%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU147+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.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 08:37:44 AM UTC 2026
% Result : Theorem 95.63s 20.34s
% Output : Refutation 97.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 77
% Syntax : Number of formulae : 525 ( 191 unt; 0 typ; 14 def)
% Number of atoms : 1441 ( 525 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 4585 ( 628 ~; 486 |; 152 &;3155 @)
% ( 23 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 5 con; 0-3 aty)
% Number of variables : 1202 ( 29 ^;1128 !; 31 ?;1202 :)
% ( 0 !>; 0 ?*; 0 @-; 14 @+)
% Comments :
%------------------------------------------------------------------------------
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(proper_subset_decl,type,
proper_subset: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $o ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $o ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i > $o ).
thf(sk13_decl,type,
sk13: $i > $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i > $i > $i ).
thf(sk20_decl,type,
sk20: $i > $i > $i ).
thf(sk21_decl,type,
sk21: $i > $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ set_intersection2 ) @ ( C @ in ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( C @ ( D @ in ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( B @ ( D @ in ) )
| ( C @ ( D @ in ) ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( C @ in ) )
& ( B @ ( C @ in ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( C @ ( D @ in ) ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( B @ ( D @ in ) )
& ( C @ ( D @ in ) ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ in ) ) ) ) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ proper_subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(67,plain,
! [A: $i] :
~ ( A @ ( A @ proper_subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(68,plain,
~ ? [A: $i] : ( A @ ( A @ proper_subset ) ),
inference(miniscope,[status(thm)],[67]) ).
thf(69,plain,
! [A: $i] :
~ ( A @ ( A @ proper_subset ) ),
inference(cnf,[status(esa)],[68]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(319,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(cnf,[status(esa)],[319]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(lifteq,[status(thm)],[320]) ).
thf(60,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(403,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ in ) )
=> ( A = empty_set ) )
& ( ( A = empty_set )
=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(404,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ in ) )
=> ( A = empty_set ) )
& ! [A: $i] :
( ( A = empty_set )
=> ~ ? [B: $i] : ( A @ ( B @ in ) ) ) ),
inference(miniscope,[status(thm)],[403]) ).
thf(405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = empty_set )
| ( C @ ( C @ sk22 @ in ) ) )
& ( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ) ),
inference(cnf,[status(esa)],[404]) ).
thf(407,plain,
! [A: $i] :
( ( A = empty_set )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(cnfConj,[status(thm)],[405]) ).
thf(410,plain,
! [A: $i] :
( ( A @ ( A @ sk22 @ in ) )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[407]) ).
thf(411,plain,
! [A: $i] :
( ( A @ ( A @ sk22 @ in ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[410]) ).
thf(57,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(378,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(11,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(92,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(93,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[92]) ).
thf(94,plain,
~ ( sk3 @ empty ),
inference(cnf,[status(esa)],[93]) ).
thf(448,plain,
( ( ( sk3 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[378,94]) ).
thf(449,plain,
( ( sk3 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[448]) ).
thf(450,plain,
sk3 != empty_set,
inference(simp,[status(thm)],[449]) ).
thf(4072,plain,
! [A: $i] :
( ( A != sk3 )
| ( empty_set != empty_set )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[411,450]) ).
thf(4073,plain,
! [A: $i] :
( ( A != sk3 )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(simp,[status(thm)],[4072]) ).
thf(4074,plain,
sk3 @ ( sk3 @ sk22 @ in ),
inference(pattern_uni,[status(thm)],[4073:[bind(A,$thf( sk3 ))]]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(137,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_union2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_union2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(138,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_union2 ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
=> ( ! [D: $i] :
( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[137]) ).
thf(139,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ set_union2 ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk9 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk7 ) ) ) )
& ( ( H
= ( G @ ( F @ set_union2 ) ) )
| ( G @ ( F @ ( G @ ( H @ sk9 ) ) @ in ) )
| ( F @ ( F @ ( G @ ( H @ sk9 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk7 ) ) ) )
& ( ( H
= ( G @ ( F @ set_union2 ) ) )
| ~ ( H @ ( G @ ( F @ sk7 ) ) )
| ~ ( G @ ( F @ ( G @ ( H @ sk8 ) ) @ in ) ) )
& ( ( H
= ( G @ ( F @ set_union2 ) ) )
| ~ ( H @ ( G @ ( F @ sk7 ) ) )
| ~ ( F @ ( F @ ( G @ ( H @ sk8 ) ) @ in ) ) )
& ( ( H
= ( G @ ( F @ set_union2 ) ) )
| ~ ( H @ ( G @ ( F @ sk7 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk8 ) ) @ in ) ) )
& ( ( C @ ( E @ in ) )
| ~ ( B @ ( E @ in ) )
| ( C
!= ( B @ ( A @ set_union2 ) ) ) )
& ( ( C @ ( E @ in ) )
| ~ ( A @ ( E @ in ) )
| ( C
!= ( B @ ( A @ set_union2 ) ) ) )
& ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_union2 ) ) ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ~ ( A @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_union2 ) ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ~ ( A @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_union2 ) ) ) ),
inference(lifteq,[status(thm)],[144]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
| ~ ( A @ ( C @ in ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(6929,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk22 @ in ) )
!= ( A @ ( C @ in ) ) )
| ( B @ ( A @ set_union2 ) @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4074,155]) ).
thf(6930,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk22 @ in ) )
!= ( A @ ( C @ in ) ) )
| ( B @ ( A @ set_union2 ) @ ( C @ in ) ) ),
inference(simp,[status(thm)],[6929]) ).
thf(6931,plain,
! [A: $i] : ( A @ ( sk3 @ set_union2 ) @ ( sk3 @ sk22 @ in ) ),
inference(pattern_uni,[status(thm)],[6930:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk3 @ sk22 ))]]) ).
thf(6965,plain,
! [A: $i] : ( A @ ( sk3 @ set_union2 ) @ ( sk3 @ sk22 @ in ) ),
inference(simp,[status(thm)],[6931]) ).
thf(7039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ set_union2 ) @ ( sk3 @ sk22 @ in ) )
!= ( B @ ( D @ in ) ) )
| ( C @ ( B @ set_union2 ) @ ( D @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6965,155]) ).
thf(7040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ set_union2 ) @ ( sk3 @ sk22 @ in ) )
!= ( B @ ( D @ in ) ) )
| ( C @ ( B @ set_union2 ) @ ( D @ in ) ) ),
inference(simp,[status(thm)],[7039]) ).
thf(7041,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) @ ( sk3 @ sk22 @ in ) ),
inference(pattern_uni,[status(thm)],[7040:[bind(A,$thf( G )),bind(B,$thf( G @ ( sk3 @ set_union2 ) )),bind(C,$thf( C )),bind(D,$thf( sk3 @ sk22 ))]]) ).
thf(7130,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) @ ( sk3 @ sk22 @ in ) ),
inference(simp,[status(thm)],[7041]) ).
thf(64,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(442,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(443,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(cnf,[status(esa)],[442]) ).
thf(444,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(lifteq,[status(thm)],[443]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(86,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(87,plain,
( ~ ? [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ? [A: $i,B: $i] :
( ~ ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(miniscope,[status(thm)],[86]) ).
