%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM042-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:08:09 AM UTC 2026
% Result : Unsatisfiable 12.12s 4.96s
% Output : Refutation 12.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 160
% Syntax : Number of formulae : 321 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 649 ( 142 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 2996 ( 312 ~; 328 |; 0 &;2356 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 79 usr; 20 con; 0-3 aty)
% Number of variables : 606 ( 0 ^; 606 !; 0 ?; 606 :)
% Comments :
%------------------------------------------------------------------------------
thf(subclass_decl,type,
subclass: $i > $i > $o ).
thf(x_decl,type,
x: $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(identity_relation_decl,type,
identity_relation: $i ).
thf(irreflexive_decl,type,
irreflexive: $i > $i > $o ).
thf(domain_of_decl,type,
domain_of: $i > $i ).
thf(symmetrization_of_decl,type,
symmetrization_of: $i > $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(rotate_decl,type,
rotate: $i > $i ).
thf(recursion_equation_functions_decl,type,
recursion_equation_functions: $i > $i ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(rest_of_decl,type,
rest_of: $i > $i ).
thf(composition_function_decl,type,
composition_function: $i ).
thf(flip_decl,type,
flip: $i > $i ).
thf(image_decl,type,
image: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(homomorphism_decl,type,
homomorphism: $i > $i > $i > $o ).
thf(operation_decl,type,
operation: $i > $o ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(range_of_decl,type,
range_of: $i > $i ).
thf(restrict_decl,type,
restrict: $i > $i > $i > $i ).
thf(universal_class_decl,type,
universal_class: $i ).
thf(union_of_range_map_decl,type,
union_of_range_map: $i ).
thf(sum_class_decl,type,
sum_class: $i > $i ).
thf(compatible_decl,type,
compatible: $i > $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(not_homomorphism1_decl,type,
not_homomorphism1: $i > $i > $i > $i ).
thf(not_homomorphism2_decl,type,
not_homomorphism2: $i > $i > $i > $i ).
thf(function_decl,type,
function: $i > $o ).
thf(null_class_decl,type,
null_class: $i ).
thf(choice_decl,type,
choice: $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(successor_relation_decl,type,
successor_relation: $i ).
thf(ordinal_numbers_decl,type,
ordinal_numbers: $i ).
thf(kind_1_ordinals_decl,type,
kind_1_ordinals: $i ).
thf(cross_product_decl,type,
cross_product: $i > $i > $i ).
thf(domain_decl,type,
domain: $i > $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(single_valued1_decl,type,
single_valued1: $i > $i ).
thf(single_valued2_decl,type,
single_valued2: $i > $i ).
thf(single_valued3_decl,type,
single_valued3: $i > $i ).
thf(successor_decl,type,
successor: $i > $i ).
thf(compose_class_decl,type,
compose_class: $i > $i ).
thf(inductive_decl,type,
inductive: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(asymmetric_decl,type,
asymmetric: $i > $i > $o ).
thf(element_relation_decl,type,
element_relation: $i ).
thf(rest_relation_decl,type,
rest_relation: $i ).
thf(first_decl,type,
first: $i > $i ).
thf(second_decl,type,
second: $i > $i ).
thf(omega_decl,type,
omega: $i ).
thf(not_subclass_element_decl,type,
not_subclass_element: $i > $i > $i ).
thf(range_decl,type,
range: $i > $i > $i > $i ).
thf(well_ordering_decl,type,
well_ordering: $i > $i > $o ).
thf(recursion_decl,type,
recursion: $i > $i > $i > $i ).
thf(add_relation_decl,type,
add_relation: $i ).
thf(ordinal_multiply_decl,type,
ordinal_multiply: $i > $i > $i ).
thf(ordinal_add_decl,type,
ordinal_add: $i > $i > $i ).
thf(integer_of_decl,type,
integer_of: $i > $i ).
thf(application_function_decl,type,
application_function: $i ).
thf(power_class_decl,type,
power_class: $i > $i ).
thf(not_well_ordering_decl,type,
not_well_ordering: $i > $i > $i ).
thf(segment_decl,type,
segment: $i > $i > $i > $i ).
thf(connected_decl,type,
connected: $i > $i > $o ).
thf(regular_decl,type,
regular: $i > $i ).
thf(maps_decl,type,
maps: $i > $i > $i > $o ).
thf(least_decl,type,
least: $i > $i > $i ).
thf(section_decl,type,
section: $i > $i > $i > $o ).
thf(domain_relation_decl,type,
domain_relation: $i ).
thf(transitive_decl,type,
transitive: $i > $i > $o ).
thf(single_valued_class_decl,type,
single_valued_class: $i > $o ).
thf(limit_ordinals_decl,type,
limit_ordinals: $i ).
thf(symmetric_difference_decl,type,
symmetric_difference: $i > $i > $i ).
thf(subset_relation_decl,type,
subset_relation: $i ).
thf(diagonalise_decl,type,
diagonalise: $i > $i ).
thf(cantor_decl,type,
cantor: $i > $i ).
thf(singleton_relation_decl,type,
singleton_relation: $i ).
thf(86,axiom,
! [A: $i] :
( ( domain_relation @ ( A @ domain_of @ ( A @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation3) ).
thf(351,plain,
! [A: $i] :
( ( domain_relation @ ( A @ domain_of @ ( A @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ irreflexive ) )
| ~ ( identity_relation @ complement @ ( B @ ( B @ ( A @ restrict ) ) @ subclass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive2) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ irreflexive ) )
| ~ ( identity_relation @ complement @ ( B @ ( B @ ( A @ restrict ) ) @ subclass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ inverse @ ( A @ union ) )
= ( A @ symmetrization_of ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetrization) ).
