TSTP Solution File: SET652+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET652+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:53:58 EDT 2023
% Result : Theorem 155.53s 28.78s
% Output : Refutation 156.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 57
% Syntax : Number of formulae : 1113 ( 289 unt; 30 typ; 0 def)
% Number of atoms : 3187 ( 657 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 12439 (1297 ~;1220 |; 36 &;9734 @)
% ( 8 <=>; 144 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 9 con; 0-2 aty)
% Number of variables : 1814 ( 0 ^;1797 !; 17 ?;1814 :)
% Comments :
%------------------------------------------------------------------------------
thf(ilf_type_type,type,
ilf_type: $i > $i > $o ).
thf(set_type_type,type,
set_type: $i ).
thf(relation_type_type,type,
relation_type: $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(binary_relation_type_type,type,
binary_relation_type: $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(subset_type_type,type,
subset_type: $i > $i ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(relation_like_type,type,
relation_like: $i > $o ).
thf(member_type_type,type,
member_type: $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i > $i > $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i ).
thf(sk11_type,type,
sk11: $i > $i > $i ).
thf(sk12_type,type,
sk12: $i > $i > $i ).
thf(sk13_type,type,
sk13: $i > $i > $i ).
thf(sk14_type,type,
sk14: $i > $i ).
thf(sk15_type,type,
sk15: $i > $i > $i ).
thf(4,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( relation_type @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
thf(38,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( relation_type @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ( ilf_type @ ( sk5 @ B @ A ) @ ( relation_type @ B @ A ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(27,axiom,
! [A: $i] : ( ilf_type @ A @ set_type ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
thf(111,plain,
! [A: $i] : ( ilf_type @ A @ set_type ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(112,plain,
! [A: $i] : ( ilf_type @ A @ set_type ),
inference(cnf,[status(esa)],[111]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ( ilf_type @ ( sk5 @ B @ A ) @ ( relation_type @ B @ A ) ) ),
inference(rewrite,[status(thm)],[39,112]) ).
thf(176,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk5 @ B @ A ) @ ( relation_type @ B @ A ) ),
inference(simp,[status(thm)],[175]) ).
thf(24,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( subset @ ( domain_of @ C ) @ A )
& ( subset @ ( range_of @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
thf(102,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( subset @ ( domain_of @ C ) @ A )
& ( subset @ ( range_of @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( subset @ ( domain_of @ C ) @ A ) ),
inference(cnf,[status(esa)],[102]) ).
thf(3844,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( subset @ ( domain_of @ C ) @ A ) ),
inference(rewrite,[status(thm)],[103,112]) ).
thf(3845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( subset @ ( domain_of @ C ) @ A ) ),
inference(simp,[status(thm)],[3844]) ).
thf(3881,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( domain_of @ E ) @ C )
| ( ( ilf_type @ ( sk5 @ B @ A ) @ ( relation_type @ B @ A ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[176,3845]) ).
thf(3882,plain,
! [B: $i,A: $i] : ( subset @ ( domain_of @ ( sk5 @ A @ B ) ) @ A ),
inference(pattern_uni,[status(thm)],[3881:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( sk5 @ F @ G ))]]) ).
thf(3967,plain,
! [B: $i,A: $i] : ( subset @ ( domain_of @ ( sk5 @ A @ B ) ) @ A ),
inference(simp,[status(thm)],[3882]) ).
thf(1,conjecture,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ C @ A ) )
=> ( ( subset @ ( range_of @ D ) @ B )
=> ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_14) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ C @ A ) )
=> ( ( subset @ ( range_of @ D ) @ B )
=> ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ ( relation_type @ C @ A ) )
=> ( ( subset @ ( range_of @ D ) @ B )
=> ( ilf_type @ D @ ( relation_type @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,plain,
subset @ ( range_of @ sk4 ) @ sk2,
inference(cnf,[status(esa)],[29]) ).
thf(20,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(94,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ set_type )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ),
inference(cnf,[status(esa)],[94]) ).
thf(3017,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ $true
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ),
inference(rewrite,[status(thm)],[95,112]) ).
thf(3018,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ),
inference(simp,[status(thm)],[3017]) ).
thf(3075,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( subset @ A @ C )
| ( ( subset @ ( range_of @ sk4 ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,3018]) ).
thf(3076,plain,
! [A: $i] :
( ~ ( subset @ A @ ( range_of @ sk4 ) )
| ( subset @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3075:[bind(A,$thf( A )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( sk2 ))]]) ).
thf(4139,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ sk2 )
| ( ( subset @ ( domain_of @ ( sk5 @ A @ B ) ) @ A )
!= ( subset @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3967,3076]) ).
thf(4140,plain,
! [A: $i] : ( subset @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[4139:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( F )),bind(C,$thf( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ F ) ))]]) ).
thf(4188,plain,
! [A: $i] : ( subset @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) @ sk2 ),
inference(simp,[status(thm)],[4140]) ).
thf(25,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ! [C: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
=> ( ilf_type @ C @ ( relation_type @ A @ B ) ) )
& ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
thf(105,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ! [C: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
=> ( ilf_type @ C @ ( relation_type @ A @ B ) ) )
& ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ),
inference(cnf,[status(esa)],[105]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(5181,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ),
inference(rewrite,[status(thm)],[108,112]) ).
thf(5182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ),
inference(simp,[status(thm)],[5181]) ).
thf(5206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ilf_type @ E @ ( subset_type @ ( cross_product @ C @ D ) ) )
| ( ( ilf_type @ ( sk5 @ B @ A ) @ ( relation_type @ B @ A ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[176,5182]) ).
thf(5207,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk5 @ A @ B ) @ ( subset_type @ ( cross_product @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[5206:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( sk5 @ F @ G ))]]) ).
thf(5282,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk5 @ A @ B ) @ ( subset_type @ ( cross_product @ A @ B ) ) ),
inference(simp,[status(thm)],[5207]) ).
thf(26,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
=> ( relation_like @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
thf(109,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
=> ( relation_like @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( relation_like @ C ) ),
inference(cnf,[status(esa)],[109]) ).
thf(5443,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( relation_like @ C ) ),
inference(rewrite,[status(thm)],[110,112]) ).
thf(5444,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( relation_like @ C ) ),
inference(simp,[status(thm)],[5443]) ).
thf(6351,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation_like @ E )
| ( ( ilf_type @ ( sk5 @ A @ B ) @ ( subset_type @ ( cross_product @ A @ B ) ) )
!= ( ilf_type @ E @ ( subset_type @ ( cross_product @ C @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5282,5444]) ).
thf(6352,plain,
! [B: $i,A: $i] : ( relation_like @ ( sk5 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[6351:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( sk5 @ F @ G ))]]) ).
thf(6388,plain,
! [B: $i,A: $i] : ( relation_like @ ( sk5 @ A @ B ) ),
inference(simp,[status(thm)],[6352]) ).
thf(10,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( ilf_type @ A @ binary_relation_type )
<=> ( ( relation_like @ A )
& ( ilf_type @ A @ set_type ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
thf(53,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( ( ilf_type @ A @ binary_relation_type )
=> ( ( relation_like @ A )
& ( ilf_type @ A @ set_type ) ) )
& ( ( ( relation_like @ A )
& ( ilf_type @ A @ set_type ) )
=> ( ilf_type @ A @ binary_relation_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(56,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( relation_like @ A )
| ~ ( ilf_type @ A @ set_type )
| ( ilf_type @ A @ binary_relation_type ) ),
inference(cnf,[status(esa)],[53]) ).
thf(57,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( relation_like @ A )
| ( ilf_type @ A @ binary_relation_type ) ),
inference(simp,[status(thm)],[56]) ).
thf(290,plain,
! [A: $i] :
( ~ $true
| ~ ( relation_like @ A )
| ( ilf_type @ A @ binary_relation_type ) ),
inference(rewrite,[status(thm)],[57,112]) ).
thf(291,plain,
! [A: $i] :
( ~ ( relation_like @ A )
| ( ilf_type @ A @ binary_relation_type ) ),
inference(simp,[status(thm)],[290]) ).
thf(6395,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ binary_relation_type )
| ( ( relation_like @ ( sk5 @ A @ B ) )
!= ( relation_like @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6388,291]) ).
thf(6396,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk5 @ A @ B ) @ binary_relation_type ),
inference(pattern_uni,[status(thm)],[6395:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( sk5 @ D @ E ))]]) ).
thf(6405,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk5 @ A @ B ) @ binary_relation_type ),
inference(simp,[status(thm)],[6396]) ).
thf(32,plain,
ilf_type @ sk4 @ ( relation_type @ sk3 @ sk1 ),
inference(cnf,[status(esa)],[29]) ).
thf(3875,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( domain_of @ C ) @ A )
| ( ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk1 ) )
!= ( ilf_type @ C @ ( relation_type @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,3845]) ).
thf(3876,plain,
subset @ ( domain_of @ sk4 ) @ sk3,
inference(pattern_uni,[status(thm)],[3875:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 )),bind(C,$thf( sk4 ))]]) ).
thf(7,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( empty @ A )
<=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ~ ( member @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
thf(44,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( ( empty @ A )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ~ ( member @ B @ A ) ) )
& ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ~ ( member @ B @ A ) )
=> ( empty @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(46,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( member @ ( sk7 @ A ) @ A )
| ( empty @ A ) ),
inference(cnf,[status(esa)],[44]) ).
thf(207,plain,
! [A: $i] :
( ~ $true
| ( member @ ( sk7 @ A ) @ A )
| ( empty @ A ) ),
inference(rewrite,[status(thm)],[46,112]) ).
thf(208,plain,
! [A: $i] :
( ( member @ ( sk7 @ A ) @ A )
| ( empty @ A ) ),
inference(simp,[status(thm)],[207]) ).
thf(16,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( subset @ A @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
thf(81,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) )
=> ( subset @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( subset @ A @ B )
| ~ ( ilf_type @ C @ set_type )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[81]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( subset @ A @ B )
| ~ $true
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(rewrite,[status(thm)],[85,112]) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(simp,[status(thm)],[249]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ B )
| ( ( subset @ ( range_of @ sk4 ) @ sk2 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35,250]) ).
thf(252,plain,
! [A: $i] :
( ~ ( member @ A @ ( range_of @ sk4 ) )
| ( member @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).
thf(265,plain,
! [A: $i] :
( ~ ( member @ A @ ( range_of @ sk4 ) )
| ( member @ A @ sk2 ) ),
inference(simp,[status(thm)],[252]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| ( member @ B @ sk2 )
| ( ( member @ ( sk7 @ A ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[208,265]) ).
thf(280,plain,
( ( empty @ ( range_of @ sk4 ) )
| ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk7 @ ( range_of @ sk4 ) ))]]) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ~ ( subset @ A @ B )
| ( member @ C @ B )
| ( ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[280,250]) ).
thf(319,plain,
! [A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ~ ( subset @ sk2 @ A )
| ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk7 @ ( range_of @ sk4 ) ))]]) ).
thf(325,plain,
! [A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ~ ( subset @ sk2 @ A )
| ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ A ) ),
inference(simp,[status(thm)],[319]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( empty @ A )
| ~ ( ilf_type @ B @ set_type )
| ~ ( member @ B @ A ) ),
inference(cnf,[status(esa)],[44]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ ( empty @ A )
| ~ $true
| ~ ( member @ B @ A ) ),
inference(rewrite,[status(thm)],[45,112]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( member @ B @ A ) ),
inference(simp,[status(thm)],[193]) ).
thf(1014,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ~ ( subset @ sk2 @ A )
| ~ ( empty @ B )
| ( ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ A )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[325,194]) ).
thf(1015,plain,
! [A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ~ ( subset @ sk2 @ A )
| ~ ( empty @ A ) ),
inference(pattern_uni,[status(thm)],[1014:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk7 @ ( range_of @ sk4 ) ))]]) ).
thf(4043,plain,
! [A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ~ ( empty @ A )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3876,1015]) ).
thf(4070,plain,
! [A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ~ ( empty @ A )
| ( ( domain_of @ sk4 )
!= sk2 )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[4043]) ).
thf(4094,plain,
( ( empty @ ( range_of @ sk4 ) )
| ~ ( empty @ sk3 )
| ( ( domain_of @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4070]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ~ ( empty @ A )
| ( ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[280,194]) ).
thf(322,plain,
( ( empty @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[321:[bind(A,$thf( sk2 )),bind(B,$thf( sk7 @ ( range_of @ sk4 ) ))]]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ~ ( empty @ sk2 )
| ~ ( member @ B @ A )
| ( ( empty @ ( range_of @ sk4 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[322,194]) ).
thf(330,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ~ ( member @ A @ ( range_of @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( B ))]]) ).
thf(338,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ~ ( member @ A @ ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[330]) ).
thf(353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ~ ( empty @ sk2 )
| ( ( member @ C @ B )
!= ( member @ D @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[250,338]) ).
thf(354,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( member @ B @ A )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( A )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( member @ B @ A )
| ~ ( empty @ sk2 ) ),
inference(simp,[status(thm)],[354]) ).
thf(15,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( relation_like @ A )
<=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ A )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ( B
= ( ordered_pair @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
thf(71,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( ( relation_like @ A )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ A )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ( B
= ( ordered_pair @ C @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ A )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ( B
= ( ordered_pair @ C @ D ) ) ) ) ) )
=> ( relation_like @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(73,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( member @ ( sk14 @ A ) @ A )
| ( relation_like @ A ) ),
inference(cnf,[status(esa)],[71]) ).
thf(267,plain,
! [A: $i] :
( ~ $true
| ( member @ ( sk14 @ A ) @ A )
| ( relation_like @ A ) ),
inference(rewrite,[status(thm)],[73,112]) ).
thf(268,plain,
! [A: $i] :
( ( member @ ( sk14 @ A ) @ A )
| ( relation_like @ A ) ),
inference(simp,[status(thm)],[267]) ).
thf(543,plain,
! [C: $i,B: $i,A: $i] :
( ( relation_like @ A )
| ~ ( subset @ B @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 )
| ( ( member @ ( sk14 @ A ) @ A )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[268,365]) ).
thf(544,plain,
! [A: $i] :
( ( relation_like @ A )
| ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk14 @ D ))]]) ).
thf(554,plain,
! [A: $i] :
( ( relation_like @ A )
| ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(simp,[status(thm)],[544]) ).
thf(4035,plain,
! [A: $i] :
( ( relation_like @ A )
| ~ ( empty @ sk2 )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3876,554]) ).
thf(4082,plain,
! [A: $i] :
( ( relation_like @ A )
| ~ ( empty @ sk2 )
| ( ( domain_of @ sk4 )
!= A )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[4035]) ).
thf(4101,plain,
( ( relation_like @ ( domain_of @ sk4 ) )
| ~ ( empty @ sk2 )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[4082]) ).
thf(13,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ A @ ( power_set @ B ) )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
thf(62,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( member @ A @ ( power_set @ B ) )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) )
=> ( member @ A @ ( power_set @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ( member @ ( sk10 @ B @ A ) @ A )
| ( member @ A @ ( power_set @ B ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ( member @ ( sk10 @ B @ A ) @ A )
| ( member @ A @ ( power_set @ B ) ) ),
inference(rewrite,[status(thm)],[64,112]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( member @ ( sk10 @ B @ A ) @ A )
| ( member @ A @ ( power_set @ B ) ) ),
inference(simp,[status(thm)],[400]) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ( member @ C @ sk2 )
| ( ( member @ ( sk10 @ B @ A ) @ A )
!= ( member @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[401,265]) ).
thf(407,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ( member @ ( sk10 @ A @ ( range_of @ sk4 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[406:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( D )),bind(C,$thf( sk10 @ D @ ( range_of @ sk4 ) ))]]) ).
thf(415,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ( member @ ( sk10 @ A @ ( range_of @ sk4 ) ) @ sk2 ) ),
inference(simp,[status(thm)],[407]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( member @ ( sk10 @ B @ A ) @ B )
| ( member @ A @ ( power_set @ B ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( member @ ( sk10 @ B @ A ) @ B )
| ( member @ A @ ( power_set @ B ) ) ),
inference(rewrite,[status(thm)],[65,112]) ).
thf(464,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk10 @ B @ A ) @ B )
| ( member @ A @ ( power_set @ B ) ) ),
inference(simp,[status(thm)],[463]) ).
thf(476,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ( member @ B @ ( power_set @ C ) )
| ( ( member @ ( sk10 @ A @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ ( sk10 @ C @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[415,464]) ).
thf(477,plain,
( ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )
| ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[476:[bind(A,$thf( sk2 )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( sk2 ))]]) ).
thf(489,plain,
member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ),
inference(simp,[status(thm)],[477]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( relation_like @ A )
| ~ ( ilf_type @ B @ set_type )
| ~ ( member @ B @ A )
| ( B
= ( ordered_pair @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( ordered_pair @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
= B )
| ~ ( ilf_type @ A @ set_type )
| ~ ( relation_like @ A )
| ~ ( ilf_type @ B @ set_type )
| ~ ( member @ B @ A ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(1550,plain,
! [B: $i,A: $i] :
( ( ( ordered_pair @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
= B )
| ~ $true
| ~ ( relation_like @ A )
| ~ $true
| ~ ( member @ B @ A ) ),
inference(rewrite,[status(thm)],[78,112]) ).
thf(1551,plain,
! [B: $i,A: $i] :
( ( ( ordered_pair @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
= B )
| ~ ( relation_like @ A )
| ~ ( member @ B @ A ) ),
inference(simp,[status(thm)],[1550]) ).
thf(1587,plain,
! [B: $i,A: $i] :
( ( ( ordered_pair @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
= B )
| ~ ( relation_like @ A )
| ( ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[489,1551]) ).
thf(1588,plain,
( ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
= ( range_of @ sk4 ) )
| ~ ( relation_like @ ( power_set @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1587:[bind(A,$thf( power_set @ sk2 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ( member @ C @ ( power_set @ D ) )
| ( ( member @ ( sk10 @ B @ A ) @ A )
!= ( member @ ( sk10 @ D @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[401,464]) ).
thf(474,plain,
! [A: $i] :
( ( member @ A @ ( power_set @ A ) )
| ( member @ A @ ( power_set @ A ) ) ),
inference(pattern_uni,[status(thm)],[473:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(488,plain,
! [A: $i] : ( member @ A @ ( power_set @ A ) ),
inference(simp,[status(thm)],[474]) ).
thf(508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ C )
| ( member @ D @ C )
| ( ( member @ A @ ( power_set @ A ) )
!= ( member @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[488,250]) ).
thf(509,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ B ) @ A )
| ( member @ B @ A ) ),
inference(pattern_uni,[status(thm)],[508:[bind(A,$thf( E )),bind(B,$thf( power_set @ E )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(521,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ B ) @ A )
| ( member @ B @ A ) ),
inference(simp,[status(thm)],[509]) ).
thf(6,axiom,
? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
thf(42,plain,
? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,plain,
ilf_type @ sk6 @ binary_relation_type,
inference(cnf,[status(esa)],[42]) ).
thf(14,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ ( range_of @ A ) )
<=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
thf(67,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( member @ B @ ( range_of @ A ) )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ C @ B ) @ A ) ) )
& ( ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ C @ B ) @ A ) )
=> ( member @ B @ ( range_of @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ binary_relation_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ set_type )
| ~ ( member @ ( ordered_pair @ C @ B ) @ A )
| ( member @ B @ ( range_of @ A ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(785,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ binary_relation_type )
| ~ $true
| ~ $true
| ~ ( member @ ( ordered_pair @ C @ B ) @ A )
| ( member @ B @ ( range_of @ A ) ) ),
inference(rewrite,[status(thm)],[68,112]) ).
thf(786,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ binary_relation_type )
| ~ ( member @ ( ordered_pair @ C @ B ) @ A )
| ( member @ B @ ( range_of @ A ) ) ),
inference(simp,[status(thm)],[785]) ).
thf(816,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ C @ B ) @ A )
| ( member @ B @ ( range_of @ A ) )
| ( ( ilf_type @ sk6 @ binary_relation_type )
!= ( ilf_type @ A @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[43,786]) ).
thf(817,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ B @ A ) @ sk6 )
| ( member @ A @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[816:[bind(A,$thf( sk6 ))]]) ).
thf(862,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ B @ A ) @ sk6 )
| ( member @ A @ ( range_of @ sk6 ) ) ),
inference(simp,[status(thm)],[817]) ).
thf(1267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( power_set @ B ) @ A )
| ( member @ C @ ( range_of @ sk6 ) )
| ( ( member @ B @ A )
!= ( member @ ( ordered_pair @ D @ C ) @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[521,862]) ).
