%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU238+1 : TPTP v9.3.1. Released v3.3.0.
% 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 8.43s 1.80s
% Output : CNFRefutation 8.43s
% 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(f26,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(f43,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(f46,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f49,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(f51,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(f53,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(f54,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(f55,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)],[f54]) ).
fof(f64,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,[],[f55]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f74,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f86,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f87,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(flattening,[],[f86]) ).
fof(f91,plain,
! [X0] :
( ~ ordinal(X0)
| ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f93,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f94,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f93]) ).
fof(f98,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f99,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f103,plain,
! [X0] :
( ~ ordinal(X0)
| ( being_limit_ordinal(X0)
<=> ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f104,plain,
! [X0] :
( ~ ordinal(X0)
| ( being_limit_ordinal(X0)
<=> ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) ) ),
inference(flattening,[],[f103]) ).
fof(f105,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,[],[f64]) ).
fof(f125,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f126,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,[],[f102]) ).
fof(f128,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,[],[f104]) ).
fof(f129,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,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ) )
& ( ( ordinal(sK13(X0))
& in(sK13(X0),X0)
& ~ in(succ(sK13(X0)),X0) )
| being_limit_ordinal(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X1,sK13(X0))],[f129]) ).
fof(f131,plain,
( ordinal(sK14)
& ( ( being_limit_ordinal(sK14)
& sK14 = succ(sK15)
& ordinal(sK15) )
| ( ! [X1] :
( ~ ordinal(X1)
| succ(X1) != sK14 )
& ~ being_limit_ordinal(sK14) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X2,sK15)],[f105]) ).
fof(f132,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f146,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f147,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f161,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(succ(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f163,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(succ(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f199,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f203,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f46]) ).
fof(f206,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f208,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal_subset(succ(X0),X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f212,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f213,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK13(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f214,plain,
! [X0] :
( ~ ordinal(X0)
| in(sK13(X0),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f215,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(succ(sK13(X0)),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f216,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f217,plain,
! [X1] :
( being_limit_ordinal(sK14)
| ~ ordinal(X1)
| succ(X1) != sK14 ),
inference(cnf_transformation,[],[f131]) ).
fof(f221,plain,
( sK14 = succ(sK15)
| ~ being_limit_ordinal(sK14) ),
inference(cnf_transformation,[],[f131]) ).
fof(f222,plain,
( ordinal(sK15)
| ~ being_limit_ordinal(sK14) ),
inference(cnf_transformation,[],[f131]) ).
fof(f230,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(set_union2(X0,singleton(X0))) ),
inference(definition_unfolding,[],[f163,f146]) ).
fof(f232,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(set_union2(X0,singleton(X0))) ),
inference(definition_unfolding,[],[f161,f146]) ).
fof(f233,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f203,f146]) ).
fof(f235,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal_subset(set_union2(X0,singleton(X0)),X1) ),
inference(definition_unfolding,[],[f208,f146]) ).
fof(f236,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(set_union2(sK13(X0),singleton(sK13(X0))),X0)
| being_limit_ordinal(X0) ),
inference(definition_unfolding,[],[f215,f146]) ).
fof(f237,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X2)
| ~ in(X2,X0)
| in(set_union2(X2,singleton(X2)),X0) ),
inference(definition_unfolding,[],[f212,f146]) ).
fof(f238,plain,
( sK14 = set_union2(sK15,singleton(sK15))
| ~ being_limit_ordinal(sK14) ),
inference(definition_unfolding,[],[f221,f146]) ).
fof(f241,plain,
! [X1] :
( being_limit_ordinal(sK14)
| ~ ordinal(X1)
| sK14 != set_union2(X1,singleton(X1)) ),
inference(definition_unfolding,[],[f217,f146]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_76,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_78,plain,
! [X0: $i] :
( ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_117,plain,
! [X0: $i] : in(X0,set_union2(X0,singleton(X0))),
inference(cnf_transformation,[],[f233]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(set_union2(X0,singleton(X0)),X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_126,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(set_union2(sK13(X0),singleton(sK13(X0))),X0) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_127,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| in(sK13(X0),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_128,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ordinal(sK13(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_129,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,[],[f237]) ).
