%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC327+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 : n008.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 03:09:19 PM UTC 2026
% Result : Theorem 0.59s 1.29s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of formulae : 79 ( 17 unt; 1 def)
% Number of atoms : 377 ( 146 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 497 ( 199 ~; 192 |; 90 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 110 !; 38 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ? [X8] :
( equalelemsP(X0)
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ( ! [X11] :
( ssList(X11)
=> app(X11,cons(X9,nil)) != X0 )
| app(cons(X9,nil),X10) != X8 ) ) )
& app(X0,X8) = X1
& ssList(X8) ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| 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 = X1
| nil != X0 )
& ? [X8] :
( equalelemsP(X0)
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ( ! [X11] :
( ssList(X11)
=> app(X11,cons(X9,nil)) != X0 )
| app(cons(X9,nil),X10) != X8 ) ) )
& app(X0,X8) = X1
& ssList(X8) ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ! [X8] :
( ~ equalelemsP(X0)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X0 )
& app(cons(X9,nil),X10) = X8 ) )
| app(X0,X8) != X1
| ~ ssList(X8) ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ! [X8] :
( ~ equalelemsP(X0)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X0 )
& app(cons(X9,nil),X10) = X8 ) )
| app(X0,X8) != X1
| ~ ssList(X8) ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f126,plain,
( ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ssList(sK7)
& ( ( nil != sK5
& nil = sK4 )
| sP0(sK5,sK4) )
& ( nil != sK6
| nil = sK7 )
& ssList(sK8)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK6
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK8
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK6)
& sK7 = app(sK6,sK8)
& sK4 = sK6
& sK5 = sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7),skolemize(X4,sK8)],[f122]) ).
fof(f143,plain,
( nil != sK5
| sP0(sK5,sK4) ),
inference(cnf_transformation,[],[f126]) ).
fof(f144,plain,
( nil = sK4
| sP0(sK5,sK4) ),
inference(cnf_transformation,[],[f126]) ).
fof(f145,plain,
( nil != sK6
| nil = sK7 ),
inference(cnf_transformation,[],[f126]) ).
fof(f146,plain,
ssList(sK8),
inference(cnf_transformation,[],[f126]) ).
fof(f147,plain,
! [X6,X7,X5] :
( app(X7,cons(X5,nil)) != sK6
| ~ ssList(X7)
| app(cons(X5,nil),X6) != sK8
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f126]) ).
fof(f148,plain,
equalelemsP(sK6),
inference(cnf_transformation,[],[f126]) ).
fof(f149,plain,
sK7 = app(sK6,sK8),
inference(cnf_transformation,[],[f126]) ).
fof(f150,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f126]) ).
fof(f151,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f126]) ).
fof(f184,plain,
( nil = sK6
| sP0(sK7,sK6) ),
inference(definition_unfolding,[],[f144,f151,f150,f150]) ).
fof(f185,plain,
( nil != sK7
| sP0(sK7,sK6) ),
inference(definition_unfolding,[],[f143,f151,f150,f151]) ).
tcf(c_54,negated_conjecture,
app(sK6,sK8) = sK7,
inference(cnf_transformation,[],[f149]) ).
tcf(c_55,negated_conjecture,
equalelemsP(sK6),
inference(cnf_transformation,[],[f148]) ).
tcf(c_56,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ( app(X2,cons(X0,nil)) != sK6 )
| ( app(cons(X0,nil),X1) != sK8 ) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_57,negated_conjecture,
ssList(sK8),
inference(cnf_transformation,[],[f146]) ).
tcf(c_58,negated_conjecture,
( ( nil = sK7 )
| ( nil != sK6 ) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_59,negated_conjecture,
( sP0(sK7,sK6)
| ( nil = sK6 ) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_60,negated_conjecture,
( sP0(sK7,sK6)
| ( nil != sK7 ) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_118,negated_conjecture,
sP0(sK7,sK6),
inference(global_subsumption_just,[status(thm)],[c_59,c_59,c_60,c_58]) ).
tcf(c_120,negated_conjecture,
sP0(sK7,sK6),
inference(global_subsumption_just,[status(thm)],[c_60,c_118]) ).
