TSTP Solution File: SET098+1 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SET098+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n024.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 : Mon Jun 24 14:40:08 EDT 2024
% Result : Theorem 137.42s 38.78s
% Output : Refutation 137.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 44
% Syntax : Number of formulae : 992 ( 414 unt; 0 typ; 0 def)
% Number of atoms : 2395 ( 682 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 9488 (1055 ~; 665 |; 150 &;7502 @)
% ( 19 <=>; 97 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 10 con; 0-3 aty)
% Number of variables : 1237 ( 0 ^1209 !; 28 ?;1237 :)
% Comments :
%------------------------------------------------------------------------------
thf(null_class_type,type,
null_class: $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(subclass_type,type,
subclass: $i > $i > $o ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(flip_type,type,
flip: $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(universal_class_type,type,
universal_class: $i ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(function_type,type,
function: $i > $o ).
thf(identity_relation_type,type,
identity_relation: $i ).
thf(image_type,type,
image: $i > $i > $i ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(restrict_type,type,
restrict: $i > $i > $i > $i ).
thf(element_relation_type,type,
element_relation: $i ).
thf(rotate_type,type,
rotate: $i > $i ).
thf(successor_relation_type,type,
successor_relation: $i ).
thf(sum_class_type,type,
sum_class: $i > $i ).
thf(power_class_type,type,
power_class: $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $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(successor_type,type,
successor: $i > $i ).
thf(inductive_type,type,
inductive: $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(sk4_type,type,
sk4: $i > $i > $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(20,axiom,
! [A: $i] :
( ( A != null_class )
=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( member @ B @ A )
& ( disjoint @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity) ).
thf(124,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)],[20]) ).
thf(125,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( sk3 @ A ) @ universal_class ) ),
inference(cnf,[status(esa)],[124]) ).
thf(128,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( sk3 @ A ) @ universal_class ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(1,conjecture,
! [A: $i] :
( ( A = null_class )
| ? [B: $i] :
( ( singleton @ B )
= A )
| ? [B: $i] :
( ( member @ B @ A )
& ? [C: $i] :
( ( member @ C @ ( intersection @ ( complement @ ( singleton @ B ) ) @ A ) )
& ( member @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_number_of_elements_in_class) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A = null_class )
| ? [B: $i] :
( ( singleton @ B )
= A )
| ? [B: $i] :
( ( member @ B @ A )
& ? [C: $i] :
( ( member @ C @ ( intersection @ ( complement @ ( singleton @ B ) ) @ A ) )
& ( member @ C @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(46,plain,
~ ! [A: $i] :
( ( A = null_class )
| ? [B: $i] :
( ( singleton @ B )
= A )
| ? [B: $i] :
( ( member @ B @ A )
& ? [C: $i] :
( ( member @ C @ ( intersection @ ( complement @ ( singleton @ B ) ) @ A ) )
& ( member @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,plain,
sk1 != null_class,
inference(cnf,[status(esa)],[46]) ).
thf(52,plain,
sk1 != null_class,
inference(lifteq,[status(thm)],[49]) ).
thf(697,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[128,52]) ).
thf(698,plain,
member @ ( sk3 @ sk1 ) @ universal_class,
inference(pattern_uni,[status(thm)],[697:[bind(A,$thf( sk1 ))]]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
<=> ( ( member @ C @ A )
| ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(185,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)],[32]) ).
thf(186,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)],[185]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[186]) ).
thf(190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(27793,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( union @ A @ B ) )
| ( ( member @ ( sk3 @ sk1 ) @ universal_class )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[698,190]) ).
thf(27794,plain,
! [A: $i] : ( member @ ( sk3 @ sk1 ) @ ( union @ universal_class @ A ) ),
inference(pattern_uni,[status(thm)],[27793:[bind(A,$thf( universal_class )),bind(B,$thf( B )),bind(C,$thf( sk3 @ sk1 ))]]) ).
thf(28120,plain,
! [A: $i] : ( member @ ( sk3 @ sk1 ) @ ( union @ universal_class @ A ) ),
inference(simp,[status(thm)],[27794]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( member @ B @ ( complement @ A ) )
<=> ( ( member @ B @ universal_class )
& ~ ( member @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(213,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)],[38]) ).
thf(214,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)],[213]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ~ ( member @ B @ A ) ),
inference(cnf,[status(esa)],[214]) ).
thf(38245,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ sk1 ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[698,217]) ).
thf(38246,plain,
~ ( member @ ( sk3 @ sk1 ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38245:[bind(A,$thf( universal_class )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(95894,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ universal_class @ A ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[28120,38246]) ).
thf(96123,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( union @ universal_class @ A )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[95894]) ).
thf(96284,plain,
! [A: $i] :
( ( union @ universal_class @ A )
!= ( complement @ universal_class ) ),
inference(simp,[status(thm)],[96123]) ).
thf(126,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( sk3 @ A ) @ A ) ),
inference(cnf,[status(esa)],[124]) ).
thf(129,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( sk3 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[126]) ).
thf(8215,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ A )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[129,52]) ).
thf(8216,plain,
member @ ( sk3 @ sk1 ) @ sk1,
inference(pattern_uni,[status(thm)],[8215:[bind(A,$thf( sk1 ))]]) ).
thf(9647,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( member @ null_class @ sk1 )
| ( A
!= ( sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,8216]) ).
thf(9648,plain,
( ( member @ ( sk3 @ ( sk3 @ sk1 ) ) @ universal_class )
| ( member @ null_class @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9647:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(39,axiom,
? [A: $i] :
( ( function @ A )
& ! [B: $i] :
( ( member @ B @ universal_class )
=> ( ( B = null_class )
| ( member @ ( apply @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice) ).
thf(219,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)],[39]) ).
thf(221,plain,
function @ sk7,
inference(cnf,[status(esa)],[219]) ).
thf(7,axiom,
! [A: $i] :
( ( function @ A )
<=> ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function_defn) ).
thf(71,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)],[7]) ).
thf(72,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)],[71]) ).
thf(74,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(1208,plain,
! [A: $i] :
( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ( ( function @ sk7 )
!= ( function @ A ) ) ),
inference(paramod_ordered,[status(thm)],[221,74]) ).
thf(1209,plain,
subclass @ sk7 @ ( cross_product @ universal_class @ universal_class ),
inference(pattern_uni,[status(thm)],[1208:[bind(A,$thf( sk7 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subclass @ A @ B )
& ( subclass @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
thf(53,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(54,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)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[54]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A ) ),
inference(simp,[status(thm)],[58]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B != null_class )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[59,52]) ).
thf(292,plain,
! [A: $i] :
( ~ ( subclass @ sk1 @ A )
| ~ ( subclass @ A @ sk1 )
| ( A != null_class ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( sk1 ))]]) ).
thf(400,plain,
( ~ ( subclass @ sk1 @ null_class )
| ~ ( subclass @ null_class @ sk1 ) ),
inference(simp,[status(thm)],[292]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( subclass @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
thf(200,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)],[36]) ).
thf(201,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)],[200]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( member @ ( sk6 @ B @ A ) @ A )
| ( subclass @ A @ B ) ),
inference(cnf,[status(esa)],[201]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( member @ ( sk6 @ B @ A ) @ A )
| ( subclass @ A @ B ) ),
inference(simp,[status(thm)],[202]) ).
thf(28,axiom,
! [A: $i] :
~ ( member @ A @ null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
thf(168,plain,
! [A: $i] :
~ ( member @ A @ null_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(169,plain,
~ ? [A: $i] : ( member @ A @ null_class ),
inference(miniscope,[status(thm)],[168]) ).
thf(170,plain,
! [A: $i] :
~ ( member @ A @ null_class ),
inference(cnf,[status(esa)],[169]) ).
thf(33466,plain,
! [C: $i,B: $i,A: $i] :
( ( subclass @ A @ B )
| ( ( member @ ( sk6 @ B @ A ) @ A )
!= ( member @ C @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[205,170]) ).
thf(33467,plain,
! [A: $i] : ( subclass @ null_class @ A ),
inference(pattern_uni,[status(thm)],[33466:[bind(A,$thf( null_class )),bind(B,$thf( D )),bind(C,$thf( sk6 @ D @ null_class ))]]) ).
thf(33729,plain,
! [A: $i] : ( subclass @ null_class @ A ),
inference(simp,[status(thm)],[33467]) ).
thf(34002,plain,
( ~ ( subclass @ sk1 @ null_class )
| ~ $true ),
inference(rewrite,[status(thm)],[400,33729]) ).
thf(34003,plain,
~ ( subclass @ sk1 @ null_class ),
inference(simp,[status(thm)],[34002]) ).
thf(34088,plain,
( ( subclass @ sk7 @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk1 @ null_class ) ),
inference(paramod_ordered,[status(thm)],[1209,34003]) ).
thf(34103,plain,
( ( sk7 != sk1 )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[34088]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',first_second) ).
thf(223,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)],[40]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( member @ B @ universal_class )
| ( ( second @ ( ordered_pair @ A @ B ) )
= B ) ),
inference(cnf,[status(esa)],[223]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( ( second @ ( ordered_pair @ A @ B ) )
= B )
| ~ ( member @ A @ universal_class )
| ~ ( member @ B @ universal_class ) ),
inference(lifteq,[status(thm)],[225]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).
thf(250,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(251,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(45869,plain,
! [B: $i,A: $i] :
( ( ( second @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) )
= B )
| ~ ( member @ A @ universal_class )
| ~ ( member @ B @ universal_class ) ),
inference(rewrite,[status(thm)],[227,252]) ).
thf(13,axiom,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of_defn) ).
thf(86,plain,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(87,plain,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
inference(cnf,[status(esa)],[86]) ).
thf(88,plain,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
inference(lifteq,[status(thm)],[87]) ).
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/sandbox/benchmark/theBenchmark.p',successor_relation_defn2) ).
thf(153,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(154,plain,
( ! [A: $i,B: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
=> ( ( member @ A @ universal_class )
& ( member @ B @ universal_class )
& ( ( successor @ A )
= B ) ) )
& ! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( member @ B @ universal_class )
& ( ( successor @ A )
= B ) )
=> ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ) ),
inference(miniscope,[status(thm)],[153]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
| ( ( successor @ A )
= B ) ),
inference(cnf,[status(esa)],[154]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( ( successor @ A )
= B )
| ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ),
inference(lifteq,[status(thm)],[158]) ).
thf(17920,plain,
! [B: $i,A: $i] :
( ( ( successor @ A )
= B )
| ~ ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ successor_relation ) ),
inference(rewrite,[status(thm)],[161,252]) ).
thf(35,axiom,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_defn) ).
thf(197,plain,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(198,plain,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[197]) ).
thf(199,plain,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
inference(lifteq,[status(thm)],[198]) ).
thf(27,axiom,
? [A: $i] :
( ( member @ A @ universal_class )
& ( inductive @ A )
& ! [B: $i] :
( ( inductive @ B )
=> ( subclass @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity) ).
thf(164,plain,
? [A: $i] :
( ( member @ A @ universal_class )
& ( inductive @ A )
& ! [B: $i] :
( ( inductive @ B )
=> ( subclass @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(167,plain,
member @ sk5 @ universal_class,
inference(cnf,[status(esa)],[164]) ).
thf(27902,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( union @ A @ B ) )
| ( ( member @ sk5 @ universal_class )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[167,190]) ).
thf(27903,plain,
! [A: $i] : ( member @ sk5 @ ( union @ universal_class @ A ) ),
inference(pattern_uni,[status(thm)],[27902:[bind(A,$thf( universal_class )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(28155,plain,
! [A: $i] : ( member @ sk5 @ ( union @ universal_class @ A ) ),
inference(simp,[status(thm)],[27903]) ).
thf(28254,plain,
! [B: $i,A: $i] :
( ( member @ sk5 @ ( successor @ A ) )
| ( ( union @ A @ ( singleton @ A ) )
!= ( union @ universal_class @ B ) ) ),
inference(paramod_ordered,[status(thm)],[199,28155]) ).
thf(28255,plain,
member @ sk5 @ ( successor @ universal_class ),
inference(pattern_uni,[status(thm)],[28254:[bind(A,$thf( universal_class )),bind(B,$thf( singleton @ universal_class ))]]) ).
thf(38391,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ sk5 @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[167,217]) ).
thf(38392,plain,
~ ( member @ sk5 @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38391:[bind(A,$thf( universal_class )),bind(B,$thf( sk5 ))]]) ).
thf(38948,plain,
( ( member @ sk5 @ ( successor @ universal_class ) )
!= ( member @ sk5 @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[28255,38392]) ).
thf(39022,plain,
( ( sk5 != sk5 )
| ( ( successor @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[38948]) ).
thf(39049,plain,
( ( successor @ universal_class )
!= ( complement @ universal_class ) ),
inference(simp,[status(thm)],[39022]) ).
thf(6,axiom,
! [A: $i] : ( subclass @ A @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(69,plain,
! [A: $i] : ( subclass @ A @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ! [C: $i] :
~ ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
thf(134,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)],[22]) ).
thf(135,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)],[134]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( disjoint @ A @ B )
| ~ ( member @ C @ A )
| ~ ( member @ C @ B ) ),
inference(cnf,[status(esa)],[135]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( power_class @ B ) )
<=> ( ( member @ A @ universal_class )
& ( subclass @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_defn) ).
thf(103,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)],[16]) ).
thf(104,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)],[103]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( subclass @ A @ B ) ),
inference(cnf,[status(esa)],[104]) ).
thf(166,plain,
inductive @ sk5,
inference(cnf,[status(esa)],[164]) ).
thf(8568,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ A )
| ( inductive @ null_class )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[129,166]) ).
thf(8569,plain,
( ( member @ ( sk3 @ sk5 ) @ sk5 )
| ( inductive @ null_class ) ),
inference(pattern_uni,[status(thm)],[8568:[bind(A,$thf( sk5 ))]]) ).
thf(11405,plain,
! [A: $i] :
( ( inductive @ null_class )
| ( ( member @ ( sk3 @ sk5 ) @ sk5 )
!= ( member @ A @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[8569,170]) ).
thf(11496,plain,
! [A: $i] :
( ( inductive @ null_class )
| ( ( sk3 @ sk5 )
!= A )
| ( sk5 != null_class ) ),
inference(simp,[status(thm)],[11405]) ).
thf(11519,plain,
( ( inductive @ null_class )
| ( sk5 != null_class ) ),
inference(simp,[status(thm)],[11496]) ).
thf(37,axiom,
! [A: $i] :
( ( inductive @ A )
<=> ( ( member @ null_class @ A )
& ( subclass @ ( image @ successor_relation @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive_defn) ).
thf(207,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)],[37]) ).
thf(208,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)],[207]) ).
thf(210,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
inference(cnf,[status(esa)],[208]) ).
thf(35129,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ B @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[210,170]) ).
thf(35130,plain,
~ ( inductive @ null_class ),
inference(pattern_uni,[status(thm)],[35129:[bind(A,$thf( null_class )),bind(B,$thf( null_class ))]]) ).
thf(35364,plain,
( $false
| ( sk5 != null_class ) ),
inference(rewrite,[status(thm)],[11519,35130]) ).
thf(35365,plain,
sk5 != null_class,
inference(simp,[status(thm)],[35364]) ).
thf(35395,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B != null_class )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[59,35365]) ).
thf(35396,plain,
! [A: $i] :
( ~ ( subclass @ sk5 @ A )
| ~ ( subclass @ A @ sk5 )
| ( A != null_class ) ),
inference(pattern_uni,[status(thm)],[35395:[bind(A,$thf( sk5 ))]]) ).
thf(35401,plain,
( ~ ( subclass @ sk5 @ null_class )
| ~ ( subclass @ null_class @ sk5 ) ),
inference(simp,[status(thm)],[35396]) ).
thf(47361,plain,
( ~ ( subclass @ sk5 @ null_class )
| ~ $true ),
inference(rewrite,[status(thm)],[35401,33729]) ).
thf(47362,plain,
~ ( subclass @ sk5 @ null_class ),
inference(simp,[status(thm)],[47361]) ).
thf(47417,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ sk5 @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[107,47362]) ).
thf(47418,plain,
~ ( member @ sk5 @ ( power_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[47417:[bind(A,$thf( sk5 )),bind(B,$thf( null_class ))]]) ).