thf(479,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ union ) )
= ( A @ symmetrization_of ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ ( omega @ subclass ) )
| ~ ( A @ inductive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
thf(347,plain,
! [A: $i] :
( ( A @ ( omega @ subclass ) )
| ~ ( A @ inductive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(142,axiom,
( ( element_relation @ inverse @ ( element_relation @ complement @ compose ) @ complement @ ( universal_class @ ( universal_class @ cross_product ) @ intersection ) @ ( universal_class @ ( universal_class @ cross_product ) @ intersection ) )
= subset_relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_relation) ).
thf(468,plain,
( ( element_relation @ inverse @ ( element_relation @ complement @ compose ) @ complement @ ( universal_class @ ( universal_class @ cross_product ) @ intersection ) @ ( universal_class @ ( universal_class @ cross_product ) @ intersection ) )
= subset_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ domain_of @ ( A @ maps ) ) )
| ~ ( B @ ( A @ range_of @ subclass ) )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps4) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ domain_of @ ( A @ maps ) ) )
| ~ ( B @ ( A @ range_of @ subclass ) )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(25,axiom,
! [B: $i,A: $i] : ( universal_class @ ( B @ ( A @ unordered_pair ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
thf(217,plain,
! [B: $i,A: $i] : ( universal_class @ ( B @ ( A @ unordered_pair ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ complement @ ( A @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ complement @ ( A @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( successor_relation @ ( B @ ( A @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) )
| ( ( A @ successor )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation3) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( successor_relation @ ( B @ ( A @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) )
| ( ( A @ successor )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ well_ordering ) )
| ( B @ ( B @ ( A @ not_well_ordering ) @ subclass ) )
| ~ ( B @ ( A @ connected ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering7) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ well_ordering ) )
| ( B @ ( B @ ( A @ not_well_ordering ) @ subclass ) )
| ~ ( B @ ( A @ connected ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(101,axiom,
! [A: $i] : ( universal_class @ ( universal_class @ cross_product ) @ ( A @ rest_of @ subclass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_of1) ).
thf(384,plain,
! [A: $i] : ( universal_class @ ( universal_class @ cross_product ) @ ( A @ rest_of @ subclass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(156,axiom,
universal_class @ ( universal_class @ cross_product ) @ ( domain_relation @ subclass ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
thf(500,plain,
universal_class @ ( universal_class @ cross_product ) @ ( domain_relation @ subclass ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(144,axiom,
! [A: $i] :
( ( A @ function )
| ~ ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ subclass ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( A @ subclass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
thf(472,plain,
! [A: $i] :
( ( A @ function )
| ~ ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ subclass ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( A @ subclass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(80,axiom,
universal_class @ ( universal_class @ cross_product ) @ ( element_relation @ subclass ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
thf(340,plain,
universal_class @ ( universal_class @ cross_product ) @ ( element_relation @ subclass ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ homomorphism ) ) )
| ( ( B @ ( A @ ( C @ not_homomorphism2 ) ) @ ( C @ apply ) @ ( B @ ( A @ ( C @ not_homomorphism1 ) ) @ ( C @ apply ) @ ordered_pair ) @ ( B @ apply ) )
!= ( B @ ( A @ ( C @ not_homomorphism2 ) ) @ ( B @ ( A @ ( C @ not_homomorphism1 ) ) @ ordered_pair ) @ ( A @ apply ) @ ( C @ apply ) ) )
| ~ ( B @ ( A @ ( C @ compatible ) ) )
| ~ ( B @ operation )
| ~ ( A @ operation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism6) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ homomorphism ) ) )
| ( ( B @ ( A @ ( C @ not_homomorphism2 ) ) @ ( C @ apply ) @ ( B @ ( A @ ( C @ not_homomorphism1 ) ) @ ( C @ apply ) @ ordered_pair ) @ ( B @ apply ) )
!= ( B @ ( A @ ( C @ not_homomorphism2 ) ) @ ( B @ ( A @ ( C @ not_homomorphism1 ) ) @ ordered_pair ) @ ( A @ apply ) @ ( C @ apply ) ) )
| ~ ( B @ ( A @ ( C @ compatible ) ) )
| ~ ( B @ operation )
| ~ ( A @ operation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ ( universal_class @ ( element_relation @ restrict ) ) @ domain_of )
= ( A @ sum_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).
thf(417,plain,
! [A: $i] :
( ( A @ ( universal_class @ ( element_relation @ restrict ) ) @ domain_of )
= ( A @ sum_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(58,axiom,
universal_class @ ( omega @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
thf(288,plain,
universal_class @ ( omega @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ singleton @ ( D @ image ) @ ( C @ image ) @ ( B @ member ) )
| ~ ( D @ ( C @ compose ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).
thf(174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ singleton @ ( D @ image ) @ ( C @ image ) @ ( B @ member ) )
| ~ ( D @ ( C @ compose ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ least ) @ member ) )
| ( C = null_class )
| ~ ( B @ ( C @ subclass ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering2) ).
thf(404,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ least ) @ member ) )
| ( C = null_class )
| ~ ( B @ ( C @ subclass ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ domain_of @ domain_of )
= ( A @ domain_of ) )
| ~ ( C @ ( B @ ( A @ compatible ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible2) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ domain_of @ domain_of )
= ( A @ domain_of ) )
| ~ ( C @ ( B @ ( A @ compatible ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(137,axiom,
! [A: $i] :
( ( universal_class @ ( universal_class @ cross_product ) @ ( A @ subclass ) )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
thf(460,plain,
! [A: $i] :
( ( universal_class @ ( universal_class @ cross_product ) @ ( A @ subclass ) )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(119,axiom,
! [A: $i] : ( universal_class @ ( universal_class @ cross_product ) @ ( A @ compose_class @ subclass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition1) ).
