%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.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 : Sun Sep 27 08:08:45 AM UTC 2026
% Result : Theorem 128.35s 30.19s
% Output : Refutation 120.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 60
% Syntax : Number of formulae : 1036 ( 120 unt; 0 typ; 19 def)
% Number of atoms : 3849 ( 704 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 8367 (1405 ~;1510 |; 221 &;5156 @)
% ( 7 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 17 con; 0-2 aty)
% Number of variables : 933 ( 6 ^; 867 !; 41 ?; 933 :)
% ( 0 !>; 0 ?*; 0 @-; 19 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(relation_non_empty_decl,type,
relation_non_empty: $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ! [B: $i] :
( ( B @ ordinal )
=> ( A @ ( B @ in ) ) )
& ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( B @ ordinal ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ element ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
( ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) ) )
& ( A @ ( B @ in ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( A @ sk18 @ ( B @ in ) )
& ( ( A @ sk18 )
!= B )
& ~ ( B @ ( A @ sk18 @ in ) )
& ( A @ ( B @ in ) ) ) ) ) ).
thf(35,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(172,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(173,plain,
( ( sk15 @ ordinal )
& ( sk15 @ epsilon_connected )
& ( sk15 @ epsilon_transitive )
& ~ ( sk15 @ empty ) ),
inference(cnf,[status(esa)],[172]) ).
thf(177,plain,
sk15 @ ordinal,
inference(cnfConj,[status(thm)],[173]) ).
thf(1,conjecture,
! [A: $i] :
~ ! [B: $i] :
( ( A @ ( B @ in ) )
<=> ( B @ ordinal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
~ ! [B: $i] :
( ( A @ ( B @ in ) )
<=> ( B @ ordinal ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ ! [A: $i] :
~ ! [B: $i] :
( ( ( B @ ordinal )
=> ( A @ ( B @ in ) ) )
& ( ( A @ ( B @ in ) )
=> ( B @ ordinal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,plain,
~ ~ ? [A: $i] :
( ! [B: $i] :
( ( B @ ordinal )
=> ( A @ ( B @ in ) ) )
& ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( B @ ordinal ) ) ),
inference(miniscope,[status(thm)],[43]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( B @ in ) )
| ~ ( B @ ordinal ) )
& ( ( A @ ordinal )
| ~ ( sk1 @ ( A @ in ) ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(47,plain,
! [A: $i] :
( ( sk1 @ ( A @ in ) )
| ~ ( A @ ordinal ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(48,plain,
! [A: $i] :
( ( sk1 @ ( A @ in ) )
| ~ ( A @ ordinal ) ),
inference(simp,[status(thm)],[47]) ).
thf(767,plain,
! [A: $i] :
( ( ( sk15 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[177,48]) ).
thf(768,plain,
! [A: $i] :
( ( ( sk15 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) ) ),
inference(simp,[status(thm)],[767]) ).
thf(769,plain,
sk1 @ ( sk15 @ in ),
inference(pattern_uni,[status(thm)],[768:[bind(A,$thf( sk15 ))]]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ epsilon_transitive )
<=> ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(134,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) )
=> ( A @ epsilon_transitive ) )
& ( ( A @ epsilon_transitive )
=> ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(135,plain,
( ! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) )
=> ( A @ epsilon_transitive ) )
& ! [A: $i] :
( ( A @ epsilon_transitive )
=> ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ) ),
inference(miniscope,[status(thm)],[134]) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ epsilon_transitive )
| ~ ( C @ ( C @ sk13 @ subset ) ) )
& ( ( C @ epsilon_transitive )
| ( C @ ( C @ sk13 @ in ) ) )
& ( ( A @ ( B @ subset ) )
| ~ ( A @ ( B @ in ) )
| ~ ( A @ epsilon_transitive ) ) ),
inference(cnf,[status(esa)],[135]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( A @ ( B @ in ) )
| ~ ( A @ epsilon_transitive ) ),
inference(cnfConj,[status(thm)],[136]) ).
thf(1716,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ in ) )
!= ( A @ ( B @ in ) ) )
| ( A @ ( B @ subset ) )
| ~ $true
| ~ ( A @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[769,137]) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ in ) )
!= ( A @ ( B @ in ) ) )
| ( A @ ( B @ subset ) )
| ~ ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[1716]) ).
thf(1718,plain,
( ( sk1 @ ( sk15 @ subset ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[1717:[bind(A,$thf( sk1 )),bind(B,$thf( sk15 ))]]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(154,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(miniscope,[status(thm)],[153]) ).
thf(155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk14 ) @ in ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk14 ) @ in ) ) )
& ( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[154]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk14 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk14 ) @ in ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(37,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(180,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(181,plain,
( ( sk16 @ ordinal )
& ( sk16 @ epsilon_connected )
& ( sk16 @ epsilon_transitive ) ),
inference(cnf,[status(esa)],[180]) ).
thf(184,plain,
sk16 @ ordinal,
inference(cnfConj,[status(thm)],[181]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ in ) )
=> ( A @ ordinal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(185,plain,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ in ) )
=> ( A @ ordinal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( A @ ordinal )
| ~ ( B @ ( A @ in ) )
| ~ ( B @ ordinal ) ),
inference(cnf,[status(esa)],[185]) ).
thf(3429,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ordinal )
!= ( B @ ordinal ) )
| ( A @ ordinal )
| ~ ( B @ ( A @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[184,186]) ).
thf(3430,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ordinal )
!= ( B @ ordinal ) )
| ( A @ ordinal )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[3429]) ).
thf(3431,plain,
! [A: $i] :
( ( A @ ordinal )
| ~ ( sk16 @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[3430:[bind(A,$thf( A )),bind(B,$thf( sk16 ))]]) ).
thf(24544,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ in ) )
!= ( sk16 @ ( C @ in ) ) )
| ( C @ ordinal )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[159,3431]) ).
thf(24545,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ in ) )
!= ( sk16 @ ( C @ in ) ) )
| ( C @ ordinal )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[24544]) ).
thf(24546,plain,
! [A: $i] :
( ( sk16 @ ( A @ sk14 ) @ ordinal )
| ( A @ ( sk16 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[24545:[bind(A,$thf( sk16 )),bind(B,$thf( D )),bind(C,$thf( sk16 @ ( D @ sk14 ) ))]]) ).
thf(24643,plain,
! [A: $i] :
( ( sk16 @ ( A @ sk14 ) @ ordinal )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[24546]) ).
thf(24932,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( sk1 @ ( B @ in ) )
| ~ $true
| ( A @ ( sk16 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24643,48]) ).
thf(24933,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( sk1 @ ( B @ in ) )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[24932]) ).
thf(24934,plain,
! [A: $i] :
( ( sk1 @ ( sk16 @ ( A @ sk14 ) @ in ) )
| ( A @ ( sk16 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[24933:[bind(A,$thf( C )),bind(B,$thf( sk16 @ ( C @ sk14 ) ))]]) ).
thf(24963,plain,
! [A: $i] :
( ( sk1 @ ( sk16 @ ( A @ sk14 ) @ in ) )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[24934]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ epsilon_connected )
<=> ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(199,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) )
=> ( A @ epsilon_connected ) )
& ( ( A @ epsilon_connected )
=> ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(200,plain,
( ! [A: $i] :
( ~ ? [B: $i] :
( ? [C: $i] :
( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) ) )
& ( A @ ( B @ in ) ) )
=> ( A @ epsilon_connected ) )
& ! [A: $i] :
( ( A @ epsilon_connected )
=> ~ ? [B: $i] :
( ? [C: $i] :
( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) ) )
& ( A @ ( B @ in ) ) ) ) ),
inference(miniscope,[status(thm)],[199]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ epsilon_connected )
| ~ ( D @ sk18 @ ( D @ sk19 @ in ) ) )
& ( ( D @ epsilon_connected )
| ( ( D @ sk18 )
!= ( D @ sk19 ) ) )
& ( ( D @ epsilon_connected )
| ~ ( D @ sk19 @ ( D @ sk18 @ in ) ) )
& ( ( D @ epsilon_connected )
| ( D @ ( D @ sk19 @ in ) ) )
& ( ( D @ epsilon_connected )
| ( D @ ( D @ sk18 @ in ) ) )
& ( ( B @ ( C @ in ) )
| ( B = C )
| ( C @ ( B @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( A @ ( B @ in ) )
| ~ ( A @ epsilon_connected ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(204,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ( A @ ( A @ sk19 @ in ) ) ),
inference(cnfConj,[status(thm)],[201]) ).
thf(211,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ( A @ ( A @ sk19 @ in ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(46,plain,
! [A: $i] :
( ( A @ ordinal )
| ~ ( sk1 @ ( A @ in ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(5525,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ in ) )
!= ( sk1 @ ( B @ in ) ) )
| ( B @ ordinal )
| ~ $true
| ( A @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[211,46]) ).
thf(5526,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ in ) )
!= ( sk1 @ ( B @ in ) ) )
| ( B @ ordinal )
| ( A @ epsilon_connected ) ),
inference(simp,[status(thm)],[5525]) ).
thf(5527,plain,
( ( sk1 @ sk19 @ ordinal )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[5526:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk19 ))]]) ).
thf(138,plain,
! [A: $i] :
( ( A @ epsilon_transitive )
| ( A @ ( A @ sk13 @ in ) ) ),
inference(cnfConj,[status(thm)],[136]) ).
thf(140,plain,
! [A: $i] :
( ( A @ epsilon_transitive )
| ( A @ ( A @ sk13 @ in ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(1682,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk13 @ in ) )
!= ( sk1 @ ( B @ in ) ) )
| ( B @ ordinal )
| ~ $true
| ( A @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[140,46]) ).
thf(1683,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk13 @ in ) )
!= ( sk1 @ ( B @ in ) ) )
| ( B @ ordinal )
| ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[1682]) ).
thf(1684,plain,
( ( sk1 @ sk13 @ ordinal )
| ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[1683:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk13 ))]]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ordinal )
<=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
thf(142,plain,
! [A: $i] :
( ( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) )
& ( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(143,plain,
( ! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) )
& ! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ) ),
inference(miniscope,[status(thm)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( ( B @ ordinal )
| ~ ( B @ epsilon_connected )
| ~ ( B @ epsilon_transitive ) )
& ( ( A @ epsilon_connected )
| ~ ( A @ ordinal ) )
& ( ( A @ epsilon_transitive )
| ~ ( A @ ordinal ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(147,plain,
! [A: $i] :
( ( A @ ordinal )
| ~ ( A @ epsilon_connected )
| ~ ( A @ epsilon_transitive ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(148,plain,
! [A: $i] :
( ( A @ ordinal )
| ~ ( A @ epsilon_connected )
| ~ ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[147]) ).
thf(1938,plain,
! [A: $i] :
( ( ( sk1 @ epsilon_transitive )
!= ( A @ epsilon_transitive ) )
| ( A @ ordinal )
| ~ ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1684,148]) ).
thf(1939,plain,
! [A: $i] :
( ( ( sk1 @ epsilon_transitive )
!= ( A @ epsilon_transitive ) )
| ( A @ ordinal )
| ~ ( A @ epsilon_connected )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[1938]) ).
thf(1940,plain,
( ( sk1 @ ordinal )
| ~ ( sk1 @ epsilon_connected )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[1939:[bind(A,$thf( sk1 ))]]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(3235,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[171]) ).
thf(3236,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[3235:[bind(A,$thf( B ))]]) ).
thf(3239,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[3236]) ).
thf(3376,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ in ) )
!= ( B @ ( B @ in ) ) )
| ~ $true
| ~ ( A @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[48,3239]) ).
thf(3377,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ in ) )
!= ( B @ ( B @ in ) ) )
| ~ ( A @ ordinal ) ),
inference(simp,[status(thm)],[3376]) ).
thf(3378,plain,
~ ( sk1 @ ordinal ),
inference(pattern_uni,[status(thm)],[3377:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(10882,plain,
( $false
| ~ ( sk1 @ epsilon_connected )
| ( sk1 @ sk13 @ ordinal ) ),
inference(rewrite,[status(thm)],[1940,3378]) ).
thf(10883,plain,
( ~ ( sk1 @ epsilon_connected )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[10882]) ).
thf(10916,plain,
( ( ( sk1 @ sk13 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ~ ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[10883,3378]) ).
thf(10917,plain,
( ( ( sk1 @ sk13 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[10916]) ).
thf(10988,plain,
( ( ( sk1 @ sk13 )
!= sk1 )
| ~ ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[10917]) ).
thf(11312,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( ( sk1 @ sk13 )
!= sk1 )
| ~ $true
| ( sk1 @ sk19 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[5527,10988]) ).
thf(11313,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( ( sk1 @ sk13 )
!= sk1 )
| ( sk1 @ sk19 @ ordinal ) ),
inference(simp,[status(thm)],[11312]) ).
thf(11314,plain,
( ( ( sk1 @ sk13 )
!= sk1 )
| ( sk1 @ sk19 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11313:[]]) ).
thf(13158,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[11314,3378]) ).
thf(13159,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13158]) ).
thf(13199,plain,
( ( ( sk1 @ sk19 )
!= sk1 )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13159]) ).
thf(17,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(98,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(99,plain,
( ( sk8 @ relation_empty_yielding )
& ( sk8 @ relation ) ),
inference(cnf,[status(esa)],[98]) ).
thf(101,plain,
sk8 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[99]) ).
thf(146,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ~ ( A @ ordinal ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(10979,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ~ ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[10883,146]) ).
thf(10980,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[10979]) ).
thf(10981,plain,
( ( sk1 @ sk13 @ epsilon_connected )
| ~ ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[10980:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(11209,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected )
| ~ $true
| ( sk1 @ sk19 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[5527,10981]) ).
thf(11210,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected )
| ( sk1 @ sk19 @ ordinal ) ),
inference(simp,[status(thm)],[11209]) ).
thf(11211,plain,
( ( sk1 @ sk13 @ epsilon_connected )
| ( sk1 @ sk19 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11210:[]]) ).
thf(206,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ( A @ ( A @ sk18 @ in ) ) ),
inference(cnfConj,[status(thm)],[201]) ).
thf(209,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ( A @ ( A @ sk18 @ in ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(1970,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ in ) )
!= ( sk1 @ ( B @ in ) ) )
| ( B @ ordinal )
| ~ $true
| ( A @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[209,46]) ).
thf(1971,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ in ) )
!= ( sk1 @ ( B @ in ) ) )
| ( B @ ordinal )
| ( A @ epsilon_connected ) ),
inference(simp,[status(thm)],[1970]) ).
thf(1972,plain,
( ( sk1 @ sk18 @ ordinal )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[1971:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk18 ))]]) ).
