TSTP Solution File: NUM139-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM139-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 11:39:57 EDT 2023
% Result : Unsatisfiable 6.26s 2.48s
% Output : Refutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 240
% Syntax : Number of formulae : 401 ( 97 unt; 80 typ; 0 def)
% Number of atoms : 649 ( 142 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 3008 ( 314 ~; 328 |; 0 &;2366 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 103 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 80 usr; 21 con; 0-3 aty)
% Number of variables : 606 ( 0 ^; 606 !; 0 ?; 606 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(not_subclass_element_type,type,
not_subclass_element: $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(power_class_type,type,
power_class: $i > $i ).
thf(x_type,type,
x: $i ).
thf(z_type,type,
z: $i ).
thf(subclass_type,type,
subclass: $i > $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(null_class_type,type,
null_class: $i ).
thf(image_type,type,
image: $i > $i > $i ).
thf(successor_relation_type,type,
successor_relation: $i ).
thf(ordinal_numbers_type,type,
ordinal_numbers: $i ).
thf(kind_1_ordinals_type,type,
kind_1_ordinals: $i ).
thf(maps_type,type,
maps: $i > $i > $i > $o ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(function_type,type,
function: $i > $o ).
thf(choice_type,type,
choice: $i ).
thf(domain_type,type,
domain: $i > $i > $i > $i ).
thf(single_valued1_type,type,
single_valued1: $i > $i ).
thf(single_valued2_type,type,
single_valued2: $i > $i ).
thf(single_valued3_type,type,
single_valued3: $i > $i ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(homomorphism_type,type,
homomorphism: $i > $i > $i > $o ).
thf(operation_type,type,
operation: $i > $o ).
thf(restrict_type,type,
restrict: $i > $i > $i > $i ).
thf(element_relation_type,type,
element_relation: $i ).
thf(universal_class_type,type,
universal_class: $i ).
thf(sum_class_type,type,
sum_class: $i > $i ).
thf(recursion_type,type,
recursion: $i > $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(add_relation_type,type,
add_relation: $i ).
thf(union_of_range_map_type,type,
union_of_range_map: $i ).
thf(ordinal_multiply_type,type,
ordinal_multiply: $i > $i > $i ).
thf(ordinal_add_type,type,
ordinal_add: $i > $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(symmetrization_of_type,type,
symmetrization_of: $i > $i ).
thf(compatible_type,type,
compatible: $i > $i > $i > $o ).
thf(connected_type,type,
connected: $i > $i > $o ).
thf(not_well_ordering_type,type,
not_well_ordering: $i > $i > $i ).
thf(well_ordering_type,type,
well_ordering: $i > $i > $o ).
thf(not_homomorphism1_type,type,
not_homomorphism1: $i > $i > $i > $i ).
thf(not_homomorphism2_type,type,
not_homomorphism2: $i > $i > $i > $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(flip_type,type,
flip: $i > $i ).
thf(inductive_type,type,
inductive: $i > $o ).
thf(omega_type,type,
omega: $i ).
thf(segment_type,type,
segment: $i > $i > $i > $i ).
thf(rotate_type,type,
rotate: $i > $i ).
thf(composition_function_type,type,
composition_function: $i ).
thf(recursion_equation_functions_type,type,
recursion_equation_functions: $i > $i ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(rest_of_type,type,
rest_of: $i > $i ).
thf(least_type,type,
least: $i > $i > $i ).
thf(section_type,type,
section: $i > $i > $i > $o ).
thf(domain_relation_type,type,
domain_relation: $i ).
thf(transitive_type,type,
transitive: $i > $i > $o ).
thf(complement_type,type,
complement: $i > $i ).
thf(identity_relation_type,type,
identity_relation: $i ).
thf(irreflexive_type,type,
irreflexive: $i > $i > $o ).
thf(compose_class_type,type,
compose_class: $i > $i ).
thf(application_function_type,type,
application_function: $i ).
thf(single_valued_class_type,type,
single_valued_class: $i > $o ).
thf(rest_relation_type,type,
rest_relation: $i ).
thf(asymmetric_type,type,
asymmetric: $i > $i > $o ).
thf(first_type,type,
first: $i > $i ).
thf(second_type,type,
second: $i > $i ).
thf(limit_ordinals_type,type,
limit_ordinals: $i ).
thf(range_type,type,
range: $i > $i > $i > $i ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(integer_of_type,type,
integer_of: $i > $i ).
