TSTP Solution File: SET069+1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET069+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 : Tue May 21 03:01:21 EDT 2024
% Result : Theorem 208.04s 39.52s
% Output : Refutation 208.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 84
% Syntax : Number of formulae : 1277 ( 516 unt; 40 typ; 0 def)
% Number of atoms : 2920 (1122 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 9249 (1491 ~; 854 |; 124 &;6673 @)
% ( 19 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 11 con; 0-3 aty)
% Number of variables : 1014 ( 0 ^ 995 !; 19 ?;1014 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(universal_class_type,type,
universal_class: $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(subclass_type,type,
subclass: $i > $i > $o ).
thf(restrict_type,type,
restrict: $i > $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(sum_class_type,type,
sum_class: $i > $i ).
thf(image_type,type,
image: $i > $i > $i ).
thf(null_class_type,type,
null_class: $i ).
thf(flip_type,type,
flip: $i > $i ).
thf(function_type,type,
function: $i > $o ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(identity_relation_type,type,
identity_relation: $i ).
thf(inductive_type,type,
inductive: $i > $o ).
thf(successor_relation_type,type,
successor_relation: $i ).
thf(power_class_type,type,
power_class: $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(first_type,type,
first: $i > $i ).
thf(second_type,type,
second: $i > $i ).
thf(rotate_type,type,
rotate: $i > $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(element_relation_type,type,
element_relation: $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(sk4_type,type,
sk4: $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_defn) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,axiom,
? [A: $i] :
( ( member @ A @ universal_class )
& ( inductive @ A )
& ! [B: $i] :
( ( inductive @ B )
=> ( subclass @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity) ).
thf(188,plain,
? [A: $i] :
( ( member @ A @ universal_class )
& ( inductive @ A )
& ! [B: $i] :
( ( inductive @ B )
=> ( subclass @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(190,plain,
inductive @ sk7,
inference(cnf,[status(esa)],[188]) ).
thf(13,axiom,
! [A: $i] :
( ( inductive @ A )
<=> ( ( member @ null_class @ A )
& ( subclass @ ( image @ successor_relation @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_defn) ).
thf(102,plain,
! [A: $i] :
( ( ( inductive @ A )
=> ( ( member @ null_class @ A )
& ( subclass @ ( image @ successor_relation @ A ) @ A ) ) )
& ( ( ( member @ null_class @ A )
& ( subclass @ ( image @ successor_relation @ A ) @ A ) )
=> ( inductive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(103,plain,
( ! [A: $i] :
( ( inductive @ A )
=> ( ( member @ null_class @ A )
& ( subclass @ ( image @ successor_relation @ A ) @ A ) ) )
& ! [A: $i] :
( ( ( member @ null_class @ A )
& ( subclass @ ( image @ successor_relation @ A ) @ A ) )
=> ( inductive @ A ) ) ),
inference(miniscope,[status(thm)],[102]) ).
thf(105,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
inference(cnf,[status(esa)],[103]) ).
thf(5701,plain,
! [A: $i] :
( ( member @ null_class @ A )
| ( ( inductive @ sk7 )
!= ( inductive @ A ) ) ),
inference(paramod_ordered,[status(thm)],[190,105]) ).
thf(5702,plain,
member @ null_class @ sk7,
inference(pattern_uni,[status(thm)],[5701:[bind(A,$thf( sk7 ))]]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ~ ( member @ B @ universal_class )
=> ( ( unordered_pair @ A @ B )
= ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pair_contains_only_other2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ~ ( member @ B @ universal_class )
=> ( ( unordered_pair @ A @ B )
= ( singleton @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(46,plain,
~ ! [A: $i,B: $i] :
( ~ ( member @ B @ universal_class )
=> ( ( unordered_pair @ A @ B )
= ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,plain,
~ ( member @ sk2 @ universal_class ),
inference(cnf,[status(esa)],[46]) ).
thf(5789,plain,
( ( member @ sk2 @ universal_class )
!= ( member @ null_class @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[5702,48]) ).
thf(5810,plain,
( ( sk2 != null_class )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[5789]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subclass @ A @ B )
& ( subclass @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subclass @ A @ B )
& ( subclass @ B @ A ) ) )
& ( ( ( subclass @ A @ B )
& ( subclass @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(51,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( subclass @ A @ B )
& ( subclass @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( subclass @ A @ B )
& ( subclass @ B @ A ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[50]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[51]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A ) ),
inference(simp,[status(thm)],[55]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ~ ( member @ sk2 @ A )
| ( B != universal_class ) ),
inference(paramod_ordered,[status(thm)],[56,48]) ).
thf(313,plain,
! [A: $i] :
( ~ ( subclass @ A @ universal_class )
| ~ ( subclass @ universal_class @ A )
| ~ ( member @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( A )),bind(B,$thf( universal_class ))]]) ).
thf(6,axiom,
! [A: $i] : ( subclass @ A @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(67,plain,
! [A: $i] : ( subclass @ A @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(68,plain,
! [A: $i] : ( subclass @ A @ universal_class ),
inference(cnf,[status(esa)],[67]) ).
thf(83891,plain,
! [A: $i] :
( ~ $true
| ~ ( subclass @ universal_class @ A )
| ~ ( member @ sk2 @ A ) ),
inference(rewrite,[status(thm)],[313,68]) ).
thf(83892,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ~ ( member @ sk2 @ A ) ),
inference(simp,[status(thm)],[83891]) ).
thf(12,axiom,
! [A: $i] :
( ( function @ A )
<=> ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_defn) ).
thf(96,plain,
! [A: $i] :
( ( ( function @ A )
=> ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) )
& ( ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
=> ( function @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(97,plain,
( ! [A: $i] :
( ( function @ A )
=> ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) )
& ! [A: $i] :
( ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
=> ( function @ A ) ) ),
inference(miniscope,[status(thm)],[96]) ).
thf(98,plain,
! [A: $i] :
( ~ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( function @ A ) ),
inference(cnf,[status(esa)],[97]) ).
thf(101,plain,
! [A: $i] :
( ~ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( function @ A ) ),
inference(simp,[status(thm)],[98]) ).
thf(191,plain,
member @ sk7 @ universal_class,
inference(cnf,[status(esa)],[188]) ).
thf(36,axiom,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( power_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class) ).
thf(218,plain,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( power_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(219,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
inference(cnf,[status(esa)],[218]) ).
thf(44927,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ sk7 @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[191,219]) ).
thf(44928,plain,
member @ ( power_class @ sk7 ) @ universal_class,
inference(pattern_uni,[status(thm)],[44927:[bind(A,$thf( sk7 ))]]) ).
thf(45357,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[44928,219]) ).
thf(45358,plain,
member @ ( power_class @ ( power_class @ sk7 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[45357:[bind(A,$thf( power_class @ sk7 ))]]) ).
thf(46405,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[45358,219]) ).
thf(46406,plain,
member @ ( power_class @ ( power_class @ ( power_class @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[46405:[bind(A,$thf( power_class @ ( power_class @ sk7 ) ))]]) ).
thf(50094,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( power_class @ sk7 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[46406,219]) ).
thf(50095,plain,
member @ ( power_class @ ( power_class @ ( power_class @ ( power_class @ sk7 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[50094:[bind(A,$thf( power_class @ ( power_class @ ( power_class @ sk7 ) ) ))]]) ).
thf(96033,plain,
( ( member @ ( power_class @ ( power_class @ ( power_class @ ( power_class @ sk7 ) ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[50095,48]) ).
thf(96181,plain,
( ( ( power_class @ ( power_class @ ( power_class @ ( power_class @ sk7 ) ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[96033]) ).
thf(96235,plain,
( ( power_class @ ( power_class @ ( power_class @ ( power_class @ sk7 ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[96181]) ).
thf(41,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation) ).
thf(236,plain,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(30,axiom,
! [A: $i] :
~ ( member @ A @ null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
thf(192,plain,
! [A: $i] :
~ ( member @ A @ null_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(193,plain,
~ ? [A: $i] : ( member @ A @ null_class ),
inference(miniscope,[status(thm)],[192]) ).
thf(194,plain,
! [A: $i] :
~ ( member @ A @ null_class ),
inference(cnf,[status(esa)],[193]) ).
thf(5661,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ B @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[105,194]) ).
thf(5662,plain,
~ ( inductive @ null_class ),
inference(pattern_uni,[status(thm)],[5661:[bind(A,$thf( null_class )),bind(B,$thf( null_class ))]]) ).
thf(5731,plain,
( ( inductive @ sk7 )
!= ( inductive @ null_class ) ),
inference(paramod_ordered,[status(thm)],[190,5662]) ).
thf(5732,plain,
sk7 != null_class,
inference(simp,[status(thm)],[5731]) ).
thf(5734,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B != null_class )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[56,5732]) ).
thf(5735,plain,
! [A: $i] :
( ~ ( subclass @ sk7 @ A )
| ~ ( subclass @ A @ sk7 )
| ( A != null_class ) ),
inference(pattern_uni,[status(thm)],[5734:[bind(A,$thf( sk7 ))]]) ).
thf(5740,plain,
( ~ ( subclass @ sk7 @ null_class )
| ~ ( subclass @ null_class @ sk7 ) ),
inference(simp,[status(thm)],[5735]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( subclass @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( ( subclass @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subclass @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(87,plain,
( ! [A: $i,B: $i] :
( ( subclass @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subclass @ A @ B ) ) ),
inference(miniscope,[status(thm)],[86]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subclass @ A @ B ) ),
inference(cnf,[status(esa)],[87]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subclass @ A @ B ) ),
inference(simp,[status(thm)],[88]) ).
thf(3166,plain,
! [C: $i,B: $i,A: $i] :
( ( subclass @ A @ B )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ C @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[91,194]) ).
thf(3167,plain,
! [A: $i] : ( subclass @ null_class @ A ),
inference(pattern_uni,[status(thm)],[3166:[bind(A,$thf( null_class )),bind(B,$thf( D )),bind(C,$thf( sk4 @ D @ null_class ))]]) ).
thf(3237,plain,
! [A: $i] : ( subclass @ null_class @ A ),
inference(simp,[status(thm)],[3167]) ).
thf(15372,plain,
( ~ ( subclass @ sk7 @ null_class )
| ~ $true ),
inference(rewrite,[status(thm)],[5740,3237]) ).
thf(15373,plain,
~ ( subclass @ sk7 @ null_class ),
inference(simp,[status(thm)],[15372]) ).
thf(15406,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk7 @ null_class ) ),
inference(paramod_ordered,[status(thm)],[236,15373]) ).
thf(15440,plain,
( ( sk7 != element_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[15406]) ).
thf(40,axiom,
? [A: $i] :
( ( function @ A )
& ! [B: $i] :
( ( member @ B @ universal_class )
=> ( ( B = null_class )
| ( member @ ( apply @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice) ).
thf(232,plain,
? [A: $i] :
( ( function @ A )
& ! [B: $i] :
( ( member @ B @ universal_class )
=> ( ( B = null_class )
| ( member @ ( apply @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(234,plain,
function @ sk8,
inference(cnf,[status(esa)],[232]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( sum_class @ B ) )
<=> ? [C: $i] :
( ( member @ A @ C )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_defn) ).
thf(72,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( sum_class @ B ) )
=> ? [C: $i] :
( ( member @ A @ C )
& ( member @ C @ B ) ) )
& ( ? [C: $i] :
( ( member @ A @ C )
& ( member @ C @ B ) )
=> ( member @ A @ ( sum_class @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(73,plain,
( ! [A: $i,B: $i] :
( ( member @ A @ ( sum_class @ B ) )
=> ? [C: $i] :
( ( member @ A @ C )
& ( member @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ? [C: $i] :
( ( member @ A @ C )
& ( member @ C @ B ) )
=> ( member @ A @ ( sum_class @ B ) ) ) ),
inference(miniscope,[status(thm)],[72]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( member @ ( sk3 @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[73]) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[76,194]) ).
thf(1172,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[1171:[bind(A,$thf( E )),bind(B,$thf( null_class )),bind(C,$thf( sk3 @ null_class @ E ))]]) ).
thf(1217,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ null_class ) ),
inference(simp,[status(thm)],[1172]) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ null_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,1217]) ).
thf(1276,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ null_class ) ) ),
inference(pattern_uni,[status(thm)],[1275:[bind(A,$thf( E )),bind(B,$thf( sum_class @ null_class )),bind(C,$thf( sk3 @ ( sum_class @ null_class ) @ E ))]]) ).
thf(1305,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ null_class ) ) ),
inference(simp,[status(thm)],[1276]) ).
thf(1537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,1305]) ).
thf(1538,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ),
inference(pattern_uni,[status(thm)],[1537:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ null_class ) )),bind(C,$thf( sk3 @ ( sum_class @ ( sum_class @ null_class ) ) @ E ))]]) ).
thf(1556,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ),
inference(simp,[status(thm)],[1538]) ).
thf(5787,plain,
! [A: $i] :
( ( member @ null_class @ sk7 )
!= ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5702,1556]) ).
thf(5800,plain,
! [A: $i] :
( ( null_class != A )
| ( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
!= sk7 ) ),
inference(simp,[status(thm)],[5787]) ).
thf(5819,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
!= sk7 ),
inference(simp,[status(thm)],[5800]) ).
thf(18,axiom,
! [A: $i] :
( ( A != null_class )
=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( member @ B @ A )
& ( disjoint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
thf(129,plain,
! [A: $i] :
( ( A != null_class )
=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( member @ B @ A )
& ( disjoint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(131,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( sk5 @ A ) @ A ) ),
inference(cnf,[status(esa)],[129]) ).
thf(134,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( sk5 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[131]) ).
thf(11334,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk5 @ A ) @ A )
!= ( member @ B @ ( sum_class @ null_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,1217]) ).
thf(11335,plain,
( ( sum_class @ null_class )
= null_class ),
inference(pattern_uni,[status(thm)],[11334:[bind(A,$thf( sum_class @ null_class )),bind(B,$thf( sk5 @ ( sum_class @ null_class ) ))]]) ).
thf(12537,plain,
( ( sum_class @ ( sum_class @ null_class ) )
!= sk7 ),
inference(rewrite,[status(thm)],[5819,11335]) ).
thf(12614,plain,
( ( sum_class @ null_class )
!= sk7 ),
inference(rewrite,[status(thm)],[12537,11335]) ).
thf(43,axiom,
! [A: $i] :
( ( member @ A @ identity_relation )
<=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( A
= ( ordered_pair @ B @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
thf(239,plain,
! [A: $i] :
( ( ( member @ A @ identity_relation )
=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( A
= ( ordered_pair @ B @ B ) ) ) )
& ( ? [B: $i] :
( ( member @ B @ universal_class )
& ( A
= ( ordered_pair @ B @ B ) ) )
=> ( member @ A @ identity_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(240,plain,
( ! [A: $i] :
( ( member @ A @ identity_relation )
=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( A
= ( ordered_pair @ B @ B ) ) ) )
& ! [A: $i] :
( ? [B: $i] :
( ( member @ B @ universal_class )
& ( A
= ( ordered_pair @ B @ B ) ) )
=> ( member @ A @ identity_relation ) ) ),
inference(miniscope,[status(thm)],[239]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ( A
!= ( ordered_pair @ B @ B ) )
| ( member @ A @ identity_relation ) ),
inference(cnf,[status(esa)],[240]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( A
!= ( ordered_pair @ B @ B ) )
| ~ ( member @ B @ universal_class )
| ( member @ A @ identity_relation ) ),
inference(lifteq,[status(thm)],[241]) ).
thf(245,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ A ) @ identity_relation ) ),
inference(simp,[status(thm)],[244]) ).
thf(57166,plain,
! [A: $i] :
( ( member @ ( ordered_pair @ A @ A ) @ identity_relation )
| ( ( member @ sk7 @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[191,245]) ).
thf(57167,plain,
member @ ( ordered_pair @ sk7 @ sk7 ) @ identity_relation,
inference(pattern_uni,[status(thm)],[57166:[bind(A,$thf( sk7 ))]]) ).
thf(57892,plain,
! [A: $i] :
( ( member @ ( ordered_pair @ sk7 @ sk7 ) @ identity_relation )
!= ( member @ A @ null_class ) ),
inference(paramod_ordered,[status(thm)],[57167,194]) ).
thf(57982,plain,
! [A: $i] :
( ( ( ordered_pair @ sk7 @ sk7 )
!= A )
| ( identity_relation != null_class ) ),
inference(simp,[status(thm)],[57892]) ).
thf(58068,plain,
identity_relation != null_class,
inference(simp,[status(thm)],[57982]) ).
thf(58111,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( A != identity_relation ) ),
inference(paramod_ordered,[status(thm)],[134,58068]) ).
thf(58112,plain,
member @ ( sk5 @ identity_relation ) @ identity_relation,
inference(pattern_uni,[status(thm)],[58111:[bind(A,$thf( identity_relation ))]]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( member @ B @ ( complement @ A ) )
<=> ( ( member @ B @ universal_class )
& ~ ( member @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( ( member @ B @ ( complement @ A ) )
=> ( ( member @ B @ universal_class )
& ~ ( member @ B @ A ) ) )
& ( ( ( member @ B @ universal_class )
& ~ ( member @ B @ A ) )
=> ( member @ B @ ( complement @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(227,plain,
( ! [A: $i,B: $i] :
( ( member @ B @ ( complement @ A ) )
=> ( ( member @ B @ universal_class )
& ~ ( member @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( member @ B @ universal_class )
& ~ ( member @ B @ A ) )
=> ( member @ B @ ( complement @ A ) ) ) ),
inference(miniscope,[status(thm)],[226]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ~ ( member @ B @ A ) ),
inference(cnf,[status(esa)],[227]) ).
thf(59076,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk5 @ identity_relation ) @ identity_relation )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58112,230]) ).
thf(59077,plain,
~ ( member @ ( sk5 @ identity_relation ) @ ( complement @ identity_relation ) ),
inference(pattern_uni,[status(thm)],[59076:[bind(A,$thf( identity_relation )),bind(B,$thf( sk5 @ identity_relation ))]]) ).
thf(130,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( sk5 @ A ) @ universal_class ) ),
inference(cnf,[status(esa)],[129]) ).
thf(133,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( sk5 @ A ) @ universal_class ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(638,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( inductive @ null_class )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[133,190]) ).
thf(639,plain,
( ( member @ ( sk5 @ sk7 ) @ universal_class )
| ( inductive @ null_class ) ),
inference(pattern_uni,[status(thm)],[638:[bind(A,$thf( sk7 ))]]) ).
thf(5721,plain,
( ( member @ ( sk5 @ sk7 ) @ universal_class )
| $false ),
inference(rewrite,[status(thm)],[639,5662]) ).
thf(5722,plain,
member @ ( sk5 @ sk7 ) @ universal_class,
inference(simp,[status(thm)],[5721]) ).
thf(48985,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk5 @ sk7 ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5722,230]) ).
thf(48986,plain,
~ ( member @ ( sk5 @ sk7 ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[48985:[bind(A,$thf( universal_class )),bind(B,$thf( sk5 @ sk7 ))]]) ).
thf(255,plain,
! [A: $i] :
( ( member @ sk7 @ universal_class )
!= ( member @ A @ null_class ) ),
inference(paramod_ordered,[status(thm)],[191,194]) ).
thf(256,plain,
! [A: $i] :
( ( sk7 != A )
| ( null_class != universal_class ) ),
inference(simp,[status(thm)],[255]) ).
thf(257,plain,
null_class != universal_class,
inference(simp,[status(thm)],[256]) ).
thf(611,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( A != universal_class )
| ( null_class != null_class ) ),
inference(paramod_ordered,[status(thm)],[133,257]) ).
thf(612,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( A != universal_class ) ),
inference(pattern_uni,[status(thm)],[611:[]]) ).
thf(728,plain,
member @ ( sk5 @ universal_class ) @ universal_class,
inference(simp,[status(thm)],[612]) ).
thf(45059,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ universal_class ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[728,219]) ).
thf(45060,plain,
member @ ( power_class @ ( sk5 @ universal_class ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[45059:[bind(A,$thf( sk5 @ universal_class ))]]) ).
thf(46022,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk5 @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[45060,219]) ).
thf(46023,plain,
member @ ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[46022:[bind(A,$thf( power_class @ ( sk5 @ universal_class ) ))]]) ).
thf(48578,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[46023,219]) ).
thf(48579,plain,
member @ ( power_class @ ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[48578:[bind(A,$thf( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ))]]) ).
thf(95467,plain,
( ( member @ ( power_class @ ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[48579,48]) ).
thf(95565,plain,
( ( ( power_class @ ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[95467]) ).
thf(95648,plain,
( ( power_class @ ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[95565]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
thf(247,plain,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
inference(cnf,[status(esa)],[247]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
inference(lifteq,[status(thm)],[248]) ).
thf(15408,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( ( subclass @ A @ B )
!= ( subclass @ sk7 @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[91,15373]) ).
thf(15409,plain,
member @ ( sk4 @ null_class @ sk7 ) @ sk7,
inference(pattern_uni,[status(thm)],[15408:[bind(A,$thf( sk7 )),bind(B,$thf( null_class ))]]) ).
thf(48906,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk4 @ null_class @ sk7 ) @ sk7 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15409,230]) ).
thf(48907,plain,
~ ( member @ ( sk4 @ null_class @ sk7 ) @ ( complement @ sk7 ) ),
inference(pattern_uni,[status(thm)],[48906:[bind(A,$thf( sk7 )),bind(B,$thf( sk4 @ null_class @ sk7 ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( singleton @ A )
= ( unordered_pair @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
thf(114,plain,
! [A: $i] :
( ( singleton @ A )
= ( unordered_pair @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(115,plain,
! [A: $i] :
( ( singleton @ A )
= ( unordered_pair @ A @ A ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(47,plain,
( ( unordered_pair @ sk1 @ sk2 )
!= ( singleton @ sk1 ) ),
inference(cnf,[status(esa)],[46]) ).
