%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU382+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n007.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 08:38:38 AM UTC 2026
% Result : Theorem 31.80s 8.63s
% Output : Refutation 33.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 806
% Syntax : Number of formulae : 1614 ( 118 unt; 0 typ; 0 def)
% Number of atoms : 9907 (1356 equ; 0 cnn)
% Maximal formula atoms : 49 ( 6 avg)
% Number of connectives : 29918 (1050 ~; 34 |;4873 &;20575 @)
% ( 243 <=>;3143 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 225 ( 223 usr; 3 con; 0-6 aty)
% Number of variables : 4626 ( 0 ^;3996 !; 630 ?;4626 :)
% Comments :
%------------------------------------------------------------------------------
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(boole_POSet_decl,type,
boole_POSet: $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(reflexive_relstr_decl,type,
reflexive_relstr: $i > $o ).
thf(transitive_relstr_decl,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_decl,type,
antisymmetric_relstr: $i > $o ).
thf(with_suprema_relstr_decl,type,
with_suprema_relstr: $i > $o ).
thf(with_infima_relstr_decl,type,
with_infima_relstr: $i > $o ).
thf(bounded_relstr_decl,type,
bounded_relstr: $i > $o ).
thf(distributive_relstr_decl,type,
distributive_relstr: $i > $o ).
thf(complemented_relstr_decl,type,
complemented_relstr: $i > $o ).
thf(lower_bounded_relstr_decl,type,
lower_bounded_relstr: $i > $o ).
thf(upper_bounded_relstr_decl,type,
upper_bounded_relstr: $i > $o ).
thf(boolean_relstr_decl,type,
boolean_relstr: $i > $o ).
thf(heyting_relstr_decl,type,
heyting_relstr: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(well_orders_decl,type,
well_orders: $i > $i > $o ).
thf(relation_field_decl,type,
relation_field: $i > $i ).
thf(well_ordering_decl,type,
well_ordering: $i > $o ).
thf(complete_relstr_decl,type,
complete_relstr: $i > $o ).
thf(up_complete_relstr_decl,type,
up_complete_relstr: $i > $o ).
thf(join_complete_relstr_decl,type,
join_complete_relstr: $i > $o ).
thf(strict_rel_str_decl,type,
strict_rel_str: $i > $o ).
thf(v1_yellow_3_decl,type,
v1_yellow_3: $i > $o ).
thf(is_reflexive_in_decl,type,
is_reflexive_in: $i > $i > $o ).
thf(is_transitive_in_decl,type,
is_transitive_in: $i > $i > $o ).
thf(is_antisymmetric_in_decl,type,
is_antisymmetric_in: $i > $i > $o ).
thf(is_connected_in_decl,type,
is_connected_in: $i > $i > $o ).
thf(is_well_founded_in_decl,type,
is_well_founded_in: $i > $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(bijective_decl,type,
bijective: $i > $i > $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(onto_decl,type,
onto: $i > $i > $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(inclusion_relation_decl,type,
inclusion_relation: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(natural_decl,type,
natural: $i > $o ).
thf(succ_decl,type,
succ: $i > $i ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(function_inverse_decl,type,
function_inverse: $i > $i ).
thf(relation_inverse_decl,type,
relation_inverse: $i > $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(identity_relation_decl,type,
identity_relation: $i > $i ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(relation_restriction_decl,type,
relation_restriction: $i > $i > $i ).
thf(relation_dom_restriction_decl,type,
relation_dom_restriction: $i > $i > $i ).
thf(relation_rng_restriction_decl,type,
relation_rng_restriction: $i > $i > $i ).
thf(being_limit_ordinal_decl,type,
being_limit_ordinal: $i > $o ).
thf(relation_image_decl,type,
relation_image: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(relation_composition_decl,type,
relation_composition: $i > $i > $i ).
thf(ordinal_subset_decl,type,
ordinal_subset: $i > $i > $o ).
thf(well_founded_relation_decl,type,
well_founded_relation: $i > $o ).
thf(connected_decl,type,
connected: $i > $o ).
thf(reflexive_decl,type,
reflexive: $i > $o ).
thf(transitive_decl,type,
transitive: $i > $o ).
thf(union_decl,type,
union: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(fiber_decl,type,
fiber: $i > $i > $i ).
thf(trivial_carrier_decl,type,
trivial_carrier: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(v2_waybel_3_decl,type,
v2_waybel_3: $i > $o ).
thf(v3_waybel_3_decl,type,
v3_waybel_3: $i > $o ).
thf(v1_waybel_2_decl,type,
v1_waybel_2: $i > $o ).
thf(v2_waybel_2_decl,type,
v2_waybel_2: $i > $o ).
thf(equipotent_decl,type,
equipotent: $i > $i > $o ).
thf(antisymmetric_decl,type,
antisymmetric: $i > $o ).
thf(connected_relstr_decl,type,
connected_relstr: $i > $o ).
thf(relation_isomorphism_decl,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(latt_str_decl,type,
latt_str: $i > $o ).
thf(distributive_lattstr_decl,type,
distributive_lattstr: $i > $o ).
thf(bounded_lattstr_decl,type,
bounded_lattstr: $i > $o ).
thf(complemented_lattstr_decl,type,
complemented_lattstr: $i > $o ).
thf(boolean_lattstr_decl,type,
boolean_lattstr: $i > $o ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(omega_decl,type,
omega: $i ).
thf(lower_bounded_semilattstr_decl,type,
lower_bounded_semilattstr: $i > $o ).
thf(upper_bounded_semilattstr_decl,type,
upper_bounded_semilattstr: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(pair_first_decl,type,
pair_first: $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(pair_second_decl,type,
pair_second: $i > $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(relation_dom_restr_as_relation_of_decl,type,
relation_dom_restr_as_relation_of: $i > $i > $i > $i > $i ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v3_membered_decl,type,
v3_membered: $i > $o ).
thf(v4_membered_decl,type,
v4_membered: $i > $o ).
thf(v5_membered_decl,type,
v5_membered: $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(top_str_decl,type,
top_str: $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(cast_to_subset_decl,type,
cast_to_subset: $i > $i ).
thf(lattice_decl,type,
lattice: $i > $o ).
thf(k2_lattice3_decl,type,
k2_lattice3: $i > $i ).
thf(relation_of_lattice_decl,type,
relation_of_lattice: $i > $i ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(directed_relstr_decl,type,
directed_relstr: $i > $o ).
thf(net_str_decl,type,
net_str: $i > $i > $o ).
thf(subnet_decl,type,
subnet: $i > $i > $i > $o ).
thf(preimage_subnetstr_decl,type,
preimage_subnetstr: $i > $i > $i > $i ).
thf(is_eventually_in_decl,type,
is_eventually_in: $i > $i > $i > $o ).
thf(apply_binary_decl,type,
apply_binary: $i > $i > $i > $i ).
thf(apply_binary_as_element_decl,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(apply_on_set_and_struct_decl,type,
apply_on_set_and_struct: $i > $i > $i > $i > $i ).
thf(proper_element_decl,type,
proper_element: $i > $i > $o ).
thf(relation_dom_as_subset_decl,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(poset_of_lattice_decl,type,
poset_of_lattice: $i > $i ).
thf(strict_latt_str_decl,type,
strict_latt_str: $i > $o ).
thf(join_commutative_decl,type,
join_commutative: $i > $o ).
thf(join_associative_decl,type,
join_associative: $i > $o ).
thf(meet_commutative_decl,type,
meet_commutative: $i > $o ).
thf(meet_associative_decl,type,
meet_associative: $i > $o ).
thf(meet_absorbing_decl,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_decl,type,
join_absorbing: $i > $o ).
thf(complete_latt_str_decl,type,
complete_latt_str: $i > $o ).
thf(boole_lattice_decl,type,
boole_lattice: $i > $i ).
thf(modular_lattstr_decl,type,
modular_lattstr: $i > $o ).
thf(subrelstr_decl,type,
subrelstr: $i > $i > $o ).
thf(incl_POSet_decl,type,
incl_POSet: $i > $i ).
thf(set_meet_decl,type,
set_meet: $i > $i ).
thf(latt_str_of_decl,type,
latt_str_of: $i > $i > $i > $i ).
thf(relation_inverse_image_decl,type,
relation_inverse_image: $i > $i > $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(full_subrelstr_decl,type,
full_subrelstr: $i > $i > $o ).
thf(k8_filter_1_decl,type,
k8_filter_1: $i > $i > $i ).
thf(rel_str_of_decl,type,
rel_str_of: $i > $i > $i ).
thf(relation_rng_as_subset_decl,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(subnetstr_decl,type,
subnetstr: $i > $i > $i > $o ).
thf(strict_net_str_decl,type,
strict_net_str: $i > $i > $o ).
thf(full_subnetstr_decl,type,
full_subnetstr: $i > $i > $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(centered_decl,type,
centered: $i > $o ).
thf(empty_carrier_subset_decl,type,
empty_carrier_subset: $i > $i ).
thf(bottom_of_semilattstr_decl,type,
bottom_of_semilattstr: $i > $i ).
thf(cup_closed_decl,type,
cup_closed: $i > $o ).
thf(diff_closed_decl,type,
diff_closed: $i > $o ).
thf(preboolean_decl,type,
preboolean: $i > $o ).
thf(function_of_composition_decl,type,
function_of_composition: $i > $i > $i > $i > $i > $i ).
thf(relation_restriction_as_relation_of_decl,type,
relation_restriction_as_relation_of: $i > $i > $i ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(join_of_latt_set_decl,type,
join_of_latt_set: $i > $i > $i ).
thf(join_on_relstr_decl,type,
join_on_relstr: $i > $i > $i ).
thf(meet_of_latt_set_decl,type,
meet_of_latt_set: $i > $i > $i ).
thf(meet_on_relstr_decl,type,
meet_on_relstr: $i > $i > $i ).
thf(meet_semilatt_str_decl,type,
meet_semilatt_str: $i > $o ).
thf(are_equipotent_decl,type,
are_equipotent: $i > $i > $o ).
thf(is_often_in_decl,type,
is_often_in: $i > $i > $i > $o ).
thf(ordered_pair_as_product_element_decl,type,
ordered_pair_as_product_element: $i > $i > $i > $i > $i ).
thf(topological_space_decl,type,
topological_space: $i > $o ).
thf(closed_subset_decl,type,
closed_subset: $i > $i > $o ).
thf(cast_as_carrier_subset_decl,type,
cast_as_carrier_subset: $i > $i ).
thf(the_mapping_decl,type,
the_mapping: $i > $i > $i ).
thf(inclusion_order_decl,type,
inclusion_order: $i > $i ).
thf(apply_on_structs_decl,type,
apply_on_structs: $i > $i > $i > $i > $i ).
thf(relstr_set_smaller_decl,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(symmetric_decl,type,
symmetric: $i > $o ).
thf(join_semilatt_str_decl,type,
join_semilatt_str: $i > $o ).
thf(identity_as_relation_of_decl,type,
identity_as_relation_of: $i > $i ).
thf(a_1_0_filter_1_decl,type,
a_1_0_filter_1: $i > $i ).
thf(a_2_2_lattice3_decl,type,
a_2_2_lattice3: $i > $i > $i ).
thf(bottom_of_relstr_decl,type,
bottom_of_relstr: $i > $i ).
thf(apply_as_element_decl,type,
apply_as_element: $i > $i > $i > $i > $i ).
thf(related_decl,type,
related: $i > $i > $i > $o ).
thf(lim_points_of_net_decl,type,
lim_points_of_net: $i > $i > $i ).
thf(v1_xcmplx_0_decl,type,
v1_xcmplx_0: $i > $o ).
thf(unordered_triple_decl,type,
unordered_triple: $i > $i > $i > $i ).
thf(the_L_meet_decl,type,
the_L_meet: $i > $i ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(latt_set_smaller_decl,type,
latt_set_smaller: $i > $i > $i > $o ).
thf(join_commut_decl,type,
join_commut: $i > $i > $i > $i ).
thf(join_decl,type,
join: $i > $i > $i > $i ).
thf(net_str_of_decl,type,
net_str_of: $i > $i > $i > $i > $i ).
thf(ex_sup_of_relstr_set_decl,type,
ex_sup_of_relstr_set: $i > $i > $o ).
thf(the_L_join_decl,type,
the_L_join: $i > $i ).
thf(k10_filter_1_decl,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(directed_subset_decl,type,
directed_subset: $i > $i > $o ).
thf(filtered_subset_decl,type,
filtered_subset: $i > $i > $o ).
thf(complements_of_subsets_decl,type,
complements_of_subsets: $i > $i > $i ).
thf(subset_complement_decl,type,
subset_complement: $i > $i > $i ).
thf(relstr_element_smaller_decl,type,
relstr_element_smaller: $i > $i > $i > $o ).
thf(function_invverse_img_as_carrier_subset_decl,type,
function_invverse_img_as_carrier_subset: $i > $i > $i > $i > $i ).
thf(point_neighbourhood_decl,type,
point_neighbourhood: $i > $i > $i > $o ).
thf(open_subset_decl,type,
open_subset: $i > $i > $o ).
thf(meet_commut_decl,type,
meet_commut: $i > $i > $i > $i ).
thf(ex_inf_of_relstr_set_decl,type,
ex_inf_of_relstr_set: $i > $i > $o ).
thf(topstr_closure_decl,type,
topstr_closure: $i > $i > $i ).
thf(k1_pcomps_1_decl,type,
k1_pcomps_1: $i > $i ).
thf(meet_decl,type,
meet: $i > $i > $i > $i ).
thf(compact_top_space_decl,type,
compact_top_space: $i > $o ).
thf(is_a_cover_of_carrier_decl,type,
is_a_cover_of_carrier: $i > $i > $o ).
thf(open_subsets_decl,type,
open_subsets: $i > $i > $o ).
thf(below_decl,type,
below: $i > $i > $i > $o ).
thf(subset_union2_decl,type,
subset_union2: $i > $i > $i > $i ).
thf(union_of_subsets_decl,type,
union_of_subsets: $i > $i > $i ).
thf(apply_netmap_decl,type,
apply_netmap: $i > $i > $i > $i ).
thf(interior_decl,type,
interior: $i > $i > $i ).
thf(related_reflexive_decl,type,
related_reflexive: $i > $i > $i > $o ).
thf(subset_difference_decl,type,
subset_difference: $i > $i > $i > $i ).
thf(upper_relstr_subset_decl,type,
upper_relstr_subset: $i > $i > $o ).
thf(cast_to_el_of_lattice_decl,type,
cast_to_el_of_lattice: $i > $i > $i ).
thf(closed_subsets_decl,type,
closed_subsets: $i > $i > $o ).
thf(latt_element_smaller_decl,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(meet_of_subsets_decl,type,
meet_of_subsets: $i > $i > $i ).
thf(the_topology_decl,type,
the_topology: $i > $i ).
thf(subset_intersection2_decl,type,
subset_intersection2: $i > $i > $i > $i ).
thf(unordered_pair_as_carrier_subset_decl,type,
unordered_pair_as_carrier_subset: $i > $i > $i > $i ).
thf(below_refl_decl,type,
below_refl: $i > $i > $i > $o ).
thf(cast_to_el_of_LattPOSet_decl,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(identity_on_carrier_decl,type,
identity_on_carrier: $i > $i ).
thf(a_2_3_lattice3_decl,type,
a_2_3_lattice3: $i > $i > $i ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ reflexive )
=> ( A @ ( B @ relation_restriction ) @ reflexive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_wellord1) ).
thf(2630,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ reflexive )
=> ( A @ ( B @ relation_restriction ) @ reflexive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equipotent ) )
<=> ? [C: $i] :
( ( ( C @ relation_rng )
= B )
& ( ( C @ relation_dom )
= A )
& ( C @ one_to_one )
& ( C @ function )
& ( C @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord2) ).
thf(1411,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( ( C @ relation_rng )
= B )
& ( ( C @ relation_dom )
= A )
& ( C @ one_to_one )
& ( C @ function )
& ( C @ relation ) )
=> ( B @ ( A @ equipotent ) ) )
& ( ( B @ ( A @ equipotent ) )
=> ? [C: $i] :
( ( ( C @ relation_rng )
= B )
& ( ( C @ relation_dom )
= A )
& ( C @ one_to_one )
& ( C @ function )
& ( C @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(749,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(6167,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(4005,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(187,axiom,
! [A: $i] :
( ( A @ finite )
<=> ? [B: $i] :
( ( omega @ ( B @ relation_dom @ in ) )
& ( ( B @ relation_rng )
= A )
& ( B @ function )
& ( B @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_finset_1) ).
thf(2109,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( omega @ ( B @ relation_dom @ in ) )
& ( ( B @ relation_rng )
= A )
& ( B @ function )
& ( B @ relation ) )
=> ( A @ finite ) )
& ( ( A @ finite )
=> ? [B: $i] :
( ( omega @ ( B @ relation_dom @ in ) )
& ( ( B @ relation_rng )
= A )
& ( B @ function )
& ( B @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] :
( ( A @ ( B @ well_orders ) )
& ( B @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_wellord2) ).
thf(846,plain,
! [A: $i] :
? [B: $i] :
( ( A @ ( B @ well_orders ) )
& ( B @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(3698,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i,G: $i] :
( ! [H: $i] :
( ( A @ the_carrier @ powerset @ ( H @ element ) )
=> ( ( H = F )
=> ( G
= ( H @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( B @ cartesian_product2 ) @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_7_2__tops_2__1) ).
thf(5390,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( ( ? [F: $i,G: $i] :
( ! [H: $i] :
( ( A @ the_carrier @ powerset @ ( H @ element ) )
=> ( ( H = F )
=> ( G
= ( H @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( B @ cartesian_product2 ) @ ( E @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ( ? [F: $i,G: $i] :
( ! [H: $i] :
( ( A @ the_carrier @ powerset @ ( H @ element ) )
=> ( ( H = F )
=> ( G
= ( H @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( B @ cartesian_product2 ) @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_founded_relation )
<=> ( A @ relation_field @ ( A @ is_well_founded_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
thf(1083,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_well_founded_in ) )
=> ( A @ well_founded_relation ) )
& ( ( A @ well_founded_relation )
=> ( A @ relation_field @ ( A @ is_well_founded_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ union @ ordinal )
& ( A @ union @ epsilon_connected )
& ( A @ union @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_ordinal1) ).
thf(1179,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ union @ ordinal )
& ( A @ union @ epsilon_connected )
& ( A @ union @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(118,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(1586,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(1501,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(3661,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(427,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ relation_of_lattice @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(4062,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ relation_of_lattice @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(211,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ connected )
<=> ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_wellord1) ).
thf(2263,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) )
=> ( A @ connected ) )
& ( ( A @ connected )
=> ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(450,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ lower_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_yellow_1) ).
thf(4169,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ lower_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(72,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(1315,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(681,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice )
= ( A @ k2_lattice3 @ ( A @ the_carrier @ rel_str_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
thf(5676,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice )
= ( A @ k2_lattice3 @ ( A @ the_carrier @ rel_str_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(788,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ empty_carrier_subset @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(6527,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ empty_carrier_subset @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(110,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( A @ function_inverse @ one_to_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(1549,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( A @ function_inverse @ one_to_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(375,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ upper_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ upper_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow_1) ).
thf(3681,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ upper_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ upper_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(526,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnet ) ) )
=> ( C @ ( A @ lim_points_of_net ) @ ( B @ ( A @ lim_points_of_net ) @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_yellow_6) ).
thf(4714,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnet ) ) )
=> ( C @ ( A @ lim_points_of_net ) @ ( B @ ( A @ lim_points_of_net ) @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(163,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ subset ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(1882,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(152,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(1808,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_wellord1) ).
thf(1073,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(696,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( C
= ( B @ ( A @ topstr_closure ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ in ) )
=> ( ( C @ ( D @ in ) )
<=> ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ~ ( ( E @ ( B @ disjoint ) )
& ( E @ ( D @ in ) )
& ( A @ ( E @ open_subset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_pre_topc) ).
thf(5793,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ in ) )
=> ( ( ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ~ ( ( E @ ( B @ disjoint ) )
& ( E @ ( D @ in ) )
& ( A @ ( E @ open_subset ) ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ~ ( ( E @ ( B @ disjoint ) )
& ( E @ ( D @ in ) )
& ( A @ ( E @ open_subset ) ) ) ) ) ) )
=> ( C
= ( B @ ( A @ topstr_closure ) ) ) )
& ( ( C
= ( B @ ( A @ topstr_closure ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ in ) )
=> ( ( ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ~ ( ( E @ ( B @ disjoint ) )
& ( E @ ( D @ in ) )
& ( A @ ( E @ open_subset ) ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ~ ( ( E @ ( B @ disjoint ) )
& ( E @ ( D @ in ) )
& ( A @ ( E @ open_subset ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(184,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr ) )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( ( A @ ( B @ full_subrelstr ) )
=> ( ( A @ ( B @ full_subrelstr ) )
& ( B @ transitive_relstr ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_yellow_0) ).
thf(2099,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr ) )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( ( A @ ( B @ full_subrelstr ) )
=> ( ( A @ ( B @ full_subrelstr ) )
& ( B @ transitive_relstr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(281,axiom,
! [A: $i] :
( ( A @ boole_lattice @ latt_str )
& ( A @ boole_lattice @ strict_latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
thf(2837,plain,
! [A: $i] :
( ( A @ boole_lattice @ latt_str )
& ( A @ boole_lattice @ strict_latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(509,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(4614,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ well_ordering )
=> ( A @ ( B @ relation_restriction ) @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_wellord1) ).
thf(1305,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ well_ordering )
=> ( A @ ( B @ relation_restriction ) @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( B @ ( A @ set_difference ) @ v5_membered )
& ( B @ ( A @ set_difference ) @ v4_membered )
& ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc41_membered) ).
thf(4747,plain,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( B @ ( A @ set_difference ) @ v5_membered )
& ( B @ ( A @ set_difference ) @ v4_membered )
& ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ latt_element_smaller ) ) )
<=> ( C @ ( B @ cast_to_el_of_LattPOSet ) @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice3) ).
thf(6214,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ cast_to_el_of_LattPOSet ) @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) )
=> ( A @ ( C @ ( B @ latt_element_smaller ) ) ) )
& ( ( A @ ( C @ ( B @ latt_element_smaller ) ) )
=> ( C @ ( B @ cast_to_el_of_LattPOSet ) @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(653,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ interior ) @ open_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tops_1) ).
thf(5501,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ interior ) @ open_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ ( B @ relation_dom_restriction ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
thf(2363,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ ( B @ relation_dom_restriction ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(161,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
<=> ( ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) ) )
& ( C @ one_to_one )
& ( ( C @ relation_rng )
= ( B @ relation_field ) )
& ( ( C @ relation_dom )
= ( A @ relation_field ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_wellord1) ).
thf(1855,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) )
=> ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) ) ) )
& ( C @ one_to_one )
& ( ( C @ relation_rng )
= ( B @ relation_field ) )
& ( ( C @ relation_dom )
= ( A @ relation_field ) ) )
=> ( C @ ( B @ ( A @ relation_isomorphism ) ) ) )
& ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) )
=> ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) ) ) )
& ( C @ one_to_one )
& ( ( C @ relation_rng )
= ( B @ relation_field ) )
& ( ( C @ relation_dom )
= ( A @ relation_field ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( B @ ( A @ set_intersection2 ) @ v3_membered )
& ( B @ ( A @ set_intersection2 ) @ v2_membered )
& ( B @ ( A @ set_intersection2 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc31_membered) ).
thf(2622,plain,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( B @ ( A @ set_intersection2 ) @ v3_membered )
& ( B @ ( A @ set_intersection2 ) @ v2_membered )
& ( B @ ( A @ set_intersection2 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(747,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ topstr_closure ) @ closed_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(6162,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ topstr_closure ) @ closed_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(783,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ below ) ) )
<=> ( ( C @ ( B @ ( A @ join ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
thf(6495,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( ( C @ ( B @ ( A @ join ) ) )
= C )
=> ( C @ ( B @ ( A @ below ) ) ) )
& ( ( C @ ( B @ ( A @ below ) ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(576,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(5069,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( B @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(3549,plain,
! [A: $i,B: $i] :
( ( B @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(2527,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B
= ( A @ ( C @ relation_dom_restriction ) ) )
<=> ( ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
=> ( ( D @ ( B @ apply ) )
= ( D @ ( C @ apply ) ) ) )
& ( ( B @ relation_dom )
= ( A @ ( C @ relation_dom @ set_intersection2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
thf(3040,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
=> ( ( D @ ( B @ apply ) )
= ( D @ ( C @ apply ) ) ) )
& ( ( B @ relation_dom )
= ( A @ ( C @ relation_dom @ set_intersection2 ) ) ) )
=> ( B
= ( A @ ( C @ relation_dom_restriction ) ) ) )
& ( ( B
= ( A @ ( C @ relation_dom_restriction ) ) )
=> ( ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
=> ( ( D @ ( B @ apply ) )
= ( D @ ( C @ apply ) ) ) )
& ( ( B @ relation_dom )
= ( A @ ( C @ relation_dom @ set_intersection2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_difference ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(3460,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_difference ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( A @ ( B @ relation_composition ) @ relation )
& ( A @ ( B @ relation_composition ) @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(2248,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( A @ ( B @ relation_composition ) @ relation )
& ( A @ ( B @ relation_composition ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(455,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(4215,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(2380,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_ordering )
<=> ( ( A @ well_founded_relation )
& ( A @ connected )
& ( A @ antisymmetric )
& ( A @ transitive )
& ( A @ reflexive ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
thf(1655,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ well_founded_relation )
& ( A @ connected )
& ( A @ antisymmetric )
& ( A @ transitive )
& ( A @ reflexive ) )
=> ( A @ well_ordering ) )
& ( ( A @ well_ordering )
=> ( ( A @ well_founded_relation )
& ( A @ connected )
& ( A @ antisymmetric )
& ( A @ transitive )
& ( A @ reflexive ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(603,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(5257,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(63,axiom,
? [A: $i] :
( ( A @ v3_waybel_3 )
& ( A @ v2_waybel_3 )
& ( A @ distributive_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_6) ).
thf(1260,plain,
? [A: $i] :
( ( A @ v3_waybel_3 )
& ( A @ v2_waybel_3 )
& ( A @ distributive_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ distributive_lattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ modular_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).
thf(2459,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ distributive_lattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ modular_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = E )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( E @ in ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_1__tops_2__1) ).
thf(5005,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ? [E: $i] :
( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = E )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( E @ in ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = E )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( E @ in ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( E @ closed_subset ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ element ) ) ) ) )
& ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
thf(5412,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( ? [E: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( E @ closed_subset ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ element ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( E @ closed_subset ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ element ) ) ) ) ) )
& ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ connected )
<=> ( A @ relation_field @ ( A @ is_connected_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
thf(1497,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_connected_in ) )
=> ( A @ connected ) )
& ( ( A @ connected )
=> ( A @ relation_field @ ( A @ is_connected_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(502,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_knaster) ).
thf(4543,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_antisymmetric_in ) )
<=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
thf(2195,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( C = D ) )
=> ( B @ ( A @ is_antisymmetric_in ) ) )
& ( ( B @ ( A @ is_antisymmetric_in ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_waybel_1) ).
thf(1705,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(3365,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(545,axiom,
! [A: $i,B: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ function )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(4870,plain,
! [A: $i,B: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ function )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( A @ ( F @ in ) )
& ( E = F )
& ( F @ ordinal ) )
& ( C = E )
& ? [F: $i] :
( ( A @ ( F @ in ) )
& ( D = F )
& ( F @ ordinal ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ( A @ ( F @ in ) )
& ( D = F )
& ( F @ ordinal ) )
& ( E = D )
& ( B @ succ @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
thf(4026,plain,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( A @ ( F @ in ) )
& ( E = F )
& ( F @ ordinal ) )
& ( C = E )
& ? [F: $i] :
( ( A @ ( F @ in ) )
& ( D = F )
& ( F @ ordinal ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ? [E: $i] :
( ? [F: $i] :
( ( A @ ( F @ in ) )
& ( D = F )
& ( F @ ordinal ) )
& ( E = D )
& ( B @ succ @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( A @ ( F @ in ) )
& ( D = F )
& ( F @ ordinal ) )
& ( E = D )
& ( B @ succ @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(139,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(1735,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(743,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = E )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( E @ in ) )
& ( B @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_2__tops_2__1) ).