thf(10963,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk18 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1972,10883]) ).
thf(10964,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[10963]) ).
thf(10965,plain,
( ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk18 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[10964:[]]) ).
thf(11515,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10965,146]) ).
thf(11516,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11515]) ).
thf(11517,plain,
( ( sk1 @ sk18 @ epsilon_connected )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11516:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(10973,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk19 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[5527,10883]) ).
thf(10974,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk19 @ ordinal ) ),
inference(simp,[status(thm)],[10973]) ).
thf(10975,plain,
( ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk19 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[10974:[]]) ).
thf(11579,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10975,146]) ).
thf(11580,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11579]) ).
thf(11581,plain,
( ( sk1 @ sk19 @ epsilon_connected )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11580:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(145,plain,
! [A: $i] :
( ( A @ epsilon_transitive )
| ~ ( A @ ordinal ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(5758,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[5527,145]) ).
thf(5759,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[5758]) ).
thf(5760,plain,
( ( sk1 @ sk19 @ epsilon_transitive )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[5759:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(10957,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ $true
| ~ ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[10883,145]) ).
thf(10958,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[10957]) ).
thf(10959,plain,
( ( sk1 @ sk13 @ epsilon_transitive )
| ~ ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[10958:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(11096,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_transitive )
| ~ $true
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[5760,10959]) ).
thf(11097,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_transitive )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11096]) ).
thf(11098,plain,
( ( sk1 @ sk13 @ epsilon_transitive )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11097:[]]) ).
thf(12437,plain,
( ~ $true
| ( ( sk1 @ sk19 @ epsilon_transitive )
!= ( sk1 @ sk13 @ epsilon_transitive ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(eqfactor_ordered,[status(thm)],[11098]) ).
thf(12440,plain,
( ( ( sk1 @ sk19 )
!= ( sk1 @ sk13 ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12437]) ).
thf(6,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(60,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(61,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
empty_set @ empty,
inference(cnfConj,[status(thm)],[61]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(107,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(108,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[107]) ).
thf(109,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(80,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(81,plain,
! [A: $i] : ( A @ ( A @ sk6 @ element ) ),
inference(cnf,[status(esa)],[80]) ).
thf(42,axiom,
( ( empty_set @ 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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(215,plain,
( ( empty_set @ 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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(216,plain,
( ( empty_set @ 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 ) ),
inference(cnf,[status(esa)],[215]) ).
thf(222,plain,
empty_set @ ordinal,
inference(cnfConj,[status(thm)],[216]) ).
thf(1331,plain,
! [A: $i] :
( ( ( empty_set @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[222,48]) ).
thf(1332,plain,
! [A: $i] :
( ( ( empty_set @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) ) ),
inference(simp,[status(thm)],[1331]) ).
thf(1333,plain,
sk1 @ ( empty_set @ in ),
inference(pattern_uni,[status(thm)],[1332:[bind(A,$thf( empty_set ))]]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(126,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(127,plain,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ empty )
& ( C @ powerset @ ( B @ element ) ) )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[126]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ empty )
| ~ ( C @ powerset @ ( B @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[127]) ).
thf(1476,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( C @ empty )
| ~ ( C @ powerset @ ( B @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1333,128]) ).
thf(1477,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( C @ empty )
| ~ ( C @ powerset @ ( B @ element ) ) ),
inference(simp,[status(thm)],[1476]) ).
thf(1478,plain,
! [A: $i] :
( ~ ( A @ empty )
| ~ ( A @ powerset @ ( sk1 @ element ) ) ),
inference(pattern_uni,[status(thm)],[1477:[bind(A,$thf( empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(1501,plain,
! [A: $i] :
( ~ ( A @ empty )
| ~ ( A @ powerset @ ( sk1 @ element ) ) ),
inference(simp,[status(thm)],[1478]) ).
thf(5669,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ~ $true
| ~ ( A @ powerset @ ( sk1 @ element ) ) ),
inference(paramod_ordered,[status(thm)],[62,1501]) ).
thf(5670,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ~ ( A @ powerset @ ( sk1 @ element ) ) ),
inference(simp,[status(thm)],[5669]) ).
thf(5671,plain,
~ ( empty_set @ powerset @ ( sk1 @ element ) ),
inference(pattern_uni,[status(thm)],[5670:[bind(A,$thf( empty_set ))]]) ).
thf(5825,plain,
! [A: $i] :
( ( ( A @ ( A @ sk6 @ element ) )
!= ( empty_set @ powerset @ ( sk1 @ element ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,5671]) ).
thf(5826,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ element ) )
!= ( empty_set @ powerset @ ( sk1 @ element ) ) ),
inference(simp,[status(thm)],[5825]) ).
thf(5855,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ( ( A @ sk6 )
!= sk1 ) ),
inference(simp,[status(thm)],[5826]) ).
thf(5871,plain,
( ( empty_set @ powerset @ sk6 )
!= sk1 ),
inference(simp,[status(thm)],[5855]) ).
thf(6090,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ( ( empty_set @ sk6 )
!= sk1 )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,5871]) ).
thf(6091,plain,
( ( ( empty_set @ sk6 )
!= sk1 )
| ~ ( empty_set @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[6090:[bind(A,$thf( empty_set @ powerset ))]]) ).
thf(8264,plain,
( ( ( empty_set @ powerset @ empty )
!= ( empty_set @ empty ) )
| ( ( empty_set @ sk6 )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,6091]) ).
thf(8265,plain,
( ( ( empty_set @ powerset @ empty )
!= ( empty_set @ empty ) )
| ( ( empty_set @ sk6 )
!= sk1 ) ),
inference(simp,[status(thm)],[8264]) ).
thf(8266,plain,
( ( ( empty_set @ powerset )
!= empty_set )
| ( ( empty_set @ sk6 )
!= sk1 ) ),
inference(simp,[status(thm)],[8265]) ).
thf(25,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(129,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(130,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[129]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[130]) ).
thf(1575,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[62,131]) ).
thf(1576,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[1575]) ).
thf(1577,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[1576:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(2328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ in ) )
!= ( empty_set @ ( C @ in ) ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[159,1577]) ).
thf(2329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ in ) )
!= ( empty_set @ ( C @ in ) ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[2328]) ).
thf(2330,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(pattern_uni,[status(thm)],[2329:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( empty_set @ ( D @ sk14 ) ))]]) ).
thf(2366,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(simp,[status(thm)],[2330]) ).
thf(139,plain,
! [A: $i] :
( ( A @ epsilon_transitive )
| ~ ( A @ ( A @ sk13 @ subset ) ) ),
inference(cnfConj,[status(thm)],[136]) ).
thf(141,plain,
! [A: $i] :
( ( A @ epsilon_transitive )
| ~ ( A @ ( A @ sk13 @ subset ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(2378,plain,
! [B: $i,A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( B @ ( B @ sk13 @ subset ) ) )
| ( B @ epsilon_transitive )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2366,141]) ).
thf(2379,plain,
! [B: $i,A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( B @ ( B @ sk13 @ subset ) ) )
| ( B @ epsilon_transitive ) ),
inference(simp,[status(thm)],[2378]) ).
thf(2384,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( B @ sk13 )
!= empty_set )
| ( B @ epsilon_transitive ) ),
inference(simp,[status(thm)],[2379]) ).
thf(2385,plain,
! [A: $i] :
( ( ( A @ sk13 )
!= empty_set )
| ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[2384]) ).
thf(24482,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk13 ) )
| ( empty_set != empty_set )
| ( B @ epsilon_transitive )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,2385]) ).
thf(24483,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk13 ) )
| ( B @ epsilon_transitive )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[24482]) ).
thf(24484,plain,
! [A: $i] :
( ( A @ epsilon_transitive )
| ~ ( A @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[24483:[bind(A,$thf( C @ sk13 )),bind(B,$thf( C ))]]) ).
thf(24490,plain,
! [A: $i] :
( ( A @ epsilon_transitive )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[24484]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(93,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(miniscope,[status(thm)],[92]) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ powerset @ ( C @ element ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ element ) ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ element ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ element ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(2232,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[1718,97]) ).
thf(2233,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[2232]) ).
thf(2234,plain,
( ( sk1 @ powerset @ ( sk15 @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[2233:[bind(A,$thf( sk15 )),bind(B,$thf( sk1 ))]]) ).
thf(25578,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ powerset @ ( sk15 @ element ) )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,2234]) ).
thf(25579,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ powerset @ ( sk15 @ element ) )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25578]) ).
thf(25580,plain,
( ( sk1 @ powerset @ ( sk15 @ element ) )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25579:[bind(A,$thf( sk1 ))]]) ).
thf(2248,plain,
( ( ( sk1 @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk15 @ subset ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1684,1718]) ).
thf(2249,plain,
( ( ( sk1 @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk15 @ subset ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[2248]) ).
thf(2250,plain,
( ( sk1 @ ( sk15 @ subset ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[2249:[]]) ).
thf(25521,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk15 @ subset ) )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,1718]) ).
thf(25522,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk15 @ subset ) )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25521]) ).
thf(25523,plain,
( ( sk1 @ ( sk15 @ subset ) )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25522:[bind(A,$thf( sk1 ))]]) ).
thf(25675,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( sk1 @ ( sk15 @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,25523]) ).
thf(25676,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( sk1 @ ( sk15 @ subset ) ) ),
inference(simp,[status(thm)],[25675]) ).
thf(25680,plain,
( ( ( sk1 @ sk13 )
!= empty_set )
| ( sk1 @ ( sk15 @ subset ) ) ),
inference(simp,[status(thm)],[25676]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(115,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11509,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10965,48]) ).
thf(11510,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11509]) ).
thf(11511,plain,
( ( sk1 @ ( sk1 @ sk18 @ in ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11510:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(168,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[168]) ).
thf(14974,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[11511,169]) ).
thf(14975,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[14974]) ).
thf(14976,plain,
( ( sk1 @ ( sk1 @ sk18 @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[14975:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(49,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(50,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(72,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(73,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[72]) ).
thf(987,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[73,97]) ).
thf(988,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) ) ),
inference(simp,[status(thm)],[987]) ).
thf(989,plain,
! [A: $i] : ( A @ powerset @ ( A @ element ) ),
inference(pattern_uni,[status(thm)],[988:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(5813,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ element ) )
!= ( empty_set @ powerset @ ( sk1 @ element ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[989,5671]) ).
thf(5814,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ element ) )
!= ( empty_set @ powerset @ ( sk1 @ element ) ) ),
inference(simp,[status(thm)],[5813]) ).
thf(5860,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ powerset ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[5814]) ).
thf(5874,plain,
( ( sk1 @ powerset )
!= ( empty_set @ powerset ) ),
inference(simp,[status(thm)],[5860]) ).
thf(6121,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset ) )
| ( B
!= ( empty_set @ powerset ) )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[52,5874]) ).
thf(6122,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ~ ( A @ empty )
| ~ ( sk1 @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[6121:[bind(A,$thf( sk1 @ powerset )),bind(B,$thf( B ))]]) ).
thf(6152,plain,
( ~ ( empty_set @ powerset @ empty )
| ~ ( sk1 @ powerset @ empty ) ),
inference(simp,[status(thm)],[6122]) ).
thf(8432,plain,
( ~ $true
| ( ( sk1 @ powerset @ empty )
!= ( empty_set @ powerset @ empty ) )
| ~ ( empty_set @ powerset @ empty ) ),
inference(eqfactor_ordered,[status(thm)],[6152]) ).
thf(8434,plain,
( ( ( sk1 @ powerset @ empty )
!= ( empty_set @ powerset @ empty ) )
| ~ ( empty_set @ powerset @ empty ) ),
inference(simp,[status(thm)],[8432]) ).
thf(11093,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_transitive )
| ~ $true
| ( sk1 @ sk19 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[5527,10959]) ).
thf(11094,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_transitive )
| ( sk1 @ sk19 @ ordinal ) ),
inference(simp,[status(thm)],[11093]) ).
thf(11095,plain,
( ( sk1 @ sk13 @ epsilon_transitive )
| ( sk1 @ sk19 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11094:[]]) ).
thf(12369,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[11095,146]) ).
thf(12370,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12369]) ).
thf(12371,plain,
( ( sk1 @ sk19 @ epsilon_connected )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[12370:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(22,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(117,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(118,plain,
( ( sk11 @ function )
& ( sk11 @ empty )
& ( sk11 @ relation ) ),
inference(cnf,[status(esa)],[117]) ).
thf(120,plain,
sk11 @ empty,
inference(cnfConj,[status(thm)],[118]) ).
thf(1071,plain,
! [A: $i] :
( ( ( sk11 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[120,109]) ).
thf(1072,plain,
! [A: $i] :
( ( ( sk11 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[1071]) ).
thf(1073,plain,
sk11 = empty_set,
inference(pattern_uni,[status(thm)],[1072:[bind(A,$thf( sk11 ))]]) ).
thf(2000,plain,
! [A: $i] :
( ( ( sk1 @ epsilon_connected )
!= ( A @ epsilon_connected ) )
| ( A @ ordinal )
| ~ $true
| ~ ( A @ epsilon_transitive )
| ( sk1 @ sk18 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1972,148]) ).
thf(2001,plain,
! [A: $i] :
( ( ( sk1 @ epsilon_connected )
!= ( A @ epsilon_connected ) )
| ( A @ ordinal )
| ~ ( A @ epsilon_transitive )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[2000]) ).
thf(2002,plain,
( ( sk1 @ ordinal )
| ~ ( sk1 @ epsilon_transitive )
| ( sk1 @ sk18 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[2001:[bind(A,$thf( sk1 ))]]) ).
thf(15567,plain,
( $false
| ~ ( sk1 @ epsilon_transitive )
| ( sk1 @ sk18 @ ordinal ) ),
inference(rewrite,[status(thm)],[2002,3378]) ).
thf(15568,plain,
( ~ ( sk1 @ epsilon_transitive )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[15567]) ).
thf(12775,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11211,48]) ).
thf(12776,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12775]) ).
thf(12777,plain,
( ( sk1 @ ( sk1 @ sk19 @ in ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[12776:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(18112,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[12777,169]) ).
thf(18113,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[18112]) ).
thf(18114,plain,
( ( sk1 @ ( sk1 @ sk19 @ element ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[18113:[bind(A,$thf( sk1 @ sk19 )),bind(B,$thf( sk1 ))]]) ).
thf(15676,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[15568,146]) ).
thf(15677,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[15676]) ).
thf(15678,plain,
( ( sk1 @ sk18 @ epsilon_connected )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[15677:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(25546,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk18 @ epsilon_connected )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,15678]) ).