thf(subset_relation_type,type,
subset_relation: $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(105,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/sandbox2/benchmark/theBenchmark.p',domain) ).
thf(384,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)],[105]) ).
thf(96,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).
thf(365,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(347,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)],[88]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',well_ordering2) ).
thf(352,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)],[90]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',rotate3) ).
thf(333,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)],[82]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',section3) ).
thf(249,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)],[43]) ).
thf(136,axiom,
! [A: $i] :
( ~ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).
thf(449,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)],[136]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',flip2) ).
thf(247,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)],[42]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( irreflexive @ A @ B )
| ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexive1) ).
thf(379,plain,
! [B: $i,A: $i] :
( ~ ( irreflexive @ A @ B )
| ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ union_of_range_map )
| ( ( sum_class @ ( range_of @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_range_map2) ).
thf(269,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)],[52]) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).
thf(408,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)],[117]) ).
thf(5,axiom,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
thf(170,plain,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,axiom,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
thf(217,plain,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).
thf(276,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( single_valued_class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).
thf(404,plain,
! [A: $i] :
( ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( single_valued_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( apply @ ( recursion @ A @ successor_relation @ union_of_range_map ) @ B )
= ( ordinal_add @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal_addition) ).
thf(185,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)],[13]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass1) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',compose2) ).
thf(257,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)],[47]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
!= null_class )
| ( asymmetric @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',asymmetric2) ).
thf(504,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)],[159]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).
thf(357,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(18,axiom,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).
thf(196,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
| ( ( successor @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).
thf(460,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
| ( ( successor @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',recursion_equation_functions5) ).
thf(421,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)],[122]) ).
thf(78,axiom,
subclass @ application_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn1) ).
thf(325,plain,
subclass @ application_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ( connected @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_ordering1) ).
thf(228,plain,
! [B: $i,A: $i] :
( ~ ( well_ordering @ A @ B )
| ( connected @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(147,axiom,
! [A: $i] :
( ( A = null_class )
| ( ( intersection @ A @ ( regular @ A ) )
= null_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
thf(475,plain,
! [A: $i] :
( ( A = null_class )
| ( ( intersection @ A @ ( regular @ A ) )
= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(75,axiom,
! [A: $i] : ( subclass @ ( rest_of @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rest_of1) ).
thf(321,plain,
! [A: $i] : ( subclass @ ( rest_of @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( unordered_pair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
thf(376,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)],[102]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ ( domain_of @ ( restrict @ A @ C @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',section2) ).
thf(253,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)],[45]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
thf(480,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( union @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(453,plain,
! [B: $i,A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( union @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ rest_relation )
| ( ( rest_of @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rest_relation2) ).
thf(396,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ rest_relation )
| ( ( rest_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( member @ ( domain_of @ A ) @ ordinal_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',recursion_equation_functions3) ).
thf(243,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)],[40]) ).
thf(160,axiom,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
thf(507,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',compose3) ).
thf(312,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)],[70]) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',rotate2) ).
thf(233,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)],[35]) ).
thf(130,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
thf(439,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',operation4) ).
thf(381,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)],[104]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
thf(302,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( intersection @ ( complement @ ( intersection @ A @ B ) ) @ ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) )
= ( symmetric_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference) ).
thf(392,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)],[109]) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',compatible4) ).
thf(424,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)],[123]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( sum_class @ ( image @ A @ ( singleton @ B ) ) )
= ( apply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( sum_class @ ( image @ A @ ( singleton @ B ) ) )
= ( apply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(125,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
thf(429,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(55,axiom,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).
thf(275,plain,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(3,axiom,
( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ ordinal_numbers ) )
= kind_1_ordinals ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kind_1_ordinals) ).
thf(165,plain,
( ( union @ ( singleton @ null_class ) @ ( image @ successor_relation @ ordinal_numbers ) )
= kind_1_ordinals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(144,axiom,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
thf(467,plain,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ element_relation )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
thf(484,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ element_relation )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',section1) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( section @ A @ B @ C )
| ( subclass @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',recursion_equation_functions1) ).
thf(435,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
thf(329,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)],[80]) ).
thf(155,axiom,
! [A: $i] :
( ( second @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_term_defn2) ).
thf(493,plain,
! [A: $i] :
( ( second @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(77,axiom,
subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rest_relation1) ).