thf(49,plain,
( ( unordered_pair @ sk1 @ sk2 )
!= ( singleton @ sk1 ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(1073,plain,
! [A: $i] :
( ( ( singleton @ A )
!= ( singleton @ sk1 ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[116,49]) ).
thf(1076,plain,
! [A: $i] :
( ( A != sk1 )
| ( A != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1073]) ).
thf(1080,plain,
sk2 != sk1,
inference(simp,[status(thm)],[1076]) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B != sk1 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[56,1080]) ).
thf(1084,plain,
! [A: $i] :
( ~ ( subclass @ sk2 @ A )
| ~ ( subclass @ A @ sk2 )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[1083:[bind(A,$thf( sk2 ))]]) ).
thf(1089,plain,
( ~ ( subclass @ sk2 @ sk1 )
| ~ ( subclass @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[1084]) ).
thf(3357,plain,
! [A: $i] :
( ~ ( subclass @ sk1 @ sk2 )
| ( ( subclass @ null_class @ A )
!= ( subclass @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[3237,1089]) ).
thf(3366,plain,
! [A: $i] :
( ~ ( subclass @ sk1 @ sk2 )
| ( sk2 != null_class )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[3357]) ).
thf(3376,plain,
( ~ ( subclass @ sk1 @ sk2 )
| ( sk2 != null_class ) ),
inference(simp,[status(thm)],[3366]) ).
thf(3806,plain,
! [A: $i] :
( ( sk2 != null_class )
| ( ( subclass @ null_class @ A )
!= ( subclass @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3237,3376]) ).
thf(3818,plain,
! [A: $i] :
( ( sk2 != null_class )
| ( sk1 != null_class )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[3806]) ).
thf(3830,plain,
( ( sk2 != null_class )
| ( sk1 != null_class ) ),
inference(simp,[status(thm)],[3818]) ).
thf(57871,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( ordered_pair @ sk7 @ sk7 ) @ identity_relation )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57167,230]) ).
thf(57872,plain,
~ ( member @ ( ordered_pair @ sk7 @ sk7 ) @ ( complement @ identity_relation ) ),
inference(pattern_uni,[status(thm)],[57871:[bind(A,$thf( identity_relation )),bind(B,$thf( ordered_pair @ sk7 @ sk7 ))]]) ).
thf(68083,plain,
~ ( member @ ( unordered_pair @ ( singleton @ sk7 ) @ ( unordered_pair @ sk7 @ ( singleton @ sk7 ) ) ) @ ( complement @ identity_relation ) ),
inference(rewrite,[status(thm)],[57872,249]) ).
thf(132,plain,
! [A: $i] :
( ( A = null_class )
| ( disjoint @ ( sk5 @ A ) @ A ) ),
inference(cnf,[status(esa)],[129]) ).
thf(135,plain,
! [A: $i] :
( ( A = null_class )
| ( disjoint @ ( sk5 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[132]) ).
thf(12688,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( sk1 != null_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[135,3830]) ).
thf(12689,plain,
( ( disjoint @ ( sk5 @ sk2 ) @ sk2 )
| ( sk1 != null_class ) ),
inference(pattern_uni,[status(thm)],[12688:[bind(A,$thf( sk2 ))]]) ).
thf(45,axiom,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( sum_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class) ).
thf(250,plain,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( sum_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(251,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
inference(cnf,[status(esa)],[250]) ).
thf(60930,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ sk7 @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[191,251]) ).
thf(60931,plain,
member @ ( sum_class @ sk7 ) @ universal_class,
inference(pattern_uni,[status(thm)],[60930:[bind(A,$thf( sk7 ))]]) ).
thf(61332,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[60931,251]) ).
thf(61333,plain,
member @ ( sum_class @ ( sum_class @ sk7 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[61332:[bind(A,$thf( sum_class @ sk7 ))]]) ).
thf(322,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( subclass @ C @ B )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[68,56]) ).
thf(323,plain,
! [A: $i] :
( ( A = universal_class )
| ~ ( subclass @ universal_class @ A ) ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( universal_class ))]]) ).
thf(1985,plain,
! [A: $i] :
( ~ ( subclass @ sk2 @ sk1 )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[68,1089]) ).
thf(1989,plain,
! [A: $i] :
( ~ ( subclass @ sk2 @ sk1 )
| ( A != sk1 )
| ( sk2 != universal_class ) ),
inference(simp,[status(thm)],[1985]) ).
thf(2004,plain,
( ~ ( subclass @ sk2 @ sk1 )
| ( sk2 != universal_class ) ),
inference(simp,[status(thm)],[1989]) ).
thf(2259,plain,
! [A: $i] :
( ( sk2 != universal_class )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[68,2004]) ).
thf(2263,plain,
! [A: $i] :
( ( sk2 != universal_class )
| ( A != sk2 )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[2259]) ).
thf(2269,plain,
( ( sk2 != universal_class )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[2263]) ).
thf(86190,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( sk1 != universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[323,2269]) ).
thf(86191,plain,
( ~ ( subclass @ universal_class @ sk2 )
| ( sk1 != universal_class ) ),
inference(pattern_uni,[status(thm)],[86190:[bind(A,$thf( sk2 ))]]) ).
thf(48603,plain,
( ( member @ ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[46023,48]) ).
thf(48716,plain,
( ( ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[48603]) ).
thf(48751,plain,
( ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) )
!= sk2 ),
inference(simp,[status(thm)],[48716]) ).
thf(64160,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sum_class @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[61333,219]) ).
thf(64161,plain,
member @ ( power_class @ ( sum_class @ ( sum_class @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[64160:[bind(A,$thf( sum_class @ ( sum_class @ sk7 ) ))]]) ).
thf(82232,plain,
( ( member @ ( power_class @ ( sum_class @ ( sum_class @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[64161,48]) ).
thf(82361,plain,
( ( ( power_class @ ( sum_class @ ( sum_class @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[82232]) ).
thf(82421,plain,
( ( power_class @ ( sum_class @ ( sum_class @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[82361]) ).
thf(37,axiom,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_defn) ).
thf(220,plain,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(221,plain,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[220]) ).
thf(222,plain,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
<=> ( ( member @ C @ A )
| ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(209,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(210,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[209]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[210]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(42137,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( union @ A @ B ) )
| ( ( member @ null_class @ sk7 )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5702,214]) ).
thf(42138,plain,
! [A: $i] : ( member @ null_class @ ( union @ sk7 @ A ) ),
inference(pattern_uni,[status(thm)],[42137:[bind(A,$thf( sk7 )),bind(B,$thf( B )),bind(C,$thf( null_class ))]]) ).
thf(42498,plain,
! [A: $i] : ( member @ null_class @ ( union @ sk7 @ A ) ),
inference(simp,[status(thm)],[42138]) ).
thf(42683,plain,
! [B: $i,A: $i] :
( ( member @ null_class @ ( successor @ A ) )
| ( ( union @ A @ ( singleton @ A ) )
!= ( union @ sk7 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[222,42498]) ).
thf(42684,plain,
member @ null_class @ ( successor @ sk7 ),
inference(pattern_uni,[status(thm)],[42683:[bind(A,$thf( sk7 )),bind(B,$thf( singleton @ sk7 ))]]) ).
thf(58108,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( A != identity_relation ) ),
inference(paramod_ordered,[status(thm)],[133,58068]) ).
thf(58109,plain,
member @ ( sk5 @ identity_relation ) @ universal_class,
inference(pattern_uni,[status(thm)],[58108:[bind(A,$thf( identity_relation ))]]) ).
thf(60846,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ identity_relation ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[58109,251]) ).
thf(60847,plain,
member @ ( sum_class @ ( sk5 @ identity_relation ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60846:[bind(A,$thf( sk5 @ identity_relation ))]]) ).
thf(61622,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[60847,251]) ).
thf(61623,plain,
member @ ( sum_class @ ( sum_class @ ( sk5 @ identity_relation ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[61622:[bind(A,$thf( sum_class @ ( sk5 @ identity_relation ) ))]]) ).
thf(45379,plain,
( ( member @ ( power_class @ sk7 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[44928,48]) ).
thf(45449,plain,
( ( ( power_class @ sk7 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[45379]) ).
thf(45515,plain,
( ( power_class @ sk7 )
!= sk2 ),
inference(simp,[status(thm)],[45449]) ).
thf(1777,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,1556]) ).
thf(1778,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1777:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )),bind(C,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) @ E ))]]) ).
thf(1817,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(simp,[status(thm)],[1778]) ).
thf(2134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,1817]) ).
thf(2135,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2134:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )),bind(C,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) @ E ))]]) ).
thf(2165,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(simp,[status(thm)],[2135]) ).
thf(2506,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,2165]) ).
thf(2507,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2506:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )),bind(C,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) @ E ))]]) ).
thf(2535,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2507]) ).
thf(2897,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,2535]) ).
thf(2898,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2897:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) )),bind(C,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) @ E ))]]) ).
thf(2932,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2898]) ).
thf(5680,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,2932]) ).
thf(5681,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[5680:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )),bind(B,$thf( null_class ))]]) ).
thf(12575,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[5681,11335]) ).
thf(12025,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk5 @ A ) @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,2165]) ).
thf(12026,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
= null_class ),
inference(pattern_uni,[status(thm)],[12025:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )),bind(B,$thf( sk5 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ))]]) ).
thf(11851,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk5 @ A ) @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,1556]) ).
thf(11852,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
= null_class ),
inference(pattern_uni,[status(thm)],[11851:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )),bind(B,$thf( sk5 @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ))]]) ).
thf(13649,plain,
( ( sum_class @ ( sum_class @ null_class ) )
= null_class ),
inference(rewrite,[status(thm)],[11852,11335]) ).
thf(14658,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
= null_class ),
inference(rewrite,[status(thm)],[12026,13649]) ).
thf(16027,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ),
inference(rewrite,[status(thm)],[12575,14658]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn1) ).
thf(216,plain,
! [A: $i,B: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(217,plain,
! [B: $i,A: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(cnf,[status(esa)],[216]) ).
thf(61342,plain,
( ( member @ ( sum_class @ sk7 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60931,48]) ).
thf(61433,plain,
( ( ( sum_class @ sk7 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[61342]) ).
thf(61488,plain,
( ( sum_class @ sk7 )
!= sk2 ),
inference(simp,[status(thm)],[61433]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B != universal_class )
| ( A != null_class ) ),
inference(paramod_ordered,[status(thm)],[56,257]) ).
thf(354,plain,
! [A: $i] :
( ~ ( subclass @ null_class @ A )
| ~ ( subclass @ A @ null_class )
| ( A != universal_class ) ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( null_class ))]]) ).
thf(357,plain,
( ~ ( subclass @ null_class @ universal_class )
| ~ ( subclass @ universal_class @ null_class ) ),
inference(simp,[status(thm)],[354]) ).
thf(1862,plain,
( ~ $true
| ~ ( subclass @ universal_class @ null_class ) ),
inference(rewrite,[status(thm)],[357,68]) ).
thf(1863,plain,
~ ( subclass @ universal_class @ null_class ),
inference(simp,[status(thm)],[1862]) ).
thf(3164,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[91,1863]) ).
thf(3165,plain,
member @ ( sk4 @ null_class @ universal_class ) @ universal_class,
inference(pattern_uni,[status(thm)],[3164:[bind(A,$thf( universal_class )),bind(B,$thf( null_class ))]]) ).
thf(44956,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk4 @ null_class @ universal_class ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[3165,219]) ).
thf(44957,plain,
member @ ( power_class @ ( sk4 @ null_class @ universal_class ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[44956:[bind(A,$thf( sk4 @ null_class @ universal_class ))]]) ).
thf(47144,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk4 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[44957,219]) ).
thf(47145,plain,
member @ ( power_class @ ( power_class @ ( sk4 @ null_class @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[47144:[bind(A,$thf( power_class @ ( sk4 @ null_class @ universal_class ) ))]]) ).
thf(233,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ sk8 @ A ) @ A ) ),
inference(cnf,[status(esa)],[232]) ).
thf(235,plain,
! [A: $i] :
( ( A = null_class )
| ~ ( member @ A @ universal_class )
| ( member @ ( apply @ sk8 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[233]) ).
thf(52493,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( apply @ sk8 @ A ) @ A )
| ( ( member @ sk7 @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[191,235]) ).
thf(52494,plain,
( ( sk7 = null_class )
| ( member @ ( apply @ sk8 @ sk7 ) @ sk7 ) ),
inference(pattern_uni,[status(thm)],[52493:[bind(A,$thf( sk7 ))]]) ).
thf(97393,plain,
member @ ( apply @ sk8 @ sk7 ) @ sk7,
inference(simplifyReflect,[status(thm)],[52494,5732]) ).
thf(97474,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( apply @ sk8 @ sk7 ) @ sk7 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[97393,230]) ).
thf(97475,plain,
~ ( member @ ( apply @ sk8 @ sk7 ) @ ( complement @ sk7 ) ),
inference(pattern_uni,[status(thm)],[97474:[bind(A,$thf( sk7 )),bind(B,$thf( apply @ sk8 @ sk7 ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( power_class @ B ) )
<=> ( ( member @ A @ universal_class )
& ( subclass @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_defn) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( power_class @ B ) )
=> ( ( member @ A @ universal_class )
& ( subclass @ A @ B ) ) )
& ( ( ( member @ A @ universal_class )
& ( subclass @ A @ B ) )
=> ( member @ A @ ( power_class @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(109,plain,
( ! [A: $i,B: $i] :
( ( member @ A @ ( power_class @ B ) )
=> ( ( member @ A @ universal_class )
& ( subclass @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( subclass @ A @ B ) )
=> ( member @ A @ ( power_class @ B ) ) ) ),
inference(miniscope,[status(thm)],[108]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( subclass @ A @ B ) ),
inference(cnf,[status(esa)],[109]) ).
thf(1984,plain,
! [A: $i] :
( ~ ( subclass @ sk1 @ sk2 )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[68,1089]) ).
thf(1996,plain,
! [A: $i] :
( ~ ( subclass @ sk1 @ sk2 )
| ( A != sk2 )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[1984]) ).
thf(2006,plain,
( ~ ( subclass @ sk1 @ sk2 )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[1996]) ).
thf(6899,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( sk1 != universal_class )
| ( ( subclass @ A @ B )
!= ( subclass @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[112,2006]) ).
thf(6900,plain,
( ~ ( member @ sk1 @ ( power_class @ sk2 ) )
| ( sk1 != universal_class ) ),
inference(pattern_uni,[status(thm)],[6899:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(99,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(cnf,[status(esa)],[97]) ).
thf(3905,plain,
! [A: $i] :
( ~ ( function @ A )
| ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[99,1863]) ).
thf(3946,plain,
! [A: $i] :
( ~ ( function @ A )
| ( A != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[3905]) ).
thf(3959,plain,
( ~ ( function @ universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[3946]) ).
thf(252,plain,
( ( member @ sk7 @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[191,48]) ).
thf(253,plain,
( ( sk7 != sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[252]) ).
thf(254,plain,
sk7 != sk2,
inference(simp,[status(thm)],[253]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B != sk2 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[56,254]) ).
thf(327,plain,
! [A: $i] :
( ~ ( subclass @ sk7 @ A )
| ~ ( subclass @ A @ sk7 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( sk7 ))]]) ).
thf(335,plain,
( ~ ( subclass @ sk7 @ sk2 )
| ~ ( subclass @ sk2 @ sk7 ) ),
inference(simp,[status(thm)],[327]) ).
thf(408,plain,
! [A: $i] :
( ~ ( subclass @ sk7 @ sk2 )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[68,335]) ).
thf(412,plain,
! [A: $i] :
( ~ ( subclass @ sk7 @ sk2 )
| ( A != sk2 )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[408]) ).
thf(429,plain,
( ~ ( subclass @ sk7 @ sk2 )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[412]) ).
thf(6884,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( sk7 != universal_class )
| ( ( subclass @ A @ B )
!= ( subclass @ sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[112,429]) ).
thf(6885,plain,
( ~ ( member @ sk7 @ ( power_class @ sk2 ) )
| ( sk7 != universal_class ) ),
inference(pattern_uni,[status(thm)],[6884:[bind(A,$thf( sk7 )),bind(B,$thf( sk2 ))]]) ).
thf(15631,plain,
( ( sk7 != universal_class )
| ( ( member @ sk7 @ ( power_class @ sk2 ) )
!= ( member @ sk7 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[191,6885]) ).
thf(15678,plain,
( ( sk7 != universal_class )
| ( sk7 != sk7 )
| ( ( power_class @ sk2 )
!= universal_class ) ),
inference(simp,[status(thm)],[15631]) ).
thf(15703,plain,
( ( sk7 != universal_class )
| ( ( power_class @ sk2 )
!= universal_class ) ),
inference(simp,[status(thm)],[15678]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(174,plain,
! [A: $i,B: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(175,plain,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
inference(cnf,[status(esa)],[174]) ).
thf(5299,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,2932]) ).
thf(5300,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[5299:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )),bind(C,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) @ E ))]]) ).
thf(5359,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[5300]) ).
thf(8444,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,5359]) ).
thf(8445,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[8444:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) )),bind(C,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) @ E ))]]) ).
thf(8539,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[8445]) ).
thf(10090,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( unordered_pair @ A @ B ) @ universal_class )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,8539]) ).
thf(10114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ A @ B )
!= C )
| ( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )
!= universal_class ) ),
inference(simp,[status(thm)],[10090]) ).
thf(10134,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )
!= universal_class ),
inference(simp,[status(thm)],[10114]) ).
thf(12523,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[10134,11335]) ).
thf(11505,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk5 @ A ) @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,2932]) ).
thf(11506,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )
= null_class ),
inference(pattern_uni,[status(thm)],[11505:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )),bind(B,$thf( sk5 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ))]]) ).
thf(16734,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )
= null_class ),
inference(rewrite,[status(thm)],[11506,14658]) ).
thf(18114,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[12523,16734]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
<=> ( ( member @ A @ universal_class )
& ( ( A = B )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( unordered_pair @ B @ C ) )
=> ( ( member @ A @ universal_class )
& ( ( A = B )
| ( A = C ) ) ) )
& ( ( ( member @ A @ universal_class )
& ( ( A = B )
| ( A = C ) ) )
=> ( member @ A @ ( unordered_pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(177,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
=> ( ( member @ A @ universal_class )
& ( ( A = B )
| ( A = C ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ universal_class )
& ( ( A = B )
| ( A = C ) ) )
=> ( member @ A @ ( unordered_pair @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[176]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( A != C )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(cnf,[status(esa)],[177]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[178]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ( member @ B @ ( unordered_pair @ A @ B ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(24705,plain,
! [B: $i,A: $i] :
( ( member @ B @ ( unordered_pair @ A @ B ) )
| ( ( member @ ( sk5 @ sk7 ) @ universal_class )
!= ( member @ B @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[5722,183]) ).
thf(24706,plain,
! [A: $i] : ( member @ ( sk5 @ sk7 ) @ ( unordered_pair @ A @ ( sk5 @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[24705:[bind(A,$thf( A )),bind(B,$thf( sk5 @ sk7 ))]]) ).
thf(38892,plain,
! [B: $i,A: $i] :
( ( member @ ( sk5 @ sk7 ) @ ( singleton @ A ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ B @ ( sk5 @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[116,24706]) ).
thf(38893,plain,
member @ ( sk5 @ sk7 ) @ ( singleton @ ( sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[38892:[bind(A,$thf( sk5 @ sk7 )),bind(B,$thf( sk5 @ sk7 ))]]) ).
thf(39273,plain,
! [A: $i] :
( ( member @ ( sk5 @ sk7 ) @ ( singleton @ ( sk5 @ sk7 ) ) )
!= ( member @ A @ null_class ) ),
inference(paramod_ordered,[status(thm)],[38893,194]) ).
thf(39373,plain,
! [A: $i] :
( ( ( sk5 @ sk7 )
!= A )
| ( ( singleton @ ( sk5 @ sk7 ) )
!= null_class ) ),
inference(simp,[status(thm)],[39273]) ).
thf(39446,plain,
( ( singleton @ ( sk5 @ sk7 ) )
!= null_class ),
inference(simp,[status(thm)],[39373]) ).
thf(39483,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( A
!= ( singleton @ ( sk5 @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,39446]) ).
thf(39484,plain,
member @ ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ) @ ( singleton @ ( sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[39483:[bind(A,$thf( singleton @ ( sk5 @ sk7 ) ))]]) ).
thf(24713,plain,
! [B: $i,A: $i] :
( ( member @ B @ ( unordered_pair @ A @ B ) )
| ( ( member @ sk7 @ universal_class )
!= ( member @ B @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[191,183]) ).
thf(24714,plain,
! [A: $i] : ( member @ sk7 @ ( unordered_pair @ A @ sk7 ) ),
inference(pattern_uni,[status(thm)],[24713:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(25608,plain,
! [B: $i,A: $i] :
( ( member @ sk7 @ ( singleton @ A ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ B @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[116,24714]) ).
thf(25609,plain,
member @ sk7 @ ( singleton @ sk7 ),
inference(pattern_uni,[status(thm)],[25608:[bind(A,$thf( sk7 )),bind(B,$thf( sk7 ))]]) ).
thf(49137,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ sk7 @ ( singleton @ sk7 ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25609,230]) ).