thf(421,plain,
! [A: $i] : ( universal_class @ ( universal_class @ cross_product ) @ ( A @ compose_class @ subclass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(59,axiom,
! [A: $i] :
( ( universal_class @ ( A @ power_class @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class2) ).
thf(289,plain,
! [A: $i] :
( ( universal_class @ ( A @ power_class @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subclass ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass1) ).
thf(448,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subclass ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ inverse @ function )
| ~ ( A @ one_to_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).
thf(316,plain,
! [A: $i] :
( ( A @ inverse @ function )
| ~ ( A @ one_to_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( null_class @ ( C @ singleton @ ( B @ ( A @ restrict ) ) @ not_subclass_element ) @ first )
= ( C @ ( B @ ( A @ domain ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( null_class @ ( C @ singleton @ ( B @ ( A @ restrict ) ) @ not_subclass_element ) @ first )
= ( C @ ( B @ ( A @ domain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( D @ rotate @ ( C @ ( B @ ( A @ ordered_pair ) @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate2) ).
thf(164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( D @ rotate @ ( C @ ( B @ ( A @ ordered_pair ) @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ connected ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering1) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ connected ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(150,axiom,
( ( subset_relation @ ( subset_relation @ inverse @ intersection ) )
= identity_relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
thf(485,plain,
( ( subset_relation @ ( subset_relation @ inverse @ intersection ) )
= identity_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ transitive ) )
| ~ ( B @ ( B @ ( A @ restrict ) ) @ ( B @ ( B @ ( A @ restrict ) ) @ ( B @ ( B @ ( A @ restrict ) ) @ compose ) @ subclass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive2) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ transitive ) )
| ~ ( B @ ( B @ ( A @ restrict ) ) @ ( B @ ( B @ ( A @ restrict ) ) @ ( B @ ( B @ ( A @ restrict ) ) @ compose ) @ subclass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( B @ domain_of @ ( A @ member ) )
| ( ( universal_class @ ( A @ singleton @ ( B @ restrict ) ) )
= null_class )
| ~ ( universal_class @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( B @ domain_of @ ( A @ member ) )
| ( ( universal_class @ ( A @ singleton @ ( B @ restrict ) ) )
= null_class )
| ~ ( universal_class @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ ( A @ sum_class @ subclass ) )
| ~ ( ordinal_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers2) ).
thf(411,plain,
! [A: $i] :
( ( A @ ( A @ sum_class @ subclass ) )
| ~ ( ordinal_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ restrict ) ) @ ( B @ ( B @ ( A @ restrict ) ) @ ( B @ ( B @ ( A @ restrict ) ) @ compose ) @ subclass ) )
| ~ ( B @ ( A @ transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive1) ).
thf(428,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ restrict ) ) @ ( B @ ( B @ ( A @ restrict ) ) @ ( B @ ( B @ ( A @ restrict ) ) @ compose ) @ subclass ) )
| ~ ( B @ ( A @ transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(160,axiom,
! [A: $i] :
( ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ not_subclass_element ) @ second )
= ( A @ single_valued2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_term_defn2) ).
thf(507,plain,
! [A: $i] :
( ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ not_subclass_element ) @ second )
= ( A @ single_valued2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ compose_class @ ( B @ ( A @ ordered_pair ) @ member ) )
| ( ( A @ ( C @ compose ) )
!= B )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition3) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ compose_class @ ( B @ ( A @ ordered_pair ) @ member ) )
| ( ( A @ ( C @ compose ) )
!= B )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( A @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( A @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ function )
| ~ ( A @ one_to_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
thf(248,plain,
! [A: $i] :
( ( A @ function )
| ~ ( A @ one_to_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ complement @ ( element_relation @ image ) @ complement )
= ( A @ power_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_definition) ).
thf(380,plain,
! [A: $i] :
( ( A @ complement @ ( element_relation @ image ) @ complement )
= ( A @ power_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(128,axiom,
! [B: $i,A: $i] : ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ compose ) @ subclass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
thf(439,plain,
! [B: $i,A: $i] : ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ compose ) @ subclass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( B @ ( union_of_range_map @ ( successor_relation @ ( A @ recursion ) ) @ apply ) )
= ( B @ ( A @ ordinal_add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_addition) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( B @ ( union_of_range_map @ ( successor_relation @ ( A @ recursion ) ) @ apply ) )
= ( B @ ( A @ ordinal_add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
thf(220,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ rotate @ ( B @ ( A @ ( C @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( B @ ( A @ ( C @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( D @ ( C @ ( B @ ( A @ ordered_pair ) @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate3) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ rotate @ ( B @ ( A @ ( C @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( B @ ( A @ ( C @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( D @ ( C @ ( B @ ( A @ ordered_pair ) @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ( A @ recursion_equation_functions @ ( B @ member ) )
| ( ( B @ rest_of @ ( A @ compose ) )
!= B )
| ~ ( ordinal_numbers @ ( B @ domain_of @ member ) )
| ~ ( B @ function )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions5) ).
