TSTP Solution File: NUM159-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM159-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 11:39:59 EDT 2023
% Result : Unsatisfiable 121.27s 23.54s
% Output : Refutation 121.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 237
% Syntax : Number of formulae : 860 ( 266 unt; 78 typ; 0 def)
% Number of atoms : 1645 ( 664 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 7345 ( 899 ~; 709 |; 0 &;5737 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 103 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 78 usr; 19 con; 0-3 aty)
% Number of variables : 1149 ( 0 ^;1149 !; 0 ?;1149 :)
% Comments :
%------------------------------------------------------------------------------
thf(subclass_type,type,
subclass: $i > $i > $o ).
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(homomorphism_type,type,
homomorphism: $i > $i > $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(rotate_type,type,
rotate: $i > $i ).
thf(recursion_equation_functions_type,type,
recursion_equation_functions: $i > $i ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(rest_of_type,type,
rest_of: $i > $i ).
thf(composition_function_type,type,
composition_function: $i ).
thf(flip_type,type,
flip: $i > $i ).
thf(operation_type,type,
operation: $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(domain_relation_type,type,
domain_relation: $i ).
thf(union_of_range_map_type,type,
union_of_range_map: $i ).
thf(sum_class_type,type,
sum_class: $i > $i ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(compatible_type,type,
compatible: $i > $i > $i > $o ).
thf(not_homomorphism1_type,type,
not_homomorphism1: $i > $i > $i > $i ).
thf(not_homomorphism2_type,type,
not_homomorphism2: $i > $i > $i > $i ).
thf(function_type,type,
function: $i > $o ).
thf(universal_class_type,type,
universal_class: $i ).
thf(null_class_type,type,
null_class: $i ).
thf(choice_type,type,
choice: $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(maps_type,type,
maps: $i > $i > $i > $o ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(compose_class_type,type,
compose_class: $i > $i ).
thf(application_function_type,type,
application_function: $i ).
thf(restrict_type,type,
restrict: $i > $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(inductive_type,type,
inductive: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(asymmetric_type,type,
asymmetric: $i > $i > $o ).
thf(element_relation_type,type,
element_relation: $i ).
thf(rest_relation_type,type,
rest_relation: $i ).
thf(first_type,type,
first: $i > $i ).
thf(second_type,type,
second: $i > $i ).
thf(omega_type,type,
omega: $i ).
thf(not_subclass_element_type,type,
not_subclass_element: $i > $i > $i ).
thf(range_type,type,
range: $i > $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(recursion_type,type,
recursion: $i > $i > $i > $i ).
thf(add_relation_type,type,
add_relation: $i ).
thf(ordinal_multiply_type,type,
ordinal_multiply: $i > $i > $i ).
thf(integer_of_type,type,
integer_of: $i > $i ).
thf(segment_type,type,
segment: $i > $i > $i > $i ).
thf(identity_relation_type,type,
identity_relation: $i ).
thf(single_valued1_type,type,
single_valued1: $i > $i ).
thf(subset_relation_type,type,
subset_relation: $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(power_class_type,type,
power_class: $i > $i ).
thf(not_well_ordering_type,type,
not_well_ordering: $i > $i > $i ).
thf(connected_type,type,
connected: $i > $i > $o ).
thf(well_ordering_type,type,
well_ordering: $i > $i > $o ).
thf(symmetrization_of_type,type,
symmetrization_of: $i > $i ).
thf(diagonalise_type,type,
diagonalise: $i > $i ).
thf(cantor_type,type,
cantor: $i > $i ).
thf(regular_type,type,
regular: $i > $i ).
thf(singleton_relation_type,type,
singleton_relation: $i ).
thf(single_valued2_type,type,
single_valued2: $i > $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(least_type,type,
least: $i > $i > $i ).
thf(section_type,type,
section: $i > $i > $i > $o ).
thf(transitive_type,type,
transitive: $i > $i > $o ).
thf(irreflexive_type,type,
irreflexive: $i > $i > $o ).
thf(single_valued3_type,type,
single_valued3: $i > $i ).
thf(single_valued_class_type,type,
single_valued_class: $i > $o ).
thf(limit_ordinals_type,type,
limit_ordinals: $i ).
thf(ordinal_add_type,type,
ordinal_add: $i > $i > $i ).
thf(76,axiom,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
thf(329,plain,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(330,plain,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
inference(lifteq,[status(thm)],[329]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(489,plain,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
inference(lifteq,[status(thm)],[488]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
inference(cnf,[status(esa)],[411]) ).
thf(413,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
inference(lifteq,[status(thm)],[412]) ).
thf(414,plain,
! [A: $i] : ( subclass @ A @ A ),
inference(simp,[status(thm)],[413]) ).
thf(1,negated_conjecture,
~ ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_kind_1_ordinal_1) ).
thf(160,plain,
~ ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(161,plain,
~ ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ),
inference(polarity_switch,[status(thm)],[160]) ).
thf(552,plain,
! [A: $i] :
( ( subclass @ A @ A )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[414,161]) ).
thf(553,plain,
! [A: $i] :
( ( A
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( A != kind_1_ordinals ) ),
inference(simp,[status(thm)],[552]) ).
thf(554,plain,
( ( image @ successor_relation @ ordinal_numbers )
!= kind_1_ordinals ),
inference(simp,[status(thm)],[553]) ).
thf(4951,plain,
! [B: $i,A: $i] :
( ( ( range_of @ ( restrict @ A @ B @ universal_class ) )
!= kind_1_ordinals )
| ( ( image @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[489,554]) ).
thf(4952,plain,
( ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) )
!= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[4951:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers ))]]) ).
thf(32,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(232,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)],[32]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( restrict @ C @ A @ B )
= ( intersection @ ( cross_product @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[232]) ).
thf(28303,plain,
( ( range_of @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) )
!= kind_1_ordinals ),
inference(rewrite,[status(thm)],[4952,233]) ).
thf(28404,plain,
( ( ( range_of @ identity_relation )
!= kind_1_ordinals )
| ( ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation )
!= ( intersection @ ( inverse @ subset_relation ) @ subset_relation ) ) ),
inference(paramod_ordered,[status(thm)],[330,28303]) ).
thf(28419,plain,
( ( ( range_of @ identity_relation )
!= kind_1_ordinals )
| ( ( cross_product @ ordinal_numbers @ universal_class )
!= ( inverse @ subset_relation ) )
| ( subset_relation != successor_relation ) ),
inference(simp,[status(thm)],[28404]) ).
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(479,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(83,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(347,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(39,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(249,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)],[39]) ).
thf(133,axiom,
subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_range_map1) ).
thf(450,plain,
subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(572,plain,
( ( subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[450,161]) ).
thf(573,plain,
( ( ( image @ successor_relation @ ordinal_numbers )
!= union_of_range_map )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[572]) ).
thf(4957,plain,
! [B: $i,A: $i] :
( ( ( range_of @ ( restrict @ A @ B @ universal_class ) )
!= union_of_range_map )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals )
| ( ( image @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[489,573]) ).
thf(4958,plain,
( ( ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) )
!= union_of_range_map )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[4957:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers ))]]) ).
thf(28324,plain,
( ( ( range_of @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) )
!= union_of_range_map )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(rewrite,[status(thm)],[4958,233]) ).
thf(67,axiom,
member @ omega @ universal_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
thf(310,plain,
member @ omega @ universal_class,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
thf(317,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
inference(cnf,[status(esa)],[317]) ).
thf(508,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ omega @ universal_class )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[310,318]) ).
thf(509,plain,
~ ( member @ omega @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[508:[bind(A,$thf( omega )),bind(B,$thf( universal_class ))]]) ).
thf(516,plain,
( ( member @ omega @ ( complement @ universal_class ) )
!= ( member @ omega @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[310,509]) ).
thf(517,plain,
( ( omega != omega )
| ( ( complement @ universal_class )
!= universal_class ) ),
inference(simp,[status(thm)],[516]) ).
thf(518,plain,
( ( complement @ universal_class )
!= universal_class ),
inference(simp,[status(thm)],[517]) ).
thf(33,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(234,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( rest_of @ A ) ) @ rest_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
thf(190,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(191,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
inference(cnf,[status(esa)],[190]) ).
thf(192,plain,
! [A: $i] :
( ( A = null_class )
| ~ ( member @ A @ universal_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(7207,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A )
| ( ( member @ omega @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[310,192]) ).
thf(7208,plain,
( ( omega = null_class )
| ( member @ ( apply @ choice @ omega ) @ omega ) ),
inference(pattern_uni,[status(thm)],[7207:[bind(A,$thf( omega ))]]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( sum_class @ ( image @ A @ ( singleton @ B ) ) )
= ( apply @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( sum_class @ ( image @ A @ ( singleton @ B ) ) )
= ( apply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(504,plain,
! [B: $i,A: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
inference(lifteq,[status(thm)],[503]) ).
thf(20765,plain,
( ( omega = null_class )
| ( member @ ( sum_class @ ( image @ choice @ ( singleton @ omega ) ) ) @ omega ) ),
inference(rewrite,[status(thm)],[7208,504]) ).
thf(5,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(170,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)],[5]) ).
thf(80,axiom,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
thf(340,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(341,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
inference(cnf,[status(esa)],[340]) ).
thf(342,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
inference(lifteq,[status(thm)],[341]) ).
thf(2116,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ null_class @ subset_relation )
= identity_relation )
| ( A
!= ( inverse @ subset_relation ) ) ),
inference(paramod_ordered,[status(thm)],[342,330]) ).
thf(2117,plain,
( ( member @ ( regular @ ( inverse @ subset_relation ) ) @ ( inverse @ subset_relation ) )
| ( ( intersection @ null_class @ subset_relation )
= identity_relation ) ),
inference(pattern_uni,[status(thm)],[2116:[bind(A,$thf( inverse @ subset_relation ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
thf(217,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,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(193,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
inference(cnf,[status(esa)],[193]) ).
thf(8316,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( unordered_pair @ A @ B ) )
| ( ( member @ omega @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[310,194]) ).
thf(8317,plain,
! [A: $i] : ( member @ omega @ ( unordered_pair @ omega @ A ) ),
inference(pattern_uni,[status(thm)],[8316:[bind(A,$thf( omega ))]]) ).
thf(8402,plain,
! [A: $i] : ( member @ omega @ ( unordered_pair @ omega @ A ) ),
inference(simp,[status(thm)],[8317]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ composition_function )
| ( ( compose @ A @ B )
= C ) ),
inference(cnf,[status(esa)],[170]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ A @ B )
= C )
| ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ composition_function ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(121,axiom,
subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_relation1) ).
thf(428,plain,
subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(546,plain,
( ( subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[428,161]) ).
thf(547,plain,
( ( ( image @ successor_relation @ ordinal_numbers )
!= rest_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[546]) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ composition_function )
| ( ( image @ successor_relation @ ordinal_numbers )
!= rest_relation )
| ( ( compose @ A @ B )
!= kind_1_ordinals )
| ( C
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[172,547]) ).
thf(741,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ ( cross_product @ universal_class @ universal_class ) ) ) @ composition_function )
| ( ( image @ successor_relation @ ordinal_numbers )
!= rest_relation )
| ( ( compose @ A @ B )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[740:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(37,axiom,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(245,plain,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(246,plain,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
inference(lifteq,[status(thm)],[245]) ).
thf(16,axiom,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
thf(198,plain,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(199,plain,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
inference(lifteq,[status(thm)],[198]) ).
thf(1105,plain,
! [B: $i,A: $i] :
( ( ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
= ( range_of @ B ) )
| ( ( inverse @ A )
!= ( inverse @ B ) ) ),
inference(paramod_ordered,[status(thm)],[246,199]) ).
thf(1106,plain,
! [A: $i] :
( ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
= ( range_of @ A ) ),
inference(pattern_uni,[status(thm)],[1105:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(117,axiom,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_definition) ).
thf(421,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(422,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
inference(lifteq,[status(thm)],[421]) ).