thf(6127,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ? [E: $i] :
( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = E )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( E @ in ) )
& ( B @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = E )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( E @ in ) )
& ( B @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( ( A @ empty )
=> ( ( A @ ( B @ element ) )
<=> ( B @ empty ) ) )
& ( ~ ( A @ empty )
=> ( ( A @ ( B @ element ) )
<=> ( A @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(4220,plain,
! [A: $i,B: $i] :
( ( ( A @ empty )
=> ( ( ( B @ empty )
=> ( A @ ( B @ element ) ) )
& ( ( A @ ( B @ element ) )
=> ( B @ empty ) ) ) )
& ( ~ ( A @ empty )
=> ( ( ( A @ ( B @ in ) )
=> ( A @ ( B @ element ) ) )
& ( ( A @ ( B @ element ) )
=> ( A @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ~ ( A @ v1_yellow_3 )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_yellow_3) ).
thf(2184,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ~ ( A @ v1_yellow_3 )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ~ ( ! [C: $i] :
( ( C @ ordinal )
=> ~ ( ! [D: $i] :
( ( D @ ordinal )
=> ( ( A @ ( D @ in ) )
=> ( D @ ( C @ ordinal_subset ) ) ) )
& ( A @ ( C @ in ) ) ) )
& ( A != empty_set )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(4435,plain,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ~ ( ! [C: $i] :
( ( C @ ordinal )
=> ~ ( ! [D: $i] :
( ( D @ ordinal )
=> ( ( A @ ( D @ in ) )
=> ( D @ ( C @ ordinal_subset ) ) ) )
& ( A @ ( C @ in ) ) ) )
& ( A != empty_set )
& ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(363,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(3577,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ boolean_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc8_waybel_1) ).
thf(829,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ boolean_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(335,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ fiber ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord1) ).
thf(3335,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) ) ) )
=> ( C
= ( B @ ( A @ fiber ) ) ) )
& ( ( C
= ( B @ ( A @ fiber ) ) )
=> ! [D: $i] :
( ( ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ element ) )
=> ( ( A @ ( B @ proper_element ) )
<=> ( B
!= ( A @ union ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
thf(1835,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ element ) )
=> ( ( ( B
!= ( A @ union ) )
=> ( A @ ( B @ proper_element ) ) )
& ( ( A @ ( B @ proper_element ) )
=> ( B
!= ( A @ union ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(359,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ antisymmetric )
<=> ( A @ relation_field @ ( A @ is_antisymmetric_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
thf(3545,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_antisymmetric_in ) )
=> ( A @ antisymmetric ) )
& ( ( A @ antisymmetric )
=> ( A @ relation_field @ ( A @ is_antisymmetric_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(45,axiom,
! [A: $i] : ( A @ inclusion_relation @ transitive ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).
thf(1127,plain,
! [A: $i] : ( A @ inclusion_relation @ transitive ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( B
= ( A @ ( C @ apply ) ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(4371,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ( B
= ( A @ ( C @ apply ) ) )
& ( C @ relation_dom @ ( A @ in ) ) )
=> ( C @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( B
= ( A @ ( C @ apply ) ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(390,axiom,
! [A: $i] :
( ( A @ identity_as_relation_of )
= ( A @ identity_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(3777,plain,
! [A: $i] :
( ( A @ identity_as_relation_of )
= ( A @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ distributive_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ boolean_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
thf(1386,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ distributive_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ boolean_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ transitive_relstr )
& ( A @ one_sorted_str ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ full_subnetstr ) ) )
& ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ strict_net_str ) )
& ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ transitive_relstr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_yellow_6) ).
thf(4137,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ transitive_relstr )
& ( A @ one_sorted_str ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ full_subnetstr ) ) )
& ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ strict_net_str ) )
& ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ transitive_relstr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(395,axiom,
? [A: $i] :
( ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_orders_2) ).
thf(3809,plain,
? [A: $i] :
( ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B
= ( A @ identity_relation ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
<=> ( ( C = D )
& ( A @ ( C @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(1623,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ in ) ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( ( C = D )
& ( A @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ identity_relation ) ) )
& ( ( B
= ( A @ identity_relation ) )
=> ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ in ) ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( ( C = D )
& ( A @ ( C @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( A @ ( C @ in ) )
=> ( ( D @ relation_rng @ ( C @ ( D @ apply ) @ in ) )
| ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
thf(3836,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( A @ ( C @ in ) )
=> ( ( D @ relation_rng @ ( C @ ( D @ apply ) @ in ) )
| ( B = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(368,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( ( C @ ordinal )
& ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
thf(3629,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ( ( C @ ordinal )
& ( A @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( ( C @ ordinal )
& ( A @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ latt_str )
& ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(2046,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ latt_str )
& ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(601,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ union_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(5252,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ union_of_subsets ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(719,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ transitive_relstr )
<=> ( A @ the_carrier @ ( A @ the_InternalRel @ is_transitive_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_orders_2) ).
thf(5935,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ the_carrier @ ( A @ the_InternalRel @ is_transitive_in ) )
=> ( A @ transitive_relstr ) )
& ( ( A @ transitive_relstr )
=> ( A @ the_carrier @ ( A @ the_InternalRel @ is_transitive_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(1576,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i,G: $i] :
( ( B @ ( G @ ( C @ apply ) @ ( F @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( G @ ( F @ ordered_pair ) ) ) )
& ( A @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
thf(3513,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( ? [F: $i,G: $i] :
( ( B @ ( G @ ( C @ apply ) @ ( F @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( G @ ( F @ ordered_pair ) ) ) )
& ( A @ ( A @ cartesian_product2 ) @ ( E @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ( ? [F: $i,G: $i] :
( ( B @ ( G @ ( C @ apply ) @ ( F @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( G @ ( F @ ordered_pair ) ) ) )
& ( A @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(595,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( ( A @ ( B @ subrelstr ) )
& ( A @ ( B @ full_subrelstr ) ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( B @ the_carrier @ ( F @ in ) )
& ( B @ the_carrier @ ( E @ in ) )
& ( D @ ( C @ ( A @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( F @ ( E @ ( B @ related ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_yellow_0) ).
thf(5195,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( ( A @ ( B @ subrelstr ) )
& ( A @ ( B @ full_subrelstr ) ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( B @ the_carrier @ ( F @ in ) )
& ( B @ the_carrier @ ( E @ in ) )
& ( D @ ( C @ ( A @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( F @ ( E @ ( B @ related ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(799,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_semilattstr )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B
= ( A @ bottom_of_semilattstr ) )
<=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattices) ).
thf(6583,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_semilattstr )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
=> ( B
= ( A @ bottom_of_semilattstr ) ) )
& ( ( B
= ( A @ bottom_of_semilattstr ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(124,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
<=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(1613,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) )
=> ( A @ one_to_one ) )
& ( ( A @ one_to_one )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(334,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
thf(3308,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_image ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( ( A = empty_set )
=> ( ( B
= ( A @ set_meet ) )
<=> ( B = empty_set ) ) )
& ( ( A != empty_set )
=> ( ( B
= ( A @ set_meet ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(2010,plain,
! [A: $i,B: $i] :
( ( ( A = empty_set )
=> ( ( ( B = empty_set )
=> ( B
= ( A @ set_meet ) ) )
& ( ( B
= ( A @ set_meet ) )
=> ( B = empty_set ) ) ) )
& ( ( A != empty_set )
=> ( ( ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ set_meet ) ) )
& ( ( B
= ( A @ set_meet ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( C @ ( B @ ( A @ unordered_triple ) ) ) )
<=> ! [E: $i] :
( ( D @ ( E @ in ) )
<=> ~ ( ( E != C )
& ( E != B )
& ( E != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_enumset1) ).
thf(4803,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( ~ ( ( E != C )
& ( E != B )
& ( E != A ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ~ ( ( E != C )
& ( E != B )
& ( E != A ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ unordered_triple ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ unordered_triple ) ) ) )
=> ! [E: $i] :
( ( ~ ( ( E != C )
& ( E != B )
& ( E != A ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ~ ( ( E != C )
& ( E != B )
& ( E != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(126,axiom,
? [A: $i] : ( A @ top_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(1645,plain,
? [A: $i] : ( A @ top_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(575,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ subnetstr ) ) )
& ( A @ ( D @ strict_net_str ) ) )
=> ( ( D
= ( C @ ( B @ ( A @ preimage_subnetstr ) ) ) )
<=> ( ( ( D @ the_carrier )
= ( C @ ( B @ ( A @ the_mapping ) @ ( A @ ( B @ function_invverse_img_as_carrier_subset ) ) ) ) )
& ( B @ ( D @ subrelstr ) )
& ( B @ ( D @ full_subrelstr ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_yellow_6) ).
thf(5056,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ subnetstr ) ) )
& ( A @ ( D @ strict_net_str ) ) )
=> ( ( ( ( ( D @ the_carrier )
= ( C @ ( B @ ( A @ the_mapping ) @ ( A @ ( B @ function_invverse_img_as_carrier_subset ) ) ) ) )
& ( B @ ( D @ subrelstr ) )
& ( B @ ( D @ full_subrelstr ) ) )
=> ( D
= ( C @ ( B @ ( A @ preimage_subnetstr ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ preimage_subnetstr ) ) ) )
=> ( ( ( D @ the_carrier )
= ( C @ ( B @ ( A @ the_mapping ) @ ( A @ ( B @ function_invverse_img_as_carrier_subset ) ) ) ) )
& ( B @ ( D @ subrelstr ) )
& ( B @ ( D @ full_subrelstr ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(170,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] : ( A @ ( B @ subrelstr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(1967,plain,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] : ( A @ ( B @ subrelstr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) )
= ( B @ ( A @ set_difference ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(6483,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) )
= ( B @ ( A @ set_difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_dom @ ( A @ ( B @ relation_inverse_image ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
thf(4156,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_dom @ ( A @ ( B @ relation_inverse_image ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(150,axiom,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(1803,plain,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(688,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ poset_of_lattice @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_lattice ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice3) ).
thf(5750,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ poset_of_lattice @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_lattice ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ well_founded_relation )
=> ( A @ ( B @ relation_restriction ) @ well_founded_relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_wellord1) ).
thf(1518,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ well_founded_relation )
=> ( A @ ( B @ relation_restriction ) @ well_founded_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(508,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_often_in ) ) )
=> ( ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ directed_relstr )
& ~ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ empty_carrier ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_yellow_6) ).
thf(4610,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_often_in ) ) )
=> ( ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ directed_relstr )
& ~ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ empty_carrier ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(621,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet_commut ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(5352,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet_commut ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(164,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ antisymmetric )
<=> ! [B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
thf(1887,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( B = C ) )
=> ( A @ antisymmetric ) )
& ( ( A @ antisymmetric )
=> ! [B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(3820,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( A @ ( B @ set_intersection2 ) @ v5_membered )
& ( A @ ( B @ set_intersection2 ) @ v4_membered )
& ( A @ ( B @ set_intersection2 ) @ v3_membered )
& ( A @ ( B @ set_intersection2 ) @ v2_membered )
& ( A @ ( B @ set_intersection2 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc36_membered) ).
thf(2328,plain,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( A @ ( B @ set_intersection2 ) @ v5_membered )
& ( A @ ( B @ set_intersection2 ) @ v4_membered )
& ( A @ ( B @ set_intersection2 ) @ v3_membered )
& ( A @ ( B @ set_intersection2 ) @ v2_membered )
& ( A @ ( B @ set_intersection2 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ set_union2 ) @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(4866,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ set_union2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnet ) ) )
=> ( ( A @ ( C @ net_str ) )
& ( C @ directed_relstr )
& ( C @ transitive_relstr )
& ~ ( C @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_yellow_6) ).
thf(1985,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnet ) ) )
=> ( ( A @ ( C @ net_str ) )
& ( C @ directed_relstr )
& ( C @ transitive_relstr )
& ~ ( C @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(330,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pboole) ).
thf(3275,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(533,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_transitive_in ) )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( E @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( A @ ( E @ ( C @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
thf(4761,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( E @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( A @ ( E @ ( C @ ordered_pair ) @ in ) ) )
=> ( B @ ( A @ is_transitive_in ) ) )
& ( ( B @ ( A @ is_transitive_in ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( E @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( A @ ( E @ ( C @ ordered_pair ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(212,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(2274,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(315,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_waybel_0) ).
thf(3125,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(3280,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(2897,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(612,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( B @ ( A @ ex_inf_of_relstr_set ) )
<=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( D @ ( E @ ( A @ related ) ) ) ) )
& ( D @ ( B @ ( A @ relstr_element_smaller ) ) ) )
=> ( D = C ) ) )
& ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_yellow_0) ).
thf(5289,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( D @ ( E @ ( A @ related ) ) ) ) )
& ( D @ ( B @ ( A @ relstr_element_smaller ) ) ) )
=> ( D = C ) ) )
& ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) )
=> ( B @ ( A @ ex_inf_of_relstr_set ) ) )
& ( ( B @ ( A @ ex_inf_of_relstr_set ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( D @ ( E @ ( A @ related ) ) ) ) )
& ( D @ ( B @ ( A @ relstr_element_smaller ) ) ) )
=> ( D = C ) ) )
& ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(3803,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(246,axiom,
? [A: $i] :
( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ modular_lattstr )
& ( A @ distributive_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_lattices) ).
thf(2571,plain,
? [A: $i] :
( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ modular_lattstr )
& ( A @ distributive_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(268,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ~ ( ( A @ being_limit_ordinal )
& ? [B: $i] :
( ( A
= ( B @ succ ) )
& ( B @ ordinal ) ) )
& ~ ( ! [B: $i] :
( ( B @ ordinal )
=> ( A
!= ( B @ succ ) ) )
& ~ ( A @ being_limit_ordinal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_ordinal1) ).
thf(2703,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ~ ( ( A @ being_limit_ordinal )
& ? [B: $i] :
( ( A
= ( B @ succ ) )
& ( B @ ordinal ) ) )
& ~ ( ! [B: $i] :
( ( B @ ordinal )
=> ( A
!= ( B @ succ ) ) )
& ~ ( A @ being_limit_ordinal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ onto ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ one_to_one )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ bijective ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_funct_2) ).
thf(1055,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ onto ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ one_to_one )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ bijective ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(500,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_membered) ).
thf(4539,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(316,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(3131,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(559,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
<=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow_0) ).
thf(4956,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) )
=> ( B @ ( A @ ex_sup_of_relstr_set ) ) )
& ( ( B @ ( A @ ex_sup_of_relstr_set ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_intersection2 ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(6274,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_intersection2 ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(610,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_pre_topc) ).
thf(5284,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(440,axiom,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ in ) )
=> ( A @ ordinal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(4130,plain,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ in ) )
=> ( A @ ordinal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_inverse @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(1313,plain,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_inverse @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ well_founded_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_wellord2) ).
thf(1279,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ well_founded_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(740,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_waybel_7) ).
thf(6113,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(404,axiom,
? [A: $i] :
( ( A @ strict_rel_str )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_orders_2) ).
thf(3845,plain,
? [A: $i] :
( ( A @ strict_rel_str )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ empty )
& ( C @ function ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(2488,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ empty )
& ( C @ function ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( B @ ( A @ meet_on_relstr ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_0) ).
thf(5744,plain,
! [A: $i,B: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( B @ ( A @ meet_on_relstr ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ relation_dom_restr_as_relation_of ) ) ) )
= ( D @ ( C @ relation_dom_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_relset_1) ).
thf(2691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ relation_dom_restr_as_relation_of ) ) ) )
= ( D @ ( C @ relation_dom_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(777,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( B @ ( C @ ( B @ ( A @ meet_commut ) ) @ ( A @ below ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
thf(6470,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( B @ ( C @ ( B @ ( A @ meet_commut ) ) @ ( A @ below ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ( A @ boole_POSet @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ boole_POSet @ ( B @ upper_relstr_subset ) )
<=> ! [C: $i,D: $i] :
( ( ( B @ ( C @ in ) )
& ( A @ ( D @ subset ) )
& ( D @ ( C @ subset ) ) )
=> ( B @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_waybel_7) ).
thf(5323,plain,
! [A: $i,B: $i] :
( ( A @ boole_POSet @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ ( C @ in ) )
& ( A @ ( D @ subset ) )
& ( D @ ( C @ subset ) ) )
=> ( B @ ( D @ in ) ) )
=> ( A @ boole_POSet @ ( B @ upper_relstr_subset ) ) )
& ( ( A @ boole_POSet @ ( B @ upper_relstr_subset ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( C @ in ) )
& ( A @ ( D @ subset ) )
& ( D @ ( C @ subset ) ) )
=> ( B @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(574,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ the_carrier @ subset_complement ) @ ( C @ in ) )
<=> ~ ( B @ ( C @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
thf(5052,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ the_carrier @ subset_complement ) @ ( C @ in ) ) )
& ( ( B @ ( A @ the_carrier @ subset_complement ) @ ( C @ in ) )
=> ~ ( B @ ( C @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ net_str ) )
& ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_waybel_0) ).
thf(4952,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ net_str ) )
& ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ set_intersection2 ) @ v2_membered )
& ( B @ ( A @ set_intersection2 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc29_membered) ).
thf(2852,plain,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ set_intersection2 ) @ v2_membered )
& ( B @ ( A @ set_intersection2 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(460,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ identity_relation @ apply ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(4253,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ identity_relation @ apply ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(735,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( B
= ( C @ ( A @ meet_of_latt_set ) ) )
<=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ ( A @ latt_set_smaller ) ) )
=> ( B @ ( D @ ( A @ below_refl ) ) ) ) )
& ( C @ ( B @ ( A @ latt_set_smaller ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice3) ).
thf(6049,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ ( A @ latt_set_smaller ) ) )
=> ( B @ ( D @ ( A @ below_refl ) ) ) ) )
& ( C @ ( B @ ( A @ latt_set_smaller ) ) ) )
=> ( B
= ( C @ ( A @ meet_of_latt_set ) ) ) )
& ( ( B
= ( C @ ( A @ meet_of_latt_set ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ ( A @ latt_set_smaller ) ) )
=> ( B @ ( D @ ( A @ below_refl ) ) ) ) )
& ( C @ ( B @ ( A @ latt_set_smaller ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(149,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ apply_binary ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_binop_1) ).
thf(1800,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ apply_binary ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(618,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ~ ( B @ ( C @ are_equipotent ) )
& ( B @ ( C @ subset ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( B @ ( C @ powerset @ in ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ subset ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(5338,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ~ ( B @ ( C @ are_equipotent ) )
& ( B @ ( C @ subset ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( B @ ( C @ powerset @ in ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ subset ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(370,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ empty_carrier_subset @ v5_membered )
& ( A @ empty_carrier_subset @ v4_membered )
& ( A @ empty_carrier_subset @ v3_membered )
& ( A @ empty_carrier_subset @ v2_membered )
& ( A @ empty_carrier_subset @ v1_membered )
& ( A @ empty_carrier_subset @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_pre_topc) ).
thf(3638,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ empty_carrier_subset @ v5_membered )
& ( A @ empty_carrier_subset @ v4_membered )
& ( A @ empty_carrier_subset @ v3_membered )
& ( A @ empty_carrier_subset @ v2_membered )
& ( A @ empty_carrier_subset @ v1_membered )
& ( A @ empty_carrier_subset @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(1087,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ ( A @ relation_rng_restriction ) @ function )
& ( B @ ( A @ relation_rng_restriction ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(4617,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ ( A @ relation_rng_restriction ) @ function )
& ( B @ ( A @ relation_rng_restriction ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(596,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ latt_set_smaller ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( D @ ( B @ ( A @ below ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice3) ).
thf(5199,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( D @ ( B @ ( A @ below ) ) ) ) )
=> ( C @ ( B @ ( A @ latt_set_smaller ) ) ) )
& ( ( C @ ( B @ ( A @ latt_set_smaller ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( D @ ( B @ ( A @ below ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(451,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B
= ( A @ relation_rng ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(4179,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_rng ) ) )
& ( ( B
= ( A @ relation_rng ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(774,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(6379,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(769,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(6310,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(275,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_founded_relation )
<=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ ( A @ fiber ) @ disjoint ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set )
& ( A @ relation_field @ ( B @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
thf(2767,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ ( A @ fiber ) @ disjoint ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set )
& ( A @ relation_field @ ( B @ subset ) ) )
=> ( A @ well_founded_relation ) )
& ( ( A @ well_founded_relation )
=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ ( A @ fiber ) @ disjoint ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set )
& ( A @ relation_field @ ( B @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(647,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ closed_subset ) )
<=> ( A @ ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) @ open_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pre_topc) ).
thf(5480,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) @ open_subset ) )
=> ( A @ ( B @ closed_subset ) ) )
& ( ( A @ ( B @ closed_subset ) )
=> ( A @ ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) @ open_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(464,axiom,
( ( empty_set @ v5_membered )
& ( empty_set @ v4_membered )
& ( empty_set @ v3_membered )
& ( empty_set @ v2_membered )
& ( empty_set @ v1_membered )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
thf(4270,plain,
( ( empty_set @ v5_membered )
& ( empty_set @ v4_membered )
& ( empty_set @ v3_membered )
& ( empty_set @ v2_membered )
& ( empty_set @ v1_membered )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ boole_lattice @ complete_latt_str )
& ( A @ boole_lattice @ boolean_lattstr )
& ( A @ boole_lattice @ complemented_lattstr )
& ( A @ boole_lattice @ bounded_lattstr )
& ( A @ boole_lattice @ upper_bounded_semilattstr )
& ( A @ boole_lattice @ lower_bounded_semilattstr )
& ( A @ boole_lattice @ modular_lattstr )
& ( A @ boole_lattice @ distributive_lattstr )
& ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_knaster) ).
thf(1931,plain,
! [A: $i] :
( ( A @ boole_lattice @ complete_latt_str )
& ( A @ boole_lattice @ boolean_lattstr )
& ( A @ boole_lattice @ complemented_lattstr )
& ( A @ boole_lattice @ bounded_lattstr )
& ( A @ boole_lattice @ upper_bounded_semilattstr )
& ( A @ boole_lattice @ lower_bounded_semilattstr )
& ( A @ boole_lattice @ modular_lattstr )
& ( A @ boole_lattice @ distributive_lattstr )
& ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equipotent ) )
=> ( A @ ( B @ equipotent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_wellord2) ).
thf(1568,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ equipotent ) )
=> ( A @ ( B @ equipotent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ boolean_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_waybel_1) ).
thf(1100,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ boolean_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ powerset @ ( C @ ( B @ ( A @ unordered_pair_as_carrier_subset ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(5617,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ powerset @ ( C @ ( B @ ( A @ unordered_pair_as_carrier_subset ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(605,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( B @ ( A @ ( C @ point_neighbourhood ) ) )
<=> ( C @ ( A @ interior ) @ ( B @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
thf(5264,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( ( C @ ( A @ interior ) @ ( B @ in ) )
=> ( B @ ( A @ ( C @ point_neighbourhood ) ) ) )
& ( ( B @ ( A @ ( C @ point_neighbourhood ) ) )
=> ( C @ ( A @ interior ) @ ( B @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ transitive )
=> ( A @ ( B @ relation_restriction ) @ transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_wellord1) ).
thf(4018,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ transitive )
=> ( A @ ( B @ relation_restriction ) @ transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(231,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(2451,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(357,axiom,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_membered) ).
thf(3525,plain,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(529,axiom,
! [A: $i] :
( ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lattice3) ).
thf(4724,plain,
! [A: $i] :
( ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(173,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ( ( A @ incl_POSet @ antisymmetric_relstr )
& ( A @ incl_POSet @ transitive_relstr )
& ( A @ incl_POSet @ reflexive_relstr )
& ( A @ incl_POSet @ strict_rel_str )
& ~ ( A @ incl_POSet @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_yellow_1) ).
thf(1978,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ( ( A @ incl_POSet @ antisymmetric_relstr )
& ( A @ incl_POSet @ transitive_relstr )
& ( A @ incl_POSet @ reflexive_relstr )
& ( A @ incl_POSet @ strict_rel_str )
& ~ ( A @ incl_POSet @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(569,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_orders_2) ).
thf(5032,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( B @ ( A @ ordinal_subset ) )
<=> ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(4686,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( ( B @ ( A @ subset ) )
=> ( B @ ( A @ ordinal_subset ) ) )
& ( ( B @ ( A @ ordinal_subset ) )
=> ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( A @ ( B @ set_intersection2 ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc28_membered) ).
thf(4556,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( A @ ( B @ set_intersection2 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( ( B @ relation_field @ ( A @ subset ) )
& ( B @ well_ordering ) )
=> ( ( A @ ( B @ relation_restriction ) @ relation_field )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_wellord1) ).
thf(1302,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( ( B @ relation_field @ ( A @ subset ) )
& ( B @ well_ordering ) )
=> ( ( A @ ( B @ relation_restriction ) @ relation_field )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( C @ ( B @ ( A @ meet ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(5892,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( C @ ( B @ ( A @ meet ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(418,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
thf(3966,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_inverse_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(505,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( D
= ( B @ singleton ) )
& ( A @ ( B @ in ) )
& ( C
= ( B @ singleton ) )
& ( A @ ( B @ in ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( C
= ( D @ singleton ) )
& ( A @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__1) ).
thf(4583,plain,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( D
= ( B @ singleton ) )
& ( A @ ( B @ in ) )
& ( C
= ( B @ singleton ) )
& ( A @ ( B @ in ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ singleton ) )
& ( A @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ singleton ) )
& ( A @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(483,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( C
= ( B @ ( A @ relation_composition ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(4443,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_composition ) ) ) )
& ( ( C
= ( B @ ( A @ relation_composition ) ) )
=> ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ~ ( B @ empty_carrier )
& ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ latt_str )
& ( B @ ( A @ k8_filter_1 ) @ strict_latt_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_1) ).
thf(2105,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ~ ( B @ empty_carrier )
& ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ latt_str )
& ( B @ ( A @ k8_filter_1 ) @ strict_latt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ( A @ one_sorted_str ) )
=> ( ( D @ ( C @ ( B @ ( A @ function_invverse_img_as_carrier_subset ) ) ) )
= ( D @ ( C @ relation_inverse_image ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_pre_topc) ).
thf(5597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ( A @ one_sorted_str ) )
=> ( ( D @ ( C @ ( B @ ( A @ function_invverse_img_as_carrier_subset ) ) ) )
= ( D @ ( C @ relation_inverse_image ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( A @ ( A @ ordinal_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(1450,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( A @ ( A @ ordinal_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(75,axiom,
! [A: $i,B: $i] : ( A @ ( A @ equipotent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_wellord2) ).
thf(1334,plain,
! [A: $i] : ( A @ ( A @ equipotent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(755,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( B @ ( A @ bottom_of_relstr @ ( A @ related ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_yellow_0) ).
thf(6189,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( B @ ( A @ bottom_of_relstr @ ( A @ related ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(586,axiom,
! [A: $i] :
( ( A @ powerset @ preboolean )
& ( A @ powerset @ diff_closed )
& ( A @ powerset @ cup_closed )
& ~ ( A @ powerset @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(5135,plain,
! [A: $i] :
( ( A @ powerset @ preboolean )
& ( A @ powerset @ diff_closed )
& ( A @ powerset @ cup_closed )
& ~ ( A @ powerset @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(310,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(3093,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(641,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ in ) )
=> ( ( B @ ( A @ topstr_closure ) @ ( C @ in ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( ( D @ ( B @ subset ) )
& ( A @ ( D @ closed_subset ) ) )
=> ( D @ ( C @ in ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_pre_topc) ).
thf(5457,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ in ) )
=> ( ( ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( ( D @ ( B @ subset ) )
& ( A @ ( D @ closed_subset ) ) )
=> ( D @ ( C @ in ) ) ) )
=> ( B @ ( A @ topstr_closure ) @ ( C @ in ) ) )
& ( ( B @ ( A @ topstr_closure ) @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( ( D @ ( B @ subset ) )
& ( A @ ( D @ closed_subset ) ) )
=> ( D @ ( C @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(624,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ closed_subsets ) )
<=> ( A @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ open_subsets ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tops_2) ).
thf(5360,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ open_subsets ) )
=> ( A @ ( B @ closed_subsets ) ) )
& ( ( A @ ( B @ closed_subsets ) )
=> ( A @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ open_subsets ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(5045,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(627,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ interior ) )
= ( B @ ( A @ the_carrier @ subset_complement ) @ ( A @ topstr_closure ) @ ( A @ the_carrier @ subset_complement ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
thf(5379,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ interior ) )
= ( B @ ( A @ the_carrier @ subset_complement ) @ ( A @ topstr_closure ) @ ( A @ the_carrier @ subset_complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(4996,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(591,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( B @ ( A @ topstr_closure ) @ ( B @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_pre_topc) ).
