TSTP Solution File: SEU383+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU383+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 11:58:38 EDT 2023
% Result : Theorem 222.01s 42.00s
% Output : Refutation 222.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 81
% Syntax : Number of formulae : 1954 ( 249 unt; 41 typ; 0 def)
% Number of atoms : 5614 (1850 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 15405 (2789 ~;2563 |; 95 &;9861 @)
% ( 6 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 11 con; 0-3 aty)
% Number of variables : 1159 ( 0 ^;1125 !; 34 ?;1159 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(reflexive_relstr_type,type,
reflexive_relstr: $i > $o ).
thf(transitive_relstr_type,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_type,type,
antisymmetric_relstr: $i > $o ).
thf(lower_bounded_relstr_type,type,
lower_bounded_relstr: $i > $o ).
thf(rel_str_type,type,
rel_str: $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(filtered_subset_type,type,
filtered_subset: $i > $i > $o ).
thf(upper_relstr_subset_type,type,
upper_relstr_subset: $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(proper_element_type,type,
proper_element: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(bottom_of_relstr_type,type,
bottom_of_relstr: $i > $i ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(v1_yellow_3_type,type,
v1_yellow_3: $i > $o ).
thf(related_type,type,
related: $i > $i > $i > $o ).
thf(finite_type,type,
finite: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(join_on_relstr_type,type,
join_on_relstr: $i > $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 ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i > $i ).
thf(sk13_type,type,
sk13: $i > $i ).
thf(sk14_type,type,
sk14: $i > $i ).
thf(sk15_type,type,
sk15: $i > $i ).
thf(sk16_type,type,
sk16: $i ).
thf(sk17_type,type,
sk17: $i > $i ).
thf(sk18_type,type,
sk18: $i > $i > $i ).
thf(sk19_type,type,
sk19: $i > $i > $i ).
thf(14,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(86,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(118,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(119,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[118]) ).
thf(120,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty @ A ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(106,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( in @ C @ A )
=> ( in @ C @ B ) )
& ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[106]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[107]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[111]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
<=> ~ ( in @ ( bottom_of_relstr @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_7) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
<=> ~ ( in @ ( bottom_of_relstr @ A ) @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(42,plain,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ~ ( in @ ( bottom_of_relstr @ A ) @ B ) )
& ( ~ ( in @ ( bottom_of_relstr @ A ) @ B )
=> ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(52,plain,
~ ( empty @ sk2 ),
inference(cnf,[status(esa)],[42]) ).
thf(180,plain,
( ( empty @ sk2 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,52]) ).
thf(182,plain,
sk2 != empty_set,
inference(simp,[status(thm)],[180]) ).
thf(2021,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[115,182]) ).
thf(2022,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk2 @ A ) @ A )
| ( in @ ( sk10 @ sk2 @ A ) @ sk2 )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2021:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(2341,plain,
( ( in @ ( sk9 @ sk2 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk2 @ empty_set ) @ sk2 ) ),
inference(simp,[status(thm)],[2022]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(83,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(84,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ( empty @ B ) ),
inference(miniscope,[status(thm)],[83]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[84]) ).
thf(1507,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( empty @ empty_set )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[86,85]) ).
thf(1508,plain,
! [A: $i] :
~ ( in @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[1507:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(11727,plain,
( $false
| ( in @ ( sk10 @ sk2 @ empty_set ) @ sk2 ) ),
inference(rewrite,[status(thm)],[2341,1508]) ).
thf(11728,plain,
in @ ( sk10 @ sk2 @ empty_set ) @ sk2,
inference(simp,[status(thm)],[11727]) ).
thf(11729,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ empty_set @ sk2 )
| ( A
!= ( sk10 @ sk2 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[120,11728]) ).
thf(11730,plain,
( ~ ( empty @ ( sk10 @ sk2 @ empty_set ) )
| ( in @ empty_set @ sk2 ) ),
inference(pattern_uni,[status(thm)],[11729:[bind(A,$thf( sk10 @ sk2 @ empty_set ))]]) ).
thf(40310,plain,
( ( in @ empty_set @ sk2 )
| ( ( empty @ ( sk10 @ sk2 @ empty_set ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,11730]) ).
thf(40422,plain,
( ( in @ empty_set @ sk2 )
| ( ( sk10 @ sk2 @ empty_set )
!= empty_set ) ),
inference(simp,[status(thm)],[40310]) ).
thf(32,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(140,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(142,plain,
one_sorted_str @ sk16,
inference(cnf,[status(esa)],[140]) ).
thf(8,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(72,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(73,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(919,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( empty @ ( the_carrier @ A ) )
| ( ( one_sorted_str @ sk16 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[142,73]) ).
thf(920,plain,
( ( empty_carrier @ sk16 )
| ~ ( empty @ ( the_carrier @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[919:[bind(A,$thf( sk16 ))]]) ).
thf(141,plain,
~ ( empty_carrier @ sk16 ),
inference(cnf,[status(esa)],[140]) ).
thf(1410,plain,
( $false
| ~ ( empty @ ( the_carrier @ sk16 ) ) ),
inference(rewrite,[status(thm)],[920,141]) ).
thf(1411,plain,
~ ( empty @ ( the_carrier @ sk16 ) ),
inference(simp,[status(thm)],[1410]) ).
thf(31,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(138,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(20,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(100,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(101,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk7 @ A ) @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[100]) ).
thf(23,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(116,plain,
? [A: $i] : ( rel_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(117,plain,
rel_str @ sk11,
inference(cnf,[status(esa)],[116]) ).
thf(39,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
thf(164,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(165,plain,
! [A: $i] :
( ~ ( rel_str @ A )
| ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(18951,plain,
! [A: $i] :
( ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) )
| ( ( rel_str @ sk11 )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[117,165]) ).
thf(18952,plain,
element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk11 ),
inference(pattern_uni,[status(thm)],[18951:[bind(A,$thf( sk11 ))]]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(98,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ),
inference(cnf,[status(esa)],[98]) ).
thf(19142,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( in @ A @ B )
| ( ( element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk11 ) )
!= ( element @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18952,99]) ).
thf(19143,plain,
( ( empty @ ( the_carrier @ sk11 ) )
| ( in @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[19142:[bind(A,$thf( bottom_of_relstr @ sk11 )),bind(B,$thf( the_carrier @ sk11 ))]]) ).
thf(24653,plain,
! [A: $i] :
( ( empty @ ( the_carrier @ sk11 ) )
| ( ( in @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk11 ) )
!= ( in @ A @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[19143,1508]) ).
thf(24692,plain,
! [A: $i] :
( ( empty @ ( the_carrier @ sk11 ) )
| ( ( bottom_of_relstr @ sk11 )
!= A )
| ( ( the_carrier @ sk11 )
!= empty_set ) ),
inference(simp,[status(thm)],[24653]) ).
thf(24725,plain,
( ( empty @ ( the_carrier @ sk11 ) )
| ( ( the_carrier @ sk11 )
!= empty_set ) ),
inference(simp,[status(thm)],[24692]) ).
thf(51,plain,
rel_str @ sk1,
inference(cnf,[status(esa)],[42]) ).
thf(36,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(154,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(155,plain,
! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ),
inference(cnf,[status(esa)],[154]) ).
thf(14668,plain,
! [A: $i] :
( ( one_sorted_str @ A )
| ( ( rel_str @ sk1 )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51,155]) ).
thf(14669,plain,
one_sorted_str @ sk1,
inference(pattern_uni,[status(thm)],[14668:[bind(A,$thf( sk1 ))]]) ).
thf(14718,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( empty @ ( the_carrier @ A ) )
| ( ( one_sorted_str @ sk1 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14669,73]) ).
thf(14719,plain,
( ( empty_carrier @ sk1 )
| ~ ( empty @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14718:[bind(A,$thf( sk1 ))]]) ).
thf(49,plain,
~ ( empty_carrier @ sk1 ),
inference(cnf,[status(esa)],[42]) ).
thf(16653,plain,
( $false
| ~ ( empty @ ( the_carrier @ sk1 ) ) ),
inference(rewrite,[status(thm)],[14719,49]) ).
thf(16654,plain,
~ ( empty @ ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[16653]) ).
thf(27142,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ ( the_carrier @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[24725,16654]) ).
thf(27161,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( the_carrier @ sk11 )
!= ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[27142]) ).
thf(54824,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[27161]) ).
thf(54966,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk1 )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,54824]) ).
thf(54967,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk11 != sk1 ) ),
inference(pattern_uni,[status(thm)],[54966:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(55076,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk11 != sk1 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,54967]) ).
thf(55077,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk11 != sk1 ) ),
inference(pattern_uni,[status(thm)],[55076:[bind(A,$thf( sk11 ))]]) ).
thf(55,plain,
( ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ~ ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 ) ),
inference(cnf,[status(esa)],[42]) ).
thf(47,plain,
element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ),
inference(cnf,[status(esa)],[42]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( ( proper_element @ B @ ( powerset @ A ) )
=> ( B != A ) )
& ( ( B != A )
=> ( proper_element @ B @ ( powerset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( B = A )
| ( proper_element @ B @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[145]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( element @ B @ ( powerset @ A ) )
| ( proper_element @ B @ ( powerset @ A ) ) ),
inference(lifteq,[status(thm)],[147]) ).
thf(13603,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( proper_element @ B @ ( powerset @ A ) )
| ( ( element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( element @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[47,150]) ).
thf(13604,plain,
( ( ( the_carrier @ sk1 )
= sk2 )
| ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[13603:[bind(A,$thf( the_carrier @ sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(46,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
| ~ ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(15682,plain,
( ( ( the_carrier @ sk1 )
= sk2 )
| ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
| ( ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13604,46]) ).
thf(15683,plain,
( ( ( the_carrier @ sk1 )
= sk2 )
| ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15682:[]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ),
inference(cnf,[status(esa)],[90]) ).
thf(16479,plain,
! [B: $i,A: $i] :
( ( ( the_carrier @ sk1 )
= sk2 )
| ( element @ A @ B )
| ( ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15683,91]) ).
thf(16480,plain,
( ( ( the_carrier @ sk1 )
= sk2 )
| ( element @ ( bottom_of_relstr @ sk1 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[16479:[bind(A,$thf( bottom_of_relstr @ sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(19004,plain,
! [A: $i] :
( ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) )
| ( ( rel_str @ sk1 )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51,165]) ).
thf(19005,plain,
element @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ),
inference(pattern_uni,[status(thm)],[19004:[bind(A,$thf( sk1 ))]]) ).
thf(19226,plain,
( ( element @ ( bottom_of_relstr @ sk1 ) @ sk2 )
| ( ( the_carrier @ sk1 )
!= ( the_carrier @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[16480,19005]) ).
thf(19227,plain,
element @ ( bottom_of_relstr @ sk1 ) @ sk2,
inference(pattern_uni,[status(thm)],[19226:[]]) ).
thf(19422,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( in @ A @ B )
| ( ( element @ ( bottom_of_relstr @ sk1 ) @ sk2 )
!= ( element @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19227,99]) ).
thf(19423,plain,
( ( empty @ sk2 )
| ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[19422:[bind(A,$thf( bottom_of_relstr @ sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(19587,plain,
( $false
| ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 ) ),
inference(rewrite,[status(thm)],[19423,52]) ).
thf(19588,plain,
in @ ( bottom_of_relstr @ sk1 ) @ sk2,
inference(simp,[status(thm)],[19587]) ).
thf(19589,plain,
( ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[55,19588]) ).
thf(19590,plain,
proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[19589]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( proper_element @ B @ ( powerset @ A ) )
| ( B != A ) ),
inference(cnf,[status(esa)],[145]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( B != A )
| ~ ( element @ B @ ( powerset @ A ) )
| ~ ( proper_element @ B @ ( powerset @ A ) ) ),
inference(lifteq,[status(thm)],[146]) ).
thf(149,plain,
! [A: $i] :
( ~ ( element @ A @ ( powerset @ A ) )
| ~ ( proper_element @ A @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(4,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(59,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(60,plain,
! [A: $i] : ( subset @ A @ A ),
inference(cnf,[status(esa)],[59]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(68,plain,
( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(miniscope,[status(thm)],[67]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(822,plain,
! [C: $i,B: $i,A: $i] :
( ( element @ B @ ( powerset @ C ) )
| ( ( subset @ A @ A )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[60,71]) ).
thf(823,plain,
! [A: $i] : ( element @ A @ ( powerset @ A ) ),
inference(pattern_uni,[status(thm)],[822:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(11244,plain,
! [A: $i] :
( ~ $true
| ~ ( proper_element @ A @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[149,823]) ).
thf(11245,plain,
! [A: $i] :
~ ( proper_element @ A @ ( powerset @ A ) ),
inference(simp,[status(thm)],[11244]) ).
thf(20080,plain,
! [A: $i] :
( ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( proper_element @ A @ ( powerset @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19590,11245]) ).
thf(20129,plain,
! [A: $i] :
( ( sk2 != A )
| ( ( powerset @ ( the_carrier @ sk1 ) )
!= ( powerset @ A ) ) ),
inference(simp,[status(thm)],[20080]) ).
thf(20138,plain,
( ( powerset @ ( the_carrier @ sk1 ) )
!= ( powerset @ sk2 ) ),
inference(simp,[status(thm)],[20129]) ).
thf(20799,plain,
( ( the_carrier @ sk1 )
!= sk2 ),
inference(simp,[status(thm)],[20138]) ).
thf(20904,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ empty_set )
!= sk2 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,20799]) ).
thf(20905,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ empty_set )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[20904:[bind(A,$thf( sk1 ))]]) ).
thf(21115,plain,
( ( ( the_carrier @ empty_set )
!= sk2 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,20905]) ).
thf(21164,plain,
( ( ( the_carrier @ empty_set )
!= sk2 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[21115]) ).
thf(248,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( rel_str @ empty_set )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,117]) ).
thf(249,plain,
( ~ ( empty @ sk11 )
| ( rel_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( sk11 ))]]) ).
thf(3526,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( in @ A @ B )
| ( ( element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( element @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[47,99]) ).
thf(3527,plain,
( ( empty @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[3526:[bind(A,$thf( sk2 )),bind(B,$thf( powerset @ ( the_carrier @ sk1 ) ))]]) ).
thf(35,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(151,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(152,plain,
~ ? [A: $i] : ( empty @ ( powerset @ A ) ),
inference(miniscope,[status(thm)],[151]) ).
thf(153,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(3862,plain,
( $false
| ( in @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[3527,153]) ).
thf(3863,plain,
in @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[3862]) ).
thf(21,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(103,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(105,plain,
~ ( empty @ sk8 ),
inference(cnf,[status(esa)],[103]) ).
thf(185,plain,
( ( empty @ sk8 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,105]) ).
thf(187,plain,
sk8 != empty_set,
inference(simp,[status(thm)],[185]) ).
thf(1627,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( A != sk8 ) ),
inference(paramod_ordered,[status(thm)],[115,187]) ).
thf(1628,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk8 ) @ sk8 )
| ( in @ ( sk10 @ A @ sk8 ) @ A )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1627:[bind(A,$thf( sk8 ))]]) ).
thf(2199,plain,
( ( in @ ( sk9 @ empty_set @ sk8 ) @ sk8 )
| ( in @ ( sk10 @ empty_set @ sk8 ) @ empty_set ) ),
inference(simp,[status(thm)],[1628]) ).
thf(8750,plain,
( ( in @ ( sk9 @ empty_set @ sk8 ) @ sk8 )
| $false ),
inference(rewrite,[status(thm)],[2199,1508]) ).
thf(8751,plain,
in @ ( sk9 @ empty_set @ sk8 ) @ sk8,
inference(simp,[status(thm)],[8750]) ).
thf(8754,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ empty_set @ sk8 )
| ( A
!= ( sk9 @ empty_set @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[120,8751]) ).
thf(8755,plain,
( ~ ( empty @ ( sk9 @ empty_set @ sk8 ) )
| ( in @ empty_set @ sk8 ) ),
inference(pattern_uni,[status(thm)],[8754:[bind(A,$thf( sk9 @ empty_set @ sk8 ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(87,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(89,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(14716,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( empty @ ( sk5 @ A ) )
| ( ( one_sorted_str @ sk1 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14669,89]) ).
thf(14717,plain,
( ( empty_carrier @ sk1 )
| ~ ( empty @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14716:[bind(A,$thf( sk1 ))]]) ).
thf(15912,plain,
( $false
| ~ ( empty @ ( sk5 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[14717,49]) ).
thf(15913,plain,
~ ( empty @ ( sk5 @ sk1 ) ),
inference(simp,[status(thm)],[15912]) ).
thf(15916,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( sk5 @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,15913]) ).
thf(15917,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ ( sk5 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[15916:[bind(A,$thf( sk1 ))]]) ).
thf(16325,plain,
( ~ ( empty @ sk1 )
| ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15917]) ).
thf(16326,plain,
( ~ ( empty @ sk1 )
| ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ sk1 ) ) ),
inference(simp,[status(thm)],[16325]) ).
thf(41292,plain,
( ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ sk1 ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,16326]) ).
thf(41348,plain,
( ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ sk1 ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[41292]) ).
thf(62055,plain,
( ( sk1 != empty_set )
| ( empty @ ( sk5 @ empty_set ) )
| ( empty @ sk1 ) ),
inference(bool_ext,[status(thm)],[41348]) ).
thf(16275,plain,
( ~ ( empty @ ( sk5 @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,15917]) ).
thf(16329,plain,
( ~ ( empty @ ( sk5 @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[16275]) ).
thf(79731,plain,
( ( sk1 != empty_set )
| ( empty @ sk1 )
| ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ ( sk5 @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[62055,16329]) ).
thf(79732,plain,
( ( sk1 != empty_set )
| ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[79731:[]]) ).
thf(81269,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( sk5 @ sk1 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,15913]) ).
thf(81349,plain,
( ( sk1 != empty_set )
| ( ( sk5 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[81269]) ).
thf(82375,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( sk5 @ sk1 )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81349]) ).
thf(82376,plain,
( ~ ( empty @ sk1 )
| ( ( sk5 @ sk1 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[82375:[bind(A,$thf( sk1 ))]]) ).
thf(88,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( element @ ( sk5 @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(14708,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ( element @ ( sk5 @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( one_sorted_str @ sk1 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14669,88]) ).
thf(14709,plain,
( ( empty_carrier @ sk1 )
| ( element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[14708:[bind(A,$thf( sk1 ))]]) ).
thf(22386,plain,
( $false
| ( element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[14709,49]) ).
thf(22387,plain,
element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[22386]) ).
thf(22507,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( in @ A @ B )
| ( ( element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( element @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22387,99]) ).
thf(22508,plain,
( ( empty @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[22507:[bind(A,$thf( sk5 @ sk1 )),bind(B,$thf( powerset @ ( the_carrier @ sk1 ) ))]]) ).
thf(30039,plain,
( $false
| ( in @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[22508,153]) ).
thf(30040,plain,
in @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[30039]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(143,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ),
inference(cnf,[status(esa)],[143]) ).
thf(30102,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30040,144]) ).
thf(30103,plain,
~ ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ ( sk5 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[30102:[bind(A,$thf( sk5 @ sk1 )),bind(B,$thf( powerset @ ( the_carrier @ sk1 ) ))]]) ).
thf(30352,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ ( sk5 @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,30103]) ).
thf(30353,plain,
( ~ ( empty @ sk1 )
| ~ ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ ( sk5 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[30352:[bind(A,$thf( sk1 ))]]) ).
thf(54,plain,
antisymmetric_relstr @ sk1,
inference(cnf,[status(esa)],[42]) ).
thf(260,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( antisymmetric_relstr @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,54]) ).
thf(261,plain,
( ~ ( empty @ sk1 )
| ( antisymmetric_relstr @ empty_set ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( sk1 ))]]) ).
thf(808,plain,
( ( antisymmetric_relstr @ empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,261]) ).
thf(809,plain,
( ( antisymmetric_relstr @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[808]) ).
thf(80995,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( empty @ sk1 )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,79732]) ).
thf(80996,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( A != empty_set )
| ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[80995:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(81467,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( empty @ sk1 ) ),
inference(simp,[status(thm)],[80996]) ).
thf(83467,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( empty @ sk1 ) ),
inference(rewrite,[status(thm)],[81467,1508]) ).
thf(83468,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( empty @ sk1 ) ),
inference(simp,[status(thm)],[83467]) ).
thf(83564,plain,
! [B: $i,A: $i] :
( ( empty @ sk1 )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[83468,91]) ).
thf(83565,plain,
( ( empty @ sk1 )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[83564:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(26983,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[24725,52]) ).
thf(27165,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( the_carrier @ sk11 )
!= sk2 ) ),
inference(simp,[status(thm)],[26983]) ).
thf(29038,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ sk11 )
!= sk2 )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,27165]) ).
thf(29039,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( ( the_carrier @ sk11 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[29038:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(10533,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk8 ) @ sk8 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8751,144]) ).
thf(10534,plain,
~ ( in @ sk8 @ ( sk9 @ empty_set @ sk8 ) ),
inference(pattern_uni,[status(thm)],[10533:[bind(A,$thf( sk9 @ empty_set @ sk8 )),bind(B,$thf( sk8 ))]]) ).
thf(19610,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
!= ( in @ sk8 @ ( sk9 @ empty_set @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[19588,10534]) ).
thf(19704,plain,
( ( ( bottom_of_relstr @ sk1 )
!= sk8 )
| ( ( sk9 @ empty_set @ sk8 )
!= sk2 ) ),
inference(simp,[status(thm)],[19610]) ).
thf(41,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( upper_relstr_subset @ B @ A )
<=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ B )
& ( related @ A @ C @ D ) )
=> ( in @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_waybel_0) ).
thf(169,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( upper_relstr_subset @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ B )
& ( related @ A @ C @ D ) )
=> ( in @ D @ B ) ) ) ) )
& ( ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ B )
& ( related @ A @ C @ D ) )
=> ( in @ D @ B ) ) ) )
=> ( upper_relstr_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ~ ( rel_str @ A )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( related @ A @ ( sk18 @ B @ A ) @ ( sk19 @ B @ A ) )
| ( upper_relstr_subset @ B @ A ) ),
inference(cnf,[status(esa)],[169]) ).
thf(206,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ ( bottom_of_relstr @ empty_set ) @ sk2 )
| ~ ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,46]) ).
thf(207,plain,
( ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ empty_set ) @ sk2 )
| ~ ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( sk1 ))]]) ).
thf(24167,plain,
( ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ empty_set ) @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[207,19590]) ).
thf(24168,plain,
( ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ empty_set ) @ sk2 ) ),
inference(simp,[status(thm)],[24167]) ).
thf(24223,plain,
( ( in @ ( bottom_of_relstr @ empty_set ) @ sk2 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,24168]) ).
thf(24320,plain,
( ( in @ ( bottom_of_relstr @ empty_set ) @ sk2 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[24223]) ).
thf(10521,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3863,144]) ).
thf(10522,plain,
~ ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ),
inference(pattern_uni,[status(thm)],[10521:[bind(A,$thf( sk2 )),bind(B,$thf( powerset @ ( the_carrier @ sk1 ) ))]]) ).
thf(26698,plain,
( ( sk1 != empty_set )
| ( ( in @ ( bottom_of_relstr @ empty_set ) @ sk2 )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[24320,10522]) ).
thf(26713,plain,
( ( sk1 != empty_set )
| ( ( bottom_of_relstr @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[26698]) ).
thf(26746,plain,
( ( sk1 != empty_set )
| ( ( bottom_of_relstr @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(simp,[status(thm)],[26713]) ).
thf(240,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( one_sorted_str @ empty_set )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,142]) ).
thf(241,plain,
( ~ ( empty @ sk16 )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( sk16 ))]]) ).
thf(875,plain,
( ( one_sorted_str @ empty_set )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,241]) ).
thf(876,plain,
( ( one_sorted_str @ empty_set )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[875]) ).
thf(2033,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( one_sorted_str @ empty_set )
| ( B != empty_set )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[115,876]) ).
thf(2034,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk16 ) @ sk16 )
| ( in @ ( sk10 @ A @ sk16 ) @ A )
| ( one_sorted_str @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2033:[bind(A,$thf( sk16 ))]]) ).
thf(2346,plain,
( ( in @ ( sk9 @ empty_set @ sk16 ) @ sk16 )
| ( in @ ( sk10 @ empty_set @ sk16 ) @ empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[2034]) ).
thf(48874,plain,
( ( in @ ( sk9 @ empty_set @ sk16 ) @ sk16 )
| $false
| ( one_sorted_str @ empty_set ) ),
inference(rewrite,[status(thm)],[2346,1508]) ).
thf(48875,plain,
( ( in @ ( sk9 @ empty_set @ sk16 ) @ sk16 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[48874]) ).
thf(22396,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,22387]) ).
thf(22397,plain,
( ~ ( empty @ sk1 )
| ( element @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[22396:[bind(A,$thf( sk1 ))]]) ).
thf(2417,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ( element @ ( sk5 @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( one_sorted_str @ sk16 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[142,88]) ).
thf(2418,plain,
( ( empty_carrier @ sk16 )
| ( element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[2417:[bind(A,$thf( sk16 ))]]) ).
thf(2618,plain,
( $false
| ( element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(rewrite,[status(thm)],[2418,141]) ).
thf(2619,plain,
element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ),
inference(simp,[status(thm)],[2618]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[68]) ).
thf(2650,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
!= ( element @ A @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[2619,70]) ).
thf(2651,plain,
subset @ ( sk5 @ sk16 ) @ ( the_carrier @ sk16 ),
inference(pattern_uni,[status(thm)],[2650:[bind(A,$thf( sk5 @ sk16 )),bind(B,$thf( the_carrier @ sk16 ))]]) ).
thf(2724,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( subset @ ( sk5 @ sk16 ) @ ( the_carrier @ empty_set ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,2651]) ).
thf(2725,plain,
( ~ ( empty @ sk16 )
| ( subset @ ( sk5 @ sk16 ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[2724:[bind(A,$thf( sk16 ))]]) ).
thf(9543,plain,
( ( subset @ ( sk5 @ sk16 ) @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,2725]) ).
thf(9604,plain,
( ( subset @ ( sk5 @ sk16 ) @ ( the_carrier @ empty_set ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[9543]) ).
thf(27,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(125,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(126,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ),
inference(cnf,[status(esa)],[125]) ).
thf(81305,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( finite @ A )
| ( ( empty @ sk1 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79732,126]) ).
thf(81306,plain,
( ( sk1 != empty_set )
| ( finite @ sk1 ) ),
inference(pattern_uni,[status(thm)],[81305:[bind(A,$thf( sk1 ))]]) ).
thf(81489,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( finite @ sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,81306]) ).
thf(81490,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( A != empty_set )
| ( finite @ sk1 ) ),
inference(pattern_uni,[status(thm)],[81489:[bind(A,$thf( sk1 ))]]) ).
thf(81552,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( finite @ sk1 ) ),
inference(simp,[status(thm)],[81490]) ).
thf(84732,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( finite @ sk1 ) ),
inference(rewrite,[status(thm)],[81552,1508]) ).
thf(84733,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( finite @ sk1 ) ),
inference(simp,[status(thm)],[84732]) ).
thf(84803,plain,
! [B: $i,A: $i] :
( ( finite @ sk1 )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[84733,144]) ).
thf(84804,plain,
( ( finite @ sk1 )
| ~ ( in @ sk1 @ ( sk9 @ empty_set @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[84803:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(16679,plain,
( ( empty @ ( the_carrier @ sk1 ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,16654]) ).
thf(16712,plain,
( ( the_carrier @ sk1 )
!= empty_set ),
inference(simp,[status(thm)],[16679]) ).
thf(16729,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( A
!= ( the_carrier @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[115,16712]) ).
thf(16730,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
| ( in @ ( sk10 @ A @ ( the_carrier @ sk1 ) ) @ A )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[16729:[bind(A,$thf( the_carrier @ sk1 )),bind(B,$thf( B ))]]) ).
thf(16786,plain,
( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
| ( in @ ( sk10 @ empty_set @ ( the_carrier @ sk1 ) ) @ empty_set ) ),
inference(simp,[status(thm)],[16730]) ).
thf(95453,plain,
( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
| $false ),
inference(rewrite,[status(thm)],[16786,1508]) ).
thf(95454,plain,
in @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ),
inference(simp,[status(thm)],[95453]) ).
thf(95583,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[95454,91]) ).
thf(95584,plain,
element @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ),
inference(pattern_uni,[status(thm)],[95583:[bind(A,$thf( sk9 @ empty_set @ ( the_carrier @ sk1 ) )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(18,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(95,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(96,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[95]) ).
thf(97,plain,
~ ( empty @ sk6 ),
inference(cnf,[status(esa)],[96]) ).
thf(181,plain,
( ( empty @ sk6 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,97]) ).
thf(183,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[181]) ).
thf(2112,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[115,183]) ).
thf(2113,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk6 ) @ sk6 )
| ( in @ ( sk10 @ A @ sk6 ) @ A )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2112:[bind(A,$thf( sk6 ))]]) ).
thf(2186,plain,
( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
| ( in @ ( sk10 @ empty_set @ sk6 ) @ empty_set ) ),
inference(simp,[status(thm)],[2113]) ).
thf(3378,plain,
( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[2186,1508]) ).
thf(3379,plain,
in @ ( sk9 @ empty_set @ sk6 ) @ sk6,
inference(simp,[status(thm)],[3378]) ).
thf(3424,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3379,91]) ).
thf(3425,plain,
element @ ( sk9 @ empty_set @ sk6 ) @ sk6,
inference(pattern_uni,[status(thm)],[3424:[bind(A,$thf( sk9 @ empty_set @ sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(3536,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ sk6 )
| ( A
!= ( sk9 @ empty_set @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[120,3425]) ).
thf(3537,plain,
( ~ ( empty @ ( sk9 @ empty_set @ sk6 ) )
| ( element @ empty_set @ sk6 ) ),
inference(pattern_uni,[status(thm)],[3536:[bind(A,$thf( sk9 @ empty_set @ sk6 ))]]) ).
thf(31203,plain,
( ( element @ empty_set @ sk6 )
| ( ( empty @ ( sk9 @ empty_set @ sk6 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,3537]) ).
thf(31295,plain,
( ( element @ empty_set @ sk6 )
| ( ( sk9 @ empty_set @ sk6 )
!= empty_set ) ),
inference(simp,[status(thm)],[31203]) ).
thf(13215,plain,
! [B: $i,A: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( proper_element @ B @ ( powerset @ A ) )
| ( B != empty_set )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[150,182]) ).
thf(13216,plain,
! [A: $i] :
( ~ ( element @ A @ ( powerset @ sk2 ) )
| ( proper_element @ A @ ( powerset @ sk2 ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[13215:[bind(A,$thf( sk2 ))]]) ).
thf(13940,plain,
( ~ ( element @ empty_set @ ( powerset @ sk2 ) )
| ( proper_element @ empty_set @ ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[13216]) ).
thf(30,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(135,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(137,plain,
! [A: $i] : ( element @ ( sk14 @ A ) @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[135]) ).
thf(136,plain,
! [A: $i] : ( empty @ ( sk14 @ A ) ),
inference(cnf,[status(esa)],[135]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( B = empty_set )
| ( ( empty @ ( sk14 @ A ) )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[136,120]) ).
thf(239,plain,
! [A: $i] :
( ( sk14 @ A )
= empty_set ),
inference(pattern_uni,[status(thm)],[238:[bind(A,$thf( C )),bind(B,$thf( sk14 @ C ))]]) ).
thf(317,plain,
! [A: $i] :
( ( sk14 @ A )
= empty_set ),
inference(simp,[status(thm)],[239]) ).
