TSTP Solution File: SEU391+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU391+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:58:42 EDT 2023
% Result : Theorem 101.21s 25.28s
% Output : Refutation 102.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1130
% Syntax : Number of formulae : 2045 ( 150 unt; 257 typ; 0 def)
% Number of atoms : 10954 (1408 equ; 0 cnn)
% Maximal formula atoms : 49 ( 6 avg)
% Number of connectives : 33162 (1256 ~; 42 |;5463 &;22740 @)
% ( 257 <=>;3404 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 436 ( 436 >; 0 *; 0 +; 0 <<)
% Number of symbols : 259 ( 257 usr; 17 con; 0-6 aty)
% Number of variables : 4983 ( 0 ^;4312 !; 671 ?;4983 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(net_str_type,type,
net_str: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(filter_of_net_str_type,type,
filter_of_net_str: $i > $i > $i ).
thf(is_eventually_in_type,type,
is_eventually_in: $i > $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(equipotent_type,type,
equipotent: $i > $i > $o ).
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(well_ordering_type,type,
well_ordering: $i > $o ).
thf(relation_isomorphism_type,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(well_orders_type,type,
well_orders: $i > $i > $o ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $i > $o ).
thf(relation_field_type,type,
relation_field: $i > $i ).
thf(pair_first_type,type,
pair_first: $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(pair_second_type,type,
pair_second: $i > $i ).
thf(finite_type,type,
finite: $i > $o ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(relation_dom_restr_as_relation_of_type,type,
relation_dom_restr_as_relation_of: $i > $i > $i > $i > $i ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(boole_POSet_type,type,
boole_POSet: $i > $i ).
thf(strict_rel_str_type,type,
strict_rel_str: $i > $o ).
thf(reflexive_relstr_type,type,
reflexive_relstr: $i > $o ).
thf(transitive_relstr_type,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_type,type,
antisymmetric_relstr: $i > $o ).
thf(lower_bounded_relstr_type,type,
lower_bounded_relstr: $i > $o ).
thf(upper_bounded_relstr_type,type,
upper_bounded_relstr: $i > $o ).
thf(bounded_relstr_type,type,
bounded_relstr: $i > $o ).
thf(up_complete_relstr_type,type,
up_complete_relstr: $i > $o ).
thf(join_complete_relstr_type,type,
join_complete_relstr: $i > $o ).
thf(v1_yellow_3_type,type,
v1_yellow_3: $i > $o ).
thf(distributive_relstr_type,type,
distributive_relstr: $i > $o ).
thf(heyting_relstr_type,type,
heyting_relstr: $i > $o ).
thf(complemented_relstr_type,type,
complemented_relstr: $i > $o ).
thf(boolean_relstr_type,type,
boolean_relstr: $i > $o ).
thf(with_suprema_relstr_type,type,
with_suprema_relstr: $i > $o ).
thf(with_infima_relstr_type,type,
with_infima_relstr: $i > $o ).
thf(complete_relstr_type,type,
complete_relstr: $i > $o ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(relation_rng_type,type,
relation_rng: $i > $i ).
thf(quasi_total_type,type,
quasi_total: $i > $i > $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(v1_membered_type,type,
v1_membered: $i > $o ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(v4_membered_type,type,
v4_membered: $i > $o ).
thf(v5_membered_type,type,
v5_membered: $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(reflexive_type,type,
reflexive: $i > $o ).
thf(transitive_type,type,
transitive: $i > $o ).
thf(antisymmetric_type,type,
antisymmetric: $i > $o ).
thf(connected_type,type,
connected: $i > $o ).
thf(well_founded_relation_type,type,
well_founded_relation: $i > $o ).
thf(top_str_type,type,
top_str: $i > $o ).
thf(rel_str_type,type,
rel_str: $i > $o ).
thf(being_limit_ordinal_type,type,
being_limit_ordinal: $i > $o ).
thf(union_type,type,
union: $i > $i ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(cast_to_subset_type,type,
cast_to_subset: $i > $i ).
thf(proper_subset_type,type,
proper_subset: $i > $i > $o ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(inclusion_relation_type,type,
inclusion_relation: $i > $i ).
thf(is_reflexive_in_type,type,
is_reflexive_in: $i > $i > $o ).
thf(is_transitive_in_type,type,
is_transitive_in: $i > $i > $o ).
thf(is_antisymmetric_in_type,type,
is_antisymmetric_in: $i > $i > $o ).
thf(is_connected_in_type,type,
is_connected_in: $i > $i > $o ).
thf(is_well_founded_in_type,type,
is_well_founded_in: $i > $i > $o ).
thf(apply_binary_type,type,
apply_binary: $i > $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(bijective_type,type,
bijective: $i > $i > $i > $o ).
thf(onto_type,type,
onto: $i > $i > $i > $o ).
thf(epsilon_transitive_type,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_type,type,
epsilon_connected: $i > $o ).
thf(relation_dom_as_subset_type,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(lattice_type,type,
lattice: $i > $o ).
thf(latt_str_type,type,
latt_str: $i > $o ).
thf(poset_of_lattice_type,type,
poset_of_lattice: $i > $i ).
thf(natural_type,type,
natural: $i > $o ).
thf(succ_type,type,
succ: $i > $i ).
thf(function_inverse_type,type,
function_inverse: $i > $i ).
thf(relation_inverse_type,type,
relation_inverse: $i > $i ).
thf(complete_latt_str_type,type,
complete_latt_str: $i > $o ).
thf(partfun_dom_restriction_type,type,
partfun_dom_restriction: $i > $i > $i > $i > $i ).
thf(subrelstr_type,type,
subrelstr: $i > $i > $o ).
thf(cast_as_carrier_subset_type,type,
cast_as_carrier_subset: $i > $i ).
thf(directed_subset_type,type,
directed_subset: $i > $i > $o ).
thf(incl_POSet_type,type,
incl_POSet: $i > $i ).
thf(relation_inverse_image_type,type,
relation_inverse_image: $i > $i > $i ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(full_subrelstr_type,type,
full_subrelstr: $i > $i > $o ).
thf(relation_image_type,type,
relation_image: $i > $i > $i ).
thf(strict_latt_str_type,type,
strict_latt_str: $i > $o ).
thf(latt_str_of_type,type,
latt_str_of: $i > $i > $i > $i ).
thf(relation_restriction_type,type,
relation_restriction: $i > $i > $i ).
thf(v2_waybel_3_type,type,
v2_waybel_3: $i > $o ).
thf(v3_waybel_3_type,type,
v3_waybel_3: $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(relation_composition_type,type,
relation_composition: $i > $i > $i ).
thf(topological_space_type,type,
topological_space: $i > $o ).
thf(open_subset_type,type,
open_subset: $i > $i > $o ).
thf(closed_subset_type,type,
closed_subset: $i > $i > $o ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(relation_dom_restriction_type,type,
relation_dom_restriction: $i > $i > $i ).
thf(relation_rng_restriction_type,type,
relation_rng_restriction: $i > $i > $i ).
thf(centered_type,type,
centered: $i > $o ).
thf(set_meet_type,type,
set_meet: $i > $i ).
thf(identity_relation_type,type,
identity_relation: $i > $i ).
thf(lower_bounded_semilattstr_type,type,
lower_bounded_semilattstr: $i > $o ).
thf(boole_lattice_type,type,
boole_lattice: $i > $i ).
thf(bottom_of_semilattstr_type,type,
bottom_of_semilattstr: $i > $i ).
thf(cup_closed_type,type,
cup_closed: $i > $o ).
thf(diff_closed_type,type,
diff_closed: $i > $o ).
thf(preboolean_type,type,
preboolean: $i > $o ).
thf(ordinal_subset_type,type,
ordinal_subset: $i > $i > $o ).
thf(rel_str_of_type,type,
rel_str_of: $i > $i > $i ).
thf(relation_rng_as_subset_type,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(function_of_composition_type,type,
function_of_composition: $i > $i > $i > $i > $i > $i ).
thf(relation_restriction_as_relation_of_type,type,
relation_restriction_as_relation_of: $i > $i > $i ).
thf(the_InternalRel_type,type,
the_InternalRel: $i > $i ).
thf(bottom_of_relstr_type,type,
bottom_of_relstr: $i > $i ).
thf(meet_semilatt_str_type,type,
meet_semilatt_str: $i > $o ).
thf(trivial_carrier_type,type,
trivial_carrier: $i > $o ).
thf(fiber_type,type,
fiber: $i > $i > $i ).
thf(filtered_subset_type,type,
filtered_subset: $i > $i > $o ).
thf(inclusion_order_type,type,
inclusion_order: $i > $i ).
thf(symmetric_type,type,
symmetric: $i > $o ).
thf(upper_bounded_semilattstr_type,type,
upper_bounded_semilattstr: $i > $o ).
thf(identity_as_relation_of_type,type,
identity_as_relation_of: $i > $i ).
thf(join_semilatt_str_type,type,
join_semilatt_str: $i > $o ).
thf(connected_relstr_type,type,
connected_relstr: $i > $o ).
thf(are_equipotent_type,type,
are_equipotent: $i > $i > $o ).
thf(omega_type,type,
omega: $i ).
thf(join_on_relstr_type,type,
join_on_relstr: $i > $i > $i ).
thf(directed_relstr_type,type,
directed_relstr: $i > $o ).
thf(dense_type,type,
dense: $i > $i > $o ).
thf(meet_commutative_type,type,
meet_commutative: $i > $o ).
thf(the_L_meet_type,type,
the_L_meet: $i > $i ).
thf(v1_binop_1_type,type,
v1_binop_1: $i > $i > $o ).
thf(meet_associative_type,type,
meet_associative: $i > $o ).
thf(v2_binop_1_type,type,
v2_binop_1: $i > $i > $o ).
thf(a_2_2_lattice3_type,type,
a_2_2_lattice3: $i > $i > $i ).
thf(latt_set_smaller_type,type,
latt_set_smaller: $i > $i > $i > $o ).
thf(join_commutative_type,type,
join_commutative: $i > $o ).
thf(join_commut_type,type,
join_commut: $i > $i > $i > $i ).
thf(join_type,type,
join: $i > $i > $i > $i ).
thf(strict_net_str_type,type,
strict_net_str: $i > $i > $o ).
thf(net_str_of_type,type,
net_str_of: $i > $i > $i > $i > $i ).
thf(full_subnetstr_type,type,
full_subnetstr: $i > $i > $i > $o ).
thf(subnetstr_type,type,
subnetstr: $i > $i > $i > $o ).
thf(related_type,type,
related: $i > $i > $i > $o ).
thf(complements_of_subsets_type,type,
complements_of_subsets: $i > $i > $i ).
thf(subset_complement_type,type,
subset_complement: $i > $i > $i ).
thf(ex_sup_of_relstr_set_type,type,
ex_sup_of_relstr_set: $i > $i > $o ).
thf(relstr_set_smaller_type,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(the_L_join_type,type,
the_L_join: $i > $i ).
thf(netstr_restr_to_element_type,type,
netstr_restr_to_element: $i > $i > $i > $i ).
thf(apply_netmap_type,type,
apply_netmap: $i > $i > $i > $i ).
thf(k10_filter_1_type,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(is_a_convergence_point_of_set_type,type,
is_a_convergence_point_of_set: $i > $i > $i > $o ).
thf(bounded_lattstr_type,type,
bounded_lattstr: $i > $o ).
thf(k2_lattice3_type,type,
k2_lattice3: $i > $i ).
thf(relation_of_lattice_type,type,
relation_of_lattice: $i > $i ).
thf(subnet_type,type,
subnet: $i > $i > $i > $o ).
thf(preimage_subnetstr_type,type,
preimage_subnetstr: $i > $i > $i > $i ).
thf(the_mapping_type,type,
the_mapping: $i > $i > $i ).
thf(relstr_element_smaller_type,type,
relstr_element_smaller: $i > $i > $i > $o ).
thf(apply_binary_as_element_type,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(function_invverse_img_as_carrier_subset_type,type,
function_invverse_img_as_carrier_subset: $i > $i > $i > $i > $i ).
thf(netstr_induced_subset_type,type,
netstr_induced_subset: $i > $i > $i > $o ).
thf(apply_on_set_and_struct_type,type,
apply_on_set_and_struct: $i > $i > $i > $i > $i ).
thf(proper_element_type,type,
proper_element: $i > $i > $o ).
thf(meet_commut_type,type,
meet_commut: $i > $i > $i > $i ).
thf(nowhere_dense_type,type,
nowhere_dense: $i > $i > $o ).
thf(boundary_set_type,type,
boundary_set: $i > $i > $o ).
thf(point_neighbourhood_type,type,
point_neighbourhood: $i > $i > $i > $o ).
thf(join_associative_type,type,
join_associative: $i > $o ).
thf(meet_absorbing_type,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_type,type,
join_absorbing: $i > $o ).
thf(ex_inf_of_relstr_set_type,type,
ex_inf_of_relstr_set: $i > $i > $o ).
thf(topstr_closure_type,type,
topstr_closure: $i > $i > $i ).
thf(distributive_lattstr_type,type,
distributive_lattstr: $i > $o ).
thf(modular_lattstr_type,type,
modular_lattstr: $i > $o ).
thf(complemented_lattstr_type,type,
complemented_lattstr: $i > $o ).
thf(boolean_lattstr_type,type,
boolean_lattstr: $i > $o ).
thf(lim_points_of_net_type,type,
lim_points_of_net: $i > $i > $i ).
thf(k1_pcomps_1_type,type,
k1_pcomps_1: $i > $i ).
thf(meet_type,type,
meet: $i > $i > $i > $i ).
thf(below_type,type,
below: $i > $i > $i > $o ).
thf(k8_filter_1_type,type,
k8_filter_1: $i > $i > $i ).
thf(compact_top_space_type,type,
compact_top_space: $i > $o ).
thf(is_a_cover_of_carrier_type,type,
is_a_cover_of_carrier: $i > $i > $o ).
thf(open_subsets_type,type,
open_subsets: $i > $i > $o ).
thf(subset_union2_type,type,
subset_union2: $i > $i > $i > $i ).
thf(union_of_subsets_type,type,
union_of_subsets: $i > $i > $i ).
thf(apply_on_structs_type,type,
apply_on_structs: $i > $i > $i > $i > $i ).
thf(subset_difference_type,type,
subset_difference: $i > $i > $i > $i ).
thf(lower_relstr_subset_type,type,
lower_relstr_subset: $i > $i > $o ).
thf(upper_relstr_subset_type,type,
upper_relstr_subset: $i > $i > $o ).
thf(interior_type,type,
interior: $i > $i > $i ).
thf(related_reflexive_type,type,
related_reflexive: $i > $i > $i > $o ).
thf(meet_of_latt_set_type,type,
meet_of_latt_set: $i > $i > $i ).
thf(cast_to_el_of_lattice_type,type,
cast_to_el_of_lattice: $i > $i > $i ).
thf(subnetstr_of_element_type,type,
subnetstr_of_element: $i > $i > $i > $i ).
thf(closed_subsets_type,type,
closed_subsets: $i > $i > $o ).
thf(empty_carrier_subset_type,type,
empty_carrier_subset: $i > $i ).
thf(neighborhood_system_type,type,
neighborhood_system: $i > $i > $i ).
thf(latt_element_smaller_type,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(meet_of_subsets_type,type,
meet_of_subsets: $i > $i > $i ).
thf(the_topology_type,type,
the_topology: $i > $i ).
thf(subset_intersection2_type,type,
subset_intersection2: $i > $i > $i > $i ).
thf(unordered_pair_as_carrier_subset_type,type,
unordered_pair_as_carrier_subset: $i > $i > $i > $i ).
thf(a_2_0_yellow19_type,type,
a_2_0_yellow19: $i > $i > $i ).
thf(below_refl_type,type,
below_refl: $i > $i > $i > $o ).
thf(cast_to_el_of_LattPOSet_type,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(join_of_latt_set_type,type,
join_of_latt_set: $i > $i > $i ).
thf(meet_on_relstr_type,type,
meet_on_relstr: $i > $i > $i ).
thf(a_2_1_yellow19_type,type,
a_2_1_yellow19: $i > $i > $i ).
thf(a_3_0_waybel_9_type,type,
a_3_0_waybel_9: $i > $i > $i > $i ).
thf(apply_on_set_and_struct2_type,type,
apply_on_set_and_struct2: $i > $i > $i > $i > $i ).
thf(identity_on_carrier_type,type,
identity_on_carrier: $i > $i ).
thf(ordered_pair_as_product_element_type,type,
ordered_pair_as_product_element: $i > $i > $i > $i > $i ).
thf(is_often_in_type,type,
is_often_in: $i > $i > $i > $o ).
thf(a_2_3_lattice3_type,type,
a_2_3_lattice3: $i > $i > $i ).
thf(is_a_cluster_point_of_netstr_type,type,
is_a_cluster_point_of_netstr: $i > $i > $i > $o ).
thf(apply_as_element_type,type,
apply_as_element: $i > $i > $i > $i > $i ).
thf(v1_waybel_2_type,type,
v1_waybel_2: $i > $o ).
thf(v2_waybel_2_type,type,
v2_waybel_2: $i > $o ).
thf(v1_xcmplx_0_type,type,
v1_xcmplx_0: $i > $o ).
thf(v1_xreal_0_type,type,
v1_xreal_0: $i > $o ).
thf(v1_int_1_type,type,
v1_int_1: $i > $o ).
thf(v1_rat_1_type,type,
v1_rat_1: $i > $o ).
thf(a_1_0_filter_1_type,type,
a_1_0_filter_1: $i > $i ).
thf(unordered_triple_type,type,
unordered_triple: $i > $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $o ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk13_type,type,
sk13: $i ).
thf(sk29_type,type,
sk29: $i ).
thf(sk31_type,type,
sk31: $i ).
thf(sk37_type,type,
sk37: $i ).
thf(sk41_type,type,
sk41: $i ).
thf(sk42_type,type,
sk42: $i ).
thf(6,axiom,
! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( well_orders @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_wellord2) ).
thf(892,plain,
! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( well_orders @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(392,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( lower_bounded_relstr @ A )
<=> ? [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_yellow_0) ).
thf(3021,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( lower_bounded_relstr @ A )
=> ? [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ B ) ) )
& ( ? [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ B ) )
=> ( lower_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(807,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(6085,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(343,axiom,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) )
& ( v4_membered @ ( set_difference @ A @ B ) )
& ( v5_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc41_membered) ).
thf(2744,plain,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) )
& ( v4_membered @ ( set_difference @ A @ B ) )
& ( v5_membered @ ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( meet_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(3661,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( meet_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(42,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_first @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).
thf(1105,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( ( B
= ( pair_first @ A ) )
=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = C ) ) )
& ( ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = C ) )
=> ( B
= ( pair_first @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(276,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(2412,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(719,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel_0) ).
thf(5390,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(863,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(6512,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(773,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( transitive_relstr @ A )
<=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_yellow_0) ).
thf(5778,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( transitive_relstr @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) )
& ( ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) )
=> ( transitive_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(68,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(1295,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( reflexive @ B )
=> ( reflexive @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord1) ).
thf(1549,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( reflexive @ B )
=> ( reflexive @ ( relation_restriction @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(570,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( ( apply_binary_as_element @ A @ B @ C @ D @ E @ F )
= ( apply_binary @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(4166,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( ( apply_binary_as_element @ A @ B @ C @ D @ E @ F )
= ( apply_binary @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(686,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
thf(5136,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(867,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( rel_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( element @ ( apply_on_set_and_struct @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_6) ).
thf(6530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( rel_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( element @ ( apply_on_set_and_struct @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(783,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( is_a_cover_of_carrier @ A @ B )
<=> ( ( cast_as_carrier_subset @ A )
= ( union_of_subsets @ ( the_carrier @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).
thf(5896,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( ( is_a_cover_of_carrier @ A @ B )
=> ( ( cast_as_carrier_subset @ A )
= ( union_of_subsets @ ( the_carrier @ A ) @ B ) ) )
& ( ( ( cast_as_carrier_subset @ A )
= ( union_of_subsets @ ( the_carrier @ A ) @ B ) )
=> ( is_a_cover_of_carrier @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ( ( subset @ B @ C )
=> ( ( ( B = empty_set )
& ( A != empty_set ) )
| ( ( function @ D )
& ( quasi_total @ D @ A @ C )
& ( relation_of2_as_subset @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(2778,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ( ( subset @ B @ C )
=> ( ( ( B = empty_set )
& ( A != empty_set ) )
| ( ( function @ D )
& ( quasi_total @ D @ A @ C )
& ( relation_of2_as_subset @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(199,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( well_founded_relation @ ( inclusion_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_wellord2) ).
thf(1995,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( well_founded_relation @ ( inclusion_relation @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(571,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( is_eventually_in @ A @ B @ C )
=> ( is_often_in @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_yellow_6) ).
thf(4169,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( is_eventually_in @ A @ B @ C )
=> ( is_often_in @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( netstr_induced_subset @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow19) ).
thf(3666,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( netstr_induced_subset @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(552,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) )
& ( join_commutative @ ( boole_lattice @ A ) )
& ( join_associative @ ( boole_lattice @ A ) )
& ( meet_commutative @ ( boole_lattice @ A ) )
& ( meet_associative @ ( boole_lattice @ A ) )
& ( meet_absorbing @ ( boole_lattice @ A ) )
& ( join_absorbing @ ( boole_lattice @ A ) )
& ( lattice @ ( boole_lattice @ A ) )
& ( distributive_lattstr @ ( boole_lattice @ A ) )
& ( modular_lattstr @ ( boole_lattice @ A ) )
& ( lower_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( upper_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( bounded_lattstr @ ( boole_lattice @ A ) )
& ( complemented_lattstr @ ( boole_lattice @ A ) )
& ( boolean_lattstr @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattice3) ).
thf(4022,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) )
& ( join_commutative @ ( boole_lattice @ A ) )
& ( join_associative @ ( boole_lattice @ A ) )
& ( meet_commutative @ ( boole_lattice @ A ) )
& ( meet_associative @ ( boole_lattice @ A ) )
& ( meet_absorbing @ ( boole_lattice @ A ) )
& ( join_absorbing @ ( boole_lattice @ A ) )
& ( lattice @ ( boole_lattice @ A ) )
& ( distributive_lattstr @ ( boole_lattice @ A ) )
& ( modular_lattstr @ ( boole_lattice @ A ) )
& ( lower_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( upper_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( bounded_lattstr @ ( boole_lattice @ A ) )
& ( complemented_lattstr @ ( boole_lattice @ A ) )
& ( boolean_lattstr @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(852,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(6431,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
thf(2787,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(835,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( is_eventually_in @ A @ B @ C )
<=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ( ( related @ B @ D @ E )
=> ( in @ ( apply_netmap @ A @ B @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_waybel_0) ).
thf(6317,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( ( is_eventually_in @ A @ B @ C )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ( ( related @ B @ D @ E )
=> ( in @ ( apply_netmap @ A @ B @ E ) @ C ) ) ) ) )
& ( ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ( ( related @ B @ D @ E )
=> ( in @ ( apply_netmap @ A @ B @ E ) @ C ) ) ) )
=> ( is_eventually_in @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
thf(5205,plain,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(457,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( ( meet_absorbing @ A )
<=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ ( meet @ A @ B @ C ) @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattices) ).
thf(3449,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( ( ( meet_absorbing @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ ( meet @ A @ B @ C ) @ C )
= C ) ) ) )
& ( ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ ( meet @ A @ B @ C ) @ C )
= C ) ) )
=> ( meet_absorbing @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(545,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( ( join_of_latt_set @ A @ B )
= ( join_on_relstr @ ( poset_of_lattice @ A ) @ B ) )
& ( ( meet_of_latt_set @ A @ B )
= ( meet_on_relstr @ ( poset_of_lattice @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_yellow_0) ).
thf(3990,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( ( join_of_latt_set @ A @ B )
= ( join_on_relstr @ ( poset_of_lattice @ A ) @ B ) )
& ( ( meet_of_latt_set @ A @ B )
= ( meet_on_relstr @ ( poset_of_lattice @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice3) ).
thf(5225,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( transitive_relstr @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( directed_relstr @ ( netstr_restr_to_element @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc26_waybel_9) ).
thf(4339,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( transitive_relstr @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( directed_relstr @ ( netstr_restr_to_element @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(32,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(1068,plain,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( neighborhood_system @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow19) ).
thf(4311,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( neighborhood_system @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
thf(2947,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) )
& ( ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) )
=> ( in @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( one_sorted_str @ A )
& ( transitive_relstr @ B )
& ( net_str @ B @ A ) )
=> ( ( transitive_relstr @ ( preimage_subnetstr @ A @ B @ C ) )
& ( strict_net_str @ ( preimage_subnetstr @ A @ B @ C ) @ A )
& ( full_subnetstr @ ( preimage_subnetstr @ A @ B @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_yellow_6) ).
thf(5625,plain,
! [A: $i,B: $i,C: $i] :
( ( ( one_sorted_str @ A )
& ( transitive_relstr @ B )
& ( net_str @ B @ A ) )
=> ( ( transitive_relstr @ ( preimage_subnetstr @ A @ B @ C ) )
& ( strict_net_str @ ( preimage_subnetstr @ A @ B @ C ) @ A )
& ( full_subnetstr @ ( preimage_subnetstr @ A @ B @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(152,axiom,
! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( function @ B )
& ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= ( singleton @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
thf(1728,plain,
! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( function @ B )
& ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= ( singleton @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( filter_of_net_str @ A @ B ) )
<=> ( ( is_eventually_in @ A @ B @ C )
& ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_yellow19) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( filter_of_net_str @ A @ B ) )
<=> ( ( is_eventually_in @ A @ B @ C )
& ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(875,plain,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ ( filter_of_net_str @ A @ B ) )
=> ( ( is_eventually_in @ A @ B @ C )
& ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) )
& ( ( ( is_eventually_in @ A @ B @ C )
& ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( in @ C @ ( filter_of_net_str @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(876,plain,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ ( filter_of_net_str @ A @ B ) )
=> ( ( is_eventually_in @ A @ B @ C )
& ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) )
& ! [C: $i] :
( ( ( is_eventually_in @ A @ B @ C )
& ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( in @ C @ ( filter_of_net_str @ A @ B ) ) ) ) ) ),
inference(miniscope,[status(thm)],[875]) ).
thf(878,plain,
~ ( empty_carrier @ sk1 ),
inference(cnf,[status(esa)],[876]) ).
thf(858,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( open_subsets @ B @ A )
<=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ C @ B )
=> ( open_subset @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_2) ).