thf(49138,plain,
~ ( member @ sk7 @ ( complement @ ( singleton @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[49137:[bind(A,$thf( singleton @ sk7 )),bind(B,$thf( sk7 ))]]) ).
thf(3906,plain,
! [A: $i] :
( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ( ( function @ sk8 )
!= ( function @ A ) ) ),
inference(paramod_ordered,[status(thm)],[234,99]) ).
thf(3907,plain,
subclass @ sk8 @ ( cross_product @ universal_class @ universal_class ),
inference(pattern_uni,[status(thm)],[3906:[bind(A,$thf( sk8 ))]]) ).
thf(3970,plain,
( ( subclass @ sk8 @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ null_class ) ),
inference(paramod_ordered,[status(thm)],[3907,1863]) ).
thf(4011,plain,
( ( sk8 != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[3970]) ).
thf(189,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ sk7 @ A ) ),
inference(cnf,[status(esa)],[188]) ).
thf(3362,plain,
! [A: $i] :
( ~ ( subclass @ sk7 @ sk2 )
| ( ( subclass @ null_class @ A )
!= ( subclass @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[3237,335]) ).
thf(3373,plain,
! [A: $i] :
( ~ ( subclass @ sk7 @ sk2 )
| ( sk2 != null_class )
| ( A != sk7 ) ),
inference(simp,[status(thm)],[3362]) ).
thf(3383,plain,
( ~ ( subclass @ sk7 @ sk2 )
| ( sk2 != null_class ) ),
inference(simp,[status(thm)],[3373]) ).
thf(34093,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( sk2 != null_class )
| ( ( subclass @ sk7 @ A )
!= ( subclass @ sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[189,3383]) ).
thf(34094,plain,
( ~ ( inductive @ sk2 )
| ( sk2 != null_class ) ),
inference(pattern_uni,[status(thm)],[34093:[bind(A,$thf( sk2 ))]]) ).
thf(34270,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ~ ( inductive @ sk2 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[134,34094]) ).
thf(34271,plain,
( ( member @ ( sk5 @ sk2 ) @ sk2 )
| ~ ( inductive @ sk2 ) ),
inference(pattern_uni,[status(thm)],[34270:[bind(A,$thf( sk2 ))]]) ).
thf(5690,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[105,48]) ).
thf(5705,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( sk2 != null_class )
| ( A != universal_class ) ),
inference(simp,[status(thm)],[5690]) ).
thf(5713,plain,
( ~ ( inductive @ universal_class )
| ( sk2 != null_class ) ),
inference(simp,[status(thm)],[5705]) ).
thf(532,plain,
! [B: $i,A: $i] :
( ( member @ ( unordered_pair @ A @ B ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[175,48]) ).
thf(534,plain,
! [B: $i,A: $i] :
( ( ( unordered_pair @ A @ B )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[532]) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
!= sk2 ),
inference(simp,[status(thm)],[534]) ).
thf(5791,plain,
! [A: $i] :
( ( member @ null_class @ sk7 )
!= ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5702,2165]) ).
thf(5806,plain,
! [A: $i] :
( ( null_class != A )
| ( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
!= sk7 ) ),
inference(simp,[status(thm)],[5791]) ).
thf(5825,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
!= sk7 ),
inference(simp,[status(thm)],[5806]) ).
thf(12532,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )
!= sk7 ),
inference(rewrite,[status(thm)],[5825,11335]) ).
thf(14301,plain,
( ( sum_class @ ( sum_class @ null_class ) )
!= sk7 ),
inference(rewrite,[status(thm)],[12532,13649]) ).
thf(5693,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,2165]) ).
thf(5694,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[5693:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )),bind(B,$thf( null_class ))]]) ).
thf(12544,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(rewrite,[status(thm)],[5694,11335]) ).
thf(14354,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ null_class ) ) ),
inference(rewrite,[status(thm)],[12544,13649]) ).
thf(39472,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( A
!= ( singleton @ ( sk5 @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[133,39446]) ).
thf(39473,plain,
member @ ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[39472:[bind(A,$thf( singleton @ ( sk5 @ sk7 ) ))]]) ).
thf(39734,plain,
( ( member @ ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[39473,48]) ).
thf(39821,plain,
( ( ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[39734]) ).
thf(39885,plain,
( ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[39821]) ).
thf(58113,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( A != identity_relation ) ),
inference(paramod_ordered,[status(thm)],[135,58068]) ).
thf(58114,plain,
disjoint @ ( sk5 @ identity_relation ) @ identity_relation,
inference(pattern_uni,[status(thm)],[58113:[bind(A,$thf( identity_relation ))]]) ).
thf(12300,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[134,5732]) ).
thf(12301,plain,
member @ ( sk5 @ sk7 ) @ sk7,
inference(pattern_uni,[status(thm)],[12300:[bind(A,$thf( sk7 ))]]) ).
thf(48988,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk5 @ sk7 ) @ sk7 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12301,230]) ).
thf(48989,plain,
~ ( member @ ( sk5 @ sk7 ) @ ( complement @ sk7 ) ),
inference(pattern_uni,[status(thm)],[48988:[bind(A,$thf( sk7 )),bind(B,$thf( sk5 @ sk7 ))]]) ).
thf(54614,plain,
( ( member @ ( sk5 @ sk7 ) @ ( singleton @ ( sk5 @ sk7 ) ) )
!= ( member @ ( sk5 @ sk7 ) @ ( complement @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[38893,48989]) ).
thf(54801,plain,
( ( ( sk5 @ sk7 )
!= ( sk5 @ sk7 ) )
| ( ( singleton @ ( sk5 @ sk7 ) )
!= ( complement @ sk7 ) ) ),
inference(simp,[status(thm)],[54614]) ).
thf(54873,plain,
( ( singleton @ ( sk5 @ sk7 ) )
!= ( complement @ sk7 ) ),
inference(simp,[status(thm)],[54801]) ).
thf(42627,plain,
! [B: $i,A: $i] :
( ( member @ null_class @ ( union @ sk7 @ A ) )
!= ( member @ B @ null_class ) ),
inference(paramod_ordered,[status(thm)],[42498,194]) ).
thf(42721,plain,
! [B: $i,A: $i] :
( ( null_class != B )
| ( ( union @ sk7 @ A )
!= null_class ) ),
inference(simp,[status(thm)],[42627]) ).
thf(42809,plain,
! [A: $i] :
( ( union @ sk7 @ A )
!= null_class ),
inference(simp,[status(thm)],[42721]) ).
thf(61077,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[45358,251]) ).
thf(61078,plain,
member @ ( sum_class @ ( power_class @ ( power_class @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[61077:[bind(A,$thf( power_class @ ( power_class @ sk7 ) ))]]) ).
thf(73525,plain,
( ( member @ ( sum_class @ ( power_class @ ( power_class @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[61078,48]) ).
thf(73632,plain,
( ( ( sum_class @ ( power_class @ ( power_class @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[73525]) ).
thf(73697,plain,
( ( sum_class @ ( power_class @ ( power_class @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[73632]) ).
thf(48927,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk4 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44957,230]) ).
thf(48928,plain,
~ ( member @ ( power_class @ ( sk4 @ null_class @ universal_class ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[48927:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk4 @ null_class @ universal_class ) ))]]) ).
thf(242,plain,
! [A: $i] :
( ~ ( member @ A @ identity_relation )
| ( member @ ( sk9 @ A ) @ universal_class ) ),
inference(cnf,[status(esa)],[240]) ).
thf(59158,plain,
! [A: $i] :
( ( member @ ( sk9 @ A ) @ universal_class )
| ( ( member @ ( sk5 @ identity_relation ) @ identity_relation )
!= ( member @ A @ identity_relation ) ) ),
inference(paramod_ordered,[status(thm)],[58112,242]) ).
thf(59159,plain,
member @ ( sk9 @ ( sk5 @ identity_relation ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[59158:[bind(A,$thf( sk5 @ identity_relation ))]]) ).
thf(60576,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk9 @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[59159,230]) ).
thf(60577,plain,
~ ( member @ ( sk9 @ ( sk5 @ identity_relation ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[60576:[bind(A,$thf( universal_class )),bind(B,$thf( sk9 @ ( sk5 @ identity_relation ) ))]]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( A != B )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(cnf,[status(esa)],[177]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[179]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(15416,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ sk7 @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[112,15373]) ).
thf(15417,plain,
~ ( member @ sk7 @ ( power_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[15416:[bind(A,$thf( sk7 )),bind(B,$thf( null_class ))]]) ).
thf(15917,plain,
( ( member @ sk7 @ ( power_class @ null_class ) )
!= ( member @ sk7 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[191,15417]) ).
thf(15953,plain,
( ( sk7 != sk7 )
| ( ( power_class @ null_class )
!= universal_class ) ),
inference(simp,[status(thm)],[15917]) ).
thf(15985,plain,
( ( power_class @ null_class )
!= universal_class ),
inference(simp,[status(thm)],[15953]) ).
thf(88925,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( A
!= ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[323,15985]) ).
thf(88926,plain,
~ ( subclass @ universal_class @ ( power_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[88925:[bind(A,$thf( power_class @ null_class ))]]) ).
thf(3363,plain,
! [A: $i] :
( ( sk2 != universal_class )
| ( ( subclass @ null_class @ A )
!= ( subclass @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[3237,2004]) ).
thf(3368,plain,
! [A: $i] :
( ( sk2 != universal_class )
| ( sk2 != null_class )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[3363]) ).
thf(3378,plain,
( ( sk2 != universal_class )
| ( sk2 != null_class ) ),
inference(simp,[status(thm)],[3368]) ).
thf(12842,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( sk2 != universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[135,3378]) ).
thf(12843,plain,
( ( disjoint @ ( sk5 @ sk2 ) @ sk2 )
| ( sk2 != universal_class ) ),
inference(pattern_uni,[status(thm)],[12842:[bind(A,$thf( sk2 ))]]) ).
thf(42910,plain,
! [A: $i] :
( ( member @ null_class @ ( successor @ sk7 ) )
!= ( member @ A @ null_class ) ),
inference(paramod_ordered,[status(thm)],[42684,194]) ).
thf(43009,plain,
! [A: $i] :
( ( null_class != A )
| ( ( successor @ sk7 )
!= null_class ) ),
inference(simp,[status(thm)],[42910]) ).
thf(43029,plain,
( ( successor @ sk7 )
!= null_class ),
inference(simp,[status(thm)],[43009]) ).
thf(43099,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( A
!= ( successor @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[134,43029]) ).
thf(43100,plain,
member @ ( sk5 @ ( successor @ sk7 ) ) @ ( successor @ sk7 ),
inference(pattern_uni,[status(thm)],[43099:[bind(A,$thf( successor @ sk7 ))]]) ).
thf(43090,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( A
!= ( successor @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[133,43029]) ).
thf(43091,plain,
member @ ( sk5 @ ( successor @ sk7 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[43090:[bind(A,$thf( successor @ sk7 ))]]) ).
thf(49010,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk5 @ ( successor @ sk7 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43091,230]) ).
thf(49011,plain,
~ ( member @ ( sk5 @ ( successor @ sk7 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[49010:[bind(A,$thf( universal_class )),bind(B,$thf( sk5 @ ( successor @ sk7 ) ))]]) ).
thf(65751,plain,
( ( member @ ( sk5 @ ( successor @ sk7 ) ) @ ( complement @ universal_class ) )
!= ( member @ ( sk5 @ ( successor @ sk7 ) ) @ ( successor @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[43100,49011]) ).
thf(65907,plain,
( ( ( sk5 @ ( successor @ sk7 ) )
!= ( sk5 @ ( successor @ sk7 ) ) )
| ( ( complement @ universal_class )
!= ( successor @ sk7 ) ) ),
inference(simp,[status(thm)],[65751]) ).
thf(66000,plain,
( ( complement @ universal_class )
!= ( successor @ sk7 ) ),
inference(simp,[status(thm)],[65907]) ).
thf(1087,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( sk1 != null_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[133,1080]) ).
thf(1088,plain,
( ( member @ ( sk5 @ sk2 ) @ universal_class )
| ( sk1 != null_class ) ),
inference(pattern_uni,[status(thm)],[1087:[bind(A,$thf( sk2 ))]]) ).
thf(13312,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( member @ ( sk5 @ sk2 ) @ universal_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[135,1088]) ).
thf(13313,plain,
( ( disjoint @ ( sk5 @ sk1 ) @ sk1 )
| ( member @ ( sk5 @ sk2 ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[13312:[bind(A,$thf( sk1 ))]]) ).
thf(61324,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[60931,219]) ).
thf(61325,plain,
member @ ( power_class @ ( sum_class @ sk7 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[61324:[bind(A,$thf( sum_class @ sk7 ))]]) ).
thf(48942,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ null_class @ sk7 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5702,230]) ).
thf(48943,plain,
~ ( member @ null_class @ ( complement @ sk7 ) ),
inference(pattern_uni,[status(thm)],[48942:[bind(A,$thf( sk7 )),bind(B,$thf( null_class ))]]) ).
thf(49354,plain,
( ( member @ null_class @ ( complement @ sk7 ) )
!= ( member @ null_class @ ( successor @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[42684,48943]) ).
thf(49539,plain,
( ( null_class != null_class )
| ( ( complement @ sk7 )
!= ( successor @ sk7 ) ) ),
inference(simp,[status(thm)],[49354]) ).
thf(49602,plain,
( ( complement @ sk7 )
!= ( successor @ sk7 ) ),
inference(simp,[status(thm)],[49539]) ).
thf(58233,plain,
( ( member @ ( sk5 @ identity_relation ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[58109,48]) ).
thf(58317,plain,
( ( ( sk5 @ identity_relation )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[58233]) ).
thf(58393,plain,
( ( sk5 @ identity_relation )
!= sk2 ),
inference(simp,[status(thm)],[58317]) ).
thf(407,plain,
! [A: $i] :
( ~ ( subclass @ sk2 @ sk7 )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[68,335]) ).
thf(418,plain,
! [A: $i] :
( ~ ( subclass @ sk2 @ sk7 )
| ( A != sk7 )
| ( sk2 != universal_class ) ),
inference(simp,[status(thm)],[407]) ).
thf(423,plain,
( ~ ( subclass @ sk2 @ sk7 )
| ( sk2 != universal_class ) ),
inference(simp,[status(thm)],[418]) ).
thf(492,plain,
! [A: $i] :
( ( sk2 != universal_class )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[68,423]) ).
thf(495,plain,
! [A: $i] :
( ( sk2 != universal_class )
| ( A != sk2 )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[492]) ).
thf(504,plain,
( ( sk2 != universal_class )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[495]) ).
thf(5945,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ~ ( inductive @ universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[133,5713]) ).
thf(5946,plain,
( ( member @ ( sk5 @ sk2 ) @ universal_class )
| ~ ( inductive @ universal_class ) ),
inference(pattern_uni,[status(thm)],[5945:[bind(A,$thf( sk2 ))]]) ).
thf(14046,plain,
( ~ ( inductive @ universal_class )
| ( ( member @ ( sk5 @ sk2 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[5946,48]) ).
thf(14063,plain,
( ~ ( inductive @ universal_class )
| ( ( sk5 @ sk2 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[14046]) ).
thf(14088,plain,
( ~ ( inductive @ universal_class )
| ( ( sk5 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[14063]) ).
thf(28,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn1) ).
thf(187,plain,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15407,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk7 @ null_class ) ),
inference(paramod_ordered,[status(thm)],[187,15373]) ).
thf(15426,plain,
( ( sk7 != successor_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[15407]) ).
thf(60848,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[44928,251]) ).
thf(60849,plain,
member @ ( sum_class @ ( power_class @ sk7 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60848:[bind(A,$thf( power_class @ sk7 ))]]) ).
thf(62255,plain,
( ( member @ ( sum_class @ ( power_class @ sk7 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60849,48]) ).
thf(62363,plain,
( ( ( sum_class @ ( power_class @ sk7 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[62255]) ).
thf(62410,plain,
( ( sum_class @ ( power_class @ sk7 ) )
!= sk2 ),
inference(simp,[status(thm)],[62363]) ).
thf(63582,plain,
( ( member @ ( power_class @ ( sum_class @ sk7 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[61325,48]) ).
thf(63674,plain,
( ( ( power_class @ ( sum_class @ sk7 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[63582]) ).
thf(63736,plain,
( ( power_class @ ( sum_class @ sk7 ) )
!= sk2 ),
inference(simp,[status(thm)],[63674]) ).
thf(58210,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk5 @ identity_relation ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58109,230]) ).
thf(58211,plain,
~ ( member @ ( sk5 @ identity_relation ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[58210:[bind(A,$thf( universal_class )),bind(B,$thf( sk5 @ identity_relation ))]]) ).
thf(61081,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ universal_class ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[728,251]) ).
thf(61082,plain,
member @ ( sum_class @ ( sk5 @ universal_class ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[61081:[bind(A,$thf( sk5 @ universal_class ))]]) ).
thf(63084,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk5 @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[61082,219]) ).
thf(63085,plain,
member @ ( power_class @ ( sum_class @ ( sk5 @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[63084:[bind(A,$thf( sum_class @ ( sk5 @ universal_class ) ))]]) ).
thf(78945,plain,
( ( member @ ( power_class @ ( sum_class @ ( sk5 @ universal_class ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[63085,48]) ).
thf(79035,plain,
( ( ( power_class @ ( sum_class @ ( sk5 @ universal_class ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[78945]) ).
thf(79120,plain,
( ( power_class @ ( sum_class @ ( sk5 @ universal_class ) ) )
!= sk2 ),
inference(simp,[status(thm)],[79035]) ).
thf(48994,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ sk7 @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[191,230]) ).
thf(48995,plain,
~ ( member @ sk7 @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[48994:[bind(A,$thf( universal_class )),bind(B,$thf( sk7 ))]]) ).
thf(49771,plain,
( ( member @ sk7 @ ( complement @ universal_class ) )
!= ( member @ sk7 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[191,48995]) ).
thf(49889,plain,
( ( sk7 != sk7 )
| ( ( complement @ universal_class )
!= universal_class ) ),
inference(simp,[status(thm)],[49771]) ).
thf(49952,plain,
( ( complement @ universal_class )
!= universal_class ),
inference(simp,[status(thm)],[49889]) ).
thf(87289,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( A
!= ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[323,49952]) ).
thf(87290,plain,
~ ( subclass @ universal_class @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[87289:[bind(A,$thf( complement @ universal_class ))]]) ).
thf(89473,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,87290]) ).
thf(89474,plain,
~ ( member @ universal_class @ ( power_class @ ( complement @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[89473:[bind(A,$thf( universal_class )),bind(B,$thf( complement @ universal_class ))]]) ).
thf(47171,plain,
( ( member @ ( power_class @ ( sk4 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[44957,48]) ).
thf(47272,plain,
( ( ( power_class @ ( sk4 @ null_class @ universal_class ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[47171]) ).
thf(47330,plain,
( ( power_class @ ( sk4 @ null_class @ universal_class ) )
!= sk2 ),
inference(simp,[status(thm)],[47272]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( member @ B @ ( domain_of @ A ) )
<=> ( ( member @ B @ universal_class )
& ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( ( member @ B @ ( domain_of @ A ) )
=> ( ( member @ B @ universal_class )
& ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) ) )
& ( ( ( member @ B @ universal_class )
& ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) )
=> ( member @ B @ ( domain_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44915,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[5722,219]) ).
thf(44916,plain,
member @ ( power_class @ ( sk5 @ sk7 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[44915:[bind(A,$thf( sk5 @ sk7 ))]]) ).
thf(49033,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk5 @ sk7 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44916,230]) ).
thf(49034,plain,
~ ( member @ ( power_class @ ( sk5 @ sk7 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[49033:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk5 @ sk7 ) ))]]) ).
thf(6904,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( sk2 != universal_class )
| ( ( subclass @ A @ B )
!= ( subclass @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[112,423]) ).
thf(6905,plain,
( ~ ( member @ sk2 @ ( power_class @ sk7 ) )
| ( sk2 != universal_class ) ),
inference(pattern_uni,[status(thm)],[6904:[bind(A,$thf( sk2 )),bind(B,$thf( sk7 ))]]) ).
thf(54682,plain,
( ( member @ ( sk5 @ sk7 ) @ ( complement @ sk7 ) )
!= ( member @ ( sk5 @ sk7 ) @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[5722,48989]) ).
thf(54794,plain,
( ( ( sk5 @ sk7 )
!= ( sk5 @ sk7 ) )
| ( ( complement @ sk7 )
!= universal_class ) ),
inference(simp,[status(thm)],[54682]) ).
thf(54871,plain,
( ( complement @ sk7 )
!= universal_class ),
inference(simp,[status(thm)],[54794]) ).
thf(88853,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( A
!= ( complement @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[323,54871]) ).
thf(88854,plain,
~ ( subclass @ universal_class @ ( complement @ sk7 ) ),
inference(pattern_uni,[status(thm)],[88853:[bind(A,$thf( complement @ sk7 ))]]) ).
thf(89602,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( complement @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[91,88854]) ).
thf(89603,plain,
member @ ( sk4 @ ( complement @ sk7 ) @ universal_class ) @ universal_class,
inference(pattern_uni,[status(thm)],[89602:[bind(A,$thf( universal_class )),bind(B,$thf( complement @ sk7 ))]]) ).
thf(93302,plain,
( ( member @ ( sk4 @ ( complement @ sk7 ) @ universal_class ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[89603,48]) ).
thf(93429,plain,
( ( ( sk4 @ ( complement @ sk7 ) @ universal_class )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[93302]) ).
thf(93496,plain,
( ( sk4 @ ( complement @ sk7 ) @ universal_class )
!= sk2 ),
inference(simp,[status(thm)],[93429]) ).
