%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM401+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 02:24:09 PM UTC 2026
% Result : Theorem 3.84s 1.21s
% Output : CNFRefutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 119 ( 17 unt; 0 def)
% Number of atoms : 426 ( 72 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 487 ( 180 ~; 224 |; 59 &)
% ( 12 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 159 ( 0 sgn 146 !; 13 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f10,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f11,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f13,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f39,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f42,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f46,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f48,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_ordinal1) ).
fof(f49,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f54,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f67,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f69,plain,
! [X0] :
( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f76,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f77,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f84,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f85,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f84]) ).
fof(f89,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f90,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f89]) ).
fof(f93,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ( in(X0,succ(X1))
<~> ordinal_subset(X0,X1) ) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f98,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f100,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f101,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f103,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f103]) ).
fof(f105,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f106,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK1(X0),X0)
& ~ subset(sK1(X0),X0) )
| epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f106]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f109]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f110]) ).
fof(f126,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f127,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ( in(X0,succ(X1))
| ordinal_subset(X0,X1) )
& ( ~ in(X0,succ(X1))
| ~ ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f93]) ).
fof(f128,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ( in(X0,succ(X1))
| ordinal_subset(X0,X1) )
& ( ~ in(X0,succ(X1))
| ~ ordinal_subset(X0,X1) ) ) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
( ordinal(sK17)
& ordinal(sK18)
& ( in(sK17,succ(sK18))
| ordinal_subset(sK17,sK18) )
& ( ~ in(sK17,succ(sK18))
| ~ ordinal_subset(sK17,sK18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f128]) ).
fof(f131,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f134,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f143,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f146,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f147,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f148,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f104]) ).
fof(f152,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f155,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f157,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f213,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f217,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f42]) ).
fof(f221,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f223,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f129]) ).
fof(f224,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f129]) ).
fof(f225,plain,
( in(sK17,succ(sK18))
| ordinal_subset(sK17,sK18) ),
inference(cnf_transformation,[],[f129]) ).
fof(f226,plain,
( ~ in(sK17,succ(sK18))
| ~ ordinal_subset(sK17,sK18) ),
inference(cnf_transformation,[],[f129]) ).
fof(f232,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f239,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f217,f147]) ).
fof(f241,plain,
( ~ in(sK17,set_union2(sK18,singleton(sK18)))
| ~ ordinal_subset(sK17,sK18) ),
inference(definition_unfolding,[],[f226,f147]) ).
fof(f242,plain,
( in(sK17,set_union2(sK18,singleton(sK18)))
| ordinal_subset(sK17,sK18) ),
inference(definition_unfolding,[],[f225,f147]) ).
fof(f247,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f148]) ).
fof(f248,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f157]) ).
fof(f250,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f155]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_51,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_132,plain,
! [X0: $i] : in(X0,set_union2(X0,singleton(X0))),
inference(cnf_transformation,[],[f239]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_138,negated_conjecture,
( ~ ordinal_subset(sK17,sK18)
| ~ in(sK17,set_union2(sK18,singleton(sK18))) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_139,negated_conjecture,
( ordinal_subset(sK17,sK18)
| in(sK17,set_union2(sK18,singleton(sK18))) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_140,negated_conjecture,
ordinal(sK18),
inference(cnf_transformation,[],[f224]) ).
tcf(c_141,negated_conjecture,
ordinal(sK17),
inference(cnf_transformation,[],[f223]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_2856,plain,
epsilon_transitive(sK18),
inference(superposition,[status(thm)],[c_140,c_51]) ).
tcf(c_2857,plain,
epsilon_transitive(sK17),
inference(superposition,[status(thm)],[c_141,c_51]) ).
tcf(c_3467,plain,
( ~ ordinal_subset(sK17,sK18)
| ~ in(sK17,sK18) ),
inference(superposition,[status(thm)],[c_73,c_138]) ).
tcf(c_3516,plain,
( ordinal_subset(sK18,sK17)
| ~ ordinal(sK18)
| ~ ordinal(sK17)
| ~ in(sK17,sK18) ),
inference(superposition,[status(thm)],[c_59,c_3467]) ).
tcf(c_3591,plain,
( ordinal_subset(sK18,sK17)
| ~ in(sK17,sK18) ),
inference(global_subsumption_just,[status(thm)],[c_3516,c_141,c_140,c_3516]) ).
tcf(c_3648,plain,
( ordinal_subset(sK17,sK18)
| in(sK17,sK18)
| in(sK17,singleton(sK18)) ),
inference(superposition,[status(thm)],[c_139,c_75]) ).
