X2),sK54(X1,X2))
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f300]) ).
fof(f506,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1)
| ~ strictorderedP(X1)
| app(sK57(X1,X2),cons(sK56(X1,X2),nil)) = X1
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f300]) ).
fof(f507,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1)
| ~ strictorderedP(X1)
| app(cons(sK54(X1,X2),nil),sK55(X1,X2)) = X2
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f300]) ).
fof(f552,plain,
! [X2,X1] :
( ~ sP6(app(X1,X2),X1)
| ~ strictorderedP(X1)
| app(cons(sK54(X1,X2),nil),sK55(X1,X2)) = X2
| ~ ssList(X2) ),
inference(equality_resolution,[],[f507]) ).
fof(f553,plain,
! [X2,X1] :
( ~ sP6(app(X1,X2),X1)
| ~ strictorderedP(X1)
| app(sK57(X1,X2),cons(sK56(X1,X2),nil)) = X1
| ~ ssList(X2) ),
inference(equality_resolution,[],[f506]) ).
fof(f554,plain,
! [X2,X1] :
( ~ sP6(app(X1,X2),X1)
| ~ strictorderedP(X1)
| lt(sK56(X1,X2),sK54(X1,X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f505]) ).
fof(f555,plain,
! [X2,X1] :
( ~ sP6(app(X1,X2),X1)
| ~ strictorderedP(X1)
| ssList(sK57(X1,X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f504]) ).
fof(f556,plain,
! [X2,X1] :
( ~ sP6(app(X1,X2),X1)
| ~ strictorderedP(X1)
| ssItem(sK56(X1,X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f503]) ).
fof(f557,plain,
! [X2,X1] :
( ~ sP6(app(X1,X2),X1)
| ~ strictorderedP(X1)
| ssList(sK55(X1,X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f502]) ).
fof(f558,plain,
! [X2,X1] :
( ~ sP6(app(X1,X2),X1)
| ~ strictorderedP(X1)
| ssItem(sK54(X1,X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f501]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( ( app(cons(sK54(X0,X1),nil),sK55(X0,X1)) = X1 )
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ~ sP6(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f552]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] :
( ( app(sK57(X0,X1),cons(sK56(X0,X1),nil)) = X0 )
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ~ sP6(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f553]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] :
( lt(sK56(X0,X1),sK54(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ~ sP6(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f554]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( ssList(sK57(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ~ sP6(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f555]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] :
( ssItem(sK56(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ~ sP6(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f556]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] :
( ssList(sK55(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ~ sP6(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f557]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] :
( ssItem(sK54(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ~ sP6(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f558]) ).
tcf(c_3370,plain,
! [X0: $i,X1: $i] :
( ssItem(sK54(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ( X0 != sK60 )
| ( app(X0,X1) != sK61 ) ),
inference(resolution_lifted,[status(thm)],[c_252,c_385]) ).
tcf(c_3371,plain,
! [X0: $i] :
( ssItem(sK54(sK60,X0))
| ~ strictorderedP(sK60)
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(unflattening,[status(thm)],[c_3370]) ).
tcf(c_3373,plain,
! [X0: $i] :
( ssItem(sK54(sK60,X0))
| ( app(sK60,X0) != sK61 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3371,c_254,c_3371]) ).
tcf(c_3374,plain,
! [X0: $i] :
( ssItem(sK54(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(renaming,[status(thm)],[c_3373]) ).
tcf(c_3385,plain,
! [X0: $i,X1: $i] :
( ssList(sK55(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ( X0 != sK60 )
| ( app(X0,X1) != sK61 ) ),
inference(resolution_lifted,[status(thm)],[c_251,c_385]) ).
tcf(c_3386,plain,
! [X0: $i] :
( ssList(sK55(sK60,X0))
| ~ strictorderedP(sK60)
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(unflattening,[status(thm)],[c_3385]) ).
tcf(c_3388,plain,
! [X0: $i] :
( ssList(sK55(sK60,X0))
| ( app(sK60,X0) != sK61 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3386,c_254,c_3386]) ).
tcf(c_3389,plain,
! [X0: $i] :
( ssList(sK55(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(renaming,[status(thm)],[c_3388]) ).