thf(636,plain,
! [A: $i] : ( element @ empty_set @ ( powerset @ A ) ),
inference(rewrite,[status(thm)],[137,317]) ).
thf(115248,plain,
( ~ $true
| ( proper_element @ empty_set @ ( powerset @ sk2 ) ) ),
inference(rewrite,[status(thm)],[13940,636]) ).
thf(115249,plain,
proper_element @ empty_set @ ( powerset @ sk2 ),
inference(simp,[status(thm)],[115248]) ).
thf(115294,plain,
! [A: $i] :
( ( proper_element @ empty_set @ ( powerset @ sk2 ) )
!= ( proper_element @ A @ ( powerset @ A ) ) ),
inference(paramod_ordered,[status(thm)],[115249,11245]) ).
thf(115331,plain,
! [A: $i] :
( ( empty_set != A )
| ( ( powerset @ sk2 )
!= ( powerset @ A ) ) ),
inference(simp,[status(thm)],[115294]) ).
thf(115332,plain,
( ( powerset @ sk2 )
!= ( powerset @ empty_set ) ),
inference(simp,[status(thm)],[115331]) ).
thf(53,plain,
filtered_subset @ sk2 @ sk1,
inference(cnf,[status(esa)],[42]) ).
thf(252,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( filtered_subset @ sk2 @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,53]) ).
thf(253,plain,
( ~ ( empty @ sk1 )
| ( filtered_subset @ sk2 @ empty_set ) ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( sk1 ))]]) ).
thf(1405,plain,
( ( filtered_subset @ sk2 @ empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,253]) ).
thf(1406,plain,
( ( filtered_subset @ sk2 @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[1405]) ).
thf(698,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( ( element @ empty_set @ ( powerset @ A ) )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[636,70]) ).
thf(699,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(pattern_uni,[status(thm)],[698:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).
thf(729,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( subset @ A @ B )
| ( empty_set != empty_set ) ),
inference(paramod_ordered,[status(thm)],[120,699]) ).
thf(730,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( subset @ A @ B ) ),
inference(pattern_uni,[status(thm)],[729:[]]) ).
thf(14660,plain,
! [A: $i] :
( ( one_sorted_str @ A )
| ( ( rel_str @ sk11 )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[117,155]) ).
thf(14661,plain,
one_sorted_str @ sk11,
inference(pattern_uni,[status(thm)],[14660:[bind(A,$thf( sk11 ))]]) ).
thf(14680,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( empty @ ( the_carrier @ A ) )
| ( ( one_sorted_str @ sk11 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14661,73]) ).
thf(14681,plain,
( ( empty_carrier @ sk11 )
| ~ ( empty @ ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[14680:[bind(A,$thf( sk11 ))]]) ).
thf(16194,plain,
( ( empty_carrier @ sk11 )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,14681]) ).
thf(16228,plain,
( ( empty_carrier @ sk11 )
| ( ( the_carrier @ sk11 )
!= empty_set ) ),
inference(simp,[status(thm)],[16194]) ).
thf(40,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bottom_of_relstr @ A )
= ( join_on_relstr @ A @ empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).
thf(166,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bottom_of_relstr @ A )
= ( join_on_relstr @ A @ empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(167,plain,
! [A: $i] :
( ~ ( rel_str @ A )
| ( ( bottom_of_relstr @ A )
= ( join_on_relstr @ A @ empty_set ) ) ),
inference(cnf,[status(esa)],[166]) ).
thf(168,plain,
! [A: $i] :
( ( ( join_on_relstr @ A @ empty_set )
= ( bottom_of_relstr @ A ) )
| ~ ( rel_str @ A ) ),
inference(lifteq,[status(thm)],[167]) ).
thf(19942,plain,
! [A: $i] :
( ( ( join_on_relstr @ A @ empty_set )
= ( bottom_of_relstr @ A ) )
| ( ( rel_str @ sk11 )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[117,168]) ).
thf(19943,plain,
( ( join_on_relstr @ sk11 @ empty_set )
= ( bottom_of_relstr @ sk11 ) ),
inference(pattern_uni,[status(thm)],[19942:[bind(A,$thf( sk11 ))]]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(162,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] : ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(miniscope,[status(thm)],[161]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ~ ( rel_str @ A )
| ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(cnf,[status(esa)],[162]) ).
thf(18061,plain,
! [B: $i,A: $i] :
( ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) )
| ( ( rel_str @ sk1 )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51,163]) ).
thf(18062,plain,
! [A: $i] : ( element @ ( join_on_relstr @ sk1 @ A ) @ ( the_carrier @ sk1 ) ),
inference(pattern_uni,[status(thm)],[18061:[bind(A,$thf( sk1 ))]]) ).
thf(18080,plain,
! [A: $i] : ( element @ ( join_on_relstr @ sk1 @ A ) @ ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[18062]) ).
thf(18208,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ ( join_on_relstr @ sk1 @ A ) @ ( the_carrier @ sk1 ) )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18080,99]) ).
thf(18209,plain,
! [A: $i] :
( ( empty @ ( the_carrier @ sk1 ) )
| ( in @ ( join_on_relstr @ sk1 @ A ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[18208:[bind(A,$thf( E )),bind(B,$thf( join_on_relstr @ sk1 @ E )),bind(C,$thf( the_carrier @ sk1 ))]]) ).
thf(18250,plain,
! [A: $i] :
( ( empty @ ( the_carrier @ sk1 ) )
| ( in @ ( join_on_relstr @ sk1 @ A ) @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[18209]) ).
thf(99534,plain,
! [A: $i] :
( $false
| ( in @ ( join_on_relstr @ sk1 @ A ) @ ( the_carrier @ sk1 ) ) ),
inference(rewrite,[status(thm)],[18250,16654]) ).
thf(99535,plain,
! [A: $i] : ( in @ ( join_on_relstr @ sk1 @ A ) @ ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[99534]) ).
thf(10565,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( in @ B @ A )
!= ( in @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[144]) ).
thf(10566,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(pattern_uni,[status(thm)],[10565:[bind(A,$thf( B ))]]) ).
thf(10568,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(simp,[status(thm)],[10566]) ).
thf(99691,plain,
! [B: $i,A: $i] :
( ( in @ ( join_on_relstr @ sk1 @ A ) @ ( the_carrier @ sk1 ) )
!= ( in @ B @ B ) ),
inference(paramod_ordered,[status(thm)],[99535,10568]) ).
thf(99787,plain,
! [B: $i,A: $i] :
( ( ( join_on_relstr @ sk1 @ A )
!= B )
| ( ( the_carrier @ sk1 )
!= B ) ),
inference(simp,[status(thm)],[99691]) ).
thf(99859,plain,
! [A: $i] :
( ( join_on_relstr @ sk1 @ A )
!= ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[99787]) ).
thf(99891,plain,
! [A: $i] :
( ( ( bottom_of_relstr @ sk11 )
!= ( the_carrier @ sk1 ) )
| ( ( join_on_relstr @ sk11 @ empty_set )
!= ( join_on_relstr @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19943,99859]) ).
thf(99942,plain,
! [A: $i] :
( ( ( bottom_of_relstr @ sk11 )
!= ( the_carrier @ sk1 ) )
| ( sk11 != sk1 )
| ( empty_set != A ) ),
inference(simp,[status(thm)],[99891]) ).
thf(99967,plain,
( ( ( bottom_of_relstr @ sk11 )
!= ( the_carrier @ sk1 ) )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[99942]) ).
thf(1629,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( B != sk8 ) ),
inference(paramod_ordered,[status(thm)],[115,187]) ).
thf(1630,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk8 @ A ) @ A )
| ( in @ ( sk10 @ sk8 @ A ) @ sk8 )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1629:[bind(A,$thf( A )),bind(B,$thf( sk8 ))]]) ).
thf(2200,plain,
( ( in @ ( sk9 @ sk8 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk8 @ empty_set ) @ sk8 ) ),
inference(simp,[status(thm)],[1630]) ).
thf(9636,plain,
( $false
| ( in @ ( sk10 @ sk8 @ empty_set ) @ sk8 ) ),
inference(rewrite,[status(thm)],[2200,1508]) ).
thf(9637,plain,
in @ ( sk10 @ sk8 @ empty_set ) @ sk8,
inference(simp,[status(thm)],[9636]) ).
thf(10651,plain,
( ( in @ ( sk10 @ sk8 @ empty_set ) @ sk8 )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[9637,10522]) ).
thf(10679,plain,
( ( ( sk10 @ sk8 @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[10651]) ).
thf(938,plain,
( ( rel_str @ empty_set )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,249]) ).
thf(939,plain,
( ( rel_str @ empty_set )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[938]) ).
thf(14666,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( one_sorted_str @ A )
| ( ( rel_str @ empty_set )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[939,155]) ).
thf(14667,plain,
( ( sk11 != empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[14666:[bind(A,$thf( empty_set ))]]) ).
thf(15345,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( one_sorted_str @ empty_set )
| ( B != sk11 ) ),
inference(paramod_ordered,[status(thm)],[115,14667]) ).
thf(15346,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk11 @ A ) @ A )
| ( in @ ( sk10 @ sk11 @ A ) @ sk11 )
| ( A != empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[15345:[bind(A,$thf( A )),bind(B,$thf( sk11 ))]]) ).
thf(15407,plain,
( ( in @ ( sk9 @ sk11 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[15346]) ).
thf(60289,plain,
( $false
| ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
| ( one_sorted_str @ empty_set ) ),
inference(rewrite,[status(thm)],[15407,1508]) ).
thf(60290,plain,
( ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[60289]) ).
thf(60412,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60290,10568]) ).
thf(60445,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( sk10 @ sk11 @ empty_set )
!= A )
| ( sk11 != A ) ),
inference(simp,[status(thm)],[60412]) ).
thf(60481,plain,
( ( one_sorted_str @ empty_set )
| ( ( sk10 @ sk11 @ empty_set )
!= sk11 ) ),
inference(simp,[status(thm)],[60445]) ).
thf(2699,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( empty @ ( sk5 @ A ) )
| ( ( one_sorted_str @ sk16 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[142,89]) ).
thf(2700,plain,
( ( empty_carrier @ sk16 )
| ~ ( empty @ ( sk5 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[2699:[bind(A,$thf( sk16 ))]]) ).
thf(2812,plain,
( $false
| ~ ( empty @ ( sk5 @ sk16 ) ) ),
inference(rewrite,[status(thm)],[2700,141]) ).
thf(2813,plain,
~ ( empty @ ( sk5 @ sk16 ) ),
inference(simp,[status(thm)],[2812]) ).
thf(2816,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( sk5 @ empty_set ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,2813]) ).
thf(2817,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ ( sk5 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[2816:[bind(A,$thf( sk16 ))]]) ).
thf(3006,plain,
( ~ ( empty @ sk16 )
| ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ sk16 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2817]) ).
thf(3010,plain,
( ~ ( empty @ sk16 )
| ( ( sk5 @ empty_set )
!= sk16 ) ),
inference(simp,[status(thm)],[3006]) ).
thf(3284,plain,
( ( ( sk5 @ empty_set )
!= sk16 )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,3010]) ).
thf(3285,plain,
( ( ( sk5 @ empty_set )
!= sk16 )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[3284]) ).
thf(11,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(78,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ~ ( finite @ A )
| ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ),
inference(cnf,[status(esa)],[78]) ).
thf(2675,plain,
! [B: $i,A: $i] :
( ~ ( finite @ A )
| ( finite @ B )
| ( ( element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
!= ( element @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[2619,79]) ).
thf(2676,plain,
( ~ ( finite @ ( the_carrier @ sk16 ) )
| ( finite @ ( sk5 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[2675:[bind(A,$thf( the_carrier @ sk16 )),bind(B,$thf( sk5 @ sk16 ))]]) ).
thf(10561,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3379,144]) ).
thf(10562,plain,
~ ( in @ sk6 @ ( sk9 @ empty_set @ sk6 ) ),
inference(pattern_uni,[status(thm)],[10561:[bind(A,$thf( sk9 @ empty_set @ sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(20030,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,19590]) ).
thf(20031,plain,
( ~ ( empty @ sk1 )
| ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[20030:[bind(A,$thf( sk1 ))]]) ).
thf(47784,plain,
( ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,20031]) ).
thf(47868,plain,
( ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[47784]) ).
thf(13585,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( proper_element @ B @ ( powerset @ A ) )
| ( ( element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
!= ( element @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[2619,150]) ).
thf(13586,plain,
( ( ( sk5 @ sk16 )
= ( the_carrier @ sk16 ) )
| ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[13585:[bind(A,$thf( the_carrier @ sk16 )),bind(B,$thf( sk5 @ sk16 ))]]) ).
thf(19298,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( in @ A @ B )
| ( ( element @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ) )
!= ( element @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19005,99]) ).
thf(19299,plain,
( ( empty @ ( the_carrier @ sk1 ) )
| ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[19298:[bind(A,$thf( bottom_of_relstr @ sk1 )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(25448,plain,
( $false
| ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ) ) ),
inference(rewrite,[status(thm)],[19299,16654]) ).
thf(25449,plain,
in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ),
inference(simp,[status(thm)],[25448]) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( B != sk6 ) ),
inference(paramod_ordered,[status(thm)],[115,183]) ).
thf(2115,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk6 @ A ) @ A )
| ( in @ ( sk10 @ sk6 @ A ) @ sk6 )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2114:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).
thf(2187,plain,
( ( in @ ( sk9 @ sk6 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk6 @ empty_set ) @ sk6 ) ),
inference(simp,[status(thm)],[2115]) ).
thf(5303,plain,
( $false
| ( in @ ( sk10 @ sk6 @ empty_set ) @ sk6 ) ),
inference(rewrite,[status(thm)],[2187,1508]) ).
thf(5304,plain,
in @ ( sk10 @ sk6 @ empty_set ) @ sk6,
inference(simp,[status(thm)],[5303]) ).
thf(10557,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk6 @ empty_set ) @ sk6 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5304,144]) ).
thf(10558,plain,
~ ( in @ sk6 @ ( sk10 @ sk6 @ empty_set ) ),
inference(pattern_uni,[status(thm)],[10557:[bind(A,$thf( sk10 @ sk6 @ empty_set )),bind(B,$thf( sk6 ))]]) ).
thf(25557,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ) )
!= ( in @ sk6 @ ( sk10 @ sk6 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[25449,10558]) ).
thf(25585,plain,
( ( ( bottom_of_relstr @ sk1 )
!= sk6 )
| ( ( sk10 @ sk6 @ empty_set )
!= ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[25557]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(61,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(62,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(26950,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( empty @ ( the_carrier @ sk16 ) )
!= ( empty @ ( the_carrier @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[24725,1411]) ).
thf(27146,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( the_carrier @ sk16 )
!= ( the_carrier @ sk11 ) ) ),
inference(simp,[status(thm)],[26950]) ).
thf(54162,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk16 != sk11 ) ),
inference(simp,[status(thm)],[27146]) ).
thf(54303,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk16 != sk11 )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,54162]) ).
thf(54304,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk16 != sk11 ) ),
inference(pattern_uni,[status(thm)],[54303:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(54433,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( B != sk11 )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[64,54304]) ).
thf(54434,plain,
! [A: $i] :
( ~ ( empty @ sk16 )
| ~ ( empty @ A )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( A != sk11 ) ),
inference(pattern_uni,[status(thm)],[54433:[bind(A,$thf( sk16 ))]]) ).
thf(54508,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ sk11 )
| ~ ( empty @ ( the_carrier @ sk11 ) ) ),
inference(simp,[status(thm)],[54434]) ).
thf(77087,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ sk11 )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[54508]) ).
thf(77097,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ sk11 )
| ( ( the_carrier @ sk11 )
!= sk11 ) ),
inference(simp,[status(thm)],[77087]) ).
thf(1414,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( the_carrier @ empty_set ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,1411]) ).
thf(1415,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[1414:[bind(A,$thf( sk16 ))]]) ).
thf(1483,plain,
( ~ ( empty @ sk16 )
| ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk16 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1415]) ).
thf(1486,plain,
( ~ ( empty @ sk16 )
| ( ( the_carrier @ empty_set )
!= sk16 ) ),
inference(simp,[status(thm)],[1483]) ).
thf(292,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( rel_str @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,51]) ).
thf(293,plain,
( ~ ( empty @ sk1 )
| ( rel_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( sk1 ))]]) ).
thf(909,plain,
( ( rel_str @ empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,293]) ).
thf(910,plain,
( ( rel_str @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[909]) ).
thf(14662,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( one_sorted_str @ A )
| ( ( rel_str @ empty_set )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[910,155]) ).
thf(14663,plain,
( ( sk1 != empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[14662:[bind(A,$thf( empty_set ))]]) ).
thf(15003,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( one_sorted_str @ empty_set )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,14663]) ).
thf(15004,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( A != empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[15003:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(15058,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[15004]) ).
thf(56491,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( one_sorted_str @ empty_set ) ),
inference(rewrite,[status(thm)],[15058,1508]) ).
thf(56492,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[56491]) ).
thf(56572,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56492,91]) ).
thf(56573,plain,
( ( one_sorted_str @ empty_set )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[56572:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(48,plain,
upper_relstr_subset @ sk2 @ sk1,
inference(cnf,[status(esa)],[42]) ).
thf(228,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( upper_relstr_subset @ sk2 @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,48]) ).
thf(229,plain,
( ~ ( empty @ sk1 )
| ( upper_relstr_subset @ sk2 @ empty_set ) ),
inference(pattern_uni,[status(thm)],[228:[bind(A,$thf( sk1 ))]]) ).
thf(1350,plain,
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,229]) ).
thf(1351,plain,
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[1350]) ).
thf(1781,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( upper_relstr_subset @ sk2 @ empty_set )
| ( B != empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,1351]) ).
thf(1782,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( upper_relstr_subset @ sk2 @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1781:[bind(A,$thf( sk1 ))]]) ).
thf(2258,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( upper_relstr_subset @ sk2 @ empty_set ) ),
inference(simp,[status(thm)],[1782]) ).
thf(74762,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( upper_relstr_subset @ sk2 @ empty_set ) ),
inference(rewrite,[status(thm)],[2258,1508]) ).
thf(74763,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( upper_relstr_subset @ sk2 @ empty_set ) ),
inference(simp,[status(thm)],[74762]) ).
thf(74856,plain,
! [B: $i,A: $i] :
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[74763,91]) ).
thf(74857,plain,
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[74856:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2834,plain,
( ( empty @ ( sk5 @ sk16 ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,2813]) ).
thf(2835,plain,
( ( sk5 @ sk16 )
!= empty_set ),
inference(simp,[status(thm)],[2834]) ).
thf(2848,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( B
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[115,2835]) ).
thf(2849,plain,
! [A: $i] :
( ( in @ ( sk9 @ ( sk5 @ sk16 ) @ A ) @ A )
| ( in @ ( sk10 @ ( sk5 @ sk16 ) @ A ) @ ( sk5 @ sk16 ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2848:[bind(A,$thf( A )),bind(B,$thf( sk5 @ sk16 ))]]) ).
thf(2860,plain,
( ( in @ ( sk9 @ ( sk5 @ sk16 ) @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) ) ),
inference(simp,[status(thm)],[2849]) ).
thf(88990,plain,
( $false
| ( in @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) ) ),
inference(rewrite,[status(thm)],[2860,1508]) ).
thf(88991,plain,
in @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ),
inference(simp,[status(thm)],[88990]) ).
thf(89090,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[88991,144]) ).
thf(89091,plain,
~ ( in @ ( sk5 @ sk16 ) @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) ),
inference(pattern_uni,[status(thm)],[89090:[bind(A,$thf( sk10 @ ( sk5 @ sk16 ) @ empty_set )),bind(B,$thf( sk5 @ sk16 ))]]) ).
thf(10549,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk8 @ empty_set ) @ sk8 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9637,144]) ).
thf(10550,plain,
~ ( in @ sk8 @ ( sk10 @ sk8 @ empty_set ) ),
inference(pattern_uni,[status(thm)],[10549:[bind(A,$thf( sk10 @ sk8 @ empty_set )),bind(B,$thf( sk8 ))]]) ).
thf(11758,plain,
( ( in @ ( sk10 @ sk2 @ empty_set ) @ sk2 )
!= ( in @ sk8 @ ( sk10 @ sk8 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[11728,10550]) ).
thf(11848,plain,
( ( ( sk10 @ sk2 @ empty_set )
!= sk8 )
| ( ( sk10 @ sk8 @ empty_set )
!= sk2 ) ),
inference(simp,[status(thm)],[11758]) ).
thf(104,plain,
finite @ sk8,
inference(cnf,[status(esa)],[103]) ).
thf(3645,plain,
( ( finite @ ( sk5 @ sk16 ) )
| ( ( finite @ ( the_carrier @ sk16 ) )
!= ( finite @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[104,2676]) ).
thf(3649,plain,
( ( finite @ ( sk5 @ sk16 ) )
| ( ( the_carrier @ sk16 )
!= sk8 ) ),
inference(simp,[status(thm)],[3645]) ).
thf(27010,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[24725,105]) ).
thf(27217,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( the_carrier @ sk11 )
!= sk8 ) ),
inference(simp,[status(thm)],[27010]) ).
thf(29896,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ sk11 )
!= sk8 )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,27217]) ).
thf(29897,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( ( the_carrier @ sk11 )
!= sk8 ) ),
inference(pattern_uni,[status(thm)],[29896:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ~ ( finite @ A )
| ( finite @ B )
| ( ( element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( element @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[47,79]) ).
thf(1233,plain,
( ~ ( finite @ ( the_carrier @ sk1 ) )
| ( finite @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1232:[bind(A,$thf( the_carrier @ sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(3380,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ empty_set @ sk6 )
| ( A
!= ( sk9 @ empty_set @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[120,3379]) ).
thf(3381,plain,
( ~ ( empty @ ( sk9 @ empty_set @ sk6 ) )
| ( in @ empty_set @ sk6 ) ),
inference(pattern_uni,[status(thm)],[3380:[bind(A,$thf( sk9 @ empty_set @ sk6 ))]]) ).
thf(10136,plain,
( ( in @ empty_set @ sk6 )
| ( ( empty @ ( sk9 @ empty_set @ sk6 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,3381]) ).
thf(10209,plain,
( ( in @ empty_set @ sk6 )
| ( ( sk9 @ empty_set @ sk6 )
!= empty_set ) ),
inference(simp,[status(thm)],[10136]) ).
thf(81493,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( finite @ sk1 )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,81306]) ).
thf(81494,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( A != empty_set )
| ( finite @ sk1 ) ),
inference(pattern_uni,[status(thm)],[81493:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(81554,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( finite @ sk1 ) ),
inference(simp,[status(thm)],[81494]) ).
thf(86415,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( finite @ sk1 ) ),
inference(rewrite,[status(thm)],[81554,1508]) ).
thf(86416,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( finite @ sk1 ) ),
inference(simp,[status(thm)],[86415]) ).
thf(19053,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( bottom_of_relstr @ sk11 ) @ empty_set )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,18952]) ).
thf(19054,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( element @ ( bottom_of_relstr @ sk11 ) @ empty_set ) ),
inference(pattern_uni,[status(thm)],[19053:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(43537,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( element @ ( bottom_of_relstr @ sk11 ) @ empty_set )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ ( the_carrier @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[24725,19054]) ).
thf(43538,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( element @ ( bottom_of_relstr @ sk11 ) @ empty_set ) ),
inference(pattern_uni,[status(thm)],[43537:[]]) ).
thf(19974,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( ( join_on_relstr @ A @ empty_set )
= ( bottom_of_relstr @ A ) )
| ( ( rel_str @ empty_set )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[939,168]) ).
thf(19975,plain,
( ( sk11 != empty_set )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[19974:[bind(A,$thf( empty_set ))]]) ).
thf(20906,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != sk2 )
| ( A
!= ( the_carrier @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[115,20799]) ).
thf(20907,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
| ( in @ ( sk10 @ A @ ( the_carrier @ sk1 ) ) @ A )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[20906:[bind(A,$thf( the_carrier @ sk1 )),bind(B,$thf( B ))]]) ).
thf(20963,plain,
( ( in @ ( sk9 @ sk2 @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
| ( in @ ( sk10 @ sk2 @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(simp,[status(thm)],[20907]) ).
thf(103243,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ sk2 @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk2 @ ( the_carrier @ sk1 ) ) @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20963,91]) ).
thf(103244,plain,
( ( in @ ( sk9 @ sk2 @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
| ( element @ ( sk10 @ sk2 @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[103243:[bind(A,$thf( sk10 @ sk2 @ ( the_carrier @ sk1 ) )),bind(B,$thf( sk2 ))]]) ).
thf(1681,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( filtered_subset @ sk2 @ empty_set )
| ( B != empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,1406]) ).
thf(1682,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( filtered_subset @ sk2 @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1681:[bind(A,$thf( sk1 ))]]) ).
thf(2228,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( filtered_subset @ sk2 @ empty_set ) ),
inference(simp,[status(thm)],[1682]) ).
thf(69538,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( filtered_subset @ sk2 @ empty_set ) ),
inference(rewrite,[status(thm)],[2228,1508]) ).
thf(69539,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( filtered_subset @ sk2 @ empty_set ) ),
inference(simp,[status(thm)],[69538]) ).
thf(69629,plain,
! [B: $i,A: $i] :
( ( filtered_subset @ sk2 @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[69539,91]) ).
thf(69630,plain,
( ( filtered_subset @ sk2 @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[69629:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(9701,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk10 @ sk8 @ empty_set ) @ sk8 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9637,91]) ).
thf(9702,plain,
element @ ( sk10 @ sk8 @ empty_set ) @ sk8,
inference(pattern_uni,[status(thm)],[9701:[bind(A,$thf( sk10 @ sk8 @ empty_set )),bind(B,$thf( sk8 ))]]) ).
thf(9815,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ sk8 )
| ( A
!= ( sk10 @ sk8 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[120,9702]) ).
thf(9816,plain,
( ~ ( empty @ ( sk10 @ sk8 @ empty_set ) )
| ( element @ empty_set @ sk8 ) ),
inference(pattern_uni,[status(thm)],[9815:[bind(A,$thf( sk10 @ sk8 @ empty_set ))]]) ).
thf(36389,plain,
( ( element @ empty_set @ sk8 )
| ( ( empty @ ( sk10 @ sk8 @ empty_set ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,9816]) ).
thf(36487,plain,
( ( element @ empty_set @ sk8 )
| ( ( sk10 @ sk8 @ empty_set )
!= empty_set ) ),
inference(simp,[status(thm)],[36389]) ).
thf(1981,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( rel_str @ empty_set )
| ( B != empty_set )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[115,939]) ).
thf(1982,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk11 ) @ sk11 )
| ( in @ ( sk10 @ A @ sk11 ) @ A )
| ( rel_str @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1981:[bind(A,$thf( sk11 ))]]) ).
thf(2327,plain,
( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
| ( in @ ( sk10 @ empty_set @ sk11 ) @ empty_set )
| ( rel_str @ empty_set ) ),
inference(simp,[status(thm)],[1982]) ).
thf(45765,plain,
( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
| $false
| ( rel_str @ empty_set ) ),
inference(rewrite,[status(thm)],[2327,1508]) ).
thf(45766,plain,
( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
| ( rel_str @ empty_set ) ),
inference(simp,[status(thm)],[45765]) ).
thf(45821,plain,
! [B: $i,A: $i] :
( ( rel_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45766,144]) ).
thf(45822,plain,
( ( rel_str @ empty_set )
| ~ ( in @ sk11 @ ( sk9 @ empty_set @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[45821:[bind(A,$thf( sk9 @ empty_set @ sk11 )),bind(B,$thf( sk11 ))]]) ).
thf(16657,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( the_carrier @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,16654]) ).
thf(16658,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[16657:[bind(A,$thf( sk1 ))]]) ).
thf(2626,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,2619]) ).
thf(2627,plain,
( ~ ( empty @ sk16 )
| ( element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[2626:[bind(A,$thf( sk16 ))]]) ).
thf(12942,plain,
! [B: $i,A: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( proper_element @ B @ ( powerset @ A ) )
| ( B != empty_set )
| ( A != sk8 ) ),
inference(paramod_ordered,[status(thm)],[150,187]) ).
thf(12943,plain,
! [A: $i] :
( ~ ( element @ A @ ( powerset @ sk8 ) )
| ( proper_element @ A @ ( powerset @ sk8 ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[12942:[bind(A,$thf( sk8 ))]]) ).
thf(13851,plain,
( ~ ( element @ empty_set @ ( powerset @ sk8 ) )
| ( proper_element @ empty_set @ ( powerset @ sk8 ) ) ),
inference(simp,[status(thm)],[12943]) ).
thf(113483,plain,
( ~ $true
| ( proper_element @ empty_set @ ( powerset @ sk8 ) ) ),
inference(rewrite,[status(thm)],[13851,636]) ).
thf(113484,plain,
proper_element @ empty_set @ ( powerset @ sk8 ),
inference(simp,[status(thm)],[113483]) ).
thf(113529,plain,
! [A: $i] :
( ( proper_element @ empty_set @ ( powerset @ sk8 ) )
!= ( proper_element @ A @ ( powerset @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113484,11245]) ).
thf(113566,plain,
! [A: $i] :
( ( empty_set != A )
| ( ( powerset @ sk8 )
!= ( powerset @ A ) ) ),
inference(simp,[status(thm)],[113529]) ).
thf(113576,plain,
( ( powerset @ sk8 )
!= ( powerset @ empty_set ) ),
inference(simp,[status(thm)],[113566]) ).
thf(14670,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ( element @ ( sk5 @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( one_sorted_str @ sk11 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14661,88]) ).
thf(14671,plain,
( ( empty_carrier @ sk11 )
| ( element @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[14670:[bind(A,$thf( sk11 ))]]) ).
thf(21284,plain,
! [B: $i,A: $i] :
( ( empty_carrier @ sk11 )
| ( B = A )
| ( proper_element @ B @ ( powerset @ A ) )
| ( ( element @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) )
!= ( element @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[14671,150]) ).
thf(21285,plain,
( ( empty_carrier @ sk11 )
| ( ( sk5 @ sk11 )
= ( the_carrier @ sk11 ) )
| ( proper_element @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[21284:[bind(A,$thf( the_carrier @ sk11 )),bind(B,$thf( sk5 @ sk11 ))]]) ).
thf(26999,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[24725,97]) ).
thf(27187,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( the_carrier @ sk11 )
!= sk6 ) ),
inference(simp,[status(thm)],[26999]) ).
thf(3524,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( in @ A @ B )
| ( ( element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
!= ( element @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2619,99]) ).
thf(3525,plain,
( ( empty @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[3524:[bind(A,$thf( sk5 @ sk16 )),bind(B,$thf( powerset @ ( the_carrier @ sk16 ) ))]]) ).
thf(27990,plain,
( $false
| ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(rewrite,[status(thm)],[3525,153]) ).
thf(27991,plain,
in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ),
inference(simp,[status(thm)],[27990]) ).
thf(81041,plain,
! [B: $i,A: $i] :
( ( sk1 != empty_set )
| ~ ( in @ A @ B )
| ( ( empty @ sk1 )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[79732,85]) ).
thf(81042,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ~ ( in @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[81041:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(85136,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
!= ( in @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[27991,81042]) ).
thf(85146,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( ( sk5 @ sk16 )
!= A )
| ( ( powerset @ ( the_carrier @ sk16 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[85136]) ).
thf(85223,plain,
( ( sk1 != empty_set )
| ( ( powerset @ ( the_carrier @ sk16 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[85146]) ).
