TSTP Solution File: SEU369+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU369+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 11:58:34 EDT 2023
% Result : Theorem 7.59s 2.73s
% Output : Refutation 8.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 179
% Syntax : Number of formulae : 292 ( 37 unt; 68 typ; 0 def)
% Number of atoms : 1195 ( 34 equ; 0 cnn)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 3245 ( 176 ~; 2 |; 762 &;2098 @)
% ( 9 <=>; 198 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 93 ( 93 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 68 usr; 2 con; 0-3 aty)
% Number of variables : 352 ( 0 ^; 296 !; 56 ?; 352 :)
% Comments :
%------------------------------------------------------------------------------
thf(element_type,type,
element: $i > $i > $o ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(boole_POSet_type,type,
boole_POSet: $i > $i ).
thf(related_reflexive_type,type,
related_reflexive: $i > $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(latt_str_type,type,
latt_str: $i > $o ).
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(lower_bounded_semilattstr_type,type,
lower_bounded_semilattstr: $i > $o ).
thf(upper_bounded_semilattstr_type,type,
upper_bounded_semilattstr: $i > $o ).
thf(bounded_lattstr_type,type,
bounded_lattstr: $i > $o ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(boolean_lattstr_type,type,
boolean_lattstr: $i > $o ).
thf(distributive_lattstr_type,type,
distributive_lattstr: $i > $o ).
thf(complemented_lattstr_type,type,
complemented_lattstr: $i > $o ).
thf(boole_lattice_type,type,
boole_lattice: $i > $i ).
thf(strict_latt_str_type,type,
strict_latt_str: $i > $o ).
thf(join_commutative_type,type,
join_commutative: $i > $o ).
thf(join_associative_type,type,
join_associative: $i > $o ).
thf(meet_commutative_type,type,
meet_commutative: $i > $o ).
thf(meet_associative_type,type,
meet_associative: $i > $o ).
thf(meet_absorbing_type,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_type,type,
join_absorbing: $i > $o ).
thf(lattice_type,type,
lattice: $i > $o ).
thf(modular_lattstr_type,type,
modular_lattstr: $i > $o ).
thf(complete_latt_str_type,type,
complete_latt_str: $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(rel_str_type,type,
rel_str: $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(reflexive_relstr_type,type,
reflexive_relstr: $i > $o ).
thf(trivial_carrier_type,type,
trivial_carrier: $i > $o ).
thf(transitive_relstr_type,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_type,type,
antisymmetric_relstr: $i > $o ).
thf(complete_relstr_type,type,
complete_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(strict_rel_str_type,type,
strict_rel_str: $i > $o ).
thf(poset_of_lattice_type,type,
poset_of_lattice: $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(quasi_total_type,type,
quasi_total: $i > $i > $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(latt_str_of_type,type,
latt_str_of: $i > $i > $i > $i ).
thf(rel_str_of_type,type,
rel_str_of: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(meet_semilatt_str_type,type,
meet_semilatt_str: $i > $o ).
thf(join_semilatt_str_type,type,
join_semilatt_str: $i > $o ).
thf(relation_type,type,
relation: $i > $o ).
thf(relation_of_lattice_type,type,
relation_of_lattice: $i > $i ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(k2_lattice3_type,type,
k2_lattice3: $i > $i ).
thf(reflexive_type,type,
reflexive: $i > $o ).
thf(antisymmetric_type,type,
antisymmetric: $i > $o ).
thf(transitive_type,type,
transitive: $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
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(the_L_meet_type,type,
the_L_meet: $i > $i ).
thf(the_InternalRel_type,type,
the_InternalRel: $i > $i ).
thf(the_L_join_type,type,
the_L_join: $i > $i ).
thf(below_type,type,
below: $i > $i > $i > $o ).
thf(related_type,type,
related: $i > $i > $i > $o ).
thf(9,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/sandbox/benchmark/theBenchmark.p',fc3_lattice3) ).
thf(174,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)],[9]) ).
thf(21,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(297,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(701,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)],[110]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
thf(207,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)],[10]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
thf(629,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)],[92]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(365,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)],[34]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
thf(481,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)],[61]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',fc1_yellow_1) ).
thf(408,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)],[44]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
thf(582,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)],[80]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
thf(677,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)],[102]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).
thf(120,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)],[3]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',cc2_yellow_0) ).
thf(247,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)],[16]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(655,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)],[94]) ).
thf(67,axiom,
? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(511,plain,
? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
thf(550,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)],[77]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(698,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)],[109]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).