thf(1268,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( ordered_pair @ A @ B ) ) @ sk6 )
| ( member @ B @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1267:[bind(A,$thf( sk6 )),bind(B,$thf( ordered_pair @ E @ F )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( ordered_pair @ A @ B ) ) @ sk6 )
| ( member @ B @ ( range_of @ sk6 ) ) ),
inference(simp,[status(thm)],[1268]) ).
thf(1957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( ordered_pair @ A @ B ) ) @ sk6 )
| ~ ( empty @ C )
| ( ( member @ B @ ( range_of @ sk6 ) )
!= ( member @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1297,194]) ).
thf(1958,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( ordered_pair @ A @ B ) ) @ sk6 )
| ~ ( empty @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1957:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( range_of @ sk6 )),bind(D,$thf( B ))]]) ).
thf(1994,plain,
! [B: $i,A: $i] :
( ~ ( relation_like @ ( power_set @ sk2 ) )
| ~ ( subset @ ( power_set @ ( range_of @ sk4 ) ) @ sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
!= ( ordered_pair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1588,1958]) ).
thf(1995,plain,
( ~ ( relation_like @ ( power_set @ sk2 ) )
| ~ ( subset @ ( power_set @ ( range_of @ sk4 ) ) @ sk6 )
| ~ ( empty @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1994:[bind(A,$thf( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )),bind(B,$thf( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ))]]) ).
thf(5202,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk1 ) )
!= ( ilf_type @ C @ ( relation_type @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,5182]) ).
thf(5203,plain,
ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[5202:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 )),bind(C,$thf( sk4 ))]]) ).
thf(5473,plain,
! [C: $i,B: $i,A: $i] :
( ( relation_like @ C )
| ( ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5203,5444]) ).
thf(5474,plain,
relation_like @ sk4,
inference(pattern_uni,[status(thm)],[5473:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 )),bind(C,$thf( sk4 ))]]) ).
thf(5544,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
| ( ( relation_like @ sk4 )
!= ( relation_like @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5474,291]) ).
thf(5545,plain,
ilf_type @ sk4 @ binary_relation_type,
inference(pattern_uni,[status(thm)],[5544:[bind(A,$thf( sk4 ))]]) ).
thf(22,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( subset @ A @ ( cross_product @ ( domain_of @ A ) @ ( range_of @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(98,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( subset @ A @ ( cross_product @ ( domain_of @ A ) @ ( range_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(99,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ binary_relation_type )
| ( subset @ A @ ( cross_product @ ( domain_of @ A ) @ ( range_of @ A ) ) ) ),
inference(cnf,[status(esa)],[98]) ).
thf(5567,plain,
! [A: $i] :
( ( subset @ A @ ( cross_product @ ( domain_of @ A ) @ ( range_of @ A ) ) )
| ( ( ilf_type @ sk4 @ binary_relation_type )
!= ( ilf_type @ A @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[5545,99]) ).
thf(5568,plain,
subset @ sk4 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ),
inference(pattern_uni,[status(thm)],[5567:[bind(A,$thf( sk4 ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(60,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ set_type )
| ~ ( ilf_type @ D @ set_type )
| ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) ) ),
inference(rewrite,[status(thm)],[61,112]) ).
thf(232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ D )
| ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) )
| ( ( subset @ ( range_of @ sk4 ) @ sk2 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35,232]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) ) ),
inference(pattern_uni,[status(thm)],[233:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(9826,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ sk4 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5568,247]) ).
thf(9827,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ sk4 ) @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[9826:[bind(A,$thf( sk4 )),bind(B,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ))]]) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) )
| ( ( subset @ ( range_of @ sk4 ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[35,232]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[235:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( range_of @ sk4 )),bind(D,$thf( sk2 ))]]) ).
thf(10266,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ sk4 ) @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9827,236]) ).
thf(10267,plain,
subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[10266:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ sk4 )),bind(B,$thf( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ? [B: $i] : ( ilf_type @ B @ ( member_type @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
thf(58,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ? [B: $i] : ( ilf_type @ B @ ( member_type @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( ilf_type @ A @ set_type )
| ( ilf_type @ ( sk9 @ A ) @ ( member_type @ A ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(341,plain,
! [A: $i] :
( ( empty @ A )
| ~ $true
| ( ilf_type @ ( sk9 @ A ) @ ( member_type @ A ) ) ),
inference(rewrite,[status(thm)],[59,112]) ).
thf(342,plain,
! [A: $i] :
( ( empty @ A )
| ( ilf_type @ ( sk9 @ A ) @ ( member_type @ A ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(55,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ A @ binary_relation_type )
| ( relation_like @ A ) ),
inference(cnf,[status(esa)],[53]) ).
thf(215,plain,
! [A: $i] :
( ~ $true
| ~ ( ilf_type @ A @ binary_relation_type )
| ( relation_like @ A ) ),
inference(rewrite,[status(thm)],[55,112]) ).
thf(216,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ binary_relation_type )
| ( relation_like @ A ) ),
inference(simp,[status(thm)],[215]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| ( relation_like @ B )
| ( ( ilf_type @ ( sk9 @ A ) @ ( member_type @ A ) )
!= ( ilf_type @ B @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[342,216]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| ( relation_like @ B )
| ( ( sk9 @ A )
!= B )
| ( ( member_type @ A )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[343]) ).
thf(347,plain,
! [A: $i] :
( ( empty @ A )
| ( relation_like @ ( sk9 @ A ) )
| ( ( member_type @ A )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[345]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( subset @ ( range_of @ C ) @ B ) ),
inference(cnf,[status(esa)],[102]) ).
thf(4407,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( subset @ ( range_of @ C ) @ B ) ),
inference(rewrite,[status(thm)],[104,112]) ).
thf(4408,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( subset @ ( range_of @ C ) @ B ) ),
inference(simp,[status(thm)],[4407]) ).
thf(4439,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( range_of @ C ) @ B )
| ( ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk1 ) )
!= ( ilf_type @ C @ ( relation_type @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,4408]) ).
thf(4440,plain,
subset @ ( range_of @ sk4 ) @ sk1,
inference(pattern_uni,[status(thm)],[4439:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 )),bind(C,$thf( sk4 ))]]) ).
thf(6796,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( range_of @ sk4 ) @ sk1 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4440,236]) ).
thf(6797,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk1 @ sk2 ),
inference(pattern_uni,[status(thm)],[6796:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(9832,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk1 @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6797,247]) ).
thf(9833,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9832:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ sk1 @ sk2 ))]]) ).
thf(3328,plain,
! [A: $i] :
( ( subset @ A @ ( cross_product @ ( domain_of @ A ) @ ( range_of @ A ) ) )
| ( ( ilf_type @ sk6 @ binary_relation_type )
!= ( ilf_type @ A @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[43,99]) ).
thf(3329,plain,
subset @ sk6 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ),
inference(pattern_uni,[status(thm)],[3328:[bind(A,$thf( sk6 ))]]) ).
thf(6854,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ sk6 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3329,236]) ).
thf(6855,plain,
subset @ ( cross_product @ sk6 @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[6854:[bind(A,$thf( sk6 )),bind(B,$thf( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ))]]) ).
thf(257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( empty @ A )
| ~ ( subset @ B @ C )
| ( member @ D @ C )
| ( ( member @ ( sk7 @ A ) @ A )
!= ( member @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[208,250]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ~ ( subset @ B @ A )
| ( member @ ( sk7 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( sk7 @ E ))]]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ~ ( subset @ B @ A )
| ( member @ ( sk7 @ B ) @ A ) ),
inference(simp,[status(thm)],[258]) ).
thf(14741,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ ( sk7 @ B ) @ A )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3876,264]) ).
thf(14742,plain,
( ( empty @ ( domain_of @ sk4 ) )
| ( member @ ( sk7 @ ( domain_of @ sk4 ) ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[14741:[bind(A,$thf( sk3 )),bind(B,$thf( domain_of @ sk4 ))]]) ).
thf(16483,plain,
! [B: $i,A: $i] :
( ( empty @ ( domain_of @ sk4 ) )
| ~ ( empty @ A )
| ( ( member @ ( sk7 @ ( domain_of @ sk4 ) ) @ sk3 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14742,194]) ).
thf(16484,plain,
( ( empty @ ( domain_of @ sk4 ) )
| ~ ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[16483:[bind(A,$thf( sk3 )),bind(B,$thf( sk7 @ ( domain_of @ sk4 ) ))]]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ( member @ ( sk15 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[81]) ).
thf(2137,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ( member @ ( sk15 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(rewrite,[status(thm)],[83,112]) ).
thf(2138,plain,
! [B: $i,A: $i] :
( ( member @ ( sk15 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[2137]) ).
thf(2151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ~ ( empty @ C )
| ( ( member @ ( sk15 @ B @ A ) @ A )
!= ( member @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2138,194]) ).
thf(2152,plain,
! [B: $i,A: $i] :
( ( subset @ B @ A )
| ~ ( empty @ B ) ),
inference(pattern_uni,[status(thm)],[2151:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( sk15 @ E @ F ))]]) ).
thf(2168,plain,
! [B: $i,A: $i] :
( ( subset @ B @ A )
| ~ ( empty @ B ) ),
inference(simp,[status(thm)],[2152]) ).
thf(3136,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ B )
| ( subset @ C @ sk2 )
| ( ( subset @ B @ A )
!= ( subset @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2168,3076]) ).
thf(3137,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( subset @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3136:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3148,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( subset @ A @ sk2 ) ),
inference(simp,[status(thm)],[3137]) ).
thf(16532,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( subset @ A @ sk2 )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16484,3148]) ).
thf(16533,plain,
( ~ ( empty @ sk3 )
| ( subset @ ( domain_of @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[16532:[bind(A,$thf( domain_of @ sk4 ))]]) ).
thf(6844,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3876,236]) ).
thf(6845,plain,
subset @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk3 @ sk2 ),
inference(pattern_uni,[status(thm)],[6844:[bind(A,$thf( domain_of @ sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( subset @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).
thf(96,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( subset @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(97,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( subset @ A @ A ) ),
inference(cnf,[status(esa)],[96]) ).
thf(199,plain,
! [A: $i] :
( ~ $true
| ( subset @ A @ A ) ),
inference(rewrite,[status(thm)],[97,112]) ).
thf(200,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[199]) ).
thf(241,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ D @ E )
| ( subset @ ( cross_product @ B @ D ) @ ( cross_product @ C @ E ) )
| ( ( subset @ A @ A )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[200,232]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ C )
| ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ C )
| ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(9036,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3876,246]) ).
thf(9037,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ ( domain_of @ sk4 ) ) @ ( cross_product @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[9036:[bind(A,$thf( A )),bind(B,$thf( domain_of @ sk4 )),bind(C,$thf( sk3 ))]]) ).
thf(9798,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( cross_product @ A @ ( domain_of @ sk4 ) ) @ ( cross_product @ A @ sk3 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9037,247]) ).
thf(9799,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ A @ ( domain_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[9798:[bind(A,$thf( G )),bind(B,$thf( cross_product @ G @ ( domain_of @ sk4 ) )),bind(C,$thf( cross_product @ G @ sk3 ))]]) ).
thf(9907,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ A @ ( domain_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[9799]) ).
thf(6846,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( range_of @ sk4 ) @ sk2 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35,236]) ).
thf(6847,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ),
inference(pattern_uni,[status(thm)],[6846:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(9031,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6847,246]) ).
thf(9032,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ A @ ( cross_product @ sk2 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[9031:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ sk2 @ sk2 ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ilf_type @ B @ ( subset_type @ A ) )
<=> ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
thf(88,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( ilf_type @ B @ ( subset_type @ A ) )
=> ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) )
& ( ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
=> ( ilf_type @ B @ ( subset_type @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(9711,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( range_of @ sk4 ) @ sk1 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4440,247]) ).
thf(9712,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk1 ),
inference(pattern_uni,[status(thm)],[9711:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(14683,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ ( sk7 @ B ) @ A )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk1 ) )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9712,264]) ).
thf(14684,plain,
( ( empty @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) )
| ( member @ ( sk7 @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14683:[bind(A,$thf( cross_product @ sk2 @ sk1 )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ))]]) ).
thf(4445,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( range_of @ E ) @ D )
| ( ( ilf_type @ ( sk5 @ B @ A ) @ ( relation_type @ B @ A ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[176,4408]) ).
thf(4446,plain,
! [B: $i,A: $i] : ( subset @ ( range_of @ ( sk5 @ A @ B ) ) @ B ),
inference(pattern_uni,[status(thm)],[4445:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( sk5 @ F @ G ))]]) ).
thf(4579,plain,
! [B: $i,A: $i] : ( subset @ ( range_of @ ( sk5 @ A @ B ) ) @ B ),
inference(simp,[status(thm)],[4446]) ).
thf(4705,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ sk2 )
| ( ( subset @ ( range_of @ ( sk5 @ A @ B ) ) @ B )
!= ( subset @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4579,3076]) ).
thf(4706,plain,
! [A: $i] : ( subset @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[4705:[bind(A,$thf( E )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( range_of @ ( sk5 @ E @ ( range_of @ sk4 ) ) ))]]) ).
thf(4743,plain,
! [A: $i] : ( subset @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) @ sk2 ),
inference(simp,[status(thm)],[4706]) ).
thf(9717,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4743,247]) ).
thf(9718,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9717:[bind(A,$thf( E )),bind(B,$thf( range_of @ ( sk5 @ E @ ( range_of @ sk4 ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(9924,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[9718]) ).
thf(218,plain,
! [A: $i] :
( ( relation_like @ A )
| ( ( ilf_type @ sk6 @ binary_relation_type )
!= ( ilf_type @ A @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[43,216]) ).
thf(219,plain,
relation_like @ sk6,
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( sk6 ))]]) ).
thf(1791,plain,
( ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
= ( range_of @ sk4 ) )
| ( ( relation_like @ ( power_set @ sk2 ) )
!= ( relation_like @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[219,1588]) ).
thf(1808,plain,
( ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
= ( range_of @ sk4 ) )
| ( ( power_set @ sk2 )
!= sk6 ) ),
inference(simp,[status(thm)],[1791]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( ilf_type @ B @ ( subset_type @ A ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(2501,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( ilf_type @ B @ ( subset_type @ A ) ) ),
inference(rewrite,[status(thm)],[89,112]) ).
thf(2502,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( ilf_type @ B @ ( subset_type @ A ) ) ),
inference(simp,[status(thm)],[2501]) ).
thf(2510,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( ilf_type @ C @ ( subset_type @ B ) )
| ( ( ilf_type @ ( sk9 @ A ) @ ( member_type @ A ) )
!= ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[342,2502]) ).
thf(2511,plain,
! [A: $i] :
( ( empty @ ( power_set @ A ) )
| ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( subset_type @ A ) ) ),
inference(pattern_uni,[status(thm)],[2510:[bind(A,$thf( power_set @ E )),bind(B,$thf( E )),bind(C,$thf( sk9 @ ( power_set @ E ) ))]]) ).
thf(2527,plain,
! [A: $i] :
( ( empty @ ( power_set @ A ) )
| ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( subset_type @ A ) ) ),
inference(simp,[status(thm)],[2511]) ).
thf(9,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ~ ( empty @ ( power_set @ A ) )
& ( ilf_type @ ( power_set @ A ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
thf(50,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ~ ( empty @ ( power_set @ A ) )
& ( ilf_type @ ( power_set @ A ) @ set_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( empty @ ( power_set @ A ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(179,plain,
! [A: $i] :
( ~ $true
| ~ ( empty @ ( power_set @ A ) ) ),
inference(rewrite,[status(thm)],[51,112]) ).
thf(180,plain,
! [A: $i] :
~ ( empty @ ( power_set @ A ) ),
inference(simp,[status(thm)],[179]) ).
thf(2556,plain,
! [A: $i] :
( $false
| ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( subset_type @ A ) ) ),
inference(rewrite,[status(thm)],[2527,180]) ).
thf(2557,plain,
! [A: $i] : ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( subset_type @ A ) ),
inference(simp,[status(thm)],[2556]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ilf_type @ C @ ( relation_type @ A @ B ) ) ),
inference(cnf,[status(esa)],[105]) ).
thf(4944,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ilf_type @ C @ ( relation_type @ A @ B ) ) ),
inference(rewrite,[status(thm)],[107,112]) ).
thf(4945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ilf_type @ C @ ( relation_type @ A @ B ) ) ),
inference(simp,[status(thm)],[4944]) ).
thf(4971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
| ( ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( subset_type @ A ) )
!= ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2557,4945]) ).
thf(4972,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) @ ( relation_type @ A @ B ) ),
inference(pattern_uni,[status(thm)],[4971:[bind(A,$thf( cross_product @ G @ H )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( sk9 @ ( power_set @ ( cross_product @ G @ H ) ) ))]]) ).
thf(5047,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) @ ( relation_type @ A @ B ) ),
inference(simp,[status(thm)],[4972]) ).
thf(27581,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( range_of @ E ) @ D )
| ( ( ilf_type @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) @ ( relation_type @ A @ B ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[5047,4408]) ).
thf(27582,plain,
! [B: $i,A: $i] : ( subset @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) ) @ B ),
inference(pattern_uni,[status(thm)],[27581:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( H )),bind(D,$thf( I )),bind(E,$thf( sk9 @ ( power_set @ ( cross_product @ H @ I ) ) ))]]) ).
thf(27619,plain,
! [B: $i,A: $i] : ( subset @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) ) @ B ),
inference(simp,[status(thm)],[27582]) ).
thf(28162,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ sk2 )
| ( ( subset @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) ) @ B )
!= ( subset @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[27619,3076]) ).
thf(28163,plain,
! [A: $i] : ( subset @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[28162:[bind(A,$thf( G )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( range_of @ ( sk9 @ ( power_set @ ( cross_product @ G @ ( range_of @ sk4 ) ) ) ) ))]]) ).
thf(28205,plain,
! [A: $i] : ( subset @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) @ sk2 ),
inference(simp,[status(thm)],[28163]) ).
thf(9791,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3876,247]) ).
thf(9792,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk3 ),
inference(pattern_uni,[status(thm)],[9791:[bind(A,$thf( domain_of @ sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(10060,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk3 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9792,236]) ).
thf(10061,plain,
subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ sk3 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[10060:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) )),bind(B,$thf( cross_product @ sk2 @ sk3 ))]]) ).
thf(19,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( ( ilf_type @ A @ ( member_type @ B ) )
<=> ( member @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
thf(91,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( ( ( ilf_type @ A @ ( member_type @ B ) )
=> ( member @ A @ B ) )
& ( ( member @ A @ B )
=> ( ilf_type @ A @ ( member_type @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( empty @ B )
| ~ ( ilf_type @ B @ set_type )
| ~ ( member @ A @ B )
| ( ilf_type @ A @ ( member_type @ B ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(2712,plain,
! [B: $i,A: $i] :
( ~ $true
| ( empty @ B )
| ~ $true
| ~ ( member @ A @ B )
| ( ilf_type @ A @ ( member_type @ B ) ) ),
inference(rewrite,[status(thm)],[92,112]) ).
thf(2713,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ~ ( member @ A @ B )
| ( ilf_type @ A @ ( member_type @ B ) ) ),
inference(simp,[status(thm)],[2712]) ).
thf(2738,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( ilf_type @ B @ ( member_type @ C ) )
| ( ( member @ A @ ( power_set @ A ) )
!= ( member @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[488,2713]) ).
thf(2739,plain,
! [A: $i] :
( ( empty @ ( power_set @ A ) )
| ( ilf_type @ A @ ( member_type @ ( power_set @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2738:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( power_set @ D ))]]) ).
thf(2788,plain,
! [A: $i] :
( ( empty @ ( power_set @ A ) )
| ( ilf_type @ A @ ( member_type @ ( power_set @ A ) ) ) ),
inference(simp,[status(thm)],[2739]) ).
thf(6516,plain,
! [A: $i] :
( $false
| ( ilf_type @ A @ ( member_type @ ( power_set @ A ) ) ) ),
inference(rewrite,[status(thm)],[2788,180]) ).
thf(6517,plain,
! [A: $i] : ( ilf_type @ A @ ( member_type @ ( power_set @ A ) ) ),
inference(simp,[status(thm)],[6516]) ).
thf(6532,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( subset_type @ B ) )
| ( ( ilf_type @ A @ ( member_type @ ( power_set @ A ) ) )
!= ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6517,2502]) ).
thf(6533,plain,
! [A: $i] : ( ilf_type @ A @ ( subset_type @ A ) ),
inference(pattern_uni,[status(thm)],[6532:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(33,plain,
~ ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ),
inference(cnf,[status(esa)],[29]) ).
thf(4961,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4945,33]) ).
thf(4962,plain,
~ ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4961:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).