thf(5169,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( B @ ( A @ topstr_closure ) @ ( B @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ function )
& ( A @ relation ) )
=> ( B @ ( A @ relation_image ) @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(2103,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ function )
& ( A @ relation ) )
=> ( B @ ( A @ relation_image ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(745,axiom,
! [A: $i,B: $i] :
( ( A @ boole_lattice @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_lattice @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ boole_lattice @ below ) ) )
<=> ( C @ ( B @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
thf(6156,plain,
! [A: $i,B: $i] :
( ( A @ boole_lattice @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_lattice @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ subset ) )
=> ( C @ ( B @ ( A @ boole_lattice @ below ) ) ) )
& ( ( C @ ( B @ ( A @ boole_lattice @ below ) ) )
=> ( C @ ( B @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ? [D: $i] :
( ! [E: $i,F: $i] :
( ( D @ ( F @ ( E @ ordered_pair ) @ in ) )
<=> ( ( B @ ( F @ ( C @ apply ) @ ( E @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ ( F @ in ) )
& ( A @ ( E @ in ) ) ) )
& ( D @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_relat_1__e6_21__wellord2) ).
thf(1696,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ? [D: $i] :
( ! [E: $i,F: $i] :
( ( ( ( B @ ( F @ ( C @ apply ) @ ( E @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ ( F @ in ) )
& ( A @ ( E @ in ) ) )
=> ( D @ ( F @ ( E @ ordered_pair ) @ in ) ) )
& ( ( D @ ( F @ ( E @ ordered_pair ) @ in ) )
=> ( ( B @ ( F @ ( C @ apply ) @ ( E @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ ( F @ in ) )
& ( A @ ( E @ in ) ) ) ) )
& ( D @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_intersection2 ) @ ( C @ ( A @ set_intersection2 ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(1975,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_intersection2 ) @ ( C @ ( A @ set_intersection2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(426,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice3) ).
thf(4055,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(4230,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ relation_dom @ ( A @ relation_rng @ subset ) )
=> ( ( B @ ( A @ relation_composition ) @ relation_dom )
= ( A @ relation_dom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
thf(1447,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ relation_dom @ ( A @ relation_rng @ subset ) )
=> ( ( B @ ( A @ relation_composition ) @ relation_dom )
= ( A @ relation_dom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(583,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(5101,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(224,axiom,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(2371,plain,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(4364,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(42,axiom,
! [A: $i] : ( A @ inclusion_relation @ relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(1119,plain,
! [A: $i] : ( A @ inclusion_relation @ relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(600,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( ( A @ ( B @ full_subrelstr ) )
<=> ( ( B @ the_InternalRel )
= ( B @ the_carrier @ ( A @ the_InternalRel @ relation_restriction_as_relation_of ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_yellow_0) ).
thf(5246,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( ( ( ( B @ the_InternalRel )
= ( B @ the_carrier @ ( A @ the_InternalRel @ relation_restriction_as_relation_of ) ) )
=> ( A @ ( B @ full_subrelstr ) ) )
& ( ( A @ ( B @ full_subrelstr ) )
=> ( ( B @ the_InternalRel )
= ( B @ the_carrier @ ( A @ the_InternalRel @ relation_restriction_as_relation_of ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( A @ ( B @ relation_image ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
thf(1526,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( A @ ( B @ relation_image ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ? [E: $i] :
( ! [F: $i] :
( ( E @ ( F @ in ) )
=> ( B @ ( F @ ( D @ ordered_pair ) @ in ) ) )
& ( E @ ( D @ in ) )
& ( C = E ) )
& ( A @ ( C @ in ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ ( D @ in ) )
=> ? [E: $i] :
( ! [F: $i] :
( ( E @ ( F @ in ) )
=> ( B @ ( F @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) ) )
& ( E @ ( D @ ( C @ apply ) @ in ) )
& ( D = E ) ) )
& ( ( C @ relation_dom )
= A )
& ( C @ function )
& ( C @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e10_24__wellord2) ).
thf(4379,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ? [E: $i] :
( ! [F: $i] :
( ( E @ ( F @ in ) )
=> ( B @ ( F @ ( D @ ordered_pair ) @ in ) ) )
& ( E @ ( D @ in ) )
& ( C = E ) )
& ( A @ ( C @ in ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ ( D @ in ) )
=> ? [E: $i] :
( ! [F: $i] :
( ( E @ ( F @ in ) )
=> ( B @ ( F @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) ) )
& ( E @ ( D @ ( C @ apply ) @ in ) )
& ( D = E ) ) )
& ( ( C @ relation_dom )
= A )
& ( C @ function )
& ( C @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(549,axiom,
? [A: $i] :
( ( A @ boolean_lattstr )
& ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ distributive_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_lattices) ).
thf(4892,plain,
? [A: $i] :
( ( A @ boolean_lattstr )
& ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ distributive_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( B = empty_set )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
<=> ( C = empty_set ) )
| ( A = empty_set ) ) )
& ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
<=> ( A
= ( C @ ( B @ ( A @ relation_dom_as_subset ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
thf(3559,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( B = empty_set )
=> ( ( ( ( C = empty_set )
=> ( B @ ( A @ ( C @ quasi_total ) ) ) )
& ( ( B @ ( A @ ( C @ quasi_total ) ) )
=> ( C = empty_set ) ) )
| ( A = empty_set ) ) )
& ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( ( A
= ( C @ ( B @ ( A @ relation_dom_as_subset ) ) ) )
=> ( B @ ( A @ ( C @ quasi_total ) ) ) )
& ( ( B @ ( A @ ( C @ quasi_total ) ) )
=> ( A
= ( C @ ( B @ ( A @ relation_dom_as_subset ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str )
& ~ ( C @ ( B @ ( A @ latt_str_of ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
thf(3582,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str )
& ~ ( C @ ( B @ ( A @ latt_str_of ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(789,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) )
= ( B @ ( A @ union_of_subsets ) @ ( A @ subset_complement ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tops_2) ).
thf(6529,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) )
= ( B @ ( A @ union_of_subsets ) @ ( A @ subset_complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(590,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ directed_subset ) )
<=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ~ ( ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ~ ( ( E @ ( D @ ( A @ related ) ) )
& ( E @ ( C @ ( A @ related ) ) )
& ( B @ ( E @ in ) ) ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_waybel_0) ).
thf(5157,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ~ ( ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ~ ( ( E @ ( D @ ( A @ related ) ) )
& ( E @ ( C @ ( A @ related ) ) )
& ( B @ ( E @ in ) ) ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) ) ) )
=> ( A @ ( B @ directed_subset ) ) )
& ( ( A @ ( B @ directed_subset ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ~ ( ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ~ ( ( E @ ( D @ ( A @ related ) ) )
& ( E @ ( C @ ( A @ related ) ) )
& ( B @ ( E @ in ) ) ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(3503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(487,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ relation_dom @ ( B @ in ) )
=> ( ( C
= ( B @ ( A @ apply ) ) )
<=> ( C = empty_set ) ) )
& ( ( A @ relation_dom @ ( B @ in ) )
=> ( ( C
= ( B @ ( A @ apply ) ) )
<=> ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(4480,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ relation_dom @ ( B @ in ) )
=> ( ( ( C = empty_set )
=> ( C
= ( B @ ( A @ apply ) ) ) )
& ( ( C
= ( B @ ( A @ apply ) ) )
=> ( C = empty_set ) ) ) )
& ( ( A @ relation_dom @ ( B @ in ) )
=> ( ( ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( C
= ( B @ ( A @ apply ) ) ) )
& ( ( C
= ( B @ ( A @ apply ) ) )
=> ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ latt_str_of ) ) )
= ( F @ ( E @ ( D @ latt_str_of ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(4531,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ latt_str_of ) ) )
= ( F @ ( E @ ( D @ latt_str_of ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(636,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ poset_of_lattice @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) )
<=> ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_element_smaller ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattice3) ).
thf(5443,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ poset_of_lattice @ the_carrier @ ( C @ element ) )
=> ( ( ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_element_smaller ) ) )
=> ( C @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) ) )
& ( ( C @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) )
=> ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_element_smaller ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(764,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) )
=> ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) ) )
& ( ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_yellow_0) ).
thf(6250,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) )
=> ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) ) )
& ( ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(570,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(5034,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(649,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( C @ the_carrier @ ( F @ element ) )
=> ! [G: $i] :
( ( C @ the_carrier @ ( G @ element ) )
=> ( ( ( G @ ( F @ ( C @ related ) ) )
& ( E = G )
& ( D = F ) )
=> ( E @ ( D @ ( B @ related ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_yellow_6) ).
thf(5487,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( C @ the_carrier @ ( F @ element ) )
=> ! [G: $i] :
( ( C @ the_carrier @ ( G @ element ) )
=> ( ( ( G @ ( F @ ( C @ related ) ) )
& ( E = G )
& ( D = F ) )
=> ( E @ ( D @ ( B @ related ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(550,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( A @ ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
thf(4910,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( A @ ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(240,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_inverse @ relation )
& ( A @ relation_inverse @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(2496,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_inverse @ relation )
& ( A @ relation_inverse @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(142,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(1768,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(593,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( ( A @ compact_top_space )
<=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) )
=> ~ ( ( C @ finite )
& ( C @ ( A @ is_a_cover_of_carrier ) )
& ( B @ ( C @ subset ) ) ) )
& ( A @ ( B @ open_subsets ) )
& ( B @ ( A @ is_a_cover_of_carrier ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_compts_1) ).
thf(5174,plain,
! [A: $i] :
( ( A @ top_str )
=> ( ( ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) )
=> ~ ( ( C @ finite )
& ( C @ ( A @ is_a_cover_of_carrier ) )
& ( B @ ( C @ subset ) ) ) )
& ( A @ ( B @ open_subsets ) )
& ( B @ ( A @ is_a_cover_of_carrier ) ) ) )
=> ( A @ compact_top_space ) )
& ( ( A @ compact_top_space )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) )
=> ~ ( ( C @ finite )
& ( C @ ( A @ is_a_cover_of_carrier ) )
& ( B @ ( C @ subset ) ) ) )
& ( A @ ( B @ open_subsets ) )
& ( B @ ( A @ is_a_cover_of_carrier ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ relation_of2_as_subset ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
<=> ( ( C @ ( A @ ( B @ relation_dom_as_subset ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).
thf(3097,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( ( C @ ( A @ ( B @ relation_dom_as_subset ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( ( C @ ( A @ ( B @ relation_dom_as_subset ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(694,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_intersection2 ) ) )
= ( B @ ( C @ ( A @ subset_intersection2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(5783,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_intersection2 ) ) )
= ( B @ ( C @ ( A @ subset_intersection2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(469,axiom,
? [A: $i] :
( ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).
thf(4323,plain,
? [A: $i] :
( ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(753,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( A @ ( B @ ( A @ interior ) @ open_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
thf(6183,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( A @ ( B @ ( A @ interior ) @ open_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ reflexive )
<=> ! [B: $i] :
( ( A @ relation_field @ ( B @ in ) )
=> ( A @ ( B @ ( B @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
thf(2473,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i] :
( ( A @ relation_field @ ( B @ in ) )
=> ( A @ ( B @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ reflexive ) )
& ( ( A @ reflexive )
=> ! [B: $i] :
( ( A @ relation_field @ ( B @ in ) )
=> ( A @ ( B @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(70,axiom,
! [A: $i] : ( A @ inclusion_relation @ antisymmetric ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).
thf(1311,plain,
! [A: $i] : ( A @ inclusion_relation @ antisymmetric ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( B @ ( C @ ( A @ subset_union2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(5862,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( B @ ( C @ ( A @ subset_union2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i,G: $i] :
( ( G
= ( F @ singleton ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C = E )
& ? [F: $i,G: $i] :
( ( G
= ( F @ singleton ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= D ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ? [F: $i,G: $i] :
( ( G
= ( F @ singleton ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= D ) )
& ( E = D )
& ( B @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
thf(3418,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i,G: $i] :
( ( G
= ( F @ singleton ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C = E )
& ? [F: $i,G: $i] :
( ( G
= ( F @ singleton ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= D ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ? [E: $i] :
( ? [F: $i,G: $i] :
( ( G
= ( F @ singleton ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= D ) )
& ( E = D )
& ( B @ ( A @ cartesian_product2 ) @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ? [F: $i,G: $i] :
( ( G
= ( F @ singleton ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= D ) )
& ( E = D )
& ( B @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(554,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice2) ).
thf(4925,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(393,axiom,
? [A: $i] :
( ( A @ connected_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_waybel_0) ).
thf(3795,plain,
? [A: $i] :
( ( A @ connected_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( B @ relation_rng @ ( A @ in ) )
& ( B @ one_to_one ) )
=> ( ( A
= ( A @ ( B @ ( B @ function_inverse @ relation_composition ) @ apply ) ) )
& ( A
= ( A @ ( B @ function_inverse @ apply ) @ ( B @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(1047,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( B @ relation_rng @ ( A @ in ) )
& ( B @ one_to_one ) )
=> ( ( A
= ( A @ ( B @ ( B @ function_inverse @ relation_composition ) @ apply ) ) )
& ( A
= ( A @ ( B @ function_inverse @ apply ) @ ( B @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(138,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ bounded_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).
thf(1730,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ bounded_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) )
=> ( A @ bounded_relstr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(894,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) )
=> ( A @ bounded_relstr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(742,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(6122,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ distributive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_waybel_1) ).
thf(825,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ distributive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_arytm_3) ).
thf(1255,plain,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ reflexive )
<=> ( A @ relation_field @ ( A @ is_reflexive_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
thf(1123,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_reflexive_in ) )
=> ( A @ reflexive ) )
& ( ( A @ reflexive )
=> ( A @ relation_field @ ( A @ is_reflexive_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(640,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( A @ the_carrier @ powerset @ powerset @ ( A @ the_topology @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(5455,plain,
! [A: $i] :
( ( A @ top_str )
=> ( A @ the_carrier @ powerset @ powerset @ ( A @ the_topology @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(656,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ the_carrier @ complements_of_subsets ) @ finite )
<=> ( B @ finite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_tops_2) ).
thf(5507,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( ( B @ finite )
=> ( B @ ( A @ the_carrier @ complements_of_subsets ) @ finite ) )
& ( ( B @ ( A @ the_carrier @ complements_of_subsets ) @ finite )
=> ( B @ finite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i,G: $i] :
( ? [H: $i] :
( ! [I: $i] :
( ( H @ ( I @ in ) )
=> ( B @ ( I @ ( G @ ordered_pair ) @ in ) ) )
& ( H @ ( G @ in ) )
& ( F = H ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e10_24__wellord2__1) ).
thf(3664,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( ( ? [F: $i,G: $i] :
( ? [H: $i] :
( ! [I: $i] :
( ( H @ ( I @ in ) )
=> ( B @ ( I @ ( G @ ordered_pair ) @ in ) ) )
& ( H @ ( G @ in ) )
& ( F = H ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( A @ cartesian_product2 ) @ ( E @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ( ? [F: $i,G: $i] :
( ? [H: $i] :
( ! [I: $i] :
( ( H @ ( I @ in ) )
=> ( B @ ( I @ ( G @ ordered_pair ) @ in ) ) )
& ( H @ ( G @ in ) )
& ( F = H ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(3471,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(552,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ identity_as_relation_of @ relation_of2_as_subset ) ) )
& ( A @ ( A @ ( A @ identity_as_relation_of @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(4915,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ identity_as_relation_of @ relation_of2_as_subset ) ) )
& ( A @ ( A @ ( A @ identity_as_relation_of @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(228,axiom,
! [A: $i] :
( ( A @ centered )
<=> ( ! [B: $i] :
~ ( ( ( B @ set_meet )
= empty_set )
& ( B @ finite )
& ( A @ ( B @ subset ) )
& ( B != empty_set ) )
& ( A != empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_compts_1) ).
thf(2409,plain,
! [A: $i] :
( ( ( ! [B: $i] :
~ ( ( ( B @ set_meet )
= empty_set )
& ( B @ finite )
& ( A @ ( B @ subset ) )
& ( B != empty_set ) )
& ( A != empty_set ) )
=> ( A @ centered ) )
& ( ( A @ centered )
=> ( ! [B: $i] :
~ ( ( ( B @ set_meet )
= empty_set )
& ( B @ finite )
& ( A @ ( B @ subset ) )
& ( B != empty_set ) )
& ( A != empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(484,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( B @ ( A @ meet_of_latt_set ) )
= ( B @ ( A @ a_2_2_lattice3 ) @ ( A @ join_of_latt_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d22_lattice3) ).
thf(4466,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( B @ ( A @ meet_of_latt_set ) )
= ( B @ ( A @ a_2_2_lattice3 ) @ ( A @ join_of_latt_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_inverse @ relation_inverse )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(1091,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_inverse @ relation_inverse )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(795,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i,G: $i] :
( ! [H: $i] :
( ( A @ the_carrier @ powerset @ ( H @ element ) )
=> ( ( H = F )
=> ( G
= ( H @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ cartesian_product2 ) @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_7_1__tops_2__1) ).
thf(6550,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( ( ? [F: $i,G: $i] :
( ! [H: $i] :
( ( A @ the_carrier @ powerset @ ( H @ element ) )
=> ( ( H = F )
=> ( G
= ( H @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ cartesian_product2 ) @ ( E @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ( ? [F: $i,G: $i] :
( ! [H: $i] :
( ( A @ the_carrier @ powerset @ ( H @ element ) )
=> ( ( H = F )
=> ( G
= ( H @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ cartesian_product2 ) @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ being_limit_ordinal )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal2) ).
thf(1021,plain,
? [A: $i] :
( ( A @ being_limit_ordinal )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(249,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( D @ ordinal )
& ( B = D )
& ( C @ ordinal )
& ( B = C ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( C @ ordinal )
& ( D = C )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
thf(2596,plain,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( D @ ordinal )
& ( B = D )
& ( C @ ordinal )
& ( B = C ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( ? [D: $i] :
( ( C @ ordinal )
& ( D = C )
& ( A @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C @ ordinal )
& ( D = C )
& ( A @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(566,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_orders_2) ).
thf(5002,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(1570,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(564,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_0) ).
thf(4989,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(620,axiom,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ meet_of_latt_set ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(5349,plain,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ meet_of_latt_set ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( C @ relation_field @ ( B @ in ) )
& ( C @ relation_field @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(1676,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( C @ relation_field @ ( B @ in ) )
& ( C @ relation_field @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ relation_rng @ ( A @ subset ) )
=> ( ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
thf(3752,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ relation_rng @ ( A @ subset ) )
=> ( ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(322,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( B @ rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(3239,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_inverse_image ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( D @ ( A @ ordered_pair ) @ in ) )
& ( C @ relation_rng @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
thf(4204,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( D @ ( A @ ordered_pair ) @ in ) )
& ( C @ relation_rng @ ( D @ in ) ) )
=> ( B @ ( C @ relation_inverse_image ) @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_inverse_image ) @ ( A @ in ) )
=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( D @ ( A @ ordered_pair ) @ in ) )
& ( C @ relation_rng @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(644,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( B @ the_carrier @ ( C @ the_carrier @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_yellow_6) ).
thf(5470,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( B @ the_carrier @ ( C @ the_carrier @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(537,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(4785,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(490,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(4499,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ set_intersection2 ) @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(3134,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ set_intersection2 ) @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ( ( C @ ( B @ disjoint ) )
<=> ( C @ ( A @ subset_complement ) @ ( B @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
thf(5085,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ( ( ( C @ ( A @ subset_complement ) @ ( B @ subset ) )
=> ( C @ ( B @ disjoint ) ) )
& ( ( C @ ( B @ disjoint ) )
=> ( C @ ( A @ subset_complement ) @ ( B @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(191,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2132,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(542,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B
= ( A @ function_inverse ) )
<=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) ) )
& ( ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) )
=> ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
& ( ( B @ relation_dom )
= ( A @ relation_rng ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(4836,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) ) )
& ( ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) )
=> ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
& ( ( B @ relation_dom )
= ( A @ relation_rng ) ) )
=> ( B
= ( A @ function_inverse ) ) )
& ( ( B
= ( A @ function_inverse ) )
=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) ) )
& ( ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) )
=> ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
& ( ( B @ relation_dom )
= ( A @ relation_rng ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(668,axiom,
! [A: $i] :
( ( A @ powerset @ union )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(5594,plain,
! [A: $i] :
( ( A @ powerset @ union )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(298,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( A @ cast_as_carrier_subset @ closed_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(2958,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( A @ cast_as_carrier_subset @ closed_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(466,axiom,
( ~ ( omega @ empty )
& ( omega @ ordinal )
& ( omega @ epsilon_connected )
& ( omega @ epsilon_transitive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal2) ).
thf(4280,plain,
( ~ ( omega @ empty )
& ( omega @ ordinal )
& ( omega @ epsilon_connected )
& ( omega @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(262,axiom,
? [A: $i] :
( ~ ( A @ v1_yellow_3 )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_yellow_3) ).
thf(2670,plain,
? [A: $i] :
( ~ ( A @ v1_yellow_3 )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(4608,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(425,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(4053,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= F ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( B @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_2__tops_2__2) ).
thf(6427,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= F ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( B @ cartesian_product2 ) @ ( F @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( B @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(261,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ v1_partfun1 ) ) )
& ( A @ the_InternalRel @ transitive )
& ( A @ the_InternalRel @ antisymmetric )
& ( A @ the_InternalRel @ reflexive )
& ( A @ the_InternalRel @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_orders_2) ).
thf(2663,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ v1_partfun1 ) ) )
& ( A @ the_InternalRel @ transitive )
& ( A @ the_InternalRel @ antisymmetric )
& ( A @ the_InternalRel @ reflexive )
& ( A @ the_InternalRel @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(662,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ powerset @ powerset @ ( C @ element ) )
=> ( ( C
= ( B @ ( A @ complements_of_subsets ) ) )
<=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
<=> ( B @ ( D @ ( A @ subset_complement ) @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(5534,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ powerset @ powerset @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( B @ ( D @ ( A @ subset_complement ) @ in ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ subset_complement ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ complements_of_subsets ) ) ) )
& ( ( C
= ( B @ ( A @ complements_of_subsets ) ) )
=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( B @ ( D @ ( A @ subset_complement ) @ in ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ subset_complement ) @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(692,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ open_subset ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ closed_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_tops_1) ).
thf(5779,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ open_subset ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ closed_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(195,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(2179,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(571,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( A @ ( C @ net_str ) )
=> ( ( B @ ( A @ ( C @ subnetstr ) ) )
<=> ( ( ( C @ ( A @ the_mapping ) )
= ( C @ the_carrier @ ( B @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( B @ the_carrier @ relation_dom_restr_as_relation_of ) ) ) ) )
& ( B @ ( C @ subrelstr ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_yellow_6) ).
thf(5038,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( A @ ( C @ net_str ) )
=> ( ( ( ( ( C @ ( A @ the_mapping ) )
= ( C @ the_carrier @ ( B @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( B @ the_carrier @ relation_dom_restr_as_relation_of ) ) ) ) )
& ( B @ ( C @ subrelstr ) ) )
=> ( B @ ( A @ ( C @ subnetstr ) ) ) )
& ( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( ( ( C @ ( A @ the_mapping ) )
= ( C @ the_carrier @ ( B @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( B @ the_carrier @ relation_dom_restr_as_relation_of ) ) ) ) )
& ( B @ ( C @ subrelstr ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(562,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( A @ the_carrier @ powerset @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
thf(4979,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( A @ the_carrier @ powerset @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( A @ the_carrier @ powerset @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(221,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( D
= ( B @ singleton ) )
& ( A @ ( B @ in ) )
& ( C
= ( B @ singleton ) )
& ( A @ ( B @ in ) ) )
=> ( C = D ) )
=> ? [B: $i] :
( ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
<=> ( ( D
= ( C @ singleton ) )
& ( A @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ( B @ function )
& ( B @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e16_22__wellord2__1) ).
thf(2345,plain,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( D
= ( B @ singleton ) )
& ( A @ ( B @ in ) )
& ( C
= ( B @ singleton ) )
& ( A @ ( B @ in ) ) )
=> ( C = D ) )
=> ? [B: $i] :
( ! [C: $i,D: $i] :
( ( ( ( D
= ( C @ singleton ) )
& ( A @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( ( D
= ( C @ singleton ) )
& ( A @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) ) )
& ( B @ function )
& ( B @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(202,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
thf(2211,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(65,axiom,
! [A: $i] :
( ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_inverse @ function )
& ( A @ relation_inverse @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(1281,plain,
! [A: $i] :
( ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_inverse @ function )
& ( A @ relation_inverse @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(206,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ reflexive_relstr )
& ( A @ trivial_carrier )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ v2_waybel_3 )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_waybel_3) ).
thf(2228,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ reflexive_relstr )
& ( A @ trivial_carrier )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ v2_waybel_3 )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ relation_of2 ) ) )
& ( C @ ( B @ ( E @ quasi_total ) ) )
& ( E @ function )
& ( B @ ( A @ ( D @ relation_of2 ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ function_of_composition ) ) ) ) @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ function_of_composition ) ) ) ) @ quasi_total ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ function_of_composition ) ) ) ) @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(2653,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ relation_of2 ) ) )
& ( C @ ( B @ ( E @ quasi_total ) ) )
& ( E @ function )
& ( B @ ( A @ ( D @ relation_of2 ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ function_of_composition ) ) ) ) @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ function_of_composition ) ) ) ) @ quasi_total ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ function_of_composition ) ) ) ) @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
thf(1027,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(203,axiom,
( ( ( empty_set @ relation_rng )
= empty_set )
& ( ( empty_set @ relation_dom )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(2213,plain,
( ( ( empty_set @ relation_rng )
= empty_set )
& ( ( empty_set @ relation_dom )
= empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(702,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ empty_carrier )
<=> ( A @ the_carrier @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
thf(5858,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( ( A @ the_carrier @ empty )
=> ( A @ empty_carrier ) )
& ( ( A @ empty_carrier )
=> ( A @ the_carrier @ empty ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(437,axiom,
! [A: $i] :
( ? [B: $i] :
( ( A @ ( B @ in ) )
& ( B @ ordinal ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( C @ ordinal )
=> ( ( A @ ( C @ in ) )
=> ( C @ ( B @ ordinal_subset ) ) ) )
& ( A @ ( B @ in ) )
& ( B @ ordinal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
thf(4104,plain,
! [A: $i] :
( ? [B: $i] :
( ( A @ ( B @ in ) )
& ( B @ ordinal ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( C @ ordinal )
=> ( ( A @ ( C @ in ) )
=> ( C @ ( B @ ordinal_subset ) ) ) )
& ( A @ ( B @ in ) )
& ( B @ ordinal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(3408,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(1740,plain,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(166,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ complete_relstr )
& ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ bounded_relstr )
& ( A @ poset_of_lattice @ upper_bounded_relstr )
& ( A @ poset_of_lattice @ lower_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_yellow_1) ).
thf(1910,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ complete_relstr )
& ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ bounded_relstr )
& ( A @ poset_of_lattice @ upper_bounded_relstr )
& ( A @ poset_of_lattice @ lower_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field @ ( A @ well_orders ) )
<=> ( A @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_wellord1) ).
thf(842,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ well_ordering )
=> ( A @ relation_field @ ( A @ well_orders ) ) )
& ( ( A @ relation_field @ ( A @ well_orders ) )
=> ( A @ well_ordering ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ relation_dom_restr_as_relation_of ) ) ) @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_1) ).
thf(1573,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ relation_dom_restr_as_relation_of ) ) ) @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(615,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(5330,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(48,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(1143,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(633,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ connected_relstr )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_waybel_3) ).
thf(5423,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ connected_relstr )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ v3_waybel_3 )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ v2_waybel_3 )
& ( A @ up_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_waybel_3) ).
thf(1328,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ v3_waybel_3 )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ v2_waybel_3 )
& ( A @ up_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ connected )
=> ( A @ ( B @ relation_restriction ) @ connected ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_wellord1) ).