thf(340,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)],[32]) ).
thf(38,axiom,
! [A: $i] :
( ( strict_latt_str @ ( boole_lattice @ A ) )
& ( latt_str @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
thf(389,plain,
! [A: $i] :
( ( strict_latt_str @ ( boole_lattice @ A ) )
& ( latt_str @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(36,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(372,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(504,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)],[65]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(587,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(75,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(542,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(57,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(460,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',fc2_yellow_1) ).
thf(421,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)],[47]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(416,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(325,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)],[29]) ).
thf(52,axiom,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_orders_2) ).
thf(443,plain,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(253,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)],[17]) ).
thf(68,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( k2_lattice3 @ A )
= ( relation_of_lattice @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
thf(514,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)],[68]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',dt_k2_lattice3) ).
thf(692,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)],[108]) ).
thf(14,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(243,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
thf(265,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)],[18]) ).
thf(26,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(312,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(40,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(397,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(687,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fc4_lattice3) ).
thf(452,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)],[55]) ).
thf(96,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(661,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)],[96]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).
thf(484,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)],[62]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
thf(665,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)],[98]) ).
thf(104,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(682,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)],[104]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fc4_yellow_1) ).
thf(285,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)],[20]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(519,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(317,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)],[28]) ).
thf(89,axiom,
! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
thf(615,plain,
! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(328,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)],[30]) ).
thf(73,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(537,plain,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(476,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)],[60]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',rc1_yellow_0) ).
thf(526,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)],[72]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(590,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)],[83]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
thf(128,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)],[6]) ).
thf(66,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(508,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fc2_lattice3) ).
thf(558,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)],[78]) ).
thf(101,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(674,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(48,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(430,plain,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
thf(689,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)],[107]) ).
thf(87,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(601,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(42,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bounded_relstr @ A )
=> ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(402,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)],[42]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(577,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)],[79]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
thf(545,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(27,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(313,plain,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',rc10_lattices) ).
thf(350,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)],[33]) ).
thf(74,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(540,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',fc7_yellow_1) ).
thf(604,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)],[88]) ).
thf(1,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',t2_yellow_1) ).
thf(2,negated_conjecture,
~ ! [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 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,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)],[2]) ).
thf(15,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) )
=> ( bounded_relstr @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(245,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)],[15]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',rc2_orders_2) ).
thf(434,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)],[50]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',fc1_orders_2) ).
thf(303,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)],[23]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',rc11_lattices) ).
thf(271,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)],[19]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(599,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(594,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(626,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)],[91]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
thf(668,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)],[99]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).
thf(135,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)],[7]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
thf(658,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)],[95]) ).
thf(105,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(685,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fc3_orders_2) ).
thf(521,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)],[71]) ).
thf(39,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(394,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)],[39]) ).
thf(24,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(306,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(473,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)],[59]) ).
thf(103,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(680,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(663,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)],[97]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',rc12_lattices) ).
thf(374,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)],[37]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( relation @ ( relation_of_lattice @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(458,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( relation @ ( relation_of_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(705,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)],[111]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(707,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)],[112]) ).
thf(51,axiom,
? [A: $i] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(441,plain,
? [A: $i] : ( join_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(31,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(338,plain,
? [A: $i] : ( rel_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(81,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(585,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(35,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(370,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fc1_yellow_0) ).
thf(446,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)],[53]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(497,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)],[64]) ).
thf(54,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(450,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(100,axiom,
! [A: $i] :
( ( boole_POSet @ A )
= ( poset_of_lattice @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_1) ).
thf(671,plain,
! [A: $i] :
( ( boole_POSet @ A )
= ( poset_of_lattice @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(63,axiom,
? [A: $i] : ( latt_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(495,plain,
? [A: $i] : ( latt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(69,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(517,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fc8_yellow_1) ).
thf(632,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)],[93]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',fc1_knaster) ).
thf(139,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)],[8]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
thf(418,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)],[46]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(300,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)],[22]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fc2_orders_2) ).
thf(620,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)],[90]) ).
thf(49,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(432,plain,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(43,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(405,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',cc1_knaster) ).
thf(210,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)],[11]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(239,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(126,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,axiom,
? [A: $i] : ( meet_semilatt_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(400,plain,
? [A: $i] : ( meet_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',fc3_yellow_1) ).
thf(464,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)],[58]) ).
thf(85,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(596,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)],[85]) ).
thf(25,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(309,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',rc13_lattices) ).