thf(88,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( D @ ( C @ disjoint ) )
| ~ ( D @ ( C @ set_intersection2 ) @ ( E @ in ) ) )
& ( ( B @ ( A @ set_intersection2 ) @ ( A @ ( B @ sk2 ) @ in ) )
| ( B @ ( A @ disjoint ) ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) @ ( A @ ( B @ sk2 ) @ in ) )
| ( B @ ( A @ disjoint ) ) ),
inference(cnfConj,[status(thm)],[88]) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( A @ set_intersection2 ) )
!= ( C @ ( B @ set_intersection2 ) ) )
| ( empty_set @ ( B @ ( C @ sk2 ) @ in ) )
| ( C @ ( B @ disjoint ) ) ),
inference(paramod_ordered,[status(thm)],[444,89]) ).
thf(965,plain,
! [A: $i] :
( ( empty_set @ ( A @ ( empty_set @ sk2 ) @ in ) )
| ( empty_set @ ( A @ disjoint ) ) ),
inference(pattern_uni,[status(thm)],[964:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( empty_set ))]]) ).
thf(406,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ),
inference(cnfConj,[status(thm)],[405]) ).
thf(408,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ),
inference(lifteq,[status(thm)],[406]) ).
thf(409,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(simp,[status(thm)],[408]) ).
thf(1036,plain,
! [A: $i] :
( $false
| ( empty_set @ ( A @ disjoint ) ) ),
inference(rewrite,[status(thm)],[965,409]) ).
thf(1037,plain,
! [A: $i] : ( empty_set @ ( A @ disjoint ) ),
inference(simp,[status(thm)],[1036]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ disjoint ) )
| ~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) ),
inference(cnfConj,[status(thm)],[88]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ disjoint ) )
| ~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(1057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( A @ disjoint ) )
!= ( C @ ( B @ disjoint ) ) )
| ~ $true
| ~ ( C @ ( B @ set_intersection2 ) @ ( D @ in ) ) ),
inference(paramod_ordered,[status(thm)],[1037,91]) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( A @ disjoint ) )
!= ( C @ ( B @ disjoint ) ) )
| ~ ( C @ ( B @ set_intersection2 ) @ ( D @ in ) ) ),
inference(simp,[status(thm)],[1057]) ).
thf(1059,plain,
! [B: $i,A: $i] :
~ ( empty_set @ ( A @ set_intersection2 ) @ ( B @ in ) ),
inference(pattern_uni,[status(thm)],[1058:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( empty_set ))]]) ).
thf(1079,plain,
! [B: $i,A: $i] :
~ ( empty_set @ ( A @ set_intersection2 ) @ ( B @ in ) ),
inference(simp,[status(thm)],[1059]) ).
thf(1085,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(rewrite,[status(thm)],[1079,444]) ).
thf(11136,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) @ ( sk3 @ sk22 @ in ) )
!= ( empty_set @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7130,1085]) ).
thf(11137,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) @ ( sk3 @ sk22 @ in ) )
!= ( empty_set @ ( C @ in ) ) ),
inference(simp,[status(thm)],[11136]) ).
thf(11190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) )
!= empty_set )
| ( ( sk3 @ sk22 )
!= C ) ),
inference(simp,[status(thm)],[11137]) ).
thf(11244,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) )
!= empty_set ),
inference(simp,[status(thm)],[11190]) ).
thf(11522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= ( C @ ( D @ ( sk3 @ set_union2 ) @ set_union2 ) ) )
| ( ( B @ ( A @ set_union2 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[321,11244]) ).
thf(11523,plain,
! [B: $i,A: $i] :
( ( B @ ( sk3 @ set_union2 ) @ ( A @ set_union2 ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[11522:[bind(A,$thf( A )),bind(B,$thf( F @ ( sk3 @ set_union2 ) )),bind(C,$thf( A )),bind(D,$thf( F ))]]) ).
thf(11637,plain,
! [B: $i,A: $i] :
( ( B @ ( sk3 @ set_union2 ) @ ( A @ set_union2 ) )
!= empty_set ),
inference(simp,[status(thm)],[11523]) ).
thf(12888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( D @ ( sk3 @ set_union2 ) ) )
| ( ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[321,11637]) ).
thf(12889,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[12888:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(13052,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( A @ set_union2 ) @ ( B @ set_union2 ) )
!= empty_set ),
inference(simp,[status(thm)],[12889]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(336,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(337,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[336]) ).
thf(338,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[337]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(81,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(82,plain,
! [B: $i,A: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(cnf,[status(esa)],[81]) ).
thf(53,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(357,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(358,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(cnf,[status(esa)],[357]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(96,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(miniscope,[status(thm)],[95]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C = D )
| ~ ( C @ ( D @ subset ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( A @ ( B @ subset ) )
| ( A != B ) )
& ( ( B @ ( A @ subset ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[96]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[97]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[105]) ).
thf(1,conjecture,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(2,negated_conjecture,
( ( empty_set @ powerset )
!= ( empty_set @ singleton ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(65,plain,
( ( empty_set @ powerset )
!= ( empty_set @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(66,plain,
( ( empty_set @ singleton )
!= ( empty_set @ powerset ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(1362,plain,
! [B: $i,A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ( B
!= ( empty_set @ powerset ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[106,66]) ).
thf(1363,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ~ ( empty_set @ singleton @ ( A @ subset ) )
| ~ ( A @ ( empty_set @ singleton @ subset ) ) ),
inference(pattern_uni,[status(thm)],[1362:[bind(A,$thf( empty_set @ singleton )),bind(B,$thf( B ))]]) ).
thf(1472,plain,
( ~ ( empty_set @ singleton @ ( empty_set @ powerset @ subset ) )
| ~ ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[1363]) ).
thf(1758,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( empty_set @ singleton @ ( empty_set @ powerset @ subset ) ) )
| ~ $true
| ~ ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[358,1472]) ).
thf(1759,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( empty_set @ singleton @ ( empty_set @ powerset @ subset ) ) )
| ~ ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[1758]) ).
thf(1768,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ( ( empty_set @ powerset )
!= empty_set )
| ~ ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[1759]) ).
thf(1791,plain,
( ( ( empty_set @ powerset )
!= empty_set )
| ~ ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[1768]) ).
thf(1842,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ( empty_set != empty_set )
| ~ ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[338,1791]) ).
thf(1843,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ~ ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[1842]) ).
thf(1844,plain,
( ~ ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) )
| ~ ( empty_set @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[1843:[bind(A,$thf( empty_set @ powerset ))]]) ).
thf(3193,plain,
! [A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ~ ( empty_set @ ( empty_set @ singleton @ subset ) )
| ~ ( empty_set @ powerset @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[338,1844]) ).
thf(3194,plain,
( ~ ( empty_set @ ( empty_set @ singleton @ subset ) )
| ~ ( empty_set @ powerset @ empty )
| ~ ( empty_set @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[3193:[bind(A,$thf( empty_set @ powerset ))]]) ).
thf(3281,plain,
( ~ ( empty_set @ ( empty_set @ singleton @ subset ) )
| ~ ( empty_set @ powerset @ empty ) ),
inference(simp,[status(thm)],[3194]) ).
