%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM397+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 14.74s 2.82s
% Output : CNFRefutation 14.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 145 ( 9 unt; 0 def)
% Number of atoms : 465 ( 33 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 532 ( 212 ~; 230 |; 72 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 206 ( 0 sgn 192 !; 14 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f10,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f11,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f16,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f17,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f34,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f35,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(f36,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f37,conjecture,
! [X0] :
( ordinal(X0)
=> ordinal(union(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_ordinal1) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ordinal(union(X0)) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f45,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f48,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f16]) ).
fof(f53,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f48]) ).
fof(f67,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f68,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f74,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f75,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f77,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f79,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
? [X0] :
( ordinal(X0)
& ~ ordinal(union(X0)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f81]) ).
fof(f85,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f87,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f88,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,[],[f67]) ).
fof(f89,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK0(X0),X0)
& ~ subset(sK0(X0),X0) )
| epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f89]) ).
fof(f91,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f92,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ( ~ in(sK2(X0),sK1(X0))
& sK1(X0) != sK2(X0)
& ~ in(sK1(X0),sK2(X0))
& in(sK2(X0),X0)
& in(sK1(X0),X0) )
| epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f92]) ).
fof(f94,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f95,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f97,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK5(X0,X5),X0)
& in(X5,sK5(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK3(X0,X1),X1)
| ( in(sK4(X0,X1),X0)
& in(sK3(X0,X1),sK4(X0,X1)) ) )
& ( ~ in(sK3(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK3(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f97]) ).
fof(f113,plain,
( ordinal(sK19)
& ~ ordinal(union(sK19)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f80]) ).
fof(f114,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f127,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f128,plain,
! [X0] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f129,plain,
! [X0] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f131,plain,
! [X0] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f132,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f133,plain,
! [X0] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f134,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f135,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f137,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f138,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f139,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK5(X0,X5),X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f140,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK5(X0,X5)) ),
inference(cnf_transformation,[],[f98]) ).
fof(f142,plain,
! [X0,X1] :
( in(sK3(X0,X1),X1)
| in(sK4(X0,X1),X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f98]) ).
fof(f149,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f53]) ).
fof(f156,plain,
empty(empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f189,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f190,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f191,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f192,plain,
ordinal(sK19),
inference(cnf_transformation,[],[f113]) ).
fof(f193,plain,
~ ordinal(union(sK19)),
inference(cnf_transformation,[],[f113]) ).
fof(f195,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f199,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f201,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f203,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK5(X0,X5)) ),
inference(equality_resolution,[],[f140]) ).
fof(f204,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK5(X0,X5),X0) ),
inference(equality_resolution,[],[f139]) ).
tcf(c_59,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_60,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_62,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_63,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_64,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_65,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_66,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_68,plain,
! [X0: $i] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_69,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( in(sK4(X0,X1),X0)
| in(sK3(X0,X1),X1)
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( in(sK5(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_86,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f149]) ).
tcf(c_87,plain,
empty(empty_set),
inference(cnf_transformation,[],[f156]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_124,negated_conjecture,
~ ordinal(union(sK19)),
inference(cnf_transformation,[],[f193]) ).
tcf(c_125,negated_conjecture,
ordinal(sK19),
inference(cnf_transformation,[],[f192]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_126]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_128,c_151]) ).
tcf(c_2615,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3582,plain,
! [X0: $i] :
( ordinal(union(sK19))
| ~ ordinal(X0)
| ( union(sK19) != X0 ) ),
inference(instantiation,[status(thm)],[c_2615]) ).
tcf(c_3584,plain,
( ordinal(union(sK19))
| ~ epsilon_connected(union(sK19))
| ~ epsilon_transitive(union(sK19)) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_3587,plain,
( ordinal(union(sK19))
| ~ ordinal(empty_set)
| ( union(sK19) != empty_set ) ),
inference(instantiation,[status(thm)],[c_3582]) ).
tcf(c_3596,plain,
! [X0: $i] :
( in(sK4(sK19,X0),sK19)
| in(sK3(sK19,X0),X0)
| ( union(sK19) = X0 ) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_3597,plain,
( in(sK4(sK19,empty_set),sK19)
| in(sK3(sK19,empty_set),empty_set)
| ( union(sK19) = empty_set ) ),
inference(instantiation,[status(thm)],[c_3596]) ).
tcf(c_3609,plain,
( epsilon_connected(union(sK19))
| ( sK1(union(sK19)) != sK2(union(sK19)) ) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_3610,plain,
( epsilon_connected(union(sK19))
| ~ in(sK1(union(sK19)),sK2(union(sK19))) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3611,plain,
( epsilon_connected(union(sK19))
| ~ in(sK2(union(sK19)),sK1(union(sK19))) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_3612,plain,
( epsilon_connected(union(sK19))
| in(sK1(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_3613,plain,
( epsilon_connected(union(sK19))
| in(sK2(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_3631,plain,
( in(sK2(union(sK19)),sK1(union(sK19)))
| in(sK1(union(sK19)),sK2(union(sK19)))
| ( sK1(union(sK19)) = sK2(union(sK19)) )
| ~ ordinal(sK2(union(sK19)))
| ~ ordinal(sK1(union(sK19))) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_3710,plain,
( epsilon_transitive(union(sK19))
| ~ subset(sK0(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_3711,plain,
( epsilon_transitive(union(sK19))
| in(sK0(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_3722,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ in(sK3(sK19,X0),X0) ),
inference(instantiation,[status(thm)],[c_131]) ).