tcf(c_3400,plain,
! [X0: $i,X1: $i] :
( ssItem(sK56(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ( X0 != sK60 )
| ( app(X0,X1) != sK61 ) ),
inference(resolution_lifted,[status(thm)],[c_250,c_385]) ).
tcf(c_3401,plain,
! [X0: $i] :
( ssItem(sK56(sK60,X0))
| ~ strictorderedP(sK60)
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(unflattening,[status(thm)],[c_3400]) ).
tcf(c_3403,plain,
! [X0: $i] :
( ssItem(sK56(sK60,X0))
| ( app(sK60,X0) != sK61 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3401,c_254,c_3401]) ).
tcf(c_3404,plain,
! [X0: $i] :
( ssItem(sK56(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(renaming,[status(thm)],[c_3403]) ).
tcf(c_3415,plain,
! [X0: $i,X1: $i] :
( ssList(sK57(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ( X0 != sK60 )
| ( app(X0,X1) != sK61 ) ),
inference(resolution_lifted,[status(thm)],[c_249,c_385]) ).
tcf(c_3416,plain,
! [X0: $i] :
( ssList(sK57(sK60,X0))
| ~ strictorderedP(sK60)
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(unflattening,[status(thm)],[c_3415]) ).
tcf(c_3418,plain,
! [X0: $i] :
( ssList(sK57(sK60,X0))
| ( app(sK60,X0) != sK61 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3416,c_254,c_3416]) ).
tcf(c_3419,plain,
! [X0: $i] :
( ssList(sK57(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(renaming,[status(thm)],[c_3418]) ).
tcf(c_3430,plain,
! [X0: $i,X1: $i] :
( lt(sK56(X0,X1),sK54(X0,X1))
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ( X0 != sK60 )
| ( app(X0,X1) != sK61 ) ),
inference(resolution_lifted,[status(thm)],[c_248,c_385]) ).
tcf(c_3431,plain,
! [X0: $i] :
( lt(sK56(sK60,X0),sK54(sK60,X0))
| ~ strictorderedP(sK60)
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(unflattening,[status(thm)],[c_3430]) ).
tcf(c_3433,plain,
! [X0: $i] :
( lt(sK56(sK60,X0),sK54(sK60,X0))
| ( app(sK60,X0) != sK61 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3431,c_254,c_3431]) ).
tcf(c_3434,plain,
! [X0: $i] :
( lt(sK56(sK60,X0),sK54(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(renaming,[status(thm)],[c_3433]) ).
tcf(c_3445,plain,
! [X0: $i,X1: $i] :
( ( app(sK57(X0,X1),cons(sK56(X0,X1),nil)) = X0 )
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ( X0 != sK60 )
| ( app(X0,X1) != sK61 ) ),
inference(resolution_lifted,[status(thm)],[c_247,c_385]) ).
tcf(c_3446,plain,
! [X0: $i] :
( ( app(sK57(sK60,X0),cons(sK56(sK60,X0),nil)) = sK60 )
| ~ strictorderedP(sK60)
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(unflattening,[status(thm)],[c_3445]) ).
tcf(c_3448,plain,
! [X0: $i] :
( ( app(sK57(sK60,X0),cons(sK56(sK60,X0),nil)) = sK60 )
| ( app(sK60,X0) != sK61 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3446,c_254,c_3446]) ).
tcf(c_3449,plain,
! [X0: $i] :
( ( app(sK57(sK60,X0),cons(sK56(sK60,X0),nil)) = sK60 )
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(renaming,[status(thm)],[c_3448]) ).
tcf(c_3460,plain,
! [X0: $i,X1: $i] :
( ( app(cons(sK54(X0,X1),nil),sK55(X0,X1)) = X1 )
| ~ strictorderedP(X0)
| ~ ssList(X1)
| ( X0 != sK60 )
| ( app(X0,X1) != sK61 ) ),
inference(resolution_lifted,[status(thm)],[c_246,c_385]) ).
tcf(c_3461,plain,
! [X0: $i] :
( ( app(cons(sK54(sK60,X0),nil),sK55(sK60,X0)) = X0 )
| ~ strictorderedP(sK60)
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(unflattening,[status(thm)],[c_3460]) ).