thf(85506,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( powerset @ ( the_carrier @ sk16 ) )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,85223]) ).
thf(85507,plain,
( ~ ( empty @ sk1 )
| ( ( powerset @ ( the_carrier @ sk16 ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[85506:[bind(A,$thf( sk1 ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( empty_carrier @ A )
=> ( v1_yellow_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_3) ).
thf(74,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( empty_carrier @ A )
=> ( v1_yellow_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(75,plain,
! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( empty_carrier @ A )
| ( v1_yellow_3 @ A ) ),
inference(cnf,[status(esa)],[74]) ).
thf(964,plain,
! [A: $i] :
( ~ ( empty_carrier @ A )
| ( v1_yellow_3 @ A )
| ( ( rel_str @ sk11 )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[117,75]) ).
thf(965,plain,
( ~ ( empty_carrier @ sk11 )
| ( v1_yellow_3 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[964:[bind(A,$thf( sk11 ))]]) ).
thf(50,plain,
reflexive_relstr @ sk1,
inference(cnf,[status(esa)],[42]) ).
thf(17,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ~ ( v1_yellow_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_3) ).
thf(92,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ~ ( v1_yellow_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(93,plain,
! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( v1_yellow_3 @ A ) ),
inference(cnf,[status(esa)],[92]) ).
thf(3218,plain,
! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( v1_yellow_3 @ A )
| ( ( reflexive_relstr @ sk1 )
!= ( reflexive_relstr @ A ) ) ),
inference(paramod_ordered,[status(thm)],[50,93]) ).
thf(3219,plain,
( ~ ( rel_str @ sk1 )
| ( empty_carrier @ sk1 )
| ~ ( v1_yellow_3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3218:[bind(A,$thf( sk1 ))]]) ).
thf(21882,plain,
( ~ $true
| $false
| ~ ( v1_yellow_3 @ sk1 ) ),
inference(rewrite,[status(thm)],[3219,49,51]) ).
thf(21883,plain,
~ ( v1_yellow_3 @ sk1 ),
inference(simp,[status(thm)],[21882]) ).
thf(21884,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( v1_yellow_3 @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,21883]) ).
thf(21885,plain,
( ~ ( empty @ sk1 )
| ~ ( v1_yellow_3 @ empty_set ) ),
inference(pattern_uni,[status(thm)],[21884:[bind(A,$thf( sk1 ))]]) ).
thf(22187,plain,
( ~ ( v1_yellow_3 @ empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,21885]) ).
thf(22223,plain,
( ~ ( v1_yellow_3 @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[22187]) ).
thf(22322,plain,
( ~ ( empty_carrier @ sk11 )
| ( sk1 != empty_set )
| ( ( v1_yellow_3 @ sk11 )
!= ( v1_yellow_3 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[965,22223]) ).
thf(22365,plain,
( ~ ( empty_carrier @ sk11 )
| ( sk1 != empty_set )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[22322]) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( subset @ B @ C )
| ( ( element @ ( sk7 @ A ) @ ( powerset @ A ) )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[101,70]) ).
thf(887,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(898,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk7 @ A ) @ A ) ),
inference(simp,[status(thm)],[887]) ).
thf(19049,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk11 ) )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,18952]) ).
thf(19050,plain,
( ~ ( empty @ sk11 )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[19049:[bind(A,$thf( sk11 ))]]) ).
thf(43088,plain,
( ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk11 ) )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19050]) ).
thf(43192,plain,
( ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk11 ) )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[43088]) ).
thf(3908,plain,
! [A: $i] :
( ( in @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( in @ A @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[3863,1508]) ).
thf(3913,plain,
! [A: $i] :
( ( sk2 != A )
| ( ( powerset @ ( the_carrier @ sk1 ) )
!= empty_set ) ),
inference(simp,[status(thm)],[3908]) ).
thf(3915,plain,
( ( powerset @ ( the_carrier @ sk1 ) )
!= empty_set ),
inference(simp,[status(thm)],[3913]) ).
thf(8815,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk8 ) @ sk8 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8751,91]) ).
thf(8816,plain,
element @ ( sk9 @ empty_set @ sk8 ) @ sk8,
inference(pattern_uni,[status(thm)],[8815:[bind(A,$thf( sk9 @ empty_set @ sk8 )),bind(B,$thf( sk8 ))]]) ).
thf(54307,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk11 != empty_set )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,54162]) ).
thf(54308,plain,
( ~ ( empty @ sk16 )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk11 != empty_set ) ),
inference(pattern_uni,[status(thm)],[54307:[bind(A,$thf( sk16 ))]]) ).
thf(2722,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ sk16 ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,2651]) ).
thf(2723,plain,
( ~ ( empty @ sk16 )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[2722:[bind(A,$thf( sk16 ))]]) ).
thf(9352,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk16 )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,2723]) ).
thf(9353,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ sk16 )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[9352:[bind(A,$thf( sk16 ))]]) ).
thf(9462,plain,
( ~ ( empty @ sk16 )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(simp,[status(thm)],[9353]) ).
thf(35197,plain,
! [B: $i,A: $i] :
( ~ ( empty @ sk16 )
| ( element @ A @ ( powerset @ B ) )
| ( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9462,71]) ).
thf(35198,plain,
( ~ ( empty @ sk16 )
| ( element @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[35197:[bind(A,$thf( sk5 @ empty_set )),bind(B,$thf( the_carrier @ empty_set ))]]) ).
thf(55078,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk1 != empty_set )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,54967]) ).
thf(55079,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk1 != empty_set ) ),
inference(pattern_uni,[status(thm)],[55078:[bind(A,$thf( sk11 ))]]) ).
thf(77844,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk1 != empty_set )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,55079]) ).
thf(77920,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk1 != empty_set )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[77844]) ).
thf(139,plain,
! [A: $i] : ( element @ ( sk15 @ A ) @ A ),
inference(cnf,[status(esa)],[138]) ).
thf(10652,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( ( in @ A @ B )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[99,10522]) ).
thf(10653,plain,
( ~ ( element @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 )
| ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10652:[bind(A,$thf( powerset @ ( the_carrier @ sk1 ) )),bind(B,$thf( sk2 ))]]) ).
thf(39252,plain,
( ~ ( element @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[10653,52]) ).
thf(39253,plain,
~ ( element @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ),
inference(simp,[status(thm)],[39252]) ).
thf(39393,plain,
! [A: $i] :
( ( element @ ( sk15 @ A ) @ A )
!= ( element @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[139,39253]) ).
thf(39446,plain,
! [A: $i] :
( ( ( sk15 @ A )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[39393]) ).
thf(39456,plain,
( ( sk15 @ sk2 )
!= ( powerset @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[39446]) ).
thf(3,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(57,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(58,plain,
one_sorted_str @ sk3,
inference(cnf,[status(esa)],[57]) ).
thf(234,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( one_sorted_str @ empty_set )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[120,58]) ).
thf(235,plain,
( ~ ( empty @ sk3 )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( sk3 ))]]) ).
thf(857,plain,
( ( one_sorted_str @ empty_set )
| ( ( empty @ sk3 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,235]) ).
thf(858,plain,
( ( one_sorted_str @ empty_set )
| ( sk3 != empty_set ) ),
inference(simp,[status(thm)],[857]) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( one_sorted_str @ empty_set )
| ( B != empty_set )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[115,858]) ).
thf(1634,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk3 ) @ sk3 )
| ( in @ ( sk10 @ A @ sk3 ) @ A )
| ( one_sorted_str @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1633:[bind(A,$thf( sk3 ))]]) ).
thf(2203,plain,
( ( in @ ( sk9 @ empty_set @ sk3 ) @ sk3 )
| ( in @ ( sk10 @ empty_set @ sk3 ) @ empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[1634]) ).
thf(35320,plain,
( ( in @ ( sk9 @ empty_set @ sk3 ) @ sk3 )
| $false
| ( one_sorted_str @ empty_set ) ),
inference(rewrite,[status(thm)],[2203,1508]) ).
thf(35321,plain,
( ( in @ ( sk9 @ empty_set @ sk3 ) @ sk3 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[35320]) ).
thf(35435,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk3 ) @ sk3 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35321,10568]) ).
thf(35477,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( sk9 @ empty_set @ sk3 )
!= A )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[35435]) ).
thf(35493,plain,
( ( one_sorted_str @ empty_set )
| ( ( sk9 @ empty_set @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[35477]) ).
thf(13479,plain,
! [B: $i,A: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( proper_element @ B @ ( powerset @ A ) )
| ( A != empty_set )
| ( B != sk6 ) ),
inference(paramod_ordered,[status(thm)],[150,183]) ).
thf(13480,plain,
! [A: $i] :
( ~ ( element @ sk6 @ ( powerset @ A ) )
| ( proper_element @ sk6 @ ( powerset @ A ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[13479:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).
thf(14023,plain,
( ~ ( element @ sk6 @ ( powerset @ empty_set ) )
| ( proper_element @ sk6 @ ( powerset @ empty_set ) ) ),
inference(simp,[status(thm)],[13480]) ).
thf(19944,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( ( join_on_relstr @ A @ empty_set )
= ( bottom_of_relstr @ A ) )
| ( ( rel_str @ empty_set )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[910,168]) ).
thf(19945,plain,
( ( sk1 != empty_set )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[19944:[bind(A,$thf( empty_set ))]]) ).
thf(19992,plain,
! [A: $i] :
( ( ( join_on_relstr @ A @ empty_set )
= ( bottom_of_relstr @ A ) )
| ( ( rel_str @ sk1 )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51,168]) ).
thf(19993,plain,
( ( join_on_relstr @ sk1 @ empty_set )
= ( bottom_of_relstr @ sk1 ) ),
inference(pattern_uni,[status(thm)],[19992:[bind(A,$thf( sk1 ))]]) ).
thf(46152,plain,
( ( sk1 != empty_set )
| ( ( bottom_of_relstr @ sk1 )
= ( bottom_of_relstr @ empty_set ) )
| ( ( join_on_relstr @ sk1 @ empty_set )
!= ( join_on_relstr @ empty_set @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[19945,19993]) ).
thf(46195,plain,
( ( ( bottom_of_relstr @ sk1 )
= ( bottom_of_relstr @ empty_set ) )
| ( sk1 != empty_set )
| ( sk1 != empty_set )
| ( empty_set != empty_set ) ),
inference(simp,[status(thm)],[46152]) ).
thf(46231,plain,
( ( ( bottom_of_relstr @ sk1 )
= ( bottom_of_relstr @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[46195]) ).
thf(46240,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( bottom_of_relstr @ sk1 )
= ( bottom_of_relstr @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,46231]) ).
thf(46241,plain,
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ sk1 )
= ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[46240:[bind(A,$thf( sk1 ))]]) ).
thf(25454,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,25449]) ).
thf(25455,plain,
( ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[25454:[bind(A,$thf( sk1 ))]]) ).
thf(52259,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ empty_set ) )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25455,10568]) ).
thf(52317,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ sk1 )
!= A )
| ( ( the_carrier @ empty_set )
!= A ) ),
inference(simp,[status(thm)],[52259]) ).
thf(52341,plain,
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ sk1 )
!= ( the_carrier @ empty_set ) ) ),
inference(simp,[status(thm)],[52317]) ).
thf(52384,plain,
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ empty_set )
!= ( the_carrier @ empty_set ) )
| ( ( bottom_of_relstr @ sk1 )
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46241,52341]) ).
thf(52385,plain,
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ empty_set )
!= ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[52384:[]]) ).
thf(52523,plain,
( ( ( bottom_of_relstr @ empty_set )
!= ( the_carrier @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,52385]) ).
thf(52585,plain,
( ( ( bottom_of_relstr @ empty_set )
!= ( the_carrier @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[52523]) ).
thf(55096,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( B != sk1 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[64,54967]) ).
thf(55097,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ~ ( empty @ A )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[55096:[bind(A,$thf( sk11 ))]]) ).
thf(55178,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk1 )
| ~ ( empty @ ( the_carrier @ sk11 ) ) ),
inference(simp,[status(thm)],[55097]) ).
thf(78248,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk1 )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[55178]) ).
thf(78251,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk1 )
| ( ( the_carrier @ sk11 )
!= sk1 ) ),
inference(simp,[status(thm)],[78248]) ).
thf(104758,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ sk11 )
!= sk1 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,78251]) ).
thf(104830,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ sk11 )
!= sk1 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[104758]) ).
thf(54413,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk16 != sk11 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,54304]) ).
thf(54414,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk16 != sk11 ) ),
inference(pattern_uni,[status(thm)],[54413:[bind(A,$thf( sk11 ))]]) ).
thf(76448,plain,
( ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk16 != sk11 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,54414]) ).
thf(76518,plain,
( ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk16 != sk11 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[76448]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ~ ( rel_str @ A )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( element @ ( sk18 @ B @ A ) @ ( the_carrier @ A ) )
| ( upper_relstr_subset @ B @ A ) ),
inference(cnf,[status(esa)],[169]) ).
thf(16733,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( B
!= ( the_carrier @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[115,16712]) ).
thf(16734,plain,
! [A: $i] :
( ( in @ ( sk9 @ ( the_carrier @ sk1 ) @ A ) @ A )
| ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ A ) @ ( the_carrier @ sk1 ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[16733:[bind(A,$thf( A )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(16788,plain,
( ( in @ ( sk9 @ ( the_carrier @ sk1 ) @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[16734]) ).
thf(96790,plain,
( $false
| ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ) ) ),
inference(rewrite,[status(thm)],[16788,1508]) ).
thf(96791,plain,
in @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ),
inference(simp,[status(thm)],[96790]) ).
thf(96980,plain,
! [A: $i] :
( ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[96791,10568]) ).
thf(97066,plain,
! [A: $i] :
( ( ( sk10 @ ( the_carrier @ sk1 ) @ empty_set )
!= A )
| ( ( the_carrier @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[96980]) ).
thf(97087,plain,
( ( sk10 @ ( the_carrier @ sk1 ) @ empty_set )
!= ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[97066]) ).
thf(2438,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ( element @ ( sk5 @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( one_sorted_str @ sk3 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58,88]) ).
thf(2439,plain,
( ( empty_carrier @ sk3 )
| ( element @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[2438:[bind(A,$thf( sk3 ))]]) ).
thf(13097,plain,
! [B: $i,A: $i] :
( ( empty_carrier @ sk3 )
| ( B = A )
| ( proper_element @ B @ ( powerset @ A ) )
| ( ( element @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) )
!= ( element @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[2439,150]) ).
thf(13098,plain,
( ( empty_carrier @ sk3 )
| ( ( sk5 @ sk3 )
= ( the_carrier @ sk3 ) )
| ( proper_element @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[13097:[bind(A,$thf( the_carrier @ sk3 )),bind(B,$thf( sk5 @ sk3 ))]]) ).
thf(3868,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,3863]) ).
thf(3869,plain,
( ~ ( empty @ sk1 )
| ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[3868:[bind(A,$thf( sk1 ))]]) ).
thf(2019,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[115,182]) ).
thf(2020,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk2 ) @ sk2 )
| ( in @ ( sk10 @ A @ sk2 ) @ A )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2019:[bind(A,$thf( sk2 ))]]) ).
thf(2340,plain,
( ( in @ ( sk9 @ empty_set @ sk2 ) @ sk2 )
| ( in @ ( sk10 @ empty_set @ sk2 ) @ empty_set ) ),
inference(simp,[status(thm)],[2020]) ).
thf(10252,plain,
( ( in @ ( sk9 @ empty_set @ sk2 ) @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[2340,1508]) ).
thf(10253,plain,
in @ ( sk9 @ empty_set @ sk2 ) @ sk2,
inference(simp,[status(thm)],[10252]) ).
thf(10545,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk2 ) @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10253,144]) ).
thf(10546,plain,
~ ( in @ sk2 @ ( sk9 @ empty_set @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10545:[bind(A,$thf( sk9 @ empty_set @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(32616,plain,
( ~ ( empty @ sk1 )
| ( ( in @ sk2 @ ( sk9 @ empty_set @ sk2 ) )
!= ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3869,10546]) ).
thf(32635,plain,
( ~ ( empty @ sk1 )
| ( sk2 != sk2 )
| ( ( sk9 @ empty_set @ sk2 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[32616]) ).
thf(32687,plain,
( ~ ( empty @ sk1 )
| ( ( sk9 @ empty_set @ sk2 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[32635]) ).
thf(25498,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25449,144]) ).
thf(25499,plain,
~ ( in @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ sk1 ) ),
inference(pattern_uni,[status(thm)],[25498:[bind(A,$thf( bottom_of_relstr @ sk1 )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(17463,plain,
( ~ ( empty @ sk1 )
| ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16658]) ).
thf(17465,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[17463]) ).
thf(18621,plain,
( ( ( the_carrier @ empty_set )
!= sk1 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,17465]) ).
thf(18671,plain,
( ( ( the_carrier @ empty_set )
!= sk1 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[18621]) ).
thf(2844,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( A
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[115,2835]) ).
thf(2845,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ ( sk5 @ sk16 ) ) @ ( sk5 @ sk16 ) )
| ( in @ ( sk10 @ A @ ( sk5 @ sk16 ) ) @ A )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2844:[bind(A,$thf( sk5 @ sk16 )),bind(B,$thf( B ))]]) ).
thf(2864,plain,
( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( sk5 @ sk16 ) )
| ( in @ ( sk10 @ empty_set @ ( sk5 @ sk16 ) ) @ empty_set ) ),
inference(simp,[status(thm)],[2845]) ).
thf(90398,plain,
( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( sk5 @ sk16 ) )
| $false ),
inference(rewrite,[status(thm)],[2864,1508]) ).
thf(90399,plain,
in @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( sk5 @ sk16 ),
inference(simp,[status(thm)],[90398]) ).
thf(90533,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( sk5 @ sk16 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[90399,91]) ).
thf(90534,plain,
element @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( sk5 @ sk16 ),
inference(pattern_uni,[status(thm)],[90533:[bind(A,$thf( sk9 @ empty_set @ ( sk5 @ sk16 ) )),bind(B,$thf( sk5 @ sk16 ))]]) ).
thf(91293,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( element @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( sk5 @ sk16 ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[13586,90534]) ).
thf(91294,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( element @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( sk5 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[91293:[]]) ).
thf(89124,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[88991,91]) ).
thf(89125,plain,
element @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ),
inference(pattern_uni,[status(thm)],[89124:[bind(A,$thf( sk10 @ ( sk5 @ sk16 ) @ empty_set )),bind(B,$thf( sk5 @ sk16 ))]]) ).
thf(89884,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( element @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[13586,89125]) ).
thf(89885,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( element @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[89884:[]]) ).
thf(15934,plain,
( ( empty @ ( sk5 @ sk1 ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,15913]) ).
thf(15967,plain,
( ( sk5 @ sk1 )
!= empty_set ),
inference(simp,[status(thm)],[15934]) ).
thf(16041,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( A
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[115,15967]) ).
thf(16042,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ ( sk5 @ sk1 ) ) @ ( sk5 @ sk1 ) )
| ( in @ ( sk10 @ A @ ( sk5 @ sk1 ) ) @ A )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[16041:[bind(A,$thf( sk5 @ sk1 )),bind(B,$thf( B ))]]) ).
thf(16098,plain,
( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( sk5 @ sk1 ) )
| ( in @ ( sk10 @ empty_set @ ( sk5 @ sk1 ) ) @ empty_set ) ),
inference(simp,[status(thm)],[16042]) ).
thf(92303,plain,
( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( sk5 @ sk1 ) )
| $false ),
inference(rewrite,[status(thm)],[16098,1508]) ).
thf(92304,plain,
in @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( sk5 @ sk1 ),
inference(simp,[status(thm)],[92303]) ).
thf(92501,plain,
! [A: $i] :
( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( sk5 @ sk1 ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[92304,10568]) ).
thf(92564,plain,
! [A: $i] :
( ( ( sk9 @ empty_set @ ( sk5 @ sk1 ) )
!= A )
| ( ( sk5 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[92501]) ).
thf(92630,plain,
( ( sk9 @ empty_set @ ( sk5 @ sk1 ) )
!= ( sk5 @ sk1 ) ),
inference(simp,[status(thm)],[92564]) ).
thf(104451,plain,
( ~ ( empty @ sk16 )
| ( ( the_carrier @ sk11 )
!= sk11 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,77097]) ).
thf(104522,plain,
( ~ ( empty @ sk16 )
| ( ( the_carrier @ sk11 )
!= sk11 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[104451]) ).
thf(641,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( element @ A @ ( powerset @ B ) )
| ( empty_set != empty_set ) ),
inference(paramod_ordered,[status(thm)],[120,636]) ).
thf(642,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( element @ A @ ( powerset @ B ) ) ),
inference(pattern_uni,[status(thm)],[641:[]]) ).
thf(81085,plain,
! [B: $i,A: $i] :
( ( sk1 != empty_set )
| ( element @ A @ ( powerset @ B ) )
| ( ( empty @ sk1 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79732,642]) ).
thf(81086,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( element @ sk1 @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[81085:[bind(A,$thf( sk1 ))]]) ).
thf(81468,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( element @ sk1 @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[81086]) ).
thf(5305,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ empty_set @ sk6 )
| ( A
!= ( sk10 @ sk6 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[120,5304]) ).
thf(5306,plain,
( ~ ( empty @ ( sk10 @ sk6 @ empty_set ) )
| ( in @ empty_set @ sk6 ) ),
inference(pattern_uni,[status(thm)],[5305:[bind(A,$thf( sk10 @ sk6 @ empty_set ))]]) ).
thf(19626,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19588,144]) ).
thf(19627,plain,
~ ( in @ sk2 @ ( bottom_of_relstr @ sk1 ) ),
inference(pattern_uni,[status(thm)],[19626:[bind(A,$thf( bottom_of_relstr @ sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(19879,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( ( in @ A @ B )
!= ( in @ sk2 @ ( bottom_of_relstr @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[99,19627]) ).
thf(19880,plain,
( ~ ( element @ sk2 @ ( bottom_of_relstr @ sk1 ) )
| ( empty @ ( bottom_of_relstr @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[19879:[bind(A,$thf( sk2 )),bind(B,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(45620,plain,
! [A: $i] :
( ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( ( element @ A @ ( powerset @ A ) )
!= ( element @ sk2 @ ( bottom_of_relstr @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[823,19880]) ).
thf(45699,plain,
! [A: $i] :
( ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( A != sk2 )
| ( ( powerset @ A )
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(simp,[status(thm)],[45620]) ).
thf(45744,plain,
( ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) ) ),
inference(simp,[status(thm)],[45699]) ).
thf(204,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ empty_set @ sk2 )
| ~ ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( A
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[120,46]) ).
thf(205,plain,
( ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( in @ empty_set @ sk2 )
| ~ ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(23829,plain,
( ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( in @ empty_set @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[205,19590]) ).
thf(23830,plain,
( ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( in @ empty_set @ sk2 ) ),
inference(simp,[status(thm)],[23829]) ).
thf(67032,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( in @ empty_set @ sk2 )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ ( bottom_of_relstr @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[45744,23830]) ).
thf(67033,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( in @ empty_set @ sk2 ) ),
inference(pattern_uni,[status(thm)],[67032:[]]) ).
thf(1805,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( rel_str @ empty_set )
| ( B != empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,910]) ).
thf(1806,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( rel_str @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1805:[bind(A,$thf( sk1 ))]]) ).
thf(2265,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( rel_str @ empty_set ) ),
inference(simp,[status(thm)],[1806]) ).
thf(39938,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( rel_str @ empty_set ) ),
inference(rewrite,[status(thm)],[2265,1508]) ).
thf(39939,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( rel_str @ empty_set ) ),
inference(simp,[status(thm)],[39938]) ).
thf(40054,plain,
! [A: $i] :
( ( rel_str @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[39939,10568]) ).
thf(40100,plain,
! [A: $i] :
( ( rel_str @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[40054]) ).
thf(40115,plain,
( ( rel_str @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[40100]) ).
thf(16045,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( B
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[115,15967]) ).
thf(16046,plain,
! [A: $i] :
( ( in @ ( sk9 @ ( sk5 @ sk1 ) @ A ) @ A )
| ( in @ ( sk10 @ ( sk5 @ sk1 ) @ A ) @ ( sk5 @ sk1 ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[16045:[bind(A,$thf( A )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(16100,plain,
( ( in @ ( sk9 @ ( sk5 @ sk1 ) @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) ) ),
inference(simp,[status(thm)],[16046]) ).
thf(93588,plain,
( $false
| ( in @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[16100,1508]) ).
thf(93589,plain,
in @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ),
inference(simp,[status(thm)],[93588]) ).
thf(93786,plain,
! [A: $i] :
( ( in @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[93589,10568]) ).
thf(93864,plain,
! [A: $i] :
( ( ( sk10 @ ( sk5 @ sk1 ) @ empty_set )
!= A )
| ( ( sk5 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[93786]) ).
thf(93923,plain,
( ( sk10 @ ( sk5 @ sk1 ) @ empty_set )
!= ( sk5 @ sk1 ) ),
inference(simp,[status(thm)],[93864]) ).
thf(37,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_waybel_0) ).
thf(156,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(157,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( rel_str @ A )
| ( element @ ( sk17 @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(25452,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,25449]) ).
thf(25453,plain,
( ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25452:[bind(A,$thf( sk1 ))]]) ).
thf(51867,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,25453]) ).
thf(51868,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[51867:[bind(A,$thf( sk1 ))]]) ).
thf(52095,plain,
( ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(simp,[status(thm)],[51868]) ).
thf(71962,plain,
( ( in @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,52095]) ).
thf(72098,plain,
( ( in @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[71962]) ).
thf(11775,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk2 @ empty_set ) @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11728,144]) ).
thf(11776,plain,
~ ( in @ sk2 @ ( sk10 @ sk2 @ empty_set ) ),
inference(pattern_uni,[status(thm)],[11775:[bind(A,$thf( sk10 @ sk2 @ empty_set )),bind(B,$thf( sk2 ))]]) ).
thf(11984,plain,
( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
!= ( in @ sk2 @ ( sk10 @ sk2 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[3379,11776]) ).
thf(11986,plain,
( ( ( sk9 @ empty_set @ sk6 )
!= sk2 )
| ( ( sk10 @ sk2 @ empty_set )
!= sk6 ) ),
inference(simp,[status(thm)],[11984]) ).
thf(86512,plain,
! [B: $i,A: $i] :
( ( finite @ sk1 )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[86416,91]) ).
thf(86513,plain,
( ( finite @ sk1 )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[86512:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(15341,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( one_sorted_str @ empty_set )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[115,14667]) ).
thf(15342,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk11 ) @ sk11 )
| ( in @ ( sk10 @ A @ sk11 ) @ A )
| ( A != empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[15341:[bind(A,$thf( sk11 ))]]) ).
thf(15405,plain,
( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
| ( in @ ( sk10 @ empty_set @ sk11 ) @ empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[15342]) ).
thf(58167,plain,
( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
| $false
| ( one_sorted_str @ empty_set ) ),
inference(rewrite,[status(thm)],[15405,1508]) ).
thf(58168,plain,
( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[58167]) ).
thf(58249,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[58168,91]) ).
thf(58250,plain,
( ( one_sorted_str @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk11 ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[58249:[bind(A,$thf( sk9 @ empty_set @ sk11 )),bind(B,$thf( sk11 ))]]) ).
thf(11755,plain,
( ( in @ ( sk10 @ sk2 @ empty_set ) @ sk2 )
!= ( in @ sk8 @ ( sk9 @ empty_set @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[11728,10534]) ).
thf(11849,plain,
( ( ( sk10 @ sk2 @ empty_set )
!= sk8 )
| ( ( sk9 @ empty_set @ sk8 )
!= sk2 ) ),
inference(simp,[status(thm)],[11755]) ).
thf(93723,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[93589,91]) ).
thf(93724,plain,
element @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ),
inference(pattern_uni,[status(thm)],[93723:[bind(A,$thf( sk10 @ ( sk5 @ sk1 ) @ empty_set )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(19051,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ empty_set ) )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,18952]) ).
thf(19052,plain,
( ~ ( empty @ sk11 )
| ( element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[19051:[bind(A,$thf( sk11 ))]]) ).
thf(21306,plain,
! [B: $i,A: $i] :
( ( empty_carrier @ sk11 )
| ( empty @ B )
| ( in @ A @ B )
| ( ( element @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) )
!= ( element @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14671,99]) ).
thf(21307,plain,
( ( empty_carrier @ sk11 )
| ( empty @ ( powerset @ ( the_carrier @ sk11 ) ) )
| ( in @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[21306:[bind(A,$thf( sk5 @ sk11 )),bind(B,$thf( powerset @ ( the_carrier @ sk11 ) ))]]) ).
thf(63426,plain,
( ( empty_carrier @ sk11 )
| $false
| ( in @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) ) ),
inference(rewrite,[status(thm)],[21307,153]) ).
thf(63427,plain,
( ( empty_carrier @ sk11 )
| ( in @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) ) ),
inference(simp,[status(thm)],[63426]) ).
thf(63503,plain,
! [B: $i,A: $i] :
( ( empty_carrier @ sk11 )
| ~ ( in @ B @ A )
| ( ( in @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[63427,144]) ).
thf(63504,plain,
( ( empty_carrier @ sk11 )
| ~ ( in @ ( powerset @ ( the_carrier @ sk11 ) ) @ ( sk5 @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[63503:[bind(A,$thf( sk5 @ sk11 )),bind(B,$thf( powerset @ ( the_carrier @ sk11 ) ))]]) ).
thf(93687,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[93589,144]) ).
thf(93688,plain,
~ ( in @ ( sk5 @ sk1 ) @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) ),
inference(pattern_uni,[status(thm)],[93687:[bind(A,$thf( sk10 @ ( sk5 @ sk1 ) @ empty_set )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(80991,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( empty @ sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,79732]) ).
thf(80992,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( A != empty_set )
| ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[80991:[bind(A,$thf( sk1 ))]]) ).
thf(81465,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( empty @ sk1 ) ),
inference(simp,[status(thm)],[80992]) ).
thf(81963,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( empty @ sk1 ) ),
inference(rewrite,[status(thm)],[81465,1508]) ).
thf(81964,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( empty @ sk1 ) ),
inference(simp,[status(thm)],[81963]) ).
thf(82102,plain,
! [A: $i] :
( ( empty @ sk1 )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[81964,10568]) ).
thf(82143,plain,
! [A: $i] :
( ( empty @ sk1 )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[82102]) ).
thf(82204,plain,
( ( empty @ sk1 )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[82143]) ).
thf(54415,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk11 != empty_set )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,54304]) ).
thf(54416,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk11 != empty_set ) ),
inference(pattern_uni,[status(thm)],[54415:[bind(A,$thf( sk16 ))]]) ).
thf(76934,plain,
( ~ ( empty @ sk16 )
| ( sk11 != empty_set )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk16 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[54416]) ).
thf(76941,plain,
( ~ ( empty @ sk16 )
| ( sk11 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk16 ) ),
inference(simp,[status(thm)],[76934]) ).
thf(1645,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( antisymmetric_relstr @ empty_set )
| ( B != empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,809]) ).
thf(1646,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( antisymmetric_relstr @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1645:[bind(A,$thf( sk1 ))]]) ).
thf(2212,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( antisymmetric_relstr @ empty_set ) ),
inference(simp,[status(thm)],[1646]) ).
thf(37999,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( antisymmetric_relstr @ empty_set ) ),
inference(rewrite,[status(thm)],[2212,1508]) ).
thf(38000,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( antisymmetric_relstr @ empty_set ) ),
inference(simp,[status(thm)],[37999]) ).