thf(6480,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( ( open_subsets @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ C @ B )
=> ( open_subset @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ C @ B )
=> ( open_subset @ C @ A ) ) )
=> ( open_subsets @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ~ ( empty @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(1486,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ~ ( empty @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(422,axiom,
! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(3230,plain,
! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(269,axiom,
! [A: $i] :
( ( boole_POSet @ A )
= ( poset_of_lattice @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_yellow_1) ).
thf(2381,plain,
! [A: $i] :
( ( boole_POSet @ A )
= ( poset_of_lattice @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(757,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( open_subsets @ B @ A )
<=> ( closed_subsets @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tops_2) ).
thf(5644,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( ( open_subsets @ B @ A )
=> ( closed_subsets @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ A ) )
& ( ( closed_subsets @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ A )
=> ( open_subsets @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(2062,plain,
! [A: $i,B: $i] :
( ( ( proper_subset @ A @ B )
=> ( ( subset @ A @ B )
& ( A != B ) ) )
& ( ( ( subset @ A @ B )
& ( A != B ) )
=> ( proper_subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B )
& ( element @ C @ ( the_carrier @ A ) )
& ( element @ D @ ( the_carrier @ B ) ) )
=> ( ( k10_filter_1 @ A @ B @ C @ D )
= ( ordered_pair @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_filter_1) ).
thf(2953,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B )
& ( element @ C @ ( the_carrier @ A ) )
& ( element @ D @ ( the_carrier @ B ) ) )
=> ( ( k10_filter_1 @ A @ B @ C @ D )
= ( ordered_pair @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(856,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) )
& ( join_commutative @ ( boole_lattice @ A ) )
& ( join_associative @ ( boole_lattice @ A ) )
& ( meet_commutative @ ( boole_lattice @ A ) )
& ( meet_associative @ ( boole_lattice @ A ) )
& ( meet_absorbing @ ( boole_lattice @ A ) )
& ( join_absorbing @ ( boole_lattice @ A ) )
& ( lattice @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lattice3) ).
thf(6458,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) )
& ( join_commutative @ ( boole_lattice @ A ) )
& ( join_associative @ ( boole_lattice @ A ) )
& ( meet_commutative @ ( boole_lattice @ A ) )
& ( meet_associative @ ( boole_lattice @ A ) )
& ( meet_absorbing @ ( boole_lattice @ A ) )
& ( join_absorbing @ ( boole_lattice @ A ) )
& ( lattice @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(2671,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(5173,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(2282,plain,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(760,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
thf(5669,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( ( B
= ( relation_inverse @ A ) )
=> ! [C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ C @ D ) @ B )
=> ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ( ( in @ ( ordered_pair @ D @ C ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ C @ D ) @ B )
=> ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ( ( in @ ( ordered_pair @ D @ C ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) )
=> ( B
= ( relation_inverse @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(45,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(1136,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1142,plain,
with_infima_relstr @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(1269,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(196,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(1971,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(444,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( ( full_subrelstr @ B @ A )
<=> ( ( the_InternalRel @ B )
= ( relation_restriction_as_relation_of @ ( the_InternalRel @ A ) @ ( the_carrier @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_yellow_0) ).
thf(3402,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( ( ( full_subrelstr @ B @ A )
=> ( ( the_InternalRel @ B )
= ( relation_restriction_as_relation_of @ ( the_InternalRel @ A ) @ ( the_carrier @ B ) ) ) )
& ( ( ( the_InternalRel @ B )
= ( relation_restriction_as_relation_of @ ( the_InternalRel @ A ) @ ( the_carrier @ B ) ) )
=> ( full_subrelstr @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(149,axiom,
? [A: $i] : ( meet_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(1692,plain,
? [A: $i] : ( meet_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_0) ).
thf(4623,plain,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(661,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(4973,plain,
! [A: $i,B: $i] :
( ( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
=> ~ ( in @ B @ A ) )
& ( ~ ( in @ B @ A )
=> ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(72,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(1305,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(750,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(5614,plain,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(724,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(5425,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( B
= ( relation_dom @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_dom @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(35,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(1076,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1078,plain,
empty @ empty_set,
inference(cnf,[status(esa)],[1076]) ).
thf(674,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
thf(5037,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ( in @ C @ B )
=> ( ( in @ C @ A )
& ( ordinal @ C ) ) )
& ( ( ( in @ C @ A )
& ( ordinal @ C ) )
=> ( in @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(141,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(1655,plain,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(3120,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( ( disjoint @ B @ C )
=> ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ( ( subset @ B @ ( subset_complement @ A @ C ) )
=> ( disjoint @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1137,plain,
rel_str @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(73,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(1310,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(625,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( function @ ( identity_on_carrier @ A ) )
& ( quasi_total @ ( identity_on_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( identity_on_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
thf(4647,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( function @ ( identity_on_carrier @ A ) )
& ( quasi_total @ ( identity_on_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( identity_on_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(3365,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(153,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( trivial_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_yellow_0) ).
thf(1735,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( trivial_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(456,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( point_neighbourhood @ C @ A @ B )
<=> ( in @ B @ ( interior @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_connsp_2) ).
thf(3446,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( point_neighbourhood @ C @ A @ B )
=> ( in @ B @ ( interior @ A @ C ) ) )
& ( ( in @ B @ ( interior @ A @ C ) )
=> ( point_neighbourhood @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(4058,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(662,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( ( function @ ( the_L_join @ A ) )
& ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(4980,plain,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( ( function @ ( the_L_join @ A ) )
& ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
thf(3717,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) ) )
& ( ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) )
=> ( in @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(849,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(6391,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation_of2_as_subset @ ( relation_restriction_as_relation_of @ A @ B ) @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_toler_1) ).
thf(1608,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation_of2_as_subset @ ( relation_restriction_as_relation_of @ A @ B ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(3439,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(562,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(4097,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( ( C
= ( complements_of_subsets @ A @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( ( in @ D @ C )
=> ( in @ ( subset_complement @ A @ D ) @ B ) )
& ( ( in @ ( subset_complement @ A @ D ) @ B )
=> ( in @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( ( in @ D @ C )
=> ( in @ ( subset_complement @ A @ D ) @ B ) )
& ( ( in @ ( subset_complement @ A @ D ) @ B )
=> ( in @ D @ C ) ) ) )
=> ( C
= ( complements_of_subsets @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(530,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( closed_subset @ B @ A )
<=> ( open_subset @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pre_topc) ).
thf(3942,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ B @ A )
=> ( open_subset @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) @ A ) )
& ( ( open_subset @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) @ A )
=> ( closed_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(285,axiom,
! [A: $i] :
( ( ~ ( v1_yellow_3 @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( the_InternalRel @ A ) )
& ( relation @ ( the_InternalRel @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_yellow_3) ).
thf(2448,plain,
! [A: $i] :
( ( ~ ( v1_yellow_3 @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( the_InternalRel @ A ) )
& ( relation @ ( the_InternalRel @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ C ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e4_7_1__tops_2__2) ).
thf(6089,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ C ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) ) )
& ( ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ C ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) )
=> ( in @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(434,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( subset @ B @ ( topstr_closure @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
thf(3338,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( subset @ B @ ( topstr_closure @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( below_refl @ A @ B @ C )
<=> ( below @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(4638,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( ( below_refl @ A @ B @ C )
=> ( below @ A @ B @ C ) )
& ( ( below @ A @ B @ C )
=> ( below_refl @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(2434,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(503,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ~ ( trivial_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_waybel_7) ).
thf(3781,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ~ ( trivial_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(646,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
<=> ~ ( in @ ( bottom_of_relstr @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_7) ).
thf(4856,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ~ ( in @ ( bottom_of_relstr @ A ) @ B ) )
& ( ~ ( in @ ( bottom_of_relstr @ A ) @ B )
=> ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) )
& ( v4_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc40_membered) ).
thf(1919,plain,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) )
& ( v4_membered @ ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(512,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ B )
& ( in @ A @ ( relation_rng @ B ) ) )
=> ( ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) )
& ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
thf(3826,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ B )
& ( in @ A @ ( relation_rng @ B ) ) )
=> ( ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) )
& ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(448,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( ( function @ ( the_L_meet @ A ) )
& ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(3414,plain,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( ( function @ ( the_L_meet @ A ) )
& ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(1761,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(692,axiom,
! [A: $i] :
( ( top_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( empty @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_tops_1) ).
thf(5161,plain,
! [A: $i] :
( ( top_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( empty @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(584,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( apply_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( identity_on_carrier @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tmap_1) ).
thf(4247,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( apply_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( identity_on_carrier @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( meet_commut @ A @ B @ C )
= ( meet @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(5005,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( meet_commut @ A @ B @ C )
= ( meet @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(5178,plain,
! [A: $i,B: $i] :
( ( ( subset @ ( singleton @ A ) @ B )
=> ( in @ A @ B ) )
& ( ( in @ A @ B )
=> ( subset @ ( singleton @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(1063,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation_of2 @ C @ A @ B )
=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) )
& ( ( subset @ C @ ( cartesian_product2 @ A @ B ) )
=> ( relation_of2 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(755,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( strict_net_str @ ( preimage_subnetstr @ A @ B @ C ) @ A )
& ( subnetstr @ ( preimage_subnetstr @ A @ B @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_yellow_6) ).
thf(5636,plain,
! [A: $i,B: $i,C: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( strict_net_str @ ( preimage_subnetstr @ A @ B @ C ) @ A )
& ( subnetstr @ ( preimage_subnetstr @ A @ B @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) )
& ( v3_membered @ ( set_intersection2 @ A @ B ) )
& ( v4_membered @ ( set_intersection2 @ A @ B ) )
& ( v5_membered @ ( set_intersection2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc35_membered) ).
thf(2046,plain,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) )
& ( v3_membered @ ( set_intersection2 @ A @ B ) )
& ( v4_membered @ ( set_intersection2 @ A @ B ) )
& ( v5_membered @ ( set_intersection2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(683,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( related_reflexive @ A @ B @ C )
<=> ( related @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
thf(5123,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( ( related_reflexive @ A @ B @ C )
=> ( related @ A @ B @ C ) )
& ( ( related @ A @ B @ C )
=> ( related_reflexive @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(713,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
thf(5301,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( relation_inverse_image @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( relation_inverse_image @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(163,axiom,
! [A: $i] :
( ( ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel_0) ).
thf(1803,plain,
! [A: $i] :
( ( ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] :
( ( subnetstr @ C @ A @ B )
& ( strict_net_str @ C @ A )
& ( full_subnetstr @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_yellow_6) ).
thf(3597,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] :
( ( subnetstr @ C @ A @ B )
& ( strict_net_str @ C @ A )
& ( full_subnetstr @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(733,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(5533,plain,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(1746,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( well_ordering @ B )
& ( equipotent @ A @ ( relation_field @ B ) )
& ! [C: $i] :
( ( relation @ C )
=> ~ ( well_orders @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_wellord2) ).
thf(898,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( well_ordering @ B )
& ( equipotent @ A @ ( relation_field @ B ) )
& ! [C: $i] :
( ( relation @ C )
=> ~ ( well_orders @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(3836,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( cartesian_product2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( cartesian_product2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(238,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_orders_2) ).
thf(2216,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(707,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( E = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ E ) ) ) ) ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ( ( relation_dom @ C )
= B )
& ! [D: $i] :
( ( in @ D @ B )
=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( E = D )
=> ( ( apply @ C @ D )
= ( subset_complement @ ( the_carrier @ A ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e4_7_2__tops_2) ).
thf(5227,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( E = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ E ) ) ) ) ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ( ( relation_dom @ C )
= B )
& ! [D: $i] :
( ( in @ D @ B )
=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( E = D )
=> ( ( apply @ C @ D )
= ( subset_complement @ ( the_carrier @ A ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(23,axiom,
? [A: $i] : ( top_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(1000,plain,
? [A: $i] : ( top_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1001,plain,
top_str @ sk10,
inference(cnf,[status(esa)],[1000]) ).
thf(770,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_waybel_0) ).
thf(5740,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(720,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
thf(5393,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(2763,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(19,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
thf(973,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(885,plain,
net_str @ sk2 @ sk1,
inference(cnf,[status(esa)],[876]) ).
thf(405,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_0) ).
thf(3088,plain,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(785,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( meet_of_latt_set @ A @ B )
= ( join_of_latt_set @ A @ ( a_2_2_lattice3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d22_lattice3) ).
thf(5921,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( meet_of_latt_set @ A @ B )
= ( join_of_latt_set @ A @ ( a_2_2_lattice3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(131,axiom,
! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ( ( relation @ ( the_InternalRel @ A ) )
& ( reflexive @ ( the_InternalRel @ A ) )
& ( antisymmetric @ ( the_InternalRel @ A ) )
& ( transitive @ ( the_InternalRel @ A ) )
& ( v1_partfun1 @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_orders_2) ).
thf(1613,plain,
! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ( ( relation @ ( the_InternalRel @ A ) )
& ( reflexive @ ( the_InternalRel @ A ) )
& ( antisymmetric @ ( the_InternalRel @ A ) )
& ( transitive @ ( the_InternalRel @ A ) )
& ( v1_partfun1 @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(2010,plain,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(532,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_6) ).
thf(3947,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(301,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(2531,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(273,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
=> ( relation_isomorphism @ B @ A @ ( function_inverse @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_wellord1) ).
thf(2405,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
=> ( relation_isomorphism @ B @ A @ ( function_inverse @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ C )
<=> ( latt_set_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattice3) ).
thf(3688,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ C )
=> ( latt_set_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) )
& ( ( latt_set_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A )
=> ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(4775,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(740,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ B )
& ( in @ E @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = E )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e4_7_2__tops_2__1) ).
thf(5553,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ B )
& ( in @ E @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = E )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ B )
& ( in @ E @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = E )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( in @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(3644,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(4415,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_union2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_union2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ C )
<=> ( latt_element_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice3) ).
thf(3821,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ C )
=> ( latt_element_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) )
& ( ( latt_element_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A )
=> ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(416,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(3148,plain,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(917,plain,
! [A: $i,B: $i] :
( ( ( ( set_difference @ A @ B )
= empty_set )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( ( set_difference @ A @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(641,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
thf(4778,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(2185,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(853,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( lim_points_of_net @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_yellow_6) ).
thf(6434,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( lim_points_of_net @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(290,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(2466,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(6208,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(91,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
thf(1408,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1409,plain,
~ ( empty @ sk41 ),
inference(cnf,[status(esa)],[1408]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) ) )
=> ( ( function_invverse_img_as_carrier_subset @ A @ B @ C @ D )
= ( relation_inverse_image @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_pre_topc) ).
thf(4238,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) ) )
=> ( ( function_invverse_img_as_carrier_subset @ A @ B @ C @ D )
= ( relation_inverse_image @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(789,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(5953,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(344,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(2755,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
thf(3495,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( B
= ( identity_relation @ A ) )
=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) )
& ( ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) )
=> ( B
= ( identity_relation @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(567,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(4130,plain,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(834,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(6315,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(1313,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(66,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A )
& ( v2_waybel_3 @ A )
& ( v3_waybel_3 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_3) ).
thf(1277,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A )
& ( v2_waybel_3 @ A )
& ( v3_waybel_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1279,plain,
up_complete_relstr @ sk29,
inference(cnf,[status(esa)],[1277]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(1992,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(663,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(4984,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc27_membered) ).
thf(2691,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1147,plain,
bounded_relstr @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(677,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(5052,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(500,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(3734,plain,
! [A: $i,B: $i] :
( ( ( B
= ( union @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( union @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ A )
& ? [I: $i] :
( ( G = I )
& ( in @ H @ I )
& ! [J: $i] :
( ( in @ J @ I )
=> ( in @ ( ordered_pair @ H @ J ) @ B ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ A )
& ? [I: $i] :
( ( G = I )
& ( in @ H @ I )
& ! [J: $i] :
( ( in @ J @ I )
=> ( in @ ( ordered_pair @ H @ J ) @ B ) ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ C ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ A )
& ? [I: $i] :
( ( G = I )
& ( in @ H @ I )
& ! [J: $i] :
( ( in @ J @ I )
=> ( in @ ( ordered_pair @ H @ J ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__2) ).
thf(5077,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ A )
& ? [I: $i] :
( ( G = I )
& ( in @ H @ I )
& ! [J: $i] :
( ( in @ J @ I )
=> ( in @ ( ordered_pair @ H @ J ) @ B ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ A )
& ? [I: $i] :
( ( G = I )
& ( in @ H @ I )
& ! [J: $i] :
( ( in @ J @ I )
=> ( in @ ( ordered_pair @ H @ J ) @ B ) ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ C ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ A )
& ? [I: $i] :
( ( G = I )
& ( in @ H @ I )
& ! [J: $i] :
( ( in @ J @ I )
=> ( in @ ( ordered_pair @ H @ J ) @ B ) ) ) ) ) )
& ( ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ C ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ A )
& ? [I: $i] :
( ( G = I )
& ( in @ H @ I )
& ! [J: $i] :
( ( in @ J @ I )
=> ( in @ ( ordered_pair @ H @ J ) @ B ) ) ) ) )
=> ( in @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_inverse_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ D ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
thf(5617,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( ( in @ A @ ( relation_inverse_image @ C @ B ) )
=> ? [D: $i] :
( ( in @ D @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ D ) @ C )
& ( in @ D @ B ) ) )
& ( ? [D: $i] :
( ( in @ D @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ D ) @ C )
& ( in @ D @ B ) )
=> ( in @ A @ ( relation_inverse_image @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( union_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( meet_of_subsets @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(5792,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( union_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( meet_of_subsets @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_waybel_9) ).
thf(5866,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(705,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ B @ A )
& ( nowhere_dense @ B @ A ) )
=> ( ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tops_1) ).
thf(5214,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ B @ A )
& ( nowhere_dense @ B @ A ) )
=> ( ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(747,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(5605,plain,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(272,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(2403,plain,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(3638,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(5193,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(2767,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(752,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
thf(5622,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ B )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(969,plain,
! [A: $i,B: $i] :
( ~ ( empty @ B )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(420,axiom,
! [A: $i] :
( ~ ( empty @ ( powerset @ A ) )
& ( cup_closed @ ( powerset @ A ) )
& ( diff_closed @ ( powerset @ A ) )
& ( preboolean @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(3216,plain,
! [A: $i] :
( ~ ( empty @ ( powerset @ A ) )
& ( cup_closed @ ( powerset @ A ) )
& ( diff_closed @ ( powerset @ A ) )
& ( preboolean @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(589,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(4270,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(90,axiom,
! [A: $i] :
( ( centered @ A )
<=> ( ( A != empty_set )
& ! [B: $i] :
~ ( ( B != empty_set )
& ( subset @ B @ A )
& ( finite @ B )
& ( ( set_meet @ B )
= empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_compts_1) ).
thf(1389,plain,
! [A: $i] :
( ( ( centered @ A )
=> ( ( A != empty_set )
& ! [B: $i] :
~ ( ( B != empty_set )
& ( subset @ B @ A )
& ( finite @ B )
& ( ( set_meet @ B )
= empty_set ) ) ) )
& ( ( ( A != empty_set )
& ! [B: $i] :
~ ( ( B != empty_set )
& ( subset @ B @ A )
& ( finite @ B )
& ( ( set_meet @ B )
= empty_set ) ) )
=> ( centered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1390,plain,
( ! [A: $i] :
( ( centered @ A )
=> ( ( A != empty_set )
& ~ ? [B: $i] :
( ( B != empty_set )
& ( subset @ B @ A )
& ( finite @ B )
& ( ( set_meet @ B )
= empty_set ) ) ) )
& ! [A: $i] :
( ( ( A != empty_set )
& ~ ? [B: $i] :
( ( B != empty_set )
& ( subset @ B @ A )
& ( finite @ B )
& ( ( set_meet @ B )
= empty_set ) ) )
=> ( centered @ A ) ) ),
inference(miniscope,[status(thm)],[1389]) ).
thf(1391,plain,
! [A: $i] :
( ~ ( centered @ A )
| ( A != empty_set ) ),
inference(cnf,[status(esa)],[1390]) ).
thf(1397,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( centered @ A ) ),
inference(lifteq,[status(thm)],[1391]) ).
thf(1398,plain,
~ ( centered @ empty_set ),
inference(simp,[status(thm)],[1397]) ).
thf(881,plain,
one_sorted_str @ sk1,
inference(cnf,[status(esa)],[876]) ).
thf(403,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ? [C: $i] : ( point_neighbourhood @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
thf(3084,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ? [C: $i] : ( point_neighbourhood @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(485,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(3657,plain,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) )
& ( v3_membered @ ( set_intersection2 @ B @ A ) )
& ( v4_membered @ ( set_intersection2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc34_membered) ).
thf(1931,plain,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) )
& ( v3_membered @ ( set_intersection2 @ B @ A ) )
& ( v4_membered @ ( set_intersection2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(772,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(5746,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( relation_image @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( relation_image @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( unordered_pair_as_carrier_subset @ A @ B @ C )
= ( unordered_pair @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_struct_0) ).
thf(3951,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( unordered_pair_as_carrier_subset @ A @ B @ C )
= ( unordered_pair @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(2158,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] :
( ( subnet @ C @ A @ B )
& ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( strict_net_str @ C @ A )
& ( directed_relstr @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_9) ).
thf(4632,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] :
( ( subnet @ C @ A @ B )
& ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( strict_net_str @ C @ A )
& ( directed_relstr @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(768,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( lower_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_waybel_0) ).
thf(5727,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( lower_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(593,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( reflexive @ ( k2_lattice3 @ A ) )
& ( antisymmetric @ ( k2_lattice3 @ A ) )
& ( transitive @ ( k2_lattice3 @ A ) )
& ( v1_partfun1 @ ( k2_lattice3 @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( k2_lattice3 @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice3) ).
thf(4302,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( reflexive @ ( k2_lattice3 @ A ) )
& ( antisymmetric @ ( k2_lattice3 @ A ) )
& ( transitive @ ( k2_lattice3 @ A ) )
& ( v1_partfun1 @ ( k2_lattice3 @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( k2_lattice3 @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(271,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_waybel_0) ).
thf(2388,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(860,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice3) ).
thf(6487,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( relstr_set_smaller @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) )
=> ( relstr_set_smaller @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(302,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(2533,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( ( C
= ( apply @ A @ B ) )
=> ( in @ ( ordered_pair @ B @ C ) @ A ) )
& ( ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( C
= ( apply @ A @ B ) ) ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( ( C
= ( apply @ A @ B ) )
=> ( C = empty_set ) )
& ( ( C = empty_set )
=> ( C
= ( apply @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(14,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(924,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(1811,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( powerset @ ( relation_dom @ C ) ) )
& ( in @ ( relation_image @ C @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
thf(2996,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ( ( in @ E @ ( powerset @ ( relation_dom @ C ) ) )
& ( in @ ( relation_image @ C @ E ) @ B ) ) )
& ( ( ( in @ E @ ( powerset @ ( relation_dom @ C ) ) )
& ( in @ ( relation_image @ C @ E ) @ B ) )
=> ( in @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(814,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
thf(6189,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(811,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( boolean_lattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( distributive_lattstr @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A )
& ( complemented_lattstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattices) ).
thf(6176,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( boolean_lattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( distributive_lattstr @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A )
& ( complemented_lattstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(206,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(2034,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(417,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) )
& ( join_commutative @ ( boole_lattice @ A ) )
& ( join_associative @ ( boole_lattice @ A ) )
& ( meet_commutative @ ( boole_lattice @ A ) )
& ( meet_associative @ ( boole_lattice @ A ) )
& ( meet_absorbing @ ( boole_lattice @ A ) )
& ( join_absorbing @ ( boole_lattice @ A ) )
& ( lattice @ ( boole_lattice @ A ) )
& ( distributive_lattstr @ ( boole_lattice @ A ) )
& ( modular_lattstr @ ( boole_lattice @ A ) )
& ( lower_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( upper_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( bounded_lattstr @ ( boole_lattice @ A ) )
& ( complemented_lattstr @ ( boole_lattice @ A ) )
& ( boolean_lattstr @ ( boole_lattice @ A ) )
& ( complete_latt_str @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_knaster) ).
thf(3152,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) )
& ( join_commutative @ ( boole_lattice @ A ) )
& ( join_associative @ ( boole_lattice @ A ) )
& ( meet_commutative @ ( boole_lattice @ A ) )
& ( meet_associative @ ( boole_lattice @ A ) )
& ( meet_absorbing @ ( boole_lattice @ A ) )
& ( join_absorbing @ ( boole_lattice @ A ) )
& ( lattice @ ( boole_lattice @ A ) )
& ( distributive_lattstr @ ( boole_lattice @ A ) )
& ( modular_lattstr @ ( boole_lattice @ A ) )
& ( lower_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( upper_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( bounded_lattstr @ ( boole_lattice @ A ) )
& ( complemented_lattstr @ ( boole_lattice @ A ) )
& ( boolean_lattstr @ ( boole_lattice @ A ) )
& ( complete_latt_str @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(826,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( transitive_relstr @ A )
& ( directed_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_yellow_6) ).
thf(6259,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( transitive_relstr @ A )
& ( directed_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(664,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( strict_net_str @ B @ A )
=> ( B
= ( net_str_of @ A @ ( the_carrier @ B ) @ ( the_InternalRel @ B ) @ ( the_mapping @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v6_waybel_0) ).
thf(4988,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( strict_net_str @ B @ A )
=> ( B
= ( net_str_of @ A @ ( the_carrier @ B ) @ ( the_InternalRel @ B ) @ ( the_mapping @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(2090,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(671,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tops_2) ).
thf(5013,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(715,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ~ ( empty @ B )
& ( directed_subset @ B @ A ) )
<=> ! [C: $i] :
( ( ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( in @ D @ B )
& ( relstr_set_smaller @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_waybel_0) ).
thf(5333,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( ~ ( empty @ B )
& ( directed_subset @ B @ A ) )
=> ! [C: $i] :
( ( ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( in @ D @ B )
& ( relstr_set_smaller @ A @ C @ D ) ) ) )
& ( ! [C: $i] :
( ( ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( in @ D @ B )
& ( relstr_set_smaller @ A @ C @ D ) ) )
=> ( ~ ( empty @ B )
& ( directed_subset @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( boundary_set @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( empty @ ( interior @ A @ B ) )
& ( v1_membered @ ( interior @ A @ B ) )
& ( v2_membered @ ( interior @ A @ B ) )
& ( v3_membered @ ( interior @ A @ B ) )
& ( v4_membered @ ( interior @ A @ B ) )
& ( v5_membered @ ( interior @ A @ B ) )
& ( boundary_set @ ( interior @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_tops_1) ).