thf(48578,plain,
( ( member @ ( sk3 @ sk1 ) @ sk1 )
!= ( member @ sk5 @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[8216,47418]) ).
thf(48604,plain,
( ( ( sk3 @ sk1 )
!= sk5 )
| ( ( power_class @ null_class )
!= sk1 ) ),
inference(simp,[status(thm)],[48578]) ).
thf(45,axiom,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( sum_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class) ).
thf(253,plain,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( sum_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(254,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
inference(cnf,[status(esa)],[253]) ).
thf(71451,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ sk5 @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[167,254]) ).
thf(71452,plain,
member @ ( sum_class @ sk5 ) @ universal_class,
inference(pattern_uni,[status(thm)],[71451:[bind(A,$thf( sk5 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( power_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class) ).
thf(195,plain,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( power_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(196,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
inference(cnf,[status(esa)],[195]) ).
thf(71840,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ sk5 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71452,196]) ).
thf(71841,plain,
member @ ( power_class @ ( sum_class @ sk5 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71840:[bind(A,$thf( sum_class @ sk5 ))]]) ).
thf(9,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation) ).
thf(80,plain,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34095,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk1 @ null_class ) ),
inference(paramod_ordered,[status(thm)],[80,34003]) ).
thf(34117,plain,
( ( sk1 != element_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[34095]) ).
thf(17,axiom,
! [A: $i] :
( ( singleton @ A )
= ( unordered_pair @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
thf(109,plain,
! [A: $i] :
( ( singleton @ A )
= ( unordered_pair @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(110,plain,
! [A: $i] :
( ( singleton @ A )
= ( unordered_pair @ A @ A ) ),
inference(cnf,[status(esa)],[109]) ).
thf(111,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',rotate_defn) ).
thf(147,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)],[24]) ).
thf(148,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 ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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(miniscope,[status(thm)],[147]) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A ) ),
inference(cnf,[status(esa)],[148]) ).
thf(14820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ C ) ) @ ( unordered_pair @ ( ordered_pair @ B @ C ) @ ( singleton @ D ) ) ) @ ( rotate @ A ) )
| ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ C @ D ) ) @ ( unordered_pair @ ( ordered_pair @ C @ D ) @ ( singleton @ B ) ) ) @ A ) ),
inference(rewrite,[status(thm)],[151,252]) ).
thf(14826,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ C ) ) @ ( unordered_pair @ ( ordered_pair @ B @ C ) @ ( singleton @ D ) ) ) @ ( rotate @ A ) )
| ( ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ C @ D ) ) @ ( unordered_pair @ ( ordered_pair @ C @ D ) @ ( singleton @ B ) ) ) @ A )
!= ( member @ E @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[14820,170]) ).
thf(14827,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ C @ A ) ) @ ( unordered_pair @ ( ordered_pair @ C @ A ) @ ( singleton @ B ) ) ) @ ( rotate @ null_class ) ),
inference(pattern_uni,[status(thm)],[14826:[bind(A,$thf( null_class )),bind(B,$thf( O )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( unordered_pair @ ( singleton @ ( ordered_pair @ M @ N ) ) @ ( unordered_pair @ ( ordered_pair @ M @ N ) @ ( singleton @ O ) ) ))]]) ).
thf(15232,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ C @ A ) ) @ ( unordered_pair @ ( ordered_pair @ C @ A ) @ ( singleton @ B ) ) ) @ ( rotate @ null_class ) ),
inference(simp,[status(thm)],[14827]) ).
thf(19162,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ C ) @ ( unordered_pair @ C @ ( singleton @ A ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ C ) @ ( unordered_pair @ C @ ( singleton @ A ) ) ) @ ( singleton @ B ) ) ) @ ( rotate @ null_class ) ),
inference(rewrite,[status(thm)],[15232,252]) ).
thf(19385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ D ) @ ( unordered_pair @ D @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ D ) @ ( singleton @ A ) ) @ ( singleton @ C ) ) ) @ ( rotate @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ D @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,19162]) ).
thf(19386,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( unordered_pair @ ( singleton @ B ) @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( rotate @ null_class ) ),
inference(pattern_uni,[status(thm)],[19385:[bind(A,$thf( singleton @ E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( singleton @ E ))]]) ).
thf(19504,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( unordered_pair @ ( singleton @ B ) @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( rotate @ null_class ) ),
inference(simp,[status(thm)],[19386]) ).
thf(23887,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( rotate @ null_class ) ),
inference(rewrite,[status(thm)],[19504,111]) ).
thf(30408,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ sk1 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[698,196]) ).
thf(30409,plain,
member @ ( power_class @ ( sk3 @ sk1 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[30408:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(71504,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ sk1 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30409,254]) ).
thf(71505,plain,
member @ ( sum_class @ ( power_class @ ( sk3 @ sk1 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71504:[bind(A,$thf( power_class @ ( sk3 @ sk1 ) ))]]) ).
thf(30539,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ sk5 @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[167,196]) ).
thf(30540,plain,
member @ ( power_class @ sk5 ) @ universal_class,
inference(pattern_uni,[status(thm)],[30539:[bind(A,$thf( sk5 ))]]) ).
thf(30798,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ sk5 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30540,196]) ).
thf(30799,plain,
member @ ( power_class @ ( power_class @ sk5 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[30798:[bind(A,$thf( power_class @ sk5 ))]]) ).
thf(32273,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30799,196]) ).
thf(32274,plain,
member @ ( power_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[32273:[bind(A,$thf( power_class @ ( power_class @ sk5 ) ))]]) ).
thf(71493,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ sk5 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30540,254]) ).
thf(71494,plain,
member @ ( sum_class @ ( power_class @ sk5 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71493:[bind(A,$thf( power_class @ sk5 ))]]) ).
thf(73026,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71494,196]) ).
thf(73027,plain,
member @ ( power_class @ ( sum_class @ ( power_class @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[73026:[bind(A,$thf( sum_class @ ( power_class @ sk5 ) ))]]) ).
thf(800,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( inductive @ null_class )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[128,166]) ).
thf(801,plain,
( ( member @ ( sk3 @ sk5 ) @ universal_class )
| ( inductive @ null_class ) ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( sk5 ))]]) ).
thf(35368,plain,
( ( member @ ( sk3 @ sk5 ) @ universal_class )
| $false ),
inference(rewrite,[status(thm)],[801,35130]) ).
thf(35369,plain,
member @ ( sk3 @ sk5 ) @ universal_class,
inference(simp,[status(thm)],[35368]) ).
thf(36050,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ sk5 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[35369,196]) ).
thf(36051,plain,
member @ ( power_class @ ( sk3 @ sk5 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[36050:[bind(A,$thf( sk3 @ sk5 ))]]) ).
thf(38263,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk3 @ sk5 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36051,217]) ).
thf(38264,plain,
~ ( member @ ( power_class @ ( sk3 @ sk5 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38263:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk3 @ sk5 ) ))]]) ).
thf(48561,plain,
( ( member @ sk5 @ ( power_class @ null_class ) )
!= ( member @ sk5 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[167,47418]) ).
thf(48658,plain,
( ( sk5 != sk5 )
| ( ( power_class @ null_class )
!= universal_class ) ),
inference(simp,[status(thm)],[48561]) ).
thf(48670,plain,
( ( power_class @ null_class )
!= universal_class ),
inference(simp,[status(thm)],[48658]) ).
thf(28411,plain,
! [A: $i] :
( ( member @ sk5 @ ( successor @ universal_class ) )
!= ( member @ A @ null_class ) ),
inference(paramod_ordered,[status(thm)],[28255,170]) ).
thf(28555,plain,
! [A: $i] :
( ( sk5 != A )
| ( ( successor @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[28411]) ).
thf(28593,plain,
( ( successor @ universal_class )
!= null_class ),
inference(simp,[status(thm)],[28555]) ).
thf(28634,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ A )
| ( A
!= ( successor @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[129,28593]) ).
thf(28635,plain,
member @ ( sk3 @ ( successor @ universal_class ) ) @ ( successor @ universal_class ),
inference(pattern_uni,[status(thm)],[28634:[bind(A,$thf( successor @ universal_class ))]]) ).
thf(38450,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ ( successor @ universal_class ) ) @ ( successor @ universal_class ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28635,217]) ).
thf(38451,plain,
~ ( member @ ( sk3 @ ( successor @ universal_class ) ) @ ( complement @ ( successor @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[38450:[bind(A,$thf( successor @ universal_class )),bind(B,$thf( sk3 @ ( successor @ universal_class ) ))]]) ).
thf(43,axiom,
! [A: $i] :
( ( member @ A @ identity_relation )
<=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( A
= ( ordered_pair @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
thf(242,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(243,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)],[242]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ( A
!= ( ordered_pair @ B @ B ) )
| ( member @ A @ identity_relation ) ),
inference(cnf,[status(esa)],[243]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( A
!= ( ordered_pair @ B @ B ) )
| ~ ( member @ B @ universal_class )
| ( member @ A @ identity_relation ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(248,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ A ) @ identity_relation ) ),
inference(simp,[status(thm)],[247]) ).
thf(66742,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ A ) ) ) @ identity_relation ) ),
inference(rewrite,[status(thm)],[248,252]) ).
thf(71241,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[36051,254]) ).
thf(71242,plain,
member @ ( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71241:[bind(A,$thf( power_class @ ( sk3 @ sk5 ) ))]]) ).
thf(77177,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71242,196]) ).
thf(77178,plain,
member @ ( power_class @ ( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[77177:[bind(A,$thf( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ))]]) ).
thf(255,plain,
! [A: $i] :
( ( member @ sk5 @ universal_class )
!= ( member @ A @ null_class ) ),
inference(paramod_ordered,[status(thm)],[167,170]) ).
thf(256,plain,
! [A: $i] :
( ( sk5 != A )
| ( universal_class != null_class ) ),
inference(simp,[status(thm)],[255]) ).
thf(257,plain,
universal_class != null_class,
inference(simp,[status(thm)],[256]) ).
thf(695,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( A != universal_class ) ),
inference(paramod_ordered,[status(thm)],[128,257]) ).
thf(696,plain,
member @ ( sk3 @ universal_class ) @ universal_class,
inference(pattern_uni,[status(thm)],[695:[bind(A,$thf( universal_class ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( sum_class @ B ) )
<=> ? [C: $i] :
( ( member @ A @ C )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_defn) ).
thf(89,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)],[14]) ).
thf(90,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)],[89]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( member @ ( sk2 @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[90]) ).
thf(2210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ B @ A ) @ B )
!= ( member @ C @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[93,170]) ).
thf(2211,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[2210:[bind(A,$thf( E )),bind(B,$thf( null_class )),bind(C,$thf( sk2 @ null_class @ E ))]]) ).
thf(2284,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ null_class ) ),
inference(simp,[status(thm)],[2211]) ).
thf(2296,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ null_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,2284]) ).
thf(2297,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ null_class ) ) ),
inference(pattern_uni,[status(thm)],[2296:[bind(A,$thf( E )),bind(B,$thf( sum_class @ null_class )),bind(C,$thf( sk2 @ ( sum_class @ null_class ) @ E ))]]) ).
thf(2350,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ null_class ) ) ),
inference(simp,[status(thm)],[2297]) ).
thf(2502,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,2350]) ).
thf(2503,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ),
inference(pattern_uni,[status(thm)],[2502:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ null_class ) )),bind(C,$thf( sk2 @ ( sum_class @ ( sum_class @ null_class ) ) @ E ))]]) ).
thf(2552,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ),
inference(simp,[status(thm)],[2503]) ).
thf(2665,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,2552]) ).
thf(2666,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2665:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )),bind(C,$thf( sk2 @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) @ E ))]]) ).
thf(2741,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(simp,[status(thm)],[2666]) ).
thf(2997,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,2741]) ).
thf(2998,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2997:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )),bind(C,$thf( sk2 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) @ E ))]]) ).
thf(3088,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(simp,[status(thm)],[2998]) ).
thf(3345,plain,
! [A: $i] :
( ( member @ ( sk3 @ universal_class ) @ universal_class )
!= ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[696,3088]) ).
thf(3349,plain,
! [A: $i] :
( ( ( sk3 @ universal_class )
!= A )
| ( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
!= universal_class ) ),
inference(simp,[status(thm)],[3345]) ).
thf(3371,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
!= universal_class ),
inference(simp,[status(thm)],[3349]) ).
thf(8719,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk3 @ A ) @ A )
!= ( member @ B @ ( sum_class @ null_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[129,2284]) ).
thf(8720,plain,
( ( sum_class @ null_class )
= null_class ),
inference(pattern_uni,[status(thm)],[8719:[bind(A,$thf( sum_class @ null_class )),bind(B,$thf( sk3 @ ( sum_class @ null_class ) ))]]) ).
thf(9576,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[3371,8720]) ).
thf(8249,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk3 @ A ) @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[129,2552]) ).
thf(8250,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
= null_class ),
inference(pattern_uni,[status(thm)],[8249:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )),bind(B,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ))]]) ).
thf(9804,plain,
( ( sum_class @ ( sum_class @ null_class ) )
= null_class ),
inference(rewrite,[status(thm)],[8250,8720]) ).
thf(10864,plain,
( ( sum_class @ ( sum_class @ null_class ) )
!= universal_class ),
inference(rewrite,[status(thm)],[9576,9804]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',flip_defn) ).
thf(173,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)],[30]) ).
thf(174,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 ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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(miniscope,[status(thm)],[173]) ).
thf(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ),
inference(cnf,[status(esa)],[174]) ).
thf(21890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ A @ B ) ) @ ( unordered_pair @ ( ordered_pair @ A @ B ) @ ( singleton @ C ) ) ) @ ( flip @ D ) )
| ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ A ) ) @ ( unordered_pair @ ( ordered_pair @ B @ A ) @ ( singleton @ C ) ) ) @ D ) ),
inference(rewrite,[status(thm)],[177,252]) ).
thf(21925,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ A @ B ) ) @ ( unordered_pair @ ( ordered_pair @ A @ B ) @ ( singleton @ C ) ) ) @ ( flip @ D ) )
| ( ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ A ) ) @ ( unordered_pair @ ( ordered_pair @ B @ A ) @ ( singleton @ C ) ) ) @ D )
!= ( member @ E @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[21890,170]) ).
thf(21926,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ A ) ) @ ( unordered_pair @ ( ordered_pair @ B @ A ) @ ( singleton @ C ) ) ) @ ( flip @ null_class ) ),
inference(pattern_uni,[status(thm)],[21925:[bind(A,$thf( N )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( null_class )),bind(E,$thf( unordered_pair @ ( singleton @ ( ordered_pair @ M @ N ) ) @ ( unordered_pair @ ( ordered_pair @ M @ N ) @ ( singleton @ O ) ) ))]]) ).
thf(22355,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ A ) ) @ ( unordered_pair @ ( ordered_pair @ B @ A ) @ ( singleton @ C ) ) ) @ ( flip @ null_class ) ),
inference(simp,[status(thm)],[21926]) ).
thf(22421,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ ( singleton @ A ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ ( singleton @ A ) ) ) @ ( singleton @ C ) ) ) @ ( flip @ null_class ) ),
inference(rewrite,[status(thm)],[22355,252]) ).
thf(22645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ C ) @ ( unordered_pair @ C @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ C ) @ ( singleton @ A ) ) @ ( singleton @ D ) ) ) @ ( flip @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ C @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,22421]) ).
thf(22646,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( unordered_pair @ ( singleton @ B ) @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( flip @ null_class ) ),
inference(pattern_uni,[status(thm)],[22645:[bind(A,$thf( singleton @ E )),bind(B,$thf( E )),bind(C,$thf( singleton @ E ))]]) ).
thf(22741,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( unordered_pair @ ( singleton @ B ) @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( flip @ null_class ) ),
inference(simp,[status(thm)],[22646]) ).
thf(25866,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( flip @ null_class ) ),
inference(rewrite,[status(thm)],[22741,111]) ).
thf(26087,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ C ) ) @ ( singleton @ ( singleton @ C ) ) ) ) @ ( singleton @ A ) ) @ ( flip @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ C ) ) ) @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,25866]) ).
