%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU238+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 02:56:18 PM UTC 2026
% Result : Theorem 10.54s 2.52s
% Output : CNFRefutation 10.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 102 ( 13 unt; 0 def)
% Number of atoms : 344 ( 42 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 431 ( 189 ~; 175 |; 40 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 120 !; 7 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f11,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f20,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f38,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f41,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f44,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f46,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(f48,axiom,
! [X0] :
( ordinal(X0)
=> ( being_limit_ordinal(X0)
<=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> in(succ(X1),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(f49,conjecture,
! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( X0 = succ(X1)
& ordinal(X1) ) )
& ~ ( ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) )
& ~ being_limit_ordinal(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(f50,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( X0 = succ(X1)
& ordinal(X1) ) )
& ~ ( ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) )
& ~ being_limit_ordinal(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f59,plain,
~ ! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X2] :
( succ(X2) = X0
& ordinal(X2) ) )
& ~ ( ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) )
& ~ being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f50]) ).
fof(f60,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f70,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f82,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f83,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(flattening,[],[f82]) ).
fof(f87,plain,
! [X0] :
( ~ ordinal(X0)
| ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f89,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f90,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f89]) ).
fof(f94,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f95,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f99,plain,
! [X0] :
( ~ ordinal(X0)
| ( being_limit_ordinal(X0)
<=> ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f100,plain,
! [X0] :
( ~ ordinal(X0)
| ( being_limit_ordinal(X0)
<=> ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) ) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
? [X0] :
( ordinal(X0)
& ( ( being_limit_ordinal(X0)
& ? [X2] :
( succ(X2) = X0
& ordinal(X2) ) )
| ( ! [X1] :
( ~ ordinal(X1)
| X0 != succ(X1) )
& ~ being_limit_ordinal(X0) ) ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f122,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f123,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| ( ( ~ in(X0,X1)
| ordinal_subset(succ(X0),X1) )
& ( ~ ordinal_subset(succ(X0),X1)
| in(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f125,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) )
& ( ? [X1] :
( ordinal(X1)
& in(X1,X0)
& ~ in(succ(X1),X0) )
| being_limit_ordinal(X0) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f126,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ) )
& ( ? [X1] :
( ordinal(X1)
& in(X1,X0)
& ~ in(succ(X1),X0) )
| being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ) )
& ( ( ordinal(sK14(X0))
& in(sK14(X0),X0)
& ~ in(succ(sK14(X0)),X0) )
| being_limit_ordinal(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f126]) ).
fof(f128,plain,
( ordinal(sK15)
& ( ( being_limit_ordinal(sK15)
& sK15 = succ(sK16)
& ordinal(sK16) )
| ( ! [X1] :
( ~ ordinal(X1)
| succ(X1) != sK15 )
& ~ being_limit_ordinal(sK15) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X0,sK15),skolemize(X2,sK16)],[f101]) ).
fof(f129,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f143,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f144,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f158,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(succ(X0)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f160,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(succ(X0)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f198,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f202,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f41]) ).
fof(f205,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f207,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal_subset(succ(X0),X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f211,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f212,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK14(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f213,plain,
! [X0] :
( ~ ordinal(X0)
| in(sK14(X0),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f214,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(succ(sK14(X0)),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f215,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f128]) ).
fof(f216,plain,
! [X1] :
( being_limit_ordinal(sK15)
| ~ ordinal(X1)
| succ(X1) != sK15 ),
inference(cnf_transformation,[],[f128]) ).
fof(f220,plain,
( sK15 = succ(sK16)
| ~ being_limit_ordinal(sK15) ),
inference(cnf_transformation,[],[f128]) ).
fof(f221,plain,
( ordinal(sK16)
| ~ being_limit_ordinal(sK15) ),
inference(cnf_transformation,[],[f128]) ).
fof(f229,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(set_union2(X0,singleton(X0))) ),
inference(definition_unfolding,[],[f160,f143]) ).
fof(f231,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(set_union2(X0,singleton(X0))) ),
inference(definition_unfolding,[],[f158,f143]) ).
fof(f232,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f202,f143]) ).
fof(f234,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal_subset(set_union2(X0,singleton(X0)),X1) ),
inference(definition_unfolding,[],[f207,f143]) ).
fof(f235,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(set_union2(sK14(X0),singleton(sK14(X0))),X0)
| being_limit_ordinal(X0) ),
inference(definition_unfolding,[],[f214,f143]) ).
fof(f236,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X2)
| ~ in(X2,X0)
| in(set_union2(X2,singleton(X2)),X0) ),
inference(definition_unfolding,[],[f211,f143]) ).
fof(f237,plain,
( sK15 = set_union2(sK16,singleton(sK16))
| ~ being_limit_ordinal(sK15) ),
inference(definition_unfolding,[],[f220,f143]) ).