thf(452,plain,
! [B: $i,A: $i] :
( ( A @ recursion_equation_functions @ ( B @ member ) )
| ( ( B @ rest_of @ ( A @ compose ) )
!= B )
| ~ ( ordinal_numbers @ ( B @ domain_of @ member ) )
| ~ ( B @ function )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ cross_product ) @ ( C @ ( A @ ordered_pair ) @ member ) )
| ~ ( D @ ( C @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
thf(334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ cross_product ) @ ( C @ ( A @ ordered_pair ) @ member ) )
| ~ ( D @ ( C @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ( A @ regular @ member ) )
| ( A = null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
thf(302,plain,
! [A: $i] :
( ( A @ ( A @ regular @ member ) )
| ( A = null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( A @ restrict ) ) @ domain_of @ subclass ) )
| ~ ( C @ ( B @ ( A @ section ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',section2) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( A @ restrict ) ) @ domain_of @ subclass ) )
| ~ ( C @ ( B @ ( A @ section ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ least ) @ ( C @ ( A @ segment ) ) )
= null_class )
| ~ ( B @ ( C @ subclass ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering4) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ least ) @ ( C @ ( A @ segment ) ) )
= null_class )
| ~ ( B @ ( C @ subclass ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ regular @ ( A @ intersection ) )
= null_class )
| ( A = null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
thf(297,plain,
! [A: $i] :
( ( ( A @ regular @ ( A @ intersection ) )
= null_class )
| ( A = null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(112,axiom,
( ( ordinal_numbers @ ( kind_1_ordinals @ complement @ intersection ) )
= limit_ordinals ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_ordinals) ).
thf(407,plain,
( ( ordinal_numbers @ ( kind_1_ordinals @ complement @ intersection ) )
= limit_ordinals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(141,axiom,
universal_class @ ( universal_class @ cross_product ) @ ( successor_relation @ subclass ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
thf(467,plain,
universal_class @ ( universal_class @ cross_product ) @ ( successor_relation @ subclass ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( element_relation @ ( B @ ( A @ ordered_pair ) @ member ) )
| ~ ( B @ ( A @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( element_relation @ ( B @ ( A @ ordered_pair ) @ member ) )
| ~ ( B @ ( A @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ asymmetric ) )
| ( ( B @ ( B @ ( A @ inverse @ ( A @ intersection ) @ restrict ) ) )
!= null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',asymmetric2) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ asymmetric ) )
| ( ( B @ ( B @ ( A @ inverse @ ( A @ intersection ) @ restrict ) ) )
!= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(17,axiom,
choice @ function,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
thf(197,plain,
choice @ function,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(91,axiom,
! [A: $i] : ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( A @ rotate @ subclass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate1) ).
thf(361,plain,
! [A: $i] : ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( A @ rotate @ subclass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( B @ complement @ ( A @ complement @ intersection ) @ complement @ ( B @ ( A @ intersection ) @ complement @ intersection ) )
= ( B @ ( A @ symmetric_difference ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference) ).
thf(435,plain,
! [B: $i,A: $i] :
( ( B @ complement @ ( A @ complement @ intersection ) @ complement @ ( B @ ( A @ intersection ) @ complement @ intersection ) )
= ( B @ ( A @ symmetric_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ inductive )
| ~ ( A @ ( A @ ( successor_relation @ image ) @ subclass ) )
| ~ ( A @ ( null_class @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive3) ).
thf(493,plain,
! [A: $i] :
( ( A @ inductive )
| ~ ( A @ ( A @ ( successor_relation @ image ) @ subclass ) )
| ~ ( A @ ( null_class @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apply ) )
= C )
| ~ ( application_function @ ( C @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn3) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apply ) )
= C )
| ~ ( application_function @ ( C @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ inverse @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one3) ).
thf(224,plain,
! [A: $i] :
( ( A @ one_to_one )
| ~ ( A @ function )
| ~ ( A @ inverse @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( A @ function )
| ~ ( B @ recursion_equation_functions @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions2) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( A @ function )
| ~ ( B @ recursion_equation_functions @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(104,axiom,
universal_class @ ( universal_class @ cross_product ) @ ( universal_class @ cross_product ) @ ( application_function @ subclass ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn1) ).
thf(388,plain,
universal_class @ ( universal_class @ cross_product ) @ ( universal_class @ cross_product ) @ ( application_function @ subclass ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ compose ) )
= C )
| ~ ( composition_function @ ( C @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function2) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ compose ) )
= C )
| ~ ( composition_function @ ( C @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(146,axiom,
! [A: $i] :
( ( ( A @ domain_of @ domain_of @ ( A @ domain_of @ domain_of @ cross_product ) )
= ( A @ domain_of ) )
| ~ ( A @ operation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation2) ).
thf(476,plain,
! [A: $i] :
( ( ( A @ domain_of @ domain_of @ ( A @ domain_of @ domain_of @ cross_product ) )
= ( A @ domain_of ) )
| ~ ( A @ operation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( universal_class @ ( A @ ( C @ restrict ) ) )
= B )
| ~ ( C @ rest_of @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_of3) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( universal_class @ ( A @ ( C @ restrict ) ) )
= B )
| ~ ( C @ rest_of @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ subclass ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subclass ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(158,axiom,
! [A: $i] :
( ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ not_subclass_element ) @ first )
= ( A @ single_valued1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_term_defn1) ).
thf(503,plain,
! [A: $i] :
( ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ not_subclass_element ) @ first )
= ( A @ single_valued1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ flip @ ( C @ ( A @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( C @ ( A @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( D @ ( C @ ( B @ ( A @ ordered_pair ) @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip3) ).
thf(244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ flip @ ( C @ ( A @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( C @ ( A @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( D @ ( C @ ( B @ ( A @ ordered_pair ) @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ ( element_relation @ well_ordering ) )
| ~ ( ordinal_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers1) ).
thf(266,plain,
! [A: $i] :
( ( A @ ( element_relation @ well_ordering ) )
| ~ ( ordinal_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(90,axiom,
! [A: $i] : ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( A @ flip @ subclass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).
thf(360,plain,
! [A: $i] : ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( A @ flip @ subclass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( element_relation @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( element_relation @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ least ) @ ( D @ ordered_pair ) @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( B @ ( C @ subclass ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering5) ).
thf(343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ least ) @ ( D @ ordered_pair ) @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( B @ ( C @ subclass ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(35,axiom,
! [A: $i] :
( ( rest_relation @ ( A @ rest_of @ ( A @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_relation3) ).