thf(324,plain,
subclass @ rest_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(60,axiom,
! [A: $i] :
( ~ ( well_ordering @ element_relation @ A )
| ~ ( subclass @ ( sum_class @ A ) @ A )
| ~ ( member @ A @ universal_class )
| ( member @ A @ ordinal_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal_numbers3) ).
thf(285,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)],[60]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( segment @ A @ B @ C )
= ( domain_of @ ( restrict @ A @ B @ ( singleton @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment) ).
thf(224,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)],[31]) ).
thf(73,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
thf(317,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',well_ordering3) ).
thf(388,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)],[107]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
thf(339,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)],[85]) ).
thf(153,axiom,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).
thf(489,plain,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(25,axiom,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
thf(212,plain,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',well_ordering8) ).
thf(457,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)],[140]) ).
thf(7,axiom,
! [A: $i] :
( ( domain @ A @ ( image @ ( inverse @ A ) @ ( singleton @ ( single_valued1 @ A ) ) ) @ ( single_valued2 @ A ) )
= ( single_valued3 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_term_defn3) ).
thf(173,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)],[7]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function3) ).
thf(371,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)],[100]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ domain_relation )
| ( ( domain_of @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation2) ).
thf(266,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ domain_relation )
| ( ( domain_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).
thf(205,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)],[22]) ).
thf(69,axiom,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
thf(311,plain,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',compose_class_definition3) ).
thf(298,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)],[64]) ).
thf(1,negated_conjecture,
~ ( member @ ( not_subclass_element @ ( intersection @ ( power_class @ x ) @ z ) @ x ) @ z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complete_induction3_1) ).
thf(161,plain,
~ ( member @ ( not_subclass_element @ ( intersection @ ( power_class @ x ) @ z ) @ x ) @ z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( complement @ B ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
thf(402,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( complement @ B ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ~ ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) )
| ( irreflexive @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexive2) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ ( restrict @ A @ B @ B ) @ ( complement @ identity_relation ) )
| ( irreflexive @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',transitive2) ).
thf(259,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)],[48]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
thf(413,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)],[119]) ).
thf(133,axiom,
member @ omega @ universal_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
thf(445,plain,
member @ omega @ universal_class,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',union_of_range_map3) ).
thf(498,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)],[157]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( intersection @ ( cross_product @ A @ B ) @ C )
= ( restrict @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
thf(335,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)],[83]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( ( compose @ B @ ( rest_of @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',recursion_equation_functions4) ).
thf(236,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)],[37]) ).
thf(11,axiom,
! [A: $i] :
( ( domain_of @ ( restrict @ element_relation @ universal_class @ A ) )
= ( sum_class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
thf(181,plain,
! [A: $i] :
( ( domain_of @ ( restrict @ element_relation @ universal_class @ A ) )
= ( sum_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).
thf(350,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)],[89]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
= ( domain_of @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).
thf(187,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)],[14]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( well_ordering @ element_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal_numbers1) ).
thf(406,plain,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( well_ordering @ element_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(6,axiom,
function @ choice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
thf(172,plain,
function @ choice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
thf(219,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(54,axiom,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).
thf(274,plain,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).
thf(230,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)],[34]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',subset_relation) ).
thf(451,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)],[137]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',well_ordering5) ).
thf(245,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)],[41]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(44,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ omega @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
thf(251,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ omega @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( ( not_well_ordering @ A @ B )
!= null_class )
| ( well_ordering @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_ordering6) ).
thf(198,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)],[19]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( subclass @ ( cross_product @ A @ A ) @ ( union @ identity_relation @ ( symmetrization_of @ B ) ) )
| ( connected @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connected2) ).
thf(345,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)],[87]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps3) ).
thf(367,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
thf(455,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(30,axiom,
inductive @ omega,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
thf(223,plain,
inductive @ omega,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
thf(226,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
thf(431,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)],[126]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( rest_of @ C ) )
| ( member @ A @ ( domain_of @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rest_of2) ).
thf(394,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)],[110]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( rest_of @ C ) )
| ( ( restrict @ C @ A @ universal_class )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rest_of3) ).
thf(306,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)],[67]) ).
thf(146,axiom,
! [A: $i] :
( ( intersection @ ( domain_of @ A ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ A ) ) )
= ( cantor @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cantor_class) ).
thf(473,plain,
! [A: $i] :
( ( intersection @ ( domain_of @ A ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ A ) ) )
= ( cantor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(2,negated_conjecture,
~ ( subclass @ ( intersection @ ( power_class @ x ) @ z ) @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complete_induction3_2) ).