tcf(c_130,negated_conjecture,
( ordinal(sK15)
| ~ being_limit_ordinal(sK14) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_131,negated_conjecture,
( ( set_union2(sK15,singleton(sK15)) = sK14 )
| ~ being_limit_ordinal(sK14) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_134,negated_conjecture,
! [X0: $i] :
( being_limit_ordinal(sK14)
| ~ ordinal(X0)
| ( set_union2(X0,singleton(X0)) != sK14 ) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_135,negated_conjecture,
ordinal(sK14),
inference(cnf_transformation,[],[f216]) ).
tcf(c_2150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3087,plain,
! [X0: $i] :
( proper_subset(set_union2(X0,singleton(X0)),sK14)
| ( set_union2(X0,singleton(X0)) = sK14 )
| ~ subset(set_union2(X0,singleton(X0)),sK14) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_3092,plain,
( being_limit_ordinal(sK14)
| ~ ordinal(sK14)
| ~ in(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_3094,plain,
( being_limit_ordinal(sK14)
| in(sK13(sK14),sK14)
| ~ ordinal(sK14) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_3095,plain,
( being_limit_ordinal(sK14)
| ordinal(sK13(sK14))
| ~ ordinal(sK14) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_3101,plain,
( in(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| ~ ordinal(sK14)
| ~ epsilon_transitive(set_union2(sK13(sK14),singleton(sK13(sK14))))
| ~ proper_subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14) ),
inference(instantiation,[status(thm)],[c_120]) ).
tcf(c_3132,plain,
! [X0: $i] :
( subset(set_union2(X0,singleton(X0)),sK14)
| ~ ordinal(sK14)
| ~ ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal_subset(set_union2(X0,singleton(X0)),sK14) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_3144,plain,
( ordinal(set_union2(sK13(sK14),singleton(sK13(sK14))))
| ~ ordinal(sK13(sK14)) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_3149,plain,
( epsilon_transitive(set_union2(sK13(sK14),singleton(sK13(sK14))))
| ~ ordinal(sK13(sK14)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_3217,plain,
! [X0: $i] :
( ordinal_subset(set_union2(X0,singleton(X0)),sK14)
| ~ ordinal(sK14)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_3433,plain,
( ordinal_subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| ~ ordinal(sK14)
| ~ ordinal(sK13(sK14))
| ~ in(sK13(sK14),sK14) ),
inference(instantiation,[status(thm)],[c_3217]) ).
tcf(c_3473,plain,
( proper_subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| ( set_union2(sK13(sK14),singleton(sK13(sK14))) = sK14 )
| ~ subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14) ),
inference(instantiation,[status(thm)],[c_3087]) ).
tcf(c_3509,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_2150]) ).
tcf(c_3728,plain,
! [X0: $i] :
( ( set_union2(sK15,singleton(sK15)) = X0 )
| ( X0 != sK14 )
| ( set_union2(sK15,singleton(sK15)) != sK14 ) ),
inference(instantiation,[status(thm)],[c_3509]) ).
tcf(c_4826,plain,
! [X0: $i] :
( ~ in(sK14,X0)
| ~ in(X0,sK14) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_5027,plain,
( subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14)
| ~ ordinal(sK14)
| ~ ordinal(set_union2(sK13(sK14),singleton(sK13(sK14))))
| ~ ordinal_subset(set_union2(sK13(sK14),singleton(sK13(sK14))),sK14) ),
inference(instantiation,[status(thm)],[c_3132]) ).
tcf(c_6751,plain,
~ in(sK14,sK14),
inference(instantiation,[status(thm)],[c_4826]) ).
tcf(c_8651,plain,
! [X0: $i] :
( ( set_union2(sK15,singleton(sK15)) = X0 )
| ~ being_limit_ordinal(sK14)
| ( X0 != sK14 ) ),
inference(resolution,[status(thm)],[c_2150,c_131]) ).
tcf(c_9181,plain,
( being_limit_ordinal(sK14)
| ~ ordinal(sK13(sK14))
| ( set_union2(sK13(sK14),singleton(sK13(sK14))) != sK14 ) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_9334,plain,
! [X0: $i] :
( ( set_union2(sK15,singleton(sK15)) = X0 )
| ( X0 != sK14 ) ),
inference(global_subsumption_just,[status(thm)],[c_8651,c_135,c_131,c_3095,c_3094,c_3092,c_3101,c_3144,c_3149,c_3433,c_3473,c_3728,c_5027,c_9181]) ).