thf(4820,plain,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( boundary_set @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( empty @ ( interior @ A @ B ) )
& ( v1_membered @ ( interior @ A @ B ) )
& ( v2_membered @ ( interior @ A @ B ) )
& ( v3_membered @ ( interior @ A @ B ) )
& ( v4_membered @ ( interior @ A @ B ) )
& ( v5_membered @ ( interior @ A @ B ) )
& ( boundary_set @ ( interior @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( relation @ E )
& ( function @ E ) )
=> ( ( in @ C @ A )
=> ( ( B = empty_set )
| ( ( apply @ ( relation_composition @ D @ E ) @ C )
= ( apply @ E @ ( apply @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
thf(2451,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( relation @ E )
& ( function @ E ) )
=> ( ( in @ C @ A )
=> ( ( B = empty_set )
| ( ( apply @ ( relation_composition @ D @ E ) @ C )
= ( apply @ E @ ( apply @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(244,axiom,
? [A: $i] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(2236,plain,
? [A: $i] : ( join_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(2880,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc29_membered) ).
thf(1682,plain,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(691,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( v3_waybel_3 @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( up_complete_relstr @ A )
& ( v2_waybel_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_waybel_3) ).
thf(5156,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( v3_waybel_3 @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( up_complete_relstr @ A )
& ( v2_waybel_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(47,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( rel_str @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice3) ).
thf(1151,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( rel_str @ ( poset_of_lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(50,axiom,
! [A: $i] :
( ( ( ordinal @ A )
& ( natural @ A ) )
=> ( ~ ( empty @ ( succ @ A ) )
& ( epsilon_transitive @ ( succ @ A ) )
& ( epsilon_connected @ ( succ @ A ) )
& ( ordinal @ ( succ @ A ) )
& ( natural @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_arytm_3) ).
thf(1183,plain,
! [A: $i] :
( ( ( ordinal @ A )
& ( natural @ A ) )
=> ( ~ ( empty @ ( succ @ A ) )
& ( epsilon_transitive @ ( succ @ A ) )
& ( epsilon_connected @ ( succ @ A ) )
& ( ordinal @ ( succ @ A ) )
& ( natural @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( quasi_total @ C @ A @ B )
<=> ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( ( quasi_total @ C @ A @ B )
<=> ( C = empty_set ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
thf(2073,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( ( quasi_total @ C @ A @ B )
=> ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) )
& ( ( A
= ( relation_dom_as_subset @ A @ B @ C ) )
=> ( quasi_total @ C @ A @ B ) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( ( ( quasi_total @ C @ A @ B )
=> ( C = empty_set ) )
& ( ( C = empty_set )
=> ( quasi_total @ C @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A )
& ( net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_waybel_0) ).
thf(2833,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A )
& ( net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(56,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] : ( subrelstr @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(1215,plain,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] : ( subrelstr @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(2772,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(716,axiom,
! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(5343,plain,
! [A: $i] :
( ( ( epsilon_connected @ A )
=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) )
& ( ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) )
=> ( epsilon_connected @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(82,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(1351,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_orders @ B @ A )
=> ( ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A )
& ( well_ordering @ ( relation_restriction @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord2) ).
thf(1600,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_orders @ B @ A )
=> ( ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A )
& ( well_ordering @ ( relation_restriction @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(651,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow19) ).
thf(4892,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(520,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( element @ ( the_topology @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(3906,plain,
! [A: $i] :
( ( top_str @ A )
=> ( element @ ( the_topology @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(577,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(4211,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(818,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ( ( directed_relstr @ A )
<=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( related @ A @ B @ D )
& ( related @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_yellow_6) ).
thf(6210,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ( ( ( directed_relstr @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( related @ A @ B @ D )
& ( related @ A @ C @ D ) ) ) ) )
& ( ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( related @ A @ B @ D )
& ( related @ A @ C @ D ) ) ) )
=> ( directed_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(465,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( trivial_carrier @ A )
& ( reflexive_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( v2_waybel_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_waybel_3) ).
thf(3510,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( trivial_carrier @ A )
& ( reflexive_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( v2_waybel_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(2437,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation_of2_as_subset @ C @ A @ B )
=> ( relation_of2 @ C @ A @ B ) )
& ( ( relation_of2 @ C @ A @ B )
=> ( relation_of2_as_subset @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2 @ D @ A @ B )
& ( function @ E )
& ( quasi_total @ E @ B @ C )
& ( relation_of2 @ E @ B @ C ) )
=> ( ( function_of_composition @ A @ B @ C @ D @ E )
= ( relation_composition @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(1928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2 @ D @ A @ B )
& ( function @ E )
& ( quasi_total @ E @ B @ C )
& ( relation_of2 @ E @ B @ C ) )
=> ( ( function_of_composition @ A @ B @ C @ D @ E )
= ( relation_composition @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(553,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_grcat_1) ).
thf(4055,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( rel_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( ( apply_on_set_and_struct @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_yellow_6) ).
thf(3068,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( rel_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( ( apply_on_set_and_struct @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(877,plain,
( sk3
| ~ ( in @ sk5 @ ( filter_of_net_str @ sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[876]) ).
thf(233,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(2190,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(450,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(3421,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(202,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( with_suprema_relstr @ ( poset_of_lattice @ A ) )
& ( with_infima_relstr @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_yellow_1) ).
thf(2002,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( with_suprema_relstr @ ( poset_of_lattice @ A ) )
& ( with_infima_relstr @ ( poset_of_lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(799,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( related @ A @ B @ C )
<=> ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
thf(6021,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
=> ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) )
& ( ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) )
=> ( related @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(624,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_waybel_0) ).
thf(4643,plain,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
thf(1943,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(836,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(6327,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(380,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(2965,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(139,axiom,
! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_wellord2) ).
thf(1651,plain,
! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(732,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( below @ ( boole_lattice @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice3) ).
thf(5530,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( ( below @ ( boole_lattice @ A ) @ B @ C )
=> ( subset @ B @ C ) )
& ( ( subset @ B @ C )
=> ( below @ ( boole_lattice @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(925,plain,
empty @ sk9,
inference(cnf,[status(esa)],[924]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(1915,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(340,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( dense @ ( cast_as_carrier_subset @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_tops_1) ).
thf(2737,plain,
! [A: $i] :
( ( top_str @ A )
=> ( dense @ ( cast_as_carrier_subset @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(396,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( strict_net_str @ D @ A )
& ( subnetstr @ D @ A @ B ) )
=> ( ( D
= ( preimage_subnetstr @ A @ B @ C ) )
<=> ( ( full_subrelstr @ D @ B )
& ( subrelstr @ D @ B )
& ( ( the_carrier @ D )
= ( function_invverse_img_as_carrier_subset @ B @ A @ ( the_mapping @ A @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_6) ).
thf(3054,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( strict_net_str @ D @ A )
& ( subnetstr @ D @ A @ B ) )
=> ( ( ( D
= ( preimage_subnetstr @ A @ B @ C ) )
=> ( ( full_subrelstr @ D @ B )
& ( subrelstr @ D @ B )
& ( ( the_carrier @ D )
= ( function_invverse_img_as_carrier_subset @ B @ A @ ( the_mapping @ A @ B ) @ C ) ) ) )
& ( ( ( full_subrelstr @ D @ B )
& ( subrelstr @ D @ B )
& ( ( the_carrier @ D )
= ( function_invverse_img_as_carrier_subset @ B @ A @ ( the_mapping @ A @ B ) @ C ) ) )
=> ( D
= ( preimage_subnetstr @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(322,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(2660,plain,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(2000,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(449,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pre_topc) ).
thf(3418,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( subnetstr_of_element @ A @ B @ C ) @ A )
& ( subnet @ ( subnetstr_of_element @ A @ B @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_waybel_9) ).
thf(5298,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( subnetstr_of_element @ A @ B @ C ) @ A )
& ( subnet @ ( subnetstr_of_element @ A @ B @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(452,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( lower_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( upper_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_waybel_0) ).
thf(3435,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( lower_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( upper_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(34,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( well_ordering @ ( inclusion_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_wellord2) ).
thf(1074,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( well_ordering @ ( inclusion_relation @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2 @ D @ A @ B )
& ( function @ E )
& ( quasi_total @ E @ B @ C )
& ( relation_of2 @ E @ B @ C ) )
=> ( ( function @ ( function_of_composition @ A @ B @ C @ D @ E ) )
& ( quasi_total @ ( function_of_composition @ A @ B @ C @ D @ E ) @ A @ C )
& ( relation_of2_as_subset @ ( function_of_composition @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(1604,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2 @ D @ A @ B )
& ( function @ E )
& ( quasi_total @ E @ B @ C )
& ( relation_of2 @ E @ B @ C ) )
=> ( ( function @ ( function_of_composition @ A @ B @ C @ D @ E ) )
& ( quasi_total @ ( function_of_composition @ A @ B @ C @ D @ E ) @ A @ C )
& ( relation_of2_as_subset @ ( function_of_composition @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) ) )
=> ( element @ ( function_invverse_img_as_carrier_subset @ A @ B @ C @ D ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_pre_topc) ).
thf(6183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) ) )
=> ( element @ ( function_invverse_img_as_carrier_subset @ A @ B @ C @ D ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(620,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice3) ).
thf(4629,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(738,axiom,
! [A: $i] :
( ? [B: $i] :
( ( ordinal @ B )
& ( in @ B @ A ) )
=> ? [B: $i] :
( ( ordinal @ B )
& ( in @ B @ A )
& ! [C: $i] :
( ( ordinal @ C )
=> ( ( in @ C @ A )
=> ( ordinal_subset @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
thf(5545,plain,
! [A: $i] :
( ? [B: $i] :
( ( ordinal @ B )
& ( in @ B @ A ) )
=> ? [B: $i] :
( ( ordinal @ B )
& ( in @ B @ A )
& ! [C: $i] :
( ( ordinal @ C )
=> ( ( in @ C @ A )
=> ( ordinal_subset @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(680,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(5070,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(80,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ~ ( ! [B: $i] :
~ ( ( in @ B @ A )
& ( B = empty_set ) )
& ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ~ ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( in @ ( apply @ B @ C ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_wellord2) ).
thf(1338,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ~ ( ! [B: $i] :
~ ( ( in @ B @ A )
& ( B = empty_set ) )
& ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ~ ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( in @ ( apply @ B @ C ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(687,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( being_limit_ordinal @ A )
<=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ B @ A )
=> ( in @ ( succ @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_ordinal1) ).
thf(5142,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( ( ( being_limit_ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ B @ A )
=> ( in @ ( succ @ B ) @ A ) ) ) )
& ( ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ B @ A )
=> ( in @ ( succ @ B ) @ A ) ) )
=> ( being_limit_ordinal @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(736,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( relation @ ( relation_of_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(5540,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( relation @ ( relation_of_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(317,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(2621,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(65,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
thf(1274,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( latt_str_of @ A @ B @ C )
= ( latt_str_of @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(2589,plain,
! [A: $i,B: $i,C: $i] :
( ( ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( latt_str_of @ A @ B @ C )
= ( latt_str_of @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(151,axiom,
! [A: $i] :
( ( strict_latt_str @ ( boole_lattice @ A ) )
& ( latt_str @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
thf(1723,plain,
! [A: $i] :
( ( strict_latt_str @ ( boole_lattice @ A ) )
& ( latt_str @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(840,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_set_smaller @ B @ C @ A )
<=> ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice3) ).
thf(6343,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( ( latt_set_smaller @ B @ C @ A )
=> ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) )
& ( ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) )
=> ( latt_set_smaller @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(38,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(1091,plain,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(3972,plain,
! [A: $i,B: $i] :
( ( ( subset @ ( singleton @ A ) @ B )
=> ( in @ A @ B ) )
& ( ( in @ A @ B )
=> ( subset @ ( singleton @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(83,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(1353,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1355,plain,
~ ( empty @ sk37 ),
inference(cnf,[status(esa)],[1353]) ).
thf(57,axiom,
! [A: $i] :
( ( ( with_suprema_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel_0) ).
thf(1217,plain,
! [A: $i] :
( ( ( with_suprema_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(144,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ~ ( ~ ( being_limit_ordinal @ A )
& ! [B: $i] :
( ( ordinal @ B )
=> ( A
!= ( succ @ B ) ) ) )
& ~ ( ? [B: $i] :
( ( ordinal @ B )
& ( A
= ( succ @ B ) ) )
& ( being_limit_ordinal @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_ordinal1) ).
thf(1666,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( ~ ( ~ ( being_limit_ordinal @ A )
& ! [B: $i] :
( ( ordinal @ B )
=> ( A
!= ( succ @ B ) ) ) )
& ~ ( ? [B: $i] :
( ( ordinal @ B )
& ( A
= ( succ @ B ) ) )
& ( being_limit_ordinal @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(4344,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ E @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ E @ G ) @ B ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ A )
& ( in @ E @ A )
& ? [F: $i] :
( ( E = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__1) ).
thf(4521,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ E @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ E @ G ) @ B ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ A )
& ( in @ E @ A )
& ? [F: $i] :
( ( E = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ A )
& ( in @ E @ A )
& ? [F: $i] :
( ( E = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) ) )
=> ( in @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(412,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ B @ A )
& ( boundary_set @ B @ A ) )
=> ( ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(3134,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ B @ A )
& ( boundary_set @ B @ A ) )
=> ( ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(721,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( join_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(5396,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( join_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(466,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( ex_inf_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_element_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ E )
=> ( related @ A @ E @ D ) ) ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_yellow_0) ).
thf(3514,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( ( ex_inf_of_relstr_set @ A @ B )
=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_element_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ E )
=> ( related @ A @ E @ D ) ) ) )
=> ( D = C ) ) ) ) )
& ( ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_element_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ E )
=> ( related @ A @ E @ D ) ) ) )
=> ( D = C ) ) ) )
=> ( ex_inf_of_relstr_set @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(519,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ( ordinal @ C )
& ( B = D )
& ( ordinal @ D ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
thf(3889,plain,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ( ordinal @ C )
& ( B = D )
& ( ordinal @ D ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) ) )
& ( ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) )
=> ( in @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(805,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_complement @ ( the_carrier @ A ) @ B )
= ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
thf(6079,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_complement @ ( the_carrier @ A ) @ B )
= ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(311,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(2601,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(279,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
thf(2428,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( transitive @ A )
=> ( is_transitive_in @ A @ ( relation_field @ A ) ) )
& ( ( is_transitive_in @ A @ ( relation_field @ A ) )
=> ( transitive @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(310,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ~ ( empty @ ( succ @ A ) )
& ( epsilon_transitive @ ( succ @ A ) )
& ( epsilon_connected @ ( succ @ A ) )
& ( ordinal @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
thf(2596,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( ~ ( empty @ ( succ @ A ) )
& ( epsilon_transitive @ ( succ @ A ) )
& ( epsilon_connected @ ( succ @ A ) )
& ( ordinal @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(602,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( directed_subset @ B @ A )
& ( lower_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_waybel_0) ).
thf(4397,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( directed_subset @ B @ A )
& ( lower_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(44,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_2) ).
thf(1123,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(846,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_transitive_in @ A @ B )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ E @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
thf(6371,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( is_transitive_in @ A @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ E @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ C @ E ) @ A ) ) )
& ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ E @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ C @ E ) @ A ) )
=> ( is_transitive_in @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(109,axiom,
! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
thf(1502,plain,
! [A: $i] :
( ( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) )
& ( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(790,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
thf(5956,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnet @ C @ A @ B )
=> ( ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( directed_relstr @ C )
& ( net_str @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_yellow_6) ).
thf(3233,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnet @ C @ A @ B )
=> ( ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( directed_relstr @ C )
& ( net_str @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(374,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ( ( relation @ ( the_L_join @ A ) )
& ( function @ ( the_L_join @ A ) )
& ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( v1_binop_1 @ ( the_L_join @ A ) @ ( the_carrier @ A ) )
& ( v1_partfun1 @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lattice2) ).
thf(2937,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ( ( relation @ ( the_L_join @ A ) )
& ( function @ ( the_L_join @ A ) )
& ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( v1_binop_1 @ ( the_L_join @ A ) @ ( the_carrier @ A ) )
& ( v1_partfun1 @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(3816,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(132,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ~ ( v1_yellow_3 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_yellow_3) ).
thf(1619,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ~ ( v1_yellow_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(300,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bottom_of_relstr @ A )
= ( join_on_relstr @ A @ empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).
thf(2528,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bottom_of_relstr @ A )
= ( join_on_relstr @ A @ empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(3664,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(459,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ( ( related_reflexive @ ( boole_POSet @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow_1) ).
thf(3471,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ( ( ( related_reflexive @ ( boole_POSet @ A ) @ B @ C )
=> ( subset @ B @ C ) )
& ( ( subset @ B @ C )
=> ( related_reflexive @ ( boole_POSet @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(786,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) )
=> ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) ) )
& ( ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) )
=> ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_yellow_0) ).
thf(5924,plain,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) )
=> ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) ) )
& ( ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) )
=> ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(568,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( succ @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( set_difference @ F @ ( singleton @ A ) ) ) )
& ( C = E )
& ? [F: $i] :
( ( in @ F @ B )
& ( E
= ( set_difference @ F @ ( singleton @ A ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( powerset @ A ) )
& ( E = D )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( set_difference @ F @ ( singleton @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
thf(4140,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( succ @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( set_difference @ F @ ( singleton @ A ) ) ) )
& ( C = E )
& ? [F: $i] :
( ( in @ F @ B )
& ( E
= ( set_difference @ F @ ( singleton @ A ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( powerset @ A ) )
& ( E = D )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( set_difference @ F @ ( singleton @ A ) ) ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( powerset @ A ) )
& ( E = D )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( set_difference @ F @ ( singleton @ A ) ) ) ) )
=> ( in @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(293,axiom,
! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
thf(2477,plain,
! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(413,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(3137,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(148,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(1687,plain,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(2179,plain,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
=> ( ( upper_relstr_subset @ B @ ( boole_POSet @ A ) )
<=> ! [C: $i,D: $i] :
( ( ( subset @ C @ D )
& ( subset @ D @ A )
& ( in @ C @ B ) )
=> ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_waybel_7) ).
thf(3546,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
=> ( ( ( upper_relstr_subset @ B @ ( boole_POSet @ A ) )
=> ! [C: $i,D: $i] :
( ( ( subset @ C @ D )
& ( subset @ D @ A )
& ( in @ C @ B ) )
=> ( in @ D @ B ) ) )
& ( ! [C: $i,D: $i] :
( ( ( subset @ C @ D )
& ( subset @ D @ A )
& ( in @ C @ B ) )
=> ( in @ D @ B ) )
=> ( upper_relstr_subset @ B @ ( boole_POSet @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(603,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(4402,plain,
! [A: $i] :
( ( ( A = empty_set )
=> ! [B: $i] :
~ ( in @ B @ A ) )
& ( ! [B: $i] :
~ ( in @ B @ A )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( function @ ( partfun_dom_restriction @ A @ B @ C @ D ) )
& ( relation_of2_as_subset @ ( partfun_dom_restriction @ A @ B @ C @ D ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(1210,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( function @ ( partfun_dom_restriction @ A @ B @ C @ D ) )
& ( relation_of2_as_subset @ ( partfun_dom_restriction @ A @ B @ C @ D ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(342,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(2741,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(526,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( subset @ ( the_carrier @ C ) @ ( the_carrier @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_yellow_6) ).
thf(3931,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( subset @ ( the_carrier @ C ) @ ( the_carrier @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(631,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(4680,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
& ( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( point_neighbourhood @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
thf(3595,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( point_neighbourhood @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(556,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(4063,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ ( unordered_pair @ A @ B ) )
& ( finite @ ( unordered_pair @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(1423,plain,
! [A: $i,B: $i] :
( ~ ( empty @ ( unordered_pair @ A @ B ) )
& ( finite @ ( unordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(430,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3307,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(536,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( neighborhood_system @ A @ B )
= ( a_2_0_yellow19 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow19) ).
thf(3958,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( neighborhood_system @ A @ B )
= ( a_2_0_yellow19 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
thf(2445,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(289,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(2464,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(345,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(2758,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(543,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( netstr_induced_subset @ C @ A @ B )
<=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( C
= ( relation_rng_as_subset @ ( the_carrier @ ( netstr_restr_to_element @ A @ B @ D ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( netstr_restr_to_element @ A @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_yellow19) ).
thf(3980,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( netstr_induced_subset @ C @ A @ B )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( C
= ( relation_rng_as_subset @ ( the_carrier @ ( netstr_restr_to_element @ A @ B @ D ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( netstr_restr_to_element @ A @ B @ D ) ) ) ) ) )
& ( ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( C
= ( relation_rng_as_subset @ ( the_carrier @ ( netstr_restr_to_element @ A @ B @ D ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( netstr_restr_to_element @ A @ B @ D ) ) ) ) )
=> ( netstr_induced_subset @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(1837,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(195,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(1968,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(879,plain,
( ~ ( is_eventually_in @ sk1 @ sk2 @ sk4 )
| ~ ( element @ sk4 @ ( powerset @ ( the_carrier @ sk1 ) ) )
| ~ sk3 ),
inference(cnf,[status(esa)],[876]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(2663,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(263,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ~ ( trivial_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( heyting_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) )
& ( boolean_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel_7) ).
thf(2332,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ~ ( trivial_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( heyting_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) )
& ( boolean_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(177,axiom,
! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_1) ).
thf(1888,plain,
! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ B @ A )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C ) )
<=> ( ( relation_dom_as_subset @ B @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
thf(4553,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ B @ A )
=> ( ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C ) )
=> ( ( relation_dom_as_subset @ B @ A @ C )
= B ) )
& ( ( ( relation_dom_as_subset @ B @ A @ C )
= B )
=> ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(235,axiom,
! [A: $i] :
( ( identity_as_relation_of @ A )
= ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(2200,plain,
! [A: $i] :
( ( identity_as_relation_of @ A )
= ( identity_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(313,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
=> ( ( ( reflexive @ A )
=> ( reflexive @ B ) )
& ( ( transitive @ A )
=> ( transitive @ B ) )
& ( ( connected @ A )
=> ( connected @ B ) )
& ( ( antisymmetric @ A )
=> ( antisymmetric @ B ) )
& ( ( well_founded_relation @ A )
=> ( well_founded_relation @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_wellord1) ).
thf(2609,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
=> ( ( ( reflexive @ A )
=> ( reflexive @ B ) )
& ( ( transitive @ A )
=> ( transitive @ B ) )
& ( ( connected @ A )
=> ( connected @ B ) )
& ( ( antisymmetric @ A )
=> ( antisymmetric @ B ) )
& ( ( well_founded_relation @ A )
=> ( well_founded_relation @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(36,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( well_orders @ A @ B )
<=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
thf(1079,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( well_orders @ A @ B )
=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) )
& ( ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) )
=> ( well_orders @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(261,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(2327,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(394,axiom,
( ! [A: $i] :
( ( ordinal @ A )
=> ( ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ B @ A )
=> ( ( in @ B @ omega )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ B ) ) )
=> ~ ( ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ! [E: $i] :
( ( ( in @ E @ C )
& ( subset @ D @ E ) )
=> ( E = D ) ) ) ) ) ) ) )
=> ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) )
=> ! [A: $i] :
( ( ordinal @ A )
=> ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_ordinal1__e18_27__finset_1__1) ).
thf(3028,plain,
( ! [A: $i] :
( ( ordinal @ A )
=> ( ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ B @ A )
=> ( ( in @ B @ omega )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ B ) ) )
=> ~ ( ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ! [E: $i] :
( ( ( in @ E @ C )
& ( subset @ D @ E ) )
=> ( E = D ) ) ) ) ) ) ) )
=> ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) )
=> ! [A: $i] :
( ( ordinal @ A )
=> ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(525,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( ~ ( empty @ ( neighborhood_system @ A @ B ) )
& ( filtered_subset @ ( neighborhood_system @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ ( neighborhood_system @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ ( neighborhood_system @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_yellow19) ).
thf(3926,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( ~ ( empty @ ( neighborhood_system @ A @ B ) )
& ( filtered_subset @ ( neighborhood_system @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ ( neighborhood_system @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ ( neighborhood_system @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(303,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(2547,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(2313,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( cartesian_product2 @ B @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ B )
& ! [H: $i] :
( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( H = F )
=> ( G
= ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e4_7_2__tops_2__1) ).
thf(3763,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ( ( in @ E @ ( cartesian_product2 @ B @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ B )
& ! [H: $i] :
( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( H = F )
=> ( G
= ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) ) )
& ( ( ( in @ E @ ( cartesian_product2 @ B @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ B )
& ! [H: $i] :
( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( H = F )
=> ( G
= ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) )
=> ( in @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(136,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
thf(1634,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( reflexive @ A )
=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) )
& ( ( is_reflexive_in @ A @ ( relation_field @ A ) )
=> ( reflexive @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(4732,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(241,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(2228,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(3647,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( in @ C @ A )
=> ( in @ C @ B ) )
& ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( ( apply_on_set_and_struct2 @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_yellow_2) ).
thf(4080,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( ( apply_on_set_and_struct2 @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(3731,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( topological_space @ B )
& ( top_str @ B )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( in @ A @ ( a_2_0_yellow19 @ B @ C ) )
<=> ? [D: $i] :
( ( point_neighbourhood @ D @ B @ C )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
thf(4123,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( topological_space @ B )
& ( top_str @ B )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( ( in @ A @ ( a_2_0_yellow19 @ B @ C ) )
=> ? [D: $i] :
( ( point_neighbourhood @ D @ B @ C )
& ( A = D ) ) )
& ( ? [D: $i] :
( ( point_neighbourhood @ D @ B @ C )
& ( A = D ) )
=> ( in @ A @ ( a_2_0_yellow19 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(839,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(6339,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(5714,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(1259,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= empty_set ) )
& ( ( ( set_intersection2 @ A @ B )
= empty_set )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(356,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A ) )
=> ( ( relation @ ( the_L_meet @ A ) )
& ( function @ ( the_L_meet @ A ) )
& ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( v1_binop_1 @ ( the_L_meet @ A ) @ ( the_carrier @ A ) )
& ( v1_partfun1 @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice2) ).
thf(2801,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A ) )
=> ( ( relation @ ( the_L_meet @ A ) )
& ( function @ ( the_L_meet @ A ) )
& ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( v1_binop_1 @ ( the_L_meet @ A ) @ ( the_carrier @ A ) )
& ( v1_partfun1 @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(331,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(2685,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(6028,plain,
! [A: $i,B: $i] :
( ( ( B
= ( powerset @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( subset @ C @ A ) )
& ( ( subset @ C @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( subset @ C @ A ) )
& ( ( subset @ C @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( powerset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(6477,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l82_funct_1) ).
thf(5577,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) )
& ( ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) )
=> ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(175,axiom,
! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( reflexive_relstr @ ( incl_POSet @ A ) )
& ( transitive_relstr @ ( incl_POSet @ A ) )
& ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow_1) ).