thf(162,plain,
~ ( subclass @ ( intersection @ ( power_class @ x ) @ z ) @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( domain_of @ A ) ) @ domain_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation3) ).
thf(255,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( domain_of @ A ) ) @ domain_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',well_ordering4) ).
thf(342,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)],[86]) ).
thf(91,axiom,
( ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers )
= limit_ordinals ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',limit_ordinals) ).
thf(355,plain,
( ( intersection @ ( complement @ kind_1_ordinals ) @ ordinal_numbers )
= limit_ordinals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( compatible @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( compatible @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
thf(295,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(50,axiom,
! [A: $i] :
( ~ ( well_ordering @ element_relation @ A )
| ~ ( subclass @ ( sum_class @ A ) @ A )
| ( member @ A @ ordinal_numbers )
| ( A = ordinal_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal_numbers4) ).
thf(263,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)],[50]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
= ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
thf(177,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)],[9]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( subclass @ ( cross_product @ B @ B ) @ ( union @ identity_relation @ ( symmetrization_of @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connected1) ).
thf(331,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)],[81]) ).
thf(131,axiom,
! [A: $i] : ( subclass @ A @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(441,plain,
! [A: $i] : ( subclass @ A @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(99,axiom,
subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_range_map1) ).
thf(370,plain,
subclass @ union_of_range_map @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',recursion_equation_functions2) ).
thf(502,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( recursion_equation_functions @ B ) )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( subclass @ ( range_of @ A ) @ B )
| ( maps @ A @ ( domain_of @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps4) ).
thf(463,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)],[142]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',flip3) ).
thf(359,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)],[93]) ).
thf(71,axiom,
subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
thf(314,plain,
subclass @ domain_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(134,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).
thf(446,plain,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).
thf(175,plain,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',transitive1) ).
thf(386,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)],[106]) ).
thf(143,axiom,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagonalisation) ).
thf(465,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(95,axiom,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( subclass @ ( sum_class @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal_numbers2) ).
thf(363,plain,
! [A: $i] :
( ~ ( member @ A @ ordinal_numbers )
| ( subclass @ ( sum_class @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( compose_class @ C ) )
| ( ( compose @ C @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition2) ).
thf(495,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)],[156]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( member @ B @ universal_class )
| ( member @ ( image @ A @ B ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
thf(482,plain,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( member @ B @ universal_class )
| ( member @ ( image @ A @ B ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(74,axiom,
! [A: $i] :
( ~ ( single_valued_class @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).
thf(319,plain,
! [A: $i] :
( ~ ( single_valued_class @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',application_function_defn4) ).
thf(304,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)],[66]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',range) ).
thf(390,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)],[108]) ).
thf(113,axiom,
! [B: $i,A: $i] : ( subclass @ ( compose @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
thf(401,plain,
! [B: $i,A: $i] : ( subclass @ ( compose @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(36,axiom,
subclass @ composition_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function1) ).
thf(235,plain,
subclass @ composition_function @ ( cross_product @ universal_class @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',application_function_defn2) ).
thf(433,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)],[127]) ).
thf(148,axiom,
( ( intersection @ ( complement @ ( compose @ element_relation @ ( complement @ identity_relation ) ) ) @ element_relation )
= singleton_relation ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_can_define_singleton) ).
thf(478,plain,
( ( intersection @ ( complement @ ( compose @ element_relation @ ( complement @ identity_relation ) ) ) @ element_relation )
= singleton_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( not_subclass_element @ A @ B ) @ B )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
thf(272,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( not_subclass_element @ A @ B ) @ B )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( ( domain_of @ ( domain_of @ B ) )
= ( domain_of @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).
thf(214,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)],[26]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).
thf(287,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)],[61]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).
thf(447,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(72,axiom,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).
thf(315,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(118,axiom,
! [A: $i] :
( ( member @ A @ omega )
| ( ( integer_of @ A )
= null_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',integer_function2) ).
thf(410,plain,
! [A: $i] :
( ( member @ A @ omega )
| ( ( integer_of @ A )
= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(15,axiom,
! [A: $i] :
( ( union @ A @ ( inverse @ A ) )
= ( symmetrization_of @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetrization) ).