tcf(c_9349,plain,
( being_limit_ordinal(sK14)
| ~ ordinal(sK15)
| ( sK14 != sK14 ) ),
inference(resolution,[status(thm)],[c_9334,c_134]) ).
tcf(c_9352,plain,
( being_limit_ordinal(sK14)
| ~ ordinal(sK15) ),
inference(equality_resolution_simp,[status(thm)],[c_9349]) ).
tcf(c_10101,plain,
being_limit_ordinal(sK14),
inference(global_subsumption_just,[status(thm)],[c_9352,c_135,c_3095,c_3094,c_3092,c_3101,c_3144,c_3149,c_3433,c_3473,c_5027,c_9181]) ).
tcf(c_12423,negated_conjecture,
set_union2(sK15,singleton(sK15)) = sK14,
inference(global_subsumption_just,[status(thm)],[c_131,c_131,c_10101]) ).
tcf(c_12460,plain,
in(sK15,sK14),
inference(superposition,[status(thm)],[c_12423,c_117]) ).
tcf(c_12688,plain,
! [X0: $i] :
( in(sK14,X0)
| ~ ordinal(sK15)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK15,X0) ),
inference(superposition,[status(thm)],[c_12423,c_129]) ).
tcf(c_12739,plain,
! [X0: $i] :
( in(sK14,X0)
| ~ in(sK15,X0)
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0) ),
inference(global_subsumption_just,[status(thm)],[c_12688,c_135,c_130,c_3095,c_3094,c_3092,c_3101,c_3144,c_3149,c_3433,c_3473,c_5027,c_9181,c_12688]) ).
tcf(c_12740,plain,
! [X0: $i] :
( in(sK14,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK15,X0) ),
inference(renaming,[status(thm)],[c_12739]) ).
tcf(c_12743,plain,
( in(sK14,sK14)
| ~ being_limit_ordinal(sK14)
| ~ ordinal(sK14) ),
inference(superposition,[status(thm)],[c_12460,c_12740]) ).
tcf(c_12747,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12743,c_10101,c_6751,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU238+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 13:21:29 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 8.43/1.80 % SZS status Started for theBenchmark.p
% 8.43/1.80 % SZS status Theorem for theBenchmark.p
% 8.43/1.80
% 8.43/1.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.43/1.80
% 8.43/1.80 % ------ iProver source info
% 8.43/1.80
% 8.43/1.80 % git: date: 2026-07-19 20:42:38 +0200
% 8.43/1.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.43/1.80 % git: non_committed_changes: false
% 8.43/1.80
% 8.43/1.80 % ------ Parsing...
% 8.43/1.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.43/1.80
% 8.43/1.80 % ------ Preprocessing... sup_sim: 0 sf_s rm: 21 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 8.43/1.80
% 8.43/1.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.43/1.80
% 8.43/1.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.43/1.80 % ------ Proving...
% 8.43/1.80 % ------ Problem Properties
% 8.43/1.80
% 8.43/1.80 %
% 8.43/1.80 % clauses 60
% 8.43/1.80 % conjectures 6
% 8.43/1.80 % EPR 38
% 8.43/1.80 % Horn 55
% 8.43/1.80 % unary 25
% 8.43/1.80 % binary 17
% 8.43/1.80 % lits 121
% 8.43/1.80 % lits eq 11
% 8.43/1.80 % fd_pure 0
% 8.43/1.80 % fd_pseudo 0
% 8.43/1.80 % fd_cond 1
% 8.43/1.80 % fd_pseudo_cond 2
% 8.43/1.80 % AC symbols 0
% 8.43/1.80
% 8.43/1.80 % ------ Input Options Time Limit: Unbounded
% 8.43/1.80
% 8.43/1.80
% 8.43/1.80 % ------
% 8.43/1.80 % Current options:
% 8.43/1.80 % ------
% 8.43/1.80
% 8.43/1.80
% 8.43/1.80 %
% 8.43/1.80
% 8.43/1.80 % ------ Proving...
% 8.43/1.80 %
% 8.43/1.80
% 8.43/1.80 % SZS status Theorem for theBenchmark.p
% 8.43/1.80
% 8.43/1.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.43/1.81
% 8.43/1.81
%------------------------------------------------------------------------------