TSTP Solution File: NUM145-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM145-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:39:58 EDT 2023
% Result : Unsatisfiable 119.78s 21.06s
% Output : Refutation 120.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 239
% Syntax : Number of formulae : 855 ( 235 unt; 79 typ; 0 def)
% Number of atoms : 1693 ( 756 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 7597 ( 854 ~; 789 |; 0 &;5954 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 103 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 79 usr; 21 con; 0-3 aty)
% Number of variables : 1033 ( 0 ^;1033 !; 0 ?;1033 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(successor_type,type,
successor: $i > $i ).
thf(x_type,type,
x: $i ).
thf(universal_class_type,type,
universal_class: $i ).
thf(inductive_type,type,
inductive: $i > $o ).
thf(subclass_type,type,
subclass: $i > $i > $o ).
thf(omega_type,type,
omega: $i ).
thf(section_type,type,
section: $i > $i > $i > $o ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(restrict_type,type,
restrict: $i > $i > $i > $i ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(transitive_type,type,
transitive: $i > $i > $o ).
thf(homomorphism_type,type,
homomorphism: $i > $i > $i > $o ).
thf(operation_type,type,
operation: $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(null_class_type,type,
null_class: $i ).
thf(image_type,type,
image: $i > $i > $i ).
thf(successor_relation_type,type,
successor_relation: $i ).
thf(ordinal_numbers_type,type,
ordinal_numbers: $i ).
thf(kind_1_ordinals_type,type,
kind_1_ordinals: $i ).
thf(maps_type,type,
maps: $i > $i > $i > $o ).
thf(complement_type,type,
complement: $i > $i ).
thf(identity_relation_type,type,
identity_relation: $i ).
thf(irreflexive_type,type,
irreflexive: $i > $i > $o ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(function_type,type,
function: $i > $o ).
thf(choice_type,type,
choice: $i ).
thf(domain_type,type,
domain: $i > $i > $i > $i ).
thf(single_valued1_type,type,
single_valued1: $i > $i ).
thf(single_valued2_type,type,
single_valued2: $i > $i ).
thf(single_valued3_type,type,
single_valued3: $i > $i ).
thf(element_relation_type,type,
element_relation: $i ).
thf(power_class_type,type,
power_class: $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(single_valued_class_type,type,
single_valued_class: $i > $o ).
thf(connected_type,type,
connected: $i > $i > $o ).
thf(not_well_ordering_type,type,
not_well_ordering: $i > $i > $i ).
thf(well_ordering_type,type,
well_ordering: $i > $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(asymmetric_type,type,
asymmetric: $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(symmetrization_of_type,type,
symmetrization_of: $i > $i ).
thf(compatible_type,type,
compatible: $i > $i > $i > $o ).
thf(segment_type,type,
segment: $i > $i > $i > $i ).
thf(least_type,type,
least: $i > $i > $i ).
thf(limit_ordinals_type,type,
limit_ordinals: $i ).
thf(first_type,type,
first: $i > $i ).
thf(not_subclass_element_type,type,
not_subclass_element: $i > $i > $i ).
thf(second_type,type,
second: $i > $i ).
thf(range_type,type,
range: $i > $i > $i > $i ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(recursion_type,type,
recursion: $i > $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(add_relation_type,type,
add_relation: $i ).
thf(union_of_range_map_type,type,
union_of_range_map: $i ).
thf(ordinal_multiply_type,type,
ordinal_multiply: $i > $i > $i ).
thf(ordinal_add_type,type,
ordinal_add: $i > $i > $i ).
thf(diagonalise_type,type,
diagonalise: $i > $i ).
thf(subset_relation_type,type,
subset_relation: $i ).
thf(cantor_type,type,
cantor: $i > $i ).
thf(regular_type,type,
regular: $i > $i ).
thf(sum_class_type,type,
sum_class: $i > $i ).
thf(not_homomorphism1_type,type,
not_homomorphism1: $i > $i > $i > $i ).
thf(not_homomorphism2_type,type,
not_homomorphism2: $i > $i > $i > $i ).
thf(singleton_relation_type,type,
singleton_relation: $i ).
thf(rotate_type,type,
rotate: $i > $i ).
thf(composition_function_type,type,
composition_function: $i ).
thf(recursion_equation_functions_type,type,
recursion_equation_functions: $i > $i ).
thf(rest_of_type,type,
rest_of: $i > $i ).
thf(flip_type,type,
flip: $i > $i ).
thf(domain_relation_type,type,
domain_relation: $i ).
thf(compose_class_type,type,
compose_class: $i > $i ).
thf(application_function_type,type,
application_function: $i ).
thf(rest_relation_type,type,
rest_relation: $i ).
thf(integer_of_type,type,
integer_of: $i > $i ).
thf(160,axiom,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
thf(506,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(507,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
inference(cnf,[status(esa)],[506]) ).
thf(508,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
inference(lifteq,[status(thm)],[507]) ).
thf(28,axiom,
( ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers )
= limit_ordinals ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_ordinals) ).
thf(220,plain,
( ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers )
= limit_ordinals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(221,plain,
( ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers )
= limit_ordinals ),
inference(lifteq,[status(thm)],[220]) ).
thf(1717,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ ( complement @ kind_1_ordinals ) @ null_class )
= limit_ordinals )
| ( A != ordinal_numbers ) ),
inference(paramod_ordered,[status(thm)],[508,221]) ).
thf(1718,plain,
( ( member @ ( regular @ ordinal_numbers ) @ ordinal_numbers )
| ( ( intersection @ ( complement @ kind_1_ordinals ) @ null_class )
= limit_ordinals ) ),
inference(pattern_uni,[status(thm)],[1717:[bind(A,$thf( ordinal_numbers ))]]) ).
thf(1,negated_conjecture,
member @ ( successor @ x ) @ universal_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1) ).
thf(161,plain,
member @ ( successor @ x ) @ universal_class,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
thf(465,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(466,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
inference(cnf,[status(esa)],[465]) ).
thf(520,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ ( successor @ x ) @ universal_class )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[161,466]) ).
thf(521,plain,
~ ( member @ ( successor @ x ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[520:[bind(A,$thf( successor @ x )),bind(B,$thf( universal_class ))]]) ).
thf(538,plain,
( ( member @ ( successor @ x ) @ ( complement @ universal_class ) )
!= ( member @ ( successor @ x ) @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[161,521]) ).
thf(540,plain,
( ( ( successor @ x )
!= ( successor @ x ) )
| ( ( complement @ universal_class )
!= universal_class ) ),
inference(simp,[status(thm)],[538]) ).
thf(542,plain,
( ( complement @ universal_class )
!= universal_class ),
inference(simp,[status(thm)],[540]) ).
thf(1679,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( null_class != universal_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[508,542]) ).
thf(1680,plain,
( ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) )
| ( null_class != universal_class ) ),
inference(pattern_uni,[status(thm)],[1679:[bind(A,$thf( complement @ universal_class ))]]) ).
thf(140,axiom,
member @ omega @ universal_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
thf(459,plain,
member @ omega @ universal_class,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ omega @ universal_class )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[459,466]) ).
thf(524,plain,
~ ( member @ omega @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[523:[bind(A,$thf( omega )),bind(B,$thf( universal_class ))]]) ).
thf(9486,plain,
( ( null_class != universal_class )
| ( ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) )
!= ( member @ omega @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1680,524]) ).
thf(9550,plain,
( ( null_class != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= omega )
| ( ( complement @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[9486]) ).
thf(9570,plain,
( ( null_class != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= omega ) ),
inference(simp,[status(thm)],[9550]) ).
thf(9588,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= omega )
| ( null_class != null_class ) ),
inference(paramod_ordered,[status(thm)],[508,9570]) ).
thf(9589,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= omega ) ),
inference(pattern_uni,[status(thm)],[9588:[]]) ).
thf(9648,plain,
( ( member @ ( regular @ universal_class ) @ universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= omega ) ),
inference(simp,[status(thm)],[9589]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
thf(479,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ union_of_range_map )
| ( ( sum_class @ ( range_of @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_range_map2) ).
thf(347,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ union_of_range_map )
| ( ( sum_class @ ( range_of @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(145,axiom,
( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) )
= subset_relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_relation) ).
thf(467,plain,
( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) )
= subset_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(468,plain,
( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) )
= subset_relation ),
inference(lifteq,[status(thm)],[467]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(74,axiom,
subclass @ composition_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function1) ).
thf(321,plain,
subclass @ composition_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
thf(188,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[188]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(2389,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B != universal_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[190,542]) ).
thf(2390,plain,
! [A: $i] :
( ~ ( subclass @ ( complement @ universal_class ) @ A )
| ~ ( subclass @ A @ ( complement @ universal_class ) )
| ( A != universal_class ) ),
inference(pattern_uni,[status(thm)],[2389:[bind(A,$thf( complement @ universal_class )),bind(B,$thf( B ))]]) ).
thf(3141,plain,
( ~ ( subclass @ ( complement @ universal_class ) @ universal_class )
| ~ ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[2390]) ).
thf(138,axiom,
! [A: $i] : ( subclass @ A @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(455,plain,
! [A: $i] : ( subclass @ A @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(3639,plain,
( ~ $true
| ~ ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(rewrite,[status(thm)],[3141,455]) ).
thf(3640,plain,
~ ( subclass @ universal_class @ ( complement @ universal_class ) ),
inference(simp,[status(thm)],[3639]) ).
thf(3651,plain,
( ( subclass @ composition_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ) )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[321,3640]) ).
thf(3698,plain,
( ( composition_function != universal_class )
| ( ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3651]) ).
thf(80,axiom,
! [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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip2) ).
thf(333,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(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( intersection @ ( complement @ ( intersection @ A @ B ) ) @ ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) )
= ( symmetric_difference @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( intersection @ ( complement @ ( intersection @ A @ B ) ) @ ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) )
= ( symmetric_difference @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( member @ B @ universal_class )
| ( member @ ( image @ A @ B ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
thf(481,plain,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( member @ B @ universal_class )
| ( member @ ( image @ A @ B ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(88,axiom,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).
thf(352,plain,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(131,axiom,
! [A: $i] :
( ( member @ A @ omega )
| ( ( integer_of @ A )
= null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',integer_function2) ).
thf(440,plain,
! [A: $i] :
( ( member @ A @ omega )
| ( ( integer_of @ A )
= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(441,plain,
! [A: $i] :
( ( member @ A @ omega )
| ( ( integer_of @ A )
= null_class ) ),
inference(cnf,[status(esa)],[440]) ).
thf(442,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( member @ A @ omega ) ),
inference(lifteq,[status(thm)],[441]) ).
thf(519,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( ( member @ ( successor @ x ) @ universal_class )
!= ( member @ A @ ( complement @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[161,466]) ).
thf(527,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( ( successor @ x )
!= A )
| ( ( complement @ B )
!= universal_class ) ),
inference(simp,[status(thm)],[519]) ).
thf(532,plain,
! [A: $i] :
( ~ ( member @ ( successor @ x ) @ A )
| ( ( complement @ A )
!= universal_class ) ),
inference(simp,[status(thm)],[527]) ).
thf(1004,plain,
! [B: $i,A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( ( complement @ B )
!= universal_class )
| ( ( member @ A @ omega )
!= ( member @ ( successor @ x ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[442,532]) ).
thf(1005,plain,
( ( ( integer_of @ ( successor @ x ) )
= null_class )
| ( ( complement @ omega )
!= universal_class ) ),
inference(pattern_uni,[status(thm)],[1004:[bind(A,$thf( successor @ x )),bind(B,$thf( omega ))]]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( union @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( union @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( union @ A @ B ) ),
inference(lifteq,[status(thm)],[275]) ).
thf(113,axiom,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(403,plain,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(404,plain,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
inference(lifteq,[status(thm)],[403]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(10,axiom,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
thf(179,plain,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(180,plain,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
inference(lifteq,[status(thm)],[179]) ).
thf(4032,plain,
! [B: $i,A: $i] :
( ( domain_of @ ( inverse @ ( restrict @ A @ B @ universal_class ) ) )
= ( image @ A @ B ) ),
inference(rewrite,[status(thm)],[346,180]) ).
thf(7,axiom,
( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ ordinal_numbers ) )
= kind_1_ordinals ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kind_1_ordinals) ).
thf(172,plain,
( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ ordinal_numbers ) )
= kind_1_ordinals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(173,plain,
( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ ordinal_numbers ) )
= kind_1_ordinals ),
inference(lifteq,[status(thm)],[172]) ).
thf(4033,plain,
! [B: $i,A: $i] :
( ( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( inverse @ ( restrict @ A @ B @ universal_class ) ) ) )
= kind_1_ordinals )
| ( ( image @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[4032,173]) ).
thf(4034,plain,
( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[4033:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers ))]]) ).
thf(4139,plain,
! [A: $i] :
( ( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) )
= kind_1_ordinals )
| ( ( inverse @ A )
!= ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[404,4034]) ).
thf(4140,plain,
( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) @ universal_class ) ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[4139:[bind(A,$thf( restrict @ successor_relation @ ordinal_numbers @ universal_class ))]]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( intersection @ ( cross_product @ A @ B ) @ C )
= ( restrict @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( intersection @ ( cross_product @ A @ B ) @ C )
= ( restrict @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( restrict @ C @ A @ B )
= ( intersection @ ( cross_product @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[208]) ).
thf(10497,plain,
( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) @ universal_class ) ) ) ) )
= kind_1_ordinals ),
inference(rewrite,[status(thm)],[4140,209]) ).
thf(17277,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= kind_1_ordinals )
| ( ( union @ A @ B )
!= ( union @ ( singleton @ null_class ) @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) @ universal_class ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[276,10497]) ).
thf(17278,plain,
( ( complement @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) @ universal_class ) ) ) ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[17277:[bind(A,$thf( singleton @ null_class )),bind(B,$thf( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) @ universal_class ) ) ) ))]]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ application_function )
| ( member @ B @ ( domain_of @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn2) ).