tcf(c_3723,plain,
( ~ empty(empty_set)
| ~ in(sK3(sK19,empty_set),empty_set) ),
inference(instantiation,[status(thm)],[c_3722]) ).
tcf(c_3765,plain,
( subset(sK0(union(sK19)),union(sK19))
| ~ in(sK0(union(sK19)),sK19) ),
inference(instantiation,[status(thm)],[c_133]) ).
tcf(c_3877,plain,
! [X0: $i] :
( ordinal(sK2(union(sK19)))
| ~ ordinal(X0)
| ~ in(sK2(union(sK19)),X0) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_3941,plain,
! [X0: $i] :
( in(sK5(sK19,X0),sK19)
| ~ in(X0,union(sK19)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_4025,plain,
! [X0: $i] :
( ~ empty(sK19)
| ~ in(sK4(sK19,X0),sK19) ),
inference(instantiation,[status(thm)],[c_131]) ).
tcf(c_4026,plain,
( ~ empty(sK19)
| ~ in(sK4(sK19,empty_set),sK19) ),
inference(instantiation,[status(thm)],[c_4025]) ).
tcf(c_4124,plain,
( epsilon_transitive(sK19)
| ~ ordinal(sK19) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_4127,plain,
! [X0: $i] :
( empty(sK19)
| in(X0,sK19)
| ~ element(X0,sK19) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_4192,plain,
! [X0: $i] :
( in(sK2(union(sK19)),sK5(X0,sK2(union(sK19))))
| ~ in(sK2(union(sK19)),union(X0)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_4277,plain,
! [X0: $i] :
( ordinal(sK2(union(sK19)))
| ~ ordinal(sK5(X0,sK2(union(sK19))))
| ~ in(sK2(union(sK19)),sK5(X0,sK2(union(sK19)))) ),
inference(instantiation,[status(thm)],[c_3877]) ).
tcf(c_4383,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(sK5(X1,X0),X2)
| ~ in(X0,sK5(X1,X0)) ),
inference(instantiation,[status(thm)],[c_331]) ).
tcf(c_4936,plain,
! [X0: $i] :
( in(sK0(union(X0)),sK5(X0,sK0(union(X0))))
| ~ in(sK0(union(X0)),union(X0)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_4961,plain,
( in(sK5(sK19,sK0(union(sK19))),sK19)
| ~ in(sK0(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_3941]) ).
tcf(c_5703,plain,
! [X0: $i,X1: $i] :
( ordinal(sK5(X0,sK2(union(sK19))))
| ~ ordinal(X1)
| ~ in(sK5(X0,sK2(union(sK19))),X1) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_7216,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK5(X0,X1),X2)
| ~ epsilon_transitive(X2)
| ~ in(sK5(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_7437,plain,
( in(sK1(union(sK19)),sK5(sK19,sK1(union(sK19))))
| ~ in(sK1(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_7444,plain,
( in(sK5(sK19,sK1(union(sK19))),sK19)
| ~ in(sK1(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_3941]) ).
tcf(c_7920,plain,
( in(sK5(sK19,sK2(union(sK19))),sK19)
| ~ in(sK2(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_3941]) ).
tcf(c_7982,plain,
( in(sK0(union(sK19)),sK5(sK19,sK0(union(sK19))))
| ~ in(sK0(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_4936]) ).
tcf(c_8094,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK5(X0,X1))
| ~ ordinal(X2)
| ~ in(sK5(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_9133,plain,
( in(sK2(union(sK19)),sK5(sK19,sK2(union(sK19))))
| ~ in(sK2(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_4192]) ).
tcf(c_11478,plain,
! [X0: $i] :
( ordinal(sK5(X0,sK2(union(sK19))))
| ~ ordinal(sK19)
| ~ in(sK5(X0,sK2(union(sK19))),sK19) ),
inference(instantiation,[status(thm)],[c_5703]) ).
tcf(c_12009,plain,
( empty(sK19)
| in(sK0(union(sK19)),sK19)
| ~ element(sK0(union(sK19)),sK19) ),
inference(instantiation,[status(thm)],[c_4127]) ).
tcf(c_12703,plain,
! [X0: $i] :
( ordinal(sK1(union(sK19)))
| ~ ordinal(X0)
| ~ in(sK1(union(sK19)),X0) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_13035,plain,
! [X0: $i] :
( element(sK0(union(sK19)),X0)
| ~ subset(sK5(sK19,sK0(union(sK19))),X0)
| ~ in(sK0(union(sK19)),sK5(sK19,sK0(union(sK19)))) ),
inference(instantiation,[status(thm)],[c_4383]) ).