thf(237,plain,
! [A: $i] :
( ( rest_relation @ ( A @ rest_of @ ( A @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ least ) @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( B @ ( C @ subclass ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering3) ).
thf(430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ least ) @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( B @ ( C @ subclass ) )
| ~ ( B @ ( A @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( ( A @ rest_of @ ( B @ compose ) )
= A )
| ~ ( B @ recursion_equation_functions @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions4) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( A @ rest_of @ ( B @ compose ) )
= A )
| ~ ( B @ recursion_equation_functions @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
identity_relation @ complement @ ( x @ subclass ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property4_1) ).
thf(161,plain,
identity_relation @ complement @ ( x @ subclass ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( B @ function )
| ~ ( B @ recursion_equation_functions @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions1) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( B @ function )
| ~ ( B @ recursion_equation_functions @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( universal_class @ ( B @ ( A @ restrict ) ) @ range_of )
= ( B @ ( A @ image ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( universal_class @ ( B @ ( A @ restrict ) ) @ range_of )
= ( B @ ( A @ image ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subclass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
thf(444,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subclass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subclass ) )
| ~ ( B @ ( A @ subclass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subclass ) )
| ~ ( B @ ( A @ subclass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ operation )
| ~ ( C @ ( B @ ( A @ homomorphism ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ operation )
| ~ ( C @ ( B @ ( A @ homomorphism ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( A @ domain_of @ ( B @ member ) )
| ( ( universal_class @ ( B @ singleton @ ( A @ restrict ) ) )
!= null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(423,plain,
! [B: $i,A: $i] :
( ~ ( A @ domain_of @ ( B @ member ) )
| ( ( universal_class @ ( B @ singleton @ ( A @ restrict ) ) )
!= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ domain_of @ domain_of @ ( A @ range_of @ subclass ) )
| ~ ( C @ ( B @ ( A @ compatible ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible3) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ domain_of @ domain_of @ ( A @ range_of @ subclass ) )
| ~ ( C @ ( B @ ( A @ compatible ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ well_ordering ) )
| ~ ( C @ ( B @ connected ) )
| ( ( A @ ( C @ ( B @ not_well_ordering ) @ ( B @ segment ) ) )
!= null_class )
| ~ ( C @ ( B @ not_well_ordering ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering8) ).
thf(291,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ well_ordering ) )
| ~ ( C @ ( B @ connected ) )
| ( ( A @ ( C @ ( B @ not_well_ordering ) @ ( B @ segment ) ) )
!= null_class )
| ~ ( C @ ( B @ not_well_ordering ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(55,axiom,
! [A: $i] :
( ( universal_class @ ( A @ sum_class @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).
thf(281,plain,
! [A: $i] :
( ( universal_class @ ( A @ sum_class @ member ) )
| ~ ( universal_class @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( null_class @ ( C @ ( B @ singleton @ ( A @ restrict ) ) @ not_subclass_element ) @ second )
= ( C @ ( B @ ( A @ range ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ( null_class @ ( C @ ( B @ singleton @ ( A @ restrict ) ) @ not_subclass_element ) @ second )
= ( C @ ( B @ ( A @ range ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ domain_of @ domain_of @ ( A @ range_of @ subclass ) )
| ~ ( A @ operation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).
thf(413,plain,
! [A: $i] :
( ( A @ domain_of @ domain_of @ ( A @ range_of @ subclass ) )
| ~ ( A @ operation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(100,axiom,
! [A: $i] :
( ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ subclass ) )
| ~ ( A @ single_valued_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class1) ).
thf(382,plain,
! [A: $i] :
( ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ subclass ) )
| ~ ( A @ single_valued_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(69,axiom,
! [A: $i] :
( ( ( A @ integer_of )
= A )
| ~ ( omega @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',integer_function1) ).
thf(313,plain,
! [A: $i] :
( ( ( A @ integer_of )
= A )
| ~ ( omega @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(140,axiom,
! [A: $i] : ( universal_class @ ( A @ subclass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(466,plain,
! [A: $i] : ( universal_class @ ( A @ subclass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( D @ flip @ ( C @ ( B @ ( A @ ordered_pair ) @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip2) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( D @ flip @ ( C @ ( B @ ( A @ ordered_pair ) @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ range_of @ subclass ) )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ range_of @ subclass ) )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ domain_of )
= B )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ domain_of )
= B )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ well_ordering ) )
| ( ( B @ ( A @ not_well_ordering ) )
!= null_class )
| ~ ( B @ ( A @ connected ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering6) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ well_ordering ) )
| ( ( B @ ( A @ not_well_ordering ) )
!= null_class )
| ~ ( B @ ( A @ connected ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(103,axiom,
universal_class @ ( universal_class @ cross_product ) @ ( rest_relation @ subclass ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_relation1) ).
thf(387,plain,
universal_class @ ( universal_class @ cross_product ) @ ( rest_relation @ subclass ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ compose ) )
= B )
| ~ ( C @ compose_class @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition2) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ compose ) )
= B )
| ~ ( C @ compose_class @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(149,axiom,
! [A: $i] :
( ( identity_relation @ ( A @ intersection ) @ domain_of @ complement )
= ( A @ diagonalise ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonalisation) ).