tcf(c_3940,plain,
( ordinal_subset(sK17,sK18)
| in(sK17,sK18)
| ( sK17 = sK18 ) ),
inference(superposition,[status(thm)],[c_3648,c_66]) ).
tcf(c_4047,plain,
( subset(sK17,sK18)
| in(sK17,sK18)
| ( sK17 = sK18 )
| ~ ordinal(sK18)
| ~ ordinal(sK17) ),
inference(superposition,[status(thm)],[c_3940,c_129]) ).
tcf(c_4119,plain,
( ordinal_subset(sK18,sK17)
| in(sK18,sK17)
| ( sK17 = sK18 )
| ~ ordinal(sK18)
| ~ ordinal(sK17) ),
inference(superposition,[status(thm)],[c_136,c_3591]) ).
tcf(c_4460,plain,
( subset(sK17,sK18)
| in(sK17,sK18)
| ( sK17 = sK18 ) ),
inference(global_subsumption_just,[status(thm)],[c_4047,c_141,c_140,c_4047]) ).
tcf(c_4462,plain,
( in(sK17,sK18)
| ( sK17 = sK18 )
| ~ subset(sK18,sK17) ),
inference(superposition,[status(thm)],[c_4460,c_60]) ).
tcf(c_4469,plain,
( ordinal_subset(sK18,sK17)
| in(sK18,sK17)
| ( sK17 = sK18 ) ),
inference(global_subsumption_just,[status(thm)],[c_4119,c_141,c_140,c_4119]) ).
tcf(c_4471,plain,
( subset(sK18,sK17)
| in(sK18,sK17)
| ( sK17 = sK18 )
| ~ ordinal(sK18)
| ~ ordinal(sK17) ),
inference(superposition,[status(thm)],[c_4469,c_129]) ).
tcf(c_6490,plain,
( ~ ordinal_subset(sK17,sK18)
| ~ in(sK17,sK18) ),
inference(superposition,[status(thm)],[c_73,c_138]) ).
tcf(c_6538,plain,
( ordinal_subset(sK18,sK17)
| ~ ordinal(sK18)
| ~ ordinal(sK17)
| ~ in(sK17,sK18) ),
inference(superposition,[status(thm)],[c_59,c_6490]) ).
tcf(c_6540,plain,
! [X0: $i] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ),
inference(equality_factoring,[status(thm)],[c_59]) ).
tcf(c_6554,plain,
( ordinal_subset(sK18,sK17)
| ~ in(sK17,sK18) ),
inference(global_subsumption_just,[status(thm)],[c_6538,c_3591]) ).
tcf(c_6575,plain,
( ordinal_subset(sK17,sK18)
| in(sK17,sK18)
| in(sK17,singleton(sK18)) ),
inference(superposition,[status(thm)],[c_139,c_75]) ).
tcf(c_6634,plain,
( ordinal_subset(sK17,sK18)
| in(sK17,sK18)
| ( sK17 = sK18 ) ),
inference(superposition,[status(thm)],[c_6575,c_66]) ).
tcf(c_6637,plain,
( subset(sK17,sK18)
| in(sK17,sK18)
| ( sK17 = sK18 )
| ~ ordinal(sK18)
| ~ ordinal(sK17) ),
inference(superposition,[status(thm)],[c_6634,c_129]) ).
tcf(c_6682,plain,
( ordinal_subset(sK18,sK17)
| in(sK18,sK17)
| ( sK17 = sK18 )
| ~ ordinal(sK18)
| ~ ordinal(sK17) ),
inference(superposition,[status(thm)],[c_136,c_6554]) ).
tcf(c_6826,plain,
( subset(sK17,sK18)
| in(sK17,sK18)
| ( sK17 = sK18 ) ),
inference(global_subsumption_just,[status(thm)],[c_6637,c_4460]) ).
tcf(c_6828,plain,
( in(sK17,sK18)
| ( sK17 = sK18 )
| ~ subset(sK18,sK17) ),
inference(superposition,[status(thm)],[c_6826,c_60]) ).
tcf(c_6830,plain,
( ordinal_subset(sK18,sK17)
| in(sK18,sK17)
| ( sK17 = sK18 ) ),
inference(global_subsumption_just,[status(thm)],[c_6682,c_4469]) ).
tcf(c_6832,plain,
( subset(sK18,sK17)
| in(sK18,sK17)
| ( sK17 = sK18 )
| ~ ordinal(sK18)
| ~ ordinal(sK17) ),
inference(superposition,[status(thm)],[c_6830,c_129]) ).