thf(1856,plain,
! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( reflexive_relstr @ ( incl_POSet @ A ) )
& ( transitive_relstr @ ( incl_POSet @ A ) )
& ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(2694,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ( ordinal_subset @ A @ B )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( ordinal_subset @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1138,plain,
~ ( empty_carrier @ sk13 ),
inference(cnf,[status(esa)],[1136]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ~ ( empty_carrier @ C )
& ( net_str @ C @ B )
& ( element @ D @ ( the_carrier @ C ) ) )
=> ( ( in @ A @ ( a_3_0_waybel_9 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( element @ E @ ( the_carrier @ C ) )
& ( A = E )
& ( related @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_waybel_9) ).
thf(4012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ~ ( empty_carrier @ C )
& ( net_str @ C @ B )
& ( element @ D @ ( the_carrier @ C ) ) )
=> ( ( ( in @ A @ ( a_3_0_waybel_9 @ B @ C @ D ) )
=> ? [E: $i] :
( ( element @ E @ ( the_carrier @ C ) )
& ( A = E )
& ( related @ C @ D @ E ) ) )
& ( ? [E: $i] :
( ( element @ E @ ( the_carrier @ C ) )
& ( A = E )
& ( related @ C @ D @ E ) )
=> ( in @ A @ ( a_3_0_waybel_9 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(762,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( related @ A @ ( bottom_of_relstr @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_yellow_0) ).
thf(5687,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( related @ A @ ( bottom_of_relstr @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(249,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(2268,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(513,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ A ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ A ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) ) )
=> ! [C: $i] :
~ ( ( in @ C @ B )
& ( empty @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow19) ).
thf(3831,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ A ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ A ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) ) )
=> ! [C: $i] :
~ ( ( in @ C @ B )
& ( empty @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(1143,plain,
transitive_relstr @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(749,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( closed_subsets @ B @ A )
<=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ C @ B )
=> ( closed_subset @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tops_2) ).
thf(5609,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( ( closed_subsets @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ C @ B )
=> ( closed_subset @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ C @ B )
=> ( closed_subset @ C @ A ) ) )
=> ( closed_subsets @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( one_to_one @ C )
& ( quasi_total @ C @ A @ B )
& ( onto @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( bijective @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_funct_2) ).
thf(1498,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( one_to_one @ C )
& ( quasi_total @ C @ A @ B )
& ( onto @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( bijective @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(125,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( boolean_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_waybel_1) ).
thf(1587,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( boolean_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(819,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( in @ B @ A )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( in @ D @ A )
& ( C
= ( singleton @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__1) ).
thf(6218,plain,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( in @ B @ A )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ A )
& ( in @ D @ A )
& ( C
= ( singleton @ D ) ) ) )
& ( ? [D: $i] :
( ( in @ D @ A )
& ( in @ D @ A )
& ( C
= ( singleton @ D ) ) )
=> ( in @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(643,axiom,
! [A: $i] :
( ( boole_POSet @ A )
= ( incl_POSet @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_yellow_1) ).
thf(4817,plain,
! [A: $i] :
( ( boole_POSet @ A )
= ( incl_POSet @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(587,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(4263,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(106,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(1493,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(866,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_tops_1) ).
thf(6518,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
thf(2830,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_union2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(3441,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_union2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(774,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(5786,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(862,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ( ( lower_bounded_semilattstr @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( B
= ( bottom_of_semilattstr @ A ) )
<=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( meet @ A @ B @ C )
= B )
& ( ( meet @ A @ C @ B )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattices) ).
thf(6501,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ( ( lower_bounded_semilattstr @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( ( B
= ( bottom_of_semilattstr @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( meet @ A @ B @ C )
= B )
& ( ( meet @ A @ C @ B )
= B ) ) ) )
& ( ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( meet @ A @ B @ C )
= B )
& ( ( meet @ A @ C @ B )
= B ) ) )
=> ( B
= ( bottom_of_semilattstr @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(324,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(2666,plain,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(592,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ( ( lower_bounded_semilattstr @ A )
<=> ? [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
& ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( meet @ A @ B @ C )
= B )
& ( ( meet @ A @ C @ B )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).
thf(4291,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ( ( ( lower_bounded_semilattstr @ A )
=> ? [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
& ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( meet @ A @ B @ C )
= B )
& ( ( meet @ A @ C @ B )
= B ) ) ) ) )
& ( ? [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
& ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( meet @ A @ B @ C )
= B )
& ( ( meet @ A @ C @ B )
= B ) ) ) )
=> ( lower_bounded_semilattstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( element @ ( ordered_pair_as_product_element @ A @ B @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(6299,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( element @ ( ordered_pair_as_product_element @ A @ B @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(535,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ C @ F @ G ) )
=> ( related @ B @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_yellow_6) ).
thf(3954,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ C @ F @ G ) )
=> ( related @ B @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(884,plain,
( sk3
| ( is_eventually_in @ sk1 @ sk2 @ sk5 ) ),
inference(cnf,[status(esa)],[876]) ).
thf(77,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(1329,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(414,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( topstr_closure @ A @ B ) )
<=> ! [D: $i] :
( ( point_neighbourhood @ D @ A @ C )
=> ~ ( disjoint @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_6) ).
thf(3141,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ ( topstr_closure @ A @ B ) )
=> ! [D: $i] :
( ( point_neighbourhood @ D @ A @ C )
=> ~ ( disjoint @ D @ B ) ) )
& ( ! [D: $i] :
( ( point_neighbourhood @ D @ A @ C )
=> ~ ( disjoint @ D @ B ) )
=> ( in @ C @ ( topstr_closure @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(2877,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) )
& ( v3_membered @ ( set_intersection2 @ B @ A ) )
& ( v4_membered @ ( set_intersection2 @ B @ A ) )
& ( v5_membered @ ( set_intersection2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc36_membered) ).
thf(1361,plain,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) )
& ( v3_membered @ ( set_intersection2 @ B @ A ) )
& ( v4_membered @ ( set_intersection2 @ B @ A ) )
& ( v5_membered @ ( set_intersection2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(681,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(5075,plain,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(445,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(3407,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(873,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( open_subset @ B @ A )
<=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
thf(6593,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ B @ A )
=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) )
& ( ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A )
=> ( open_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(419,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ( ~ ( empty_carrier @ ( incl_POSet @ A ) )
& ( strict_rel_str @ ( incl_POSet @ A ) )
& ( reflexive_relstr @ ( incl_POSet @ A ) )
& ( transitive_relstr @ ( incl_POSet @ A ) )
& ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_yellow_1) ).
thf(3210,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ( ~ ( empty_carrier @ ( incl_POSet @ A ) )
& ( strict_rel_str @ ( incl_POSet @ A ) )
& ( reflexive_relstr @ ( incl_POSet @ A ) )
& ( transitive_relstr @ ( incl_POSet @ A ) )
& ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(496,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(3714,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(498,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( interior @ A @ B )
= ( subset_complement @ ( the_carrier @ A ) @ ( topstr_closure @ A @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
thf(3728,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( interior @ A @ B )
= ( subset_complement @ ( the_carrier @ A ) @ ( topstr_closure @ A @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(771,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ B @ C ) @ ( relation_of_lattice @ A ) )
<=> ( below_refl @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_1) ).
thf(5743,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ B @ C ) @ ( relation_of_lattice @ A ) )
=> ( below_refl @ A @ B @ C ) )
& ( ( below_refl @ A @ B @ C )
=> ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ B @ C ) @ ( relation_of_lattice @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(278,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( lower_bounded_relstr @ ( poset_of_lattice @ A ) )
& ( with_suprema_relstr @ ( poset_of_lattice @ A ) )
& ( with_infima_relstr @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_yellow_1) ).
thf(2419,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( lower_bounded_relstr @ ( poset_of_lattice @ A ) )
& ( with_suprema_relstr @ ( poset_of_lattice @ A ) )
& ( with_infima_relstr @ ( poset_of_lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(832,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( v2_waybel_3 @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( v3_waybel_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_waybel_3) ).
thf(6304,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( v2_waybel_3 @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( v3_waybel_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(9,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
thf(901,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( well_orders @ A @ ( relation_field @ A ) )
=> ( well_ordering @ A ) )
& ( ( well_ordering @ A )
=> ( well_orders @ A @ ( relation_field @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(1414,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(173,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_second @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
thf(1842,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( ( B
= ( pair_second @ A ) )
=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = D ) ) )
& ( ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = D ) )
=> ( B
= ( pair_second @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(159,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(1791,plain,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(648,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( fiber @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D != B )
& ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord1) ).
thf(4861,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( fiber @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( D != B )
& ( in @ ( ordered_pair @ D @ B ) @ A ) ) )
& ( ( ( D != B )
& ( in @ ( ordered_pair @ D @ B ) @ A ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( D != B )
& ( in @ ( ordered_pair @ D @ B ) @ A ) ) )
& ( ( ( D != B )
& ( in @ ( ordered_pair @ D @ B ) @ A ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( fiber @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(2172,plain,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(305,axiom,
! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(2551,plain,
! [A: $i] :
~ ( proper_subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(1207,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( succ @ A ) ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ A ) )
& ? [E: $i] :
( ( in @ E @ B )
& ( D
= ( set_difference @ E @ ( singleton @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
thf(2978,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( succ @ A ) ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( powerset @ A ) )
& ? [E: $i] :
( ( in @ E @ B )
& ( D
= ( set_difference @ E @ ( singleton @ A ) ) ) ) ) )
& ( ( ( in @ D @ ( powerset @ A ) )
& ? [E: $i] :
( ( in @ E @ B )
& ( D
= ( set_difference @ E @ ( singleton @ A ) ) ) ) )
=> ( in @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(320,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2649,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(478,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( in @ B @ A )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
=> ? [B: $i] :
( ( relation @ B )
& ( function @ B )
& ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( in @ C @ A )
& ( D
= ( singleton @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1__e16_22__wellord2__1) ).
thf(3611,plain,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( in @ B @ A )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
=> ? [B: $i] :
( ( relation @ B )
& ( function @ B )
& ! [C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ C @ D ) @ B )
=> ( ( in @ C @ A )
& ( in @ C @ A )
& ( D
= ( singleton @ C ) ) ) )
& ( ( ( in @ C @ A )
& ( in @ C @ A )
& ( D
= ( singleton @ C ) ) )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(40,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(1099,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(102,axiom,
! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
thf(1478,plain,
! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(69,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(1297,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc30_membered) ).
thf(1451,plain,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
thf(2845,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( B
= ( identity_relation @ A ) )
=> ! [C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ C @ D ) @ B )
=> ( ( in @ C @ A )
& ( C = D ) ) )
& ( ( ( in @ C @ A )
& ( C = D ) )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ C @ D ) @ B )
=> ( ( in @ C @ A )
& ( C = D ) ) )
& ( ( ( in @ C @ A )
& ( C = D ) )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) )
=> ( B
= ( identity_relation @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(197,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( distributive_relstr @ A )
& ( v2_waybel_3 @ A )
& ( v3_waybel_3 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_6) ).
thf(1974,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( distributive_relstr @ A )
& ( v2_waybel_3 @ A )
& ( v3_waybel_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(30,axiom,
! [A: $i] :
( ( cast_to_subset @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(1060,plain,
! [A: $i] :
( ( cast_to_subset @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(3937,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(479,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(3628,plain,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
thf(2697,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(5801,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_intersection2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_intersection2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(718,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(5369,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_rng_restriction @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) )
& ( ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) )
& ( ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_rng_restriction @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B )
& ( element @ D @ A ) )
=> ( ( apply_as_element @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(6186,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B )
& ( element @ D @ A ) )
=> ( ( apply_as_element @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_wellord1) ).
thf(1759,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(133,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(1627,plain,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(6349,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(1825,plain,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(5947,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(75,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(1324,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(2285,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ D @ C )
<=> ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
thf(3787,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( in @ D @ C )
=> ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) )
& ( ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) )
=> ( in @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(116,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(1539,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(363,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(2836,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( ( one_to_one @ A )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) )
=> ( one_to_one @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(100,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A )
& ( complemented_relstr @ A )
& ( boolean_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_waybel_1) ).
thf(1456,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A )
& ( complemented_relstr @ A )
& ( boolean_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(62,axiom,
! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( ( full_subrelstr @ B @ A )
=> ( ( transitive_relstr @ B )
& ( full_subrelstr @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_yellow_0) ).
thf(1266,plain,
! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( ( full_subrelstr @ B @ A )
=> ( ( transitive_relstr @ B )
& ( full_subrelstr @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(221,axiom,
! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
thf(2153,plain,
! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(169,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(1831,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(729,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( net_str @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
thf(5498,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( net_str @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(52,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( lower_bounded_relstr @ ( poset_of_lattice @ A ) )
& ( upper_bounded_relstr @ ( poset_of_lattice @ A ) )
& ( bounded_relstr @ ( poset_of_lattice @ A ) )
& ( with_suprema_relstr @ ( poset_of_lattice @ A ) )
& ( with_infima_relstr @ ( poset_of_lattice @ A ) )
& ( complete_relstr @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_yellow_1) ).
thf(1192,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( lower_bounded_relstr @ ( poset_of_lattice @ A ) )
& ( upper_bounded_relstr @ ( poset_of_lattice @ A ) )
& ( bounded_relstr @ ( poset_of_lattice @ A ) )
& ( with_suprema_relstr @ ( poset_of_lattice @ A ) )
& ( with_infima_relstr @ ( poset_of_lattice @ A ) )
& ( complete_relstr @ ( poset_of_lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(21,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
thf(984,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( well_ordering @ A )
=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) )
& ( ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) )
=> ( well_ordering @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(911,plain,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(841,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(6346,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(565,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(4120,plain,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(24,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) )
=> ( bounded_relstr @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(1002,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) )
=> ( bounded_relstr @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(358,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_waybel_0) ).
thf(2813,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(501,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier_subset @ A )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_pre_topc) ).
thf(3760,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier_subset @ A )
= empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(539,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
<=> ( ordinal_subset @ ( succ @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_ordinal1) ).
thf(3967,plain,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( ( in @ A @ B )
=> ( ordinal_subset @ ( succ @ A ) @ B ) )
& ( ( ordinal_subset @ ( succ @ A ) @ B )
=> ( in @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(446,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( nowhere_dense @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(3409,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( nowhere_dense @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(408,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(3109,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( ( subset @ A @ B )
=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) )
& ( ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) )
=> ( subset @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(558,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ! [B: $i] :
~ ( ( subset @ B @ ( relation_field @ A ) )
& ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ( disjoint @ ( fiber @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
thf(4069,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( well_founded_relation @ A )
=> ! [B: $i] :
~ ( ( subset @ B @ ( relation_field @ A ) )
& ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ( disjoint @ ( fiber @ A @ C ) @ B ) ) ) )
& ( ! [B: $i] :
~ ( ( subset @ B @ ( relation_field @ A ) )
& ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ( disjoint @ ( fiber @ A @ C ) @ B ) ) )
=> ( well_founded_relation @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(2140,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( powerset @ C ) )
& ? [F: $i] :
( ( F = E )
& ? [G: $i] :
( ( element @ G @ ( the_carrier @ A ) )
& ( in @ G @ B )
& ( relstr_set_smaller @ A @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e11_2_1__waybel_0__1) ).
thf(4086,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ( ( in @ E @ ( powerset @ C ) )
& ? [F: $i] :
( ( F = E )
& ? [G: $i] :
( ( element @ G @ ( the_carrier @ A ) )
& ( in @ G @ B )
& ( relstr_set_smaller @ A @ F @ G ) ) ) ) )
& ( ( ( in @ E @ ( powerset @ C ) )
& ? [F: $i] :
( ( F = E )
& ? [G: $i] :
( ( element @ G @ ( the_carrier @ A ) )
& ( in @ G @ B )
& ( relstr_set_smaller @ A @ F @ G ) ) ) )
=> ( in @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B )
& ( element @ D @ A ) )
=> ( element @ ( apply_as_element @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(6514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B )
& ( element @ D @ A ) )
=> ( element @ ( apply_as_element @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(3824,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(514,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(3834,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( ( function @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( reflexive @ B )
& ( quasi_total @ B @ A @ A ) )
=> ( ( function @ B )
& ( one_to_one @ B )
& ( quasi_total @ B @ A @ A )
& ( onto @ B @ A @ A )
& ( bijective @ B @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_funct_2) ).
thf(2203,plain,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( ( function @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( reflexive @ B )
& ( quasi_total @ B @ A @ A ) )
=> ( ( function @ B )
& ( one_to_one @ B )
& ( quasi_total @ B @ A @ A )
& ( onto @ B @ A @ A )
& ( bijective @ B @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( well_ordering @ B )
& ( subset @ A @ ( relation_field @ B ) ) )
=> ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_wellord1) ).
thf(2043,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( well_ordering @ B )
& ( subset @ A @ ( relation_field @ B ) ) )
=> ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
( ( relation @ D )
& ! [E: $i,F: $i] :
( ( in @ ( ordered_pair @ E @ F ) @ D )
<=> ( ( in @ E @ A )
& ( in @ F @ A )
& ( in @ ( ordered_pair @ ( apply @ C @ E ) @ ( apply @ C @ F ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_relat_1__e6_21__wellord2) ).
thf(2883,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
( ( relation @ D )
& ! [E: $i,F: $i] :
( ( ( in @ ( ordered_pair @ E @ F ) @ D )
=> ( ( in @ E @ A )
& ( in @ F @ A )
& ( in @ ( ordered_pair @ ( apply @ C @ E ) @ ( apply @ C @ F ) ) @ B ) ) )
& ( ( ( in @ E @ A )
& ( in @ F @ A )
& ( in @ ( ordered_pair @ ( apply @ C @ E ) @ ( apply @ C @ F ) ) @ B ) )
=> ( in @ ( ordered_pair @ E @ F ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(797,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).
thf(6011,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(33,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(1071,plain,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(607,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_waybel_0) ).
thf(4448,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(464,axiom,
! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(3508,plain,
! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(2617,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(684,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( connected_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_waybel_0) ).
thf(5126,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( connected_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(4,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( well_ordering @ A )
& ( relation_isomorphism @ A @ B @ C ) )
=> ( well_ordering @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_wellord1) ).
thf(888,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( well_ordering @ A )
& ( relation_isomorphism @ A @ B @ C ) )
=> ( well_ordering @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(667,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below @ A @ B @ C )
& ( below @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).
thf(4995,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below @ A @ B @ C )
& ( below @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(693,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( open_subset @ B @ A )
<=> ( in @ B @ ( the_topology @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_pre_topc) ).
thf(5170,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ B @ A )
=> ( in @ B @ ( the_topology @ A ) ) )
& ( ( in @ B @ ( the_topology @ A ) )
=> ( open_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(569,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ( strict_net_str @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_waybel_0) ).
thf(4163,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ( strict_net_str @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ A ) ) )
=> ( element @ ( apply_on_structs @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_waybel_0) ).
thf(3476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ A ) ) )
=> ( element @ ( apply_on_structs @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(1333,plain,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(506,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( connected_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel_3) ).
thf(3802,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( connected_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(373,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow_0) ).
thf(2926,plain,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ( ex_sup_of_relstr_set @ A @ B )
=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) )
& ( ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) )
=> ( ex_sup_of_relstr_set @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
thf(1814,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( B
= ( relation_dom_restriction @ C @ A ) )
=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) )
& ( ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
=> ( B
= ( relation_dom_restriction @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(421,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
thf(3225,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( transitive @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) )
& ( ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( transitive @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(337,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( function_inverse @ A ) )
<=> ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(2702,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( B
= ( function_inverse @ A ) )
=> ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) ) )
& ( ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) )
=> ( B
= ( function_inverse @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(765,axiom,
! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
thf(5711,plain,
! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(210,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
thf(2057,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( antisymmetric @ A )
=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) )
& ( ( is_antisymmetric_in @ A @ ( relation_field @ A ) )
=> ( antisymmetric @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(473,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(3592,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(547,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( finite @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
<=> ( finite @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_tops_2) ).
thf(3999,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( ( finite @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
=> ( finite @ B ) )
& ( ( finite @ B )
=> ( finite @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(726,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ D @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = D )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1__e4_7_2__tops_2__1) ).
thf(5447,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ( in @ C @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ D @ B )
& ( in @ D @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = D )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) ) )
& ( ( ( in @ D @ B )
& ( in @ D @ B )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = D )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ~ ( empty_carrier @ C )
& ( net_str @ C @ B ) )
=> ( ( in @ A @ ( a_2_1_yellow19 @ B @ C ) )
<=> ? [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
& ( A = D )
& ( is_eventually_in @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
thf(4004,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ~ ( empty_carrier @ C )
& ( net_str @ C @ B ) )
=> ( ( ( in @ A @ ( a_2_1_yellow19 @ B @ C ) )
=> ? [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
& ( A = D )
& ( is_eventually_in @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
& ( A = D )
& ( is_eventually_in @ B @ C @ D ) )
=> ( in @ A @ ( a_2_1_yellow19 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(594,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( below_refl @ A @ B @ C )
<=> ( related_reflexive @ ( poset_of_lattice @ A ) @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( cast_to_el_of_LattPOSet @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice3) ).
thf(4308,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below_refl @ A @ B @ C )
=> ( related_reflexive @ ( poset_of_lattice @ A ) @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( cast_to_el_of_LattPOSet @ A @ C ) ) )
& ( ( related_reflexive @ ( poset_of_lattice @ A ) @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( cast_to_el_of_LattPOSet @ A @ C ) )
=> ( below_refl @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( heyting_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) )
& ( boolean_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel_7) ).
thf(926,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( heyting_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) )
& ( boolean_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(613,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( heyting_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( distributive_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_waybel_1) ).
thf(4550,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( heyting_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( distributive_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(1278,plain,
transitive_relstr @ sk29,
inference(cnf,[status(esa)],[1277]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(1648,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(328,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
thf(2677,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( connected @ A )
=> ( is_connected_in @ A @ ( relation_field @ A ) ) )
& ( ( is_connected_in @ A @ ( relation_field @ A ) )
=> ( connected @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(1146,plain,
reflexive_relstr @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(801,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( below @ A @ ( meet_commut @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
thf(6026,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( below @ A @ ( meet_commut @ A @ B @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
thf(1483,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( meet_commut @ A @ B @ C )
= ( meet_commut @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(3079,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( meet_commut @ A @ B @ C )
= ( meet_commut @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(615,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
thf(4562,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(339,axiom,
! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
thf(2734,plain,
! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(758,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(5647,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( B
= ( relation_rng @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_rng @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(861,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(6492,plain,
! [A: $i] :
( ( ( relation @ A )
=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) )
& ( ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) )
=> ( relation @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(3343,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(965,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(714,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( natural @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).
thf(5327,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( natural @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(307,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(2556,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(41,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(1103,plain,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(517,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( distributive_lattstr @ A )
& ( modular_lattstr @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_lattices) ).
thf(3871,plain,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( distributive_lattstr @ A )
& ( modular_lattstr @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(2275,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ( ( set_difference @ A @ B )
= A ) )
& ( ( ( set_difference @ A @ B )
= A )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(2524,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(608,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( poset_of_lattice @ A )
= ( rel_str_of @ ( the_carrier @ A ) @ ( k2_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice3) ).
thf(4453,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( poset_of_lattice @ A )
= ( rel_str_of @ ( the_carrier @ A ) @ ( k2_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(135,axiom,
! [A: $i] :
( ( bottom_of_relstr @ ( boole_POSet @ A ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).
thf(1631,plain,
! [A: $i] :
( ( bottom_of_relstr @ ( boole_POSet @ A ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ( ~ ( empty_carrier @ ( latt_str_of @ A @ B @ C ) )
& ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
thf(5043,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ( ~ ( empty_carrier @ ( latt_str_of @ A @ B @ C ) )
& ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(655,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
thf(4943,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( ( empty_carrier @ A )
=> ( empty @ ( the_carrier @ A ) ) )
& ( ( empty @ ( the_carrier @ A ) )
=> ( empty_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(432,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( latt_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice3) ).
thf(3319,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( latt_set_smaller @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ B @ D ) ) )
=> ( latt_set_smaller @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(3636,plain,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(425,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(3240,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ( ( in @ ( ordered_pair @ C @ D ) @ B )
=> ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ( ( in @ ( ordered_pair @ C @ D ) @ B )
=> ( in @ ( ordered_pair @ C @ D ) @ A ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(2188,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(404,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(3086,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(3945,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(384,axiom,
! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_orders_2) ).
thf(2991,plain,
! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(1965,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( subset_union2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(4946,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( subset_union2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( A != empty_set )
& ( subset @ A @ ( relation_rng @ B ) )
& ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(1256,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( A != empty_set )
& ( subset @ A @ ( relation_rng @ B ) )
& ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ A )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
thf(2827,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ A )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(764,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_well_founded_in @ A @ B )
<=> ! [C: $i] :
~ ( ( subset @ C @ B )
& ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ( disjoint @ ( fiber @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
thf(5698,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( is_well_founded_in @ A @ B )
=> ! [C: $i] :
~ ( ( subset @ C @ B )
& ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ( disjoint @ ( fiber @ A @ D ) @ C ) ) ) )
& ( ! [C: $i] :
~ ( ( subset @ C @ B )
& ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ( disjoint @ ( fiber @ A @ D ) @ C ) ) )
=> ( is_well_founded_in @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
thf(3372,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) )
& ( ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) )
=> ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( pair_first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( pair_second @ ( ordered_pair @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).
thf(904,plain,
! [A: $i,B: $i] :
( ( ( pair_first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( pair_second @ ( ordered_pair @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(668,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty @ ( empty_carrier_subset @ A ) )
& ( v1_membered @ ( empty_carrier_subset @ A ) )
& ( v2_membered @ ( empty_carrier_subset @ A ) )
& ( v3_membered @ ( empty_carrier_subset @ A ) )
& ( v4_membered @ ( empty_carrier_subset @ A ) )
& ( v5_membered @ ( empty_carrier_subset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_pre_topc) ).
thf(4998,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty @ ( empty_carrier_subset @ A ) )
& ( v1_membered @ ( empty_carrier_subset @ A ) )
& ( v2_membered @ ( empty_carrier_subset @ A ) )
& ( v3_membered @ ( empty_carrier_subset @ A ) )
& ( v4_membered @ ( empty_carrier_subset @ A ) )
& ( v5_membered @ ( empty_carrier_subset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(418,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( C
= ( lim_points_of_net @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
<=> ! [E: $i] :
( ( point_neighbourhood @ E @ A @ D )
=> ( is_eventually_in @ A @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_yellow_6) ).