thf(483,plain,
! [A: $i] :
( ( identity_relation @ ( A @ intersection ) @ domain_of @ complement )
= ( A @ diagonalise ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( D @ ( C @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( D @ ( C @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ function )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ function )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ segment ) ) )
= ( C @ singleton @ ( B @ ( A @ restrict ) ) @ domain_of ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ segment ) ) )
= ( C @ singleton @ ( B @ ( A @ restrict ) ) @ domain_of ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ section ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ restrict ) ) @ domain_of @ subclass ) )
| ~ ( B @ ( A @ subclass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',section3) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ section ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ restrict ) ) @ domain_of @ subclass ) )
| ~ ( B @ ( A @ subclass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ inverse @ domain_of )
= ( A @ range_of ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
thf(367,plain,
! [A: $i] :
( ( A @ inverse @ domain_of )
= ( A @ range_of ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ compatible ) ) )
| ~ ( C @ domain_of @ domain_of @ ( A @ range_of @ subclass ) )
| ( ( B @ domain_of @ domain_of )
!= ( A @ domain_of ) )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible4) ).
thf(455,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ compatible ) ) )
| ~ ( C @ domain_of @ domain_of @ ( A @ range_of @ subclass ) )
| ( ( B @ domain_of @ domain_of )
!= ( A @ domain_of ) )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ inverse @ ( A @ intersection ) @ restrict ) ) )
= null_class )
| ~ ( B @ ( A @ asymmetric ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',asymmetric1) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ inverse @ ( A @ intersection ) @ restrict ) ) )
= null_class )
| ~ ( B @ ( A @ asymmetric ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(159,axiom,
( ( element_relation @ ( identity_relation @ complement @ ( element_relation @ compose ) @ complement @ intersection ) )
= singleton_relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_can_define_singleton) ).
thf(505,plain,
( ( element_relation @ ( identity_relation @ complement @ ( element_relation @ compose ) @ complement @ intersection ) )
= singleton_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( identity_relation @ complement @ ( B @ ( B @ ( A @ restrict ) ) @ subclass ) )
| ~ ( B @ ( A @ irreflexive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive1) ).
thf(426,plain,
! [B: $i,A: $i] :
( ( identity_relation @ complement @ ( B @ ( B @ ( A @ restrict ) ) @ subclass ) )
| ~ ( B @ ( A @ irreflexive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(2,negated_conjecture,
~ ( x @ symmetrization_of @ domain_of @ ( x @ irreflexive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property4_2) ).
thf(162,plain,
~ ( x @ symmetrization_of @ domain_of @ ( x @ irreflexive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43,axiom,
omega @ inductive,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
thf(255,plain,
omega @ inductive,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ rest_of @ ( C @ ( A @ ordered_pair ) @ member ) )
| ( ( universal_class @ ( A @ ( B @ restrict ) ) )
!= C )
| ~ ( B @ domain_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_of4) ).
thf(487,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ rest_of @ ( C @ ( A @ ordered_pair ) @ member ) )
| ( ( universal_class @ ( A @ ( B @ restrict ) ) )
!= C )
| ~ ( B @ domain_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(88,axiom,
! [A: $i] :
( ( A = ordinal_numbers )
| ( ordinal_numbers @ ( A @ member ) )
| ~ ( A @ ( A @ sum_class @ subclass ) )
| ~ ( A @ ( element_relation @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers4) ).
thf(355,plain,
! [A: $i] :
( ( A = ordinal_numbers )
| ( ordinal_numbers @ ( A @ member ) )
| ~ ( A @ ( A @ sum_class @ subclass ) )
| ~ ( A @ ( element_relation @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ ( A @ ( successor_relation @ image ) @ subclass ) )
| ~ ( A @ inductive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).
thf(458,plain,
! [A: $i] :
( ( A @ ( A @ ( successor_relation @ image ) @ subclass ) )
| ~ ( A @ inductive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ subclass ) )
| ~ ( C @ ( B @ ( A @ section ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',section1) ).
thf(409,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ subclass ) )
| ~ ( C @ ( B @ ( A @ section ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( ( A @ rest_of )
= B )
| ~ ( rest_relation @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_relation2) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( ( A @ rest_of )
= B )
| ~ ( rest_relation @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( ( A @ range_of @ sum_class )
= B )
| ~ ( union_of_range_map @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_range_map2) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( ( A @ range_of @ sum_class )
= B )
| ~ ( union_of_range_map @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( B @ complement @ ( A @ complement @ intersection ) @ complement )
= ( B @ ( A @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(470,plain,
! [B: $i,A: $i] :
( ( B @ complement @ ( A @ complement @ intersection ) @ complement )
= ( B @ ( A @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(78,axiom,
universal_class @ ( universal_class @ cross_product ) @ ( universal_class @ cross_product ) @ ( composition_function @ subclass ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function1) ).
thf(336,plain,
universal_class @ ( universal_class @ cross_product ) @ ( universal_class @ cross_product ) @ ( composition_function @ subclass ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ homomorphism ) ) )
| ( A @ domain_of @ ( B @ ( A @ ( C @ not_homomorphism2 ) ) @ ( B @ ( A @ ( C @ not_homomorphism1 ) ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( A @ ( C @ compatible ) ) )
| ~ ( B @ operation )
| ~ ( A @ operation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism5) ).
thf(446,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ homomorphism ) ) )
| ( A @ domain_of @ ( B @ ( A @ ( C @ not_homomorphism2 ) ) @ ( B @ ( A @ ( C @ not_homomorphism1 ) ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( A @ ( C @ compatible ) ) )
| ~ ( B @ operation )
| ~ ( A @ operation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ( ( A @ domain_of )
= B )
| ~ ( domain_relation @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation2) ).