fof(f121,definition,
! [X1,X0] :
( ~ sP0(X1,X0)
| ! [X8] :
( ~ equalelemsP(X0)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X0 )
& app(cons(X9,nil),X10) = X8 ) )
| app(X0,X8) != X1
| ~ ssList(X8) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f122,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| sP0(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f99,f121]) ).
fof(f123,plain,
! [X1,X0] :
( ~ sP0(X1,X0)
| ! [X8] :
( ~ equalelemsP(X0)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X0 )
& app(cons(X9,nil),X10) = X8 ) )
| app(X0,X8) != X1
| ~ ssList(X8) ) ),
inference(nnf_transformation,[],[f121]) ).
fof(f124,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ! [X2] :
( ~ equalelemsP(X1)
| ? [X3] :
( ssItem(X3)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X3,nil)) = X1 )
& app(cons(X3,nil),X4) = X2 ) )
| app(X1,X2) != X0
| ~ ssList(X2) ) ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ! [X2] :
( ~ equalelemsP(X1)
| ( ssItem(sK1(X1,X2))
& ssList(sK2(X1,X2))
& ssList(sK3(X1,X2))
& app(sK3(X1,X2),cons(sK1(X1,X2),nil)) = X1
& app(cons(sK1(X1,X2),nil),sK2(X1,X2)) = X2 )
| app(X1,X2) != X0
| ~ ssList(X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X3,sK1(X1,X2)),skolemize(X4,sK2(X1,X2)),skolemize(X5,sK3(X1,X2))],[f124]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ equalelemsP(X1)
| ssItem(sK1(X1,X2))
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ equalelemsP(X1)
| ssList(sK2(X1,X2))
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ equalelemsP(X1)
| ssList(sK3(X1,X2))
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ equalelemsP(X1)
| app(sK3(X1,X2),cons(sK1(X1,X2),nil)) = X1
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ equalelemsP(X1)
| app(cons(sK1(X1,X2),nil),sK2(X1,X2)) = X2
| app(X1,X2) != X0
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f188,plain,
! [X2,X1] :
( ~ sP0(app(X1,X2),X1)
| ~ equalelemsP(X1)
| app(cons(sK1(X1,X2),nil),sK2(X1,X2)) = X2
| ~ ssList(X2) ),
inference(equality_resolution,[],[f138]) ).
fof(f189,plain,
! [X2,X1] :
( ~ sP0(app(X1,X2),X1)
| ~ equalelemsP(X1)
| app(sK3(X1,X2),cons(sK1(X1,X2),nil)) = X1
| ~ ssList(X2) ),
inference(equality_resolution,[],[f137]) ).
fof(f190,plain,
! [X2,X1] :
( ~ sP0(app(X1,X2),X1)
| ~ equalelemsP(X1)
| ssList(sK3(X1,X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f136]) ).
fof(f191,plain,
! [X2,X1] :
( ~ sP0(app(X1,X2),X1)
| ~ equalelemsP(X1)
| ssList(sK2(X1,X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f135]) ).
fof(f192,plain,
! [X2,X1] :
( ~ sP0(app(X1,X2),X1)
| ~ equalelemsP(X1)
| ssItem(sK1(X1,X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f134]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( app(cons(sK1(X0,X1),nil),sK2(X0,X1)) = X1 )
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ~ sP0(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( app(sK3(X0,X1),cons(sK1(X0,X1),nil)) = X0 )
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ~ sP0(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ssList(sK3(X0,X1))
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ~ sP0(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ssList(sK2(X0,X1))
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ~ sP0(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ~ sP0(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_635,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ( X0 != sK6 )
| ( app(X0,X1) != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_120]) ).
tcf(c_636,plain,
! [X0: $i] :
( ssItem(sK1(sK6,X0))
| ~ equalelemsP(sK6)
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(unflattening,[status(thm)],[c_635]) ).
tcf(c_638,plain,
! [X0: $i] :
( ssItem(sK1(sK6,X0))
| ( app(sK6,X0) != sK7 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_636,c_55,c_636]) ).