thf(449,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ application_function )
| ( member @ B @ ( domain_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( second @ ( not_subclass_element @ ( restrict @ A @ ( singleton @ B ) @ C ) @ null_class ) )
= ( range @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ( second @ ( not_subclass_element @ ( restrict @ A @ ( singleton @ B ) @ C ) @ null_class ) )
= ( range @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(50,axiom,
! [A: $i] :
( ( first @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_term_defn1) ).
thf(268,plain,
! [A: $i] :
( ( first @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(269,plain,
! [A: $i] :
( ( first @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued1 @ A ) ),
inference(lifteq,[status(thm)],[268]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( subclass @ ( sum_class @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers2) ).
thf(408,plain,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( subclass @ ( sum_class @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( subclass @ ( cross_product @ A @ A ) @ ( union @ identity_relation @ ( symmetrization_of @ B ) ) )
| ( connected @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected2) ).
thf(216,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ ( cross_product @ A @ A ) @ ( union @ identity_relation @ ( symmetrization_of @ B ) ) )
| ( connected @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ ( cross_product @ A @ A ) @ ( union @ identity_relation @ ( symmetrization_of @ B ) ) )
| ( connected @ B @ A ) ),
inference(cnf,[status(esa)],[216]) ).
thf(15,axiom,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_definition) ).
thf(191,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(192,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( power_class @ B ) )
| ( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
!= ( complement @ B ) ) ),
inference(paramod_ordered,[status(thm)],[192,192]) ).
thf(858,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[857:[bind(A,$thf( E )),bind(B,$thf( image @ element_relation @ ( complement @ E ) ))]]) ).
thf(878,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(simp,[status(thm)],[858]) ).
thf(2,negated_conjecture,
~ ( member @ x @ ( successor @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2) ).
thf(162,plain,
~ ( member @ x @ ( successor @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(163,plain,
~ ( member @ x @ ( successor @ x ) ),
inference(polarity_switch,[status(thm)],[162]) ).
thf(509,plain,
( ( member @ ( successor @ x ) @ universal_class )
!= ( member @ x @ ( successor @ x ) ) ),
inference(paramod_ordered,[status(thm)],[161,163]) ).
thf(511,plain,
( ( ( successor @ x )
!= x )
| ( ( successor @ x )
!= universal_class ) ),
inference(simp,[status(thm)],[509]) ).
thf(77,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
thf(328,plain,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(37,axiom,
inductive @ omega,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
thf(239,plain,
inductive @ omega,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(3,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ omega @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
thf(164,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ omega @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(165,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ omega @ A ) ),
inference(cnf,[status(esa)],[164]) ).
thf(3654,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( subclass @ omega @ A )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,3640]) ).
thf(3696,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( omega != universal_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3654]) ).
thf(3707,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( omega != universal_class ) ),
inference(simp,[status(thm)],[3696]) ).
thf(3724,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ~ ( inductive @ ( complement @ universal_class ) )
| ( B != universal_class )
| ( A != omega ) ),
inference(paramod_ordered,[status(thm)],[190,3707]) ).
thf(3725,plain,
! [A: $i] :
( ~ ( subclass @ omega @ A )
| ~ ( subclass @ A @ omega )
| ~ ( inductive @ ( complement @ universal_class ) )
| ( A != universal_class ) ),
inference(pattern_uni,[status(thm)],[3724:[bind(A,$thf( omega ))]]) ).
thf(3742,plain,
( ~ ( subclass @ omega @ universal_class )
| ~ ( subclass @ universal_class @ omega )
| ~ ( inductive @ ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3725]) ).
thf(16901,plain,
( ~ $true
| ~ ( subclass @ universal_class @ omega )
| ~ ( inductive @ ( complement @ universal_class ) ) ),
inference(rewrite,[status(thm)],[3742,455]) ).
thf(16902,plain,
( ~ ( subclass @ universal_class @ omega )
| ~ ( inductive @ ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[16901]) ).
thf(16970,plain,
( ~ ( subclass @ universal_class @ omega )
| ( ( inductive @ ( complement @ universal_class ) )
!= ( inductive @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[239,16902]) ).
thf(17006,plain,
( ~ ( subclass @ universal_class @ omega )
| ( ( complement @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[16970]) ).
thf(17038,plain,
( ( ( complement @ universal_class )
!= omega )
| ( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[328,17006]) ).
thf(17113,plain,
( ( ( complement @ universal_class )
!= omega )
| ( element_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[17038]) ).
thf(103,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
thf(384,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
| ( ( successor @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation2) ).
thf(472,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
| ( ( successor @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(102,axiom,
subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
thf(383,plain,
subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(3667,plain,
( ( subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[383,3640]) ).
thf(3693,plain,
( ( domain_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3667]) ).
thf(1760,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) )
| ( A != element_relation ) ),
inference(paramod_ordered,[status(thm)],[508,328]) ).
thf(1761,plain,
( ( member @ ( regular @ element_relation ) @ element_relation )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[1760:[bind(A,$thf( element_relation ))]]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( first @ ( not_subclass_element @ ( restrict @ A @ B @ ( singleton @ C ) ) @ null_class ) )
= ( domain @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain) ).
thf(245,plain,
! [C: $i,B: $i,A: $i] :
( ( first @ ( not_subclass_element @ ( restrict @ A @ B @ ( singleton @ C ) ) @ null_class ) )
= ( domain @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ( domain @ A @ B @ C )
= ( first @ ( not_subclass_element @ ( restrict @ A @ B @ ( singleton @ C ) ) @ null_class ) ) ),
inference(lifteq,[status(thm)],[245]) ).
thf(30694,plain,
! [C: $i,B: $i,A: $i] :
( ( domain @ A @ B @ C )
= ( first @ ( not_subclass_element @ ( intersection @ ( cross_product @ B @ ( singleton @ C ) ) @ A ) @ null_class ) ) ),
inference(rewrite,[status(thm)],[246,209]) ).
thf(510,plain,
( ( member @ omega @ universal_class )
!= ( member @ x @ ( successor @ x ) ) ),
inference(paramod_ordered,[status(thm)],[459,163]) ).
thf(512,plain,
( ( omega != x )
| ( ( successor @ x )
!= universal_class ) ),
inference(simp,[status(thm)],[510]) ).
thf(2509,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( B != x )
| ( ( successor @ x )
!= universal_class )
| ( A != omega ) ),
inference(paramod_ordered,[status(thm)],[190,512]) ).
thf(2510,plain,
! [A: $i] :
( ~ ( subclass @ omega @ A )
| ~ ( subclass @ A @ omega )
| ( A != x )
| ( ( successor @ x )
!= universal_class ) ),
inference(pattern_uni,[status(thm)],[2509:[bind(A,$thf( omega ))]]) ).
thf(3182,plain,
( ~ ( subclass @ omega @ x )
| ~ ( subclass @ x @ omega )
| ( ( successor @ x )
!= universal_class ) ),
inference(simp,[status(thm)],[2510]) ).
thf(5392,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ~ ( subclass @ x @ omega )
| ( ( successor @ x )
!= universal_class )
| ( ( subclass @ omega @ A )
!= ( subclass @ omega @ x ) ) ),
inference(paramod_ordered,[status(thm)],[165,3182]) ).
thf(5393,plain,
( ~ ( inductive @ x )
| ~ ( subclass @ x @ omega )
| ( ( successor @ x )
!= universal_class ) ),
inference(pattern_uni,[status(thm)],[5392:[bind(A,$thf( x ))]]) ).
thf(120,axiom,
! [A: $i] : ( subclass @ ( compose_class @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition1) ).
thf(417,plain,
! [A: $i] : ( subclass @ ( compose_class @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ C ) ),
inference(cnf,[status(esa)],[230]) ).
thf(21415,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( subclass @ ( domain_of @ ( inverse @ A ) ) @ C ) ),
inference(rewrite,[status(thm)],[231,180]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ( connected @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering1) ).
thf(301,plain,
! [B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ( connected @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(129,axiom,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( well_ordering @ element_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers1) ).
thf(436,plain,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( well_ordering @ element_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( intersection @ A @ ( cross_product @ B @ C ) )
= ( restrict @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( intersection @ A @ ( cross_product @ B @ C ) )
= ( restrict @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1774,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ null_class @ universal_class )
| ( A
!= ( successor @ x ) ) ),
inference(paramod_ordered,[status(thm)],[508,161]) ).
thf(1775,plain,
( ( member @ ( regular @ ( successor @ x ) ) @ ( successor @ x ) )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[1774:[bind(A,$thf( successor @ x ))]]) ).
thf(12047,plain,
( ( member @ null_class @ universal_class )
| ( ( member @ ( regular @ ( successor @ x ) ) @ ( successor @ x ) )
!= ( member @ x @ ( successor @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[1775,163]) ).
thf(12051,plain,
( ( member @ null_class @ universal_class )
| ( ( regular @ ( successor @ x ) )
!= x )
| ( ( successor @ x )
!= ( successor @ x ) ) ),
inference(simp,[status(thm)],[12047]) ).
thf(12062,plain,
( ( member @ null_class @ universal_class )
| ( ( regular @ ( successor @ x ) )
!= x ) ),
inference(simp,[status(thm)],[12051]) ).
thf(117,axiom,
! [A: $i] :
( ( domain_of @ ( restrict @ element_relation @ universal_class @ A ) )
= ( sum_class @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).
thf(412,plain,
! [A: $i] :
( ( domain_of @ ( restrict @ element_relation @ universal_class @ A ) )
= ( sum_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(413,plain,
! [A: $i] :
( ( domain_of @ ( restrict @ element_relation @ universal_class @ A ) )
= ( sum_class @ A ) ),
inference(lifteq,[status(thm)],[412]) ).
thf(10501,plain,
! [A: $i] :
( ( domain_of @ ( intersection @ ( cross_product @ universal_class @ A ) @ element_relation ) )
= ( sum_class @ A ) ),
inference(rewrite,[status(thm)],[413,209]) ).
thf(107,axiom,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(389,plain,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9463,plain,
! [B: $i,A: $i] :
( ( null_class != universal_class )
| ~ ( member @ A @ B )
| ( ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) )
!= ( member @ A @ ( complement @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1680,466]) ).
thf(9464,plain,
( ( null_class != universal_class )
| ~ ( member @ ( regular @ ( complement @ universal_class ) ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[9463:[bind(A,$thf( regular @ ( complement @ universal_class ) )),bind(B,$thf( universal_class ))]]) ).
thf(39,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) )
| ( operation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation4) ).
thf(242,plain,
! [A: $i] :
( ~ ( function @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) )
| ( operation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(243,plain,
! [A: $i] :
( ~ ( function @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) )
| ( operation @ A ) ),
inference(cnf,[status(esa)],[242]) ).
thf(244,plain,
! [A: $i] :
( ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
!= ( domain_of @ A ) )
| ~ ( function @ A )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) )
| ( operation @ A ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(27920,plain,
! [A: $i] :
( ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
!= ( domain_of @ A ) )
| ~ ( function @ A )
| ~ ( subclass @ ( domain_of @ ( inverse @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
| ( operation @ A ) ),
inference(rewrite,[status(thm)],[244,180]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
thf(357,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1350,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ B ) ) ) )
| ( ( power_class @ ( image @ element_relation @ ( complement @ A ) ) )
!= ( power_class @ B ) ) ),
inference(paramod_ordered,[status(thm)],[878,192]) ).
thf(1351,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1350:[bind(A,$thf( E )),bind(B,$thf( image @ element_relation @ ( complement @ E ) ))]]) ).
thf(1409,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[1351]) ).
thf(1915,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ~ ( member @ x @ null_class )
| ( A
!= ( successor @ x ) ) ),
inference(paramod_ordered,[status(thm)],[508,163]) ).
thf(1916,plain,
( ( member @ ( regular @ ( successor @ x ) ) @ ( successor @ x ) )
| ~ ( member @ x @ null_class ) ),
inference(pattern_uni,[status(thm)],[1915:[bind(A,$thf( successor @ x ))]]) ).
thf(14425,plain,
( ~ ( member @ x @ null_class )
| ( ( member @ ( regular @ ( successor @ x ) ) @ ( successor @ x ) )
!= ( member @ x @ ( successor @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[1916,163]) ).
thf(14443,plain,
( ~ ( member @ x @ null_class )
| ( ( regular @ ( successor @ x ) )
!= x )
| ( ( successor @ x )
!= ( successor @ x ) ) ),
inference(simp,[status(thm)],[14425]) ).
thf(14458,plain,
( ~ ( member @ x @ null_class )
| ( ( regular @ ( successor @ x ) )
!= x ) ),
inference(simp,[status(thm)],[14443]) ).
thf(14463,plain,
( ( ( regular @ ( successor @ x ) )
!= x )
| ( ( member @ null_class @ universal_class )
!= ( member @ x @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[12062,14458]) ).
thf(14510,plain,
( ( ( regular @ ( successor @ x ) )
!= x )
| ( null_class != x )
| ( null_class != universal_class ) ),
inference(simp,[status(thm)],[14463]) ).
thf(390,plain,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
inference(lifteq,[status(thm)],[389]) ).
thf(17456,plain,
! [C: $i,B: $i,A: $i] :
( ( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( successor @ C ) )
| ( ( union @ A @ B )
!= ( union @ C @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[276,390]) ).
thf(17457,plain,
! [A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ ( singleton @ A ) ) ) )
= ( successor @ A ) ),
inference(pattern_uni,[status(thm)],[17456:[bind(A,$thf( D )),bind(B,$thf( singleton @ D )),bind(C,$thf( D ))]]) ).
thf(17610,plain,
! [A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ ( singleton @ A ) ) ) )
= ( successor @ A ) ),
inference(simp,[status(thm)],[17457]) ).