thf(3187,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( C
= ( lim_points_of_net @ A @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ D @ C )
=> ! [E: $i] :
( ( point_neighbourhood @ E @ A @ D )
=> ( is_eventually_in @ A @ B @ E ) ) )
& ( ! [E: $i] :
( ( point_neighbourhood @ E @ A @ D )
=> ( is_eventually_in @ A @ B @ E ) )
=> ( in @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ D @ C )
=> ! [E: $i] :
( ( point_neighbourhood @ E @ A @ D )
=> ( is_eventually_in @ A @ B @ E ) ) )
& ( ! [E: $i] :
( ( point_neighbourhood @ E @ A @ D )
=> ( is_eventually_in @ A @ B @ E ) )
=> ( in @ D @ C ) ) ) )
=> ( C
= ( lim_points_of_net @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(353,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(2789,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(833,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(6312,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( related_reflexive @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
thf(4677,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( related_reflexive @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(327,axiom,
! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_yellow_1) ).
thf(2674,plain,
! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(160,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(1795,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(472,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(3590,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(516,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( union_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_complement @ A @ ( meet_of_subsets @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tops_2) ).
thf(3868,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( union_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_complement @ A @ ( meet_of_subsets @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(638,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_arytm_3) ).
thf(4769,plain,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( below_refl @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(3964,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( below_refl @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1311,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[1310]) ).
thf(1312,plain,
~ ( empty @ sk31 ),
inference(cnf,[status(esa)],[1311]) ).
thf(411,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ex_inf_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_yellow_0) ).
thf(3123,plain,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ( ex_inf_of_relstr_set @ A @ B )
=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) ) ) )
& ( ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) ) )
=> ( ex_inf_of_relstr_set @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(2442,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(823,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).
thf(6248,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(649,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( bounded_lattstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).
thf(4887,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( bounded_lattstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(84,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C )
& ( quasi_total @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(1356,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C )
& ( quasi_total @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(798,axiom,
! [A: $i] :
( ( element @ A @ omega )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_arytm_3) ).
thf(6016,plain,
! [A: $i] :
( ( element @ A @ omega )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(803,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_set_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ E )
=> ( related @ A @ D @ E ) ) ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_yellow_0) ).
thf(6048,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( ( ex_sup_of_relstr_set @ A @ B )
=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_set_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ E )
=> ( related @ A @ D @ E ) ) ) )
=> ( D = C ) ) ) ) )
& ( ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_set_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ E )
=> ( related @ A @ D @ E ) ) ) )
=> ( D = C ) ) ) )
=> ( ex_sup_of_relstr_set @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(95,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(1428,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(224,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( upper_bounded_semilattstr @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( upper_bounded_relstr @ ( poset_of_lattice @ A ) )
& ( with_suprema_relstr @ ( poset_of_lattice @ A ) )
& ( with_infima_relstr @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow_1) ).
thf(2161,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( upper_bounded_semilattstr @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) )
& ( upper_bounded_relstr @ ( poset_of_lattice @ A ) )
& ( with_suprema_relstr @ ( poset_of_lattice @ A ) )
& ( with_infima_relstr @ ( poset_of_lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(792,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
thf(5965,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_composition @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_composition @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1139,plain,
complete_relstr @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(2891,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ( ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) )
& ( latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(1271,plain,
! [A: $i,B: $i,C: $i] :
( ( ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ( ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) )
& ( latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(6532,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(5595,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(572,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(4171,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(581,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( lim_points_of_net @ A @ B ) )
=> ( is_a_cluster_point_of_netstr @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_waybel_9) ).
thf(4236,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( lim_points_of_net @ A @ B ) )
=> ( is_a_cluster_point_of_netstr @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(176,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_yellow_1) ).
thf(1865,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(579,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ~ ( empty_carrier @ ( net_str_of @ A @ B @ C @ D ) )
& ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_waybel_0) ).
thf(4218,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ~ ( empty_carrier @ ( net_str_of @ A @ B @ C @ D ) )
& ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(629,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_waybel_0) ).
thf(4672,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(387,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i,D: $i] :
( ( subnet @ D @ A @ B )
=> ( ( D
= ( preimage_subnetstr @ A @ B @ C ) )
=> ( is_eventually_in @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_yellow_6) ).
thf(3002,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i,D: $i] :
( ( subnet @ D @ A @ B )
=> ( ( D
= ( preimage_subnetstr @ A @ B @ C ) )
=> ( is_eventually_in @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A )
& ~ ( empty_carrier @ B )
& ( latt_str @ B ) )
=> ( ( strict_latt_str @ ( k8_filter_1 @ A @ B ) )
& ( latt_str @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_1) ).
thf(3340,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A )
& ~ ( empty_carrier @ B )
& ( latt_str @ B ) )
=> ( ( strict_latt_str @ ( k8_filter_1 @ A @ B ) )
& ( latt_str @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(200,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(1997,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(494,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( distributive_lattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( modular_lattstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_lattices) ).
thf(3700,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( distributive_lattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( modular_lattstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(4060,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(979,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(6024,plain,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(297,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(2521,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(424,axiom,
! [A: $i] : ( in @ A @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(3238,plain,
! [A: $i] : ( in @ A @ ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( inclusion_relation @ A ) )
<=> ( ( ( relation_field @ B )
= A )
& ! [C: $i,D: $i] :
( ( ( in @ C @ A )
& ( in @ D @ A ) )
=> ( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( subset @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord2) ).
thf(4828,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( B
= ( inclusion_relation @ A ) )
=> ( ( ( relation_field @ B )
= A )
& ! [C: $i,D: $i] :
( ( ( in @ C @ A )
& ( in @ D @ A ) )
=> ( ( ( in @ ( ordered_pair @ C @ D ) @ B )
=> ( subset @ C @ D ) )
& ( ( subset @ C @ D )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
& ( ( ( ( relation_field @ B )
= A )
& ! [C: $i,D: $i] :
( ( ( in @ C @ A )
& ( in @ D @ A ) )
=> ( ( ( in @ ( ordered_pair @ C @ D ) @ B )
=> ( subset @ C @ D ) )
& ( ( subset @ C @ D )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) )
=> ( B
= ( inclusion_relation @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1144,plain,
upper_bounded_relstr @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ A ) ) )
=> ( ( apply_on_structs @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_waybel_0) ).
thf(4667,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ ( the_carrier @ A ) @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ A ) ) )
=> ( ( apply_on_structs @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(763,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( latt_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice3) ).
thf(5689,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( latt_element_smaller @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ D @ B ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ D @ B ) ) )
=> ( latt_element_smaller @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(174,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(1853,plain,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(179,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ~ ( trivial_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ~ ( v1_yellow_3 @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A )
& ( complemented_relstr @ A )
& ( boolean_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_7) ).
thf(1894,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ~ ( trivial_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ~ ( v1_yellow_3 @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A )
& ( complemented_relstr @ A )
& ( boolean_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(383,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( bounded_lattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).
thf(2987,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( bounded_lattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc38_membered) ).
thf(1806,plain,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc39_membered) ).
thf(1011,plain,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(653,axiom,
! [A: $i] :
( ( A = omega )
<=> ( ( in @ empty_set @ A )
& ( being_limit_ordinal @ A )
& ( ordinal @ A )
& ! [B: $i] :
( ( ordinal @ B )
=> ( ( ( in @ empty_set @ B )
& ( being_limit_ordinal @ B ) )
=> ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_ordinal2) ).
thf(4914,plain,
! [A: $i] :
( ( ( A = omega )
=> ( ( in @ empty_set @ A )
& ( being_limit_ordinal @ A )
& ( ordinal @ A )
& ! [B: $i] :
( ( ordinal @ B )
=> ( ( ( in @ empty_set @ B )
& ( being_limit_ordinal @ B ) )
=> ( subset @ A @ B ) ) ) ) )
& ( ( ( in @ empty_set @ A )
& ( being_limit_ordinal @ A )
& ( ordinal @ A )
& ! [B: $i] :
( ( ordinal @ B )
=> ( ( ( in @ empty_set @ B )
& ( being_limit_ordinal @ B ) )
=> ( subset @ A @ B ) ) ) )
=> ( A = omega ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(779,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ! [D: $i] :
( ( ( strict_net_str @ D @ A )
& ( net_str @ D @ A ) )
=> ( ( D
= ( netstr_restr_to_element @ A @ B @ C ) )
<=> ( ! [E: $i] :
( ( in @ E @ ( the_carrier @ D ) )
<=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) ) )
& ( ( the_InternalRel @ D )
= ( relation_restriction_as_relation_of @ ( the_InternalRel @ B ) @ ( the_carrier @ D ) ) )
& ( ( the_mapping @ A @ D )
= ( partfun_dom_restriction @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_waybel_9) ).
thf(5827,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ! [D: $i] :
( ( ( strict_net_str @ D @ A )
& ( net_str @ D @ A ) )
=> ( ( ( D
= ( netstr_restr_to_element @ A @ B @ C ) )
=> ( ! [E: $i] :
( ( ( in @ E @ ( the_carrier @ D ) )
=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) ) )
& ( ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) )
=> ( in @ E @ ( the_carrier @ D ) ) ) )
& ( ( the_InternalRel @ D )
= ( relation_restriction_as_relation_of @ ( the_InternalRel @ B ) @ ( the_carrier @ D ) ) )
& ( ( the_mapping @ A @ D )
= ( partfun_dom_restriction @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ D ) ) ) ) )
& ( ( ! [E: $i] :
( ( ( in @ E @ ( the_carrier @ D ) )
=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) ) )
& ( ? [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
& ( F = E )
& ( related @ B @ C @ F ) )
=> ( in @ E @ ( the_carrier @ D ) ) ) )
& ( ( the_InternalRel @ D )
= ( relation_restriction_as_relation_of @ ( the_InternalRel @ B ) @ ( the_carrier @ D ) ) )
& ( ( the_mapping @ A @ D )
= ( partfun_dom_restriction @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ D ) ) ) )
=> ( D
= ( netstr_restr_to_element @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(216,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(2097,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(784,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( directed_relstr @ C )
& ( net_str @ C @ A ) )
=> ( ( subnet @ C @ A @ B )
<=> ? [D: $i] :
( ( function @ D )
& ( quasi_total @ D @ ( the_carrier @ C ) @ ( the_carrier @ B ) )
& ( relation_of2_as_subset @ D @ ( the_carrier @ C ) @ ( the_carrier @ B ) )
& ( ( the_mapping @ A @ C )
= ( function_of_composition @ ( the_carrier @ C ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ D @ ( the_mapping @ A @ B ) ) )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
& ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( related @ C @ F @ G )
=> ( related @ B @ E @ ( apply_on_set_and_struct @ ( the_carrier @ C ) @ B @ D @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_yellow_6) ).
thf(5901,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( directed_relstr @ C )
& ( net_str @ C @ A ) )
=> ( ( ( subnet @ C @ A @ B )
=> ? [D: $i] :
( ( function @ D )
& ( quasi_total @ D @ ( the_carrier @ C ) @ ( the_carrier @ B ) )
& ( relation_of2_as_subset @ D @ ( the_carrier @ C ) @ ( the_carrier @ B ) )
& ( ( the_mapping @ A @ C )
= ( function_of_composition @ ( the_carrier @ C ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ D @ ( the_mapping @ A @ B ) ) )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
& ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( related @ C @ F @ G )
=> ( related @ B @ E @ ( apply_on_set_and_struct @ ( the_carrier @ C ) @ B @ D @ G ) ) ) ) ) ) ) )
& ( ? [D: $i] :
( ( function @ D )
& ( quasi_total @ D @ ( the_carrier @ C ) @ ( the_carrier @ B ) )
& ( relation_of2_as_subset @ D @ ( the_carrier @ C ) @ ( the_carrier @ B ) )
& ( ( the_mapping @ A @ C )
= ( function_of_composition @ ( the_carrier @ C ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ D @ ( the_mapping @ A @ B ) ) )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
& ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( related @ C @ F @ G )
=> ( related @ B @ E @ ( apply_on_set_and_struct @ ( the_carrier @ C ) @ B @ D @ G ) ) ) ) ) ) )
=> ( subnet @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) )
& ( v3_membered @ ( set_intersection2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc31_membered) ).
thf(1542,plain,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) )
& ( v3_membered @ ( set_intersection2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(375,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ ( netstr_restr_to_element @ A @ B @ C ) ) )
=> ( ( D = E )
=> ( ( apply_netmap @ A @ B @ D )
= ( apply_netmap @ A @ ( netstr_restr_to_element @ A @ B @ C ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_waybel_9) ).
thf(2943,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ ( netstr_restr_to_element @ A @ B @ C ) ) )
=> ( ( D = E )
=> ( ( apply_netmap @ A @ B @ D )
= ( apply_netmap @ A @ ( netstr_restr_to_element @ A @ B @ C ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(495,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ! [B: $i] :
( ( in @ B @ ( relation_field @ A ) )
=> ( in @ ( ordered_pair @ B @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
thf(3710,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( reflexive @ A )
=> ! [B: $i] :
( ( in @ B @ ( relation_field @ A ) )
=> ( in @ ( ordered_pair @ B @ B ) @ A ) ) )
& ( ! [B: $i] :
( ( in @ B @ ( relation_field @ A ) )
=> ( in @ ( ordered_pair @ B @ B ) @ A ) )
=> ( reflexive @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(880,plain,
( ( in @ sk4 @ ( filter_of_net_str @ sk1 @ sk2 ) )
| ~ sk3 ),
inference(cnf,[status(esa)],[876]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(1801,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(2378,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(777,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(5795,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( in @ A @ C )
& ( in @ B @ D ) ) )
& ( ( ( in @ A @ C )
& ( in @ B @ D ) )
=> ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(600,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ex_inf_of_relstr_set @ A @ B )
=> ( ( C
= ( meet_on_relstr @ A @ B ) )
<=> ( ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_yellow_0) ).
thf(4374,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ex_inf_of_relstr_set @ A @ B )
=> ( ( ( C
= ( meet_on_relstr @ A @ B ) )
=> ( ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) ) ) )
& ( ( ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) ) )
=> ( C
= ( meet_on_relstr @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( netstr_induced_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow19) ).
thf(3066,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( netstr_induced_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(371,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( trivial_carrier @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_yellow_0) ).
thf(2896,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( trivial_carrier @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(816,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_knaster) ).
thf(6196,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(639,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(4773,plain,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(122,axiom,
! [A: $i] :
? [B: $i] :
( ( relation_of2 @ B @ A @ A )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( quasi_total @ B @ A @ A )
& ( onto @ B @ A @ A )
& ( bijective @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_2) ).
thf(1571,plain,
! [A: $i] :
? [B: $i] :
( ( relation_of2 @ B @ A @ A )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( quasi_total @ B @ A @ A )
& ( onto @ B @ A @ A )
& ( bijective @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(97,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(1439,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(743,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( cartesian_product2 @ A @ B ) )
& ? [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
= D )
& ( in @ E @ A )
& ( F
= ( singleton @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
thf(5584,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( cartesian_product2 @ A @ B ) )
& ? [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
= D )
& ( in @ E @ A )
& ( F
= ( singleton @ E ) ) ) ) )
& ( ( ( in @ D @ ( cartesian_product2 @ A @ B ) )
& ? [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
= D )
& ( in @ E @ A )
& ( F
= ( singleton @ E ) ) ) )
=> ( in @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(673,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( is_often_in @ A @ B @ C )
=> ( subnet @ ( preimage_subnetstr @ A @ B @ C ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_yellow_6) ).
thf(5035,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( is_often_in @ A @ B @ C )
=> ( subnet @ ( preimage_subnetstr @ A @ B @ C ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( cartesian_product2 @ A @ A ) )
& ? [F: $i,G: $i] :
( ( E
= ( ordered_pair @ F @ G ) )
& ( in @ ( ordered_pair @ ( apply @ C @ F ) @ ( apply @ C @ G ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
thf(2025,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ( ( in @ E @ ( cartesian_product2 @ A @ A ) )
& ? [F: $i,G: $i] :
( ( E
= ( ordered_pair @ F @ G ) )
& ( in @ ( ordered_pair @ ( apply @ C @ F ) @ ( apply @ C @ G ) ) @ B ) ) ) )
& ( ( ( in @ E @ ( cartesian_product2 @ A @ A ) )
& ? [F: $i,G: $i] :
( ( E
= ( ordered_pair @ F @ G ) )
& ( in @ ( ordered_pair @ ( apply @ C @ F ) @ ( apply @ C @ G ) ) @ B ) ) )
=> ( in @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(3668,plain,
! [A: $i,B: $i] :
( ( ( B
= ( singleton @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) )
=> ( B
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattices) ).
thf(4993,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_wellord1) ).
thf(1381,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(288,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(2461,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(793,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(5987,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( equipotent @ A @ B )
=> ( equipotent @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_wellord2) ).
thf(890,plain,
! [A: $i,B: $i] :
( ( equipotent @ A @ B )
=> ( equipotent @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(458,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_antisymmetric_in @ A @ B )
<=> ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ C ) @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
thf(3456,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( is_antisymmetric_in @ A @ B )
=> ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ C ) @ A ) )
=> ( C = D ) ) )
& ( ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ C ) @ A ) )
=> ( C = D ) )
=> ( is_antisymmetric_in @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) )
& ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
thf(2182,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) )
& ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(796,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( latt_str @ A )
& ( ( bottom_of_semilattstr @ A )
= ( join_of_latt_set @ A @ empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice3) ).
thf(6004,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( latt_str @ A )
& ( ( bottom_of_semilattstr @ A )
= ( join_of_latt_set @ A @ empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(795,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ( ( in @ A @ ( a_1_0_filter_1 @ B ) )
<=> ? [C: $i,D: $i] :
( ( element @ C @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ B ) )
& ( A
= ( ordered_pair_as_product_element @ ( the_carrier @ B ) @ ( the_carrier @ B ) @ C @ D ) )
& ( below_refl @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
thf(5994,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ( ( ( in @ A @ ( a_1_0_filter_1 @ B ) )
=> ? [C: $i,D: $i] :
( ( element @ C @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ B ) )
& ( A
= ( ordered_pair_as_product_element @ ( the_carrier @ B ) @ ( the_carrier @ B ) @ C @ D ) )
& ( below_refl @ B @ C @ D ) ) )
& ( ? [C: $i,D: $i] :
( ( element @ C @ ( the_carrier @ B ) )
& ( element @ D @ ( the_carrier @ B ) )
& ( A
= ( ordered_pair_as_product_element @ ( the_carrier @ B ) @ ( the_carrier @ B ) @ C @ D ) )
& ( below_refl @ B @ C @ D ) )
=> ( in @ A @ ( a_1_0_filter_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
thf(3073,plain,
! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( ( proper_element @ B @ A )
=> ( B
!= ( union @ A ) ) )
& ( ( B
!= ( union @ A ) )
=> ( proper_element @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(745,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(5599,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(710,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ D @ C )
<=> ( ( closed_subset @ D @ A )
& ( subset @ B @ D ) ) ) )
& ( ( topstr_closure @ A @ B )
= ( meet_of_subsets @ ( the_carrier @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_pre_topc) ).
thf(5286,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( in @ D @ C )
=> ( ( closed_subset @ D @ A )
& ( subset @ B @ D ) ) )
& ( ( ( closed_subset @ D @ A )
& ( subset @ B @ D ) )
=> ( in @ D @ C ) ) ) )
& ( ( topstr_closure @ A @ B )
= ( meet_of_subsets @ ( the_carrier @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(542,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
thf(3977,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(2410,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(7,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(895,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(388,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(3006,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(2329,plain,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(190,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bounded_relstr @ A )
=> ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(1952,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bounded_relstr @ A )
=> ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(2765,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(828,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(6270,plain,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(883,plain,
( sk3
| ( element @ sk5 @ ( powerset @ ( the_carrier @ sk1 ) ) ) ),
inference(cnf,[status(esa)],[876]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(2369,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( ( relation_restriction_as_relation_of @ A @ B )
= ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_toler_1) ).
thf(2797,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( ( relation_restriction_as_relation_of @ A @ B )
= ( relation_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( net_str_of @ A @ B @ C @ D )
= ( net_str_of @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_waybel_0) ).
thf(3310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( net_str_of @ A @ B @ C @ D )
= ( net_str_of @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(217,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(2101,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( ( B
= ( relation_rng @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_rng @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(381,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i,C: $i] :
( ( is_a_convergence_point_of_set @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ D @ A )
& ( in @ C @ D ) )
=> ( in @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_waybel_7) ).
thf(2967,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i,C: $i] :
( ( ( is_a_convergence_point_of_set @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ D @ A )
& ( in @ C @ D ) )
=> ( in @ D @ B ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ D @ A )
& ( in @ C @ D ) )
=> ( in @ D @ B ) ) )
=> ( is_a_convergence_point_of_set @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(619,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( strict_latt_str @ A )
=> ( A
= ( latt_str_of @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ ( the_L_meet @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(4626,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( strict_latt_str @ A )
=> ( A
= ( latt_str_of @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ ( the_L_meet @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(650,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ~ ( v1_yellow_3 @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_yellow_3) ).
thf(4890,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ~ ( v1_yellow_3 @ A )
=> ~ ( empty_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(379,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_orders_2) ).
thf(2962,plain,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
& ( F = D )
& ( closed_subset @ F @ A )
& ( subset @ B @ D ) )
& ( C = E )
& ? [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
& ( F = E )
& ( closed_subset @ F @ A )
& ( subset @ B @ E ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ? [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
& ( F = D )
& ( closed_subset @ F @ A )
& ( subset @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e1_40__pre_topc__1) ).
thf(5254,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
& ( F = D )
& ( closed_subset @ F @ A )
& ( subset @ B @ D ) )
& ( C = E )
& ? [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
& ( F = E )
& ( closed_subset @ F @ A )
& ( subset @ B @ E ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ? [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
& ( F = D )
& ( closed_subset @ F @ A )
& ( subset @ B @ D ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ? [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
& ( F = D )
& ( closed_subset @ F @ A )
& ( subset @ B @ D ) ) )
=> ( in @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_wellord1) ).
thf(1528,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(756,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( relation_of_lattice @ A )
= ( a_1_0_filter_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_1) ).
thf(5641,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( relation_of_lattice @ A )
= ( a_1_0_filter_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(759,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( open_subset @ ( interior @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
thf(5667,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( open_subset @ ( interior @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(1496,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(521,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( in @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( topstr_closure @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ D @ A )
& ( subset @ B @ D ) )
=> ( in @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).
thf(3908,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( in @ C @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ ( topstr_closure @ A @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ D @ A )
& ( subset @ B @ D ) )
=> ( in @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ D @ A )
& ( subset @ B @ D ) )
=> ( in @ C @ D ) ) )
=> ( in @ C @ ( topstr_closure @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(6485,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel_1) ).
thf(1694,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(658,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(4965,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( closed_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(389,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( net_str @ C @ A )
=> ( ( subnetstr @ C @ A @ B )
<=> ( ( subrelstr @ C @ B )
& ( ( the_mapping @ A @ C )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_yellow_6) ).
thf(3009,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( net_str @ C @ A )
=> ( ( ( subnetstr @ C @ A @ B )
=> ( ( subrelstr @ C @ B )
& ( ( the_mapping @ A @ C )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ C ) ) ) ) )
& ( ( ( subrelstr @ C @ B )
& ( ( the_mapping @ A @ C )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ C ) ) ) )
=> ( subnetstr @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(606,axiom,
! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_waybel_0) ).
thf(4441,plain,
! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(610,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( reflexive_relstr @ A )
& ( with_suprema_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( with_suprema_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_waybel_0) ).
thf(4458,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( reflexive_relstr @ A )
& ( with_suprema_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( with_suprema_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(647,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(4859,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(523,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(3921,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(101,axiom,
! [A: $i] :
( ( lower_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( ( bottom_of_semilattstr @ ( boole_lattice @ A ) )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lattice3) ).
thf(1472,plain,
! [A: $i] :
( ( lower_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( ( bottom_of_semilattstr @ ( boole_lattice @ A ) )
= empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(192,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( symmetric @ A )
& ( transitive @ A ) )
=> ( ( relation @ A )
& ( reflexive @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_partfun1) ).
thf(1958,plain,
! [A: $i] :
( ( ( relation @ A )
& ( symmetric @ A )
& ( transitive @ A ) )
=> ( ( relation @ A )
& ( reflexive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( cartesian_product2 @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [H: $i] :
( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( H = F )
=> ( G
= ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e4_7_1__tops_2__1) ).
thf(6440,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ( ( in @ E @ ( cartesian_product2 @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [H: $i] :
( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( H = F )
=> ( G
= ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) ) )
& ( ( ( in @ E @ ( cartesian_product2 @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [H: $i] :
( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( H = F )
=> ( G
= ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) )
=> ( in @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(1551,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(28,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( heyting_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_waybel_1) ).
thf(1049,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( heyting_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(735,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(5538,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ( ( ( finite @ C )
& ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( in @ D @ B )
& ( relstr_set_smaller @ A @ empty_set @ D ) )
& ! [D: $i,E: $i] :
( ( ( in @ D @ C )
& ( subset @ E @ C )
& ? [F: $i] :
( ( element @ F @ ( the_carrier @ A ) )
& ( in @ F @ B )
& ( relstr_set_smaller @ A @ E @ F ) ) )
=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ A ) )
& ( in @ F @ B )
& ( relstr_set_smaller @ A @ ( set_union2 @ E @ ( singleton @ D ) ) @ F ) ) ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( in @ D @ B )
& ( relstr_set_smaller @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_finset_1__e11_2_1__waybel_0) ).
thf(4690,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ( ( ( finite @ C )
& ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( in @ D @ B )
& ( relstr_set_smaller @ A @ empty_set @ D ) )
& ! [D: $i,E: $i] :
( ( ( in @ D @ C )
& ( subset @ E @ C )
& ? [F: $i] :
( ( element @ F @ ( the_carrier @ A ) )
& ( in @ F @ B )
& ( relstr_set_smaller @ A @ E @ F ) ) )
=> ? [F: $i] :
( ( element @ F @ ( the_carrier @ A ) )
& ( in @ F @ B )
& ( relstr_set_smaller @ A @ ( set_union2 @ E @ ( singleton @ D ) ) @ F ) ) ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
& ( in @ D @ B )
& ( relstr_set_smaller @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(2318,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(250,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(2271,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(609,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( subset @ ( interior @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
thf(4456,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( subset @ ( interior @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1145,plain,
antisymmetric_relstr @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_waybel_1) ).
thf(1018,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(870,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).
thf(6564,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(717,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(5358,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(685,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( transitive_relstr @ A )
<=> ( is_transitive_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_orders_2) ).
thf(5133,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( transitive_relstr @ A )
=> ( is_transitive_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) )
& ( ( is_transitive_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) )
=> ( transitive_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(1181,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_enumset1) ).