thf(1121,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ connected )
=> ( A @ ( B @ relation_restriction ) @ connected ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(538,axiom,
! [A: $i] :
( ( A @ relation )
<=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ ordered_pair ) ) )
& ( A @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(4789,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ ordered_pair ) ) )
& ( A @ ( B @ in ) ) )
=> ( A @ relation ) )
& ( ( A @ relation )
=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ ordered_pair ) ) )
& ( A @ ( B @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_image ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
thf(4636,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ relation_image ) @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_image ) @ ( A @ in ) )
=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(438,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B
= ( A @ relation_inverse ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
<=> ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(4109,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_inverse ) ) )
& ( ( B
= ( A @ relation_inverse ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( E = F ) )
& ( A @ ( E @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__1) ).
thf(3205,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ? [E: $i] :
( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( E = F ) )
& ( A @ ( E @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( E = F ) )
& ( A @ ( E @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(587,axiom,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ powerset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(5145,plain,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ powerset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( A @ ( B @ set_intersection2 ) @ v4_membered )
& ( A @ ( B @ set_intersection2 ) @ v3_membered )
& ( A @ ( B @ set_intersection2 ) @ v2_membered )
& ( A @ ( B @ set_intersection2 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc34_membered) ).
thf(3254,plain,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( A @ ( B @ set_intersection2 ) @ v4_membered )
& ( A @ ( B @ set_intersection2 ) @ v3_membered )
& ( A @ ( B @ set_intersection2 ) @ v2_membered )
& ( A @ ( B @ set_intersection2 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(494,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(4512,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(2685,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_restriction ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(1111,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ latt_str )
& ( B @ complete_latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ( ( C @ ( B @ a_2_3_lattice3 ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_lattice3) ).
thf(5577,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ latt_str )
& ( B @ complete_latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) )
=> ( C @ ( B @ a_2_3_lattice3 ) @ ( A @ in ) ) )
& ( ( C @ ( B @ a_2_3_lattice3 ) @ ( A @ in ) )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(58,axiom,
? [A: $i] :
( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ~ ( A @ v1_yellow_3 )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ trivial_carrier )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_7) ).
thf(1227,plain,
? [A: $i] :
( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ~ ( A @ v1_yellow_3 )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ trivial_carrier )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(717,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ ex_sup_of_relstr_set ) )
=> ( ( C
= ( B @ ( A @ join_on_relstr ) ) )
<=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_yellow_0) ).
thf(5919,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ ex_sup_of_relstr_set ) )
=> ( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
=> ( C
= ( B @ ( A @ join_on_relstr ) ) ) )
& ( ( C
= ( B @ ( A @ join_on_relstr ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(730,axiom,
! [A: $i,B: $i] :
( ( ( A @ poset_of_lattice @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ cast_to_el_of_lattice ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice3) ).
thf(5978,plain,
! [A: $i,B: $i] :
( ( ( A @ poset_of_lattice @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ cast_to_el_of_lattice ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(286,axiom,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ordinal ) ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(2858,plain,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ordinal ) ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(711,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ below ) ) )
& ( C @ ( B @ ( A @ below ) ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattices) ).
thf(5889,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ below ) ) )
& ( C @ ( B @ ( A @ below ) ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( B @ ( C @ relation_rng @ subset ) )
& ( A @ ( C @ relation_dom @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
thf(4095,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( B @ ( C @ relation_rng @ subset ) )
& ( A @ ( C @ relation_dom @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ related_reflexive ) ) )
<=> ( C @ ( B @ ( A @ related ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
thf(5951,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( ( C @ ( B @ ( A @ related ) ) )
=> ( C @ ( B @ ( A @ related_reflexive ) ) ) )
& ( ( C @ ( B @ ( A @ related_reflexive ) ) )
=> ( C @ ( B @ ( A @ related ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( A @ function_inverse )
= ( A @ relation_inverse ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
thf(989,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( A @ function_inverse )
= ( A @ relation_inverse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ poset_of_lattice @ the_carrier @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(6218,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ poset_of_lattice @ the_carrier @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(4263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(4676,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(98,axiom,
! [A: $i] : ( A @ identity_relation @ relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(1493,plain,
! [A: $i] : ( A @ identity_relation @ relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ related_reflexive ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
thf(5830,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ related_reflexive ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(787,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ compact_top_space )
<=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( ( B @ ( A @ the_carrier @ meet_of_subsets ) )
= empty_set )
& ( A @ ( B @ closed_subsets ) )
& ( B @ centered ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_compts_1) ).
thf(6518,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ( ( ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( ( B @ ( A @ the_carrier @ meet_of_subsets ) )
= empty_set )
& ( A @ ( B @ closed_subsets ) )
& ( B @ centered ) ) )
=> ( A @ compact_top_space ) )
& ( ( A @ compact_top_space )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( ( B @ ( A @ the_carrier @ meet_of_subsets ) )
= empty_set )
& ( A @ ( B @ closed_subsets ) )
& ( B @ centered ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(685,axiom,
( ( ! [A: $i] :
( ( A @ ordinal )
=> ( ( ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( ( omega @ ( B @ in ) )
=> ! [C: $i] :
( ( B @ powerset @ powerset @ ( C @ element ) )
=> ~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( ( E @ ( D @ subset ) )
& ( C @ ( E @ in ) ) )
=> ( E = D ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set ) ) ) ) ) )
& ( A @ being_limit_ordinal ) )
=> ( ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) )
| ( A = empty_set ) ) ) )
& ! [A: $i] :
( ( A @ ordinal )
=> ( ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) )
=> ( ( omega @ ( A @ succ @ in ) )
=> ! [B: $i] :
( ( A @ succ @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ) ) )
& ( ( omega @ ( empty_set @ in ) )
=> ! [A: $i] :
( ( empty_set @ powerset @ powerset @ ( A @ element ) )
=> ~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( ( C @ ( B @ subset ) )
& ( A @ ( C @ in ) ) )
=> ( C = B ) )
& ( A @ ( B @ in ) ) )
& ( A != empty_set ) ) ) ) )
=> ! [A: $i] :
( ( A @ ordinal )
=> ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_ordinal2__e18_27__finset_1) ).
thf(5694,plain,
( ( ! [A: $i] :
( ( A @ ordinal )
=> ( ( ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( ( omega @ ( B @ in ) )
=> ! [C: $i] :
( ( B @ powerset @ powerset @ ( C @ element ) )
=> ~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( ( E @ ( D @ subset ) )
& ( C @ ( E @ in ) ) )
=> ( E = D ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set ) ) ) ) ) )
& ( A @ being_limit_ordinal ) )
=> ( ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) )
| ( A = empty_set ) ) ) )
& ! [A: $i] :
( ( A @ ordinal )
=> ( ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) )
=> ( ( omega @ ( A @ succ @ in ) )
=> ! [B: $i] :
( ( A @ succ @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ) ) )
& ( ( omega @ ( empty_set @ in ) )
=> ! [A: $i] :
( ( empty_set @ powerset @ powerset @ ( A @ element ) )
=> ~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( ( C @ ( B @ subset ) )
& ( A @ ( C @ in ) ) )
=> ( C = B ) )
& ( A @ ( B @ in ) ) )
& ( A != empty_set ) ) ) ) )
=> ! [A: $i] :
( ( A @ ordinal )
=> ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ full_subnetstr ) ) )
& ( A @ ( C @ strict_net_str ) )
& ~ ( C @ empty_carrier )
& ( B @ ( A @ ( C @ subnetstr ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_yellow_6) ).
thf(2868,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ full_subnetstr ) ) )
& ( A @ ( C @ strict_net_str ) )
& ~ ( C @ empty_carrier )
& ( B @ ( A @ ( C @ subnetstr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(767,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( B = empty_set )
& ( B @ ( A @ is_a_cover_of_carrier ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tops_2) ).
thf(6304,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( B = empty_set )
& ( B @ ( A @ is_a_cover_of_carrier ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(695,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc20_membered) ).
thf(5786,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( C @ ( B @ ( A @ relation_dom_as_subset ) ) )
= ( C @ relation_dom ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(1842,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( C @ ( B @ ( A @ relation_dom_as_subset ) ) )
= ( C @ relation_dom ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(117,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_dom @ finite )
=> ( A @ relation_rng @ finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
thf(1584,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_dom @ finite )
=> ( A @ relation_rng @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(784,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ strict_rel_str )
=> ( A
= ( A @ the_InternalRel @ ( A @ the_carrier @ rel_str_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(6501,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ strict_rel_str )
=> ( A
= ( A @ the_InternalRel @ ( A @ the_carrier @ rel_str_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(792,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ powerset @ ( B @ ( A @ complements_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(6539,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ powerset @ ( B @ ( A @ complements_of_subsets ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(793,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_join @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function )
& ( A @ the_L_join @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice2) ).
thf(6541,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_join @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function )
& ( A @ the_L_join @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ subnet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_yellow_6) ).
thf(3775,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ subnet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(290,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= ( C @ singleton ) ) )
& ( ( B @ relation_dom )
= A )
& ( B @ function )
& ( B @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
thf(2877,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= ( C @ singleton ) ) )
& ( ( B @ relation_dom )
= A )
& ( B @ function )
& ( B @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ relation_dom @ ( A @ subset ) )
=> ( A @ ( B @ relation_image ) @ ( B @ relation_inverse_image ) @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
thf(4167,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ relation_dom @ ( A @ subset ) )
=> ( A @ ( B @ relation_image ) @ ( B @ relation_inverse_image ) @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(93,axiom,
! [A: $i] :
( ( ( A @ ordinal )
& ( A @ empty ) )
=> ( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_arytm_3) ).
thf(1461,plain,
! [A: $i] :
( ( ( A @ ordinal )
& ( A @ empty ) )
=> ( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(478,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).
thf(4425,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(85,axiom,
? [A: $i] :
( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_waybel_0) ).
thf(1424,plain,
? [A: $i] :
( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(642,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).
thf(5464,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(530,axiom,
! [A: $i] :
( ( A @ succ )
= ( A @ singleton @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
thf(4744,plain,
! [A: $i] :
( ( A @ succ )
= ( A @ singleton @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(748,axiom,
! [A: $i] :
( ( A @ boole_POSet )
= ( A @ boole_lattice @ poset_of_lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_1) ).
thf(6164,plain,
! [A: $i] :
( ( A @ boole_POSet )
= ( A @ boole_lattice @ poset_of_lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(153,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ ordered_pair ) ) )
=> ! [B: $i] :
( ( B
= ( A @ pair_first ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).
thf(1810,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ ordered_pair ) ) )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = C ) )
=> ( B
= ( A @ pair_first ) ) )
& ( ( B
= ( A @ pair_first ) )
=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(147,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(1791,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(704,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(5865,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(680,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ ex_inf_of_relstr_set ) )
=> ( ( C
= ( B @ ( A @ meet_on_relstr ) ) )
<=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_yellow_0) ).
thf(5662,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ ex_inf_of_relstr_set ) )
=> ( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) ) )
=> ( C
= ( B @ ( A @ meet_on_relstr ) ) ) )
& ( ( C
= ( B @ ( A @ meet_on_relstr ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(4621,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(256,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2649,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(19,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(985,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
thf(1249,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(2153,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_waybel_0) ).
thf(1131,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(387,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( A @ relation_dom @ ( B @ ( A @ relation_composition ) @ relation_dom @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(3770,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( A @ relation_dom @ ( B @ ( A @ relation_composition ) @ relation_dom @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(652,axiom,
! [A: $i] :
( ( A @ boole_POSet @ bottom_of_relstr )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_yellow_1) ).
thf(5498,plain,
! [A: $i] :
( ( A @ boole_POSet @ bottom_of_relstr )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(32,axiom,
? [A: $i] :
( ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_waybel_1) ).
thf(1060,plain,
? [A: $i] :
( ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(772,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
<=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( E @ ( D @ ( A @ related ) ) ) ) )
& ( D @ ( B @ ( A @ relstr_set_smaller ) ) ) )
=> ( D = C ) ) )
& ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_yellow_0) ).
thf(6346,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( E @ ( D @ ( A @ related ) ) ) ) )
& ( D @ ( B @ ( A @ relstr_set_smaller ) ) ) )
=> ( D = C ) ) )
& ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) )
=> ( B @ ( A @ ex_sup_of_relstr_set ) ) )
& ( ( B @ ( A @ ex_sup_of_relstr_set ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( E @ ( D @ ( A @ related ) ) ) ) )
& ( D @ ( B @ ( A @ relstr_set_smaller ) ) ) )
=> ( D = C ) ) )
& ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ relation_composition ) @ relation_rng )
= ( A @ relation_rng @ ( B @ relation_image ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
thf(1246,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ relation_composition ) @ relation_rng )
= ( A @ relation_rng @ ( B @ relation_image ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_intersection2 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(6152,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_intersection2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(381,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(3703,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( A @ ( B @ relation_restriction ) @ relation_field @ subset ) )
& ( B @ relation_field @ ( A @ ( B @ relation_restriction ) @ relation_field @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_wellord1) ).
thf(1324,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( A @ ( B @ relation_restriction ) @ relation_field @ subset ) )
& ( B @ relation_field @ ( A @ ( B @ relation_restriction ) @ relation_field @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ well_orders ) )
=> ( ( A @ ( B @ relation_restriction ) @ well_ordering )
& ( ( A @ ( B @ relation_restriction ) @ relation_field )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord2) ).
thf(1114,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ well_orders ) )
=> ( ( A @ ( B @ relation_restriction ) @ well_ordering )
& ( ( A @ ( B @ relation_restriction ) @ relation_field )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( A @ ( B @ set_intersection2 ) @ v3_membered )
& ( A @ ( B @ set_intersection2 ) @ v2_membered )
& ( A @ ( B @ set_intersection2 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc32_membered) ).
thf(3787,plain,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( A @ ( B @ set_intersection2 ) @ v3_membered )
& ( A @ ( B @ set_intersection2 ) @ v2_membered )
& ( A @ ( B @ set_intersection2 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ relation_rng @ ( A @ relation_dom @ subset ) )
=> ( ( A @ ( B @ relation_composition ) @ relation_rng )
= ( A @ relation_rng ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
thf(1456,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ relation_rng @ ( A @ relation_dom @ subset ) )
=> ( ( A @ ( B @ relation_composition ) @ relation_rng )
= ( A @ relation_rng ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(208,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(2243,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(779,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ the_carrier @ subset_complement ) )
= ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
thf(6475,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ the_carrier @ subset_complement ) )
= ( B @ ( A @ cast_as_carrier_subset @ ( A @ the_carrier @ subset_difference ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(287,axiom,
! [A: $i] :
( ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(2862,plain,
! [A: $i] :
( ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(442,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(4135,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(3064,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_union2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_union2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( ( A @ succ @ powerset @ powerset @ ( B @ element ) )
& ( A @ ordinal ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ? [E: $i] :
( ( D
= ( A @ singleton @ ( E @ set_difference ) ) )
& ( B @ ( E @ in ) ) )
& ( A @ powerset @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
thf(1720,plain,
! [A: $i,B: $i] :
( ( ( A @ succ @ powerset @ powerset @ ( B @ element ) )
& ( A @ ordinal ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( ? [E: $i] :
( ( D
= ( A @ singleton @ ( E @ set_difference ) ) )
& ( B @ ( E @ in ) ) )
& ( A @ powerset @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ? [E: $i] :
( ( D
= ( A @ singleton @ ( E @ set_difference ) ) )
& ( B @ ( E @ in ) ) )
& ( A @ powerset @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(462,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ v1_yellow_3 ) )
=> ( ( A @ the_InternalRel @ relation )
& ~ ( A @ the_InternalRel @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_yellow_3) ).
thf(4259,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ v1_yellow_3 ) )
=> ( ( A @ the_InternalRel @ relation )
& ~ ( A @ the_InternalRel @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(750,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ bottom_of_relstr @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
thf(6171,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ bottom_of_relstr @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(353,axiom,
! [A: $i] :
( ( A = omega )
<=> ( ! [B: $i] :
( ( B @ ordinal )
=> ( ( ( B @ being_limit_ordinal )
& ( B @ ( empty_set @ in ) ) )
=> ( B @ ( A @ subset ) ) ) )
& ( A @ ordinal )
& ( A @ being_limit_ordinal )
& ( A @ ( empty_set @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_ordinal2) ).
thf(3476,plain,
! [A: $i] :
( ( ( ! [B: $i] :
( ( B @ ordinal )
=> ( ( ( B @ being_limit_ordinal )
& ( B @ ( empty_set @ in ) ) )
=> ( B @ ( A @ subset ) ) ) )
& ( A @ ordinal )
& ( A @ being_limit_ordinal )
& ( A @ ( empty_set @ in ) ) )
=> ( A = omega ) )
& ( ( A = omega )
=> ( ! [B: $i] :
( ( B @ ordinal )
=> ( ( ( B @ being_limit_ordinal )
& ( B @ ( empty_set @ in ) ) )
=> ( B @ ( A @ subset ) ) ) )
& ( A @ ordinal )
& ( A @ being_limit_ordinal )
& ( A @ ( empty_set @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(3755,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(175,axiom,
! [A: $i] : ( A @ succ @ ( A @ in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(1991,plain,
! [A: $i] : ( A @ succ @ ( A @ in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(746,axiom,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(6160,plain,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(536,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ relation_dom @ ( A @ in ) )
=> ( ( A @ ( C @ ( B @ relation_composition ) @ apply ) )
= ( A @ ( B @ apply ) @ ( C @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
thf(4782,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ relation_dom @ ( A @ in ) )
=> ( ( A @ ( C @ ( B @ relation_composition ) @ apply ) )
= ( A @ ( B @ apply ) @ ( C @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(178,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(2043,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(782,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ directed_relstr )
<=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ related ) ) )
& ( D @ ( B @ ( A @ related ) ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_yellow_6) ).
thf(6486,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ related ) ) )
& ( D @ ( B @ ( A @ related ) ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) )
=> ( A @ directed_relstr ) )
& ( ( A @ directed_relstr )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ related ) ) )
& ( D @ ( B @ ( A @ related ) ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(699,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(5833,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(637,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ powerset @ ( C @ ( B @ ( A @ relation_rng_as_subset ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(5447,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ powerset @ ( C @ ( B @ ( A @ relation_rng_as_subset ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ join_of_latt_set ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(6038,plain,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ join_of_latt_set ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(706,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(5872,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ in ) )
& ( C @ ( B @ in ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(2529,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ in ) )
& ( C @ ( B @ in ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(399,axiom,
! [A: $i,B: $i] :
( ( A @ singleton @ ( A @ singleton @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ singleton @ rel_str_of ) @ trivial_carrier )
& ( B @ ( A @ singleton @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ singleton @ rel_str_of ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_yellow_0) ).
thf(3824,plain,
! [A: $i,B: $i] :
( ( A @ singleton @ ( A @ singleton @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ singleton @ rel_str_of ) @ trivial_carrier )
& ( B @ ( A @ singleton @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ singleton @ rel_str_of ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ relation_rng )
= empty_set )
| ( ( A @ relation_dom )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(2634,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ relation_rng )
= empty_set )
| ( ( A @ relation_dom )
= empty_set ) )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(687,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ strict_latt_str )
=> ( A
= ( A @ the_L_meet @ ( A @ the_L_join @ ( A @ the_carrier @ latt_str_of ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(5747,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ strict_latt_str )
=> ( A
= ( A @ the_L_meet @ ( A @ the_L_join @ ( A @ the_carrier @ latt_str_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ bijective ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ onto ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ one_to_one )
& ( C @ function ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_2) ).
thf(938,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ bijective ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ onto ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ one_to_one )
& ( C @ function ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_difference ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(4644,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_difference ) ) ) )
& ( ( C
= ( B @ ( A @ set_difference ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( B @ ( C @ fiber ) @ ( B @ ( A @ ( C @ relation_restriction ) @ fiber ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_wellord1) ).
thf(1187,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( B @ ( C @ fiber ) @ ( B @ ( A @ ( C @ relation_restriction ) @ fiber ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(2440,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
& ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(597,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ in ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
thf(5209,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ in ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
=> ( C @ ( B @ ( A @ relstr_element_smaller ) ) ) )
& ( ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ in ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( B @ ( A @ set_intersection2 ) @ v4_membered )
& ( B @ ( A @ set_intersection2 ) @ v3_membered )
& ( B @ ( A @ set_intersection2 ) @ v2_membered )
& ( B @ ( A @ set_intersection2 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc33_membered) ).
thf(1663,plain,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( B @ ( A @ set_intersection2 ) @ v4_membered )
& ( B @ ( A @ set_intersection2 ) @ v3_membered )
& ( B @ ( A @ set_intersection2 ) @ v2_membered )
& ( B @ ( A @ set_intersection2 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join_commut ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattices) ).
thf(5887,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join_commut ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(165,axiom,
? [A: $i] :
( ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_lattices) ).
thf(1895,plain,
? [A: $i] :
( ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(553,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( ( B @ ( A @ relation_restriction_as_relation_of ) )
= ( B @ ( A @ relation_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_toler_1) ).
thf(4921,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( ( B @ ( A @ relation_restriction_as_relation_of ) )
= ( B @ ( A @ relation_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(682,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( B @ ( B @ ( A @ interior ) @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tops_1) ).
thf(5679,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( B @ ( B @ ( A @ interior ) @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(805,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ upper_relstr_subset ) )
<=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( A @ related ) ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_waybel_0) ).
thf(6637,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( A @ related ) ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) ) ) )
=> ( A @ ( B @ upper_relstr_subset ) ) )
& ( ( A @ ( B @ upper_relstr_subset ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( A @ related ) ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ bounded_relstr )
=> ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(1251,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ bounded_relstr )
=> ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(786,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_eventually_in ) ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( D @ ( B @ related ) ) )
=> ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) ) ) )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_waybel_0) ).
thf(6507,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( D @ ( B @ related ) ) )
=> ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) ) ) )
& ( B @ the_carrier @ ( D @ element ) ) )
=> ( C @ ( B @ ( A @ is_eventually_in ) ) ) )
& ( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( D @ ( B @ related ) ) )
=> ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) ) ) )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ being_limit_ordinal )
<=> ( A
= ( A @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_ordinal1) ).
thf(1680,plain,
! [A: $i] :
( ( ( A
= ( A @ union ) )
=> ( A @ being_limit_ordinal ) )
& ( ( A @ being_limit_ordinal )
=> ( A
= ( A @ union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(691,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C
= ( B @ ( A @ join_of_latt_set ) ) )
<=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ ( A @ latt_element_smaller ) ) )
=> ( D @ ( C @ ( A @ below ) ) ) ) )
& ( B @ ( C @ ( A @ latt_element_smaller ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattice3) ).
thf(5762,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ ( A @ latt_element_smaller ) ) )
=> ( D @ ( C @ ( A @ below ) ) ) ) )
& ( B @ ( C @ ( A @ latt_element_smaller ) ) ) )
=> ( C
= ( B @ ( A @ join_of_latt_set ) ) ) )
& ( ( C
= ( B @ ( A @ join_of_latt_set ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ ( A @ latt_element_smaller ) ) )
=> ( D @ ( C @ ( A @ below ) ) ) ) )
& ( B @ ( C @ ( A @ latt_element_smaller ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
thf(5969,plain,
! [A: $i,B: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(3890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(97,axiom,
( ( empty_set @ ordinal )
& ( empty_set @ epsilon_connected )
& ( empty_set @ epsilon_transitive )
& ( empty_set @ empty )
& ( empty_set @ one_to_one )
& ( empty_set @ function )
& ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(1483,plain,
( ( empty_set @ ordinal )
& ( empty_set @ epsilon_connected )
& ( empty_set @ epsilon_transitive )
& ( empty_set @ empty )
& ( empty_set @ one_to_one )
& ( empty_set @ function )
& ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(6084,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(168,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(1927,plain,
! [A: $i] :
( ( A @ relation )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ boolean_relstr )
& ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ heyting_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_waybel_7) ).
thf(856,plain,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ boolean_relstr )
& ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ heyting_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_as_element ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(4503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_as_element ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( B @ strict_net_str ) )
=> ( B
= ( B @ ( A @ the_mapping ) @ ( B @ the_InternalRel @ ( B @ the_carrier @ ( A @ net_str_of ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v6_waybel_0) ).
thf(5882,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( B @ strict_net_str ) )
=> ( B
= ( B @ ( A @ the_mapping ) @ ( B @ the_InternalRel @ ( B @ the_carrier @ ( A @ net_str_of ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ antisymmetric )
=> ( A @ ( B @ relation_restriction ) @ antisymmetric ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
thf(3696,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ antisymmetric )
=> ( A @ ( B @ relation_restriction ) @ antisymmetric ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(801,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(6598,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(17,axiom,
? [A: $i] :
( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(965,plain,
? [A: $i] :
( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(770,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ( ( B @ a_1_0_filter_1 @ ( A @ in ) )
<=> ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ below_refl ) ) )
& ( A
= ( D @ ( C @ ( B @ the_carrier @ ( B @ the_carrier @ ordered_pair_as_product_element ) ) ) ) )
& ( B @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
thf(6314,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ( ( ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ below_refl ) ) )
& ( A
= ( D @ ( C @ ( B @ the_carrier @ ( B @ the_carrier @ ordered_pair_as_product_element ) ) ) ) )
& ( B @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( C @ element ) ) )
=> ( B @ a_1_0_filter_1 @ ( A @ in ) ) )
& ( ( B @ a_1_0_filter_1 @ ( A @ in ) )
=> ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ below_refl ) ) )
& ( A
= ( D @ ( C @ ( B @ the_carrier @ ( B @ the_carrier @ ordered_pair_as_product_element ) ) ) ) )
& ( B @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ordered_pair ) @ pair_second )
= B )
& ( ( B @ ( A @ ordered_pair ) @ pair_first )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
thf(1510,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ordered_pair ) @ pair_second )
= B )
& ( ( B @ ( A @ ordered_pair ) @ pair_first )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_dom @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l29_wellord1) ).
thf(4412,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_dom @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ! [E: $i] :
( ( ( E @ function )
& ( E @ relation ) )
=> ( ( A @ ( C @ in ) )
=> ( ( ( C @ ( E @ ( D @ relation_composition ) @ apply ) )
= ( C @ ( D @ apply ) @ ( E @ apply ) ) )
| ( B = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_2) ).
thf(4256,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ! [E: $i] :
( ( ( E @ function )
& ( E @ relation ) )
=> ( ( A @ ( C @ in ) )
=> ( ( ( C @ ( E @ ( D @ relation_composition ) @ apply ) )
= ( C @ ( D @ apply ) @ ( E @ apply ) ) )
| ( B = empty_set ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation )
& ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_composition ) @ function )
& ( B @ ( A @ relation_composition ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(3839,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation )
& ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_composition ) @ function )
& ( B @ ( A @ relation_composition ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(356,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(3523,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( ( A @ relation_empty_yielding )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ relation_empty_yielding )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(1374,plain,
! [A: $i,B: $i] :
( ( ( A @ relation_empty_yielding )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ relation_empty_yielding )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(506,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
thf(4599,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B
= ( A @ inclusion_relation ) )
<=> ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ in ) )
& ( A @ ( C @ in ) ) )
=> ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
<=> ( D @ ( C @ subset ) ) ) )
& ( ( B @ relation_field )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).
thf(3372,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ in ) )
& ( A @ ( C @ in ) ) )
=> ( ( ( D @ ( C @ subset ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( D @ ( C @ subset ) ) ) ) )
& ( ( B @ relation_field )
= A ) )
=> ( B
= ( A @ inclusion_relation ) ) )
& ( ( B
= ( A @ inclusion_relation ) )
=> ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ in ) )
& ( A @ ( C @ in ) ) )
=> ( ( ( D @ ( C @ subset ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( D @ ( C @ subset ) ) ) ) )
& ( ( B @ relation_field )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(156,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ empty_carrier )
=> ( A @ v1_yellow_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow_3) ).
thf(1833,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ empty_carrier )
=> ( A @ v1_yellow_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(718,axiom,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(5933,plain,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(369,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(3636,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(205,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(2225,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(199,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(2188,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(417,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B
= ( A @ relation_dom ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(3945,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_dom ) ) )
& ( ( B
= ( A @ relation_dom ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(327,axiom,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(3266,plain,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ? [E: $i] :
( ( A @ ( E @ in ) )
& ( D = E )
& ( E @ ordinal ) )
& ( B @ succ @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
thf(2991,plain,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ? [C: $i] :
! [D: $i] :
( ( ( ? [E: $i] :
( ( A @ ( E @ in ) )
& ( D = E )
& ( E @ ordinal ) )
& ( B @ succ @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ? [E: $i] :
( ( A @ ( E @ in ) )
& ( D = E )
& ( E @ ordinal ) )
& ( B @ succ @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(348,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ~ ( A @ v1_yellow_3 )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_yellow_3) ).