thf(38114,plain,
! [A: $i] :
( ( antisymmetric_relstr @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[38000,10568]) ).
thf(38143,plain,
! [A: $i] :
( ( antisymmetric_relstr @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[38114]) ).
thf(38194,plain,
( ( antisymmetric_relstr @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[38143]) ).
thf(54163,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ sk16 )
!= ( the_carrier @ sk11 ) )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,27146]) ).
thf(54164,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( ( the_carrier @ sk16 )
!= ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[54163:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(25475,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ) )
!= ( in @ sk8 @ ( sk9 @ empty_set @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[25449,10534]) ).
thf(25599,plain,
( ( ( bottom_of_relstr @ sk1 )
!= sk8 )
| ( ( sk9 @ empty_set @ sk8 )
!= ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[25475]) ).
thf(35199,plain,
( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,9462]) ).
thf(35285,plain,
( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[35199]) ).
thf(58640,plain,
! [B: $i,A: $i] :
( ( sk16 != empty_set )
| ( element @ A @ ( powerset @ B ) )
| ( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35285,71]) ).
thf(58641,plain,
( ( sk16 != empty_set )
| ( element @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[58640:[bind(A,$thf( sk5 @ empty_set )),bind(B,$thf( the_carrier @ empty_set ))]]) ).
thf(67010,plain,
! [A: $i] :
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( finite @ A )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45744,126]) ).
thf(67011,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( finite @ ( bottom_of_relstr @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[67010:[bind(A,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(20804,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= ( powerset @ sk2 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,20138]) ).
thf(20805,plain,
( ~ ( empty @ sk1 )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= ( powerset @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[20804:[bind(A,$thf( sk1 ))]]) ).
thf(50091,plain,
( ( ( powerset @ ( the_carrier @ empty_set ) )
!= ( powerset @ sk2 ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,20805]) ).
thf(50161,plain,
( ( ( powerset @ ( the_carrier @ empty_set ) )
!= ( powerset @ sk2 ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[50091]) ).
thf(43,plain,
lower_bounded_relstr @ sk1,
inference(cnf,[status(esa)],[42]) ).
thf(230,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( lower_bounded_relstr @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,43]) ).
thf(231,plain,
( ~ ( empty @ sk1 )
| ( lower_bounded_relstr @ empty_set ) ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( sk1 ))]]) ).
thf(678,plain,
( ( lower_bounded_relstr @ empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,231]) ).
thf(679,plain,
( ( lower_bounded_relstr @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[678]) ).
thf(1885,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( lower_bounded_relstr @ empty_set )
| ( A != empty_set )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,679]) ).
thf(1886,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( lower_bounded_relstr @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1885:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(2292,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( lower_bounded_relstr @ empty_set ) ),
inference(simp,[status(thm)],[1886]) ).
thf(44326,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( lower_bounded_relstr @ empty_set ) ),
inference(rewrite,[status(thm)],[2292,1508]) ).
thf(44327,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( lower_bounded_relstr @ empty_set ) ),
inference(simp,[status(thm)],[44326]) ).
thf(44404,plain,
! [B: $i,A: $i] :
( ( lower_bounded_relstr @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44327,91]) ).
thf(44405,plain,
( ( lower_bounded_relstr @ empty_set )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[44404:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(276,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( reflexive_relstr @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,50]) ).
thf(277,plain,
( ~ ( empty @ sk1 )
| ( reflexive_relstr @ empty_set ) ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( sk1 ))]]) ).
thf(817,plain,
( ( reflexive_relstr @ empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,277]) ).
thf(818,plain,
( ( reflexive_relstr @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[817]) ).
thf(2110,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( reflexive_relstr @ empty_set )
| ( A != empty_set )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,818]) ).
thf(2111,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( reflexive_relstr @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2110:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(2185,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( reflexive_relstr @ empty_set ) ),
inference(simp,[status(thm)],[2111]) ).
thf(33992,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( reflexive_relstr @ empty_set ) ),
inference(rewrite,[status(thm)],[2185,1508]) ).
thf(33993,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( reflexive_relstr @ empty_set ) ),
inference(simp,[status(thm)],[33992]) ).
thf(44382,plain,
! [B: $i,A: $i] :
( ( lower_bounded_relstr @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44327,144]) ).
thf(44383,plain,
( ( lower_bounded_relstr @ empty_set )
| ~ ( in @ sk1 @ ( sk10 @ sk1 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[44382:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(18008,plain,
! [B: $i,A: $i] :
( ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) )
| ( ( rel_str @ sk11 )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[117,163]) ).
thf(18009,plain,
! [A: $i] : ( element @ ( join_on_relstr @ sk11 @ A ) @ ( the_carrier @ sk11 ) ),
inference(pattern_uni,[status(thm)],[18008:[bind(A,$thf( sk11 ))]]) ).
thf(18091,plain,
! [A: $i] : ( element @ ( join_on_relstr @ sk11 @ A ) @ ( the_carrier @ sk11 ) ),
inference(simp,[status(thm)],[18009]) ).
thf(20704,plain,
! [A: $i] :
( ( element @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk11 ) )
| ( ( join_on_relstr @ sk11 @ A )
!= ( join_on_relstr @ sk1 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[19993,18091]) ).
thf(20775,plain,
! [A: $i] :
( ( element @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk11 ) )
| ( sk11 != sk1 )
| ( A != empty_set ) ),
inference(simp,[status(thm)],[20704]) ).
thf(20790,plain,
( ( element @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk11 ) )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[20775]) ).
thf(1649,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( antisymmetric_relstr @ empty_set )
| ( A != empty_set )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,809]) ).
thf(1650,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( antisymmetric_relstr @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1649:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(2214,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( antisymmetric_relstr @ empty_set ) ),
inference(simp,[status(thm)],[1650]) ).
thf(38900,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( antisymmetric_relstr @ empty_set ) ),
inference(rewrite,[status(thm)],[2214,1508]) ).
thf(38901,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( antisymmetric_relstr @ empty_set ) ),
inference(simp,[status(thm)],[38900]) ).
thf(924,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( empty @ ( the_carrier @ A ) )
| ( ( one_sorted_str @ sk3 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58,73]) ).
thf(925,plain,
( ( empty_carrier @ sk3 )
| ~ ( empty @ ( the_carrier @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[924:[bind(A,$thf( sk3 ))]]) ).
thf(81037,plain,
( ( sk1 != empty_set )
| ( empty_carrier @ sk3 )
| ( ( empty @ ( the_carrier @ sk3 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,925]) ).
thf(81380,plain,
( ( empty_carrier @ sk3 )
| ( sk1 != empty_set )
| ( ( the_carrier @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[81037]) ).
thf(46863,plain,
( ( sk11 != empty_set )
| ( ( bottom_of_relstr @ sk11 )
= ( bottom_of_relstr @ empty_set ) )
| ( ( join_on_relstr @ sk11 @ empty_set )
!= ( join_on_relstr @ empty_set @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[19975,19943]) ).
thf(46959,plain,
( ( ( bottom_of_relstr @ sk11 )
= ( bottom_of_relstr @ empty_set ) )
| ( sk11 != empty_set )
| ( sk11 != empty_set )
| ( empty_set != empty_set ) ),
inference(simp,[status(thm)],[46863]) ).
thf(46994,plain,
( ( ( bottom_of_relstr @ sk11 )
= ( bottom_of_relstr @ empty_set ) )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[46959]) ).
thf(1424,plain,
( ( empty @ ( the_carrier @ sk16 ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,1411]) ).
thf(1425,plain,
( ( the_carrier @ sk16 )
!= empty_set ),
inference(simp,[status(thm)],[1424]) ).
thf(1851,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != empty_set )
| ( B
!= ( the_carrier @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[115,1425]) ).
thf(1852,plain,
! [A: $i] :
( ( in @ ( sk9 @ ( the_carrier @ sk16 ) @ A ) @ A )
| ( in @ ( sk10 @ ( the_carrier @ sk16 ) @ A ) @ ( the_carrier @ sk16 ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1851:[bind(A,$thf( A )),bind(B,$thf( the_carrier @ sk16 ))]]) ).
thf(2280,plain,
( ( in @ ( sk9 @ ( the_carrier @ sk16 ) @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ) ) ),
inference(simp,[status(thm)],[1852]) ).
thf(87618,plain,
( $false
| ( in @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ) ) ),
inference(rewrite,[status(thm)],[2280,1508]) ).
thf(87619,plain,
in @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ),
inference(simp,[status(thm)],[87618]) ).
thf(87709,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[87619,144]) ).
thf(87710,plain,
~ ( in @ ( the_carrier @ sk16 ) @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) ),
inference(pattern_uni,[status(thm)],[87709:[bind(A,$thf( sk10 @ ( the_carrier @ sk16 ) @ empty_set )),bind(B,$thf( the_carrier @ sk16 ))]]) ).
thf(19200,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ ( the_carrier @ sk1 ) )
| ( A
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[120,19005]) ).
thf(19201,plain,
( ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( element @ empty_set @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[19200:[bind(A,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(1809,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( rel_str @ empty_set )
| ( A != empty_set )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,910]) ).
thf(1810,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( rel_str @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1809:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(2266,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( rel_str @ empty_set ) ),
inference(simp,[status(thm)],[1810]) ).
thf(40683,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( rel_str @ empty_set ) ),
inference(rewrite,[status(thm)],[2266,1508]) ).
thf(40684,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( rel_str @ empty_set ) ),
inference(simp,[status(thm)],[40683]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(121,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(32497,plain,
( ~ ( empty @ sk1 )
| ( ( in @ sk2 @ ( bottom_of_relstr @ sk1 ) )
!= ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3869,19627]) ).
thf(32629,plain,
( ~ ( empty @ sk1 )
| ( sk2 != sk2 )
| ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[32497]) ).
thf(32679,plain,
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[32629]) ).
thf(56403,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,32679]) ).
thf(56462,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[56403]) ).
thf(54325,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( B != sk11 )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[64,54162]) ).
thf(54326,plain,
! [A: $i] :
( ~ ( empty @ sk16 )
| ~ ( empty @ A )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( A != sk11 ) ),
inference(pattern_uni,[status(thm)],[54325:[bind(A,$thf( sk16 ))]]) ).
thf(54407,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ sk11 )
| ( ( the_carrier @ sk11 )
!= empty_set ) ),
inference(simp,[status(thm)],[54326]) ).
thf(45650,plain,
! [A: $i] :
( ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( ( element @ ( sk15 @ A ) @ A )
!= ( element @ sk2 @ ( bottom_of_relstr @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[139,19880]) ).
thf(45718,plain,
! [A: $i] :
( ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( ( sk15 @ A )
!= sk2 )
| ( A
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(simp,[status(thm)],[45650]) ).
thf(45747,plain,
( ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( ( sk15 @ ( bottom_of_relstr @ sk1 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[45718]) ).
thf(30049,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,30040]) ).
thf(30050,plain,
( ~ ( empty @ sk1 )
| ( in @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[30049:[bind(A,$thf( sk1 ))]]) ).
thf(125854,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( in @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ empty_set ) ) )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30050,10568]) ).
thf(125937,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( sk5 @ sk1 )
!= A )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= A ) ),
inference(simp,[status(thm)],[125854]) ).
thf(126014,plain,
( ~ ( empty @ sk1 )
| ( ( sk5 @ sk1 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[125937]) ).
thf(126321,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,126014]) ).
thf(126322,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ sk1 )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[126321:[bind(A,$thf( sk1 ))]]) ).
thf(126426,plain,
( ~ ( empty @ sk1 )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[126322]) ).
thf(20686,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,19993]) ).
thf(20687,plain,
( ~ ( empty @ sk1 )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[20686:[bind(A,$thf( sk1 ))]]) ).
thf(92374,plain,
( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( sk5 @ sk1 ) )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[92304,30103]) ).
thf(92555,plain,
( ( ( sk9 @ empty_set @ ( sk5 @ sk1 ) )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(simp,[status(thm)],[92374]) ).
thf(92628,plain,
( ( sk9 @ empty_set @ ( sk5 @ sk1 ) )
!= ( powerset @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[92555]) ).
thf(19671,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
!= ( in @ sk6 @ ( sk10 @ sk6 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[19588,10558]) ).
thf(19700,plain,
( ( ( bottom_of_relstr @ sk1 )
!= sk6 )
| ( ( sk10 @ sk6 @ empty_set )
!= sk2 ) ),
inference(simp,[status(thm)],[19671]) ).
thf(19047,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ ( the_carrier @ sk11 ) )
| ( A
!= ( bottom_of_relstr @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,18952]) ).
thf(19048,plain,
( ~ ( empty @ ( bottom_of_relstr @ sk11 ) )
| ( element @ empty_set @ ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[19047:[bind(A,$thf( bottom_of_relstr @ sk11 ))]]) ).
thf(42489,plain,
( ( element @ empty_set @ ( the_carrier @ sk11 ) )
| ( ( empty @ ( bottom_of_relstr @ sk11 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19048]) ).
thf(42594,plain,
( ( element @ empty_set @ ( the_carrier @ sk11 ) )
| ( ( bottom_of_relstr @ sk11 )
!= empty_set ) ),
inference(simp,[status(thm)],[42489]) ).
thf(9640,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ empty_set @ sk8 )
| ( A
!= ( sk10 @ sk8 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[120,9637]) ).
thf(9641,plain,
( ~ ( empty @ ( sk10 @ sk8 @ empty_set ) )
| ( in @ empty_set @ sk8 ) ),
inference(pattern_uni,[status(thm)],[9640:[bind(A,$thf( sk10 @ sk8 @ empty_set ))]]) ).
thf(35868,plain,
( ( in @ empty_set @ sk8 )
| ( ( empty @ ( sk10 @ sk8 @ empty_set ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,9641]) ).
thf(35970,plain,
( ( in @ empty_set @ sk8 )
| ( ( sk10 @ sk8 @ empty_set )
!= empty_set ) ),
inference(simp,[status(thm)],[35868]) ).
thf(28052,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27991,144]) ).
thf(28053,plain,
~ ( in @ ( powerset @ ( the_carrier @ sk16 ) ) @ ( sk5 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[28052:[bind(A,$thf( sk5 @ sk16 )),bind(B,$thf( powerset @ ( the_carrier @ sk16 ) ))]]) ).
thf(28835,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( in @ ( powerset @ ( the_carrier @ empty_set ) ) @ ( sk5 @ sk16 ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,28053]) ).
thf(28836,plain,
( ~ ( empty @ sk16 )
| ~ ( in @ ( powerset @ ( the_carrier @ empty_set ) ) @ ( sk5 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[28835:[bind(A,$thf( sk16 ))]]) ).
thf(81335,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( the_carrier @ sk1 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,16654]) ).
thf(81356,plain,
( ( sk1 != empty_set )
| ( ( the_carrier @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[81335]) ).
thf(82491,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ sk1 )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81356]) ).
thf(82492,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ sk1 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[82491:[bind(A,$thf( sk1 ))]]) ).
thf(29,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(131,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(132,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk13 @ A ) @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(1881,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( lower_bounded_relstr @ empty_set )
| ( B != empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,679]) ).
thf(1882,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( lower_bounded_relstr @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1881:[bind(A,$thf( sk1 ))]]) ).
thf(2291,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( lower_bounded_relstr @ empty_set ) ),
inference(simp,[status(thm)],[1882]) ).
thf(41687,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( lower_bounded_relstr @ empty_set ) ),
inference(rewrite,[status(thm)],[2291,1508]) ).
thf(41688,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( lower_bounded_relstr @ empty_set ) ),
inference(simp,[status(thm)],[41687]) ).
thf(41803,plain,
! [A: $i] :
( ( lower_bounded_relstr @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41688,10568]) ).
thf(41848,plain,
! [A: $i] :
( ( lower_bounded_relstr @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[41803]) ).
thf(41882,plain,
( ( lower_bounded_relstr @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[41848]) ).
thf(1525,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( finite @ ( the_carrier @ empty_set ) )
| ( finite @ sk2 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,1233]) ).
thf(1526,plain,
( ~ ( empty @ sk1 )
| ~ ( finite @ ( the_carrier @ empty_set ) )
| ( finite @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1525:[bind(A,$thf( sk1 ))]]) ).
thf(74055,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk11 != empty_set )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,54308]) ).
thf(74123,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk11 != empty_set )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[74055]) ).
thf(1985,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( rel_str @ empty_set )
| ( A != empty_set )
| ( B != sk11 ) ),
inference(paramod_ordered,[status(thm)],[115,939]) ).
thf(1986,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk11 @ A ) @ A )
| ( in @ ( sk10 @ sk11 @ A ) @ sk11 )
| ( rel_str @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1985:[bind(A,$thf( A )),bind(B,$thf( sk11 ))]]) ).
thf(2328,plain,
( ( in @ ( sk9 @ sk11 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
| ( rel_str @ empty_set ) ),
inference(simp,[status(thm)],[1986]) ).
thf(47424,plain,
( $false
| ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
| ( rel_str @ empty_set ) ),
inference(rewrite,[status(thm)],[2328,1508]) ).
thf(47425,plain,
( ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
| ( rel_str @ empty_set ) ),
inference(simp,[status(thm)],[47424]) ).
thf(47502,plain,
! [B: $i,A: $i] :
( ( rel_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[47425,91]) ).
thf(47503,plain,
( ( rel_str @ empty_set )
| ( element @ ( sk10 @ sk11 @ empty_set ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[47502:[bind(A,$thf( sk10 @ sk11 @ empty_set )),bind(B,$thf( sk11 ))]]) ).
thf(22485,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( proper_element @ B @ ( powerset @ A ) )
| ( ( element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( element @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[22387,150]) ).
thf(22486,plain,
( ( ( sk5 @ sk1 )
= ( the_carrier @ sk1 ) )
| ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[22485:[bind(A,$thf( the_carrier @ sk1 )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(94608,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( element @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22486,93724]) ).
thf(94609,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( element @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[94608:[]]) ).
thf(27108,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( empty @ ( sk5 @ sk1 ) )
!= ( empty @ ( the_carrier @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[24725,15913]) ).
thf(27174,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( sk5 @ sk1 )
!= ( the_carrier @ sk11 ) ) ),
inference(simp,[status(thm)],[27108]) ).
thf(14999,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( one_sorted_str @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,14663]) ).
thf(15000,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( A != empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[14999:[bind(A,$thf( sk1 ))]]) ).
thf(15056,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[15000]) ).
thf(54518,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( one_sorted_str @ empty_set ) ),
inference(rewrite,[status(thm)],[15056,1508]) ).
thf(54519,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[54518]) ).
thf(54598,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54519,91]) ).
thf(54599,plain,
( ( one_sorted_str @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[54598:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(90441,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( the_carrier @ sk16 ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[13586,90399]) ).
thf(90442,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( the_carrier @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[90441:[]]) ).
thf(54825,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ sk11 )
!= ( the_carrier @ sk1 ) )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,27161]) ).
thf(54826,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( ( the_carrier @ sk11 )
!= ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[54825:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(44,plain,
transitive_relstr @ sk1,
inference(cnf,[status(esa)],[42]) ).
thf(258,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( transitive_relstr @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,44]) ).
thf(259,plain,
( ~ ( empty @ sk1 )
| ( transitive_relstr @ empty_set ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( sk1 ))]]) ).
thf(687,plain,
( ( transitive_relstr @ empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,259]) ).
thf(688,plain,
( ( transitive_relstr @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[687]) ).
thf(2049,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( transitive_relstr @ empty_set )
| ( A != empty_set )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,688]) ).
thf(2050,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( transitive_relstr @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2049:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(2164,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( transitive_relstr @ empty_set ) ),
inference(simp,[status(thm)],[2050]) ).
thf(31573,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( transitive_relstr @ empty_set ) ),
inference(rewrite,[status(thm)],[2164,1508]) ).
thf(31574,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( transitive_relstr @ empty_set ) ),
inference(simp,[status(thm)],[31573]) ).
thf(31628,plain,
! [B: $i,A: $i] :
( ( transitive_relstr @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31574,144]) ).
thf(31629,plain,
( ( transitive_relstr @ empty_set )
| ~ ( in @ sk1 @ ( sk10 @ sk1 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[31628:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(19672,plain,
! [A: $i] :
( ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[19588,10568]) ).
thf(19697,plain,
! [A: $i] :
( ( ( bottom_of_relstr @ sk1 )
!= A )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[19672]) ).
thf(19728,plain,
( ( bottom_of_relstr @ sk1 )
!= sk2 ),
inference(simp,[status(thm)],[19697]) ).
thf(19742,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != sk2 )
| ( B
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[115,19728]) ).
thf(19743,plain,
! [A: $i] :
( ( in @ ( sk9 @ ( bottom_of_relstr @ sk1 ) @ A ) @ A )
| ( in @ ( sk10 @ ( bottom_of_relstr @ sk1 ) @ A ) @ ( bottom_of_relstr @ sk1 ) )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[19742:[bind(A,$thf( A )),bind(B,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(19792,plain,
( ( in @ ( sk9 @ ( bottom_of_relstr @ sk1 ) @ sk2 ) @ sk2 )
| ( in @ ( sk10 @ ( bottom_of_relstr @ sk1 ) @ sk2 ) @ ( bottom_of_relstr @ sk1 ) ) ),
inference(simp,[status(thm)],[19743]) ).
thf(102374,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ ( bottom_of_relstr @ sk1 ) @ sk2 ) @ sk2 )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ ( bottom_of_relstr @ sk1 ) @ sk2 ) @ ( bottom_of_relstr @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19792,91]) ).
thf(102375,plain,
( ( in @ ( sk9 @ ( bottom_of_relstr @ sk1 ) @ sk2 ) @ sk2 )
| ( element @ ( sk10 @ ( bottom_of_relstr @ sk1 ) @ sk2 ) @ ( bottom_of_relstr @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[102374:[bind(A,$thf( sk10 @ ( bottom_of_relstr @ sk1 ) @ sk2 )),bind(B,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(81025,plain,
( ( sk1 != empty_set )
| ( ( the_carrier @ sk11 )
!= ( the_carrier @ sk1 ) )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,54826]) ).
thf(81355,plain,
( ( sk1 != empty_set )
| ( sk11 != sk1 )
| ( ( the_carrier @ sk11 )
!= sk1 ) ),
inference(simp,[status(thm)],[81025]) ).
thf(95547,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[95454,144]) ).
thf(95548,plain,
~ ( in @ ( the_carrier @ sk1 ) @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[95547:[bind(A,$thf( sk9 @ empty_set @ ( the_carrier @ sk1 ) )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(133,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( sk13 @ A ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(22420,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( element @ A @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[22387,70]) ).
thf(22421,plain,
subset @ ( sk5 @ sk1 ) @ ( the_carrier @ sk1 ),
inference(pattern_uni,[status(thm)],[22420:[bind(A,$thf( sk5 @ sk1 )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(56550,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56492,144]) ).
thf(56551,plain,
( ( one_sorted_str @ empty_set )
| ~ ( in @ sk1 @ ( sk10 @ sk1 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[56550:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(19355,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( bottom_of_relstr @ empty_set ) @ sk2 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,19227]) ).
thf(19356,plain,
( ~ ( empty @ sk1 )
| ( element @ ( bottom_of_relstr @ empty_set ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[19355:[bind(A,$thf( sk1 ))]]) ).
thf(24955,plain,
( ( element @ ( bottom_of_relstr @ empty_set ) @ sk2 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19356]) ).
thf(25042,plain,
( ( element @ ( bottom_of_relstr @ empty_set ) @ sk2 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[24955]) ).
thf(19693,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[19588,10522]) ).
thf(19698,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[19693]) ).
thf(19729,plain,
( ( bottom_of_relstr @ sk1 )
!= ( powerset @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[19698]) ).
thf(18953,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) )
| ( ( rel_str @ empty_set )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[910,165]) ).
thf(18954,plain,
( ( sk1 != empty_set )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[18953:[bind(A,$thf( empty_set ))]]) ).
thf(81157,plain,
( ( sk1 != empty_set )
| ~ ( empty @ sk11 )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,55079]) ).
thf(81454,plain,
( ( sk1 != empty_set )
| ~ ( empty @ sk11 )
| ( ( the_carrier @ sk11 )
!= sk1 ) ),
inference(simp,[status(thm)],[81157]) ).
thf(87743,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[87619,91]) ).
thf(87744,plain,
element @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ),
inference(pattern_uni,[status(thm)],[87743:[bind(A,$thf( sk10 @ ( the_carrier @ sk16 ) @ empty_set )),bind(B,$thf( the_carrier @ sk16 ))]]) ).
thf(25558,plain,
! [A: $i] :
( ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[25449,10568]) ).
thf(25598,plain,
! [A: $i] :
( ( ( bottom_of_relstr @ sk1 )
!= A )
| ( ( the_carrier @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[25558]) ).
thf(25636,plain,
( ( bottom_of_relstr @ sk1 )
!= ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[25598]) ).
thf(35679,plain,
! [B: $i,A: $i] :
( ( sk16 != empty_set )
| ( element @ A @ ( powerset @ B ) )
| ( ( subset @ ( sk5 @ sk16 ) @ ( the_carrier @ empty_set ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9604,71]) ).
thf(35680,plain,
( ( sk16 != empty_set )
| ( element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[35679:[bind(A,$thf( sk5 @ sk16 )),bind(B,$thf( the_carrier @ empty_set ))]]) ).
thf(10634,plain,
( ( in @ ( sk9 @ empty_set @ sk2 ) @ sk2 )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[10253,10522]) ).
thf(10677,plain,
( ( ( sk9 @ empty_set @ sk2 )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[10634]) ).
thf(10693,plain,
( ( sk9 @ empty_set @ sk2 )
!= ( powerset @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[10677]) ).
thf(29756,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ sk11 )
!= sk6 )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,27187]) ).
thf(29757,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( ( the_carrier @ sk11 )
!= sk6 ) ),
inference(pattern_uni,[status(thm)],[29756:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( in @ A @ sk2 )
| ~ ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( B
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[64,46]) ).
thf(346,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( in @ A @ sk2 )
| ~ ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[345:[bind(A,$thf( A )),bind(B,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(31359,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( in @ A @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[346,19590]) ).
thf(31360,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[31359]) ).
thf(102,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[100]) ).
thf(23885,plain,
( ( in @ empty_set @ sk2 )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,23830]) ).
thf(23970,plain,
( ( in @ empty_set @ sk2 )
| ( ( bottom_of_relstr @ sk1 )
!= empty_set ) ),
inference(simp,[status(thm)],[23885]) ).
thf(81485,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( finite @ sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81306]) ).
thf(81486,plain,
( ~ ( empty @ sk1 )
| ( finite @ sk1 ) ),
inference(pattern_uni,[status(thm)],[81485:[bind(A,$thf( sk1 ))]]) ).
thf(84991,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( ( in @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( in @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[3863,81042]) ).
thf(85147,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( sk2 != A )
| ( ( powerset @ ( the_carrier @ sk1 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[84991]) ).
thf(85222,plain,
( ( sk1 != empty_set )
| ( ( powerset @ ( the_carrier @ sk1 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[85147]) ).
thf(85366,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( powerset @ ( the_carrier @ sk1 ) )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,85222]) ).
thf(85367,plain,
( ~ ( empty @ sk1 )
| ( ( powerset @ ( the_carrier @ sk1 ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[85366:[bind(A,$thf( sk1 ))]]) ).
thf(160,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( rel_str @ A )
| ( upper_relstr_subset @ ( sk17 @ A ) @ A ) ),
inference(cnf,[status(esa)],[156]) ).
thf(90594,plain,
! [A: $i] :
( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( sk5 @ sk16 ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[90399,10568]) ).
thf(90677,plain,
! [A: $i] :
( ( ( sk9 @ empty_set @ ( sk5 @ sk16 ) )
!= A )
| ( ( sk5 @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[90594]) ).
thf(90702,plain,
( ( sk9 @ empty_set @ ( sk5 @ sk16 ) )
!= ( sk5 @ sk16 ) ),
inference(simp,[status(thm)],[90677]) ).
thf(34047,plain,
! [B: $i,A: $i] :
( ( reflexive_relstr @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33993,144]) ).
thf(34048,plain,
( ( reflexive_relstr @ empty_set )
| ~ ( in @ sk1 @ ( sk10 @ sk1 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[34047:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(1481,plain,
( ~ ( empty @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,1415]) ).
thf(1487,plain,
( ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[1481]) ).
thf(10317,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk2 ) @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10253,91]) ).
thf(10318,plain,
element @ ( sk9 @ empty_set @ sk2 ) @ sk2,
inference(pattern_uni,[status(thm)],[10317:[bind(A,$thf( sk9 @ empty_set @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(10393,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ sk2 )
| ( A
!= ( sk9 @ empty_set @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[120,10318]) ).
thf(10394,plain,
( ~ ( empty @ ( sk9 @ empty_set @ sk2 ) )
| ( element @ empty_set @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10393:[bind(A,$thf( sk9 @ empty_set @ sk2 ))]]) ).
thf(19809,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( in @ sk2 @ ( bottom_of_relstr @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,19627]) ).
thf(19810,plain,
( ~ ( empty @ sk1 )
| ~ ( in @ sk2 @ ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[19809:[bind(A,$thf( sk1 ))]]) ).
thf(32571,plain,
( ~ ( empty @ sk1 )
| ( ( in @ sk2 @ ( bottom_of_relstr @ empty_set ) )
!= ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3869,19810]) ).
thf(32624,plain,
( ~ ( empty @ sk1 )
| ( sk2 != sk2 )
| ( ( bottom_of_relstr @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[32571]) ).
thf(32677,plain,
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[32624]) ).
thf(56279,plain,
( ( ( bottom_of_relstr @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,32677]) ).
thf(56340,plain,
( ( ( bottom_of_relstr @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[56279]) ).
thf(107544,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk1 )
| ( ( the_carrier @ sk11 )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81355]) ).
thf(107545,plain,
( ~ ( empty @ sk1 )
| ( sk11 != sk1 )
| ( ( the_carrier @ sk11 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[107544:[bind(A,$thf( sk1 ))]]) ).
thf(12940,plain,
! [B: $i,A: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( proper_element @ B @ ( powerset @ A ) )
| ( A != empty_set )
| ( B != sk8 ) ),
inference(paramod_ordered,[status(thm)],[150,187]) ).
thf(12941,plain,
! [A: $i] :
( ~ ( element @ sk8 @ ( powerset @ A ) )
| ( proper_element @ sk8 @ ( powerset @ A ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[12940:[bind(A,$thf( A )),bind(B,$thf( sk8 ))]]) ).
thf(13850,plain,
( ~ ( element @ sk8 @ ( powerset @ empty_set ) )
| ( proper_element @ sk8 @ ( powerset @ empty_set ) ) ),
inference(simp,[status(thm)],[12941]) ).
thf(22571,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,22421]) ).
thf(22572,plain,
( ~ ( empty @ sk1 )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[22571:[bind(A,$thf( sk1 ))]]) ).
thf(50561,plain,
( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,22572]) ).
thf(50646,plain,
( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[50561]) ).
thf(25713,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( in @ ( the_carrier @ empty_set ) @ ( bottom_of_relstr @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,25499]) ).
thf(25714,plain,
( ~ ( empty @ sk1 )
| ~ ( in @ ( the_carrier @ empty_set ) @ ( bottom_of_relstr @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25713:[bind(A,$thf( sk1 ))]]) ).
thf(52953,plain,
( ~ ( in @ ( the_carrier @ empty_set ) @ ( bottom_of_relstr @ sk1 ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,25714]) ).