thf(3643,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ~ ( subclass @ universal_class @ null_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[508,3640]) ).
thf(3644,plain,
( ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) )
| ~ ( subclass @ universal_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[3643:[bind(A,$thf( complement @ universal_class ))]]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( single_valued_class @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class1) ).
thf(195,plain,
! [A: $i] :
( ~ ( single_valued_class @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(196,plain,
! [A: $i] :
( ~ ( single_valued_class @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(cnf,[status(esa)],[195]) ).
thf(16,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
thf(193,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(194,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(100,axiom,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
thf(380,plain,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(601,plain,
! [B: $i,A: $i] :
( ( member @ ( unordered_pair @ A @ B ) @ universal_class )
!= ( member @ x @ ( successor @ x ) ) ),
inference(paramod_ordered,[status(thm)],[380,163]) ).
thf(602,plain,
! [B: $i,A: $i] :
( ( ( unordered_pair @ A @ B )
!= x )
| ( ( successor @ x )
!= universal_class ) ),
inference(simp,[status(thm)],[601]) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( singleton @ A )
!= x )
| ( ( successor @ x )
!= universal_class )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[194,602]) ).
thf(1132,plain,
! [A: $i] :
( ( ( singleton @ A )
!= x )
| ( ( successor @ x )
!= universal_class ) ),
inference(pattern_uni,[status(thm)],[1131:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(141,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
thf(460,plain,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( restrict @ A @ B @ C )
= ( intersection @ A @ ( cross_product @ B @ C ) ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(36002,plain,
! [C: $i,B: $i,A: $i] :
( ( intersection @ ( cross_product @ B @ C ) @ A )
= ( intersection @ A @ ( cross_product @ B @ C ) ) ),
inference(rewrite,[status(thm)],[258,209]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( unordered_pair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( unordered_pair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(57,axiom,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
thf(283,plain,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(284,plain,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
inference(lifteq,[status(thm)],[283]) ).
thf(10508,plain,
( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ) )
= kind_1_ordinals ),
inference(rewrite,[status(thm)],[4034,209]) ).
thf(17451,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= kind_1_ordinals )
| ( ( union @ A @ B )
!= ( union @ ( singleton @ null_class ) @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[276,10508]) ).
thf(17452,plain,
( ( complement @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[17451:[bind(A,$thf( singleton @ null_class )),bind(B,$thf( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ))]]) ).
thf(36155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( complement @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( domain_of @ ( inverse @ ( intersection @ A @ ( cross_product @ B @ C ) ) ) ) ) ) )
= kind_1_ordinals )
| ( ( intersection @ ( cross_product @ B @ C ) @ A )
!= ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ),
inference(paramod_ordered,[status(thm)],[36002,17452]) ).
thf(36156,plain,
( ( complement @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( domain_of @ ( inverse @ ( intersection @ successor_relation @ ( cross_product @ ordinal_numbers @ universal_class ) ) ) ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[36155:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers )),bind(C,$thf( universal_class ))]]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ composition_function )
| ( ( compose @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function2) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ composition_function )
| ( ( compose @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
thf(228,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(36007,plain,
! [C: $i,B: $i,A: $i] :
( ( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ A @ ( cross_product @ B @ C ) ) )
= subset_relation )
| ( ( intersection @ ( cross_product @ B @ C ) @ A )
!= ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[36002,468]) ).
thf(36008,plain,
( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) @ ( cross_product @ universal_class @ universal_class ) ) )
= subset_relation ),
inference(pattern_uni,[status(thm)],[36007:[bind(A,$thf( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) )),bind(B,$thf( universal_class )),bind(C,$thf( universal_class ))]]) ).
thf(72,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ~ ( member @ ( ordered_pair @ D @ E ) @ ( domain_of @ B ) )
| ( ( apply @ C @ ( ordered_pair @ ( apply @ A @ D ) @ ( apply @ A @ E ) ) )
= ( apply @ A @ ( apply @ B @ ( ordered_pair @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism4) ).
thf(316,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ~ ( member @ ( ordered_pair @ D @ E ) @ ( domain_of @ B ) )
| ( ( apply @ C @ ( ordered_pair @ ( apply @ A @ D ) @ ( apply @ A @ E ) ) )
= ( apply @ A @ ( apply @ B @ ( ordered_pair @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(11,axiom,
function @ choice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
thf(181,plain,
function @ choice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(229,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(cnf,[status(esa)],[228]) ).
thf(20153,plain,
! [A: $i] :
( ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( ( function @ choice )
!= ( function @ A ) ) ),
inference(paramod_ordered,[status(thm)],[181,229]) ).
thf(20154,plain,
subclass @ ( compose @ choice @ ( inverse @ choice ) ) @ identity_relation,
inference(pattern_uni,[status(thm)],[20153:[bind(A,$thf( choice ))]]) ).
thf(20205,plain,
! [A: $i] :
( ( subclass @ ( compose @ choice @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) @ identity_relation )
| ( ( inverse @ A )
!= ( inverse @ choice ) ) ),
inference(paramod_ordered,[status(thm)],[404,20154]) ).
thf(20206,plain,
subclass @ ( compose @ choice @ ( domain_of @ ( flip @ ( cross_product @ choice @ universal_class ) ) ) ) @ identity_relation,
inference(pattern_uni,[status(thm)],[20205:[bind(A,$thf( choice ))]]) ).
thf(17304,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= kind_1_ordinals )
| ( ( union @ A @ B )
!= ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ ordinal_numbers ) ) ) ),
inference(paramod_ordered,[status(thm)],[276,173]) ).
thf(17305,plain,
( ( complement @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[17304:[bind(A,$thf( singleton @ null_class )),bind(B,$thf( image @ successor_relation @ ordinal_numbers ))]]) ).
thf(4046,plain,
! [C: $i,B: $i,A: $i] :
( ( ( complement @ ( domain_of @ ( inverse @ ( restrict @ A @ B @ universal_class ) ) ) )
= ( power_class @ C ) )
| ( ( image @ A @ B )
!= ( image @ element_relation @ ( complement @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[4032,192]) ).
thf(4047,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) ) )
= ( power_class @ A ) ),
inference(pattern_uni,[status(thm)],[4046:[bind(A,$thf( element_relation )),bind(B,$thf( complement @ D )),bind(C,$thf( D ))]]) ).
thf(4115,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) ) )
= ( power_class @ A ) ),
inference(simp,[status(thm)],[4047]) ).
thf(10496,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ( complement @ A ) @ universal_class ) @ element_relation ) ) ) )
= ( power_class @ A ) ),
inference(rewrite,[status(thm)],[4115,209]) ).
thf(17859,plain,
! [A: $i] :
( ( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) )
= ( power_class @ A ) )
| ( ( complement @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17305,10496]) ).
thf(17860,plain,
( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) )
= ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) ) ),
inference(pattern_uni,[status(thm)],[17859:[bind(A,$thf( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ))]]) ).
thf(17724,plain,
! [A: $i] :
( ( ( complement @ ( image @ element_relation @ kind_1_ordinals ) )
= ( power_class @ A ) )
| ( ( complement @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17305,192]) ).
thf(17725,plain,
( ( complement @ ( image @ element_relation @ kind_1_ordinals ) )
= ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) ) ),
inference(pattern_uni,[status(thm)],[17724:[bind(A,$thf( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ))]]) ).
thf(25449,plain,
( ( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) )
= ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) )
| ( ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) )
!= ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17860,17725]) ).
thf(25450,plain,
( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) )
= ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ),
inference(pattern_uni,[status(thm)],[25449:[]]) ).
thf(25979,plain,
! [A: $i] :
( ( ( complement @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) )
= ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) )
| ( ( inverse @ A )
!= ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) ),
inference(paramod_ordered,[status(thm)],[404,25450]) ).
thf(25980,plain,
( ( complement @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) @ universal_class ) ) ) ) )
= ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ),
inference(pattern_uni,[status(thm)],[25979:[bind(A,$thf( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ))]]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible3) ).
thf(218,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) ) ),
inference(cnf,[status(esa)],[218]) ).
thf(14533,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( subclass @ ( domain_of @ ( inverse @ A ) ) @ ( domain_of @ ( domain_of @ C ) ) ) ),
inference(rewrite,[status(thm)],[219,180]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( domain_of @ B ) )
| ( ( restrict @ B @ A @ universal_class )
!= C )
| ( member @ ( ordered_pair @ A @ C ) @ ( rest_of @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_of4) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( domain_of @ B ) )
| ( ( restrict @ B @ A @ universal_class )
!= C )
| ( member @ ( ordered_pair @ A @ C ) @ ( rest_of @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1713,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ null_class @ ordinal_numbers )
= limit_ordinals )
| ( A
!= ( complement @ kind_1_ordinals ) ) ),
inference(paramod_ordered,[status(thm)],[508,221]) ).
thf(1714,plain,
( ( member @ ( regular @ ( complement @ kind_1_ordinals ) ) @ ( complement @ kind_1_ordinals ) )
| ( ( intersection @ null_class @ ordinal_numbers )
= limit_ordinals ) ),
inference(pattern_uni,[status(thm)],[1713:[bind(A,$thf( complement @ kind_1_ordinals ))]]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( intersection @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( recursion @ null_class @ ( apply @ add_relation @ A ) @ union_of_range_map )
= ( ordinal_multiply @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_multiplication) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( recursion @ null_class @ ( apply @ add_relation @ A ) @ union_of_range_map )
= ( ordinal_multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(152,axiom,
! [A: $i] :
( ~ ( member @ A @ omega )
| ( ( integer_of @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',integer_function1) ).
thf(485,plain,
! [A: $i] :
( ~ ( member @ A @ omega )
| ( ( integer_of @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(89,axiom,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate1) ).
thf(353,plain,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( compose_class @ C ) )
| ( ( compose @ C @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition2) ).
thf(492,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( compose_class @ C ) )
| ( ( compose @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(17697,plain,
! [A: $i] :
( ( ( power_class @ ( image @ element_relation @ kind_1_ordinals ) )
= ( complement @ ( image @ element_relation @ ( power_class @ A ) ) ) )
| ( ( complement @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17305,878]) ).
thf(17698,plain,
( ( power_class @ ( image @ element_relation @ kind_1_ordinals ) )
= ( complement @ ( image @ element_relation @ ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[17697:[bind(A,$thf( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ))]]) ).
thf(25519,plain,
( ( ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) ) ) )
= ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) )
| ( ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) )
!= ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17860,17698]) ).
thf(25520,plain,
( ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) ) ) )
= ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ),
inference(pattern_uni,[status(thm)],[25519:[]]) ).
thf(26770,plain,
! [A: $i] :
( ( ( power_class @ ( image @ element_relation @ kind_1_ordinals ) )
= ( power_class @ A ) )
| ( ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) ) ) )
!= ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[25520,192]) ).
thf(26771,plain,
( ( power_class @ ( image @ element_relation @ kind_1_ordinals ) )
= ( power_class @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) ) ),
inference(pattern_uni,[status(thm)],[26770:[bind(A,$thf( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ))]]) ).
thf(36145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( power_class @ ( domain_of @ ( inverse @ ( intersection @ A @ ( cross_product @ B @ C ) ) ) ) )
= ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) )
| ( ( intersection @ ( cross_product @ B @ C ) @ A )
!= ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ),
inference(paramod_ordered,[status(thm)],[36002,26771]) ).
thf(36146,plain,
( ( power_class @ ( domain_of @ ( inverse @ ( intersection @ element_relation @ ( cross_product @ kind_1_ordinals @ universal_class ) ) ) ) )
= ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ),
inference(pattern_uni,[status(thm)],[36145:[bind(A,$thf( element_relation )),bind(B,$thf( kind_1_ordinals )),bind(C,$thf( universal_class ))]]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( range @ A @ B @ C )
= ( second @ ( not_subclass_element @ ( restrict @ A @ ( singleton @ B ) @ C ) @ null_class ) ) ),
inference(lifteq,[status(thm)],[247]) ).
thf(31860,plain,
! [C: $i,B: $i,A: $i] :
( ( range @ A @ B @ C )
= ( second @ ( not_subclass_element @ ( intersection @ ( cross_product @ ( singleton @ B ) @ C ) @ A ) @ null_class ) ) ),
inference(rewrite,[status(thm)],[248,209]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ rest_relation )
| ( ( rest_of @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_relation2) ).
thf(428,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ rest_relation )
| ( ( rest_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( segment @ A @ B @ C )
= ( domain_of @ ( restrict @ A @ B @ ( singleton @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment) ).
thf(312,plain,
! [C: $i,B: $i,A: $i] :
( ( segment @ A @ B @ C )
= ( domain_of @ ( restrict @ A @ B @ ( singleton @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( subclass @ ( cross_product @ B @ B ) @ ( union @ identity_relation @ ( symmetrization_of @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected1) ).
thf(206,plain,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( subclass @ ( cross_product @ B @ B ) @ ( union @ identity_relation @ ( symmetrization_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(105,axiom,
subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_relation1) ).
thf(387,plain,
subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1563,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) )
| ( A != rest_relation ) ),
inference(paramod_ordered,[status(thm)],[508,387]) ).
thf(1564,plain,
( ( member @ ( regular @ rest_relation ) @ rest_relation )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[1563:[bind(A,$thf( rest_relation ))]]) ).
thf(12089,plain,
! [B: $i,A: $i] :
( ( ( regular @ ( successor @ x ) )
!= x )
| ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ null_class @ universal_class )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12062,466]) ).
thf(12090,plain,
( ( ( regular @ ( successor @ x ) )
!= x )
| ~ ( member @ null_class @ ( complement @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[12089:[bind(A,$thf( null_class )),bind(B,$thf( universal_class ))]]) ).
thf(36012,plain,
! [C: $i,B: $i,A: $i] :
( ( ( intersection @ A @ ( cross_product @ B @ C ) )
= subset_relation )
| ( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) )
!= ( intersection @ ( cross_product @ B @ C ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[468,36002]) ).