thf(3458,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ~ ( A @ v1_yellow_3 )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ connected_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_waybel_0) ).
thf(1795,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ connected_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(654,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(5503,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(267,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( B @ ( A @ meet_of_latt_set ) )
= ( B @ ( A @ poset_of_lattice @ meet_on_relstr ) ) )
& ( ( B @ ( A @ join_of_latt_set ) )
= ( B @ ( A @ poset_of_lattice @ join_on_relstr ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_yellow_0) ).
thf(2695,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( B @ ( A @ meet_of_latt_set ) )
= ( B @ ( A @ poset_of_lattice @ meet_on_relstr ) ) )
& ( ( B @ ( A @ join_of_latt_set ) )
= ( B @ ( A @ poset_of_lattice @ join_on_relstr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_on_structs ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_waybel_0) ).
thf(3272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_on_structs ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ~ ( A @ empty ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ apply_as_element ) ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(4801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ~ ( A @ empty ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ apply_as_element ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(763,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( ( A @ ( C @ net_str ) )
& ( C @ directed_relstr )
& ( C @ transitive_relstr )
& ~ ( C @ empty_carrier ) )
=> ( ( B @ ( A @ ( C @ subnet ) ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ? [F: $i] :
( ! [G: $i] :
( ( C @ the_carrier @ ( G @ element ) )
=> ( ( G @ ( F @ ( C @ related ) ) )
=> ( G @ ( D @ ( B @ ( C @ the_carrier @ apply_on_set_and_struct ) ) ) @ ( E @ ( B @ related ) ) ) ) )
& ( C @ the_carrier @ ( F @ element ) ) ) )
& ( ( C @ ( A @ the_mapping ) )
= ( B @ ( A @ the_mapping ) @ ( D @ ( A @ the_carrier @ ( B @ the_carrier @ ( C @ the_carrier @ function_of_composition ) ) ) ) ) )
& ( B @ the_carrier @ ( C @ the_carrier @ ( D @ relation_of2_as_subset ) ) )
& ( B @ the_carrier @ ( C @ the_carrier @ ( D @ quasi_total ) ) )
& ( D @ function ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_yellow_6) ).
thf(6229,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( ( A @ ( C @ net_str ) )
& ( C @ directed_relstr )
& ( C @ transitive_relstr )
& ~ ( C @ empty_carrier ) )
=> ( ( ? [D: $i] :
( ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ? [F: $i] :
( ! [G: $i] :
( ( C @ the_carrier @ ( G @ element ) )
=> ( ( G @ ( F @ ( C @ related ) ) )
=> ( G @ ( D @ ( B @ ( C @ the_carrier @ apply_on_set_and_struct ) ) ) @ ( E @ ( B @ related ) ) ) ) )
& ( C @ the_carrier @ ( F @ element ) ) ) )
& ( ( C @ ( A @ the_mapping ) )
= ( B @ ( A @ the_mapping ) @ ( D @ ( A @ the_carrier @ ( B @ the_carrier @ ( C @ the_carrier @ function_of_composition ) ) ) ) ) )
& ( B @ the_carrier @ ( C @ the_carrier @ ( D @ relation_of2_as_subset ) ) )
& ( B @ the_carrier @ ( C @ the_carrier @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( B @ ( A @ ( C @ subnet ) ) ) )
& ( ( B @ ( A @ ( C @ subnet ) ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ? [F: $i] :
( ! [G: $i] :
( ( C @ the_carrier @ ( G @ element ) )
=> ( ( G @ ( F @ ( C @ related ) ) )
=> ( G @ ( D @ ( B @ ( C @ the_carrier @ apply_on_set_and_struct ) ) ) @ ( E @ ( B @ related ) ) ) ) )
& ( C @ the_carrier @ ( F @ element ) ) ) )
& ( ( C @ ( A @ the_mapping ) )
= ( B @ ( A @ the_mapping ) @ ( D @ ( A @ the_carrier @ ( B @ the_carrier @ ( C @ the_carrier @ function_of_composition ) ) ) ) ) )
& ( B @ the_carrier @ ( C @ the_carrier @ ( D @ relation_of2_as_subset ) ) )
& ( B @ the_carrier @ ( C @ the_carrier @ ( D @ quasi_total ) ) )
& ( D @ function ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(673,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_membered) ).
thf(5612,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(561,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ subnetstr ) ) )
& ( B @ ( A @ ( C @ full_subnetstr ) ) )
& ~ ( C @ empty_carrier ) )
=> ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( C @ the_carrier @ ( F @ element ) )
=> ! [G: $i] :
( ( C @ the_carrier @ ( G @ element ) )
=> ( ( ( E @ ( D @ ( B @ related ) ) )
& ( E = G )
& ( D = F ) )
=> ( G @ ( F @ ( C @ related ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_yellow_6) ).
thf(4975,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ subnetstr ) ) )
& ( B @ ( A @ ( C @ full_subnetstr ) ) )
& ~ ( C @ empty_carrier ) )
=> ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( C @ the_carrier @ ( F @ element ) )
=> ! [G: $i] :
( ( C @ the_carrier @ ( G @ element ) )
=> ( ( ( E @ ( D @ ( B @ related ) ) )
& ( E = G )
& ( D = F ) )
=> ( G @ ( F @ ( C @ related ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(106,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( ( A @ relation_dom )
= ( A @ function_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ function_inverse @ relation_dom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
thf(1520,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( ( A @ relation_dom )
= ( A @ function_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ function_inverse @ relation_dom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(3404,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(408,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
thf(3868,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) )
& ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) )
= ( H @ ( G @ ( F @ ( E @ net_str_of ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_waybel_0) ).
thf(5185,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) )
= ( H @ ( G @ ( F @ ( E @ net_str_of ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(634,axiom,
! [A: $i] :
( ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_yellow_1) ).
thf(5427,plain,
! [A: $i] :
( ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(371,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ inclusion_order @ relation_of2_as_subset ) ) )
& ( A @ ( A @ ( A @ inclusion_order @ v1_partfun1 ) ) )
& ( A @ inclusion_order @ transitive )
& ( A @ inclusion_order @ antisymmetric )
& ( A @ inclusion_order @ reflexive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
thf(3646,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ inclusion_order @ relation_of2_as_subset ) ) )
& ( A @ ( A @ ( A @ inclusion_order @ v1_partfun1 ) ) )
& ( A @ inclusion_order @ transitive )
& ( A @ inclusion_order @ antisymmetric )
& ( A @ inclusion_order @ reflexive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(436,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(4099,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(302,axiom,
! [A: $i] :
( ( ! [B: $i] :
~ ( ! [C: $i] :
( C
!= ( B @ singleton ) )
& ( A @ ( B @ in ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( D
= ( B @ singleton ) )
& ( C
= ( B @ singleton ) )
& ( A @ ( B @ in ) ) )
=> ( C = D ) ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= ( C @ singleton ) ) )
& ( ( B @ relation_dom )
= A )
& ( B @ function )
& ( B @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
thf(3002,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ! [C: $i] :
( C
!= ( B @ singleton ) )
& ( A @ ( B @ in ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( D
= ( B @ singleton ) )
& ( C
= ( B @ singleton ) )
& ( A @ ( B @ in ) ) )
=> ( C = D ) ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= ( C @ singleton ) ) )
& ( ( B @ relation_dom )
= A )
& ( B @ function )
& ( B @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(638,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ union_of_subsets ) )
= ( B @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(5449,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ union_of_subsets ) )
= ( B @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(3091,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(715,axiom,
! [A: $i] :
? [B: $i] :
( ~ ( A @ powerset @ ( B @ proper_element ) )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(5908,plain,
! [A: $i] :
? [B: $i] :
( ~ ( A @ powerset @ ( B @ proper_element ) )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(790,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ latt_set_smaller ) ) )
<=> ( C @ ( B @ cast_to_el_of_LattPOSet ) @ ( A @ ( B @ poset_of_lattice @ relstr_element_smaller ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice3) ).
thf(6532,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ cast_to_el_of_LattPOSet ) @ ( A @ ( B @ poset_of_lattice @ relstr_element_smaller ) ) )
=> ( A @ ( C @ ( B @ latt_set_smaller ) ) ) )
& ( ( A @ ( C @ ( B @ latt_set_smaller ) ) )
=> ( C @ ( B @ cast_to_el_of_LattPOSet ) @ ( A @ ( B @ poset_of_lattice @ relstr_element_smaller ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( B @ the_carrier @ ( D @ ( C @ ( B @ ( A @ apply_on_structs ) ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_waybel_0) ).
thf(5282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( B @ the_carrier @ ( D @ ( C @ ( B @ ( A @ apply_on_structs ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(4236,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(588,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ meet ) ) )
= ( C @ ( B @ ( A @ the_L_meet @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattices) ).
thf(5148,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ meet ) ) )
= ( C @ ( B @ ( A @ the_L_meet @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ join_commut ) ) )
= ( B @ ( C @ ( A @ join_commut ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
thf(6649,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ join_commut ) ) )
= ( B @ ( C @ ( A @ join_commut ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( A @ finite )
=> ( A @ ( B @ relation_image ) @ finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
thf(4433,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( A @ finite )
=> ( A @ ( B @ relation_image ) @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(78,axiom,
? [A: $i] :
( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ connected_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_3) ).
thf(1356,plain,
? [A: $i] :
( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ connected_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(780,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
thf(6478,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(705,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ closed_subset ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tops_1) ).
thf(5870,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ closed_subset ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(577,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ point_neighbourhood ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
thf(5071,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ point_neighbourhood ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ cartesian_product2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(2538,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ cartesian_product2 ) ) ) )
& ( ( C
= ( B @ ( A @ cartesian_product2 ) ) )
=> ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(752,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ open_subsets ) )
<=> ( A @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ closed_subsets ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tops_2) ).
thf(6179,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ closed_subsets ) )
=> ( A @ ( B @ open_subsets ) ) )
& ( ( A @ ( B @ open_subsets ) )
=> ( A @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ closed_subsets ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
<=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(3551,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ in ) )
=> ( ( B @ singleton @ ( A @ set_difference ) )
= A ) )
& ( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
=> ~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(22,axiom,
? [A: $i] :
( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
thf(996,plain,
? [A: $i] :
( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ apply_netmap ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_waybel_0) ).
thf(5610,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ apply_netmap ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(431,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ? [E: $i,F: $i] :
( ( F
= ( E @ singleton ) )
& ( A @ ( E @ in ) )
& ( ( F @ ( E @ ordered_pair ) )
= D ) )
& ( B @ ( A @ cartesian_product2 ) @ ( D @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
thf(4073,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( ? [E: $i,F: $i] :
( ( F
= ( E @ singleton ) )
& ( A @ ( E @ in ) )
& ( ( F @ ( E @ ordered_pair ) )
= D ) )
& ( B @ ( A @ cartesian_product2 ) @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ? [E: $i,F: $i] :
( ( F
= ( E @ singleton ) )
& ( A @ ( E @ in ) )
& ( ( F @ ( E @ ordered_pair ) )
= D ) )
& ( B @ ( A @ cartesian_product2 ) @ ( D @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ meet_of_subsets ) )
= ( B @ set_meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(6604,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ meet_of_subsets ) )
= ( B @ set_meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(365,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i] :
( ( B
= ( A @ relation_rng ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(3586,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
=> ( B
= ( A @ relation_rng ) ) )
& ( ( B
= ( A @ relation_rng ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(728,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(5972,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_dom_restriction ) )
= ( B @ ( A @ identity_relation @ relation_composition ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
thf(1194,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_dom_restriction ) )
= ( B @ ( A @ identity_relation @ relation_composition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(527,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(4716,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(4337,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_intersection2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(263,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ in ) )
<=> ( B @ ( A @ succ @ ordinal_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
thf(2679,plain,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( ( B @ ( A @ succ @ ordinal_subset ) )
=> ( B @ ( A @ in ) ) )
& ( ( B @ ( A @ in ) )
=> ( B @ ( A @ succ @ ordinal_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(768,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(6308,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(236,axiom,
! [A: $i] :
( ( ( A @ boole_lattice @ bottom_of_semilattstr )
= empty_set )
& ( A @ boole_lattice @ lower_bounded_semilattstr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice3) ).
thf(2478,plain,
! [A: $i] :
( ( ( A @ boole_lattice @ bottom_of_semilattstr )
= empty_set )
& ( A @ boole_lattice @ lower_bounded_semilattstr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ relation_of2 ) ) )
& ( C @ ( B @ ( E @ quasi_total ) ) )
& ( E @ function )
& ( B @ ( A @ ( D @ relation_of2 ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ function_of_composition ) ) ) ) )
= ( E @ ( D @ relation_composition ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(3251,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ relation_of2 ) ) )
& ( C @ ( B @ ( E @ quasi_total ) ) )
& ( E @ function )
& ( B @ ( A @ ( D @ relation_of2 ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ function_of_composition ) ) ) ) )
= ( E @ ( D @ relation_composition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(386,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ being_limit_ordinal )
<=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( A @ ( B @ succ @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_ordinal1) ).
thf(3764,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( A @ ( B @ succ @ in ) ) ) )
=> ( A @ being_limit_ordinal ) )
& ( ( A @ being_limit_ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( A @ ( B @ succ @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(5520,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(1806,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_waybel_0) ).
thf(1011,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(697,axiom,
! [A: $i] :
( ( A @ boole_POSet )
= ( A @ powerset @ incl_POSet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_yellow_1) ).
thf(5827,plain,
! [A: $i] :
( ( A @ boole_POSet )
= ( A @ powerset @ incl_POSet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ relation_inverse_image ) @ ( A @ ( C @ relation_inverse_image ) @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
thf(3270,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ relation_inverse_image ) @ ( A @ ( C @ relation_inverse_image ) @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(650,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ antisymmetric_relstr )
<=> ( A @ the_carrier @ ( A @ the_InternalRel @ is_antisymmetric_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_orders_2) ).
thf(5491,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ the_carrier @ ( A @ the_InternalRel @ is_antisymmetric_in ) )
=> ( A @ antisymmetric_relstr ) )
& ( ( A @ antisymmetric_relstr )
=> ( A @ the_carrier @ ( A @ the_InternalRel @ is_antisymmetric_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(714,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( A @ powerset @ ( B @ proper_element ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
thf(5901,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( ( B != A )
=> ( A @ powerset @ ( B @ proper_element ) ) )
& ( ( A @ powerset @ ( B @ proper_element ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(143,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ k2_lattice3 )
= ( A @ relation_of_lattice ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
thf(1771,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ k2_lattice3 )
= ( A @ relation_of_lattice ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(2945,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(486,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ bottom_of_relstr )
= ( empty_set @ ( A @ join_on_relstr ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_yellow_0) ).
thf(4477,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ bottom_of_relstr )
= ( empty_set @ ( A @ join_on_relstr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(171,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ transitive )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ ( D @ ( B @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_wellord1) ).
thf(1969,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ ( D @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ transitive ) )
& ( ( A @ transitive )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ ( D @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ~ ( ! [C: $i] :
( ( C @ relation )
=> ~ ( A @ ( C @ well_orders ) ) )
& ( B @ relation_field @ ( A @ equipotent ) )
& ( B @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_wellord2) ).
thf(1307,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ~ ( ! [C: $i] :
( ( C @ relation )
=> ~ ( A @ ( C @ well_orders ) ) )
& ( B @ relation_field @ ( A @ equipotent ) )
& ( B @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_membered) ).
thf(2180,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(480,axiom,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(4430,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( D @ relation_rng @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(2632,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( D @ relation_rng @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(501,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(4541,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(580,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( B @ ( C @ ( A @ meet_commut ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(5082,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( B @ ( C @ ( A @ meet_commut ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(635,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ ex_inf_of_relstr_set ) )
& ( empty_set @ ( A @ ex_sup_of_relstr_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_0) ).
thf(5439,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ ex_inf_of_relstr_set ) )
& ( empty_set @ ( A @ ex_sup_of_relstr_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_difference ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(3932,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_difference ) )
= A )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_difference ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(806,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ open_subset ) )
<=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ closed_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
thf(6645,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ closed_subset ) )
=> ( A @ ( B @ open_subset ) ) )
& ( ( A @ ( B @ open_subset ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ closed_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= ( C @ relation_rng ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(2593,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= ( C @ relation_rng ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ meet_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(5885,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ meet_of_subsets ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(210,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ~ ( ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( C @ ( C @ ( B @ apply ) @ in ) ) )
& ( ( B @ relation_dom )
= A ) ) )
& ! [B: $i] :
~ ( ( B = empty_set )
& ( A @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_wellord2) ).
thf(2252,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ~ ( ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( C @ ( C @ ( B @ apply ) @ in ) ) )
& ( ( B @ relation_dom )
= A ) ) )
& ! [B: $i] :
~ ( ( B = empty_set )
& ( A @ ( B @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(214,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
thf(2278,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_inverse_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ element ) )
& ( A @ ( C @ element ) )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( B @ ( A @ cartesian_product2 ) @ ( D @ ( C @ ( B @ ( A @ ordered_pair_as_product_element ) ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(4684,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ element ) )
& ( A @ ( C @ element ) )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( B @ ( A @ cartesian_product2 ) @ ( D @ ( C @ ( B @ ( A @ ordered_pair_as_product_element ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(663,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ strict_latt_str ) )
=> ( ( B
= ( A @ boole_lattice ) )
<=> ( ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( B @ the_L_meet @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_intersection2 ) ) ) )
& ( ( D @ ( C @ ( B @ the_L_join @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_union2 ) ) ) ) ) ) )
& ( ( B @ the_carrier )
= ( A @ powerset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice3) ).
thf(5552,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ strict_latt_str ) )
=> ( ( ( ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( B @ the_L_meet @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_intersection2 ) ) ) )
& ( ( D @ ( C @ ( B @ the_L_join @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_union2 ) ) ) ) ) ) )
& ( ( B @ the_carrier )
= ( A @ powerset ) ) )
=> ( B
= ( A @ boole_lattice ) ) )
& ( ( B
= ( A @ boole_lattice ) )
=> ( ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( B @ the_L_meet @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_intersection2 ) ) ) )
& ( ( D @ ( C @ ( B @ the_L_join @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_union2 ) ) ) ) ) ) )
& ( ( B @ the_carrier )
= ( A @ powerset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(524,axiom,
? [A: $i] :
( ( A @ strict_latt_str )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(4694,plain,
? [A: $i] :
( ( A @ strict_latt_str )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ? [E: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( E @ closed_subset ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ element ) ) )
& ( A @ the_carrier @ powerset @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
thf(5367,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( ? [E: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( E @ closed_subset ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ element ) ) )
& ( A @ the_carrier @ powerset @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ? [E: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( E @ closed_subset ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ element ) ) )
& ( A @ the_carrier @ powerset @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(657,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_LattPOSet ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
thf(5511,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_LattPOSet ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc9_waybel_1) ).
thf(811,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(2182,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( C @ ( B @ subset ) )
=> ( ( ( C @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
| ( ( A != empty_set )
& ( B = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).
thf(4882,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( C @ ( B @ subset ) )
=> ( ( ( C @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
| ( ( A != empty_set )
& ( B = empty_set ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(421,axiom,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ symmetric )
& ( B @ reflexive )
& ( B @ relation )
& ( A @ ( A @ ( B @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_partfun1) ).
thf(4009,plain,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ symmetric )
& ( B @ reflexive )
& ( B @ relation )
& ( A @ ( A @ ( B @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(217,axiom,
! [A: $i] :
( ( A @ epsilon_transitive )
<=> ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(2314,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) )
=> ( A @ epsilon_transitive ) )
& ( ( A @ epsilon_transitive )
=> ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(190,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ relation_restriction ) )
= ( B @ ( B @ cartesian_product2 ) @ ( A @ set_intersection2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
thf(2129,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ relation_restriction ) )
= ( B @ ( B @ cartesian_product2 ) @ ( A @ set_intersection2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(428,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( A @ ( C @ net_str ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
thf(4064,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( A @ ( C @ net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(176,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
<=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(1993,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(678,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ below_refl ) ) )
<=> ( C @ ( A @ cast_to_el_of_LattPOSet ) @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ ( A @ poset_of_lattice @ related_reflexive ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
thf(5656,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( A @ cast_to_el_of_LattPOSet ) @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ ( A @ poset_of_lattice @ related_reflexive ) ) )
=> ( C @ ( B @ ( A @ below_refl ) ) ) )
& ( ( C @ ( B @ ( A @ below_refl ) ) )
=> ( C @ ( A @ cast_to_el_of_LattPOSet ) @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ ( A @ poset_of_lattice @ related_reflexive ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ boole_POSet @ distributive_relstr )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_waybel_1) ).
thf(1149,plain,
! [A: $i] :
( ( A @ boole_POSet @ distributive_relstr )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ element ) )
& ( A @ ( C @ element ) )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ ordered_pair_as_product_element ) ) ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(2874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ element ) )
& ( A @ ( C @ element ) )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ ordered_pair_as_product_element ) ) ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(773,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ cast_as_carrier_subset @ ( B @ ( A @ the_carrier @ subset_intersection2 ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_pre_topc) ).
thf(6376,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ cast_as_carrier_subset @ ( B @ ( A @ the_carrier @ subset_intersection2 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc39_membered) ).
thf(1688,plain,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ relation )
=> ( ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
thf(2401,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ relation )
=> ( ( ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(367,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_often_in ) ) )
=> ( B @ ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ subnet ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_yellow_6) ).
thf(3627,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_often_in ) ) )
=> ( B @ ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ subnet ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(3110,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(762,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ is_a_cover_of_carrier ) )
<=> ( ( A @ cast_as_carrier_subset )
= ( B @ ( A @ the_carrier @ union_of_subsets ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_pre_topc) ).
thf(6223,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( ( ( A @ cast_as_carrier_subset )
= ( B @ ( A @ the_carrier @ union_of_subsets ) ) )
=> ( B @ ( A @ is_a_cover_of_carrier ) ) )
& ( ( B @ ( A @ is_a_cover_of_carrier ) )
=> ( ( A @ cast_as_carrier_subset )
= ( B @ ( A @ the_carrier @ union_of_subsets ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( B @ ( A @ relation_composition ) @ relation )
& ( B @ ( A @ relation_composition ) @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(4085,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( B @ ( A @ relation_composition ) @ relation )
& ( B @ ( A @ relation_composition ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(785,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ subset_complement ) @ ( C @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(6504,plain,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ subset_complement ) @ ( C @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(771,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( A @ ( C @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(6325,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ( ( B
= ( A @ powerset ) )
=> ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(489,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4497,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(582,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( B @ ( A @ ex_inf_of_relstr_set ) )
<=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_yellow_0) ).
thf(5089,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) )
=> ( B @ ( A @ ex_inf_of_relstr_set ) ) )
& ( ( B @ ( A @ ex_inf_of_relstr_set ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ below_refl ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(5495,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ below_refl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(447,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ relation_of_lattice )
= ( A @ a_1_0_filter_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_1) ).
thf(4158,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ relation_of_lattice )
= ( A @ a_1_0_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( C = E )
& ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
thf(5619,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( C = E )
& ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) @ finite )
& ~ ( B @ ( A @ unordered_pair ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(2365,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) @ finite )
& ~ ( B @ ( A @ unordered_pair ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(300,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ? [B: $i] :
! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( ? [D: $i] :
( ( ( omega @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ powerset @ powerset @ ( E @ element ) )
=> ~ ( ! [F: $i] :
~ ( ! [G: $i] :
( ( ( G @ ( F @ subset ) )
& ( E @ ( G @ in ) ) )
=> ( G = F ) )
& ( E @ ( F @ in ) ) )
& ( E != empty_set ) ) ) )
& ( C = D )
& ( D @ ordinal ) )
& ( A @ succ @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e18_27__finset_1__1) ).
thf(2962,plain,
! [A: $i] :
( ( A @ ordinal )
=> ? [B: $i] :
! [C: $i] :
( ( ( ? [D: $i] :
( ( ( omega @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ powerset @ powerset @ ( E @ element ) )
=> ~ ( ! [F: $i] :
~ ( ! [G: $i] :
( ( ( G @ ( F @ subset ) )
& ( E @ ( G @ in ) ) )
=> ( G = F ) )
& ( E @ ( F @ in ) ) )
& ( E != empty_set ) ) ) )
& ( C = D )
& ( D @ ordinal ) )
& ( A @ succ @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( ? [D: $i] :
( ( ( omega @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ powerset @ powerset @ ( E @ element ) )
=> ~ ( ! [F: $i] :
~ ( ! [G: $i] :
( ( ( G @ ( F @ subset ) )
& ( E @ ( G @ in ) ) )
=> ( G = F ) )
& ( E @ ( F @ in ) ) )
& ( E != empty_set ) ) ) )
& ( C = D )
& ( D @ ordinal ) )
& ( A @ succ @ ( C @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(602,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ apply_netmap ) ) )
= ( C @ ( B @ ( A @ the_mapping ) @ ( A @ ( B @ apply_on_structs ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_waybel_0) ).
thf(5254,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ apply_netmap ) ) )
= ( C @ ( B @ ( A @ the_mapping ) @ ( A @ ( B @ apply_on_structs ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( C @ function_inverse @ ( A @ ( B @ relation_isomorphism ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_wellord1) ).
thf(1445,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( C @ function_inverse @ ( A @ ( B @ relation_isomorphism ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
thf(1528,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( B @ ( A @ set_difference ) @ v4_membered )
& ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc40_membered) ).
thf(3241,plain,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( B @ ( A @ set_difference ) @ v4_membered )
& ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( ( A @ succ @ powerset @ powerset @ ( B @ element ) )
& ( A @ ordinal ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( E
= ( A @ singleton @ ( F @ set_difference ) ) )
& ( B @ ( F @ in ) ) )
& ( C = E )
& ? [F: $i] :
( ( D
= ( A @ singleton @ ( F @ set_difference ) ) )
& ( B @ ( F @ in ) ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ( D
= ( A @ singleton @ ( F @ set_difference ) ) )
& ( B @ ( F @ in ) ) )
& ( E = D )
& ( A @ powerset @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
thf(2797,plain,
! [A: $i,B: $i] :
( ( ( A @ succ @ powerset @ powerset @ ( B @ element ) )
& ( A @ ordinal ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( E
= ( A @ singleton @ ( F @ set_difference ) ) )
& ( B @ ( F @ in ) ) )
& ( C = E )
& ? [F: $i] :
( ( D
= ( A @ singleton @ ( F @ set_difference ) ) )
& ( B @ ( F @ in ) ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ? [E: $i] :
( ? [F: $i] :
( ( D
= ( A @ singleton @ ( F @ set_difference ) ) )
& ( B @ ( F @ in ) ) )
& ( E = D )
& ( A @ powerset @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( D
= ( A @ singleton @ ( F @ set_difference ) ) )
& ( B @ ( F @ in ) ) )
& ( E = D )
& ( A @ powerset @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ordinal )
<=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
thf(1076,plain,
! [A: $i] :
( ( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) )
& ( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(250,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_reflexive_in ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ ( C @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
thf(2614,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ ( C @ ordered_pair ) @ in ) ) )
=> ( B @ ( A @ is_reflexive_in ) ) )
& ( ( B @ ( A @ is_reflexive_in ) )
=> ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ ( C @ ordered_pair ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_yellow_1) ).
thf(1203,plain,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(277,axiom,
? [A: $i] : ( A @ meet_semilatt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(2784,plain,
? [A: $i] : ( A @ meet_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(294,axiom,
! [A: $i] :
( ( A @ function )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).
thf(2927,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( C = D ) )
=> ( A @ function ) )
& ( ( A @ function )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(3455,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(732,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( E @ ( B @ subset ) )
& ( A @ ( F @ closed_subset ) )
& ( F = E )
& ( A @ the_carrier @ powerset @ ( F @ element ) ) )
& ( C = E )
& ? [F: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( F @ closed_subset ) )
& ( F = D )
& ( A @ the_carrier @ powerset @ ( F @ element ) ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( F @ closed_subset ) )
& ( F = D )
& ( A @ the_carrier @ powerset @ ( F @ element ) ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e1_40__pre_topc__1) ).