thf(25547,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk18 @ epsilon_connected )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25546]) ).
thf(25548,plain,
( ( sk1 @ sk18 @ epsilon_connected )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25547:[bind(A,$thf( sk1 ))]]) ).
thf(26163,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( sk1 @ sk18 @ epsilon_connected )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,25548]) ).
thf(26164,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(simp,[status(thm)],[26163]) ).
thf(26169,plain,
( ( ( sk1 @ sk13 )
!= empty_set )
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(simp,[status(thm)],[26164]) ).
thf(3462,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ordinal )
!= ( B @ ordinal ) )
| ( A @ ordinal )
| ~ ( B @ ( A @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[177,186]) ).
thf(3463,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ordinal )
!= ( B @ ordinal ) )
| ( A @ ordinal )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[3462]) ).
thf(3464,plain,
! [A: $i] :
( ( A @ ordinal )
| ~ ( sk15 @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[3463:[bind(A,$thf( A )),bind(B,$thf( sk15 ))]]) ).
thf(24728,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ in ) )
!= ( sk15 @ ( C @ in ) ) )
| ( C @ ordinal )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[159,3464]) ).
thf(24729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ in ) )
!= ( sk15 @ ( C @ in ) ) )
| ( C @ ordinal )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[24728]) ).
thf(24730,plain,
! [A: $i] :
( ( sk15 @ ( A @ sk14 ) @ ordinal )
| ( A @ ( sk15 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[24729:[bind(A,$thf( sk15 )),bind(B,$thf( D )),bind(C,$thf( sk15 @ ( D @ sk14 ) ))]]) ).
thf(24827,plain,
! [A: $i] :
( ( sk15 @ ( A @ sk14 ) @ ordinal )
| ( A @ ( sk15 @ subset ) ) ),
inference(simp,[status(thm)],[24730]) ).
thf(2981,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) )
| ~ $true
| ~ ( A @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[48,169]) ).
thf(2982,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) )
| ~ ( A @ ordinal ) ),
inference(simp,[status(thm)],[2981]) ).
thf(2983,plain,
! [A: $i] :
( ( sk1 @ ( A @ element ) )
| ~ ( A @ ordinal ) ),
inference(pattern_uni,[status(thm)],[2982:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 ))]]) ).
thf(25154,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( sk1 @ ( B @ element ) )
| ~ $true
| ( A @ ( sk15 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24827,2983]) ).
thf(25155,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( sk1 @ ( B @ element ) )
| ( A @ ( sk15 @ subset ) ) ),
inference(simp,[status(thm)],[25154]) ).
thf(25156,plain,
! [A: $i] :
( ( sk1 @ ( sk15 @ ( A @ sk14 ) @ element ) )
| ( A @ ( sk15 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[25155:[bind(A,$thf( C )),bind(B,$thf( sk15 @ ( C @ sk14 ) ))]]) ).
thf(25167,plain,
! [A: $i] :
( ( sk1 @ ( sk15 @ ( A @ sk14 ) @ element ) )
| ( A @ ( sk15 @ subset ) ) ),
inference(simp,[status(thm)],[25156]) ).
thf(11202,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected )
| ~ $true
| ( sk1 @ sk18 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1972,10981]) ).
thf(11203,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[11202]) ).
thf(11204,plain,
( ( sk1 @ sk13 @ epsilon_connected )
| ( sk1 @ sk18 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11203:[]]) ).
thf(12611,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11204,3378]) ).
thf(12612,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12611]) ).
thf(12674,plain,
( ( ( sk1 @ sk18 )
!= sk1 )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12612]) ).
thf(5737,plain,
! [A: $i] :
( ( ( sk1 @ epsilon_connected )
!= ( A @ epsilon_connected ) )
| ( A @ ordinal )
| ~ $true
| ~ ( A @ epsilon_transitive )
| ( sk1 @ sk19 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[5527,148]) ).
thf(5738,plain,
! [A: $i] :
( ( ( sk1 @ epsilon_connected )
!= ( A @ epsilon_connected ) )
| ( A @ ordinal )
| ~ ( A @ epsilon_transitive )
| ( sk1 @ sk19 @ ordinal ) ),
inference(simp,[status(thm)],[5737]) ).
thf(5739,plain,
( ( sk1 @ ordinal )
| ~ ( sk1 @ epsilon_transitive )
| ( sk1 @ sk19 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[5738:[bind(A,$thf( sk1 ))]]) ).
thf(28328,plain,
( $false
| ~ ( sk1 @ epsilon_transitive )
| ( sk1 @ sk19 @ ordinal ) ),
inference(rewrite,[status(thm)],[5739,3378]) ).
thf(28329,plain,
( ~ ( sk1 @ epsilon_transitive )
| ( sk1 @ sk19 @ ordinal ) ),
inference(simp,[status(thm)],[28328]) ).
thf(28421,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[28329,145]) ).
thf(28422,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[28421]) ).
thf(28423,plain,
( ( sk1 @ sk19 @ epsilon_transitive )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[28422:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(28452,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[28329,146]) ).
thf(28453,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[28452]) ).
thf(28454,plain,
( ( sk1 @ sk19 @ epsilon_connected )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[28453:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(28752,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk19 @ epsilon_connected )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,28454]) ).
thf(28753,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk19 @ epsilon_connected )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[28752]) ).
thf(28754,plain,
( ( sk1 @ sk19 @ epsilon_connected )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[28753:[bind(A,$thf( sk1 ))]]) ).
thf(174,plain,
~ ( sk15 @ empty ),
inference(cnfConj,[status(thm)],[173]) ).
thf(336,plain,
( ( ( sk15 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,174]) ).
thf(337,plain,
( ( sk15 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[336]) ).
thf(340,plain,
sk15 != empty_set,
inference(simp,[status(thm)],[337]) ).
thf(2021,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[1972,145]) ).
thf(2022,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[2021]) ).
thf(2023,plain,
( ( sk1 @ sk18 @ epsilon_transitive )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[2022:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(11053,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_transitive )
| ~ $true
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[2023,10959]) ).
thf(11054,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_transitive )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11053]) ).
thf(11055,plain,
( ( sk1 @ sk13 @ epsilon_transitive )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11054:[]]) ).
thf(10960,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ~ ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[10883,48]) ).
thf(10961,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[10960]) ).
thf(10962,plain,
( ( sk1 @ ( sk1 @ sk13 @ in ) )
| ~ ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[10961:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(11836,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ~ ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[10962,169]) ).
thf(11837,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[11836]) ).
thf(11838,plain,
( ( sk1 @ ( sk1 @ sk13 @ element ) )
| ~ ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[11837:[bind(A,$thf( sk1 @ sk13 )),bind(B,$thf( sk1 ))]]) ).
thf(13762,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ element ) )
| ~ $true
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[2023,11838]) ).
thf(13763,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[13762]) ).
thf(13764,plain,
( ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[13763:[]]) ).
thf(6137,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset ) )
| ( ( empty_set @ powerset )
!= empty_set )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,5874]) ).
thf(6138,plain,
( ( ( empty_set @ powerset )
!= empty_set )
| ~ ( sk1 @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[6137:[bind(A,$thf( sk1 @ powerset ))]]) ).
thf(15658,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[15568,48]) ).
thf(15659,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[15658]) ).
thf(15660,plain,
( ( sk1 @ ( sk1 @ sk18 @ in ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[15659:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(17089,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( A @ ( B @ in ) ) )
| ( A @ ( B @ subset ) )
| ~ $true
| ~ ( A @ epsilon_transitive )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[15660,137]) ).
thf(17090,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( A @ ( B @ in ) ) )
| ( A @ ( B @ subset ) )
| ~ ( A @ epsilon_transitive )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[17089]) ).
thf(17091,plain,
( ( sk1 @ ( sk1 @ sk18 @ subset ) )
| ~ ( sk1 @ epsilon_transitive )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[17090:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk18 ))]]) ).
thf(17257,plain,
( ( sk1 @ ( sk1 @ sk18 @ subset ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[17091]) ).
thf(17995,plain,
( ( ( sk1 @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ sk18 @ subset ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1684,17257]) ).
thf(17996,plain,
( ( ( sk1 @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ sk18 @ subset ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[17995]) ).
thf(17997,plain,
( ( sk1 @ ( sk1 @ sk18 @ subset ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[17996:[]]) ).
thf(22049,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[17997,97]) ).
thf(22050,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[22049]) ).
thf(22051,plain,
( ( sk1 @ powerset @ ( sk1 @ sk18 @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[22050:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 ))]]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(110,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(111,plain,
( ( sk10 @ function )
& ( sk10 @ relation_empty_yielding )
& ( sk10 @ relation ) ),
inference(cnf,[status(esa)],[110]) ).
thf(112,plain,
sk10 @ relation,
inference(cnfConj,[status(thm)],[111]) ).
thf(5,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(55,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(56,plain,
! [A: $i] :
( ( ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ empty )
| ~ ( A @ relation ) )
& ( ( A @ function )
| ~ ( A @ function )
| ~ ( A @ empty )
| ~ ( A @ relation ) )
& ( ( A @ relation )
| ~ ( A @ function )
| ~ ( A @ empty )
| ~ ( A @ relation ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(59,plain,
! [A: $i] :
( ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ empty )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(555,plain,
! [A: $i] :
( ( ( sk10 @ relation )
!= ( A @ relation ) )
| ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[112,59]) ).
thf(556,plain,
! [A: $i] :
( ( ( sk10 @ relation )
!= ( A @ relation ) )
| ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[555]) ).
thf(557,plain,
( ( sk10 @ one_to_one )
| ~ ( sk10 @ function )
| ~ ( sk10 @ empty ) ),
inference(pattern_uni,[status(thm)],[556:[bind(A,$thf( sk10 ))]]) ).
thf(114,plain,
sk10 @ function,
inference(cnfConj,[status(thm)],[111]) ).
thf(23129,plain,
( ( sk10 @ one_to_one )
| ~ $true
| ~ ( sk10 @ empty ) ),
inference(rewrite,[status(thm)],[557,114]) ).
thf(23130,plain,
( ( sk10 @ one_to_one )
| ~ ( sk10 @ empty ) ),
inference(simp,[status(thm)],[23129]) ).
thf(5729,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[5527,3378]) ).
thf(5730,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[5729]) ).
thf(5770,plain,
( ( ( sk1 @ sk19 )
!= sk1 )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[5730]) ).
thf(1358,plain,
! [A: $i] :
( ( empty_set != empty_set )
| ( sk1 @ ( A @ in ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,1333]) ).
thf(1359,plain,
! [A: $i] :
( ( sk1 @ ( A @ in ) )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[1358:[]]) ).
thf(3217,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) )
| ~ $true
| ~ ( A @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[48,171]) ).
thf(3218,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) )
| ~ ( A @ ordinal ) ),
inference(simp,[status(thm)],[3217]) ).
thf(3219,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ in ) )
| ~ ( A @ ordinal ) ),
inference(pattern_uni,[status(thm)],[3218:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 ))]]) ).
thf(12768,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11211,3219]) ).
thf(12769,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12768]) ).
thf(12770,plain,
( ~ ( sk1 @ sk19 @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[12769:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(13798,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ element ) )
| ~ $true
| ( sk1 @ sk18 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1972,11838]) ).
thf(13799,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[13798]) ).
thf(13800,plain,
( ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk18 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[13799:[]]) ).
thf(12655,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11204,48]) ).
thf(12656,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12655]) ).
thf(12657,plain,
( ( sk1 @ ( sk1 @ sk18 @ in ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[12656:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(17796,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[12657,169]) ).
thf(17797,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[17796]) ).
thf(17798,plain,
( ( sk1 @ ( sk1 @ sk18 @ element ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[17797:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 ))]]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk14 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk14 ) @ in ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(29103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk16 @ ( A @ sk14 ) @ in ) )
!= ( C @ ( B @ ( C @ sk14 ) @ in ) ) )
| ( C @ ( B @ subset ) )
| ~ $true
| ( A @ ( sk16 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24963,160]) ).
thf(29104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk16 @ ( A @ sk14 ) @ in ) )
!= ( C @ ( B @ ( C @ sk14 ) @ in ) ) )
| ( C @ ( B @ subset ) )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[29103]) ).
thf(29105,plain,
( ( sk1 @ ( sk16 @ subset ) )
| ( sk1 @ ( sk16 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[29104:[bind(A,$thf( sk1 )),bind(B,$thf( sk16 )),bind(C,$thf( sk1 ))]]) ).
thf(29282,plain,
sk1 @ ( sk16 @ subset ),
inference(simp,[status(thm)],[29105]) ).
thf(24943,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_connected )
| ~ $true
| ( A @ ( sk16 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24643,146]) ).
thf(24944,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_connected )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[24943]) ).
thf(24945,plain,
! [A: $i] :
( ( sk16 @ ( A @ sk14 ) @ epsilon_connected )
| ( A @ ( sk16 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[24944:[bind(A,$thf( C )),bind(B,$thf( sk16 @ ( C @ sk14 ) ))]]) ).
thf(24971,plain,
! [A: $i] :
( ( sk16 @ ( A @ sk14 ) @ epsilon_connected )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[24945]) ).
thf(23,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(122,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(123,plain,
( ( sk12 @ function )
& ( sk12 @ relation ) ),
inference(cnf,[status(esa)],[122]) ).
thf(125,plain,
sk12 @ function,
inference(cnfConj,[status(thm)],[123]) ).
thf(15611,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[15568,3378]) ).
thf(15612,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[15611]) ).
thf(15706,plain,
( ( ( sk1 @ sk18 )
!= sk1 )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[15612]) ).
thf(5807,plain,
! [B: $i,A: $i] :
( ( ( B @ powerset @ ( A @ element ) )
!= ( empty_set @ powerset @ ( sk1 @ element ) ) )
| ~ $true
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[97,5671]) ).
thf(5808,plain,
! [B: $i,A: $i] :
( ( ( B @ powerset @ ( A @ element ) )
!= ( empty_set @ powerset @ ( sk1 @ element ) ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[5807]) ).
thf(5809,plain,
~ ( empty_set @ ( sk1 @ subset ) ),
inference(pattern_uni,[status(thm)],[5808:[bind(A,$thf( sk1 )),bind(B,$thf( empty_set ))]]) ).
thf(5914,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ ( sk1 @ subset ) ) )
| ~ $true
| ( A @ ( A @ ( B @ sk14 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[159,5809]) ).
thf(5915,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ ( sk1 @ subset ) ) )
| ( A @ ( A @ ( B @ sk14 ) @ in ) ) ),
inference(simp,[status(thm)],[5914]) ).