thf(6568,plain,
! [A: $i] :
( ( ilf_type @ A @ ( subset_type @ A ) )
!= ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6533,4962]) ).
thf(6583,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( subset_type @ A )
!= ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[6568]) ).
thf(6596,plain,
( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= ( subset_type @ sk4 ) ),
inference(simp,[status(thm)],[6583]) ).
thf(6602,plain,
( ( cross_product @ sk3 @ sk2 )
!= sk4 ),
inference(simp,[status(thm)],[6596]) ).
thf(8,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
thf(48,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( ilf_type @ ( sk8 @ A ) @ ( subset_type @ A ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(201,plain,
! [A: $i] :
( ~ $true
| ( ilf_type @ ( sk8 @ A ) @ ( subset_type @ A ) ) ),
inference(rewrite,[status(thm)],[49,112]) ).
thf(202,plain,
! [A: $i] : ( ilf_type @ ( sk8 @ A ) @ ( subset_type @ A ) ),
inference(simp,[status(thm)],[201]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ binary_relation_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( member @ B @ ( range_of @ A ) )
| ( member @ ( ordered_pair @ ( sk11 @ B @ A ) @ B ) @ A ) ),
inference(cnf,[status(esa)],[67]) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ binary_relation_type )
| ~ $true
| ~ ( member @ B @ ( range_of @ A ) )
| ( member @ ( ordered_pair @ ( sk11 @ B @ A ) @ B ) @ A ) ),
inference(rewrite,[status(thm)],[70,112]) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ binary_relation_type )
| ~ ( member @ B @ ( range_of @ A ) )
| ( member @ ( ordered_pair @ ( sk11 @ B @ A ) @ B ) @ A ) ),
inference(simp,[status(thm)],[1040]) ).
thf(6574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
| ( ( ilf_type @ A @ ( subset_type @ A ) )
!= ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6533,4945]) ).
thf(6575,plain,
! [B: $i,A: $i] : ( ilf_type @ ( cross_product @ A @ B ) @ ( relation_type @ A @ B ) ),
inference(pattern_uni,[status(thm)],[6574:[bind(A,$thf( cross_product @ E @ F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( cross_product @ E @ F ))]]) ).
thf(6590,plain,
! [B: $i,A: $i] : ( ilf_type @ ( cross_product @ A @ B ) @ ( relation_type @ A @ B ) ),
inference(simp,[status(thm)],[6575]) ).
thf(15017,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( domain_of @ E ) @ C )
| ( ( ilf_type @ ( cross_product @ A @ B ) @ ( relation_type @ A @ B ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[6590,3845]) ).
thf(15018,plain,
! [B: $i,A: $i] : ( subset @ ( domain_of @ ( cross_product @ A @ B ) ) @ A ),
inference(pattern_uni,[status(thm)],[15017:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( cross_product @ F @ G ))]]) ).
thf(15041,plain,
! [B: $i,A: $i] : ( subset @ ( domain_of @ ( cross_product @ A @ B ) ) @ A ),
inference(simp,[status(thm)],[15018]) ).
thf(16087,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ sk2 )
| ( ( subset @ ( domain_of @ ( cross_product @ A @ B ) ) @ A )
!= ( subset @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[15041,3076]) ).
thf(16088,plain,
! [A: $i] : ( subset @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[16087:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( F )),bind(C,$thf( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ F ) ))]]) ).
thf(16146,plain,
! [A: $i] : ( subset @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ sk2 ),
inference(simp,[status(thm)],[16088]) ).
thf(16222,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16146,236]) ).
thf(16223,plain,
! [A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[16222:[bind(A,$thf( F )),bind(B,$thf( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ F ) )),bind(C,$thf( sk2 ))]]) ).
thf(16308,plain,
! [A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[16223]) ).
thf(4948,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
| ( ( ilf_type @ ( sk8 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[202,4945]) ).
thf(4949,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk8 @ ( cross_product @ A @ B ) ) @ ( relation_type @ A @ B ) ),
inference(pattern_uni,[status(thm)],[4948:[bind(A,$thf( cross_product @ F @ G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( sk8 @ ( cross_product @ F @ G ) ))]]) ).
thf(5039,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk8 @ ( cross_product @ A @ B ) ) @ ( relation_type @ A @ B ) ),
inference(simp,[status(thm)],[4949]) ).
thf(5113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( domain_of @ E ) @ C )
| ( ( ilf_type @ ( sk8 @ ( cross_product @ A @ B ) ) @ ( relation_type @ A @ B ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[5039,3845]) ).
thf(5114,plain,
! [B: $i,A: $i] : ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[5113:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( H )),bind(E,$thf( sk8 @ ( cross_product @ G @ H ) ))]]) ).
thf(5143,plain,
! [B: $i,A: $i] : ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ A ),
inference(simp,[status(thm)],[5114]) ).
thf(9772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ C ) @ ( cross_product @ sk2 @ D ) )
| ( ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ A )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5143,247]) ).
thf(9773,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[9772:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( domain_of @ ( sk8 @ ( cross_product @ G @ H ) ) )),bind(D,$thf( G ))]]) ).
thf(9901,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) ) @ ( cross_product @ sk2 @ A ) ),
inference(simp,[status(thm)],[9773]) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( member @ C @ B )
| ( ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[489,250]) ).
thf(494,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ sk2 ) @ A )
| ( member @ ( range_of @ sk4 ) @ A ) ),
inference(pattern_uni,[status(thm)],[493:[bind(A,$thf( power_set @ sk2 )),bind(B,$thf( B )),bind(C,$thf( range_of @ sk4 ))]]) ).
thf(505,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ sk2 ) @ A )
| ( member @ ( range_of @ sk4 ) @ A ) ),
inference(simp,[status(thm)],[494]) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( power_set @ sk2 ) @ A )
| ~ ( empty @ B )
| ( ( member @ ( range_of @ sk4 ) @ A )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[505,194]) ).
thf(754,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ sk2 ) @ A )
| ~ ( empty @ A ) ),
inference(pattern_uni,[status(thm)],[753:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( range_of @ sk4 ))]]) ).
thf(5623,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( subset @ sk4 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )
!= ( subset @ ( power_set @ sk2 ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5568,754]) ).
thf(5645,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( power_set @ sk2 )
!= sk4 )
| ( ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) )
!= A ) ),
inference(simp,[status(thm)],[5623]) ).
thf(5669,plain,
( ~ ( empty @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )
| ( ( power_set @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[5645]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( member @ A @ ( power_set @ B ) )
| ~ ( ilf_type @ C @ set_type )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[62]) ).
thf(611,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( member @ A @ ( power_set @ B ) )
| ~ $true
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(rewrite,[status(thm)],[66,112]) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( power_set @ B ) )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(simp,[status(thm)],[611]) ).
thf(643,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( power_set @ B ) )
| ( member @ C @ B )
| ( ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[489,612]) ).
thf(644,plain,
! [A: $i] :
( ~ ( member @ ( power_set @ sk2 ) @ ( power_set @ A ) )
| ( member @ ( range_of @ sk4 ) @ A ) ),
inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( power_set @ sk2 )),bind(B,$thf( B )),bind(C,$thf( range_of @ sk4 ))]]) ).
thf(685,plain,
! [A: $i] :
( ~ ( member @ ( power_set @ sk2 ) @ ( power_set @ A ) )
| ( member @ ( range_of @ sk4 ) @ A ) ),
inference(simp,[status(thm)],[644]) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( power_set @ B ) @ A )
| ( member @ ( range_of @ sk4 ) @ C )
| ( ( member @ B @ A )
!= ( member @ ( power_set @ sk2 ) @ ( power_set @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[521,685]) ).
thf(1271,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ A ) )
| ( member @ ( range_of @ sk4 ) @ A ) ),
inference(pattern_uni,[status(thm)],[1270:[bind(A,$thf( power_set @ E )),bind(B,$thf( power_set @ sk2 )),bind(C,$thf( E ))]]) ).
thf(1298,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ A ) )
| ( member @ ( range_of @ sk4 ) @ A ) ),
inference(simp,[status(thm)],[1271]) ).
thf(259,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ~ ( empty @ D )
| ( ( member @ C @ B )
!= ( member @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[250,194]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ~ ( empty @ B ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(11917,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( empty @ B )
| ( ( subset @ ( range_of @ sk4 ) @ sk1 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4440,260]) ).
thf(11918,plain,
! [A: $i] :
( ~ ( member @ A @ ( range_of @ sk4 ) )
| ~ ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[11917:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(12153,plain,
! [A: $i] :
( ~ ( member @ A @ ( range_of @ sk4 ) )
| ~ ( empty @ sk1 ) ),
inference(simp,[status(thm)],[11918]) ).
thf(12984,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ A ) )
| ~ ( empty @ sk1 )
| ( ( member @ ( range_of @ sk4 ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,12153]) ).
thf(12985,plain,
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( range_of @ sk4 ) ) )
| ~ ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12984:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(23385,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( subset @ A @ A )
!= ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( range_of @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[200,12985]) ).
thf(23481,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( A
!= ( power_set @ ( power_set @ sk2 ) ) )
| ( A
!= ( power_set @ ( range_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[23385]) ).
thf(23515,plain,
( ~ ( empty @ sk1 )
| ( ( power_set @ ( power_set @ sk2 ) )
!= ( power_set @ ( range_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[23481]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( relation_like @ A )
| ( member @ B @ sk2 )
| ( ( member @ ( sk14 @ A ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[268,265]) ).
thf(278,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk14 @ ( range_of @ sk4 ) ))]]) ).
thf(1607,plain,
! [B: $i,A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ( ( ordered_pair @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
= B )
| ~ ( relation_like @ A )
| ( ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[278,1551]) ).
thf(1608,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ( ( ordered_pair @ ( sk12 @ ( sk14 @ ( range_of @ sk4 ) ) @ sk2 ) @ ( sk13 @ ( sk14 @ ( range_of @ sk4 ) ) @ sk2 ) )
= ( sk14 @ ( range_of @ sk4 ) ) )
| ~ ( relation_like @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1607:[bind(A,$thf( sk2 )),bind(B,$thf( sk14 @ ( range_of @ sk4 ) ))]]) ).
thf(8962,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) )
| ( ( subset @ ( range_of @ sk4 ) @ sk1 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4440,246]) ).
thf(8963,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8962:[bind(A,$thf( A )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( sk1 ))]]) ).
thf(532,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 )
| ( ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[489,365]) ).
thf(533,plain,
( ~ ( subset @ ( power_set @ sk2 ) @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[532:[bind(A,$thf( power_set @ sk2 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(1272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ ( power_set @ B ) @ A )
| ~ ( empty @ C )
| ( ( member @ B @ A )
!= ( member @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[521,194]) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ B ) @ A )
| ~ ( empty @ A ) ),
inference(pattern_uni,[status(thm)],[1272:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4038,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ ( power_set @ B ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3876,1273]) ).
thf(4075,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( ( domain_of @ sk4 )
!= ( power_set @ B ) )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[4038]) ).
thf(4097,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( ( domain_of @ sk4 )
!= ( power_set @ A ) ) ),
inference(simp,[status(thm)],[4075]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ B @ ( subset_type @ A ) )
| ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(2572,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ B @ ( subset_type @ A ) )
| ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ),
inference(rewrite,[status(thm)],[90,112]) ).
thf(2573,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ B @ ( subset_type @ A ) )
| ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ),
inference(simp,[status(thm)],[2572]) ).
thf(5310,plain,
! [B: $i,A: $i] :
( ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( ilf_type @ B @ ( subset_type @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[5203,2573]) ).
thf(5311,plain,
ilf_type @ sk4 @ ( member_type @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5310:[bind(A,$thf( cross_product @ sk3 @ sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( empty @ B )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ A @ ( member_type @ B ) )
| ( member @ A @ B ) ),
inference(cnf,[status(esa)],[91]) ).
thf(2872,plain,
! [B: $i,A: $i] :
( ~ $true
| ( empty @ B )
| ~ $true
| ~ ( ilf_type @ A @ ( member_type @ B ) )
| ( member @ A @ B ) ),
inference(rewrite,[status(thm)],[93,112]) ).
thf(2873,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ~ ( ilf_type @ A @ ( member_type @ B ) )
| ( member @ A @ B ) ),
inference(simp,[status(thm)],[2872]) ).
thf(5346,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ A @ B )
| ( ( ilf_type @ sk4 @ ( member_type @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) ) )
!= ( ilf_type @ A @ ( member_type @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[5311,2873]) ).
thf(5347,plain,
( ( empty @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) )
| ( member @ sk4 @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[5346:[bind(A,$thf( sk4 )),bind(B,$thf( power_set @ ( cross_product @ sk3 @ sk1 ) ))]]) ).
thf(5381,plain,
( $false
| ( member @ sk4 @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[5347,180]) ).
thf(5382,plain,
member @ sk4 @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ),
inference(simp,[status(thm)],[5381]) ).
thf(13025,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( member @ sk4 @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( member @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5382,12153]) ).
thf(13053,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( sk4 != A )
| ( ( power_set @ ( cross_product @ sk3 @ sk1 ) )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[13025]) ).
thf(13095,plain,
( ~ ( empty @ sk1 )
| ( ( power_set @ ( cross_product @ sk3 @ sk1 ) )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[13053]) ).
thf(9805,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ sk6 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3329,247]) ).
thf(9806,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ sk6 ) @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[9805:[bind(A,$thf( sk6 )),bind(B,$thf( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ))]]) ).
thf(10137,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ sk6 ) @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9806,247]) ).
thf(10138,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ sk6 ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[10137:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ sk6 )),bind(B,$thf( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) ))]]) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ A ) )
| ~ ( empty @ B )
| ( ( member @ ( range_of @ sk4 ) @ A )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1298,194]) ).
thf(1379,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ A ) )
| ~ ( empty @ A ) ),
inference(pattern_uni,[status(thm)],[1378:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( range_of @ sk4 ))]]) ).
thf(16534,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ A ) )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16484,1379]) ).
thf(16535,plain,
( ~ ( empty @ sk3 )
| ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( domain_of @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[16534:[bind(A,$thf( domain_of @ sk4 ))]]) ).
thf(30634,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( ( subset @ A @ A )
!= ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( domain_of @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[200,16535]) ).
thf(30687,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( A
!= ( power_set @ ( power_set @ sk2 ) ) )
| ( A
!= ( power_set @ ( domain_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[30634]) ).
thf(30799,plain,
( ~ ( empty @ sk3 )
| ( ( power_set @ ( domain_of @ sk4 ) )
!= ( power_set @ ( power_set @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30687]) ).
thf(28314,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28205,236]) ).
thf(28315,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[28314:[bind(A,$thf( G )),bind(B,$thf( range_of @ ( sk9 @ ( power_set @ ( cross_product @ G @ ( range_of @ sk4 ) ) ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(28398,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[28315]) ).
thf(243,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ C )
| ( subset @ ( cross_product @ B @ D ) @ ( cross_product @ C @ E ) )
| ( ( subset @ A @ A )
!= ( subset @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[200,232]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ C )
| ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).
thf(7451,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ sk6 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3329,244]) ).
thf(7452,plain,
! [A: $i] : ( subset @ ( cross_product @ sk6 @ A ) @ ( cross_product @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[7451:[bind(A,$thf( A )),bind(B,$thf( sk6 )),bind(C,$thf( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ))]]) ).
thf(7466,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ sk4 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5568,244]) ).
thf(7467,plain,
! [A: $i] : ( subset @ ( cross_product @ sk4 @ A ) @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[7466:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ))]]) ).
thf(6968,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk1 @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6797,236]) ).
thf(6969,plain,
subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk1 @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[6968:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ sk1 @ sk2 ))]]) ).
thf(7943,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk1 @ sk2 ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6969,236]) ).
thf(7944,plain,
subset @ ( cross_product @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( cross_product @ sk1 @ sk2 ) @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[7943:[bind(A,$thf( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ sk1 @ sk2 ) @ sk2 ))]]) ).
thf(2591,plain,
! [B: $i,A: $i] :
( ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( ( ilf_type @ sk6 @ binary_relation_type )
!= ( ilf_type @ B @ ( subset_type @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,2573]) ).
thf(2612,plain,
! [B: $i,A: $i] :
( ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( sk6 != B )
| ( ( subset_type @ A )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2591]) ).
thf(2629,plain,
! [A: $i] :
( ( ilf_type @ sk6 @ ( member_type @ ( power_set @ A ) ) )
| ( ( subset_type @ A )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2612]) ).
thf(2984,plain,
! [C: $i,B: $i,A: $i] :
( ( ( subset_type @ A )
!= binary_relation_type )
| ( ilf_type @ C @ ( subset_type @ B ) )
| ( ( ilf_type @ sk6 @ ( member_type @ ( power_set @ A ) ) )
!= ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2629,2502]) ).
thf(2985,plain,
! [A: $i] :
( ( ( subset_type @ A )
!= binary_relation_type )
| ( ilf_type @ sk6 @ ( subset_type @ A ) ) ),
inference(pattern_uni,[status(thm)],[2984:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk6 ))]]) ).
thf(27586,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( domain_of @ E ) @ C )
| ( ( ilf_type @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) @ ( relation_type @ A @ B ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[5047,3845]) ).
thf(27587,plain,
! [B: $i,A: $i] : ( subset @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[27586:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( H )),bind(D,$thf( I )),bind(E,$thf( sk9 @ ( power_set @ ( cross_product @ H @ I ) ) ))]]) ).
thf(27609,plain,
! [B: $i,A: $i] : ( subset @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) ) @ A ),
inference(simp,[status(thm)],[27587]) ).
thf(27702,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ sk2 )
| ( ( subset @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) ) @ A )
!= ( subset @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[27609,3076]) ).
thf(27703,plain,
! [A: $i] : ( subset @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[27702:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( H )),bind(C,$thf( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ H ) ) ) ))]]) ).
thf(27763,plain,
! [A: $i] : ( subset @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) @ sk2 ),
inference(simp,[status(thm)],[27703]) ).
thf(27808,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27763,247]) ).
thf(27809,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[27808:[bind(A,$thf( H )),bind(B,$thf( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ H ) ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(27942,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[27809]) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ( ( member @ ( sk10 @ B @ A ) @ A )
!= ( member @ A @ ( power_set @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[401]) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ( ( sk10 @ B @ A )
!= A )
| ( A
!= ( power_set @ B ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(417,plain,
! [A: $i] :
( ( member @ ( power_set @ A ) @ ( power_set @ A ) )
| ( ( sk10 @ A @ ( power_set @ A ) )
!= ( power_set @ A ) ) ),
inference(simp,[status(thm)],[412]) ).
thf(283,plain,
! [C: $i,B: $i,A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( subset @ A @ B )
| ( member @ C @ B )
| ( ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[278,250]) ).
thf(284,plain,
! [A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( subset @ sk2 @ A )
| ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk14 @ ( range_of @ sk4 ) ))]]) ).
thf(288,plain,
! [A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( subset @ sk2 @ A )
| ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ A ) ),
inference(simp,[status(thm)],[284]) ).
thf(2906,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( empty @ C )
| ( member @ B @ C )
| ( ( ilf_type @ ( sk9 @ A ) @ ( member_type @ A ) )
!= ( ilf_type @ B @ ( member_type @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[342,2873]) ).
thf(2907,plain,
! [A: $i] :
( ( empty @ A )
| ( empty @ A )
| ( member @ ( sk9 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[2906:[bind(A,$thf( D )),bind(B,$thf( sk9 @ D )),bind(C,$thf( D ))]]) ).
thf(2954,plain,
! [A: $i] :
( ( empty @ A )
| ( member @ ( sk9 @ A ) @ A ) ),
inference(simp,[status(thm)],[2907]) ).
thf(3769,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| ( member @ B @ sk2 )
| ( ( member @ ( sk9 @ A ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2954,265]) ).
thf(3770,plain,
( ( empty @ ( range_of @ sk4 ) )
| ( member @ ( sk9 @ ( range_of @ sk4 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3769:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk9 @ ( range_of @ sk4 ) ))]]) ).
thf(3808,plain,
! [B: $i,A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ ( sk9 @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3770,2713]) ).
thf(3809,plain,
( ( empty @ ( range_of @ sk4 ) )
| ( empty @ sk2 )
| ( ilf_type @ ( sk9 @ ( range_of @ sk4 ) ) @ ( member_type @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3808:[bind(A,$thf( sk9 @ ( range_of @ sk4 ) )),bind(B,$thf( sk2 ))]]) ).
thf(2740,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[489,2713]) ).
thf(2741,plain,
( ( empty @ ( power_set @ sk2 ) )
| ( ilf_type @ ( range_of @ sk4 ) @ ( member_type @ ( power_set @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[2740:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( power_set @ sk2 ))]]) ).