thf(36013,plain,
( ( intersection @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) @ ( cross_product @ universal_class @ universal_class ) )
= subset_relation ),
inference(pattern_uni,[status(thm)],[36012:[bind(A,$thf( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) )),bind(B,$thf( universal_class )),bind(C,$thf( universal_class ))]]) ).
thf(36022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( domain_of @ ( intersection @ A @ ( cross_product @ B @ C ) ) )
= ( sum_class @ D ) )
| ( ( intersection @ ( cross_product @ B @ C ) @ A )
!= ( intersection @ ( cross_product @ universal_class @ D ) @ element_relation ) ) ),
inference(paramod_ordered,[status(thm)],[36002,10501]) ).
thf(36023,plain,
! [A: $i] :
( ( domain_of @ ( intersection @ element_relation @ ( cross_product @ universal_class @ A ) ) )
= ( sum_class @ A ) ),
inference(pattern_uni,[status(thm)],[36022:[bind(A,$thf( element_relation )),bind(B,$thf( universal_class )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(36408,plain,
! [A: $i] :
( ( domain_of @ ( intersection @ element_relation @ ( cross_product @ universal_class @ A ) ) )
= ( sum_class @ A ) ),
inference(simp,[status(thm)],[36023]) ).
thf(137,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).
thf(453,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( compatible @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
thf(292,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( compatible @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
thf(232,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(233,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
inference(cnf,[status(esa)],[232]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
thf(270,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(20215,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ ( compose @ choice @ ( inverse @ null_class ) ) @ identity_relation )
| ( A != choice ) ),
inference(paramod_ordered,[status(thm)],[508,20154]) ).
thf(20216,plain,
( ( member @ ( regular @ choice ) @ choice )
| ( subclass @ ( compose @ choice @ ( inverse @ null_class ) ) @ identity_relation ) ),
inference(pattern_uni,[status(thm)],[20215:[bind(A,$thf( choice ))]]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( asymmetric @ A @ B )
| ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
= null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',asymmetric1) ).
thf(201,plain,
! [B: $i,A: $i] :
( ~ ( asymmetric @ A @ B )
| ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ ( image @ C @ ( singleton @ D ) ) ) )
| ~ ( member @ ( ordered_pair @ D @ A ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ D @ A ) @ ( compose @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose3) ).
thf(381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ ( image @ C @ ( singleton @ D ) ) ) )
| ~ ( member @ ( ordered_pair @ D @ A ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ D @ A ) @ ( compose @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1821,plain,
! [A: $i] :
( ( A = null_class )
| ( ( member @ ( regular @ A ) @ A )
!= ( member @ ( successor @ x ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[508,521]) ).
thf(1931,plain,
! [A: $i] :
( ( A = null_class )
| ( ( regular @ A )
!= ( successor @ x ) )
| ( A
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[1821]) ).
thf(2000,plain,
( ( ( complement @ universal_class )
= null_class )
| ( ( regular @ ( complement @ universal_class ) )
!= ( successor @ x ) ) ),
inference(simp,[status(thm)],[1931]) ).
thf(21669,plain,
( ( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) )
| ( ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) )
!= ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17725,17698]) ).
thf(21670,plain,
( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ),
inference(pattern_uni,[status(thm)],[21669:[]]) ).
thf(22096,plain,
! [A: $i] :
( ( ( power_class @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ A ) ) ) )
| ( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21670,878]) ).
thf(22097,plain,
( ( power_class @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[22096:[bind(A,$thf( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ))]]) ).
thf(9446,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) )
| ( A != universal_class )
| ( null_class != null_class ) ),
inference(paramod_ordered,[status(thm)],[508,1680]) ).
thf(9447,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) )
| ( A != universal_class ) ),
inference(pattern_uni,[status(thm)],[9446:[]]) ).
thf(9571,plain,
( ( member @ ( regular @ universal_class ) @ universal_class )
| ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[9447]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( apply @ ( recursion @ A @ successor_relation @ union_of_range_map ) @ B )
= ( ordinal_add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_addition) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( apply @ ( recursion @ A @ successor_relation @ union_of_range_map ) @ B )
= ( ordinal_add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( apply @ ( recursion @ A @ successor_relation @ union_of_range_map ) @ B )
= ( ordinal_add @ A @ B ) ),
inference(lifteq,[status(thm)],[255]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( sum_class @ ( image @ A @ ( singleton @ B ) ) )
= ( apply @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( sum_class @ ( image @ A @ ( singleton @ B ) ) )
= ( apply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
inference(lifteq,[status(thm)],[290]) ).
thf(17146,plain,
! [B: $i,A: $i] :
( ( sum_class @ ( image @ ( recursion @ A @ successor_relation @ union_of_range_map ) @ ( singleton @ B ) ) )
= ( ordinal_add @ A @ B ) ),
inference(rewrite,[status(thm)],[256,291]) ).
thf(1813,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( function @ null_class )
| ( A != choice ) ),
inference(paramod_ordered,[status(thm)],[508,181]) ).
thf(1814,plain,
( ( member @ ( regular @ choice ) @ choice )
| ( function @ null_class ) ),
inference(pattern_uni,[status(thm)],[1813:[bind(A,$thf( choice ))]]) ).
thf(3775,plain,
( ( function @ null_class )
| ( ( member @ ( regular @ choice ) @ choice )
!= ( member @ x @ ( successor @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[1814,163]) ).
thf(3778,plain,
( ( function @ null_class )
| ( ( regular @ choice )
!= x )
| ( ( successor @ x )
!= choice ) ),
inference(simp,[status(thm)],[3775]) ).
thf(1347,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ) )
= ( power_class @ B ) )
| ( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
!= ( complement @ B ) ) ),
inference(paramod_ordered,[status(thm)],[878,192]) ).
thf(1348,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( power_class @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[1347:[bind(A,$thf( E )),bind(B,$thf( image @ element_relation @ ( power_class @ E ) ))]]) ).
thf(1408,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( power_class @ A ) ) ) ),
inference(simp,[status(thm)],[1348]) ).
thf(5092,plain,
! [B: $i,A: $i] :
( ( ( power_class @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ B ) ) ) )
| ( ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ) )
!= ( complement @ ( image @ element_relation @ ( power_class @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1408,878]) ).
thf(5093,plain,
! [A: $i] :
( ( power_class @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[5092:[bind(A,$thf( E )),bind(B,$thf( image @ element_relation @ ( complement @ E ) ))]]) ).
thf(5366,plain,
! [A: $i] :
( ( power_class @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[5093]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( rest_of @ C ) )
| ( member @ A @ ( domain_of @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_of2) ).
thf(424,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( rest_of @ C ) )
| ( member @ A @ ( domain_of @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( subclass @ ( not_well_ordering @ A @ B ) @ B )
| ( well_ordering @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering7) ).
thf(197,plain,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( subclass @ ( not_well_ordering @ A @ B ) @ B )
| ( well_ordering @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( member @ ( domain_of @ A ) @ ordinal_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions3) ).
thf(329,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( member @ ( domain_of @ A ) @ ordinal_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(36034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ A @ ( cross_product @ B @ C ) ) @ universal_class ) ) ) ) )
= kind_1_ordinals )
| ( ( intersection @ ( cross_product @ B @ C ) @ A )
!= ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ),
inference(paramod_ordered,[status(thm)],[36002,10497]) ).
thf(36035,plain,
( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ successor_relation @ ( cross_product @ ordinal_numbers @ universal_class ) ) @ universal_class ) ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[36034:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers )),bind(C,$thf( universal_class ))]]) ).
thf(142,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class2) ).
thf(461,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ application_function )
| ( ( apply @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn3) ).
thf(456,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ application_function )
| ( ( apply @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1006,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( ( member @ A @ omega )
!= ( member @ x @ ( successor @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[442,163]) ).
thf(1008,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( A != x )
| ( ( successor @ x )
!= omega ) ),
inference(simp,[status(thm)],[1006]) ).
thf(1012,plain,
( ( ( integer_of @ x )
= null_class )
| ( ( successor @ x )
!= omega ) ),
inference(simp,[status(thm)],[1008]) ).
thf(93,axiom,
! [A: $i] :
( ~ ( well_ordering @ element_relation @ A )
| ~ ( subclass @ ( sum_class @ A ) @ A )
| ~ ( member @ A @ universal_class )
| ( member @ A @ ordinal_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers3) ).
thf(361,plain,
! [A: $i] :
( ~ ( well_ordering @ element_relation @ A )
| ~ ( subclass @ ( sum_class @ A ) @ A )
| ~ ( member @ A @ universal_class )
| ( member @ A @ ordinal_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
!= null_class )
| ( asymmetric @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',asymmetric2) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
!= null_class )
| ( asymmetric @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
!= null_class )
| ( asymmetric @ A @ B ) ),
inference(cnf,[status(esa)],[236]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
!= null_class )
| ( asymmetric @ A @ B ) ),
inference(lifteq,[status(thm)],[237]) ).
thf(23841,plain,
! [B: $i,A: $i] :
( ( ( intersection @ ( cross_product @ B @ B ) @ ( intersection @ A @ ( inverse @ A ) ) )
!= null_class )
| ( asymmetric @ A @ B ) ),
inference(rewrite,[status(thm)],[238,209]) ).
thf(1194,plain,
! [A: $i] :
( ( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) ) ) )
= subset_relation )
| ( ( inverse @ A )
!= ( inverse @ element_relation ) ) ),
inference(paramod_ordered,[status(thm)],[404,468]) ).
thf(1195,plain,
( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( domain_of @ ( flip @ ( cross_product @ element_relation @ universal_class ) ) ) ) ) ) )
= subset_relation ),
inference(pattern_uni,[status(thm)],[1194:[bind(A,$thf( element_relation ))]]) ).
thf(16942,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[387,16902]) ).
thf(16981,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( rest_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[16942]) ).
thf(58,axiom,
! [A: $i] :
( ( intersection @ ( domain_of @ A ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ A ) ) )
= ( cantor @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cantor_class) ).
thf(285,plain,
! [A: $i] :
( ( intersection @ ( domain_of @ A ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ A ) ) )
= ( cantor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',section1) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1539,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ ( inverse @ subset_relation ) @ null_class )
= identity_relation )
| ( A != subset_relation ) ),
inference(paramod_ordered,[status(thm)],[508,284]) ).
thf(1540,plain,
( ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ subset_relation ) @ null_class )
= identity_relation ) ),
inference(pattern_uni,[status(thm)],[1539:[bind(A,$thf( subset_relation ))]]) ).
thf(106,axiom,
subclass @ application_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn1) ).
thf(388,plain,
subclass @ application_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(855,plain,
! [A: $i] :
( ( ( power_class @ A )
!= universal_class )
| ( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
!= ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[192,542]) ).
thf(869,plain,
! [A: $i] :
( ( ( power_class @ A )
!= universal_class )
| ( ( image @ element_relation @ ( complement @ A ) )
!= universal_class ) ),
inference(simp,[status(thm)],[855]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( domain_of @ A ) ) @ domain_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation3) ).
thf(499,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( domain_of @ A ) ) @ domain_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( complement @ D ) )
| ( ( member @ ( unordered_pair @ A @ B ) @ universal_class )
!= ( member @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[380,466]) ).
thf(598,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ A @ B ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[597:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( unordered_pair @ E @ F )),bind(D,$thf( universal_class ))]]) ).
thf(608,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ A @ B ) @ ( complement @ universal_class ) ),
inference(simp,[status(thm)],[598]) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( singleton @ A ) @ ( complement @ universal_class ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[194,608]) ).
thf(1138,plain,
! [A: $i] :
~ ( member @ ( singleton @ A ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[1137:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).
thf(266,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(267,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
inference(cnf,[status(esa)],[266]) ).
thf(40312,plain,
! [A: $i] :
( ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( ( inductive @ omega )
!= ( inductive @ A ) ) ),
inference(paramod_ordered,[status(thm)],[239,267]) ).
thf(40313,plain,
subclass @ ( image @ successor_relation @ omega ) @ omega,
inference(pattern_uni,[status(thm)],[40312:[bind(A,$thf( omega ))]]) ).
thf(40375,plain,
( ( subclass @ ( image @ successor_relation @ omega ) @ omega )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[40313,3640]) ).
thf(40406,plain,
( ( ( image @ successor_relation @ omega )
!= universal_class )
| ( ( complement @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[40375]) ).
thf(1682,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) )
| ( A != successor_relation ) ),
inference(paramod_ordered,[status(thm)],[508,460]) ).
thf(1683,plain,
( ( member @ ( regular @ successor_relation ) @ successor_relation )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[1682:[bind(A,$thf( successor_relation ))]]) ).
thf(153,axiom,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive3) ).
thf(488,plain,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(83,axiom,
! [A: $i] :
( ~ ( well_ordering @ element_relation @ A )
| ~ ( subclass @ ( sum_class @ A ) @ A )
| ( member @ A @ ordinal_numbers )
| ( A = ordinal_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers4) ).
thf(339,plain,
! [A: $i] :
( ~ ( well_ordering @ element_relation @ A )
| ~ ( subclass @ ( sum_class @ A ) @ A )
| ( member @ A @ ordinal_numbers )
| ( A = ordinal_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(5417,plain,
! [A: $i] :
( ~ ( subclass @ omega @ x )
| ( ( successor @ x )
!= universal_class )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ x @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[455,3182]) ).
thf(5472,plain,
! [A: $i] :
( ~ ( subclass @ omega @ x )
| ( ( successor @ x )
!= universal_class )
| ( A != x )
| ( omega != universal_class ) ),
inference(simp,[status(thm)],[5417]) ).
thf(5496,plain,
( ~ ( subclass @ omega @ x )
| ( ( successor @ x )
!= universal_class )
| ( omega != universal_class ) ),
inference(simp,[status(thm)],[5472]) ).
thf(17073,plain,
( ( ( complement @ universal_class )
!= omega )
| ( ( subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[383,17006]) ).