thf(5001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( complement @ ( range_of @ ( restrict @ A @ B @ universal_class ) ) )
= ( power_class @ C ) )
| ( ( image @ A @ B )
!= ( image @ element_relation @ ( complement @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[489,422]) ).
thf(5002,plain,
! [A: $i] :
( ( complement @ ( range_of @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) )
= ( power_class @ A ) ),
inference(pattern_uni,[status(thm)],[5001:[bind(A,$thf( element_relation )),bind(B,$thf( complement @ D )),bind(C,$thf( D ))]]) ).
thf(5015,plain,
! [A: $i] :
( ( complement @ ( range_of @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) )
= ( power_class @ A ) ),
inference(simp,[status(thm)],[5002]) ).
thf(12179,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) )
= ( power_class @ B ) )
| ( ( range_of @ A )
!= ( range_of @ ( restrict @ element_relation @ ( complement @ B ) @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1106,5015]) ).
thf(12180,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) @ universal_class ) ) ) ) )
= ( power_class @ A ) ),
inference(pattern_uni,[status(thm)],[12179:[bind(A,$thf( restrict @ element_relation @ ( complement @ F ) @ universal_class )),bind(B,$thf( F ))]]) ).
thf(12302,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) @ universal_class ) ) ) ) )
= ( power_class @ A ) ),
inference(simp,[status(thm)],[12180]) ).
thf(37150,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ ( cross_product @ ( complement @ A ) @ universal_class ) @ element_relation ) @ universal_class ) ) ) ) )
= ( power_class @ A ) ),
inference(rewrite,[status(thm)],[12302,233]) ).
thf(132,axiom,
! [A: $i] : ( subclass @ ( compose_class @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition1) ).
thf(449,plain,
! [A: $i] : ( subclass @ ( compose_class @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(18,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(201,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)],[18]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ C ) ),
inference(cnf,[status(esa)],[201]) ).
thf(235,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( rest_of @ A ) ) @ rest_relation ) ),
inference(cnf,[status(esa)],[234]) ).
thf(29115,plain,
! [A: $i] :
( ( member @ ( ordered_pair @ A @ ( rest_of @ A ) ) @ rest_relation )
| ( ( member @ omega @ universal_class )
!= ( member @ A @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[310,235]) ).
thf(29116,plain,
member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ rest_relation,
inference(pattern_uni,[status(thm)],[29115:[bind(A,$thf( omega ))]]) ).
thf(29301,plain,
( ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ rest_relation )
!= ( member @ omega @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[29116,509]) ).
thf(29363,plain,
( ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= omega )
| ( ( complement @ universal_class )
!= rest_relation ) ),
inference(simp,[status(thm)],[29301]) ).
thf(48,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(269,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)],[48]) ).
thf(100,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ omega @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
thf(384,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ omega @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(126,axiom,
( ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers )
= limit_ordinals ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_ordinals) ).
thf(437,plain,
( ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers )
= limit_ordinals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(438,plain,
( ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers )
= limit_ordinals ),
inference(lifteq,[status(thm)],[437]) ).
thf(28405,plain,
( ( ( range_of @ limit_ordinals )
!= kind_1_ordinals )
| ( ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation )
!= ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[438,28303]) ).
thf(28423,plain,
( ( ( range_of @ limit_ordinals )
!= kind_1_ordinals )
| ( ( cross_product @ ordinal_numbers @ universal_class )
!= ( complement @ kind_1_ordinals ) )
| ( ordinal_numbers != successor_relation ) ),
inference(simp,[status(thm)],[28405]) ).
thf(8439,plain,
! [A: $i] :
( ( member @ omega @ ( unordered_pair @ omega @ A ) )
!= ( member @ omega @ ( complement @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[8402,509]) ).
thf(8475,plain,
! [A: $i] :
( ( omega != omega )
| ( ( unordered_pair @ omega @ A )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[8439]) ).
thf(8490,plain,
! [A: $i] :
( ( unordered_pair @ omega @ A )
!= ( complement @ universal_class ) ),
inference(simp,[status(thm)],[8475]) ).
thf(143,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(472,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)],[143]) ).
thf(46,axiom,
inductive @ omega,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
thf(265,plain,
inductive @ omega,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
thf(219,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(220,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
inference(cnf,[status(esa)],[219]) ).
thf(20015,plain,
! [A: $i] :
( ( member @ null_class @ A )
| ( ( inductive @ omega )
!= ( inductive @ A ) ) ),
inference(paramod_ordered,[status(thm)],[265,220]) ).
thf(20016,plain,
member @ null_class @ omega,
inference(pattern_uni,[status(thm)],[20015:[bind(A,$thf( omega ))]]) ).
thf(20170,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ null_class @ omega )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20016,318]) ).
thf(20171,plain,
~ ( member @ null_class @ ( complement @ omega ) ),
inference(pattern_uni,[status(thm)],[20170:[bind(A,$thf( null_class )),bind(B,$thf( omega ))]]) ).
thf(20296,plain,
( ( member @ null_class @ ( complement @ omega ) )
!= ( member @ null_class @ omega ) ),
inference(paramod_ordered,[status(thm)],[20016,20171]) ).
thf(20349,plain,
( ( null_class != null_class )
| ( ( complement @ omega )
!= omega ) ),
inference(simp,[status(thm)],[20296]) ).
thf(20381,plain,
( ( complement @ omega )
!= omega ),
inference(simp,[status(thm)],[20349]) ).
thf(75,axiom,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonalisation) ).
thf(327,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(328,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
inference(lifteq,[status(thm)],[327]) ).
thf(1370,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)],[328,422]) ).
thf(1371,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(pattern_uni,[status(thm)],[1370:[bind(A,$thf( D )),bind(B,$thf( domain_of @ ( intersection @ D @ identity_relation ) ))]]) ).
thf(1405,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(simp,[status(thm)],[1371]) ).
thf(3445,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)],[328,1405]) ).
thf(3446,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) )
= ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ),
inference(pattern_uni,[status(thm)],[3445:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(6,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(173,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)],[6]) ).
thf(174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ),
inference(cnf,[status(esa)],[173]) ).
thf(11,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(185,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)],[11]) ).
thf(218,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(8456,plain,
! [B: $i,A: $i] :
( ( member @ omega @ ( singleton @ A ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ omega @ B ) ) ),
inference(paramod_ordered,[status(thm)],[218,8402]) ).
thf(8457,plain,
member @ omega @ ( singleton @ omega ),
inference(pattern_uni,[status(thm)],[8456:[bind(A,$thf( omega )),bind(B,$thf( omega ))]]) ).
thf(8538,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ omega @ ( singleton @ omega ) )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8457,318]) ).
thf(8539,plain,
~ ( member @ omega @ ( complement @ ( singleton @ omega ) ) ),
inference(pattern_uni,[status(thm)],[8538:[bind(A,$thf( omega )),bind(B,$thf( singleton @ omega ))]]) ).
thf(63,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(301,plain,
! [A: $i] :
( ( first @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(29299,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ rest_relation )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29116,318]) ).
thf(29300,plain,
~ ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ ( complement @ rest_relation ) ),
inference(pattern_uni,[status(thm)],[29299:[bind(A,$thf( ordered_pair @ omega @ ( rest_of @ omega ) )),bind(B,$thf( rest_relation ))]]) ).
thf(29445,plain,
( ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ ( complement @ rest_relation ) )
!= ( member @ null_class @ omega ) ),
inference(paramod_ordered,[status(thm)],[20016,29300]) ).
thf(29490,plain,
( ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= null_class )
| ( ( complement @ rest_relation )
!= omega ) ),
inference(simp,[status(thm)],[29445]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(4955,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ ( range_of @ ( restrict @ A @ B @ universal_class ) ) @ kind_1_ordinals )
| ( ( image @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[489,161]) ).
thf(4956,plain,
~ ( subclass @ ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[4955:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers ))]]) ).
thf(28302,plain,
~ ( subclass @ ( range_of @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) @ kind_1_ordinals ),
inference(rewrite,[status(thm)],[4956,233]) ).
thf(1979,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( null_class != kind_1_ordinals )
| ( A
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[342,554]) ).
thf(1980,plain,
( ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) )
| ( null_class != kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[1979:[bind(A,$thf( image @ successor_relation @ ordinal_numbers ))]]) ).
thf(2431,plain,
! [B: $i,A: $i] :
( ( null_class != kind_1_ordinals )
| ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1980,318]) ).
thf(2432,plain,
( ( null_class != kind_1_ordinals )
| ~ ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) ),
inference(pattern_uni,[status(thm)],[2431:[bind(A,$thf( regular @ ( image @ successor_relation @ ordinal_numbers ) )),bind(B,$thf( image @ successor_relation @ ordinal_numbers ))]]) ).
thf(56,axiom,
! [A: $i] :
( ( member @ A @ omega )
| ( ( integer_of @ A )
= null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',integer_function2) ).
thf(286,plain,
! [A: $i] :
( ( member @ A @ omega )
| ( ( integer_of @ A )
= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(287,plain,
! [A: $i] :
( ( member @ A @ omega )
| ( ( integer_of @ A )
= null_class ) ),
inference(cnf,[status(esa)],[286]) ).
thf(288,plain,
! [A: $i] :
( ( ( integer_of @ A )
= null_class )
| ( member @ A @ omega ) ),
inference(lifteq,[status(thm)],[287]) ).
thf(74,axiom,
! [A: $i] :
( ( union @ A @ ( inverse @ A ) )
= ( symmetrization_of @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetrization) ).
thf(325,plain,
! [A: $i] :
( ( union @ A @ ( inverse @ A ) )
= ( symmetrization_of @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(326,plain,
! [A: $i] :
( ( union @ A @ ( inverse @ A ) )
= ( symmetrization_of @ A ) ),
inference(lifteq,[status(thm)],[325]) ).
thf(1612,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)],[246,326]) ).
thf(1613,plain,
! [A: $i] :
( ( union @ A @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
= ( symmetrization_of @ A ) ),
inference(pattern_uni,[status(thm)],[1612:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(5068,plain,
! [A: $i] :
( ( ( domain_of @ ( inverse @ A ) )
!= kind_1_ordinals )
| ( ( range_of @ A )
!= ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[199,4952]) ).
thf(5069,plain,
( ( domain_of @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) )
!= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[5068:[bind(A,$thf( restrict @ successor_relation @ ordinal_numbers @ universal_class ))]]) ).
thf(28297,plain,
( ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) )
!= kind_1_ordinals ),
inference(rewrite,[status(thm)],[5069,233]) ).
thf(28488,plain,
( ( ( domain_of @ ( inverse @ identity_relation ) )
!= kind_1_ordinals )
| ( ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation )
!= ( intersection @ ( inverse @ subset_relation ) @ subset_relation ) ) ),
inference(paramod_ordered,[status(thm)],[330,28297]) ).
thf(28518,plain,
( ( ( domain_of @ ( inverse @ identity_relation ) )
!= kind_1_ordinals )
| ( ( cross_product @ ordinal_numbers @ universal_class )
!= ( inverse @ subset_relation ) )
| ( subset_relation != successor_relation ) ),
inference(simp,[status(thm)],[28488]) ).
thf(8441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ C ) )
| ( ( member @ omega @ ( unordered_pair @ omega @ A ) )
!= ( member @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8402,318]) ).
thf(8442,plain,
! [A: $i] :
~ ( member @ omega @ ( complement @ ( unordered_pair @ omega @ A ) ) ),
inference(pattern_uni,[status(thm)],[8441:[bind(A,$thf( E )),bind(B,$thf( omega )),bind(C,$thf( unordered_pair @ omega @ E ))]]) ).
thf(8500,plain,
! [A: $i] :
~ ( member @ omega @ ( complement @ ( unordered_pair @ omega @ A ) ) ),
inference(simp,[status(thm)],[8442]) ).