thf(5916,plain,
sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ),
inference(pattern_uni,[status(thm)],[5915:[bind(A,$thf( sk1 )),bind(B,$thf( empty_set ))]]) ).
thf(6354,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( sk1 @ ( A @ in ) ) )
| ( A @ ordinal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5916,46]) ).
thf(6355,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( sk1 @ ( A @ in ) ) )
| ( A @ ordinal ) ),
inference(simp,[status(thm)],[6354]) ).
thf(6356,plain,
sk1 @ ( empty_set @ sk14 ) @ ordinal,
inference(pattern_uni,[status(thm)],[6355:[bind(A,$thf( sk1 @ ( empty_set @ sk14 ) ))]]) ).
thf(6517,plain,
! [A: $i] :
( ( ( sk1 @ ( empty_set @ sk14 ) @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6356,145]) ).
thf(6518,plain,
! [A: $i] :
( ( ( sk1 @ ( empty_set @ sk14 ) @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[6517]) ).
thf(6519,plain,
sk1 @ ( empty_set @ sk14 ) @ epsilon_transitive,
inference(pattern_uni,[status(thm)],[6518:[bind(A,$thf( sk1 @ ( empty_set @ sk14 ) ))]]) ).
thf(10932,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[2023,10883]) ).
thf(10933,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[10932]) ).
thf(10934,plain,
( ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[10933:[]]) ).
thf(11424,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[10934,3219]) ).
thf(11425,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11424]) ).
thf(11426,plain,
( ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11425:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(29325,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk16 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29282,97]) ).
thf(29326,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk16 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) ) ),
inference(simp,[status(thm)],[29325]) ).
thf(29327,plain,
sk1 @ powerset @ ( sk16 @ element ),
inference(pattern_uni,[status(thm)],[29326:[bind(A,$thf( sk16 )),bind(B,$thf( sk1 ))]]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in ) )
| ( B @ empty )
| ~ ( B @ ( A @ element ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(29387,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk16 @ element ) )
!= ( B @ ( A @ element ) ) )
| ( B @ ( A @ in ) )
| ( B @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29327,133]) ).
thf(29388,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk16 @ element ) )
!= ( B @ ( A @ element ) ) )
| ( B @ ( A @ in ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[29387]) ).
thf(29389,plain,
( ( sk1 @ powerset @ ( sk16 @ in ) )
| ( sk1 @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[29388:[bind(A,$thf( sk16 )),bind(B,$thf( sk1 @ powerset ))]]) ).
thf(29483,plain,
! [A: $i] :
( ( ( sk1 @ powerset @ ( sk16 @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ $true
| ( sk1 @ powerset @ empty ) ),
inference(paramod_ordered,[status(thm)],[29389,3239]) ).
thf(29484,plain,
! [A: $i] :
( ( ( sk1 @ powerset @ ( sk16 @ in ) )
!= ( A @ ( A @ in ) ) )
| ( sk1 @ powerset @ empty ) ),
inference(simp,[status(thm)],[29483]) ).
thf(29589,plain,
! [A: $i] :
( ( ( sk1 @ powerset )
!= A )
| ( sk16 != A )
| ( sk1 @ powerset @ empty ) ),
inference(simp,[status(thm)],[29484]) ).
thf(29621,plain,
( ( ( sk1 @ powerset )
!= sk16 )
| ( sk1 @ powerset @ empty ) ),
inference(simp,[status(thm)],[29589]) ).
thf(17095,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[15660,169]) ).
thf(17096,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[17095]) ).
thf(17097,plain,
( ( sk1 @ ( sk1 @ sk18 @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[17096:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 ))]]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ~ ( ~ ( A @ ( B @ in ) )
& ( A != B )
& ~ ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(187,plain,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ~ ( ~ ( A @ ( B @ in ) )
& ( A != B )
& ~ ( B @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ in ) )
| ( A = B )
| ( B @ ( A @ in ) )
| ~ ( B @ ordinal )
| ~ ( A @ ordinal ) ),
inference(cnf,[status(esa)],[187]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ in ) )
| ( B @ ( A @ in ) )
| ~ ( B @ ordinal )
| ~ ( A @ ordinal )
| ( A = B ) ),
inference(lifteq,[status(thm)],[188]) ).
thf(11283,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( ( sk1 @ sk13 )
!= sk1 )
| ~ $true
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[2023,10988]) ).
thf(11284,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( ( sk1 @ sk13 )
!= sk1 )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11283]) ).
thf(11285,plain,
( ( ( sk1 @ sk13 )
!= sk1 )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11284:[]]) ).
thf(15,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(87,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_non_empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(88,plain,
( ( sk7 @ function )
& ( sk7 @ relation_non_empty )
& ( sk7 @ relation ) ),
inference(cnf,[status(esa)],[87]) ).
thf(90,plain,
sk7 @ relation_non_empty,
inference(cnfConj,[status(thm)],[88]) ).
thf(1246,plain,
! [A: $i] :
( ( A != sk7 )
| ( empty_set @ relation_non_empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,90]) ).
thf(1247,plain,
( ( empty_set @ relation_non_empty )
| ~ ( sk7 @ empty ) ),
inference(pattern_uni,[status(thm)],[1246:[bind(A,$thf( sk7 ))]]) ).
thf(1888,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[1684,146]) ).
thf(1889,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[1888]) ).
thf(1890,plain,
( ( sk1 @ sk13 @ epsilon_connected )
| ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[1889:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(11305,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( ( sk1 @ sk13 )
!= sk1 )
| ~ $true
| ( sk1 @ sk18 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1972,10988]) ).
thf(11306,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( ( sk1 @ sk13 )
!= sk1 )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[11305]) ).
thf(11307,plain,
( ( ( sk1 @ sk13 )
!= sk1 )
| ( sk1 @ sk18 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11306:[]]) ).
thf(13100,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[11307,146]) ).
thf(13101,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13100]) ).
thf(13102,plain,
( ( sk1 @ sk18 @ epsilon_connected )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[13101:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(2024,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[1972,48]) ).
thf(2025,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[2024]) ).
thf(2026,plain,
( ( sk1 @ ( sk1 @ sk18 @ in ) )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[2025:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(3229,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[2026,171]) ).
thf(3230,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[3229]) ).
thf(3231,plain,
( ~ ( sk1 @ sk18 @ ( sk1 @ in ) )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[3230:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 ))]]) ).
thf(5761,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[5527,48]) ).
thf(5762,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[5761]) ).
thf(5763,plain,
( ( sk1 @ ( sk1 @ sk19 @ in ) )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[5762:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(7030,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[5763,169]) ).
thf(7031,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[7030]) ).
thf(7032,plain,
( ( sk1 @ ( sk1 @ sk19 @ element ) )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[7031:[bind(A,$thf( sk1 @ sk19 )),bind(B,$thf( sk1 ))]]) ).
thf(12,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(76,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(77,plain,
( ( sk5 @ relation )
& ~ ( sk5 @ empty ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
~ ( sk5 @ empty ),
inference(cnfConj,[status(thm)],[77]) ).
thf(12781,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11211,146]) ).
thf(12782,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12781]) ).
thf(12783,plain,
( ( sk1 @ sk19 @ epsilon_connected )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[12782:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(14419,plain,
( ~ $true
| ( ( sk1 @ sk19 @ epsilon_connected )
!= ( sk1 @ sk13 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(eqfactor_ordered,[status(thm)],[12783]) ).
thf(14423,plain,
( ( ( sk1 @ sk19 @ epsilon_connected )
!= ( sk1 @ sk13 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[14419]) ).
thf(25524,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ~ $true
| ( sk1 @ sk18 @ ordinal )
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,15568]) ).
thf(25525,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk18 @ ordinal )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25524]) ).
thf(25526,plain,
( ( sk1 @ sk18 @ ordinal )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25525:[bind(A,$thf( sk1 ))]]) ).
thf(18,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(102,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(103,plain,
( ( sk9 @ one_to_one )
& ( sk9 @ function )
& ( sk9 @ relation ) ),
inference(cnf,[status(esa)],[102]) ).
thf(106,plain,
sk9 @ one_to_one,
inference(cnfConj,[status(thm)],[103]) ).
thf(11084,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_transitive )
| ~ $true
| ( sk1 @ sk18 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1972,10959]) ).
thf(11085,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_transitive )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[11084]) ).
thf(11086,plain,
( ( sk1 @ sk13 @ epsilon_transitive )
| ( sk1 @ sk18 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11085:[]]) ).
thf(12235,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[11086,3219]) ).
thf(12236,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12235]) ).
thf(12237,plain,
( ~ ( sk1 @ sk18 @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[12236:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(5817,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ~ ( empty_set @ ( sk1 @ element ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,5671]) ).
thf(5818,plain,
( ~ ( empty_set @ ( sk1 @ element ) )
| ~ ( empty_set @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[5817:[bind(A,$thf( empty_set @ powerset ))]]) ).
thf(7508,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ element ) )
!= ( empty_set @ ( sk1 @ element ) ) )
| ~ $true
| ~ ( empty_set @ powerset @ empty ) ),
inference(paramod_ordered,[status(thm)],[989,5818]) ).
thf(7509,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ element ) )
!= ( empty_set @ ( sk1 @ element ) ) )
| ~ ( empty_set @ powerset @ empty ) ),
inference(simp,[status(thm)],[7508]) ).
thf(7568,plain,
! [A: $i] :
( ( ( A @ powerset )
!= empty_set )
| ( A != sk1 )
| ~ ( empty_set @ powerset @ empty ) ),
inference(simp,[status(thm)],[7509]) ).
thf(7581,plain,
( ( ( sk1 @ powerset )
!= empty_set )
| ~ ( empty_set @ powerset @ empty ) ),
inference(simp,[status(thm)],[7568]) ).
thf(2331,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ in ) )
!= ( sk1 @ ( C @ in ) ) )
| ( C @ ordinal )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[159,46]) ).
thf(2332,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ in ) )
!= ( sk1 @ ( C @ in ) ) )
| ( C @ ordinal )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[2331]) ).
thf(2333,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk14 ) @ ordinal )
| ( A @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[2332:[bind(A,$thf( sk1 )),bind(B,$thf( D )),bind(C,$thf( sk1 @ ( D @ sk14 ) ))]]) ).
thf(2367,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk14 ) @ ordinal )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[2333]) ).
thf(221,plain,
empty_set @ epsilon_transitive,
inference(cnfConj,[status(thm)],[216]) ).
thf(11503,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10965,3219]) ).
thf(11504,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11503]) ).
thf(11505,plain,
( ~ ( sk1 @ sk18 @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11504:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(11573,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10975,48]) ).
thf(11574,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11573]) ).
thf(11575,plain,
( ( sk1 @ ( sk1 @ sk19 @ in ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11574:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(15287,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[11575,169]) ).
thf(15288,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[15287]) ).
thf(15289,plain,
( ( sk1 @ ( sk1 @ sk19 @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[15288:[bind(A,$thf( sk1 @ sk19 )),bind(B,$thf( sk1 ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(74,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(89,plain,
sk7 @ relation,
inference(cnfConj,[status(thm)],[88]) ).
thf(116,plain,
! [A: $i] :
( ( A @ function )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[115]) ).
thf(15642,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[15568,3219]) ).
thf(15643,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[15642]) ).
thf(15644,plain,
( ~ ( sk1 @ sk18 @ ( sk1 @ in ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[15643:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(25585,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ~ ( sk1 @ sk18 @ ( sk1 @ in ) )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,15644]) ).
thf(25586,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ~ ( sk1 @ sk18 @ ( sk1 @ in ) )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25585]) ).
thf(25587,plain,
( ~ ( sk1 @ sk18 @ ( sk1 @ in ) )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25586:[bind(A,$thf( sk1 ))]]) ).
thf(8,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(68,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(69,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[68]) ).
thf(70,plain,
~ ( sk4 @ empty ),
inference(cnf,[status(esa)],[69]) ).
thf(229,plain,
( ( ( sk4 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,70]) ).
thf(230,plain,
( ( sk4 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[229]) ).
thf(233,plain,
sk4 != empty_set,
inference(simp,[status(thm)],[230]) ).
thf(11168,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected )
| ~ $true
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[2023,10981]) ).
thf(11169,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11168]) ).
thf(11170,plain,
( ( sk1 @ sk13 @ epsilon_connected )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11169:[]]) ).
thf(220,plain,
empty_set @ one_to_one,
inference(cnfConj,[status(thm)],[216]) ).
thf(100,plain,
sk8 @ relation,
inference(cnfConj,[status(thm)],[99]) ).
thf(455,plain,
! [A: $i] :
( ( ( sk8 @ relation )
!= ( A @ relation ) )
| ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,59]) ).
thf(456,plain,
! [A: $i] :
( ( ( sk8 @ relation )
!= ( A @ relation ) )
| ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[455]) ).
thf(457,plain,
( ( sk8 @ one_to_one )
| ~ ( sk8 @ function )
| ~ ( sk8 @ empty ) ),
inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( sk8 ))]]) ).
thf(16656,plain,
! [A: $i] :
( ( ( A @ function )
!= ( sk8 @ function ) )
| ( sk8 @ one_to_one )
| ~ $true
| ~ ( sk8 @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[116,457]) ).
thf(16657,plain,
! [A: $i] :
( ( ( A @ function )
!= ( sk8 @ function ) )
| ( sk8 @ one_to_one )
| ~ ( sk8 @ empty )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[16656]) ).
thf(16658,plain,
( ( sk8 @ one_to_one )
| ~ ( sk8 @ empty )
| ~ ( sk8 @ empty ) ),
inference(pattern_uni,[status(thm)],[16657:[bind(A,$thf( sk8 ))]]) ).
thf(16697,plain,
( ( sk8 @ one_to_one )
| ~ ( sk8 @ empty ) ),
inference(simp,[status(thm)],[16658]) ).
thf(11518,plain,
( ~ $true
| ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ sk13 @ ordinal ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(eqfactor_ordered,[status(thm)],[10965]) ).
thf(11520,plain,
( ( ( sk1 @ sk18 )
!= ( sk1 @ sk13 ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11518]) ).
thf(12245,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[11086,48]) ).
thf(12246,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12245]) ).
thf(12247,plain,
( ( sk1 @ ( sk1 @ sk18 @ in ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[12246:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(12648,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11204,3219]) ).
thf(12649,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12648]) ).
thf(12650,plain,
( ~ ( sk1 @ sk18 @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[12649:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(3205,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[769,171]) ).
thf(3206,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) ) ),
inference(simp,[status(thm)],[3205]) ).