thf(26088,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ A ) ) @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( flip @ null_class ) ),
inference(pattern_uni,[status(thm)],[26087:[bind(A,$thf( singleton @ ( singleton @ ( singleton @ H ) ) )),bind(B,$thf( singleton @ ( singleton @ H ) )),bind(C,$thf( H ))]]) ).
thf(26223,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ A ) ) @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( flip @ null_class ) ),
inference(simp,[status(thm)],[26088]) ).
thf(26483,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( flip @ null_class ) ),
inference(rewrite,[status(thm)],[26223,111]) ).
thf(30589,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ universal_class ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[696,196]) ).
thf(30590,plain,
member @ ( power_class @ ( sk3 @ universal_class ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[30589:[bind(A,$thf( sk3 @ universal_class ))]]) ).
thf(71254,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30590,254]) ).
thf(71255,plain,
member @ ( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71254:[bind(A,$thf( power_class @ ( sk3 @ universal_class ) ))]]) ).
thf(77626,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71255,196]) ).
thf(77627,plain,
member @ ( power_class @ ( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[77626:[bind(A,$thf( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ))]]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',compose_defn2) ).
thf(112,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)],[18]) ).
thf(113,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 ) ) ) ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ C @ universal_class )
& ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) ) )
=> ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) ) ) ),
inference(miniscope,[status(thm)],[112]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ universal_class )
| ~ ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) )
| ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ universal_class )
| ~ ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) )
| ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_defn) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
inference(cnf,[status(esa)],[77]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(1265,plain,
! [B: $i,A: $i] :
( ( image @ B @ A )
= ( domain_of @ ( inverse @ ( restrict @ B @ A @ universal_class ) ) ) ),
inference(rewrite,[status(thm)],[79,88]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( restrict @ B @ A @ C )
= ( intersection @ B @ ( cross_product @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_defn) ).
thf(239,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)],[42]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( restrict @ B @ A @ C )
= ( intersection @ B @ ( cross_product @ A @ C ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( restrict @ B @ A @ C )
= ( intersection @ B @ ( cross_product @ A @ C ) ) ),
inference(lifteq,[status(thm)],[240]) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ( image @ B @ A )
= ( domain_of @ ( inverse @ ( intersection @ B @ ( cross_product @ A @ universal_class ) ) ) ) ),
inference(rewrite,[status(thm)],[1265,241]) ).
thf(5708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ universal_class )
| ~ ( member @ D @ ( domain_of @ ( inverse @ ( intersection @ B @ ( cross_product @ ( image @ A @ ( singleton @ C ) ) @ universal_class ) ) ) ) )
| ( member @ ( unordered_pair @ ( singleton @ C ) @ ( unordered_pair @ C @ ( singleton @ D ) ) ) @ ( compose @ B @ A ) ) ),
inference(rewrite,[status(thm)],[117,1553,252]) ).
thf(35183,plain,
! [A: $i] :
( ( member @ null_class @ A )
| ( ( inductive @ sk5 )
!= ( inductive @ A ) ) ),
inference(paramod_ordered,[status(thm)],[166,210]) ).
thf(35184,plain,
member @ null_class @ sk5,
inference(pattern_uni,[status(thm)],[35183:[bind(A,$thf( sk5 ))]]) ).
thf(38294,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ null_class @ sk5 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35184,217]) ).
thf(38295,plain,
~ ( member @ null_class @ ( complement @ sk5 ) ),
inference(pattern_uni,[status(thm)],[38294:[bind(A,$thf( sk5 )),bind(B,$thf( null_class ))]]) ).
thf(38643,plain,
( ( member @ null_class @ ( complement @ sk5 ) )
!= ( member @ null_class @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[35184,38295]) ).
thf(38783,plain,
( ( null_class != null_class )
| ( ( complement @ sk5 )
!= sk5 ) ),
inference(simp,[status(thm)],[38643]) ).
thf(38812,plain,
( ( complement @ sk5 )
!= sk5 ),
inference(simp,[status(thm)],[38783]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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(cnf,[status(esa)],[148]) ).
thf(152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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(simp,[status(thm)],[149]) ).
thf(15632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ C ) ) @ ( unordered_pair @ ( ordered_pair @ B @ C ) @ ( singleton @ D ) ) ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ C @ D ) ) @ ( unordered_pair @ ( ordered_pair @ C @ D ) @ ( singleton @ B ) ) ) @ A )
| ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ C ) ) @ ( unordered_pair @ ( ordered_pair @ B @ C ) @ ( singleton @ D ) ) ) @ ( rotate @ A ) ) ),
inference(rewrite,[status(thm)],[152,252]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[186]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(29603,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( union @ A @ B ) )
| ( ( member @ ( sk3 @ sk1 ) @ sk1 )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8216,191]) ).
thf(29604,plain,
! [A: $i] : ( member @ ( sk3 @ sk1 ) @ ( union @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[29603:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 @ sk1 ))]]) ).
thf(3294,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,3088]) ).
thf(3295,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3294:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )),bind(C,$thf( sk2 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) @ E ))]]) ).
thf(3381,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(simp,[status(thm)],[3295]) ).
thf(3616,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,3381]) ).
thf(3617,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3616:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) )),bind(C,$thf( sk2 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) @ E ))]]) ).
thf(3707,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)],[3617]) ).
thf(4384,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ universal_class )
!= ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[698,3707]) ).
thf(4456,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= A )
| ( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )
!= universal_class ) ),
inference(simp,[status(thm)],[4384]) ).
thf(4488,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )
!= universal_class ),
inference(simp,[status(thm)],[4456]) ).
thf(9597,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[4488,8720]) ).
thf(8185,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk3 @ A ) @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[129,3088]) ).
thf(8186,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
= null_class ),
inference(pattern_uni,[status(thm)],[8185:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )),bind(B,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ))]]) ).
thf(11317,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
= null_class ),
inference(rewrite,[status(thm)],[8186,9804]) ).
thf(11684,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[9597,11317]) ).
thf(38721,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ null_class @ ( complement @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[210,38295]) ).
thf(38722,plain,
~ ( inductive @ ( complement @ sk5 ) ),
inference(pattern_uni,[status(thm)],[38721:[bind(A,$thf( complement @ sk5 ))]]) ).
thf(4387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ 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)],[93,3707]) ).
thf(4388,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4387:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )),bind(C,$thf( sk2 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) @ E ))]]) ).
thf(4484,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)],[4388]) ).
thf(9600,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)],[4484,8720]) ).
thf(5306,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ 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)],[93,4484]) ).
thf(5307,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[5306:[bind(A,$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( sk2 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) @ E ))]]) ).
thf(5442,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)],[5307]) ).
thf(8829,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk3 @ A ) @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[129,5442]) ).
thf(8830,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )
= null_class ),
inference(pattern_uni,[status(thm)],[8829:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) )),bind(B,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ))]]) ).
thf(8566,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk3 @ A ) @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[129,3707]) ).
thf(8567,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )
= null_class ),
inference(pattern_uni,[status(thm)],[8566:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) )),bind(B,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ))]]) ).
thf(11755,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )
= null_class ),
inference(rewrite,[status(thm)],[8567,11317]) ).
thf(13296,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
= null_class ),
inference(rewrite,[status(thm)],[8830,11755]) ).
thf(13970,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ null_class ) ) ),
inference(rewrite,[status(thm)],[9600,13296]) ).
thf(27924,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( union @ A @ B ) )
| ( ( member @ ( sk3 @ sk1 ) @ sk1 )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8216,190]) ).
thf(27925,plain,
! [A: $i] : ( member @ ( sk3 @ sk1 ) @ ( union @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[27924:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 @ sk1 ))]]) ).
thf(28038,plain,
! [A: $i] : ( member @ ( sk3 @ sk1 ) @ ( union @ sk1 @ A ) ),
inference(simp,[status(thm)],[27925]) ).
thf(29051,plain,
! [B: $i,A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( successor @ A ) )
| ( ( union @ A @ ( singleton @ A ) )
!= ( union @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[199,28038]) ).
thf(29052,plain,
member @ ( sk3 @ sk1 ) @ ( successor @ sk1 ),
inference(pattern_uni,[status(thm)],[29051:[bind(A,$thf( sk1 )),bind(B,$thf( singleton @ sk1 ))]]) ).
thf(38425,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ sk1 ) @ ( successor @ sk1 ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29052,217]) ).
thf(38426,plain,
~ ( member @ ( sk3 @ sk1 ) @ ( complement @ ( successor @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[38425:[bind(A,$thf( successor @ sk1 )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(29216,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( successor @ sk1 ) )
!= ( member @ A @ null_class ) ),
inference(paramod_ordered,[status(thm)],[29052,170]) ).
thf(29374,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= A )
| ( ( successor @ sk1 )
!= null_class ) ),
inference(simp,[status(thm)],[29216]) ).
thf(29433,plain,
( ( successor @ sk1 )
!= null_class ),
inference(simp,[status(thm)],[29374]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B != null_class )
| ( A != universal_class ) ),
inference(paramod_ordered,[status(thm)],[59,257]) ).
thf(419,plain,
! [A: $i] :
( ~ ( subclass @ universal_class @ A )
| ~ ( subclass @ A @ universal_class )
| ( A != null_class ) ),
inference(pattern_uni,[status(thm)],[418:[bind(A,$thf( universal_class ))]]) ).
thf(422,plain,
( ~ ( subclass @ universal_class @ null_class )
| ~ ( subclass @ null_class @ universal_class ) ),
inference(simp,[status(thm)],[419]) ).
thf(70,plain,
! [A: $i] : ( subclass @ A @ universal_class ),
inference(cnf,[status(esa)],[69]) ).
thf(1333,plain,
( ~ ( subclass @ universal_class @ null_class )
| ~ $true ),
inference(rewrite,[status(thm)],[422,70]) ).
thf(1334,plain,
~ ( subclass @ universal_class @ null_class ),
inference(simp,[status(thm)],[1333]) ).
thf(1355,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ null_class ) ),
inference(paramod_ordered,[status(thm)],[80,1334]) ).
thf(1359,plain,
( ( element_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[1355]) ).
thf(38409,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ sk1 ) @ sk1 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8216,217]) ).
thf(38410,plain,
~ ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) ),
inference(pattern_uni,[status(thm)],[38409:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(95900,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ universal_class @ A ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[28120,38410]) ).
thf(96093,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( union @ universal_class @ A )
!= ( complement @ sk1 ) ) ),
inference(simp,[status(thm)],[95900]) ).
thf(96270,plain,
! [A: $i] :
( ( union @ universal_class @ A )
!= ( complement @ sk1 ) ),
inference(simp,[status(thm)],[96093]) ).
thf(38403,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ sk5 @ ( successor @ universal_class ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28255,217]) ).
thf(38404,plain,
~ ( member @ sk5 @ ( complement @ ( successor @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[38403:[bind(A,$thf( successor @ universal_class )),bind(B,$thf( sk5 ))]]) ).
thf(44072,plain,
( ( member @ sk5 @ ( complement @ ( successor @ universal_class ) ) )
!= ( member @ sk5 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[167,38404]) ).
thf(44117,plain,
( ( sk5 != sk5 )
| ( ( complement @ ( successor @ universal_class ) )
!= universal_class ) ),
inference(simp,[status(thm)],[44072]) ).
thf(44179,plain,
( ( complement @ ( successor @ universal_class ) )
!= universal_class ),
inference(simp,[status(thm)],[44117]) ).
thf(28638,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( A
!= ( successor @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[128,28593]) ).
thf(28639,plain,
member @ ( sk3 @ ( successor @ universal_class ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[28638:[bind(A,$thf( successor @ universal_class ))]]) ).
thf(30536,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ ( successor @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[28639,196]) ).
thf(30537,plain,
member @ ( power_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[30536:[bind(A,$thf( sk3 @ ( successor @ universal_class ) ))]]) ).
thf(38394,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30537,217]) ).
thf(38395,plain,
~ ( member @ ( power_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38394:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk3 @ ( successor @ universal_class ) ) ))]]) ).
thf(11,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn1) ).
thf(83,plain,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1357,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ null_class ) ),
inference(paramod_ordered,[status(thm)],[83,1334]) ).
thf(1366,plain,
( ( successor_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[1357]) ).
thf(39177,plain,
( ( member @ ( sk3 @ sk1 ) @ ( complement @ universal_class ) )
!= ( member @ ( sk3 @ sk1 ) @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[8216,38246]) ).
thf(39254,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( complement @ universal_class )
!= sk1 ) ),
inference(simp,[status(thm)],[39177]) ).
thf(39276,plain,
( ( complement @ universal_class )
!= sk1 ),
inference(simp,[status(thm)],[39254]) ).
thf(31028,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ sk1 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30409,196]) ).
thf(31029,plain,
member @ ( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[31028:[bind(A,$thf( power_class @ ( sk3 @ sk1 ) ))]]) ).
thf(96015,plain,
! [B: $i,A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( successor @ A ) )
| ( ( union @ A @ ( singleton @ A ) )
!= ( union @ universal_class @ B ) ) ),
inference(paramod_ordered,[status(thm)],[199,28120]) ).
thf(96016,plain,
member @ ( sk3 @ sk1 ) @ ( successor @ universal_class ),
inference(pattern_uni,[status(thm)],[96015:[bind(A,$thf( universal_class )),bind(B,$thf( singleton @ universal_class ))]]) ).
thf(96357,plain,
( ( member @ ( sk3 @ sk1 ) @ ( successor @ universal_class ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ ( successor @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[96016,38426]) ).
thf(96687,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( successor @ universal_class )
!= ( complement @ ( successor @ sk1 ) ) ) ),
inference(simp,[status(thm)],[96357]) ).
thf(96797,plain,
( ( successor @ universal_class )
!= ( complement @ ( successor @ sk1 ) ) ),
inference(simp,[status(thm)],[96687]) ).
thf(75855,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sum_class @ sk5 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71841,217]) ).
thf(75856,plain,
~ ( member @ ( power_class @ ( sum_class @ sk5 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[75855:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sum_class @ sk5 ) ))]]) ).
thf(108835,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ A @ sk1 ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[29604,38246]) ).
thf(109035,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( union @ A @ sk1 )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[108835]) ).
thf(109274,plain,
! [A: $i] :
( ( union @ A @ sk1 )
!= ( complement @ universal_class ) ),
inference(simp,[status(thm)],[109035]) ).
thf(150,plain,
! [D: $i,C: $i,B: $i,A: $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 ) ) ),
inference(cnf,[status(esa)],[148]) ).
thf(14141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ C ) ) @ ( unordered_pair @ ( ordered_pair @ B @ C ) @ ( singleton @ D ) ) ) @ ( rotate @ A ) )
| ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ C ) ) @ ( unordered_pair @ ( ordered_pair @ B @ C ) @ ( singleton @ D ) ) ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ),
inference(rewrite,[status(thm)],[150,252]) ).
thf(44077,plain,
( ( member @ sk5 @ ( complement @ ( successor @ universal_class ) ) )
!= ( member @ sk5 @ ( successor @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[28255,38404]) ).
thf(44144,plain,
( ( sk5 != sk5 )
| ( ( complement @ ( successor @ universal_class ) )
!= ( successor @ universal_class ) ) ),
inference(simp,[status(thm)],[44077]) ).
thf(44187,plain,
( ( complement @ ( successor @ universal_class ) )
!= ( successor @ universal_class ) ),
inference(simp,[status(thm)],[44144]) ).
thf(6060,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ 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)],[93,5442]) ).
thf(6061,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[6060:[bind(A,$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( sk2 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) @ E ))]]) ).
thf(6174,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)],[6061]) ).
thf(6749,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( 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)],[93,6174]) ).
thf(6750,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[6749:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) )),bind(C,$thf( sk2 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) @ E ))]]) ).
thf(6894,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 @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[6750]) ).
thf(8169,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( ( member @ ( sk3 @ A ) @ A )
!= ( member @ B @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[129,6894]) ).
thf(8170,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) )
= null_class ),
inference(pattern_uni,[status(thm)],[8169:[bind(A,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) )),bind(B,$thf( sk3 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ))]]) ).
thf(15250,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) )
= null_class ),
inference(rewrite,[status(thm)],[8170,13296]) ).
thf(31328,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30590,196]) ).
thf(31329,plain,
member @ ( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[31328:[bind(A,$thf( power_class @ ( sk3 @ universal_class ) ))]]) ).