thf(3359,plain,
! [A: $i] :
( ( sk1 != universal_class )
| ( ( subclass @ null_class @ A )
!= ( subclass @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3237,2006]) ).
thf(3369,plain,
! [A: $i] :
( ( sk1 != universal_class )
| ( sk1 != null_class )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[3359]) ).
thf(3379,plain,
( ( sk1 != universal_class )
| ( sk1 != null_class ) ),
inference(simp,[status(thm)],[3369]) ).
thf(3470,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( sk1 != universal_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[133,3379]) ).
thf(3471,plain,
( ( member @ ( sk5 @ sk1 ) @ universal_class )
| ( sk1 != universal_class ) ),
inference(pattern_uni,[status(thm)],[3470:[bind(A,$thf( sk1 ))]]) ).
thf(8771,plain,
( ( sk1 != universal_class )
| ( ( member @ ( sk5 @ sk1 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[3471,48]) ).
thf(8797,plain,
( ( sk1 != universal_class )
| ( ( sk5 @ sk1 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[8771]) ).
thf(8819,plain,
( ( sk1 != universal_class )
| ( ( sk5 @ sk1 )
!= sk2 ) ),
inference(simp,[status(thm)],[8797]) ).
thf(1880,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ null_class ) ),
inference(paramod_ordered,[status(thm)],[236,1863]) ).
thf(1890,plain,
( ( element_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[1880]) ).
thf(62239,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( power_class @ sk7 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60849,230]) ).
thf(62240,plain,
~ ( member @ ( sum_class @ ( power_class @ sk7 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[62239:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( power_class @ sk7 ) ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( inverse @ A )
= ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_defn) ).
thf(93,plain,
! [A: $i] :
( ( inverse @ A )
= ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5686,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,1556]) ).
thf(5687,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ),
inference(pattern_uni,[status(thm)],[5686:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )),bind(B,$thf( null_class ))]]) ).
thf(12542,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ null_class ) ) ),
inference(rewrite,[status(thm)],[5687,11335]) ).
thf(12642,plain,
~ ( inductive @ ( sum_class @ null_class ) ),
inference(rewrite,[status(thm)],[12542,11335]) ).
thf(6922,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( sk2 != universal_class )
| ( ( subclass @ A @ B )
!= ( subclass @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[112,2004]) ).
thf(6923,plain,
( ~ ( member @ sk2 @ ( power_class @ sk1 ) )
| ( sk2 != universal_class ) ),
inference(pattern_uni,[status(thm)],[6922:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) )
<=> ( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_defn) ).
thf(152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) )
=> ( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A ) ) )
& ( ( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A ) )
=> ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(45669,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk5 @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[44916,219]) ).
thf(45670,plain,
member @ ( power_class @ ( power_class @ ( sk5 @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[45669:[bind(A,$thf( power_class @ ( sk5 @ sk7 ) ))]]) ).
thf(48216,plain,
( ( member @ ( power_class @ ( power_class @ ( sk5 @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[45670,48]) ).
thf(48317,plain,
( ( ( power_class @ ( power_class @ ( sk5 @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[48216]) ).
thf(48376,plain,
( ( power_class @ ( power_class @ ( sk5 @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[48317]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( function @ A )
| ( B != sk8 ) ),
inference(paramod_ordered,[status(thm)],[56,234]) ).
thf(261,plain,
! [A: $i] :
( ~ ( subclass @ A @ sk8 )
| ~ ( subclass @ sk8 @ A )
| ( function @ A ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( A )),bind(B,$thf( sk8 ))]]) ).
thf(24,axiom,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate) ).
thf(163,plain,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(164,plain,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(cnf,[status(esa)],[163]) ).
thf(25865,plain,
! [A: $i] :
( ( member @ sk7 @ ( singleton @ sk7 ) )
!= ( member @ A @ null_class ) ),
inference(paramod_ordered,[status(thm)],[25609,194]) ).
thf(25912,plain,
! [A: $i] :
( ( sk7 != A )
| ( ( singleton @ sk7 )
!= null_class ) ),
inference(simp,[status(thm)],[25865]) ).
thf(25962,plain,
( ( singleton @ sk7 )
!= null_class ),
inference(simp,[status(thm)],[25912]) ).
thf(25994,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( A
!= ( singleton @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[133,25962]) ).
thf(25995,plain,
member @ ( sk5 @ ( singleton @ sk7 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[25994:[bind(A,$thf( singleton @ sk7 ))]]) ).
thf(44970,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ ( singleton @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[25995,219]) ).
thf(44971,plain,
member @ ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[44970:[bind(A,$thf( sk5 @ ( singleton @ sk7 ) ))]]) ).
thf(47803,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[44971,219]) ).
thf(47804,plain,
member @ ( power_class @ ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[47803:[bind(A,$thf( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ))]]) ).
thf(89467,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[91,87290]) ).
thf(89468,plain,
member @ ( sk4 @ ( complement @ universal_class ) @ universal_class ) @ universal_class,
inference(pattern_uni,[status(thm)],[89467:[bind(A,$thf( universal_class )),bind(B,$thf( complement @ universal_class ))]]) ).
thf(91562,plain,
( ( member @ ( sk4 @ ( complement @ universal_class ) @ universal_class ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[89468,48]) ).
thf(91678,plain,
( ( ( sk4 @ ( complement @ universal_class ) @ universal_class )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[91562]) ).
thf(91720,plain,
( ( sk4 @ ( complement @ universal_class ) @ universal_class )
!= sk2 ),
inference(simp,[status(thm)],[91678]) ).
thf(60923,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[5722,251]) ).
thf(60924,plain,
member @ ( sum_class @ ( sk5 @ sk7 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60923:[bind(A,$thf( sk5 @ sk7 ))]]) ).
thf(62774,plain,
( ( member @ ( sum_class @ ( sk5 @ sk7 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60924,48]) ).
thf(62894,plain,
( ( ( sum_class @ ( sk5 @ sk7 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[62774]) ).
thf(62934,plain,
( ( sum_class @ ( sk5 @ sk7 ) )
!= sk2 ),
inference(simp,[status(thm)],[62894]) ).
thf(62952,plain,
( ( sk2 != null_class )
| ( ( sum_class @ ( sk5 @ sk7 ) )
!= ( sum_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[11335,62934]) ).
thf(63006,plain,
( ( sk2 != null_class )
| ( ( sk5 @ sk7 )
!= null_class ) ),
inference(simp,[status(thm)],[62952]) ).
thf(85468,plain,
( ( member @ ( power_class @ ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[47804,48]) ).
thf(85572,plain,
( ( ( power_class @ ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[85468]) ).
thf(85639,plain,
( ( power_class @ ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[85572]) ).
thf(25657,plain,
! [B: $i,A: $i] :
( ( member @ sk7 @ ( unordered_pair @ A @ sk7 ) )
!= ( member @ B @ null_class ) ),
inference(paramod_ordered,[status(thm)],[24714,194]) ).
thf(25706,plain,
! [B: $i,A: $i] :
( ( sk7 != B )
| ( ( unordered_pair @ A @ sk7 )
!= null_class ) ),
inference(simp,[status(thm)],[25657]) ).
thf(25773,plain,
! [A: $i] :
( ( unordered_pair @ A @ sk7 )
!= null_class ),
inference(simp,[status(thm)],[25706]) ).
thf(34151,plain,
! [B: $i,A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( A
!= ( unordered_pair @ B @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[133,25773]) ).
thf(34152,plain,
! [A: $i] : ( member @ ( sk5 @ ( unordered_pair @ A @ sk7 ) ) @ universal_class ),
inference(pattern_uni,[status(thm)],[34151:[bind(A,$thf( unordered_pair @ C @ sk7 )),bind(B,$thf( C ))]]) ).
thf(34192,plain,
! [A: $i] : ( member @ ( sk5 @ ( unordered_pair @ A @ sk7 ) ) @ universal_class ),
inference(simp,[status(thm)],[34152]) ).
thf(36641,plain,
! [A: $i] :
( ( member @ ( sk5 @ ( unordered_pair @ A @ sk7 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[34192,48]) ).
thf(36730,plain,
! [A: $i] :
( ( ( sk5 @ ( unordered_pair @ A @ sk7 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[36641]) ).
thf(36800,plain,
! [A: $i] :
( ( sk5 @ ( unordered_pair @ A @ sk7 ) )
!= sk2 ),
inference(simp,[status(thm)],[36730]) ).
thf(58206,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ identity_relation ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[58109,219]) ).
thf(58207,plain,
member @ ( power_class @ ( sk5 @ identity_relation ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[58206:[bind(A,$thf( sk5 @ identity_relation ))]]) ).
thf(60997,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[58207,251]) ).
thf(60998,plain,
member @ ( sum_class @ ( power_class @ ( sk5 @ identity_relation ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60997:[bind(A,$thf( power_class @ ( sk5 @ identity_relation ) ))]]) ).
thf(62754,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk5 @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[60924,219]) ).
thf(62755,plain,
member @ ( power_class @ ( sum_class @ ( sk5 @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[62754:[bind(A,$thf( sum_class @ ( sk5 @ sk7 ) ))]]) ).
thf(77395,plain,
( ( member @ ( power_class @ ( sum_class @ ( sk5 @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[62755,48]) ).
thf(77531,plain,
( ( ( power_class @ ( sum_class @ ( sk5 @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[77395]) ).
thf(77581,plain,
( ( power_class @ ( sum_class @ ( sk5 @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[77531]) ).
thf(25303,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( unordered_pair @ A @ B ) )
| ( ( member @ sk7 @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[191,185]) ).
thf(25304,plain,
! [A: $i] : ( member @ sk7 @ ( unordered_pair @ sk7 @ A ) ),
inference(pattern_uni,[status(thm)],[25303:[bind(A,$thf( sk7 ))]]) ).
thf(25568,plain,
! [A: $i] : ( member @ sk7 @ ( unordered_pair @ sk7 @ A ) ),
inference(simp,[status(thm)],[25304]) ).
thf(34799,plain,
! [B: $i,A: $i] :
( ( member @ sk7 @ ( unordered_pair @ sk7 @ A ) )
!= ( member @ B @ null_class ) ),
inference(paramod_ordered,[status(thm)],[25568,194]) ).
thf(34887,plain,
! [B: $i,A: $i] :
( ( sk7 != B )
| ( ( unordered_pair @ sk7 @ A )
!= null_class ) ),
inference(simp,[status(thm)],[34799]) ).
thf(34948,plain,
! [A: $i] :
( ( unordered_pair @ sk7 @ A )
!= null_class ),
inference(simp,[status(thm)],[34887]) ).
thf(622,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( subclass @ successor_relation @ null_class )
| ( A
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[133,187]) ).
thf(623,plain,
( ( member @ ( sk5 @ ( cross_product @ universal_class @ universal_class ) ) @ universal_class )
| ( subclass @ successor_relation @ null_class ) ),
inference(pattern_uni,[status(thm)],[622:[bind(A,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(2455,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( unordered_pair @ A @ B ) @ universal_class )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,2165]) ).
thf(2516,plain,
! [C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ A @ B )
!= C )
| ( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
!= universal_class ) ),
inference(simp,[status(thm)],[2455]) ).
thf(2536,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
!= universal_class ),
inference(simp,[status(thm)],[2516]) ).
thf(12548,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[2536,11335]) ).
thf(14408,plain,
( ( sum_class @ ( sum_class @ null_class ) )
!= universal_class ),
inference(rewrite,[status(thm)],[12548,13649]) ).
thf(42,axiom,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip) ).
thf(237,plain,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(238,plain,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(cnf,[status(esa)],[237]) ).
thf(61328,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ sk7 ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60931,230]) ).
thf(61329,plain,
~ ( member @ ( sum_class @ sk7 ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[61328:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ sk7 ))]]) ).
thf(62762,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk5 @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[60924,251]) ).
thf(62763,plain,
member @ ( sum_class @ ( sum_class @ ( sk5 @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[62762:[bind(A,$thf( sum_class @ ( sk5 @ sk7 ) ))]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( restrict @ B @ A @ C )
= ( intersection @ B @ ( cross_product @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_defn) ).
thf(61,plain,
! [A: $i,B: $i,C: $i] :
( ( restrict @ B @ A @ C )
= ( intersection @ B @ ( cross_product @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( subclass @ successor_relation @ A )
| ( B
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[56,187]) ).
thf(293,plain,
! [A: $i] :
( ~ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( cross_product @ universal_class @ universal_class ) @ A )
| ( subclass @ successor_relation @ A ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( A )),bind(B,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(10085,plain,
! [C: $i,B: $i,A: $i] :
( ( subclass @ A @ B )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[91,8539]) ).
thf(10086,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[10085:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )),bind(B,$thf( D )),bind(C,$thf( sk4 @ D @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ))]]) ).
thf(10180,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) @ A ),
inference(simp,[status(thm)],[10086]) ).
thf(11112,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk5 @ A ) @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,8539]) ).
thf(11113,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )
= null_class ),
inference(pattern_uni,[status(thm)],[11112:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )),bind(B,$thf( sk5 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ))]]) ).
thf(20071,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
= null_class ),
inference(rewrite,[status(thm)],[11113,16734]) ).
thf(21774,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) @ A ),
inference(rewrite,[status(thm)],[10180,20071]) ).
thf(12531,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[8539,11335]) ).
thf(20903,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ),
inference(rewrite,[status(thm)],[12531,20071]) ).
thf(5960,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( sk7 != universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[133,5810]) ).
thf(5961,plain,
( ( member @ ( sk5 @ sk2 ) @ universal_class )
| ( sk7 != universal_class ) ),
inference(pattern_uni,[status(thm)],[5960:[bind(A,$thf( sk2 ))]]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) )
<=> ( ( member @ C @ universal_class )
& ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn2) ).
thf(117,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) )
=> ( ( member @ C @ universal_class )
& ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) ) ) )
& ( ( ( member @ C @ universal_class )
& ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) ) )
=> ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(48936,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk5 @ ( successor @ sk7 ) ) @ ( successor @ sk7 ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43100,230]) ).
thf(48937,plain,
~ ( member @ ( sk5 @ ( successor @ sk7 ) ) @ ( complement @ ( successor @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[48936:[bind(A,$thf( successor @ sk7 )),bind(B,$thf( sk5 @ ( successor @ sk7 ) ))]]) ).
thf(99460,plain,
( ( member @ ( sk5 @ ( successor @ sk7 ) ) @ ( complement @ ( successor @ sk7 ) ) )
!= ( member @ ( sk5 @ ( successor @ sk7 ) ) @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[43091,48937]) ).
thf(99626,plain,
( ( ( sk5 @ ( successor @ sk7 ) )
!= ( sk5 @ ( successor @ sk7 ) ) )
| ( ( complement @ ( successor @ sk7 ) )
!= universal_class ) ),
inference(simp,[status(thm)],[99460]) ).
thf(99760,plain,
( ( complement @ ( successor @ sk7 ) )
!= universal_class ),
inference(simp,[status(thm)],[99626]) ).
thf(88699,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( sk1 != null_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[323,3379]) ).
thf(88700,plain,
( ~ ( subclass @ universal_class @ sk1 )
| ( sk1 != null_class ) ),
inference(pattern_uni,[status(thm)],[88699:[bind(A,$thf( sk1 ))]]) ).
thf(89435,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( subclass @ sk7 @ A )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[189,87290]) ).
thf(89535,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( sk7 != universal_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[89435]) ).
thf(89553,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[89535]) ).
thf(60973,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ ( singleton @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[25995,251]) ).
thf(60974,plain,
member @ ( sum_class @ ( sk5 @ ( singleton @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60973:[bind(A,$thf( sk5 @ ( singleton @ sk7 ) ))]]) ).
thf(72647,plain,
( ( member @ ( sum_class @ ( sk5 @ ( singleton @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60974,48]) ).
thf(72751,plain,
( ( ( sum_class @ ( sk5 @ ( singleton @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[72647]) ).
thf(72796,plain,
( ( sum_class @ ( sk5 @ ( singleton @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[72751]) ).
thf(57067,plain,
! [A: $i] :
( ( member @ ( ordered_pair @ A @ A ) @ identity_relation )
| ( ( member @ ( power_class @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[44928,245]) ).
thf(57068,plain,
member @ ( ordered_pair @ ( power_class @ sk7 ) @ ( power_class @ sk7 ) ) @ identity_relation,
inference(pattern_uni,[status(thm)],[57067:[bind(A,$thf( power_class @ sk7 ))]]) ).
thf(100018,plain,
member @ ( unordered_pair @ ( singleton @ ( power_class @ sk7 ) ) @ ( unordered_pair @ ( power_class @ sk7 ) @ ( singleton @ ( power_class @ sk7 ) ) ) ) @ identity_relation,
inference(rewrite,[status(thm)],[57068,249]) ).
thf(13232,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( sk1 != universal_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[135,3379]) ).
thf(13233,plain,
( ( disjoint @ ( sk5 @ sk1 ) @ sk1 )
| ( sk1 != universal_class ) ),
inference(pattern_uni,[status(thm)],[13232:[bind(A,$thf( sk1 ))]]) ).
thf(3994,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( subclass @ sk8 @ null_class )
| ( A
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[133,3907]) ).
thf(3995,plain,
( ( member @ ( sk5 @ ( cross_product @ universal_class @ universal_class ) ) @ universal_class )
| ( subclass @ sk8 @ null_class ) ),
inference(pattern_uni,[status(thm)],[3994:[bind(A,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(60156,plain,
( ( member @ ( sk5 @ identity_relation ) @ ( complement @ identity_relation ) )
!= ( member @ ( sk5 @ identity_relation ) @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[58109,59077]) ).
thf(60366,plain,
( ( ( sk5 @ identity_relation )
!= ( sk5 @ identity_relation ) )
| ( ( complement @ identity_relation )
!= universal_class ) ),
inference(simp,[status(thm)],[60156]) ).
thf(60406,plain,
( ( complement @ identity_relation )
!= universal_class ),
inference(simp,[status(thm)],[60366]) ).
thf(86682,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( A
!= ( complement @ identity_relation ) ) ),
inference(paramod_ordered,[status(thm)],[323,60406]) ).
thf(86683,plain,
~ ( subclass @ universal_class @ ( complement @ identity_relation ) ),
inference(pattern_uni,[status(thm)],[86682:[bind(A,$thf( complement @ identity_relation ))]]) ).
thf(48884,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk5 @ sk7 ) @ ( singleton @ ( sk5 @ sk7 ) ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[38893,230]) ).
thf(48885,plain,
~ ( member @ ( sk5 @ sk7 ) @ ( complement @ ( singleton @ ( sk5 @ sk7 ) ) ) ),
inference(pattern_uni,[status(thm)],[48884:[bind(A,$thf( singleton @ ( sk5 @ sk7 ) )),bind(B,$thf( sk5 @ sk7 ))]]) ).
thf(1386,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( member @ ( sk5 @ sk2 ) @ universal_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[133,1088]) ).
thf(1387,plain,
( ( member @ ( sk5 @ sk1 ) @ universal_class )
| ( member @ ( sk5 @ sk2 ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[1386:[bind(A,$thf( sk1 ))]]) ).
thf(46429,plain,
( ( member @ ( power_class @ ( power_class @ sk7 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[45358,48]) ).
thf(46540,plain,
( ( ( power_class @ ( power_class @ sk7 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[46429]) ).
thf(46588,plain,
( ( power_class @ ( power_class @ sk7 ) )
!= sk2 ),
inference(simp,[status(thm)],[46540]) ).
thf(63103,plain,
( ( member @ ( sum_class @ ( sk5 @ universal_class ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[61082,48]) ).
thf(63180,plain,
( ( ( sum_class @ ( sk5 @ universal_class ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[63103]) ).
thf(63249,plain,
( ( sum_class @ ( sk5 @ universal_class ) )
!= sk2 ),
inference(simp,[status(thm)],[63180]) ).
thf(63280,plain,
( ( sk2 != null_class )
| ( ( sum_class @ ( sk5 @ universal_class ) )
!= ( sum_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[11335,63249]) ).
thf(63332,plain,
( ( sk2 != null_class )
| ( ( sk5 @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[63280]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
<=> ( ( member @ A @ universal_class )
& ( member @ B @ universal_class )
& ( ( successor @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn2) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
=> ( ( member @ A @ universal_class )
& ( member @ B @ universal_class )
& ( ( successor @ A )
= B ) ) )
& ( ( ( member @ A @ universal_class )
& ( member @ B @ universal_class )
& ( ( successor @ A )
= B ) )
=> ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(63092,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk5 @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[61082,251]) ).
thf(63093,plain,
member @ ( sum_class @ ( sum_class @ ( sk5 @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[63092:[bind(A,$thf( sum_class @ ( sk5 @ universal_class ) ))]]) ).
thf(86192,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( sk2 != universal_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[323,2269]) ).
thf(86193,plain,
( ~ ( subclass @ universal_class @ sk1 )
| ( sk2 != universal_class ) ),
inference(pattern_uni,[status(thm)],[86192:[bind(A,$thf( sk1 ))]]) ).
thf(62758,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sk5 @ sk7 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60924,230]) ).
thf(62759,plain,
~ ( member @ ( sum_class @ ( sk5 @ sk7 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[62758:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sk5 @ sk7 ) ))]]) ).
thf(44940,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ ( successor @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[43091,219]) ).
thf(44941,plain,
member @ ( power_class @ ( sk5 @ ( successor @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[44940:[bind(A,$thf( sk5 @ ( successor @ sk7 ) ))]]) ).
thf(46753,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk5 @ ( successor @ sk7 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[44941,219]) ).