thf(17118,plain,
( ( ( complement @ universal_class )
!= omega )
| ( domain_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[17073]) ).
thf(1002,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( ( member @ A @ omega )
!= ( member @ ( successor @ x ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[442,521]) ).
thf(1011,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( A
!= ( successor @ x ) )
| ( ( complement @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[1002]) ).
thf(1016,plain,
( ( ( integer_of @ ( successor @ x ) )
= null_class )
| ( ( complement @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[1011]) ).
thf(9475,plain,
( ( null_class != universal_class )
| ( ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) )
!= ( member @ ( successor @ x ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1680,521]) ).
thf(9531,plain,
( ( null_class != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= ( successor @ x ) )
| ( ( complement @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[9475]) ).
thf(9568,plain,
( ( null_class != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= ( successor @ x ) ) ),
inference(simp,[status(thm)],[9531]) ).
thf(10431,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= ( successor @ x ) )
| ( null_class != null_class ) ),
inference(paramod_ordered,[status(thm)],[508,9568]) ).
thf(10432,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= ( successor @ x ) ) ),
inference(pattern_uni,[status(thm)],[10431:[]]) ).
thf(10487,plain,
( ( member @ ( regular @ universal_class ) @ universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= ( successor @ x ) ) ),
inference(simp,[status(thm)],[10432]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( ( domain_of @ ( domain_of @ B ) )
= ( domain_of @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible2) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( ( domain_of @ ( domain_of @ B ) )
= ( domain_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( ( domain_of @ ( domain_of @ B ) )
= ( domain_of @ A ) ) ),
inference(cnf,[status(esa)],[210]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( domain_of @ ( domain_of @ B ) )
= ( domain_of @ A ) )
| ~ ( compatible @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[211]) ).
thf(9433,plain,
! [A: $i] :
( ( null_class != universal_class )
| ( ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) )
!= ( member @ ( singleton @ A ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1680,1138]) ).
thf(9525,plain,
! [A: $i] :
( ( null_class != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= ( singleton @ A ) )
| ( ( complement @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[9433]) ).
thf(9566,plain,
! [A: $i] :
( ( null_class != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= ( singleton @ A ) ) ),
inference(simp,[status(thm)],[9525]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ B @ C ) ),
inference(cnf,[status(esa)],[224]) ).
thf(14509,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( ( regular @ ( successor @ x ) )
!= x )
| ( ( member @ A @ omega )
!= ( member @ x @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[442,14458]) ).
thf(14515,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( ( regular @ ( successor @ x ) )
!= x )
| ( A != x )
| ( null_class != omega ) ),
inference(simp,[status(thm)],[14509]) ).
thf(14529,plain,
( ( ( integer_of @ x )
= null_class )
| ( ( regular @ ( successor @ x ) )
!= x )
| ( null_class != omega ) ),
inference(simp,[status(thm)],[14515]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ D )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ C @ A ) @ B ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ C @ A ) @ B ) @ ( rotate @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate3) ).
thf(393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ D )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ C @ A ) @ B ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ C @ A ) @ B ) @ ( rotate @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(14508,plain,
( ( ( regular @ ( successor @ x ) )
!= x )
| ( ( member @ omega @ universal_class )
!= ( member @ x @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[459,14458]) ).
thf(14516,plain,
( ( ( regular @ ( successor @ x ) )
!= x )
| ( omega != x )
| ( null_class != universal_class ) ),
inference(simp,[status(thm)],[14508]) ).
thf(10191,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != universal_class )
| ~ ( member @ ( regular @ ( complement @ universal_class ) ) @ universal_class )
| ( null_class != null_class ) ),
inference(paramod_ordered,[status(thm)],[508,9464]) ).
thf(10192,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != universal_class )
| ~ ( member @ ( regular @ ( complement @ universal_class ) ) @ universal_class ) ),
inference(pattern_uni,[status(thm)],[10191:[]]) ).
thf(10270,plain,
( ( member @ ( regular @ universal_class ) @ universal_class )
| ~ ( member @ ( regular @ ( complement @ universal_class ) ) @ universal_class ) ),
inference(simp,[status(thm)],[10192]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
thf(371,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( function @ B )
| ~ ( member @ ( domain_of @ B ) @ ordinal_numbers )
| ( ( compose @ A @ ( rest_of @ B ) )
!= B )
| ( member @ B @ ( recursion_equation_functions @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions5) ).
thf(503,plain,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( function @ B )
| ~ ( member @ ( domain_of @ B ) @ ordinal_numbers )
| ( ( compose @ A @ ( rest_of @ B ) )
!= B )
| ( member @ B @ ( recursion_equation_functions @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(56,axiom,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonalisation) ).
thf(281,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(282,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
inference(lifteq,[status(thm)],[281]) ).
thf(901,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( power_class @ B ) )
| ( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
!= ( complement @ B ) ) ),
inference(paramod_ordered,[status(thm)],[282,192]) ).
thf(902,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(pattern_uni,[status(thm)],[901:[bind(A,$thf( D )),bind(B,$thf( domain_of @ ( intersection @ D @ identity_relation ) ))]]) ).
thf(923,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(simp,[status(thm)],[902]) ).
thf(1477,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) )
= ( power_class @ ( domain_of @ ( intersection @ B @ identity_relation ) ) ) )
| ( ( diagonalise @ A )
!= ( diagonalise @ B ) ) ),
inference(paramod_ordered,[status(thm)],[282,923]) ).
thf(1478,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(pattern_uni,[status(thm)],[1477:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(22138,plain,
! [A: $i] :
( ( ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( power_class @ A ) )
| ( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21670,192]) ).
thf(22139,plain,
( ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) ) ),
inference(pattern_uni,[status(thm)],[22138:[bind(A,$thf( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ))]]) ).
thf(22657,plain,
! [A: $i] :
( ( ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) )
| ( ( power_class @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
!= ( power_class @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22139,192]) ).
thf(22658,plain,
( ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[22657:[bind(A,$thf( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ))]]) ).
thf(1537,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ ( inverse @ null_class ) @ subset_relation )
= identity_relation )
| ( A != subset_relation ) ),
inference(paramod_ordered,[status(thm)],[508,284]) ).
thf(1538,plain,
( ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ null_class ) @ subset_relation )
= identity_relation ) ),
inference(pattern_uni,[status(thm)],[1537:[bind(A,$thf( subset_relation ))]]) ).
thf(4334,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ null_class ) @ null_class )
= identity_relation )
| ( A != subset_relation ) ),
inference(paramod_ordered,[status(thm)],[508,1538]) ).
thf(4335,plain,
( ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ null_class ) @ null_class )
= identity_relation ) ),
inference(pattern_uni,[status(thm)],[4334:[bind(A,$thf( subset_relation ))]]) ).
thf(4384,plain,
( ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ null_class ) @ null_class )
= identity_relation ) ),
inference(simp,[status(thm)],[4335]) ).
thf(898,plain,
! [A: $i] :
( ( ( diagonalise @ A )
!= universal_class )
| ( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
!= ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[282,542]) ).
thf(911,plain,
! [A: $i] :
( ( ( diagonalise @ A )
!= universal_class )
| ( ( domain_of @ ( intersection @ A @ identity_relation ) )
!= universal_class ) ),
inference(simp,[status(thm)],[898]) ).
thf(118,axiom,
subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_range_map1) ).
thf(414,plain,
subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1856,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) )
| ( A != union_of_range_map ) ),
inference(paramod_ordered,[status(thm)],[508,414]) ).
thf(1857,plain,
( ( member @ ( regular @ union_of_range_map ) @ union_of_range_map )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[1856:[bind(A,$thf( union_of_range_map ))]]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
= ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
= ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(4038,plain,
! [C: $i,B: $i,A: $i] :
( ( ( complement @ ( domain_of @ ( inverse @ ( restrict @ A @ B @ universal_class ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ C ) ) ) )
| ( ( image @ A @ B )
!= ( image @ element_relation @ ( power_class @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[4032,878]) ).
thf(4039,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( power_class @ A ) @ universal_class ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[4038:[bind(A,$thf( element_relation )),bind(B,$thf( power_class @ D )),bind(C,$thf( D ))]]) ).
thf(4112,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( power_class @ A ) @ universal_class ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(simp,[status(thm)],[4039]) ).
thf(7871,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( power_class @ A ) @ universal_class ) ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ B ) ) ) )
| ( ( power_class @ ( image @ element_relation @ ( complement @ A ) ) )
!= ( power_class @ ( image @ element_relation @ ( complement @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4112,878]) ).
thf(7872,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( power_class @ A ) @ universal_class ) ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[7871:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(15042,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ( power_class @ A ) @ universal_class ) @ element_relation ) ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ A ) ) ) ),
inference(rewrite,[status(thm)],[7872,209]) ).
thf(9465,plain,
! [B: $i,A: $i] :
( ( null_class != universal_class )
| ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1680,466]) ).
thf(9466,plain,
( ( null_class != universal_class )
| ~ ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ ( complement @ universal_class ) ) ) ),
inference(pattern_uni,[status(thm)],[9465:[bind(A,$thf( regular @ ( complement @ universal_class ) )),bind(B,$thf( complement @ universal_class ))]]) ).
thf(20999,plain,
( ( null_class != universal_class )
| ( ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ ( complement @ universal_class ) ) )
!= ( member @ ( regular @ ( complement @ universal_class ) ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1680,9466]) ).
thf(21155,plain,
( ( null_class != universal_class )
| ( ( regular @ ( complement @ universal_class ) )
!= ( regular @ ( complement @ universal_class ) ) )
| ( ( complement @ ( complement @ universal_class ) )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[20999]) ).
thf(21199,plain,
( ( null_class != universal_class )
| ( ( complement @ ( complement @ universal_class ) )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[21155]) ).
thf(21224,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != universal_class )
| ( ( complement @ ( complement @ universal_class ) )
!= ( complement @ universal_class ) )
| ( null_class != null_class ) ),
inference(paramod_ordered,[status(thm)],[508,21199]) ).
thf(21225,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != universal_class )
| ( ( complement @ ( complement @ universal_class ) )
!= ( complement @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[21224:[]]) ).
thf(21412,plain,
( ( member @ ( regular @ universal_class ) @ universal_class )
| ( ( complement @ ( complement @ universal_class ) )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[21225]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ ( domain_of @ ( restrict @ A @ C @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',section2) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ ( domain_of @ ( restrict @ A @ C @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( complement @ ( domain_of @ ( inverse @ ( intersection @ A @ ( cross_product @ B @ C ) ) ) ) )
= ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) )
| ( ( intersection @ ( cross_product @ B @ C ) @ A )
!= ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ),
inference(paramod_ordered,[status(thm)],[36002,25450]) ).
thf(36130,plain,
( ( complement @ ( domain_of @ ( inverse @ ( intersection @ element_relation @ ( cross_product @ kind_1_ordinals @ universal_class ) ) ) ) )
= ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ),
inference(pattern_uni,[status(thm)],[36129:[bind(A,$thf( element_relation )),bind(B,$thf( kind_1_ordinals )),bind(C,$thf( universal_class ))]]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( subclass @ ( range_of @ A ) @ B )
| ( maps @ A @ ( domain_of @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps4) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( subclass @ ( range_of @ A ) @ B )
| ( maps @ A @ ( domain_of @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(3732,plain,
( ( omega != universal_class )
| ( ( inductive @ ( complement @ universal_class ) )
!= ( inductive @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[239,3707]) ).
thf(3738,plain,
( ( omega != universal_class )
| ( ( complement @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[3732]) ).
thf(3665,plain,
( ( subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[414,3640]) ).
thf(3686,plain,
( ( union_of_range_map != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3665]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( rest_of @ C ) )
| ( ( restrict @ C @ A @ universal_class )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_of3) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( rest_of @ C ) )
| ( ( restrict @ C @ A @ universal_class )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(26031,plain,
! [A: $i] :
( ( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( power_class @ A ) )
| ( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25450,192]) ).
thf(26032,plain,
( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) )
= ( power_class @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) ) ),
inference(pattern_uni,[status(thm)],[26031:[bind(A,$thf( domain_of @ ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ))]]) ).
thf(1547,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ null_class ) )
= kind_1_ordinals )
| ( A != ordinal_numbers ) ),
inference(paramod_ordered,[status(thm)],[508,173]) ).
thf(1548,plain,
( ( member @ ( regular @ ordinal_numbers ) @ ordinal_numbers )
| ( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ null_class ) )
= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[1547:[bind(A,$thf( ordinal_numbers ))]]) ).
thf(4036,plain,
! [C: $i,B: $i,A: $i] :
( ( ( complement @ ( domain_of @ ( inverse @ ( restrict @ A @ B @ universal_class ) ) ) )
= ( power_class @ ( domain_of @ ( intersection @ C @ identity_relation ) ) ) )
| ( ( image @ A @ B )
!= ( image @ element_relation @ ( diagonalise @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[4032,923]) ).
thf(4037,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( diagonalise @ A ) @ universal_class ) ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(pattern_uni,[status(thm)],[4036:[bind(A,$thf( element_relation )),bind(B,$thf( diagonalise @ D )),bind(C,$thf( D ))]]) ).
thf(4111,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( diagonalise @ A ) @ universal_class ) ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(simp,[status(thm)],[4037]) ).
thf(7719,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( diagonalise @ A ) @ universal_class ) ) ) )
= ( complement @ ( image @ element_relation @ ( diagonalise @ B ) ) ) )
| ( ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
!= ( power_class @ ( domain_of @ ( intersection @ B @ identity_relation ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4111,923]) ).
thf(7720,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( diagonalise @ A ) @ universal_class ) ) ) )
= ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[7719:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(14534,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ( diagonalise @ A ) @ universal_class ) @ element_relation ) ) ) )
= ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) ) ),
inference(rewrite,[status(thm)],[7720,209]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( ( not_well_ordering @ A @ B )
!= null_class )
| ( well_ordering @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering6) ).