thf(2790,plain,
( $false
| ( ilf_type @ ( range_of @ sk4 ) @ ( member_type @ ( power_set @ sk2 ) ) ) ),
inference(rewrite,[status(thm)],[2741,180]) ).
thf(2791,plain,
ilf_type @ ( range_of @ sk4 ) @ ( member_type @ ( power_set @ sk2 ) ),
inference(simp,[status(thm)],[2790]) ).
thf(2797,plain,
! [B: $i,A: $i] :
( ( ilf_type @ B @ ( subset_type @ A ) )
| ( ( ilf_type @ ( range_of @ sk4 ) @ ( member_type @ ( power_set @ sk2 ) ) )
!= ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2791,2502]) ).
thf(2798,plain,
ilf_type @ ( range_of @ sk4 ) @ ( subset_type @ sk2 ),
inference(pattern_uni,[status(thm)],[2797:[bind(A,$thf( sk2 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(2810,plain,
( ( ilf_type @ ( range_of @ sk4 ) @ ( subset_type @ sk2 ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2798,33]) ).
thf(2819,plain,
( ( ( range_of @ sk4 )
!= sk4 )
| ( ( relation_type @ sk3 @ sk2 )
!= ( subset_type @ sk2 ) ) ),
inference(simp,[status(thm)],[2810]) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( power_set @ B ) @ A )
| ( member @ C @ sk2 )
| ( ( member @ B @ A )
!= ( member @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[521,265]) ).
thf(1266,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ A ) @ ( range_of @ sk4 ) )
| ( member @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1265:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1296,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ A ) @ ( range_of @ sk4 ) )
| ( member @ A @ sk2 ) ),
inference(simp,[status(thm)],[1266]) ).
thf(1331,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( power_set @ A ) @ ( range_of @ sk4 ) )
| ( member @ B @ ( power_set @ C ) )
| ( ( member @ A @ sk2 )
!= ( member @ ( sk10 @ C @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1296,464]) ).
thf(1332,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ ( sk10 @ sk2 @ A ) ) @ ( range_of @ sk4 ) )
| ( member @ A @ ( power_set @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1331:[bind(A,$thf( sk10 @ sk2 @ E )),bind(B,$thf( E )),bind(C,$thf( sk2 ))]]) ).
thf(1347,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ ( sk10 @ sk2 @ A ) ) @ ( range_of @ sk4 ) )
| ( member @ A @ ( power_set @ sk2 ) ) ),
inference(simp,[status(thm)],[1332]) ).
thf(1657,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( sk10 @ sk2 @ A ) ) @ ( range_of @ sk4 ) )
| ( member @ ( range_of @ sk4 ) @ B )
| ( ( member @ A @ ( power_set @ sk2 ) )
!= ( member @ ( power_set @ sk2 ) @ ( power_set @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1347,685]) ).
thf(1658,plain,
( ~ ( subset @ ( power_set @ ( sk10 @ sk2 @ ( power_set @ sk2 ) ) ) @ ( range_of @ sk4 ) )
| ( member @ ( range_of @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1657:[bind(A,$thf( power_set @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(1702,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( sk10 @ sk2 @ ( power_set @ sk2 ) ) ) @ ( range_of @ sk4 ) )
| ~ ( empty @ A )
| ( ( member @ ( range_of @ sk4 ) @ sk2 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1658,194]) ).
thf(1703,plain,
( ~ ( subset @ ( power_set @ ( sk10 @ sk2 @ ( power_set @ sk2 ) ) ) @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1702:[bind(A,$thf( sk2 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(16209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ B ) @ ( cross_product @ D @ B ) )
| ( ( subset @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16146,244]) ).
thf(16210,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ B ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[16209:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ G ) )),bind(D,$thf( sk2 ))]]) ).
thf(16304,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ B ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(simp,[status(thm)],[16210]) ).
thf(14736,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ ( sk7 @ B ) @ A )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6847,264]) ).
thf(14737,plain,
( ( empty @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) )
| ( member @ ( sk7 @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14736:[bind(A,$thf( cross_product @ sk2 @ sk2 )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ))]]) ).
thf(6524,plain,
! [A: $i] :
( ( ilf_type @ A @ ( member_type @ ( power_set @ A ) ) )
!= ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6517,4962]) ).
thf(6540,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( member_type @ ( power_set @ A ) )
!= ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[6524]) ).
thf(6552,plain,
( ( member_type @ ( power_set @ sk4 ) )
!= ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[6540]) ).
thf(13029,plain,
! [B: $i,A: $i] :
( ( relation_like @ A )
| ~ ( empty @ sk1 )
| ( ( member @ ( sk14 @ A ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[268,12153]) ).
thf(13030,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[13029:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk14 @ ( range_of @ sk4 ) ))]]) ).
thf(495,plain,
! [A: $i] :
( ( member @ A @ sk2 )
| ( ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )
!= ( member @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[489,265]) ).
thf(501,plain,
! [A: $i] :
( ( member @ A @ sk2 )
| ( ( range_of @ sk4 )
!= A )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(504,plain,
( ( member @ ( range_of @ sk4 ) @ sk2 )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[501]) ).
thf(750,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ sk2 ) @ A )
| ( member @ B @ sk2 )
| ( ( member @ ( range_of @ sk4 ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[505,265]) ).
thf(751,plain,
( ~ ( subset @ ( power_set @ sk2 ) @ ( range_of @ sk4 ) )
| ( member @ ( range_of @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[750:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(123,plain,
( ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[32,33]) ).
thf(124,plain,
( ( sk4 != sk4 )
| ( ( relation_type @ sk3 @ sk2 )
!= ( relation_type @ sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
( ( relation_type @ sk3 @ sk2 )
!= ( relation_type @ sk3 @ sk1 ) ),
inference(simp,[status(thm)],[124]) ).
thf(12995,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| ~ ( empty @ sk1 )
| ( ( member @ ( sk9 @ A ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2954,12153]) ).
thf(12996,plain,
( ( empty @ ( range_of @ sk4 ) )
| ~ ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[12995:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk9 @ ( range_of @ sk4 ) ))]]) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ( relation_like @ A )
| ~ ( empty @ B )
| ( ( member @ ( sk14 @ A ) @ A )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[268,194]) ).
thf(272,plain,
! [A: $i] :
( ( relation_like @ A )
| ~ ( empty @ A ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk14 @ D ))]]) ).
thf(273,plain,
! [A: $i] :
( ( relation_like @ A )
| ~ ( empty @ A ) ),
inference(simp,[status(thm)],[272]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( ilf_type @ B @ binary_relation_type )
| ( ( relation_like @ A )
!= ( relation_like @ B ) ) ),
inference(paramod_ordered,[status(thm)],[273,291]) ).
thf(369,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ilf_type @ A @ binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[368:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(13169,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ilf_type @ A @ binary_relation_type )
| ( ( empty @ ( range_of @ sk4 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12996,369]) ).
thf(13170,plain,
( ~ ( empty @ sk1 )
| ( ilf_type @ ( range_of @ sk4 ) @ binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[13169:[bind(A,$thf( range_of @ sk4 ))]]) ).
thf(13033,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ~ ( empty @ sk1 )
| ( ( member @ ( sk15 @ B @ A ) @ A )
!= ( member @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2138,12153]) ).
thf(13034,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ~ ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[13033:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( D )),bind(C,$thf( sk15 @ D @ ( range_of @ sk4 ) ))]]) ).
thf(13080,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ~ ( empty @ sk1 ) ),
inference(simp,[status(thm)],[13034]) ).
thf(23368,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( subset @ ( range_of @ sk4 ) @ A )
!= ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( range_of @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13080,12985]) ).
thf(23418,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( power_set @ ( power_set @ sk2 ) )
!= ( range_of @ sk4 ) )
| ( A
!= ( power_set @ ( range_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[23368]) ).
thf(23507,plain,
( ~ ( empty @ sk1 )
| ( ( power_set @ ( power_set @ sk2 ) )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[23418]) ).
thf(2153,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ~ ( empty @ sk2 )
| ( ( member @ ( sk15 @ B @ A ) @ A )
!= ( member @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2138,338]) ).
thf(2154,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2153:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( D )),bind(C,$thf( sk15 @ D @ ( range_of @ sk4 ) ))]]) ).
thf(2169,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ~ ( empty @ sk2 ) ),
inference(simp,[status(thm)],[2154]) ).
thf(5110,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( range_of @ E ) @ D )
| ( ( ilf_type @ ( sk8 @ ( cross_product @ A @ B ) ) @ ( relation_type @ A @ B ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[5039,4408]) ).
thf(5111,plain,
! [B: $i,A: $i] : ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ B ),
inference(pattern_uni,[status(thm)],[5110:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( H )),bind(E,$thf( sk8 @ ( cross_product @ G @ H ) ))]]) ).
thf(5142,plain,
! [B: $i,A: $i] : ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ B ),
inference(simp,[status(thm)],[5111]) ).
thf(5985,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ sk2 )
| ( ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ B )
!= ( subset @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5142,3076]) ).
thf(5986,plain,
! [A: $i] : ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[5985:[bind(A,$thf( F )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( range_of @ ( sk8 @ ( cross_product @ F @ ( range_of @ sk4 ) ) ) ))]]) ).
thf(6023,plain,
! [A: $i] : ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ sk2 ),
inference(simp,[status(thm)],[5986]) ).
thf(9058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ C ) @ ( cross_product @ B @ D ) )
| ( ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6023,246]) ).
thf(9059,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( range_of @ ( sk8 @ ( cross_product @ B @ ( range_of @ sk4 ) ) ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9058:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( range_of @ ( sk8 @ ( cross_product @ G @ ( range_of @ sk4 ) ) ) )),bind(D,$thf( sk2 ))]]) ).
thf(9155,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( range_of @ ( sk8 @ ( cross_product @ B @ ( range_of @ sk4 ) ) ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(simp,[status(thm)],[9059]) ).
thf(408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ~ ( empty @ C )
| ( ( member @ ( sk10 @ B @ A ) @ A )
!= ( member @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[401,194]) ).
thf(409,plain,
! [B: $i,A: $i] :
( ( member @ B @ ( power_set @ A ) )
| ~ ( empty @ B ) ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( sk10 @ E @ F ))]]) ).
thf(416,plain,
! [B: $i,A: $i] :
( ( member @ B @ ( power_set @ A ) )
| ~ ( empty @ B ) ),
inference(simp,[status(thm)],[409]) ).
thf(6839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ ( range_of @ sk4 ) ) @ ( cross_product @ D @ sk2 ) )
| ( ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ A )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5143,236]) ).
thf(6840,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6839:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( domain_of @ ( sk8 @ ( cross_product @ G @ H ) ) )),bind(D,$thf( G ))]]) ).
thf(6923,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk2 ) ),
inference(simp,[status(thm)],[6840]) ).
thf(4044,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ A )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ ( power_set @ sk2 ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3876,505]) ).
thf(4077,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ A )
| ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[4044]) ).
thf(4098,plain,
( ( member @ ( range_of @ sk4 ) @ sk3 )
| ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) ) ),
inference(simp,[status(thm)],[4077]) ).
thf(5828,plain,
! [B: $i,A: $i] :
( ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) )
| ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 )
| ( ( member @ ( range_of @ sk4 ) @ sk3 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4098,365]) ).
thf(5829,plain,
( ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) )
| ~ ( subset @ sk3 @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5828:[bind(A,$thf( sk3 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(16244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ C ) @ ( cross_product @ B @ D ) )
| ( ( subset @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16146,246]) ).
thf(16245,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ B ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[16244:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ G ) )),bind(D,$thf( sk2 ))]]) ).
thf(16315,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ B ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(simp,[status(thm)],[16245]) ).
thf(16528,plain,
! [B: $i,A: $i] :
( ~ ( empty @ sk3 )
| ( subset @ B @ A )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16484,2168]) ).
thf(16529,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( subset @ ( domain_of @ sk4 ) @ A ) ),
inference(pattern_uni,[status(thm)],[16528:[bind(A,$thf( A )),bind(B,$thf( domain_of @ sk4 ))]]) ).
thf(30547,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( ( subset @ ( domain_of @ sk4 ) @ A )
!= ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( domain_of @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16529,16535]) ).
thf(30761,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( ( domain_of @ sk4 )
!= ( power_set @ ( power_set @ sk2 ) ) )
| ( A
!= ( power_set @ ( domain_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[30547]) ).
thf(30789,plain,
( ~ ( empty @ sk3 )
| ( ( domain_of @ sk4 )
!= ( power_set @ ( power_set @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30761]) ).
thf(4613,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( subset @ ( power_set @ sk2 ) @ A )
!= ( subset @ ( range_of @ sk4 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[4440,754]) ).
thf(4641,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[4613]) ).
thf(4664,plain,
( ~ ( empty @ sk1 )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[4641]) ).
thf(1380,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ A ) )
| ~ ( empty @ sk2 )
| ( ( member @ ( range_of @ sk4 ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,338]) ).
thf(1381,plain,
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( range_of @ sk4 ) ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1380:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(2199,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ( subset @ ( range_of @ sk4 ) @ A )
!= ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( range_of @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2169,1381]) ).
thf(2212,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ( power_set @ ( power_set @ sk2 ) )
!= ( range_of @ sk4 ) )
| ( A
!= ( power_set @ ( range_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[2199]) ).
thf(2237,plain,
( ~ ( empty @ sk2 )
| ( ( power_set @ ( power_set @ sk2 ) )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[2212]) ).
thf(7272,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ sk6 @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6855,236]) ).
thf(7273,plain,
subset @ ( cross_product @ ( cross_product @ sk6 @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[7272:[bind(A,$thf( cross_product @ sk6 @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) @ sk2 ))]]) ).
thf(434,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ B )
| ~ ( subset @ C @ D )
| ( member @ E @ D )
| ( ( member @ B @ ( power_set @ A ) )
!= ( member @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[416,250]) ).
thf(435,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( subset @ ( power_set @ C ) @ B )
| ( member @ A @ B ) ),
inference(pattern_uni,[status(thm)],[434:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( power_set @ F )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( subset @ ( power_set @ C ) @ B )
| ( member @ A @ B ) ),
inference(simp,[status(thm)],[435]) ).
thf(7472,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk1 @ sk2 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6797,244]) ).
thf(7473,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ A ) @ ( cross_product @ ( cross_product @ sk1 @ sk2 ) @ A ) ),
inference(pattern_uni,[status(thm)],[7472:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ sk1 @ sk2 ))]]) ).
thf(4610,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ A )
| ( ( subset @ ( power_set @ sk2 ) @ A )
!= ( subset @ ( range_of @ sk4 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[4440,505]) ).
thf(4634,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ A )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[4610]) ).
thf(4660,plain,
( ( member @ ( range_of @ sk4 ) @ sk1 )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[4634]) ).
thf(28268,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28205,247]) ).
thf(28269,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[28268:[bind(A,$thf( G )),bind(B,$thf( range_of @ ( sk9 @ ( power_set @ ( cross_product @ G @ ( range_of @ sk4 ) ) ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(28426,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk9 @ ( power_set @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[28269]) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ B @ ( range_of @ sk6 ) )
| ( ( member @ A @ ( power_set @ A ) )
!= ( member @ ( ordered_pair @ C @ B ) @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[488,862]) ).
thf(1200,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ B @ ( range_of @ sk6 ) )
| ( A
!= ( ordered_pair @ C @ B ) )
| ( ( power_set @ A )
!= sk6 ) ),
inference(simp,[status(thm)],[1181]) ).
thf(1215,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( range_of @ sk6 ) )
| ( ( power_set @ ( ordered_pair @ B @ A ) )
!= sk6 ) ),
inference(simp,[status(thm)],[1200]) ).
thf(5058,plain,
( ( ilf_type @ ( range_of @ sk4 ) @ ( subset_type @ sk2 ) )
!= ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2798,4962]) ).
thf(5096,plain,
( ( ( range_of @ sk4 )
!= sk4 )
| ( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= ( subset_type @ sk2 ) ) ),
inference(simp,[status(thm)],[5058]) ).
thf(5383,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 )
| ( ( member @ sk4 @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5382,365]) ).
thf(5384,plain,
( ~ ( subset @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5383:[bind(A,$thf( power_set @ ( cross_product @ sk3 @ sk1 ) )),bind(B,$thf( sk4 ))]]) ).
thf(6174,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ sk2 )
| ( ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ A )
!= ( subset @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5143,3076]) ).
thf(6175,plain,
! [A: $i] : ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[6174:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( G )),bind(C,$thf( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ G ) ) ))]]) ).
thf(6211,plain,
! [A: $i] : ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ sk2 ),
inference(simp,[status(thm)],[6175]) ).
thf(8996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ C ) @ ( cross_product @ B @ D ) )
| ( ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6211,246]) ).
thf(8997,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ B ) ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8996:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ H ) ) )),bind(D,$thf( sk2 ))]]) ).
thf(9140,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ B ) ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(simp,[status(thm)],[8997]) ).
thf(9696,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4188,247]) ).
thf(9697,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9696:[bind(A,$thf( F )),bind(B,$thf( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ F ) )),bind(C,$thf( sk2 ))]]) ).
thf(9914,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[9697]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( ( ilf_type @ A @ set_type )
!= ( ilf_type @ B @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[112,216]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( A != B )
| ( binary_relation_type != set_type ) ),
inference(simp,[status(thm)],[222]) ).
thf(229,plain,
! [A: $i] :
( ( relation_like @ A )
| ( binary_relation_type != set_type ) ),
inference(simp,[status(thm)],[226]) ).
thf(1784,plain,
! [A: $i] :
( ( binary_relation_type != set_type )
| ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
= ( range_of @ sk4 ) )
| ( ( relation_like @ A )
!= ( relation_like @ ( power_set @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[229,1588]) ).
thf(1785,plain,
( ( binary_relation_type != set_type )
| ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
= ( range_of @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[1784:[bind(A,$thf( power_set @ sk2 ))]]) ).
thf(2001,plain,
! [B: $i,A: $i] :
( ( binary_relation_type != set_type )
| ~ ( subset @ ( power_set @ ( range_of @ sk4 ) ) @ sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
!= ( ordered_pair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1785,1958]) ).
thf(2002,plain,
( ( binary_relation_type != set_type )
| ~ ( subset @ ( power_set @ ( range_of @ sk4 ) ) @ sk6 )
| ~ ( empty @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[2001:[bind(A,$thf( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )),bind(B,$thf( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ))]]) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ~ ( empty @ sk2 )
| ( ( member @ ( sk10 @ B @ A ) @ A )
!= ( member @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[401,338]) ).
thf(403,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[402:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( D )),bind(C,$thf( sk10 @ D @ ( range_of @ sk4 ) ))]]) ).
thf(413,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ~ ( empty @ sk2 ) ),
inference(simp,[status(thm)],[403]) ).
thf(419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ sk2 )
| ~ ( subset @ B @ C )
| ( member @ D @ C )
| ( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
!= ( member @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[413,250]) ).
thf(420,plain,
! [B: $i,A: $i] :
( ~ ( empty @ sk2 )
| ~ ( subset @ ( power_set @ B ) @ A )
| ( member @ ( range_of @ sk4 ) @ A ) ),
inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( F )),bind(B,$thf( power_set @ F )),bind(C,$thf( C )),bind(D,$thf( range_of @ sk4 ))]]) ).
thf(428,plain,
! [B: $i,A: $i] :
( ~ ( empty @ sk2 )
| ~ ( subset @ ( power_set @ B ) @ A )
| ( member @ ( range_of @ sk4 ) @ A ) ),
inference(simp,[status(thm)],[420]) ).
thf(16593,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( ilf_type @ A @ binary_relation_type )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16484,369]) ).
thf(16594,plain,
( ~ ( empty @ sk3 )
| ( ilf_type @ ( domain_of @ sk4 ) @ binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[16593:[bind(A,$thf( domain_of @ sk4 ))]]) ).
thf(14651,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ ( sk7 @ B ) @ A )
| ( ( subset @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk3 @ sk2 ) )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6845,264]) ).
thf(14652,plain,
( ( empty @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )
| ( member @ ( sk7 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14651:[bind(A,$thf( cross_product @ sk3 @ sk2 )),bind(B,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ))]]) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ( ( member @ ( sk10 @ B @ A ) @ A )
!= ( member @ A @ ( power_set @ B ) ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(2794,plain,
( ( ilf_type @ ( range_of @ sk4 ) @ ( member_type @ ( power_set @ sk2 ) ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2791,33]) ).