thf(46754,plain,
member @ ( power_class @ ( power_class @ ( sk5 @ ( successor @ sk7 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[46753:[bind(A,$thf( power_class @ ( sk5 @ ( successor @ sk7 ) ) ))]]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subclass @ A @ B ) ),
inference(cnf,[status(esa)],[87]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subclass @ A @ B ) ),
inference(simp,[status(thm)],[89]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) )
<=> ( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_defn) ).
thf(197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) )
=> ( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ) )
& ( ( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
& ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) )
=> ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(48933,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44971,230]) ).
thf(48934,plain,
~ ( member @ ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[48933:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ))]]) ).
thf(681,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[133,191]) ).
thf(682,plain,
( ( member @ ( sk5 @ sk7 ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[681:[bind(A,$thf( sk7 ))]]) ).
thf(1338,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A
!= ( sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[133,682]) ).
thf(1339,plain,
( ( member @ ( sk5 @ ( sk5 @ sk7 ) ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[1338:[bind(A,$thf( sk5 @ sk7 ))]]) ).
thf(2312,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A
!= ( sk5 @ ( sk5 @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[133,1339]) ).
thf(2313,plain,
( ( member @ ( sk5 @ ( sk5 @ ( sk5 @ sk7 ) ) ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[2312:[bind(A,$thf( sk5 @ ( sk5 @ sk7 ) ))]]) ).
thf(12708,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( function @ null_class )
| ( A != sk8 ) ),
inference(paramod_ordered,[status(thm)],[135,234]) ).
thf(12709,plain,
( ( disjoint @ ( sk5 @ sk8 ) @ sk8 )
| ( function @ null_class ) ),
inference(pattern_uni,[status(thm)],[12708:[bind(A,$thf( sk8 ))]]) ).
thf(59459,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[58207,219]) ).
thf(59460,plain,
member @ ( power_class @ ( power_class @ ( sk5 @ identity_relation ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[59459:[bind(A,$thf( power_class @ ( sk5 @ identity_relation ) ))]]) ).
thf(62235,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[60849,219]) ).
thf(62236,plain,
member @ ( power_class @ ( sum_class @ ( power_class @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[62235:[bind(A,$thf( sum_class @ ( power_class @ sk7 ) ))]]) ).
thf(75680,plain,
( ( member @ ( power_class @ ( sum_class @ ( power_class @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[62236,48]) ).
thf(75801,plain,
( ( ( power_class @ ( sum_class @ ( power_class @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[75680]) ).
thf(75832,plain,
( ( power_class @ ( sum_class @ ( power_class @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[75801]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( member @ B @ universal_class ) ),
inference(cnf,[status(esa)],[227]) ).
thf(48875,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ null_class @ ( successor @ sk7 ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42684,230]) ).
thf(48876,plain,
~ ( member @ null_class @ ( complement @ ( successor @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[48875:[bind(A,$thf( successor @ sk7 )),bind(B,$thf( null_class ))]]) ).
thf(50992,plain,
( ( member @ null_class @ ( complement @ ( successor @ sk7 ) ) )
!= ( member @ null_class @ ( successor @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[42684,48876]) ).
thf(51177,plain,
( ( null_class != null_class )
| ( ( complement @ ( successor @ sk7 ) )
!= ( successor @ sk7 ) ) ),
inference(simp,[status(thm)],[50992]) ).
thf(51275,plain,
( ( complement @ ( successor @ sk7 ) )
!= ( successor @ sk7 ) ),
inference(simp,[status(thm)],[51177]) ).
thf(12740,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ~ ( inductive @ universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[135,5713]) ).
thf(12741,plain,
( ( disjoint @ ( sk5 @ sk2 ) @ sk2 )
| ~ ( inductive @ universal_class ) ),
inference(pattern_uni,[status(thm)],[12740:[bind(A,$thf( sk2 ))]]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( inductive @ A )
| ( B != sk7 ) ),
inference(paramod_ordered,[status(thm)],[56,190]) ).
thf(317,plain,
! [A: $i] :
( ~ ( subclass @ A @ sk7 )
| ~ ( subclass @ sk7 @ A )
| ( inductive @ A ) ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(106,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
inference(cnf,[status(esa)],[103]) ).
thf(5999,plain,
! [A: $i] :
( ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( ( inductive @ sk7 )
!= ( inductive @ A ) ) ),
inference(paramod_ordered,[status(thm)],[190,106]) ).
thf(6000,plain,
subclass @ ( image @ successor_relation @ sk7 ) @ sk7,
inference(pattern_uni,[status(thm)],[5999:[bind(A,$thf( sk7 ))]]) ).
thf(34085,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ~ ( subclass @ sk2 @ sk7 )
| ( ( subclass @ sk7 @ A )
!= ( subclass @ sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[189,335]) ).
thf(34086,plain,
( ~ ( inductive @ sk2 )
| ~ ( subclass @ sk2 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[34085:[bind(A,$thf( sk2 ))]]) ).
thf(35123,plain,
( ~ ( inductive @ sk2 )
| ( ( subclass @ ( image @ successor_relation @ sk7 ) @ sk7 )
!= ( subclass @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[6000,34086]) ).
thf(35198,plain,
( ~ ( inductive @ sk2 )
| ( ( image @ successor_relation @ sk7 )
!= sk2 )
| ( sk7 != sk7 ) ),
inference(simp,[status(thm)],[35123]) ).
thf(35229,plain,
( ~ ( inductive @ sk2 )
| ( ( image @ successor_relation @ sk7 )
!= sk2 ) ),
inference(simp,[status(thm)],[35198]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_defn) ).
thf(223,plain,
! [A: $i,B: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
inference(cnf,[status(esa)],[223]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
inference(lifteq,[status(thm)],[224]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( restrict @ B @ A @ C )
= ( intersection @ B @ ( cross_product @ A @ C ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( restrict @ B @ A @ C )
= ( intersection @ B @ ( cross_product @ A @ C ) ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(46289,plain,
! [B: $i,A: $i] :
( ( image @ B @ A )
= ( range_of @ ( intersection @ B @ ( cross_product @ A @ universal_class ) ) ) ),
inference(rewrite,[status(thm)],[225,63]) ).
thf(83394,plain,
( ~ ( inductive @ sk2 )
| ( ( range_of @ ( intersection @ successor_relation @ ( cross_product @ sk7 @ universal_class ) ) )
!= sk2 ) ),
inference(rewrite,[status(thm)],[35229,46289]) ).
thf(63088,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sk5 @ universal_class ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[61082,230]) ).
thf(63089,plain,
~ ( member @ ( sum_class @ ( sk5 @ universal_class ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[63088:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sk5 @ universal_class ) ))]]) ).
thf(34264,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ~ ( inductive @ sk2 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[133,34094]) ).
thf(34265,plain,
( ( member @ ( sk5 @ sk2 ) @ universal_class )
| ~ ( inductive @ sk2 ) ),
inference(pattern_uni,[status(thm)],[34264:[bind(A,$thf( sk2 ))]]) ).
thf(76071,plain,
( ~ ( inductive @ sk2 )
| ( ( member @ ( sk5 @ sk2 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[34265,48]) ).
thf(76174,plain,
( ~ ( inductive @ sk2 )
| ( ( sk5 @ sk2 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[76071]) ).
thf(76230,plain,
( ~ ( inductive @ sk2 )
| ( ( sk5 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[76174]) ).
thf(3358,plain,
! [A: $i] :
( ~ ( subclass @ sk2 @ sk1 )
| ( ( subclass @ null_class @ A )
!= ( subclass @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3237,1089]) ).
thf(3371,plain,
! [A: $i] :
( ~ ( subclass @ sk2 @ sk1 )
| ( sk1 != null_class )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[3358]) ).
thf(3381,plain,
( ~ ( subclass @ sk2 @ sk1 )
| ( sk1 != null_class ) ),
inference(simp,[status(thm)],[3371]) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( singleton @ A ) @ universal_class )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[116,175]) ).
thf(1064,plain,
! [A: $i] : ( member @ ( singleton @ A ) @ universal_class ),
inference(pattern_uni,[status(thm)],[1063:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(60941,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ ( successor @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[43091,251]) ).
thf(60942,plain,
member @ ( sum_class @ ( sk5 @ ( successor @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60941:[bind(A,$thf( sk5 @ ( successor @ sk7 ) ))]]) ).
thf(60240,plain,
( ( member @ ( sk5 @ identity_relation ) @ ( complement @ identity_relation ) )
!= ( member @ ( sk5 @ identity_relation ) @ identity_relation ) ),
inference(paramod_ordered,[status(thm)],[58112,59077]) ).
thf(60362,plain,
( ( ( sk5 @ identity_relation )
!= ( sk5 @ identity_relation ) )
| ( ( complement @ identity_relation )
!= identity_relation ) ),
inference(simp,[status(thm)],[60240]) ).
thf(60404,plain,
( ( complement @ identity_relation )
!= identity_relation ),
inference(simp,[status(thm)],[60362]) ).
thf(64168,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sum_class @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[61333,251]) ).
thf(64169,plain,
member @ ( sum_class @ ( sum_class @ ( sum_class @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[64168:[bind(A,$thf( sum_class @ ( sum_class @ sk7 ) ))]]) ).
thf(83051,plain,
( ( member @ ( sum_class @ ( sum_class @ ( sum_class @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[64169,48]) ).
thf(83178,plain,
( ( ( sum_class @ ( sum_class @ ( sum_class @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[83051]) ).
thf(83259,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[83178]) ).
thf(6918,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( sk2 != null_class )
| ( ( subclass @ A @ B )
!= ( subclass @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[112,3376]) ).
thf(6919,plain,
( ~ ( member @ sk1 @ ( power_class @ sk2 ) )
| ( sk2 != null_class ) ),
inference(pattern_uni,[status(thm)],[6918:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1773,plain,
! [A: $i] :
( ( member @ sk7 @ universal_class )
!= ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[191,1556]) ).
thf(1792,plain,
! [A: $i] :
( ( sk7 != A )
| ( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
!= universal_class ) ),
inference(simp,[status(thm)],[1773]) ).
thf(1799,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
!= universal_class ),
inference(simp,[status(thm)],[1792]) ).
thf(12549,plain,
( ( sum_class @ ( sum_class @ null_class ) )
!= universal_class ),
inference(rewrite,[status(thm)],[1799,11335]) ).
thf(13504,plain,
( ( sum_class @ null_class )
!= universal_class ),
inference(rewrite,[status(thm)],[12549,11335]) ).
thf(61618,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60847,230]) ).
thf(61619,plain,
~ ( member @ ( sum_class @ ( sk5 @ identity_relation ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[61618:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sk5 @ identity_relation ) ))]]) ).
thf(12178,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( sk1 != universal_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[134,3379]) ).
thf(12179,plain,
( ( member @ ( sk5 @ sk1 ) @ sk1 )
| ( sk1 != universal_class ) ),
inference(pattern_uni,[status(thm)],[12178:[bind(A,$thf( sk1 ))]]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ C @ B )
| ( member @ A @ ( sum_class @ B ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ C @ B )
| ( member @ A @ ( sum_class @ B ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(57156,plain,
! [A: $i] :
( ( member @ ( ordered_pair @ A @ A ) @ identity_relation )
| ( ( member @ ( sk5 @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[5722,245]) ).
thf(57157,plain,
member @ ( ordered_pair @ ( sk5 @ sk7 ) @ ( sk5 @ sk7 ) ) @ identity_relation,
inference(pattern_uni,[status(thm)],[57156:[bind(A,$thf( sk5 @ sk7 ))]]) ).
thf(100926,plain,
member @ ( unordered_pair @ ( singleton @ ( sk5 @ sk7 ) ) @ ( unordered_pair @ ( sk5 @ sk7 ) @ ( singleton @ ( sk5 @ sk7 ) ) ) ) @ identity_relation,
inference(rewrite,[status(thm)],[57157,249]) ).
thf(60921,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk5 @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[45060,251]) ).
thf(60922,plain,
member @ ( sum_class @ ( power_class @ ( sk5 @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60921:[bind(A,$thf( power_class @ ( sk5 @ universal_class ) ))]]) ).
thf(62433,plain,
( ( sk2 != null_class )
| ( ( sum_class @ ( power_class @ sk7 ) )
!= ( sum_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[11335,62410]) ).
thf(62487,plain,
( ( sk2 != null_class )
| ( ( power_class @ sk7 )
!= null_class ) ),
inference(simp,[status(thm)],[62433]) ).
thf(1881,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ null_class ) ),
inference(paramod_ordered,[status(thm)],[187,1863]) ).
thf(1889,plain,
( ( successor_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[1881]) ).
thf(59463,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58207,230]) ).
thf(59464,plain,
~ ( member @ ( power_class @ ( sk5 @ identity_relation ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[59463:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk5 @ identity_relation ) ))]]) ).
thf(43317,plain,
( ( member @ ( sk5 @ ( successor @ sk7 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[43091,48]) ).
thf(43401,plain,
( ( ( sk5 @ ( successor @ sk7 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[43317]) ).
thf(43463,plain,
( ( sk5 @ ( successor @ sk7 ) )
!= sk2 ),
inference(simp,[status(thm)],[43401]) ).
thf(49125,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( power_class @ sk7 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45358,230]) ).
thf(49126,plain,
~ ( member @ ( power_class @ ( power_class @ sk7 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[49125:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( power_class @ sk7 ) ))]]) ).
thf(8447,plain,
! [C: $i,B: $i,A: $i] :
( ( subclass @ A @ B )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[91,5359]) ).
thf(8448,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[8447:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) )),bind(B,$thf( D )),bind(C,$thf( sk4 @ D @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ))]]) ).
thf(8488,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) @ A ),
inference(simp,[status(thm)],[8448]) ).
thf(12574,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) @ A ),
inference(rewrite,[status(thm)],[8488,11335]) ).
thf(20771,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ null_class ) ) @ A ),
inference(rewrite,[status(thm)],[12574,20071]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B
!= ( singleton @ sk1 ) )
| ( A
!= ( unordered_pair @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[56,49]) ).
thf(271,plain,
! [A: $i] :
( ~ ( subclass @ ( unordered_pair @ sk1 @ sk2 ) @ A )
| ~ ( subclass @ A @ ( unordered_pair @ sk1 @ sk2 ) )
| ( A
!= ( singleton @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( unordered_pair @ sk1 @ sk2 )),bind(B,$thf( B ))]]) ).
thf(339,plain,
( ~ ( subclass @ ( unordered_pair @ sk1 @ sk2 ) @ ( singleton @ sk1 ) )
| ~ ( subclass @ ( singleton @ sk1 ) @ ( unordered_pair @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[271]) ).
thf(3845,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( sk2 != null_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[133,3830]) ).
thf(3846,plain,
( ( member @ ( sk5 @ sk1 ) @ universal_class )
| ( sk2 != null_class ) ),
inference(pattern_uni,[status(thm)],[3845:[bind(A,$thf( sk1 ))]]) ).
thf(10967,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( sk2 != null_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[134,3830]) ).
thf(10968,plain,
( ( member @ ( sk5 @ sk1 ) @ sk1 )
| ( sk2 != null_class ) ),
inference(pattern_uni,[status(thm)],[10967:[bind(A,$thf( sk1 ))]]) ).
thf(700,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( subclass @ element_relation @ null_class )
| ( A
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[133,236]) ).
thf(701,plain,
( ( member @ ( sk5 @ ( cross_product @ universal_class @ universal_class ) ) @ universal_class )
| ( subclass @ element_relation @ null_class ) ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(14493,plain,
( ( ( sk5 @ sk2 )
!= sk2 )
| ( ( inductive @ sk7 )
!= ( inductive @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[190,14088]) ).
thf(14494,plain,
( ( ( sk5 @ sk2 )
!= sk2 )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[14493]) ).
thf(48190,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( sk5 @ sk7 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[45670,219]) ).
thf(48191,plain,
member @ ( power_class @ ( power_class @ ( power_class @ ( sk5 @ sk7 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[48190:[bind(A,$thf( power_class @ ( power_class @ ( sk5 @ sk7 ) ) ))]]) ).
thf(94339,plain,
( ( member @ ( power_class @ ( power_class @ ( power_class @ ( sk5 @ sk7 ) ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[48191,48]) ).
thf(94463,plain,
( ( ( power_class @ ( power_class @ ( power_class @ ( sk5 @ sk7 ) ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[94339]) ).
thf(94552,plain,
( ( power_class @ ( power_class @ ( power_class @ ( sk5 @ sk7 ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[94463]) ).
thf(56173,plain,
( ( member @ sk7 @ ( complement @ ( singleton @ sk7 ) ) )
!= ( member @ sk7 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[191,49138]) ).
thf(56345,plain,
( ( sk7 != sk7 )
| ( ( complement @ ( singleton @ sk7 ) )
!= universal_class ) ),
inference(simp,[status(thm)],[56173]) ).
thf(56366,plain,
( ( complement @ ( singleton @ sk7 ) )
!= universal_class ),
inference(simp,[status(thm)],[56345]) ).
thf(88719,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( A
!= ( complement @ ( singleton @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[323,56366]) ).
thf(88720,plain,
~ ( subclass @ universal_class @ ( complement @ ( singleton @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[88719:[bind(A,$thf( complement @ ( singleton @ sk7 ) ))]]) ).
thf(90493,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( complement @ ( singleton @ sk7 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,88720]) ).
thf(90494,plain,
~ ( member @ universal_class @ ( power_class @ ( complement @ ( singleton @ sk7 ) ) ) ),
inference(pattern_uni,[status(thm)],[90493:[bind(A,$thf( universal_class )),bind(B,$thf( complement @ ( singleton @ sk7 ) ))]]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ~ ( member @ A @ universal_class )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[56,48]) ).
thf(311,plain,
! [A: $i] :
( ~ ( subclass @ A @ sk2 )
| ~ ( subclass @ sk2 @ A )
| ~ ( member @ A @ universal_class ) ),
inference(pattern_uni,[status(thm)],[310:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(34982,plain,
! [B: $i,A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( A
!= ( unordered_pair @ sk7 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[133,34948]) ).
thf(34983,plain,
! [A: $i] : ( member @ ( sk5 @ ( unordered_pair @ sk7 @ A ) ) @ universal_class ),
inference(pattern_uni,[status(thm)],[34982:[bind(A,$thf( unordered_pair @ sk7 @ D )),bind(B,$thf( D ))]]) ).
thf(35022,plain,
! [A: $i] : ( member @ ( sk5 @ ( unordered_pair @ sk7 @ A ) ) @ universal_class ),
inference(simp,[status(thm)],[34983]) ).
thf(38075,plain,
! [A: $i] :
( ( member @ ( sk5 @ ( unordered_pair @ sk7 @ A ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[35022,48]) ).
thf(38173,plain,
! [A: $i] :
( ( ( sk5 @ ( unordered_pair @ sk7 @ A ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[38075]) ).
thf(38200,plain,
! [A: $i] :
( ( sk5 @ ( unordered_pair @ sk7 @ A ) )
!= sk2 ),
inference(simp,[status(thm)],[38173]) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( subclass @ C @ A )
| ( B != universal_class ) ),
inference(paramod_ordered,[status(thm)],[56,68]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ universal_class )
| ~ ( subclass @ universal_class @ A )
| ( subclass @ B @ A ) ),
inference(pattern_uni,[status(thm)],[320:[bind(A,$thf( A )),bind(B,$thf( universal_class ))]]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ universal_class )
| ~ ( subclass @ universal_class @ A )
| ( subclass @ B @ A ) ),
inference(simp,[status(thm)],[321]) ).
thf(91897,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ ( subclass @ universal_class @ A )
| ( subclass @ B @ A ) ),
inference(rewrite,[status(thm)],[332,68]) ).
thf(91898,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( subclass @ B @ A ) ),
inference(simp,[status(thm)],[91897]) ).
thf(26004,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( A
!= ( singleton @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[135,25962]) ).
thf(26005,plain,
disjoint @ ( sk5 @ ( singleton @ sk7 ) ) @ ( singleton @ sk7 ),
inference(pattern_uni,[status(thm)],[26004:[bind(A,$thf( singleton @ sk7 ))]]) ).
thf(46779,plain,
( ( member @ ( power_class @ ( sk5 @ ( successor @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[44941,48]) ).
thf(46895,plain,
( ( ( power_class @ ( sk5 @ ( successor @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[46779]) ).
thf(46919,plain,
( ( power_class @ ( sk5 @ ( successor @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[46895]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
<=> ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( intersection @ A @ B ) )
=> ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( member @ C @ ( intersection @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(124,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
=> ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( member @ C @ ( intersection @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[123]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(cnf,[status(esa)],[124]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(89743,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( power_class @ null_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[91,88926]) ).
thf(89744,plain,
member @ ( sk4 @ ( power_class @ null_class ) @ universal_class ) @ universal_class,
inference(pattern_uni,[status(thm)],[89743:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ null_class ))]]) ).
thf(3282,plain,
( ( member @ ( sk4 @ null_class @ universal_class ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[3165,48]) ).
thf(3292,plain,
( ( ( sk4 @ null_class @ universal_class )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[3282]) ).
thf(3306,plain,
( ( sk4 @ null_class @ universal_class )
!= sk2 ),
inference(simp,[status(thm)],[3292]) ).
thf(89297,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( subclass @ sk7 @ A )
!= ( subclass @ universal_class @ ( complement @ identity_relation ) ) ) ),
inference(paramod_ordered,[status(thm)],[189,86683]) ).
thf(89381,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( sk7 != universal_class )
| ( A
!= ( complement @ identity_relation ) ) ),
inference(simp,[status(thm)],[89297]) ).
thf(89409,plain,
( ~ ( inductive @ ( complement @ identity_relation ) )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[89381]) ).