thf(3539,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( empty_set @ ( empty_set @ singleton @ subset ) ) )
| ~ $true
| ~ ( empty_set @ powerset @ empty ) ),
inference(paramod_ordered,[status(thm)],[82,3281]) ).
thf(3540,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( empty_set @ ( empty_set @ singleton @ subset ) ) )
| ~ ( empty_set @ powerset @ empty ) ),
inference(simp,[status(thm)],[3539]) ).
thf(3555,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= empty_set )
| ( A
!= ( empty_set @ singleton ) )
| ~ ( empty_set @ powerset @ empty ) ),
inference(simp,[status(thm)],[3540]) ).
thf(3579,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ singleton @ set_union2 ) )
!= empty_set )
| ~ ( empty_set @ powerset @ empty ) ),
inference(simp,[status(thm)],[3555]) ).
thf(6651,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= ( C @ ( empty_set @ singleton @ set_union2 ) ) )
| ( ( B @ ( A @ set_union2 ) )
!= empty_set )
| ~ ( empty_set @ powerset @ empty ) ),
inference(paramod_ordered,[status(thm)],[321,3579]) ).
thf(6652,plain,
! [A: $i] :
( ( ( empty_set @ singleton @ ( A @ set_union2 ) )
!= empty_set )
| ~ ( empty_set @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[6651:[bind(A,$thf( A )),bind(B,$thf( empty_set @ singleton )),bind(C,$thf( A ))]]) ).
thf(12375,plain,
! [B: $i,A: $i] :
( ( A
!= ( empty_set @ singleton @ ( B @ set_union2 ) ) )
| ( empty_set != empty_set )
| ~ ( empty_set @ powerset @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[338,6652]) ).
thf(12376,plain,
! [B: $i,A: $i] :
( ( A
!= ( empty_set @ singleton @ ( B @ set_union2 ) ) )
| ~ ( empty_set @ powerset @ empty )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[12375]) ).
thf(12377,plain,
! [A: $i] :
( ~ ( empty_set @ powerset @ empty )
| ~ ( empty_set @ singleton @ ( A @ set_union2 ) @ empty ) ),
inference(pattern_uni,[status(thm)],[12376:[bind(A,$thf( empty_set @ singleton @ ( C @ set_union2 ) )),bind(B,$thf( C ))]]) ).
thf(12468,plain,
! [A: $i] :
( ~ ( empty_set @ powerset @ empty )
| ~ ( empty_set @ singleton @ ( A @ set_union2 ) @ empty ) ),
inference(simp,[status(thm)],[12377]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ set_intersection2 ) @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(169,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ set_intersection2 ) @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ set_intersection2 ) @ ( A @ subset ) )
| ~ ( C @ ( A @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_difference ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(276,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_difference ) )
= A )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_difference ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1378,plain,
! [B: $i,A: $i] :
( ( A != sk3 )
| ( B != empty_set )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[106,450]) ).
thf(1379,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( sk3 @ ( A @ subset ) )
| ~ ( A @ ( sk3 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[1378:[bind(A,$thf( sk3 ))]]) ).
thf(1479,plain,
( ~ ( sk3 @ ( empty_set @ subset ) )
| ~ ( empty_set @ ( sk3 @ subset ) ) ),
inference(simp,[status(thm)],[1379]) ).
thf(1571,plain,
( ~ $true
| ~ ( empty_set @ ( sk3 @ subset ) ) ),
inference(rewrite,[status(thm)],[1479,358]) ).
thf(1572,plain,
~ ( empty_set @ ( sk3 @ subset ) ),
inference(simp,[status(thm)],[1571]) ).
thf(1601,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( empty_set @ ( sk3 @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,1572]) ).
thf(1602,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( empty_set @ ( sk3 @ subset ) ) ),
inference(simp,[status(thm)],[1601]) ).
thf(1609,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= empty_set )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[1602]) ).
thf(1616,plain,
! [A: $i] :
( ( A @ ( sk3 @ set_union2 ) )
!= empty_set ),
inference(simp,[status(thm)],[1609]) ).
thf(5241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= ( C @ ( sk3 @ set_union2 ) ) )
| ( ( B @ ( A @ set_union2 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[321,1616]) ).
thf(5242,plain,
! [A: $i] :
( ( sk3 @ ( A @ set_union2 ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[5241:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(269,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(107,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(108,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[107]) ).
thf(109,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk6 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk4 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ( ( F @ ( G @ ( H @ sk6 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk6 ) ) )
= F )
| ( H @ ( G @ ( F @ sk4 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk4 ) ) )
| ( ( F @ ( G @ ( H @ sk5 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk4 ) ) )
| ( ( F @ ( G @ ( H @ sk5 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk4 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk5 ) ) @ in ) ) )
& ( ( C @ ( E @ in ) )
| ( E != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C @ ( E @ in ) )
| ( E != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ) ),
inference(cnf,[status(esa)],[108]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[114]) ).
thf(131,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ in ) ),
inference(simp,[status(thm)],[130]) ).
thf(845,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( empty_set @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[131,409]) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( empty_set @ ( C @ in ) ) ),
inference(simp,[status(thm)],[845]) ).
thf(856,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( A != C ) ),
inference(simp,[status(thm)],[846]) ).
thf(861,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[856]) ).
thf(5347,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( B @ set_union2 ) ) )
| ( empty_set != empty_set )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[411,5242]) ).
thf(5348,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( B @ set_union2 ) ) )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(simp,[status(thm)],[5347]) ).
thf(5349,plain,
! [A: $i] : ( sk3 @ ( A @ set_union2 ) @ ( sk3 @ ( A @ set_union2 ) @ sk22 @ in ) ),
inference(pattern_uni,[status(thm)],[5348:[bind(A,$thf( sk3 @ ( C @ set_union2 ) )),bind(B,$thf( C ))]]) ).
thf(5405,plain,
! [A: $i] : ( sk3 @ ( A @ set_union2 ) @ ( sk3 @ ( A @ set_union2 ) @ sk22 @ in ) ),
inference(simp,[status(thm)],[5349]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(379,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(5287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( D @ ( C @ set_union2 ) ) )
| ( A @ ( B @ set_union2 ) @ ( C @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[321,82]) ).
thf(5288,plain,
! [B: $i,A: $i] : ( A @ ( B @ set_union2 ) @ ( A @ subset ) ),
inference(pattern_uni,[status(thm)],[5287:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
<=> ( ( A != B )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( ( ( A != B )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ proper_subset ) ) )
& ( ( B @ ( A @ proper_subset ) )
=> ( ( A != B )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(202,plain,
( ! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ proper_subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
=> ( ( A != B )
& ( B @ ( A @ subset ) ) ) ) ),
inference(miniscope,[status(thm)],[201]) ).
thf(203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ proper_subset ) )
| ( C = D )
| ~ ( D @ ( C @ subset ) ) )
& ( ( A != B )
| ~ ( B @ ( A @ proper_subset ) ) )
& ( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ proper_subset ) ) ) ),
inference(cnf,[status(esa)],[202]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ proper_subset ) ) ),
inference(cnfConj,[status(thm)],[203]) ).
thf(16281,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) ) )
| ~ $true
| ~ ( empty_set @ powerset @ empty )
| ~ ( B @ ( A @ proper_subset ) ) ),
inference(paramod_ordered,[status(thm)],[204,1844]) ).