tcf(c_3463,plain,
! [X0: $i] :
( ( app(cons(sK54(sK60,X0),nil),sK55(sK60,X0)) = X0 )
| ( app(sK60,X0) != sK61 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3461,c_254,c_3461]) ).
tcf(c_3464,plain,
! [X0: $i] :
( ( app(cons(sK54(sK60,X0),nil),sK55(sK60,X0)) = X0 )
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(renaming,[status(thm)],[c_3463]) ).
tcf(c_9202,plain,
! [X0: $i] :
( ( app(cons(sK54(sK60,X0),nil),sK55(sK60,X0)) = X0 )
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(demodulation,[status(thm)],[c_3464]) ).
tcf(c_9203,plain,
! [X0: $i] :
( ( app(sK57(sK60,X0),cons(sK56(sK60,X0),nil)) = sK60 )
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(demodulation,[status(thm)],[c_3449]) ).
tcf(c_9204,plain,
! [X0: $i] :
( lt(sK56(sK60,X0),sK54(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(demodulation,[status(thm)],[c_3434]) ).
tcf(c_9205,plain,
! [X0: $i] :
( ssList(sK57(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(demodulation,[status(thm)],[c_3419]) ).
tcf(c_9206,plain,
! [X0: $i] :
( ssItem(sK56(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(demodulation,[status(thm)],[c_3404]) ).
tcf(c_9207,plain,
! [X0: $i] :
( ssList(sK55(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(demodulation,[status(thm)],[c_3389]) ).
tcf(c_9208,plain,
! [X0: $i] :
( ssItem(sK54(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != sK61 ) ),
inference(demodulation,[status(thm)],[c_3374]) ).
tcf(c_12189,plain,
! [X0: $i] :
( ssList(sK57(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_9205,c_9215]) ).
tcf(c_12199,plain,
! [X0: $i] :
( ssItem(sK56(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_9206,c_9215]) ).
tcf(c_12209,plain,
! [X0: $i] :
( ssList(sK55(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_9207,c_9215]) ).
tcf(c_12219,plain,
! [X0: $i] :
( ssItem(sK54(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_9208,c_9215]) ).
tcf(c_12229,plain,
! [X0: $i] :
( lt(sK56(sK60,X0),sK54(sK60,X0))
| ~ ssList(X0)
| ( app(sK60,X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_9204,c_9215]) ).
tcf(c_12239,plain,
! [X0: $i] :
( ( app(cons(sK54(sK60,X0),nil),sK55(sK60,X0)) = X0 )
| ~ ssList(X0)
| ( app(sK60,X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_9202,c_9215]) ).
tcf(c_12249,plain,
! [X0: $i] :
( ( app(sK57(sK60,X0),cons(sK56(sK60,X0),nil)) = sK60 )
| ~ ssList(X0)
| ( app(sK60,X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_9203,c_9215]) ).
tcf(c_12259,plain,
( ( app(sK57(sK60,sK62),cons(sK56(sK60,sK62),nil)) = sK60 )
| ~ ssList(sK62) ),
inference(superposition,[status(thm)],[c_9201,c_12249]) ).
tcf(c_12260,plain,
( ( app(cons(sK54(sK60,sK62),nil),sK55(sK60,sK62)) = sK62 )
| ~ ssList(sK62) ),
inference(superposition,[status(thm)],[c_9201,c_12239]) ).
tcf(c_12261,plain,
( lt(sK56(sK60,sK62),sK54(sK60,sK62))
| ~ ssList(sK62) ),
inference(superposition,[status(thm)],[c_9201,c_12229]) ).
tcf(c_12262,plain,
( ssItem(sK54(sK60,sK62))
| ~ ssList(sK62) ),
inference(superposition,[status(thm)],[c_9201,c_12219]) ).
tcf(c_12263,plain,
( ssList(sK55(sK60,sK62))
| ~ ssList(sK62) ),
inference(superposition,[status(thm)],[c_9201,c_12209]) ).
tcf(c_12264,plain,
( ssItem(sK56(sK60,sK62))
| ~ ssList(sK62) ),
inference(superposition,[status(thm)],[c_9201,c_12199]) ).
tcf(c_12265,plain,
( ssList(sK57(sK60,sK62))
| ~ ssList(sK62) ),
inference(superposition,[status(thm)],[c_9201,c_12189]) ).