thf(296,plain,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( ( not_well_ordering @ A @ B )
!= null_class )
| ( well_ordering @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
inference(cnf,[status(esa)],[174]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ( ( domain_of @ A )
= B )
| ~ ( maps @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(286,plain,
! [A: $i] :
( ( intersection @ ( domain_of @ A ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ A ) ) )
= ( cantor @ A ) ),
inference(lifteq,[status(thm)],[285]) ).
thf(1383,plain,
! [B: $i,A: $i] :
( ( ( power_class @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ B ) ) ) )
| ( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
!= ( complement @ B ) ) ),
inference(paramod_ordered,[status(thm)],[282,878]) ).
thf(1384,plain,
! [A: $i] :
( ( power_class @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1383:[bind(A,$thf( D )),bind(B,$thf( domain_of @ ( intersection @ D @ identity_relation ) ))]]) ).
thf(1420,plain,
! [A: $i] :
( ( power_class @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) ) ),
inference(simp,[status(thm)],[1384]) ).
thf(5983,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( diagonalise @ B ) ) ) )
| ( ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
!= ( power_class @ ( domain_of @ ( intersection @ B @ identity_relation ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[923,1420]) ).
thf(5984,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( diagonalise @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[5983:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(1444,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ B ) ) ) )
| ( ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
!= ( power_class @ B ) ) ),
inference(paramod_ordered,[status(thm)],[923,192]) ).
thf(1445,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1444:[bind(A,$thf( D )),bind(B,$thf( domain_of @ ( intersection @ D @ identity_relation ) ))]]) ).
thf(1520,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) ) ),
inference(simp,[status(thm)],[1445]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass1) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( member @ A @ B )
| ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).
thf(391,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( member @ A @ B )
| ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(3656,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[328,3640]) ).
thf(3695,plain,
( ( element_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3656]) ).
thf(1355,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ B ) ) ) )
| ( ( power_class @ A )
!= ( power_class @ B ) ) ),
inference(paramod_ordered,[status(thm)],[192,878]) ).
thf(1356,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[1355:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( not_subclass_element @ A @ B ) @ B )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
thf(350,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( not_subclass_element @ A @ B ) @ B )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(133,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
thf(445,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(935,plain,
! [A: $i] :
( ( ( intersection @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) @ subset_relation )
= identity_relation )
| ( ( inverse @ A )
!= ( inverse @ subset_relation ) ) ),
inference(paramod_ordered,[status(thm)],[404,284]) ).
thf(936,plain,
( ( intersection @ ( domain_of @ ( flip @ ( cross_product @ subset_relation @ universal_class ) ) ) @ subset_relation )
= identity_relation ),
inference(pattern_uni,[status(thm)],[935:[bind(A,$thf( subset_relation ))]]) ).
thf(3645,plain,
( ( subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[387,3640]) ).
thf(3700,plain,
( ( rest_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3645]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( compose @ C @ D ) )
| ( member @ B @ ( image @ C @ ( image @ D @ ( singleton @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).
thf(335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( compose @ C @ D ) )
| ( member @ B @ ( image @ C @ ( image @ D @ ( singleton @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(31,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).
thf(226,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(227,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
inference(cnf,[status(esa)],[226]) ).
thf(18309,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( domain_of @ ( inverse @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
inference(rewrite,[status(thm)],[227,180]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
inference(cnf,[status(esa)],[184]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
inference(lifteq,[status(thm)],[185]) ).
thf(187,plain,
! [A: $i] : ( subclass @ A @ A ),
inference(simp,[status(thm)],[186]) ).
thf(4692,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( diagonalise @ A ) @ universal_class ) ) ) )
= ( power_class @ B ) )
| ( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
!= ( complement @ B ) ) ),
inference(paramod_ordered,[status(thm)],[282,4115]) ).
thf(4693,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( diagonalise @ A ) @ universal_class ) ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(pattern_uni,[status(thm)],[4692:[bind(A,$thf( D )),bind(B,$thf( domain_of @ ( intersection @ D @ identity_relation ) ))]]) ).
thf(4786,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( diagonalise @ A ) @ universal_class ) ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(simp,[status(thm)],[4693]) ).
thf(11601,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ( diagonalise @ A ) @ universal_class ) @ element_relation ) ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(rewrite,[status(thm)],[4786,209]) ).
thf(3650,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[460,3640]) ).
thf(3683,plain,
( ( successor_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3650]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions1) ).
thf(451,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( complement @ B ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
thf(434,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( complement @ B ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ ( domain_of @ ( restrict @ C @ B @ A ) ) @ A )
| ( section @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',section3) ).
thf(303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ ( domain_of @ ( restrict @ C @ B @ A ) ) @ A )
| ( section @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(271,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( function @ A ) ),
inference(cnf,[status(esa)],[270]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B )
| ( ( segment @ A @ C @ ( least @ A @ C ) )
= null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering4) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B )
| ( ( segment @ A @ C @ ( least @ A @ C ) )
= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ element_relation )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
thf(483,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ element_relation )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(4040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( power_class @ ( domain_of @ ( inverse @ ( restrict @ A @ B @ universal_class ) ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ C ) ) ) )
| ( ( image @ A @ B )
!= ( image @ element_relation @ ( complement @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[4032,878]) ).
thf(4041,plain,
! [A: $i] :
( ( power_class @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[4040:[bind(A,$thf( element_relation )),bind(B,$thf( complement @ D )),bind(C,$thf( D ))]]) ).
thf(4113,plain,
! [A: $i] :
( ( power_class @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ A ) ) ) ),
inference(simp,[status(thm)],[4041]) ).
thf(8264,plain,
! [B: $i,A: $i] :
( ( ( power_class @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ B ) ) ) )
| ( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
!= ( complement @ ( image @ element_relation @ ( power_class @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4113,878]) ).
thf(8265,plain,
! [A: $i] :
( ( power_class @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[8264:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(15968,plain,
! [A: $i] :
( ( power_class @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ( complement @ A ) @ universal_class ) @ element_relation ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(rewrite,[status(thm)],[8265,209]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( subclass @ ( not_well_ordering @ A @ B ) @ B )
| ( well_ordering @ A @ B ) ),
inference(cnf,[status(esa)],[197]) ).
thf(6327,plain,
! [A: $i] :
( ~ ( inductive @ x )
| ( ( successor @ x )
!= universal_class )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ x @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[455,5393]) ).
thf(6363,plain,
! [A: $i] :
( ~ ( inductive @ x )
| ( ( successor @ x )
!= universal_class )
| ( A != x )
| ( omega != universal_class ) ),
inference(simp,[status(thm)],[6327]) ).
thf(6376,plain,
( ~ ( inductive @ x )
| ( ( successor @ x )
!= universal_class )
| ( omega != universal_class ) ),
inference(simp,[status(thm)],[6363]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( ( compose @ C @ A )
!= B )
| ( member @ ( ordered_pair @ A @ B ) @ ( compose_class @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition3) ).
thf(367,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( ( compose @ C @ A )
!= B )
| ( member @ ( ordered_pair @ A @ B ) @ ( compose_class @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( irreflexive @ A @ B )
| ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive1) ).
thf(240,plain,
! [B: $i,A: $i] :
( ~ ( irreflexive @ A @ B )
| ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( transitive @ A @ B )
| ( subclass @ ( compose @ ( restrict @ A @ B @ B ) @ ( restrict @ A @ B @ B ) ) @ ( restrict @ A @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive1) ).
thf(251,plain,
! [B: $i,A: $i] :
( ~ ( transitive @ A @ B )
| ( subclass @ ( compose @ ( restrict @ A @ B @ B ) @ ( restrict @ A @ B @ B ) ) @ ( restrict @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(54,axiom,
! [A: $i] :
( ( union @ A @ ( inverse @ A ) )
= ( symmetrization_of @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetrization) ).
thf(277,plain,
! [A: $i] :
( ( union @ A @ ( inverse @ A ) )
= ( symmetrization_of @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(278,plain,
! [A: $i] :
( ( union @ A @ ( inverse @ A ) )
= ( symmetrization_of @ A ) ),
inference(lifteq,[status(thm)],[277]) ).
thf(40363,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ ( image @ null_class @ omega ) @ omega )
| ( A != successor_relation ) ),
inference(paramod_ordered,[status(thm)],[508,40313]) ).
thf(40364,plain,
( ( member @ ( regular @ successor_relation ) @ successor_relation )
| ( subclass @ ( image @ null_class @ omega ) @ omega ) ),
inference(pattern_uni,[status(thm)],[40363:[bind(A,$thf( successor_relation ))]]) ).
thf(64,axiom,
! [A: $i] :
( ( second @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_term_defn2) ).
thf(299,plain,
! [A: $i] :
( ( second @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( operation @ A )
| ~ ( operation @ B )
| ~ ( compatible @ C @ A @ B )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ C @ A @ B ) @ ( not_homomorphism2 @ C @ A @ B ) ) @ ( domain_of @ A ) )
| ( homomorphism @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism5) ).
thf(438,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( operation @ A )
| ~ ( operation @ B )
| ~ ( compatible @ C @ A @ B )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ C @ A @ B ) @ ( not_homomorphism2 @ C @ A @ B ) ) @ ( domain_of @ A ) )
| ( homomorphism @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
inference(cnf,[status(esa)],[222]) ).
thf(36166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( inverse @ ( intersection @ A @ ( cross_product @ B @ C ) ) ) ) )
= kind_1_ordinals )
| ( ( intersection @ ( cross_product @ B @ C ) @ A )
!= ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ),
inference(paramod_ordered,[status(thm)],[36002,10508]) ).
thf(36167,plain,
( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( inverse @ ( intersection @ successor_relation @ ( cross_product @ ordinal_numbers @ universal_class ) ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[36166:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers )),bind(C,$thf( universal_class ))]]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( member @ ( not_subclass_element @ A @ B ) @ A )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( member @ ( not_subclass_element @ A @ B ) @ A )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1872,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) )
| ( A != domain_relation ) ),
inference(paramod_ordered,[status(thm)],[508,383]) ).
thf(1873,plain,
( ( member @ ( regular @ domain_relation ) @ domain_relation )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[1872:[bind(A,$thf( domain_relation ))]]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B )
| ~ ( member @ D @ C )
| ( member @ ( least @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering3) ).
thf(426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B )
| ~ ( member @ D @ C )
| ( member @ ( least @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(28194,plain,
! [A: $i] :
( ( ( power_class @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) )
= ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) )
| ( ( inverse @ A )
!= ( inverse @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) ) ) ),
inference(paramod_ordered,[status(thm)],[404,26771]) ).
thf(28195,plain,
( ( power_class @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ) @ universal_class ) ) ) ) )
= ( power_class @ ( image @ element_relation @ kind_1_ordinals ) ) ),
inference(pattern_uni,[status(thm)],[28194:[bind(A,$thf( intersection @ ( cross_product @ kind_1_ordinals @ universal_class ) @ element_relation ))]]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ domain_relation )
| ( ( domain_of @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation2) ).
thf(342,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ domain_relation )
| ( ( domain_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(522,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( ( member @ omega @ universal_class )
!= ( member @ A @ ( complement @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[459,466]) ).
thf(526,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( omega != A )
| ( ( complement @ B )
!= universal_class ) ),
inference(simp,[status(thm)],[522]) ).
thf(531,plain,
! [A: $i] :
( ~ ( member @ omega @ A )
| ( ( complement @ A )
!= universal_class ) ),
inference(simp,[status(thm)],[526]) ).
thf(1133,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)],[194,380]) ).
thf(1134,plain,
! [A: $i] : ( member @ ( singleton @ A ) @ universal_class ),
inference(pattern_uni,[status(thm)],[1133:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(1565,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ rest_relation @ null_class )
| ( A
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[508,387]) ).
thf(1566,plain,
( ( member @ ( regular @ ( cross_product @ universal_class @ universal_class ) ) @ ( cross_product @ universal_class @ universal_class ) )
| ( subclass @ rest_relation @ null_class ) ),
inference(pattern_uni,[status(thm)],[1565:[bind(A,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(16953,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[383,16902]) ).
thf(16974,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( domain_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[16953]) ).
thf(3774,plain,
! [A: $i] :
( ( function @ null_class )
| ( ( complement @ A )
!= universal_class )
| ( ( member @ ( regular @ choice ) @ choice )
!= ( member @ ( successor @ x ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1814,532]) ).
thf(3783,plain,
! [A: $i] :
( ( function @ null_class )
| ( ( complement @ A )
!= universal_class )
| ( ( regular @ choice )
!= ( successor @ x ) )
| ( choice != A ) ),
inference(simp,[status(thm)],[3774]) ).
thf(3786,plain,
( ( function @ null_class )
| ( ( complement @ choice )
!= universal_class )
| ( ( regular @ choice )
!= ( successor @ x ) ) ),
inference(simp,[status(thm)],[3783]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( function @ A )
| ( ( domain_of @ ( domain_of @ B ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) )
| ( compatible @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible4) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( function @ A )
| ( ( domain_of @ ( domain_of @ B ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) )
| ( compatible @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(69,axiom,
! [A: $i] :
( ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( single_valued_class @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class2) ).
thf(310,plain,
! [A: $i] :
( ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( single_valued_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one3) ).
thf(199,plain,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1715,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ ( complement @ null_class ) @ ordinal_numbers )
= limit_ordinals )
| ( A != kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[508,221]) ).
thf(1716,plain,
( ( member @ ( regular @ kind_1_ordinals ) @ kind_1_ordinals )
| ( ( intersection @ ( complement @ null_class ) @ ordinal_numbers )
= limit_ordinals ) ),
inference(pattern_uni,[status(thm)],[1715:[bind(A,$thf( kind_1_ordinals ))]]) ).
thf(3649,plain,
! [A: $i] :
( ( subclass @ ( compose_class @ A ) @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[417,3640]) ).