thf(2799,plain,
( ( ( range_of @ sk4 )
!= sk4 )
| ( ( relation_type @ sk3 @ sk2 )
!= ( member_type @ ( power_set @ sk2 ) ) ) ),
inference(simp,[status(thm)],[2794]) ).
thf(2793,plain,
! [A: $i] :
( ( relation_like @ A )
| ( ( ilf_type @ ( range_of @ sk4 ) @ ( member_type @ ( power_set @ sk2 ) ) )
!= ( ilf_type @ A @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[2791,216]) ).
thf(2800,plain,
! [A: $i] :
( ( relation_like @ A )
| ( ( range_of @ sk4 )
!= A )
| ( ( member_type @ ( power_set @ sk2 ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2793]) ).
thf(2804,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ( ( member_type @ ( power_set @ sk2 ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2800]) ).
thf(6869,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ sk4 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5568,236]) ).
thf(6870,plain,
subset @ ( cross_product @ sk4 @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[6869:[bind(A,$thf( sk4 )),bind(B,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ))]]) ).
thf(9763,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ sk4 @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6870,247]) ).
thf(9764,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ sk4 @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9763:[bind(A,$thf( cross_product @ sk4 @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ sk2 ))]]) ).
thf(2003,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ ( range_of @ sk6 ) )
| ( ( subset @ A @ A )
!= ( subset @ ( power_set @ ( ordered_pair @ B @ C ) ) @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[200,1958]) ).
thf(2009,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ ( range_of @ sk6 ) )
| ( A
!= ( power_set @ ( ordered_pair @ B @ C ) ) )
| ( A != sk6 ) ),
inference(simp,[status(thm)],[2003]) ).
thf(2011,plain,
! [B: $i,A: $i] :
( ~ ( empty @ ( range_of @ sk6 ) )
| ( ( power_set @ ( ordered_pair @ A @ B ) )
!= sk6 ) ),
inference(simp,[status(thm)],[2009]) ).
thf(7376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ B ) @ ( cross_product @ D @ B ) )
| ( ( subset @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4188,244]) ).
thf(7377,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ B ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[7376:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ G ) )),bind(D,$thf( sk2 ))]]) ).
thf(7533,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ B ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(simp,[status(thm)],[7377]) ).
thf(237,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ~ ( subset @ G @ H )
| ( subset @ ( cross_product @ E @ G ) @ ( cross_product @ F @ H ) )
| ( ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) )
!= ( subset @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[232,232]) ).
thf(238,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ E )
| ~ ( subset @ D @ F )
| ~ ( subset @ A @ B )
| ( subset @ ( cross_product @ ( cross_product @ C @ D ) @ A ) @ ( cross_product @ ( cross_product @ E @ F ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( J )),bind(D,$thf( L )),bind(E,$thf( cross_product @ I @ J )),bind(F,$thf( cross_product @ K @ L ))]]) ).
thf(248,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ E )
| ~ ( subset @ D @ F )
| ~ ( subset @ A @ B )
| ( subset @ ( cross_product @ ( cross_product @ C @ D ) @ A ) @ ( cross_product @ ( cross_product @ E @ F ) @ B ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(6873,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ A @ A )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[200,236]) ).
thf(6874,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6873:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(7661,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk2 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6874,236]) ).
thf(7662,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ A @ sk2 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7661:[bind(A,$thf( G )),bind(B,$thf( cross_product @ G @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ G @ sk2 ))]]) ).
thf(7725,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ A @ sk2 ) @ sk2 ) ),
inference(simp,[status(thm)],[7662]) ).
thf(14784,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ ( sk7 @ B ) @ A )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk3 ) )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9792,264]) ).
thf(14785,plain,
( ( empty @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) )
| ( member @ ( sk7 @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[14784:[bind(A,$thf( cross_product @ sk2 @ sk3 )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ))]]) ).
thf(7461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ B ) @ ( cross_product @ D @ B ) )
| ( ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6023,244]) ).
thf(7462,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk8 @ ( cross_product @ B @ ( range_of @ sk4 ) ) ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[7461:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( range_of @ ( sk8 @ ( cross_product @ G @ ( range_of @ sk4 ) ) ) )),bind(D,$thf( sk2 ))]]) ).
thf(7518,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk8 @ ( cross_product @ B @ ( range_of @ sk4 ) ) ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(simp,[status(thm)],[7462]) ).
thf(4021,plain,
( ~ ( empty @ sk2 )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ ( power_set @ sk2 ) @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3876,533]) ).
thf(4076,plain,
( ~ ( empty @ sk2 )
| ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[4021]) ).
thf(9784,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk1 @ sk2 ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6969,247]) ).
thf(9785,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ ( cross_product @ sk1 @ sk2 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9784:[bind(A,$thf( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ sk1 @ sk2 ) @ sk2 ))]]) ).
thf(5308,plain,
( ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[5203,33]) ).
thf(5323,plain,
( ( sk4 != sk4 )
| ( ( subset_type @ ( cross_product @ sk3 @ sk1 ) )
!= ( relation_type @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[5308]) ).
thf(5334,plain,
( ( subset_type @ ( cross_product @ sk3 @ sk1 ) )
!= ( relation_type @ sk3 @ sk2 ) ),
inference(simp,[status(thm)],[5323]) ).
thf(9702,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk3 @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6845,247]) ).
thf(9703,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9702:[bind(A,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ sk3 @ sk2 ))]]) ).
thf(16180,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16146,247]) ).
thf(16181,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[16180:[bind(A,$thf( F )),bind(B,$thf( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ F ) )),bind(C,$thf( sk2 ))]]) ).
thf(16297,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[16181]) ).
thf(327,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ( empty @ ( power_set @ A ) )
!= ( empty @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,180]) ).
thf(334,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ( power_set @ A )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(2732,plain,
! [B: $i,A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[280,2713]) ).
thf(2733,plain,
( ( empty @ ( range_of @ sk4 ) )
| ( empty @ sk2 )
| ( ilf_type @ ( sk7 @ ( range_of @ sk4 ) ) @ ( member_type @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[2732:[bind(A,$thf( sk7 @ ( range_of @ sk4 ) )),bind(B,$thf( sk2 ))]]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( ( ilf_type @ ( sk8 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ B @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[202,216]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( ( sk8 @ A )
!= B )
| ( ( subset_type @ A )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[217]) ).
thf(230,plain,
! [A: $i] :
( ( relation_like @ ( sk8 @ A ) )
| ( ( subset_type @ A )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[223]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( ( subset_type @ A )
!= binary_relation_type )
| ( ilf_type @ B @ binary_relation_type )
| ( ( relation_like @ ( sk8 @ A ) )
!= ( relation_like @ B ) ) ),
inference(paramod_ordered,[status(thm)],[230,291]) ).
thf(300,plain,
! [A: $i] :
( ( ( subset_type @ A )
!= binary_relation_type )
| ( ilf_type @ ( sk8 @ A ) @ binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( C )),bind(B,$thf( sk8 @ C ))]]) ).
thf(302,plain,
! [A: $i] :
( ( ( subset_type @ A )
!= binary_relation_type )
| ( ilf_type @ ( sk8 @ A ) @ binary_relation_type ) ),
inference(simp,[status(thm)],[300]) ).
thf(1573,plain,
! [B: $i,A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ( ( ordered_pair @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
= B )
| ~ ( relation_like @ A )
| ( ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[280,1551]) ).
thf(1574,plain,
( ( empty @ ( range_of @ sk4 ) )
| ( ( ordered_pair @ ( sk12 @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 ) @ ( sk13 @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 ) )
= ( sk7 @ ( range_of @ sk4 ) ) )
| ~ ( relation_like @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1573:[bind(A,$thf( sk2 )),bind(B,$thf( sk7 @ ( range_of @ sk4 ) ))]]) ).
thf(1750,plain,
! [A: $i] :
( ( binary_relation_type != set_type )
| ( empty @ ( range_of @ sk4 ) )
| ( ( ordered_pair @ ( sk12 @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 ) @ ( sk13 @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 ) )
= ( sk7 @ ( range_of @ sk4 ) ) )
| ( ( relation_like @ A )
!= ( relation_like @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[229,1574]) ).
thf(1751,plain,
( ( binary_relation_type != set_type )
| ( empty @ ( range_of @ sk4 ) )
| ( ( ordered_pair @ ( sk12 @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 ) @ ( sk13 @ ( sk7 @ ( range_of @ sk4 ) ) @ sk2 ) )
= ( sk7 @ ( range_of @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[1750:[bind(A,$thf( sk2 ))]]) ).
thf(6802,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4743,236]) ).
thf(6803,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6802:[bind(A,$thf( E )),bind(B,$thf( range_of @ ( sk5 @ E @ ( range_of @ sk4 ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(6915,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[6803]) ).
thf(2512,plain,
! [B: $i,A: $i] :
( ( ilf_type @ B @ ( subset_type @ A ) )
| ( ( ilf_type @ sk6 @ binary_relation_type )
!= ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,2502]) ).
thf(2516,plain,
! [B: $i,A: $i] :
( ( ilf_type @ B @ ( subset_type @ A ) )
| ( sk6 != B )
| ( ( member_type @ ( power_set @ A ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2512]) ).
thf(2528,plain,
! [A: $i] :
( ( ilf_type @ sk6 @ ( subset_type @ A ) )
| ( ( member_type @ ( power_set @ A ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2516]) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ~ ( subset @ B @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 )
| ( ( member @ ( sk7 @ A ) @ A )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[208,365]) ).
thf(537,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[536:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk7 @ D ))]]) ).
thf(562,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(simp,[status(thm)],[537]) ).
thf(4040,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ sk2 )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3876,562]) ).
thf(4074,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ sk2 )
| ( ( domain_of @ sk4 )
!= A )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[4040]) ).
thf(4096,plain,
( ( empty @ ( domain_of @ sk4 ) )
| ~ ( empty @ sk2 )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[4074]) ).
thf(5768,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ( range_of @ sk4 )
!= sk3 )
| ~ ( subset @ ( power_set @ sk2 ) @ A )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4096,754]) ).
thf(5769,plain,
( ~ ( empty @ sk2 )
| ( ( range_of @ sk4 )
!= sk3 )
| ~ ( subset @ ( power_set @ sk2 ) @ ( domain_of @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[5768:[bind(A,$thf( domain_of @ sk4 ))]]) ).
thf(1233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( power_set @ ( ordered_pair @ B @ A ) )
!= sk6 )
| ~ ( empty @ C )
| ( ( member @ A @ ( range_of @ sk6 ) )
!= ( member @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1215,194]) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ( ( power_set @ ( ordered_pair @ B @ A ) )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1233:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( range_of @ sk6 )),bind(D,$thf( A ))]]) ).
thf(1818,plain,
! [B: $i,A: $i] :
( ( binary_relation_type != set_type )
| ( ( power_set @ ( range_of @ sk4 ) )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
!= ( ordered_pair @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1785,1234]) ).
thf(1819,plain,
( ( binary_relation_type != set_type )
| ( ( power_set @ ( range_of @ sk4 ) )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1818:[bind(A,$thf( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )),bind(B,$thf( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ))]]) ).
thf(1786,plain,
! [B: $i,A: $i] :
( ~ ( relation_like @ ( power_set @ sk2 ) )
| ( ( power_set @ ( range_of @ sk4 ) )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
!= ( ordered_pair @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1588,1234]) ).
thf(1787,plain,
( ~ ( relation_like @ ( power_set @ sk2 ) )
| ( ( power_set @ ( range_of @ sk4 ) )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1786:[bind(A,$thf( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )),bind(B,$thf( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ))]]) ).
thf(5542,plain,
( ( ( power_set @ ( range_of @ sk4 ) )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( relation_like @ ( power_set @ sk2 ) )
!= ( relation_like @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[5474,1787]) ).
thf(5551,plain,
( ( ( power_set @ ( range_of @ sk4 ) )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( power_set @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[5542]) ).
thf(10034,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk3 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9792,247]) ).
thf(10035,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[10034:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) )),bind(B,$thf( cross_product @ sk2 @ sk3 ))]]) ).
thf(6864,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6023,236]) ).
thf(6865,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6864:[bind(A,$thf( F )),bind(B,$thf( range_of @ ( sk8 @ ( cross_product @ F @ ( range_of @ sk4 ) ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(6926,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[6865]) ).
thf(7443,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ ( range_of @ sk4 ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,244]) ).
thf(7444,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[7443:[bind(A,$thf( A )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( sk2 ))]]) ).
thf(8470,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ A ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7444,236]) ).
thf(8471,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ A ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8470:[bind(A,$thf( H )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ H )),bind(C,$thf( cross_product @ sk2 @ H ))]]) ).
thf(8530,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ A ) @ sk2 ) ),
inference(simp,[status(thm)],[8471]) ).
thf(5466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation_like @ D )
| ( ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( subset_type @ A ) )
!= ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2557,5444]) ).
thf(5467,plain,
! [B: $i,A: $i] : ( relation_like @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[5466:[bind(A,$thf( cross_product @ G @ H )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( sk9 @ ( power_set @ ( cross_product @ G @ H ) ) ))]]) ).
thf(5513,plain,
! [B: $i,A: $i] : ( relation_like @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) ),
inference(simp,[status(thm)],[5467]) ).
thf(5704,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ binary_relation_type )
| ( ( relation_like @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) )
!= ( relation_like @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5513,291]) ).
thf(5705,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) @ binary_relation_type ),
inference(pattern_uni,[status(thm)],[5704:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( sk9 @ ( power_set @ ( cross_product @ F @ G ) ) ))]]) ).
thf(5714,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk9 @ ( power_set @ ( cross_product @ A @ B ) ) ) @ binary_relation_type ),
inference(simp,[status(thm)],[5705]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ set_type )
| ( ( sk14 @ A )
!= ( ordered_pair @ B @ C ) )
| ( relation_like @ A ) ),
inference(cnf,[status(esa)],[71]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ A )
!= ( ordered_pair @ B @ C ) )
| ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ set_type )
| ( relation_like @ A ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ A )
!= ( ordered_pair @ B @ C ) )
| ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ set_type )
| ( relation_like @ A ) ),
inference(simp,[status(thm)],[79]) ).
thf(1771,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ A )
!= ( ordered_pair @ B @ C ) )
| ~ $true
| ~ $true
| ~ $true
| ( relation_like @ A ) ),
inference(rewrite,[status(thm)],[80,112]) ).
thf(1772,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ A )
!= ( ordered_pair @ B @ C ) )
| ( relation_like @ A ) ),
inference(simp,[status(thm)],[1771]) ).
thf(4047,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ ( power_set @ sk2 ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3876,754]) ).
thf(4072,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[4047]) ).
thf(4095,plain,
( ~ ( empty @ sk3 )
| ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) ) ),
inference(simp,[status(thm)],[4072]) ).
thf(2585,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) )
| ( ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( subset_type @ A ) )
!= ( ilf_type @ C @ ( subset_type @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[2557,2573]) ).
thf(2586,plain,
! [A: $i] : ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( member_type @ ( power_set @ A ) ) ),
inference(pattern_uni,[status(thm)],[2585:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( sk9 @ ( power_set @ E ) ))]]) ).
thf(2631,plain,
! [A: $i] : ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( member_type @ ( power_set @ A ) ) ),
inference(simp,[status(thm)],[2586]) ).
thf(5067,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
!= ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,4962]) ).
thf(5098,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= set_type ) ),
inference(simp,[status(thm)],[5067]) ).
thf(5107,plain,
( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= set_type ),
inference(simp,[status(thm)],[5098]) ).
thf(5307,plain,
( ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) )
!= ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5203,4962]) ).
thf(5326,plain,
( ( sk4 != sk4 )
| ( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= ( subset_type @ ( cross_product @ sk3 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[5307]) ).
thf(5337,plain,
( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= ( subset_type @ ( cross_product @ sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[5326]) ).
thf(7571,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ sk4 @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6870,236]) ).
thf(7572,plain,
subset @ ( cross_product @ ( cross_product @ sk4 @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[7571:[bind(A,$thf( cross_product @ sk4 @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ sk2 ))]]) ).
thf(2756,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( empty @ C )
| ( ilf_type @ B @ ( member_type @ C ) )
| ( ( member @ ( sk7 @ A ) @ A )
!= ( member @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[208,2713]) ).
thf(2757,plain,
! [A: $i] :
( ( empty @ A )
| ( empty @ A )
| ( ilf_type @ ( sk7 @ A ) @ ( member_type @ A ) ) ),
inference(pattern_uni,[status(thm)],[2756:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(2781,plain,
! [A: $i] :
( ( empty @ A )
| ( ilf_type @ ( sk7 @ A ) @ ( member_type @ A ) ) ),
inference(simp,[status(thm)],[2757]) ).
thf(7144,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6847,236]) ).
thf(7145,plain,
subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[7144:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ sk2 @ sk2 ))]]) ).
thf(8672,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ sk2 ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7145,236]) ).
thf(8673,plain,
subset @ ( cross_product @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( cross_product @ sk2 @ sk2 ) @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[8672:[bind(A,$thf( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ sk2 @ sk2 ) @ sk2 ))]]) ).
thf(5344,plain,
( ( ilf_type @ sk4 @ ( member_type @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) ) )
!= ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5311,4962]) ).
thf(5363,plain,
( ( sk4 != sk4 )
| ( ( member_type @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[5344]) ).
thf(5374,plain,
( ( member_type @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[5363]) ).
thf(9931,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk1 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9712,247]) ).
thf(9932,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9931:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ sk2 @ sk1 ))]]) ).
thf(3073,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ C )
| ( subset @ A @ C )
| ( ( subset @ ( range_of @ sk4 ) @ sk2 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35,3018]) ).
thf(3074,plain,
! [A: $i] :
( ~ ( subset @ sk2 @ A )
| ( subset @ ( range_of @ sk4 ) @ A ) ),
inference(pattern_uni,[status(thm)],[3073:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).
thf(3104,plain,
! [A: $i] :
( ~ ( subset @ sk2 @ A )
| ( subset @ ( range_of @ sk4 ) @ A ) ),
inference(simp,[status(thm)],[3074]) ).
thf(4051,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3876,3104]) ).
thf(4085,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ( ( domain_of @ sk4 )
!= sk2 )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[4051]) ).
thf(4102,plain,
( ( subset @ ( range_of @ sk4 ) @ sk3 )
| ( ( domain_of @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4085]) ).
thf(4887,plain,
! [A: $i] :
( ( ( domain_of @ sk4 )
!= sk2 )
| ~ ( empty @ A )
| ( ( subset @ ( power_set @ sk2 ) @ A )
!= ( subset @ ( range_of @ sk4 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4102,754]) ).
thf(4904,plain,
! [A: $i] :
( ( ( domain_of @ sk4 )
!= sk2 )
| ~ ( empty @ A )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[4887]) ).
thf(4934,plain,
( ( ( domain_of @ sk4 )
!= sk2 )
| ~ ( empty @ sk3 )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[4904]) ).
thf(1969,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( range_of @ sk6 ) )
| ( ( subset @ A @ A )
!= ( subset @ ( power_set @ ( ordered_pair @ B @ C ) ) @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[200,1297]) ).
thf(1971,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( range_of @ sk6 ) )
| ( A
!= ( power_set @ ( ordered_pair @ B @ C ) ) )
| ( A != sk6 ) ),
inference(simp,[status(thm)],[1969]) ).
thf(1984,plain,
! [B: $i,A: $i] :
( ( member @ B @ ( range_of @ sk6 ) )
| ( ( power_set @ ( ordered_pair @ A @ B ) )
!= sk6 ) ),
inference(simp,[status(thm)],[1971]) ).
thf(5345,plain,
( ( ilf_type @ sk4 @ ( member_type @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[5311,33]) ).
thf(5358,plain,
( ( sk4 != sk4 )
| ( ( member_type @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( relation_type @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[5345]) ).
thf(5369,plain,
( ( member_type @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( relation_type @ sk3 @ sk2 ) ),
inference(simp,[status(thm)],[5358]) ).
thf(498,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ( ( member @ ( sk10 @ B @ A ) @ B )
!= ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[489,464]) ).
thf(500,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ( ( sk10 @ B @ A )
!= ( range_of @ sk4 ) )
| ( B
!= ( power_set @ sk2 ) ) ),
inference(simp,[status(thm)],[498]) ).
thf(503,plain,
! [A: $i] :
( ( member @ A @ ( power_set @ ( power_set @ sk2 ) ) )
| ( ( sk10 @ ( power_set @ sk2 ) @ A )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[500]) ).
thf(9067,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) )
| ( ( subset @ sk4 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5568,246]) ).
thf(9068,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ sk4 ) @ ( cross_product @ A @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[9067:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ))]]) ).
thf(454,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ( ( member @ ( sk10 @ A @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[415]) ).