thf(3207,plain,
~ ( sk15 @ ( sk1 @ in ) ),
inference(pattern_uni,[status(thm)],[3206:[bind(A,$thf( sk15 )),bind(B,$thf( sk1 ))]]) ).
thf(6361,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( A @ ( B @ in ) ) )
| ( A @ ( B @ subset ) )
| ~ $true
| ~ ( A @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[5916,137]) ).
thf(6362,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( A @ ( B @ in ) ) )
| ( A @ ( B @ subset ) )
| ~ ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[6361]) ).
thf(6363,plain,
( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ subset ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[6362:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ ( empty_set @ sk14 ) ))]]) ).
thf(10097,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[6363,97]) ).
thf(10098,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[10097]) ).
thf(10099,plain,
( ( sk1 @ powerset @ ( sk1 @ ( empty_set @ sk14 ) @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[10098:[bind(A,$thf( sk1 @ ( empty_set @ sk14 ) )),bind(B,$thf( sk1 ))]]) ).
thf(28552,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk19 @ epsilon_transitive )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,28423]) ).
thf(28553,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk19 @ epsilon_transitive )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[28552]) ).
thf(28554,plain,
( ( sk1 @ sk19 @ epsilon_transitive )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[28553:[bind(A,$thf( sk1 ))]]) ).
thf(6369,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5916,169]) ).
thf(6370,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) ) ),
inference(simp,[status(thm)],[6369]) ).
thf(6371,plain,
sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ element ),
inference(pattern_uni,[status(thm)],[6370:[bind(A,$thf( sk1 @ ( empty_set @ sk14 ) )),bind(B,$thf( sk1 ))]]) ).
thf(6526,plain,
! [A: $i] :
( ( ( sk1 @ ( empty_set @ sk14 ) @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6356,146]) ).
thf(6527,plain,
! [A: $i] :
( ( ( sk1 @ ( empty_set @ sk14 ) @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected ) ),
inference(simp,[status(thm)],[6526]) ).
thf(6528,plain,
sk1 @ ( empty_set @ sk14 ) @ epsilon_connected,
inference(pattern_uni,[status(thm)],[6527:[bind(A,$thf( sk1 @ ( empty_set @ sk14 ) ))]]) ).
thf(13184,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[11314,3219]) ).
thf(13185,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13184]) ).
thf(13186,plain,
( ~ ( sk1 @ sk19 @ ( sk1 @ in ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[13185:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(10954,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ~ ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[10883,3219]) ).
thf(10955,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[10954]) ).
thf(10956,plain,
( ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ~ ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[10955:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(11717,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk19 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[5527,10956]) ).
thf(11718,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ sk19 @ ordinal ) ),
inference(simp,[status(thm)],[11717]) ).
thf(11719,plain,
( ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ sk19 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11718:[]]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(163,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(164,plain,
! [A: $i] :
( ( ( A @ ordinal )
| ~ ( A @ empty ) )
& ( ( A @ epsilon_connected )
| ~ ( A @ empty ) )
& ( ( A @ epsilon_transitive )
| ~ ( A @ empty ) ) ),
inference(cnf,[status(esa)],[163]) ).
thf(165,plain,
! [A: $i] :
( ( A @ epsilon_transitive )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[164]) ).
thf(853,plain,
! [A: $i] :
( ( ( sk16 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[184,48]) ).
thf(854,plain,
! [A: $i] :
( ( ( sk16 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) ) ),
inference(simp,[status(thm)],[853]) ).
thf(855,plain,
sk1 @ ( sk16 @ in ),
inference(pattern_uni,[status(thm)],[854:[bind(A,$thf( sk16 ))]]) ).
thf(2984,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk16 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[855,169]) ).
thf(2985,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk16 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) ) ),
inference(simp,[status(thm)],[2984]) ).
thf(2986,plain,
sk1 @ ( sk16 @ element ),
inference(pattern_uni,[status(thm)],[2985:[bind(A,$thf( sk16 )),bind(B,$thf( sk1 ))]]) ).
thf(5767,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[5527,146]) ).
thf(5768,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[5767]) ).
thf(5769,plain,
( ( sk1 @ sk19 @ epsilon_connected )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[5768:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(25539,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ sk18 @ element ) )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,17097]) ).
thf(25540,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ sk18 @ element ) )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25539]) ).
thf(25541,plain,
( ( sk1 @ ( sk1 @ sk18 @ element ) )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25540:[bind(A,$thf( sk1 ))]]) ).
thf(1295,plain,
! [A: $i] :
( ( empty_set != empty_set )
| ( A @ one_to_one )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,220]) ).
thf(1296,plain,
! [A: $i] :
( ( A @ one_to_one )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[1295:[]]) ).
thf(5810,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ element ) )
!= ( empty_set @ powerset @ ( sk1 @ element ) ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[169,5671]) ).
thf(5811,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ element ) )
!= ( empty_set @ powerset @ ( sk1 @ element ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[5810]) ).
thf(5812,plain,
~ ( empty_set @ powerset @ ( sk1 @ in ) ),
inference(pattern_uni,[status(thm)],[5811:[bind(A,$thf( sk1 )),bind(B,$thf( empty_set @ powerset ))]]) ).
thf(6032,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ in ) )
!= ( empty_set @ powerset @ ( sk1 @ in ) ) )
| ~ $true
| ( A @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[209,5812]) ).
thf(6033,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ in ) )
!= ( empty_set @ powerset @ ( sk1 @ in ) ) )
| ( A @ epsilon_connected ) ),
inference(simp,[status(thm)],[6032]) ).
thf(6047,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ( ( A @ sk18 )
!= sk1 )
| ( A @ epsilon_connected ) ),
inference(simp,[status(thm)],[6033]) ).
thf(6060,plain,
( ( ( empty_set @ powerset @ sk18 )
!= sk1 )
| ( empty_set @ powerset @ epsilon_connected ) ),
inference(simp,[status(thm)],[6047]) ).
thf(224,plain,
empty_set @ epsilon_connected,
inference(cnfConj,[status(thm)],[216]) ).
thf(1760,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[1684,48]) ).
thf(1761,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[1760]) ).
thf(1762,plain,
( ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[1761:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(8540,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_connected )
| ~ $true
| ( A @ ( sk1 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[2367,146]) ).
thf(8541,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_connected )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[8540]) ).
thf(8542,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk14 ) @ epsilon_connected )
| ( A @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[8541:[bind(A,$thf( C )),bind(B,$thf( sk1 @ ( C @ sk14 ) ))]]) ).
thf(8562,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk14 ) @ epsilon_connected )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[8542]) ).
thf(12731,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11211,3378]) ).
thf(12732,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12731]) ).
thf(12796,plain,
( ( ( sk1 @ sk19 )
!= sk1 )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12732]) ).
thf(12351,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[11095,3219]) ).
thf(12352,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12351]) ).
thf(12353,plain,
( ~ ( sk1 @ sk19 @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[12352:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(13461,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11517,3219]) ).
thf(13462,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(simp,[status(thm)],[13461]) ).
thf(13463,plain,
( ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[13462:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(14,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(82,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(83,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[82]) ).
thf(86,plain,
empty_set @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[83]) ).
thf(350,plain,
! [B: $i,A: $i] :
( ( B != empty_set )
| ( A @ relation_empty_yielding )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[52,86]) ).
thf(351,plain,
! [A: $i] :
( ( A @ relation_empty_yielding )
| ~ ( empty_set @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[350:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(9354,plain,
! [A: $i] :
( ( A @ relation_empty_yielding )
| ~ $true
| ~ ( A @ empty ) ),
inference(rewrite,[status(thm)],[351,62]) ).
thf(9355,plain,
! [A: $i] :
( ( A @ relation_empty_yielding )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[9354]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(1843,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ $true
| ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[1684,145]) ).
thf(1844,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[1843]) ).
thf(1845,plain,
( ( sk1 @ sk13 @ epsilon_transitive )
| ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[1844:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(1876,plain,
( ~ $true
| ( ( sk1 @ sk13 @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ epsilon_transitive ) ),
inference(eqfactor_ordered,[status(thm)],[1845]) ).
thf(1878,plain,
( ( ( sk1 @ sk13 )
!= sk1 )
| ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[1876]) ).
thf(11433,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[10934,48]) ).
thf(11434,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11433]) ).
thf(11435,plain,
( ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11434:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(53,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,plain,
sk2 @ empty,
inference(cnf,[status(esa)],[53]) ).
thf(1158,plain,
! [A: $i] :
( ( ( sk2 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[54,109]) ).
thf(1159,plain,
! [A: $i] :
( ( ( sk2 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[1158]) ).
thf(1160,plain,
sk2 = empty_set,
inference(pattern_uni,[status(thm)],[1159:[bind(A,$thf( sk2 ))]]) ).
thf(8531,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( sk1 @ ( B @ in ) )
| ~ $true
| ( A @ ( sk1 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[2367,48]) ).
thf(8532,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( sk1 @ ( B @ in ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[8531]) ).
thf(8533,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( A @ sk14 ) @ in ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[8532:[bind(A,$thf( C )),bind(B,$thf( sk1 @ ( C @ sk14 ) ))]]) ).
thf(8555,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( A @ sk14 ) @ in ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[8533]) ).
thf(23161,plain,
( ( ( sk10 @ empty )
!= ( empty_set @ empty ) )
| ( sk10 @ one_to_one )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,23130]) ).
thf(23162,plain,
( ( ( sk10 @ empty )
!= ( empty_set @ empty ) )
| ( sk10 @ one_to_one ) ),
inference(simp,[status(thm)],[23161]) ).
thf(23163,plain,
( ( sk10 != empty_set )
| ( sk10 @ one_to_one ) ),
inference(simp,[status(thm)],[23162]) ).
thf(13190,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[11314,48]) ).
thf(13191,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13190]) ).
thf(13192,plain,
( ( sk1 @ ( sk1 @ sk19 @ in ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[13191:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(20999,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[13192,169]) ).
thf(21000,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[20999]) ).
thf(21001,plain,
( ( sk1 @ ( sk1 @ sk19 @ element ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[21000:[bind(A,$thf( sk1 @ sk19 )),bind(B,$thf( sk1 ))]]) ).
thf(12144,plain,
( ~ $true
| ( ( sk1 @ sk18 @ epsilon_transitive )
!= ( sk1 @ sk13 @ epsilon_transitive ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(eqfactor_ordered,[status(thm)],[11055]) ).
thf(12151,plain,
( ( ( sk1 @ sk18 )
!= ( sk1 @ sk13 ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12144]) ).
thf(124,plain,
sk12 @ relation,
inference(cnfConj,[status(thm)],[123]) ).
thf(1563,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1333,131]) ).
thf(1564,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty ) ),
inference(simp,[status(thm)],[1563]) ).
thf(1565,plain,
~ ( sk1 @ empty ),
inference(pattern_uni,[status(thm)],[1564:[bind(A,$thf( empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(1586,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,1565]) ).
thf(1587,plain,
( ( sk1 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[1586]) ).
thf(1588,plain,
sk1 != empty_set,
inference(simp,[status(thm)],[1587]) ).
thf(13627,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ sk19 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11581,48]) ).
thf(13628,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ sk19 @ epsilon_connected ) ),
inference(simp,[status(thm)],[13627]) ).
thf(13629,plain,
( ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ sk19 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[13628:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(18419,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk19 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[13629,169]) ).
thf(18420,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ sk19 @ epsilon_connected ) ),
inference(simp,[status(thm)],[18419]) ).
thf(18421,plain,
( ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk19 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[18420:[bind(A,$thf( sk1 @ sk13 )),bind(B,$thf( sk1 ))]]) ).
thf(25157,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_connected )
| ~ $true
| ( A @ ( sk15 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24827,146]) ).
thf(25158,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_connected )
| ( A @ ( sk15 @ subset ) ) ),
inference(simp,[status(thm)],[25157]) ).
thf(25159,plain,
! [A: $i] :
( ( sk15 @ ( A @ sk14 ) @ epsilon_connected )
| ( A @ ( sk15 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[25158:[bind(A,$thf( C )),bind(B,$thf( sk15 @ ( C @ sk14 ) ))]]) ).
thf(25169,plain,
! [A: $i] :
( ( sk15 @ ( A @ sk14 ) @ epsilon_connected )
| ( A @ ( sk15 @ subset ) ) ),
inference(simp,[status(thm)],[25159]) ).
thf(14424,plain,
( ( ( sk1 @ sk19 )
!= ( sk1 @ sk13 ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[14419]) ).
thf(12253,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[11086,146]) ).
thf(12254,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12253]) ).
thf(12255,plain,
( ( sk1 @ sk18 @ epsilon_connected )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[12254:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(2643,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[2250,97]) ).
thf(2644,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[2643]) ).
thf(2645,plain,
( ( sk1 @ powerset @ ( sk15 @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[2644:[bind(A,$thf( sk15 )),bind(B,$thf( sk1 ))]]) ).
thf(12361,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[11095,48]) ).
thf(12362,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12361]) ).
thf(12363,plain,
( ( sk1 @ ( sk1 @ sk19 @ in ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[12362:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(17644,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[12363,169]) ).
thf(17645,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk19 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[17644]) ).
thf(17646,plain,
( ( sk1 @ ( sk1 @ sk19 @ element ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[17645:[bind(A,$thf( sk1 @ sk19 )),bind(B,$thf( sk1 ))]]) ).
thf(29328,plain,
! [A: $i] :
( ( ( A @ ( A @ sk13 @ subset ) )
!= ( sk1 @ ( sk16 @ subset ) ) )
| ( A @ epsilon_transitive )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29282,141]) ).
thf(29329,plain,
! [A: $i] :
( ( ( A @ ( A @ sk13 @ subset ) )
!= ( sk1 @ ( sk16 @ subset ) ) )
| ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[29328]) ).
thf(29349,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( A @ sk13 )
!= sk16 )
| ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[29329]) ).
thf(29353,plain,
( ( ( sk1 @ sk13 )
!= sk16 )
| ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[29349]) ).
thf(105,plain,
sk9 @ function,
inference(cnfConj,[status(thm)],[103]) ).
thf(13062,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[11307,3378]) ).
thf(13063,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13062]) ).
thf(13103,plain,
( ( ( sk1 @ sk18 )
!= sk1 )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13063]) ).
thf(3223,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk16 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[855,171]) ).
thf(3224,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk16 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) ) ),
inference(simp,[status(thm)],[3223]) ).
thf(3225,plain,
~ ( sk16 @ ( sk1 @ in ) ),
inference(pattern_uni,[status(thm)],[3224:[bind(A,$thf( sk16 )),bind(B,$thf( sk1 ))]]) ).