tcf(c_7144,plain,
( subset(sK18,sK17)
| in(sK18,sK17)
| ( sK17 = sK18 ) ),
inference(global_subsumption_just,[status(thm)],[c_6832,c_141,c_140,c_4471]) ).
tcf(c_7146,plain,
( in(sK18,sK17)
| ( sK17 = sK18 )
| ~ subset(sK17,sK18) ),
inference(superposition,[status(thm)],[c_7144,c_60]) ).
tcf(c_7148,plain,
( in(sK18,sK17)
| in(sK17,sK18)
| ( sK17 = sK18 ) ),
inference(superposition,[status(thm)],[c_7144,c_6828]) ).
tcf(c_7406,plain,
( subset(sK17,sK18)
| in(sK18,sK17)
| ( sK17 = sK18 )
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_7148,c_69]) ).
tcf(c_7420,plain,
( in(sK18,sK17)
| ( sK17 = sK18 ) ),
inference(global_subsumption_just,[status(thm)],[c_7146,c_2856,c_7146,c_7406]) ).
tcf(c_7422,plain,
( subset(sK18,sK17)
| ( sK17 = sK18 )
| ~ epsilon_transitive(sK17) ),
inference(superposition,[status(thm)],[c_7420,c_69]) ).
tcf(c_7423,plain,
( ( sK17 = sK18 )
| ~ in(sK17,sK18) ),
inference(superposition,[status(thm)],[c_7420,c_49]) ).
tcf(c_7424,plain,
( ( sK17 = sK18 )
| ~ empty(sK17) ),
inference(superposition,[status(thm)],[c_7420,c_147]) ).
tcf(c_7438,plain,
sK17 = sK18,
inference(global_subsumption_just,[status(thm)],[c_7424,c_2857,c_4462,c_7423,c_7422]) ).
tcf(c_7472,plain,
( ~ ordinal_subset(sK17,sK18)
| ~ in(sK18,set_union2(sK18,singleton(sK18))) ),
inference(superposition,[status(thm)],[c_7438,c_138]) ).
tcf(c_8309,plain,
~ ordinal_subset(sK17,sK18),
inference(superposition,[status(thm)],[c_132,c_7472]) ).
tcf(c_8315,plain,
~ ordinal_subset(sK18,sK18),
inference(superposition,[status(thm)],[c_7438,c_8309]) ).
tcf(c_8514,plain,
~ ordinal(sK18),
inference(superposition,[status(thm)],[c_6540,c_8315]) ).
tcf(c_8515,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8514,c_140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM401+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.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 03:53:08 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...
% 3.84/1.21 % SZS status Started for theBenchmark.p
% 3.84/1.21 % SZS status Theorem for theBenchmark.p
% 3.84/1.21
% 3.84/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.84/1.21
% 3.84/1.21 % ------ iProver source info
% 3.84/1.21
% 3.84/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 3.84/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.84/1.21 % git: non_committed_changes: false
% 3.84/1.21
% 3.84/1.21 % ------ Parsing...
% 3.84/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.84/1.21
% 3.84/1.21 % ------ 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 %
% 3.84/1.21
% 3.84/1.21 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.84/1.21
% 3.84/1.21 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 3.84/1.21 % ------ Proving...
% 3.84/1.21 % ------ Problem Properties
% 3.84/1.21
% 3.84/1.21 %
% 3.84/1.21 % clauses 66
% 3.84/1.21 % conjectures 4
% 3.84/1.21 % EPR 39
% 3.84/1.21 % Horn 57
% 3.84/1.21 % unary 27
% 3.84/1.21 % binary 22
% 3.84/1.21 % lits 128
% 3.84/1.21 % lits eq 16
% 3.84/1.21 % fd_pure 0
% 3.84/1.21 % fd_pseudo 0
% 3.84/1.21 % fd_cond 1
% 3.84/1.21 % fd_pseudo_cond 8
% 3.84/1.21 % AC symbols 0
% 3.84/1.21
% 3.84/1.21 % ------ Input Options Time Limit: Unbounded
% 3.84/1.21
% 3.84/1.21
% 3.84/1.21 % ------
% 3.84/1.21 % Current options:
% 3.84/1.21 % ------
% 3.84/1.21
% 3.84/1.21
% 3.84/1.21 %
% 3.84/1.21
% 3.84/1.21 % ------ Proving...
% 3.84/1.21 %
% 3.84/1.21
% 3.84/1.21 % SZS status Theorem for theBenchmark.p
% 3.84/1.21
% 3.84/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.84/1.21
% 3.84/1.21
%------------------------------------------------------------------------------