thf(16282,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) ) )
| ~ ( empty_set @ powerset @ empty )
| ~ ( B @ ( A @ proper_subset ) ) ),
inference(simp,[status(thm)],[16281]) ).
thf(16283,plain,
( ~ ( empty_set @ powerset @ empty )
| ~ ( empty_set @ powerset @ ( empty_set @ singleton @ proper_subset ) ) ),
inference(pattern_uni,[status(thm)],[16282:[bind(A,$thf( empty_set @ singleton )),bind(B,$thf( empty_set @ powerset ))]]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk9 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk7 ) ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk9 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk7 ) ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk9 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk7 ) ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(3546,plain,
( ( ( empty_set @ powerset @ empty )
!= ( empty_set @ empty ) )
| ~ ( empty_set @ ( empty_set @ singleton @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[378,3281]) ).
thf(3547,plain,
( ( ( empty_set @ powerset @ empty )
!= ( empty_set @ empty ) )
| ~ ( empty_set @ ( empty_set @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[3546]) ).
thf(3557,plain,
( ( ( empty_set @ powerset )
!= empty_set )
| ~ ( empty_set @ ( empty_set @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[3547]) ).
thf(3696,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( empty_set @ ( empty_set @ singleton @ subset ) ) )
| ( ( empty_set @ powerset )
!= empty_set )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,3557]) ).
thf(3697,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( empty_set @ ( empty_set @ singleton @ subset ) ) )
| ( ( empty_set @ powerset )
!= empty_set ) ),
inference(simp,[status(thm)],[3696]) ).
thf(3714,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= empty_set )
| ( A
!= ( empty_set @ singleton ) )
| ( ( empty_set @ powerset )
!= empty_set ) ),
inference(simp,[status(thm)],[3697]) ).
thf(3717,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ singleton @ set_union2 ) )
!= empty_set )
| ( ( empty_set @ powerset )
!= empty_set ) ),
inference(simp,[status(thm)],[3714]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(174,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)],[20]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(185,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3962,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( sk3 @ set_union2 ) ) )
| ( empty_set != empty_set )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[411,1616]) ).
thf(3963,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( sk3 @ set_union2 ) ) )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(simp,[status(thm)],[3962]) ).
thf(3964,plain,
! [A: $i] : ( A @ ( sk3 @ set_union2 ) @ ( A @ ( sk3 @ set_union2 ) @ sk22 @ in ) ),
inference(pattern_uni,[status(thm)],[3963:[bind(A,$thf( D @ ( sk3 @ set_union2 ) )),bind(B,$thf( D ))]]) ).
thf(4186,plain,
! [A: $i] : ( A @ ( sk3 @ set_union2 ) @ ( A @ ( sk3 @ set_union2 ) @ sk22 @ in ) ),
inference(simp,[status(thm)],[3964]) ).
thf(5251,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= ( C @ ( sk3 @ set_union2 ) ) )
| ( C @ ( sk3 @ set_union2 ) @ ( B @ ( A @ set_union2 ) @ sk22 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[321,4186]) ).
thf(5252,plain,
! [A: $i] : ( A @ ( sk3 @ set_union2 ) @ ( sk3 @ ( A @ set_union2 ) @ sk22 @ in ) ),
inference(pattern_uni,[status(thm)],[5251:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(42,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(287,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(288,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
inference(cnf,[status(esa)],[287]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(182,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
inference(cnf,[status(esa)],[182]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(264,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(265,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
inference(cnf,[status(esa)],[264]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(78,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(79,plain,
~ ? [A: $i,B: $i] :
( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
inference(miniscope,[status(thm)],[78]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ proper_subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(903,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ set_difference ) @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ~ ( C @ ( D @ proper_subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[265,80]) ).
thf(904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ set_difference ) @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ~ ( C @ ( D @ proper_subset ) ) ),
inference(simp,[status(thm)],[903]) ).
thf(905,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ set_difference ) @ ( A @ proper_subset ) ),
inference(pattern_uni,[status(thm)],[904:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ set_difference ) )),bind(D,$thf( E ))]]) ).
thf(917,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ set_difference ) @ ( A @ proper_subset ) ),
inference(simp,[status(thm)],[905]) ).
thf(117,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( B @ ( A @ sk4 ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= A ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= A ) ),
inference(lifteq,[status(thm)],[117]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= A ) ),
inference(simp,[status(thm)],[124]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
| ~ ( C @ ( B @ ( A @ sk7 ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk7 ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk7 ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( A @ ( C @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(421,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ( ( B
= ( A @ powerset ) )
=> ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(47,axiom,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(325,plain,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(214,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_intersection2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(215,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_intersection2 ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
=> ( ! [D: $i] :
( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[214]) ).
thf(216,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk14 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk12 ) ) ) )
& ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ( G @ ( F @ ( G @ ( H @ sk14 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk12 ) ) ) )
& ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ( F @ ( F @ ( G @ ( H @ sk14 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk12 ) ) ) )
& ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ~ ( H @ ( G @ ( F @ sk12 ) ) )
| ~ ( G @ ( F @ ( G @ ( H @ sk13 ) ) @ in ) )
| ~ ( F @ ( F @ ( G @ ( H @ sk13 ) ) @ in ) ) )
& ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ~ ( H @ ( G @ ( F @ sk12 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk13 ) ) @ in ) ) )
& ( ( C @ ( E @ in ) )
| ~ ( B @ ( E @ in ) )
| ~ ( A @ ( E @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( B @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( A @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ) ),
inference(cnf,[status(esa)],[215]) ).
thf(221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(289,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(284,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(4269,plain,
! [A: $i] :
( ( A
!= ( sk3 @ sk22 ) )
| ( sk3 @ ( empty_set @ in ) )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[411,4074]) ).
thf(4270,plain,
( ( sk3 @ ( empty_set @ in ) )
| ( sk3 @ sk22 @ ( sk3 @ sk22 @ sk22 @ in ) ) ),
inference(pattern_uni,[status(thm)],[4269:[bind(A,$thf( sk3 @ sk22 ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(211,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(lifteq,[status(thm)],[165]) ).
thf(1135,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( empty_set @ ( C @ set_intersection2 ) ) )
| ( ( A @ ( B @ set_intersection2 ) )
= empty_set ) ),
inference(paramod_ordered,[status(thm)],[166,444]) ).
thf(1136,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_intersection2 ) )
= empty_set ),
inference(pattern_uni,[status(thm)],[1135:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).
thf(110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(121,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ in ) ),
inference(simp,[status(thm)],[120]) ).
thf(925,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ~ ( C @ ( D @ proper_subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,80]) ).
thf(926,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ~ ( C @ ( D @ proper_subset ) ) ),
inference(simp,[status(thm)],[925]) ).
thf(927,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( A @ proper_subset ) ),
inference(pattern_uni,[status(thm)],[926:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ set_intersection2 ) )),bind(D,$thf( E ))]]) ).
thf(937,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( A @ proper_subset ) ),
inference(simp,[status(thm)],[927]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(353,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(380,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[379]) ).