thf(34895,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[31329,196]) ).
thf(34896,plain,
member @ ( power_class @ ( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[34895:[bind(A,$thf( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ))]]) ).
thf(77159,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71242,217]) ).
thf(77160,plain,
~ ( member @ ( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[77159:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ))]]) ).
thf(71529,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ universal_class ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[696,254]) ).
thf(71530,plain,
member @ ( sum_class @ ( sk3 @ universal_class ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71529:[bind(A,$thf( sk3 @ universal_class ))]]) ).
thf(73717,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sk3 @ universal_class ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71530,217]) ).
thf(73718,plain,
~ ( member @ ( sum_class @ ( sk3 @ universal_class ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[73717:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sk3 @ universal_class ) ))]]) ).
thf(47400,plain,
( ( subclass @ sk7 @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk5 @ null_class ) ),
inference(paramod_ordered,[status(thm)],[1209,47362]) ).
thf(47431,plain,
( ( sk7 != sk5 )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[47400]) ).
thf(72023,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ sk5 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71452,254]) ).
thf(72024,plain,
member @ ( sum_class @ ( sum_class @ sk5 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[72023:[bind(A,$thf( sum_class @ sk5 ))]]) ).
thf(76507,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sum_class @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[72024,254]) ).
thf(76508,plain,
member @ ( sum_class @ ( sum_class @ ( sum_class @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[76507:[bind(A,$thf( sum_class @ ( sum_class @ sk5 ) ))]]) ).
thf(816,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( subclass @ element_relation @ null_class )
| ( A
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[128,80]) ).
thf(817,plain,
( ( member @ ( sk3 @ ( cross_product @ universal_class @ universal_class ) ) @ universal_class )
| ( subclass @ element_relation @ null_class ) ),
inference(pattern_uni,[status(thm)],[816:[bind(A,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(71455,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ ( successor @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[28639,254]) ).
thf(71456,plain,
member @ ( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71455:[bind(A,$thf( sk3 @ ( successor @ universal_class ) ))]]) ).
thf(81024,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71456,217]) ).
thf(81025,plain,
~ ( member @ ( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[81024:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ))]]) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( union @ A @ B ) )
| ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[186]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ~ ( member @ B @ sk1 ) ),
inference(cnf,[status(esa)],[46]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ~ ( member @ B @ sk1 ) ),
inference(simp,[status(thm)],[47]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ~ ( member @ B @ sk1 )
| ( ( member @ A @ sk1 )
!= ( member @ B @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[50]) ).
thf(264,plain,
! [A: $i] :
( ~ ( member @ A @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ~ ( member @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(277,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 )
| ( ( member @ sk5 @ universal_class )
!= ( member @ A @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[167,264]) ).
thf(280,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 )
| ( sk5 != A )
| ( ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 )
!= universal_class ) ),
inference(simp,[status(thm)],[277]) ).
thf(284,plain,
( ~ ( member @ sk5 @ sk1 )
| ( ( intersection @ ( complement @ ( singleton @ sk5 ) ) @ sk1 )
!= universal_class ) ),
inference(simp,[status(thm)],[280]) ).
thf(880,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A
!= ( sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,698]) ).
thf(881,plain,
( ( member @ ( sk3 @ ( sk3 @ sk1 ) ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[880:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
<=> ( ( member @ A @ universal_class )
& ( ( A = B )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(228,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)],[41]) ).
thf(176,plain,
! [D: $i,C: $i,B: $i,A: $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 ) ) ),
inference(cnf,[status(esa)],[174]) ).
thf(20276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ A @ B ) ) @ ( unordered_pair @ ( ordered_pair @ A @ B ) @ ( singleton @ C ) ) ) @ ( flip @ D ) )
| ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ A @ B ) ) @ ( unordered_pair @ ( ordered_pair @ A @ B ) @ ( singleton @ C ) ) ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ),
inference(rewrite,[status(thm)],[176,252]) ).
thf(40567,plain,
( ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) )
!= ( member @ null_class @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[35184,38410]) ).
thf(40710,plain,
( ( ( sk3 @ sk1 )
!= null_class )
| ( ( complement @ sk1 )
!= sk5 ) ),
inference(simp,[status(thm)],[40567]) ).
thf(108765,plain,
! [B: $i,A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ A @ sk1 ) )
!= ( member @ B @ null_class ) ),
inference(paramod_ordered,[status(thm)],[29604,170]) ).
thf(109057,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ sk1 )
!= B )
| ( ( union @ A @ sk1 )
!= null_class ) ),
inference(simp,[status(thm)],[108765]) ).
thf(109152,plain,
! [A: $i] :
( ( union @ A @ sk1 )
!= null_class ),
inference(simp,[status(thm)],[109057]) ).
thf(798,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( function @ null_class )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[128,221]) ).
thf(799,plain,
( ( member @ ( sk3 @ sk7 ) @ universal_class )
| ( function @ null_class ) ),
inference(pattern_uni,[status(thm)],[798:[bind(A,$thf( sk7 ))]]) ).
thf(30525,plain,
! [A: $i] :
( ( function @ null_class )
| ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[799,196]) ).
thf(30526,plain,
( ( function @ null_class )
| ( member @ ( power_class @ ( sk3 @ sk7 ) ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[30525:[bind(A,$thf( sk3 @ sk7 ))]]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( member @ B @ universal_class ) ),
inference(cnf,[status(esa)],[214]) ).
thf(38285,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ sk5 ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35369,217]) ).
thf(38286,plain,
~ ( member @ ( sk3 @ sk5 ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38285:[bind(A,$thf( universal_class )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(40161,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ ( sk3 @ sk5 ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[210,38286]) ).
thf(40227,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( sk3 @ sk5 )
!= null_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[40161]) ).
thf(40246,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( sk3 @ sk5 )
!= null_class ) ),
inference(simp,[status(thm)],[40227]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',cross_product_defn) ).
thf(141,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)],[23]) ).
thf(142,plain,
( ! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
=> ( ( member @ A @ C )
& ( member @ B @ D ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ A @ C )
& ( member @ B @ D ) )
=> ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[141]) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ D ) ),
inference(cnf,[status(esa)],[142]) ).
thf(13138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ ( cross_product @ C @ D ) )
| ( member @ B @ D ) ),
inference(rewrite,[status(thm)],[145,252]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ element_relation )
<=> ( ( member @ B @ universal_class )
& ( member @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation_defn) ).
thf(179,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)],[31]) ).
thf(127,plain,
! [A: $i] :
( ( A = null_class )
| ( disjoint @ ( sk3 @ A ) @ A ) ),
inference(cnf,[status(esa)],[124]) ).
thf(130,plain,
! [A: $i] :
( ( A = null_class )
| ( disjoint @ ( sk3 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[127]) ).
thf(28650,plain,
! [A: $i] :
( ( disjoint @ ( sk3 @ A ) @ A )
| ( A
!= ( successor @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[130,28593]) ).
thf(28651,plain,
disjoint @ ( sk3 @ ( successor @ universal_class ) ) @ ( successor @ universal_class ),
inference(pattern_uni,[status(thm)],[28650:[bind(A,$thf( successor @ universal_class ))]]) ).
thf(108841,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ A @ sk1 ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[29604,38410]) ).
thf(109128,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( union @ A @ sk1 )
!= ( complement @ sk1 ) ) ),
inference(simp,[status(thm)],[108841]) ).
thf(109186,plain,
! [A: $i] :
( ( union @ A @ sk1 )
!= ( complement @ sk1 ) ),
inference(simp,[status(thm)],[109128]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( member @ A @ universal_class ) ),
inference(cnf,[status(esa)],[104]) ).
thf(229,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)],[228]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( unordered_pair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
inference(cnf,[status(esa)],[229]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ~ ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[233]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
<=> ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(118,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)],[19]) ).
thf(119,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)],[118]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ A ) ),
inference(cnf,[status(esa)],[119]) ).
thf(71299,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ sk5 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[35369,254]) ).
thf(71300,plain,
member @ ( sum_class @ ( sk3 @ sk5 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71299:[bind(A,$thf( sk3 @ sk5 ))]]) ).
thf(12,axiom,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip) ).
thf(84,plain,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(73735,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71530,196]) ).
thf(73736,plain,
member @ ( power_class @ ( sum_class @ ( sk3 @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[73735:[bind(A,$thf( sum_class @ ( sk3 @ universal_class ) ))]]) ).
thf(35366,plain,
( ( member @ ( sk3 @ sk5 ) @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[8569,35130]) ).
thf(35367,plain,
member @ ( sk3 @ sk5 ) @ sk5,
inference(simp,[status(thm)],[35366]) ).
thf(71227,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[31029,254]) ).
thf(71228,plain,
member @ ( sum_class @ ( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71227:[bind(A,$thf( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ))]]) ).
thf(36710,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[36051,196]) ).
thf(36711,plain,
member @ ( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[36710:[bind(A,$thf( power_class @ ( sk3 @ sk5 ) ))]]) ).
thf(38313,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36711,217]) ).
thf(38314,plain,
~ ( member @ ( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38313:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ))]]) ).
thf(34071,plain,
! [B: $i,A: $i] :
( ( member @ ( sk6 @ B @ A ) @ A )
| ( ( subclass @ A @ B )
!= ( subclass @ sk1 @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[205,34003]) ).
thf(34072,plain,
member @ ( sk6 @ null_class @ sk1 ) @ sk1,
inference(pattern_uni,[status(thm)],[34071:[bind(A,$thf( sk1 )),bind(B,$thf( null_class ))]]) ).
thf(38291,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk6 @ null_class @ sk1 ) @ sk1 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34072,217]) ).
thf(38292,plain,
~ ( member @ ( sk6 @ null_class @ sk1 ) @ ( complement @ sk1 ) ),
inference(pattern_uni,[status(thm)],[38291:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 @ null_class @ sk1 ))]]) ).
thf(29830,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( A
!= ( successor @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,29433]) ).
thf(29831,plain,
member @ ( sk3 @ ( successor @ sk1 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[29830:[bind(A,$thf( successor @ sk1 ))]]) ).
thf(38415,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ ( successor @ sk1 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29831,217]) ).
thf(38416,plain,
~ ( member @ ( sk3 @ ( successor @ sk1 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38415:[bind(A,$thf( universal_class )),bind(B,$thf( sk3 @ ( successor @ sk1 ) ))]]) ).
thf(49227,plain,
( ( member @ ( sk3 @ sk1 ) @ ( complement @ ( successor @ sk1 ) ) )
!= ( member @ ( sk3 @ sk1 ) @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[8216,38426]) ).
thf(49313,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( complement @ ( successor @ sk1 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[49227]) ).
thf(49338,plain,
( ( complement @ ( successor @ sk1 ) )
!= sk1 ),
inference(simp,[status(thm)],[49313]) ).
thf(38422,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk3 @ sk1 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30409,217]) ).
thf(38423,plain,
~ ( member @ ( power_class @ ( sk3 @ sk1 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38422:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk3 @ sk1 ) ))]]) ).
thf(47420,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk5 @ null_class ) ),
inference(paramod_ordered,[status(thm)],[83,47362]) ).
thf(47436,plain,
( ( sk5 != successor_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[47420]) ).
thf(38251,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31029,217]) ).
thf(38252,plain,
~ ( member @ ( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38251:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ))]]) ).
thf(33490,plain,
! [B: $i,A: $i] :
( ( member @ ( sk6 @ B @ A ) @ A )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[205,1334]) ).
thf(33491,plain,
member @ ( sk6 @ null_class @ universal_class ) @ universal_class,
inference(pattern_uni,[status(thm)],[33490:[bind(A,$thf( universal_class )),bind(B,$thf( null_class ))]]) ).
thf(71378,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk6 @ null_class @ universal_class ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[33491,254]) ).
thf(71379,plain,
member @ ( sum_class @ ( sk6 @ null_class @ universal_class ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71378:[bind(A,$thf( sk6 @ null_class @ universal_class ))]]) ).
thf(80563,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk6 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71379,196]) ).
thf(80564,plain,
member @ ( power_class @ ( sum_class @ ( sk6 @ null_class @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[80563:[bind(A,$thf( sum_class @ ( sk6 @ null_class @ universal_class ) ))]]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
inference(cnf,[status(esa)],[54]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(61,plain,
! [A: $i] : ( subclass @ A @ A ),
inference(simp,[status(thm)],[60]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( function @ B ) )
=> ( member @ ( image @ B @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
thf(171,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)],[29]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( function @ B )
| ( member @ ( image @ B @ A ) @ universal_class ) ),
inference(cnf,[status(esa)],[171]) ).
thf(19678,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( function @ B )
| ( member @ ( domain_of @ ( inverse @ ( intersection @ B @ ( cross_product @ A @ universal_class ) ) ) ) @ universal_class ) ),
inference(rewrite,[status(thm)],[172,1553]) ).
thf(29462,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( union @ A @ B ) )
| ( ( member @ ( sk3 @ sk1 ) @ universal_class )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[698,191]) ).
thf(29463,plain,
! [A: $i] : ( member @ ( sk3 @ sk1 ) @ ( union @ A @ universal_class ) ),
inference(pattern_uni,[status(thm)],[29462:[bind(A,$thf( A )),bind(B,$thf( universal_class )),bind(C,$thf( sk3 @ sk1 ))]]) ).
thf(102915,plain,
! [B: $i,A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ A @ universal_class ) )
!= ( member @ B @ null_class ) ),
inference(paramod_ordered,[status(thm)],[29463,170]) ).
thf(103186,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ sk1 )
!= B )
| ( ( union @ A @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[102915]) ).
thf(103369,plain,
! [A: $i] :
( ( union @ A @ universal_class )
!= null_class ),
inference(simp,[status(thm)],[103186]) ).
thf(71212,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30799,254]) ).
thf(71213,plain,
member @ ( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71212:[bind(A,$thf( power_class @ ( power_class @ sk5 ) ))]]) ).
thf(76710,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71213,217]) ).
thf(76711,plain,
~ ( member @ ( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[76710:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ))]]) ).
thf(3923,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ( ( subclass @ A @ B )
!= ( subclass @ universal_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[107,1334]) ).
thf(3924,plain,
~ ( member @ universal_class @ ( power_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[3923:[bind(A,$thf( universal_class )),bind(B,$thf( null_class ))]]) ).
thf(9693,plain,
( ( member @ ( sk3 @ sk1 ) @ sk1 )
!= ( member @ universal_class @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[8216,3924]) ).
thf(9700,plain,
( ( ( sk3 @ sk1 )
!= universal_class )
| ( ( power_class @ null_class )
!= sk1 ) ),
inference(simp,[status(thm)],[9693]) ).
thf(245,plain,
! [A: $i] :
( ~ ( member @ A @ identity_relation )
| ( member @ ( sk8 @ A ) @ universal_class ) ),
inference(cnf,[status(esa)],[243]) ).
thf(64832,plain,
! [B: $i,A: $i] :
( ( A = null_class )
| ( member @ ( sk8 @ B ) @ universal_class )
| ( ( member @ ( sk3 @ A ) @ A )
!= ( member @ B @ identity_relation ) ) ),
inference(paramod_ordered,[status(thm)],[129,245]) ).
thf(64833,plain,
( ( identity_relation = null_class )
| ( member @ ( sk8 @ ( sk3 @ identity_relation ) ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[64832:[bind(A,$thf( identity_relation )),bind(B,$thf( sk3 @ identity_relation ))]]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk6 @ B @ A ) @ B )
| ( subclass @ A @ B ) ),
inference(cnf,[status(esa)],[201]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk6 @ B @ A ) @ B )
| ( subclass @ A @ B ) ),
inference(simp,[status(thm)],[203]) ).
thf(180,plain,
( ! [A: $i,B: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ element_relation )
=> ( ( member @ B @ universal_class )
& ( member @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( member @ B @ universal_class )
& ( member @ A @ B ) )
=> ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ) ),
inference(miniscope,[status(thm)],[179]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ element_relation )
| ( member @ B @ universal_class ) ),
inference(cnf,[status(esa)],[180]) ).
thf(24762,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ element_relation )
| ( member @ B @ universal_class ) ),
inference(rewrite,[status(thm)],[182,252]) ).
thf(49112,plain,
( ( member @ ( sk3 @ sk1 ) @ ( complement @ ( successor @ sk1 ) ) )
!= ( member @ ( sk3 @ sk1 ) @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[698,38426]) ).