thf(62243,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[60849,251]) ).
thf(62244,plain,
member @ ( sum_class @ ( sum_class @ ( power_class @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[62243:[bind(A,$thf( sum_class @ ( power_class @ sk7 ) ))]]) ).
thf(76972,plain,
( ( member @ ( sum_class @ ( sum_class @ ( power_class @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[62244,48]) ).
thf(77075,plain,
( ( ( sum_class @ ( sum_class @ ( power_class @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[76972]) ).
thf(77131,plain,
( ( sum_class @ ( sum_class @ ( power_class @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[77075]) ).
thf(15418,plain,
! [A: $i] :
( ~ ( function @ A )
| ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk7 @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[99,15373]) ).
thf(15432,plain,
! [A: $i] :
( ~ ( function @ A )
| ( A != sk7 )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[15418]) ).
thf(15446,plain,
( ~ ( function @ sk7 )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[15432]) ).
thf(63566,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sum_class @ sk7 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[61325,230]) ).
thf(63567,plain,
~ ( member @ ( power_class @ ( sum_class @ sk7 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[63566:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sum_class @ sk7 ) ))]]) ).
thf(38955,plain,
! [B: $i,A: $i] :
( ( member @ ( sk5 @ sk7 ) @ ( unordered_pair @ A @ ( sk5 @ sk7 ) ) )
!= ( member @ B @ null_class ) ),
inference(paramod_ordered,[status(thm)],[24706,194]) ).
thf(39053,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk7 )
!= B )
| ( ( unordered_pair @ A @ ( sk5 @ sk7 ) )
!= null_class ) ),
inference(simp,[status(thm)],[38955]) ).
thf(39134,plain,
! [A: $i] :
( ( unordered_pair @ A @ ( sk5 @ sk7 ) )
!= null_class ),
inference(simp,[status(thm)],[39053]) ).
thf(60955,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk4 @ null_class @ universal_class ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[3165,251]) ).
thf(60956,plain,
member @ ( sum_class @ ( sk4 @ null_class @ universal_class ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60955:[bind(A,$thf( sk4 @ null_class @ universal_class ))]]) ).
thf(71565,plain,
( ( member @ ( sum_class @ ( sk4 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60956,48]) ).
thf(71695,plain,
( ( ( sum_class @ ( sk4 @ null_class @ universal_class ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[71565]) ).
thf(71715,plain,
( ( sum_class @ ( sk4 @ null_class @ universal_class ) )
!= sk2 ),
inference(simp,[status(thm)],[71695]) ).
thf(10082,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk3 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,8539]) ).
thf(10083,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10082:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )),bind(C,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) @ E ))]]) ).
thf(10179,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[10083]) ).
thf(23566,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(rewrite,[status(thm)],[10179,20071]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( ( unordered_pair @ A @ sk2 )
!= ( singleton @ sk1 ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[56,49]) ).
thf(279,plain,
! [A: $i] :
( ~ ( subclass @ A @ sk1 )
| ~ ( subclass @ sk1 @ A )
| ( ( unordered_pair @ A @ sk2 )
!= ( singleton @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[278:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_defn) ).
thf(64,plain,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(63570,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sum_class @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[61325,251]) ).
thf(63571,plain,
member @ ( sum_class @ ( power_class @ ( sum_class @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[63570:[bind(A,$thf( power_class @ ( sum_class @ sk7 ) ))]]) ).
thf(81195,plain,
( ( member @ ( sum_class @ ( power_class @ ( sum_class @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[63571,48]) ).
thf(81303,plain,
( ( ( sum_class @ ( power_class @ ( sum_class @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[81195]) ).
thf(81379,plain,
( ( sum_class @ ( power_class @ ( sum_class @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[81303]) ).
thf(86196,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( sk2 != universal_class )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[323,504]) ).
thf(86197,plain,
( ~ ( subclass @ universal_class @ sk7 )
| ( sk2 != universal_class ) ),
inference(pattern_uni,[status(thm)],[86196:[bind(A,$thf( sk7 ))]]) ).
thf(180,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( unordered_pair @ B @ C ) )
| ( member @ A @ universal_class ) ),
inference(cnf,[status(esa)],[177]) ).
thf(99797,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( A
!= ( complement @ ( successor @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[323,99760]) ).
thf(99798,plain,
~ ( subclass @ universal_class @ ( complement @ ( successor @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[99797:[bind(A,$thf( complement @ ( successor @ sk7 ) ))]]) ).
thf(1142,plain,
( ( inductive @ null_class )
| ( ( member @ ( sk5 @ sk7 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[639,48]) ).
thf(1144,plain,
( ( inductive @ null_class )
| ( ( sk5 @ sk7 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[1142]) ).
thf(1149,plain,
( ( inductive @ null_class )
| ( ( sk5 @ sk7 )
!= sk2 ) ),
inference(simp,[status(thm)],[1144]) ).
thf(5719,plain,
( $false
| ( ( sk5 @ sk7 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[1149,5662]) ).
thf(5720,plain,
( ( sk5 @ sk7 )
!= sk2 ),
inference(simp,[status(thm)],[5719]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ( B != successor_relation ) ),
inference(paramod_ordered,[status(thm)],[56,187]) ).
thf(291,plain,
! [A: $i] :
( ~ ( subclass @ A @ successor_relation )
| ~ ( subclass @ successor_relation @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( A )),bind(B,$thf( successor_relation ))]]) ).
thf(39489,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( A
!= ( singleton @ ( sk5 @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[135,39446]) ).
thf(39490,plain,
disjoint @ ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ) @ ( singleton @ ( sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[39489:[bind(A,$thf( singleton @ ( sk5 @ sk7 ) ))]]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( ( unordered_pair @ sk1 @ A )
!= ( singleton @ sk1 ) )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[56,49]) ).
thf(281,plain,
! [A: $i] :
( ~ ( subclass @ A @ sk2 )
| ~ ( subclass @ sk2 @ A )
| ( ( unordered_pair @ sk1 @ A )
!= ( singleton @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(34081,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( sk1 != universal_class )
| ( ( subclass @ sk7 @ A )
!= ( subclass @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[189,2006]) ).
thf(34119,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( sk1 != universal_class )
| ( sk7 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[34081]) ).
thf(34127,plain,
( ~ ( inductive @ sk2 )
| ( sk1 != universal_class )
| ( sk7 != sk1 ) ),
inference(simp,[status(thm)],[34119]) ).
thf(89609,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( complement @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,88854]) ).
thf(89610,plain,
~ ( member @ universal_class @ ( power_class @ ( complement @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[89609:[bind(A,$thf( universal_class )),bind(B,$thf( complement @ sk7 ))]]) ).
thf(25612,plain,
! [A: $i] :
( ( member @ sk7 @ ( unordered_pair @ A @ sk7 ) )
!= ( member @ sk7 @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[24714,15417]) ).
thf(25703,plain,
! [A: $i] :
( ( sk7 != sk7 )
| ( ( unordered_pair @ A @ sk7 )
!= ( power_class @ null_class ) ) ),
inference(simp,[status(thm)],[25612]) ).
thf(25771,plain,
! [A: $i] :
( ( unordered_pair @ A @ sk7 )
!= ( power_class @ null_class ) ),
inference(simp,[status(thm)],[25703]) ).
thf(83683,plain,
( ( member @ ( power_class @ ( power_class @ ( sk5 @ ( successor @ sk7 ) ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[46754,48]) ).
thf(83837,plain,
( ( ( power_class @ ( power_class @ ( sk5 @ ( successor @ sk7 ) ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[83683]) ).
thf(83877,plain,
( ( power_class @ ( power_class @ ( sk5 @ ( successor @ sk7 ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[83837]) ).
thf(3265,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A
!= ( sk4 @ null_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[133,3165]) ).
thf(3266,plain,
( ( member @ ( sk5 @ ( sk4 @ null_class @ universal_class ) ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[3265:[bind(A,$thf( sk4 @ null_class @ universal_class ))]]) ).
thf(43103,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( A
!= ( successor @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[135,43029]) ).
thf(43104,plain,
disjoint @ ( sk5 @ ( successor @ sk7 ) ) @ ( successor @ sk7 ),
inference(pattern_uni,[status(thm)],[43103:[bind(A,$thf( successor @ sk7 ))]]) ).
thf(61614,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[60847,219]) ).
thf(61615,plain,
member @ ( power_class @ ( sum_class @ ( sk5 @ identity_relation ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[61614:[bind(A,$thf( sum_class @ ( sk5 @ identity_relation ) ))]]) ).
thf(74186,plain,
( ( member @ ( power_class @ ( sum_class @ ( sk5 @ identity_relation ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[61615,48]) ).
thf(74281,plain,
( ( ( power_class @ ( sum_class @ ( sk5 @ identity_relation ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[74186]) ).
thf(74335,plain,
( ( power_class @ ( sum_class @ ( sk5 @ identity_relation ) ) )
!= sk2 ),
inference(simp,[status(thm)],[74281]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ! [C: $i] :
~ ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ! [C: $i] :
~ ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ! [C: $i] :
~ ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(140,plain,
( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( disjoint @ A @ B ) ) ),
inference(miniscope,[status(thm)],[139]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( member @ ( sk6 @ B @ A ) @ A )
| ( disjoint @ A @ B ) ),
inference(cnf,[status(esa)],[140]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( member @ ( sk6 @ B @ A ) @ A )
| ( disjoint @ A @ B ) ),
inference(simp,[status(thm)],[141]) ).
thf(49394,plain,
( ( member @ null_class @ ( complement @ sk7 ) )
!= ( member @ null_class @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[5702,48943]) ).
thf(49558,plain,
( ( null_class != null_class )
| ( ( complement @ sk7 )
!= sk7 ) ),
inference(simp,[status(thm)],[49394]) ).
thf(49608,plain,
( ( complement @ sk7 )
!= sk7 ),
inference(simp,[status(thm)],[49558]) ).
thf(34274,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ~ ( inductive @ sk2 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[135,34094]) ).
thf(34275,plain,
( ( disjoint @ ( sk5 @ sk2 ) @ sk2 )
| ~ ( inductive @ sk2 ) ),
inference(pattern_uni,[status(thm)],[34274:[bind(A,$thf( sk2 ))]]) ).
thf(77697,plain,
( ( member @ ( sum_class @ ( sum_class @ ( sk5 @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[62763,48]) ).
thf(77805,plain,
( ( ( sum_class @ ( sum_class @ ( sk5 @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[77697]) ).
thf(77893,plain,
( ( sum_class @ ( sum_class @ ( sk5 @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[77805]) ).
thf(57963,plain,
! [A: $i] :
( ( member @ ( sk9 @ A ) @ universal_class )
| ( ( member @ ( ordered_pair @ sk7 @ sk7 ) @ identity_relation )
!= ( member @ A @ identity_relation ) ) ),
inference(paramod_ordered,[status(thm)],[57167,242]) ).
thf(57964,plain,
member @ ( sk9 @ ( ordered_pair @ sk7 @ sk7 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[57963:[bind(A,$thf( ordered_pair @ sk7 @ sk7 ))]]) ).
thf(65156,plain,
member @ ( sk9 @ ( unordered_pair @ ( singleton @ sk7 ) @ ( unordered_pair @ sk7 @ ( singleton @ sk7 ) ) ) ) @ universal_class,
inference(rewrite,[status(thm)],[57964,249]) ).
thf(6920,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( sk2 != null_class )
| ( ( subclass @ A @ B )
!= ( subclass @ sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[112,3383]) ).
thf(6921,plain,
( ~ ( member @ sk7 @ ( power_class @ sk2 ) )
| ( sk2 != null_class ) ),
inference(pattern_uni,[status(thm)],[6920:[bind(A,$thf( sk7 )),bind(B,$thf( sk2 ))]]) ).
thf(17552,plain,
( ( sk2 != null_class )
| ( ( member @ sk7 @ ( power_class @ sk2 ) )
!= ( member @ sk7 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[191,6921]) ).
thf(17612,plain,
( ( sk2 != null_class )
| ( sk7 != sk7 )
| ( ( power_class @ sk2 )
!= universal_class ) ),
inference(simp,[status(thm)],[17552]) ).
thf(17628,plain,
( ( sk2 != null_class )
| ( ( power_class @ sk2 )
!= universal_class ) ),
inference(simp,[status(thm)],[17612]) ).
thf(60590,plain,
( ( member @ ( sk9 @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[59159,48]) ).
thf(60696,plain,
( ( ( sk9 @ ( sk5 @ identity_relation ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[60590]) ).
thf(60720,plain,
( ( sk9 @ ( sk5 @ identity_relation ) )
!= sk2 ),
inference(simp,[status(thm)],[60696]) ).
thf(10979,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( function @ null_class )
| ( A != sk8 ) ),
inference(paramod_ordered,[status(thm)],[134,234]) ).
thf(10980,plain,
( ( member @ ( sk5 @ sk8 ) @ sk8 )
| ( function @ null_class ) ),
inference(pattern_uni,[status(thm)],[10979:[bind(A,$thf( sk8 ))]]) ).
thf(49047,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[46023,230]) ).
thf(49048,plain,
~ ( member @ ( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[49047:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( power_class @ ( sk5 @ universal_class ) ) ))]]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( subclass @ A @ B )
| ( member @ A @ ( power_class @ B ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( subclass @ A @ B )
| ( member @ A @ ( power_class @ B ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(89336,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( complement @ identity_relation ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,86683]) ).
thf(89337,plain,
~ ( member @ universal_class @ ( power_class @ ( complement @ identity_relation ) ) ),
inference(pattern_uni,[status(thm)],[89336:[bind(A,$thf( universal_class )),bind(B,$thf( complement @ identity_relation ))]]) ).
thf(79,plain,
( ! [A: $i,B: $i] :
( ( member @ B @ ( domain_of @ A ) )
=> ( ( member @ B @ universal_class )
& ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) ) )
& ! [A: $i,B: $i] :
( ( ( member @ B @ universal_class )
& ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) )
=> ( member @ B @ ( domain_of @ A ) ) ) ),
inference(miniscope,[status(thm)],[78]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( domain_of @ A ) )
| ( member @ B @ universal_class ) ),
inference(cnf,[status(esa)],[79]) ).
thf(35148,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ~ ( inductive @ sk2 )
| ( ( subclass @ A @ B )
!= ( subclass @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[112,34086]) ).
thf(35149,plain,
( ~ ( member @ sk2 @ ( power_class @ sk7 ) )
| ~ ( inductive @ sk2 ) ),
inference(pattern_uni,[status(thm)],[35148:[bind(A,$thf( sk2 )),bind(B,$thf( sk7 ))]]) ).
thf(96879,plain,
( ( member @ ( sk5 @ sk7 ) @ ( complement @ ( singleton @ ( sk5 @ sk7 ) ) ) )
!= ( member @ ( sk5 @ sk7 ) @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[5722,48885]) ).
thf(97067,plain,
( ( ( sk5 @ sk7 )
!= ( sk5 @ sk7 ) )
| ( ( complement @ ( singleton @ ( sk5 @ sk7 ) ) )
!= universal_class ) ),
inference(simp,[status(thm)],[96879]) ).
thf(97191,plain,
( ( complement @ ( singleton @ ( sk5 @ sk7 ) ) )
!= universal_class ),
inference(simp,[status(thm)],[97067]) ).
thf(60959,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk5 @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[44916,251]) ).
thf(60960,plain,
member @ ( sum_class @ ( power_class @ ( sk5 @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60959:[bind(A,$thf( power_class @ ( sk5 @ sk7 ) ))]]) ).
thf(12752,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( A != universal_class )
| ( null_class != null_class ) ),
inference(paramod_ordered,[status(thm)],[135,257]) ).
thf(12753,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( A != universal_class ) ),
inference(pattern_uni,[status(thm)],[12752:[]]) ).
thf(13390,plain,
disjoint @ ( sk5 @ universal_class ) @ universal_class,
inference(simp,[status(thm)],[12753]) ).
thf(46045,plain,
( ( member @ ( power_class @ ( sk5 @ universal_class ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[45060,48]) ).
thf(46115,plain,
( ( ( power_class @ ( sk5 @ universal_class ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[46045]) ).
thf(46173,plain,
( ( power_class @ ( sk5 @ universal_class ) )
!= sk2 ),
inference(simp,[status(thm)],[46115]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( union @ A @ B ) )
| ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[210]) ).
thf(65,plain,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(12690,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( sk2 != null_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[135,3830]) ).
thf(12691,plain,
( ( disjoint @ ( sk5 @ sk1 ) @ sk1 )
| ( sk2 != null_class ) ),
inference(pattern_uni,[status(thm)],[12690:[bind(A,$thf( sk1 ))]]) ).
thf(61634,plain,
( ( member @ ( sum_class @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60847,48]) ).
thf(61721,plain,
( ( ( sum_class @ ( sk5 @ identity_relation ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[61634]) ).
thf(61763,plain,
( ( sum_class @ ( sk5 @ identity_relation ) )
!= sk2 ),
inference(simp,[status(thm)],[61721]) ).
thf(61811,plain,
( ( sk2 != null_class )
| ( ( sum_class @ ( sk5 @ identity_relation ) )
!= ( sum_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[11335,61763]) ).
thf(61867,plain,
( ( sk2 != null_class )
| ( ( sk5 @ identity_relation )
!= null_class ) ),
inference(simp,[status(thm)],[61811]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subclass @ B @ A )
| ( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[187,56]) ).
thf(299,plain,
( ( ( cross_product @ universal_class @ universal_class )
= successor_relation )
| ~ ( subclass @ ( cross_product @ universal_class @ universal_class ) @ successor_relation ) ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( successor_relation )),bind(B,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(10929,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( sk7 != universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[134,5810]) ).
thf(10930,plain,
( ( member @ ( sk5 @ sk2 ) @ sk2 )
| ( sk7 != universal_class ) ),
inference(pattern_uni,[status(thm)],[10929:[bind(A,$thf( sk2 ))]]) ).
thf(34754,plain,
! [A: $i] :
( ( member @ sk7 @ ( unordered_pair @ sk7 @ A ) )
!= ( member @ sk7 @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[25568,15417]) ).
thf(34872,plain,
! [A: $i] :
( ( sk7 != sk7 )
| ( ( unordered_pair @ sk7 @ A )
!= ( power_class @ null_class ) ) ),
inference(simp,[status(thm)],[34754]) ).
thf(34937,plain,
! [A: $i] :
( ( unordered_pair @ sk7 @ A )
!= ( power_class @ null_class ) ),
inference(simp,[status(thm)],[34872]) ).
thf(49843,plain,
( ( member @ sk7 @ ( complement @ universal_class ) )
!= ( member @ sk7 @ ( singleton @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[25609,48995]) ).
thf(49900,plain,
( ( sk7 != sk7 )
| ( ( complement @ universal_class )
!= ( singleton @ sk7 ) ) ),
inference(simp,[status(thm)],[49843]) ).
thf(49954,plain,
( ( complement @ universal_class )
!= ( singleton @ sk7 ) ),
inference(simp,[status(thm)],[49900]) ).
thf(89752,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( power_class @ null_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,88926]) ).
thf(89753,plain,
~ ( member @ universal_class @ ( power_class @ ( power_class @ null_class ) ) ),
inference(pattern_uni,[status(thm)],[89752:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ null_class ))]]) ).
thf(607,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( function @ null_class )
| ( A != sk8 ) ),
inference(paramod_ordered,[status(thm)],[133,234]) ).
thf(608,plain,
( ( member @ ( sk5 @ sk8 ) @ universal_class )
| ( function @ null_class ) ),
inference(pattern_uni,[status(thm)],[607:[bind(A,$thf( sk8 ))]]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( member @ A @ universal_class )
| ( B != sk7 ) ),
inference(paramod_ordered,[status(thm)],[56,191]) ).
thf(267,plain,
! [A: $i] :
( ~ ( subclass @ A @ sk7 )
| ~ ( subclass @ sk7 @ A )
| ( member @ A @ universal_class ) ),
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(12307,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( member @ ( sk5 @ sk2 ) @ universal_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[134,1088]) ).
thf(12308,plain,
( ( member @ ( sk5 @ sk1 ) @ sk1 )
| ( member @ ( sk5 @ sk2 ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[12307:[bind(A,$thf( sk1 ))]]) ).
thf(12551,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[5359,11335]) ).
thf(20291,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ null_class ) ) ),
inference(rewrite,[status(thm)],[12551,20071]) ).
thf(63562,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sum_class @ sk7 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[61325,219]) ).
thf(63563,plain,
member @ ( power_class @ ( power_class @ ( sum_class @ sk7 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[63562:[bind(A,$thf( power_class @ ( sum_class @ sk7 ) ))]]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( member @ ( sk6 @ B @ A ) @ B )
| ( disjoint @ A @ B ) ),
inference(cnf,[status(esa)],[140]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( member @ ( sk6 @ B @ A ) @ B )
| ( disjoint @ A @ B ) ),
inference(simp,[status(thm)],[142]) ).
thf(14948,plain,
! [C: $i,B: $i,A: $i] :
( ( disjoint @ A @ B )
| ( ( member @ ( sk6 @ B @ A ) @ B )
!= ( member @ C @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[145,194]) ).
thf(14949,plain,
! [A: $i] : ( disjoint @ A @ null_class ),
inference(pattern_uni,[status(thm)],[14948:[bind(A,$thf( E )),bind(B,$thf( null_class )),bind(C,$thf( sk6 @ null_class @ E ))]]) ).
thf(15004,plain,
! [A: $i] : ( disjoint @ A @ null_class ),
inference(simp,[status(thm)],[14949]) ).