thf(6008,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( E @ ( B @ subset ) )
& ( A @ ( F @ closed_subset ) )
& ( F = E )
& ( A @ the_carrier @ powerset @ ( F @ element ) ) )
& ( C = E )
& ? [F: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( F @ closed_subset ) )
& ( F = D )
& ( A @ the_carrier @ powerset @ ( F @ element ) ) )
& ( C = D ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ? [E: $i] :
( ? [F: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( F @ closed_subset ) )
& ( F = D )
& ( A @ the_carrier @ powerset @ ( F @ element ) ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( D @ ( B @ subset ) )
& ( A @ ( F @ closed_subset ) )
& ( F = D )
& ( A @ the_carrier @ powerset @ ( F @ element ) ) )
& ( E = D )
& ( A @ the_carrier @ powerset @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ connected ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
thf(1551,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ connected ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ the_carrier @ ( D @ element ) )
& ( A @ the_carrier @ ( C @ element ) )
& ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_filter_1) ).
thf(4986,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ the_carrier @ ( D @ element ) )
& ( A @ the_carrier @ ( C @ element ) )
& ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(405,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ function_inverse @ function )
& ( A @ function_inverse @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(3849,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ function_inverse @ function )
& ( A @ function_inverse @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(666,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(5587,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(303,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(3031,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ in ) )
=> ( A = empty_set ) )
& ( ( A = empty_set )
=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(523,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(4690,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ rel_str )
& ~ ( B @ empty_carrier )
& ~ ( A @ empty ) )
=> ( B @ the_carrier @ ( D @ ( C @ ( B @ ( A @ apply_on_set_and_struct ) ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_6) ).
thf(4868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ rel_str )
& ~ ( B @ empty_carrier )
& ~ ( A @ empty ) )
=> ( B @ the_carrier @ ( D @ ( C @ ( B @ ( A @ apply_on_set_and_struct ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ( ( E = C )
=> ( D
= ( E @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) ) )
=> ( D = E ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ( ( E = D )
=> ( ( D @ ( C @ apply ) )
= ( E @ ( A @ the_carrier @ subset_complement ) ) ) ) ) )
& ( ( C @ relation_dom )
= ( B @ ( A @ the_carrier @ complements_of_subsets ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e4_7_1__tops_2) ).
thf(6276,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ( ( E = C )
=> ( D
= ( E @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) ) )
=> ( D = E ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ( ( E = D )
=> ( ( D @ ( C @ apply ) )
= ( E @ ( A @ the_carrier @ subset_complement ) ) ) ) ) )
& ( ( C @ relation_dom )
= ( B @ ( A @ the_carrier @ complements_of_subsets ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ well_ordering ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_wellord2) ).
thf(944,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ well_ordering ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(94,axiom,
! [A: $i] :
( ( omega @ ( A @ element ) )
=> ( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_arytm_3) ).
thf(1467,plain,
! [A: $i] :
( ( omega @ ( A @ element ) )
=> ( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(754,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( empty_set @ ( A @ relstr_element_smaller ) ) )
& ( B @ ( empty_set @ ( A @ relstr_set_smaller ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
thf(6185,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( empty_set @ ( A @ relstr_element_smaller ) ) )
& ( B @ ( empty_set @ ( A @ relstr_set_smaller ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(690,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ identity_on_carrier @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ identity_on_carrier @ quasi_total ) ) )
& ( A @ identity_on_carrier @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
thf(5757,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ identity_on_carrier @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ identity_on_carrier @ quasi_total ) ) )
& ( A @ identity_on_carrier @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(498,axiom,
? [A: $i] : ( A @ latt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(4529,plain,
? [A: $i] : ( A @ latt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) )
<=> ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
thf(2124,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) )
=> ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) )
=> ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(756,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ latt_element_smaller ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ below ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_lattice3) ).
thf(6191,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ below ) ) ) ) )
=> ( C @ ( B @ ( A @ latt_element_smaller ) ) ) )
& ( ( C @ ( B @ ( A @ latt_element_smaller ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ below ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(468,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
thf(4319,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(319,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ! [B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( D = E )
& ( E @ ordinal ) )
& ( B = D )
& ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( B = C ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( D = C )
& ( A @ succ @ ( D @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e18_27__finset_1__1) ).
thf(3146,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ! [B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( D = E )
& ( E @ ordinal ) )
& ( B = D )
& ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( B = C ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( ? [D: $i] :
( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( D = C )
& ( A @ succ @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( D = C )
& ( A @ succ @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(547,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(4879,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(1145,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_wellord1) ).
thf(1018,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) )
=> ( ( B @ ( A @ ( C @ relation_dom_restriction ) @ apply ) )
= ( B @ ( C @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
thf(1845,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) )
=> ( ( B @ ( A @ ( C @ relation_dom_restriction ) @ apply ) )
= ( B @ ( C @ apply ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(23,axiom,
! [A: $i] :
( ( ( A @ identity_relation @ relation_rng )
= A )
& ( ( A @ identity_relation @ relation_dom )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
thf(1003,plain,
! [A: $i] :
( ( ( A @ identity_relation @ relation_rng )
= A )
& ( ( A @ identity_relation @ relation_dom )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(121,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc15_membered) ).
thf(1598,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(658,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ cast_as_carrier_subset )
= ( A @ the_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(5514,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ cast_as_carrier_subset )
= ( A @ the_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(260,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(2661,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(2192,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
& ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(1605,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
& ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ connected_relstr )
& ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ v2_waybel_3 )
& ( A @ connected_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_waybel_3) ).
thf(1647,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ connected_relstr )
& ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ v2_waybel_3 )
& ( A @ connected_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(731,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ( ( E = C )
=> ( D
= ( E @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) ) )
=> ( D = E ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ( ( E = D )
=> ( ( D @ ( C @ apply ) )
= ( E @ ( A @ the_carrier @ subset_complement ) ) ) ) ) )
& ( ( C @ relation_dom )
= B )
& ( C @ function )
& ( C @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e4_7_2__tops_2) ).
thf(5980,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ( ( E = C )
=> ( D
= ( E @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) ) )
=> ( D = E ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( D @ in ) )
=> ! [E: $i] :
( ( A @ the_carrier @ powerset @ ( E @ element ) )
=> ( ( E = D )
=> ( ( D @ ( C @ apply ) )
= ( E @ ( A @ the_carrier @ subset_complement ) ) ) ) ) )
& ( ( C @ relation_dom )
= B )
& ( C @ function )
& ( C @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ boole_lattice @ boolean_lattstr )
& ( A @ boole_lattice @ complemented_lattstr )
& ( A @ boole_lattice @ bounded_lattstr )
& ( A @ boole_lattice @ upper_bounded_semilattstr )
& ( A @ boole_lattice @ lower_bounded_semilattstr )
& ( A @ boole_lattice @ modular_lattstr )
& ( A @ boole_lattice @ distributive_lattstr )
& ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice3) ).
thf(2720,plain,
! [A: $i] :
( ( A @ boole_lattice @ boolean_lattstr )
& ( A @ boole_lattice @ complemented_lattstr )
& ( A @ boole_lattice @ bounded_lattstr )
& ( A @ boole_lattice @ upper_bounded_semilattstr )
& ( A @ boole_lattice @ lower_bounded_semilattstr )
& ( A @ boole_lattice @ modular_lattstr )
& ( A @ boole_lattice @ distributive_lattstr )
& ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(109,axiom,
? [A: $i] :
( ( A @ v3_waybel_3 )
& ( A @ v2_waybel_3 )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_3) ).
thf(1531,plain,
? [A: $i] :
( ( A @ v3_waybel_3 )
& ( A @ v2_waybel_3 )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(284,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ( C @ ( B @ ( A @ is_often_in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_yellow_6) ).
thf(2850,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ( C @ ( B @ ( A @ is_often_in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= F ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_1__tops_2__2) ).
thf(6384,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= F ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ cartesian_product2 ) @ ( F @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ! [I: $i] :
( ( A @ the_carrier @ powerset @ ( I @ element ) )
=> ( ( I = G )
=> ( H
= ( I @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( B @ ( A @ the_carrier @ complements_of_subsets ) @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(798,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ in ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
thf(6577,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ in ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
=> ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
& ( ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ in ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(639,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ union_of_subsets ) )
= ( B @ ( A @ meet_of_subsets ) @ ( A @ subset_complement ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_2) ).
thf(5452,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ union_of_subsets ) )
= ( B @ ( A @ meet_of_subsets ) @ ( A @ subset_complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(573,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ lower_bounded_relstr )
<=> ? [B: $i] :
( ( B @ ( A @ the_carrier @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_yellow_0) ).
thf(5047,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ? [B: $i] :
( ( B @ ( A @ the_carrier @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( B @ element ) ) )
=> ( A @ lower_bounded_relstr ) )
& ( ( A @ lower_bounded_relstr )
=> ? [B: $i] :
( ( B @ ( A @ the_carrier @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(671,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ identity_on_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_as_element ) ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_tmap_1) ).
thf(5607,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ identity_on_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_as_element ) ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ( A @ one_sorted_str ) )
=> ( A @ the_carrier @ powerset @ ( D @ ( C @ ( B @ ( A @ function_invverse_img_as_carrier_subset ) ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_pre_topc) ).
thf(6472,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ( A @ one_sorted_str ) )
=> ( A @ the_carrier @ powerset @ ( D @ ( C @ ( B @ ( A @ function_invverse_img_as_carrier_subset ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(123,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(1611,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(585,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( C
= ( B @ ( A @ lim_points_of_net ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
<=> ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_yellow_6) ).
thf(5111,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) ) ) ) )
=> ( C
= ( B @ ( A @ lim_points_of_net ) ) ) )
& ( ( C
= ( B @ ( A @ lim_points_of_net ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ relation_dom_as_subset ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(5388,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ relation_dom_as_subset ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(141,axiom,
( ! [A: $i] :
( ( A @ ordinal )
=> ( ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( ( omega @ ( B @ in ) )
=> ! [C: $i] :
( ( B @ powerset @ powerset @ ( C @ element ) )
=> ~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( ( E @ ( D @ subset ) )
& ( C @ ( E @ in ) ) )
=> ( E = D ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set ) ) ) ) ) )
=> ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ) ) )
=> ! [A: $i] :
( ( A @ ordinal )
=> ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_ordinal1__e18_27__finset_1__1) ).
thf(1743,plain,
( ! [A: $i] :
( ( A @ ordinal )
=> ( ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( ( omega @ ( B @ in ) )
=> ! [C: $i] :
( ( B @ powerset @ powerset @ ( C @ element ) )
=> ~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( ( E @ ( D @ subset ) )
& ( C @ ( E @ in ) ) )
=> ( E = D ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set ) ) ) ) ) )
=> ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ) ) )
=> ! [A: $i] :
( ( A @ ordinal )
=> ( ( omega @ ( A @ in ) )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ latt_str )
& ~ ( B @ empty_carrier ) )
=> ( ( C @ ( B @ a_2_2_lattice3 ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_lattice3) ).
thf(4939,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ latt_str )
& ~ ( B @ empty_carrier ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) )
=> ( C @ ( B @ a_2_2_lattice3 ) @ ( A @ in ) ) )
& ( ( C @ ( B @ a_2_2_lattice3 ) @ ( A @ in ) )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(5171,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(721,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ open_subset ) )
<=> ( A @ the_topology @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_pre_topc) ).
thf(5944,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ the_topology @ ( B @ in ) )
=> ( A @ ( B @ open_subset ) ) )
& ( ( A @ ( B @ open_subset ) )
=> ( A @ the_topology @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(648,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ unordered_pair_as_carrier_subset ) ) )
= ( C @ ( B @ unordered_pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_struct_0) ).
thf(5484,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ unordered_pair_as_carrier_subset ) ) )
= ( C @ ( B @ unordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(350,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_yellow_1) ).
thf(3462,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(452,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ transitive )
<=> ( A @ relation_field @ ( A @ is_transitive_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_relat_2) ).
thf(4200,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_transitive_in ) )
=> ( A @ transitive ) )
& ( ( A @ transitive )
=> ( A @ relation_field @ ( A @ is_transitive_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(485,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ bottom_of_semilattstr )
= ( empty_set @ ( A @ join_of_latt_set ) ) )
& ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice3) ).
thf(4469,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ bottom_of_semilattstr )
= ( empty_set @ ( A @ join_of_latt_set ) ) )
& ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(280,axiom,
? [A: $i] :
( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_lattices) ).
thf(2821,plain,
? [A: $i] :
( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(4092,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
thf(3940,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B
= ( A @ identity_relation ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= C ) )
& ( ( B @ relation_dom )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(2165,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= C ) )
& ( ( B @ relation_dom )
= A ) )
=> ( B
= ( A @ identity_relation ) ) )
& ( ( B
= ( A @ identity_relation ) )
=> ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= C ) )
& ( ( B @ relation_dom )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(3691,plain,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equipotent ) )
<=> ( B @ ( A @ are_equipotent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r2_wellord2) ).
thf(4020,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ are_equipotent ) )
=> ( B @ ( A @ equipotent ) ) )
& ( ( B @ ( A @ equipotent ) )
=> ( B @ ( A @ are_equipotent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(716,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ~ ( ( B = empty_set )
& ( ( B @ ( A @ complements_of_subsets ) )
!= empty_set ) )
& ~ ( ( ( B @ ( A @ complements_of_subsets ) )
= empty_set )
& ( B != empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).
thf(5912,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ~ ( ( B = empty_set )
& ( ( B @ ( A @ complements_of_subsets ) )
!= empty_set ) )
& ~ ( ( ( B @ ( A @ complements_of_subsets ) )
= empty_set )
& ( B != empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ below_refl ) ) )
<=> ( C @ ( B @ ( A @ below ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(5753,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( ( C @ ( B @ ( A @ below ) ) )
=> ( C @ ( B @ ( A @ below_refl ) ) ) )
& ( ( C @ ( B @ ( A @ below_refl ) ) )
=> ( C @ ( B @ ( A @ below ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(229,axiom,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(2429,plain,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(722,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( ( B @ ( A @ complements_of_subsets ) )
= empty_set )
& ( B != empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(5948,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( ( B @ ( A @ complements_of_subsets ) )
= empty_set )
& ( B != empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(444,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ in ) )
& ( B @ ( D @ in ) ) )
& ( B @ ( C @ in ) ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(4145,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ in ) )
& ( B @ ( D @ in ) ) )
& ( B @ ( C @ in ) ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ rel_str )
& ~ ( B @ empty_carrier )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_on_set_and_struct ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_yellow_6) ).
thf(1830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ rel_str )
& ~ ( B @ empty_carrier )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_on_set_and_struct ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ epsilon_connected )
<=> ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(1336,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) )
=> ( A @ epsilon_connected ) )
& ( ( A @ epsilon_connected )
=> ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ complements_of_subsets ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(5955,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ complements_of_subsets ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( A @ ( B @ ordinal_subset ) )
| ( B @ ( A @ ordinal_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(1053,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( A @ ( B @ ordinal_subset ) )
| ( B @ ( A @ ordinal_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(684,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_often_in ) ) )
<=> ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ? [E: $i] :
( ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) )
& ( E @ ( D @ ( B @ related ) ) )
& ( B @ the_carrier @ ( E @ element ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_waybel_0) ).
thf(5684,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ? [E: $i] :
( ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) )
& ( E @ ( D @ ( B @ related ) ) )
& ( B @ the_carrier @ ( E @ element ) ) ) )
=> ( C @ ( B @ ( A @ is_often_in ) ) ) )
& ( ( C @ ( B @ ( A @ is_often_in ) ) )
=> ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ? [E: $i] :
( ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) )
& ( E @ ( D @ ( B @ related ) ) )
& ( B @ the_carrier @ ( E @ element ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(3448,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_union2 ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(5262,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_union2 ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ( A @ boole_POSet @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_POSet @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ boole_POSet @ related_reflexive ) ) )
<=> ( C @ ( B @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yellow_1) ).
thf(5276,plain,
! [A: $i,B: $i] :
( ( A @ boole_POSet @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_POSet @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ subset ) )
=> ( C @ ( B @ ( A @ boole_POSet @ related_reflexive ) ) ) )
& ( ( C @ ( B @ ( A @ boole_POSet @ related_reflexive ) ) )
=> ( C @ ( B @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
<=> ( B @ ( A @ cartesian_product2 ) @ ( C @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(1785,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ cartesian_product2 ) @ ( C @ subset ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ ( C @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(2276,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(568,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(5030,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(2219,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(441,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(4132,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(218,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(2322,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow_2) ).
thf(951,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ boole_POSet @ the_carrier )
= ( A @ powerset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel_7) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ boole_POSet @ the_carrier )
= ( A @ powerset ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(808,plain,
~ ! [A: $i] :
( ( A @ boole_POSet @ the_carrier )
= ( A @ powerset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ v3_waybel_3 )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ v2_waybel_2 )
& ( A @ v1_waybel_2 )
& ~ ( A @ v1_yellow_3 )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_waybel_4) ).
thf(1285,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ v3_waybel_3 )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ v2_waybel_2 )
& ( A @ v1_waybel_2 )
& ~ ( A @ v1_yellow_3 )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(3853,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(584,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ topstr_closure ) @ ( C @ in ) )
<=> ! [D: $i] :
( ( C @ ( A @ ( D @ point_neighbourhood ) ) )
=> ~ ( B @ ( D @ disjoint ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_6) ).
thf(5106,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( C @ ( A @ ( D @ point_neighbourhood ) ) )
=> ~ ( B @ ( D @ disjoint ) ) )
=> ( B @ ( A @ topstr_closure ) @ ( C @ in ) ) )
& ( ( B @ ( A @ topstr_closure ) @ ( C @ in ) )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ point_neighbourhood ) ) )
=> ~ ( B @ ( D @ disjoint ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(2500,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ( ( B
= ( A @ union ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(312,axiom,
! [A: $i] :
( ( A @ incl_POSet )
= ( A @ inclusion_order @ ( A @ rel_str_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow_1) ).
thf(3107,plain,
! [A: $i] :
( ( A @ incl_POSet )
= ( A @ inclusion_order @ ( A @ rel_str_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( A @ ( B @ strict_net_str ) )
& ( A @ ( B @ net_str ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_waybel_0) ).
thf(2843,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( A @ ( B @ strict_net_str ) )
& ( A @ ( B @ net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(555,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_lattice2) ).
thf(4932,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(625,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(5364,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(416,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_union2 ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(3943,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_union2 ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc38_membered) ).
thf(2939,plain,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(645,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( B @ rel_str )
=> ( ( A @ ( B @ subrelstr ) )
<=> ( ( A @ the_InternalRel @ ( B @ the_InternalRel @ subset ) )
& ( A @ the_carrier @ ( B @ the_carrier @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_yellow_0) ).
thf(5472,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( B @ rel_str )
=> ( ( ( ( A @ the_InternalRel @ ( B @ the_InternalRel @ subset ) )
& ( A @ the_carrier @ ( B @ the_carrier @ subset ) ) )
=> ( A @ ( B @ subrelstr ) ) )
& ( ( A @ ( B @ subrelstr ) )
=> ( ( A @ the_InternalRel @ ( B @ the_InternalRel @ subset ) )
& ( A @ the_carrier @ ( B @ the_carrier @ subset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
& ( A @ well_ordering ) )
=> ( B @ well_ordering ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_wellord1) ).
thf(1372,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
& ( A @ well_ordering ) )
=> ( B @ well_ordering ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(411,axiom,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(3914,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(517,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(4671,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_restriction ) @ ( A @ in ) )
<=> ( ( B @ ( B @ cartesian_product2 ) @ ( A @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
thf(4414,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( B @ ( B @ cartesian_product2 ) @ ( A @ in ) )
& ( C @ ( A @ in ) ) )
=> ( B @ ( C @ relation_restriction ) @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_restriction ) @ ( A @ in ) )
=> ( ( B @ ( B @ cartesian_product2 ) @ ( A @ in ) )
& ( C @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( D = F ) )
& ( A @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e10_24__wellord2__1) ).
thf(2056,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ! [D: $i,E: $i] :
( ( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( D = F ) )
& ( A @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( D = F ) )
& ( A @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(613,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(5319,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(344,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(3415,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(737,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ directed_subset ) )
& ~ ( B @ empty ) )
<=> ! [C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( D @ in ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_waybel_0) ).
thf(6073,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ! [C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( D @ in ) )
& ( A @ the_carrier @ ( D @ element ) ) ) )
=> ( ( A @ ( B @ directed_subset ) )
& ~ ( B @ empty ) ) )
& ( ( ( A @ ( B @ directed_subset ) )
& ~ ( B @ empty ) )
=> ! [C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( D @ in ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ unordered_pair ) @ subset ) )
<=> ( ( C @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(3829,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( C @ ( B @ ( A @ unordered_pair ) @ subset ) ) )
& ( ( C @ ( B @ ( A @ unordered_pair ) @ subset ) )
=> ( ( C @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(619,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ topstr_closure ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(5347,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ topstr_closure ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(512,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(4624,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(2711,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(1506,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(739,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = D )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( D @ in ) )
& ( B @ ( D @ in ) ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e4_7_2__tops_2__1) ).
thf(6086,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ! [D: $i,E: $i] :
( ( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = D )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( D @ in ) )
& ( B @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = D )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( D @ in ) )
& ( B @ ( D @ in ) ) ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(38,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(1094,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ natural )
& ( A @ ordinal ) )
=> ( ( A @ succ @ natural )
& ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_arytm_3) ).
thf(978,plain,
! [A: $i] :
( ( ( A @ natural )
& ( A @ ordinal ) )
=> ( ( A @ succ @ natural )
& ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(495,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( ( ( A @ well_founded_relation )
=> ( B @ well_founded_relation ) )
& ( ( A @ antisymmetric )
=> ( B @ antisymmetric ) )
& ( ( A @ connected )
=> ( B @ connected ) )
& ( ( A @ transitive )
=> ( B @ transitive ) )
& ( ( A @ reflexive )
=> ( B @ reflexive ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_wellord1) ).
thf(4516,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( ( ( A @ well_founded_relation )
=> ( B @ well_founded_relation ) )
& ( ( A @ antisymmetric )
=> ( B @ antisymmetric ) )
& ( ( A @ connected )
=> ( B @ connected ) )
& ( ( A @ transitive )
=> ( B @ transitive ) )
& ( ( A @ reflexive )
=> ( B @ reflexive ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ subnetstr ) ) )
& ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ strict_net_str ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_yellow_6) ).
thf(4150,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ subnetstr ) ) )
& ( A @ ( C @ ( B @ ( A @ preimage_subnetstr ) ) @ strict_net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(713,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_waybel_0) ).
thf(5895,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ union_of_subsets ) )
= ( B @ ( A @ meet_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(6220,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ union_of_subsets ) )
= ( B @ ( A @ meet_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(3288,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( C @ relation_rng @ ( B @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(2760,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( C @ relation_rng @ ( B @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(2924,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(525,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_connected_in ) )
<=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( C != D )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
thf(4698,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( C != D )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( A @ is_connected_in ) ) )
& ( ( B @ ( A @ is_connected_in ) )
=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( C != D )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(385,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finset_1) ).
thf(3757,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(92,axiom,
! [A: $i] : ( A @ inclusion_relation @ reflexive ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
thf(1459,plain,
! [A: $i] : ( A @ inclusion_relation @ reflexive ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(291,axiom,
? [A: $i] :
( ( A @ trivial_carrier )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_yellow_0) ).
thf(2885,plain,
? [A: $i] :
( ( A @ trivial_carrier )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( B @ ( A @ relation_rng_restriction ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
thf(2960,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( B @ ( A @ relation_rng_restriction ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( B @ ( A @ set_intersection2 ) @ v5_membered )
& ( B @ ( A @ set_intersection2 ) @ v4_membered )
& ( B @ ( A @ set_intersection2 ) @ v3_membered )
& ( B @ ( A @ set_intersection2 ) @ v2_membered )
& ( B @ ( A @ set_intersection2 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc35_membered) ).
thf(3533,plain,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( B @ ( A @ set_intersection2 ) @ v5_membered )
& ( B @ ( A @ set_intersection2 ) @ v4_membered )
& ( B @ ( A @ set_intersection2 ) @ v3_membered )
& ( B @ ( A @ set_intersection2 ) @ v2_membered )
& ( B @ ( A @ set_intersection2 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(216,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(2310,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(413,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ subset ) )
=> ( ( ( C @ ( B @ ( A @ is_often_in ) ) )
=> ( D @ ( B @ ( A @ is_often_in ) ) ) )
& ( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ( D @ ( B @ ( A @ is_eventually_in ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_waybel_0) ).
thf(3928,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ subset ) )
=> ( ( ( C @ ( B @ ( A @ is_often_in ) ) )
=> ( D @ ( B @ ( A @ is_often_in ) ) ) )
& ( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ( D @ ( B @ ( A @ is_eventually_in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(145,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i,D: $i] :
( ( B @ ( A @ ( D @ subnet ) ) )
=> ( ( D
= ( C @ ( B @ ( A @ preimage_subnetstr ) ) ) )
=> ( C @ ( D @ ( A @ is_eventually_in ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_yellow_6) ).
thf(1781,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i,D: $i] :
( ( B @ ( A @ ( D @ subnet ) ) )
=> ( ( D
= ( C @ ( B @ ( A @ preimage_subnetstr ) ) ) )
=> ( C @ ( D @ ( A @ is_eventually_in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(54,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(1189,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ set_intersection2 ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc27_membered) ).
thf(4678,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ set_intersection2 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(720,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( B @ ( C @ in ) )
=> ( A @ ( C @ closed_subset ) ) ) )
=> ( A @ ( B @ ( A @ the_carrier @ meet_of_subsets ) @ closed_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_pre_topc) ).
thf(5939,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( B @ ( C @ in ) )
=> ( A @ ( C @ closed_subset ) ) ) )
=> ( A @ ( B @ ( A @ the_carrier @ meet_of_subsets ) @ closed_subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(465,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(4278,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(3401,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ~ ( ( ( A @ ( B @ relation_inverse_image ) )
= empty_set )
& ( B @ relation_rng @ ( A @ subset ) )
& ( A != empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
thf(2088,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ~ ( ( ( A @ ( B @ relation_inverse_image ) )
= empty_set )
& ( B @ relation_rng @ ( A @ subset ) )
& ( A != empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(734,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ? [C: $i] :
( ( ( B @ ( A @ topstr_closure ) )
= ( C @ ( A @ the_carrier @ meet_of_subsets ) ) )
& ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
<=> ( ( D @ ( B @ subset ) )
& ( A @ ( D @ closed_subset ) ) ) ) )
& ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_pre_topc) ).
thf(6041,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ? [C: $i] :
( ( ( B @ ( A @ topstr_closure ) )
= ( C @ ( A @ the_carrier @ meet_of_subsets ) ) )
& ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( ( ( D @ ( B @ subset ) )
& ( A @ ( D @ closed_subset ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D @ ( B @ subset ) )
& ( A @ ( D @ closed_subset ) ) ) ) ) )
& ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ connected_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ connected_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_waybel_3) ).
thf(1553,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ connected_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ connected_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(5660,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(477,axiom,
! [A: $i] :
( ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
thf(4419,plain,
! [A: $i] :
( ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( F
= ( H @ ( G @ ordered_pair ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( F = E )
& ( A @ ( A @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
thf(4559,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( B @ relation ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( F
= ( H @ ( G @ ordered_pair ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( F = E )
& ( A @ ( A @ cartesian_product2 ) @ ( F @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ( B @ ( H @ ( C @ apply ) @ ( G @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( E
= ( H @ ( G @ ordered_pair ) ) ) )
& ( F = E )
& ( A @ ( A @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(535,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(4780,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(83,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ boolean_relstr )
& ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ heyting_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ trivial_carrier )
& ~ ( A @ boole_POSet @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_waybel_7) ).
thf(1390,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ boolean_relstr )
& ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ heyting_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ trivial_carrier )
& ~ ( A @ boole_POSet @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ full_subnetstr ) ) )
& ( A @ ( C @ strict_net_str ) )
& ( B @ ( A @ ( C @ subnetstr ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_yellow_6) ).
thf(2305,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ full_subnetstr ) ) )
& ( A @ ( C @ strict_net_str ) )
& ( B @ ( A @ ( C @ subnetstr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function )
& ( B @ ( A @ the_mapping ) @ relation )
& ~ ( B @ ( A @ the_mapping ) @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_yellow_6) ).