thf(381,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk21 ) @ in ) )
| ( ( E @ ( F @ sk20 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk21 ) )
= E )
| ( ( E @ ( F @ sk20 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk21 ) @ in ) )
| ( F @ ( E @ ( F @ sk20 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk21 ) )
= E )
| ( F @ ( E @ ( F @ sk20 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[380]) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[381]) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[385]) ).
thf(397,plain,
! [A: $i] : ( A @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[396]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(243,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( B @ ( A @ sk4 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk5 ) ) @ in ) ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk4 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk5 ) ) @ in ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[111]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk4 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk5 ) ) @ in ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_difference ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(292,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_difference ) ) ) )
& ( ( C
= ( B @ ( A @ set_difference ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(32,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(248,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(6,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(76,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(77,plain,
sk1 @ empty,
inference(cnf,[status(esa)],[76]) ).
thf(532,plain,
! [A: $i] :
( ( ( sk1 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[77,338]) ).
thf(533,plain,
! [A: $i] :
( ( ( sk1 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[532]) ).
thf(534,plain,
sk1 = empty_set,
inference(pattern_uni,[status(thm)],[533:[bind(A,$thf( sk1 ))]]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[97]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(102,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[101]) ).
thf(249,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[248]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[249]) ).
thf(11138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) @ ( sk3 @ sk22 @ in ) )
!= ( D @ ( C @ in ) ) )
| ~ ( D @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7130,250]) ).
thf(11139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) @ ( sk3 @ sk22 @ in ) )
!= ( D @ ( C @ in ) ) )
| ~ ( D @ empty ) ),
inference(simp,[status(thm)],[11138]) ).
thf(11140,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) @ empty ),
inference(pattern_uni,[status(thm)],[11139:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( sk3 @ sk22 )),bind(D,$thf( G @ ( I @ ( sk3 @ set_union2 ) @ set_union2 ) ))]]) ).
thf(11202,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( sk3 @ set_union2 ) @ set_union2 ) @ empty ),
inference(simp,[status(thm)],[11140]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(83,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(84,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ~ ? [B: $i] : ( A @ ( B @ set_union2 ) @ empty ) ),
inference(miniscope,[status(thm)],[83]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ set_union2 ) @ empty )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[84]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
=> ~ ( A @ ( B @ proper_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
=> ~ ( A @ ( B @ proper_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(188,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(189,plain,
( ~ ? [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
& ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ~ ? [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(miniscope,[status(thm)],[188]) ).
thf(190,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( D @ ( C @ disjoint ) )
| ~ ( D @ ( E @ in ) )
| ~ ( C @ ( E @ in ) ) )
& ( ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ disjoint ) ) )
& ( ( A @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ disjoint ) ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ disjoint ) ) ),
inference(cnfConj,[status(thm)],[190]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(195,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[196]) ).
thf(1127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( D @ ( C @ set_intersection2 ) ) )
| ~ ( A @ ( B @ set_intersection2 ) @ ( C @ proper_subset ) ) ),
inference(paramod_ordered,[status(thm)],[166,937]) ).
thf(1128,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ set_intersection2 ) @ ( A @ proper_subset ) ),
inference(pattern_uni,[status(thm)],[1127:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(11314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( C @ ( D @ ( sk3 @ set_union2 ) @ set_union2 ) ) )
| ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(paramod_ordered,[status(thm)],[321,11202]) ).
thf(11315,plain,
! [B: $i,A: $i] :
~ ( B @ ( sk3 @ set_union2 ) @ ( A @ set_union2 ) @ empty ),
inference(pattern_uni,[status(thm)],[11314:[bind(A,$thf( F @ ( sk3 @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F ))]]) ).
thf(11461,plain,
! [B: $i,A: $i] :
~ ( B @ ( sk3 @ set_union2 ) @ ( A @ set_union2 ) @ empty ),
inference(simp,[status(thm)],[11315]) ).
thf(11858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( D @ ( sk3 @ set_union2 ) ) )
| ~ ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) @ empty ) ),
inference(paramod_ordered,[status(thm)],[321,11461]) ).
thf(11859,plain,
! [B: $i,A: $i] :
~ ( sk3 @ ( A @ set_union2 ) @ ( B @ set_union2 ) @ empty ),
inference(pattern_uni,[status(thm)],[11858:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(12020,plain,
! [B: $i,A: $i] :
~ ( sk3 @ ( A @ set_union2 ) @ ( B @ set_union2 ) @ empty ),
inference(simp,[status(thm)],[11859]) ).
thf(46,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(322,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(323,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[322]) ).
thf(324,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[323]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(359,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(360,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(cnf,[status(esa)],[359]) ).
thf(361,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(lifteq,[status(thm)],[360]) ).
thf(799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ~ ( C @ ( D @ proper_subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,80]) ).
thf(800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ~ ( C @ ( D @ proper_subset ) ) ),
inference(simp,[status(thm)],[799]) ).
thf(801,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ set_union2 ) @ proper_subset ) ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ set_union2 ) ))]]) ).
thf(805,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ set_union2 ) @ proper_subset ) ),
inference(simp,[status(thm)],[801]) ).
thf(5237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= ( D @ ( C @ set_union2 ) ) )
| ~ ( C @ ( B @ ( A @ set_union2 ) @ proper_subset ) ) ),
inference(paramod_ordered,[status(thm)],[321,805]) ).
thf(5238,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ set_union2 ) @ proper_subset ) ),
inference(pattern_uni,[status(thm)],[5237:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(354,plain,
~ ? [A: $i] :
( ( A @ singleton )
= empty_set ),
inference(miniscope,[status(thm)],[353]) ).
thf(355,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(cnf,[status(esa)],[354]) ).
thf(356,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(lifteq,[status(thm)],[355]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(418,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(419,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(cnf,[status(esa)],[418]) ).
thf(420,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(lifteq,[status(thm)],[419]) ).
thf(1117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_intersection2 ) )
!= ( D @ ( C @ set_intersection2 ) ) )
| ( C @ ( B @ ( A @ set_intersection2 ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[166,288]) ).
thf(1118,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1117:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(328,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(5235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( D @ ( C @ set_union2 ) ) )
| ~ ( C @ ( A @ ( B @ set_union2 ) @ proper_subset ) ) ),
inference(paramod_ordered,[status(thm)],[321,805]) ).
thf(5236,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ set_union2 ) @ proper_subset ) ),
inference(pattern_uni,[status(thm)],[5235:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(7897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( C @ ( D @ set_union2 ) ) )
| ~ ( C @ ( A @ ( B @ set_union2 ) @ proper_subset ) ) ),
inference(paramod_ordered,[status(thm)],[321,5236]) ).
thf(7898,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ set_union2 ) @ proper_subset ) ),
inference(pattern_uni,[status(thm)],[7897:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(50,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(339,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(10135,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( empty_set @ singleton @ set_union2 ) ) )
| ( empty_set != empty_set )
| ( ( empty_set @ powerset )
!= empty_set )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[338,3717]) ).
thf(10136,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( empty_set @ singleton @ set_union2 ) ) )
| ( ( empty_set @ powerset )
!= empty_set )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[10135]) ).