thf(34073,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( sk7 != universal_class )
| ( ( subclass @ sk7 @ A )
!= ( subclass @ sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[189,429]) ).
thf(34074,plain,
( ~ ( inductive @ sk2 )
| ( sk7 != universal_class ) ),
inference(pattern_uni,[status(thm)],[34073:[bind(A,$thf( sk2 ))]]) ).
thf(83942,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( ( member @ sk2 @ A )
!= ( member @ null_class @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[5702,83892]) ).
thf(84199,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( sk2 != null_class )
| ( A != sk7 ) ),
inference(simp,[status(thm)],[83942]) ).
thf(84350,plain,
( ~ ( subclass @ universal_class @ sk7 )
| ( sk2 != null_class ) ),
inference(simp,[status(thm)],[84199]) ).
thf(45048,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[39473,219]) ).
thf(45049,plain,
member @ ( power_class @ ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[45048:[bind(A,$thf( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ))]]) ).
thf(3454,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( sk2 != universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[133,3378]) ).
thf(3455,plain,
( ( member @ ( sk5 @ sk2 ) @ universal_class )
| ( sk2 != universal_class ) ),
inference(pattern_uni,[status(thm)],[3454:[bind(A,$thf( sk2 ))]]) ).
thf(94,plain,
! [A: $i] :
( ( inverse @ A )
= ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(95,plain,
! [A: $i] :
( ( inverse @ A )
= ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(854,plain,
! [B: $i,A: $i] :
( ( ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
= ( range_of @ B ) )
| ( ( inverse @ A )
!= ( inverse @ B ) ) ),
inference(paramod_ordered,[status(thm)],[95,66]) ).
thf(855,plain,
! [A: $i] :
( ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
= ( range_of @ A ) ),
inference(pattern_uni,[status(thm)],[854:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(48982,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk5 @ universal_class ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45060,230]) ).
thf(48983,plain,
~ ( member @ ( power_class @ ( sk5 @ universal_class ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[48982:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk5 @ universal_class ) ))]]) ).
thf(1069,plain,
! [C: $i,B: $i,A: $i] :
( ( ( singleton @ A )
!= sk2 )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[116,538]) ).
thf(1070,plain,
! [A: $i] :
( ( singleton @ A )
!= sk2 ),
inference(pattern_uni,[status(thm)],[1069:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
= null_class )
| ( member @ B @ ( domain_of @ A ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
= null_class )
| ~ ( member @ B @ universal_class )
| ( member @ B @ ( domain_of @ A ) ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
= null_class )
| ~ ( member @ B @ universal_class )
| ( member @ B @ ( domain_of @ A ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(2012,plain,
! [B: $i,A: $i] :
( ( ( intersection @ A @ ( cross_product @ ( singleton @ B ) @ universal_class ) )
= null_class )
| ~ ( member @ B @ universal_class )
| ( member @ B @ ( domain_of @ A ) ) ),
inference(rewrite,[status(thm)],[84,63]) ).
thf(74938,plain,
( ( member @ ( sum_class @ ( sum_class @ ( sk5 @ identity_relation ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[61623,48]) ).
thf(75080,plain,
( ( ( sum_class @ ( sum_class @ ( sk5 @ identity_relation ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[74938]) ).
thf(75110,plain,
( ( sum_class @ ( sum_class @ ( sk5 @ identity_relation ) ) )
!= sk2 ),
inference(simp,[status(thm)],[75080]) ).
thf(71162,plain,
( ( member @ ( sum_class @ ( sk5 @ ( successor @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60942,48]) ).
thf(71274,plain,
( ( ( sum_class @ ( sk5 @ ( successor @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[71162]) ).
thf(71335,plain,
( ( sum_class @ ( sk5 @ ( successor @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[71274]) ).
thf(6881,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[112,1863]) ).
thf(6882,plain,
~ ( member @ universal_class @ ( power_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[6881:[bind(A,$thf( universal_class )),bind(B,$thf( null_class ))]]) ).
thf(13455,plain,
( ( member @ ( sk5 @ sk7 ) @ sk7 )
!= ( member @ universal_class @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[12301,6882]) ).
thf(13477,plain,
( ( ( sk5 @ sk7 )
!= universal_class )
| ( ( power_class @ null_class )
!= sk7 ) ),
inference(simp,[status(thm)],[13455]) ).
thf(49407,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ null_class @ ( complement @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,48943]) ).
thf(49408,plain,
~ ( inductive @ ( complement @ sk7 ) ),
inference(pattern_uni,[status(thm)],[49407:[bind(A,$thf( complement @ sk7 ))]]) ).
thf(89707,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( subclass @ sk7 @ A )
!= ( subclass @ universal_class @ ( power_class @ null_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[189,88926]) ).
thf(89806,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( sk7 != universal_class )
| ( A
!= ( power_class @ null_class ) ) ),
inference(simp,[status(thm)],[89707]) ).
thf(89832,plain,
( ~ ( inductive @ ( power_class @ null_class ) )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[89806]) ).
thf(49131,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk5 @ universal_class ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[728,230]) ).
thf(49132,plain,
~ ( member @ ( sk5 @ universal_class ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[49131:[bind(A,$thf( universal_class )),bind(B,$thf( sk5 @ universal_class ))]]) ).
thf(12931,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( member @ ( sk5 @ sk1 ) @ universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[135,3846]) ).
thf(12932,plain,
( ( disjoint @ ( sk5 @ sk2 ) @ sk2 )
| ( member @ ( sk5 @ sk1 ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[12931:[bind(A,$thf( sk2 ))]]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[124]) ).
thf(49050,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk5 @ ( singleton @ sk7 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25995,230]) ).
thf(49051,plain,
~ ( member @ ( sk5 @ ( singleton @ sk7 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[49050:[bind(A,$thf( universal_class )),bind(B,$thf( sk5 @ ( singleton @ sk7 ) ))]]) ).
thf(26133,plain,
( ( member @ ( sk5 @ ( singleton @ sk7 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[25995,48]) ).
thf(26194,plain,
( ( ( sk5 @ ( singleton @ sk7 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[26133]) ).
thf(26232,plain,
( ( sk5 @ ( singleton @ sk7 ) )
!= sk2 ),
inference(simp,[status(thm)],[26194]) ).
thf(59918,plain,
( ( member @ ( sk5 @ identity_relation ) @ ( complement @ universal_class ) )
!= ( member @ ( sk5 @ identity_relation ) @ identity_relation ) ),
inference(paramod_ordered,[status(thm)],[58112,58211]) ).
thf(60037,plain,
( ( ( sk5 @ identity_relation )
!= ( sk5 @ identity_relation ) )
| ( ( complement @ universal_class )
!= identity_relation ) ),
inference(simp,[status(thm)],[59918]) ).
thf(60082,plain,
( ( complement @ universal_class )
!= identity_relation ),
inference(simp,[status(thm)],[60037]) ).
thf(25822,plain,
( ( member @ sk7 @ ( power_class @ null_class ) )
!= ( member @ sk7 @ ( singleton @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[25609,15417]) ).
thf(25928,plain,
( ( sk7 != sk7 )
| ( ( power_class @ null_class )
!= ( singleton @ sk7 ) ) ),
inference(simp,[status(thm)],[25822]) ).
thf(25974,plain,
( ( power_class @ null_class )
!= ( singleton @ sk7 ) ),
inference(simp,[status(thm)],[25928]) ).
thf(97238,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( A
!= ( complement @ ( singleton @ ( sk5 @ sk7 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[323,97191]) ).
thf(97239,plain,
~ ( subclass @ universal_class @ ( complement @ ( singleton @ ( sk5 @ sk7 ) ) ) ),
inference(pattern_uni,[status(thm)],[97238:[bind(A,$thf( complement @ ( singleton @ ( sk5 @ sk7 ) ) ))]]) ).
thf(44960,plain,
! [A: $i] :
( ( function @ null_class )
| ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk5 @ sk8 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[608,219]) ).
thf(44961,plain,
( ( function @ null_class )
| ( member @ ( power_class @ ( sk5 @ sk8 ) ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[44960:[bind(A,$thf( sk5 @ sk8 ))]]) ).
thf(89329,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( complement @ identity_relation ) ) ) ),
inference(paramod_ordered,[status(thm)],[91,86683]) ).
thf(89330,plain,
member @ ( sk4 @ ( complement @ identity_relation ) @ universal_class ) @ universal_class,
inference(pattern_uni,[status(thm)],[89329:[bind(A,$thf( universal_class )),bind(B,$thf( complement @ identity_relation ))]]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( domain_of @ A ) )
| ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) ),
inference(cnf,[status(esa)],[79]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class )
| ~ ( member @ B @ ( domain_of @ A ) ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(2354,plain,
! [B: $i,A: $i] :
( ( ( intersection @ A @ ( cross_product @ ( singleton @ B ) @ universal_class ) )
!= null_class )
| ~ ( member @ B @ ( domain_of @ A ) ) ),
inference(rewrite,[status(thm)],[85,63]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( subclass @ successor_relation @ ( cross_product @ A @ universal_class ) )
| ( B != universal_class ) ),
inference(paramod_ordered,[status(thm)],[56,187]) ).
thf(295,plain,
! [A: $i] :
( ~ ( subclass @ A @ universal_class )
| ~ ( subclass @ universal_class @ A )
| ( subclass @ successor_relation @ ( cross_product @ A @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( A )),bind(B,$thf( universal_class ))]]) ).
thf(73828,plain,
! [A: $i] :
( ~ $true
| ~ ( subclass @ universal_class @ A )
| ( subclass @ successor_relation @ ( cross_product @ A @ universal_class ) ) ),
inference(rewrite,[status(thm)],[295,68]) ).
thf(73829,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( subclass @ successor_relation @ ( cross_product @ A @ universal_class ) ) ),
inference(simp,[status(thm)],[73828]) ).
thf(54276,plain,
( ( member @ ( sk5 @ sk7 ) @ ( singleton @ ( sk5 @ sk7 ) ) )
!= ( member @ ( sk5 @ sk7 ) @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[38893,48986]) ).
thf(54452,plain,
( ( ( sk5 @ sk7 )
!= ( sk5 @ sk7 ) )
| ( ( singleton @ ( sk5 @ sk7 ) )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[54276]) ).
thf(54543,plain,
( ( singleton @ ( sk5 @ sk7 ) )
!= ( complement @ universal_class ) ),
inference(simp,[status(thm)],[54452]) ).
thf(9823,plain,
( ( sk2 != null_class )
| ( ( member @ ( sk5 @ sk1 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[3846,48]) ).
thf(9858,plain,
( ( sk2 != null_class )
| ( ( sk5 @ sk1 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[9823]) ).
thf(9863,plain,
( ( sk2 != null_class )
| ( ( sk5 @ sk1 )
!= sk2 ) ),
inference(simp,[status(thm)],[9858]) ).
thf(25870,plain,
( ( sk7 != universal_class )
| ( ( member @ sk7 @ ( power_class @ sk2 ) )
!= ( member @ sk7 @ ( singleton @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[25609,6885]) ).
thf(25925,plain,
( ( sk7 != universal_class )
| ( sk7 != sk7 )
| ( ( power_class @ sk2 )
!= ( singleton @ sk7 ) ) ),
inference(simp,[status(thm)],[25870]) ).
thf(25971,plain,
( ( sk7 != universal_class )
| ( ( power_class @ sk2 )
!= ( singleton @ sk7 ) ) ),
inference(simp,[status(thm)],[25925]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( disjoint @ A @ B )
| ~ ( member @ C @ A )
| ~ ( member @ C @ B ) ),
inference(cnf,[status(esa)],[140]) ).
thf(96881,plain,
( ( member @ ( sk5 @ sk7 ) @ ( complement @ ( singleton @ ( sk5 @ sk7 ) ) ) )
!= ( member @ ( sk5 @ sk7 ) @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[12301,48885]) ).
thf(97094,plain,
( ( ( sk5 @ sk7 )
!= ( sk5 @ sk7 ) )
| ( ( complement @ ( singleton @ ( sk5 @ sk7 ) ) )
!= sk7 ) ),
inference(simp,[status(thm)],[96881]) ).
thf(97195,plain,
( ( complement @ ( singleton @ ( sk5 @ sk7 ) ) )
!= sk7 ),
inference(simp,[status(thm)],[97094]) ).
thf(60572,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk9 @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[59159,219]) ).
thf(60573,plain,
member @ ( power_class @ ( sk9 @ ( sk5 @ identity_relation ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60572:[bind(A,$thf( sk9 @ ( sk5 @ identity_relation ) ))]]) ).
thf(12563,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(rewrite,[status(thm)],[2535,11335]) ).
thf(19046,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ null_class ) ),
inference(rewrite,[status(thm)],[12563,16734]) ).
thf(71971,plain,
( ( member @ ( sum_class @ ( power_class @ ( sk5 @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60960,48]) ).
thf(72093,plain,
( ( ( sum_class @ ( power_class @ ( sk5 @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[71971]) ).
thf(72149,plain,
( ( sum_class @ ( power_class @ ( sk5 @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[72093]) ).
thf(86567,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( sk2 != null_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[323,3378]) ).
thf(86568,plain,
( ~ ( subclass @ universal_class @ sk2 )
| ( sk2 != null_class ) ),
inference(pattern_uni,[status(thm)],[86567:[bind(A,$thf( sk2 ))]]) ).
thf(47829,plain,
( ( member @ ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[44971,48]) ).
thf(47949,plain,
( ( ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[47829]) ).
thf(47979,plain,
( ( power_class @ ( sk5 @ ( singleton @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[47949]) ).
thf(8115,plain,
( ( sk2 != universal_class )
| ( ( member @ ( sk5 @ sk2 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[3455,48]) ).
thf(8134,plain,
( ( sk2 != universal_class )
| ( ( sk5 @ sk2 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[8115]) ).
thf(8151,plain,
( ( sk2 != universal_class )
| ( ( sk5 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[8134]) ).
thf(11279,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( sk2 != universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[134,3378]) ).
thf(11280,plain,
( ( member @ ( sk5 @ sk2 ) @ sk2 )
| ( sk2 != universal_class ) ),
inference(pattern_uni,[status(thm)],[11279:[bind(A,$thf( sk2 ))]]) ).
thf(99918,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ ( complement @ ( successor @ sk7 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,99798]) ).
thf(99919,plain,
~ ( member @ universal_class @ ( power_class @ ( complement @ ( successor @ sk7 ) ) ) ),
inference(pattern_uni,[status(thm)],[99918:[bind(A,$thf( universal_class )),bind(B,$thf( complement @ ( successor @ sk7 ) ))]]) ).
thf(80410,plain,
( ( member @ ( power_class @ ( power_class @ ( sum_class @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[63563,48]) ).
thf(80501,plain,
( ( ( power_class @ ( power_class @ ( sum_class @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[80410]) ).
thf(80580,plain,
( ( power_class @ ( power_class @ ( sum_class @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[80501]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ element_relation )
<=> ( ( member @ B @ universal_class )
& ( member @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation_defn) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( ( member @ ( ordered_pair @ A @ B ) @ element_relation )
=> ( ( member @ B @ universal_class )
& ( member @ A @ B ) ) )
& ( ( ( member @ B @ universal_class )
& ( member @ A @ B ) )
=> ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(3208,plain,
! [C: $i,B: $i,A: $i] :
( ( subclass @ A @ B )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[91,2535]) ).
thf(3209,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[3208:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) )),bind(B,$thf( D )),bind(C,$thf( sk4 @ D @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ))]]) ).
thf(3229,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) @ A ),
inference(simp,[status(thm)],[3209]) ).
thf(12538,plain,
! [A: $i] : ( subclass @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) @ A ),
inference(rewrite,[status(thm)],[3229,11335]) ).
thf(18943,plain,
! [A: $i] : ( subclass @ ( sum_class @ null_class ) @ A ),
inference(rewrite,[status(thm)],[12538,16734]) ).
thf(100,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(cnf,[status(esa)],[97]) ).
thf(4418,plain,
! [A: $i] :
( ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( ( function @ sk8 )
!= ( function @ A ) ) ),
inference(paramod_ordered,[status(thm)],[234,100]) ).
thf(4419,plain,
subclass @ ( compose @ sk8 @ ( inverse @ sk8 ) ) @ identity_relation,
inference(pattern_uni,[status(thm)],[4418:[bind(A,$thf( sk8 ))]]) ).
thf(11449,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( member @ ( sk5 @ sk1 ) @ universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[134,3846]) ).
thf(11450,plain,
( ( member @ ( sk5 @ sk2 ) @ sk2 )
| ( member @ ( sk5 @ sk1 ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[11449:[bind(A,$thf( sk2 ))]]) ).
thf(90094,plain,
( ( member @ ( sk4 @ ( complement @ identity_relation ) @ universal_class ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[89330,48]) ).
thf(90187,plain,
( ( ( sk4 @ ( complement @ identity_relation ) @ universal_class )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[90094]) ).
thf(90258,plain,
( ( sk4 @ ( complement @ identity_relation ) @ universal_class )
!= sk2 ),
inference(simp,[status(thm)],[90187]) ).
thf(26000,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( A
!= ( singleton @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[134,25962]) ).
thf(26001,plain,
member @ ( sk5 @ ( singleton @ sk7 ) ) @ ( singleton @ sk7 ),
inference(pattern_uni,[status(thm)],[26000:[bind(A,$thf( singleton @ sk7 ))]]) ).
thf(54343,plain,
( ( member @ ( sk5 @ sk7 ) @ ( complement @ universal_class ) )
!= ( member @ ( sk5 @ sk7 ) @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[12301,48986]) ).
thf(54513,plain,
( ( ( sk5 @ sk7 )
!= ( sk5 @ sk7 ) )
| ( ( complement @ universal_class )
!= sk7 ) ),
inference(simp,[status(thm)],[54343]) ).
thf(54560,plain,
( ( complement @ universal_class )
!= sk7 ),
inference(simp,[status(thm)],[54513]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ( member @ B @ A )
| ( member @ B @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[227]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ( member @ B @ A )
| ( member @ B @ ( complement @ A ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(5784,plain,
! [A: $i] :
( ( member @ null_class @ sk7 )
!= ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5702,2932]) ).
thf(5803,plain,
! [A: $i] :
( ( null_class != A )
| ( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )
!= sk7 ) ),
inference(simp,[status(thm)],[5784]) ).
thf(5822,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )
!= sk7 ),
inference(simp,[status(thm)],[5803]) ).
thf(12567,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) )
!= sk7 ),
inference(rewrite,[status(thm)],[5822,11335]) ).
thf(15294,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
!= sk7 ),
inference(rewrite,[status(thm)],[12567,14658]) ).
thf(51038,plain,
( ( member @ null_class @ ( complement @ ( successor @ sk7 ) ) )
!= ( member @ null_class @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[5702,48876]) ).
thf(51172,plain,
( ( null_class != null_class )
| ( ( complement @ ( successor @ sk7 ) )
!= sk7 ) ),
inference(simp,[status(thm)],[51038]) ).
thf(51273,plain,
( ( complement @ ( successor @ sk7 ) )
!= sk7 ),
inference(simp,[status(thm)],[51172]) ).
thf(958,plain,
( ( function @ null_class )
| ( ( member @ ( sk5 @ sk8 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[608,48]) ).
thf(960,plain,
( ( function @ null_class )
| ( ( sk5 @ sk8 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[958]) ).
thf(961,plain,
( ( function @ null_class )
| ( ( sk5 @ sk8 )
!= sk2 ) ),
inference(simp,[status(thm)],[960]) ).
thf(10061,plain,
! [A: $i] :
( ( member @ null_class @ sk7 )
!= ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5702,8539]) ).
thf(10105,plain,
! [A: $i] :
( ( null_class != A )
| ( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )
!= sk7 ) ),
inference(simp,[status(thm)],[10061]) ).
thf(10186,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )
!= sk7 ),
inference(simp,[status(thm)],[10105]) ).
thf(12565,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) )
!= sk7 ),
inference(rewrite,[status(thm)],[10186,11335]) ).
thf(18840,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )
!= sk7 ),
inference(rewrite,[status(thm)],[12565,16734]) ).
thf(6892,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( sk1 != null_class )
| ( ( subclass @ A @ B )
!= ( subclass @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[112,3381]) ).
thf(6893,plain,
( ~ ( member @ sk2 @ ( power_class @ sk1 ) )
| ( sk1 != null_class ) ),
inference(pattern_uni,[status(thm)],[6892:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(68602,plain,
( ( member @ ( power_class @ ( sk9 @ ( sk5 @ identity_relation ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60573,48]) ).
thf(68719,plain,
( ( ( power_class @ ( sk9 @ ( sk5 @ identity_relation ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[68602]) ).
thf(68768,plain,
( ( power_class @ ( sk9 @ ( sk5 @ identity_relation ) ) )
!= sk2 ),
inference(simp,[status(thm)],[68719]) ).
thf(73047,plain,
( ( member @ ( sum_class @ ( power_class @ ( sk5 @ identity_relation ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60998,48]) ).
thf(73176,plain,
( ( ( sum_class @ ( power_class @ ( sk5 @ identity_relation ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[73047]) ).
thf(73232,plain,
( ( sum_class @ ( power_class @ ( sk5 @ identity_relation ) ) )
!= sk2 ),
inference(simp,[status(thm)],[73176]) ).
thf(4526,plain,
! [A: $i] :
( ( subclass @ ( compose @ sk8 @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) @ identity_relation )
| ( ( inverse @ A )
!= ( inverse @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[95,4419]) ).
thf(4527,plain,
subclass @ ( compose @ sk8 @ ( domain_of @ ( flip @ ( cross_product @ sk8 @ universal_class ) ) ) ) @ identity_relation,
inference(pattern_uni,[status(thm)],[4526:[bind(A,$thf( sk8 ))]]) ).