thf(49299,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( complement @ ( successor @ sk1 ) )
!= universal_class ) ),
inference(simp,[status(thm)],[49112]) ).
thf(49334,plain,
( ( complement @ ( successor @ sk1 ) )
!= universal_class ),
inference(simp,[status(thm)],[49299]) ).
thf(29842,plain,
! [A: $i] :
( ( disjoint @ ( sk3 @ A ) @ A )
| ( A
!= ( successor @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[130,29433]) ).
thf(29843,plain,
disjoint @ ( sk3 @ ( successor @ sk1 ) ) @ ( successor @ sk1 ),
inference(pattern_uni,[status(thm)],[29842:[bind(A,$thf( successor @ sk1 ))]]) ).
thf(24105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ C ) ) @ ( singleton @ ( singleton @ C ) ) ) ) @ ( singleton @ A ) ) @ ( rotate @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ C ) ) ) @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,23887]) ).
thf(24106,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ A ) ) @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( rotate @ null_class ) ),
inference(pattern_uni,[status(thm)],[24105:[bind(A,$thf( singleton @ ( singleton @ ( singleton @ H ) ) )),bind(B,$thf( singleton @ ( singleton @ H ) )),bind(C,$thf( H ))]]) ).
thf(24166,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ A ) ) @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( rotate @ null_class ) ),
inference(simp,[status(thm)],[24106]) ).
thf(24249,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( rotate @ null_class ) ),
inference(rewrite,[status(thm)],[24166,111]) ).
thf(85,plain,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(cnf,[status(esa)],[84]) ).
thf(22643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ C ) @ ( singleton @ A ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ C ) @ ( unordered_pair @ C @ ( singleton @ B ) ) ) @ ( singleton @ D ) ) ) @ ( flip @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ C @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,22421]) ).
thf(22644,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( unordered_pair @ ( singleton @ B ) @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( flip @ null_class ) ),
inference(pattern_uni,[status(thm)],[22643:[bind(A,$thf( singleton @ E )),bind(B,$thf( E )),bind(C,$thf( singleton @ E ))]]) ).
thf(22740,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( unordered_pair @ ( singleton @ B ) @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( flip @ null_class ) ),
inference(simp,[status(thm)],[22644]) ).
thf(24957,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( flip @ null_class ) ),
inference(rewrite,[status(thm)],[22740,111]) ).
thf(25175,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ C ) ) ) ) @ ( unordered_pair @ ( singleton @ A ) @ ( singleton @ B ) ) ) @ ( flip @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ ( singleton @ ( singleton @ C ) ) @ ( singleton @ ( singleton @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,24957]) ).
thf(25176,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( flip @ null_class ) ),
inference(pattern_uni,[status(thm)],[25175:[bind(A,$thf( singleton @ ( singleton @ E ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(25257,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( flip @ null_class ) ),
inference(simp,[status(thm)],[25176]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ sk1 )
| ( ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
!= ( member @ A @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[50]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ sk1 )
| ( ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
!= ( member @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(792,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( subclass @ successor_relation @ null_class )
| ( A
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[128,83]) ).
thf(793,plain,
( ( member @ ( sk3 @ ( cross_product @ universal_class @ universal_class ) ) @ universal_class )
| ( subclass @ successor_relation @ null_class ) ),
inference(pattern_uni,[status(thm)],[792:[bind(A,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(81042,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71456,196]) ).
thf(81043,plain,
member @ ( power_class @ ( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[81042:[bind(A,$thf( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ))]]) ).
thf(73008,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( power_class @ sk5 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71494,217]) ).
thf(73009,plain,
~ ( member @ ( sum_class @ ( power_class @ sk5 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[73008:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( power_class @ sk5 ) ))]]) ).
thf(40647,plain,
( ( member @ ( sk3 @ sk1 ) @ ( successor @ sk1 ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[29052,38410]) ).
thf(40664,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( successor @ sk1 )
!= ( complement @ sk1 ) ) ),
inference(simp,[status(thm)],[40647]) ).
thf(40735,plain,
( ( successor @ sk1 )
!= ( complement @ sk1 ) ),
inference(simp,[status(thm)],[40664]) ).
thf(71215,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ sk1 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[698,254]) ).
thf(71216,plain,
member @ ( sum_class @ ( sk3 @ sk1 ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71215:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(72412,plain,
( ( member @ null_class @ universal_class )
| ( ( sum_class @ ( sk3 @ sk1 ) )
!= ( sum_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[8720,71216]) ).
thf(72468,plain,
( ( member @ null_class @ universal_class )
| ( ( sk3 @ sk1 )
!= null_class ) ),
inference(simp,[status(thm)],[72412]) ).
thf(76080,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sum_class @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71841,254]) ).
thf(76081,plain,
member @ ( sum_class @ ( power_class @ ( sum_class @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[76080:[bind(A,$thf( power_class @ ( sum_class @ sk5 ) ))]]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ~ ( member @ B @ sk1 )
| ( ( member @ sk5 @ universal_class )
!= ( member @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[167,50]) ).
thf(269,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ~ ( member @ B @ sk1 )
| ( sk5 != A )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[258]) ).
thf(275,plain,
! [A: $i] :
( ~ ( member @ A @ ( intersection @ ( complement @ ( singleton @ sk5 ) ) @ sk1 ) )
| ~ ( member @ A @ sk1 )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[269]) ).
thf(209,plain,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
inference(cnf,[status(esa)],[208]) ).
thf(212,plain,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
inference(simp,[status(thm)],[209]) ).
thf(36310,plain,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( domain_of @ ( inverse @ ( intersection @ successor_relation @ ( cross_product @ A @ universal_class ) ) ) ) @ A )
| ( inductive @ A ) ),
inference(rewrite,[status(thm)],[212,1553]) ).
thf(71498,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ ( successor @ sk1 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[29831,254]) ).
thf(71499,plain,
member @ ( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71498:[bind(A,$thf( sk3 @ ( successor @ sk1 ) ))]]) ).
thf(78304,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71499,254]) ).
thf(78305,plain,
member @ ( sum_class @ ( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[78304:[bind(A,$thf( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ))]]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( member @ B @ universal_class )
| ( ( first @ ( ordered_pair @ A @ B ) )
= A ) ),
inference(cnf,[status(esa)],[223]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( ( first @ ( ordered_pair @ A @ B ) )
= A )
| ~ ( member @ A @ universal_class )
| ~ ( member @ B @ universal_class ) ),
inference(lifteq,[status(thm)],[224]) ).
thf(44807,plain,
! [B: $i,A: $i] :
( ( ( first @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) )
= A )
| ~ ( member @ A @ universal_class )
| ~ ( member @ B @ universal_class ) ),
inference(rewrite,[status(thm)],[226,252]) ).
thf(49234,plain,
( ( member @ ( sk3 @ sk1 ) @ ( complement @ ( successor @ sk1 ) ) )
!= ( member @ ( sk3 @ sk1 ) @ ( successor @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[29052,38426]) ).
thf(49291,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( complement @ ( successor @ sk1 ) )
!= ( successor @ sk1 ) ) ),
inference(simp,[status(thm)],[49234]) ).
thf(49331,plain,
( ( complement @ ( successor @ sk1 ) )
!= ( successor @ sk1 ) ),
inference(simp,[status(thm)],[49291]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_defn) ).
thf(192,plain,
! [A: $i,B: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(30566,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ ( successor @ sk1 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[29831,196]) ).
thf(30567,plain,
member @ ( power_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[30566:[bind(A,$thf( sk3 @ ( successor @ sk1 ) ))]]) ).
thf(9980,plain,
! [A: $i] :
( ( disjoint @ ( sk3 @ A ) @ A )
| ( A != universal_class ) ),
inference(paramod_ordered,[status(thm)],[130,257]) ).
thf(9981,plain,
disjoint @ ( sk3 @ universal_class ) @ universal_class,
inference(pattern_uni,[status(thm)],[9980:[bind(A,$thf( universal_class ))]]) ).
thf(165,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ sk5 @ A ) ),
inference(cnf,[status(esa)],[164]) ).
thf(72827,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71300,254]) ).
thf(72828,plain,
member @ ( sum_class @ ( sum_class @ ( sk3 @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[72827:[bind(A,$thf( sum_class @ ( sk3 @ sk5 ) ))]]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( member @ A @ ( sk2 @ B @ A ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(77608,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71255,217]) ).
thf(77609,plain,
~ ( member @ ( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[77608:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ))]]) ).
thf(40651,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[210,38410]) ).
thf(40677,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( sk3 @ sk1 )
!= null_class )
| ( A
!= ( complement @ sk1 ) ) ),
inference(simp,[status(thm)],[40651]) ).
thf(40739,plain,
( ~ ( inductive @ ( complement @ sk1 ) )
| ( ( sk3 @ sk1 )
!= null_class ) ),
inference(simp,[status(thm)],[40677]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ sk1 )
| ( B != A )
| ( ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[262]) ).
thf(276,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ A @ sk1 )
| ( ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[271]) ).
thf(96811,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 )
| ( ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[276]) ).
thf(33768,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sk6 @ null_class @ universal_class ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[33491,196]) ).
thf(33769,plain,
member @ ( power_class @ ( sk6 @ null_class @ universal_class ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[33768:[bind(A,$thf( sk6 @ null_class @ universal_class ))]]) ).
thf(37522,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk6 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[33769,196]) ).
thf(37523,plain,
member @ ( power_class @ ( power_class @ ( sk6 @ null_class @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[37522:[bind(A,$thf( power_class @ ( sk6 @ null_class @ universal_class ) ))]]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(162,plain,
! [A: $i,B: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(163,plain,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
inference(cnf,[status(esa)],[162]) ).
thf(1011,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)],[111,163]) ).
thf(1012,plain,
! [A: $i] : ( member @ ( singleton @ A ) @ universal_class ),
inference(pattern_uni,[status(thm)],[1011:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(278,plain,
! [A: $i] :
( ~ ( member @ A @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ( ( member @ sk5 @ universal_class )
!= ( member @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[167,264]) ).
thf(281,plain,
! [A: $i] :
( ~ ( member @ A @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ( sk5 != A )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[278]) ).
thf(285,plain,
( ~ ( member @ sk5 @ ( intersection @ ( complement @ ( singleton @ sk5 ) ) @ sk1 ) )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[281]) ).
thf(19383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ D ) @ ( singleton @ A ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ D ) @ ( unordered_pair @ D @ ( singleton @ B ) ) ) @ ( singleton @ C ) ) ) @ ( rotate @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ D @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,19162]) ).
thf(19384,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( unordered_pair @ ( singleton @ B ) @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( rotate @ null_class ) ),
inference(pattern_uni,[status(thm)],[19383:[bind(A,$thf( singleton @ E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( singleton @ E ))]]) ).
thf(19503,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( unordered_pair @ ( singleton @ B ) @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( rotate @ null_class ) ),
inference(simp,[status(thm)],[19384]) ).
thf(20859,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( unordered_pair @ ( singleton @ ( singleton @ B ) ) @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( rotate @ null_class ) ),
inference(rewrite,[status(thm)],[19503,111]) ).
thf(21074,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ C ) ) ) ) @ ( unordered_pair @ ( singleton @ A ) @ ( singleton @ B ) ) ) @ ( rotate @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ ( singleton @ ( singleton @ C ) ) @ ( singleton @ ( singleton @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,20859]) ).
thf(21075,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( rotate @ null_class ) ),
inference(pattern_uni,[status(thm)],[21074:[bind(A,$thf( singleton @ ( singleton @ E ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(21150,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) ) @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ B ) ) ) @ ( singleton @ A ) ) ) @ ( rotate @ null_class ) ),
inference(simp,[status(thm)],[21075]) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ B @ D )
| ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) ),
inference(cnf,[status(esa)],[142]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ B @ D )
| ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(13468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ B @ D )
| ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ ( cross_product @ C @ D ) ) ),
inference(rewrite,[status(thm)],[146,252]) ).
thf(38412,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ sk5 ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30540,217]) ).
thf(38413,plain,
~ ( member @ ( power_class @ sk5 ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38412:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ sk5 ))]]) ).
thf(44363,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ ( power_class @ sk5 ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[210,38413]) ).
thf(44374,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( power_class @ sk5 )
!= null_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[44363]) ).
thf(44448,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( power_class @ sk5 )
!= null_class ) ),
inference(simp,[status(thm)],[44374]) ).
thf(8313,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ A )
| ( function @ null_class )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[129,221]) ).
thf(8314,plain,
( ( member @ ( sk3 @ sk7 ) @ sk7 )
| ( function @ null_class ) ),
inference(pattern_uni,[status(thm)],[8313:[bind(A,$thf( sk7 ))]]) ).
thf(78077,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71499,196]) ).
thf(78078,plain,
member @ ( power_class @ ( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[78077:[bind(A,$thf( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ))]]) ).
thf(38441,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ universal_class ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[696,217]) ).
thf(38442,plain,
~ ( member @ ( sk3 @ universal_class ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38441:[bind(A,$thf( universal_class )),bind(B,$thf( sk3 @ universal_class ))]]) ).
thf(37882,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[36711,196]) ).
thf(37883,plain,
member @ ( power_class @ ( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[37882:[bind(A,$thf( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ))]]) ).
thf(40575,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ sk1 @ A ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[28038,38410]) ).
thf(40700,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( union @ sk1 @ A )
!= ( complement @ sk1 ) ) ),
inference(simp,[status(thm)],[40575]) ).
thf(40746,plain,
! [A: $i] :
( ( union @ sk1 @ A )
!= ( complement @ sk1 ) ),
inference(simp,[status(thm)],[40700]) ).
thf(29336,plain,
( ( member @ ( sk3 @ sk1 ) @ ( successor @ sk1 ) )
!= ( member @ universal_class @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[29052,3924]) ).
thf(29372,plain,
( ( ( sk3 @ sk1 )
!= universal_class )
| ( ( successor @ sk1 )
!= ( power_class @ null_class ) ) ),
inference(simp,[status(thm)],[29336]) ).
thf(29826,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ A )
| ( A
!= ( successor @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[129,29433]) ).
thf(29827,plain,
member @ ( sk3 @ ( successor @ sk1 ) ) @ ( successor @ sk1 ),
inference(pattern_uni,[status(thm)],[29826:[bind(A,$thf( successor @ sk1 ))]]) ).
thf(38453,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ ( successor @ sk1 ) ) @ ( successor @ sk1 ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29827,217]) ).
thf(38454,plain,
~ ( member @ ( sk3 @ ( successor @ sk1 ) ) @ ( complement @ ( successor @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[38453:[bind(A,$thf( successor @ sk1 )),bind(B,$thf( sk3 @ ( successor @ sk1 ) ))]]) ).
thf(38358,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk6 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33769,217]) ).
thf(38359,plain,
~ ( member @ ( power_class @ ( sk6 @ null_class @ universal_class ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38358:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk6 @ null_class @ universal_class ) ))]]) ).
thf(40640,plain,
( ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) )
!= ( member @ ( sk3 @ sk1 ) @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[8216,38410]) ).
thf(40695,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( complement @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[40640]) ).
thf(40743,plain,
( ( complement @ sk1 )
!= sk1 ),
inference(simp,[status(thm)],[40695]) ).
thf(72423,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ sk1 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71216,254]) ).
thf(72424,plain,
member @ ( sum_class @ ( sum_class @ ( sk3 @ sk1 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[72423:[bind(A,$thf( sum_class @ ( sk3 @ sk1 ) ))]]) ).
thf(76955,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71213,254]) ).
thf(76956,plain,
member @ ( sum_class @ ( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[76955:[bind(A,$thf( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ))]]) ).
thf(80545,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sk6 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71379,217]) ).
thf(80546,plain,
~ ( member @ ( sum_class @ ( sk6 @ null_class @ universal_class ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[80545:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sk6 @ null_class @ universal_class ) ))]]) ).
thf(822,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[128,167]) ).
thf(823,plain,
( ( member @ ( sk3 @ sk5 ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[822:[bind(A,$thf( sk5 ))]]) ).
thf(1643,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[128,823]) ).
thf(1644,plain,
( ( member @ ( sk3 @ ( sk3 @ sk5 ) ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[1643:[bind(A,$thf( sk3 @ sk5 ))]]) ).