thf(10137,plain,
! [A: $i] :
( ( ( empty_set @ powerset )
!= empty_set )
| ~ ( A @ ( empty_set @ singleton @ set_union2 ) @ empty ) ),
inference(pattern_uni,[status(thm)],[10136:[bind(A,$thf( D @ ( empty_set @ singleton @ set_union2 ) )),bind(B,$thf( D ))]]) ).
thf(10195,plain,
! [A: $i] :
( ( ( empty_set @ powerset )
!= empty_set )
| ~ ( A @ ( empty_set @ singleton @ set_union2 ) @ empty ) ),
inference(simp,[status(thm)],[10137]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(171,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
= A )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnf,[status(esa)],[171]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
inference(lifteq,[status(thm)],[172]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( B @ ( A @ sk4 ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= B ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= B ) ),
inference(lifteq,[status(thm)],[112]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= B ) ),
inference(simp,[status(thm)],[128]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(134,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( D @ ( C @ in ) ) )
| ~ ( D @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,250]) ).
thf(781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( D @ ( C @ in ) ) )
| ~ ( D @ empty ) ),
inference(simp,[status(thm)],[780]) ).
thf(782,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ unordered_pair ) ))]]) ).
thf(792,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(simp,[status(thm)],[782]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(266,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ proper_subset ) )
| ( A = B )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[203]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ proper_subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[206]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ proper_subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[209]) ).
thf(17714,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ ( B @ proper_subset ) )
| ~ $true
| ( B = C ) ),
inference(paramod_ordered,[status(thm)],[358,210]) ).
thf(17715,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ ( B @ proper_subset ) )
| ( B = C ) ),
inference(simp,[status(thm)],[17714]) ).
thf(17716,plain,
! [A: $i] :
( ( A @ ( empty_set @ proper_subset ) )
| ( empty_set = A ) ),
inference(pattern_uni,[status(thm)],[17715:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
| ~ ( C @ ( B @ ( A @ sk7 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk7 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(lifteq,[status(thm)],[143]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk7 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(175,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)],[174]) ).
thf(176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk10 ) @ in ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk10 ) @ in ) ) )
& ( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[175]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk10 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk10 ) @ in ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_union2 ) ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_union2 ) ) ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(149,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( A @ ( C @ in ) )
| ~ ( B @ ( A @ set_union2 ) @ ( C @ in ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(412,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(16263,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) ) )
| ( ( empty_set @ powerset )
!= empty_set )
| ~ $true
| ~ ( B @ ( A @ proper_subset ) ) ),
inference(paramod_ordered,[status(thm)],[204,1791]) ).
thf(16264,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ powerset @ ( empty_set @ singleton @ subset ) ) )
| ( ( empty_set @ powerset )
!= empty_set )
| ~ ( B @ ( A @ proper_subset ) ) ),
inference(simp,[status(thm)],[16263]) ).
thf(16265,plain,
( ( ( empty_set @ powerset )
!= empty_set )
| ~ ( empty_set @ powerset @ ( empty_set @ singleton @ proper_subset ) ) ),
inference(pattern_uni,[status(thm)],[16264:[bind(A,$thf( empty_set @ singleton )),bind(B,$thf( empty_set @ powerset ))]]) ).
thf(2110,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( sk3 @ set_union2 ) ) )
| ( empty_set != empty_set )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[338,1616]) ).
thf(2111,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( sk3 @ set_union2 ) ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[2110]) ).
thf(2112,plain,
! [A: $i] :
~ ( A @ ( sk3 @ set_union2 ) @ empty ),
inference(pattern_uni,[status(thm)],[2111:[bind(A,$thf( D @ ( sk3 @ set_union2 ) )),bind(B,$thf( D ))]]) ).
thf(2128,plain,
! [A: $i] :
~ ( A @ ( sk3 @ set_union2 ) @ empty ),
inference(simp,[status(thm)],[2112]) ).
thf(5277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= ( C @ ( sk3 @ set_union2 ) ) )
| ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(paramod_ordered,[status(thm)],[321,2128]) ).
thf(5278,plain,
! [A: $i] :
~ ( sk3 @ ( A @ set_union2 ) @ empty ),
inference(pattern_uni,[status(thm)],[5277:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ disjoint ) ) ),
inference(cnfConj,[status(thm)],[190]) ).
thf(18569,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ singleton ) )
| ( empty_set != empty_set )
| ( A @ ( empty_set @ proper_subset ) ) ),
inference(paramod_ordered,[status(thm)],[17716,356]) ).
thf(18570,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ singleton ) )
| ( A @ ( empty_set @ proper_subset ) ) ),
inference(simp,[status(thm)],[18569]) ).
thf(18571,plain,
! [A: $i] : ( A @ singleton @ ( empty_set @ proper_subset ) ),
inference(pattern_uni,[status(thm)],[18570:[bind(A,$thf( C @ singleton )),bind(B,$thf( C ))]]) ).
thf(19124,plain,
! [A: $i] : ( A @ singleton @ ( empty_set @ proper_subset ) ),
inference(simp,[status(thm)],[18571]) ).
thf(20454,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( empty_set @ proper_subset ) )
!= ( B @ ( C @ proper_subset ) ) )
| ~ $true
| ~ ( C @ ( B @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[19124,80]) ).
thf(20455,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( empty_set @ proper_subset ) )
!= ( B @ ( C @ proper_subset ) ) )
| ~ ( C @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[20454]) ).
thf(20456,plain,
! [A: $i] :
~ ( empty_set @ ( A @ singleton @ subset ) ),
inference(pattern_uni,[status(thm)],[20455:[bind(A,$thf( D )),bind(B,$thf( D @ singleton )),bind(C,$thf( empty_set ))]]) ).
thf(20549,plain,
! [A: $i] :
~ ( empty_set @ ( A @ singleton @ subset ) ),
inference(simp,[status(thm)],[20456]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ proper_subset ) )
| ~ ( B @ ( A @ proper_subset ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(802,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ~ ( B @ ( C @ proper_subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,80]) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ~ ( B @ ( C @ proper_subset ) ) ),
inference(simp,[status(thm)],[802]) ).
thf(804,plain,
! [A: $i] :
~ ( empty_set @ ( A @ proper_subset ) ),
inference(pattern_uni,[status(thm)],[803:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk10 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk10 ) @ in ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
| ( B @ ( A @ ( B @ ( C @ sk9 ) ) @ in ) )
| ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk7 ) ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( C @ sk9 ) ) @ in ) )
| ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk7 ) ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( C @ sk9 ) ) @ in ) )
| ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk7 ) ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(186,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(cnf,[status(esa)],[185]) ).
thf(187,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(lifteq,[status(thm)],[186]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(274,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk12 ) ) ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk12 ) ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk12 ) ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_intersection2 ) @ ( C @ ( A @ set_intersection2 ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(245,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_intersection2 ) @ ( C @ ( A @ set_intersection2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(362,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
inference(cnf,[status(esa)],[211]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
inference(lifteq,[status(thm)],[212]) ).
thf(3951,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ singleton ) )
| ( empty_set != empty_set )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[411,356]) ).
thf(3952,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ singleton ) )
| ( A @ ( A @ sk22 @ in ) ) ),
inference(simp,[status(thm)],[3951]) ).