thf(6399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( unordered_triple @ A @ B @ C ) )
=> ! [E: $i] :
( ( ( in @ E @ D )
=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) )
& ( ~ ( ( E != A )
& ( E != B )
& ( E != C ) )
=> ( in @ E @ D ) ) ) )
& ( ! [E: $i] :
( ( ( in @ E @ D )
=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) )
& ( ~ ( ( E != A )
& ( E != B )
& ( E != C ) )
=> ( in @ E @ D ) ) )
=> ( D
= ( unordered_triple @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(130,axiom,
! [A: $i] : ( relation @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(1611,plain,
! [A: $i] : ( relation @ ( inclusion_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(121,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(1566,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(844,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnet @ C @ A @ B )
=> ( subset @ ( lim_points_of_net @ A @ B ) @ ( lim_points_of_net @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_yellow_6) ).
thf(6367,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnet @ C @ A @ B )
=> ( subset @ ( lim_points_of_net @ A @ B ) @ ( lim_points_of_net @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(533,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(3949,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc37_membered) ).
thf(2518,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(660,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( closed_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
thf(4971,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( closed_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(114,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(1531,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
=> ( ( relation_rng @ A )
= empty_set ) )
& ( ( ( relation_rng @ A )
= empty_set )
=> ( ( relation_dom @ A )
= empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
thf(2689,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(767,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_lattices) ).
thf(5716,plain,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ( in @ D @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = D )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1__e4_7_1__tops_2__1) ).
thf(3376,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ D @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ( in @ D @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = D )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) ) )
& ( ( ( in @ D @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ( in @ D @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = D )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
thf(3640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) )
& ( ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) )
=> ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(112,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_waybel_1) ).
thf(1516,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(748,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
thf(5607,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(1961,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ E @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ E @ G ) @ B ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ A )
& ? [F: $i] :
( ( D = F )
& ( in @ E @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ E @ G ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1__e10_24__wellord2__1) ).
thf(1225,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ E @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ E @ G ) @ B ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ D @ A )
& ( in @ D @ A )
& ? [F: $i] :
( ( D = F )
& ( in @ E @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ E @ G ) @ B ) ) ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ A )
& ? [F: $i] :
( ( D = F )
& ( in @ E @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ E @ G ) @ B ) ) ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ( ( B != empty_set )
=> ! [E: $i] :
( ( in @ E @ ( relation_inverse_image @ D @ C ) )
<=> ( ( in @ E @ A )
& ( in @ ( apply @ D @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
thf(5399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ( ( B != empty_set )
=> ! [E: $i] :
( ( ( in @ E @ ( relation_inverse_image @ D @ C ) )
=> ( ( in @ E @ A )
& ( in @ ( apply @ D @ E ) @ C ) ) )
& ( ( ( in @ E @ A )
& ( in @ ( apply @ D @ E ) @ C ) )
=> ( in @ E @ ( relation_inverse_image @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(2060,plain,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( unordered_pair_as_carrier_subset @ A @ B @ C ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(4272,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( unordered_pair_as_carrier_subset @ A @ B @ C ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(402,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( nowhere_dense @ B @ A )
=> ( boundary_set @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(3082,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( nowhere_dense @ B @ A )
=> ( boundary_set @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( equipotent @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_wellord2) ).
thf(886,plain,
! [A: $i] : ( equipotent @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(887,plain,
! [A: $i] : ( equipotent @ A @ A ),
inference(cnf,[status(esa)],[886]) ).
thf(623,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(4641,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(227,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(2175,plain,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(274,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(2407,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(652,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( ( topological_space @ A )
<=> ( ( in @ ( the_carrier @ A ) @ ( the_topology @ A ) )
& ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( subset @ B @ ( the_topology @ A ) )
=> ( in @ ( union_of_subsets @ ( the_carrier @ A ) @ B ) @ ( the_topology @ A ) ) ) )
& ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( in @ B @ ( the_topology @ A ) )
& ( in @ C @ ( the_topology @ A ) ) )
=> ( in @ ( subset_intersection2 @ ( the_carrier @ A ) @ B @ C ) @ ( the_topology @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_pre_topc) ).
thf(4894,plain,
! [A: $i] :
( ( top_str @ A )
=> ( ( ( topological_space @ A )
=> ( ( in @ ( the_carrier @ A ) @ ( the_topology @ A ) )
& ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( subset @ B @ ( the_topology @ A ) )
=> ( in @ ( union_of_subsets @ ( the_carrier @ A ) @ B ) @ ( the_topology @ A ) ) ) )
& ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( in @ B @ ( the_topology @ A ) )
& ( in @ C @ ( the_topology @ A ) ) )
=> ( in @ ( subset_intersection2 @ ( the_carrier @ A ) @ B @ C ) @ ( the_topology @ A ) ) ) ) ) ) )
& ( ( ( in @ ( the_carrier @ A ) @ ( the_topology @ A ) )
& ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( subset @ B @ ( the_topology @ A ) )
=> ( in @ ( union_of_subsets @ ( the_carrier @ A ) @ B ) @ ( the_topology @ A ) ) ) )
& ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( in @ B @ ( the_topology @ A ) )
& ( in @ C @ ( the_topology @ A ) ) )
=> ( in @ ( subset_intersection2 @ ( the_carrier @ A ) @ B @ C ) @ ( the_topology @ A ) ) ) ) ) )
=> ( topological_space @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(477,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( heyting_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_waybel_1) ).
thf(3608,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( heyting_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join_commut @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
thf(6596,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join_commut @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(3019,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(848,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(6389,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(599,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ ( succ @ A ) )
& ? [D: $i] :
( ( ordinal @ D )
& ( C = D )
& ( ( in @ D @ omega )
=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( powerset @ D ) ) )
=> ~ ( ( E != empty_set )
& ! [F: $i] :
~ ( ( in @ F @ E )
& ! [G: $i] :
( ( ( in @ G @ E )
& ( subset @ F @ G ) )
=> ( G = F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e18_27__finset_1__1) ).
thf(4346,plain,
! [A: $i] :
( ( ordinal @ A )
=> ? [B: $i] :
! [C: $i] :
( ( ( in @ C @ B )
=> ( ( in @ C @ ( succ @ A ) )
& ? [D: $i] :
( ( ordinal @ D )
& ( C = D )
& ( ( in @ D @ omega )
=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( powerset @ D ) ) )
=> ~ ( ( E != empty_set )
& ! [F: $i] :
~ ( ( in @ F @ E )
& ! [G: $i] :
( ( ( in @ G @ E )
& ( subset @ F @ G ) )
=> ( G = F ) ) ) ) ) ) ) ) )
& ( ( ( in @ C @ ( succ @ A ) )
& ? [D: $i] :
( ( ordinal @ D )
& ( C = D )
& ( ( in @ D @ omega )
=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( powerset @ D ) ) )
=> ~ ( ( E != empty_set )
& ! [F: $i] :
~ ( ( in @ F @ E )
& ! [G: $i] :
( ( ( in @ G @ E )
& ( subset @ F @ G ) )
=> ( G = F ) ) ) ) ) ) ) )
=> ( in @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( element @ ( apply_on_set_and_struct2 @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_yellow_2) ).
thf(4020,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ( function @ C )
& ( quasi_total @ C @ A @ ( the_carrier @ B ) )
& ( relation_of2 @ C @ A @ ( the_carrier @ B ) )
& ( element @ D @ A ) )
=> ( element @ ( apply_on_set_and_struct2 @ A @ B @ C @ D ) @ ( the_carrier @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(470,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ ( relation_field @ A ) )
& ( in @ C @ ( relation_field @ A ) )
& ( B != C )
& ~ ( in @ ( ordered_pair @ B @ C ) @ A )
& ~ ( in @ ( ordered_pair @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
thf(3554,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( connected @ A )
=> ! [B: $i,C: $i] :
~ ( ( in @ B @ ( relation_field @ A ) )
& ( in @ C @ ( relation_field @ A ) )
& ( B != C )
& ~ ( in @ ( ordered_pair @ B @ C ) @ A )
& ~ ( in @ ( ordered_pair @ C @ B ) @ A ) ) )
& ( ! [B: $i,C: $i] :
~ ( ( in @ B @ ( relation_field @ A ) )
& ( in @ C @ ( relation_field @ A ) )
& ( B != C )
& ~ ( in @ ( ordered_pair @ B @ C ) @ A )
& ~ ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( connected @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(690,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(5154,plain,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(158,axiom,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i] :
( C
!= ( singleton @ B ) ) ) )
=> ? [B: $i] :
( ( relation @ B )
& ( function @ B )
& ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
thf(1763,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i] :
( C
!= ( singleton @ B ) ) ) )
=> ? [B: $i] :
( ( relation @ B )
& ( function @ B )
& ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= ( singleton @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(843,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_connected_in @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( in @ C @ B )
& ( in @ D @ B )
& ( C != D )
& ~ ( in @ ( ordered_pair @ C @ D ) @ A )
& ~ ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
thf(6352,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( is_connected_in @ A @ B )
=> ! [C: $i,D: $i] :
~ ( ( in @ C @ B )
& ( in @ D @ B )
& ( C != D )
& ~ ( in @ ( ordered_pair @ C @ D ) @ A )
& ~ ( in @ ( ordered_pair @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
~ ( ( in @ C @ B )
& ( in @ D @ B )
& ( C != D )
& ~ ( in @ ( ordered_pair @ C @ D ) @ A )
& ~ ( in @ ( ordered_pair @ D @ C ) @ A ) )
=> ( is_connected_in @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(260,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
thf(2322,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(471,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
thf(3564,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( relation_inverse_image @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) )
& ( ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) )
& ( ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( relation_inverse_image @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(407,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_lattices) ).
thf(3095,plain,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(79,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( connected @ ( inclusion_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_wellord2) ).
thf(1336,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( connected @ ( inclusion_relation @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(58,axiom,
! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( rel_str @ ( incl_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
thf(1220,plain,
! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( rel_str @ ( incl_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(529,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(3940,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(287,axiom,
( ( empty @ empty_set )
& ( v1_membered @ empty_set )
& ( v2_membered @ empty_set )
& ( v3_membered @ empty_set )
& ( v4_membered @ empty_set )
& ( v5_membered @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
thf(2454,plain,
( ( empty @ empty_set )
& ( v1_membered @ empty_set )
& ( v2_membered @ empty_set )
& ( v3_membered @ empty_set )
& ( v4_membered @ empty_set )
& ( v5_membered @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(769,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(5731,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( ( element @ B @ A )
=> ( in @ B @ A ) )
& ( ( in @ B @ A )
=> ( element @ B @ A ) ) ) )
& ( ( empty @ A )
=> ( ( ( element @ B @ A )
=> ( empty @ B ) )
& ( ( empty @ B )
=> ( element @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(574,axiom,
! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_yellow_1) ).
thf(4190,plain,
! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(509,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ empty_set )
& ( ex_inf_of_relstr_set @ A @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).
thf(3818,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ empty_set )
& ( ex_inf_of_relstr_set @ A @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(1300,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( subnetstr_of_element @ A @ B @ C )
= ( netstr_restr_to_element @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_waybel_9) ).
thf(3691,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( subnetstr_of_element @ A @ B @ C )
= ( netstr_restr_to_element @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(137,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_waybel_0) ).
thf(1637,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(854,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(6436,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) )
& ( ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) )
=> ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ? [F: $i] :
( ( C = F )
& ( in @ E @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ E @ G ) @ B ) ) ) )
=> ( D = E ) )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ! [D: $i] :
~ ? [E: $i] :
( ( C = E )
& ( in @ D @ E )
& ! [F: $i] :
( ( in @ F @ E )
=> ( in @ ( ordered_pair @ D @ F ) @ B ) ) ) ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ( ( relation_dom @ C )
= A )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( D = E )
& ( in @ ( apply @ C @ D ) @ E )
& ! [F: $i] :
( ( in @ F @ E )
=> ( in @ ( ordered_pair @ ( apply @ C @ D ) @ F ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e10_24__wellord2) ).
thf(2486,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ? [F: $i] :
( ( C = F )
& ( in @ E @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ E @ G ) @ B ) ) ) )
=> ( D = E ) )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ! [D: $i] :
~ ? [E: $i] :
( ( C = E )
& ( in @ D @ E )
& ! [F: $i] :
( ( in @ F @ E )
=> ( in @ ( ordered_pair @ D @ F ) @ B ) ) ) ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ( ( relation_dom @ C )
= A )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( D = E )
& ( in @ ( apply @ C @ D ) @ E )
& ! [F: $i] :
( ( in @ F @ E )
=> ( in @ ( ordered_pair @ ( apply @ C @ D ) @ F ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(564,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( ( ordered_pair_as_product_element @ A @ B @ C @ D )
= ( ordered_pair @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(4117,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( ( ordered_pair_as_product_element @ A @ B @ C @ D )
= ( ordered_pair @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(123,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(1579,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(688,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ C @ B )
=> ( closed_subset @ C @ A ) ) )
=> ( closed_subset @ ( meet_of_subsets @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_pre_topc) ).
thf(5147,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ C @ B )
=> ( closed_subset @ C @ A ) ) )
=> ( closed_subset @ ( meet_of_subsets @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(838,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(6337,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(1749,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ ( singleton @ B ) )
=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) )
& ( ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
=> ( subset @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc22_waybel_9) ).
thf(4267,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(831,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( meet_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_complement @ A @ ( union_of_subsets @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tops_2) ).
thf(6301,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( meet_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_complement @ A @ ( union_of_subsets @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) )
& ( v3_membered @ ( set_intersection2 @ A @ B ) )
& ( v4_membered @ ( set_intersection2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc33_membered) ).
thf(991,plain,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) )
& ( v3_membered @ ( set_intersection2 @ A @ B ) )
& ( v4_membered @ ( set_intersection2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(703,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(5208,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(788,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( is_a_cover_of_carrier @ A @ B )
& ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tops_2) ).
thf(5949,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( is_a_cover_of_carrier @ A @ B )
& ( B = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(493,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( closed_subsets @ B @ A )
<=> ( open_subsets @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_tops_2) ).
thf(3697,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( ( closed_subsets @ B @ A )
=> ( open_subsets @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ A ) )
& ( ( open_subsets @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ A )
=> ( closed_subsets @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(308,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( directed_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_yellow_6) ).
thf(2558,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( directed_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( open_subset @ ( interior @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).
thf(3970,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( open_subset @ ( interior @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1141,plain,
with_suprema_relstr @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(115,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
thf(1536,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( well_founded_relation @ A )
=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) )
& ( ( is_well_founded_in @ A @ ( relation_field @ A ) )
=> ( well_founded_relation @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(438,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( ( full_subrelstr @ B @ A )
& ( subrelstr @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ A @ C @ D )
& ( in @ E @ ( the_carrier @ B ) )
& ( in @ F @ ( the_carrier @ B ) ) )
=> ( related @ B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_yellow_0) ).
thf(3356,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( ( full_subrelstr @ B @ A )
& ( subrelstr @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ A @ C @ D )
& ( in @ E @ ( the_carrier @ B ) )
& ( in @ F @ ( the_carrier @ B ) ) )
=> ( related @ B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(845,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(6369,plain,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(1955,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(731,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i] :
( ( ordinal @ F )
& ( D = F )
& ( in @ F @ A ) )
& ( C = E )
& ? [F: $i] :
( ( ordinal @ F )
& ( E = F )
& ( in @ F @ A ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( succ @ B ) )
& ( E = D )
& ? [F: $i] :
( ( ordinal @ F )
& ( D = F )
& ( in @ F @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
thf(5504,plain,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i] :
( ( ordinal @ F )
& ( D = F )
& ( in @ F @ A ) )
& ( C = E )
& ? [F: $i] :
( ( ordinal @ F )
& ( E = F )
& ( in @ F @ A ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( succ @ B ) )
& ( E = D )
& ? [F: $i] :
( ( ordinal @ F )
& ( D = F )
& ( in @ F @ A ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( succ @ B ) )
& ( E = D )
& ? [F: $i] :
( ( ordinal @ F )
& ( D = F )
& ( in @ F @ A ) ) )
=> ( in @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( equipotent @ A @ B )
<=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ( one_to_one @ C )
& ( ( relation_dom @ C )
= A )
& ( ( relation_rng @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord2) ).
thf(2357,plain,
! [A: $i,B: $i] :
( ( ( equipotent @ A @ B )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ( one_to_one @ C )
& ( ( relation_dom @ C )
= A )
& ( ( relation_rng @ C )
= B ) ) )
& ( ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ( one_to_one @ C )
& ( ( relation_dom @ C )
= A )
& ( ( relation_rng @ C )
= B ) )
=> ( equipotent @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( transitive @ B )
=> ( transitive @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
thf(2320,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( transitive @ B )
=> ( transitive @ ( relation_restriction @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(665,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(4991,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(815,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(6193,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( bijective @ C @ A @ B ) )
=> ( ( function @ C )
& ( one_to_one @ C )
& ( quasi_total @ C @ A @ B )
& ( onto @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_2) ).
thf(1094,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( bijective @ C @ A @ B ) )
=> ( ( function @ C )
& ( one_to_one @ C )
& ( quasi_total @ C @ A @ B )
& ( onto @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1140,plain,
lower_bounded_relstr @ sk13,
inference(cnf,[status(esa)],[1136]) ).
thf(761,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow_0) ).
thf(5685,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(161,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ ( union @ A ) )
& ( epsilon_connected @ ( union @ A ) )
& ( ordinal @ ( union @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_ordinal1) ).
thf(1797,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ ( union @ A ) )
& ( epsilon_connected @ ( union @ A ) )
& ( ordinal @ ( union @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(537,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( antisymmetric_relstr @ A )
<=> ( is_antisymmetric_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_orders_2) ).
thf(3961,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( antisymmetric_relstr @ A )
=> ( is_antisymmetric_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) )
& ( ( is_antisymmetric_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) )
=> ( antisymmetric_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(399,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( empty_carrier @ A )
=> ( v1_yellow_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_3) ).
thf(3071,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( empty_carrier @ A )
=> ( v1_yellow_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(86,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_waybel_0) ).
thf(1372,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(426,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( meet @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_meet @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
thf(3256,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( meet @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_meet @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(822,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( is_often_in @ A @ B @ C )
=> ( ~ ( empty_carrier @ ( preimage_subnetstr @ A @ B @ C ) )
& ( directed_relstr @ ( preimage_subnetstr @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_yellow_6) ).
thf(6245,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( is_often_in @ A @ B @ C )
=> ( ~ ( empty_carrier @ ( preimage_subnetstr @ A @ B @ C ) )
& ( directed_relstr @ ( preimage_subnetstr @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(357,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_associative @ A )
& ( meet_semilatt_str @ A ) )
=> ( ( relation @ ( the_L_meet @ A ) )
& ( function @ ( the_L_meet @ A ) )
& ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( v2_binop_1 @ ( the_L_meet @ A ) @ ( the_carrier @ A ) )
& ( v1_partfun1 @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_lattice2) ).
thf(2807,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_associative @ A )
& ( meet_semilatt_str @ A ) )
=> ( ( relation @ ( the_L_meet @ A ) )
& ( function @ ( the_L_meet @ A ) )
& ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( v2_binop_1 @ ( the_L_meet @ A ) @ ( the_carrier @ A ) )
& ( v1_partfun1 @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(522,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_reflexive_in @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( ordered_pair @ C @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
thf(3914,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( is_reflexive_in @ A @ B )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( ordered_pair @ C @ C ) @ A ) ) )
& ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( ordered_pair @ C @ C ) @ A ) )
=> ( is_reflexive_in @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(186,axiom,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(1940,plain,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(2479,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) )
& ( ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) )
=> ( in @ ( ordered_pair @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(406,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( closed_subset @ B @ A )
<=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
thf(3092,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ B @ A )
=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) )
& ( ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A )
=> ( closed_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( latt_str @ B ) )
=> ( ( in @ A @ ( a_2_2_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_lattice3) ).
thf(2818,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( latt_str @ B ) )
=> ( ( ( in @ A @ ( a_2_2_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) )
=> ( in @ A @ ( a_2_2_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(120,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( complemented_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( complemented_relstr @ A )
& ( boolean_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_waybel_1) ).
thf(1553,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( complemented_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( complemented_relstr @ A )
& ( boolean_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(734,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(5536,plain,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) )
& ( v3_membered @ ( set_intersection2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc32_membered) ).
thf(2209,plain,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) )
& ( v3_membered @ ( set_intersection2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(204,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( boolean_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( complemented_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_waybel_1) ).
thf(2013,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( boolean_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( distributive_relstr @ A )
& ( complemented_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ( in @ ( relation_image @ C @ E ) @ B )
& ( D = F )
& ( in @ ( relation_image @ C @ F ) @ B ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( powerset @ ( relation_dom @ C ) ) )
& ( F = E )
& ( in @ ( relation_image @ C @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
thf(3478,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ( in @ ( relation_image @ C @ E ) @ B )
& ( D = F )
& ( in @ ( relation_image @ C @ F ) @ B ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ? [F: $i] :
( ( in @ F @ ( powerset @ ( relation_dom @ C ) ) )
& ( F = E )
& ( in @ ( relation_image @ C @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( in @ F @ ( powerset @ ( relation_dom @ C ) ) )
& ( F = E )
& ( in @ ( relation_image @ C @ E ) @ B ) )
=> ( in @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(1839,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(626,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( C
= ( join_of_latt_set @ A @ B ) )
<=> ( ( latt_element_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_element_smaller @ A @ D @ B )
=> ( below @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattice3) ).
thf(4651,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( C
= ( join_of_latt_set @ A @ B ) )
=> ( ( latt_element_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_element_smaller @ A @ D @ B )
=> ( below @ A @ C @ D ) ) ) ) )
& ( ( ( latt_element_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_element_smaller @ A @ D @ B )
=> ( below @ A @ C @ D ) ) ) )
=> ( C
= ( join_of_latt_set @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( E
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( F
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ A ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( E
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
thf(2626,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( E
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( F
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ A ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( E
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) ) ) )
& ( ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ A ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( E
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) ) )
=> ( in @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( equipotent @ A @ B )
<=> ( are_equipotent @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r2_wellord2) ).
thf(2352,plain,
! [A: $i,B: $i] :
( ( ( equipotent @ A @ B )
=> ( are_equipotent @ A @ B ) )
& ( ( are_equipotent @ A @ B )
=> ( equipotent @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(1949,plain,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(4763,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(366,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A )
& ( connected_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( connected_relstr @ A )
& ( v2_waybel_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_waybel_3) ).
thf(2870,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A )
& ( connected_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( connected_relstr @ A )
& ( v2_waybel_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(48,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
<=> ( ( ( relation_dom @ C )
= ( relation_field @ A ) )
& ( ( relation_rng @ C )
= ( relation_field @ B ) )
& ( one_to_one @ C )
& ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
<=> ( ( in @ D @ ( relation_field @ A ) )
& ( in @ E @ ( relation_field @ A ) )
& ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_wellord1) ).
thf(1157,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( relation_isomorphism @ A @ B @ C )
=> ( ( ( relation_dom @ C )
= ( relation_field @ A ) )
& ( ( relation_rng @ C )
= ( relation_field @ B ) )
& ( one_to_one @ C )
& ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ A )
=> ( ( in @ D @ ( relation_field @ A ) )
& ( in @ E @ ( relation_field @ A ) )
& ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) )
& ( ( ( in @ D @ ( relation_field @ A ) )
& ( in @ E @ ( relation_field @ A ) )
& ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) )
& ( ( ( ( relation_dom @ C )
= ( relation_field @ A ) )
& ( ( relation_rng @ C )
= ( relation_field @ B ) )
& ( one_to_one @ C )
& ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ A )
=> ( ( in @ D @ ( relation_field @ A ) )
& ( in @ E @ ( relation_field @ A ) )
& ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) )
& ( ( ( in @ D @ ( relation_field @ A ) )
& ( in @ E @ ( relation_field @ A ) )
& ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) )
=> ( relation_isomorphism @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
thf(1834,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(51,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
thf(1189,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(437,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( ( compact_top_space @ A )
<=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( is_a_cover_of_carrier @ A @ B )
& ( open_subsets @ B @ A )
& ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( subset @ C @ B )
& ( is_a_cover_of_carrier @ A @ C )
& ( finite @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_compts_1) ).
thf(3346,plain,
! [A: $i] :
( ( top_str @ A )
=> ( ( ( compact_top_space @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( is_a_cover_of_carrier @ A @ B )
& ( open_subsets @ B @ A )
& ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( subset @ C @ B )
& ( is_a_cover_of_carrier @ A @ C )
& ( finite @ C ) ) ) ) ) )
& ( ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( is_a_cover_of_carrier @ A @ B )
& ( open_subsets @ B @ A )
& ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( subset @ C @ B )
& ( is_a_cover_of_carrier @ A @ C )
& ( finite @ C ) ) ) ) )
=> ( compact_top_space @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(256,axiom,
! [A: $i] :
? [B: $i] :
( ( relation_of2 @ B @ A @ A )
& ( relation @ B )
& ( reflexive @ B )
& ( symmetric @ B )
& ( antisymmetric @ B )
& ( transitive @ B )
& ( v1_partfun1 @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_partfun1) ).
thf(2305,plain,
! [A: $i] :
? [B: $i] :
( ( relation_of2 @ B @ A @ A )
& ( relation @ B )
& ( reflexive @ B )
& ( symmetric @ B )
& ( antisymmetric @ B )
& ( transitive @ B )
& ( v1_partfun1 @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(611,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ? [E: $i] :
( ( ordinal @ E )
& ( C = E )
& ( ( in @ E @ omega )
=> ! [F: $i] :
( ( element @ F @ ( powerset @ ( powerset @ E ) ) )
=> ~ ( ( F != empty_set )
& ! [G: $i] :
~ ( ( in @ G @ F )
& ! [H: $i] :
( ( ( in @ H @ F )
& ( subset @ G @ H ) )
=> ( H = G ) ) ) ) ) ) )
& ( B = D )
& ? [E: $i] :
( ( ordinal @ E )
& ( D = E )
& ( ( in @ E @ omega )
=> ! [F: $i] :
( ( element @ F @ ( powerset @ ( powerset @ E ) ) )
=> ~ ( ( F != empty_set )
& ! [G: $i] :
~ ( ( in @ G @ F )
& ! [H: $i] :
( ( ( in @ H @ F )
& ( subset @ G @ H ) )
=> ( H = G ) ) ) ) ) ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( succ @ A ) )
& ( D = C )
& ? [E: $i] :
( ( ordinal @ E )
& ( C = E )
& ( ( in @ E @ omega )
=> ! [F: $i] :
( ( element @ F @ ( powerset @ ( powerset @ E ) ) )
=> ~ ( ( F != empty_set )
& ! [G: $i] :
~ ( ( in @ G @ F )
& ! [H: $i] :
( ( ( in @ H @ F )
& ( subset @ G @ H ) )
=> ( H = G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e18_27__finset_1__1) ).