thf(222,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)],[12]) ).
thf(719,plain,
$false,
inference(e,[status(thm)],[174,297,701,207,629,365,481,408,582,677,120,247,655,511,550,698,340,389,372,504,587,542,460,421,416,325,443,253,514,692,243,265,312,397,687,452,661,484,665,682,285,519,317,615,328,537,476,526,590,128,508,558,674,430,689,601,402,577,545,313,350,540,604,113,245,434,303,271,599,594,626,668,135,658,685,521,394,306,473,680,663,374,123,458,705,707,441,338,585,370,446,497,450,671,495,517,632,139,418,300,620,432,405,210,239,126,400,464,596,309,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU369+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 13:02:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.01 % [INFO] Parsing done (179ms).
% 1.38/1.02 % [INFO] Running in sequential loop mode.
% 1.87/1.21 % [INFO] eprover registered as external prover.
% 1.87/1.21 % [INFO] cvc4 registered as external prover.
% 1.87/1.22 % [INFO] Scanning for conjecture ...
% 2.07/1.30 % [INFO] Found a conjecture and 120 axioms. Running axiom selection ...
% 2.46/1.38 % [INFO] Axiom selection finished. Selected 110 axioms (removed 10 axioms).
% 2.86/1.48 % [INFO] Problem is first-order (TPTP FOF).
% 2.86/1.49 % [INFO] Type checking passed.
% 2.86/1.49 % [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 ...
% 7.59/2.72 % External prover 'e' found a proof!
% 7.59/2.72 % [INFO] Killing All external provers ...
% 7.59/2.72 % Time passed: 2214ms (effective reasoning time: 1702ms)
% 7.59/2.72 % 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)>
% 7.59/2.73 % Axioms used in derivation (110): redefinition_m2_relset_1, fc1_yellow_1, rc2_yellow_0, cc3_lattices, rc2_xboole_0, fc1_xboole_0, rc12_lattices, cc6_lattices, existence_l1_lattices, d5_tarski, t1_subset, fc4_lattice3, fc4_subset_1, existence_l3_lattices, d2_lattice3, rc2_partfun1, cc4_lattices, rc2_orders_2, cc1_lattice3, dt_m2_relset_1, dt_k4_lattice3, dt_u1_orders_2, reflexivity_r3_lattices, d9_orders_2, rc1_lattice3, rc11_lattices, rc3_lattices, dt_l1_lattices, dt_k3_yellow_1, rc2_lattice3, t6_boole, rc2_subset_1, existence_l2_lattices, redefinition_r3_orders_2, t2_lattice3, fc3_subset_1, t5_subset, existence_m1_relset_1, cc2_yellow_0, dt_l3_lattices, fc2_subset_1, fc2_lattice3, fc1_lattice3, dt_l2_lattices, fc8_yellow_1, dt_k3_lattice3, cc5_lattices, t4_subset, dt_k9_filter_1, rc13_lattices, d3_lattice3, fc2_orders_2, t7_boole, existence_l1_orders_2, rc1_orders_2, rc3_struct_0, fc1_subset_1, reflexivity_r3_orders_2, dt_g1_orders_2, rc1_subset_1, fc4_yellow_1, cc1_lattices, abstractness_v1_orders_2, cc4_yellow_0, redefinition_r3_lattices, t3_subset, cc1_relset_1, rc9_lattices, dt_u1_lattices, existence_m1_subset_1, commutativity_k2_tarski, fc3_orders_2, d2_yellow_1, existence_m2_relset_1, fc1_yellow_0, dt_l1_orders_2, fc1_orders_2, free_g1_orders_2, fc1_struct_0, fc2_yellow_1, fc1_knaster, reflexivity_r1_tarski, dt_k2_lattice3, t7_lattice3, cc1_knaster, dt_g3_lattices, rc6_lattices, free_g3_lattices, cc7_lattices, fc3_lattice3, cc5_yellow_0, dt_k1_lattice3, abstractness_v3_lattices, cc1_yellow_0, redefinition_k2_lattice3, fc3_yellow_1, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, rc1_yellow_0, cc2_lattice3, existence_l1_struct_0, fc7_yellow_1, rc10_lattices, dt_u2_lattices, fc3_lattices, cc3_yellow_0, antisymmetry_r2_hidden, cc2_lattices
% 7.59/2.73 % No. of inferences in proof: 224
% 7.59/2.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2214 ms resp. 1702 ms w/o parsing
% 8.22/2.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.22/2.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------