thf(10,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(182,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)],[10]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ union_of_range_map )
| ( ( sum_class @ ( range_of @ A ) )
= B ) ),
inference(cnf,[status(esa)],[182]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( ( sum_class @ ( range_of @ A ) )
= B )
| ~ ( member @ ( ordered_pair @ A @ B ) @ union_of_range_map ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
thf(372,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(9,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(179,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ domain_relation )
| ( ( domain_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ domain_relation )
| ( ( domain_of @ A )
= B ) ),
inference(cnf,[status(esa)],[179]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( ( domain_of @ A )
= B )
| ~ ( member @ ( ordered_pair @ A @ B ) @ domain_relation ) ),
inference(lifteq,[status(thm)],[180]) ).
thf(5199,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ domain_relation )
| ( B != kind_1_ordinals )
| ( ( domain_of @ A )
!= ( domain_of @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[181,5069]) ).
thf(5200,plain,
! [A: $i] :
( ~ ( member @ ( ordered_pair @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ A ) @ domain_relation )
| ( A != kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[5199:[bind(A,$thf( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) )),bind(B,$thf( B ))]]) ).
thf(5251,plain,
~ ( member @ ( ordered_pair @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals ) @ domain_relation ),
inference(simp,[status(thm)],[5200]) ).
thf(20194,plain,
( ( member @ ( ordered_pair @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals ) @ domain_relation )
!= ( member @ null_class @ omega ) ),
inference(paramod_ordered,[status(thm)],[20016,5251]) ).
thf(20197,plain,
( ( ( ordered_pair @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals )
!= null_class )
| ( omega != domain_relation ) ),
inference(simp,[status(thm)],[20194]) ).
thf(28313,plain,
( ( ( ordered_pair @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) @ kind_1_ordinals )
!= null_class )
| ( omega != domain_relation ) ),
inference(rewrite,[status(thm)],[20197,233]) ).
thf(1510,plain,
! [B: $i,A: $i] :
( ( ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
= ( domain_of @ ( inverse @ B ) ) )
| ( ( range_of @ A )
!= ( range_of @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1106,199]) ).
thf(1511,plain,
! [A: $i] :
( ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
= ( domain_of @ ( inverse @ A ) ) ),
inference(pattern_uni,[status(thm)],[1510:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(2125,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ null_class @ ordinal_numbers )
= limit_ordinals )
| ( A
!= ( complement @ kind_1_ordinals ) ) ),
inference(paramod_ordered,[status(thm)],[342,438]) ).
thf(2126,plain,
( ( member @ ( regular @ ( complement @ kind_1_ordinals ) ) @ ( complement @ kind_1_ordinals ) )
| ( ( intersection @ null_class @ ordinal_numbers )
= limit_ordinals ) ),
inference(pattern_uni,[status(thm)],[2125:[bind(A,$thf( complement @ kind_1_ordinals ))]]) ).
thf(138,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(460,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions2) ).
thf(188,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ A ) ),
inference(cnf,[status(esa)],[188]) ).
thf(55,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(284,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)],[55]) ).
thf(30,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(228,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)],[30]) ).
thf(57,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(289,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)],[57]) ).
thf(20167,plain,
( ( member @ omega @ ( complement @ universal_class ) )
!= ( member @ null_class @ omega ) ),
inference(paramod_ordered,[status(thm)],[20016,509]) ).
thf(20206,plain,
( ( omega != null_class )
| ( ( complement @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[20167]) ).
thf(2851,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ domain_relation )
| ( ( domain_of @ A )
!= kind_1_ordinals )
| ( B
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[181,554]) ).
thf(2852,plain,
! [A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( image @ successor_relation @ ordinal_numbers ) ) @ domain_relation )
| ( ( domain_of @ A )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[2851:[bind(A,$thf( A )),bind(B,$thf( image @ successor_relation @ ordinal_numbers ))]]) ).
thf(7995,plain,
( ( member @ ( apply @ choice @ omega ) @ omega )
| ( inductive @ null_class )
| ( omega != omega ) ),
inference(paramod_ordered,[status(thm)],[7208,265]) ).
thf(7996,plain,
( ( member @ ( apply @ choice @ omega ) @ omega )
| ( inductive @ null_class ) ),
inference(pattern_uni,[status(thm)],[7995:[]]) ).
thf(20772,plain,
( ( member @ ( sum_class @ ( image @ choice @ ( singleton @ omega ) ) ) @ omega )
| ( inductive @ null_class ) ),
inference(rewrite,[status(thm)],[7996,504]) ).
thf(507,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( ( member @ omega @ universal_class )
!= ( member @ A @ ( complement @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[310,318]) ).
thf(511,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( omega != A )
| ( ( complement @ B )
!= universal_class ) ),
inference(simp,[status(thm)],[507]) ).
thf(515,plain,
! [A: $i] :
( ~ ( member @ omega @ A )
| ( ( complement @ A )
!= universal_class ) ),
inference(simp,[status(thm)],[511]) ).
thf(29252,plain,
! [A: $i] :
( ( ( complement @ A )
!= universal_class )
| ( ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ rest_relation )
!= ( member @ omega @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29116,515]) ).
thf(29358,plain,
! [A: $i] :
( ( ( complement @ A )
!= universal_class )
| ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= omega )
| ( rest_relation != A ) ),
inference(simp,[status(thm)],[29252]) ).
thf(29378,plain,
( ( ( complement @ rest_relation )
!= universal_class )
| ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= omega ) ),
inference(simp,[status(thm)],[29358]) ).
thf(20060,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ ( ordered_pair @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals ) @ domain_relation ) ) ),
inference(paramod_ordered,[status(thm)],[220,5251]) ).
thf(20067,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( ordered_pair @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals )
!= null_class )
| ( A != domain_relation ) ),
inference(simp,[status(thm)],[20060]) ).
thf(20103,plain,
( ~ ( inductive @ domain_relation )
| ( ( ordered_pair @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals )
!= null_class ) ),
inference(simp,[status(thm)],[20067]) ).
thf(28334,plain,
( ~ ( inductive @ domain_relation )
| ( ( ordered_pair @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) @ kind_1_ordinals )
!= null_class ) ),
inference(rewrite,[status(thm)],[20103,233]) ).
thf(144,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).
thf(475,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(153,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(492,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)],[153]) ).
thf(95,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(376,plain,
subclass @ composition_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(140,axiom,
! [B: $i,A: $i] : ( subclass @ ( compose @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
thf(464,plain,
! [B: $i,A: $i] : ( subclass @ ( compose @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1409,plain,
! [B: $i,A: $i] :
( ( subclass @ ( compose @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[464,161]) ).
thf(1418,plain,
! [B: $i,A: $i] :
( ( ( compose @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[1409]) ).
thf(34,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(236,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)],[34]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A ) ),
inference(cnf,[status(esa)],[236]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A )
| ~ ( member @ A @ ( cross_product @ B @ C ) ) ),
inference(lifteq,[status(thm)],[237]) ).
thf(2118,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ ( inverse @ null_class ) @ subset_relation )
= identity_relation )
| ( A != subset_relation ) ),
inference(paramod_ordered,[status(thm)],[342,330]) ).
thf(2119,plain,
( ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ null_class ) @ subset_relation )
= identity_relation ) ),
inference(pattern_uni,[status(thm)],[2118:[bind(A,$thf( subset_relation ))]]) ).
thf(15652,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ null_class ) @ null_class )
= identity_relation )
| ( A != subset_relation ) ),
inference(paramod_ordered,[status(thm)],[342,2119]) ).
thf(15653,plain,
( ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ null_class ) @ null_class )
= identity_relation ) ),
inference(pattern_uni,[status(thm)],[15652:[bind(A,$thf( subset_relation ))]]) ).
thf(15678,plain,
( ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ null_class ) @ null_class )
= identity_relation ) ),
inference(simp,[status(thm)],[15653]) ).
thf(3,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(165,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)],[3]) ).
thf(166,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(cnf,[status(esa)],[165]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
= ( ordered_pair @ A @ B ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(24,axiom,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
thf(216,plain,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(904,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)],[216,318]) ).
thf(905,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ A @ B ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[904:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( unordered_pair @ E @ F )),bind(D,$thf( universal_class ))]]) ).
thf(915,plain,
! [B: $i,A: $i] :
~ ( member @ ( unordered_pair @ A @ B ) @ ( complement @ universal_class ) ),
inference(simp,[status(thm)],[905]) ).
thf(26123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( complement @ universal_class ) )
| ( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[229,915]) ).
thf(26124,plain,
! [B: $i,A: $i] :
~ ( member @ ( ordered_pair @ A @ B ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[26123:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( singleton @ F )),bind(D,$thf( unordered_pair @ F @ ( singleton @ H ) ))]]) ).
thf(26170,plain,
! [B: $i,A: $i] :
~ ( member @ ( ordered_pair @ A @ B ) @ ( complement @ universal_class ) ),
inference(simp,[status(thm)],[26124]) ).
thf(26352,plain,
! [F: $i,E: $i,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 )
!= ( member @ ( ordered_pair @ E @ F ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[166,26170]) ).
thf(26353,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( rotate @ ( complement @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[26352:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( complement @ universal_class )),bind(E,$thf( ordered_pair @ G @ H )),bind(F,$thf( A ))]]) ).
thf(26464,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( rotate @ ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[26353]) ).
thf(27845,plain,
! [G: $i,F: $i,E: $i,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 )
!= ( member @ ( ordered_pair @ ( ordered_pair @ E @ F ) @ G ) @ ( rotate @ ( complement @ universal_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[174,26464]) ).
thf(27846,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ ( rotate @ ( complement @ universal_class ) ) ) ),
inference(pattern_uni,[status(thm)],[27845:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( rotate @ ( complement @ universal_class ) )),bind(E,$thf( B )),bind(F,$thf( A )),bind(G,$thf( C ))]]) ).
thf(108,axiom,
( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ ordinal_numbers ) )
= kind_1_ordinals ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kind_1_ordinals) ).
thf(399,plain,
( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ ordinal_numbers ) )
= kind_1_ordinals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(400,plain,
( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ ordinal_numbers ) )
= kind_1_ordinals ),
inference(lifteq,[status(thm)],[399]) ).
thf(5003,plain,
! [B: $i,A: $i] :
( ( ( union @ ( singleton @ null_class ) @ ( range_of @ ( restrict @ A @ B @ universal_class ) ) )
= kind_1_ordinals )
| ( ( image @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[489,400]) ).
thf(5004,plain,
( ( union @ ( singleton @ null_class ) @ ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[5003:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers ))]]) ).
thf(28341,plain,
( ( union @ ( singleton @ null_class ) @ ( range_of @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) )
= kind_1_ordinals ),
inference(rewrite,[status(thm)],[5004,233]) ).
thf(29257,plain,
( ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ rest_relation )
!= ( member @ omega @ ( complement @ ( singleton @ omega ) ) ) ),
inference(paramod_ordered,[status(thm)],[29116,8539]) ).
thf(29337,plain,
( ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= omega )
| ( ( complement @ ( singleton @ omega ) )
!= rest_relation ) ),
inference(simp,[status(thm)],[29257]) ).
thf(129,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).
thf(443,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(22,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(211,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)],[22]) ).
thf(96,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
thf(377,plain,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(542,plain,
( ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[377,161]) ).
thf(543,plain,
( ( ( image @ successor_relation @ ordinal_numbers )
!= element_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[542]) ).
thf(645,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ composition_function )
| ( ( image @ successor_relation @ ordinal_numbers )
!= element_relation )
| ( ( compose @ A @ B )
!= kind_1_ordinals )
| ( C
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[172,543]) ).
thf(646,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ ( cross_product @ universal_class @ universal_class ) ) ) @ composition_function )
| ( ( image @ successor_relation @ ordinal_numbers )
!= element_relation )
| ( ( compose @ A @ B )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[645:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( cross_product @ universal_class @ universal_class ))]]) ).
thf(41,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(253,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)],[41]) ).
thf(106,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(397,plain,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(601,plain,
! [A: $i] :
( ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[397,161]) ).
thf(602,plain,
! [A: $i] :
( ( ( flip @ A )
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[601]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one3) ).
thf(221,plain,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(59,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(293,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)],[59]) ).
thf(135,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(453,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)],[135]) ).