thf(53104,plain,
( ~ ( in @ ( the_carrier @ empty_set ) @ ( bottom_of_relstr @ sk1 ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[52953]) ).
thf(11911,plain,
( ( in @ ( sk10 @ sk2 @ empty_set ) @ sk2 )
!= ( in @ sk2 @ ( sk10 @ sk2 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[11728,11776]) ).
thf(11988,plain,
( ( ( sk10 @ sk2 @ empty_set )
!= sk2 )
| ( ( sk10 @ sk2 @ empty_set )
!= sk2 ) ),
inference(simp,[status(thm)],[11911]) ).
thf(12012,plain,
( ( sk10 @ sk2 @ empty_set )
!= sk2 ),
inference(simp,[status(thm)],[11988]) ).
thf(47062,plain,
( ( sk11 != empty_set )
| ( ( bottom_of_relstr @ empty_set )
!= sk2 )
| ( ( bottom_of_relstr @ sk11 )
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46994,19728]) ).
thf(47146,plain,
( ( sk11 != empty_set )
| ( ( bottom_of_relstr @ empty_set )
!= sk2 )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[47062]) ).
thf(17413,plain,
( ~ ( empty @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,16658]) ).
thf(17467,plain,
( ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[17413]) ).
thf(54970,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk1 != empty_set )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,54824]) ).
thf(54971,plain,
( ~ ( empty @ sk11 )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk1 != empty_set ) ),
inference(pattern_uni,[status(thm)],[54970:[bind(A,$thf( sk11 ))]]) ).
thf(45881,plain,
! [A: $i] :
( ( rel_str @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45766,10568]) ).
thf(45926,plain,
! [A: $i] :
( ( rel_str @ empty_set )
| ( ( sk9 @ empty_set @ sk11 )
!= A )
| ( sk11 != A ) ),
inference(simp,[status(thm)],[45881]) ).
thf(45956,plain,
( ( rel_str @ empty_set )
| ( ( sk9 @ empty_set @ sk11 )
!= sk11 ) ),
inference(simp,[status(thm)],[45926]) ).
thf(6,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(65,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19353,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ sk2 )
| ( A
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[120,19227]) ).
thf(19354,plain,
( ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( element @ empty_set @ sk2 ) ),
inference(pattern_uni,[status(thm)],[19353:[bind(A,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(24779,plain,
( ( element @ empty_set @ sk2 )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19354]) ).
thf(24858,plain,
( ( element @ empty_set @ sk2 )
| ( ( bottom_of_relstr @ sk1 )
!= empty_set ) ),
inference(simp,[status(thm)],[24779]) ).
thf(25450,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ empty_set @ ( the_carrier @ sk1 ) )
| ( A
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[120,25449]) ).
thf(25451,plain,
( ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( in @ empty_set @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25450:[bind(A,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(51509,plain,
( ( in @ empty_set @ ( the_carrier @ sk1 ) )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,25451]) ).
thf(51640,plain,
( ( in @ empty_set @ ( the_carrier @ sk1 ) )
| ( ( bottom_of_relstr @ sk1 )
!= empty_set ) ),
inference(simp,[status(thm)],[51509]) ).
thf(2045,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( transitive_relstr @ empty_set )
| ( B != empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,688]) ).
thf(2046,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( transitive_relstr @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2045:[bind(A,$thf( sk1 ))]]) ).
thf(2350,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( transitive_relstr @ empty_set ) ),
inference(simp,[status(thm)],[2046]) ).
thf(51132,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( transitive_relstr @ empty_set ) ),
inference(rewrite,[status(thm)],[2350,1508]) ).
thf(51133,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( transitive_relstr @ empty_set ) ),
inference(simp,[status(thm)],[51132]) ).
thf(51210,plain,
! [B: $i,A: $i] :
( ( transitive_relstr @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51133,91]) ).
thf(51211,plain,
( ( transitive_relstr @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[51210:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2842,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( sk5 @ empty_set )
!= empty_set )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,2835]) ).
thf(2843,plain,
( ~ ( empty @ sk16 )
| ( ( sk5 @ empty_set )
!= empty_set ) ),
inference(pattern_uni,[status(thm)],[2842:[bind(A,$thf( sk16 ))]]) ).
thf(3049,plain,
( ( ( sk5 @ empty_set )
!= empty_set )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,2843]) ).
thf(3050,plain,
( ( ( sk5 @ empty_set )
!= empty_set )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[3049]) ).
thf(16039,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( sk5 @ empty_set )
!= empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,15967]) ).
thf(16040,plain,
( ~ ( empty @ sk1 )
| ( ( sk5 @ empty_set )
!= empty_set ) ),
inference(pattern_uni,[status(thm)],[16039:[bind(A,$thf( sk1 ))]]) ).
thf(77494,plain,
( ~ ( empty @ sk11 )
| ( sk11 != sk1 )
| ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[55077]) ).
thf(77500,plain,
( ~ ( empty @ sk11 )
| ( sk11 != sk1 )
| ( ( the_carrier @ empty_set )
!= sk11 ) ),
inference(simp,[status(thm)],[77494]) ).
thf(101487,plain,
( ( sk11 != sk1 )
| ( ( the_carrier @ empty_set )
!= sk11 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,77500]) ).
thf(101553,plain,
( ( sk11 != sk1 )
| ( ( the_carrier @ empty_set )
!= sk11 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[101487]) ).
thf(25639,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( bottom_of_relstr @ empty_set )
!= ( the_carrier @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,25636]) ).
thf(25640,plain,
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ empty_set )
!= ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25639:[bind(A,$thf( sk1 ))]]) ).
thf(63579,plain,
! [A: $i] :
( ( empty_carrier @ sk11 )
| ( ( in @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[63427,10568]) ).
thf(63642,plain,
! [A: $i] :
( ( empty_carrier @ sk11 )
| ( ( sk5 @ sk11 )
!= A )
| ( ( powerset @ ( the_carrier @ sk11 ) )
!= A ) ),
inference(simp,[status(thm)],[63579]) ).
thf(63677,plain,
( ( empty_carrier @ sk11 )
| ( ( sk5 @ sk11 )
!= ( powerset @ ( the_carrier @ sk11 ) ) ) ),
inference(simp,[status(thm)],[63642]) ).
thf(10579,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( in @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,10522]) ).
thf(10580,plain,
( ~ ( empty @ sk1 )
| ~ ( in @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10579:[bind(A,$thf( sk1 ))]]) ).
thf(2037,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( one_sorted_str @ empty_set )
| ( A != empty_set )
| ( B != sk16 ) ),
inference(paramod_ordered,[status(thm)],[115,876]) ).
thf(2038,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk16 @ A ) @ A )
| ( in @ ( sk10 @ sk16 @ A ) @ sk16 )
| ( one_sorted_str @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2037:[bind(A,$thf( A )),bind(B,$thf( sk16 ))]]) ).
thf(2347,plain,
( ( in @ ( sk9 @ sk16 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk16 @ empty_set ) @ sk16 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[2038]) ).
thf(50199,plain,
( $false
| ( in @ ( sk10 @ sk16 @ empty_set ) @ sk16 )
| ( one_sorted_str @ empty_set ) ),
inference(rewrite,[status(thm)],[2347,1508]) ).
thf(50200,plain,
( ( in @ ( sk10 @ sk16 @ empty_set ) @ sk16 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[50199]) ).
thf(50315,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( in @ ( sk10 @ sk16 @ empty_set ) @ sk16 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[50200,10568]) ).
thf(50344,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( sk10 @ sk16 @ empty_set )
!= A )
| ( sk16 != A ) ),
inference(simp,[status(thm)],[50315]) ).
thf(50377,plain,
( ( one_sorted_str @ empty_set )
| ( ( sk10 @ sk16 @ empty_set )
!= sk16 ) ),
inference(simp,[status(thm)],[50344]) ).
thf(11796,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk10 @ sk2 @ empty_set ) @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11728,91]) ).
thf(11797,plain,
element @ ( sk10 @ sk2 @ empty_set ) @ sk2,
inference(pattern_uni,[status(thm)],[11796:[bind(A,$thf( sk10 @ sk2 @ empty_set )),bind(B,$thf( sk2 ))]]) ).
thf(14504,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ sk2 )
| ( A
!= ( sk10 @ sk2 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[120,11797]) ).
thf(14505,plain,
( ~ ( empty @ ( sk10 @ sk2 @ empty_set ) )
| ( element @ empty_set @ sk2 ) ),
inference(pattern_uni,[status(thm)],[14504:[bind(A,$thf( sk10 @ sk2 @ empty_set ))]]) ).
thf(1537,plain,
( ( finite @ sk2 )
| ( ( finite @ ( the_carrier @ sk1 ) )
!= ( finite @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[104,1233]) ).
thf(1540,plain,
( ( finite @ sk2 )
| ( ( the_carrier @ sk1 )
!= sk8 ) ),
inference(simp,[status(thm)],[1537]) ).
thf(89031,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[13586,88991]) ).
thf(89032,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[89031:[]]) ).
thf(10671,plain,
( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3379,10522]) ).
thf(10678,plain,
( ( ( sk9 @ empty_set @ sk6 )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[10671]) ).
thf(10670,plain,
( ( in @ ( sk10 @ sk6 @ empty_set ) @ sk6 )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[5304,10522]) ).
thf(10676,plain,
( ( ( sk10 @ sk6 @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[10670]) ).
thf(38956,plain,
! [B: $i,A: $i] :
( ( antisymmetric_relstr @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38901,144]) ).
thf(38957,plain,
( ( antisymmetric_relstr @ empty_set )
| ~ ( in @ sk1 @ ( sk10 @ sk1 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[38956:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(8894,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ sk8 )
| ( A
!= ( sk9 @ empty_set @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[120,8816]) ).
thf(8895,plain,
( ~ ( empty @ ( sk9 @ empty_set @ sk8 ) )
| ( element @ empty_set @ sk8 ) ),
inference(pattern_uni,[status(thm)],[8894:[bind(A,$thf( sk9 @ empty_set @ sk8 ))]]) ).
thf(52917,plain,
( ~ ( empty @ sk1 )
| ~ ( in @ ( the_carrier @ empty_set ) @ ( bottom_of_relstr @ empty_set ) )
| ( ( bottom_of_relstr @ sk1 )
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46241,25714]) ).
thf(52918,plain,
( ~ ( empty @ sk1 )
| ~ ( in @ ( the_carrier @ empty_set ) @ ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[52917:[]]) ).
thf(696,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( element @ A @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[47,70]) ).
thf(697,plain,
subset @ sk2 @ ( the_carrier @ sk1 ),
inference(pattern_uni,[status(thm)],[696:[bind(A,$thf( sk2 )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(1847,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( A
!= ( the_carrier @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[115,1425]) ).
thf(1848,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ ( the_carrier @ sk16 ) ) @ ( the_carrier @ sk16 ) )
| ( in @ ( sk10 @ A @ ( the_carrier @ sk16 ) ) @ A )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1847:[bind(A,$thf( the_carrier @ sk16 )),bind(B,$thf( B ))]]) ).
thf(2278,plain,
( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( the_carrier @ sk16 ) )
| ( in @ ( sk10 @ empty_set @ ( the_carrier @ sk16 ) ) @ empty_set ) ),
inference(simp,[status(thm)],[1848]) ).
thf(79297,plain,
( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( the_carrier @ sk16 ) )
| $false ),
inference(rewrite,[status(thm)],[2278,1508]) ).
thf(79298,plain,
in @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( the_carrier @ sk16 ),
inference(simp,[status(thm)],[79297]) ).
thf(79479,plain,
! [A: $i] :
( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( the_carrier @ sk16 ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[79298,10568]) ).
thf(79564,plain,
! [A: $i] :
( ( ( sk9 @ empty_set @ ( the_carrier @ sk16 ) )
!= A )
| ( ( the_carrier @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[79479]) ).
thf(79603,plain,
( ( sk9 @ empty_set @ ( the_carrier @ sk16 ) )
!= ( the_carrier @ sk16 ) ),
inference(simp,[status(thm)],[79564]) ).
thf(32523,plain,
( ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,3869]) ).
thf(32630,plain,
( ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[32523]) ).
thf(85107,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) )
!= ( in @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[32630,81042]) ).
thf(85169,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( sk2 != A )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= sk1 ) ),
inference(simp,[status(thm)],[85107]) ).
thf(85244,plain,
( ( sk1 != empty_set )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= sk1 ) ),
inference(simp,[status(thm)],[85169]) ).
thf(93428,plain,
! [B: $i,A: $i] :
( ( sk1 != empty_set )
| ( subset @ A @ B )
| ( ( empty @ sk1 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79732,730]) ).
thf(93429,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( subset @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[93428:[bind(A,$thf( sk1 ))]]) ).
thf(93438,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( subset @ sk1 @ A ) ),
inference(simp,[status(thm)],[93429]) ).
thf(98613,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( subset @ sk1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,93438]) ).
thf(98614,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( subset @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[98613:[bind(A,$thf( sk1 ))]]) ).
thf(98688,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( subset @ sk1 @ A ) ),
inference(simp,[status(thm)],[98614]) ).
thf(98716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ sk1 )
| ( element @ B @ ( powerset @ C ) )
| ( ( subset @ sk1 @ A )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[98688,71]) ).
thf(98717,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( element @ sk1 @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[98716:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(78247,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk1 )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[55178]) ).
thf(78260,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk1 )
| ( ( the_carrier @ sk11 )
!= sk11 ) ),
inference(simp,[status(thm)],[78247]) ).
thf(32620,plain,
( ~ ( empty @ sk1 )
| ( ( in @ sk2 @ ( sk10 @ sk2 @ empty_set ) )
!= ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3869,11776]) ).
thf(32638,plain,
( ~ ( empty @ sk1 )
| ( sk2 != sk2 )
| ( ( sk10 @ sk2 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[32620]) ).
thf(32689,plain,
( ~ ( empty @ sk1 )
| ( ( sk10 @ sk2 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[32638]) ).
thf(13213,plain,
! [B: $i,A: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( proper_element @ B @ ( powerset @ A ) )
| ( A != empty_set )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[150,182]) ).
thf(13214,plain,
! [A: $i] :
( ~ ( element @ sk2 @ ( powerset @ A ) )
| ( proper_element @ sk2 @ ( powerset @ A ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[13213:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(13939,plain,
( ~ ( element @ sk2 @ ( powerset @ empty_set ) )
| ( proper_element @ sk2 @ ( powerset @ empty_set ) ) ),
inference(simp,[status(thm)],[13214]) ).
thf(3512,plain,
! [B: $i,A: $i] :
( ( empty_carrier @ sk3 )
| ( empty @ B )
| ( in @ A @ B )
| ( ( element @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) )
!= ( element @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2439,99]) ).
thf(3513,plain,
( ( empty_carrier @ sk3 )
| ( empty @ ( powerset @ ( the_carrier @ sk3 ) ) )
| ( in @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[3512:[bind(A,$thf( sk5 @ sk3 )),bind(B,$thf( powerset @ ( the_carrier @ sk3 ) ))]]) ).
thf(53152,plain,
( ( empty_carrier @ sk3 )
| $false
| ( in @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) ) ),
inference(rewrite,[status(thm)],[3513,153]) ).
thf(53153,plain,
( ( empty_carrier @ sk3 )
| ( in @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) ) ),
inference(simp,[status(thm)],[53152]) ).
thf(48952,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk16 ) @ sk16 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[48875,91]) ).
thf(48953,plain,
( ( one_sorted_str @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk16 ) @ sk16 ) ),
inference(pattern_uni,[status(thm)],[48952:[bind(A,$thf( sk9 @ empty_set @ sk16 )),bind(B,$thf( sk16 ))]]) ).
thf(126338,plain,
( ( sk1 != empty_set )
| ( ( sk5 @ sk1 )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( ( empty @ sk1 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,126014]) ).
thf(126339,plain,
( ( sk1 != empty_set )
| ( ( sk5 @ sk1 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[126338:[]]) ).
thf(45843,plain,
! [B: $i,A: $i] :
( ( rel_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45766,91]) ).
thf(45844,plain,
( ( rel_str @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk11 ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[45843:[bind(A,$thf( sk9 @ empty_set @ sk11 )),bind(B,$thf( sk11 ))]]) ).
thf(79387,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( the_carrier @ sk16 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[79298,144]) ).
thf(79388,plain,
~ ( in @ ( the_carrier @ sk16 ) @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[79387:[bind(A,$thf( sk9 @ empty_set @ ( the_carrier @ sk16 ) )),bind(B,$thf( the_carrier @ sk16 ))]]) ).
thf(99614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ ( join_on_relstr @ sk1 @ A ) @ ( the_carrier @ sk1 ) )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[99535,144]) ).
thf(99615,plain,
! [A: $i] :
~ ( in @ ( the_carrier @ sk1 ) @ ( join_on_relstr @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[99614:[bind(A,$thf( E )),bind(B,$thf( join_on_relstr @ sk1 @ E )),bind(C,$thf( the_carrier @ sk1 ))]]) ).
thf(99809,plain,
! [A: $i] :
~ ( in @ ( the_carrier @ sk1 ) @ ( join_on_relstr @ sk1 @ A ) ),
inference(simp,[status(thm)],[99615]) ).
thf(1787,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( upper_relstr_subset @ sk2 @ empty_set )
| ( A != empty_set )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,1351]) ).
thf(1788,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( upper_relstr_subset @ sk2 @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1787:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(2259,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( upper_relstr_subset @ sk2 @ empty_set ) ),
inference(simp,[status(thm)],[1788]) ).
thf(77126,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( upper_relstr_subset @ sk2 @ empty_set ) ),
inference(rewrite,[status(thm)],[2259,1508]) ).
thf(77127,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( upper_relstr_subset @ sk2 @ empty_set ) ),
inference(simp,[status(thm)],[77126]) ).
thf(77263,plain,
! [A: $i] :
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[77127,10568]) ).
thf(77333,plain,
! [A: $i] :
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[77263]) ).
thf(77346,plain,
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[77333]) ).
thf(19202,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,19005]) ).
thf(19203,plain,
( ~ ( empty @ sk1 )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[19202:[bind(A,$thf( sk1 ))]]) ).
thf(254,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty_carrier @ empty_set )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,141]) ).
thf(255,plain,
( ~ ( empty @ sk16 )
| ~ ( empty_carrier @ empty_set ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$thf( sk16 ))]]) ).
thf(771,plain,
( ~ ( empty_carrier @ empty_set )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,255]) ).
thf(772,plain,
( ~ ( empty_carrier @ empty_set )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[771]) ).
thf(979,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty_carrier @ A )
| ( sk16 != empty_set )
| ( empty_set != empty_set ) ),
inference(paramod_ordered,[status(thm)],[120,772]) ).
thf(980,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty_carrier @ A )
| ( sk16 != empty_set ) ),
inference(pattern_uni,[status(thm)],[979:[]]) ).
thf(1637,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( one_sorted_str @ empty_set )
| ( A != empty_set )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[115,858]) ).
thf(1638,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk3 @ A ) @ A )
| ( in @ ( sk10 @ sk3 @ A ) @ sk3 )
| ( one_sorted_str @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1637:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(2206,plain,
( ( in @ ( sk9 @ sk3 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk3 @ empty_set ) @ sk3 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[1638]) ).
thf(36548,plain,
( $false
| ( in @ ( sk10 @ sk3 @ empty_set ) @ sk3 )
| ( one_sorted_str @ empty_set ) ),
inference(rewrite,[status(thm)],[2206,1508]) ).
thf(36549,plain,
( ( in @ ( sk10 @ sk3 @ empty_set ) @ sk3 )
| ( one_sorted_str @ empty_set ) ),
inference(simp,[status(thm)],[36548]) ).
thf(36663,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( in @ ( sk10 @ sk3 @ empty_set ) @ sk3 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36549,10568]) ).
thf(36709,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( sk10 @ sk3 @ empty_set )
!= A )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[36663]) ).
thf(36738,plain,
( ( one_sorted_str @ empty_set )
| ( ( sk10 @ sk3 @ empty_set )
!= sk3 ) ),
inference(simp,[status(thm)],[36709]) ).
thf(21890,plain,
( ~ ( empty_carrier @ sk11 )
| ( ( v1_yellow_3 @ sk11 )
!= ( v1_yellow_3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[965,21883]) ).
thf(21913,plain,
( ~ ( empty_carrier @ sk11 )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[21890]) ).
thf(22240,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty_carrier @ sk11 )
| ( sk1 != empty_set )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,21913]) ).
thf(22241,plain,
( ~ ( empty @ sk11 )
| ~ ( empty_carrier @ sk11 )
| ( sk1 != empty_set ) ),
inference(pattern_uni,[status(thm)],[22240:[bind(A,$thf( sk11 ))]]) ).
thf(1485,plain,
( ~ ( empty @ sk16 )
| ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk16 ) ) ),
inference(simp,[status(thm)],[1483]) ).
thf(8580,plain,
( ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk16 ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,1485]) ).
thf(8619,plain,
( ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk16 ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[8580]) ).
thf(83538,plain,
! [B: $i,A: $i] :
( ( empty @ sk1 )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[83468,144]) ).
thf(83539,plain,
( ( empty @ sk1 )
| ~ ( in @ sk1 @ ( sk10 @ sk1 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[83538:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(66783,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[45744,97]) ).
thf(67061,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( ( bottom_of_relstr @ sk1 )
!= sk6 ) ),
inference(simp,[status(thm)],[66783]) ).
thf(34107,plain,
! [A: $i] :
( ( reflexive_relstr @ empty_set )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33993,10568]) ).
thf(34147,plain,
! [A: $i] :
( ( reflexive_relstr @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[34107]) ).
thf(34180,plain,
( ( reflexive_relstr @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[34147]) ).
thf(25715,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( in @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,25499]) ).
thf(25716,plain,
( ~ ( empty @ sk1 )
| ~ ( in @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[25715:[bind(A,$thf( sk1 ))]]) ).
thf(54305,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk16 != sk11 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,54162]) ).
thf(54306,plain,
( ~ ( empty @ sk11 )
| ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk16 != sk11 ) ),
inference(pattern_uni,[status(thm)],[54305:[bind(A,$thf( sk11 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( related @ A @ ( bottom_of_relstr @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_yellow_0) ).
thf(76,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( related @ A @ ( bottom_of_relstr @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( empty_carrier @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( lower_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ( related @ A @ ( bottom_of_relstr @ A ) @ B ) ),
inference(cnf,[status(esa)],[76]) ).
thf(24423,plain,
( ~ ( in @ sk2 @ ( bottom_of_relstr @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19810]) ).
thf(24505,plain,
( ~ ( in @ sk2 @ ( bottom_of_relstr @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[24423]) ).
thf(38054,plain,
! [B: $i,A: $i] :
( ( antisymmetric_relstr @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38000,144]) ).
thf(38055,plain,
( ( antisymmetric_relstr @ empty_set )
| ~ ( in @ sk1 @ ( sk9 @ empty_set @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[38054:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(27998,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,27991]) ).
thf(27999,plain,
( ~ ( empty @ sk16 )
| ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[27998:[bind(A,$thf( sk16 ))]]) ).
thf(47005,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( bottom_of_relstr @ sk11 )
= ( bottom_of_relstr @ empty_set ) )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,46994]) ).
thf(47006,plain,
( ~ ( empty @ sk11 )
| ( ( bottom_of_relstr @ sk11 )
= ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[47005:[bind(A,$thf( sk11 ))]]) ).
thf(47283,plain,
( ~ ( empty @ sk11 )
| ( ( bottom_of_relstr @ empty_set )
!= sk2 )
| ( ( bottom_of_relstr @ sk11 )
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[47006,19728]) ).
thf(47383,plain,
( ~ ( empty @ sk11 )
| ( ( bottom_of_relstr @ empty_set )
!= sk2 )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[47283]) ).
thf(100046,plain,
! [A: $i] :
( ~ ( in @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ sk11 ) )
| ( ( join_on_relstr @ sk11 @ empty_set )
!= ( join_on_relstr @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19943,99809]) ).
thf(100212,plain,
! [A: $i] :
( ~ ( in @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ sk11 ) )
| ( sk11 != sk1 )
| ( empty_set != A ) ),
inference(simp,[status(thm)],[100046]) ).
thf(100302,plain,
( ~ ( in @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ sk11 ) )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[100212]) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( subset @ B @ C )
| ( ( element @ ( sk13 @ A ) @ ( powerset @ A ) )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[132,70]) ).
thf(1310,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk13 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[1309:[bind(A,$thf( D )),bind(B,$thf( sk13 @ D )),bind(C,$thf( D ))]]) ).
thf(1329,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk13 @ A ) @ A ) ),
inference(simp,[status(thm)],[1310]) ).
thf(92438,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( sk5 @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[92304,91]) ).
thf(92439,plain,
element @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( sk5 @ sk1 ),
inference(pattern_uni,[status(thm)],[92438:[bind(A,$thf( sk9 @ empty_set @ ( sk5 @ sk1 ) )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(93319,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( element @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( the_carrier @ sk1 ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22486,92439]) ).
thf(93320,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( element @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[93319:[]]) ).
thf(2710,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( empty @ ( sk5 @ A ) )
| ( ( one_sorted_str @ sk3 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58,89]) ).
thf(2711,plain,
( ( empty_carrier @ sk3 )
| ~ ( empty @ ( sk5 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[2710:[bind(A,$thf( sk3 ))]]) ).
thf(81250,plain,
( ( sk1 != empty_set )
| ( empty_carrier @ sk3 )
| ( ( empty @ ( sk5 @ sk3 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,2711]) ).
thf(81437,plain,
( ( empty_carrier @ sk3 )
| ( sk1 != empty_set )
| ( ( sk5 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[81250]) ).
thf(1430,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ empty_set )
!= empty_set )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,1425]) ).
thf(1431,plain,
( ~ ( empty @ sk16 )
| ( ( the_carrier @ empty_set )
!= empty_set ) ),
inference(pattern_uni,[status(thm)],[1430:[bind(A,$thf( sk16 ))]]) ).
thf(1611,plain,
( ( ( the_carrier @ empty_set )
!= empty_set )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,1431]) ).
thf(1612,plain,
( ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[1611]) ).
thf(76516,plain,
( ~ ( empty @ sk11 )
| ( sk16 != sk11 )
| ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[54414]) ).
thf(76522,plain,
( ~ ( empty @ sk11 )
| ( sk16 != sk11 )
| ( ( the_carrier @ empty_set )
!= sk11 ) ),
inference(simp,[status(thm)],[76516]) ).
thf(28747,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( the_carrier @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[13586,27991]) ).
thf(28748,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( the_carrier @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[28747:[]]) ).
thf(50510,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,22572]) ).
thf(50511,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ sk1 )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[50510:[bind(A,$thf( sk1 ))]]) ).
thf(50668,plain,
( ~ ( empty @ sk1 )
| ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(simp,[status(thm)],[50511]) ).
thf(710,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( subset @ sk2 @ ( the_carrier @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,697]) ).
thf(711,plain,
( ~ ( empty @ sk1 )
| ( subset @ sk2 @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[710:[bind(A,$thf( sk1 ))]]) ).
thf(3486,plain,
( ( subset @ sk2 @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,711]) ).
thf(3487,plain,
( ( subset @ sk2 @ ( the_carrier @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[3486]) ).
thf(3759,plain,
! [B: $i,A: $i] :
( ( sk1 != empty_set )
| ( element @ A @ ( powerset @ B ) )
| ( ( subset @ sk2 @ ( the_carrier @ empty_set ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3487,71]) ).
thf(3760,plain,
( ( sk1 != empty_set )
| ( element @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[3759:[bind(A,$thf( sk2 )),bind(B,$thf( the_carrier @ empty_set ))]]) ).
thf(499,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( element @ B @ C )
| ( A
!= ( sk15 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[64,139]) ).
thf(500,plain,
! [B: $i,A: $i] :
( ~ ( empty @ ( sk15 @ B ) )
| ~ ( empty @ A )
| ( element @ A @ B ) ),
inference(pattern_uni,[status(thm)],[499:[bind(A,$thf( sk15 @ D )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(605,plain,
! [B: $i,A: $i] :
( ~ ( empty @ ( sk15 @ B ) )
| ~ ( empty @ A )
| ( element @ A @ B ) ),
inference(simp,[status(thm)],[500]) ).
thf(11120,plain,
( ( in @ ( sk10 @ sk6 @ empty_set ) @ sk6 )
!= ( in @ sk2 @ ( sk9 @ empty_set @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[5304,10546]) ).
thf(11129,plain,
( ( ( sk10 @ sk6 @ empty_set )
!= sk2 )
| ( ( sk9 @ empty_set @ sk2 )
!= sk6 ) ),
inference(simp,[status(thm)],[11120]) ).
thf(19738,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != sk2 )
| ( A
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[115,19728]) ).
thf(19739,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ ( bottom_of_relstr @ sk1 ) ) @ ( bottom_of_relstr @ sk1 ) )
| ( in @ ( sk10 @ A @ ( bottom_of_relstr @ sk1 ) ) @ A )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[19738:[bind(A,$thf( bottom_of_relstr @ sk1 )),bind(B,$thf( B ))]]) ).
thf(19790,plain,
( ( in @ ( sk9 @ sk2 @ ( bottom_of_relstr @ sk1 ) ) @ ( bottom_of_relstr @ sk1 ) )
| ( in @ ( sk10 @ sk2 @ ( bottom_of_relstr @ sk1 ) ) @ sk2 ) ),
inference(simp,[status(thm)],[19739]) ).
thf(77426,plain,
( ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk11 != sk1 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,55077]) ).
thf(77497,plain,
( ~ ( empty @ ( the_carrier @ empty_set ) )
| ( sk11 != sk1 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[77426]) ).
thf(20684,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( bottom_of_relstr @ sk1 )
= empty_set )
| ( A
!= ( join_on_relstr @ sk1 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[120,19993]) ).
thf(20685,plain,
( ~ ( empty @ ( join_on_relstr @ sk1 @ empty_set ) )
| ( ( bottom_of_relstr @ sk1 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[20684:[bind(A,$thf( join_on_relstr @ sk1 @ empty_set ))]]) ).
thf(49180,plain,
( ~ ( empty @ ( bottom_of_relstr @ sk1 ) )
| ( ( bottom_of_relstr @ sk1 )
= empty_set ) ),
inference(rewrite,[status(thm)],[20685,19993]) ).
thf(1455,plain,
( ( empty_carrier @ sk3 )
| ( ( empty @ ( the_carrier @ sk3 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,925]) ).
thf(1456,plain,
( ( empty_carrier @ sk3 )
| ( ( the_carrier @ sk3 )
!= empty_set ) ),
inference(simp,[status(thm)],[1455]) ).
thf(54636,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[54519,10568]) ).
thf(54663,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[54636]) ).
thf(54691,plain,
( ( one_sorted_str @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[54663]) ).
thf(39262,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( element @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,39253]) ).
thf(39263,plain,
( ~ ( empty @ sk1 )
| ~ ( element @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[39262:[bind(A,$thf( sk1 ))]]) ).
thf(61478,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( element @ ( sk15 @ A ) @ A )
!= ( element @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[139,39263]) ).
thf(61564,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( sk15 @ A )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[61478]) ).
thf(61597,plain,
( ~ ( empty @ sk1 )
| ( ( sk15 @ sk2 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[61564]) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( rel_str @ A )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( upper_relstr_subset @ B @ A )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ C @ B )
| ~ ( related @ A @ C @ D )
| ( in @ D @ B ) ),
inference(cnf,[status(esa)],[169]) ).
thf(84829,plain,
! [B: $i,A: $i] :
( ( finite @ sk1 )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[84733,91]) ).