thf(457,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ( ( member @ ( sk10 @ A @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(16472,plain,
! [B: $i,A: $i] :
( ( empty @ ( domain_of @ sk4 ) )
| ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ ( sk7 @ ( domain_of @ sk4 ) ) @ sk3 )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14742,2713]) ).
thf(16473,plain,
( ( empty @ ( domain_of @ sk4 ) )
| ( empty @ sk3 )
| ( ilf_type @ ( sk7 @ ( domain_of @ sk4 ) ) @ ( member_type @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[16472:[bind(A,$thf( sk7 @ ( domain_of @ sk4 ) )),bind(B,$thf( sk3 ))]]) ).
thf(7441,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3876,244]) ).
thf(7442,plain,
! [A: $i] : ( subset @ ( cross_product @ ( domain_of @ sk4 ) @ A ) @ ( cross_product @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[7441:[bind(A,$thf( A )),bind(B,$thf( domain_of @ sk4 )),bind(C,$thf( sk3 ))]]) ).
thf(9846,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( cross_product @ ( domain_of @ sk4 ) @ A ) @ ( cross_product @ sk3 @ A ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7442,247]) ).
thf(9847,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ A ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[9846:[bind(A,$thf( H )),bind(B,$thf( cross_product @ ( domain_of @ sk4 ) @ H )),bind(C,$thf( cross_product @ sk3 @ H ))]]) ).
thf(9925,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ A ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[9847]) ).
thf(510,plain,
! [B: $i,A: $i] :
( ( member @ B @ sk2 )
| ( ( member @ A @ ( power_set @ A ) )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[488,265]) ).
thf(516,plain,
! [B: $i,A: $i] :
( ( member @ B @ sk2 )
| ( A != B )
| ( ( power_set @ A )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[510]) ).
thf(520,plain,
! [A: $i] :
( ( member @ A @ sk2 )
| ( ( power_set @ A )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[516]) ).
thf(735,plain,
! [C: $i,B: $i,A: $i] :
( ( ( power_set @ A )
!= ( range_of @ sk4 ) )
| ( member @ B @ ( power_set @ C ) )
| ( ( member @ A @ sk2 )
!= ( member @ ( sk10 @ C @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[520,464]) ).
thf(736,plain,
! [A: $i] :
( ( ( power_set @ ( sk10 @ sk2 @ A ) )
!= ( range_of @ sk4 ) )
| ( member @ A @ ( power_set @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[735:[bind(A,$thf( sk10 @ sk2 @ E )),bind(B,$thf( E )),bind(C,$thf( sk2 ))]]) ).
thf(740,plain,
! [A: $i] :
( ( ( power_set @ ( sk10 @ sk2 @ A ) )
!= ( range_of @ sk4 ) )
| ( member @ A @ ( power_set @ sk2 ) ) ),
inference(simp,[status(thm)],[736]) ).
thf(952,plain,
! [B: $i,A: $i] :
( ( ( power_set @ ( sk10 @ sk2 @ A ) )
!= ( range_of @ sk4 ) )
| ( member @ ( range_of @ sk4 ) @ B )
| ( ( member @ A @ ( power_set @ sk2 ) )
!= ( member @ ( power_set @ sk2 ) @ ( power_set @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[740,685]) ).
thf(953,plain,
( ( ( power_set @ ( sk10 @ sk2 @ ( power_set @ sk2 ) ) )
!= ( range_of @ sk4 ) )
| ( member @ ( range_of @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[952:[bind(A,$thf( power_set @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(1990,plain,
! [B: $i,A: $i] :
( ( ( power_set @ sk2 )
!= sk6 )
| ~ ( subset @ ( power_set @ ( range_of @ sk4 ) ) @ sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
!= ( ordered_pair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1808,1958]) ).
thf(1991,plain,
( ( ( power_set @ sk2 )
!= sk6 )
| ~ ( subset @ ( power_set @ ( range_of @ sk4 ) ) @ sk6 )
| ~ ( empty @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1990:[bind(A,$thf( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )),bind(B,$thf( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ))]]) ).
thf(15012,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( range_of @ E ) @ D )
| ( ( ilf_type @ ( cross_product @ A @ B ) @ ( relation_type @ A @ B ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[6590,4408]) ).
thf(15013,plain,
! [B: $i,A: $i] : ( subset @ ( range_of @ ( cross_product @ A @ B ) ) @ B ),
inference(pattern_uni,[status(thm)],[15012:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( cross_product @ F @ G ))]]) ).
thf(15039,plain,
! [B: $i,A: $i] : ( subset @ ( range_of @ ( cross_product @ A @ B ) ) @ B ),
inference(simp,[status(thm)],[15013]) ).
thf(253,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ~ ( subset @ D @ E )
| ( member @ F @ E )
| ( ( member @ C @ B )
!= ( member @ F @ D ) ) ),
inference(paramod_ordered,[status(thm)],[250,250]) ).
thf(254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ~ ( subset @ B @ D )
| ( member @ C @ D ) ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ~ ( subset @ B @ D )
| ( member @ C @ D ) ),
inference(simp,[status(thm)],[254]) ).
thf(2760,plain,
! [B: $i,A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[278,2713]) ).
thf(2761,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ( empty @ sk2 )
| ( ilf_type @ ( sk14 @ ( range_of @ sk4 ) ) @ ( member_type @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[2760:[bind(A,$thf( sk14 @ ( range_of @ sk4 ) )),bind(B,$thf( sk2 ))]]) ).
thf(2574,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) )
| ( ( ilf_type @ ( sk8 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ C @ ( subset_type @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[202,2573]) ).
thf(2575,plain,
! [A: $i] : ( ilf_type @ ( sk8 @ A ) @ ( member_type @ ( power_set @ A ) ) ),
inference(pattern_uni,[status(thm)],[2574:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk8 @ D ))]]) ).
thf(2623,plain,
! [A: $i] : ( ilf_type @ ( sk8 @ A ) @ ( member_type @ ( power_set @ A ) ) ),
inference(simp,[status(thm)],[2575]) ).
thf(2633,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( ( ilf_type @ ( sk8 @ A ) @ ( member_type @ ( power_set @ A ) ) )
!= ( ilf_type @ B @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[2623,216]) ).
thf(2642,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( ( sk8 @ A )
!= B )
| ( ( member_type @ ( power_set @ A ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2633]) ).
thf(2645,plain,
! [A: $i] :
( ( relation_like @ ( sk8 @ A ) )
| ( ( member_type @ ( power_set @ A ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2642]) ).
thf(16537,plain,
( ~ ( empty @ sk3 )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[16484,4664]) ).
thf(16637,plain,
( ~ ( empty @ sk3 )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) )
| ( ( domain_of @ sk4 )
!= sk1 ) ),
inference(simp,[status(thm)],[16537]) ).
thf(164,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[112,33]) ).
thf(165,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( relation_type @ sk3 @ sk2 )
!= set_type ) ),
inference(simp,[status(thm)],[164]) ).
thf(166,plain,
( ( relation_type @ sk3 @ sk2 )
!= set_type ),
inference(simp,[status(thm)],[165]) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ A ) )
| ( member @ B @ sk2 )
| ( ( member @ ( range_of @ sk4 ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,265]) ).
thf(1374,plain,
( ~ ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( range_of @ sk4 ) ) )
| ( member @ ( range_of @ sk4 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(10078,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk3 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9792,246]) ).
thf(10079,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) ) @ ( cross_product @ A @ ( cross_product @ sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[10078:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) )),bind(C,$thf( cross_product @ sk2 @ sk3 ))]]) ).
thf(9048,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) )
| ( ( subset @ sk6 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3329,246]) ).
thf(9049,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ sk6 ) @ ( cross_product @ A @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[9048:[bind(A,$thf( A )),bind(B,$thf( sk6 )),bind(C,$thf( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ))]]) ).
thf(13028,plain,
! [A: $i] :
( ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) )
| ~ ( empty @ sk1 )
| ( ( member @ ( range_of @ sk4 ) @ sk3 )
!= ( member @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4098,12153]) ).
thf(13047,plain,
! [A: $i] :
( ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) )
| ~ ( empty @ sk1 )
| ( ( range_of @ sk4 )
!= A )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[13028]) ).
thf(13090,plain,
( ( ( domain_of @ sk4 )
!= ( power_set @ sk2 ) )
| ~ ( empty @ sk1 )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[13047]) ).
thf(5445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation_like @ D )
| ( ( ilf_type @ ( sk8 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[202,5444]) ).
thf(5446,plain,
! [B: $i,A: $i] : ( relation_like @ ( sk8 @ ( cross_product @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[5445:[bind(A,$thf( cross_product @ F @ G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( sk8 @ ( cross_product @ F @ G ) ))]]) ).
thf(5510,plain,
! [B: $i,A: $i] : ( relation_like @ ( sk8 @ ( cross_product @ A @ B ) ) ),
inference(simp,[status(thm)],[5446]) ).
thf(5688,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ binary_relation_type )
| ( ( relation_like @ ( sk8 @ ( cross_product @ A @ B ) ) )
!= ( relation_like @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5510,291]) ).
thf(5689,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk8 @ ( cross_product @ A @ B ) ) @ binary_relation_type ),
inference(pattern_uni,[status(thm)],[5688:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( sk8 @ ( cross_product @ E @ F ) ))]]) ).
thf(5698,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk8 @ ( cross_product @ A @ B ) ) @ binary_relation_type ),
inference(simp,[status(thm)],[5689]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( empty @ A )
| ( ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[278,194]) ).
thf(286,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( sk2 )),bind(B,$thf( sk14 @ ( range_of @ sk4 ) ))]]) ).
thf(9951,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk1 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9712,244]) ).
thf(9952,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ A ) @ ( cross_product @ ( cross_product @ sk2 @ sk1 ) @ A ) ),
inference(pattern_uni,[status(thm)],[9951:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ sk2 @ sk1 ))]]) ).
thf(4604,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( ( subset @ ( power_set @ B ) @ A )
!= ( subset @ ( range_of @ sk4 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[4440,1273]) ).
thf(4637,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( ( power_set @ B )
!= ( range_of @ sk4 ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[4604]) ).
thf(4662,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( power_set @ A )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[4637]) ).
thf(6871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ ( range_of @ sk4 ) ) @ ( cross_product @ D @ sk2 ) )
| ( ( subset @ ( range_of @ ( sk5 @ A @ B ) ) @ B )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4579,236]) ).
thf(6872,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk5 @ A @ B ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6871:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( range_of @ ( sk5 @ F @ G ) )),bind(D,$thf( G ))]]) ).
thf(6927,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk5 @ A @ B ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) ),
inference(simp,[status(thm)],[6872]) ).
thf(2559,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( ( ilf_type @ ( sk9 @ ( power_set @ A ) ) @ ( subset_type @ A ) )
!= ( ilf_type @ B @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[2557,216]) ).
thf(2563,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( ( sk9 @ ( power_set @ A ) )
!= B )
| ( ( subset_type @ A )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2559]) ).
thf(2568,plain,
! [A: $i] :
( ( relation_like @ ( sk9 @ ( power_set @ A ) ) )
| ( ( subset_type @ A )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2563]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ D @ sk2 )
| ( ( member @ C @ B )
!= ( member @ D @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[250,265]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( member @ B @ A )
| ( member @ B @ sk2 ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( A )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ ( range_of @ sk4 ) )
| ~ ( member @ B @ A )
| ( member @ B @ sk2 ) ),
inference(simp,[status(thm)],[276]) ).
thf(203,plain,
! [A: $i] :
( ( ilf_type @ ( sk8 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[202,33]) ).
thf(204,plain,
! [A: $i] :
( ( ( sk8 @ A )
!= sk4 )
| ( ( subset_type @ A )
!= ( relation_type @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ B )
| ( member @ C @ sk2 )
| ( ( member @ B @ ( power_set @ A ) )
!= ( member @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[416,265]) ).
thf(441,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ sk2 )
| ~ ( empty @ B )
| ( B != C )
| ( ( power_set @ A )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[436]) ).
thf(445,plain,
! [B: $i,A: $i] :
( ( member @ B @ sk2 )
| ~ ( empty @ B )
| ( ( power_set @ A )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[441]) ).
thf(571,plain,
! [C: $i,B: $i,A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( subset @ sk2 @ A )
| ~ ( empty @ B )
| ( ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ A )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[288,194]) ).
thf(572,plain,
! [A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( subset @ sk2 @ A )
| ~ ( empty @ A ) ),
inference(pattern_uni,[status(thm)],[571:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk14 @ ( range_of @ sk4 ) ))]]) ).
thf(4041,plain,
! [A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( empty @ A )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3876,572]) ).
thf(4080,plain,
! [A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( empty @ A )
| ( ( domain_of @ sk4 )
!= sk2 )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[4041]) ).
thf(4099,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ~ ( empty @ sk3 )
| ( ( domain_of @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[4080]) ).
thf(17,axiom,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
thf(86,plain,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2145,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ C @ sk2 )
| ( ( member @ ( sk15 @ B @ A ) @ A )
!= ( member @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2138,265]) ).
thf(2146,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ( member @ ( sk15 @ A @ ( range_of @ sk4 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2145:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( D )),bind(C,$thf( sk15 @ D @ ( range_of @ sk4 ) ))]]) ).
thf(2166,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ( member @ ( sk15 @ A @ ( range_of @ sk4 ) ) @ sk2 ) ),
inference(simp,[status(thm)],[2146]) ).
thf(5063,plain,
! [A: $i] :
( ~ ( relation_like @ A )
| ( ( ilf_type @ A @ binary_relation_type )
!= ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[291,4962]) ).
thf(5095,plain,
! [A: $i] :
( ~ ( relation_like @ A )
| ( A != sk4 )
| ( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[5063]) ).
thf(5105,plain,
( ~ ( relation_like @ sk4 )
| ( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[5095]) ).
thf(5538,plain,
( ~ $true
| ( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= binary_relation_type ) ),
inference(rewrite,[status(thm)],[5105,5474]) ).
thf(5539,plain,
( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= binary_relation_type ),
inference(simp,[status(thm)],[5538]) ).
thf(1448,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ sk2 )
| ( ( subset @ A @ A )
!= ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( range_of @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[200,1374]) ).
thf(1454,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ sk2 )
| ( A
!= ( power_set @ ( power_set @ sk2 ) ) )
| ( A
!= ( power_set @ ( range_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[1448]) ).
thf(1464,plain,
( ( member @ ( range_of @ sk4 ) @ sk2 )
| ( ( power_set @ ( power_set @ sk2 ) )
!= ( power_set @ ( range_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[1454]) ).
thf(12029,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( empty @ B )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3876,260]) ).
thf(12030,plain,
! [A: $i] :
( ~ ( member @ A @ ( domain_of @ sk4 ) )
| ~ ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[12029:[bind(A,$thf( domain_of @ sk4 )),bind(B,$thf( sk3 )),bind(C,$thf( C ))]]) ).
thf(12209,plain,
! [A: $i] :
( ~ ( member @ A @ ( domain_of @ sk4 ) )
| ~ ( empty @ sk3 ) ),
inference(simp,[status(thm)],[12030]) ).
thf(19271,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( ( member @ sk4 @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( member @ A @ ( domain_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5382,12209]) ).
thf(19309,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( sk4 != A )
| ( ( power_set @ ( cross_product @ sk3 @ sk1 ) )
!= ( domain_of @ sk4 ) ) ),
inference(simp,[status(thm)],[19271]) ).
thf(19352,plain,
( ~ ( empty @ sk3 )
| ( ( power_set @ ( cross_product @ sk3 @ sk1 ) )
!= ( domain_of @ sk4 ) ) ),
inference(simp,[status(thm)],[19309]) ).
thf(1844,plain,
! [B: $i,A: $i] :
( ( ( power_set @ sk2 )
!= sk6 )
| ( ( power_set @ ( range_of @ sk4 ) )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( ordered_pair @ ( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) @ ( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ) )
!= ( ordered_pair @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1808,1234]) ).
thf(1845,plain,
( ( ( power_set @ sk2 )
!= sk6 )
| ( ( power_set @ ( range_of @ sk4 ) )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1844:[bind(A,$thf( sk13 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )),bind(B,$thf( sk12 @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) ))]]) ).
thf(2076,plain,
( ( ( power_set @ sk2 )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( power_set @ ( range_of @ sk4 ) )
!= ( power_set @ sk2 ) )
| ( sk6 != sk6 ) ),
inference(eqfactor_ordered,[status(thm)],[1845]) ).
thf(2079,plain,
( ( ( power_set @ sk2 )
!= sk6 )
| ~ ( empty @ ( range_of @ sk6 ) )
| ( ( range_of @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[2076]) ).
thf(15118,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ sk2 )
| ( ( subset @ ( range_of @ ( cross_product @ A @ B ) ) @ B )
!= ( subset @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[15039,3076]) ).
thf(15119,plain,
! [A: $i] : ( subset @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[15118:[bind(A,$thf( E )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( range_of @ ( cross_product @ E @ ( range_of @ sk4 ) ) ))]]) ).
thf(15159,plain,
! [A: $i] : ( subset @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ sk2 ),
inference(simp,[status(thm)],[15119]) ).
thf(15940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ C ) @ ( cross_product @ B @ D ) )
| ( ( subset @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15159,246]) ).
thf(15941,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( range_of @ ( cross_product @ B @ ( range_of @ sk4 ) ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15940:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( range_of @ ( cross_product @ F @ ( range_of @ sk4 ) ) )),bind(D,$thf( sk2 ))]]) ).
thf(16000,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( range_of @ ( cross_product @ B @ ( range_of @ sk4 ) ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(simp,[status(thm)],[15941]) ).
thf(13026,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ~ ( empty @ sk1 )
| ( ( member @ ( sk10 @ B @ A ) @ A )
!= ( member @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[401,12153]) ).
thf(13027,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ~ ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[13026:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( D )),bind(C,$thf( sk10 @ D @ ( range_of @ sk4 ) ))]]) ).
thf(13079,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ~ ( empty @ sk1 ) ),
inference(simp,[status(thm)],[13027]) ).
thf(239,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ~ ( subset @ E @ F )
| ( subset @ ( cross_product @ E @ G ) @ ( cross_product @ F @ H ) )
| ( ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) )
!= ( subset @ G @ H ) ) ),
inference(paramod_ordered,[status(thm)],[232,232]) ).
thf(240,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ E )
| ~ ( subset @ D @ F )
| ~ ( subset @ A @ B )
| ( subset @ ( cross_product @ A @ ( cross_product @ C @ D ) ) @ ( cross_product @ B @ ( cross_product @ E @ F ) ) ) ),
inference(pattern_uni,[status(thm)],[239:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( J )),bind(D,$thf( L )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( cross_product @ I @ J )),bind(H,$thf( cross_product @ K @ L ))]]) ).
thf(245,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ E )
| ~ ( subset @ D @ F )
| ~ ( subset @ A @ B )
| ( subset @ ( cross_product @ A @ ( cross_product @ C @ D ) ) @ ( cross_product @ B @ ( cross_product @ E @ F ) ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(28,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ A ) @ set_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
thf(113,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ A ) @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ C ) @ ( cross_product @ sk2 @ D ) )
| ( ( subset @ ( range_of @ ( cross_product @ A @ B ) ) @ B )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15039,247]) ).
thf(15055,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( cross_product @ A @ B ) ) ) @ ( cross_product @ sk2 @ B ) ),
inference(pattern_uni,[status(thm)],[15054:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( range_of @ ( cross_product @ F @ G ) )),bind(D,$thf( G ))]]) ).
thf(15192,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( cross_product @ A @ B ) ) ) @ ( cross_product @ sk2 @ B ) ),
inference(simp,[status(thm)],[15055]) ).
thf(269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation_like @ A )
| ~ ( subset @ B @ C )
| ( member @ D @ C )
| ( ( member @ ( sk14 @ A ) @ A )
!= ( member @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[268,250]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ~ ( subset @ B @ A )
| ( member @ ( sk14 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( sk14 @ E ))]]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ~ ( subset @ B @ A )
| ( member @ ( sk14 @ B ) @ A ) ),
inference(simp,[status(thm)],[270]) ).
thf(6828,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6211,236]) ).
thf(6829,plain,
! [A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6828:[bind(A,$thf( G )),bind(B,$thf( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ G ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(6920,plain,
! [A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[6829]) ).
thf(9708,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk1 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8963,247]) ).
thf(9709,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[9708:[bind(A,$thf( G )),bind(B,$thf( cross_product @ G @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ G @ sk1 ))]]) ).
thf(9920,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[9709]) ).
thf(3452,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( subset @ sk6 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
!= ( subset @ ( power_set @ sk2 ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3329,754]) ).