thf(40072,plain,
( ( member @ ( sk3 @ sk5 ) @ ( complement @ universal_class ) )
!= ( member @ ( sk3 @ sk5 ) @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[35367,38286]) ).
thf(40213,plain,
( ( ( sk3 @ sk5 )
!= ( sk3 @ sk5 ) )
| ( ( complement @ universal_class )
!= sk5 ) ),
inference(simp,[status(thm)],[40072]) ).
thf(40240,plain,
( ( complement @ universal_class )
!= sk5 ),
inference(simp,[status(thm)],[40213]) ).
thf(25514,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ C ) ) ) ) @ ( singleton @ A ) ) @ ( flip @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ C ) ) ) @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,25257]) ).
thf(25515,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( flip @ null_class ) ),
inference(pattern_uni,[status(thm)],[25514:[bind(A,$thf( singleton @ ( singleton @ ( singleton @ H ) ) )),bind(B,$thf( singleton @ ( singleton @ H ) )),bind(C,$thf( H ))]]) ).
thf(25621,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( flip @ null_class ) ),
inference(simp,[status(thm)],[25515]) ).
thf(25643,plain,
! [A: $i] :
~ ( member @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( flip @ null_class ) ),
inference(rewrite,[status(thm)],[25621,111]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( disjoint @ A @ B ) ),
inference(cnf,[status(esa)],[135]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( disjoint @ A @ B ) ),
inference(simp,[status(thm)],[136]) ).
thf(11920,plain,
! [C: $i,B: $i,A: $i] :
( ( disjoint @ A @ B )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ C @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[139,170]) ).
thf(11921,plain,
! [A: $i] : ( disjoint @ null_class @ A ),
inference(pattern_uni,[status(thm)],[11920:[bind(A,$thf( null_class )),bind(B,$thf( D )),bind(C,$thf( sk4 @ D @ null_class ))]]) ).
thf(12004,plain,
! [A: $i] : ( disjoint @ null_class @ A ),
inference(simp,[status(thm)],[11921]) ).
thf(10212,plain,
! [A: $i] :
( ( disjoint @ ( sk3 @ A ) @ A )
| ( inductive @ null_class )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[130,166]) ).
thf(10213,plain,
( ( disjoint @ ( sk3 @ sk5 ) @ sk5 )
| ( inductive @ null_class ) ),
inference(pattern_uni,[status(thm)],[10212:[bind(A,$thf( sk5 ))]]) ).
thf(35362,plain,
( ( disjoint @ ( sk3 @ sk5 ) @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[10213,35130]) ).
thf(35363,plain,
disjoint @ ( sk3 @ sk5 ) @ sk5,
inference(simp,[status(thm)],[35362]) ).
thf(33226,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[31029,196]) ).
thf(33227,plain,
member @ ( power_class @ ( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[33226:[bind(A,$thf( power_class @ ( power_class @ ( sk3 @ sk1 ) ) ))]]) ).
thf(81273,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71456,254]) ).
thf(81274,plain,
member @ ( sum_class @ ( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[81273:[bind(A,$thf( sum_class @ ( sk3 @ ( successor @ universal_class ) ) ))]]) ).
thf(1443,plain,
( ( member @ null_class @ universal_class )
| ( ( member @ ( sk3 @ ( sk3 @ sk1 ) ) @ universal_class )
!= ( member @ null_class @ universal_class ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[881]) ).
thf(1449,plain,
( ( member @ null_class @ universal_class )
| ( ( sk3 @ ( sk3 @ sk1 ) )
!= null_class )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[1443]) ).
thf(1456,plain,
( ( member @ null_class @ universal_class )
| ( ( sk3 @ ( sk3 @ sk1 ) )
!= null_class ) ),
inference(simp,[status(thm)],[1449]) ).
thf(48567,plain,
( ( member @ sk5 @ ( successor @ universal_class ) )
!= ( member @ sk5 @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[28255,47418]) ).
thf(48625,plain,
( ( sk5 != sk5 )
| ( ( successor @ universal_class )
!= ( power_class @ null_class ) ) ),
inference(simp,[status(thm)],[48567]) ).
thf(48685,plain,
( ( successor @ universal_class )
!= ( power_class @ null_class ) ),
inference(simp,[status(thm)],[48625]) ).
thf(211,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
inference(cnf,[status(esa)],[208]) ).
thf(35666,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( domain_of @ ( inverse @ ( intersection @ successor_relation @ ( cross_product @ A @ universal_class ) ) ) ) @ A ) ),
inference(rewrite,[status(thm)],[211,1553]) ).
thf(38276,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk3 @ universal_class ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30590,217]) ).
thf(38277,plain,
~ ( member @ ( power_class @ ( sk3 @ universal_class ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38276:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk3 @ universal_class ) ))]]) ).
thf(359,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ( B != element_relation ) ),
inference(paramod_ordered,[status(thm)],[59,80]) ).
thf(360,plain,
! [A: $i] :
( ~ ( subclass @ A @ element_relation )
| ~ ( subclass @ element_relation @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[359:[bind(A,$thf( A )),bind(B,$thf( element_relation ))]]) ).
thf(39182,plain,
( ( member @ ( sk3 @ sk1 ) @ ( successor @ sk1 ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[29052,38246]) ).
thf(39222,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( successor @ sk1 )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[39182]) ).
thf(39267,plain,
( ( successor @ sk1 )
!= ( complement @ universal_class ) ),
inference(simp,[status(thm)],[39222]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(1563,plain,
! [B: $i,A: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( domain_of @ ( inverse @ ( intersection @ A @ ( cross_product @ ( singleton @ B ) @ universal_class ) ) ) ) ) ),
inference(rewrite,[status(thm)],[194,1553]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',domain_of) ).
thf(95,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)],[15]) ).
thf(96,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)],[95]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( domain_of @ A ) )
| ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) ),
inference(cnf,[status(esa)],[96]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class )
| ~ ( member @ B @ ( domain_of @ A ) ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(3190,plain,
! [B: $i,A: $i] :
( ( ( intersection @ A @ ( cross_product @ ( singleton @ B ) @ universal_class ) )
!= null_class )
| ~ ( member @ B @ ( domain_of @ A ) ) ),
inference(rewrite,[status(thm)],[102,241]) ).
thf(76728,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71213,196]) ).
thf(76729,plain,
member @ ( power_class @ ( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[76728:[bind(A,$thf( sum_class @ ( power_class @ ( power_class @ sk5 ) ) ))]]) ).
thf(76295,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sum_class @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[72024,196]) ).
thf(76296,plain,
member @ ( power_class @ ( sum_class @ ( sum_class @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[76295:[bind(A,$thf( sum_class @ ( sum_class @ sk5 ) ))]]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( A != B )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(cnf,[status(esa)],[229]) ).
thf(236,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[231]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(9655,plain,
! [A: $i] :
( ~ ( member @ A @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ( ( member @ ( sk3 @ sk1 ) @ sk1 )
!= ( member @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[8216,264]) ).
thf(9656,plain,
~ ( member @ ( sk3 @ sk1 ) @ ( intersection @ ( complement @ ( singleton @ ( sk3 @ sk1 ) ) ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9655:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(12060,plain,
( ( member @ ( sk3 @ sk1 ) @ ( intersection @ ( complement @ ( singleton @ ( sk3 @ sk1 ) ) ) @ sk1 ) )
!= ( member @ ( sk3 @ sk1 ) @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[698,9656]) ).
thf(12186,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( intersection @ ( complement @ ( singleton @ ( sk3 @ sk1 ) ) ) @ sk1 )
!= universal_class ) ),
inference(simp,[status(thm)],[12060]) ).
thf(12201,plain,
( ( intersection @ ( complement @ ( singleton @ ( sk3 @ sk1 ) ) ) @ sk1 )
!= universal_class ),
inference(simp,[status(thm)],[12186]) ).
thf(10042,plain,
! [A: $i] :
( ( disjoint @ ( sk3 @ A ) @ A )
| ( function @ null_class )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[130,221]) ).
thf(10043,plain,
( ( disjoint @ ( sk3 @ sk7 ) @ sk7 )
| ( function @ null_class ) ),
inference(pattern_uni,[status(thm)],[10042:[bind(A,$thf( sk7 ))]]) ).
thf(4,axiom,
! [A: $i] :
( ( inverse @ A )
= ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_defn) ).
thf(64,plain,
! [A: $i] :
( ( inverse @ A )
= ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32710,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30537,196]) ).
thf(32711,plain,
member @ ( power_class @ ( power_class @ ( sk3 @ ( successor @ universal_class ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[32710:[bind(A,$thf( power_class @ ( sk3 @ ( successor @ universal_class ) ) ))]]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( member @ B @ universal_class )
| ( ( successor @ A )
!= B )
| ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ),
inference(cnf,[status(esa)],[154]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( ( successor @ A )
!= B )
| ~ ( member @ A @ universal_class )
| ~ ( member @ B @ universal_class )
| ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ),
inference(lifteq,[status(thm)],[155]) ).
thf(160,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( member @ ( successor @ A ) @ universal_class )
| ( member @ ( ordered_pair @ A @ ( successor @ A ) ) @ successor_relation ) ),
inference(simp,[status(thm)],[159]) ).
thf(17436,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( member @ ( successor @ A ) @ universal_class )
| ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ ( successor @ A ) ) ) ) @ successor_relation ) ),
inference(rewrite,[status(thm)],[160,252]) ).
thf(75873,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sum_class @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71841,196]) ).
thf(75874,plain,
member @ ( power_class @ ( power_class @ ( sum_class @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[75873:[bind(A,$thf( power_class @ ( sum_class @ sk5 ) ))]]) ).
thf(44577,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ ( sk3 @ universal_class ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[210,38442]) ).
thf(44591,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( sk3 @ universal_class )
!= null_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[44577]) ).
thf(44654,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( sk3 @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[44591]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( function @ A )
| ( B != sk7 ) ),
inference(paramod_ordered,[status(thm)],[59,221]) ).
thf(298,plain,
! [A: $i] :
( ~ ( subclass @ A @ sk7 )
| ~ ( subclass @ sk7 @ A )
| ( function @ A ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(38388,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ ( successor @ universal_class ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28639,217]) ).
thf(38389,plain,
~ ( member @ ( sk3 @ ( successor @ universal_class ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38388:[bind(A,$thf( universal_class )),bind(B,$thf( sk3 @ ( successor @ universal_class ) ))]]) ).
thf(32969,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30567,196]) ).
thf(32970,plain,
member @ ( power_class @ ( power_class @ ( sk3 @ ( successor @ sk1 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[32969:[bind(A,$thf( power_class @ ( sk3 @ ( successor @ sk1 ) ) ))]]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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(cnf,[status(esa)],[174]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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(simp,[status(thm)],[175]) ).
thf(23036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ A @ B ) ) @ ( unordered_pair @ ( ordered_pair @ A @ B ) @ ( singleton @ C ) ) ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ~ ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ B @ A ) ) @ ( unordered_pair @ ( ordered_pair @ B @ A ) @ ( singleton @ C ) ) ) @ D )
| ( member @ ( unordered_pair @ ( singleton @ ( ordered_pair @ A @ B ) ) @ ( unordered_pair @ ( ordered_pair @ A @ B ) @ ( singleton @ C ) ) ) @ ( flip @ D ) ) ),
inference(rewrite,[status(thm)],[178,252]) ).
thf(75,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(cnf,[status(esa)],[72]) ).
thf(1487,plain,
! [A: $i] :
( ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( ( function @ sk7 )
!= ( function @ A ) ) ),
inference(paramod_ordered,[status(thm)],[221,75]) ).
thf(1488,plain,
subclass @ ( compose @ sk7 @ ( inverse @ sk7 ) ) @ identity_relation,
inference(pattern_uni,[status(thm)],[1487:[bind(A,$thf( sk7 ))]]) ).
thf(34060,plain,
! [A: $i] :
( ~ ( function @ A )
| ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk1 @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[74,34003]) ).
thf(34110,plain,
! [A: $i] :
( ~ ( function @ A )
| ( A != sk1 )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[34060]) ).
thf(34127,plain,
( ~ ( function @ sk1 )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[34110]) ).
thf(37266,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[32274,196]) ).
thf(37267,plain,
member @ ( power_class @ ( power_class @ ( power_class @ ( power_class @ sk5 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[37266:[bind(A,$thf( power_class @ ( power_class @ ( power_class @ sk5 ) ) ))]]) ).
thf(39112,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ sk1 @ A ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[28038,38246]) ).
thf(39210,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( union @ sk1 @ A )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[39112]) ).
thf(39263,plain,
! [A: $i] :
( ( union @ sk1 @ A )
!= ( complement @ universal_class ) ),
inference(simp,[status(thm)],[39210]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ~ ( member @ A @ B )
| ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ),
inference(cnf,[status(esa)],[180]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ~ ( member @ A @ B )
| ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ),
inference(simp,[status(thm)],[181]) ).
thf(26867,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ~ ( member @ A @ B )
| ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ element_relation ) ),
inference(rewrite,[status(thm)],[184,252]) ).
thf(204,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[201]) ).
thf(1354,plain,
! [A: $i] :
( ~ ( function @ A )
| ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[74,1334]) ).
thf(1363,plain,
! [A: $i] :
( ~ ( function @ A )
| ( A != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[1354]) ).
thf(1371,plain,
( ~ ( function @ universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[1363]) ).
thf(10917,plain,
! [A: $i] :
( ( function @ null_class )
| ( ( member @ ( sk3 @ sk7 ) @ sk7 )
!= ( member @ A @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[8314,170]) ).
thf(10989,plain,
! [A: $i] :
( ( function @ null_class )
| ( ( sk3 @ sk7 )
!= A )
| ( sk7 != null_class ) ),
inference(simp,[status(thm)],[10917]) ).
thf(11018,plain,
( ( function @ null_class )
| ( sk7 != null_class ) ),
inference(simp,[status(thm)],[10989]) ).
thf(7965,plain,
( ( ( intersection @ ( complement @ ( singleton @ sk5 ) ) @ sk1 )
!= universal_class )
| ( ( member @ sk5 @ sk1 )
!= ( member @ sk5 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[167,284]) ).
thf(7979,plain,
( ( ( intersection @ ( complement @ ( singleton @ sk5 ) ) @ sk1 )
!= universal_class )
| ( sk5 != sk5 )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[7965]) ).
thf(8010,plain,
( ( ( intersection @ ( complement @ ( singleton @ sk5 ) ) @ sk1 )
!= universal_class )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[7979]) ).
thf(47383,plain,
! [B: $i,A: $i] :
( ( member @ ( sk6 @ B @ A ) @ A )
| ( ( subclass @ A @ B )
!= ( subclass @ sk5 @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[205,47362]) ).
thf(47384,plain,
member @ ( sk6 @ null_class @ sk5 ) @ sk5,
inference(pattern_uni,[status(thm)],[47383:[bind(A,$thf( sk5 )),bind(B,$thf( null_class ))]]) ).
thf(47461,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk6 @ null_class @ sk5 ) @ sk5 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47384,217]) ).
thf(47462,plain,
~ ( member @ ( sk6 @ null_class @ sk5 ) @ ( complement @ sk5 ) ),
inference(pattern_uni,[status(thm)],[47461:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 @ null_class @ sk5 ))]]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( cross_product @ A @ B ) )
=> ( C
= ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product) ).
thf(131,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)],[21]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( cross_product @ A @ B ) )
| ( C
= ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ordered_pair @ ( first @ C ) @ ( second @ C ) )
= C )
| ~ ( member @ C @ ( cross_product @ A @ B ) ) ),
inference(lifteq,[status(thm)],[132]) ).
thf(11085,plain,
! [C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( singleton @ ( first @ C ) ) @ ( unordered_pair @ ( first @ C ) @ ( singleton @ ( second @ C ) ) ) )
= C )
| ~ ( member @ C @ ( cross_product @ A @ B ) ) ),
inference(rewrite,[status(thm)],[133,252]) ).
thf(71315,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30567,254]) ).
thf(71316,plain,
member @ ( sum_class @ ( power_class @ ( sk3 @ ( successor @ sk1 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71315:[bind(A,$thf( power_class @ ( sk3 @ ( successor @ sk1 ) ) ))]]) ).
thf(73939,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71530,254]) ).