thf(84830,plain,
( ( finite @ sk1 )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[84829:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(28125,plain,
! [A: $i] :
( ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
!= ( in @ A @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[27991,1508]) ).
thf(28171,plain,
! [A: $i] :
( ( ( sk5 @ sk16 )
!= A )
| ( ( powerset @ ( the_carrier @ sk16 ) )
!= empty_set ) ),
inference(simp,[status(thm)],[28125]) ).
thf(28182,plain,
( ( powerset @ ( the_carrier @ sk16 ) )
!= empty_set ),
inference(simp,[status(thm)],[28171]) ).
thf(17464,plain,
( ~ ( empty @ sk1 )
| ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk1 ) ) ),
inference(simp,[status(thm)],[17463]) ).
thf(41603,plain,
( ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk1 ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,17464]) ).
thf(41661,plain,
( ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk1 ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[41603]) ).
thf(9400,plain,
( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ sk16 ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,2723]) ).
thf(9461,plain,
( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ sk16 ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[9400]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(127,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(129,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( sk12 @ A ) ) ),
inference(cnf,[status(esa)],[127]) ).
thf(22252,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ~ ( empty_carrier @ sk11 )
| ( B != sk1 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[64,21913]) ).
thf(22253,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ~ ( empty @ A )
| ~ ( empty_carrier @ sk11 )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[22252:[bind(A,$thf( sk11 ))]]) ).
thf(22301,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk1 )
| ~ ( empty_carrier @ sk11 ) ),
inference(simp,[status(thm)],[22253]) ).
thf(52400,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( the_carrier @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,52341]) ).
thf(52457,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( the_carrier @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[52400]) ).
thf(24592,plain,
! [B: $i,A: $i] :
( ( empty @ ( the_carrier @ sk11 ) )
| ~ ( in @ B @ A )
| ( ( in @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk11 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19143,144]) ).
thf(24593,plain,
( ( empty @ ( the_carrier @ sk11 ) )
| ~ ( in @ ( the_carrier @ sk11 ) @ ( bottom_of_relstr @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[24592:[bind(A,$thf( bottom_of_relstr @ sk11 )),bind(B,$thf( the_carrier @ sk11 ))]]) ).
thf(134,plain,
! [A: $i] :
( ( empty @ A )
| ( finite @ ( sk13 @ A ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(89213,plain,
( ( in @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) )
!= ( in @ ( powerset @ ( the_carrier @ sk16 ) ) @ ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[88991,28053]) ).
thf(89248,plain,
( ( ( sk10 @ ( sk5 @ sk16 ) @ empty_set )
!= ( powerset @ ( the_carrier @ sk16 ) ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(simp,[status(thm)],[89213]) ).
thf(89308,plain,
( ( sk10 @ ( sk5 @ sk16 ) @ empty_set )
!= ( powerset @ ( the_carrier @ sk16 ) ) ),
inference(simp,[status(thm)],[89248]) ).
thf(27006,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( empty @ ( sk5 @ sk16 ) )
!= ( empty @ ( the_carrier @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[24725,2813]) ).
thf(27152,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( sk5 @ sk16 )
!= ( the_carrier @ sk11 ) ) ),
inference(simp,[status(thm)],[27006]) ).
thf(55180,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( sk5 @ sk16 )
!= ( the_carrier @ sk11 ) )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,27152]) ).
thf(55181,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( ( sk5 @ sk16 )
!= ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[55180:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(48990,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk16 ) @ sk16 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[48875,10568]) ).
thf(49021,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( sk9 @ empty_set @ sk16 )
!= A )
| ( sk16 != A ) ),
inference(simp,[status(thm)],[48990]) ).
thf(49071,plain,
( ( one_sorted_str @ empty_set )
| ( ( sk9 @ empty_set @ sk16 )
!= sk16 ) ),
inference(simp,[status(thm)],[49021]) ).
thf(10572,plain,
( ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 )
!= ( in @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3863,10522]) ).
thf(10681,plain,
( ( ( powerset @ ( the_carrier @ sk1 ) )
!= sk2 )
| ( ( powerset @ ( the_carrier @ sk1 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[10572]) ).
thf(10695,plain,
( ( powerset @ ( the_carrier @ sk1 ) )
!= sk2 ),
inference(simp,[status(thm)],[10681]) ).
thf(10711,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= sk2 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,10695]) ).
thf(10712,plain,
( ~ ( empty @ sk1 )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[10711:[bind(A,$thf( sk1 ))]]) ).
thf(15527,plain,
( ( ( powerset @ ( the_carrier @ empty_set ) )
!= sk2 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,10712]) ).
thf(15592,plain,
( ( ( powerset @ ( the_carrier @ empty_set ) )
!= sk2 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[15527]) ).
thf(43732,plain,
( ( element @ empty_set @ ( the_carrier @ sk1 ) )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19201]) ).
thf(43828,plain,
( ( element @ empty_set @ ( the_carrier @ sk1 ) )
| ( ( bottom_of_relstr @ sk1 )
!= empty_set ) ),
inference(simp,[status(thm)],[43732]) ).
thf(22573,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( subset @ ( sk5 @ sk1 ) @ ( the_carrier @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,22421]) ).
thf(22574,plain,
( ~ ( empty @ sk1 )
| ( subset @ ( sk5 @ sk1 ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[22573:[bind(A,$thf( sk1 ))]]) ).
thf(50735,plain,
( ( subset @ ( sk5 @ sk1 ) @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,22574]) ).
thf(50819,plain,
( ( subset @ ( sk5 @ sk1 ) @ ( the_carrier @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[50735]) ).
thf(529,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( element @ sk2 @ ( powerset @ ( the_carrier @ A ) ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,47]) ).
thf(530,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( element @ sk2 @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[529:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(128,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk12 @ A ) @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[127]) ).
thf(104275,plain,
( ( sk1 != empty_set )
| ( sk11 != empty_set )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,77920]) ).
thf(104360,plain,
( ( sk1 != empty_set )
| ( sk11 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk1 ) ),
inference(simp,[status(thm)],[104275]) ).
thf(55331,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( sk5 @ sk1 )
!= ( the_carrier @ sk11 ) )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,27174]) ).
thf(55332,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( ( sk5 @ sk1 )
!= ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[55331:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(123245,plain,
! [A: $i] :
( ~ ( empty @ sk16 )
| ( ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ empty_set ) ) )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27999,10568]) ).
thf(123312,plain,
! [A: $i] :
( ~ ( empty @ sk16 )
| ( ( sk5 @ sk16 )
!= A )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= A ) ),
inference(simp,[status(thm)],[123245]) ).
thf(123390,plain,
( ~ ( empty @ sk16 )
| ( ( sk5 @ sk16 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[123312]) ).
thf(123416,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk16 )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,123390]) ).
thf(123417,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ sk16 )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[123416:[bind(A,$thf( sk16 ))]]) ).
thf(123512,plain,
( ~ ( empty @ sk16 )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[123417]) ).
thf(77086,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ sk11 )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk16 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[54508]) ).
thf(77099,plain,
( ~ ( empty @ sk16 )
| ~ ( empty @ sk11 )
| ( ( the_carrier @ sk11 )
!= sk16 ) ),
inference(simp,[status(thm)],[77086]) ).
thf(39016,plain,
! [A: $i] :
( ( antisymmetric_relstr @ empty_set )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[38901,10568]) ).
thf(39046,plain,
! [A: $i] :
( ( antisymmetric_relstr @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[39016]) ).
thf(39069,plain,
( ( antisymmetric_relstr @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[39046]) ).
thf(66825,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( element @ empty_set @ sk2 )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ ( bottom_of_relstr @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[45744,19354]) ).
thf(66826,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( element @ empty_set @ sk2 ) ),
inference(pattern_uni,[status(thm)],[66825:[]]) ).
thf(20353,plain,
! [A: $i] :
( ( element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk1 ) )
| ( ( join_on_relstr @ sk11 @ empty_set )
!= ( join_on_relstr @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19943,18080]) ).
thf(20420,plain,
! [A: $i] :
( ( element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk1 ) )
| ( sk11 != sk1 )
| ( empty_set != A ) ),
inference(simp,[status(thm)],[20353]) ).
thf(20422,plain,
( ( element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk1 ) )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[20420]) ).
thf(41765,plain,
! [B: $i,A: $i] :
( ( lower_bounded_relstr @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[41688,91]) ).
thf(41766,plain,
( ( lower_bounded_relstr @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[41765:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(11361,plain,
( ( in @ ( sk10 @ sk8 @ empty_set ) @ sk8 )
!= ( in @ sk8 @ ( sk10 @ sk8 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[9637,10550]) ).
thf(11388,plain,
( ( ( sk10 @ sk8 @ empty_set )
!= sk8 )
| ( ( sk10 @ sk8 @ empty_set )
!= sk8 ) ),
inference(simp,[status(thm)],[11361]) ).
thf(11414,plain,
( ( sk10 @ sk8 @ empty_set )
!= sk8 ),
inference(simp,[status(thm)],[11388]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( filtered_subset @ sk2 @ A )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,53]) ).
thf(430,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( filtered_subset @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(1687,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( filtered_subset @ sk2 @ empty_set )
| ( A != empty_set )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,1406]) ).
thf(1688,plain,
! [A: $i] :
( ( in @ ( sk9 @ sk1 @ A ) @ A )
| ( in @ ( sk10 @ sk1 @ A ) @ sk1 )
| ( filtered_subset @ sk2 @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[1687:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(2229,plain,
( ( in @ ( sk9 @ sk1 @ empty_set ) @ empty_set )
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( filtered_subset @ sk2 @ empty_set ) ),
inference(simp,[status(thm)],[1688]) ).
thf(71632,plain,
( $false
| ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( filtered_subset @ sk2 @ empty_set ) ),
inference(rewrite,[status(thm)],[2229,1508]) ).
thf(71633,plain,
( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
| ( filtered_subset @ sk2 @ empty_set ) ),
inference(simp,[status(thm)],[71632]) ).
thf(30350,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( in @ ( powerset @ ( the_carrier @ empty_set ) ) @ ( sk5 @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,30103]) ).
thf(30351,plain,
( ~ ( empty @ sk1 )
| ~ ( in @ ( powerset @ ( the_carrier @ empty_set ) ) @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[30350:[bind(A,$thf( sk1 ))]]) ).
thf(30047,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,30040]) ).
thf(30048,plain,
( ~ ( empty @ sk1 )
| ( in @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[30047:[bind(A,$thf( sk1 ))]]) ).
thf(75202,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk1 != empty_set )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,54971]) ).
thf(75270,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk1 != empty_set )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[75202]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( in @ ( bottom_of_relstr @ A ) @ sk2 )
| ~ ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,46]) ).
thf(348,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ A ) @ sk2 )
| ~ ( proper_element @ sk2 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[347:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(31873,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ A ) @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[348,19590]) ).
thf(31874,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( in @ ( bottom_of_relstr @ A ) @ sk2 ) ),
inference(simp,[status(thm)],[31873]) ).
thf(3009,plain,
( ~ ( empty @ sk16 )
| ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ sk16 ) ) ),
inference(simp,[status(thm)],[3006]) ).
thf(81196,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ sk16 ) )
| ( ( empty @ sk16 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,3009]) ).
thf(81344,plain,
( ( sk1 != empty_set )
| ( ( sk5 @ empty_set )
!= sk16 )
| ( sk16 != sk1 ) ),
inference(simp,[status(thm)],[81196]) ).
thf(105687,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( sk5 @ empty_set )
!= sk16 )
| ( sk16 != sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81344]) ).
thf(105688,plain,
( ~ ( empty @ sk1 )
| ( ( sk5 @ empty_set )
!= sk16 )
| ( sk16 != sk1 ) ),
inference(pattern_uni,[status(thm)],[105687:[bind(A,$thf( sk1 ))]]) ).
thf(20910,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A != sk2 )
| ( B
!= ( the_carrier @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[115,20799]) ).
thf(20911,plain,
! [A: $i] :
( ( in @ ( sk9 @ ( the_carrier @ sk1 ) @ A ) @ A )
| ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ A ) @ ( the_carrier @ sk1 ) )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[20910:[bind(A,$thf( A )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(20965,plain,
( ( in @ ( sk9 @ ( the_carrier @ sk1 ) @ sk2 ) @ sk2 )
| ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ sk2 ) @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[20911]) ).
thf(103884,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ ( the_carrier @ sk1 ) @ sk2 ) @ sk2 )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ sk2 ) @ ( the_carrier @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20965,91]) ).
thf(103885,plain,
( ( in @ ( sk9 @ ( the_carrier @ sk1 ) @ sk2 ) @ sk2 )
| ( element @ ( sk10 @ ( the_carrier @ sk1 ) @ sk2 ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[103884:[bind(A,$thf( sk10 @ ( the_carrier @ sk1 ) @ sk2 )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(81291,plain,
( ( sk1 != empty_set )
| ( sk16 != sk11 )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,54304]) ).
thf(81364,plain,
( ( sk1 != empty_set )
| ( sk16 != sk11 )
| ( ( the_carrier @ sk11 )
!= sk1 ) ),
inference(simp,[status(thm)],[81291]) ).
thf(108947,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk16 != sk11 )
| ( ( the_carrier @ sk11 )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81364]) ).
thf(108948,plain,
( ~ ( empty @ sk1 )
| ( sk16 != sk11 )
| ( ( the_carrier @ sk11 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[108947:[bind(A,$thf( sk1 ))]]) ).
thf(28837,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( in @ ( powerset @ ( the_carrier @ sk16 ) ) @ ( sk5 @ empty_set ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,28053]) ).
thf(28838,plain,
( ~ ( empty @ sk16 )
| ~ ( in @ ( powerset @ ( the_carrier @ sk16 ) ) @ ( sk5 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[28837:[bind(A,$thf( sk16 ))]]) ).
thf(2524,plain,
( ( ( the_carrier @ empty_set )
!= sk16 )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,1486]) ).
thf(2525,plain,
( ( ( the_carrier @ empty_set )
!= sk16 )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[2524]) ).
thf(10256,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ empty_set @ sk2 )
| ( A
!= ( sk9 @ empty_set @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[120,10253]) ).
thf(10257,plain,
( ~ ( empty @ ( sk9 @ empty_set @ sk2 ) )
| ( in @ empty_set @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10256:[bind(A,$thf( sk9 @ empty_set @ sk2 ))]]) ).
thf(37525,plain,
( ( in @ empty_set @ sk2 )
| ( ( empty @ ( sk9 @ empty_set @ sk2 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,10257]) ).
thf(37646,plain,
( ( in @ empty_set @ sk2 )
| ( ( sk9 @ empty_set @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[37525]) ).
thf(77913,plain,
( ~ ( empty @ sk11 )
| ( sk1 != empty_set )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[55079]) ).
thf(77915,plain,
( ~ ( empty @ sk11 )
| ( sk1 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk11 ) ),
inference(simp,[status(thm)],[77913]) ).
thf(104124,plain,
( ( sk1 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk11 )
| ( ( empty @ sk11 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,77915]) ).
thf(104208,plain,
( ( sk1 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk11 )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[104124]) ).
thf(5349,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk10 @ sk6 @ empty_set ) @ sk6 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5304,91]) ).
thf(5350,plain,
element @ ( sk10 @ sk6 @ empty_set ) @ sk6,
inference(pattern_uni,[status(thm)],[5349:[bind(A,$thf( sk10 @ sk6 @ empty_set )),bind(B,$thf( sk6 ))]]) ).
thf(77221,plain,
! [B: $i,A: $i] :
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[77127,91]) ).
thf(77222,plain,
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[77221:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(86486,plain,
! [B: $i,A: $i] :
( ( finite @ sk1 )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[86416,144]) ).
thf(86487,plain,
( ( finite @ sk1 )
| ~ ( in @ sk1 @ ( sk10 @ sk1 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[86486:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(81092,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( sk5 @ sk16 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,2813]) ).
thf(81407,plain,
( ( sk1 != empty_set )
| ( ( sk5 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[81092]) ).
thf(16886,plain,
( ( ( sk5 @ empty_set )
!= empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,16040]) ).
thf(16935,plain,
( ( ( sk5 @ empty_set )
!= empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[16886]) ).
thf(46256,plain,
( ( sk1 != empty_set )
| ~ ( in @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ empty_set ) )
| ( ( bottom_of_relstr @ sk1 )
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46231,25499]) ).
thf(46257,plain,
( ( sk1 != empty_set )
| ~ ( in @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[46256:[]]) ).
thf(189,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,153]) ).
thf(191,plain,
! [A: $i] :
( ( powerset @ A )
!= empty_set ),
inference(simp,[status(thm)],[189]) ).
thf(25810,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( ( in @ A @ B )
!= ( in @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[99,25499]) ).
thf(25811,plain,
( ~ ( element @ ( the_carrier @ sk1 ) @ ( bottom_of_relstr @ sk1 ) )
| ( empty @ ( bottom_of_relstr @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25810:[bind(A,$thf( the_carrier @ sk1 )),bind(B,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(58288,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58168,10568]) ).
thf(58329,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( sk9 @ empty_set @ sk11 )
!= A )
| ( sk11 != A ) ),
inference(simp,[status(thm)],[58288]) ).
thf(58363,plain,
( ( one_sorted_str @ empty_set )
| ( ( sk9 @ empty_set @ sk11 )
!= sk11 ) ),
inference(simp,[status(thm)],[58329]) ).
thf(36603,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk3 @ empty_set ) @ sk3 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[36549,144]) ).
thf(36604,plain,
( ( one_sorted_str @ empty_set )
| ~ ( in @ sk3 @ ( sk10 @ sk3 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[36603:[bind(A,$thf( sk10 @ sk3 @ empty_set )),bind(B,$thf( sk3 ))]]) ).
thf(96885,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[96791,144]) ).
thf(96886,plain,
~ ( in @ ( the_carrier @ sk1 ) @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) ),
inference(pattern_uni,[status(thm)],[96885:[bind(A,$thf( sk10 @ ( the_carrier @ sk1 ) @ empty_set )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(39994,plain,
! [B: $i,A: $i] :
( ( rel_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39939,144]) ).
thf(39995,plain,
( ( rel_str @ empty_set )
| ~ ( in @ sk1 @ ( sk9 @ empty_set @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[39994:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ B )
| ( A
!= ( sk15 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[120,139]) ).
thf(291,plain,
! [A: $i] :
( ~ ( empty @ ( sk15 @ A ) )
| ( element @ empty_set @ A ) ),
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( sk15 @ C )),bind(B,$thf( C ))]]) ).
thf(313,plain,
! [A: $i] :
( ~ ( empty @ ( sk15 @ A ) )
| ( element @ empty_set @ A ) ),
inference(simp,[status(thm)],[291]) ).
thf(40739,plain,
! [B: $i,A: $i] :
( ( rel_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40684,144]) ).
thf(40740,plain,
( ( rel_str @ empty_set )
| ~ ( in @ sk1 @ ( sk10 @ sk1 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[40739:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(50255,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk16 @ empty_set ) @ sk16 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50200,144]) ).
thf(50256,plain,
( ( one_sorted_str @ empty_set )
| ~ ( in @ sk16 @ ( sk10 @ sk16 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[50255:[bind(A,$thf( sk10 @ sk16 @ empty_set )),bind(B,$thf( sk16 ))]]) ).
thf(93317,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( element @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( sk5 @ sk1 ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22486,92439]) ).
thf(93318,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( element @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[93317:[]]) ).
thf(2357,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( finite @ sk2 )
| ( ( the_carrier @ empty_set )
!= sk8 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,1540]) ).
thf(2358,plain,
( ~ ( empty @ sk1 )
| ( finite @ sk2 )
| ( ( the_carrier @ empty_set )
!= sk8 ) ),
inference(pattern_uni,[status(thm)],[2357:[bind(A,$thf( sk1 ))]]) ).
thf(123448,plain,
( ( ( sk5 @ sk16 )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,123390]) ).
thf(123502,plain,
( ( ( sk5 @ sk16 )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[123448]) ).
thf(101469,plain,
( ( sk1 != empty_set )
| ( sk11 != sk1 )
| ( ( the_carrier @ empty_set )
!= sk11 )
| ( ( empty @ sk11 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,77500]) ).
thf(101556,plain,
( ( sk1 != empty_set )
| ( sk11 != sk1 )
| ( ( the_carrier @ empty_set )
!= sk11 )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[101469]) ).
thf(101575,plain,
( ( sk1 != empty_set )
| ( sk11 != sk1 )
| ( ( the_carrier @ empty_set )
!= sk11 ) ),
inference(simp,[status(thm)],[101556]) ).
thf(16327,plain,
( ~ ( empty @ sk1 )
| ( ( sk5 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[16325]) ).
thf(17066,plain,
( ( ( sk5 @ empty_set )
!= sk1 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,16327]) ).
thf(17115,plain,
( ( ( sk5 @ empty_set )
!= sk1 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[17066]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( upper_relstr_subset @ sk2 @ A )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,48]) ).
thf(382,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( upper_relstr_subset @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(78176,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,55178]) ).
thf(78256,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[78176]) ).
thf(89882,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( element @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[13586,89125]) ).
thf(89883,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( element @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[89882:[]]) ).
thf(53291,plain,
! [A: $i] :
( ( empty_carrier @ sk3 )
| ( ( in @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53153,10568]) ).
thf(53335,plain,
! [A: $i] :
( ( empty_carrier @ sk3 )
| ( ( sk5 @ sk3 )
!= A )
| ( ( powerset @ ( the_carrier @ sk3 ) )
!= A ) ),
inference(simp,[status(thm)],[53291]) ).
thf(53366,plain,
( ( empty_carrier @ sk3 )
| ( ( sk5 @ sk3 )
!= ( powerset @ ( the_carrier @ sk3 ) ) ) ),
inference(simp,[status(thm)],[53335]) ).
thf(19609,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
!= ( in @ sk6 @ ( sk9 @ empty_set @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[19588,10562]) ).
thf(19702,plain,
( ( ( bottom_of_relstr @ sk1 )
!= sk6 )
| ( ( sk9 @ empty_set @ sk6 )
!= sk2 ) ),
inference(simp,[status(thm)],[19609]) ).
thf(39357,plain,
! [A: $i] :
( ( element @ A @ ( powerset @ A ) )
!= ( element @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[823,39253]) ).
thf(39412,plain,
! [A: $i] :
( ( A
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( ( powerset @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[39357]) ).
thf(39483,plain,
( ( powerset @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[39412]) ).
thf(39563,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( powerset @ ( powerset @ ( the_carrier @ empty_set ) ) )
!= sk2 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,39483]) ).
thf(39564,plain,
( ~ ( empty @ sk1 )
| ( ( powerset @ ( powerset @ ( the_carrier @ empty_set ) ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[39563:[bind(A,$thf( sk1 ))]]) ).
thf(80979,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( the_carrier @ sk16 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,1411]) ).
thf(81372,plain,
( ( sk1 != empty_set )
| ( ( the_carrier @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[80979]) ).
thf(159,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( rel_str @ A )
| ( filtered_subset @ ( sk17 @ A ) @ A ) ),
inference(cnf,[status(esa)],[156]) ).
thf(14710,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( one_sorted_str @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,14669]) ).
thf(14711,plain,
( ~ ( empty @ sk1 )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[14710:[bind(A,$thf( sk1 ))]]) ).
thf(21221,plain,
! [B: $i,A: $i] :
( ( empty_carrier @ sk11 )
| ( subset @ A @ B )
| ( ( element @ ( sk5 @ sk11 ) @ ( powerset @ ( the_carrier @ sk11 ) ) )
!= ( element @ A @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[14671,70]) ).
thf(21222,plain,
( ( empty_carrier @ sk11 )
| ( subset @ ( sk5 @ sk11 ) @ ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[21221:[bind(A,$thf( sk5 @ sk11 )),bind(B,$thf( the_carrier @ sk11 ))]]) ).
thf(72655,plain,
( ~ ( in @ ( the_carrier @ empty_set ) @ ( bottom_of_relstr @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,52918]) ).
thf(72821,plain,
( ~ ( in @ ( the_carrier @ empty_set ) @ ( bottom_of_relstr @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[72655]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( one_sorted_str @ A )
| ( B != sk16 ) ),
inference(paramod_ordered,[status(thm)],[64,142]) ).
thf(406,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk16 )
| ( one_sorted_str @ A ) ),
inference(pattern_uni,[status(thm)],[405:[bind(A,$thf( A )),bind(B,$thf( sk16 ))]]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk9 @ B @ A ) @ B )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[107]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ ( sk9 @ B @ A ) @ B )
| ( in @ ( sk10 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(11101,plain,
( ( in @ ( sk10 @ sk8 @ empty_set ) @ sk8 )
!= ( in @ sk2 @ ( sk9 @ empty_set @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[9637,10546]) ).
thf(11127,plain,
( ( ( sk10 @ sk8 @ empty_set )
!= sk2 )
| ( ( sk9 @ empty_set @ sk2 )
!= sk8 ) ),
inference(simp,[status(thm)],[11101]) ).
thf(60350,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60290,144]) ).
thf(60351,plain,
( ( one_sorted_str @ empty_set )
| ~ ( in @ sk11 @ ( sk10 @ sk11 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[60350:[bind(A,$thf( sk10 @ sk11 @ empty_set )),bind(B,$thf( sk11 ))]]) ).
thf(37846,plain,
( ( element @ empty_set @ sk2 )
| ( ( empty @ ( sk9 @ empty_set @ sk2 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,10394]) ).
thf(37944,plain,
( ( element @ empty_set @ sk2 )
| ( ( sk9 @ empty_set @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[37846]) ).
thf(433,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ~ ( empty_carrier @ A )
| ( B != sk16 ) ),
inference(paramod_ordered,[status(thm)],[64,141]) ).
thf(434,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk16 )
| ~ ( empty_carrier @ A ) ),
inference(pattern_uni,[status(thm)],[433:[bind(A,$thf( A )),bind(B,$thf( sk16 ))]]) ).
thf(93659,plain,
( ( in @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[93589,30103]) ).
thf(93859,plain,
( ( ( sk10 @ ( sk5 @ sk1 ) @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(simp,[status(thm)],[93659]) ).
thf(93919,plain,
( ( sk10 @ ( sk5 @ sk1 ) @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[93859]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ~ ( rel_str @ A )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( in @ ( sk19 @ B @ A ) @ B )
| ( upper_relstr_subset @ B @ A ) ),
inference(cnf,[status(esa)],[169]) ).
thf(22398,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,22387]) ).
thf(22399,plain,
( ~ ( empty @ sk1 )
| ( element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[22398:[bind(A,$thf( sk1 ))]]) ).
thf(18388,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ ( join_on_relstr @ sk11 @ A ) @ ( the_carrier @ sk11 ) )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18091,99]) ).
thf(18389,plain,
! [A: $i] :
( ( empty @ ( the_carrier @ sk11 ) )
| ( in @ ( join_on_relstr @ sk11 @ A ) @ ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[18388:[bind(A,$thf( E )),bind(B,$thf( join_on_relstr @ sk11 @ E )),bind(C,$thf( the_carrier @ sk11 ))]]) ).
thf(18457,plain,
! [A: $i] :
( ( empty @ ( the_carrier @ sk11 ) )
| ( in @ ( join_on_relstr @ sk11 @ A ) @ ( the_carrier @ sk11 ) ) ),
inference(simp,[status(thm)],[18389]) ).
thf(32226,plain,
! [B: $i,A: $i] :
( ( sk1 != empty_set )
| ~ ( finite @ A )
| ( finite @ B )
| ( ( element @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) )
!= ( element @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[3760,79]) ).
thf(32227,plain,
( ( sk1 != empty_set )
| ~ ( finite @ ( the_carrier @ empty_set ) )
| ( finite @ sk2 ) ),
inference(pattern_uni,[status(thm)],[32226:[bind(A,$thf( the_carrier @ empty_set )),bind(B,$thf( sk2 ))]]) ).
thf(14678,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( empty @ ( sk5 @ A ) )
| ( ( one_sorted_str @ sk11 )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14661,89]) ).
thf(14679,plain,
( ( empty_carrier @ sk11 )
| ~ ( empty @ ( sk5 @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[14678:[bind(A,$thf( sk11 ))]]) ).
thf(10858,plain,
( ( in @ ( sk9 @ empty_set @ sk2 ) @ sk2 )
!= ( in @ sk8 @ ( sk9 @ empty_set @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[10253,10534]) ).
thf(10898,plain,
( ( ( sk9 @ empty_set @ sk2 )
!= sk8 )
| ( ( sk9 @ empty_set @ sk8 )
!= sk2 ) ),
inference(simp,[status(thm)],[10858]) ).
thf(84994,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( in @ B @ sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81042]) ).
thf(84995,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ~ ( in @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[84994:[bind(A,$thf( sk1 ))]]) ).
thf(85184,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ~ ( in @ A @ sk1 ) ),
inference(simp,[status(thm)],[84995]) ).
thf(73909,plain,
( ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk16 != sk11 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,54306]) ).
thf(73977,plain,
( ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk16 != sk11 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[73909]) ).
thf(41743,plain,
! [B: $i,A: $i] :
( ( lower_bounded_relstr @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[41688,144]) ).
thf(41744,plain,
( ( lower_bounded_relstr @ empty_set )
| ~ ( in @ sk1 @ ( sk9 @ empty_set @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[41743:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(54968,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk11 != sk1 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,54824]) ).
thf(54969,plain,
( ~ ( empty @ sk11 )
| ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk11 != sk1 ) ),
inference(pattern_uni,[status(thm)],[54968:[bind(A,$thf( sk11 ))]]) ).
thf(75055,plain,
( ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk11 != sk1 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,54969]) ).
thf(75123,plain,
( ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk11 != sk1 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[75055]) ).
thf(92495,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( sk5 @ sk1 ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22486,92304]) ).
thf(92496,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[92495:[]]) ).
thf(27136,plain,
! [A: $i] :
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( finite @ A )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[24725,126]) ).
thf(27137,plain,
( ( ( the_carrier @ sk11 )
!= empty_set )
| ( finite @ ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[27136:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(29613,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( finite @ ( the_carrier @ sk11 ) )
| ( A
!= ( the_carrier @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[120,27137]) ).
thf(29614,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( finite @ ( the_carrier @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[29613:[bind(A,$thf( the_carrier @ sk11 ))]]) ).
thf(35397,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk3 ) @ sk3 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35321,91]) ).
thf(35398,plain,
( ( one_sorted_str @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk3 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[35397:[bind(A,$thf( sk9 @ empty_set @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(123686,plain,
( ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,123512]) ).
thf(123738,plain,
( ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[123686]) ).
thf(11380,plain,
( ( in @ ( sk10 @ sk6 @ empty_set ) @ sk6 )
!= ( in @ sk8 @ ( sk10 @ sk8 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[5304,10550]) ).
thf(11387,plain,
( ( ( sk10 @ sk6 @ empty_set )
!= sk8 )
| ( ( sk10 @ sk8 @ empty_set )
!= sk6 ) ),
inference(simp,[status(thm)],[11380]) ).
thf(54988,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( B != sk1 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[64,54824]) ).
thf(54989,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ~ ( empty @ A )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[54988:[bind(A,$thf( sk11 ))]]) ).
thf(55050,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk1 )
| ( ( the_carrier @ sk11 )
!= empty_set ) ),
inference(simp,[status(thm)],[54989]) ).
thf(76025,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,55050]) ).
thf(76094,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[76025]) ).
thf(20333,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ sk11 ) )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,19943]) ).
thf(20334,plain,
( ~ ( empty @ sk11 )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[20333:[bind(A,$thf( sk11 ))]]) ).