thf(3691,plain,
! [A: $i] :
( ( ( compose_class @ A )
!= universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3649]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B )
| ~ ( member @ D @ C )
| ~ ( member @ ( ordered_pair @ D @ ( least @ A @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering5) ).
thf(331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B )
| ~ ( member @ D @ C )
| ~ ( member @ ( ordered_pair @ D @ ( least @ A @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(20217,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ ( compose @ choice @ ( inverse @ choice ) ) @ null_class )
| ( A != identity_relation ) ),
inference(paramod_ordered,[status(thm)],[508,20154]) ).
thf(20218,plain,
( ( member @ ( regular @ identity_relation ) @ identity_relation )
| ( subclass @ ( compose @ choice @ ( inverse @ choice ) ) @ null_class ) ),
inference(pattern_uni,[status(thm)],[20217:[bind(A,$thf( identity_relation ))]]) ).
thf(143,axiom,
! [A: $i] :
( ~ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
thf(463,plain,
! [A: $i] :
( ~ ( 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)],[143]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
thf(359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(17030,plain,
( ( ( complement @ universal_class )
!= omega )
| ( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[460,17006]) ).
thf(17124,plain,
( ( ( complement @ universal_class )
!= omega )
| ( successor_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[17030]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) )
| ( irreflexive @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive2) ).
thf(177,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) )
| ( irreflexive @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [A: $i] :
( ( domain @ A @ ( image @ ( inverse @ A ) @ ( singleton @ ( single_valued1 @ A ) ) ) @ ( single_valued2 @ A ) )
= ( single_valued3 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_term_defn3) ).
thf(182,plain,
! [A: $i] :
( ( domain @ A @ ( image @ ( inverse @ A ) @ ( singleton @ ( single_valued1 @ A ) ) ) @ ( single_valued2 @ A ) )
= ( single_valued3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13644,plain,
! [B: $i,A: $i] :
( ( ( regular @ ( complement @ universal_class ) )
!= omega )
| ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ ( regular @ universal_class ) @ universal_class )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9648,466]) ).
thf(13645,plain,
( ( ( regular @ ( complement @ universal_class ) )
!= omega )
| ~ ( member @ ( regular @ universal_class ) @ ( complement @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[13644:[bind(A,$thf( regular @ universal_class )),bind(B,$thf( universal_class ))]]) ).
thf(17419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( symmetrization_of @ C ) )
| ( ( union @ A @ B )
!= ( union @ C @ ( inverse @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[276,278]) ).
thf(17420,plain,
! [A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ ( inverse @ A ) ) ) )
= ( symmetrization_of @ A ) ),
inference(pattern_uni,[status(thm)],[17419:[bind(A,$thf( D )),bind(B,$thf( inverse @ D )),bind(C,$thf( D ))]]) ).
thf(17600,plain,
! [A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ ( inverse @ A ) ) ) )
= ( symmetrization_of @ A ) ),
inference(simp,[status(thm)],[17420]) ).
thf(16947,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[414,16902]) ).
thf(16987,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( union_of_range_map != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[16947]) ).
thf(104,axiom,
! [A: $i] : ( subclass @ ( rest_of @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_of1) ).
thf(386,plain,
! [A: $i] : ( subclass @ ( rest_of @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(3646,plain,
! [A: $i] :
( ( subclass @ ( rest_of @ A ) @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[386,3640]) ).
thf(3697,plain,
! [A: $i] :
( ( ( rest_of @ A )
!= universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3646]) ).
thf(1535,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ null_class @ subset_relation )
= identity_relation )
| ( A
!= ( inverse @ subset_relation ) ) ),
inference(paramod_ordered,[status(thm)],[508,284]) ).
thf(1536,plain,
( ( member @ ( regular @ ( inverse @ subset_relation ) ) @ ( inverse @ subset_relation ) )
| ( ( intersection @ null_class @ subset_relation )
= identity_relation ) ),
inference(pattern_uni,[status(thm)],[1535:[bind(A,$thf( inverse @ subset_relation ))]]) ).
thf(71,axiom,
( ( intersection @ ( complement @ ( compose @ element_relation @ ( complement @ identity_relation ) ) ) @ element_relation )
= singleton_relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_can_define_singleton) ).
thf(314,plain,
( ( intersection @ ( complement @ ( compose @ element_relation @ ( complement @ identity_relation ) ) ) @ element_relation )
= singleton_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(3655,plain,
( ( subclass @ application_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ) )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[388,3640]) ).
thf(3684,plain,
( ( application_function != universal_class )
| ( ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[3655]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( ( successor @ A )
!= B )
| ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation3) ).
thf(363,plain,
! [B: $i,A: $i] :
( ( ( successor @ A )
!= B )
| ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( ( sum_class @ ( range_of @ A ) )
!= B )
| ( member @ ( ordered_pair @ A @ B ) @ union_of_range_map ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_range_map3) ).
thf(495,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( ( sum_class @ ( range_of @ A ) )
!= B )
| ( member @ ( ordered_pair @ A @ B ) @ union_of_range_map ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(16918,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[328,16902]) ).
thf(16983,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( element_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[16918]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( symmetric_difference @ A @ B )
= ( intersection @ ( complement @ ( intersection @ A @ B ) ) @ ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[249]) ).
thf(20213,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ ( compose @ null_class @ ( inverse @ choice ) ) @ identity_relation )
| ( A != choice ) ),
inference(paramod_ordered,[status(thm)],[508,20154]) ).
thf(20214,plain,
( ( member @ ( regular @ choice ) @ choice )
| ( subclass @ ( compose @ null_class @ ( inverse @ choice ) ) @ identity_relation ) ),
inference(pattern_uni,[status(thm)],[20213:[bind(A,$thf( choice ))]]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( rotate @ D ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate2) ).
thf(319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( rotate @ D ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ~ ( transitive @ A @ B )
| ( subclass @ ( compose @ ( restrict @ A @ B @ B ) @ ( restrict @ A @ B @ B ) ) @ ( restrict @ A @ B @ B ) ) ),
inference(cnf,[status(esa)],[251]) ).
thf(34615,plain,
! [B: $i,A: $i] :
( ~ ( transitive @ A @ B )
| ( subclass @ ( compose @ ( intersection @ ( cross_product @ B @ B ) @ A ) @ ( intersection @ ( cross_product @ B @ B ) @ A ) ) @ ( intersection @ ( cross_product @ B @ B ) @ A ) ) ),
inference(rewrite,[status(thm)],[252,209]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
inference(cnf,[status(esa)],[170]) ).
thf(3759,plain,
( ( function @ null_class )
| ( ( member @ ( regular @ choice ) @ choice )
!= ( member @ ( successor @ x ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1814,521]) ).
thf(3780,plain,
( ( function @ null_class )
| ( ( regular @ choice )
!= ( successor @ x ) )
| ( ( complement @ universal_class )
!= choice ) ),
inference(simp,[status(thm)],[3759]) ).
thf(19008,plain,
! [A: $i] :
( ( ( complement @ ( image @ element_relation @ kind_1_ordinals ) )
= ( power_class @ A ) )
| ( ( complement @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ) ) ) )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17452,192]) ).
thf(19009,plain,
( ( complement @ ( image @ element_relation @ kind_1_ordinals ) )
= ( power_class @ ( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[19008:[bind(A,$thf( intersection @ ( complement @ ( singleton @ null_class ) ) @ ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ) ) ))]]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class )
| ~ ( member @ B @ ( domain_of @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class )
| ~ ( member @ B @ ( domain_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(5103,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( power_class @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( power_class @ B ) ) ) )
| ( ( power_class @ ( image @ element_relation @ ( complement @ A ) ) )
!= ( power_class @ ( image @ element_relation @ ( complement @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[878,1408]) ).
thf(5104,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( power_class @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( power_class @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[5103:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(1557,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( union @ ( singleton @ null_class ) @ ( image @ null_class @ ordinal_numbers ) )
= kind_1_ordinals )
| ( A != successor_relation ) ),
inference(paramod_ordered,[status(thm)],[508,173]) ).
thf(1558,plain,
( ( member @ ( regular @ successor_relation ) @ successor_relation )
| ( ( union @ ( singleton @ null_class ) @ ( image @ null_class @ ordinal_numbers ) )
= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[1557:[bind(A,$thf( successor_relation ))]]) ).
thf(10237,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( null_class != universal_class )
| ( ( member @ A @ omega )
!= ( member @ ( regular @ ( complement @ universal_class ) ) @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[442,9464]) ).
thf(10246,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( null_class != universal_class )
| ( A
!= ( regular @ ( complement @ universal_class ) ) )
| ( omega != universal_class ) ),
inference(simp,[status(thm)],[10237]) ).
thf(10268,plain,
( ( ( integer_of @ ( regular @ ( complement @ universal_class ) ) )
= null_class )
| ( null_class != universal_class )
| ( omega != universal_class ) ),
inference(simp,[status(thm)],[10246]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
inference(cnf,[status(esa)],[234]) ).
thf(127,axiom,
! [B: $i,A: $i] : ( subclass @ ( compose @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
thf(433,plain,
! [B: $i,A: $i] : ( subclass @ ( compose @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( subclass @ ( cross_product @ B @ B ) @ ( union @ identity_relation @ ( symmetrization_of @ A ) ) ) ),
inference(cnf,[status(esa)],[206]) ).
thf(1307,plain,
! [B: $i,A: $i] :
( ( ( union @ B @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
= ( symmetrization_of @ B ) )
| ( ( inverse @ A )
!= ( inverse @ B ) ) ),
inference(paramod_ordered,[status(thm)],[404,278]) ).
thf(1308,plain,
! [A: $i] :
( ( union @ A @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
= ( symmetrization_of @ A ) ),
inference(pattern_uni,[status(thm)],[1307:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(22098,plain,
! [A: $i] :
( ( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) )
| ( ( power_class @ ( image @ element_relation @ kind_1_ordinals ) )
!= ( power_class @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21670,878]) ).
thf(22099,plain,
( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ kind_1_ordinals ) ) ) ) ),
inference(pattern_uni,[status(thm)],[22098:[bind(A,$thf( image @ element_relation @ kind_1_ordinals ))]]) ).
thf(59,axiom,
! [A: $i] :
( ( A = null_class )
| ( ( intersection @ A @ ( regular @ A ) )
= null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
thf(287,plain,
! [A: $i] :
( ( A = null_class )
| ( ( intersection @ A @ ( regular @ A ) )
= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
thf(378,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(17062,plain,
( ( ( complement @ universal_class )
!= omega )
| ( ( subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[387,17006]) ).
thf(17131,plain,
( ( ( complement @ universal_class )
!= omega )
| ( rest_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[17062]) ).
thf(16910,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[460,16902]) ).
thf(16993,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( successor_relation != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[16910]) ).
thf(52,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
= ( domain_of @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation2) ).
thf(272,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
= ( domain_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(5992,plain,
! [B: $i,A: $i] :
( ( ( power_class @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ B ) ) ) )
| ( ( complement @ ( image @ element_relation @ ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) )
!= ( complement @ ( image @ element_relation @ ( power_class @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1420,878]) ).
thf(5993,plain,
! [A: $i] :
( ( power_class @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[5992:[bind(A,$thf( D )),bind(B,$thf( domain_of @ ( intersection @ D @ identity_relation ) ))]]) ).
thf(6252,plain,
! [A: $i] :
( ( power_class @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) ) ),
inference(simp,[status(thm)],[5993]) ).
thf(1917,plain,
! [A: $i] :
( ( A = null_class )
| ( ( member @ ( regular @ A ) @ A )
!= ( member @ x @ ( successor @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[508,163]) ).
thf(1933,plain,
! [A: $i] :
( ( A = null_class )
| ( ( regular @ A )
!= x )
| ( A
!= ( successor @ x ) ) ),
inference(simp,[status(thm)],[1917]) ).
thf(2003,plain,
( ( ( successor @ x )
= null_class )
| ( ( regular @ ( successor @ x ) )
!= x ) ),
inference(simp,[status(thm)],[1933]) ).
thf(300,plain,
! [A: $i] :
( ( second @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued2 @ A ) ),
inference(lifteq,[status(thm)],[299]) ).
thf(315,plain,
( ( intersection @ ( complement @ ( compose @ element_relation @ ( complement @ identity_relation ) ) ) @ element_relation )
= singleton_relation ),
inference(lifteq,[status(thm)],[314]) ).
thf(264,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( function @ A )
| ( ( domain_of @ ( domain_of @ B ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) )
| ( compatible @ A @ B @ C ) ),
inference(cnf,[status(esa)],[263]) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( domain_of @ ( domain_of @ B ) )
!= ( domain_of @ A ) )
| ~ ( function @ A )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) )
| ( compatible @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[264]) ).
thf(38366,plain,
! [C: $i,B: $i,A: $i] :
( ( ( domain_of @ ( domain_of @ B ) )
!= ( domain_of @ A ) )
| ~ ( function @ A )
| ~ ( subclass @ ( domain_of @ ( inverse @ A ) ) @ ( domain_of @ ( domain_of @ C ) ) )
| ( compatible @ A @ B @ C ) ),
inference(rewrite,[status(thm)],[265,180]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( subclass @ ( compose @ ( restrict @ A @ B @ B ) @ ( restrict @ A @ B @ B ) ) @ ( restrict @ A @ B @ B ) )
| ( transitive @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive2) ).
thf(168,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ ( compose @ ( restrict @ A @ B @ B ) @ ( restrict @ A @ B @ B ) ) @ ( restrict @ A @ B @ B ) )
| ( transitive @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12116,plain,
( ( ( regular @ ( successor @ x ) )
!= x )
| ( ( member @ null_class @ universal_class )
!= ( member @ x @ ( successor @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[12062,163]) ).