thf(73940,plain,
member @ ( sum_class @ ( sum_class @ ( sk3 @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[73939:[bind(A,$thf( sum_class @ ( sk3 @ universal_class ) ))]]) ).
thf(21403,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ C ) ) ) ) @ ( singleton @ A ) ) @ ( rotate @ null_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ C ) ) ) @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,21150]) ).
thf(21404,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( rotate @ null_class ) ),
inference(pattern_uni,[status(thm)],[21403:[bind(A,$thf( singleton @ ( singleton @ ( singleton @ H ) ) )),bind(B,$thf( singleton @ ( singleton @ H ) )),bind(C,$thf( H ))]]) ).
thf(21506,plain,
! [A: $i] :
~ ( member @ ( unordered_pair @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( rotate @ null_class ) ),
inference(simp,[status(thm)],[21404]) ).
thf(21527,plain,
! [A: $i] :
~ ( member @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ ( singleton @ A ) ) ) ) ) @ ( rotate @ null_class ) ),
inference(rewrite,[status(thm)],[21506,111]) ).
thf(102983,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ A @ universal_class ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[29463,38246]) ).
thf(103178,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( union @ A @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[102983]) ).
thf(103366,plain,
! [A: $i] :
( ( union @ A @ universal_class )
!= ( complement @ universal_class ) ),
inference(simp,[status(thm)],[103178]) ).
thf(10,axiom,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate) ).
thf(81,plain,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( domain_of @ A ) )
| ( member @ B @ universal_class ) ),
inference(cnf,[status(esa)],[96]) ).
thf(40549,plain,
( ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) )
!= ( member @ ( sk3 @ sk1 ) @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[698,38410]) ).
thf(40660,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( complement @ sk1 )
!= universal_class ) ),
inference(simp,[status(thm)],[40549]) ).
thf(40734,plain,
( ( complement @ sk1 )
!= universal_class ),
inference(simp,[status(thm)],[40660]) ).
thf(361,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( subclass @ element_relation @ A )
| ( B
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[59,80]) ).
thf(362,plain,
! [A: $i] :
( ~ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( cross_product @ universal_class @ universal_class ) @ A )
| ( subclass @ element_relation @ A ) ),
inference(pattern_uni,[status(thm)],[361:[bind(A,$thf( A )),bind(B,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(73,plain,
! [A: $i] :
( ~ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( function @ A ) ),
inference(cnf,[status(esa)],[72]) ).
thf(76,plain,
! [A: $i] :
( ~ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( function @ A ) ),
inference(simp,[status(thm)],[73]) ).
thf(38236,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32274,217]) ).
thf(38237,plain,
~ ( member @ ( power_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38236:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( power_class @ ( power_class @ sk5 ) ) ))]]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ B )
| ( disjoint @ A @ B ) ),
inference(cnf,[status(esa)],[135]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ B )
| ( disjoint @ A @ B ) ),
inference(simp,[status(thm)],[137]) ).
thf(71205,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( power_class @ sk5 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[32274,254]) ).
thf(71206,plain,
member @ ( sum_class @ ( power_class @ ( power_class @ ( power_class @ sk5 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71205:[bind(A,$thf( power_class @ ( power_class @ ( power_class @ sk5 ) ) ))]]) ).
thf(78059,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71499,217]) ).
thf(78060,plain,
~ ( member @ ( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[78059:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sk3 @ ( successor @ sk1 ) ) ))]]) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ C ) ),
inference(cnf,[status(esa)],[142]) ).
thf(12744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ ( cross_product @ C @ D ) )
| ( member @ A @ C ) ),
inference(rewrite,[status(thm)],[144,252]) ).
thf(65,plain,
! [A: $i] :
( ( inverse @ A )
= ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( subclass @ A @ B )
| ( member @ A @ ( power_class @ B ) ) ),
inference(cnf,[status(esa)],[104]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ~ ( subclass @ A @ B )
| ( member @ A @ ( power_class @ B ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( inductive @ A )
| ( B != sk5 ) ),
inference(paramod_ordered,[status(thm)],[59,166]) ).
thf(330,plain,
! [A: $i] :
( ~ ( subclass @ A @ sk5 )
| ~ ( subclass @ sk5 @ A )
| ( inductive @ A ) ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(2663,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ universal_class )
!= ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[698,2552]) ).
thf(2707,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= A )
| ( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
!= universal_class ) ),
inference(simp,[status(thm)],[2663]) ).
thf(2727,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) )
!= universal_class ),
inference(simp,[status(thm)],[2707]) ).
thf(9585,plain,
( ( sum_class @ ( sum_class @ null_class ) )
!= universal_class ),
inference(rewrite,[status(thm)],[2727,8720]) ).
thf(9741,plain,
( ( sum_class @ null_class )
!= universal_class ),
inference(rewrite,[status(thm)],[9585,8720]) ).
thf(71330,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[36711,254]) ).
thf(71331,plain,
member @ ( sum_class @ ( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71330:[bind(A,$thf( power_class @ ( power_class @ ( sk3 @ sk5 ) ) ))]]) ).
thf(12334,plain,
! [C: $i,B: $i,A: $i] :
( ( disjoint @ A @ B )
| ( ( member @ ( sk4 @ B @ A ) @ B )
!= ( member @ C @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[140,170]) ).
thf(12335,plain,
! [A: $i] : ( disjoint @ A @ null_class ),
inference(pattern_uni,[status(thm)],[12334:[bind(A,$thf( E )),bind(B,$thf( null_class )),bind(C,$thf( sk4 @ null_class @ E ))]]) ).
thf(12432,plain,
! [A: $i] : ( disjoint @ A @ null_class ),
inference(simp,[status(thm)],[12335]) ).
thf(3952,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( power_class @ B ) )
| ~ ( subclass @ null_class @ sk1 )
| ( ( subclass @ A @ B )
!= ( subclass @ sk1 @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[107,400]) ).
thf(3953,plain,
( ~ ( member @ sk1 @ ( power_class @ null_class ) )
| ~ ( subclass @ null_class @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3952:[bind(A,$thf( sk1 )),bind(B,$thf( null_class ))]]) ).
thf(33998,plain,
( ~ ( member @ sk1 @ ( power_class @ null_class ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3953,33729]) ).
thf(33999,plain,
~ ( member @ sk1 @ ( power_class @ null_class ) ),
inference(simp,[status(thm)],[33998]) ).
thf(35920,plain,
( ( member @ ( sk3 @ sk5 ) @ sk5 )
!= ( member @ sk1 @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[35367,33999]) ).
thf(35967,plain,
( ( ( sk3 @ sk5 )
!= sk1 )
| ( ( power_class @ null_class )
!= sk5 ) ),
inference(simp,[status(thm)],[35920]) ).
thf(38279,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ sk5 ) @ sk5 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35367,217]) ).
thf(38280,plain,
~ ( member @ ( sk3 @ sk5 ) @ ( complement @ sk5 ) ),
inference(pattern_uni,[status(thm)],[38279:[bind(A,$thf( sk5 )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(39846,plain,
( ( member @ ( sk3 @ sk5 ) @ ( complement @ sk5 ) )
!= ( member @ ( sk3 @ sk5 ) @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[35369,38280]) ).
thf(39942,plain,
( ( ( sk3 @ sk5 )
!= ( sk3 @ sk5 ) )
| ( ( complement @ sk5 )
!= universal_class ) ),
inference(simp,[status(thm)],[39846]) ).
thf(40007,plain,
( ( complement @ sk5 )
!= universal_class ),
inference(simp,[status(thm)],[39942]) ).
thf(9898,plain,
! [A: $i] :
( ( disjoint @ ( sk3 @ A ) @ A )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[130,52]) ).
thf(9899,plain,
disjoint @ ( sk3 @ sk1 ) @ sk1,
inference(pattern_uni,[status(thm)],[9898:[bind(A,$thf( sk1 ))]]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
| ( member @ B @ universal_class ) ),
inference(cnf,[status(esa)],[154]) ).
thf(16970,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ successor_relation )
| ( member @ B @ universal_class ) ),
inference(rewrite,[status(thm)],[157,252]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ sk1 )
| ( ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
!= ( member @ B @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[50]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ sk1 )
| ( ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
!= ( member @ B @ sk1 ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(39186,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[210,38246]) ).
thf(39233,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( sk3 @ sk1 )
!= null_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[39186]) ).
thf(39270,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( sk3 @ sk1 )
!= null_class ) ),
inference(simp,[status(thm)],[39233]) ).
thf(77853,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71255,254]) ).
thf(77854,plain,
member @ ( sum_class @ ( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[77853:[bind(A,$thf( sum_class @ ( power_class @ ( sk3 @ universal_class ) ) ))]]) ).
thf(38349,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk6 @ null_class @ universal_class ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33491,217]) ).
thf(38350,plain,
~ ( member @ ( sk6 @ null_class @ universal_class ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38349:[bind(A,$thf( universal_class )),bind(B,$thf( sk6 @ null_class @ universal_class ))]]) ).
thf(96415,plain,
( ( member @ ( sk3 @ sk1 ) @ ( successor @ universal_class ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[96016,38410]) ).
thf(96652,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( successor @ universal_class )
!= ( complement @ sk1 ) ) ),
inference(simp,[status(thm)],[96415]) ).
thf(96777,plain,
( ( successor @ universal_class )
!= ( complement @ sk1 ) ),
inference(simp,[status(thm)],[96652]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(967,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( member @ null_class @ universal_class )
| ( A
!= ( sk3 @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[128,696]) ).
thf(968,plain,
( ( member @ ( sk3 @ ( sk3 @ universal_class ) ) @ universal_class )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[967:[bind(A,$thf( sk3 @ universal_class ))]]) ).
thf(35923,plain,
( ( member @ ( sk3 @ sk5 ) @ sk5 )
!= ( member @ universal_class @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[35367,3924]) ).
thf(35935,plain,
( ( ( sk3 @ sk5 )
!= universal_class )
| ( ( power_class @ null_class )
!= sk5 ) ),
inference(simp,[status(thm)],[35923]) ).
thf(38328,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31329,217]) ).
thf(38329,plain,
~ ( member @ ( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38328:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ))]]) ).
thf(1506,plain,
( ( subclass @ ( compose @ sk7 @ ( inverse @ sk7 ) ) @ identity_relation )
!= ( subclass @ universal_class @ null_class ) ),
inference(paramod_ordered,[status(thm)],[1488,1334]) ).
thf(1547,plain,
( ( ( compose @ sk7 @ ( inverse @ sk7 ) )
!= universal_class )
| ( identity_relation != null_class ) ),
inference(simp,[status(thm)],[1506]) ).
thf(77404,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71242,254]) ).
thf(77405,plain,
member @ ( sum_class @ ( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[77404:[bind(A,$thf( sum_class @ ( power_class @ ( sk3 @ sk5 ) ) ))]]) ).
thf(279,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 )
| ( ( member @ A @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
!= ( member @ A @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[264]) ).
thf(282,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 )
| ( ( member @ A @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
!= ( member @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(38944,plain,
( ( member @ sk5 @ ( complement @ universal_class ) )
!= ( member @ sk5 @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[167,38392]) ).
thf(38984,plain,
( ( sk5 != sk5 )
| ( ( complement @ universal_class )
!= universal_class ) ),
inference(simp,[status(thm)],[38944]) ).
thf(39036,plain,
( ( complement @ universal_class )
!= universal_class ),
inference(simp,[status(thm)],[38984]) ).
thf(1229,plain,
! [A: $i] :
( ( member @ ( sk3 @ A ) @ universal_class )
| ( subclass @ sk7 @ null_class )
| ( A
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[128,1209]) ).
thf(1230,plain,
( ( member @ ( sk3 @ ( cross_product @ universal_class @ universal_class ) ) @ universal_class )
| ( subclass @ sk7 @ null_class ) ),
inference(pattern_uni,[status(thm)],[1229:[bind(A,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(28165,plain,
! [B: $i,A: $i] :
( ( member @ sk5 @ ( union @ universal_class @ A ) )
!= ( member @ B @ null_class ) ),
inference(paramod_ordered,[status(thm)],[28155,170]) ).
thf(28307,plain,
! [B: $i,A: $i] :
( ( sk5 != B )
| ( ( union @ universal_class @ A )
!= null_class ) ),
inference(simp,[status(thm)],[28165]) ).
thf(28351,plain,
! [A: $i] :
( ( union @ universal_class @ A )
!= null_class ),
inference(simp,[status(thm)],[28307]) ).
thf(9571,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(rewrite,[status(thm)],[6894,8720]) ).
thf(16727,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ),
inference(rewrite,[status(thm)],[9571,15250]) ).
thf(38712,plain,
( ( member @ ( sk3 @ sk1 ) @ sk1 )
!= ( member @ null_class @ ( complement @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8216,38295]) ).
thf(38742,plain,
( ( ( sk3 @ sk1 )
!= null_class )
| ( ( complement @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[38712]) ).
thf(71394,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk6 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[33769,254]) ).
thf(71395,plain,
member @ ( sum_class @ ( power_class @ ( sk6 @ null_class @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71394:[bind(A,$thf( power_class @ ( sk6 @ null_class @ universal_class ) ))]]) ).
thf(28952,plain,
! [B: $i,A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ sk1 @ A ) )
!= ( member @ B @ null_class ) ),
inference(paramod_ordered,[status(thm)],[28038,170]) ).
thf(29099,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ sk1 )
!= B )
| ( ( union @ sk1 @ A )
!= null_class ) ),
inference(simp,[status(thm)],[28952]) ).
thf(29184,plain,
! [A: $i] :
( ( union @ sk1 @ A )
!= null_class ),
inference(simp,[status(thm)],[29099]) ).
thf(220,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ sk7 @ A ) @ A ) ),
inference(cnf,[status(esa)],[219]) ).
thf(222,plain,
! [A: $i] :
( ( A = null_class )
| ~ ( member @ A @ universal_class )
| ( member @ ( apply @ sk7 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(40772,plain,
! [A: $i] :
( ( A = null_class )
| ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ ( domain_of @ ( inverse @ ( intersection @ sk7 @ ( cross_product @ ( singleton @ A ) @ universal_class ) ) ) ) ) @ A ) ),
inference(rewrite,[status(thm)],[222,1563]) ).
thf(48493,plain,
( ( member @ ( sk3 @ sk5 ) @ sk5 )
!= ( member @ sk5 @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[35367,47418]) ).
thf(48606,plain,
( ( ( sk3 @ sk5 )
!= sk5 )
| ( ( power_class @ null_class )
!= sk5 ) ),
inference(simp,[status(thm)],[48493]) ).
thf(12160,plain,
( ( member @ ( sk3 @ sk1 ) @ ( intersection @ ( complement @ ( singleton @ ( sk3 @ sk1 ) ) ) @ sk1 ) )
!= ( member @ ( sk3 @ sk1 ) @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[8216,9656]) ).
thf(12189,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( intersection @ ( complement @ ( singleton @ ( sk3 @ sk1 ) ) ) @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[12160]) ).
thf(12202,plain,
( ( intersection @ ( complement @ ( singleton @ ( sk3 @ sk1 ) ) ) @ sk1 )
!= sk1 ),
inference(simp,[status(thm)],[12189]) ).
thf(9579,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ),
inference(rewrite,[status(thm)],[3381,8720]) ).
thf(12995,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ null_class ) ),
inference(rewrite,[status(thm)],[9579,11755]) ).
thf(97,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)],[96]) ).
thf(100,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)],[97]) ).
thf(101,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)],[100]) ).
thf(2903,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)],[101,241]) ).
thf(76276,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sum_class @ sk5 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[72024,217]) ).
thf(76277,plain,
~ ( member @ ( sum_class @ ( sum_class @ sk5 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[76276:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sum_class @ sk5 ) ))]]) ).
thf(72202,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sk3 @ sk1 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71216,217]) ).
thf(72203,plain,
~ ( member @ ( sum_class @ ( sk3 @ sk1 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[72202:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sk3 @ sk1 ) ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn1) ).
thf(67,plain,
! [A: $i,B: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1351,plain,
( ( subclass @ sk7 @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ null_class ) ),
inference(paramod_ordered,[status(thm)],[1209,1334]) ).
thf(1358,plain,
( ( sk7 != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[1351]) ).