thf(3056,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function )
& ( B @ ( A @ the_mapping ) @ relation )
& ~ ( B @ ( A @ the_mapping ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ relation_rng_restriction ) @ relation_rng )
= ( A @ ( B @ relation_rng @ set_intersection2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
thf(1453,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ relation_rng_restriction ) @ relation_rng )
= ( A @ ( B @ relation_rng @ set_intersection2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(616,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(5332,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( B @ ( B @ ( A @ relation_restriction_as_relation_of ) @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_toler_1) ).
thf(2658,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( B @ ( B @ ( A @ relation_restriction_as_relation_of ) @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ ( C @ relation_dom_restriction ) @ apply ) )
= ( B @ ( C @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
thf(1590,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ ( C @ relation_dom_restriction ) @ apply ) )
= ( B @ ( C @ apply ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(366,axiom,
! [A: $i] :
( ( A @ identity_relation @ transitive )
& ( A @ identity_relation @ antisymmetric )
& ( A @ identity_relation @ symmetric )
& ( A @ identity_relation @ reflexive )
& ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_partfun1) ).
thf(3613,plain,
! [A: $i] :
( ( A @ identity_relation @ transitive )
& ( A @ identity_relation @ antisymmetric )
& ( A @ identity_relation @ symmetric )
& ( A @ identity_relation @ reflexive )
& ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(407,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(3864,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_waybel_1) ).
thf(896,plain,
! [A: $i] :
( ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = F ) )
& ( D = F )
& ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( F = E )
& ( C @ powerset @ ( F @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e11_2_1__waybel_0__1) ).
thf(6607,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = F ) )
& ( D = F )
& ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( F = E )
& ( C @ powerset @ ( F @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( F = E )
& ( C @ powerset @ ( F @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( B @ ( A @ relation_composition ) @ relation_rng @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(1481,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( B @ ( A @ relation_composition ) @ relation_rng @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(946,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ rel_str_of ) @ rel_str )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(4126,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ rel_str_of ) @ rel_str )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(321,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ subset ) )
=> ( ( B @ relation_rng @ ( A @ relation_rng @ subset ) )
& ( B @ relation_dom @ ( A @ relation_dom @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(3235,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ subset ) )
=> ( ( B @ relation_rng @ ( A @ relation_rng @ subset ) )
& ( B @ relation_dom @ ( A @ relation_dom @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(488,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(4495,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(655,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( A @ bottom_of_semilattstr @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(5505,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( A @ bottom_of_semilattstr @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( A @ powerset @ powerset @ ( B @ element ) ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ ( C @ relation_image ) @ in ) )
& ( D = F )
& ( B @ ( E @ ( C @ relation_image ) @ in ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ? [F: $i] :
( ( B @ ( E @ ( C @ relation_image ) @ in ) )
& ( F = E )
& ( C @ relation_dom @ powerset @ ( F @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
thf(2135,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( A @ powerset @ powerset @ ( B @ element ) ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ ( C @ relation_image ) @ in ) )
& ( D = F )
& ( B @ ( E @ ( C @ relation_image ) @ in ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( C @ relation_image ) @ in ) )
& ( F = E )
& ( C @ relation_dom @ powerset @ ( F @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ? [F: $i] :
( ( B @ ( E @ ( C @ relation_image ) @ in ) )
& ( F = E )
& ( C @ relation_dom @ powerset @ ( F @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(2406,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(433,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ~ ( ~ ( A @ ( B @ in ) )
& ( A != B )
& ~ ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(4089,plain,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ~ ( ~ ( A @ ( B @ in ) )
& ( A != B )
& ~ ( B @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(628,axiom,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
thf(5382,plain,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(244,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_dom )
= empty_set )
<=> ( ( A @ relation_rng )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(2532,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ relation_rng )
= empty_set )
=> ( ( A @ relation_dom )
= empty_set ) )
& ( ( ( A @ relation_dom )
= empty_set )
=> ( ( A @ relation_rng )
= empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(520,axiom,
! [A: $i] :
( ( A @ inclusion_order )
= ( A @ inclusion_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_yellow_1) ).
thf(4681,plain,
! [A: $i] :
( ( A @ inclusion_order )
= ( A @ inclusion_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( A @ ( B @ relation_dom_restriction ) @ relation_rng @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
thf(1508,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( A @ ( B @ relation_dom_restriction ) @ relation_rng @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(2764,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(1822,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(318,axiom,
! [A: $i] :
( ( A @ incl_POSet @ antisymmetric_relstr )
& ( A @ incl_POSet @ transitive_relstr )
& ( A @ incl_POSet @ reflexive_relstr )
& ( A @ incl_POSet @ strict_rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_yellow_1) ).
thf(3136,plain,
! [A: $i] :
( ( A @ incl_POSet @ antisymmetric_relstr )
& ( A @ incl_POSet @ transitive_relstr )
& ( A @ incl_POSet @ reflexive_relstr )
& ( A @ incl_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(338,axiom,
! [A: $i] :
( ( ( A @ transitive )
& ( A @ symmetric )
& ( A @ relation ) )
=> ( ( A @ reflexive )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_partfun1) ).
thf(3368,plain,
! [A: $i] :
( ( ( A @ transitive )
& ( A @ symmetric )
& ( A @ relation ) )
=> ( ( A @ reflexive )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(4527,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ reflexive )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ function ) )
=> ( ( A @ ( A @ ( B @ bijective ) ) )
& ( A @ ( A @ ( B @ onto ) ) )
& ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ one_to_one )
& ( B @ function ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_funct_2) ).
thf(3780,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ reflexive )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ function ) )
=> ( ( A @ ( A @ ( B @ bijective ) ) )
& ( A @ ( A @ ( B @ onto ) ) )
& ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ one_to_one )
& ( B @ function ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(532,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(4759,plain,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(631,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ cast_as_carrier_subset )
= ( A @ the_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(5409,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ cast_as_carrier_subset )
= ( A @ the_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(791,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( C @ ( B @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(6536,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( C @ ( B @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(419,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(3993,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ~ ( A @ empty ) )
=> ( ( B @ ( A @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ rel_str_of ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_2) ).
thf(2120,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ~ ( A @ empty ) )
=> ( ( B @ ( A @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ rel_str_of ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(659,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ identity_on_carrier )
= ( A @ the_carrier @ identity_as_relation_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_grcat_1) ).
thf(5517,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ identity_on_carrier )
= ( A @ the_carrier @ identity_as_relation_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(239,axiom,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(2494,plain,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(611,axiom,
! [A: $i] : ( A @ powerset @ powerset @ ( A @ k1_pcomps_1 @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(5287,plain,
! [A: $i] : ( A @ powerset @ powerset @ ( A @ k1_pcomps_1 @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(28,axiom,
? [A: $i] :
( ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_waybel_1) ).
thf(1030,plain,
? [A: $i] :
( ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(726,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( B @ top_str )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ! [D: $i] :
( ( B @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( ( ( C @ ( A @ interior ) )
= C )
=> ( A @ ( C @ open_subset ) ) )
& ( ( B @ ( D @ open_subset ) )
=> ( ( D @ ( B @ interior ) )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
thf(5963,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( B @ top_str )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ! [D: $i] :
( ( B @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( ( ( C @ ( A @ interior ) )
= C )
=> ( A @ ( C @ open_subset ) ) )
& ( ( B @ ( D @ open_subset ) )
=> ( ( D @ ( B @ interior ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_intersection2 ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(2956,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_intersection2 ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(377,axiom,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_rng @ ( A @ relation_dom @ cartesian_product2 ) @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(3694,plain,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_rng @ ( A @ relation_dom @ cartesian_product2 ) @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(278,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ~ ( B @ ( C @ are_equipotent ) )
& ( B @ ( C @ subset ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ subset ) )
=> ( D @ ( E @ in ) ) )
& ( B @ ( D @ in ) ) )
& ( B @ ( C @ in ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ subset ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(2786,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ~ ( B @ ( C @ are_equipotent ) )
& ( B @ ( C @ subset ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ subset ) )
=> ( D @ ( E @ in ) ) )
& ( B @ ( D @ in ) ) )
& ( B @ ( C @ in ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ subset ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(741,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( F @ ( E @ ( B @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_yellow_0) ).
thf(6118,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( F @ ( E @ ( B @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(693,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ interior ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(5781,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ interior ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(701,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( ( A @ topological_space )
<=> ( ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( ( A @ the_topology @ ( C @ in ) )
& ( A @ the_topology @ ( B @ in ) ) )
=> ( A @ the_topology @ ( C @ ( B @ ( A @ the_carrier @ subset_intersection2 ) ) @ in ) ) ) ) )
& ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( A @ the_topology @ ( B @ subset ) )
=> ( A @ the_topology @ ( B @ ( A @ the_carrier @ union_of_subsets ) @ in ) ) ) )
& ( A @ the_topology @ ( A @ the_carrier @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_pre_topc) ).
thf(5837,plain,
! [A: $i] :
( ( A @ top_str )
=> ( ( ( ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( ( A @ the_topology @ ( C @ in ) )
& ( A @ the_topology @ ( B @ in ) ) )
=> ( A @ the_topology @ ( C @ ( B @ ( A @ the_carrier @ subset_intersection2 ) ) @ in ) ) ) ) )
& ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( A @ the_topology @ ( B @ subset ) )
=> ( A @ the_topology @ ( B @ ( A @ the_carrier @ union_of_subsets ) @ in ) ) ) )
& ( A @ the_topology @ ( A @ the_carrier @ in ) ) )
=> ( A @ topological_space ) )
& ( ( A @ topological_space )
=> ( ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( ( A @ the_topology @ ( C @ in ) )
& ( A @ the_topology @ ( B @ in ) ) )
=> ( A @ the_topology @ ( C @ ( B @ ( A @ the_carrier @ subset_intersection2 ) ) @ in ) ) ) ) )
& ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( A @ the_topology @ ( B @ subset ) )
=> ( A @ the_topology @ ( B @ ( A @ the_carrier @ union_of_subsets ) @ in ) ) ) )
& ( A @ the_topology @ ( A @ the_carrier @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) )
<=> ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
thf(1440,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) ) )
& ( ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) )
=> ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) )
& ~ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_waybel_0) ).
thf(5590,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) )
& ~ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(796,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ open_subsets ) )
<=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( B @ ( C @ in ) )
=> ( A @ ( C @ open_subset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_2) ).
thf(6569,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( B @ ( C @ in ) )
=> ( A @ ( C @ open_subset ) ) ) )
=> ( A @ ( B @ open_subsets ) ) )
& ( ( A @ ( B @ open_subsets ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( B @ ( C @ in ) )
=> ( A @ ( C @ open_subset ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ point_neighbourhood ) ) )
=> ( A @ the_carrier @ powerset @ ( C @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
thf(5336,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ point_neighbourhood ) ) )
=> ( A @ the_carrier @ powerset @ ( C @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(276,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( ( B @ ( A @ ( C @ full_subnetstr ) ) )
<=> ( ( B @ ( C @ subrelstr ) )
& ( B @ ( C @ full_subrelstr ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_yellow_6) ).
thf(2779,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnetstr ) ) )
=> ( ( ( ( B @ ( C @ subrelstr ) )
& ( B @ ( C @ full_subrelstr ) ) )
=> ( B @ ( A @ ( C @ full_subnetstr ) ) ) )
& ( ( B @ ( A @ ( C @ full_subnetstr ) ) )
=> ( ( B @ ( C @ subrelstr ) )
& ( B @ ( C @ full_subrelstr ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_image ) )
= ( A @ ( B @ relation_dom @ set_intersection2 ) @ ( B @ relation_image ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
thf(3658,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_image ) )
= ( A @ ( B @ relation_dom @ set_intersection2 ) @ ( B @ relation_image ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( A @ powerset @ powerset @ ( B @ element ) ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ( B @ ( E @ ( C @ relation_image ) @ in ) )
& ( C @ relation_dom @ powerset @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
thf(1774,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation )
& ( A @ powerset @ powerset @ ( B @ element ) ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( ( B @ ( E @ ( C @ relation_image ) @ in ) )
& ( C @ relation_dom @ powerset @ ( E @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ( ( B @ ( E @ ( C @ relation_image ) @ in ) )
& ( C @ relation_dom @ powerset @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ subnetstr ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_yellow_6) ).
thf(2683,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ subnetstr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= F ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( A @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__2) ).
thf(3705,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= F ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( A @ cartesian_product2 ) @ ( F @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( A @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(757,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( A @ relation_of_lattice @ ( C @ ( B @ ( A @ the_carrier @ ( A @ the_carrier @ ordered_pair_as_product_element ) ) ) @ in ) )
<=> ( C @ ( B @ ( A @ below_refl ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
thf(6201,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ ( A @ below_refl ) ) )
=> ( A @ relation_of_lattice @ ( C @ ( B @ ( A @ the_carrier @ ( A @ the_carrier @ ordered_pair_as_product_element ) ) ) @ in ) ) )
& ( ( A @ relation_of_lattice @ ( C @ ( B @ ( A @ the_carrier @ ( A @ the_carrier @ ordered_pair_as_product_element ) ) ) @ in ) )
=> ( C @ ( B @ ( A @ below_refl ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ ( E @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( F @ in ) )
& ( A @ the_carrier @ ( F @ element ) ) )
& ( C @ ( E @ subset ) )
& ( C @ ( D @ in ) ) )
=> ? [F: $i] :
( ( F @ ( D @ singleton @ ( E @ set_union2 ) @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( F @ in ) )
& ( A @ the_carrier @ ( F @ element ) ) ) )
& ? [D: $i] :
( ( D @ ( empty_set @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( D @ in ) )
& ( A @ the_carrier @ ( D @ element ) ) )
& ( C @ finite ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( D @ in ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_finset_1__e11_2_1__waybel_0) ).
thf(3291,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ ( E @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( F @ in ) )
& ( A @ the_carrier @ ( F @ element ) ) )
& ( C @ ( E @ subset ) )
& ( C @ ( D @ in ) ) )
=> ? [F: $i] :
( ( F @ ( D @ singleton @ ( E @ set_union2 ) @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( F @ in ) )
& ( A @ the_carrier @ ( F @ element ) ) ) )
& ? [D: $i] :
( ( D @ ( empty_set @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( D @ in ) )
& ( A @ the_carrier @ ( D @ element ) ) )
& ( C @ finite ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( D @ in ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ rel_str_of ) )
= ( D @ ( C @ rel_str_of ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(2587,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ rel_str_of ) )
= ( D @ ( C @ rel_str_of ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(3892,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) )
& ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(326,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(3264,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(528,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
<=> ( ( B @ relation_dom @ ( A @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
thf(4719,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ( B @ relation_dom @ ( A @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) )
=> ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
=> ( ( B @ relation_dom @ ( A @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(670,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc19_membered) ).
thf(5601,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(307,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(3062,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ powerset @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(6600,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ powerset @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(606,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ meet_absorbing )
<=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( C @ ( B @ ( A @ meet ) ) @ ( A @ join ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattices) ).
thf(5268,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( C @ ( B @ ( A @ meet ) ) @ ( A @ join ) ) )
= C ) ) )
=> ( A @ meet_absorbing ) )
& ( ( A @ meet_absorbing )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( C @ ( B @ ( A @ meet ) ) @ ( A @ join ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
<=> ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).
thf(2233,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ~ ( B @ empty )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ function ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(1593,plain,
! [A: $i,B: $i] :
( ~ ( B @ empty )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ function ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ poset_of_lattice @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( A @ ( B @ poset_of_lattice @ relstr_element_smaller ) ) )
<=> ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_set_smaller ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattice3) ).
thf(5356,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ poset_of_lattice @ the_carrier @ ( C @ element ) )
=> ( ( ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_set_smaller ) ) )
=> ( C @ ( A @ ( B @ poset_of_lattice @ relstr_element_smaller ) ) ) )
& ( ( C @ ( A @ ( B @ poset_of_lattice @ relstr_element_smaller ) ) )
=> ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_set_smaller ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_dom )
= ( A @ relation_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ relation_inverse @ relation_dom ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(1380,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_dom )
= ( A @ relation_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ relation_inverse @ relation_dom ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(579,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ closed_subset ) )
<=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
thf(5078,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) )
=> ( A @ ( B @ closed_subset ) ) )
& ( ( A @ ( B @ closed_subset ) )
=> ( A @ ( B @ ( A @ the_carrier @ subset_complement ) @ open_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(496,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ related ) ) )
<=> ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
thf(4523,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( C @ ( B @ ( A @ related ) ) ) )
& ( ( C @ ( B @ ( A @ related ) ) )
=> ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i] :
( ? [G: $i] :
( ( G @ ( F @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( G @ in ) )
& ( A @ the_carrier @ ( G @ element ) ) )
& ( F = E ) )
& ( C @ powerset @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e11_2_1__waybel_0__1) ).
thf(5522,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( ? [F: $i] :
( ? [G: $i] :
( ( G @ ( F @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( G @ in ) )
& ( A @ the_carrier @ ( G @ element ) ) )
& ( F = E ) )
& ( C @ powerset @ ( E @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( G @ ( F @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( G @ in ) )
& ( A @ the_carrier @ ( G @ element ) ) )
& ( F = E ) )
& ( C @ powerset @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(1673,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_intersection2 ) ) )
= ( C @ ( B @ set_intersection2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(5477,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_intersection2 ) ) )
= ( C @ ( B @ set_intersection2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(180,axiom,
! [A: $i] :
( ( A @ incl_POSet @ rel_str )
& ( A @ incl_POSet @ strict_rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
thf(2050,plain,
! [A: $i] :
( ( A @ incl_POSet @ rel_str )
& ( A @ incl_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(398,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(3822,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(534,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field )
= ( A @ relation_rng @ ( A @ relation_dom @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(4777,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field )
= ( A @ relation_rng @ ( A @ relation_dom @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
thf(1495,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(467,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(4286,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_image ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(454,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_waybel_0) ).
thf(4210,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ set_difference ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc37_membered) ).
thf(4427,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ set_difference ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(560,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_join @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function )
& ( A @ the_L_join @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lattice2) ).
thf(4968,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_join @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function )
& ( A @ the_L_join @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(5835,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ with_suprema_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ upper_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc9_waybel_0) ).
thf(1197,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ with_suprema_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ upper_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(2091,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_intersection2 ) )
= empty_set )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ singleton @ finite )
& ~ ( A @ singleton @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(2714,plain,
! [A: $i] :
( ( A @ singleton @ finite )
& ~ ( A @ singleton @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(551,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(4912,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(220,axiom,
? [A: $i] :
( ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(2340,plain,
? [A: $i] :
( ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(403,axiom,
? [A: $i] : ( A @ join_semilatt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(3843,plain,
? [A: $i] : ( A @ join_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(257,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(2651,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ well_orders ) )
<=> ( ( B @ ( A @ is_well_founded_in ) )
& ( B @ ( A @ is_connected_in ) )
& ( B @ ( A @ is_antisymmetric_in ) )
& ( B @ ( A @ is_transitive_in ) )
& ( B @ ( A @ is_reflexive_in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_wellord1) ).
thf(928,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ( ( B @ ( A @ is_well_founded_in ) )
& ( B @ ( A @ is_connected_in ) )
& ( B @ ( A @ is_antisymmetric_in ) )
& ( B @ ( A @ is_transitive_in ) )
& ( B @ ( A @ is_reflexive_in ) ) )
=> ( B @ ( A @ well_orders ) ) )
& ( ( B @ ( A @ well_orders ) )
=> ( ( B @ ( A @ is_well_founded_in ) )
& ( B @ ( A @ is_connected_in ) )
& ( B @ ( A @ is_antisymmetric_in ) )
& ( B @ ( A @ is_transitive_in ) )
& ( B @ ( A @ is_reflexive_in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ boolean_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ distributive_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
thf(1473,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ boolean_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ distributive_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_union2 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(5215,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_union2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(1129,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(380,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(3701,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(589,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( ( ( B @ ( A @ topstr_closure ) )
= B )
& ( A @ topological_space ) )
=> ( A @ ( B @ closed_subset ) ) )
& ( ( A @ ( B @ closed_subset ) )
=> ( ( B @ ( A @ topstr_closure ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_pre_topc) ).
thf(5151,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( ( ( B @ ( A @ topstr_closure ) )
= B )
& ( A @ topological_space ) )
=> ( A @ ( B @ closed_subset ) ) )
& ( ( A @ ( B @ closed_subset ) )
=> ( ( B @ ( A @ topstr_closure ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(676,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_semilattstr )
<=> ? [B: $i] :
( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_lattices) ).
thf(5637,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ? [B: $i] :
( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
& ( A @ the_carrier @ ( B @ element ) ) )
=> ( A @ lower_bounded_semilattstr ) )
& ( ( A @ lower_bounded_semilattstr )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(459,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_well_founded_in ) )
<=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ ( A @ fiber ) @ disjoint ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set )
& ( B @ ( C @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_wellord1) ).
thf(4239,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ ( A @ fiber ) @ disjoint ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set )
& ( B @ ( C @ subset ) ) )
=> ( B @ ( A @ is_well_founded_in ) ) )
& ( ( B @ ( A @ is_well_founded_in ) )
=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ ( A @ fiber ) @ disjoint ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set )
& ( B @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(725,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
<=> ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) ) ) )
& ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
thf(5958,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) ) ) ) )
& ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ union_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) )
= ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(6595,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ union_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) )
= ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(1880,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(794,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ lim_points_of_net ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_yellow_6) ).
thf(6548,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ lim_points_of_net ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(4501,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( B != empty_set )
=> ! [E: $i] :
( ( C @ ( D @ relation_inverse_image ) @ ( E @ in ) )
<=> ( ( C @ ( E @ ( D @ apply ) @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_2) ).
thf(3918,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( B != empty_set )
=> ! [E: $i] :
( ( ( ( C @ ( E @ ( D @ apply ) @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( D @ relation_inverse_image ) @ ( E @ in ) ) )
& ( ( C @ ( D @ relation_inverse_image ) @ ( E @ in ) )
=> ( ( C @ ( E @ ( D @ apply ) @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(336,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(3362,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_restriction ) @ relation_field @ ( A @ in ) )
=> ( ( B @ ( A @ in ) )
& ( C @ relation_field @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_wellord1) ).
thf(1352,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_restriction ) @ relation_field @ ( A @ in ) )
=> ( ( B @ ( A @ in ) )
& ( C @ relation_field @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(539,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( B @ v1_xcmplx_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_membered) ).
thf(4799,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( B @ v1_xcmplx_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) )
= ( F @ ( E @ ( D @ apply_binary ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(2847,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) )
= ( F @ ( E @ ( D @ apply_binary ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(343,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).
thf(3411,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_dom_restriction ) @ relation_dom )
= ( A @ ( B @ relation_dom @ set_intersection2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
thf(2485,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_dom_restriction ) @ relation_dom )
= ( A @ ( B @ relation_dom @ set_intersection2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
=> ( ( A @ ( B @ ( C @ relation_composition ) @ apply ) )
= ( A @ ( C @ apply ) @ ( B @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
thf(3772,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
=> ( ( A @ ( B @ ( C @ relation_composition ) @ apply ) )
= ( A @ ( C @ apply ) @ ( B @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(546,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( B @ ( A @ subset ) ) )
=> ( A @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(4876,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( B @ ( A @ subset ) ) )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ unordered_pair_as_carrier_subset ) ) )
= ( B @ ( C @ ( A @ unordered_pair_as_carrier_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(5975,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ unordered_pair_as_carrier_subset ) ) )
= ( B @ ( C @ ( A @ unordered_pair_as_carrier_subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(758,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ transitive_relstr )
<=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_0) ).
thf(6205,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) ) ) )
=> ( A @ transitive_relstr ) )
& ( ( A @ transitive_relstr )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(493,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
thf(4506,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) )
<=> ( ( A @ ( B @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
thf(4066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ( A @ ( B @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) )
=> ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) ) )
& ( ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) )
=> ( ( A @ ( B @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ the_carrier @ ( D @ element ) )
& ( A @ the_carrier @ ( C @ element ) )
& ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( A @ k8_filter_1 ) @ the_carrier @ ( D @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_1) ).
thf(5280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ the_carrier @ ( D @ element ) )
& ( A @ the_carrier @ ( C @ element ) )
& ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( A @ k8_filter_1 ) @ the_carrier @ ( D @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_waybel_1) ).
thf(992,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(396,axiom,
! [A: $i] :
~ ( A @ succ @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(3817,plain,
! [A: $i] :
~ ( A @ succ @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(167,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(1923,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(683,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= ( C @ ( B @ ( A @ the_L_join @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattices) ).
thf(5681,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= ( C @ ( B @ ( A @ the_L_join @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(599,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = D )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( D @ in ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( D @ in ) ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e4_7_1__tops_2__1) ).
thf(5219,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ one_sorted_str ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) )
& ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = C )
=> ( D
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ! [D: $i,E: $i] :
( ( ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = D )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( D @ in ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ! [F: $i] :
( ( A @ the_carrier @ powerset @ ( F @ element ) )
=> ( ( F = D )
=> ( E
= ( F @ ( A @ the_carrier @ subset_complement ) ) ) ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( D @ in ) )
& ( B @ ( A @ the_carrier @ complements_of_subsets ) @ ( D @ in ) ) ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(643,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ in ) )
& ( A @ ( B @ open_subset ) ) )
=> ( C @ ( A @ ( B @ point_neighbourhood ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
thf(5468,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ in ) )
& ( A @ ( B @ open_subset ) ) )
=> ( C @ ( A @ ( B @ point_neighbourhood ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_waybel_0) ).
thf(850,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_yellow_0) ).
thf(1713,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(5354,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(430,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(4071,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(314,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ ordered_pair ) ) )
=> ! [B: $i] :
( ( B
= ( A @ pair_second ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).
thf(3113,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ ordered_pair ) ) )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = D ) )
=> ( B
= ( A @ pair_second ) ) )
& ( ( B
= ( A @ pair_second ) )
=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
=> ( B = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(352,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(3474,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(255,axiom,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ bijective ) ) )
& ( A @ ( A @ ( B @ onto ) ) )
& ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( A @ ( A @ ( B @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_2) ).
thf(2640,plain,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ bijective ) ) )
& ( A @ ( A @ ( B @ onto ) ) )
& ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( A @ ( A @ ( B @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(707,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(5877,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(515,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(4642,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(513,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ v2_waybel_3 )
& ( A @ up_complete_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ v3_waybel_3 )
& ( A @ lower_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_waybel_3) ).
thf(4627,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ v2_waybel_3 )
& ( A @ up_complete_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ v3_waybel_3 )
& ( A @ lower_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(677,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ v1_partfun1 ) ) )
& ( A @ k2_lattice3 @ transitive )
& ( A @ k2_lattice3 @ antisymmetric )
& ( A @ k2_lattice3 @ reflexive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattice3) ).
thf(5649,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ v1_partfun1 ) ) )
& ( A @ k2_lattice3 @ transitive )
& ( A @ k2_lattice3 @ antisymmetric )
& ( A @ k2_lattice3 @ reflexive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(448,axiom,
? [A: $i] :
( ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(4161,plain,
? [A: $i] :
( ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ~ ( ( C @ ( B @ in ) )
& ( C @ ( A @ subset_complement ) @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(6575,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ~ ( ( C @ ( B @ in ) )
& ( C @ ( A @ subset_complement ) @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(234,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ empty_carrier_subset )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_pre_topc) ).
thf(2470,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ empty_carrier_subset )
= empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(736,axiom,
! [A: $i,B: $i] :
( ( A @ boole_lattice @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_lattice @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ ( A @ boole_lattice @ meet ) ) )
= ( C @ ( B @ set_intersection2 ) ) )
& ( ( C @ ( B @ ( A @ boole_lattice @ join ) ) )
= ( C @ ( B @ set_union2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).
thf(6067,plain,
! [A: $i,B: $i] :
( ( A @ boole_lattice @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_lattice @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ ( A @ boole_lattice @ meet ) ) )
= ( C @ ( B @ set_intersection2 ) ) )
& ( ( C @ ( B @ ( A @ boole_lattice @ join ) ) )
= ( C @ ( B @ set_union2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ reflexive ) )
=> ( ( B @ ( A @ rel_str_of ) @ antisymmetric_relstr )
& ( B @ ( A @ rel_str_of ) @ transitive_relstr )
& ( B @ ( A @ rel_str_of ) @ reflexive_relstr )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_orders_2) ).