thf(3953,plain,
! [A: $i] : ( A @ singleton @ ( A @ singleton @ sk22 @ in ) ),
inference(pattern_uni,[status(thm)],[3952:[bind(A,$thf( C @ singleton )),bind(B,$thf( C ))]]) ).
thf(4181,plain,
! [A: $i] : ( A @ singleton @ ( A @ singleton @ sk22 @ in ) ),
inference(simp,[status(thm)],[3953]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(251,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
& ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(11520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( D @ ( sk3 @ set_union2 ) ) )
| ( ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[321,11244]) ).
thf(11521,plain,
! [B: $i,A: $i] :
( ( B @ ( sk3 @ ( A @ set_union2 ) @ set_union2 ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[11520:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(11636,plain,
! [B: $i,A: $i] :
( ( B @ ( sk3 @ ( A @ set_union2 ) @ set_union2 ) )
!= empty_set ),
inference(simp,[status(thm)],[11521]) ).
thf(12685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( sk3 @ ( C @ set_union2 ) ) )
| ( ( D @ ( A @ ( B @ set_union2 ) @ set_union2 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[321,11636]) ).
thf(12686,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk3 @ set_union2 ) @ set_union2 ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[12685:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(12810,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk3 @ set_union2 ) @ set_union2 ) )
!= empty_set ),
inference(simp,[status(thm)],[12686]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(198,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(5253,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= ( C @ ( sk3 @ set_union2 ) ) )
| ( B @ ( A @ set_union2 ) @ ( C @ ( sk3 @ set_union2 ) @ sk22 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[321,4186]) ).
thf(5254,plain,
! [A: $i] : ( sk3 @ ( A @ set_union2 ) @ ( A @ ( sk3 @ set_union2 ) @ sk22 @ in ) ),
inference(pattern_uni,[status(thm)],[5253:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(7001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= ( C @ ( sk3 @ set_union2 ) ) )
| ( B @ ( A @ set_union2 ) @ ( sk3 @ sk22 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[321,6965]) ).
thf(7002,plain,
! [A: $i] : ( sk3 @ ( A @ set_union2 ) @ ( sk3 @ sk22 @ in ) ),
inference(pattern_uni,[status(thm)],[7001:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ~ ( B @ ( D @ in ) )
| ~ ( A @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ~ ( B @ ( D @ in ) )
| ~ ( A @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
| ~ ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) ) ),
inference(simp,[status(thm)],[225]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(241,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1177,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( empty_set @ set_intersection2 ) )
!= ( C @ ( B @ set_intersection2 ) ) )
| ( empty_set @ ( B @ ( C @ sk2 ) @ in ) )
| ( C @ ( B @ disjoint ) ) ),
inference(paramod_ordered,[status(thm)],[1136,89]) ).
thf(1178,plain,
! [A: $i] :
( ( empty_set @ ( empty_set @ ( A @ sk2 ) @ in ) )
| ( A @ ( empty_set @ disjoint ) ) ),
inference(pattern_uni,[status(thm)],[1177:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).
thf(1625,plain,
! [A: $i] :
( $false
| ( A @ ( empty_set @ disjoint ) ) ),
inference(rewrite,[status(thm)],[1178,1085]) ).
thf(1626,plain,
! [A: $i] : ( A @ ( empty_set @ disjoint ) ),
inference(simp,[status(thm)],[1625]) ).
thf(1115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( D @ ( C @ set_intersection2 ) ) )
| ( C @ ( A @ ( B @ set_intersection2 ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[166,288]) ).
thf(1116,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ set_intersection2 ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1115:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( C @ ( D @ set_intersection2 ) ) )
| ( C @ ( A @ ( B @ set_intersection2 ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[166,1116]) ).
thf(1551,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ set_intersection2 ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1550:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ disjoint ) )
| ~ ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) ) ),
inference(cnfConj,[status(thm)],[190]) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ disjoint ) )
| ~ ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(342,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ in ) )
| ( D = B )
| ( D = A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ unordered_pair ) @ ( C @ in ) )
| ( C = B )
| ( C = A ) ),
inference(simp,[status(thm)],[122]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(370,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_intersection2 ) )
= empty_set )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(12687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( D @ ( sk3 @ ( C @ set_union2 ) @ set_union2 ) ) )
| ( ( A @ ( B @ set_union2 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[321,11636]) ).
thf(12688,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( B @ set_union2 ) @ ( A @ set_union2 ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[12687:[bind(A,$thf( sk3 @ ( E @ set_union2 ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(12811,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( B @ set_union2 ) @ ( A @ set_union2 ) )
!= empty_set ),
inference(simp,[status(thm)],[12688]) ).
thf(14134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( sk3 @ ( D @ set_union2 ) ) )
| ( ( A @ ( B @ set_union2 ) @ ( C @ set_union2 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[321,12811]) ).
thf(14135,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ set_union2 ) @ ( B @ set_union2 ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[14134:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(14279,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ set_union2 ) @ ( B @ set_union2 ) )
!= empty_set ),
inference(simp,[status(thm)],[14135]) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= A )
| ( C @ ( B @ ( A @ sk4 ) ) ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= A ) ),
inference(lifteq,[status(thm)],[113]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= A ) ),
inference(simp,[status(thm)],[126]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(72,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6740,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( empty_set @ singleton @ set_union2 ) ) )
| ( empty_set != empty_set )
| ~ ( empty_set @ powerset @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[338,3579]) ).
thf(6741,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( empty_set @ singleton @ set_union2 ) ) )
| ~ ( empty_set @ powerset @ empty )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[6740]) ).
thf(6742,plain,
! [A: $i] :
( ~ ( empty_set @ powerset @ empty )
| ~ ( A @ ( empty_set @ singleton @ set_union2 ) @ empty ) ),
inference(pattern_uni,[status(thm)],[6741:[bind(A,$thf( D @ ( empty_set @ singleton @ set_union2 ) )),bind(B,$thf( D ))]]) ).
thf(6835,plain,
! [A: $i] :
( ~ ( empty_set @ powerset @ empty )
| ~ ( A @ ( empty_set @ singleton @ set_union2 ) @ empty ) ),
inference(simp,[status(thm)],[6742]) ).
thf(5227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( empty_set @ ( C @ set_union2 ) ) )
| ( ( A @ ( B @ set_union2 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[321,324]) ).
thf(5228,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_union2 ) )
= A ),
inference(pattern_uni,[status(thm)],[5227:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).
thf(73,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(272,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk6 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk4 ) ) ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk6 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk6 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
| ~ ( C @ ( B @ ( A @ sk7 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk7 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(lifteq,[status(thm)],[147]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk7 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_union2 ) ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(776,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( empty_set @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,409]) ).
thf(777,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( empty_set @ ( C @ in ) ) ),
inference(simp,[status(thm)],[776]) ).
thf(787,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( B != C ) ),
inference(simp,[status(thm)],[777]) ).
thf(790,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[787]) ).
thf(14132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( sk3 @ ( D @ set_union2 ) @ ( C @ set_union2 ) ) )
| ( ( A @ ( B @ set_union2 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[321,12811]) ).
thf(14133,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ ( B @ set_union2 ) @ set_union2 ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[14132:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( E @ set_union2 ) )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(14278,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ ( B @ set_union2 ) @ set_union2 ) )
!= empty_set ),
inference(simp,[status(thm)],[14133]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ disjoint ) )
| ~ ( B @ ( A @ disjoint ) ) ),
inference(cnf,[status(esa)],[167]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(262,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(135,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[134]) ).