thf(4463,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ? [E: $i] :
( ( ordinal @ E )
& ( C = E )
& ( ( in @ E @ omega )
=> ! [F: $i] :
( ( element @ F @ ( powerset @ ( powerset @ E ) ) )
=> ~ ( ( F != empty_set )
& ! [G: $i] :
~ ( ( in @ G @ F )
& ! [H: $i] :
( ( ( in @ H @ F )
& ( subset @ G @ H ) )
=> ( H = G ) ) ) ) ) ) )
& ( B = D )
& ? [E: $i] :
( ( ordinal @ E )
& ( D = E )
& ( ( in @ E @ omega )
=> ! [F: $i] :
( ( element @ F @ ( powerset @ ( powerset @ E ) ) )
=> ~ ( ( F != empty_set )
& ! [G: $i] :
~ ( ( in @ G @ F )
& ! [H: $i] :
( ( ( in @ H @ F )
& ( subset @ G @ H ) )
=> ( H = G ) ) ) ) ) ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ ( succ @ A ) )
& ( D = C )
& ? [E: $i] :
( ( ordinal @ E )
& ( C = E )
& ( ( in @ E @ omega )
=> ! [F: $i] :
( ( element @ F @ ( powerset @ ( powerset @ E ) ) )
=> ~ ( ( F != empty_set )
& ! [G: $i] :
~ ( ( in @ G @ F )
& ! [H: $i] :
( ( ( in @ H @ F )
& ( subset @ G @ H ) )
=> ( H = G ) ) ) ) ) ) ) ) )
& ( ? [D: $i] :
( ( in @ D @ ( succ @ A ) )
& ( D = C )
& ? [E: $i] :
( ( ordinal @ E )
& ( C = E )
& ( ( in @ E @ omega )
=> ! [F: $i] :
( ( element @ F @ ( powerset @ ( powerset @ E ) ) )
=> ~ ( ( F != empty_set )
& ! [G: $i] :
~ ( ( in @ G @ F )
& ! [H: $i] :
( ( ( in @ H @ F )
& ( subset @ G @ H ) )
=> ( H = G ) ) ) ) ) ) ) )
=> ( in @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(1289,plain,
~ ( empty_carrier @ sk29 ),
inference(cnf,[status(esa)],[1277]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(2226,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(780,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(5860,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( in @ A @ C )
& ( in @ B @ D ) ) )
& ( ( ( in @ A @ C )
& ( in @ B @ D ) )
=> ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_ordering @ B )
=> ( well_ordering @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_wellord1) ).
thf(2071,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_ordering @ B )
=> ( well_ordering @ ( relation_restriction @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(350,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(2775,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(679,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(5068,plain,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(354,axiom,
! [A: $i] :
( ( v1_partfun1 @ ( identity_as_relation_of @ A ) @ A @ A )
& ( relation_of2_as_subset @ ( identity_as_relation_of @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(2792,plain,
! [A: $i] :
( ( v1_partfun1 @ ( identity_as_relation_of @ A ) @ A @ A )
& ( relation_of2_as_subset @ ( identity_as_relation_of @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(617,axiom,
( ( ( ( in @ empty_set @ omega )
=> ! [A: $i] :
( ( element @ A @ ( powerset @ ( powerset @ empty_set ) ) )
=> ~ ( ( A != empty_set )
& ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i] :
( ( ( in @ C @ A )
& ( subset @ B @ C ) )
=> ( C = B ) ) ) ) ) )
& ! [A: $i] :
( ( ordinal @ A )
=> ( ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) )
=> ( ( in @ ( succ @ A ) @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( succ @ A ) ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) )
& ! [A: $i] :
( ( ordinal @ A )
=> ( ( ( being_limit_ordinal @ A )
& ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ B @ A )
=> ( ( in @ B @ omega )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ B ) ) )
=> ~ ( ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ! [E: $i] :
( ( ( in @ E @ C )
& ( subset @ D @ E ) )
=> ( E = D ) ) ) ) ) ) ) ) )
=> ( ( A = empty_set )
| ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) ) ) )
=> ! [A: $i] :
( ( ordinal @ A )
=> ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_ordinal2__e18_27__finset_1) ).
thf(4574,plain,
( ( ( ( in @ empty_set @ omega )
=> ! [A: $i] :
( ( element @ A @ ( powerset @ ( powerset @ empty_set ) ) )
=> ~ ( ( A != empty_set )
& ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i] :
( ( ( in @ C @ A )
& ( subset @ B @ C ) )
=> ( C = B ) ) ) ) ) )
& ! [A: $i] :
( ( ordinal @ A )
=> ( ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) )
=> ( ( in @ ( succ @ A ) @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( succ @ A ) ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) )
& ! [A: $i] :
( ( ordinal @ A )
=> ( ( ( being_limit_ordinal @ A )
& ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ B @ A )
=> ( ( in @ B @ omega )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ B ) ) )
=> ~ ( ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ! [E: $i] :
( ( ( in @ E @ C )
& ( subset @ D @ E ) )
=> ( E = D ) ) ) ) ) ) ) ) )
=> ( ( A = empty_set )
| ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) ) ) )
=> ! [A: $i] :
( ( ordinal @ A )
=> ( ( in @ A @ omega )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(505,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( neighborhood_system @ A @ B ) )
<=> ( point_neighbourhood @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_yellow19) ).
thf(3797,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ ( neighborhood_system @ A @ B ) )
=> ( point_neighbourhood @ C @ A @ B ) )
& ( ( point_neighbourhood @ C @ A @ B )
=> ( in @ C @ ( neighborhood_system @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(678,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ B )
=> ( ( C
= ( join_on_relstr @ A @ B ) )
<=> ( ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_yellow_0) ).
thf(5055,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ B )
=> ( ( ( C
= ( join_on_relstr @ A @ B ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) )
& ( ( ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) )
=> ( C
= ( join_on_relstr @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(754,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(5632,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(76,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(1326,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(896,plain,
relation_empty_yielding @ sk7,
inference(cnf,[status(esa)],[895]) ).
thf(670,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_waybel_0) ).
thf(5008,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(306,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(2554,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
= ( rel_str_of @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(1508,plain,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
= ( rel_str_of @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(585,axiom,
! [A: $i] :
( ( function @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(4250,plain,
! [A: $i] :
( ( ( function @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) )
& ( ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) )
=> ( function @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ~ ( empty_carrier @ ( rel_str_of @ A @ B ) )
& ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_orders_2) ).
thf(3369,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ~ ( empty_carrier @ ( rel_str_of @ A @ B ) )
& ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( connected @ B )
=> ( connected @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
thf(1629,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( connected @ B )
=> ( connected @ ( relation_restriction @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(2431,plain,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(659,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(4969,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
thf(2526,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(586,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( element @ ( apply_netmap @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_waybel_0) ).
thf(4261,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( element @ ( apply_netmap @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(16,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(963,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(804,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( netstr_induced_subset @ C @ A @ B )
=> ( is_eventually_in @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_yellow19) ).
thf(6077,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( netstr_induced_subset @ C @ A @ B )
=> ( is_eventually_in @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( complete_latt_str @ B )
& ( latt_str @ B ) )
=> ( ( in @ A @ ( a_2_3_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_lattice3) ).
thf(4197,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( complete_latt_str @ B )
& ( latt_str @ B ) )
=> ( ( ( in @ A @ ( a_2_3_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) )
=> ( in @ A @ ( a_2_3_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( relation_of2_as_subset @ ( relation_dom_restr_as_relation_of @ A @ B @ C @ D ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_1) ).
thf(914,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( relation_of2_as_subset @ ( relation_dom_restr_as_relation_of @ A @ B @ C @ D ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(723,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( B
= ( meet_of_latt_set @ A @ C ) )
<=> ( ( latt_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_set_smaller @ A @ D @ C )
=> ( below_refl @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice3) ).
thf(5408,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( B
= ( meet_of_latt_set @ A @ C ) )
=> ( ( latt_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_set_smaller @ A @ D @ C )
=> ( below_refl @ A @ D @ B ) ) ) ) )
& ( ( ( latt_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_set_smaller @ A @ D @ C )
=> ( below_refl @ A @ D @ B ) ) ) )
=> ( B
= ( meet_of_latt_set @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(578,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( ( full_subnetstr @ C @ A @ B )
<=> ( ( full_subrelstr @ C @ B )
& ( subrelstr @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_yellow_6) ).
thf(4214,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( ( ( full_subnetstr @ C @ A @ B )
=> ( ( full_subrelstr @ C @ B )
& ( subrelstr @ C @ B ) ) )
& ( ( ( full_subrelstr @ C @ B )
& ( subrelstr @ C @ B ) )
=> ( full_subnetstr @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(67,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(1294,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(234,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(2198,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(601,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( succ @ B ) )
& ? [E: $i] :
( ( ordinal @ E )
& ( D = E )
& ( in @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
thf(4387,plain,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( succ @ B ) )
& ? [E: $i] :
( ( ordinal @ E )
& ( D = E )
& ( in @ E @ A ) ) ) )
& ( ( ( in @ D @ ( succ @ B ) )
& ? [E: $i] :
( ( ordinal @ E )
& ( D = E )
& ( in @ E @ A ) ) )
=> ( in @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(329,axiom,
? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(2680,plain,
? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(872,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( upper_relstr_subset @ B @ A )
<=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ B )
& ( related @ A @ C @ D ) )
=> ( in @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_waybel_0) ).
thf(6586,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( upper_relstr_subset @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ B )
& ( related @ A @ C @ D ) )
=> ( in @ D @ B ) ) ) ) )
& ( ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ B )
& ( related @ A @ C @ D ) )
=> ( in @ D @ B ) ) ) )
=> ( upper_relstr_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(143,axiom,
! [A: $i] :
( ~ ( empty @ ( singleton @ A ) )
& ( finite @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(1661,plain,
! [A: $i] :
( ~ ( empty @ ( singleton @ A ) )
& ( finite @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_intersection2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc28_membered) ).
thf(2623,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_intersection2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(3552,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(865,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(6516,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(378,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_0) ).
thf(2956,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(825,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( proper_subset @ A @ B )
=> ( in @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).
thf(6257,plain,
! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( proper_subset @ A @ B )
=> ( in @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(105,axiom,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(1491,plain,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(270,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(2384,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(2475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(492,axiom,
! [A: $i] :
( ( the_carrier @ ( boole_POSet @ A ) )
= ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_waybel_7) ).
thf(3694,plain,
! [A: $i] :
( ( the_carrier @ ( boole_POSet @ A ) )
= ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1077,plain,
relation @ empty_set,
inference(cnf,[status(esa)],[1076]) ).
thf(739,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ B @ E @ F ) )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_yellow_0) ).
thf(5549,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ B @ E @ F ) )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(824,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( below @ A @ B @ C )
<=> ( ( join @ A @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
thf(6252,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below @ A @ B @ C )
=> ( ( join @ A @ B @ C )
= C ) )
& ( ( ( join @ A @ B @ C )
= C )
=> ( below @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
& ! [C: $i] :
~ ( ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [D: $i] :
~ ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( E = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ E ) ) ) ) ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ( ( relation_dom @ C )
= ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [D: $i] :
( ( in @ D @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( E = D )
=> ( ( apply @ C @ D )
= ( subset_complement @ ( the_carrier @ A ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e4_7_1__tops_2) ).
thf(5869,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
& ! [C: $i] :
~ ( ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [D: $i] :
~ ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( E = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ E ) ) ) ) ) )
=> ? [C: $i] :
( ( relation @ C )
& ( function @ C )
& ( ( relation_dom @ C )
= ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [D: $i] :
( ( in @ D @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( E = D )
=> ( ( apply @ C @ D )
= ( subset_complement @ ( the_carrier @ A ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(1513,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ( in @ E @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = E )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e4_7_1__tops_2__1) ).
thf(2902,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) )
& ( in @ C @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = C )
=> ( E
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ( in @ E @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = E )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ( in @ E @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) )
& ! [F: $i] :
( ( element @ F @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( F = E )
=> ( D
= ( subset_complement @ ( the_carrier @ A ) @ F ) ) ) ) )
=> ( in @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( unordered_pair_as_carrier_subset @ A @ B @ C )
= ( unordered_pair_as_carrier_subset @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(5211,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( unordered_pair_as_carrier_subset @ A @ B @ C )
= ( unordered_pair_as_carrier_subset @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( union_of_subsets @ A @ B ) )
= ( meet_of_subsets @ A @ ( complements_of_subsets @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(6386,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( union_of_subsets @ A @ B ) )
= ( meet_of_subsets @ A @ ( complements_of_subsets @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(871,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( distributive_lattstr @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A )
& ( complemented_lattstr @ A )
& ( boolean_lattstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_lattices) ).
thf(6569,plain,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( distributive_lattstr @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A )
& ( complemented_lattstr @ A )
& ( boolean_lattstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ( ( in @ C @ A )
=> ( ( B = empty_set )
| ( in @ ( apply @ D @ C ) @ ( relation_rng @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(2230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ( ( in @ C @ A )
=> ( ( B = empty_set )
| ( in @ ( apply @ D @ C ) @ ( relation_rng @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(207,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
thf(2036,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_founded_relation @ B )
=> ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_wellord1) ).
thf(2739,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_founded_relation @ B )
=> ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(700,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ D @ C )
<=> ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
thf(5196,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( in @ D @ C )
=> ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) )
& ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B )
=> ( in @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(81,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( ( open_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_tops_1) ).
thf(1348,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( ( open_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(254,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( connected_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_3) ).
thf(2287,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( connected_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(546,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ( element @ ( bottom_of_semilattstr @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(3997,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ( element @ ( bottom_of_semilattstr @ A ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ B )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ B )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ B @ C ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ B )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e4_7_2__tops_2__2) ).
thf(6131,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ B )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ B )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ B @ C ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ B )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) ) )
& ( ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ B @ C ) )
& ( F = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ B )
& ! [I: $i] :
( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( I = G )
=> ( H
= ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) )
=> ( in @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(544,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(3987,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(428,axiom,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(3264,plain,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( ( B
= ( set_meet @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) )
& ( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) )
& ( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( set_meet @ A ) ) ) ) )
& ( ( A = empty_set )
=> ( ( ( B
= ( set_meet @ A ) )
=> ( B = empty_set ) )
& ( ( B = empty_set )
=> ( B
= ( set_meet @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(312,axiom,
! [A: $i] :
( ( ( empty @ A )
& ( ordinal @ A ) )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_arytm_3) ).
thf(2604,plain,
! [A: $i] :
( ( ( empty @ A )
& ( ordinal @ A ) )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(821,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(6237,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(71,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(1303,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
thf(5601,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) )
& ( ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) )
=> ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(1116,plain,
! [A: $i,B: $i] :
( ( ( ( set_difference @ A @ B )
= empty_set )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( ( set_difference @ A @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(220,axiom,
! [A: $i] :
( ( reflexive @ ( inclusion_order @ A ) )
& ( antisymmetric @ ( inclusion_order @ A ) )
& ( transitive @ ( inclusion_order @ A ) )
& ( v1_partfun1 @ ( inclusion_order @ A ) @ A @ A )
& ( relation_of2_as_subset @ ( inclusion_order @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
thf(2142,plain,
! [A: $i] :
( ( reflexive @ ( inclusion_order @ A ) )
& ( antisymmetric @ ( inclusion_order @ A ) )
& ( transitive @ ( inclusion_order @ A ) )
& ( v1_partfun1 @ ( inclusion_order @ A ) @ A @ A )
& ( relation_of2_as_subset @ ( inclusion_order @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(5187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ ( unordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ C )
& ( in @ B @ C ) ) )
& ( ( ( in @ A @ C )
& ( in @ B @ C ) )
=> ( subset @ ( unordered_pair @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(2258,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ ( singleton @ B ) )
=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) )
& ( ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
=> ( subset @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(2302,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(2683,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(563,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( the_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
= ( a_3_0_waybel_9 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_waybel_9) ).
thf(4114,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( the_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
= ( a_3_0_waybel_9 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(4687,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(634,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(4706,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( relation_image @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) )
& ( ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) )
& ( ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( relation_image @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( open_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tops_1) ).
thf(4670,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( open_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( partfun_dom_restriction @ A @ B @ C @ D )
= ( relation_dom_restriction @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_partfun1) ).
thf(1678,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ C )
& ( relation_of2 @ C @ A @ B ) )
=> ( ( partfun_dom_restriction @ A @ B @ C @ D )
= ( relation_dom_restriction @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(2155,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(247,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(2255,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(476,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(3601,plain,
! [A: $i] :
( ( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) )
& ( ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) )
=> ( epsilon_transitive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(2233,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(1148,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( ( reflexive @ B )
& ( antisymmetric @ B )
& ( transitive @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( reflexive_relstr @ ( rel_str_of @ A @ B ) )
& ( transitive_relstr @ ( rel_str_of @ A @ B ) )
& ( antisymmetric_relstr @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_orders_2) ).
thf(1673,plain,
! [A: $i,B: $i] :
( ( ( reflexive @ B )
& ( antisymmetric @ B )
& ( transitive @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( reflexive_relstr @ ( rel_str_of @ A @ B ) )
& ( transitive_relstr @ ( rel_str_of @ A @ B ) )
& ( antisymmetric_relstr @ ( rel_str_of @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
thf(3145,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(390,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( trivial_carrier @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( connected_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_waybel_0) ).
thf(3015,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( trivial_carrier @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( connected_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(433,axiom,
! [A: $i] :
( ( finite @ A )
<=> ? [B: $i] :
( ( relation @ B )
& ( function @ B )
& ( ( relation_rng @ B )
= A )
& ( in @ ( relation_dom @ B ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_finset_1) ).
thf(3328,plain,
! [A: $i] :
( ( ( finite @ A )
=> ? [B: $i] :
( ( relation @ B )
& ( function @ B )
& ( ( relation_rng @ B )
= A )
& ( in @ ( relation_dom @ B ) @ omega ) ) )
& ( ? [B: $i] :
( ( relation @ B )
& ( function @ B )
& ( ( relation_rng @ B )
= A )
& ( in @ ( relation_dom @ B ) @ omega ) )
=> ( finite @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(616,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( is_often_in @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ? [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
& ( related @ B @ D @ E )
& ( in @ ( apply_netmap @ A @ B @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_waybel_0) ).
thf(4565,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( ( is_often_in @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ? [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
& ( related @ B @ D @ E )
& ( in @ ( apply_netmap @ A @ B @ E ) @ C ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ? [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
& ( related @ B @ D @ E )
& ( in @ ( apply_netmap @ A @ B @ E ) @ C ) ) )
=> ( is_often_in @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_restr_as_relation_of @ A @ B @ C @ D )
= ( relation_dom_restriction @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_relset_1) ).
thf(1657,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_restr_as_relation_of @ A @ B @ C @ D )
= ( relation_dom_restriction @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_restriction @ C @ B ) )
<=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
thf(5990,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( ( in @ A @ ( relation_restriction @ C @ B ) )
=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) )
& ( ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) )
=> ( in @ A @ ( relation_restriction @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(29,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(1056,plain,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(239,axiom,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(2223,plain,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(2668,plain,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(96,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(1436,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i] :
( ( G = E )
& ? [H: $i] :
( ( element @ H @ ( the_carrier @ A ) )
& ( in @ H @ B )
& ( relstr_set_smaller @ A @ G @ H ) ) )
& ( D = F )
& ? [G: $i] :
( ( G = F )
& ? [H: $i] :
( ( element @ H @ ( the_carrier @ A ) )
& ( in @ H @ B )
& ( relstr_set_smaller @ A @ G @ H ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( powerset @ C ) )
& ( F = E )
& ? [G: $i] :
( ( G = E )
& ? [H: $i] :
( ( element @ H @ ( the_carrier @ A ) )
& ( in @ H @ B )
& ( relstr_set_smaller @ A @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e11_2_1__waybel_0__1) ).
thf(6535,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i] :
( ( G = E )
& ? [H: $i] :
( ( element @ H @ ( the_carrier @ A ) )
& ( in @ H @ B )
& ( relstr_set_smaller @ A @ G @ H ) ) )
& ( D = F )
& ? [G: $i] :
( ( G = F )
& ? [H: $i] :
( ( element @ H @ ( the_carrier @ A ) )
& ( in @ H @ B )
& ( relstr_set_smaller @ A @ G @ H ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ? [F: $i] :
( ( in @ F @ ( powerset @ C ) )
& ( F = E )
& ? [G: $i] :
( ( G = E )
& ? [H: $i] :
( ( element @ H @ ( the_carrier @ A ) )
& ( in @ H @ B )
& ( relstr_set_smaller @ A @ G @ H ) ) ) ) )
& ( ? [F: $i] :
( ( in @ F @ ( powerset @ C ) )
& ( F = E )
& ? [G: $i] :
( ( G = E )
& ? [H: $i] :
( ( element @ H @ ( the_carrier @ A ) )
& ( in @ H @ B )
& ( relstr_set_smaller @ A @ G @ H ) ) ) )
=> ( in @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(672,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( cartesian_product2 @ A @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ A )
& ? [H: $i] :
( ( F = H )
& ( in @ G @ H )
& ! [I: $i] :
( ( in @ I @ H )
=> ( in @ ( ordered_pair @ G @ I ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e10_24__wellord2__1) ).
thf(5019,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( ( in @ E @ D )
=> ( ( in @ E @ ( cartesian_product2 @ A @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ A )
& ? [H: $i] :
( ( F = H )
& ( in @ G @ H )
& ! [I: $i] :
( ( in @ I @ H )
=> ( in @ ( ordered_pair @ G @ I ) @ B ) ) ) ) ) )
& ( ( ( in @ E @ ( cartesian_product2 @ A @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ A )
& ? [H: $i] :
( ( F = H )
& ( in @ G @ H )
& ! [I: $i] :
( ( in @ I @ H )
=> ( in @ ( ordered_pair @ G @ I ) @ B ) ) ) ) )
=> ( in @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(560,axiom,
! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(4083,plain,
! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(897,plain,
relation @ sk7,
inference(cnf,[status(esa)],[895]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ ( relation_dom @ B ) )
=> ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
thf(2417,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ ( relation_dom @ B ) )
=> ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ D ) @ C ) )
<=> ( ( relation_rng_as_subset @ A @ B @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
thf(3426,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ D ) @ C ) )
=> ( ( relation_rng_as_subset @ A @ B @ C )
= B ) )
& ( ( ( relation_rng_as_subset @ A @ B @ C )
= B )
=> ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(178,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(1891,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(2619,plain,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(850,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_associative @ A )
& ( join_semilatt_str @ A ) )
=> ( ( relation @ ( the_L_join @ A ) )
& ( function @ ( the_L_join @ A ) )
& ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( v2_binop_1 @ ( the_L_join @ A ) @ ( the_carrier @ A ) )
& ( v1_partfun1 @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattice2) ).
thf(6393,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_associative @ A )
& ( join_semilatt_str @ A ) )
=> ( ( relation @ ( the_L_join @ A ) )
& ( function @ ( the_L_join @ A ) )
& ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( v2_binop_1 @ ( the_L_join @ A ) @ ( the_carrier @ A ) )
& ( v1_partfun1 @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnet @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_yellow_6) ).
thf(5176,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnet @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(701,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( top_str @ B )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
=> ( ( ( open_subset @ D @ B )
=> ( ( interior @ B @ D )
= D ) )
& ( ( ( interior @ A @ C )
= C )
=> ( open_subset @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_1) ).
thf(5200,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( top_str @ B )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
=> ( ( ( open_subset @ D @ B )
=> ( ( interior @ B @ D )
= D ) )
& ( ( ( interior @ A @ C )
= C )
=> ( open_subset @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(709,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i,D: $i] :
( ( subset @ C @ D )
=> ( ( ( is_eventually_in @ A @ B @ C )
=> ( is_eventually_in @ A @ B @ D ) )
& ( ( is_often_in @ A @ B @ C )
=> ( is_often_in @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_0) ).
thf(5283,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i,D: $i] :
( ( subset @ C @ D )
=> ( ( ( is_eventually_in @ A @ B @ C )
=> ( is_eventually_in @ A @ B @ D ) )
& ( ( is_often_in @ A @ B @ C )
=> ( is_often_in @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(6273,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_difference @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ~ ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ~ ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(507,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_yellow_1) ).
thf(3805,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(321,axiom,
( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(2651,plain,
( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(304,axiom,
? [A: $i] : ( latt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(2549,plain,
? [A: $i] : ( latt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(2731,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(1829,plain,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(393,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) )
<=> ~ ( in @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l40_tops_1) ).
thf(3025,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) )
=> ~ ( in @ C @ B ) )
& ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(467,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(3543,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(689,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(5151,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(124,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(1582,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(742,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( distributive_lattstr @ A )
& ( bounded_lattstr @ A )
& ( complemented_lattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( boolean_lattstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattices) ).
thf(5581,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( distributive_lattstr @ A )
& ( bounded_lattstr @ A )
& ( complemented_lattstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( boolean_lattstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( the_mapping @ A @ B ) )
& ( relation @ ( the_mapping @ A @ B ) )
& ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_yellow_6) ).
thf(4410,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( the_mapping @ A @ B ) )
& ( relation @ ( the_mapping @ A @ B ) )
& ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(5958,plain,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(3886,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(409,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
thf(3113,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( antisymmetric @ A )
=> ! [B: $i,C: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( B = C ) ) )
& ( ! [B: $i,C: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( B = C ) )
=> ( antisymmetric @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
thf(2699,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(246,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( connected_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( connected_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_waybel_3) ).
thf(2241,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( connected_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( connected_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(730,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(5500,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(218,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) )
& ( reflexive @ ( identity_relation @ A ) )
& ( symmetric @ ( identity_relation @ A ) )
& ( antisymmetric @ ( identity_relation @ A ) )
& ( transitive @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_partfun1) ).
thf(2127,plain,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) )
& ( reflexive @ ( identity_relation @ A ) )
& ( symmetric @ ( identity_relation @ A ) )
& ( antisymmetric @ ( identity_relation @ A ) )
& ( transitive @ ( identity_relation @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(583,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).
thf(4242,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(837,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ( ( compact_top_space @ A )
<=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( centered @ B )
& ( closed_subsets @ B @ A )
& ( ( meet_of_subsets @ ( the_carrier @ A ) @ B )
= empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_compts_1) ).