thf(48529,plain,
( ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ sk11 ) )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,20334]) ).
thf(48612,plain,
( ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ sk11 ) )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[48529]) ).
thf(6782,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ empty_set @ sk6 )
| ( A
!= ( sk10 @ sk6 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[120,5350]) ).
thf(6783,plain,
( ~ ( empty @ ( sk10 @ sk6 @ empty_set ) )
| ( element @ empty_set @ sk6 ) ),
inference(pattern_uni,[status(thm)],[6782:[bind(A,$thf( sk10 @ sk6 @ empty_set ))]]) ).
thf(33302,plain,
( ( element @ empty_set @ sk6 )
| ( ( empty @ ( sk10 @ sk6 @ empty_set ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,6783]) ).
thf(33396,plain,
( ( element @ empty_set @ sk6 )
| ( ( sk10 @ sk6 @ empty_set )
!= empty_set ) ),
inference(simp,[status(thm)],[33302]) ).
thf(2624,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,2619]) ).
thf(2625,plain,
( ~ ( empty @ sk16 )
| ( element @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[2624:[bind(A,$thf( sk16 ))]]) ).
thf(19204,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,19005]) ).
thf(19205,plain,
( ~ ( empty @ sk1 )
| ( element @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[19204:[bind(A,$thf( sk1 ))]]) ).
thf(44168,plain,
( ( element @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19205]) ).
thf(44272,plain,
( ( element @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[44168]) ).
thf(19736,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( bottom_of_relstr @ empty_set )
!= sk2 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,19728]) ).
thf(19737,plain,
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ empty_set )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[19736:[bind(A,$thf( sk1 ))]]) ).
thf(30176,plain,
! [A: $i] :
( ( in @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[30040,10568]) ).
thf(30208,plain,
! [A: $i] :
( ( ( sk5 @ sk1 )
!= A )
| ( ( powerset @ ( the_carrier @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[30176]) ).
thf(30228,plain,
( ( sk5 @ sk1 )
!= ( powerset @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[30208]) ).
thf(30270,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,30228]) ).
thf(30271,plain,
( ~ ( empty @ sk1 )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[30270:[bind(A,$thf( sk1 ))]]) ).
thf(2106,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( reflexive_relstr @ empty_set )
| ( B != empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[115,818]) ).
thf(2107,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ A @ sk1 ) @ A )
| ( reflexive_relstr @ empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[2106:[bind(A,$thf( sk1 ))]]) ).
thf(2184,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( in @ ( sk10 @ empty_set @ sk1 ) @ empty_set )
| ( reflexive_relstr @ empty_set ) ),
inference(simp,[status(thm)],[2107]) ).
thf(32933,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| $false
| ( reflexive_relstr @ empty_set ) ),
inference(rewrite,[status(thm)],[2184,1508]) ).
thf(32934,plain,
( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
| ( reflexive_relstr @ empty_set ) ),
inference(simp,[status(thm)],[32933]) ).
thf(33010,plain,
! [B: $i,A: $i] :
( ( reflexive_relstr @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[32934,91]) ).
thf(33011,plain,
( ( reflexive_relstr @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[33010:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(87802,plain,
! [A: $i] :
( ( in @ ( sk10 @ ( the_carrier @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[87619,10568]) ).
thf(87863,plain,
! [A: $i] :
( ( ( sk10 @ ( the_carrier @ sk16 ) @ empty_set )
!= A )
| ( ( the_carrier @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[87802]) ).
thf(87902,plain,
( ( sk10 @ ( the_carrier @ sk16 ) @ empty_set )
!= ( the_carrier @ sk16 ) ),
inference(simp,[status(thm)],[87863]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( one_sorted_str @ A )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[64,58]) ).
thf(394,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk3 )
| ( one_sorted_str @ A ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(81056,plain,
( ( sk1 != empty_set )
| ( ( empty @ sk6 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,97]) ).
thf(81389,plain,
( ( sk1 != empty_set )
| ( sk6 != sk1 ) ),
inference(simp,[status(thm)],[81056]) ).
thf(2966,plain,
( ( empty_carrier @ sk3 )
| ( ( empty @ ( sk5 @ sk3 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,2711]) ).
thf(2967,plain,
( ( empty_carrier @ sk3 )
| ( ( sk5 @ sk3 )
!= empty_set ) ),
inference(simp,[status(thm)],[2966]) ).
thf(102126,plain,
( ( sk16 != sk11 )
| ( ( the_carrier @ empty_set )
!= sk11 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,76522]) ).
thf(102194,plain,
( ( sk16 != sk11 )
| ( ( the_carrier @ empty_set )
!= sk11 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[102126]) ).
thf(130,plain,
! [A: $i] :
( ( empty @ A )
| ( finite @ ( sk12 @ A ) ) ),
inference(cnf,[status(esa)],[127]) ).
thf(66817,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[45744,105]) ).
thf(67109,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( ( bottom_of_relstr @ sk1 )
!= sk8 ) ),
inference(simp,[status(thm)],[66817]) ).
thf(94610,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( element @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22486,93724]) ).
thf(94611,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( element @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[94610:[]]) ).
thf(81057,plain,
( ( sk1 != empty_set )
| ( empty_carrier @ sk11 )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,14681]) ).
thf(81438,plain,
( ( empty_carrier @ sk11 )
| ( sk1 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk1 ) ),
inference(simp,[status(thm)],[81057]) ).
thf(76865,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk11 != empty_set )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,54416]) ).
thf(76936,plain,
( ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk11 != empty_set )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[76865]) ).
thf(61381,plain,
( ~ ( element @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,39263]) ).
thf(61526,plain,
( ~ ( element @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[61381]) ).
thf(78491,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( ( element @ ( sk15 @ A ) @ A )
!= ( element @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[139,61526]) ).
thf(78535,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( ( sk15 @ A )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[78491]) ).
thf(78628,plain,
( ( sk1 != empty_set )
| ( ( sk15 @ sk2 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[78535]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(80,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32988,plain,
! [B: $i,A: $i] :
( ( reflexive_relstr @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[32934,144]) ).
thf(32989,plain,
( ( reflexive_relstr @ empty_set )
| ~ ( in @ sk1 @ ( sk9 @ empty_set @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[32988:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(25478,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ) )
!= ( in @ sk8 @ ( sk10 @ sk8 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[25449,10550]) ).
thf(25597,plain,
( ( ( bottom_of_relstr @ sk1 )
!= sk8 )
| ( ( sk10 @ sk8 @ empty_set )
!= ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[25478]) ).
thf(33048,plain,
! [A: $i] :
( ( reflexive_relstr @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32934,10568]) ).
thf(33089,plain,
! [A: $i] :
( ( reflexive_relstr @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[33048]) ).
thf(33112,plain,
( ( reflexive_relstr @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[33089]) ).
thf(35375,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk3 ) @ sk3 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35321,144]) ).
thf(35376,plain,
( ( one_sorted_str @ empty_set )
| ~ ( in @ sk3 @ ( sk9 @ empty_set @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[35375:[bind(A,$thf( sk9 @ empty_set @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(40761,plain,
! [B: $i,A: $i] :
( ( rel_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40684,91]) ).
thf(40762,plain,
( ( rel_str @ empty_set )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[40761:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(60372,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60290,91]) ).
thf(60373,plain,
( ( one_sorted_str @ empty_set )
| ( element @ ( sk10 @ sk11 @ empty_set ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[60372:[bind(A,$thf( sk10 @ sk11 @ empty_set )),bind(B,$thf( sk11 ))]]) ).
thf(33826,plain,
( ( in @ empty_set @ sk8 )
| ( ( empty @ ( sk9 @ empty_set @ sk8 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,8755]) ).
thf(33947,plain,
( ( in @ empty_set @ sk8 )
| ( ( sk9 @ empty_set @ sk8 )
!= empty_set ) ),
inference(simp,[status(thm)],[33826]) ).
thf(101473,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ~ ( empty @ sk11 )
| ( B != sk1 )
| ( ( the_carrier @ empty_set )
!= sk11 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[64,77500]) ).
thf(101474,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ~ ( empty @ A )
| ~ ( empty @ sk11 )
| ( A != sk1 )
| ( ( the_carrier @ empty_set )
!= sk11 ) ),
inference(pattern_uni,[status(thm)],[101473:[bind(A,$thf( sk11 ))]]) ).
thf(101584,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk1 )
| ( ( the_carrier @ empty_set )
!= sk11 ) ),
inference(simp,[status(thm)],[101474]) ).
thf(926,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ( empty_carrier @ A )
| ~ ( empty @ ( the_carrier @ A ) )
| ( ( one_sorted_str @ empty_set )
!= ( one_sorted_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[235,73]) ).
thf(927,plain,
( ~ ( empty @ sk3 )
| ( empty_carrier @ empty_set )
| ~ ( empty @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[926:[bind(A,$thf( empty_set ))]]) ).
thf(22533,plain,
! [B: $i,A: $i] :
( ~ ( finite @ A )
| ( finite @ B )
| ( ( element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
!= ( element @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[22387,79]) ).
thf(22534,plain,
( ~ ( finite @ ( the_carrier @ sk1 ) )
| ( finite @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[22533:[bind(A,$thf( the_carrier @ sk1 )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk9 @ B @ A ) @ B )
| ~ ( in @ ( sk10 @ B @ A ) @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[107]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ ( sk9 @ B @ A ) @ B )
| ~ ( in @ ( sk10 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(26,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ~ ( v1_yellow_3 @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_yellow_3) ).
thf(123,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ~ ( v1_yellow_3 @ A )
=> ~ ( empty_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(39374,plain,
( ( element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk11 ) )
!= ( element @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[18952,39253]) ).
thf(39411,plain,
( ( ( bottom_of_relstr @ sk11 )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( ( the_carrier @ sk11 )
!= sk2 ) ),
inference(simp,[status(thm)],[39374]) ).
thf(18982,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) )
| ( ( rel_str @ empty_set )
!= ( rel_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[939,165]) ).
thf(18983,plain,
( ( sk11 != empty_set )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[18982:[bind(A,$thf( empty_set ))]]) ).
thf(42209,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,18983]) ).
thf(42210,plain,
( ~ ( empty @ sk11 )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[42209:[bind(A,$thf( sk11 ))]]) ).
thf(104412,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk16 )
| ~ ( empty @ sk11 )
| ( ( the_carrier @ empty_set )
!= sk11 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,77097]) ).
thf(104413,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk16 )
| ~ ( empty @ sk11 )
| ( ( the_carrier @ empty_set )
!= sk11 ) ),
inference(pattern_uni,[status(thm)],[104412:[bind(A,$thf( sk11 ))]]) ).
thf(104548,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk16 )
| ( ( the_carrier @ empty_set )
!= sk11 ) ),
inference(simp,[status(thm)],[104413]) ).
thf(19613,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ sk2 )
!= ( in @ sk8 @ ( sk10 @ sk8 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[19588,10550]) ).
thf(19695,plain,
( ( ( bottom_of_relstr @ sk1 )
!= sk8 )
| ( ( sk10 @ sk8 @ empty_set )
!= sk2 ) ),
inference(simp,[status(thm)],[19613]) ).
thf(27653,plain,
( ( ( bottom_of_relstr @ empty_set )
!= ( the_carrier @ sk1 ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,25640]) ).
thf(27706,plain,
( ( ( bottom_of_relstr @ empty_set )
!= ( the_carrier @ sk1 ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[27653]) ).
thf(46379,plain,
( ( sk1 != empty_set )
| ( in @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( ( bottom_of_relstr @ sk1 )
!= ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46231,25449]) ).
thf(46380,plain,
( ( sk1 != empty_set )
| ( in @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[46379:[]]) ).
thf(43303,plain,
( ( element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19052]) ).
thf(43398,plain,
( ( element @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ empty_set ) )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[43303]) ).
thf(54576,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54519,144]) ).
thf(54577,plain,
( ( one_sorted_str @ empty_set )
| ~ ( in @ sk1 @ ( sk9 @ empty_set @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[54576:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2898,plain,
! [B: $i,A: $i] :
( ( empty_carrier @ sk3 )
| ( subset @ A @ B )
| ( ( element @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) )
!= ( element @ A @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[2439,70]) ).
thf(2899,plain,
( ( empty_carrier @ sk3 )
| ( subset @ ( sk5 @ sk3 ) @ ( the_carrier @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[2898:[bind(A,$thf( sk5 @ sk3 )),bind(B,$thf( the_carrier @ sk3 ))]]) ).
thf(71765,plain,
! [A: $i] :
( ( filtered_subset @ sk2 @ empty_set )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71633,10568]) ).
thf(71818,plain,
! [A: $i] :
( ( filtered_subset @ sk2 @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[71765]) ).
thf(71866,plain,
( ( filtered_subset @ sk2 @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[71818]) ).
thf(9977,plain,
( ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ sk16 ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,3009]) ).
thf(10016,plain,
( ( ( empty @ ( sk5 @ empty_set ) )
!= ( empty @ sk16 ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[9977]) ).
thf(93782,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22486,93589]) ).
thf(93783,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( sk10 @ ( sk5 @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[93782:[]]) ).
thf(81010,plain,
( ( sk1 != empty_set )
| ( ( empty @ sk2 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,52]) ).
thf(81423,plain,
( ( sk1 != empty_set )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[81010]) ).
thf(81721,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk2 != sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81423]) ).
thf(81722,plain,
( ~ ( empty @ sk1 )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[81721:[bind(A,$thf( sk1 ))]]) ).
thf(28124,plain,
! [A: $i] :
( ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[27991,10568]) ).
thf(28166,plain,
! [A: $i] :
( ( ( sk5 @ sk16 )
!= A )
| ( ( powerset @ ( the_carrier @ sk16 ) )
!= A ) ),
inference(simp,[status(thm)],[28124]) ).
thf(28177,plain,
( ( sk5 @ sk16 )
!= ( powerset @ ( the_carrier @ sk16 ) ) ),
inference(simp,[status(thm)],[28166]) ).
thf(28446,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ sk16 ) ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,28177]) ).
thf(28447,plain,
( ~ ( empty @ sk16 )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[28446:[bind(A,$thf( sk16 ))]]) ).
thf(55810,plain,
( ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ sk16 ) ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,28447]) ).
thf(55864,plain,
( ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ sk16 ) ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[55810]) ).
thf(74898,plain,
! [A: $i] :
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[74763,10568]) ).
thf(74956,plain,
! [A: $i] :
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[74898]) ).
thf(75007,plain,
( ( upper_relstr_subset @ sk2 @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[74956]) ).
thf(89185,plain,
! [A: $i] :
( ( in @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( sk5 @ sk16 ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[88991,10568]) ).
thf(89270,plain,
! [A: $i] :
( ( ( sk10 @ ( sk5 @ sk16 ) @ empty_set )
!= A )
| ( ( sk5 @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[89185]) ).
thf(89319,plain,
( ( sk10 @ ( sk5 @ sk16 ) @ empty_set )
!= ( sk5 @ sk16 ) ),
inference(simp,[status(thm)],[89270]) ).
thf(90622,plain,
( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( sk5 @ sk16 ) )
!= ( in @ ( powerset @ ( the_carrier @ sk16 ) ) @ ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[90399,28053]) ).
thf(90633,plain,
( ( ( sk9 @ empty_set @ ( sk5 @ sk16 ) )
!= ( powerset @ ( the_carrier @ sk16 ) ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(simp,[status(thm)],[90622]) ).
thf(90692,plain,
( ( sk9 @ empty_set @ ( sk5 @ sk16 ) )
!= ( powerset @ ( the_carrier @ sk16 ) ) ),
inference(simp,[status(thm)],[90633]) ).
thf(700,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( ( element @ ( sk15 @ A ) @ A )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[139,70]) ).
thf(701,plain,
! [A: $i] : ( subset @ ( sk15 @ ( powerset @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( powerset @ E )),bind(B,$thf( sk15 @ ( powerset @ E ) )),bind(C,$thf( E ))]]) ).
thf(705,plain,
! [A: $i] : ( subset @ ( sk15 @ ( powerset @ A ) ) @ A ),
inference(simp,[status(thm)],[701]) ).
thf(71724,plain,
! [B: $i,A: $i] :
( ( filtered_subset @ sk2 @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[71633,91]) ).
thf(71725,plain,
( ( filtered_subset @ sk2 @ empty_set )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[71724:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(20257,plain,
( ( ( bottom_of_relstr @ empty_set )
!= sk2 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19737]) ).
thf(20306,plain,
( ( ( bottom_of_relstr @ empty_set )
!= sk2 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[20257]) ).
thf(82599,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ sk16 )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81372]) ).
thf(82600,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ sk16 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[82599:[bind(A,$thf( sk1 ))]]) ).
thf(104142,plain,
( ( sk1 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk11 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,77915]) ).
thf(104209,plain,
( ( sk1 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk11 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[104142]) ).
thf(81001,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( ( empty @ ( powerset @ A ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,153]) ).
thf(81341,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( ( powerset @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[81001]) ).
thf(87430,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( ( powerset @ B )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81341]) ).
thf(87431,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( powerset @ A )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[87430:[bind(A,$thf( sk1 ))]]) ).
thf(87482,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( ( powerset @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[87431]) ).
thf(89033,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[13586,88991]) ).
thf(89034,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( sk10 @ ( sk5 @ sk16 ) @ empty_set ) @ ( the_carrier @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[89033:[]]) ).
thf(126576,plain,
( ( sk1 != empty_set )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) )
| ( ( empty @ sk1 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,126426]) ).
thf(126577,plain,
( ( sk1 != empty_set )
| ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[126576:[]]) ).
thf(46072,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,19945]) ).
thf(46073,plain,
( ~ ( empty @ sk1 )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[46072:[bind(A,$thf( sk1 ))]]) ).
thf(24652,plain,
! [A: $i] :
( ( empty @ ( the_carrier @ sk11 ) )
| ( ( in @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk11 ) )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19143,10568]) ).
thf(24685,plain,
! [A: $i] :
( ( empty @ ( the_carrier @ sk11 ) )
| ( ( bottom_of_relstr @ sk11 )
!= A )
| ( ( the_carrier @ sk11 )
!= A ) ),
inference(simp,[status(thm)],[24652]) ).
thf(24721,plain,
( ( empty @ ( the_carrier @ sk11 ) )
| ( ( bottom_of_relstr @ sk11 )
!= ( the_carrier @ sk11 ) ) ),
inference(simp,[status(thm)],[24685]) ).
thf(11121,plain,
( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
!= ( in @ sk2 @ ( sk9 @ empty_set @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3379,10546]) ).
thf(11126,plain,
( ( ( sk9 @ empty_set @ sk6 )
!= sk2 )
| ( ( sk9 @ empty_set @ sk2 )
!= sk6 ) ),
inference(simp,[status(thm)],[11121]) ).
thf(70528,plain,
( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,50668]) ).
thf(70614,plain,
( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[70528]) ).
thf(48930,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk16 ) @ sk16 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[48875,144]) ).
thf(48931,plain,
( ( one_sorted_str @ empty_set )
| ~ ( in @ sk16 @ ( sk9 @ empty_set @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[48930:[bind(A,$thf( sk9 @ empty_set @ sk16 )),bind(B,$thf( sk16 ))]]) ).
thf(262,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty_carrier @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,49]) ).
thf(263,plain,
( ~ ( empty @ sk1 )
| ~ ( empty_carrier @ empty_set ) ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( sk1 ))]]) ).
thf(11816,plain,
( ( in @ ( sk10 @ sk2 @ empty_set ) @ sk2 )
!= ( in @ sk6 @ ( sk10 @ sk6 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[11728,10558]) ).
thf(11842,plain,
( ( ( sk10 @ sk2 @ empty_set )
!= sk6 )
| ( ( sk10 @ sk6 @ empty_set )
!= sk2 ) ),
inference(simp,[status(thm)],[11816]) ).
thf(41047,plain,
( ( element @ empty_set @ sk2 )
| ( ( empty @ ( sk10 @ sk2 @ empty_set ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,14505]) ).
thf(41138,plain,
( ( element @ empty_set @ sk2 )
| ( ( sk10 @ sk2 @ empty_set )
!= empty_set ) ),
inference(simp,[status(thm)],[41047]) ).
thf(41992,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,18954]) ).
thf(41993,plain,
( ~ ( empty @ sk1 )
| ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[41992:[bind(A,$thf( sk1 ))]]) ).
thf(22238,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty_carrier @ empty_set )
| ( sk11 != sk1 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,21913]) ).
thf(22239,plain,
( ~ ( empty @ sk11 )
| ~ ( empty_carrier @ empty_set )
| ( sk11 != sk1 ) ),
inference(pattern_uni,[status(thm)],[22238:[bind(A,$thf( sk11 ))]]) ).
thf(25373,plain,
( ~ ( empty_carrier @ empty_set )
| ( sk11 != sk1 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,22239]) ).
thf(25422,plain,
( ~ ( empty_carrier @ empty_set )
| ( sk11 != sk1 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[25373]) ).
thf(14255,plain,
( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
!= ( in @ sk6 @ ( sk9 @ empty_set @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[3379,10562]) ).
thf(14264,plain,
( ( ( sk9 @ empty_set @ sk6 )
!= sk6 )
| ( ( sk9 @ empty_set @ sk6 )
!= sk6 ) ),
inference(simp,[status(thm)],[14255]) ).
thf(14279,plain,
( ( sk9 @ empty_set @ sk6 )
!= sk6 ),
inference(simp,[status(thm)],[14264]) ).
thf(66716,plain,
! [A: $i] :
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( A = empty_set )
| ( ( empty @ ( bottom_of_relstr @ sk1 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45744,120]) ).
thf(66717,plain,
( ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ sk2 ) )
| ( ( bottom_of_relstr @ sk1 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[66716:[bind(A,$thf( bottom_of_relstr @ sk1 ))]]) ).
thf(40799,plain,
! [A: $i] :
( ( rel_str @ empty_set )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40684,10568]) ).
thf(40828,plain,
! [A: $i] :
( ( rel_str @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[40799]) ).
thf(40878,plain,
( ( rel_str @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[40828]) ).
thf(81106,plain,
( ( sk1 != empty_set )
| ( ( empty @ sk8 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,105]) ).
thf(81369,plain,
( ( sk1 != empty_set )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[81106]) ).
thf(55695,plain,
( ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,30271]) ).
thf(55748,plain,
( ( ( sk5 @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[55695]) ).
thf(11604,plain,
( ( in @ ( sk10 @ sk6 @ empty_set ) @ sk6 )
!= ( in @ sk6 @ ( sk10 @ sk6 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[5304,10558]) ).
thf(11615,plain,
( ( ( sk10 @ sk6 @ empty_set )
!= sk6 )
| ( ( sk10 @ sk6 @ empty_set )
!= sk6 ) ),
inference(simp,[status(thm)],[11604]) ).
thf(11636,plain,
( ( sk10 @ sk6 @ empty_set )
!= sk6 ),
inference(simp,[status(thm)],[11615]) ).
thf(51248,plain,
! [A: $i] :
( ( transitive_relstr @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51133,10568]) ).
thf(51275,plain,
! [A: $i] :
( ( transitive_relstr @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[51248]) ).
thf(51313,plain,
( ( transitive_relstr @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[51275]) ).
thf(10599,plain,
( ( in @ ( sk9 @ empty_set @ sk8 ) @ sk8 )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[8751,10522]) ).
thf(10674,plain,
( ( ( sk9 @ empty_set @ sk8 )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[10599]) ).
thf(81645,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk6 != sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81389]) ).
thf(81646,plain,
( ~ ( empty @ sk1 )
| ( sk6 != sk1 ) ),
inference(pattern_uni,[status(thm)],[81645:[bind(A,$thf( sk1 ))]]) ).
thf(30173,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( the_carrier @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22486,30040]) ).
thf(30174,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( the_carrier @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[30173:[]]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ~ ( rel_str @ A )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( element @ ( sk19 @ B @ A ) @ ( the_carrier @ A ) )
| ( upper_relstr_subset @ B @ A ) ),
inference(cnf,[status(esa)],[169]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( lower_bounded_relstr @ A )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,43]) ).
thf(386,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( lower_bounded_relstr @ A ) ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(22178,plain,
( ~ ( empty_carrier @ sk11 )
| ~ ( empty @ sk1 )
| ( ( v1_yellow_3 @ sk11 )
!= ( v1_yellow_3 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[965,21885]) ).
thf(22222,plain,
( ~ ( empty_carrier @ sk11 )
| ~ ( empty @ sk1 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[22178]) ).
thf(996,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( subset @ B @ C )
| ( ( element @ ( sk12 @ A ) @ ( powerset @ A ) )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[128,70]) ).
thf(997,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk12 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[996:[bind(A,$thf( D )),bind(B,$thf( sk12 @ D )),bind(C,$thf( D ))]]) ).
thf(1008,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk12 @ A ) @ A ) ),
inference(simp,[status(thm)],[997]) ).
thf(56967,plain,
( ( sk1 != empty_set )
| ( ( in @ sk2 @ ( sk10 @ sk2 @ empty_set ) )
!= ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[32630,11776]) ).
thf(56980,plain,
( ( sk1 != empty_set )
| ( sk2 != sk2 )
| ( ( sk10 @ sk2 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[56967]) ).
thf(57034,plain,
( ( sk1 != empty_set )
| ( ( sk10 @ sk2 @ empty_set )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[56980]) ).
thf(445,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( antisymmetric_relstr @ A )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,54]) ).
thf(446,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( antisymmetric_relstr @ A ) ),
inference(pattern_uni,[status(thm)],[445:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(3004,plain,
( ~ ( empty @ ( sk5 @ empty_set ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,2817]) ).
thf(3007,plain,
( ~ ( empty @ ( sk5 @ empty_set ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[3004]) ).
thf(20706,plain,
( ( ( bottom_of_relstr @ sk11 )
= ( bottom_of_relstr @ sk1 ) )
| ( ( join_on_relstr @ sk11 @ empty_set )
!= ( join_on_relstr @ sk1 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[19943,19993]) ).
thf(20776,plain,
( ( ( bottom_of_relstr @ sk11 )
= ( bottom_of_relstr @ sk1 ) )
| ( sk11 != sk1 )
| ( empty_set != empty_set ) ),
inference(simp,[status(thm)],[20706]) ).
thf(20792,plain,
( ( ( bottom_of_relstr @ sk11 )
= ( bottom_of_relstr @ sk1 ) )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[20776]) ).
thf(93780,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22486,93589]) ).
thf(93781,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[93780:[]]) ).
thf(77015,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,54508]) ).
thf(77095,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ ( the_carrier @ sk11 ) )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[77015]) ).
thf(103709,plain,
( ~ ( empty @ sk11 )
| ( sk16 != empty_set )
| ( ( empty @ ( the_carrier @ sk11 ) )
!= ( empty @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[77095]) ).
thf(103717,plain,
( ~ ( empty @ sk11 )
| ( sk16 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk11 ) ),
inference(simp,[status(thm)],[103709]) ).
thf(101445,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk11 )
| ( sk1 != empty_set )
| ( ( the_carrier @ empty_set )
!= sk11 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,77500]) ).
thf(101446,plain,
( ~ ( empty @ sk11 )
| ~ ( empty @ sk11 )
| ( sk1 != empty_set )
| ( ( the_carrier @ empty_set )
!= sk11 ) ),
inference(pattern_uni,[status(thm)],[101445:[bind(A,$thf( sk11 ))]]) ).
thf(101576,plain,
( ~ ( empty @ sk11 )
| ( sk1 != empty_set )
| ( ( the_carrier @ empty_set )
!= sk11 ) ),
inference(simp,[status(thm)],[101446]) ).
thf(81174,plain,
( ( sk1 != empty_set )
| ( empty_carrier @ sk11 )
| ( ( empty @ ( sk5 @ sk11 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,14679]) ).
thf(81391,plain,
( ( empty_carrier @ sk11 )
| ( sk1 != empty_set )
| ( ( sk5 @ sk11 )
!= sk1 ) ),
inference(simp,[status(thm)],[81174]) ).
thf(83606,plain,
! [A: $i] :
( ( empty @ sk1 )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[83468,10568]) ).
thf(83649,plain,
! [A: $i] :
( ( empty @ sk1 )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[83606]) ).
thf(83707,plain,
( ( empty @ sk1 )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[83649]) ).
thf(103489,plain,
( ( sk11 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk16 )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,76941]) ).
thf(103558,plain,
( ( sk11 != empty_set )
| ( ( the_carrier @ sk11 )
!= sk16 )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[103489]) ).
thf(27996,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( in @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[120,27991]) ).
thf(27997,plain,
( ~ ( empty @ sk16 )
| ( in @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[27996:[bind(A,$thf( sk16 ))]]) ).
thf(14672,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( one_sorted_str @ empty_set )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,14661]) ).
thf(14673,plain,
( ~ ( empty @ sk11 )
| ( one_sorted_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[14672:[bind(A,$thf( sk11 ))]]) ).
thf(49690,plain,
( ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ sk1 ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,20687]) ).
thf(49773,plain,
( ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ sk1 ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[49690]) ).
thf(74656,plain,
( ~ ( empty @ sk11 )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,54407]) ).
thf(74724,plain,
( ~ ( empty @ sk11 )
| ( ( the_carrier @ sk11 )
!= empty_set )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[74656]) ).
thf(449,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ~ ( empty_carrier @ A )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,49]) ).
thf(450,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ~ ( empty_carrier @ A ) ),
inference(pattern_uni,[status(thm)],[449:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(91295,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( element @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( the_carrier @ sk16 ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[13586,90534]) ).
thf(91296,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( element @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( the_carrier @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[91295:[]]) ).
thf(105322,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ sk11 )
!= sk11 )
| ( ( empty @ sk11 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,78260]) ).
thf(105396,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ sk11 )
!= sk11 )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[105322]) ).
thf(82060,plain,
! [B: $i,A: $i] :
( ( empty @ sk1 )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[81964,91]) ).
thf(82061,plain,
( ( empty @ sk1 )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[82060:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(158,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( sk17 @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(101083,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ sk2 @ ( bottom_of_relstr @ sk1 ) ) @ ( bottom_of_relstr @ sk1 ) )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk2 @ ( bottom_of_relstr @ sk1 ) ) @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19790,91]) ).
thf(101084,plain,
( ( in @ ( sk9 @ sk2 @ ( bottom_of_relstr @ sk1 ) ) @ ( bottom_of_relstr @ sk1 ) )
| ( element @ ( sk10 @ sk2 @ ( bottom_of_relstr @ sk1 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[101083:[bind(A,$thf( sk10 @ sk2 @ ( bottom_of_relstr @ sk1 ) )),bind(B,$thf( sk2 ))]]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ~ ( in @ ( sk10 @ B @ A ) @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[107]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( in @ ( sk9 @ B @ A ) @ A )
| ~ ( in @ ( sk10 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( rel_str @ A )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( in @ ( sk18 @ B @ A ) @ B )
| ( upper_relstr_subset @ B @ A ) ),
inference(cnf,[status(esa)],[169]) ).
thf(40016,plain,
! [B: $i,A: $i] :
( ( rel_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39939,91]) ).
thf(40017,plain,
( ( rel_str @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[40016:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(92402,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( sk5 @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[92304,144]) ).
thf(92403,plain,
~ ( in @ ( sk5 @ sk1 ) @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[92402:[bind(A,$thf( sk9 @ empty_set @ ( sk5 @ sk1 ) )),bind(B,$thf( sk5 @ sk1 ))]]) ).
thf(104603,plain,
( ~ ( empty @ sk11 )
| ( ( the_carrier @ sk11 )
!= sk16 )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,77099]) ).