tcf(c_639,plain,
! [X0: $i] :
( ssItem(sK1(sK6,X0))
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(renaming,[status(thm)],[c_638]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i] :
( ssList(sK2(X0,X1))
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ( X0 != sK6 )
| ( app(X0,X1) != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_120]) ).
tcf(c_651,plain,
! [X0: $i] :
( ssList(sK2(sK6,X0))
| ~ equalelemsP(sK6)
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(unflattening,[status(thm)],[c_650]) ).
tcf(c_653,plain,
! [X0: $i] :
( ssList(sK2(sK6,X0))
| ( app(sK6,X0) != sK7 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_651,c_55,c_651]) ).
tcf(c_654,plain,
! [X0: $i] :
( ssList(sK2(sK6,X0))
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(renaming,[status(thm)],[c_653]) ).
tcf(c_665,plain,
! [X0: $i,X1: $i] :
( ssList(sK3(X0,X1))
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ( X0 != sK6 )
| ( app(X0,X1) != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_120]) ).
tcf(c_666,plain,
! [X0: $i] :
( ssList(sK3(sK6,X0))
| ~ equalelemsP(sK6)
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(unflattening,[status(thm)],[c_665]) ).
tcf(c_668,plain,
! [X0: $i] :
( ssList(sK3(sK6,X0))
| ( app(sK6,X0) != sK7 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_666,c_55,c_666]) ).
tcf(c_669,plain,
! [X0: $i] :
( ssList(sK3(sK6,X0))
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(renaming,[status(thm)],[c_668]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i] :
( ( app(sK3(X0,X1),cons(sK1(X0,X1),nil)) = X0 )
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ( X0 != sK6 )
| ( app(X0,X1) != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_120]) ).
tcf(c_681,plain,
! [X0: $i] :
( ( app(sK3(sK6,X0),cons(sK1(sK6,X0),nil)) = sK6 )
| ~ equalelemsP(sK6)
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(unflattening,[status(thm)],[c_680]) ).
tcf(c_683,plain,
! [X0: $i] :
( ( app(sK3(sK6,X0),cons(sK1(sK6,X0),nil)) = sK6 )
| ( app(sK6,X0) != sK7 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_681,c_55,c_681]) ).
tcf(c_684,plain,
! [X0: $i] :
( ( app(sK3(sK6,X0),cons(sK1(sK6,X0),nil)) = sK6 )
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(renaming,[status(thm)],[c_683]) ).
tcf(c_695,plain,
! [X0: $i,X1: $i] :
( ( app(cons(sK1(X0,X1),nil),sK2(X0,X1)) = X1 )
| ~ equalelemsP(X0)
| ~ ssList(X1)
| ( X0 != sK6 )
| ( app(X0,X1) != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_120]) ).
tcf(c_696,plain,
! [X0: $i] :
( ( app(cons(sK1(sK6,X0),nil),sK2(sK6,X0)) = X0 )
| ~ equalelemsP(sK6)
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(unflattening,[status(thm)],[c_695]) ).
tcf(c_698,plain,
! [X0: $i] :
( ( app(cons(sK1(sK6,X0),nil),sK2(sK6,X0)) = X0 )
| ( app(sK6,X0) != sK7 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_696,c_55,c_696]) ).
tcf(c_699,plain,
! [X0: $i] :
( ( app(cons(sK1(sK6,X0),nil),sK2(sK6,X0)) = X0 )
| ~ ssList(X0)
| ( app(sK6,X0) != sK7 ) ),
inference(renaming,[status(thm)],[c_698]) ).
tcf(c_2409,plain,
( ssItem(sK1(sK6,sK8))
| ~ ssList(sK8) ),
inference(superposition,[status(thm)],[c_54,c_639]) ).
tcf(c_2410,plain,
ssItem(sK1(sK6,sK8)),
inference(forward_subsumption_resolution,[status(thm)],[c_2409,c_57]) ).
tcf(c_2427,plain,
( ssList(sK2(sK6,sK8))
| ~ ssList(sK8) ),
inference(superposition,[status(thm)],[c_54,c_654]) ).