thf(497,plain,
! [B: $i,A: $i] :
( ( ( A @ domain_of )
= B )
| ~ ( domain_relation @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subclass ) )
| ( A @ ( B @ ( A @ not_subclass_element ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
thf(495,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subclass ) )
| ( A @ ( B @ ( A @ not_subclass_element ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ compose ) @ ( A @ ( D @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( A @ ( D @ ordered_pair ) @ member ) )
| ~ ( D @ singleton @ ( C @ image ) @ ( B @ image ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose3) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ compose ) @ ( A @ ( D @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( A @ ( D @ ordered_pair ) @ member ) )
| ~ ( D @ singleton @ ( C @ image ) @ ( B @ image ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ function )
| ~ ( C @ ( B @ ( A @ compatible ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ function )
| ~ ( C @ ( B @ ( A @ compatible ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ unordered_pair ) @ ( A @ singleton @ unordered_pair ) )
= ( B @ ( A @ ordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ unordered_pair ) @ ( A @ singleton @ unordered_pair ) )
= ( B @ ( A @ ordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( application_function @ ( B @ ( A @ apply ) @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) )
| ~ ( A @ domain_of @ ( B @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( universal_class @ cross_product ) @ ( C @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn4) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( application_function @ ( B @ ( A @ apply ) @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) )
| ~ ( A @ domain_of @ ( B @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( universal_class @ cross_product ) @ ( C @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ integer_of )
= null_class )
| ( omega @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',integer_function2) ).
thf(272,plain,
! [A: $i] :
( ( ( A @ integer_of )
= null_class )
| ( omega @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cross_product ) @ intersection ) )
= ( B @ ( A @ ( C @ restrict ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cross_product ) @ intersection ) )
= ( B @ ( A @ ( C @ restrict ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( composition_function @ ( B @ ( A @ compose ) @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function3) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( composition_function @ ( B @ ( A @ compose ) @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ image ) @ sum_class )
= ( B @ ( A @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ image ) @ sum_class )
= ( B @ ( A @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ operation )
| ~ ( A @ domain_of @ domain_of @ ( A @ range_of @ subclass ) )
| ( ( A @ domain_of @ domain_of @ ( A @ domain_of @ domain_of @ cross_product ) )
!= ( A @ domain_of ) )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation4) ).
thf(432,plain,
! [A: $i] :
( ( A @ operation )
| ~ ( A @ domain_of @ domain_of @ ( A @ range_of @ subclass ) )
| ( ( A @ domain_of @ domain_of @ ( A @ domain_of @ domain_of @ cross_product ) )
!= ( A @ domain_of ) )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( A @ ( choice @ apply ) @ member ) )
| ( A = null_class )
| ~ ( universal_class @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
thf(190,plain,
! [A: $i] :
( ( A @ ( A @ ( choice @ apply ) @ member ) )
| ( A = null_class )
| ~ ( universal_class @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(120,axiom,
universal_class @ ( universal_class @ cross_product ) @ ( union_of_range_map @ subclass ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_range_map1) ).
thf(422,plain,
universal_class @ ( universal_class @ cross_product ) @ ( union_of_range_map @ subclass ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ compatible ) ) )
| ~ ( C @ ( B @ ( A @ homomorphism ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ compatible ) ) )
| ~ ( C @ ( B @ ( A @ homomorphism ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( union_of_range_map @ ( B @ ( A @ ordered_pair ) @ member ) )
| ( ( A @ range_of @ sum_class )
!= B )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_range_map3) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( union_of_range_map @ ( B @ ( A @ ordered_pair ) @ member ) )
| ( ( A @ range_of @ sum_class )
!= B )
| ~ ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( ( A @ successor )
= B )
| ~ ( successor_relation @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation2) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( ( A @ successor )
= B )
| ~ ( successor_relation @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( ordinal_numbers @ ( A @ domain_of @ member ) )
| ~ ( B @ recursion_equation_functions @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions3) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ordinal_numbers @ ( A @ domain_of @ member ) )
| ~ ( B @ recursion_equation_functions @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( union_of_range_map @ ( A @ ( add_relation @ apply ) @ ( null_class @ recursion ) ) )
= ( B @ ( A @ ordinal_multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_multiplication) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( union_of_range_map @ ( A @ ( add_relation @ apply ) @ ( null_class @ recursion ) ) )
= ( B @ ( A @ ordinal_multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subclass ) )
| ~ ( B @ ( B @ ( A @ not_subclass_element ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subclass ) )
| ~ ( B @ ( B @ ( A @ not_subclass_element ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(16,axiom,
( ( ordinal_numbers @ ( successor_relation @ image ) @ ( null_class @ singleton @ union ) )
= kind_1_ordinals ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kind_1_ordinals) ).
thf(195,plain,
( ( ordinal_numbers @ ( successor_relation @ image ) @ ( null_class @ singleton @ union ) )
= kind_1_ordinals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ domain_of @ ( A @ member ) )
| ~ ( C @ rest_of @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rest_of2) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ domain_of @ ( A @ member ) )
| ~ ( C @ rest_of @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
thf(474,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(109,axiom,
! [A: $i] :
( ( universal_class @ ( A @ cross_product ) @ flip @ domain_of )
= ( A @ inverse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(400,plain,
! [A: $i] :
( ( universal_class @ ( A @ cross_product ) @ flip @ domain_of )
= ( A @ inverse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ function )
| ~ ( A @ operation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
thf(283,plain,
! [A: $i] :
( ( A @ function )
| ~ ( A @ operation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(116,axiom,
! [A: $i] :
( ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ subclass ) )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
thf(415,plain,
! [A: $i] :
( ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ subclass ) )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ second @ ( A @ first @ ordered_pair ) )
= A )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ second @ ( A @ first @ ordered_pair ) )
= A )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ operation )
| ~ ( C @ ( B @ ( A @ homomorphism ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ operation )
| ~ ( C @ ( B @ ( A @ homomorphism ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ connected ) )
| ~ ( B @ symmetrization_of @ ( identity_relation @ union ) @ ( A @ ( A @ cross_product ) @ subclass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected2) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ connected ) )
| ~ ( B @ symmetrization_of @ ( identity_relation @ union ) @ ( A @ ( A @ cross_product ) @ subclass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ domain_of @ ( B @ member ) )
| ~ ( application_function @ ( C @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn2) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ domain_of @ ( B @ member ) )
| ~ ( application_function @ ( C @ ( B @ ordered_pair ) @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ singleton @ ( A @ union ) )
= ( A @ successor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(332,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ union ) )
= ( A @ successor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ single_valued2 @ ( A @ single_valued1 @ singleton @ ( A @ inverse @ image ) @ ( A @ domain ) ) )
= ( A @ single_valued3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_term_defn3) ).