thf(10976,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[5760,10883]) ).
thf(10977,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[10976]) ).
thf(10978,plain,
( ( sk1 @ sk13 @ ordinal )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[10977:[]]) ).
thf(25549,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ sk18 @ subset ) )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,17257]) ).
thf(25550,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ sk18 @ subset ) )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25549]) ).
thf(25551,plain,
( ( sk1 @ ( sk1 @ sk18 @ subset ) )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25550:[bind(A,$thf( sk1 ))]]) ).
thf(2372,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2366,97]) ).
thf(2373,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) ) ),
inference(simp,[status(thm)],[2372]) ).
thf(2374,plain,
! [A: $i] : ( A @ powerset @ ( empty_set @ element ) ),
inference(pattern_uni,[status(thm)],[2373:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).
thf(2398,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( empty_set @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2374,133]) ).
thf(2399,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( empty_set @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty ) ),
inference(simp,[status(thm)],[2398]) ).
thf(2400,plain,
! [A: $i] :
( ( A @ powerset @ ( empty_set @ in ) )
| ( A @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[2399:[bind(A,$thf( D )),bind(B,$thf( empty_set )),bind(C,$thf( D @ powerset ))]]) ).
thf(2413,plain,
! [A: $i] :
( ( A @ powerset @ ( empty_set @ in ) )
| ( A @ powerset @ empty ) ),
inference(simp,[status(thm)],[2400]) ).
thf(11708,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk18 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1972,10956]) ).
thf(11709,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[11708]) ).
thf(11710,plain,
( ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ sk18 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11709:[]]) ).
thf(166,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[164]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(161,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(64,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28370,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ~ $true
| ( sk1 @ sk19 @ ordinal )
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,28329]) ).
thf(28371,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk19 @ ordinal )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[28370]) ).
thf(28372,plain,
( ( sk1 @ sk19 @ ordinal )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[28371:[bind(A,$thf( sk1 ))]]) ).
thf(13088,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[11307,3219]) ).
thf(13089,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13088]) ).
thf(13090,plain,
( ~ ( sk1 @ sk18 @ ( sk1 @ in ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[13089:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(149,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5629,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ powerset @ ( A @ element ) )
!= ( C @ powerset @ ( sk1 @ element ) ) )
| ~ ( C @ empty )
| ~ $true
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[97,1501]) ).
thf(5630,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ powerset @ ( A @ element ) )
!= ( C @ powerset @ ( sk1 @ element ) ) )
| ~ ( C @ empty )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[5629]) ).
thf(5631,plain,
! [A: $i] :
( ~ ( A @ empty )
| ~ ( A @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[5630:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(5698,plain,
! [A: $i] :
( ~ ( A @ empty )
| ~ ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[5631]) ).
thf(176,plain,
sk15 @ epsilon_connected,
inference(cnfConj,[status(thm)],[173]) ).
thf(12201,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[11086,3378]) ).
thf(12202,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12201]) ).
thf(12259,plain,
( ( ( sk1 @ sk18 )
!= sk1 )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12202]) ).
thf(13807,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ element ) )
| ~ $true
| ( sk1 @ sk19 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[5527,11838]) ).
thf(13808,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk19 @ ordinal ) ),
inference(simp,[status(thm)],[13807]) ).
thf(13809,plain,
( ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk19 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[13808:[]]) ).
thf(12661,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11204,146]) ).
thf(12662,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[12661]) ).
thf(12663,plain,
( ( sk1 @ sk18 @ epsilon_connected )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[12662:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ element ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(838,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ element ) )
!= ( C @ powerset @ ( B @ element ) ) )
| ( C @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,95]) ).
thf(839,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ element ) )
!= ( C @ powerset @ ( B @ element ) ) )
| ( C @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[838]) ).
thf(840,plain,
! [A: $i] : ( A @ ( A @ powerset @ sk6 @ subset ) ),
inference(pattern_uni,[status(thm)],[839:[bind(A,$thf( E @ powerset )),bind(B,$thf( E @ powerset @ sk6 )),bind(C,$thf( E ))]]) ).
thf(843,plain,
! [A: $i] : ( A @ ( A @ powerset @ sk6 @ subset ) ),
inference(simp,[status(thm)],[840]) ).
thf(8347,plain,
( ( ( sk1 @ powerset @ empty )
!= ( empty_set @ empty ) )
| ( ( empty_set @ powerset )
!= empty_set )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,6138]) ).
thf(8348,plain,
( ( ( sk1 @ powerset @ empty )
!= ( empty_set @ empty ) )
| ( ( empty_set @ powerset )
!= empty_set ) ),
inference(simp,[status(thm)],[8347]) ).
thf(8349,plain,
( ( ( sk1 @ powerset )
!= empty_set )
| ( ( empty_set @ powerset )
!= empty_set ) ),
inference(simp,[status(thm)],[8348]) ).
thf(9,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(71,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2027,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[1972,146]) ).
thf(2028,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[2027]) ).
thf(2029,plain,
( ( sk1 @ sk18 @ epsilon_connected )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[2028:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(13619,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk19 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11581,3219]) ).
thf(13620,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ sk19 @ epsilon_connected ) ),
inference(simp,[status(thm)],[13619]) ).
thf(13621,plain,
( ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ sk19 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[13620:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(11898,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ in ) )
| ~ $true
| ( sk1 @ sk18 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1972,10962]) ).
thf(11899,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[11898]) ).
thf(11900,plain,
( ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ sk18 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11899:[]]) ).
thf(13468,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[11517,48]) ).
thf(13469,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(simp,[status(thm)],[13468]) ).
thf(13470,plain,
( ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[13469:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(18265,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[13470,169]) ).
thf(18266,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(simp,[status(thm)],[18265]) ).
thf(18267,plain,
( ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk18 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[18266:[bind(A,$thf( sk1 @ sk13 )),bind(B,$thf( sk1 ))]]) ).
thf(23716,plain,
( ( ( empty_set @ powerset @ empty )
!= ( empty_set @ empty ) )
| ( ( sk1 @ powerset @ empty )
!= ( empty_set @ powerset @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,8434]) ).
thf(23717,plain,
( ( ( empty_set @ powerset @ empty )
!= ( empty_set @ empty ) )
| ( ( sk1 @ powerset @ empty )
!= ( empty_set @ powerset @ empty ) ) ),
inference(simp,[status(thm)],[23716]) ).
thf(23722,plain,
( ( ( empty_set @ powerset )
!= empty_set )
| ( ( sk1 @ powerset @ empty )
!= ( empty_set @ powerset @ empty ) ) ),
inference(simp,[status(thm)],[23717]) ).
thf(5994,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ in ) )
!= ( empty_set @ powerset @ ( sk1 @ in ) ) )
| ~ $true
| ( A @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[211,5812]) ).
thf(5995,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ in ) )
!= ( empty_set @ powerset @ ( sk1 @ in ) ) )
| ( A @ epsilon_connected ) ),
inference(simp,[status(thm)],[5994]) ).
thf(6049,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ( ( A @ sk19 )
!= sk1 )
| ( A @ epsilon_connected ) ),
inference(simp,[status(thm)],[5995]) ).
thf(6061,plain,
( ( ( empty_set @ powerset @ sk19 )
!= sk1 )
| ( empty_set @ powerset @ epsilon_connected ) ),
inference(simp,[status(thm)],[6049]) ).
thf(113,plain,
sk10 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[111]) ).
thf(9495,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( A @ sk14 ) @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) )
| ~ $true
| ( A @ ( sk1 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[8555,169]) ).
thf(9496,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( A @ sk14 ) @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[9495]) ).
thf(9497,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( A @ sk14 ) @ element ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[9496:[bind(A,$thf( D )),bind(B,$thf( sk1 @ ( D @ sk14 ) )),bind(C,$thf( sk1 ))]]) ).
thf(9592,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( A @ sk14 ) @ element ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[9497]) ).
thf(2213,plain,
( ~ $true
| ( ( sk1 @ sk18 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ epsilon_connected ) ),
inference(eqfactor_ordered,[status(thm)],[2029]) ).
thf(2214,plain,
( ( ( sk1 @ sk18 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[2213]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( B = C )
| ( C @ ( B @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( A @ ( B @ in ) )
| ~ ( A @ epsilon_connected ) ),
inference(cnfConj,[status(thm)],[201]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C @ ( B @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( A @ ( B @ in ) )
| ~ ( A @ epsilon_connected )
| ( B = C ) ),
inference(lifteq,[status(thm)],[202]) ).
thf(2403,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ powerset ) )
| ( empty_set @ ( empty_set @ element ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,2374]) ).
thf(2404,plain,
! [A: $i] :
( ( empty_set @ ( empty_set @ element ) )
| ~ ( A @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[2403:[bind(A,$thf( C @ powerset )),bind(B,$thf( C ))]]) ).
thf(2415,plain,
! [A: $i] :
( ( empty_set @ ( empty_set @ element ) )
| ~ ( A @ powerset @ empty ) ),
inference(simp,[status(thm)],[2404]) ).
thf(13094,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[11307,48]) ).
thf(13095,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13094]) ).
thf(13096,plain,
( ( sk1 @ ( sk1 @ sk18 @ in ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[13095:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(20772,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[13096,169]) ).
thf(20773,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[20772]) ).
thf(20774,plain,
( ( sk1 @ ( sk1 @ sk18 @ element ) )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[20773:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 ))]]) ).
thf(2772,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk15 @ element ) )
!= ( B @ ( A @ element ) ) )
| ( B @ ( A @ in ) )
| ( B @ empty )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[2645,133]) ).
thf(2773,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk15 @ element ) )
!= ( B @ ( A @ element ) ) )
| ( B @ ( A @ in ) )
| ( B @ empty )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[2772]) ).
thf(2774,plain,
( ( sk1 @ powerset @ ( sk15 @ in ) )
| ( sk1 @ powerset @ empty )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[2773:[bind(A,$thf( sk15 )),bind(B,$thf( sk1 @ powerset ))]]) ).
thf(24929,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_transitive )
| ~ $true
| ( A @ ( sk16 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24643,145]) ).
thf(24930,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_transitive )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[24929]) ).
thf(24931,plain,
! [A: $i] :
( ( sk16 @ ( A @ sk14 ) @ epsilon_transitive )
| ( A @ ( sk16 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[24930:[bind(A,$thf( C )),bind(B,$thf( sk16 @ ( C @ sk14 ) ))]]) ).
thf(24961,plain,
! [A: $i] :
( ( sk16 @ ( A @ sk14 ) @ epsilon_transitive )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[24931]) ).
thf(203,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ( ( A @ sk18 )
!= ( A @ sk19 ) ) ),
inference(cnfConj,[status(thm)],[201]) ).
thf(212,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ( ( A @ sk19 )
!= ( A @ sk18 ) ) ),
inference(lifteq,[status(thm)],[203]) ).
thf(213,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ( ( A @ sk19 )
!= ( A @ sk18 ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(91,plain,
sk7 @ function,
inference(cnfConj,[status(thm)],[88]) ).
thf(11582,plain,
( ~ $true
| ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ sk13 @ ordinal ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(eqfactor_ordered,[status(thm)],[10975]) ).
thf(11583,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ sk13 @ ordinal ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11582]) ).
thf(15650,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[15568,145]) ).
thf(15651,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_transitive )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[15650]) ).
thf(15652,plain,
( ( sk1 @ sk18 @ epsilon_transitive )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[15651:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(25588,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk18 @ epsilon_transitive )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,15652]) ).
thf(25589,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ sk18 @ epsilon_transitive )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25588]) ).
thf(25590,plain,
( ( sk1 @ sk18 @ epsilon_transitive )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25589:[bind(A,$thf( sk1 ))]]) ).
thf(26287,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( sk1 @ sk18 @ epsilon_transitive )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,25590]) ).
thf(26288,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[26287]) ).
thf(26303,plain,
( ( ( sk1 @ sk13 )
!= empty_set )
| ( sk1 @ sk18 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[26288]) ).
thf(11489,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10965,3378]) ).
thf(11490,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ ordinal ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11489]) ).
thf(11521,plain,
( ( ( sk1 @ sk18 )
!= sk1 )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11490]) ).
thf(1877,plain,
( ( ( sk1 @ sk13 @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[1876]) ).
thf(17955,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[17257,97]) ).
thf(17956,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[17955]) ).
thf(17957,plain,
( ( sk1 @ powerset @ ( sk1 @ sk18 @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[17956:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 ))]]) ).
thf(11567,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10975,3219]) ).
thf(11568,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11567]) ).
thf(11569,plain,
( ~ ( sk1 @ sk19 @ ( sk1 @ in ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11568:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(25536,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( ( sk1 @ sk18 )
!= sk1 )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,15706]) ).
thf(25537,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( ( sk1 @ sk18 )
!= sk1 )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25536]) ).
thf(25538,plain,
( ( ( sk1 @ sk18 )
!= sk1 )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25537:[bind(A,$thf( sk1 ))]]) ).
thf(25857,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( ( sk1 @ sk18 )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,25538]) ).
thf(25858,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( ( sk1 @ sk18 )
!= sk1 ) ),
inference(simp,[status(thm)],[25857]) ).
thf(25859,plain,
( ( ( sk1 @ sk13 )
!= empty_set )
| ( ( sk1 @ sk18 )
!= sk1 ) ),
inference(simp,[status(thm)],[25858]) ).
thf(11519,plain,
( ( ( sk1 @ sk18 @ ordinal )
!= ( sk1 @ sk13 @ ordinal ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11518]) ).
thf(2972,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[769,169]) ).
thf(2973,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) ) ),
inference(simp,[status(thm)],[2972]) ).
thf(2974,plain,
sk1 @ ( sk15 @ element ),
inference(pattern_uni,[status(thm)],[2973:[bind(A,$thf( sk15 )),bind(B,$thf( sk1 ))]]) ).
thf(28447,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ element ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[28329,2983]) ).
thf(28448,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[28447]) ).
thf(28449,plain,
( ( sk1 @ ( sk1 @ sk19 @ element ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[28448:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(28406,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[28329,3219]) ).
thf(28407,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[28406]) ).
thf(28408,plain,
( ~ ( sk1 @ sk19 @ ( sk1 @ in ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[28407:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(2960,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1333,169]) ).
thf(2961,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) ) ),
inference(simp,[status(thm)],[2960]) ).
thf(2962,plain,
sk1 @ ( empty_set @ element ),
inference(pattern_uni,[status(thm)],[2961:[bind(A,$thf( empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(24898,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk16 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ~ $true
| ( sk16 @ ( A @ sk14 ) @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[24643,97]) ).