thf(3484,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( power_set @ sk2 )
!= sk6 )
| ( ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) )
!= A ) ),
inference(simp,[status(thm)],[3452]) ).
thf(3500,plain,
( ~ ( empty @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
| ( ( power_set @ sk2 )
!= sk6 ) ),
inference(simp,[status(thm)],[3484]) ).
thf(14671,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ ( sk7 @ B ) @ A )
| ( ( subset @ ( range_of @ sk4 ) @ sk1 )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4440,264]) ).
thf(14672,plain,
( ( empty @ ( range_of @ sk4 ) )
| ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14671:[bind(A,$thf( sk1 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(15211,plain,
! [B: $i,A: $i] :
( ( empty @ ( range_of @ sk4 ) )
| ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ ( sk7 @ ( range_of @ sk4 ) ) @ sk1 )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14672,2713]) ).
thf(15212,plain,
( ( empty @ ( range_of @ sk4 ) )
| ( empty @ sk1 )
| ( ilf_type @ ( sk7 @ ( range_of @ sk4 ) ) @ ( member_type @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[15211:[bind(A,$thf( sk7 @ ( range_of @ sk4 ) )),bind(B,$thf( sk1 ))]]) ).
thf(8957,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) )
| ( ( subset @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk3 @ sk2 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6845,246]) ).
thf(8958,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ A @ ( cross_product @ sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8957:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ sk3 @ sk2 ))]]) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( member @ B @ ( power_set @ C ) )
| ( ( member @ ( sk7 @ A ) @ A )
!= ( member @ ( sk10 @ C @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[208,464]) ).
thf(480,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( member @ B @ ( power_set @ C ) )
| ( ( sk7 @ A )
!= ( sk10 @ C @ B ) )
| ( A != C ) ),
inference(simp,[status(thm)],[471]) ).
thf(483,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ A @ ( power_set @ B ) )
| ( ( sk10 @ B @ A )
!= ( sk7 @ B ) ) ),
inference(simp,[status(thm)],[480]) ).
thf(9073,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk1 @ sk2 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6797,246]) ).
thf(9074,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ A @ ( cross_product @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[9073:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ sk1 @ sk2 ))]]) ).
thf(15918,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15159,236]) ).
thf(15919,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15918:[bind(A,$thf( E )),bind(B,$thf( range_of @ ( cross_product @ E @ ( range_of @ sk4 ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(15993,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[15919]) ).
thf(6525,plain,
! [A: $i] :
( ( ilf_type @ A @ ( member_type @ ( power_set @ A ) ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[6517,33]) ).
thf(6541,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( member_type @ ( power_set @ A ) )
!= ( relation_type @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[6525]) ).
thf(6553,plain,
( ( relation_type @ sk3 @ sk2 )
!= ( member_type @ ( power_set @ sk4 ) ) ),
inference(simp,[status(thm)],[6541]) ).
thf(7382,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk3 @ sk2 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6845,244]) ).
thf(7383,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ A ) @ ( cross_product @ ( cross_product @ sk3 @ sk2 ) @ A ) ),
inference(pattern_uni,[status(thm)],[7382:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ sk3 @ sk2 ))]]) ).
thf(7849,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( cross_product @ ( domain_of @ sk4 ) @ A ) @ ( cross_product @ sk3 @ A ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7442,236]) ).
thf(7850,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ A ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk3 @ A ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7849:[bind(A,$thf( H )),bind(B,$thf( cross_product @ ( domain_of @ sk4 ) @ H )),bind(C,$thf( cross_product @ sk3 @ H ))]]) ).
thf(7911,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ A ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk3 @ A ) @ sk2 ) ),
inference(simp,[status(thm)],[7850]) ).
thf(9828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ C ) @ ( cross_product @ sk2 @ D ) )
| ( ( subset @ ( range_of @ ( sk5 @ A @ B ) ) @ B )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4579,247]) ).
thf(9829,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk5 @ A @ B ) ) ) @ ( cross_product @ sk2 @ B ) ),
inference(pattern_uni,[status(thm)],[9828:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( range_of @ ( sk5 @ F @ G ) )),bind(D,$thf( G ))]]) ).
thf(9916,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk5 @ A @ B ) ) ) @ ( cross_product @ sk2 @ B ) ),
inference(simp,[status(thm)],[9829]) ).
thf(27854,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27763,236]) ).
thf(27855,plain,
! [A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[27854:[bind(A,$thf( H )),bind(B,$thf( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ H ) ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(27953,plain,
! [A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk9 @ ( power_set @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[27855]) ).
thf(982,plain,
! [B: $i,A: $i] :
( ( ( power_set @ ( sk10 @ sk2 @ ( power_set @ sk2 ) ) )
!= ( range_of @ sk4 ) )
| ~ ( empty @ A )
| ( ( member @ ( range_of @ sk4 ) @ sk2 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[953,194]) ).
thf(983,plain,
( ( ( power_set @ ( sk10 @ sk2 @ ( power_set @ sk2 ) ) )
!= ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[982:[bind(A,$thf( sk2 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(6561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation_like @ D )
| ( ( ilf_type @ A @ ( subset_type @ A ) )
!= ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6533,5444]) ).
thf(6562,plain,
! [B: $i,A: $i] : ( relation_like @ ( cross_product @ A @ B ) ),
inference(pattern_uni,[status(thm)],[6561:[bind(A,$thf( cross_product @ E @ F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( cross_product @ E @ F ))]]) ).
thf(6589,plain,
! [B: $i,A: $i] : ( relation_like @ ( cross_product @ A @ B ) ),
inference(simp,[status(thm)],[6562]) ).
thf(7387,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ ( range_of @ sk4 ) @ sk1 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4440,244]) ).
thf(7388,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[7387:[bind(A,$thf( A )),bind(B,$thf( range_of @ sk4 )),bind(C,$thf( sk1 ))]]) ).
thf(7755,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk1 @ A ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7388,236]) ).
thf(7756,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk1 @ A ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7755:[bind(A,$thf( H )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ H )),bind(C,$thf( cross_product @ sk1 @ H ))]]) ).
thf(7805,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk1 @ A ) @ sk2 ) ),
inference(simp,[status(thm)],[7756]) ).
thf(9749,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6211,247]) ).
thf(9750,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9749:[bind(A,$thf( G )),bind(B,$thf( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ G ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(9894,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[9750]) ).
thf(10498,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk3 @ sk2 ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9703,236]) ).
thf(10499,plain,
subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ ( cross_product @ sk3 @ sk2 ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[10498:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )),bind(B,$thf( cross_product @ sk2 @ ( cross_product @ sk3 @ sk2 ) ))]]) ).
thf(16591,plain,
( ~ ( empty @ sk3 )
| ( empty @ ( range_of @ sk4 ) )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[16484,12996]) ).
thf(16611,plain,
( ( empty @ ( range_of @ sk4 ) )
| ~ ( empty @ sk3 )
| ( ( domain_of @ sk4 )
!= sk1 ) ),
inference(simp,[status(thm)],[16591]) ).
thf(16588,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( relation_like @ A )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16484,273]) ).
thf(16589,plain,
( ~ ( empty @ sk3 )
| ( relation_like @ ( domain_of @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[16588:[bind(A,$thf( domain_of @ sk4 ))]]) ).
thf(458,plain,
! [A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ( ( sk10 @ A @ ( range_of @ sk4 ) )
!= ( range_of @ sk4 ) )
| ( ( power_set @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[454]) ).
thf(1406,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ( subset @ A @ A )
!= ( subset @ ( power_set @ ( power_set @ sk2 ) ) @ ( power_set @ ( range_of @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[200,1381]) ).
thf(1410,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( A
!= ( power_set @ ( power_set @ sk2 ) ) )
| ( A
!= ( power_set @ ( range_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[1406]) ).
thf(1413,plain,
( ~ ( empty @ sk2 )
| ( ( power_set @ ( power_set @ sk2 ) )
!= ( power_set @ ( range_of @ sk4 ) ) ) ),
inference(simp,[status(thm)],[1410]) ).
thf(9957,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk1 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9712,236]) ).
thf(9958,plain,
subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ sk1 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[9957:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ sk2 @ sk1 ))]]) ).
thf(404,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( power_set @ B ) )
| ~ ( subset @ C @ D )
| ( member @ E @ D )
| ( ( member @ ( sk10 @ B @ A ) @ A )
!= ( member @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[401,250]) ).
thf(405,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( power_set @ B ) )
| ~ ( subset @ C @ A )
| ( member @ ( sk10 @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[404:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( sk10 @ F @ G ))]]) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( power_set @ B ) )
| ~ ( subset @ C @ A )
| ( member @ ( sk10 @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[405]) ).
thf(6830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ ( range_of @ sk4 ) ) @ ( cross_product @ D @ sk2 ) )
| ( ( subset @ ( domain_of @ ( sk5 @ A @ B ) ) @ A )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[3967,236]) ).
thf(6831,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk5 @ A @ B ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6830:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( domain_of @ ( sk5 @ F @ G ) )),bind(D,$thf( F ))]]) ).
thf(6921,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk5 @ A @ B ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk2 ) ),
inference(simp,[status(thm)],[6831]) ).
thf(16578,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ~ ( subset @ ( power_set @ sk2 ) @ A )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16484,754]) ).
thf(16579,plain,
( ~ ( empty @ sk3 )
| ~ ( subset @ ( power_set @ sk2 ) @ ( domain_of @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[16578:[bind(A,$thf( domain_of @ sk4 ))]]) ).
thf(2809,plain,
! [A: $i] :
( ( relation_like @ A )
| ( ( ilf_type @ ( range_of @ sk4 ) @ ( subset_type @ sk2 ) )
!= ( ilf_type @ A @ binary_relation_type ) ) ),
inference(paramod_ordered,[status(thm)],[2798,216]) ).
thf(2817,plain,
! [A: $i] :
( ( relation_like @ A )
| ( ( range_of @ sk4 )
!= A )
| ( ( subset_type @ sk2 )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2809]) ).
thf(2821,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ( ( subset_type @ sk2 )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[2817]) ).
thf(255,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ~ ( member @ G @ E )
| ( member @ G @ F )
| ( ( subset @ ( cross_product @ A @ C ) @ ( cross_product @ B @ D ) )
!= ( subset @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[232,250]) ).
thf(256,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ D )
| ~ ( subset @ C @ E )
| ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( member @ A @ ( cross_product @ D @ E ) ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( I )),bind(D,$thf( K )),bind(E,$thf( cross_product @ H @ I )),bind(F,$thf( cross_product @ J @ K ))]]) ).
thf(263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ D )
| ~ ( subset @ C @ E )
| ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( member @ A @ ( cross_product @ D @ E ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(4052,plain,
! [A: $i] :
( ( subset @ A @ sk2 )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3876,3076]) ).
thf(4064,plain,
! [A: $i] :
( ( subset @ A @ sk2 )
| ( ( domain_of @ sk4 )
!= A )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[4052]) ).
thf(4092,plain,
( ( subset @ ( domain_of @ sk4 ) @ sk2 )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[4064]) ).
thf(5395,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ( member @ sk4 @ ( power_set @ ( cross_product @ sk3 @ sk1 ) ) )
!= ( member @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5382,338]) ).
thf(5406,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( sk4 != A )
| ( ( power_set @ ( cross_product @ sk3 @ sk1 ) )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[5395]) ).
thf(5420,plain,
( ~ ( empty @ sk2 )
| ( ( power_set @ ( cross_product @ sk3 @ sk1 ) )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[5406]) ).
thf(10163,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ sk6 ) @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9806,236]) ).
thf(10164,plain,
subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ sk6 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[10163:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ sk6 )),bind(B,$thf( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) ))]]) ).
thf(10054,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk3 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9792,244]) ).
thf(10055,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) ) @ A ) @ ( cross_product @ ( cross_product @ sk2 @ sk3 ) @ A ) ),
inference(pattern_uni,[status(thm)],[10054:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ sk4 ) )),bind(C,$thf( cross_product @ sk2 @ sk3 ))]]) ).
thf(492,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ( member @ ( range_of @ sk4 ) @ ( power_set @ sk2 ) )
!= ( member @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[489,338]) ).
thf(499,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ( range_of @ sk4 )
!= A )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[492]) ).
thf(502,plain,
( ~ ( empty @ sk2 )
| ( ( power_set @ sk2 )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[499]) ).
thf(16790,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( member @ ( sk14 @ B ) @ A )
| ( ( subset @ ( domain_of @ sk4 ) @ sk3 )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3876,274]) ).
thf(16791,plain,
( ( relation_like @ ( domain_of @ sk4 ) )
| ( member @ ( sk14 @ ( domain_of @ sk4 ) ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[16790:[bind(A,$thf( sk3 )),bind(B,$thf( domain_of @ sk4 ))]]) ).
thf(6361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ilf_type @ D @ ( member_type @ ( power_set @ C ) ) )
| ( ( ilf_type @ ( sk5 @ A @ B ) @ ( subset_type @ ( cross_product @ A @ B ) ) )
!= ( ilf_type @ D @ ( subset_type @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[5282,2573]) ).
thf(6362,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk5 @ A @ B ) @ ( member_type @ ( power_set @ ( cross_product @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[6361:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( cross_product @ G @ H )),bind(D,$thf( sk5 @ G @ H ))]]) ).
thf(6389,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk5 @ A @ B ) @ ( member_type @ ( power_set @ ( cross_product @ A @ B ) ) ) ),
inference(simp,[status(thm)],[6362]) ).
thf(9296,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( cross_product @ A @ ( domain_of @ sk4 ) ) @ ( cross_product @ A @ sk3 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9037,236]) ).
thf(9297,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ A @ ( domain_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ A @ sk3 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9296:[bind(A,$thf( G )),bind(B,$thf( cross_product @ G @ ( domain_of @ sk4 ) )),bind(C,$thf( cross_product @ G @ sk3 ))]]) ).
thf(9358,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ A @ ( domain_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ A @ sk3 ) @ sk2 ) ),
inference(simp,[status(thm)],[9297]) ).
thf(7419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ B ) @ ( cross_product @ D @ B ) )
| ( ( subset @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6211,244]) ).
thf(7420,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ B ) ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[7419:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ H ) ) )),bind(D,$thf( sk2 ))]]) ).
thf(7543,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk8 @ ( cross_product @ ( range_of @ sk4 ) @ B ) ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(simp,[status(thm)],[7420]) ).
thf(9815,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6023,247]) ).
thf(9816,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9815:[bind(A,$thf( F )),bind(B,$thf( range_of @ ( sk8 @ ( cross_product @ F @ ( range_of @ sk4 ) ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(9911,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk8 @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[9816]) ).
thf(16493,plain,
! [A: $i] :
( ( empty @ ( domain_of @ sk4 ) )
| ~ ( empty @ sk1 )
| ( ( member @ ( sk7 @ ( domain_of @ sk4 ) ) @ sk3 )
!= ( member @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14742,12153]) ).
thf(16506,plain,
! [A: $i] :
( ( empty @ ( domain_of @ sk4 ) )
| ~ ( empty @ sk1 )
| ( ( sk7 @ ( domain_of @ sk4 ) )
!= A )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[16493]) ).
thf(16517,plain,
( ( empty @ ( domain_of @ sk4 ) )
| ~ ( empty @ sk1 )
| ( ( range_of @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[16506]) ).
thf(15876,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15159,247]) ).
thf(15877,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15876:[bind(A,$thf( E )),bind(B,$thf( range_of @ ( cross_product @ E @ ( range_of @ sk4 ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(15982,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[15877]) ).
thf(6612,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ binary_relation_type )
| ( ( relation_like @ ( cross_product @ A @ B ) )
!= ( relation_like @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6589,291]) ).
thf(6613,plain,
! [B: $i,A: $i] : ( ilf_type @ ( cross_product @ A @ B ) @ binary_relation_type ),
inference(pattern_uni,[status(thm)],[6612:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( cross_product @ D @ E ))]]) ).
thf(6622,plain,
! [B: $i,A: $i] : ( ilf_type @ ( cross_product @ A @ B ) @ binary_relation_type ),
inference(simp,[status(thm)],[6613]) ).
thf(16063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ ( range_of @ sk4 ) ) @ ( cross_product @ D @ sk2 ) )
| ( ( subset @ ( domain_of @ ( cross_product @ A @ B ) ) @ A )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15041,236]) ).
thf(16064,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( cross_product @ A @ B ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[16063:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( domain_of @ ( cross_product @ F @ G ) )),bind(D,$thf( F ))]]) ).
thf(16138,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( cross_product @ A @ B ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk2 ) ),
inference(simp,[status(thm)],[16064]) ).
thf(6817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ ( range_of @ sk4 ) ) @ ( cross_product @ D @ sk2 ) )
| ( ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ B )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5142,236]) ).
thf(6818,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6817:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( range_of @ ( sk8 @ ( cross_product @ G @ H ) ) )),bind(D,$thf( H ))]]) ).
thf(6917,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) ),
inference(simp,[status(thm)],[6818]) ).
thf(13017,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ ( power_set @ B ) @ A )
| ~ ( empty @ sk1 )
| ( ( member @ B @ A )
!= ( member @ C @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[521,12153]) ).
thf(13018,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ A ) @ ( range_of @ sk4 ) )
| ~ ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[13017:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(13076,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ A ) @ ( range_of @ sk4 ) )
| ~ ( empty @ sk1 ) ),
inference(simp,[status(thm)],[13018]) ).
thf(15094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ ( range_of @ sk4 ) ) @ ( cross_product @ D @ sk2 ) )
| ( ( subset @ ( range_of @ ( cross_product @ A @ B ) ) @ B )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15039,236]) ).
thf(15095,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( cross_product @ A @ B ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15094:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( range_of @ ( cross_product @ F @ G ) )),bind(D,$thf( G ))]]) ).
thf(15203,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( cross_product @ A @ B ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) ),
inference(simp,[status(thm)],[15095]) ).
thf(10240,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ sk4 ) @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9827,247]) ).
thf(10241,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ sk4 ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[10240:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ sk4 )),bind(B,$thf( cross_product @ sk2 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ))]]) ).
thf(2827,plain,
! [A: $i] :
( ( ( subset_type @ sk2 )
!= binary_relation_type )
| ( ilf_type @ A @ binary_relation_type )
| ( ( relation_like @ ( range_of @ sk4 ) )
!= ( relation_like @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2821,291]) ).
thf(2828,plain,
( ( ( subset_type @ sk2 )
!= binary_relation_type )
| ( ilf_type @ ( range_of @ sk4 ) @ binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[2827:[bind(A,$thf( range_of @ sk4 ))]]) ).
thf(6137,plain,
( ( ( range_of @ sk4 )
!= sk4 )
| ( ( cross_product @ sk3 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[5096]) ).
thf(3549,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ( ( subset @ sk6 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
!= ( subset @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3329,3104]) ).
thf(3572,plain,
! [A: $i] :
( ( subset @ ( range_of @ sk4 ) @ A )
| ( sk6 != sk2 )
| ( ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) )
!= A ) ),
inference(simp,[status(thm)],[3549]) ).
thf(3613,plain,
( ( subset @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[3572]) ).
thf(5,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( range_of @ A ) @ set_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
thf(40,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( range_of @ A ) @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6789,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) @ sk2 )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4188,236]) ).
thf(6790,plain,
! [A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6789:[bind(A,$thf( F )),bind(B,$thf( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ F ) )),bind(C,$thf( sk2 ))]]) ).
thf(6913,plain,
! [A: $i] : ( subset @ ( cross_product @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) ),
inference(simp,[status(thm)],[6790]) ).
thf(5062,plain,
( ( ilf_type @ ( range_of @ sk4 ) @ ( member_type @ ( power_set @ sk2 ) ) )
!= ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2791,4962]) ).
thf(5087,plain,
( ( ( range_of @ sk4 )
!= sk4 )
| ( ( member_type @ ( power_set @ sk2 ) )
!= ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[5062]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( ilf_type @ ( sk5 @ B @ A ) @ ( relation_type @ B @ A ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[176,33]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ B @ A )
!= sk4 )
| ( ( relation_type @ B @ A )
!= ( relation_type @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ B @ A )
!= sk4 )
| ( B != sk3 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[178]) ).
thf(186,plain,
( ( sk5 @ sk3 @ sk2 )
!= sk4 ),
inference(simp,[status(thm)],[185]) ).
thf(8951,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ C ) @ ( cross_product @ B @ D ) )
| ( ( subset @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ A ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4188,246]) ).
thf(8952,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ B ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8951:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ G ) )),bind(D,$thf( sk2 ))]]) ).
thf(9160,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( domain_of @ ( sk5 @ ( range_of @ sk4 ) @ B ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(simp,[status(thm)],[8952]) ).