thf(15422,plain,
( ( subclass @ sk8 @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk7 @ null_class ) ),
inference(paramod_ordered,[status(thm)],[3907,15373]) ).
thf(15437,plain,
( ( sk8 != sk7 )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[15422]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( member @ B @ universal_class ) )
=> ( ( ( first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( second @ ( ordered_pair @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_second) ).
thf(158,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( member @ B @ universal_class ) )
=> ( ( ( first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( second @ ( ordered_pair @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( unordered_pair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
inference(cnf,[status(esa)],[177]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ~ ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[181]) ).
thf(86194,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( sk7 != universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[323,504]) ).
thf(86195,plain,
( ~ ( subclass @ universal_class @ sk2 )
| ( sk7 != universal_class ) ),
inference(pattern_uni,[status(thm)],[86194:[bind(A,$thf( sk2 ))]]) ).
thf(59488,plain,
( ( member @ ( power_class @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[58207,48]) ).
thf(59617,plain,
( ( ( power_class @ ( sk5 @ identity_relation ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[59488]) ).
thf(59674,plain,
( ( power_class @ ( sk5 @ identity_relation ) )
!= sk2 ),
inference(simp,[status(thm)],[59617]) ).
thf(10068,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,8539]) ).
thf(10069,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10068:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )),bind(B,$thf( null_class ))]]) ).
thf(12550,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[10069,11335]) ).
thf(18217,plain,
~ ( inductive @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(rewrite,[status(thm)],[12550,16734]) ).
thf(50123,plain,
( ( member @ ( power_class @ ( power_class @ ( power_class @ sk7 ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[46406,48]) ).
thf(50217,plain,
( ( ( power_class @ ( power_class @ ( power_class @ sk7 ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[50123]) ).
thf(50262,plain,
( ( power_class @ ( power_class @ ( power_class @ sk7 ) ) )
!= sk2 ),
inference(simp,[status(thm)],[50217]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( member @ A @ ( sk3 @ B @ A ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
inference(cnf,[status(esa)],[51]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(58,plain,
! [A: $i] : ( subclass @ A @ A ),
inference(simp,[status(thm)],[57]) ).
thf(56268,plain,
( ( member @ sk7 @ ( complement @ ( singleton @ sk7 ) ) )
!= ( member @ sk7 @ ( singleton @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[25609,49138]) ).
thf(56328,plain,
( ( sk7 != sk7 )
| ( ( complement @ ( singleton @ sk7 ) )
!= ( singleton @ sk7 ) ) ),
inference(simp,[status(thm)],[56268]) ).
thf(56362,plain,
( ( complement @ ( singleton @ sk7 ) )
!= ( singleton @ sk7 ) ),
inference(simp,[status(thm)],[56328]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( subclass @ successor_relation @ ( cross_product @ universal_class @ A ) )
| ( B != universal_class ) ),
inference(paramod_ordered,[status(thm)],[56,187]) ).
thf(297,plain,
! [A: $i] :
( ~ ( subclass @ A @ universal_class )
| ~ ( subclass @ universal_class @ A )
| ( subclass @ successor_relation @ ( cross_product @ universal_class @ A ) ) ),
inference(pattern_uni,[status(thm)],[296:[bind(A,$thf( A )),bind(B,$thf( universal_class ))]]) ).
thf(76248,plain,
! [A: $i] :
( ~ $true
| ~ ( subclass @ universal_class @ A )
| ( subclass @ successor_relation @ ( cross_product @ universal_class @ A ) ) ),
inference(rewrite,[status(thm)],[297,68]) ).
thf(76249,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( subclass @ successor_relation @ ( cross_product @ universal_class @ A ) ) ),
inference(simp,[status(thm)],[76248]) ).
thf(12674,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( sk7 != universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[135,5810]) ).
thf(12675,plain,
( ( disjoint @ ( sk5 @ sk2 ) @ sk2 )
| ( sk7 != universal_class ) ),
inference(pattern_uni,[status(thm)],[12674:[bind(A,$thf( sk2 ))]]) ).
thf(11070,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ~ ( inductive @ universal_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[134,5713]) ).
thf(11071,plain,
( ( member @ ( sk5 @ sk2 ) @ sk2 )
| ~ ( inductive @ universal_class ) ),
inference(pattern_uni,[status(thm)],[11070:[bind(A,$thf( sk2 ))]]) ).
thf(15518,plain,
( ( member @ ( sk4 @ null_class @ sk7 ) @ sk7 )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[15409,48]) ).
thf(15544,plain,
( ( ( sk4 @ null_class @ sk7 )
!= sk2 )
| ( sk7 != universal_class ) ),
inference(simp,[status(thm)],[15518]) ).
thf(5285,plain,
! [B: $i,A: $i] :
( ( member @ ( singleton @ A ) @ universal_class )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1064,2932]) ).
thf(5316,plain,
! [B: $i,A: $i] :
( ( ( singleton @ A )
!= B )
| ( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )
!= universal_class ) ),
inference(simp,[status(thm)],[5285]) ).
thf(5363,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )
!= universal_class ),
inference(simp,[status(thm)],[5316]) ).
thf(12555,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[5363,11335]) ).
thf(15218,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[12555,14658]) ).
thf(70423,plain,
( ( member @ ( sum_class @ ( power_class @ ( sk5 @ universal_class ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60922,48]) ).
thf(70520,plain,
( ( ( sum_class @ ( power_class @ ( sk5 @ universal_class ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[70423]) ).
thf(70591,plain,
( ( sum_class @ ( power_class @ ( sk5 @ universal_class ) ) )
!= sk2 ),
inference(simp,[status(thm)],[70520]) ).
thf(93864,plain,
( ( member @ ( sk4 @ ( power_class @ null_class ) @ universal_class ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[89744,48]) ).
thf(93965,plain,
( ( ( sk4 @ ( power_class @ null_class ) @ universal_class )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[93864]) ).
thf(94020,plain,
( ( sk4 @ ( power_class @ null_class ) @ universal_class )
!= sk2 ),
inference(simp,[status(thm)],[93965]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
<=> ( ( member @ A @ C )
& ( member @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_defn) ).
thf(146,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
=> ( ( member @ A @ C )
& ( member @ B @ D ) ) )
& ( ( ( member @ A @ C )
& ( member @ B @ D ) )
=> ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(806,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A
!= ( sk5 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[133,728]) ).
thf(807,plain,
( ( member @ ( sk5 @ ( sk5 @ universal_class ) ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[806:[bind(A,$thf( sk5 @ universal_class ))]]) ).
thf(1624,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A
!= ( sk5 @ ( sk5 @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[133,807]) ).
thf(1625,plain,
( ( member @ ( sk5 @ ( sk5 @ ( sk5 @ universal_class ) ) ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[1624:[bind(A,$thf( sk5 @ ( sk5 @ universal_class ) ))]]) ).
thf(79349,plain,
( ( member @ ( sum_class @ ( sum_class @ ( sk5 @ universal_class ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[63093,48]) ).
thf(79480,plain,
( ( ( sum_class @ ( sum_class @ ( sk5 @ universal_class ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[79349]) ).
thf(79534,plain,
( ( sum_class @ ( sum_class @ ( sk5 @ universal_class ) ) )
!= sk2 ),
inference(simp,[status(thm)],[79480]) ).
thf(56818,plain,
( ( member @ ( power_class @ ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[45049,48]) ).
thf(56923,plain,
( ( ( power_class @ ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[56818]) ).
thf(57002,plain,
( ( power_class @ ( sk5 @ ( singleton @ ( sk5 @ sk7 ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[56923]) ).
thf(49027,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk4 @ null_class @ universal_class ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3165,230]) ).
thf(49028,plain,
~ ( member @ ( sk4 @ null_class @ universal_class ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[49027:[bind(A,$thf( universal_class )),bind(B,$thf( sk4 @ null_class @ universal_class ))]]) ).
thf(51056,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ null_class @ ( complement @ ( successor @ sk7 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,48876]) ).
thf(51057,plain,
~ ( inductive @ ( complement @ ( successor @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[51056:[bind(A,$thf( complement @ ( successor @ sk7 ) ))]]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( function @ B ) )
=> ( member @ ( image @ B @ A ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
thf(195,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( function @ B ) )
=> ( member @ ( image @ B @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(66795,plain,
( ( member @ ( power_class @ ( power_class @ ( sk5 @ identity_relation ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[59460,48]) ).
thf(66905,plain,
( ( ( power_class @ ( power_class @ ( sk5 @ identity_relation ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[66795]) ).
thf(66953,plain,
( ( power_class @ ( power_class @ ( sk5 @ identity_relation ) ) )
!= sk2 ),
inference(simp,[status(thm)],[66905]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( member @ sk7 @ A )
| ( B != universal_class ) ),
inference(paramod_ordered,[status(thm)],[56,191]) ).
thf(269,plain,
! [A: $i] :
( ~ ( subclass @ A @ universal_class )
| ~ ( subclass @ universal_class @ A )
| ( member @ sk7 @ A ) ),
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( A )),bind(B,$thf( universal_class ))]]) ).
thf(65612,plain,
! [A: $i] :
( ~ $true
| ~ ( subclass @ universal_class @ A )
| ( member @ sk7 @ A ) ),
inference(rewrite,[status(thm)],[269,68]) ).
thf(65613,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ( member @ sk7 @ A ) ),
inference(simp,[status(thm)],[65612]) ).
thf(55348,plain,
( ( function @ null_class )
| ( ( member @ ( power_class @ ( sk5 @ sk8 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[44961,48]) ).
thf(55472,plain,
( ( function @ null_class )
| ( ( power_class @ ( sk5 @ sk8 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[55348]) ).
thf(55526,plain,
( ( function @ null_class )
| ( ( power_class @ ( sk5 @ sk8 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[55472]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ A ) ),
inference(cnf,[status(esa)],[124]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( cross_product @ A @ B ) )
=> ( C
= ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product) ).
thf(136,plain,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( cross_product @ A @ B ) )
=> ( C
= ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(823,plain,
( ( member @ ( sk5 @ universal_class ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[728,48]) ).
thf(825,plain,
( ( ( sk5 @ universal_class )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[823]) ).
thf(828,plain,
( ( sk5 @ universal_class )
!= sk2 ),
inference(simp,[status(thm)],[825]) ).
thf(15918,plain,
( ( member @ ( sk5 @ sk7 ) @ sk7 )
!= ( member @ sk7 @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[12301,15417]) ).
thf(15970,plain,
( ( ( sk5 @ sk7 )
!= sk7 )
| ( ( power_class @ null_class )
!= sk7 ) ),
inference(simp,[status(thm)],[15918]) ).
thf(64164,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sum_class @ sk7 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[61333,230]) ).
thf(64165,plain,
~ ( member @ ( sum_class @ ( sum_class @ sk7 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[64164:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sum_class @ sk7 ) ))]]) ).
thf(42911,plain,
( ( member @ sk2 @ universal_class )
!= ( member @ null_class @ ( successor @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[42684,48]) ).
thf(43021,plain,
( ( sk2 != null_class )
| ( ( successor @ sk7 )
!= universal_class ) ),
inference(simp,[status(thm)],[42911]) ).
thf(87875,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ~ ( inductive @ sk2 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[323,34074]) ).
thf(87876,plain,
( ~ ( subclass @ universal_class @ sk7 )
| ~ ( inductive @ sk2 ) ),
inference(pattern_uni,[status(thm)],[87875:[bind(A,$thf( sk7 ))]]) ).
thf(64180,plain,
( ( member @ ( sum_class @ ( sum_class @ sk7 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[61333,48]) ).
thf(64275,plain,
( ( ( sum_class @ ( sum_class @ sk7 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[64180]) ).
thf(64314,plain,
( ( sum_class @ ( sum_class @ sk7 ) )
!= sk2 ),
inference(simp,[status(thm)],[64275]) ).
thf(64365,plain,
( ( sk2 != null_class )
| ( ( sum_class @ ( sum_class @ sk7 ) )
!= ( sum_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[11335,64314]) ).
thf(64432,plain,
( ( sk2 != null_class )
| ( ( sum_class @ sk7 )
!= null_class ) ),
inference(simp,[status(thm)],[64365]) ).
thf(10965,plain,
! [A: $i] :
( ( member @ ( sk5 @ A ) @ A )
| ( sk1 != null_class )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[134,3830]) ).
thf(10966,plain,
( ( member @ ( sk5 @ sk2 ) @ sk2 )
| ( sk1 != null_class ) ),
inference(pattern_uni,[status(thm)],[10965:[bind(A,$thf( sk2 ))]]) ).
thf(45693,plain,
( ( member @ ( power_class @ ( sk5 @ sk7 ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[44916,48]) ).
thf(45777,plain,
( ( ( power_class @ ( sk5 @ sk7 ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[45693]) ).
thf(45849,plain,
( ( power_class @ ( sk5 @ sk7 ) )
!= sk2 ),
inference(simp,[status(thm)],[45777]) ).
thf(25868,plain,
( ( sk2 != null_class )
| ( ( member @ sk7 @ ( power_class @ sk2 ) )
!= ( member @ sk7 @ ( singleton @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[25609,6921]) ).
thf(25894,plain,
( ( sk2 != null_class )
| ( sk7 != sk7 )
| ( ( power_class @ sk2 )
!= ( singleton @ sk7 ) ) ),
inference(simp,[status(thm)],[25868]) ).
thf(25949,plain,
( ( sk2 != null_class )
| ( ( power_class @ sk2 )
!= ( singleton @ sk7 ) ) ),
inference(simp,[status(thm)],[25894]) ).
thf(1390,plain,
( ( sk1 != null_class )
| ( ( member @ ( sk5 @ sk2 ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[1088,48]) ).
thf(1393,plain,
( ( sk1 != null_class )
| ( ( sk5 @ sk2 )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[1390]) ).
thf(1399,plain,
( ( sk1 != null_class )
| ( ( sk5 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[1393]) ).
thf(84808,plain,
( ( member @ ( power_class @ ( power_class @ ( sk4 @ null_class @ universal_class ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[47145,48]) ).
thf(84941,plain,
( ( ( power_class @ ( power_class @ ( sk4 @ null_class @ universal_class ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[84808]) ).
thf(85001,plain,
( ( power_class @ ( power_class @ ( sk4 @ null_class @ universal_class ) ) )
!= sk2 ),
inference(simp,[status(thm)],[84941]) ).
thf(14565,plain,
! [C: $i,B: $i,A: $i] :
( ( disjoint @ A @ B )
| ( ( member @ ( sk6 @ B @ A ) @ A )
!= ( member @ C @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[144,194]) ).
thf(14566,plain,
! [A: $i] : ( disjoint @ null_class @ A ),
inference(pattern_uni,[status(thm)],[14565:[bind(A,$thf( null_class )),bind(B,$thf( D )),bind(C,$thf( sk6 @ D @ null_class ))]]) ).
thf(14621,plain,
! [A: $i] : ( disjoint @ null_class @ A ),
inference(simp,[status(thm)],[14566]) ).
thf(60890,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk9 @ ( sk5 @ identity_relation ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[59159,251]) ).
thf(60891,plain,
member @ ( sum_class @ ( sk9 @ ( sk5 @ identity_relation ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[60890:[bind(A,$thf( sk9 @ ( sk5 @ identity_relation ) ))]]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[210]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(13305,plain,
! [A: $i] :
( ( disjoint @ ( sk5 @ A ) @ A )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[135,5732]) ).
thf(13306,plain,
disjoint @ ( sk5 @ sk7 ) @ sk7,
inference(pattern_uni,[status(thm)],[13305:[bind(A,$thf( sk7 ))]]) ).
thf(48894,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ sk7 ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44928,230]) ).
thf(48895,plain,
~ ( member @ ( power_class @ sk7 ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[48894:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ sk7 ))]]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[87]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( member @ A @ universal_class ) ),
inference(cnf,[status(esa)],[109]) ).
thf(69874,plain,
( ( member @ ( sum_class @ ( sk9 @ ( sk5 @ identity_relation ) ) ) @ universal_class )
!= ( member @ sk2 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[60891,48]) ).
thf(70010,plain,
( ( ( sum_class @ ( sk9 @ ( sk5 @ identity_relation ) ) )
!= sk2 )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[69874]) ).
thf(70052,plain,
( ( sum_class @ ( sk9 @ ( sk5 @ identity_relation ) ) )
!= sk2 ),
inference(simp,[status(thm)],[70010]) ).
thf(120395,plain,
$false,
inference(cvc4,[status(thm)],[69,5810,83892,101,96235,15440,234,12614,59077,48986,95648,249,48907,3830,68083,12689,61333,86191,48751,82421,42684,61623,45515,247,16027,217,61488,47145,97475,6900,3959,15703,18114,39484,49138,38893,56,4011,60847,34271,5713,538,14301,14354,39885,58114,11335,54873,42809,73697,58109,257,174,48928,60577,185,88926,50095,12843,66000,13313,44928,61325,49602,58393,2269,504,14088,15426,62410,48943,63736,58211,79120,189,46,89474,34094,47330,78,49034,6905,93496,8819,1890,62240,93,12642,6923,152,48376,261,216,164,47804,91720,63006,85639,36800,60998,77581,34948,623,5946,14408,15409,238,61329,97393,25773,62763,61,293,133,14658,116,60931,3378,21774,89468,1863,20903,5961,117,99760,88700,89553,72796,100018,13233,3995,220,86683,102,48885,1387,46588,48989,63332,13649,44957,60406,192,429,165,63093,86193,3471,62759,46754,92,197,48934,43100,2313,15417,12709,59460,75832,229,5702,60974,44971,51275,12741,62755,1089,15373,317,83394,63089,76230,3381,1064,63249,60942,60404,188,59159,83259,6919,13504,3237,61619,46406,12179,77,100926,60922,62487,5662,61078,1889,59464,43463,96,49126,20771,339,3846,10968,701,2006,14494,129,94552,90494,311,38200,91898,26005,134,46919,128,237,105,89744,3306,89409,77131,15446,45060,5722,63567,39134,71715,60849,23566,49952,279,64,81379,86197,180,99798,5720,423,46289,12301,60924,291,39490,281,34127,176,89610,191,25771,83877,3266,43104,74335,64169,144,49608,34275,335,236,34086,34265,77893,65156,86,63571,43029,49,17628,60720,10980,49048,113,219,43091,89337,81,230,76,35149,97191,60960,187,62934,13390,1339,46173,323,213,91,3165,66,251,108,48937,44916,1080,12691,49011,60956,61867,135,299,10930,226,34937,49954,89753,46023,223,608,267,12308,20291,25995,35022,63563,15004,209,34074,61615,84350,112,63085,45049,123,3455,194,145,88854,48,3376,855,63,48983,1070,24706,6885,95,2012,6921,58068,75110,71335,13477,49408,89832,67,49132,12932,127,49051,26232,60082,50,25974,97239,44961,89330,2354,73829,54543,9863,25971,72,175,89603,143,97195,60573,19046,62244,72149,58207,86568,47979,8151,11280,99919,80580,99,203,18943,4419,11450,24714,90258,218,26001,54560,231,15294,250,6882,25568,51273,961,18840,42498,6893,3383,114,68768,73232,4527,34192,15437,158,58112,48876,186,2004,139,86195,61763,59674,18217,50262,75,58,235,56362,48995,76249,12675,16734,11071,15544,15218,214,70591,94020,3907,146,39473,1625,64161,190,183,79534,48579,57002,49028,3379,51057,56366,39446,807,195,44941,45358,25962,66953,65613,55526,242,239,88720,126,136,828,45670,25609,15970,64165,163,43021,87876,64432,728,54871,10966,45849,68,25949,1399,85001,254,14621,60891,15985,62236,215,20071,61082,13306,222,48895,232,100,48191,90,111,64314,87290,70052,5732,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET069+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 11:04:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.86/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/1.00 % [INFO] Parsing done (137ms).
% 1.15/1.01 % [INFO] Running in sequential loop mode.
% 1.81/1.25 % [INFO] eprover registered as external prover.
% 1.81/1.25 % [INFO] cvc4 registered as external prover.
% 1.81/1.26 % [INFO] Scanning for conjecture ...
% 1.99/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 43 axioms. Running axiom selection ...
% 2.14/1.38 % [INFO] Axiom selection finished. Selected 43 axioms (removed 0 axioms).
% 2.14/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.14/1.44 % [INFO] Type checking passed.
% 2.14/1.45 % [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 ...
% 208.04/39.51 % External prover 'cvc4' found a proof!
% 208.04/39.51 % [INFO] Killing All external provers ...
% 208.04/39.52 % Time passed: 38985ms (effective reasoning time: 38505ms)
% 208.04/39.52 % 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)>
% 208.04/39.52 % Axioms used in derivation (43): sum_class_defn, image_defn, cross_product_defn, extensionality, infinity, first_second, rotate, null_class_defn, sum_class, restrict_defn, compose_defn1, inductive_defn, unordered_pair, cross_product, flip_defn, function_defn, element_relation_defn, identity_relation, unordered_pair_defn, successor_relation_defn1, power_class_defn, intersection, inverse_defn, replacement, element_relation, singleton_set_defn, subclass_defn, domain_of, power_class, flip, compose_defn2, choice, complement, disjoint_defn, apply_defn, regularity, successor_defn, ordered_pair_defn, class_elements_are_sets, range_of_defn, union_defn, successor_relation_defn2, rotate_defn
% 208.04/39.52 % No. of inferences in proof: 1237
% 208.04/39.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 38985 ms resp. 38505 ms w/o parsing
% 208.68/39.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 208.68/39.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------