thf(2754,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ reflexive ) )
=> ( ( B @ ( A @ rel_str_of ) @ antisymmetric_relstr )
& ( B @ ( A @ rel_str_of ) @ transitive_relstr )
& ( B @ ( A @ rel_str_of ) @ reflexive_relstr )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(4335,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(751,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ closed_subsets ) )
<=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( B @ ( C @ in ) )
=> ( A @ ( C @ closed_subset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tops_2) ).
thf(6173,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
=> ( ( ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( B @ ( C @ in ) )
=> ( A @ ( C @ closed_subset ) ) ) )
=> ( A @ ( B @ closed_subsets ) ) )
& ( ( A @ ( B @ closed_subsets ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( B @ ( C @ in ) )
=> ( A @ ( C @ closed_subset ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(578,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] :
( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_0) ).
thf(5073,plain,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] :
( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ join_commut ) ) )
= ( C @ ( B @ ( A @ join ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
thf(4949,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ join_commut ) ) )
= ( C @ ( B @ ( A @ join ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_dom_restriction ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(1184,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_dom_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(160,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ rel_str )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
thf(1848,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ rel_str )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(664,axiom,
! [A: $i] :
( ( ( A @ incl_POSet @ the_InternalRel )
= ( A @ inclusion_order ) )
& ( ( A @ incl_POSet @ the_carrier )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_1) ).
thf(5569,plain,
! [A: $i] :
( ( ( A @ incl_POSet @ the_InternalRel )
= ( A @ inclusion_order ) )
& ( ( A @ incl_POSet @ the_carrier )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( A @ ( B @ set_intersection2 ) @ v2_membered )
& ( A @ ( B @ set_intersection2 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc30_membered) ).
thf(2453,plain,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( A @ ( B @ set_intersection2 ) @ v2_membered )
& ( A @ ( B @ set_intersection2 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(3052,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(6724,plain,
$false,
inference(e,[status(thm)],[2630,1411,6167,4005,2109,846,3698,5390,1083,1179,1586,1501,3661,4062,2263,4169,1315,5676,6527,1549,3681,4714,1882,1808,1073,5793,2099,2837,4614,1305,4747,6214,5501,2363,1855,2622,6162,6495,5069,3549,2527,3040,3460,2248,4215,2380,1655,5257,1260,2459,5005,5412,1497,4543,2195,1705,3365,4870,4026,1735,6127,4220,2184,4435,3577,829,3335,1835,3545,1127,4371,3777,1386,4137,3809,1623,3836,3629,2046,5252,5935,1576,3513,5195,6583,1613,3308,2010,4803,1645,5056,1967,6483,4156,1803,5750,1518,4610,5352,1887,3820,2328,4866,1985,3275,4761,2274,3125,3280,2897,5289,3803,2571,2703,1055,4539,3131,4956,6274,5284,4130,1313,1279,6113,3845,2488,5744,2691,6470,5323,5052,4952,2852,4253,6049,1800,5338,3638,1087,4617,5199,4179,6379,6310,2767,5480,4270,1931,1568,1100,5617,5264,4018,2451,3525,4724,1978,5032,4686,4556,1302,5892,3966,4583,4443,2105,5597,1450,1334,6189,5135,3093,5457,5360,5045,5379,4996,5169,2103,6156,1696,1975,4055,4230,1447,5101,2371,4364,1119,5246,1526,4379,4892,3559,3582,6529,5157,3503,4480,4531,5443,6250,5034,5487,4910,2496,1768,5174,3097,5783,4323,6183,2473,1311,5862,3418,4925,3795,1047,1730,894,6122,825,1255,1123,5455,5507,3664,3471,4915,2409,4466,1091,6550,1021,2596,5002,1570,4989,5349,1676,3752,3239,4204,5470,4785,4499,3134,5085,2132,4836,5594,2958,4280,2670,4608,4053,6427,2663,5534,5779,2179,5038,4979,2345,2211,1281,2228,2653,1027,2213,5858,4104,3408,1740,1910,842,1573,5330,1143,5423,1328,1121,4789,4636,4109,3205,5145,3254,4512,2685,1111,5577,1227,5919,5978,2858,5889,4095,5951,989,6218,4263,4676,1493,5830,6518,5694,2868,6304,5786,1842,1584,6501,6539,6541,3775,2877,4167,1461,4425,1424,5464,4744,6164,1810,1791,5865,5662,4621,2649,985,1249,2153,1131,3770,5498,1060,6346,1246,6152,3703,1324,1114,3787,1456,2243,6475,2862,4135,3064,1720,4259,6171,3476,3755,1991,6160,4782,2043,6486,5833,5447,6038,5872,2529,3824,2634,5747,938,4644,1187,2440,5209,1663,5887,1895,4921,5679,6637,1251,6507,1680,5762,5969,3890,1483,6084,1927,856,4503,5882,3696,6598,965,6314,1510,4412,4256,3839,3523,1374,4599,3372,1833,5933,3636,2225,2188,3945,3266,2991,3458,1795,5503,2695,3272,4801,6229,5612,4975,1520,3404,3868,5185,5427,3646,4099,3002,5449,3091,5908,6532,5282,4236,5148,6649,4433,1356,6478,5870,5071,2538,6179,3551,996,5610,4073,6604,3586,5972,1194,4716,4337,2679,6308,2478,3251,3764,5520,1806,1011,5827,3270,5491,5901,1771,2945,4477,1969,1307,2180,4430,2632,4541,5082,5439,3932,6645,2593,5885,2252,2278,4684,5552,4694,5367,5511,811,2182,4882,4009,2314,2129,4064,1993,5656,1149,2874,6376,1688,2401,3627,3110,6223,4085,6504,6325,4497,5089,5495,4158,5619,2365,2962,5254,1445,1528,3241,2797,1076,2614,1203,2784,2927,3455,6008,1551,4986,3849,5587,3031,4690,4868,6276,944,1467,6185,5757,4529,2124,6191,4319,3146,4879,1145,1018,1845,1003,1598,5514,2661,2192,1605,1647,5980,2720,1531,2850,6384,6577,5452,5047,5607,6472,1611,5111,5388,1743,4939,5171,5944,5484,3462,4200,4469,2821,4092,3940,2165,3691,4020,5912,5753,2429,5948,4145,1830,1336,5955,1053,5684,3448,5262,5276,1785,2276,5030,2219,4132,2322,951,808,1285,3853,5106,2500,3107,2843,4932,5364,3943,2939,5472,1372,3914,4671,4414,2056,5319,3415,6073,3829,5347,4624,2711,1506,6086,1094,978,4516,4150,5895,6220,3288,2760,2924,4698,3757,1459,2885,2960,3533,2310,3928,1781,1189,4678,5939,4278,3401,2088,6041,1553,5660,4419,4559,4780,1390,2305,3056,1453,5332,2658,1590,3613,3864,896,6607,1481,946,4126,3235,4495,5505,2135,2406,4089,5382,2532,4681,1508,2764,1822,3136,3368,4527,3780,4759,5409,6536,3993,2120,5517,2494,5287,1030,5963,2956,3694,2786,6118,5781,5837,1440,5590,6569,5336,2779,3658,1774,2683,3705,6201,3291,2587,3892,3264,4719,5601,3062,6600,5268,2233,1593,5356,1380,5078,4523,5522,1673,5477,2050,3822,4777,1495,4286,4210,4427,4968,5835,1197,2091,2714,4912,2340,3843,2651,928,1473,5215,1129,3701,5151,5637,4239,5958,6595,1880,6548,4501,3918,3362,1352,4799,2847,3411,2485,3772,4876,5975,6205,4506,4066,5280,992,3817,1923,5681,5219,5468,850,1713,5354,4071,3113,3474,2640,5877,4642,4627,5649,4161,6575,2470,6067,2754,4335,6173,5073,4949,1184,1848,5569,2453,3052]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU382+2 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.14/0.40 % Computer : n007.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 09:21:10 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 1.31/1.21 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.64/1.98 % [INFO] Parsing done (762ms).
% 3.64/2.01 % [INFO] Running in sequential loop mode.
% 5.41/2.61 % [INFO] eprover registered as external prover.
% 5.41/2.62 % [INFO] Scanning for conjecture ...
% 6.26/2.98 % [INFO] Found a conjecture (or negated_conjecture) and 842 axioms. Running axiom selection ...
% 8.53/3.45 % [INFO] Axiom selection finished. Selected 805 axioms (removed 37 axioms).
% 10.11/3.81 % [INFO] Problem is first-order (TPTP FOF).
% 10.11/3.84 % [INFO] Type checking passed.
% 10.11/3.84 % [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 ...
% 31.80/8.62 % External prover 'e' found a proof!
% 31.80/8.62 % [INFO] Killing All external provers ...
% 31.80/8.62 % Time passed: 8081ms (effective reasoning time: 6606ms)
% 31.80/8.62 % 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)>
% 31.80/8.63 % Axioms used in derivation (805): t8_waybel_0, d1_lattices, t15_finset_1, existence_m2_yellow_6, d1_enumset1, redefinition_m2_relset_1, t30_yellow_0, dt_k7_grcat_1, d16_lattice3, d7_yellow_0, redefinition_r1_ordinal1, t32_yellow_6, d1_wellord2, l3_wellord1, t29_yellow_0, t61_yellow_0, fc1_yellow_1, cc2_finset_1, fc1_zfmisc_1, d1_finset_1, d1_tarski, rc1_waybel_6, s1_xboole_0__e4_27_3_1__finset_1, t30_relat_1, t147_funct_1, t45_pre_topc, d4_funct_1, rc5_waybel_1, t32_wellord1, t19_xboole_1, t99_relat_1, fc2_partfun1, s3_subset_1__e2_37_1_1__pre_topc, t17_xboole_1, t90_relat_1, s3_funct_1__e16_22__wellord2, cc10_waybel_1, t43_subset_1, t54_wellord1, rc2_waybel_0, s1_tarski__e2_37_1_1__pre_topc__1, fc1_ordinal2, l82_funct_1, fraenkel_a_1_0_filter_1, idempotence_k3_xboole_0, t1_boole, d8_yellow_0, rc7_yellow_6, t39_wellord1, cc4_funct_2, fc2_pre_topc, fc37_membered, redefinition_k5_subset_1, d13_lattices, t3_xboole_1, dt_k4_relset_1, dt_k5_relset_1, d5_relat_1, fc1_finsub_1, d6_relat_2, d4_ordinal1, rc4_finset_1, l1_wellord1, l2_wellord1, fc1_xboole_0, cc6_lattices, t7_mcart_1, d16_lattices, t17_tops_2, cc10_membered, s1_tarski__e4_27_3_1__finset_1__1, dt_k2_subset_1, cc5_waybel_1, d10_yellow_0, fc5_yellow_1, d5_tarski, d12_relat_1, s1_xboole_0__e18_27__finset_1__1, t29_lattice3, t44_relat_1, redefinition_k7_funct_2, t10_tops_2, rc12_lattices, existence_l1_lattices, cc9_waybel_1, cc2_arytm_3, t26_lattices, fc4_relat_1, fc4_funct_1, t1_subset, t28_lattice3, fc34_membered, fc4_lattice3, t144_relat_1, fc31_membered, t22_funct_1, existence_l3_lattices, rc1_membered, dt_k5_lattices, fc4_tops_1, fc3_relat_1, d8_funct_1, fc4_subset_1, d13_yellow_0, dt_k1_tops_1, fc4_lattice2, d6_orders_2, d5_ordinal2, rc2_yellow_0, d13_pre_topc, d6_pre_topc, t12_pre_topc, dt_k8_relset_1, dt_k1_waybel_0, t32_ordinal1, d12_yellow_6, t117_relat_1, t47_relat_1, fc9_relat_1, t2_boole, t1_yellow_1, dt_k4_subset_1, fc6_tops_1, redefinition_k1_pcomps_1, s1_tarski__e4_7_2__tops_2__1, l40_tops_1, t99_zfmisc_1, rc2_orders_2, t47_setfam_1, fc1_funct_1, d8_yellow_6, t34_lattice3, s1_tarski__e10_24__wellord2__2, t60_yellow_0, l3_subset_1, d2_lattice3, cc6_waybel_1, d1_wellord1, rc2_partfun1, cc4_lattices, d1_tops_2, cc12_waybel_0, d9_funct_1, rc3_funct_1, dt_k6_partfun1, fc1_pre_topc, t56_relat_1, cc4_waybel_3, d3_compts_1, cc1_relat_1, d22_lattice3, idempotence_k5_subset_1, t20_yellow_6, t55_funct_1, dt_k10_filter_1, d11_waybel_0, dt_k1_toler_1, d1_struct_0, t6_yellow_6, t37_xboole_1, fc2_waybel_7, cc1_lattice3, fc2_lattice2, dt_m2_relset_1, t18_finset_1, t26_wellord2, dt_k7_funct_2, cc11_waybel_0, rc13_waybel_0, redefinition_k6_setfam_1, dt_k1_pre_topc, cc14_waybel_0, commutativity_k3_xboole_0, s1_tarski__e6_22__wellord2__1, fc28_membered, fc3_lattice2, t62_funct_1, t46_pre_topc, d3_pre_topc, d2_tarski, dt_k2_binop_1, d4_subset_1, cc2_finsub_1, fc2_xboole_0, dt_u1_waybel_0, dt_u1_orders_2, rc6_pre_topc, fc32_membered, fc30_membered, fc11_finset_1, t5_tex_2, d12_waybel_0, dt_k4_lattice3, fc5_pre_topc, involutiveness_k3_subset_1, d2_tops_2, rc1_funct_1, dt_g1_waybel_0, reflexivity_r3_lattices, d1_xboole_0, d9_orders_2, rc1_lattice3, d2_tex_2, l50_zfmisc_1, rc3_lattices, t23_funct_1, t46_funct_2, s1_tarski__e6_21__wellord2__1, dt_l1_lattices, t52_pre_topc, t64_relat_1, rc1_tops_1, rc11_lattices, d6_ordinal1, dt_k5_lattice3, fc17_yellow_6, t118_zfmisc_1, fc10_finset_1, d3_wellord1, cc2_funct_2, t14_relset_1, t26_finset_1, rc2_lattice3, rc3_relat_1, t6_boole, t4_wellord2, existence_l2_lattices, d1_relat_1, cc5_waybel_0, dt_l1_pre_topc, t34_funct_1, t16_relset_1, dt_k3_yellow_1, d13_relat_1, t46_zfmisc_1, rc2_subset_1, s1_xboole_0__e6_21__wellord2__1, fc9_finset_1, dt_k6_subset_1, d14_yellow_0, t1_xboole_1, redefinition_r3_orders_2, rc3_partfun1, d9_relat_2, s1_xboole_0__e2_37_1_1__pre_topc__1, rc2_waybel_7, t16_yellow_0, t28_wellord2, t31_ordinal1, t116_relat_1, fc33_membered, t31_lattice3, cc2_ordinal1, t2_lattice3, t5_subset, t30_lattice3, commutativity_k2_xboole_0, rc4_waybel_1, fc3_subset_1, rc1_waybel_7, d4_relat_1, fc1_waybel_7, d12_relat_2, cc9_waybel_0, redefinition_k10_filter_1, cc1_arytm_3, cc1_waybel_3, existence_m1_relset_1, dt_l3_lattices, fc2_tops_1, d13_yellow_6, t17_wellord1, fc2_subset_1, fc2_lattice3, dt_k8_funct_2, t4_xboole_0, s1_xboole_0__e4_7_1__tops_2__1, d4_wellord2, cc19_membered, commutativity_k5_subset_1, l25_zfmisc_1, fraenkel_a_2_3_lattice3, t1_zfmisc_1, cc2_yellow_0, t5_wellord2, d5_wellord1, d1_ordinal1, t3_wellord2, t50_lattice3, dt_l2_lattices, cc3_funct_2, fc2_funct_1, dt_l1_waybel_0, t5_wellord1, t8_funct_1, fc6_membered, dt_k3_lattice3, t166_relat_1, l32_xboole_1, t8_zfmisc_1, fc1_lattice3, s1_relat_1__e6_21__wellord2, rc3_waybel_7, s1_tarski__e4_7_2__tops_2__2, rc4_funct_1, redefinition_k8_relset_1, t13_compts_1, d4_lattice3, t44_pre_topc, abstractness_v6_waybel_0, t23_wellord1, t2_tarski, s1_ordinal1__e8_6__wellord2, fc8_yellow_1, t33_xboole_1, existence_l1_waybel_0, t11_tops_2, d3_lattices, t146_funct_1, d21_lattice3, d2_pre_topc, d13_funct_1, dt_k4_relat_1, t4_subset, fc3_xboole_0, t178_relat_1, s2_finset_1__e11_2_1__waybel_0, dt_k2_funct_1, s3_subset_1__e1_40__pre_topc, rc1_arytm_3, t41_yellow_6, cc1_partfun1, t19_wellord1, fc13_relat_1, dt_k9_filter_1, rc13_lattices, t4_boole, cc5_lattices, d5_pre_topc, cc4_waybel_4, d2_xboole_0, t20_wellord1, cc1_funct_2, d4_tarski, t13_tops_2, t18_wellord1, d2_yellow_0, d16_relat_2, t9_zfmisc_1, t174_relat_1, t12_tops_2, d3_lattice3, redefinition_k5_setfam_1, s1_tarski__e6_27__finset_1__1, involutiveness_k4_relat_1, fc2_orders_2, cc1_ordinal1, d8_pre_topc, reflexivity_r2_wellord2, t30_tops_1, s1_funct_1__e4_7_2__tops_2__1, dt_k1_domain_1, t44_yellow_0, dt_k6_yellow_6, t7_boole, t21_wellord1, cc1_funct_1, fc9_waybel_1, d17_lattice3, t118_relat_1, s1_tarski__e16_22__wellord2__2, t143_relat_1, t15_yellow_0, reflexivity_r3_orders_2, t48_xboole_1, t3_ordinal1, dt_k1_wellord2, d8_waybel_0, cc20_membered, existence_l1_orders_2, cc3_waybel_3, t23_ordinal1, d1_yellow_1, redefinition_k3_yellow_6, s1_tarski__e10_24__wellord2__1, rc1_orders_2, s2_ordinal1__e18_27__finset_1__1, d10_relat_1, rc3_struct_0, d2_subset_1, commutativity_k4_lattices, fc1_subset_1, t33_zfmisc_1, fc5_funct_1, t13_finset_1, t24_wellord1, redefinition_k1_toler_1, commutativity_k2_struct_0, fc29_membered, redefinition_k6_partfun1, fc38_membered, l4_wellord1, cc13_waybel_0, fc5_lattice2, fc3_ordinal1, dt_g1_orders_2, rc2_funct_1, t3_lattice3, d11_relat_1, cc1_yellow_2, t21_funct_2, d2_compts_1, dt_k8_filter_1, t9_funct_2, t160_relat_1, fc10_relat_1, rc1_subset_1, cc4_membered, fc4_yellow_1, cc3_ordinal1, t74_relat_1, redefinition_k1_domain_1, connectedness_r1_ordinal1, t8_wellord1, cc1_lattices, rc1_funct_2, t2_wellord2, rc3_ordinal1, s1_xboole_0__e1_40__pre_topc__1, cc4_yellow_0, s1_tarski__e11_2_1__waybel_0__1, s1_xboole_0__e6_27__finset_1, t45_relat_1, dt_k2_struct_0, fc15_yellow_6, t140_relat_1, d14_relat_1, s1_funct_1__e10_24__wellord2__1, s1_xboole_0__e16_22__wellord2__1, cc18_membered, fc6_yellow_1, d7_xboole_0, fc5_relat_1, abstractness_v1_orders_2, t83_xboole_1, redefinition_r3_lattices, l28_zfmisc_1, redefinition_k1_waybel_0, cc3_yellow_3, t6_yellow_0, t55_tops_1, cc2_funct_1, d2_wellord1, t3_subset, cc1_relset_1, t22_relset_1, t33_ordinal1, dt_k6_setfam_1, rc9_lattices, t115_relat_1, dt_u1_lattices, existence_m1_subset_1, dt_k16_lattice3, t46_setfam_1, dt_k15_lattice3, s1_tarski__e4_7_1__tops_2__2, t17_finset_1, l4_zfmisc_1, rc4_waybel_0, t24_ordinal1, s1_ordinal2__e18_27__finset_1, fc1_waybel_1, d2_zfmisc_1, fc11_relat_1, d2_mcart_1, d4_yellow_0, l3_zfmisc_1, commutativity_k2_tarski, dt_k3_yellow_0, d7_relat_1, rc1_ordinal1, s1_xboole_0__e4_7_2__tops_2__1, d20_waybel_0, t106_zfmisc_1, rc6_yellow_6, d18_yellow_6, t145_funct_1, fc1_finset_1, l71_subset_1, existence_m1_connsp_2, cc7_waybel_1, fc39_membered, cc15_membered, t19_yellow_6, t28_yellow_6, dt_k7_relat_1, redefinition_k4_subset_1, t7_wellord2, l2_zfmisc_1, t25_wellord1, s2_funct_1__e4_7_2__tops_2, d8_relat_1, t42_ordinal1, t94_relat_1, t48_setfam_1, d4_wellord1, cc3_lattices, d5_subset_1, t92_zfmisc_1, t146_relat_1, d9_yellow_0, t70_funct_1, t31_wellord1, dt_k2_yellow_1, t41_ordinal1, commutativity_k4_subset_1, fc6_waybel_0, d7_wellord1, dt_k5_subset_1, t16_tops_2, s1_xboole_0__e11_2_1__waybel_0__1, t38_zfmisc_1, l55_zfmisc_1, s1_tarski__e8_6__wellord2__1, t10_ordinal1, rc1_waybel_3, d5_orders_2, d1_zfmisc_1, fc3_orders_2, dt_k8_relat_1, d8_setfam_1, rc2_waybel_3, t69_enumset1, t26_xboole_1, t63_xboole_1, t1_waybel_0, t22_wellord1, d2_yellow_1, rc2_relat_1, existence_m2_relset_1, fc1_yellow_0, t72_funct_1, t6_wellord2, t18_yellow_1, t25_wellord2, redefinition_k2_binop_1, s1_tarski__e16_22__wellord2__1, dt_l1_orders_2, d5_yellow_6, fraenkel_a_2_2_lattice3, t17_pre_topc, rc1_yellow_3, t51_tops_1, involutiveness_k7_setfam_1, t6_funct_2, dt_m1_connsp_2, t91_tmap_1, fc1_orders_2, t8_xboole_1, cc1_finsub_1, d3_tarski, fc1_struct_0, cc6_funct_2, cc7_yellow_0, existence_l1_pre_topc, t39_zfmisc_1, t119_zfmisc_1, rc1_relat_1, t54_funct_1, fc2_yellow_1, fc1_knaster, rc2_finset_1, fc35_membered, dt_k5_relat_1, reflexivity_r1_tarski, d11_yellow_0, free_g1_orders_2, t37_relat_1, t28_xboole_1, d1_relset_1, cc5_waybel_3, cc6_waybel_3, d8_filter_1, redefinition_k3_lattices, s1_xboole_0__e10_24__wellord2__1, t5_tops_2, dt_k4_lattices, t60_relat_1, t6_zfmisc_1, t31_yellow_6, cc1_yellow_3, reflexivity_r1_ordinal1, s1_tarski__e18_27__finset_1__1, t2_xboole_1, cc17_membered, d11_grcat_1, rc6_lattices, d1_funct_2, dt_k6_relat_1, dt_k2_lattice3, t7_lattice3, d1_connsp_2, s1_xboole_0__e6_22__wellord2, cc8_waybel_1, fc36_membered, rc1_pboole, d12_funct_1, d2_lattices, rc10_waybel_0, cc1_knaster, d3_ordinal1, dt_g3_lattices, fc6_relat_1, free_g1_waybel_0, cc10_waybel_0, free_g3_lattices, existence_m1_yellow_0, t46_relat_1, d4_xboole_0, d14_relat_2, fc3_lattice3, t35_funct_1, t36_xboole_1, cc2_waybel_3, rc7_pre_topc, dt_k1_yellow_0, rc2_ordinal1, cc7_lattices, dt_m1_yellow_0, cc5_yellow_0, dt_k5_setfam_1, rc3_finset_1, t68_funct_1, t20_relat_1, dt_k1_lattices, t22_pre_topc, dt_k7_setfam_1, t21_funct_1, d1_relat_2, fc1_relat_1, d6_wellord1, redefinition_k2_lattice3, fc3_yellow_1, l23_zfmisc_1, t11_waybel_7, rc1_ordinal2, t54_subset_1, rc1_finset_1, dt_k1_lattice3, redefinition_k5_pre_topc, rc2_tops_1, cc1_finset_1, s2_funct_1__e10_24__wellord2, fc12_finset_1, dt_k2_wellord1, abstractness_v3_lattices, fc2_arytm_3, s1_funct_1__e16_22__wellord2__1, t136_zfmisc_1, cc1_yellow_0, redefinition_k2_struct_0, d6_relat_1, t8_boole, rc1_xboole_0, redefinition_k8_funct_2, fc3_tops_1, dt_u1_pre_topc, fc3_funct_1, t16_wellord1, rc2_tex_2, t48_pre_topc, rc5_struct_0, t12_xboole_1, t4_yellow_1, fc7_relat_1, dt_m1_yellow_6, d9_yellow_6, fc1_ordinal1, t49_wellord1, t26_orders_2, d1_lattice3, s1_xboole_0__e8_6__wellord2__1, t10_zfmisc_1, t2_subset, dt_k5_pre_topc, dt_m2_yellow_6, cc1_membered, d3_relat_1, t37_zfmisc_1, redefinition_k1_yellow_1, fc2_relat_1, d2_ordinal1, fc12_relat_1, t65_relat_1, t21_relat_1, d8_lattice3, fc13_yellow_3, d1_setfam_1, symmetry_r1_xboole_0, redefinition_r2_wellord2, t86_relat_1, t2_yellow_1, fc40_membered, s1_tarski__e4_7_1__tops_2__1, s1_tarski__e1_40__pre_topc__1, fc8_relat_1, fc41_membered, l30_wellord2, t15_pre_topc, t32_filter_1, t9_tarski, t145_relat_1, cc3_arytm_3, commutativity_k3_lattices, d10_xboole_0, t1_lattice3, symmetry_r2_wellord2, fc2_finset_1, t7_xboole_1, rc1_yellow_0, idempotence_k2_xboole_0, cc2_membered, d8_lattices, t42_yellow_0, s1_funct_1__e4_7_1__tops_2__1, dt_k1_pcomps_1, cc2_lattice3, d1_funct_1, cc3_membered, t50_subset_1, fc2_ordinal1, existence_l1_struct_0, t7_tarski, rc1_partfun1, redefinition_k5_relset_1, t3_boole, d5_funct_1, redefinition_k6_subset_1, fc7_yellow_1, d8_relat_2, dt_k11_yellow_6, dt_k3_waybel_0, existence_m1_yellow_6, t57_funct_1, dt_k2_lattices, d4_relat_2, t3_xboole_0, t5_connsp_2, rc10_lattices, t12_relset_1, redefinition_k4_relset_1, d1_waybel_0, cc5_funct_2, rc1_waybel_0, rc12_waybel_0, t21_yellow_6, dt_u2_lattices, t25_relat_1, d1_tops_1, fc14_finset_1, l29_wellord1, cc16_membered, d9_lattice3, t25_orders_2, idempotence_k4_subset_1, s2_funct_1__e16_22__wellord2__1, rc2_xboole_0, fc27_membered, s2_funct_1__e4_7_1__tops_2, fc4_ordinal1, t40_xboole_1, dt_k3_yellow_6, fc13_finset_1, cc2_yellow_3, d1_binop_1, t45_xboole_1, t44_tops_1, d1_pre_topc, dt_k6_pre_topc, fc3_lattices, cc3_yellow_0, t65_zfmisc_1, t29_tops_1, d3_xboole_0, dt_k3_lattices, t71_relat_1, t23_relset_1, d1_mcart_1, cc2_lattices, t167_relat_1, dt_k3_subset_1, l1_zfmisc_1, t53_wellord1, t30_yellow_6, dt_k1_yellow_1, d2_relat_1, t39_xboole_1, t23_lattices, t119_relat_1, antisymmetry_r2_hidden, t88_relat_1, dt_k2_yellow_0, rc2_funct_2, redefinition_k4_lattices, dt_k2_pre_topc
% 31.80/8.63 % No. of inferences in proof: 1614
% 31.80/8.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8081 ms resp. 6606 ms w/o parsing
% 33.25/8.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 33.25/8.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------