thf(104672,plain,
( ~ ( empty @ sk11 )
| ( ( the_carrier @ sk11 )
!= sk16 )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[104603]) ).
thf(95642,plain,
! [A: $i] :
( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk1 ) ) @ ( the_carrier @ sk1 ) )
!= ( in @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[95454,10568]) ).
thf(95692,plain,
! [A: $i] :
( ( ( sk9 @ empty_set @ ( the_carrier @ sk1 ) )
!= A )
| ( ( the_carrier @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[95642]) ).
thf(95773,plain,
( ( sk9 @ empty_set @ ( the_carrier @ sk1 ) )
!= ( the_carrier @ sk1 ) ),
inference(simp,[status(thm)],[95692]) ).
thf(82887,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( sk5 @ sk16 )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81407]) ).
thf(82888,plain,
( ~ ( empty @ sk1 )
| ( ( sk5 @ sk16 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[82887:[bind(A,$thf( sk1 ))]]) ).
thf(69670,plain,
! [A: $i] :
( ( filtered_subset @ sk2 @ empty_set )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[69539,10568]) ).
thf(69735,plain,
! [A: $i] :
( ( filtered_subset @ sk2 @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[69670]) ).
thf(69762,plain,
( ( filtered_subset @ sk2 @ empty_set )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[69735]) ).
thf(79421,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( the_carrier @ sk16 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[79298,91]) ).
thf(79422,plain,
element @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( the_carrier @ sk16 ),
inference(pattern_uni,[status(thm)],[79421:[bind(A,$thf( sk9 @ empty_set @ ( the_carrier @ sk16 ) )),bind(B,$thf( the_carrier @ sk16 ))]]) ).
thf(47540,plain,
! [A: $i] :
( ( rel_str @ empty_set )
| ( ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47425,10568]) ).
thf(47585,plain,
! [A: $i] :
( ( rel_str @ empty_set )
| ( ( sk10 @ sk11 @ empty_set )
!= A )
| ( sk11 != A ) ),
inference(simp,[status(thm)],[47540]) ).
thf(47615,plain,
( ( rel_str @ empty_set )
| ( ( sk10 @ sk11 @ empty_set )
!= sk11 ) ),
inference(simp,[status(thm)],[47585]) ).
thf(58227,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk11 ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[58168,144]) ).
thf(58228,plain,
( ( one_sorted_str @ empty_set )
| ~ ( in @ sk11 @ ( sk9 @ empty_set @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[58227:[bind(A,$thf( sk9 @ empty_set @ sk11 )),bind(B,$thf( sk11 ))]]) ).
thf(47480,plain,
! [B: $i,A: $i] :
( ( rel_str @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk10 @ sk11 @ empty_set ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[47425,144]) ).
thf(47481,plain,
( ( rel_str @ empty_set )
| ~ ( in @ sk11 @ ( sk10 @ sk11 @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[47480:[bind(A,$thf( sk10 @ sk11 @ empty_set )),bind(B,$thf( sk11 ))]]) ).
thf(53218,plain,
! [B: $i,A: $i] :
( ( empty_carrier @ sk3 )
| ~ ( in @ B @ A )
| ( ( in @ ( sk5 @ sk3 ) @ ( powerset @ ( the_carrier @ sk3 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[53153,144]) ).
thf(53219,plain,
( ( empty_carrier @ sk3 )
| ~ ( in @ ( powerset @ ( the_carrier @ sk3 ) ) @ ( sk5 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[53218:[bind(A,$thf( sk5 @ sk3 )),bind(B,$thf( powerset @ ( the_carrier @ sk3 ) ))]]) ).
thf(90499,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) @ ( sk5 @ sk16 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[90399,144]) ).
thf(90500,plain,
~ ( in @ ( sk5 @ sk16 ) @ ( sk9 @ empty_set @ ( sk5 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[90499:[bind(A,$thf( sk9 @ empty_set @ ( sk5 @ sk16 ) )),bind(B,$thf( sk5 @ sk16 ))]]) ).
thf(81569,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk8 != sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,81369]) ).
thf(81570,plain,
( ~ ( empty @ sk1 )
| ( sk8 != sk1 ) ),
inference(pattern_uni,[status(thm)],[81569:[bind(A,$thf( sk1 ))]]) ).
thf(81,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ? [C: $i] :
( ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) ),
inference(miniscope,[status(thm)],[80]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ~ ( empty @ C ) ),
inference(cnf,[status(esa)],[81]) ).
thf(10823,plain,
( ( in @ ( sk9 @ empty_set @ sk8 ) @ sk8 )
!= ( in @ sk8 @ ( sk9 @ empty_set @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[8751,10534]) ).
thf(10901,plain,
( ( ( sk9 @ empty_set @ sk8 )
!= sk8 )
| ( ( sk9 @ empty_set @ sk8 )
!= sk8 ) ),
inference(simp,[status(thm)],[10823]) ).
thf(10909,plain,
( ( sk9 @ empty_set @ sk8 )
!= sk8 ),
inference(simp,[status(thm)],[10901]) ).
thf(81248,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( the_carrier @ empty_set ) )
!= ( empty @ sk16 ) )
| ( ( empty @ sk16 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79732,1485]) ).
thf(81368,plain,
( ( sk1 != empty_set )
| ( ( the_carrier @ empty_set )
!= sk16 )
| ( sk16 != sk1 ) ),
inference(simp,[status(thm)],[81248]) ).
thf(56610,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[56492,10568]) ).
thf(56649,plain,
! [A: $i] :
( ( one_sorted_str @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[56610]) ).
thf(56685,plain,
( ( one_sorted_str @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[56649]) ).
thf(90439,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( sk5 @ sk16 ) )
| ( ( sk5 @ sk16 )
!= ( sk5 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[13586,90399]) ).
thf(90440,plain,
( ( proper_element @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
| ( in @ ( sk9 @ empty_set @ ( the_carrier @ sk16 ) ) @ ( sk5 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[90439:[]]) ).
thf(46834,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ empty_set ) )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[120,19975]) ).
thf(46835,plain,
( ~ ( empty @ sk11 )
| ( ( join_on_relstr @ empty_set @ empty_set )
= ( bottom_of_relstr @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[46834:[bind(A,$thf( sk11 ))]]) ).
thf(66,plain,
empty @ sk4,
inference(cnf,[status(esa)],[65]) ).
thf(272,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk4 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[66,120]) ).
thf(273,plain,
sk4 = empty_set,
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( sk4 ))]]) ).
thf(35020,plain,
! [B: $i,A: $i] :
( ( sk16 != empty_set )
| ( element @ A @ ( powerset @ B ) )
| ( ( subset @ ( sk5 @ empty_set ) @ ( the_carrier @ sk16 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9461,71]) ).
thf(35021,plain,
( ( sk16 != empty_set )
| ( element @ ( sk5 @ empty_set ) @ ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[35020:[bind(A,$thf( sk5 @ empty_set )),bind(B,$thf( the_carrier @ sk16 ))]]) ).
thf(16727,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( the_carrier @ empty_set )
!= empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,16712]) ).
thf(16728,plain,
( ~ ( empty @ sk1 )
| ( ( the_carrier @ empty_set )
!= empty_set ) ),
inference(pattern_uni,[status(thm)],[16727:[bind(A,$thf( sk1 ))]]) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( finite @ B )
| ( finite @ C )
| ( ( element @ empty_set @ ( powerset @ A ) )
!= ( element @ C @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[636,79]) ).
thf(1225,plain,
! [A: $i] :
( ~ ( finite @ A )
| ( finite @ empty_set ) ),
inference(pattern_uni,[status(thm)],[1224:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( empty_set ))]]) ).
thf(6923,plain,
! [A: $i] :
( ( finite @ empty_set )
| ( ( finite @ sk8 )
!= ( finite @ A ) ) ),
inference(paramod_ordered,[status(thm)],[104,1225]) ).
thf(6924,plain,
finite @ empty_set,
inference(pattern_uni,[status(thm)],[6923:[bind(A,$thf( sk8 ))]]) ).
thf(38978,plain,
! [B: $i,A: $i] :
( ( antisymmetric_relstr @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38901,91]) ).
thf(38979,plain,
( ( antisymmetric_relstr @ empty_set )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[38978:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(16127,plain,
( ( empty_carrier @ sk11 )
| ( ( empty @ ( sk5 @ sk11 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,14679]) ).
thf(16160,plain,
( ( empty_carrier @ sk11 )
| ( ( sk5 @ sk11 )
!= empty_set ) ),
inference(simp,[status(thm)],[16127]) ).
thf(11841,plain,
( ( in @ ( sk10 @ sk2 @ empty_set ) @ sk2 )
!= ( in @ ( powerset @ ( the_carrier @ sk1 ) ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[11728,10522]) ).
thf(11847,plain,
( ( ( sk10 @ sk2 @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[11841]) ).
thf(11871,plain,
( ( sk10 @ sk2 @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[11847]) ).
thf(421,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( rel_str @ A )
| ( B != sk11 ) ),
inference(paramod_ordered,[status(thm)],[64,117]) ).
thf(422,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk11 )
| ( rel_str @ A ) ),
inference(pattern_uni,[status(thm)],[421:[bind(A,$thf( A )),bind(B,$thf( sk11 ))]]) ).
thf(789,plain,
( ~ ( empty_carrier @ empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,263]) ).
thf(790,plain,
( ~ ( empty_carrier @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[789]) ).
thf(50277,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk16 @ empty_set ) @ sk16 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50200,91]) ).
thf(50278,plain,
( ( one_sorted_str @ empty_set )
| ( element @ ( sk10 @ sk16 @ empty_set ) @ sk16 ) ),
inference(pattern_uni,[status(thm)],[50277:[bind(A,$thf( sk10 @ sk16 @ empty_set )),bind(B,$thf( sk16 ))]]) ).
thf(38720,plain,
( ~ ( in @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,10580]) ).
thf(38832,plain,
( ~ ( in @ ( powerset @ ( the_carrier @ empty_set ) ) @ sk2 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[38720]) ).
thf(505,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( rel_str @ A )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,51]) ).
thf(506,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( rel_str @ A ) ),
inference(pattern_uni,[status(thm)],[505:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(473,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( reflexive_relstr @ A )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,50]) ).
thf(474,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( reflexive_relstr @ A ) ),
inference(pattern_uni,[status(thm)],[473:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(85833,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,85244]) ).
thf(85834,plain,
( ~ ( empty @ sk1 )
| ( ( powerset @ ( the_carrier @ empty_set ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[85833:[bind(A,$thf( sk1 ))]]) ).
thf(921,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( empty @ ( the_carrier @ A ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,73]) ).
thf(928,plain,
! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( the_carrier @ A )
!= empty_set ) ),
inference(simp,[status(thm)],[921]) ).
thf(304,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( element @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,47]) ).
thf(305,plain,
( ~ ( empty @ sk1 )
| ( element @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[304:[bind(A,$thf( sk1 ))]]) ).
thf(11084,plain,
( ( in @ ( sk9 @ empty_set @ sk2 ) @ sk2 )
!= ( in @ sk2 @ ( sk9 @ empty_set @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[10253,10546]) ).
thf(11128,plain,
( ( ( sk9 @ empty_set @ sk2 )
!= sk2 )
| ( ( sk9 @ empty_set @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[11084]) ).
thf(11155,plain,
( ( sk9 @ empty_set @ sk2 )
!= sk2 ),
inference(simp,[status(thm)],[11128]) ).
thf(56963,plain,
( ( sk1 != empty_set )
| ( ( in @ sk2 @ ( sk9 @ empty_set @ sk2 ) )
!= ( in @ sk2 @ ( powerset @ ( the_carrier @ empty_set ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[32630,10546]) ).
thf(56985,plain,
( ( sk1 != empty_set )
| ( sk2 != sk2 )
| ( ( sk9 @ empty_set @ sk2 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[56963]) ).
thf(57038,plain,
( ( sk1 != empty_set )
| ( ( sk9 @ empty_set @ sk2 )
!= ( powerset @ ( the_carrier @ empty_set ) ) ) ),
inference(simp,[status(thm)],[56985]) ).
thf(43953,plain,
( ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19203]) ).
thf(44059,plain,
( ( element @ ( bottom_of_relstr @ empty_set ) @ ( the_carrier @ sk1 ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[43953]) ).
thf(84871,plain,
! [A: $i] :
( ( finite @ sk1 )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[84733,10568]) ).
thf(84940,plain,
! [A: $i] :
( ( finite @ sk1 )
| ( ( sk9 @ empty_set @ sk1 )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[84871]) ).
thf(84988,plain,
( ( finite @ sk1 )
| ( ( sk9 @ empty_set @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[84940]) ).
thf(37245,plain,
( ( finite @ sk2 )
| ( ( the_carrier @ empty_set )
!= sk8 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,2358]) ).
thf(37314,plain,
( ( finite @ sk2 )
| ( ( the_carrier @ empty_set )
!= sk8 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[37245]) ).
thf(31688,plain,
! [A: $i] :
( ( transitive_relstr @ empty_set )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31574,10568]) ).
thf(31717,plain,
! [A: $i] :
( ( transitive_relstr @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[31688]) ).
thf(31757,plain,
( ( transitive_relstr @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[31717]) ).
thf(32767,plain,
( ( in @ empty_set @ sk6 )
| ( ( empty @ ( sk10 @ sk6 @ empty_set ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,5306]) ).
thf(32873,plain,
( ( in @ empty_set @ sk6 )
| ( ( sk10 @ sk6 @ empty_set )
!= empty_set ) ),
inference(simp,[status(thm)],[32767]) ).
thf(34360,plain,
( ( element @ empty_set @ sk8 )
| ( ( empty @ ( sk9 @ empty_set @ sk8 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,8895]) ).
thf(34455,plain,
( ( element @ empty_set @ sk8 )
| ( ( sk9 @ empty_set @ sk8 )
!= empty_set ) ),
inference(simp,[status(thm)],[34360]) ).
thf(25978,plain,
( ( finite @ ( sk5 @ sk1 ) )
| ( ( finite @ ( the_carrier @ sk1 ) )
!= ( finite @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[104,22534]) ).
thf(26007,plain,
( ( finite @ ( sk5 @ sk1 ) )
| ( ( the_carrier @ sk1 )
!= sk8 ) ),
inference(simp,[status(thm)],[25978]) ).
thf(10895,plain,
( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
!= ( in @ sk8 @ ( sk9 @ empty_set @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[3379,10534]) ).
thf(10896,plain,
( ( ( sk9 @ empty_set @ sk6 )
!= sk8 )
| ( ( sk9 @ empty_set @ sk8 )
!= sk6 ) ),
inference(simp,[status(thm)],[10895]) ).
thf(13481,plain,
! [B: $i,A: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( proper_element @ B @ ( powerset @ A ) )
| ( B != empty_set )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[150,183]) ).
thf(13482,plain,
! [A: $i] :
( ~ ( element @ A @ ( powerset @ sk6 ) )
| ( proper_element @ A @ ( powerset @ sk6 ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[13481:[bind(A,$thf( sk6 ))]]) ).
thf(14024,plain,
( ~ ( element @ empty_set @ ( powerset @ sk6 ) )
| ( proper_element @ empty_set @ ( powerset @ sk6 ) ) ),
inference(simp,[status(thm)],[13482]) ).
thf(116812,plain,
( ~ $true
| ( proper_element @ empty_set @ ( powerset @ sk6 ) ) ),
inference(rewrite,[status(thm)],[14024,636]) ).
thf(116813,plain,
proper_element @ empty_set @ ( powerset @ sk6 ),
inference(simp,[status(thm)],[116812]) ).
thf(116858,plain,
! [A: $i] :
( ( proper_element @ empty_set @ ( powerset @ sk6 ) )
!= ( proper_element @ A @ ( powerset @ A ) ) ),
inference(paramod_ordered,[status(thm)],[116813,11245]) ).
thf(116895,plain,
! [A: $i] :
( ( empty_set != A )
| ( ( powerset @ sk6 )
!= ( powerset @ A ) ) ),
inference(simp,[status(thm)],[116858]) ).
thf(116906,plain,
( ( powerset @ sk6 )
!= ( powerset @ empty_set ) ),
inference(simp,[status(thm)],[116895]) ).
thf(20331,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( bottom_of_relstr @ sk11 )
= empty_set )
| ( A
!= ( join_on_relstr @ sk11 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[120,19943]) ).
thf(20332,plain,
( ~ ( empty @ ( join_on_relstr @ sk11 @ empty_set ) )
| ( ( bottom_of_relstr @ sk11 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[20331:[bind(A,$thf( join_on_relstr @ sk11 @ empty_set ))]]) ).
thf(48211,plain,
( ~ ( empty @ ( bottom_of_relstr @ sk11 ) )
| ( ( bottom_of_relstr @ sk11 )
= empty_set ) ),
inference(rewrite,[status(thm)],[20332,19943]) ).
thf(17522,plain,
( ( ( the_carrier @ empty_set )
!= empty_set )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,16728]) ).
thf(17572,plain,
( ( ( the_carrier @ empty_set )
!= empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[17522]) ).
thf(441,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( transitive_relstr @ A )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,44]) ).
thf(442,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( transitive_relstr @ A ) ),
inference(pattern_uni,[status(thm)],[441:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(20157,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( bottom_of_relstr @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[120,19729]) ).
thf(20158,plain,
( ~ ( empty @ sk1 )
| ( ( bottom_of_relstr @ empty_set )
!= ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[20157:[bind(A,$thf( sk1 ))]]) ).
thf(25474,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ sk1 ) )
!= ( in @ sk6 @ ( sk9 @ empty_set @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[25449,10562]) ).
thf(25593,plain,
( ( ( bottom_of_relstr @ sk1 )
!= sk6 )
| ( ( sk9 @ empty_set @ sk6 )
!= ( the_carrier @ sk1 ) ) ),
inference(simp,[status(thm)],[25474]) ).
thf(31650,plain,
! [B: $i,A: $i] :
( ( transitive_relstr @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31574,91]) ).
thf(31651,plain,
( ( transitive_relstr @ empty_set )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[31650:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(44442,plain,
! [A: $i] :
( ( lower_bounded_relstr @ empty_set )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44327,10568]) ).
thf(44472,plain,
! [A: $i] :
( ( lower_bounded_relstr @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[44442]) ).
thf(44505,plain,
( ( lower_bounded_relstr @ empty_set )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[44472]) ).
thf(11381,plain,
( ( in @ ( sk9 @ empty_set @ sk6 ) @ sk6 )
!= ( in @ sk8 @ ( sk10 @ sk8 @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[3379,10550]) ).
thf(11390,plain,
( ( ( sk9 @ empty_set @ sk6 )
!= sk8 )
| ( ( sk10 @ sk8 @ empty_set )
!= sk6 ) ),
inference(simp,[status(thm)],[11381]) ).
thf(92497,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( the_carrier @ sk1 ) )
| ( ( sk5 @ sk1 )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22486,92304]) ).
thf(92498,plain,
( ( proper_element @ ( sk5 @ sk1 ) @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ( in @ ( sk9 @ empty_set @ ( sk5 @ sk1 ) ) @ ( the_carrier @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[92497:[]]) ).
thf(36625,plain,
! [B: $i,A: $i] :
( ( one_sorted_str @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk3 @ empty_set ) @ sk3 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[36549,91]) ).
thf(36626,plain,
( ( one_sorted_str @ empty_set )
| ( element @ ( sk10 @ sk3 @ empty_set ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[36625:[bind(A,$thf( sk10 @ sk3 @ empty_set )),bind(B,$thf( sk3 ))]]) ).
thf(722,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( subset @ sk2 @ ( the_carrier @ A ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[64,697]) ).
thf(723,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( subset @ sk2 @ ( the_carrier @ A ) ) ),
inference(pattern_uni,[status(thm)],[722:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(61672,plain,
( ( ( powerset @ ( powerset @ ( the_carrier @ empty_set ) ) )
!= sk2 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,39564]) ).
thf(61755,plain,
( ( ( powerset @ ( powerset @ ( the_carrier @ empty_set ) ) )
!= sk2 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[61672]) ).
thf(28031,plain,
( ( in @ ( sk5 @ sk16 ) @ ( powerset @ ( the_carrier @ sk16 ) ) )
!= ( in @ sk2 @ ( bottom_of_relstr @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[27991,19627]) ).
thf(28167,plain,
( ( ( sk5 @ sk16 )
!= sk2 )
| ( ( bottom_of_relstr @ sk1 )
!= ( powerset @ ( the_carrier @ sk16 ) ) ) ),
inference(simp,[status(thm)],[28031]) ).
thf(52189,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ empty_set ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,25455]) ).
thf(52296,plain,
( ( in @ ( bottom_of_relstr @ sk1 ) @ ( the_carrier @ empty_set ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[52189]) ).
thf(51188,plain,
! [B: $i,A: $i] :
( ( transitive_relstr @ empty_set )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51133,144]) ).
thf(51189,plain,
( ( transitive_relstr @ empty_set )
| ~ ( in @ sk1 @ ( sk9 @ empty_set @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[51188:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(34069,plain,
! [B: $i,A: $i] :
( ( reflexive_relstr @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33993,91]) ).
thf(34070,plain,
( ( reflexive_relstr @ empty_set )
| ( element @ ( sk10 @ sk1 @ empty_set ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[34069:[bind(A,$thf( sk10 @ sk1 @ empty_set )),bind(B,$thf( sk1 ))]]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ( element @ A @ C ) ),
inference(cnf,[status(esa)],[121]) ).
thf(10894,plain,
( ( in @ ( sk10 @ sk6 @ empty_set ) @ sk6 )
!= ( in @ sk8 @ ( sk9 @ empty_set @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[5304,10534]) ).
thf(10902,plain,
( ( ( sk10 @ sk6 @ empty_set )
!= sk8 )
| ( ( sk9 @ empty_set @ sk8 )
!= sk6 ) ),
inference(simp,[status(thm)],[10894]) ).
thf(99589,plain,
! [A: $i] :
( ( in @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk1 ) )
| ( ( join_on_relstr @ sk11 @ empty_set )
!= ( join_on_relstr @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19943,99535]) ).
thf(99756,plain,
! [A: $i] :
( ( in @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk1 ) )
| ( sk11 != sk1 )
| ( empty_set != A ) ),
inference(simp,[status(thm)],[99589]) ).
thf(99851,plain,
( ( in @ ( bottom_of_relstr @ sk11 ) @ ( the_carrier @ sk1 ) )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[99756]) ).
thf(96921,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[96791,91]) ).
thf(96922,plain,
element @ ( sk10 @ ( the_carrier @ sk1 ) @ empty_set ) @ ( the_carrier @ sk1 ),
inference(pattern_uni,[status(thm)],[96921:[bind(A,$thf( sk10 @ ( the_carrier @ sk1 ) @ empty_set )),bind(B,$thf( the_carrier @ sk1 ))]]) ).
thf(82034,plain,
! [B: $i,A: $i] :
( ( empty @ sk1 )
| ~ ( in @ B @ A )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[81964,144]) ).
thf(82035,plain,
( ( empty @ sk1 )
| ~ ( in @ sk1 @ ( sk9 @ empty_set @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[82034:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(38076,plain,
! [B: $i,A: $i] :
( ( antisymmetric_relstr @ empty_set )
| ( element @ A @ B )
| ( ( in @ ( sk9 @ empty_set @ sk1 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38000,91]) ).
thf(38077,plain,
( ( antisymmetric_relstr @ empty_set )
| ( element @ ( sk9 @ empty_set @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[38076:[bind(A,$thf( sk9 @ empty_set @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(86556,plain,
! [A: $i] :
( ( finite @ sk1 )
| ( ( in @ ( sk10 @ sk1 @ empty_set ) @ sk1 )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[86416,10568]) ).
thf(86594,plain,
! [A: $i] :
( ( finite @ sk1 )
| ( ( sk10 @ sk1 @ empty_set )
!= A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[86556]) ).
thf(86647,plain,
( ( finite @ sk1 )
| ( ( sk10 @ sk1 @ empty_set )
!= sk1 ) ),
inference(simp,[status(thm)],[86594]) ).
thf(155979,plain,
$false,
inference(e,[status(thm)],[40422,1411,138,101,55077,21164,249,3863,8755,82376,30353,809,83565,29039,19704,88,170,26746,48875,22397,9604,84804,120,95584,31295,115332,1406,115,730,16228,99967,10679,60481,3285,2676,10562,47868,13586,25585,77097,1486,56573,19005,74857,89091,11848,3649,142,29897,1233,10209,60290,86416,43538,153,19975,103244,69630,36487,45822,16658,2627,113576,21285,27187,85507,22365,898,43192,3915,8816,54308,35198,77920,39456,35493,14023,52585,104830,99859,41348,76518,20031,174,97087,22223,2723,42,13098,14669,32687,25499,18671,91294,89885,16712,92630,104522,52,81468,3425,5306,67033,40115,125,93923,157,72098,11986,10534,86513,58250,39253,11849,57,93724,19052,63504,93688,82204,76941,38194,93,54164,25599,58641,67011,50161,44405,33993,78,44383,20790,261,38901,1415,164,81380,46994,87710,35321,19201,253,40684,121,56462,54407,45747,126426,20687,106,92628,19700,42594,35970,28836,82492,132,41882,1526,116,20905,74123,47503,94609,27174,3537,54599,90442,54826,61,31629,102375,81355,293,95548,89,1351,133,20963,22421,11728,56551,25042,74,19729,54967,8751,14661,18954,15967,81454,87744,25636,35680,60,117,10693,29757,31574,925,54508,85,81964,31360,102,11730,83468,52095,23970,81486,85367,160,90702,34048,1487,70,18091,10394,27165,56340,107545,910,13850,50646,53104,12012,165,81356,79732,47146,17467,54971,45956,92,65,24858,97,14681,51640,51211,3050,16040,101553,229,25640,9641,63677,10580,50377,54416,156,3381,14505,1540,10318,169,89032,46241,10678,10676,27161,38957,8895,52918,32679,19048,697,79603,85244,98717,78260,32689,13939,53153,317,48953,126339,45844,79388,99809,77346,88991,19203,980,36738,22241,1425,8619,83539,53,141,67061,34180,25716,54306,58168,77,24505,38055,3010,642,25455,27999,47383,11797,100302,1329,81306,19588,93320,81437,1612,679,76522,28748,50668,35285,2813,3760,10550,605,11129,19790,77497,27146,49180,1456,54691,61597,173,19943,84830,28182,41661,9461,129,22301,52457,24593,52341,134,89308,105,55181,22572,21883,49071,15592,24320,19227,25451,16329,43828,92304,50819,19627,530,19354,73,128,25714,104360,55332,123512,77099,39069,27217,66826,113484,20422,30103,41766,11414,45744,18080,430,71633,44327,30351,30050,161,64,30048,39939,965,75270,31874,74763,105688,166,103885,78251,108948,28838,44,2525,90534,37646,104208,5350,77222,259,86487,81407,16935,46257,191,25811,58363,772,45766,711,36604,59,39263,118,96886,2817,39995,313,40740,49,19728,50256,93318,2358,123502,101575,17115,38000,71,14667,382,54,55079,10257,78256,144,3487,47425,89883,53366,19702,39564,81372,159,14711,86,21222,72821,406,113,11127,93438,60351,76,37944,9702,434,98,30040,187,93919,172,22399,18457,19945,32227,14679,10898,85184,73977,24168,41744,75123,858,103,92496,140,29614,123390,35398,123738,11387,76094,155,19054,98688,48612,33396,10253,2625,91,56492,44272,19737,30271,2725,33011,22387,87902,394,81389,2967,102194,93589,36549,130,67109,2439,94611,2835,20805,636,54414,81438,6783,11245,135,76936,24725,19880,241,78628,80,32989,25597,33112,35376,40762,60373,33947,101584,927,22534,112,939,123,145,39411,3009,42210,104548,19695,89125,27706,255,77500,46380,55050,43398,54577,2899,71866,823,10016,93783,81722,55864,75007,27152,19050,48,89319,22574,90692,705,54162,150,71725,20306,50200,82600,61526,27137,95,104209,87482,89034,126577,95454,46073,24721,19810,11126,70614,19993,51133,48931,263,50,18952,9462,11842,41138,14671,16327,22486,127,81423,41993,67,90399,25422,182,52385,14279,55178,30228,81042,66717,20334,79298,92439,32677,40878,10558,81344,54824,81369,154,2843,55748,9637,11636,51313,10674,85222,81646,30174,1485,2711,10568,72,175,386,22222,1008,32934,57034,446,143,3007,43,99535,876,20792,93781,103717,231,99,101576,87,81391,83707,103558,27997,14673,49773,74724,10712,39483,450,688,91296,25453,105396,104,81349,699,15913,32630,82061,1508,17464,158,101084,114,126014,171,139,40017,19143,10546,28053,54969,92403,104672,46231,95773,14663,58,10695,82888,69762,75,79422,19356,85223,5304,21885,235,47615,58228,47481,53219,19590,22239,90500,81570,54519,82,10909,3379,81368,56685,20138,54304,51,90440,46835,183,273,35021,17465,16728,6924,15917,151,77095,87619,168,38979,19205,16160,818,11871,422,790,50278,38832,77127,126,506,69539,474,81364,85834,928,305,11155,16326,96791,57038,44059,84988,79,77915,37314,31757,32873,20799,11776,2619,34455,26007,2651,10896,116906,48211,3869,41688,17572,20965,277,442,20158,25593,115249,31651,116813,44505,9816,23830,11390,92498,36626,19792,723,61755,28167,131,47,52296,163,21913,51189,1431,34070,122,10522,47006,10902,99851,16654,84733,63427,96922,100,90,18983,82035,28177,27991,28447,83,81341,25449,38077,86647]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU383+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 13:29:18 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.84/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.99 % [INFO] Parsing done (141ms).
% 1.19/0.99 % [INFO] Running in sequential loop mode.
% 1.76/1.20 % [INFO] eprover registered as external prover.
% 1.76/1.20 % [INFO] cvc4 registered as external prover.
% 1.76/1.20 % [INFO] Scanning for conjecture ...
% 1.90/1.27 % [INFO] Found a conjecture and 44 axioms. Running axiom selection ...
% 2.19/1.32 % [INFO] Axiom selection finished. Selected 39 axioms (removed 5 axioms).
% 2.19/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.19/1.37 % [INFO] Type checking passed.
% 2.19/1.37 % [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 ...
% 222.01/41.99 % External prover 'e' found a proof!
% 222.01/42.00 % [INFO] Killing All external provers ...
% 222.01/42.00 % Time passed: 41474ms (effective reasoning time: 40998ms)
% 222.01/42.00 % 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)>
% 222.01/42.00 % Axioms used in derivation (39): cc2_finset_1, rc4_finset_1, t5_tex_2, t5_subset, t2_tarski, t4_subset, t44_yellow_0, rc1_subset_1, cc3_yellow_3, d20_waybel_0, dt_l1_orders_2, existence_l1_struct_0, antisymmetry_r2_hidden, fc1_xboole_0, t1_subset, t6_boole, rc2_subset_1, t7_boole, existence_l1_orders_2, rc3_struct_0, fc1_subset_1, t3_subset, existence_m1_subset_1, dt_k3_yellow_0, fc1_struct_0, reflexivity_r1_tarski, d11_yellow_0, cc1_yellow_3, rc10_waybel_0, dt_k1_yellow_0, rc3_finset_1, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, cc2_yellow_3, rc2_xboole_0
% 222.01/42.00 % No. of inferences in proof: 1913
% 222.01/42.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 41474 ms resp. 40998 ms w/o parsing
% 222.41/42.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 222.41/42.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------