thf(24899,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk16 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ( sk16 @ ( A @ sk14 ) @ ordinal ) ),
inference(simp,[status(thm)],[24898]) ).
thf(24900,plain,
! [A: $i] :
( ( A @ powerset @ ( sk16 @ element ) )
| ( sk16 @ ( A @ sk14 ) @ ordinal ) ),
inference(pattern_uni,[status(thm)],[24899:[bind(A,$thf( A )),bind(B,$thf( sk16 )),bind(C,$thf( A ))]]) ).
thf(40,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(190,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(191,plain,
( ( sk17 @ ordinal )
& ( sk17 @ epsilon_connected )
& ( sk17 @ epsilon_transitive )
& ( sk17 @ empty )
& ( sk17 @ one_to_one )
& ( sk17 @ function )
& ( sk17 @ relation ) ),
inference(cnf,[status(esa)],[190]) ).
thf(195,plain,
sk17 @ empty,
inference(cnfConj,[status(thm)],[191]) ).
thf(1243,plain,
! [A: $i] :
( ( ( sk17 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[195,109]) ).
thf(1244,plain,
! [A: $i] :
( ( ( sk17 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[1243]) ).
thf(1245,plain,
sk17 = empty_set,
inference(pattern_uni,[status(thm)],[1244:[bind(A,$thf( sk17 ))]]) ).
thf(434,plain,
! [A: $i] :
( ( ( sk7 @ relation )
!= ( A @ relation ) )
| ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[89,59]) ).
thf(435,plain,
! [A: $i] :
( ( ( sk7 @ relation )
!= ( A @ relation ) )
| ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[434]) ).
thf(436,plain,
( ( sk7 @ one_to_one )
| ~ ( sk7 @ function )
| ~ ( sk7 @ empty ) ),
inference(pattern_uni,[status(thm)],[435:[bind(A,$thf( sk7 ))]]) ).
thf(14576,plain,
( ( sk7 @ one_to_one )
| ~ $true
| ~ ( sk7 @ empty ) ),
inference(rewrite,[status(thm)],[436,91]) ).
thf(14577,plain,
( ( sk7 @ one_to_one )
| ~ ( sk7 @ empty ) ),
inference(simp,[status(thm)],[14576]) ).
thf(167,plain,
! [A: $i] :
( ( A @ ordinal )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[164]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ element ) )
| ~ ( C @ powerset @ ( B @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[161]) ).
thf(3268,plain,
( ( ( sk1 @ ( sk15 @ in ) )
!= ( sk15 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[769,3207]) ).
thf(3269,plain,
( ( sk1 @ ( sk15 @ in ) )
!= ( sk15 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[3268]) ).
thf(3286,plain,
( ( sk15 != sk1 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[3269]) ).
thf(3293,plain,
sk15 != sk1,
inference(simp,[status(thm)],[3286]) ).
thf(10139,plain,
( ( ( sk1 @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ subset ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[1684,6363]) ).
thf(10140,plain,
( ( ( sk1 @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ subset ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[10139]) ).
thf(10141,plain,
( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ subset ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[10140:[]]) ).
thf(10221,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10141,97]) ).
thf(10222,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ powerset @ ( A @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[10221]) ).
thf(10223,plain,
( ( sk1 @ powerset @ ( sk1 @ ( empty_set @ sk14 ) @ element ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[10222:[bind(A,$thf( sk1 @ ( empty_set @ sk14 ) )),bind(B,$thf( sk1 ))]]) ).
thf(5755,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[5527,3219]) ).
thf(5756,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ~ ( A @ ( sk1 @ in ) )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[5755]) ).
thf(5757,plain,
( ~ ( sk1 @ sk19 @ ( sk1 @ in ) )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[5756:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(29392,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset ) )
| ( empty_set @ ( sk16 @ element ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,29327]) ).
thf(29393,plain,
( ( empty_set @ ( sk16 @ element ) )
| ~ ( sk1 @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[29392:[bind(A,$thf( sk1 @ powerset ))]]) ).
thf(65,plain,
( ( sk3 @ relation )
& ( sk3 @ empty ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
sk3 @ empty,
inference(cnfConj,[status(thm)],[65]) ).
thf(1179,plain,
! [A: $i] :
( ( ( sk3 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[66,109]) ).
thf(1180,plain,
! [A: $i] :
( ( ( sk3 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[1179]) ).
thf(1181,plain,
sk3 = empty_set,
inference(pattern_uni,[status(thm)],[1180:[bind(A,$thf( sk3 ))]]) ).
thf(6972,plain,
( ~ $true
| ( ( sk1 @ sk19 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ epsilon_connected ) ),
inference(eqfactor_ordered,[status(thm)],[5769]) ).
thf(6973,plain,
( ( ( sk1 @ sk19 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[6972]) ).
thf(10337,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) )
| ~ $true
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[1359,171]) ).
thf(10338,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[10337]) ).
thf(10339,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ in ) )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[10338:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 ))]]) ).
thf(63,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[61]) ).
thf(17317,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[12247,169]) ).
thf(17318,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[17317]) ).
thf(17319,plain,
( ( sk1 @ ( sk1 @ sk18 @ element ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[17318:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 ))]]) ).
thf(28429,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[28329,48]) ).
thf(28430,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( sk1 @ ( A @ in ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[28429]) ).
thf(28431,plain,
( ( sk1 @ ( sk1 @ sk19 @ in ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[28430:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(25783,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( sk1 @ sk18 @ ordinal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,25526]) ).
thf(25784,plain,
( ( ( sk1 @ sk13 @ empty )
!= ( empty_set @ empty ) )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[25783]) ).
thf(25786,plain,
( ( ( sk1 @ sk13 )
!= empty_set )
| ( sk1 @ sk18 @ ordinal ) ),
inference(simp,[status(thm)],[25784]) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( B != sk7 )
| ( A @ relation_non_empty )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[52,90]) ).
thf(441,plain,
! [A: $i] :
( ( A @ relation_non_empty )
| ~ ( sk7 @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[440:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(6419,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5916,171]) ).
thf(6420,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) ) ),
inference(simp,[status(thm)],[6419]) ).
thf(6421,plain,
~ ( sk1 @ ( empty_set @ sk14 ) @ ( sk1 @ in ) ),
inference(pattern_uni,[status(thm)],[6420:[bind(A,$thf( sk1 @ ( empty_set @ sk14 ) )),bind(B,$thf( sk1 ))]]) ).
thf(3331,plain,
( ( ( sk1 @ ( sk16 @ in ) )
!= ( sk16 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[855,3225]) ).
thf(3332,plain,
( ( sk1 @ ( sk16 @ in ) )
!= ( sk16 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[3331]) ).
thf(3335,plain,
( ( sk16 != sk1 )
| ( sk16 != sk1 ) ),
inference(simp,[status(thm)],[3332]) ).
thf(3344,plain,
sk16 != sk1,
inference(simp,[status(thm)],[3335]) ).
thf(12150,plain,
( ( ( sk1 @ sk18 @ epsilon_transitive )
!= ( sk1 @ sk13 @ epsilon_transitive ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12144]) ).
thf(24940,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( sk1 @ ( B @ element ) )
| ~ $true
| ( A @ ( sk16 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24643,2983]) ).
thf(24941,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( sk1 @ ( B @ element ) )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[24940]) ).
thf(24942,plain,
! [A: $i] :
( ( sk1 @ ( sk16 @ ( A @ sk14 ) @ element ) )
| ( A @ ( sk16 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[24941:[bind(A,$thf( C )),bind(B,$thf( sk16 @ ( C @ sk14 ) ))]]) ).
thf(24969,plain,
! [A: $i] :
( ( sk1 @ ( sk16 @ ( A @ sk14 ) @ element ) )
| ( A @ ( sk16 @ subset ) ) ),
inference(simp,[status(thm)],[24942]) ).
thf(182,plain,
sk16 @ epsilon_transitive,
inference(cnfConj,[status(thm)],[181]) ).
thf(12439,plain,
( ( ( sk1 @ sk19 @ epsilon_transitive )
!= ( sk1 @ sk13 @ epsilon_transitive ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12437]) ).
thf(14314,plain,
( ~ $true
| ( ( sk1 @ sk18 @ epsilon_connected )
!= ( sk1 @ sk13 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(eqfactor_ordered,[status(thm)],[12663]) ).
thf(14321,plain,
( ( ( sk1 @ sk18 )
!= ( sk1 @ sk13 ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[14314]) ).
thf(175,plain,
sk15 @ epsilon_transitive,
inference(cnfConj,[status(thm)],[173]) ).
thf(25110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk15 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ~ $true
| ( sk15 @ ( A @ sk14 ) @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[24827,97]) ).
thf(25111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk15 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ( sk15 @ ( A @ sk14 ) @ ordinal ) ),
inference(simp,[status(thm)],[25110]) ).
thf(25112,plain,
! [A: $i] :
( ( A @ powerset @ ( sk15 @ element ) )
| ( sk15 @ ( A @ sk14 ) @ ordinal ) ),
inference(pattern_uni,[status(thm)],[25111:[bind(A,$thf( A )),bind(B,$thf( sk15 )),bind(C,$thf( A ))]]) ).
thf(8980,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ~ $true
| ( sk1 @ ( A @ sk14 ) @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[8562,97]) ).
thf(8981,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ( sk1 @ ( A @ sk14 ) @ epsilon_connected ) ),
inference(simp,[status(thm)],[8980]) ).
thf(8982,plain,
! [A: $i] :
( ( A @ powerset @ ( sk1 @ element ) )
| ( sk1 @ ( A @ sk14 ) @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[8981:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(11919,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ in ) )
| ~ $true
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[5760,10962]) ).
thf(11920,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11919]) ).
thf(11921,plain,
( ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11920:[]]) ).
thf(2990,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ epsilon_connected ) ),
inference(paramod_ordered,[status(thm)],[2026,169]) ).
thf(2991,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk18 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[2990]) ).
thf(2992,plain,
( ( sk1 @ ( sk1 @ sk18 @ element ) )
| ( sk1 @ epsilon_connected ) ),
inference(pattern_uni,[status(thm)],[2991:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 ))]]) ).
thf(13810,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ element ) )
| ~ $true
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[5760,11838]) ).
thf(13811,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[13810]) ).
thf(13812,plain,
( ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[13811:[]]) ).
thf(28375,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ~ ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[28329,3378]) ).
thf(28376,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[28375]) ).
thf(28485,plain,
( ( ( sk1 @ sk19 )
!= sk1 )
| ~ ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[28376]) ).
thf(28931,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( ( sk1 @ sk19 )
!= sk1 )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,28485]) ).
thf(28932,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( ( sk1 @ sk19 )
!= sk1 )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[28931]) ).
thf(28933,plain,
( ( ( sk1 @ sk19 )
!= sk1 )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[28932:[bind(A,$thf( sk1 ))]]) ).
thf(2215,plain,
( ( ( sk1 @ sk18 )
!= sk1 )
| ( sk1 @ epsilon_connected ) ),
inference(simp,[status(thm)],[2213]) ).
thf(218,plain,
empty_set @ function,
inference(cnfConj,[status(thm)],[216]) ).
thf(104,plain,
sk9 @ relation,
inference(cnfConj,[status(thm)],[103]) ).
thf(25566,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ sk18 @ in ) )
| ~ $true
| ~ ( A @ sk13 @ empty ) ),
inference(paramod_ordered,[status(thm)],[24490,15660]) ).
thf(25567,plain,
! [A: $i] :
( ( ( A @ epsilon_transitive )
!= ( sk1 @ epsilon_transitive ) )
| ( sk1 @ ( sk1 @ sk18 @ in ) )
| ~ ( A @ sk13 @ empty ) ),
inference(simp,[status(thm)],[25566]) ).
thf(25568,plain,
( ( sk1 @ ( sk1 @ sk18 @ in ) )
| ~ ( sk1 @ sk13 @ empty ) ),
inference(pattern_uni,[status(thm)],[25567:[bind(A,$thf( sk1 ))]]) ).
thf(11584,plain,
( ( ( sk1 @ sk19 )
!= ( sk1 @ sk13 ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11582]) ).
thf(11315,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( ( sk1 @ sk13 )
!= sk1 )
| ~ $true
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[5760,10988]) ).
thf(11316,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( ( sk1 @ sk13 )
!= sk1 )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11315]) ).
thf(11317,plain,
( ( ( sk1 @ sk13 )
!= sk1 )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11316:[]]) ).
thf(22555,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk1 @ sk18 @ element ) )
!= ( B @ ( A @ element ) ) )
| ( B @ ( A @ in ) )
| ( B @ empty )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[22051,133]) ).
thf(22556,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk1 @ sk18 @ element ) )
!= ( B @ ( A @ element ) ) )
| ( B @ ( A @ in ) )
| ( B @ empty )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[22555]) ).
thf(22557,plain,
( ( sk1 @ powerset @ ( sk1 @ sk18 @ in ) )
| ( sk1 @ powerset @ empty )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[22556:[bind(A,$thf( sk1 @ sk18 )),bind(B,$thf( sk1 @ powerset ))]]) ).
thf(11553,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10975,3378]) ).
thf(11554,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11553]) ).
thf(11585,plain,
( ( ( sk1 @ sk19 )
!= sk1 )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[11554]) ).
thf(11916,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ in ) )
| ~ $true
| ( sk1 @ sk19 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[5527,10962]) ).
thf(11917,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ sk19 @ ordinal ) ),
inference(simp,[status(thm)],[11916]) ).
thf(11918,plain,
( ( sk1 @ ( sk1 @ sk13 @ in ) )
| ( sk1 @ sk19 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[11917:[]]) ).
thf(16737,plain,
( ( ( sk8 @ empty )
!= ( empty_set @ empty ) )
| ( sk8 @ one_to_one )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,16697]) ).
thf(16738,plain,
( ( ( sk8 @ empty )
!= ( empty_set @ empty ) )
| ( sk8 @ one_to_one ) ),
inference(simp,[status(thm)],[16737]) ).
thf(16739,plain,
( ( sk8 != empty_set )
| ( sk8 @ one_to_one ) ),
inference(simp,[status(thm)],[16738]) ).
thf(13196,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ~ $true
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[11314,146]) ).
thf(13197,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ordinal )
!= ( A @ ordinal ) )
| ( A @ epsilon_connected )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[13196]) ).
thf(13198,plain,
( ( sk1 @ sk19 @ epsilon_connected )
| ( ( sk1 @ sk13 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[13197:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(7561,plain,
( ( ( empty_set @ powerset @ empty )
!= ( empty_set @ empty ) )
| ~ ( empty_set @ ( sk1 @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,5818]) ).