thf(28584,plain,
( ~ ( subclass @ ( range_of @ identity_relation ) @ kind_1_ordinals )
| ( ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation )
!= ( intersection @ ( inverse @ subset_relation ) @ subset_relation ) ) ),
inference(paramod_ordered,[status(thm)],[330,28302]) ).
thf(28622,plain,
( ~ ( subclass @ ( range_of @ identity_relation ) @ kind_1_ordinals )
| ( ( cross_product @ ordinal_numbers @ universal_class )
!= ( inverse @ subset_relation ) )
| ( subset_relation != successor_relation ) ),
inference(simp,[status(thm)],[28584]) ).
thf(68,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(311,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)],[68]) ).
thf(312,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)],[311]) ).
thf(53,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(280,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( complement @ B ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(8642,plain,
! [A: $i] :
( ( member @ omega @ ( unordered_pair @ omega @ A ) )
!= ( member @ omega @ ( complement @ ( singleton @ omega ) ) ) ),
inference(paramod_ordered,[status(thm)],[8402,8539]) ).
thf(8710,plain,
! [A: $i] :
( ( omega != omega )
| ( ( unordered_pair @ omega @ A )
!= ( complement @ ( singleton @ omega ) ) ) ),
inference(simp,[status(thm)],[8642]) ).
thf(8727,plain,
! [A: $i] :
( ( unordered_pair @ omega @ A )
!= ( complement @ ( singleton @ omega ) ) ),
inference(simp,[status(thm)],[8710]) ).
thf(5666,plain,
! [A: $i] :
( ~ ( member @ ( ordered_pair @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) @ kind_1_ordinals ) @ domain_relation )
| ( ( inverse @ A )
!= ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[246,5251]) ).
thf(5667,plain,
~ ( member @ ( ordered_pair @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) @ universal_class ) ) ) @ kind_1_ordinals ) @ domain_relation ),
inference(pattern_uni,[status(thm)],[5666:[bind(A,$thf( restrict @ successor_relation @ ordinal_numbers @ universal_class ))]]) ).
thf(28330,plain,
~ ( member @ ( ordered_pair @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) @ universal_class ) ) ) @ kind_1_ordinals ) @ domain_relation ),
inference(rewrite,[status(thm)],[5667,233]) ).
thf(19,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(203,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)],[19]) ).
thf(204,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(cnf,[status(esa)],[203]) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ C @ A )
!= B )
| ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ A @ B ) @ ( compose_class @ C ) ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( compose @ B @ A ) ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ A @ ( compose @ B @ A ) ) @ ( compose_class @ B ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(66,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(307,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)],[66]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
inference(cnf,[status(esa)],[247]) ).
thf(98,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(380,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)],[98]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',section1) ).
thf(439,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(2414,plain,
! [A: $i] :
( ( null_class != kind_1_ordinals )
| ( ( complement @ A )
!= universal_class )
| ( ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( member @ omega @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1980,515]) ).
thf(2457,plain,
! [A: $i] :
( ( null_class != kind_1_ordinals )
| ( ( complement @ A )
!= universal_class )
| ( ( regular @ ( image @ successor_relation @ ordinal_numbers ) )
!= omega )
| ( ( image @ successor_relation @ ordinal_numbers )
!= A ) ),
inference(simp,[status(thm)],[2414]) ).
thf(2473,plain,
( ( null_class != kind_1_ordinals )
| ( ( complement @ ( image @ successor_relation @ ordinal_numbers ) )
!= universal_class )
| ( ( regular @ ( image @ successor_relation @ ordinal_numbers ) )
!= omega ) ),
inference(simp,[status(thm)],[2457]) ).
thf(1426,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)],[218,915]) ).
thf(1427,plain,
! [A: $i] :
~ ( member @ ( singleton @ A ) @ ( complement @ universal_class ) ),
inference(pattern_uni,[status(thm)],[1426:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(20189,plain,
! [A: $i] :
( ( member @ ( singleton @ A ) @ ( complement @ universal_class ) )
!= ( member @ null_class @ omega ) ),
inference(paramod_ordered,[status(thm)],[20016,1427]) ).
thf(20216,plain,
! [A: $i] :
( ( ( singleton @ A )
!= null_class )
| ( ( complement @ universal_class )
!= omega ) ),
inference(simp,[status(thm)],[20189]) ).
thf(5050,plain,
! [A: $i] :
( ( ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) )
!= kind_1_ordinals )
| ( ( range_of @ A )
!= ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1106,4952]) ).
thf(5051,plain,
( ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) @ universal_class ) ) ) )
!= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[5050:[bind(A,$thf( restrict @ successor_relation @ ordinal_numbers @ universal_class ))]]) ).
thf(28340,plain,
( ( 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)],[5051,233]) ).
thf(91,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(366,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)],[91]) ).
thf(1422,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)],[218,216]) ).
thf(1423,plain,
! [A: $i] : ( member @ ( singleton @ A ) @ universal_class ),
inference(pattern_uni,[status(thm)],[1422:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(8283,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ B @ ( unordered_pair @ B @ C ) )
| ( ( member @ ( singleton @ A ) @ universal_class )
!= ( member @ B @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[1423,194]) ).
thf(8284,plain,
! [B: $i,A: $i] : ( member @ ( singleton @ B ) @ ( unordered_pair @ ( singleton @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[8283:[bind(A,$thf( D )),bind(B,$thf( singleton @ D ))]]) ).
thf(8386,plain,
! [B: $i,A: $i] : ( member @ ( singleton @ B ) @ ( unordered_pair @ ( singleton @ B ) @ A ) ),
inference(simp,[status(thm)],[8284]) ).
thf(26105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ ( singleton @ D ) @ ( ordered_pair @ A @ B ) )
| ( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
!= ( unordered_pair @ ( singleton @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[229,8386]) ).
thf(26106,plain,
! [B: $i,A: $i] : ( member @ ( singleton @ A ) @ ( ordered_pair @ A @ B ) ),
inference(pattern_uni,[status(thm)],[26105:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( unordered_pair @ E @ ( singleton @ G ) )),bind(D,$thf( E ))]]) ).
thf(26202,plain,
! [B: $i,A: $i] : ( member @ ( singleton @ A ) @ ( ordered_pair @ A @ B ) ),
inference(simp,[status(thm)],[26106]) ).
thf(302,plain,
! [A: $i] :
( ( first @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued1 @ A ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(84,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(349,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ element_relation )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(4,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(167,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)],[4]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( ( compose @ B @ ( rest_of @ A ) )
= A ) ),
inference(cnf,[status(esa)],[167]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( ( compose @ B @ ( rest_of @ A ) )
= A )
| ~ ( member @ A @ ( recursion_equation_functions @ B ) ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(1537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( A
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals )
| ( ( compose @ B @ ( rest_of @ A ) )
!= ( compose @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[169,1418]) ).
thf(1538,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( recursion_equation_functions @ A ) )
| ( B
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[1537:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( rest_of @ E ))]]) ).
thf(1547,plain,
! [A: $i] :
( ~ ( member @ ( image @ successor_relation @ ordinal_numbers ) @ ( recursion_equation_functions @ A ) )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[1538]) ).
thf(1565,plain,
! [A: $i] :
( ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals )
| ( ( member @ ( image @ successor_relation @ ordinal_numbers ) @ ( recursion_equation_functions @ A ) )
!= ( member @ omega @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[310,1547]) ).
thf(1570,plain,
! [A: $i] :
( ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals )
| ( ( image @ successor_relation @ ordinal_numbers )
!= omega )
| ( ( recursion_equation_functions @ A )
!= universal_class ) ),
inference(simp,[status(thm)],[1565]) ).
thf(104,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(392,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)],[104]) ).
thf(112,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(407,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)],[112]) ).
thf(122,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(429,plain,
subclass @ application_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(51,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(275,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)],[51]) ).
thf(12391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( complement @ D ) )
| ( ( member @ ( singleton @ B ) @ ( unordered_pair @ ( singleton @ B ) @ A ) )
!= ( member @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[8386,318]) ).
thf(12392,plain,
! [B: $i,A: $i] :
~ ( member @ ( singleton @ B ) @ ( complement @ ( unordered_pair @ ( singleton @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[12391:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( singleton @ H )),bind(D,$thf( unordered_pair @ ( singleton @ H ) @ G ))]]) ).
thf(12459,plain,
! [B: $i,A: $i] :
~ ( member @ ( singleton @ B ) @ ( complement @ ( unordered_pair @ ( singleton @ B ) @ A ) ) ),
inference(simp,[status(thm)],[12392]) ).
thf(26150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( singleton @ D ) @ ( complement @ ( ordered_pair @ A @ B ) ) )
| ( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
!= ( unordered_pair @ ( singleton @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[229,12459]) ).
thf(26151,plain,
! [B: $i,A: $i] :
~ ( member @ ( singleton @ A ) @ ( complement @ ( ordered_pair @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[26150:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( unordered_pair @ E @ ( singleton @ G ) )),bind(D,$thf( E ))]]) ).
thf(26182,plain,
! [B: $i,A: $i] :
~ ( member @ ( singleton @ A ) @ ( complement @ ( ordered_pair @ A @ B ) ) ),
inference(simp,[status(thm)],[26151]) ).
thf(1882,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) )
| ( A != rest_relation ) ),
inference(paramod_ordered,[status(thm)],[342,428]) ).
thf(1883,plain,
( ( member @ ( regular @ rest_relation ) @ rest_relation )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[1882:[bind(A,$thf( rest_relation ))]]) ).
thf(119,axiom,
! [A: $i] : ( subclass @ ( rest_of @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_of1) ).
thf(425,plain,
! [A: $i] : ( subclass @ ( rest_of @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(597,plain,
! [A: $i] :
( ( subclass @ ( rest_of @ A ) @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[425,161]) ).
thf(598,plain,
! [A: $i] :
( ( ( rest_of @ A )
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[597]) ).
thf(8536,plain,
( ( member @ omega @ ( complement @ universal_class ) )
!= ( member @ omega @ ( singleton @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[8457,509]) ).
thf(8565,plain,
( ( omega != omega )
| ( ( complement @ universal_class )
!= ( singleton @ omega ) ) ),
inference(simp,[status(thm)],[8536]) ).
thf(8582,plain,
( ( complement @ universal_class )
!= ( singleton @ omega ) ),
inference(simp,[status(thm)],[8565]) ).
thf(61,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(297,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)],[61]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( domain_of @ A )
= B )
| ~ ( maps @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[196]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ( connected @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering1) ).
thf(361,plain,
! [B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ( connected @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(149,axiom,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive3) ).
thf(484,plain,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(4918,plain,
! [B: $i,A: $i] :
( ( ( range_of @ ( restrict @ A @ B @ universal_class ) )
!= element_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals )
| ( ( image @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[489,543]) ).
thf(4919,plain,
( ( ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) )
!= element_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[4918:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers ))]]) ).
thf(28318,plain,
( ( ( range_of @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) )
!= element_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(rewrite,[status(thm)],[4919,233]) ).
thf(1365,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)],[422,422]) ).
thf(1366,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[1365:[bind(A,$thf( E )),bind(B,$thf( image @ element_relation @ ( complement @ E ) ))]]) ).
thf(1404,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(simp,[status(thm)],[1366]) ).
thf(3307,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)],[1404,422]) ).
thf(3308,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( power_class @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[3307:[bind(A,$thf( E )),bind(B,$thf( image @ element_relation @ ( power_class @ E ) ))]]) ).
thf(3403,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)],[3308]) ).
thf(110,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(403,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)],[110]) ).
thf(2022,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ~ ( subclass @ null_class @ kind_1_ordinals )
| ( A
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[342,161]) ).
thf(2023,plain,
( ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) )
| ~ ( subclass @ null_class @ kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[2022:[bind(A,$thf( image @ successor_relation @ ordinal_numbers ))]]) ).
thf(2502,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ null_class @ kind_1_ordinals )
| ~ ( member @ A @ ( complement @ B ) )
| ( ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2023,318]) ).
thf(2503,plain,
( ~ ( subclass @ null_class @ kind_1_ordinals )
| ~ ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) ) ),
inference(pattern_uni,[status(thm)],[2502:[bind(A,$thf( regular @ ( image @ successor_relation @ ordinal_numbers ) )),bind(B,$thf( image @ successor_relation @ ordinal_numbers ))]]) ).