thf(6329,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ( ( ( compact_top_space @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( centered @ B )
& ( closed_subsets @ B @ A )
& ( ( meet_of_subsets @ ( the_carrier @ A ) @ B )
= empty_set ) ) ) )
& ( ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ~ ( ( centered @ B )
& ( closed_subsets @ B @ A )
& ( ( meet_of_subsets @ ( the_carrier @ A ) @ B )
= empty_set ) ) )
=> ( compact_top_space @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(89,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( being_limit_ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal2) ).
thf(1384,plain,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( being_limit_ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(447,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( apply_netmap @ A @ B @ C )
= ( apply_on_structs @ B @ A @ ( the_mapping @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_waybel_0) ).
thf(3411,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( apply_netmap @ A @ B @ C )
= ( apply_on_structs @ B @ A @ ( the_mapping @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(439,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).
thf(3360,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( relstr_element_smaller @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) )
=> ( relstr_element_smaller @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(1378,plain,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(427,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ B @ A )
=> ( ( topstr_closure @ A @ B )
= B ) )
& ( ( ( topological_space @ A )
& ( ( topstr_closure @ A @ B )
= B ) )
=> ( closed_subset @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).
thf(3259,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ B @ A )
=> ( ( topstr_closure @ A @ B )
= B ) )
& ( ( ( topological_space @ A )
& ( ( topstr_closure @ A @ B )
= B ) )
=> ( closed_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(4066,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(820,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( is_a_cluster_point_of_netstr @ A @ B @ C )
<=> ! [D: $i] :
( ( point_neighbourhood @ D @ A @ C )
=> ( is_often_in @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_waybel_9) ).
thf(6233,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( is_a_cluster_point_of_netstr @ A @ B @ C )
=> ! [D: $i] :
( ( point_neighbourhood @ D @ A @ C )
=> ( is_often_in @ A @ B @ D ) ) )
& ( ! [D: $i] :
( ( point_neighbourhood @ D @ A @ C )
=> ( is_often_in @ A @ B @ D ) )
=> ( is_a_cluster_point_of_netstr @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(806,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_intersection2 @ ( the_carrier @ A ) @ B @ ( cast_as_carrier_subset @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
thf(6082,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_intersection2 @ ( the_carrier @ A ) @ B @ ( cast_as_carrier_subset @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(676,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
thf(5046,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( ( proper_element @ B @ ( powerset @ A ) )
=> ( B != A ) )
& ( ( B != A )
=> ( proper_element @ B @ ( powerset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] :
( ( subnetstr @ C @ A @ B )
& ~ ( empty_carrier @ C )
& ( strict_net_str @ C @ A )
& ( full_subnetstr @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_yellow_6) ).
thf(4206,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] :
( ( subnetstr @ C @ A @ B )
& ~ ( empty_carrier @ C )
& ( strict_net_str @ C @ A )
& ( full_subnetstr @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(1597,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1431,plain,
~ ( empty_carrier @ sk42 ),
inference(cnf,[status(esa)],[1428]) ).
thf(25,axiom,
! [A: $i] :
( ( being_limit_ordinal @ A )
<=> ( A
= ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
thf(1004,plain,
! [A: $i] :
( ( ( being_limit_ordinal @ A )
=> ( A
= ( union @ A ) ) )
& ( ( A
= ( union @ A ) )
=> ( being_limit_ordinal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(580,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A )
& ( complemented_lattstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_lattices) ).
thf(4221,plain,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( lattice @ A )
& ( lower_bounded_semilattstr @ A )
& ( upper_bounded_semilattstr @ A )
& ( bounded_lattstr @ A )
& ( complemented_lattstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(727,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
thf(5473,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_dom_restriction @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) )
& ( ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) )
& ( ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_dom_restriction @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(267,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice3) ).
thf(2372,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B )
& ( element @ C @ ( the_carrier @ A ) )
& ( element @ D @ ( the_carrier @ B ) ) )
=> ( element @ ( k10_filter_1 @ A @ B @ C @ D ) @ ( the_carrier @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_1) ).
thf(3474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B )
& ( element @ C @ ( the_carrier @ A ) )
& ( element @ D @ ( the_carrier @ B ) ) )
=> ( element @ ( k10_filter_1 @ A @ B @ C @ D ) @ ( the_carrier @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(188,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pboole) ).
thf(1945,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(657,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( v3_waybel_3 @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A )
& ~ ( v1_yellow_3 @ A )
& ( v1_waybel_2 @ A )
& ( v2_waybel_2 @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_waybel_4) ).
thf(4949,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( v3_waybel_3 @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A )
& ~ ( v1_yellow_3 @ A )
& ( v1_waybel_2 @ A )
& ( v2_waybel_2 @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ ( singleton @ A ) @ ( singleton @ A ) )
=> ( ~ ( empty_carrier @ ( rel_str_of @ ( singleton @ A ) @ B ) )
& ( strict_rel_str @ ( rel_str_of @ ( singleton @ A ) @ B ) )
& ( trivial_carrier @ ( rel_str_of @ ( singleton @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_yellow_0) ).
thf(5183,plain,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ ( singleton @ A ) @ ( singleton @ A ) )
=> ( ~ ( empty_carrier @ ( rel_str_of @ ( singleton @ A ) @ B ) )
& ( strict_rel_str @ ( rel_str_of @ ( singleton @ A ) @ B ) )
& ( trivial_carrier @ ( rel_str_of @ ( singleton @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(365,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( empty_carrier @ C )
& ( full_subnetstr @ C @ A @ B )
& ( subnetstr @ C @ A @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ B @ D @ E ) )
=> ( related @ C @ F @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_yellow_6) ).
thf(2866,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( empty_carrier @ C )
& ( full_subnetstr @ C @ A @ B )
& ( subnetstr @ C @ A @ B ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ B @ D @ E ) )
=> ( related @ C @ F @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(93,axiom,
! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
thf(1416,plain,
! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( element @ ( apply_binary_as_element @ A @ B @ C @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(3052,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( element @ ( apply_binary_as_element @ A @ B @ C @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(291,axiom,
( ( epsilon_transitive @ omega )
& ( epsilon_connected @ omega )
& ( ordinal @ omega )
& ~ ( empty @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal2) ).
thf(2470,plain,
( ( epsilon_transitive @ omega )
& ( epsilon_connected @ omega )
& ( ordinal @ omega )
& ~ ( empty @ omega ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( ( strict_latt_str @ B )
& ( latt_str @ B ) )
=> ( ( B
= ( boole_lattice @ A ) )
<=> ( ( ( the_carrier @ B )
= ( powerset @ A ) )
& ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( ( apply_binary @ ( the_L_join @ B ) @ C @ D )
= ( subset_union2 @ A @ C @ D ) )
& ( ( apply_binary @ ( the_L_meet @ B ) @ C @ D )
= ( subset_intersection2 @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice3) ).
thf(4174,plain,
! [A: $i,B: $i] :
( ( ( strict_latt_str @ B )
& ( latt_str @ B ) )
=> ( ( ( B
= ( boole_lattice @ A ) )
=> ( ( ( the_carrier @ B )
= ( powerset @ A ) )
& ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( ( apply_binary @ ( the_L_join @ B ) @ C @ D )
= ( subset_union2 @ A @ C @ D ) )
& ( ( apply_binary @ ( the_L_meet @ B ) @ C @ D )
= ( subset_intersection2 @ A @ C @ D ) ) ) ) ) ) )
& ( ( ( ( the_carrier @ B )
= ( powerset @ A ) )
& ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( ( apply_binary @ ( the_L_join @ B ) @ C @ D )
= ( subset_union2 @ A @ C @ D ) )
& ( ( apply_binary @ ( the_L_meet @ B ) @ C @ D )
= ( subset_intersection2 @ A @ C @ D ) ) ) ) ) )
=> ( B
= ( boole_lattice @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(429,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( directed_subset @ B @ A )
<=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ~ ( ( in @ C @ B )
& ( in @ D @ B )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ~ ( ( in @ E @ B )
& ( related @ A @ C @ E )
& ( related @ A @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_waybel_0) ).
thf(3296,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( directed_subset @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ~ ( ( in @ C @ B )
& ( in @ D @ B )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ~ ( ( in @ E @ B )
& ( related @ A @ C @ E )
& ( related @ A @ D @ E ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ~ ( ( in @ C @ B )
& ( in @ D @ B )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ~ ( ( in @ E @ B )
& ( related @ A @ C @ E )
& ( related @ A @ D @ E ) ) ) ) ) )
=> ( directed_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(636,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= D )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) )
& ( C = E )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( cartesian_product2 @ A @ B ) )
& ( E = D )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= D )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
thf(4734,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= D )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) )
& ( C = E )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( cartesian_product2 @ A @ B ) )
& ( E = D )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= D )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( cartesian_product2 @ A @ B ) )
& ( E = D )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= D )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) ) )
=> ( in @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(810,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ( filter_of_net_str @ A @ B )
= ( a_2_1_yellow19 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_yellow19) ).
thf(6173,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ( filter_of_net_str @ A @ B )
= ( a_2_1_yellow19 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B )
& ( C = E )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ E ) @ B ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
thf(4274,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B )
& ( C = E )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ E ) @ B ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) )
=> ( in @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(1653,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(737,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(5542,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(524,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( open_subset @ B @ A )
& ( in @ C @ B ) )
=> ( point_neighbourhood @ B @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_connsp_2) ).
thf(3924,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( open_subset @ B @ A )
& ( in @ C @ B ) )
=> ( point_neighbourhood @ B @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(728,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_7) ).
thf(5494,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_element_smaller @ B @ C @ A )
<=> ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice3) ).
thf(5789,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( ( latt_element_smaller @ B @ C @ A )
=> ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) )
& ( ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) )
=> ( latt_element_smaller @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(642,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( C
= ( topstr_closure @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
<=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ~ ( ( open_subset @ E @ A )
& ( in @ D @ E )
& ( disjoint @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_pre_topc) ).
thf(4784,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( C
= ( topstr_closure @ A @ B ) )
=> ! [D: $i] :
( ( in @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ D @ C )
=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ~ ( ( open_subset @ E @ A )
& ( in @ D @ E )
& ( disjoint @ B @ E ) ) ) )
& ( ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ~ ( ( open_subset @ E @ A )
& ( in @ D @ E )
& ( disjoint @ B @ E ) ) )
=> ( in @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( in @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ D @ C )
=> ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ~ ( ( open_subset @ E @ A )
& ( in @ D @ E )
& ( disjoint @ B @ E ) ) ) )
& ( ! [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
=> ~ ( ( open_subset @ E @ A )
& ( in @ D @ E )
& ( disjoint @ B @ E ) ) )
=> ( in @ D @ C ) ) ) )
=> ( C
= ( topstr_closure @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(245,axiom,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_orders_2) ).
thf(2238,plain,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(4313,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( unordered_pair @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( unordered_pair @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(455,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ~ ( v1_yellow_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_3) ).
thf(3443,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ~ ( v1_yellow_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(5445,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(314,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(2615,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(182,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(1917,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( rel_str @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(225,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(2170,plain,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(37,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( apply_binary @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
thf(1088,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( apply_binary @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(385,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( k2_lattice3 @ A )
= ( relation_of_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
thf(2993,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( k2_lattice3 @ A )
= ( relation_of_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(98,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(1449,plain,
? [A: $i] : ( rel_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(53,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(1204,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ D @ A ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(6265,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( ( in @ A @ ( relation_image @ C @ B ) )
=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ D @ A ) @ C )
& ( in @ D @ B ) ) )
& ( ? [D: $i] :
( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ D @ A ) @ C )
& ( in @ D @ B ) )
=> ( in @ A @ ( relation_image @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(527,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_0) ).
thf(3933,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( ( subrelstr @ B @ A )
=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) )
& ( ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) )
=> ( subrelstr @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(711,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( ( join @ ( boole_lattice @ A ) @ B @ C )
= ( set_union2 @ B @ C ) )
& ( ( meet @ ( boole_lattice @ A ) @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_lattice3) ).
thf(5293,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( ( join @ ( boole_lattice @ A ) @ B @ C )
= ( set_union2 @ B @ C ) )
& ( ( meet @ ( boole_lattice @ A ) @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(654,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( upper_relstr_subset @ C @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ( ( is_a_convergence_point_of_set @ A @ C @ B )
<=> ( subset @ ( neighborhood_system @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_yellow19) ).
thf(4940,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( upper_relstr_subset @ C @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ( ( ( is_a_convergence_point_of_set @ A @ C @ B )
=> ( subset @ ( neighborhood_system @ A @ B ) @ C ) )
& ( ( subset @ ( neighborhood_system @ A @ B ) @ C )
=> ( is_a_convergence_point_of_set @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(180,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(1912,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(882,plain,
~ ( empty_carrier @ sk2 ),
inference(cnf,[status(esa)],[876]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( antisymmetric @ B )
=> ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
thf(2177,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( antisymmetric @ B )
=> ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(548,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( boundary_set @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(4002,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( boundary_set @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(29686,plain,
$false,
inference(cvc4,[status(thm)],[892,3021,6085,2744,3661,1105,2412,5390,6512,5778,1295,1549,4166,5136,6530,5896,2778,1995,4169,3666,4022,6431,2787,6317,5205,3449,3990,5225,4339,1068,4311,2947,5625,1728,878,6480,1486,3230,2381,5644,2062,2953,6458,2671,5173,2282,5669,1142,1269,1971,3402,1692,4623,4973,1305,5614,5425,1078,5037,1655,3120,1137,1310,4647,3365,1735,3446,4058,4980,3717,6391,1608,3439,4097,3942,2448,6089,3338,4638,2434,3781,4856,1919,3826,3414,1761,5161,4247,5005,5178,1063,5636,2046,5123,5301,1803,3597,5533,1746,898,3836,2216,5227,1001,5740,5393,2763,973,885,3088,5921,1613,2010,3947,2531,2405,3688,4775,5553,3644,4415,3821,3148,917,4778,2185,6434,2466,6208,1409,4238,5953,2755,3495,4130,6315,1313,1279,1992,4984,2691,1147,5052,3734,5077,5617,5792,5866,5214,5605,2403,3638,5193,2767,5622,969,3216,4270,1398,881,3084,3657,1931,5746,3951,2158,4632,5727,4302,2388,6487,2533,924,1811,2996,6189,6176,2034,3152,6259,4988,2090,5013,5333,4820,2451,2236,2880,1682,1136,5156,1151,1183,2073,2833,1215,2772,5343,1351,1600,4892,3906,4211,6210,3510,2437,1928,4055,3068,877,2190,3421,2002,6021,4643,1943,6327,2965,1651,5530,925,1915,2737,3054,2660,2000,3418,5298,3435,1074,1604,6183,4629,5545,5070,1338,5142,5540,2621,1274,2589,1723,6343,1091,3972,1355,1217,1666,4344,4521,3134,5396,3514,3889,6079,2601,2428,2596,4397,1123,6371,1502,5956,3233,2937,3816,1619,2528,3664,3471,5924,4140,2477,3137,1687,2179,3546,4402,1210,2741,3931,4680,3595,4063,1423,3307,3958,2445,2464,2758,3980,1837,1968,879,2663,2332,1888,4553,2200,2609,1079,2327,3028,3926,2547,2313,3763,1634,4732,2228,3647,4080,3731,4123,6339,5714,1259,2801,2685,6028,6477,5577,1856,2694,1138,4012,5687,2268,3831,1143,5609,1498,1587,6218,4817,4263,1493,6518,2830,3441,5786,6501,2666,4291,6299,3954,884,1329,3141,2877,1361,5075,3407,6593,3210,3714,3728,5743,2419,6304,901,1414,1842,1791,4861,2172,2551,1207,2978,2649,3611,1099,1478,1297,1451,2845,1974,1060,3937,3628,2697,5801,5369,6186,1759,1627,6349,1825,5947,1324,2285,3787,1539,2836,1456,1266,2153,1831,5498,1192,984,911,6346,4120,1002,2813,3760,3967,3409,3109,4069,2140,4086,6514,3824,3834,2203,2043,2883,6011,1071,4448,3508,2617,5126,888,4995,5170,4163,3476,1333,3802,2926,1814,3225,2702,5711,2057,3592,3999,5447,4004,4308,926,4550,1278,1648,2677,1146,6026,1483,3079,4562,2734,5647,6492,3343,965,5327,2556,1103,3871,2275,2524,4453,1631,5043,4943,3319,3636,1389,3240,2188,3086,3945,875,2991,1965,4946,1256,2827,5698,3372,904,4998,3187,2789,6312,4677,2674,1795,3590,3868,4769,3964,1312,3123,2442,6248,4887,1356,6016,6048,1428,2161,5965,1139,2891,1271,6532,5595,4171,4236,1865,4218,4672,3002,3340,1997,3700,4060,979,6024,2521,3238,4828,1144,4667,5689,1853,1408,1894,2987,1806,1011,4914,5827,2097,5901,1542,2943,3710,880,1801,2378,5795,4374,3066,2896,6196,4773,1571,1439,5584,5035,2025,3668,4993,1381,2461,5987,890,3456,2182,6004,5994,3073,5599,5286,3977,2410,895,3006,2329,1952,2765,6270,883,2369,2797,1000,3310,2101,2967,4626,4890,2962,5254,1528,5641,5667,1496,3908,6485,1694,4965,1076,3009,4441,4458,1277,4859,3921,1472,1958,6440,1551,1049,5538,4690,2318,2271,4456,1145,1018,6564,5358,5133,1181,6399,1611,1566,6367,3949,2518,4971,1531,2689,5716,3376,3640,1516,5607,1961,1225,5399,2060,4272,3082,887,4641,2175,2407,4894,3608,6596,3019,6389,4346,4020,3554,5154,1763,6352,2322,3564,3095,1336,1220,3940,2454,5731,4190,3818,1300,3691,1637,6436,2486,4117,1579,5147,6337,1749,4267,6301,991,5208,5949,3697,2558,3970,1141,1536,3356,6369,1353,1955,5504,2357,2320,4991,6193,1094,1140,5685,1797,3961,3071,1372,3256,6245,2807,3914,1940,2479,3092,2818,1553,5536,2209,2013,3478,1839,4651,2626,2352,1949,4763,2870,1157,1834,1189,3346,2305,4463,1289,2226,5860,2071,2775,5068,2792,4574,3797,5055,5632,1326,896,5008,2554,1508,4250,3369,1629,2431,4969,2526,4261,963,6077,4197,914,5408,4214,1294,2198,4387,2680,6586,1661,2623,3552,6516,2956,6257,1491,2384,2475,3694,1077,5549,6252,5869,1513,2902,5211,6386,6569,2230,2036,2739,5196,1348,2287,3997,6131,3987,3264,2604,6237,1303,5601,1116,2142,5187,2258,2302,2683,4114,4687,4706,4670,1678,2155,2255,3601,2233,1148,1673,3145,3015,3328,4565,1657,5990,1056,2223,2668,1436,6535,5019,4083,897,2417,3426,1891,2619,6393,5176,5200,5283,6273,3805,2651,886,2549,2731,1829,3025,3543,5151,1582,5581,4410,5958,3886,3113,2699,2241,5500,2127,4242,6329,1384,3411,3360,1378,3259,4066,6233,6082,5046,4206,1597,1431,1004,4221,5473,2372,3474,1945,4949,5183,2866,1416,3052,2470,4174,3296,4734,6173,4274,1653,5542,3924,5494,5789,4784,2238,4313,3443,5445,2615,1917,2170,1088,2993,1449,1204,6265,3933,5293,4940,1912,882,2177,4002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU391+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 13:27:43 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.09 % [INFO] Parsing done (246ms).
% 1.91/1.10 % [INFO] Running in sequential loop mode.
% 2.42/1.31 % [INFO] eprover registered as external prover.
% 2.61/1.31 % [INFO] cvc4 registered as external prover.
% 2.61/1.31 % [INFO] Scanning for conjecture ...
% 2.83/1.45 % [INFO] Found a conjecture and 900 axioms. Running axiom selection ...
% 3.85/1.63 % [INFO] Axiom selection finished. Selected 872 axioms (removed 28 axioms).
% 5.13/2.01 % [INFO] Problem is first-order (TPTP FOF).
% 5.13/2.05 % [INFO] Type checking passed.
% 5.13/2.05 % [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 ...
% 101.21/25.27 % External prover 'cvc4' found a proof!
% 101.21/25.27 % [INFO] Killing All external provers ...
% 101.21/25.27 % Time passed: 24754ms (effective reasoning time: 24172ms)
% 101.21/25.28 % 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)>
% 101.21/25.28 % Axioms used in derivation (872): t8_waybel_0, d1_lattices, t15_finset_1, existence_m2_yellow_6, dt_k5_waybel_9, d1_enumset1, redefinition_m2_relset_1, t30_yellow_0, dt_k7_grcat_1, d16_lattice3, d7_yellow_0, cc1_tops_1, redefinition_r1_ordinal1, t32_yellow_6, fc8_tops_1, d1_wellord2, l3_wellord1, 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, 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, cc12_membered, fc15_waybel_0, t29_yellow_0, t17_xboole_1, t90_relat_1, s3_funct_1__e16_22__wellord2, cc10_waybel_1, t43_subset_1, t54_wellord1, t12_waybel_9, t45_pre_topc, 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, 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, d7_waybel_9, t39_wellord1, 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, d10_yellow_0, fc5_yellow_1, d5_tarski, d12_relat_1, t29_lattice3, t44_relat_1, redefinition_k7_funct_2, t10_tops_2, rc12_lattices, cc5_waybel_1, fraenkel_a_2_1_yellow19, existence_l1_lattices, cc9_waybel_1, cc2_arytm_3, rc3_tops_1, t26_lattices, fc4_relat_1, d1_yellow19, s1_xboole_0__e18_27__finset_1__1, fc4_funct_1, t1_subset, t28_lattice3, fc34_membered, fc4_lattice3, t144_relat_1, fc31_membered, t22_funct_1, existence_l3_lattices, fc8_yellow_6, rc1_membered, dt_k5_lattices, fc4_tops_1, t9_yellow19, fc2_waybel_0, fc3_relat_1, t8_waybel_7, 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_k1_yellow19, dt_k8_relset_1, 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, dt_k1_waybel_0, cc5_tops_1, l40_tops_1, t99_zfmisc_1, rc2_orders_2, t47_setfam_1, fc1_funct_1, d8_yellow_6, rc4_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, cc3_tops_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, t21_ordinal1, t26_wellord2, dt_k7_funct_2, cc11_waybel_0, t4_yellow19, 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_orders_2, rc6_pre_topc, fc32_membered, fc30_membered, fc11_finset_1, t5_tex_2, t2_yellow19, d12_waybel_0, dt_k4_lattice3, fc5_pre_topc, involutiveness_k3_subset_1, d2_tops_2, dt_k2_yellow19, rc1_funct_1, dt_u1_waybel_0, rc11_waybel_0, dt_g1_waybel_0, reflexivity_r3_lattices, d1_xboole_0, d9_orders_2, rc1_lattice3, d2_tex_2, fc1_yellow19, 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, t3_yellow19, 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, rc5_tops_1, fc5_waybel_0, 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, 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, d8_xboole_0, fc2_lattice3, t5_wellord2, d5_wellord1, d1_ordinal1, t3_wellord2, t50_lattice3, dt_l2_lattices, fc2_funct_1, dt_l1_waybel_0, t5_wellord1, t8_funct_1, fc6_membered, rc4_tops_1, 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, fc10_tops_1, cc3_funct_2, 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, dt_k3_lattice3, t16_waybel_9, existence_l1_waybel_0, t11_tops_2, d3_lattices, t146_funct_1, d13_funct_1, dt_k4_relat_1, t4_subset, fc3_xboole_0, t178_relat_1, s2_finset_1__e11_2_1__waybel_0, dt_m1_yellow19, 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, d21_lattice3, cc11_membered, d2_pre_topc, fc26_waybel_9, 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, cc1_ordinal1, cc6_tops_1, rc8_waybel_0, fc2_yellow_0, 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, fc2_orders_2, dt_k7_yellow_2, d9_waybel_9, 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, d8_waybel_0, cc20_membered, existence_l1_orders_2, cc3_waybel_3, t23_ordinal1, d1_yellow_1, fc9_tops_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, rc4_waybel_7, dt_k1_wellord2, cc13_waybel_0, fc5_lattice2, fc3_ordinal1, rc9_waybel_0, rc2_funct_1, t3_lattice3, d11_relat_1, cc1_yellow_2, t21_funct_2, dt_g1_orders_2, dt_k2_partfun1, 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_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_k6_waybel_9, s1_tarski__e11_2_1__waybel_0__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, t29_waybel_9, t33_ordinal1, 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, t22_relset_1, cc13_membered, t24_ordinal1, s1_ordinal2__e18_27__finset_1, antisymmetry_r2_xboole_0, dt_k6_setfam_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, cc2_tops_1, 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, redefinition_k2_binop_1, s1_tarski__e16_22__wellord2__1, dt_l1_orders_2, d5_yellow_6, fraenkel_a_2_2_lattice3, t25_wellord2, d2_yellow19, 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, cc1_yellow_3, reflexivity_r1_ordinal1, cc17_membered, d11_grcat_1, rc6_lattices, d1_funct_2, t31_yellow_6, redefinition_k7_yellow_2, dt_k6_relat_1, dt_k2_lattice3, t4_waybel_7, s1_tarski__e18_27__finset_1__1, t7_lattice3, d1_connsp_2, fraenkel_a_2_0_yellow19, t2_xboole_1, 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, 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, rc1_waybel_9, l23_zfmisc_1, rc2_tex_2, t48_pre_topc, 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, rc5_struct_0, cc4_tops_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, d5_waybel_7, fc40_membered, s1_tarski__e4_7_1__tops_2__1, s1_tarski__e1_40__pre_topc__1, fc8_relat_1, 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, cc14_membered, d3_yellow19, fc41_membered, 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, t60_xboole_1, rc1_partfun1, existence_m1_yellow19, t3_boole, d5_funct_1, redefinition_k6_subset_1, fc7_yellow_1, fc22_waybel_9, dt_k6_waybel_9, t7_tarski, dt_k11_yellow_6, dt_k3_waybel_0, fc3_waybel_0, redefinition_k5_relset_1, rc7_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, fraenkel_a_3_0_waybel_9, d8_relat_2, t25_relat_1, d1_tops_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, redefinition_k2_partfun1, fc14_finset_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, irreflexivity_r2_xboole_0, cc3_yellow_0, t65_zfmisc_1, t29_tops_1, d3_xboole_0, dt_k3_lattices, t71_relat_1, t23_relset_1, d1_mcart_1, 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, fc4_waybel_0, cc2_lattices, rc2_funct_2, redefinition_k4_lattices, dt_k2_pre_topc
% 101.21/25.28 % No. of inferences in proof: 1788
% 101.21/25.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24754 ms resp. 24172 ms w/o parsing
% 102.72/25.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 102.72/25.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------