tcf(c_17692,plain,
! [X0: $i,X1: $i] :
( ordinal(sK5(X0,X1))
| ~ ordinal(sK19)
| ~ in(sK5(X0,X1),sK19) ),
inference(instantiation,[status(thm)],[c_8094]) ).
tcf(c_21903,plain,
( ordinal(sK5(sK19,sK2(union(sK19))))
| ~ ordinal(sK19)
| ~ in(sK5(sK19,sK2(union(sK19))),sK19) ),
inference(instantiation,[status(thm)],[c_11478]) ).
tcf(c_23183,plain,
( ordinal(sK1(union(sK19)))
| ~ ordinal(sK5(sK19,sK1(union(sK19))))
| ~ in(sK1(union(sK19)),sK5(sK19,sK1(union(sK19)))) ),
inference(instantiation,[status(thm)],[c_12703]) ).
tcf(c_23381,plain,
! [X0: $i] :
( subset(sK5(sK19,sK0(union(sK19))),X0)
| ~ epsilon_transitive(X0)
| ~ in(sK5(sK19,sK0(union(sK19))),X0) ),
inference(instantiation,[status(thm)],[c_7216]) ).
tcf(c_27724,plain,
! [X0: $i] :
( ordinal(sK5(sK19,X0))
| ~ ordinal(sK19)
| ~ in(sK5(sK19,X0),sK19) ),
inference(instantiation,[status(thm)],[c_17692]) ).
tcf(c_29546,plain,
( ordinal(sK2(union(sK19)))
| ~ ordinal(sK5(sK19,sK2(union(sK19))))
| ~ in(sK2(union(sK19)),sK5(sK19,sK2(union(sK19)))) ),
inference(instantiation,[status(thm)],[c_4277]) ).
tcf(c_34661,plain,
( ordinal(sK5(sK19,sK1(union(sK19))))
| ~ ordinal(sK19)
| ~ in(sK5(sK19,sK1(union(sK19))),sK19) ),
inference(instantiation,[status(thm)],[c_27724]) ).
tcf(c_34973,plain,
( subset(sK5(sK19,sK0(union(sK19))),sK19)
| ~ epsilon_transitive(sK19)
| ~ in(sK5(sK19,sK0(union(sK19))),sK19) ),
inference(instantiation,[status(thm)],[c_23381]) ).
tcf(c_53581,plain,
( element(sK0(union(sK19)),sK19)
| ~ subset(sK5(sK19,sK0(union(sK19))),sK19)
| ~ in(sK0(union(sK19)),sK5(sK19,sK0(union(sK19)))) ),
inference(instantiation,[status(thm)],[c_13035]) ).
tcf(c_53582,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_53581,c_34973,c_34661,c_29546,c_23183,c_21903,c_12009,c_9133,c_7982,c_7920,c_7444,c_7437,c_4961,c_4124,c_4026,c_3765,c_3723,c_3710,c_3711,c_3631,c_3609,c_3610,c_3611,c_3612,c_3613,c_3597,c_3587,c_3584,c_124,c_86,c_87,c_125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM397+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 03:52:54 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...
% 14.74/2.82 % SZS status Started for theBenchmark.p
% 14.74/2.82 % SZS status Theorem for theBenchmark.p
% 14.74/2.82
% 14.74/2.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.74/2.82
% 14.74/2.82 % ------ iProver source info
% 14.74/2.82
% 14.74/2.82 % git: date: 2026-07-19 20:42:38 +0200
% 14.74/2.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.74/2.82 % git: non_committed_changes: false
% 14.74/2.82
% 14.74/2.82 % ------ Parsing...
% 14.74/2.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.74/2.82
% 14.74/2.82 % ------ Preprocessing... sup_sim: 0 sf_s rm: 22 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 14.74/2.82
% 14.74/2.82 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.74/2.82
% 14.74/2.82 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.74/2.82 % ------ Proving...
% 14.74/2.82 % ------ Problem Properties
% 14.74/2.82
% 14.74/2.82 %
% 14.74/2.82 % clauses 58
% 14.74/2.82 % conjectures 2
% 14.74/2.82 % EPR 40
% 14.74/2.82 % Horn 49
% 14.74/2.82 % unary 20
% 14.74/2.82 % binary 22
% 14.74/2.82 % lits 121
% 14.74/2.82 % lits eq 8
% 14.74/2.82 % fd_pure 0
% 14.74/2.82 % fd_pseudo 0
% 14.74/2.82 % fd_cond 1
% 14.74/2.82 % fd_pseudo_cond 6
% 14.74/2.82 % AC symbols 0
% 14.74/2.82
% 14.74/2.82 % ------ Input Options Time Limit: Unbounded
% 14.74/2.82
% 14.74/2.82
% 14.74/2.82 % ------
% 14.74/2.82 % Current options:
% 14.74/2.82 % ------
% 14.74/2.82
% 14.74/2.82
% 14.74/2.82 %
% 14.74/2.82
% 14.74/2.82 % ------ Proving...
% 14.74/2.82 %
% 14.74/2.82
% 14.74/2.82 % SZS status Theorem for theBenchmark.p
% 14.74/2.82
% 14.74/2.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.74/2.83
% 14.74/2.83
%------------------------------------------------------------------------------