thf(18217,plain,
( ~ ( subclass @ null_class @ kind_1_ordinals )
| ( ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) )
!= ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) ) ) ),
inference(paramod_ordered,[status(thm)],[2023,2503]) ).
thf(18359,plain,
( ~ ( subclass @ null_class @ kind_1_ordinals )
| ( ( regular @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) )
| ( ( complement @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(simp,[status(thm)],[18217]) ).
thf(18379,plain,
( ~ ( subclass @ null_class @ kind_1_ordinals )
| ( ( complement @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(simp,[status(thm)],[18359]) ).
thf(102,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(388,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)],[102]) ).
thf(87,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(356,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)],[87]) ).
thf(116,axiom,
subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
thf(420,plain,
subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(156,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
thf(499,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(20183,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ null_class @ null_class )
| ( A != omega ) ),
inference(paramod_ordered,[status(thm)],[342,20016]) ).
thf(20184,plain,
( ( member @ ( regular @ omega ) @ omega )
| ( member @ null_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[20183:[bind(A,$thf( omega ))]]) ).
thf(8544,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ null_class @ ( singleton @ omega ) )
| ( A != omega ) ),
inference(paramod_ordered,[status(thm)],[342,8457]) ).
thf(8545,plain,
( ( member @ ( regular @ omega ) @ omega )
| ( member @ null_class @ ( singleton @ omega ) ) ),
inference(pattern_uni,[status(thm)],[8544:[bind(A,$thf( omega ))]]) ).
thf(26319,plain,
! [F: $i,E: $i,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 )
!= ( member @ ( ordered_pair @ E @ F ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[174,26170]) ).
thf(26320,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ C @ B ) @ A ) @ ( flip @ ( complement @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[26319:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( complement @ universal_class )),bind(E,$thf( ordered_pair @ G @ H )),bind(F,$thf( C ))]]) ).
thf(26459,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ C @ B ) @ A ) @ ( flip @ ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[26320]) ).
thf(27655,plain,
! [G: $i,F: $i,E: $i,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 )
!= ( member @ ( ordered_pair @ ( ordered_pair @ G @ F ) @ E ) @ ( flip @ ( complement @ universal_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[174,26459]) ).
thf(27656,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ ( flip @ ( complement @ universal_class ) ) ) ),
inference(pattern_uni,[status(thm)],[27655:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( flip @ ( complement @ universal_class ) )),bind(E,$thf( C )),bind(F,$thf( A )),bind(G,$thf( B ))]]) ).
thf(2449,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) )
| ( A != kind_1_ordinals )
| ( null_class != null_class ) ),
inference(paramod_ordered,[status(thm)],[342,1980]) ).
thf(2450,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) )
| ( A != kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[2449:[]]) ).
thf(2472,plain,
( ( member @ ( regular @ kind_1_ordinals ) @ kind_1_ordinals )
| ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(simp,[status(thm)],[2450]) ).
thf(42,axiom,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
thf(255,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(256,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
inference(cnf,[status(esa)],[255]) ).
thf(3323,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)],[328,1404]) ).
thf(3324,plain,
! [A: $i] :
( ( power_class @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( complement @ ( image @ element_relation @ ( power_class @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3323:[bind(A,$thf( D )),bind(B,$thf( domain_of @ ( intersection @ D @ identity_relation ) ))]]) ).
thf(3407,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)],[3324]) ).
thf(29050,plain,
! [B: $i,A: $i] :
( ( member @ ( ordered_pair @ B @ ( rest_of @ B ) ) @ rest_relation )
| ( ( member @ ( singleton @ A ) @ universal_class )
!= ( member @ B @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[1423,235]) ).
thf(29051,plain,
! [A: $i] : ( member @ ( ordered_pair @ ( singleton @ A ) @ ( rest_of @ ( singleton @ A ) ) ) @ rest_relation ),
inference(pattern_uni,[status(thm)],[29050:[bind(A,$thf( C )),bind(B,$thf( singleton @ C ))]]) ).
thf(29248,plain,
! [A: $i] : ( member @ ( ordered_pair @ ( singleton @ A ) @ ( rest_of @ ( singleton @ A ) ) ) @ rest_relation ),
inference(simp,[status(thm)],[29051]) ).
thf(1888,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( inductive @ null_class )
| ( A != omega ) ),
inference(paramod_ordered,[status(thm)],[342,265]) ).
thf(1889,plain,
( ( member @ ( regular @ omega ) @ omega )
| ( inductive @ null_class ) ),
inference(pattern_uni,[status(thm)],[1888:[bind(A,$thf( omega ))]]) ).
thf(3433,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)],[1405,422]) ).
thf(3434,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3433:[bind(A,$thf( D )),bind(B,$thf( domain_of @ ( intersection @ D @ identity_relation ) ))]]) ).
thf(3555,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( diagonalise @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) ) ) ) ),
inference(simp,[status(thm)],[3434]) ).
thf(44,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(259,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)],[44]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
!= null_class )
| ( asymmetric @ A @ B ) ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
!= null_class )
| ( asymmetric @ A @ B ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(37778,plain,
! [B: $i,A: $i] :
( ( ( intersection @ ( cross_product @ B @ B ) @ ( intersection @ A @ ( inverse @ A ) ) )
!= null_class )
| ( asymmetric @ A @ B ) ),
inference(rewrite,[status(thm)],[261,233]) ).
thf(28586,plain,
( ~ ( subclass @ ( range_of @ limit_ordinals ) @ kind_1_ordinals )
| ( ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation )
!= ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[438,28302]) ).
thf(28608,plain,
( ~ ( subclass @ ( range_of @ limit_ordinals ) @ kind_1_ordinals )
| ( ( cross_product @ ordinal_numbers @ universal_class )
!= ( complement @ kind_1_ordinals ) )
| ( ordinal_numbers != successor_relation ) ),
inference(simp,[status(thm)],[28586]) ).
thf(26093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ universal_class )
| ( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[229,216]) ).
thf(26094,plain,
! [B: $i,A: $i] : ( member @ ( ordered_pair @ A @ B ) @ universal_class ),
inference(pattern_uni,[status(thm)],[26093:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( singleton @ F )),bind(D,$thf( unordered_pair @ F @ ( singleton @ H ) ))]]) ).
thf(26191,plain,
! [B: $i,A: $i] : ( member @ ( ordered_pair @ A @ B ) @ universal_class ),
inference(simp,[status(thm)],[26094]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( compatible @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( compatible @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(47,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(266,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)],[47]) ).
thf(88,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(359,plain,
! [A: $i] :
( ( second @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(360,plain,
! [A: $i] :
( ( second @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued2 @ A ) ),
inference(lifteq,[status(thm)],[359]) ).
thf(107,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(398,plain,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(27697,plain,
! [G: $i,F: $i,E: $i,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 )
!= ( member @ ( ordered_pair @ ( ordered_pair @ G @ F ) @ E ) @ ( flip @ ( complement @ universal_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[166,26459]) ).
thf(27698,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( rotate @ ( flip @ ( complement @ universal_class ) ) ) ),
inference(pattern_uni,[status(thm)],[27697:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( flip @ ( complement @ universal_class ) )),bind(E,$thf( A )),bind(F,$thf( C )),bind(G,$thf( B ))]]) ).
thf(2120,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( ( intersection @ ( inverse @ subset_relation ) @ null_class )
= identity_relation )
| ( A != subset_relation ) ),
inference(paramod_ordered,[status(thm)],[342,330]) ).
thf(2121,plain,
( ( member @ ( regular @ subset_relation ) @ subset_relation )
| ( ( intersection @ ( inverse @ subset_relation ) @ null_class )
= identity_relation ) ),
inference(pattern_uni,[status(thm)],[2120:[bind(A,$thf( subset_relation ))]]) ).
thf(123,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(430,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)],[123]) ).
thf(94,axiom,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(374,plain,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(375,plain,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
inference(lifteq,[status(thm)],[374]) ).
thf(9964,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( B != kind_1_ordinals )
| ( ( domain_of @ A )
!= ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) @ universal_class ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[197,5051]) ).
thf(9965,plain,
! [B: $i,A: $i] :
( ~ ( maps @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) @ universal_class ) ) ) @ A @ B )
| ( A != kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[9964:[bind(A,$thf( domain_of @ ( flip @ ( cross_product @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) @ universal_class ) ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(10246,plain,
! [A: $i] :
~ ( maps @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) @ universal_class ) ) ) @ kind_1_ordinals @ A ),
inference(simp,[status(thm)],[9965]) ).
thf(28331,plain,
! [A: $i] :
~ ( maps @ ( domain_of @ ( flip @ ( cross_product @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) @ universal_class ) ) ) @ kind_1_ordinals @ A ),
inference(rewrite,[status(thm)],[10246,233]) ).
thf(1102,plain,
! [A: $i] :
( ( ( intersection @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) @ subset_relation )
= identity_relation )
| ( ( inverse @ A )
!= ( inverse @ subset_relation ) ) ),
inference(paramod_ordered,[status(thm)],[246,330]) ).
thf(1103,plain,
( ( intersection @ ( domain_of @ ( flip @ ( cross_product @ subset_relation @ universal_class ) ) ) @ subset_relation )
= identity_relation ),
inference(pattern_uni,[status(thm)],[1102:[bind(A,$thf( subset_relation ))]]) ).
thf(29425,plain,
( ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ ( complement @ rest_relation ) )
!= ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ rest_relation ) ),
inference(paramod_ordered,[status(thm)],[29116,29300]) ).
thf(29480,plain,
( ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= ( ordered_pair @ omega @ ( rest_of @ omega ) ) )
| ( ( complement @ rest_relation )
!= rest_relation ) ),
inference(simp,[status(thm)],[29425]) ).
thf(29522,plain,
( ( complement @ rest_relation )
!= rest_relation ),
inference(simp,[status(thm)],[29480]) ).
thf(5664,plain,
( ( member @ ( ordered_pair @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals ) @ domain_relation )
!= ( member @ omega @ universal_class ) ),
inference(paramod_ordered,[status(thm)],[310,5251]) ).
thf(5672,plain,
( ( ( ordered_pair @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals )
!= omega )
| ( universal_class != domain_relation ) ),
inference(simp,[status(thm)],[5664]) ).
thf(28339,plain,
( ( ( ordered_pair @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) @ kind_1_ordinals )
!= omega )
| ( universal_class != domain_relation ) ),
inference(rewrite,[status(thm)],[5672,233]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
inference(cnf,[status(esa)],[175]) ).
thf(118,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(423,plain,
! [A: $i] :
( ~ ( single_valued_class @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(576,plain,
( ( subclass @ composition_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[376,161]) ).
thf(577,plain,
( ( ( image @ successor_relation @ ordinal_numbers )
!= composition_function )
| ( ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[576]) ).
thf(58,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(291,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)],[58]) ).
thf(3310,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)],[1404,422]) ).
thf(3311,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3310:[bind(A,$thf( E )),bind(B,$thf( image @ element_relation @ ( complement @ E ) ))]]) ).
thf(3404,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( power_class @ A ) ) )
= ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[3311]) ).
thf(544,plain,
( ( subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[420,161]) ).
thf(545,plain,
( ( ( image @ successor_relation @ ordinal_numbers )
!= domain_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[544]) ).
thf(130,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
thf(445,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(99,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(382,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)],[99]) ).
thf(5091,plain,
! [A: $i] :
( ~ ( subclass @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) @ kind_1_ordinals )
| ( ( range_of @ A )
!= ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1106,4956]) ).
thf(5092,plain,
~ ( subclass @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) @ universal_class ) ) ) ) @ kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[5091:[bind(A,$thf( restrict @ successor_relation @ ordinal_numbers @ universal_class ))]]) ).
thf(28342,plain,
~ ( subclass @ ( 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)],[5092,233]) ).