thf(190,plain,
! [A: $i] :
( ( union @ A @ ( inverse @ A ) )
= ( symmetrization_of @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( recursion @ null_class @ ( apply @ add_relation @ A ) @ union_of_range_map )
= ( ordinal_multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal_multiplication) ).
thf(183,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)],[12]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class )
| ~ ( member @ B @ ( domain_of @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(373,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)],[101]) ).
thf(24,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
thf(210,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ~ ( asymmetric @ A @ B )
| ( ( restrict @ ( intersection @ A @ ( inverse @ A ) ) @ B @ B )
= null_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',asymmetric1) ).
thf(326,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)],[79]) ).
thf(129,axiom,
! [A: $i] :
( ( first @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_term_defn1) ).
thf(437,plain,
! [A: $i] :
( ( first @ ( not_subclass_element @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
= ( single_valued1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
thf(283,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)],[59]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ( intersection @ A @ ( cross_product @ B @ C ) )
= ( restrict @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
thf(415,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)],[120]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ composition_function )
| ( ( compose @ A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function2) ).
thf(239,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)],[38]) ).
thf(39,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
thf(242,plain,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).
thf(427,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ ( ordered_pair @ B @ C ) ) @ application_function )
| ( ( apply @ A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn3) ).
thf(442,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)],[132]) ).
thf(98,axiom,
! [A: $i] : ( subclass @ ( compose_class @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition1) ).
thf(369,plain,
! [A: $i] : ( subclass @ ( compose_class @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( connected @ A @ B )
| ( subclass @ ( not_well_ordering @ A @ B ) @ B )
| ( well_ordering @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_ordering7) ).
thf(322,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)],[76]) ).
thf(152,axiom,
! [A: $i] :
( ~ ( member @ A @ omega )
| ( ( integer_of @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',integer_function1) ).
thf(486,plain,
! [A: $i] :
( ~ ( member @ A @ omega )
| ( ( integer_of @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(84,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( rest_of @ A ) ) @ rest_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rest_relation3) ).
thf(337,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( ordered_pair @ A @ ( rest_of @ A ) ) @ rest_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',rest_of4) ).
thf(469,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)],[145]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
thf(309,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)],[68]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( member @ ( not_subclass_element @ A @ B ) @ A )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
thf(491,plain,
! [B: $i,A: $i] :
( ( member @ ( not_subclass_element @ A @ B ) @ A )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(510,plain,
$false,
inference(e,[status(thm)],[384,365,347,352,333,249,449,247,379,269,408,170,217,276,404,185,417,257,504,357,196,460,421,325,228,261,475,179,321,376,253,480,221,453,396,243,507,312,233,439,201,381,302,392,424,192,429,275,165,467,484,361,435,329,493,324,285,224,317,388,339,489,212,457,173,371,266,205,311,298,161,279,402,291,281,259,413,445,498,335,236,181,350,187,406,172,219,274,230,451,245,208,251,198,345,367,399,455,223,226,431,167,394,306,473,162,255,342,355,194,295,263,177,331,441,370,502,463,359,314,446,175,386,465,363,495,482,203,319,304,390,401,235,433,478,272,214,287,447,315,410,190,183,373,210,326,437,283,415,239,242,427,442,369,322,486,337,469,309,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM139-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:26:33 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.05 % [INFO] Parsing done (192ms).
% 1.51/1.06 % [INFO] Running in sequential loop mode.
% 1.98/1.27 % [INFO] eprover registered as external prover.
% 1.98/1.27 % [INFO] cvc4 registered as external prover.
% 1.98/1.27 % [INFO] Scanning for conjecture ...
% 2.25/1.36 % [INFO] Found a conjecture and 158 axioms. Running axiom selection ...
% 2.45/1.43 % [INFO] Axiom selection finished. Selected 158 axioms (removed 0 axioms).
% 2.88/1.52 % [INFO] Problem is propositional (TPTP CNF).
% 2.95/1.53 % [INFO] Type checking passed.
% 2.95/1.54 % [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 ...
% 5.87/2.48 % External prover 'e' found a proof!
% 5.87/2.48 % [INFO] Killing All external provers ...
% 5.87/2.48 % Time passed: 1949ms (effective reasoning time: 1414ms)
% 5.87/2.48 % 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)>
% 5.87/2.48 % 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
% 5.87/2.48 % No. of inferences in proof: 321
% 6.26/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1949 ms resp. 1414 ms w/o parsing
% 6.34/2.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.34/2.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------