thf(12117,plain,
( ( ( regular @ ( successor @ x ) )
!= x )
| ( null_class != x )
| ( ( successor @ x )
!= universal_class ) ),
inference(simp,[status(thm)],[12116]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B )
| ( C = null_class )
| ( member @ ( least @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering2) ).
thf(405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B )
| ( C = null_class )
| ( member @ ( least @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ( member @ B @ ( domain_of @ A ) )
| ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ ( apply @ A @ B ) ) ) @ application_function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn4) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ) )
| ~ ( member @ B @ ( domain_of @ A ) )
| ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ ( apply @ A @ B ) ) ) @ application_function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ D )
| ( member @ ( ordered_pair @ A @ C ) @ ( cross_product @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
thf(447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ D )
| ( member @ ( ordered_pair @ A @ C ) @ ( cross_product @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(5416,plain,
! [A: $i] :
( ~ ( subclass @ x @ omega )
| ( ( successor @ x )
!= universal_class )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ omega @ x ) ) ),
inference(paramod_ordered,[status(thm)],[455,3182]) ).
thf(5469,plain,
! [A: $i] :
( ~ ( subclass @ x @ omega )
| ( ( successor @ x )
!= universal_class )
| ( A != omega )
| ( universal_class != x ) ),
inference(simp,[status(thm)],[5416]) ).
thf(5494,plain,
( ~ ( subclass @ x @ omega )
| ( ( successor @ x )
!= universal_class )
| ( universal_class != x ) ),
inference(simp,[status(thm)],[5469]) ).
thf(7367,plain,
! [A: $i] :
( ( ( successor @ x )
!= universal_class )
| ( universal_class != x )
| ( ( subclass @ A @ universal_class )
!= ( subclass @ x @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[455,5494]) ).
thf(7402,plain,
! [A: $i] :
( ( ( successor @ x )
!= universal_class )
| ( universal_class != x )
| ( A != x )
| ( omega != universal_class ) ),
inference(simp,[status(thm)],[7367]) ).
thf(7419,plain,
( ( ( successor @ x )
!= universal_class )
| ( universal_class != x )
| ( omega != universal_class ) ),
inference(simp,[status(thm)],[7402]) ).
thf(24824,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ ( regular @ choice ) @ choice )
| ( subclass @ ( compose @ null_class @ ( inverse @ null_class ) ) @ identity_relation )
| ( A != choice ) ),
inference(paramod_ordered,[status(thm)],[508,20214]) ).
thf(24825,plain,
( ( member @ ( regular @ choice ) @ choice )
| ( member @ ( regular @ choice ) @ choice )
| ( subclass @ ( compose @ null_class @ ( inverse @ null_class ) ) @ identity_relation ) ),
inference(pattern_uni,[status(thm)],[24824:[bind(A,$thf( choice ))]]) ).
thf(24884,plain,
( ( member @ ( regular @ choice ) @ choice )
| ( subclass @ ( compose @ null_class @ ( inverse @ null_class ) ) @ identity_relation ) ),
inference(simp,[status(thm)],[24825]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ D )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ ( flip @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip3) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ D )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ ( flip @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( operation @ A )
| ~ ( operation @ B )
| ~ ( compatible @ C @ A @ B )
| ( ( apply @ B @ ( ordered_pair @ ( apply @ C @ ( not_homomorphism1 @ C @ A @ B ) ) @ ( apply @ C @ ( not_homomorphism2 @ C @ A @ B ) ) ) )
!= ( apply @ C @ ( apply @ A @ ( ordered_pair @ ( not_homomorphism1 @ C @ A @ B ) @ ( not_homomorphism2 @ C @ A @ B ) ) ) ) )
| ( homomorphism @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism6) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( operation @ A )
| ~ ( operation @ B )
| ~ ( compatible @ C @ A @ B )
| ( ( apply @ B @ ( ordered_pair @ ( apply @ C @ ( not_homomorphism1 @ C @ A @ B ) ) @ ( apply @ C @ ( not_homomorphism2 @ C @ A @ B ) ) ) )
!= ( apply @ C @ ( apply @ A @ ( ordered_pair @ ( not_homomorphism1 @ C @ A @ B ) @ ( not_homomorphism2 @ C @ A @ B ) ) ) ) )
| ( homomorphism @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).
thf(294,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( ( restrict @ B @ ( singleton @ A ) @ universal_class )
= null_class )
| ( member @ A @ ( domain_of @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(400,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( ( restrict @ B @ ( singleton @ A ) @ universal_class )
= null_class )
| ( member @ A @ ( domain_of @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ ( compose @ A @ B ) ) ) @ composition_function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function3) ).
thf(415,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ ( compose @ A @ B ) ) ) @ composition_function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(110,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( rest_of @ A ) ) @ rest_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_relation3) ).
thf(395,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( rest_of @ A ) ) @ rest_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ~ ( irreflexive @ A @ B )
| ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) ) ),
inference(cnf,[status(esa)],[240]) ).
thf(25009,plain,
! [B: $i,A: $i] :
( ~ ( irreflexive @ A @ B )
| ( subclass @ ( intersection @ ( cross_product @ B @ B ) @ A ) @ ( complement @ identity_relation ) ) ),
inference(rewrite,[status(thm)],[241,209]) ).
thf(14478,plain,
( ( ( regular @ ( successor @ x ) )
!= x )
| ( ( member @ ( successor @ x ) @ universal_class )
!= ( member @ x @ null_class ) ) ),
inference(paramod_ordered,[status(thm)],[161,14458]) ).
thf(14511,plain,
( ( ( regular @ ( successor @ x ) )
!= x )
| ( ( successor @ x )
!= x )
| ( null_class != universal_class ) ),
inference(simp,[status(thm)],[14478]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( recursion @ null_class @ ( apply @ add_relation @ A ) @ union_of_range_map )
= ( ordinal_multiply @ A @ B ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(4019,plain,
! [B: $i,A: $i] :
( ( recursion @ null_class @ ( sum_class @ ( image @ add_relation @ ( singleton @ A ) ) ) @ union_of_range_map )
= ( ordinal_multiply @ A @ B ) ),
inference(rewrite,[status(thm)],[254,291]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions2) ).
thf(501,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(200,plain,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
inference(cnf,[status(esa)],[199]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( ( compose @ B @ ( rest_of @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions4) ).
thf(322,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( ( compose @ B @ ( rest_of @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
thf(337,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( not_well_ordering @ B @ C ) )
| ( ( segment @ B @ ( not_well_ordering @ B @ C ) @ A )
!= null_class )
| ~ ( connected @ B @ C )
| ( well_ordering @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering8) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( not_well_ordering @ B @ C ) )
| ( ( segment @ B @ ( not_well_ordering @ B @ C ) @ A )
!= null_class )
| ~ ( connected @ B @ C )
| ( well_ordering @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(90,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
thf(354,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(17067,plain,
( ( ( complement @ universal_class )
!= omega )
| ( ( subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ universal_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[414,17006]) ).
thf(17123,plain,
( ( ( complement @ universal_class )
!= omega )
| ( union_of_range_map != universal_class )
| ( ( cross_product @ universal_class @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[17067]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B )
| ( ( segment @ A @ C @ ( least @ A @ C ) )
= null_class ) ),
inference(cnf,[status(esa)],[213]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ( ( segment @ A @ C @ ( least @ A @ C ) )
= null_class )
| ~ ( well_ordering @ A @ B )
| ~ ( subclass @ C @ B ) ),
inference(lifteq,[status(thm)],[214]) ).
thf(20231,plain,
( ( subclass @ ( compose @ choice @ ( inverse @ choice ) ) @ identity_relation )
!= ( subclass @ universal_class @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[20154,3640]) ).
thf(20263,plain,
( ( ( compose @ choice @ ( inverse @ choice ) )
!= universal_class )
| ( ( complement @ universal_class )
!= identity_relation ) ),
inference(simp,[status(thm)],[20231]) ).
thf(49345,plain,
$false,
inference(e,[status(thm)],[1718,9648,479,347,468,234,3698,333,249,481,352,1005,17278,308,449,247,269,408,170,217,276,878,440,511,17113,384,472,3693,1761,30694,5393,417,21415,301,436,257,174,404,12062,10501,389,184,9464,27920,357,1409,14510,17610,3644,196,1132,542,460,36002,421,284,36156,325,228,36008,316,20206,25980,10497,216,14533,475,1714,179,443,321,253,485,353,492,164,36146,31860,397,221,25520,428,312,206,1564,602,12090,36013,16902,36408,453,292,233,380,270,20216,201,381,220,2000,22097,512,9571,17146,192,275,165,3778,5366,424,467,229,197,329,36035,461,456,1012,361,23841,1195,16981,285,224,403,188,1540,388,869,499,1138,40406,1683,488,339,5496,193,17118,1016,10487,212,328,9566,225,14529,393,14516,10270,371,503,1478,22658,4384,173,911,1857,266,205,508,1814,15042,412,1680,21412,166,36130,161,279,3738,3686,375,3707,26032,1548,14534,180,296,176,286,291,5984,1520,259,191,1916,281,204,391,3695,236,181,1356,350,445,936,466,17305,3700,335,18309,17860,187,172,1408,11601,3683,230,451,434,303,17725,245,9570,271,3182,208,387,14458,213,483,15968,198,6376,345,367,240,251,278,455,40364,1775,299,20154,226,438,431,25450,521,223,608,267,17006,36167,490,1873,426,1420,255,28195,342,194,162,531,1134,209,3640,282,414,1566,16974,3786,263,310,199,1716,3691,331,20218,463,26771,359,17124,177,182,13645,17600,1538,16987,3697,17452,1536,386,314,3684,10496,363,524,495,16983,218,250,465,10508,20214,319,17698,34615,171,3780,390,19009,418,5104,1558,10268,235,433,207,1308,22139,22099,287,290,378,40313,17131,16993,272,6252,383,2003,300,315,38366,168,12117,405,190,373,21199,21670,447,7419,24884,410,305,210,294,195,400,532,283,415,239,242,9466,506,268,395,25009,459,14511,4019,277,442,501,163,200,9568,322,337,469,5494,354,923,17123,215,222,232,20263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM145-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:08:39 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.93/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/1.03 % [INFO] Parsing done (174ms).
% 1.34/1.04 % [INFO] Running in sequential loop mode.
% 2.17/1.24 % [INFO] eprover registered as external prover.
% 2.17/1.24 % [INFO] cvc4 registered as external prover.
% 2.17/1.24 % [INFO] Scanning for conjecture ...
% 2.23/1.32 % [INFO] Found a conjecture and 158 axioms. Running axiom selection ...
% 2.54/1.39 % [INFO] Axiom selection finished. Selected 158 axioms (removed 0 axioms).
% 2.87/1.47 % [INFO] Problem is propositional (TPTP CNF).
% 2.97/1.48 % [INFO] Type checking passed.
% 2.97/1.48 % [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 ...
% 119.78/21.05 % External prover 'e' found a proof!
% 119.78/21.05 % [INFO] Killing All external provers ...
% 119.78/21.05 % Time passed: 20522ms (effective reasoning time: 20013ms)
% 119.78/21.05 % 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)>
% 119.78/21.06 % Axioms used in derivation (158): range, recursion_equation_functions1, equal_implies_subclass1, rest_relation2, complement1, one_to_one2, omega_is_inductive1, cartesian_product4, rotate2, homomorphism4, maps4, range_of, transitive1, function3, recursion_equation_functions5, operation4, regularity1, symmetrization, singleton_set, identity_relation, union, flip3, element_relation2, unordered_pairs_in_universal, rest_of4, compose2, homomorphism3, compatible3, application_function_defn2, symmetric_difference, cartesian_product1, compose_can_define_singleton, image, definition_of_domain_relation1, replacement, well_ordering4, not_subclass_members1, compose_class_definition3, definition_of_composition_function2, successor, ordered_pair, successor_relation1, irreflexive1, rest_of2, domain, homomorphism1, rest_relation3, one_to_one3, single_valued_term_defn3, single_valued_class1, compose3, omega_is_inductive2, rotate1, choice1, section1, single_valued_term_defn1, power_class2, regularity2, equal_implies_subclass2, element_relation3, homomorphism6, recursion_equation_functions4, intersection1, well_ordering3, flip2, well_ordering6, transitive2, inverse, segment, asymmetric2, connected1, sum_class_definition, ordinal_multiplication, inductive2, compatible2, sum_class2, subclass_members, cartesian_product2, maps1, not_subclass_members2, ordinal_numbers2, inductive1, single_valued_term_defn2, successor_relation3, function1, maps3, domain2, compatible4, intersection3, limit_ordinals, kind_1_ordinals, ordinal_numbers4, single_valued_class2, compose_class_definition1, unordered_pair_member, apply, well_ordering7, element_relation1, operation1, application_function_defn1, asymmetric1, restriction1, union_of_range_map1, ordinal_addition, cartesian_product3, section2, definition_of_domain_relation3, flip1, homomorphism5, maps2, ordinal_numbers1, compatible1, unordered_pair2, application_function_defn4, recursion_equation_functions3, well_ordering2, complement2, operation2, connected2, union_of_range_map3, rotate3, well_ordering8, compose_class_definition2, one_to_one1, subclass_implies_equal, function2, rest_of1, cantor_class, successor_relation2, rest_relation1, domain1, restriction2, omega_in_universal, ordinal_numbers3, well_ordering1, diagonalisation, intersection2, class_elements_are_sets, integer_function2, section3, rest_of3, inductive3, integer_function1, irreflexive2, operation3, well_ordering5, application_function_defn3, definition_of_domain_relation2, choice2, definition_of_composition_function1, homomorphism2, power_class_definition, union_of_range_map2, definition_of_composition_function3, unordered_pair3, recursion_equation_functions2, subset_relation, compose1
% 119.78/21.06 % No. of inferences in proof: 776
% 119.78/21.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20522 ms resp. 20013 ms w/o parsing
% 120.18/21.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 120.18/21.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------