thf(96344,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sk3 @ sk1 ) @ ( successor @ universal_class ) )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[96016,217]) ).
thf(96345,plain,
~ ( member @ ( sk3 @ sk1 ) @ ( complement @ ( successor @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[96344:[bind(A,$thf( successor @ universal_class )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(99125,plain,
( ( member @ ( sk3 @ sk1 ) @ ( complement @ ( successor @ universal_class ) ) )
!= ( member @ ( sk3 @ sk1 ) @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[8216,96345]) ).
thf(99260,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( complement @ ( successor @ universal_class ) )
!= sk1 ) ),
inference(simp,[status(thm)],[99125]) ).
thf(99306,plain,
( ( complement @ ( successor @ universal_class ) )
!= sk1 ),
inference(simp,[status(thm)],[99260]) ).
thf(38242,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( power_class @ sk5 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30799,217]) ).
thf(38243,plain,
~ ( member @ ( power_class @ ( power_class @ sk5 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38242:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( power_class @ sk5 ) ))]]) ).
thf(246,plain,
! [A: $i] :
( ~ ( member @ A @ identity_relation )
| ( A
= ( ordered_pair @ ( sk8 @ A ) @ ( sk8 @ A ) ) ) ),
inference(cnf,[status(esa)],[243]) ).
thf(249,plain,
! [A: $i] :
( ( ( ordered_pair @ ( sk8 @ A ) @ ( sk8 @ A ) )
= A )
| ~ ( member @ A @ identity_relation ) ),
inference(lifteq,[status(thm)],[246]) ).
thf(68888,plain,
! [A: $i] :
( ( ( unordered_pair @ ( singleton @ ( sk8 @ A ) ) @ ( unordered_pair @ ( sk8 @ A ) @ ( singleton @ ( sk8 @ A ) ) ) )
= A )
| ~ ( member @ A @ identity_relation ) ),
inference(rewrite,[status(thm)],[249,252]) ).
thf(73229,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( power_class @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71494,254]) ).
thf(73230,plain,
member @ ( sum_class @ ( sum_class @ ( power_class @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[73229:[bind(A,$thf( sum_class @ ( power_class @ sk5 ) ))]]) ).
thf(34102,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk1 @ null_class ) ),
inference(paramod_ordered,[status(thm)],[83,34003]) ).
thf(34113,plain,
( ( sk1 != successor_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[34102]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ( member @ B @ A )
| ( member @ B @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[214]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ( member @ B @ A )
| ( member @ B @ ( complement @ A ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(71458,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( sk3 @ ( successor @ universal_class ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[30537,254]) ).
thf(71459,plain,
member @ ( sum_class @ ( power_class @ ( sk3 @ ( successor @ universal_class ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71458:[bind(A,$thf( power_class @ ( sk3 @ ( successor @ universal_class ) ) ))]]) ).
thf(6139,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)],[163,5442]) ).
thf(6144,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)],[6139]) ).
thf(6159,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)],[6144]) ).
thf(9596,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)],[6159,8720]) ).
thf(12900,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[9596,11755]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ element_relation )
| ( member @ A @ B ) ),
inference(cnf,[status(esa)],[180]) ).
thf(26288,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ element_relation )
| ( member @ A @ B ) ),
inference(rewrite,[status(thm)],[183,252]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( A != C )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(cnf,[status(esa)],[229]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[230]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ universal_class )
| ( member @ B @ ( unordered_pair @ A @ B ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(47368,plain,
! [A: $i] :
( ~ ( function @ A )
| ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk5 @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[74,47362]) ).
thf(47424,plain,
! [A: $i] :
( ~ ( function @ A )
| ( A != sk5 )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[47368]) ).
thf(47437,plain,
( ~ ( function @ sk5 )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[47424]) ).
thf(82,plain,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(cnf,[status(esa)],[81]) ).
thf(71822,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ sk5 ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71452,217]) ).
thf(71823,plain,
~ ( member @ ( sum_class @ sk5 ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[71822:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ sk5 ))]]) ).
thf(72624,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ sk5 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71300,196]) ).
thf(72625,plain,
member @ ( power_class @ ( sum_class @ ( sk3 @ sk5 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[72624:[bind(A,$thf( sum_class @ ( sk3 @ sk5 ) ))]]) ).
thf(80802,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk6 @ null_class @ universal_class ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71379,254]) ).
thf(80803,plain,
member @ ( sum_class @ ( sum_class @ ( sk6 @ null_class @ universal_class ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[80802:[bind(A,$thf( sum_class @ ( sk6 @ null_class @ universal_class ) ))]]) ).
thf(7536,plain,
! [A: $i] :
( ( member @ sk5 @ universal_class )
!= ( member @ A @ ( sum_class @ ( sum_class @ ( 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)],[167,6894]) ).
thf(7556,plain,
! [A: $i] :
( ( sk5 != A )
| ( ( sum_class @ ( sum_class @ ( 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)],[7536]) ).
thf(7571,plain,
( ( sum_class @ ( sum_class @ ( 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)],[7556]) ).
thf(9593,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[7571,8720]) ).
thf(13846,plain,
( ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) )
!= universal_class ),
inference(rewrite,[status(thm)],[9593,13296]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ( ( member @ sk5 @ universal_class )
!= ( member @ B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[167,50]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ( sk5 != B )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[260]) ).
thf(272,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ sk5 @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) )
| ( sk1 != universal_class ) ),
inference(simp,[status(thm)],[265]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) )
| ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(5051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ C ) @ ( unordered_pair @ C @ ( singleton @ D ) ) ) @ ( compose @ B @ A ) )
| ( member @ D @ ( domain_of @ ( inverse @ ( intersection @ B @ ( cross_product @ ( image @ A @ ( singleton @ C ) ) @ universal_class ) ) ) ) ) ),
inference(rewrite,[status(thm)],[116,1553,252]) ).
thf(1666,plain,
( ( member @ null_class @ universal_class )
| ( ( member @ ( sk3 @ sk5 ) @ universal_class )
!= ( member @ null_class @ universal_class ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[823]) ).
thf(1671,plain,
( ( member @ null_class @ universal_class )
| ( ( sk3 @ sk5 )
!= null_class )
| ( universal_class != universal_class ) ),
inference(simp,[status(thm)],[1666]) ).
thf(1678,plain,
( ( member @ null_class @ universal_class )
| ( ( sk3 @ sk5 )
!= null_class ) ),
inference(simp,[status(thm)],[1671]) ).
thf(72606,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( sum_class @ ( sk3 @ sk5 ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71300,217]) ).
thf(72607,plain,
~ ( member @ ( sum_class @ ( sk3 @ sk5 ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[72606:[bind(A,$thf( universal_class )),bind(B,$thf( sum_class @ ( sk3 @ sk5 ) ))]]) ).
thf(71348,plain,
! [A: $i] :
( ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[31329,254]) ).
thf(71349,plain,
member @ ( sum_class @ ( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[71348:[bind(A,$thf( power_class @ ( power_class @ ( sk3 @ universal_class ) ) ))]]) ).
thf(48,plain,
! [A: $i] :
( ( singleton @ A )
!= sk1 ),
inference(cnf,[status(esa)],[46]) ).
thf(51,plain,
! [A: $i] :
( ( singleton @ A )
!= sk1 ),
inference(lifteq,[status(thm)],[48]) ).
thf(71436,plain,
! [A: $i] :
( ( function @ null_class )
| ( member @ ( sum_class @ A ) @ universal_class )
| ( ( member @ ( sk3 @ sk7 ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[799,254]) ).
thf(71437,plain,
( ( function @ null_class )
| ( member @ ( sum_class @ ( sk3 @ sk7 ) ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[71436:[bind(A,$thf( sk3 @ sk7 ))]]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ sk1 )
| ( ( member @ sk5 @ universal_class )
!= ( member @ B @ ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[167,50]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ B @ sk1 )
| ( sk5 != B )
| ( ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 )
!= universal_class ) ),
inference(simp,[status(thm)],[259]) ).
thf(273,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 )
| ~ ( member @ sk5 @ sk1 )
| ( ( intersection @ ( complement @ ( singleton @ A ) ) @ sk1 )
!= universal_class ) ),
inference(simp,[status(thm)],[266]) ).
thf(9595,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(rewrite,[status(thm)],[6174,8720]) ).
thf(16341,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ),
inference(rewrite,[status(thm)],[9595,15250]) ).
thf(7454,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( sum_class @ B ) )
| ( ( member @ ( sk2 @ B @ A ) @ B )
!= ( member @ C @ ( sum_class @ ( sum_class @ ( 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)],[93,6894]) ).
thf(7455,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[7454:[bind(A,$thf( E )),bind(B,$thf( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) )),bind(C,$thf( sk2 @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) @ E ))]]) ).
thf(7582,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 @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[7455]) ).
thf(17140,plain,
! [A: $i] :
~ ( member @ A @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ ( sum_class @ null_class ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[7582,15250]) ).
thf(72220,plain,
! [A: $i] :
( ( member @ ( power_class @ A ) @ universal_class )
| ( ( member @ ( sum_class @ ( sk3 @ sk1 ) ) @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[71216,196]) ).
thf(72221,plain,
member @ ( power_class @ ( sum_class @ ( sk3 @ sk1 ) ) ) @ universal_class,
inference(pattern_uni,[status(thm)],[72220:[bind(A,$thf( sum_class @ ( sk3 @ sk1 ) ))]]) ).
thf(38297,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ A ) )
| ( ( member @ ( power_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ universal_class )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30567,217]) ).
thf(38298,plain,
~ ( member @ ( power_class @ ( sk3 @ ( successor @ sk1 ) ) ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[38297:[bind(A,$thf( universal_class )),bind(B,$thf( power_class @ ( sk3 @ ( successor @ sk1 ) ) ))]]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ C @ B )
| ( member @ A @ ( sum_class @ B ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ C @ B )
| ( member @ A @ ( sum_class @ B ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
| ( member @ A @ universal_class ) ),
inference(cnf,[status(esa)],[154]) ).
thf(16558,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ successor_relation )
| ( member @ A @ universal_class ) ),
inference(rewrite,[status(thm)],[156,252]) ).
thf(102989,plain,
! [A: $i] :
( ( member @ ( sk3 @ sk1 ) @ ( union @ A @ universal_class ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[29463,38410]) ).
thf(103151,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( union @ A @ universal_class )
!= ( complement @ sk1 ) ) ),
inference(simp,[status(thm)],[102989]) ).
thf(103349,plain,
! [A: $i] :
( ( union @ A @ universal_class )
!= ( complement @ sk1 ) ),
inference(simp,[status(thm)],[103151]) ).
thf(47407,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ sk5 @ null_class ) ),
inference(paramod_ordered,[status(thm)],[80,47362]) ).
thf(47430,plain,
( ( sk5 != element_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= null_class ) ),
inference(simp,[status(thm)],[47407]) ).
thf(68,plain,
! [B: $i,A: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(cnf,[status(esa)],[67]) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) )
| ( member @ C @ universal_class ) ),
inference(cnf,[status(esa)],[113]) ).
thf(4826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( unordered_pair @ ( singleton @ C ) @ ( unordered_pair @ C @ ( singleton @ D ) ) ) @ ( compose @ B @ A ) )
| ( member @ C @ universal_class ) ),
inference(rewrite,[status(thm)],[115,252]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[119]) ).
thf(34216,plain,
( ( member @ ( sk3 @ sk1 ) @ sk1 )
!= ( member @ sk1 @ ( power_class @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[8216,33999]) ).
thf(34261,plain,
( ( ( sk3 @ sk1 )
!= sk1 )
| ( ( power_class @ null_class )
!= sk1 ) ),
inference(simp,[status(thm)],[34216]) ).
thf(99137,plain,
( ( member @ ( sk3 @ sk1 ) @ ( successor @ sk1 ) )
!= ( member @ ( sk3 @ sk1 ) @ ( complement @ ( successor @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[29052,96345]) ).
thf(99192,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) )
| ( ( successor @ sk1 )
!= ( complement @ ( successor @ universal_class ) ) ) ),
inference(simp,[status(thm)],[99137]) ).
thf(99278,plain,
( ( successor @ sk1 )
!= ( complement @ ( successor @ universal_class ) ) ),
inference(simp,[status(thm)],[99192]) ).
thf(232,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( unordered_pair @ B @ C ) )
| ( member @ A @ universal_class ) ),
inference(cnf,[status(esa)],[229]) ).
thf(149157,plain,
$false,
inference(e,[status(thm)],[96284,9648,34103,28120,45869,88,17920,39049,69,138,48604,71841,170,34117,217,23887,71505,32274,73027,38264,48670,38451,66742,77178,10864,26483,698,77627,5708,153,38812,15632,29604,30799,11684,38722,13970,38426,29433,1359,96270,44179,257,38395,185,33729,1366,52,34003,39276,31029,96797,75856,109274,14141,44187,15250,196,35130,34896,77160,73718,47431,76508,817,36051,81025,189,46,93,284,881,228,20276,40710,109152,30526,30590,216,40246,13138,179,28651,109186,106,238,121,71300,84,73736,35367,71228,164,1334,38314,253,38292,38416,49338,38423,47436,38252,80564,61,221,89,19678,103369,38246,147,76711,9700,22421,64833,74,206,38392,35369,24762,49334,29843,24249,38410,85,34072,25257,270,793,81043,73009,40735,72468,76081,70,275,36310,35184,78305,38295,44807,49331,192,30567,9981,165,72828,92,252,197,77609,40739,21890,96811,37523,1012,285,9804,47418,36711,21150,141,13468,44448,8314,78078,28038,28155,19162,53,109,38442,37883,124,40746,77,29372,38454,38359,24957,31329,40743,72424,76956,80546,1644,40240,25643,12004,173,35363,33227,81274,1456,48685,129,35666,38277,134,360,205,39267,1563,3190,76729,128,76296,237,12201,72024,166,264,10043,64,32711,17436,75874,44654,33491,298,71379,13296,38389,191,33769,32970,23036,1488,34127,71494,37267,59,39263,118,26867,204,71,1371,11018,8010,47462,14820,11085,71316,86,73940,1209,21527,219,103366,81,25866,98,40734,362,76,245,38413,103,38237,38404,140,799,213,71206,78060,12744,66,108,330,130,9741,223,71331,167,38286,12432,47384,35967,40007,28639,9899,16970,267,71255,39270,241,80,77854,28593,30537,162,38350,96777,112,123,968,35935,71499,9656,38329,1547,77405,28255,282,39036,1230,28351,16727,95,38742,50,71395,29184,199,40772,96016,48606,8216,12202,12995,2903,76277,72203,67,1358,99306,38243,35365,68888,30540,73230,34113,250,1553,218,29831,71459,11317,71242,171,139,30409,38280,12900,26288,235,207,71216,47437,82,71823,72625,29463,75,29052,80803,13846,71452,11755,47362,272,5051,1678,72607,71349,51,71437,190,8720,273,16341,168,17140,210,107,71456,195,72221,696,38298,94,239,242,71530,16558,71213,20859,103349,47430,131,68,28635,33999,163,200,254,4826,122,3924,83,34261,96345,111,99278,232,29827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET098+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Jun 23 14:19:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.02/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.06 % [INFO] Parsing done (147ms).
% 1.29/1.06 % [INFO] Running in sequential loop mode.
% 1.83/1.27 % [INFO] eprover registered as external prover.
% 1.83/1.28 % [INFO] Scanning for conjecture ...
% 2.05/1.35 % [INFO] Found a conjecture (or negated_conjecture) and 43 axioms. Running axiom selection ...
% 2.26/1.40 % [INFO] Axiom selection finished. Selected 43 axioms (removed 0 axioms).
% 2.26/1.45 % [INFO] Problem is first-order (TPTP FOF).
% 2.26/1.46 % [INFO] Type checking passed.
% 2.26/1.46 % [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 ...
% 137.42/38.77 % External prover 'e' found a proof!
% 137.42/38.78 % [INFO] Killing All external provers ...
% 137.42/38.78 % Time passed: 38254ms (effective reasoning time: 37709ms)
% 137.42/38.78 % 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)>
% 137.42/38.78 % 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
% 137.42/38.78 % No. of inferences in proof: 992
% 137.42/38.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 38254 ms resp. 37709 ms w/o parsing
% 137.74/38.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 137.74/38.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------