fof(f240,plain,
! [X1] :
( being_limit_ordinal(sK15)
| ~ ordinal(X1)
| sK15 != set_union2(X1,singleton(X1)) ),
inference(definition_unfolding,[],[f216,f143]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_76,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_78,plain,
! [X0: $i] :
( ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_119,plain,
! [X0: $i] : in(X0,set_union2(X0,singleton(X0))),
inference(cnf_transformation,[],[f232]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(set_union2(X0,singleton(X0)),X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_128,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(set_union2(sK14(X0),singleton(sK14(X0))),X0) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_129,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| in(sK14(X0),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_130,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ordinal(sK14(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( in(set_union2(X0,singleton(X0)),X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_132,negated_conjecture,
( ordinal(sK16)
| ~ being_limit_ordinal(sK15) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_133,negated_conjecture,
( ( set_union2(sK16,singleton(sK16)) = sK15 )
| ~ being_limit_ordinal(sK15) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_136,negated_conjecture,
! [X0: $i] :
( being_limit_ordinal(sK15)
| ~ ordinal(X0)
| ( set_union2(X0,singleton(X0)) != sK15 ) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_137,negated_conjecture,
ordinal(sK15),
inference(cnf_transformation,[],[f215]) ).
tcf(c_2158,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3095,plain,
! [X0: $i] :
( proper_subset(set_union2(X0,singleton(X0)),sK15)
| ( set_union2(X0,singleton(X0)) = sK15 )
| ~ subset(set_union2(X0,singleton(X0)),sK15) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_3100,plain,
( being_limit_ordinal(sK15)
| ~ ordinal(sK15)
| ~ in(set_union2(sK14(sK15),singleton(sK14(sK15))),sK15) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_3102,plain,
( being_limit_ordinal(sK15)
| in(sK14(sK15),sK15)
| ~ ordinal(sK15) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_3103,plain,
( being_limit_ordinal(sK15)
| ordinal(sK14(sK15))
| ~ ordinal(sK15) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_3109,plain,
( in(set_union2(sK14(sK15),singleton(sK14(sK15))),sK15)
| ~ ordinal(sK15)
| ~ epsilon_transitive(set_union2(sK14(sK15),singleton(sK14(sK15))))
| ~ proper_subset(set_union2(sK14(sK15),singleton(sK14(sK15))),sK15) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_3140,plain,
! [X0: $i] :
( subset(set_union2(X0,singleton(X0)),sK15)
| ~ ordinal(sK15)
| ~ ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal_subset(set_union2(X0,singleton(X0)),sK15) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_3152,plain,
( ordinal(set_union2(sK14(sK15),singleton(sK14(sK15))))
| ~ ordinal(sK14(sK15)) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_3157,plain,
( epsilon_transitive(set_union2(sK14(sK15),singleton(sK14(sK15))))
| ~ ordinal(sK14(sK15)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_3225,plain,
! [X0: $i] :
( ordinal_subset(set_union2(X0,singleton(X0)),sK15)
| ~ ordinal(sK15)
| ~ ordinal(X0)
| ~ in(X0,sK15) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_3441,plain,
( ordinal_subset(set_union2(sK14(sK15),singleton(sK14(sK15))),sK15)
| ~ ordinal(sK15)
| ~ ordinal(sK14(sK15))
| ~ in(sK14(sK15),sK15) ),
inference(instantiation,[status(thm)],[c_3225]) ).
tcf(c_3481,plain,
( proper_subset(set_union2(sK14(sK15),singleton(sK14(sK15))),sK15)
| ( set_union2(sK14(sK15),singleton(sK14(sK15))) = sK15 )
| ~ subset(set_union2(sK14(sK15),singleton(sK14(sK15))),sK15) ),
inference(instantiation,[status(thm)],[c_3095]) ).
tcf(c_3517,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,singleton(X0)) = X2 )
| ( X2 != X1 )
| ( set_union2(X0,singleton(X0)) != X1 ) ),
inference(instantiation,[status(thm)],[c_2158]) ).
tcf(c_3736,plain,
! [X0: $i] :
( ( set_union2(sK16,singleton(sK16)) = X0 )
| ( X0 != sK15 )
| ( set_union2(sK16,singleton(sK16)) != sK15 ) ),
inference(instantiation,[status(thm)],[c_3517]) ).
tcf(c_4834,plain,
! [X0: $i] :
( ~ in(sK15,X0)
| ~ in(X0,sK15) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_5035,plain,
( subset(set_union2(sK14(sK15),singleton(sK14(sK15))),sK15)
| ~ ordinal(sK15)
| ~ ordinal(set_union2(sK14(sK15),singleton(sK14(sK15))))
| ~ ordinal_subset(set_union2(sK14(sK15),singleton(sK14(sK15))),sK15) ),
inference(instantiation,[status(thm)],[c_3140]) ).
tcf(c_6759,plain,
~ in(sK15,sK15),
inference(instantiation,[status(thm)],[c_4834]) ).
tcf(c_8659,plain,
! [X0: $i] :
( ( set_union2(sK16,singleton(sK16)) = X0 )
| ~ being_limit_ordinal(sK15)
| ( X0 != sK15 ) ),
inference(resolution,[status(thm)],[c_2158,c_133]) ).