tcf(c_2428,plain,
ssList(sK2(sK6,sK8)),
inference(forward_subsumption_resolution,[status(thm)],[c_2427,c_57]) ).
tcf(c_2435,plain,
( ssList(sK3(sK6,sK8))
| ~ ssList(sK8) ),
inference(superposition,[status(thm)],[c_54,c_669]) ).
tcf(c_2436,plain,
ssList(sK3(sK6,sK8)),
inference(forward_subsumption_resolution,[status(thm)],[c_2435,c_57]) ).
tcf(c_2443,plain,
( ( app(sK3(sK6,sK8),cons(sK1(sK6,sK8),nil)) = sK6 )
| ~ ssList(sK8) ),
inference(superposition,[status(thm)],[c_54,c_684]) ).
tcf(c_2444,plain,
app(sK3(sK6,sK8),cons(sK1(sK6,sK8),nil)) = sK6,
inference(forward_subsumption_resolution,[status(thm)],[c_2443,c_57]) ).
tcf(c_2451,plain,
( ( app(cons(sK1(sK6,sK8),nil),sK2(sK6,sK8)) = sK8 )
| ~ ssList(sK8) ),
inference(superposition,[status(thm)],[c_54,c_699]) ).
tcf(c_2452,plain,
app(cons(sK1(sK6,sK8),nil),sK2(sK6,sK8)) = sK8,
inference(forward_subsumption_resolution,[status(thm)],[c_2451,c_57]) ).
tcf(c_2453,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(sK1(sK6,sK8))
| ~ ssList(sK2(sK6,sK8))
| ( app(X0,cons(sK1(sK6,sK8),nil)) != sK6 ) ),
inference(superposition,[status(thm)],[c_2452,c_56]) ).
tcf(c_2454,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(X0,cons(sK1(sK6,sK8),nil)) != sK6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2453,c_2410,c_2428]) ).
tcf(c_2462,plain,
~ ssList(sK3(sK6,sK8)),
inference(superposition,[status(thm)],[c_2444,c_2454]) ).
tcf(c_2463,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2462,c_2436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC327+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 17:39:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.59/1.29 % SZS status Started for theBenchmark.p
% 0.59/1.29 % SZS status Theorem for theBenchmark.p
% 0.59/1.29
% 0.59/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.59/1.29
% 0.59/1.29 % ------ iProver source info
% 0.59/1.29
% 0.59/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.59/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.59/1.29 % git: non_committed_changes: false
% 0.59/1.29
% 0.59/1.29 % ------ Parsing...
% 0.59/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.59/1.29
% 0.59/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 0.59/1.29
% 0.59/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.59/1.29
% 0.59/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.59/1.29 % ------ Proving...
% 0.59/1.29 % ------ Problem Properties
% 0.59/1.29
% 0.59/1.29 %
% 0.59/1.29 % clauses 44
% 0.59/1.29 % conjectures 7
% 0.59/1.29 % EPR 10
% 0.59/1.29 % Horn 36
% 0.59/1.29 % unary 11
% 0.59/1.29 % binary 4
% 0.59/1.29 % lits 126
% 0.59/1.29 % lits eq 40
% 0.59/1.29 % fd_pure 0
% 0.59/1.29 % fd_pseudo 0
% 0.59/1.29 % fd_cond 4
% 0.59/1.29 % fd_pseudo_cond 5
% 0.59/1.29 % AC symbols 0
% 0.59/1.29
% 0.59/1.29 % ------ Schedule dynamic 5 is on
% 0.59/1.29
% 0.59/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.59/1.29
% 0.59/1.29
% 0.59/1.29 % ------
% 0.59/1.29 % Current options:
% 0.59/1.29 % ------
% 0.59/1.29
% 0.59/1.29
% 0.59/1.29 %
% 0.59/1.29
% 0.59/1.29 % ------ Proving...
% 0.59/1.29 %
% 0.59/1.29
% 0.59/1.29 % SZS status Theorem for theBenchmark.p
% 0.59/1.29
% 0.59/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.59/1.29
% 0.59/1.29
%------------------------------------------------------------------------------