tcf(c_12266,plain,
ssList(sK57(sK60,sK62)),
inference(forward_subsumption_resolution,[status(thm)],[c_12265,c_9212]) ).
tcf(c_12267,plain,
ssItem(sK56(sK60,sK62)),
inference(forward_subsumption_resolution,[status(thm)],[c_12264,c_9212]) ).
tcf(c_12268,plain,
ssList(sK55(sK60,sK62)),
inference(forward_subsumption_resolution,[status(thm)],[c_12263,c_9212]) ).
tcf(c_12269,plain,
ssItem(sK54(sK60,sK62)),
inference(forward_subsumption_resolution,[status(thm)],[c_12262,c_9212]) ).
tcf(c_12270,plain,
lt(sK56(sK60,sK62),sK54(sK60,sK62)),
inference(forward_subsumption_resolution,[status(thm)],[c_12261,c_9212]) ).
tcf(c_12271,plain,
app(cons(sK54(sK60,sK62),nil),sK55(sK60,sK62)) = sK62,
inference(forward_subsumption_resolution,[status(thm)],[c_12260,c_9212]) ).
tcf(c_12272,plain,
app(sK57(sK60,sK62),cons(sK56(sK60,sK62),nil)) = sK60,
inference(forward_subsumption_resolution,[status(thm)],[c_12259,c_9212]) ).
tcf(c_12273,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(sK55(sK60,sK62))
| ~ ssItem(sK54(sK60,sK62))
| ~ lt(X1,sK54(sK60,sK62))
| ( app(X0,cons(X1,nil)) != sK60 ) ),
inference(superposition,[status(thm)],[c_12271,c_9213]) ).
tcf(c_12274,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ~ lt(X1,sK54(sK60,sK62))
| ( app(X0,cons(X1,nil)) != sK60 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12273,c_12268,c_12269]) ).
tcf(c_12288,plain,
( ~ ssList(sK57(sK60,sK62))
| ~ ssItem(sK56(sK60,sK62))
| ~ lt(sK56(sK60,sK62),sK54(sK60,sK62)) ),
inference(superposition,[status(thm)],[c_12272,c_12274]) ).
tcf(c_12289,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12288,c_12266,c_12267,c_12270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC343+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 17:46:04 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 3.81/1.28 % SZS status Started for theBenchmark.p
% 3.81/1.28 % SZS status Theorem for theBenchmark.p
% 3.81/1.28
% 3.81/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.81/1.28
% 3.81/1.28 % ------ iProver source info
% 3.81/1.28
% 3.81/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.81/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.81/1.28 % git: non_committed_changes: false
% 3.81/1.28
% 3.81/1.28 % ------ Parsing...
% 3.81/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.81/1.28
% 3.81/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 3.81/1.28
% 3.81/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.81/1.28
% 3.81/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.81/1.28 % ------ Proving...
% 3.81/1.28 % ------ Problem Properties
% 3.81/1.28
% 3.81/1.28 %
% 3.81/1.28 % clauses 195
% 3.81/1.28 % conjectures 7
% 3.81/1.28 % EPR 55
% 3.81/1.28 % Horn 127
% 3.81/1.28 % unary 22
% 3.81/1.28 % binary 41
% 3.81/1.28 % lits 654
% 3.81/1.28 % lits eq 93
% 3.81/1.28 % fd_pure 0
% 3.81/1.28 % fd_pseudo 0
% 3.81/1.28 % fd_cond 21
% 3.81/1.28 % fd_pseudo_cond 14
% 3.81/1.28 % AC symbols 0
% 3.81/1.28
% 3.81/1.28 % ------ Schedule dynamic 5 is on
% 3.81/1.28
% 3.81/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.81/1.28
% 3.81/1.28
% 3.81/1.28 % ------
% 3.81/1.28 % Current options:
% 3.81/1.28 % ------
% 3.81/1.28
% 3.81/1.28
% 3.81/1.28 %
% 3.81/1.28
% 3.81/1.28 % ------ Proving...
% 3.81/1.28 %
% 3.81/1.28
% 3.81/1.28 % SZS status Theorem for theBenchmark.p
% 3.81/1.28
% 3.81/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.81/1.28
% 3.81/1.28
%------------------------------------------------------------------------------