thf(7562,plain,
( ( ( empty_set @ powerset @ empty )
!= ( empty_set @ empty ) )
| ~ ( empty_set @ ( sk1 @ element ) ) ),
inference(simp,[status(thm)],[7561]) ).
thf(7574,plain,
( ( ( empty_set @ powerset )
!= empty_set )
| ~ ( empty_set @ ( sk1 @ element ) ) ),
inference(simp,[status(thm)],[7562]) ).
thf(6359,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5916,3239]) ).
thf(6360,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
!= ( A @ ( A @ in ) ) ),
inference(simp,[status(thm)],[6359]) ).
thf(6435,plain,
! [A: $i] :
( ( sk1 != A )
| ( ( sk1 @ ( empty_set @ sk14 ) )
!= A ) ),
inference(simp,[status(thm)],[6360]) ).
thf(6444,plain,
( ( sk1 @ ( empty_set @ sk14 ) )
!= sk1 ),
inference(simp,[status(thm)],[6435]) ).
thf(207,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ~ ( A @ sk19 @ ( A @ sk18 @ in ) ) ),
inference(cnfConj,[status(thm)],[201]) ).
thf(214,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ~ ( A @ sk19 @ ( A @ sk18 @ in ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(75,plain,
! [A: $i] :
( ( A @ relation )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[74]) ).
thf(2954,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[1762,169]) ).
thf(2955,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[2954]) ).
thf(2956,plain,
( ( sk1 @ ( sk1 @ sk13 @ element ) )
| ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[2955:[bind(A,$thf( sk1 @ sk13 )),bind(B,$thf( sk1 ))]]) ).
thf(8499,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ~ $true
| ( sk1 @ ( A @ sk14 ) @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[2367,97]) ).
thf(8500,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ( sk1 @ ( A @ sk14 ) @ ordinal ) ),
inference(simp,[status(thm)],[8499]) ).
thf(8501,plain,
! [A: $i] :
( ( A @ powerset @ ( sk1 @ element ) )
| ( sk1 @ ( A @ sk14 ) @ ordinal ) ),
inference(pattern_uni,[status(thm)],[8500:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(6028,plain,
! [A: $i] :
( ( ( A @ ( A @ sk13 @ in ) )
!= ( empty_set @ powerset @ ( sk1 @ in ) ) )
| ~ $true
| ( A @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[140,5812]) ).
thf(6029,plain,
! [A: $i] :
( ( ( A @ ( A @ sk13 @ in ) )
!= ( empty_set @ powerset @ ( sk1 @ in ) ) )
| ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[6028]) ).
thf(6042,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ( ( A @ sk13 )
!= sk1 )
| ( A @ epsilon_transitive ) ),
inference(simp,[status(thm)],[6029]) ).
thf(6055,plain,
( ( ( empty_set @ powerset @ sk13 )
!= sk1 )
| ( empty_set @ powerset @ epsilon_transitive ) ),
inference(simp,[status(thm)],[6042]) ).
thf(11720,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ~ $true
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[5760,10956]) ).
thf(11721,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11720]) ).
thf(11722,plain,
( ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11721:[]]) ).
thf(183,plain,
sk16 @ epsilon_connected,
inference(cnfConj,[status(thm)],[181]) ).
thf(8528,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_transitive )
| ~ $true
| ( A @ ( sk1 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[2367,145]) ).
thf(8529,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_transitive )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[8528]) ).
thf(8530,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk14 ) @ epsilon_transitive )
| ( A @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[8529:[bind(A,$thf( C )),bind(B,$thf( sk1 @ ( C @ sk14 ) ))]]) ).
thf(8553,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk14 ) @ epsilon_transitive )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[8530]) ).
thf(8752,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ~ $true
| ( sk1 @ ( A @ sk14 ) @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[8553,97]) ).
thf(8753,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ( sk1 @ ( A @ sk14 ) @ epsilon_transitive ) ),
inference(simp,[status(thm)],[8752]) ).
thf(8754,plain,
! [A: $i] :
( ( A @ powerset @ ( sk1 @ element ) )
| ( sk1 @ ( A @ sk14 ) @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[8753:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(12317,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ~ $true
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[11095,3378]) ).
thf(12318,plain,
( ( ( sk1 @ sk19 @ ordinal )
!= ( sk1 @ ordinal ) )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12317]) ).
thf(12374,plain,
( ( ( sk1 @ sk19 )
!= sk1 )
| ( sk1 @ sk13 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[12318]) ).
thf(3014,plain,
! [A: $i] :
( ( empty_set != empty_set )
| ( sk1 @ ( A @ element ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,2962]) ).
thf(3015,plain,
! [A: $i] :
( ( sk1 @ ( A @ element ) )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[3014:[]]) ).
thf(238,plain,
( ( ( sk5 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,78]) ).
thf(239,plain,
( ( sk5 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[238]) ).
thf(242,plain,
sk5 != empty_set,
inference(simp,[status(thm)],[239]) ).
thf(11212,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected )
| ~ $true
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[5760,10981]) ).
thf(11213,plain,
( ( ( sk1 @ epsilon_connected )
!= ( sk1 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[11212]) ).
thf(11214,plain,
( ( sk1 @ sk13 @ epsilon_connected )
| ( sk1 @ sk19 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[11213:[]]) ).
thf(205,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ~ ( A @ sk18 @ ( A @ sk19 @ in ) ) ),
inference(cnfConj,[status(thm)],[201]) ).
thf(210,plain,
! [A: $i] :
( ( A @ epsilon_connected )
| ~ ( A @ sk18 @ ( A @ sk19 @ in ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(79,plain,
sk5 @ relation,
inference(cnfConj,[status(thm)],[77]) ).
thf(3175,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ~ $true
| ( sk1 @ epsilon_transitive ) ),
inference(paramod_ordered,[status(thm)],[1762,171]) ).
thf(3176,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk13 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ( sk1 @ epsilon_transitive ) ),
inference(simp,[status(thm)],[3175]) ).
thf(3177,plain,
( ~ ( sk1 @ sk13 @ ( sk1 @ in ) )
| ( sk1 @ epsilon_transitive ) ),
inference(pattern_uni,[status(thm)],[3176:[bind(A,$thf( sk1 @ sk13 )),bind(B,$thf( sk1 ))]]) ).
thf(14608,plain,
( ( ( sk7 @ empty )
!= ( empty_set @ empty ) )
| ( sk7 @ one_to_one )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,14577]) ).
thf(14609,plain,
( ( ( sk7 @ empty )
!= ( empty_set @ empty ) )
| ( sk7 @ one_to_one ) ),
inference(simp,[status(thm)],[14608]) ).
thf(14610,plain,
( ( sk7 != empty_set )
| ( sk7 @ one_to_one ) ),
inference(simp,[status(thm)],[14609]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(178,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(2697,plain,
( ( ( sk7 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ relation_non_empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,1247]) ).
thf(2698,plain,
( ( ( sk7 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ relation_non_empty ) ),
inference(simp,[status(thm)],[2697]) ).
thf(2699,plain,
( ( sk7 != empty_set )
| ( empty_set @ relation_non_empty ) ),
inference(simp,[status(thm)],[2698]) ).
thf(10438,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk1 @ ( empty_set @ sk14 ) @ element ) )
!= ( B @ ( A @ element ) ) )
| ( B @ ( A @ in ) )
| ( B @ empty )
| ~ $true
| ( sk1 @ sk13 @ ordinal ) ),
inference(paramod_ordered,[status(thm)],[10223,133]) ).
thf(10439,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ powerset @ ( sk1 @ ( empty_set @ sk14 ) @ element ) )
!= ( B @ ( A @ element ) ) )
| ( B @ ( A @ in ) )
| ( B @ empty )
| ( sk1 @ sk13 @ ordinal ) ),
inference(simp,[status(thm)],[10438]) ).
thf(10440,plain,
( ( sk1 @ powerset @ ( sk1 @ ( empty_set @ sk14 ) @ in ) )
| ( sk1 @ powerset @ empty )
| ( sk1 @ sk13 @ ordinal ) ),
inference(pattern_uni,[status(thm)],[10439:[bind(A,$thf( sk1 @ ( empty_set @ sk14 ) )),bind(B,$thf( sk1 @ powerset ))]]) ).
thf(23293,plain,
! [A: $i] :
( ( ( A @ powerset @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( empty_set @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,2415]) ).
thf(23294,plain,
! [A: $i] :
( ( ( A @ powerset @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( empty_set @ element ) ) ),
inference(simp,[status(thm)],[23293]) ).
thf(23296,plain,
! [A: $i] :
( ( ( A @ powerset )
!= empty_set )
| ( empty_set @ ( empty_set @ element ) ) ),
inference(simp,[status(thm)],[23294]) ).
thf(14320,plain,
( ( ( sk1 @ sk18 @ epsilon_connected )
!= ( sk1 @ sk13 @ epsilon_connected ) )
| ( sk1 @ sk13 @ epsilon_connected ) ),
inference(simp,[status(thm)],[14314]) ).
thf(25143,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_transitive )
| ~ $true
| ( A @ ( sk15 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24827,145]) ).
thf(25144,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( A @ sk14 ) @ ordinal )
!= ( B @ ordinal ) )
| ( B @ epsilon_transitive )
| ( A @ ( sk15 @ subset ) ) ),
inference(simp,[status(thm)],[25143]) ).
thf(25145,plain,
! [A: $i] :
( ( sk15 @ ( A @ sk14 ) @ epsilon_transitive )
| ( A @ ( sk15 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[25144:[bind(A,$thf( C )),bind(B,$thf( sk15 @ ( C @ sk14 ) ))]]) ).
thf(25190,plain,
! [A: $i] :
( ( sk15 @ ( A @ sk14 ) @ epsilon_transitive )
| ( A @ ( sk15 @ subset ) ) ),
inference(simp,[status(thm)],[25145]) ).
thf(54600,plain,
$false,
inference(e,[status(thm)],[1718,24963,13199,101,11211,11517,11581,12440,8266,25580,2250,1501,25680,170,115,14976,8434,12371,1073,15568,18114,26169,25167,12674,10959,28423,28754,142,25548,340,11055,153,13764,174,6138,185,22051,23130,5770,1359,12770,5874,13800,17798,29282,52,25523,184,24971,110,125,1577,15706,6519,11426,29621,17097,189,11285,1247,1890,46,24490,13102,3231,7032,12657,78,11314,3431,14423,211,25526,106,12237,11838,15678,7581,2367,221,12777,132,11505,15289,74,3378,89,133,10965,116,25587,233,17257,11307,11170,220,102,16697,60,117,11520,24643,10975,160,12247,70,3239,12650,3207,10099,28554,6371,6528,13186,11719,6356,137,165,2986,92,5769,25541,97,1296,6060,224,10962,1762,8562,28454,169,12796,141,989,12353,13463,9355,156,1878,11435,53,109,1160,8555,23163,21001,12151,2023,5818,124,29389,6363,1588,18421,129,13629,6152,25169,14424,73,128,12783,12255,2645,24827,17646,134,1333,29353,105,13103,3225,10978,25551,2413,11710,166,148,161,64,28372,15660,180,13090,149,5698,176,12259,13809,12663,843,8349,71,10883,2029,6091,13621,49,11900,18267,23722,86,159,6061,187,172,113,5671,9592,2214,76,98,208,2415,20774,2774,81,3219,24961,140,213,91,11583,769,26303,11521,1877,17957,11569,25859,11519,2974,28449,11095,28408,2962,24900,1245,14577,80,167,5812,162,3293,10223,5757,1684,2234,209,112,29393,5916,1181,6973,145,5763,10339,1845,48,855,63,11575,11098,5871,95,17319,28431,25786,199,441,6421,3344,25538,12150,177,24969,182,12439,14321,1972,5809,72,175,25112,43,8982,11921,2992,17997,13812,87,15644,28933,2215,218,104,25568,11584,11317,22557,11585,186,13470,171,11918,55,2026,114,16739,13198,7574,6444,214,75,2956,25590,8501,82,15652,2374,6055,2385,2983,168,13192,11722,3464,190,183,5527,8754,12374,146,28329,13096,5760,3015,107,242,126,11214,2366,10956,11204,12363,10981,210,10141,79,3177,28485,10988,131,14610,68,62,178,2699,29327,10440,163,90,23296,122,8553,10934,1565,215,14320,100,11086,25190,222,11511]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.72 % Computer : n003.cluster.edu
% 0.24/0.72 % Model : x86_64 x86_64
% 0.24/0.72 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.72 % Memory : 8046.5625MB
% 0.24/0.72 % OS : Linux 6.8.0-71-generic
% 0.24/0.72 % CPULimit : 300
% 0.24/0.72 % WCLimit : 300
% 0.24/0.72 % DateTime : Sat Sep 26 02:40:39 UTC 2026
% 0.24/0.73 % CPUTime :
% 0.24/0.73 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.37/1.58 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.15/1.91 % [INFO] Parsing done (320ms).
% 2.15/1.93 % [INFO] Running in sequential loop mode.
% 3.26/2.55 % [INFO] eprover registered as external prover.
% 3.26/2.56 % [INFO] Scanning for conjecture ...
% 3.67/2.71 % [INFO] Found a conjecture (or negated_conjecture) and 40 axioms. Running axiom selection ...
% 3.84/2.84 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 4.06/2.95 % [INFO] Problem is first-order (TPTP FOF).
% 4.06/2.96 % [INFO] Type checking passed.
% 4.06/2.97 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 128.35/30.18 % External prover 'e' found a proof!
% 128.35/30.18 % [INFO] Killing All external provers ...
% 128.35/30.19 % Time passed: 29244ms (effective reasoning time: 28248ms)
% 128.35/30.19 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 128.35/30.19 % Axioms used in derivation (40): d4_ordinal1, rc3_funct_1, cc1_relat_1, rc1_funct_1, rc4_funct_1, t4_subset, cc1_ordinal1, rc3_ordinal1, rc2_relat_1, d3_ordinal1, rc2_ordinal1, fc2_ordinal1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, cc2_ordinal1, t5_subset, rc5_funct_1, t7_boole, cc1_funct_1, t23_ordinal1, rc2_funct_1, cc3_ordinal1, cc2_funct_1, t3_subset, t24_ordinal1, existence_m1_subset_1, rc1_ordinal1, d3_tarski, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, d2_ordinal1, fc12_relat_1
% 128.35/30.19 % No. of inferences in proof: 1017
% 128.35/30.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 29244 ms resp. 28248 ms w/o parsing
% 120.29/30.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 120.29/30.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------