tcf(c_9189,plain,
( being_limit_ordinal(sK15)
| ~ ordinal(sK14(sK15))
| ( set_union2(sK14(sK15),singleton(sK14(sK15))) != sK15 ) ),
inference(instantiation,[status(thm)],[c_136]) ).
tcf(c_9342,plain,
! [X0: $i] :
( ( set_union2(sK16,singleton(sK16)) = X0 )
| ( X0 != sK15 ) ),
inference(global_subsumption_just,[status(thm)],[c_8659,c_137,c_133,c_3103,c_3102,c_3100,c_3109,c_3152,c_3157,c_3441,c_3481,c_3736,c_5035,c_9189]) ).
tcf(c_9357,plain,
( being_limit_ordinal(sK15)
| ~ ordinal(sK16)
| ( sK15 != sK15 ) ),
inference(resolution,[status(thm)],[c_9342,c_136]) ).
tcf(c_9360,plain,
( being_limit_ordinal(sK15)
| ~ ordinal(sK16) ),
inference(equality_resolution_simp,[status(thm)],[c_9357]) ).
tcf(c_10109,plain,
being_limit_ordinal(sK15),
inference(global_subsumption_just,[status(thm)],[c_9360,c_137,c_3103,c_3102,c_3100,c_3109,c_3152,c_3157,c_3441,c_3481,c_5035,c_9189]) ).
tcf(c_12431,negated_conjecture,
set_union2(sK16,singleton(sK16)) = sK15,
inference(global_subsumption_just,[status(thm)],[c_133,c_133,c_10109]) ).
tcf(c_12468,plain,
in(sK16,sK15),
inference(superposition,[status(thm)],[c_12431,c_119]) ).
tcf(c_12696,plain,
! [X0: $i] :
( in(sK15,X0)
| ~ ordinal(sK16)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK16,X0) ),
inference(superposition,[status(thm)],[c_12431,c_131]) ).
tcf(c_12747,plain,
! [X0: $i] :
( in(sK15,X0)
| ~ in(sK16,X0)
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0) ),
inference(global_subsumption_just,[status(thm)],[c_12696,c_137,c_132,c_3103,c_3102,c_3100,c_3109,c_3152,c_3157,c_3441,c_3481,c_5035,c_9189,c_12696]) ).
tcf(c_12748,plain,
! [X0: $i] :
( in(sK15,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK16,X0) ),
inference(renaming,[status(thm)],[c_12747]) ).
tcf(c_12751,plain,
( in(sK15,sK15)
| ~ being_limit_ordinal(sK15)
| ~ ordinal(sK15) ),
inference(superposition,[status(thm)],[c_12468,c_12748]) ).
tcf(c_12755,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12751,c_10109,c_6759,c_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU238+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.58 % Computer : n006.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Thu Sep 24 13:21:43 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.63 Running first-order theorem proving
% 0.11/0.63 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.64
% 0.16/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.64
% 0.16/0.64 % Detected problem language: tptp
% 0.16/0.65 % Proving...
% 10.54/2.52 % SZS status Started for theBenchmark.p
% 10.54/2.52 % SZS status Theorem for theBenchmark.p
% 10.54/2.52
% 10.54/2.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.54/2.52
% 10.54/2.52 % ------ iProver source info
% 10.54/2.52
% 10.54/2.52 % git: date: 2026-07-19 20:42:38 +0200
% 10.54/2.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.54/2.52 % git: non_committed_changes: false
% 10.54/2.52
% 10.54/2.52 % ------ Parsing...
% 10.54/2.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.54/2.52
% 10.54/2.52 % ------ Preprocessing... sup_sim: 0 sf_s rm: 23 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 10.54/2.52
% 10.54/2.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.54/2.52
% 10.54/2.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.54/2.52 % ------ Proving...
% 10.54/2.52 % ------ Problem Properties
% 10.54/2.52
% 10.54/2.52 %
% 10.54/2.52 % clauses 60
% 10.54/2.52 % conjectures 6
% 10.54/2.52 % EPR 38
% 10.54/2.52 % Horn 55
% 10.54/2.52 % unary 25
% 10.54/2.52 % binary 17
% 10.54/2.52 % lits 121
% 10.54/2.52 % lits eq 11
% 10.54/2.52 % fd_pure 0
% 10.54/2.52 % fd_pseudo 0
% 10.54/2.52 % fd_cond 1
% 10.54/2.52 % fd_pseudo_cond 2
% 10.54/2.52 % AC symbols 0
% 10.54/2.52
% 10.54/2.52 % ------ Input Options Time Limit: Unbounded
% 10.54/2.52
% 10.54/2.52
% 10.54/2.52 % ------
% 10.54/2.52 % Current options:
% 10.54/2.52 % ------
% 10.54/2.52
% 10.54/2.52
% 10.54/2.52 %
% 10.54/2.52
% 10.54/2.52 % ------ Proving...
% 10.54/2.52 %
% 10.54/2.52
% 10.54/2.52 % SZS status Theorem for theBenchmark.p
% 10.54/2.52
% 10.54/2.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.54/2.52
% 10.54/2.52
%------------------------------------------------------------------------------