thf(200,plain,
! [A: $i] :
( ( A @ single_valued2 @ ( A @ single_valued1 @ singleton @ ( A @ inverse @ image ) @ ( A @ domain ) ) )
= ( A @ single_valued3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cross_product ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ restrict ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cross_product ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ restrict ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(130,axiom,
! [A: $i] :
( ( A @ single_valued_class )
| ~ ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ subclass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class2) ).
thf(442,plain,
! [A: $i] :
( ( A @ single_valued_class )
| ~ ( identity_relation @ ( A @ inverse @ ( A @ compose ) @ subclass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( A @ symmetrization_of @ ( identity_relation @ union ) @ ( B @ ( B @ cross_product ) @ subclass ) )
| ~ ( B @ ( A @ connected ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected1) ).
thf(501,plain,
! [B: $i,A: $i] :
( ( A @ symmetrization_of @ ( identity_relation @ union ) @ ( B @ ( B @ cross_product ) @ subclass ) )
| ~ ( B @ ( A @ connected ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(95,axiom,
! [A: $i] :
( ( ordinal_numbers @ ( A @ member ) )
| ~ ( universal_class @ ( A @ member ) )
| ~ ( A @ ( A @ sum_class @ subclass ) )
| ~ ( A @ ( element_relation @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_numbers3) ).
thf(369,plain,
! [A: $i] :
( ( ordinal_numbers @ ( A @ member ) )
| ~ ( universal_class @ ( A @ member ) )
| ~ ( A @ ( A @ sum_class @ subclass ) )
| ~ ( A @ ( element_relation @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(79,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ apply ) @ ( D @ ( A @ apply ) @ ordered_pair ) @ ( C @ apply ) )
= ( E @ ( D @ ordered_pair ) @ ( B @ apply ) @ ( A @ apply ) ) )
| ~ ( B @ domain_of @ ( E @ ( D @ ordered_pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ homomorphism ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism4) ).
thf(337,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ apply ) @ ( D @ ( A @ apply ) @ ordered_pair ) @ ( C @ apply ) )
= ( E @ ( D @ ordered_pair ) @ ( B @ apply ) @ ( A @ apply ) ) )
| ~ ( B @ domain_of @ ( E @ ( D @ ordered_pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ homomorphism ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ( universal_class @ ( B @ ( A @ image ) @ member ) )
| ~ ( universal_class @ ( B @ member ) )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( universal_class @ ( B @ ( A @ image ) @ member ) )
| ~ ( universal_class @ ( B @ member ) )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ member ) )
| ~ ( D @ ( C @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
thf(215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ member ) )
| ~ ( D @ ( C @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(152,axiom,
! [A: $i] :
( ( A @ ( element_relation @ inverse @ compose ) @ diagonalise @ ( A @ domain_of @ intersection ) )
= ( A @ cantor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cantor_class) ).
thf(491,plain,
! [A: $i] :
( ( A @ ( element_relation @ inverse @ compose ) @ diagonalise @ ( A @ domain_of @ intersection ) )
= ( A @ cantor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ( null_class @ member ) )
| ~ ( A @ inductive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
thf(222,plain,
! [A: $i] :
( ( A @ ( null_class @ member ) )
| ~ ( A @ inductive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(520,plain,
$false,
inference(e,[status(thm)],[351,365,479,347,468,481,217,440,202,385,384,500,472,340,185,417,288,174,404,389,460,421,289,448,316,261,164,321,485,353,397,411,428,507,206,307,248,380,439,270,220,233,452,334,302,349,392,297,407,275,467,229,252,197,361,435,493,285,224,188,388,169,256,193,476,212,371,503,244,266,360,311,343,237,430,166,161,279,180,444,375,176,423,402,291,281,259,413,382,313,466,172,419,362,318,387,323,483,198,330,462,345,367,455,226,505,426,162,255,487,355,458,409,263,182,470,336,446,497,495,218,250,231,378,272,235,246,300,432,190,422,305,210,326,294,341,268,358,195,437,474,400,283,415,239,242,395,464,332,200,178,277,442,501,369,337,309,215,491,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM042-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 01:55:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.19/1.20 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.27/1.63 % [INFO] Parsing done (426ms).
% 2.27/1.65 % [INFO] Running in sequential loop mode.
% 3.39/2.24 % [INFO] eprover registered as external prover.
% 3.39/2.25 % [INFO] Scanning for conjecture ...
% 3.79/2.44 % [INFO] Found a conjecture (or negated_conjecture) and 158 axioms. Running axiom selection ...
% 4.19/2.64 % [INFO] Axiom selection finished. Selected 158 axioms (removed 0 axioms).
% 4.87/2.85 % [INFO] Problem is propositional (TPTP CNF).
% 4.87/2.88 % [INFO] Type checking passed.
% 4.87/2.88 % [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 ...
% 12.12/4.95 % External prover 'e' found a proof!
% 12.12/4.95 % [INFO] Killing All external provers ...
% 12.12/4.95 % Time passed: 4414ms (effective reasoning time: 3290ms)
% 12.12/4.95 % 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
% 12.12/4.96 % No. of inferences in proof: 321
% 12.12/4.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4414 ms resp. 3290 ms w/o parsing
% 12.95/5.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.95/5.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------