thf(136,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[135]) ).
thf(340,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(cnf,[status(esa)],[339]) ).
thf(341,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(lifteq,[status(thm)],[340]) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( C @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[397,250]) ).
thf(470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( C @ empty ) ),
inference(simp,[status(thm)],[469]) ).
thf(471,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(pattern_uni,[status(thm)],[470:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ singleton ))]]) ).
thf(474,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(simp,[status(thm)],[471]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(400,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(8025,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) @ ( A @ subset ) )
!= ( empty_set @ ( empty_set @ singleton @ subset ) ) )
| ( ( empty_set @ powerset )
!= empty_set )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5288,3557]) ).
thf(8026,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) @ ( A @ subset ) )
!= ( empty_set @ ( empty_set @ singleton @ subset ) ) )
| ( ( empty_set @ powerset )
!= empty_set ) ),
inference(simp,[status(thm)],[8025]) ).
thf(8081,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= empty_set )
| ( A
!= ( empty_set @ singleton ) )
| ( ( empty_set @ powerset )
!= empty_set ) ),
inference(simp,[status(thm)],[8026]) ).
thf(8093,plain,
! [A: $i] :
( ( ( empty_set @ singleton @ ( A @ set_union2 ) )
!= empty_set )
| ( ( empty_set @ powerset )
!= empty_set ) ),
inference(simp,[status(thm)],[8081]) ).
thf(500,plain,
! [A: $i] :
( ( empty_set != empty_set )
| ( ( A @ singleton )
!= ( empty_set @ powerset ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[338,66]) ).
thf(501,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( empty_set @ powerset ) )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[500:[]]) ).
thf(11316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( D @ ( sk3 @ set_union2 ) ) )
| ~ ( C @ ( A @ ( B @ set_union2 ) @ set_union2 ) @ empty ) ),
inference(paramod_ordered,[status(thm)],[321,11202]) ).
thf(11317,plain,
! [B: $i,A: $i] :
~ ( B @ ( sk3 @ ( A @ set_union2 ) @ set_union2 ) @ empty ),
inference(pattern_uni,[status(thm)],[11316:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(11462,plain,
! [B: $i,A: $i] :
~ ( B @ ( sk3 @ ( A @ set_union2 ) @ set_union2 ) @ empty ),
inference(simp,[status(thm)],[11317]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ~ ( B @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_union2 ) ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ~ ( B @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_union2 ) ) ) ),
inference(lifteq,[status(thm)],[146]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) @ ( C @ in ) )
| ~ ( B @ ( C @ in ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(18888,plain,
! [A: $i] :
( ( A != sk3 )
| ( empty_set != empty_set )
| ( A @ ( empty_set @ proper_subset ) ) ),
inference(paramod_ordered,[status(thm)],[17716,450]) ).
thf(18889,plain,
! [A: $i] :
( ( A != sk3 )
| ( A @ ( empty_set @ proper_subset ) ) ),
inference(simp,[status(thm)],[18888]) ).
thf(18890,plain,
sk3 @ ( empty_set @ proper_subset ),
inference(pattern_uni,[status(thm)],[18889:[bind(A,$thf( sk3 ))]]) ).
thf(34158,plain,
$false,
inference(e,[status(thm)],[69,13052,12468,170,276,5242,269,861,5405,379,5288,16283,153,3717,174,185,5252,288,184,917,125,357,157,421,1572,325,228,289,78,284,4270,164,321,211,1136,106,121,937,353,397,411,243,265,89,133,292,248,534,102,11202,85,201,6652,70,192,137,92,11244,197,1128,12020,324,361,65,5238,403,188,356,169,420,1118,328,7898,339,1791,10195,173,129,134,792,266,805,1616,17716,264,161,180,444,149,412,16265,5278,166,191,20549,204,71,4186,3579,804,181,86,159,187,7130,274,81,230,245,362,76,213,91,4181,66,251,155,12810,198,5254,7002,226,167,241,80,1626,1551,194,342,123,1472,11461,95,67,370,14279,338,1085,177,182,127,2128,11637,359,336,12811,72,11636,250,450,6965,1844,6835,319,5228,171,418,75,272,4074,82,119,378,214,287,1116,151,19124,790,14278,168,262,210,107,136,341,358,195,474,400,94,8093,131,442,501,11462,5236,163,200,322,18890,83,1037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU147+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.23/0.49 % Computer : n009.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 08:40:14 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.30/1.25 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.89/1.55 % [INFO] Parsing done (298ms).
% 1.89/1.58 % [INFO] Running in sequential loop mode.
% 2.73/1.95 % [INFO] eprover registered as external prover.
% 2.73/1.96 % [INFO] Scanning for conjecture ...
% 2.73/2.05 % [INFO] Found a conjecture (or negated_conjecture) and 69 axioms. Running axiom selection ...
% 3.11/2.13 % [INFO] Axiom selection finished. Selected 62 axioms (removed 7 axioms).
% 3.48/2.23 % [INFO] Problem is first-order (TPTP FOF).
% 3.48/2.24 % [INFO] Type checking passed.
% 3.48/2.25 % [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 ...
% 95.63/20.33 % External prover 'e' found a proof!
% 95.63/20.33 % [INFO] Killing All external provers ...
% 95.63/20.34 % Time passed: 19664ms (effective reasoning time: 18748ms)
% 95.63/20.34 % 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)>
% 95.63/20.34 % Axioms used in derivation (62): fc1_xboole_0, t2_boole, d1_xboole_0, t6_boole, l2_zfmisc_1, t2_xboole_1, t19_xboole_1, t17_xboole_1, d1_tarski, idempotence_k3_xboole_0, t1_boole, t3_xboole_1, t37_xboole_1, commutativity_k3_xboole_0, d2_tarski, fc2_xboole_0, t1_xboole_1, commutativity_k2_xboole_0, t4_xboole_0, d8_xboole_0, t2_tarski, t33_xboole_1, l32_xboole_1, t4_boole, fc3_xboole_0, d2_xboole_0, t7_boole, t48_xboole_1, d7_xboole_0, t83_xboole_1, l4_zfmisc_1, antisymmetry_r2_xboole_0, l3_zfmisc_1, commutativity_k2_tarski, d1_zfmisc_1, t69_enumset1, t26_xboole_1, t63_xboole_1, t8_xboole_1, t28_xboole_1, d3_tarski, reflexivity_r1_tarski, d4_xboole_0, t36_xboole_1, t8_boole, rc1_xboole_0, t12_xboole_1, symmetry_r1_xboole_0, idempotence_k2_xboole_0, d10_xboole_0, t7_xboole_1, t60_xboole_1, t3_xboole_0, t3_boole, rc2_xboole_0, t45_xboole_1, t40_xboole_1, l1_zfmisc_1, irreflexivity_r2_xboole_0, d3_xboole_0, t39_xboole_1, antisymmetry_r2_hidden
% 95.63/20.34 % No. of inferences in proof: 511
% 95.63/20.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19664 ms resp. 18748 ms w/o parsing
% 97.06/20.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 97.06/20.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------