thf(9834,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk2 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6874,247]) ).
thf(9835,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ A @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[9834:[bind(A,$thf( G )),bind(B,$thf( cross_product @ G @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ G @ sk2 ))]]) ).
thf(9919,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[9835]) ).
thf(7436,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ A ) @ ( cross_product @ C @ A ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6847,244]) ).
thf(7437,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ A ) @ ( cross_product @ ( cross_product @ sk2 @ sk2 ) @ A ) ),
inference(pattern_uni,[status(thm)],[7436:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ sk2 @ sk2 ))]]) ).
thf(3456,plain,
! [A: $i] :
( ( subset @ A @ sk2 )
| ( ( subset @ sk6 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
!= ( subset @ A @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3329,3076]) ).
thf(3479,plain,
! [A: $i] :
( ( subset @ A @ sk2 )
| ( sk6 != A )
| ( ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[3456]) ).
thf(3497,plain,
( ( subset @ sk6 @ sk2 )
| ( ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) )
!= ( range_of @ sk4 ) ) ),
inference(simp,[status(thm)],[3479]) ).
thf(9800,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk1 @ A ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7388,247]) ).
thf(9801,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[9800:[bind(A,$thf( H )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ H )),bind(C,$thf( cross_product @ sk1 @ H ))]]) ).
thf(9908,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[9801]) ).
thf(5060,plain,
( ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk1 ) )
!= ( ilf_type @ sk4 @ ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,4962]) ).
thf(5102,plain,
( ( sk4 != sk4 )
| ( ( relation_type @ sk3 @ sk1 )
!= ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[5060]) ).
thf(5109,plain,
( ( relation_type @ sk3 @ sk1 )
!= ( subset_type @ ( cross_product @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[5102]) ).
thf(14786,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ ( sk7 @ B ) @ A )
| ( ( subset @ sk4 @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5568,264]) ).
thf(14787,plain,
( ( empty @ sk4 )
| ( member @ ( sk7 @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[14786:[bind(A,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(B,$thf( sk4 ))]]) ).
thf(344,plain,
! [A: $i] :
( ( empty @ A )
| ( ( ilf_type @ ( sk9 @ A ) @ ( member_type @ A ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[342,33]) ).
thf(346,plain,
! [A: $i] :
( ( empty @ A )
| ( ( sk9 @ A )
!= sk4 )
| ( ( member_type @ A )
!= ( relation_type @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[344]) ).
thf(9190,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ ( range_of @ sk4 ) ) @ ( cross_product @ C @ sk2 ) )
| ( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ A @ sk1 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8963,236]) ).
thf(9191,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ A @ sk1 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9190:[bind(A,$thf( G )),bind(B,$thf( cross_product @ G @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ G @ sk1 ))]]) ).
thf(9262,plain,
! [A: $i] : ( subset @ ( cross_product @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ A @ sk1 ) @ sk2 ) ),
inference(simp,[status(thm)],[9191]) ).
thf(9700,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ sk6 @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6855,247]) ).
thf(9701,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ sk6 @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9700:[bind(A,$thf( cross_product @ sk6 @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) @ sk2 ))]]) ).
thf(9786,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6847,247]) ).
thf(9787,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9786:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ sk2 @ sk2 ))]]) ).
thf(7056,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk3 @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6845,236]) ).
thf(7057,plain,
subset @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk3 @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[7056:[bind(A,$thf( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ sk3 @ sk2 ))]]) ).
thf(9838,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk3 @ sk2 ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7057,247]) ).
thf(9839,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ ( cross_product @ sk3 @ sk2 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9838:[bind(A,$thf( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ sk3 @ sk2 ) @ sk2 ))]]) ).
thf(18482,plain,
! [B: $i,A: $i] :
( ( relation_like @ ( domain_of @ sk4 ) )
| ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ ( sk14 @ ( domain_of @ sk4 ) ) @ sk3 )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16791,2713]) ).
thf(18483,plain,
( ( relation_like @ ( domain_of @ sk4 ) )
| ( empty @ sk3 )
| ( ilf_type @ ( sk14 @ ( domain_of @ sk4 ) ) @ ( member_type @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[18482:[bind(A,$thf( sk14 @ ( domain_of @ sk4 ) )),bind(B,$thf( sk3 ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( cross_product @ A @ B ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
thf(36,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( cross_product @ A @ B ) @ set_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(167,plain,
( ( sk3 != sk3 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[125]) ).
thf(168,plain,
sk2 != sk1,
inference(simp,[status(thm)],[167]) ).
thf(9766,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk2 @ sk2 ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7145,247]) ).
thf(9767,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ ( cross_product @ sk2 @ sk2 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9766:[bind(A,$thf( cross_product @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ sk2 @ sk2 ) @ sk2 ))]]) ).
thf(292,plain,
! [A: $i] :
( ~ ( relation_like @ A )
| ( ( ilf_type @ A @ binary_relation_type )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[291,33]) ).
thf(301,plain,
! [A: $i] :
( ~ ( relation_like @ A )
| ( A != sk4 )
| ( ( relation_type @ sk3 @ sk2 )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[292]) ).
thf(303,plain,
( ~ ( relation_like @ sk4 )
| ( ( relation_type @ sk3 @ sk2 )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[301]) ).
thf(5536,plain,
( ~ $true
| ( ( relation_type @ sk3 @ sk2 )
!= binary_relation_type ) ),
inference(rewrite,[status(thm)],[303,5474]) ).
thf(5537,plain,
( ( relation_type @ sk3 @ sk2 )
!= binary_relation_type ),
inference(simp,[status(thm)],[5536]) ).
thf(8573,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ ( range_of @ sk4 ) ) @ ( cross_product @ B @ sk2 ) )
| ( ( subset @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ sk3 @ sk2 ) @ sk2 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7057,236]) ).
thf(8574,plain,
subset @ ( cross_product @ ( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) ) @ ( cross_product @ ( cross_product @ ( cross_product @ sk3 @ sk2 ) @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[8573:[bind(A,$thf( cross_product @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( range_of @ sk4 ) )),bind(B,$thf( cross_product @ ( cross_product @ sk3 @ sk2 ) @ sk2 ))]]) ).
thf(9975,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ A @ B ) @ ( cross_product @ A @ C ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) @ ( cross_product @ sk2 @ sk1 ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9712,246]) ).
thf(9976,plain,
! [A: $i] : ( subset @ ( cross_product @ A @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ A @ ( cross_product @ sk2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[9975:[bind(A,$thf( A )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ ( range_of @ sk4 ) )),bind(C,$thf( cross_product @ sk2 @ sk1 ))]]) ).
thf(6569,plain,
! [A: $i] :
( ( ilf_type @ A @ ( subset_type @ A ) )
!= ( ilf_type @ sk4 @ ( relation_type @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[6533,33]) ).
thf(6587,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( subset_type @ A )
!= ( relation_type @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[6569]) ).
thf(6600,plain,
( ( relation_type @ sk3 @ sk2 )
!= ( subset_type @ sk4 ) ),
inference(simp,[status(thm)],[6587]) ).
thf(304,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ( ilf_type @ A @ binary_relation_type )
| ( ( relation_like @ ( range_of @ sk4 ) )
!= ( relation_like @ A ) ) ),
inference(paramod_ordered,[status(thm)],[286,291]) ).
thf(305,plain,
( ~ ( empty @ sk2 )
| ( ilf_type @ ( range_of @ sk4 ) @ binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[304:[bind(A,$thf( range_of @ sk4 ))]]) ).
thf(293,plain,
! [B: $i,A: $i] :
( ( binary_relation_type != set_type )
| ( ilf_type @ B @ binary_relation_type )
| ( ( relation_like @ A )
!= ( relation_like @ B ) ) ),
inference(paramod_ordered,[status(thm)],[229,291]) ).
thf(294,plain,
! [A: $i] :
( ( binary_relation_type != set_type )
| ( ilf_type @ A @ binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(15905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ B ) @ ( cross_product @ D @ B ) )
| ( ( subset @ ( range_of @ ( cross_product @ A @ ( range_of @ sk4 ) ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15159,244]) ).
thf(15906,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( cross_product @ B @ ( range_of @ sk4 ) ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[15905:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( range_of @ ( cross_product @ F @ ( range_of @ sk4 ) ) )),bind(D,$thf( sk2 ))]]) ).
thf(15989,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( cross_product @ B @ ( range_of @ sk4 ) ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(simp,[status(thm)],[15906]) ).
thf(10471,plain,
! [B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ B ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk3 @ sk2 ) ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9703,247]) ).
thf(10472,plain,
subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk2 @ ( cross_product @ sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[10471:[bind(A,$thf( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( domain_of @ sk4 ) @ ( range_of @ sk4 ) ) )),bind(B,$thf( cross_product @ sk2 @ ( cross_product @ sk3 @ sk2 ) ))]]) ).
thf(16538,plain,
! [B: $i,A: $i] :
( ~ ( empty @ sk3 )
| ( member @ B @ ( power_set @ A ) )
| ( ( empty @ ( domain_of @ sk4 ) )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16484,416]) ).
thf(16539,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( member @ ( domain_of @ sk4 ) @ ( power_set @ A ) ) ),
inference(pattern_uni,[status(thm)],[16538:[bind(A,$thf( A )),bind(B,$thf( domain_of @ sk4 ))]]) ).
thf(14763,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( member @ ( sk7 @ B ) @ A )
| ( ( subset @ sk6 @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3329,264]) ).
thf(14764,plain,
( ( empty @ sk6 )
| ( member @ ( sk7 @ sk6 ) @ ( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[14763:[bind(A,$thf( cross_product @ ( domain_of @ sk6 ) @ ( range_of @ sk6 ) )),bind(B,$thf( sk6 ))]]) ).
thf(16710,plain,
! [B: $i,A: $i] :
( ( relation_like @ B )
| ( member @ ( sk14 @ B ) @ A )
| ( ( subset @ ( range_of @ sk4 ) @ sk1 )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4440,274]) ).
thf(16711,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[16710:[bind(A,$thf( sk1 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(8968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ B @ C ) @ ( cross_product @ B @ D ) )
| ( ( subset @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4743,246]) ).
thf(8969,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( range_of @ ( sk5 @ B @ ( range_of @ sk4 ) ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8968:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( range_of @ ( sk5 @ F @ ( range_of @ sk4 ) ) )),bind(D,$thf( sk2 ))]]) ).
thf(9124,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ A @ ( range_of @ ( sk5 @ B @ ( range_of @ sk4 ) ) ) ) @ ( cross_product @ A @ sk2 ) ),
inference(simp,[status(thm)],[8969]) ).
thf(9758,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ B ) @ ( cross_product @ sk2 @ C ) )
| ( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ A ) @ ( cross_product @ sk2 @ A ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7444,247]) ).
thf(9759,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[9758:[bind(A,$thf( H )),bind(B,$thf( cross_product @ ( range_of @ sk4 ) @ H )),bind(C,$thf( cross_product @ sk2 @ H ))]]) ).
thf(9898,plain,
! [A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( cross_product @ ( range_of @ sk4 ) @ A ) ) @ ( cross_product @ sk2 @ ( cross_product @ sk2 @ A ) ) ),
inference(simp,[status(thm)],[9759]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( member @ ( sk15 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[81]) ).
thf(2371,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( member @ ( sk15 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(rewrite,[status(thm)],[84,112]) ).
thf(2372,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk15 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[2371]) ).
thf(7393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ C @ B ) @ ( cross_product @ D @ B ) )
| ( ( subset @ ( range_of @ ( sk5 @ A @ ( range_of @ sk4 ) ) ) @ sk2 )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4743,244]) ).
thf(7394,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk5 @ B @ ( range_of @ sk4 ) ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[7393:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( range_of @ ( sk5 @ F @ ( range_of @ sk4 ) ) )),bind(D,$thf( sk2 ))]]) ).
thf(7538,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ ( sk5 @ B @ ( range_of @ sk4 ) ) ) @ A ) @ ( cross_product @ sk2 @ A ) ),
inference(simp,[status(thm)],[7394]) ).
thf(449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ A ) )
| ~ ( subset @ B @ C )
| ( member @ D @ C )
| ( ( member @ ( sk10 @ A @ ( range_of @ sk4 ) ) @ sk2 )
!= ( member @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[415,250]) ).
thf(450,plain,
! [B: $i,A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ B ) )
| ~ ( subset @ sk2 @ A )
| ( member @ ( sk10 @ B @ ( range_of @ sk4 ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[449:[bind(A,$thf( E )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( sk10 @ E @ ( range_of @ sk4 ) ))]]) ).
thf(459,plain,
! [B: $i,A: $i] :
( ( member @ ( range_of @ sk4 ) @ ( power_set @ B ) )
| ~ ( subset @ sk2 @ A )
| ( member @ ( sk10 @ B @ ( range_of @ sk4 ) ) @ A ) ),
inference(simp,[status(thm)],[450]) ).
thf(9751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ C ) @ ( cross_product @ sk2 @ D ) )
| ( ( subset @ ( domain_of @ ( sk5 @ A @ B ) ) @ A )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[3967,247]) ).
thf(9752,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk5 @ A @ B ) ) ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[9751:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( domain_of @ ( sk5 @ F @ G ) )),bind(D,$thf( F ))]]) ).
thf(9895,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( sk5 @ A @ B ) ) ) @ ( cross_product @ sk2 @ A ) ),
inference(simp,[status(thm)],[9752]) ).
thf(17556,plain,
! [B: $i,A: $i] :
( ( relation_like @ ( range_of @ sk4 ) )
| ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ ( sk14 @ ( range_of @ sk4 ) ) @ sk1 )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16711,2713]) ).
thf(17557,plain,
( ( relation_like @ ( range_of @ sk4 ) )
| ( empty @ sk1 )
| ( ilf_type @ ( sk14 @ ( range_of @ sk4 ) ) @ ( member_type @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[17556:[bind(A,$thf( sk14 @ ( range_of @ sk4 ) )),bind(B,$thf( sk1 ))]]) ).
thf(5376,plain,
( ( cross_product @ sk3 @ sk2 )
!= ( cross_product @ sk3 @ sk1 ) ),
inference(simp,[status(thm)],[5337]) ).
thf(13015,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( power_set @ sk2 ) @ A )
| ~ ( empty @ sk1 )
| ( ( member @ ( range_of @ sk4 ) @ A )
!= ( member @ B @ ( range_of @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[505,12153]) ).
thf(13016,plain,
( ~ ( subset @ ( power_set @ sk2 ) @ ( range_of @ sk4 ) )
| ~ ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[13015:[bind(A,$thf( range_of @ sk4 )),bind(B,$thf( range_of @ sk4 ))]]) ).
thf(16019,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ C ) @ ( cross_product @ sk2 @ D ) )
| ( ( subset @ ( domain_of @ ( cross_product @ A @ B ) ) @ A )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15041,247]) ).
thf(16020,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( cross_product @ A @ B ) ) ) @ ( cross_product @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[16019:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( domain_of @ ( cross_product @ F @ G ) )),bind(D,$thf( F ))]]) ).
thf(16125,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( domain_of @ ( cross_product @ A @ B ) ) ) @ ( cross_product @ sk2 @ A ) ),
inference(simp,[status(thm)],[16020]) ).
thf(530,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 )
| ( ( member @ A @ ( power_set @ A ) )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[488,365]) ).
thf(531,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ A ) @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[530:[bind(A,$thf( D )),bind(B,$thf( power_set @ D )),bind(C,$thf( D ))]]) ).
thf(560,plain,
! [A: $i] :
( ~ ( subset @ ( power_set @ A ) @ ( range_of @ sk4 ) )
| ~ ( empty @ sk2 ) ),
inference(simp,[status(thm)],[531]) ).
thf(9734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( cross_product @ ( range_of @ sk4 ) @ C ) @ ( cross_product @ sk2 @ D ) )
| ( ( subset @ ( range_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) @ B )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5142,247]) ).
thf(9735,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) ) @ ( cross_product @ sk2 @ B ) ),
inference(pattern_uni,[status(thm)],[9734:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( range_of @ ( sk8 @ ( cross_product @ G @ H ) ) )),bind(D,$thf( H ))]]) ).
thf(9880,plain,
! [B: $i,A: $i] : ( subset @ ( cross_product @ ( range_of @ sk4 ) @ ( range_of @ ( sk8 @ ( cross_product @ A @ B ) ) ) ) @ ( cross_product @ sk2 @ B ) ),
inference(simp,[status(thm)],[9735]) ).
thf(23,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( ordered_pair @ A @ B ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
thf(100,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( ordered_pair @ A @ B ) @ set_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(52181,plain,
$false,
inference(e,[status(thm)],[4188,6405,4094,365,4101,1995,10267,347,9833,6855,16533,6845,9907,9032,88,14684,5444,9924,1808,28205,10061,4408,6602,202,1041,16308,9901,247,5669,23515,1608,8963,533,4097,13095,10138,30799,2168,28398,7452,7467,4440,7944,2985,27942,417,288,3809,2819,1703,16304,42,14737,4743,6552,1298,13030,504,3148,751,16146,125,13170,5182,3845,23507,2713,1379,2169,9155,1347,416,325,6923,5829,16315,9712,29,30789,4664,216,2237,7273,443,27763,5311,7473,4660,28426,280,1215,5096,5384,9140,9914,2002,428,16594,14652,411,2799,2804,15041,9764,265,2011,7533,248,60,4962,7725,14785,5545,5142,6388,7518,4076,9785,5334,2954,9703,16297,12985,102,334,2733,302,38,1751,16484,6915,2528,33,260,862,5769,16529,1296,1819,5551,1787,10035,6926,229,2873,8530,1234,5714,1772,4095,3018,2631,53,109,2798,488,554,5107,5337,489,7572,2781,96,8673,1588,1297,5374,3770,9932,4934,1984,5369,503,9068,6211,457,3967,16473,6533,9925,953,7444,1991,15039,105,244,266,2761,2645,5513,16637,166,32,1273,180,1374,264,10079,9049,13090,5698,562,286,291,9952,413,176,4662,6870,5474,44,2791,6927,2568,281,204,71,5039,445,4099,5282,2557,2573,86,572,4096,7145,2166,5539,236,1464,19352,2079,16000,5143,219,13079,1574,81,245,98,208,113,15192,274,6920,230,9920,3500,15212,6969,8958,16535,91,483,520,9074,6847,15993,6553,1381,7383,278,7911,9916,505,27953,685,521,983,6589,7805,1015,3876,9894,10499,35,16611,16589,112,2629,6517,342,1958,754,458,1551,194,1413,9958,1845,5047,48,414,9037,6921,16579,2821,6596,263,50,67,4092,5420,10164,10055,502,1785,5203,338,1658,16791,6389,7388,9358,7543,9911,3329,16517,15982,612,6622,16138,6917,13076,15203,43,15159,250,10241,99,4945,2828,6137,5510,4102,3613,40,5382,14742,6023,6913,401,13080,5087,786,186,3104,12209,9160,9919,7437,58,3497,9908,5109,14787,5568,346,4098,9262,9701,246,27619,9792,9787,2623,9839,18483,12153,9806,36,168,9767,5537,8574,273,4579,9976,6600,305,294,15989,268,6590,10472,16539,27609,9827,94,415,2502,12996,14764,16711,9124,14672,9898,200,62,6797,2372,6874,740,7538,464,459,9895,178,17557,3076,5376,369,2138,111,322,13016,16125,560,9880,7057,232,100,7442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET652+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 19:16:49 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.93/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (137ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 1.83/1.27 % [INFO] eprover registered as external prover.
% 1.83/1.28 % [INFO] cvc4 registered as external prover.
% 1.83/1.28 % [INFO] Scanning for conjecture ...
% 2.00/1.36 % [INFO] Found a conjecture and 26 axioms. Running axiom selection ...
% 2.13/1.41 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.39/1.45 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.46 % [INFO] Type checking passed.
% 2.44/1.47 % [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 ...
% 155.53/28.77 % External prover 'e' found a proof!
% 155.53/28.77 % [INFO] Killing All external provers ...
% 155.53/28.77 % Time passed: 28253ms (effective reasoning time: 27774ms)
% 155.53/28.77 % 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)>
% 155.53/28.78 % Axioms used in derivation (26): p12, p18, p15, p26, p3, p22, p11, p2, p17, p9, p1, p24, p13, p16, p20, p10, p19, p4, p7, p5, p23, p21, p25, p14, p6, p8
% 155.53/28.78 % No. of inferences in proof: 1083
% 155.53/28.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 28253 ms resp. 27774 ms w/o parsing
% 156.25/29.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 156.25/29.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------