thf(78,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(335,plain,
! [A: $i] :
( ( intersection @ ( domain_of @ A ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ A ) ) )
= ( cantor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( union @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( union @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(29446,plain,
( ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ ( complement @ rest_relation ) )
!= ( member @ omega @ ( singleton @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[8457,29300]) ).
thf(29515,plain,
( ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= omega )
| ( ( complement @ rest_relation )
!= ( singleton @ omega ) ) ),
inference(simp,[status(thm)],[29446]) ).
thf(8548,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ omega @ null_class )
| ( A
!= ( singleton @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[342,8457]) ).
thf(8549,plain,
( ( member @ ( regular @ ( singleton @ omega ) ) @ ( singleton @ omega ) )
| ( member @ omega @ null_class ) ),
inference(pattern_uni,[status(thm)],[8548:[bind(A,$thf( singleton @ omega ))]]) ).
thf(4961,plain,
! [B: $i,A: $i] :
( ( ( range_of @ ( restrict @ A @ B @ universal_class ) )
!= domain_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals )
| ( ( image @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[489,545]) ).
thf(4962,plain,
( ( ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) )
!= domain_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[4961:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers ))]]) ).
thf(28307,plain,
( ( ( range_of @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) )
!= domain_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(rewrite,[status(thm)],[4962,233]) ).
thf(20259,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ null_class @ ( complement @ omega ) ) ) ),
inference(paramod_ordered,[status(thm)],[220,20171]) ).
thf(20260,plain,
~ ( inductive @ ( complement @ omega ) ),
inference(pattern_uni,[status(thm)],[20259:[bind(A,$thf( complement @ omega ))]]) ).
thf(31,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(230,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)],[31]) ).
thf(134,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(451,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)],[134]) ).
thf(8501,plain,
! [A: $i] :
( ( ( complement @ A )
!= universal_class )
| ( ( member @ omega @ ( singleton @ omega ) )
!= ( member @ omega @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8457,515]) ).
thf(8502,plain,
( ( complement @ ( singleton @ omega ) )
!= universal_class ),
inference(pattern_uni,[status(thm)],[8501:[bind(A,$thf( singleton @ omega ))]]) ).
thf(64,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).
thf(303,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(17,axiom,
function @ choice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
thf(200,plain,
function @ choice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2256,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( function @ null_class )
| ( A != choice ) ),
inference(paramod_ordered,[status(thm)],[342,200]) ).
thf(2257,plain,
( ( member @ ( regular @ choice ) @ choice )
| ( function @ null_class ) ),
inference(pattern_uni,[status(thm)],[2256:[bind(A,$thf( choice ))]]) ).
thf(125,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(434,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)],[125]) ).
thf(49,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(271,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)],[49]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
thf(207,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(cnf,[status(esa)],[207]) ).
thf(40,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(251,plain,
! [A: $i] :
( ( domain_of @ ( restrict @ element_relation @ universal_class @ A ) )
= ( sum_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(252,plain,
! [A: $i] :
( ( domain_of @ ( restrict @ element_relation @ universal_class @ A ) )
= ( sum_class @ A ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(28312,plain,
! [A: $i] :
( ( domain_of @ ( intersection @ ( cross_product @ universal_class @ A ) @ element_relation ) )
= ( sum_class @ A ) ),
inference(rewrite,[status(thm)],[252,233]) ).
thf(82,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(345,plain,
( ( intersection @ ( complement @ ( compose @ element_relation @ ( complement @ identity_relation ) ) ) @ element_relation )
= singleton_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ~ ( member @ ( ordered_pair @ C @ ( ordered_pair @ D @ ( cross_product @ universal_class @ universal_class ) ) ) @ composition_function )
| ( ( image @ successor_relation @ ordinal_numbers )
!= element_relation )
| ( A != kind_1_ordinals )
| ( ( compose @ B @ ( rest_of @ A ) )
!= ( compose @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[169,646]) ).
thf(1002,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ ( recursion_equation_functions @ A ) )
| ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ ( rest_of @ B ) @ ( cross_product @ universal_class @ universal_class ) ) ) @ composition_function )
| ( ( image @ successor_relation @ ordinal_numbers )
!= element_relation )
| ( B != kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[1001:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( rest_of @ E ))]]) ).
thf(1029,plain,
! [A: $i] :
( ~ ( member @ kind_1_ordinals @ ( recursion_equation_functions @ A ) )
| ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ ( rest_of @ kind_1_ordinals ) @ ( cross_product @ universal_class @ universal_class ) ) ) @ composition_function )
| ( ( image @ successor_relation @ ordinal_numbers )
!= element_relation ) ),
inference(simp,[status(thm)],[1002]) ).
thf(145,axiom,
! [A: $i] : ( subclass @ A @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(477,plain,
! [A: $i] : ( subclass @ A @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(28489,plain,
( ( ( domain_of @ ( inverse @ limit_ordinals ) )
!= kind_1_ordinals )
| ( ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation )
!= ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[438,28297]) ).
thf(28516,plain,
( ( ( domain_of @ ( inverse @ limit_ordinals ) )
!= kind_1_ordinals )
| ( ( cross_product @ ordinal_numbers @ universal_class )
!= ( complement @ kind_1_ordinals ) )
| ( ordinal_numbers != successor_relation ) ),
inference(simp,[status(thm)],[28489]) ).
thf(5117,plain,
! [A: $i] :
( ~ ( subclass @ ( domain_of @ ( inverse @ A ) ) @ kind_1_ordinals )
| ( ( range_of @ A )
!= ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[199,4956]) ).
thf(5118,plain,
~ ( subclass @ ( domain_of @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) @ kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[5117:[bind(A,$thf( restrict @ successor_relation @ ordinal_numbers @ universal_class ))]]) ).
thf(28322,plain,
~ ( subclass @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ) @ kind_1_ordinals ),
inference(rewrite,[status(thm)],[5118,233]) ).
thf(139,axiom,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( well_ordering @ element_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers1) ).
thf(462,plain,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( well_ordering @ element_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(12406,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( singleton @ C ) @ ( singleton @ A ) )
| ( ( unordered_pair @ A @ A )
!= ( unordered_pair @ ( singleton @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[218,8386]) ).
thf(12407,plain,
! [A: $i] : ( member @ ( singleton @ A ) @ ( singleton @ ( singleton @ A ) ) ),
inference(pattern_uni,[status(thm)],[12406:[bind(A,$thf( singleton @ E )),bind(B,$thf( singleton @ E )),bind(C,$thf( E ))]]) ).
thf(12463,plain,
! [A: $i] : ( member @ ( singleton @ A ) @ ( singleton @ ( singleton @ A ) ) ),
inference(simp,[status(thm)],[12407]) ).
thf(12514,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ C ) )
| ( ( member @ ( singleton @ A ) @ ( singleton @ ( singleton @ A ) ) )
!= ( member @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12463,318]) ).
thf(12515,plain,
! [A: $i] :
~ ( member @ ( singleton @ A ) @ ( complement @ ( singleton @ ( singleton @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[12514:[bind(A,$thf( F )),bind(B,$thf( singleton @ F )),bind(C,$thf( singleton @ ( singleton @ F ) ))]]) ).
thf(12573,plain,
! [A: $i] :
~ ( member @ ( singleton @ A ) @ ( complement @ ( singleton @ ( singleton @ A ) ) ) ),
inference(simp,[status(thm)],[12515]) ).
thf(519,plain,
! [A: $i] :
( ( subclass @ A @ universal_class )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[477,161]) ).
thf(520,plain,
! [A: $i] :
( ( A
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( universal_class != kind_1_ordinals ) ),
inference(simp,[status(thm)],[519]) ).
thf(521,plain,
universal_class != kind_1_ordinals,
inference(simp,[status(thm)],[520]) ).
thf(136,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(455,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)],[136]) ).
thf(28,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(223,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)],[28]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions1) ).
thf(299,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(35,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(239,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)],[35]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( ( domain_of @ ( domain_of @ B ) )
= ( domain_of @ A ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( domain_of @ ( domain_of @ B ) )
= ( domain_of @ A ) )
| ~ ( compatible @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[240]) ).
thf(29,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(226,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)],[29]) ).
thf(5593,plain,
! [A: $i] :
( ( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( inverse @ A ) ) )
= kind_1_ordinals )
| ( ( range_of @ A )
!= ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[199,5004]) ).
thf(5594,plain,
( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[5593:[bind(A,$thf( restrict @ successor_relation @ ordinal_numbers @ universal_class ))]]) ).
thf(28311,plain,
( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) ) )
= kind_1_ordinals ),
inference(rewrite,[status(thm)],[5594,233]) ).
thf(159,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(505,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)],[159]) ).
thf(2155,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ null_class @ universal_class )
| ( A != omega ) ),
inference(paramod_ordered,[status(thm)],[342,310]) ).
thf(2156,plain,
( ( member @ ( regular @ omega ) @ omega )
| ( member @ null_class @ universal_class ) ),
inference(pattern_uni,[status(thm)],[2155:[bind(A,$thf( omega ))]]) ).
thf(2068,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) )
| ( A != element_relation ) ),
inference(paramod_ordered,[status(thm)],[342,377]) ).
thf(2069,plain,
( ( member @ ( regular @ element_relation ) @ element_relation )
| ( subclass @ null_class @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(pattern_uni,[status(thm)],[2068:[bind(A,$thf( element_relation ))]]) ).
thf(32905,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ B @ ( complement @ C ) )
| ( ( member @ ( ordered_pair @ ( singleton @ A ) @ ( rest_of @ ( singleton @ A ) ) ) @ rest_relation )
!= ( member @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29248,318]) ).
thf(32906,plain,
! [A: $i] :
~ ( member @ ( ordered_pair @ ( singleton @ A ) @ ( rest_of @ ( singleton @ A ) ) ) @ ( complement @ rest_relation ) ),
inference(pattern_uni,[status(thm)],[32905:[bind(A,$thf( H )),bind(B,$thf( ordered_pair @ ( singleton @ H ) @ ( rest_of @ ( singleton @ H ) ) )),bind(C,$thf( rest_relation ))]]) ).
thf(32989,plain,
! [A: $i] :
~ ( member @ ( ordered_pair @ ( singleton @ A ) @ ( rest_of @ ( singleton @ A ) ) ) @ ( complement @ rest_relation ) ),
inference(simp,[status(thm)],[32906]) ).
thf(10534,plain,
! [B: $i,A: $i] :
( ( member @ omega @ ( unordered_pair @ omega @ A ) )
!= ( member @ omega @ ( complement @ ( unordered_pair @ omega @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8402,8500]) ).
thf(10612,plain,
! [B: $i,A: $i] :
( ( omega != omega )
| ( ( unordered_pair @ omega @ A )
!= ( complement @ ( unordered_pair @ omega @ B ) ) ) ),
inference(simp,[status(thm)],[10534]) ).
thf(10643,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ omega @ A )
!= ( complement @ ( unordered_pair @ omega @ B ) ) ),
inference(simp,[status(thm)],[10612]) ).
thf(152,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(490,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)],[152]) ).
thf(120,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(426,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)],[120]) ).
thf(20273,plain,
! [A: $i] :
( ( member @ ( singleton @ A ) @ universal_class )
!= ( member @ null_class @ ( complement @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[1423,20171]) ).
thf(20338,plain,
! [A: $i] :
( ( ( singleton @ A )
!= null_class )
| ( ( complement @ omega )
!= universal_class ) ),
inference(simp,[status(thm)],[20273]) ).
thf(2,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(162,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)],[2]) ).
thf(21,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(209,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)],[21]) ).
thf(137,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(458,plain,
! [A: $i] :
( ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( single_valued_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(28343,plain,
~ ( member @ ( ordered_pair @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) @ kind_1_ordinals ) @ domain_relation ),
inference(rewrite,[status(thm)],[5251,233]) ).
thf(917,plain,
! [A: $i] :
( ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[398,161]) ).
thf(927,plain,
! [A: $i] :
( ( ( rotate @ A )
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[917]) ).
thf(60,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(295,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)],[60]) ).
thf(54,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(282,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)],[54]) ).
thf(20007,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ omega @ ( complement @ ( unordered_pair @ omega @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[220,8500]) ).
thf(20073,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( omega != null_class )
| ( A
!= ( complement @ ( unordered_pair @ omega @ B ) ) ) ),
inference(simp,[status(thm)],[20007]) ).
thf(20109,plain,
! [A: $i] :
( ~ ( inductive @ ( complement @ ( unordered_pair @ omega @ A ) ) )
| ( omega != null_class ) ),
inference(simp,[status(thm)],[20073]) ).
thf(77,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(331,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)],[77]) ).
thf(128,axiom,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( subclass @ ( sum_class @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers2) ).
thf(441,plain,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( subclass @ ( sum_class @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(36,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(242,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)],[36]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( ( restrict @ B @ ( singleton @ A ) @ universal_class )
= null_class )
| ( member @ A @ ( domain_of @ B ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( ( restrict @ B @ ( singleton @ A ) @ universal_class )
= null_class )
| ~ ( member @ A @ universal_class )
| ( member @ A @ ( domain_of @ B ) ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(31890,plain,
! [B: $i,A: $i] :
( ( ( intersection @ ( cross_product @ ( singleton @ A ) @ universal_class ) @ B )
= null_class )
| ~ ( member @ A @ universal_class )
| ( member @ A @ ( domain_of @ B ) ) ),
inference(rewrite,[status(thm)],[244,233]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(584,plain,
( ( subclass @ application_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[429,161]) ).
thf(585,plain,
( ( ( image @ successor_relation @ ordinal_numbers )
!= application_function )
| ( ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[584]) ).
thf(92,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(370,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( domain_of @ A ) ) @ domain_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(146,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
thf(478,plain,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(574,plain,
( ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[478,161]) ).
thf(575,plain,
( ( ( image @ successor_relation @ ordinal_numbers )
!= successor_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[574]) ).
thf(5005,plain,
! [B: $i,A: $i] :
( ( ( range_of @ ( restrict @ A @ B @ universal_class ) )
!= successor_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals )
| ( ( image @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[489,575]) ).
thf(5006,plain,
( ( ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) )
!= successor_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[5005:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers ))]]) ).
thf(28315,plain,
( ( ( range_of @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) )
!= successor_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(rewrite,[status(thm)],[5006,233]) ).
thf(20141,plain,
! [A: $i] :
( ( member @ omega @ ( complement @ ( unordered_pair @ omega @ A ) ) )
!= ( member @ null_class @ omega ) ),
inference(paramod_ordered,[status(thm)],[20016,8500]) ).
thf(20225,plain,
! [A: $i] :
( ( omega != null_class )
| ( ( complement @ ( unordered_pair @ omega @ A ) )
!= omega ) ),
inference(simp,[status(thm)],[20141]) ).
thf(8684,plain,
( ( member @ omega @ ( complement @ ( singleton @ omega ) ) )
!= ( member @ omega @ ( singleton @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[8457,8539]) ).
thf(8715,plain,
( ( omega != omega )
| ( ( complement @ ( singleton @ omega ) )
!= ( singleton @ omega ) ) ),
inference(simp,[status(thm)],[8684]) ).
thf(8729,plain,
( ( complement @ ( singleton @ omega ) )
!= ( singleton @ omega ) ),
inference(simp,[status(thm)],[8715]) ).
thf(336,plain,
! [A: $i] :
( ( intersection @ ( domain_of @ A ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ A ) ) )
= ( cantor @ A ) ),
inference(lifteq,[status(thm)],[335]) ).
thf(27887,plain,
! [G: $i,F: $i,E: $i,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 )
!= ( member @ ( ordered_pair @ ( ordered_pair @ E @ F ) @ G ) @ ( rotate @ ( complement @ universal_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[166,26464]) ).
thf(27888,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( rotate @ ( rotate @ ( complement @ universal_class ) ) ) ),
inference(pattern_uni,[status(thm)],[27887:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( rotate @ ( complement @ universal_class ) )),bind(E,$thf( B )),bind(F,$thf( C )),bind(G,$thf( A ))]]) ).
thf(8546,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( member @ omega @ ( singleton @ null_class ) )
| ( A != omega ) ),
inference(paramod_ordered,[status(thm)],[342,8457]) ).
thf(8547,plain,
( ( member @ ( regular @ omega ) @ omega )
| ( member @ omega @ ( singleton @ null_class ) ) ),
inference(pattern_uni,[status(thm)],[8546:[bind(A,$thf( omega ))]]) ).
thf(12231,plain,
! [B: $i,A: $i] :
( ( ( complement @ ( domain_of @ ( inverse @ A ) ) )
= ( power_class @ B ) )
| ( ( range_of @ A )
!= ( range_of @ ( restrict @ element_relation @ ( complement @ B ) @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[199,5015]) ).
thf(12232,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) ) )
= ( power_class @ A ) ),
inference(pattern_uni,[status(thm)],[12231:[bind(A,$thf( restrict @ element_relation @ ( complement @ F ) @ universal_class )),bind(B,$thf( F ))]]) ).
thf(12322,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( restrict @ element_relation @ ( complement @ A ) @ universal_class ) ) ) )
= ( power_class @ A ) ),
inference(simp,[status(thm)],[12232]) ).
thf(28321,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( inverse @ ( intersection @ ( cross_product @ ( complement @ A ) @ universal_class ) @ element_relation ) ) ) )
= ( power_class @ A ) ),
inference(rewrite,[status(thm)],[12322,233]) ).
thf(599,plain,
! [A: $i] :
( ( subclass @ ( compose_class @ A ) @ ( cross_product @ universal_class @ universal_class ) )
!= ( subclass @ ( image @ successor_relation @ ordinal_numbers ) @ kind_1_ordinals ) ),
inference(paramod_ordered,[status(thm)],[449,161]) ).
thf(600,plain,
! [A: $i] :
( ( ( compose_class @ A )
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[599]) ).
thf(8506,plain,
( ( member @ ( apply @ choice @ omega ) @ omega )
| ( member @ omega @ ( singleton @ null_class ) )
| ( omega != omega ) ),
inference(paramod_ordered,[status(thm)],[7208,8457]) ).
thf(8507,plain,
( ( member @ ( apply @ choice @ omega ) @ omega )
| ( member @ omega @ ( singleton @ null_class ) ) ),
inference(pattern_uni,[status(thm)],[8506:[]]) ).
thf(25596,plain,
( ( member @ ( sum_class @ ( image @ choice @ ( singleton @ omega ) ) ) @ omega )
| ( member @ omega @ ( singleton @ null_class ) ) ),
inference(rewrite,[status(thm)],[8507,504]) ).
thf(29270,plain,
( ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ rest_relation )
!= ( member @ null_class @ ( complement @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[29116,20171]) ).
thf(29350,plain,
( ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= null_class )
| ( ( complement @ omega )
!= rest_relation ) ),
inference(simp,[status(thm)],[29270]) ).
thf(155,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(497,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)],[155]) ).
thf(20054,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ ( singleton @ B ) @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[220,1427]) ).
thf(20070,plain,
! [B: $i,A: $i] :
( ~ ( inductive @ A )
| ( ( singleton @ B )
!= null_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[20054]) ).
thf(20106,plain,
! [A: $i] :
( ~ ( inductive @ ( complement @ universal_class ) )
| ( ( singleton @ A )
!= null_class ) ),
inference(simp,[status(thm)],[20070]) ).
thf(101,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(386,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)],[101]) ).
thf(2433,plain,
( ( null_class != kind_1_ordinals )
| ( ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( member @ omega @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1980,509]) ).
thf(2458,plain,
( ( null_class != kind_1_ordinals )
| ( ( regular @ ( image @ successor_relation @ ordinal_numbers ) )
!= omega )
| ( ( image @ successor_relation @ ordinal_numbers )
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[2433]) ).
thf(90,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(363,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)],[90]) ).
thf(154,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(495,plain,
! [B: $i,A: $i] :
( ~ ( irreflexive @ A @ B )
| ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(20133,plain,
! [A: $i] :
( ( ( complement @ A )
!= universal_class )
| ( ( member @ omega @ A )
!= ( member @ null_class @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[20016,515]) ).
thf(20218,plain,
! [A: $i] :
( ( ( complement @ A )
!= universal_class )
| ( omega != null_class )
| ( A != omega ) ),
inference(simp,[status(thm)],[20133]) ).
thf(20242,plain,
( ( ( complement @ omega )
!= universal_class )
| ( omega != null_class ) ),
inference(simp,[status(thm)],[20218]) ).
thf(250,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(cnf,[status(esa)],[249]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass1) ).
thf(465,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(231,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(cnf,[status(esa)],[230]) ).
thf(148,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(482,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)],[148]) ).
thf(72,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(319,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)],[72]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
inference(cnf,[status(esa)],[257]) ).
thf(103,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(390,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)],[103]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( rest_of @ C ) )
| ( ( restrict @ C @ A @ universal_class )
= B ) ),
inference(cnf,[status(esa)],[211]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( ( restrict @ C @ A @ universal_class )
= B )
| ~ ( member @ ( ordered_pair @ A @ B ) @ ( rest_of @ C ) ) ),
inference(lifteq,[status(thm)],[212]) ).
thf(16115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( rest_of @ C ) )
| ( ( range_of @ B )
!= kind_1_ordinals )
| ( ( restrict @ C @ A @ universal_class )
!= ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[213,4952]) ).
thf(16116,plain,
! [A: $i] :
( ~ ( member @ ( ordered_pair @ ordinal_numbers @ A ) @ ( rest_of @ successor_relation ) )
| ( ( range_of @ A )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[16115:[bind(A,$thf( ordinal_numbers )),bind(B,$thf( B )),bind(C,$thf( successor_relation ))]]) ).
thf(17565,plain,
! [A: $i] :
( ~ ( member @ ( ordered_pair @ ordinal_numbers @ A ) @ ( rest_of @ successor_relation ) )
| ( ( range_of @ A )
!= kind_1_ordinals ) ),
inference(simp,[status(thm)],[16116]) ).
thf(109,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(401,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) )
| ( irreflexive @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(115,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(418,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)],[115]) ).
thf(28333,plain,
! [A: $i] :
( ( complement @ ( range_of @ ( intersection @ ( cross_product @ ( complement @ A ) @ universal_class ) @ element_relation ) ) )
= ( power_class @ A ) ),
inference(rewrite,[status(thm)],[5015,233]) ).
thf(85,axiom,
! [A: $i] :
( ~ ( member @ A @ omega )
| ( ( integer_of @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',integer_function1) ).
thf(351,plain,
! [A: $i] :
( ~ ( member @ A @ omega )
| ( ( integer_of @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(8403,plain,
! [B: $i,A: $i] :
( ( ( complement @ B )
!= universal_class )
| ( ( member @ omega @ ( unordered_pair @ omega @ A ) )
!= ( member @ omega @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8402,515]) ).
thf(8404,plain,
! [A: $i] :
( ( complement @ ( unordered_pair @ omega @ A ) )
!= universal_class ),
inference(pattern_uni,[status(thm)],[8403:[bind(A,$thf( D )),bind(B,$thf( unordered_pair @ omega @ D ))]]) ).
thf(8488,plain,
! [A: $i] :
( ( complement @ ( unordered_pair @ omega @ A ) )
!= universal_class ),
inference(simp,[status(thm)],[8404]) ).
thf(97,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(378,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)],[97]) ).
thf(20032,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ omega @ ( complement @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[220,509]) ).
thf(20085,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( omega != null_class )
| ( A
!= ( complement @ universal_class ) ) ),
inference(simp,[status(thm)],[20032]) ).
thf(20123,plain,
( ~ ( inductive @ ( complement @ universal_class ) )
| ( omega != null_class ) ),
inference(simp,[status(thm)],[20085]) ).
thf(9095,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( B != kind_1_ordinals )
| ( ( domain_of @ A )
!= ( domain_of @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[197,5069]) ).
thf(9096,plain,
! [B: $i,A: $i] :
( ~ ( maps @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ A @ B )
| ( A != kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[9095:[bind(A,$thf( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(10357,plain,
! [A: $i] :
~ ( maps @ ( inverse @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) @ kind_1_ordinals @ A ),
inference(simp,[status(thm)],[9096]) ).
thf(28338,plain,
! [A: $i] :
~ ( maps @ ( inverse @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) ) @ kind_1_ordinals @ A ),
inference(rewrite,[status(thm)],[10357,233]) ).
thf(5549,plain,
! [A: $i] :
( ( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) )
= kind_1_ordinals )
| ( ( range_of @ A )
!= ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) ) ) ),
inference(paramod_ordered,[status(thm)],[1106,5004]) ).
thf(5550,plain,
( ( union @ ( singleton @ null_class ) @ ( domain_of @ ( domain_of @ ( flip @ ( cross_product @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) @ universal_class ) ) ) ) )
= kind_1_ordinals ),
inference(pattern_uni,[status(thm)],[5549:[bind(A,$thf( restrict @ successor_relation @ ordinal_numbers @ universal_class ))]]) ).
thf(28301,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)],[5550,233]) ).
thf(346,plain,
( ( intersection @ ( complement @ ( compose @ element_relation @ ( complement @ identity_relation ) ) ) @ element_relation )
= singleton_relation ),
inference(lifteq,[status(thm)],[345]) ).
thf(23,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(214,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)],[23]) ).
thf(20006,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ omega @ ( complement @ ( singleton @ omega ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[220,8539]) ).
thf(20092,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( omega != null_class )
| ( A
!= ( complement @ ( singleton @ omega ) ) ) ),
inference(simp,[status(thm)],[20006]) ).
thf(20131,plain,
( ~ ( inductive @ ( complement @ ( singleton @ omega ) ) )
| ( omega != null_class ) ),
inference(simp,[status(thm)],[20092]) ).
thf(131,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(447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(70,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class2) ).
thf(315,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(124,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(432,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)],[124]) ).
thf(4953,plain,
! [B: $i,A: $i] :
( ( ( range_of @ ( restrict @ A @ B @ universal_class ) )
!= rest_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals )
| ( ( image @ A @ B )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[489,547]) ).
thf(4954,plain,
( ( ( range_of @ ( restrict @ successor_relation @ ordinal_numbers @ universal_class ) )
!= rest_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(pattern_uni,[status(thm)],[4953:[bind(A,$thf( successor_relation )),bind(B,$thf( ordinal_numbers ))]]) ).
thf(28329,plain,
( ( ( range_of @ ( intersection @ ( cross_product @ ordinal_numbers @ universal_class ) @ successor_relation ) )
!= rest_relation )
| ( ( cross_product @ universal_class @ universal_class )
!= kind_1_ordinals ) ),
inference(rewrite,[status(thm)],[4954,233]) ).
thf(111,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(405,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)],[111]) ).
thf(50,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(273,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)],[50]) ).
thf(29399,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( member @ null_class @ A )
!= ( member @ ( ordered_pair @ omega @ ( rest_of @ omega ) ) @ ( complement @ rest_relation ) ) ) ),
inference(paramod_ordered,[status(thm)],[220,29300]) ).
thf(29519,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= null_class )
| ( A
!= ( complement @ rest_relation ) ) ),
inference(simp,[status(thm)],[29399]) ).
thf(29528,plain,
( ~ ( inductive @ ( complement @ rest_relation ) )
| ( ( ordered_pair @ omega @ ( rest_of @ omega ) )
!= null_class ) ),
inference(simp,[status(thm)],[29519]) ).
thf(3715,plain,
( ( null_class != kind_1_ordinals )
| ( ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( complement @ ( image @ successor_relation @ ordinal_numbers ) ) )
!= ( member @ ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) @ ( image @ successor_relation @ ordinal_numbers ) ) ) ),
inference(paramod_ordered,[status(thm)],[1980,2432]) ).
thf(3723,plain,
( ( null_class != kind_1_ordinals )
| ( ( regular @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( regular @ ( image @ successor_relation @ ordinal_numbers ) ) )
| ( ( complement @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(simp,[status(thm)],[3715]) ).
thf(3733,plain,
( ( null_class != kind_1_ordinals )
| ( ( complement @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(simp,[status(thm)],[3723]) ).
thf(45,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(262,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)],[45]) ).
thf(3814,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != kind_1_ordinals )
| ( ( complement @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( image @ successor_relation @ ordinal_numbers ) )
| ( null_class != null_class ) ),
inference(paramod_ordered,[status(thm)],[342,3733]) ).
thf(3815,plain,
! [A: $i] :
( ( member @ ( regular @ A ) @ A )
| ( A != kind_1_ordinals )
| ( ( complement @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(pattern_uni,[status(thm)],[3814:[]]) ).
thf(3822,plain,
( ( member @ ( regular @ kind_1_ordinals ) @ kind_1_ordinals )
| ( ( complement @ ( image @ successor_relation @ ordinal_numbers ) )
!= ( image @ successor_relation @ ordinal_numbers ) ) ),
inference(simp,[status(thm)],[3815]) ).
thf(65,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
thf(305,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
thf(415,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(20140,plain,
( ( member @ omega @ ( complement @ ( singleton @ omega ) ) )
!= ( member @ null_class @ omega ) ),
inference(paramod_ordered,[status(thm)],[20016,8539]) ).
thf(20222,plain,
( ( omega != null_class )
| ( ( complement @ ( singleton @ omega ) )
!= omega ) ),
inference(simp,[status(thm)],[20140]) ).
thf(105,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(395,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( not_subclass_element @ A @ B ) @ B )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(20135,plain,
( ( member @ ( apply @ choice @ omega ) @ omega )
| ( member @ null_class @ null_class )
| ( omega != omega ) ),
inference(paramod_ordered,[status(thm)],[7208,20016]) ).
thf(20136,plain,
( ( member @ ( apply @ choice @ omega ) @ omega )
| ( member @ null_class @ null_class ) ),
inference(pattern_uni,[status(thm)],[20135:[]]) ).
thf(23569,plain,
( ( member @ ( sum_class @ ( image @ choice @ ( singleton @ omega ) ) ) @ omega )
| ( member @ null_class @ null_class ) ),
inference(rewrite,[status(thm)],[20136,504]) ).
thf(20300,plain,
( ( member @ omega @ ( singleton @ omega ) )
!= ( member @ null_class @ ( complement @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[8457,20171]) ).
thf(20339,plain,
( ( omega != null_class )
| ( ( complement @ omega )
!= ( singleton @ omega ) ) ),
inference(simp,[status(thm)],[20300]) ).
thf(10584,plain,
! [A: $i] :
( ( member @ omega @ ( complement @ ( unordered_pair @ omega @ A ) ) )
!= ( member @ omega @ ( singleton @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[8457,8500]) ).
thf(10611,plain,
! [A: $i] :
( ( omega != omega )
| ( ( complement @ ( unordered_pair @ omega @ A ) )
!= ( singleton @ omega ) ) ),
inference(simp,[status(thm)],[10584]) ).
thf(10642,plain,
! [A: $i] :
( ( complement @ ( unordered_pair @ omega @ A ) )
!= ( singleton @ omega ) ),
inference(simp,[status(thm)],[10611]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(cnf,[status(esa)],[177]) ).
thf(52,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(277,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ rest_relation )
| ( ( rest_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(157,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(501,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)],[157]) ).
thf(73,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(322,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)],[73]) ).
thf(150,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(486,plain,
! [B: $i,A: $i] :
( ( member @ ( not_subclass_element @ A @ B ) @ A )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(79,axiom,
! [A: $i] :
( ( A = null_class )
| ( ( intersection @ A @ ( regular @ A ) )
= null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
thf(337,plain,
! [A: $i] :
( ( A = null_class )
| ( ( intersection @ A @ ( regular @ A ) )
= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(142,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(469,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)],[142]) ).
thf(20244,plain,
! [A: $i] :
( ( member @ omega @ ( unordered_pair @ omega @ A ) )
!= ( member @ null_class @ ( complement @ omega ) ) ),
inference(paramod_ordered,[status(thm)],[8402,20171]) ).
thf(20350,plain,
! [A: $i] :
( ( omega != null_class )
| ( ( unordered_pair @ omega @ A )
!= ( complement @ omega ) ) ),
inference(simp,[status(thm)],[20244]) ).
thf(86,axiom,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).
thf(354,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ D ) ),
inference(cnf,[status(esa)],[214]) ).
thf(3315,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)],[422,1404]) ).
thf(3316,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ ( image @ element_relation @ ( complement @ A ) ) ) ) )
= ( power_class @ ( image @ element_relation @ ( complement @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[3315:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(222,plain,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
inference(cnf,[status(esa)],[221]) ).
thf(254,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(cnf,[status(esa)],[253]) ).
thf(227,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(cnf,[status(esa)],[226]) ).
thf(56142,plain,
$false,
inference(e,[status(thm)],[28419,479,347,249,28324,518,234,20765,170,2117,217,8402,741,37150,449,247,202,29363,269,384,28423,8490,472,340,20381,3446,174,185,8539,301,29490,257,28302,2432,288,1613,28518,8500,184,372,504,28313,1511,2126,460,189,284,325,228,289,20206,2852,421,20772,29378,28334,475,492,179,376,1418,238,15678,27846,28341,20171,216,29337,443,211,646,253,602,397,221,293,453,28622,411,1405,428,265,312,280,8727,28330,206,307,233,248,380,439,2473,20216,201,28340,28303,220,366,26202,302,349,1570,392,407,429,275,165,26182,1883,598,160,8582,297,26170,1423,197,361,329,1106,229,484,28318,3403,8386,317,403,188,18379,388,356,169,420,499,20184,8545,2023,488,193,27656,26464,2472,547,328,256,3407,554,29248,1889,3555,515,37778,173,503,28608,26191,343,266,360,311,398,27698,2121,425,430,161,573,375,28331,1103,29522,166,28339,176,423,29116,286,577,291,3404,545,259,445,382,28342,335,236,181,313,29515,8549,2119,172,28307,219,20260,230,451,245,318,8502,303,377,2257,509,434,271,208,28312,345,20016,251,1029,915,330,477,28516,198,28322,462,12573,521,399,455,223,299,241,167,8457,226,28311,505,2156,438,2069,32989,10643,490,426,20338,162,209,26459,342,458,194,28343,927,374,255,2503,1547,295,282,414,327,20109,310,199,331,441,1980,31890,359,177,182,585,370,28315,20225,8729,336,27888,8547,28321,600,25596,1427,29350,497,1404,20106,29300,175,386,2458,450,363,495,218,20242,250,465,231,482,203,319,258,390,17565,401,418,28333,351,8488,378,207,20123,12463,28338,478,28301,346,214,235,246,20131,447,315,432,28329,405,190,422,273,29528,3733,262,3822,305,326,437,12459,400,28297,415,239,242,195,20222,395,23569,464,575,20339,200,10642,178,277,501,322,486,337,469,20350,354,543,215,3316,222,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM159-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 18 16:53:58 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.44/1.05 % [INFO] Parsing done (207ms).
% 1.44/1.06 % [INFO] Running in sequential loop mode.
% 2.12/1.32 % [INFO] eprover registered as external prover.
% 2.12/1.32 % [INFO] cvc4 registered as external prover.
% 2.12/1.32 % [INFO] Scanning for conjecture ...
% 2.32/1.41 % [INFO] Found a conjecture and 158 axioms. Running axiom selection ...
% 2.59/1.50 % [INFO] Axiom selection finished. Selected 158 axioms (removed 0 axioms).
% 2.78/1.60 % [INFO] Problem is propositional (TPTP CNF).
% 2.78/1.61 % [INFO] Type checking passed.
% 3.00/1.61 % [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 ...
% 121.27/23.53 % External prover 'e' found a proof!
% 121.27/23.53 % [INFO] Killing All external provers ...
% 121.27/23.53 % Time passed: 23044ms (effective reasoning time: 22471ms)
% 121.27/23.53 % 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)>
% 121.27/23.54 % 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
% 121.27/23.54 % No. of inferences in proof: 782
% 121.27/23.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23044 ms resp. 22471 ms w/o parsing
% 121.27/23.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 121.70/23.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------