%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU345+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:38:31 AM UTC 2026
% Result : Theorem 9.00s 5.32s
% Output : Refutation 9.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 88
% Syntax : Number of formulae : 178 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 642 ( 88 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 2263 ( 104 ~; 2 |; 311 &;1695 @)
% ( 5 <=>; 146 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 2 con; 0-6 aty)
% Number of variables : 367 ( 0 ^; 332 !; 35 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
thf(lower_bounded_semilattstr_decl,type,
lower_bounded_semilattstr: $i > $o ).
thf(boole_lattice_decl,type,
boole_lattice: $i > $i ).
thf(bottom_of_semilattstr_decl,type,
bottom_of_semilattstr: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(apply_binary_decl,type,
apply_binary: $i > $i > $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(strict_latt_str_decl,type,
strict_latt_str: $i > $o ).
thf(latt_str_of_decl,type,
latt_str_of: $i > $i > $i > $i ).
thf(latt_str_decl,type,
latt_str: $i > $o ).
thf(meet_semilatt_str_decl,type,
meet_semilatt_str: $i > $o ).
thf(the_L_meet_decl,type,
the_L_meet: $i > $i ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(join_commutative_decl,type,
join_commutative: $i > $o ).
thf(join_semilatt_str_decl,type,
join_semilatt_str: $i > $o ).
thf(the_L_join_decl,type,
the_L_join: $i > $i ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(apply_binary_as_element_decl,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(join_associative_decl,type,
join_associative: $i > $o ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(meet_commutative_decl,type,
meet_commutative: $i > $o ).
thf(meet_associative_decl,type,
meet_associative: $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subset_union2_decl,type,
subset_union2: $i > $i > $i > $i ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(meet_commut_decl,type,
meet_commut: $i > $i > $i > $i ).
thf(meet_decl,type,
meet: $i > $i > $i > $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(join_decl,type,
join: $i > $i > $i > $i ).
thf(subset_intersection2_decl,type,
subset_intersection2: $i > $i > $i > $i ).
thf(meet_absorbing_decl,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_decl,type,
join_absorbing: $i > $o ).
thf(lattice_decl,type,
lattice: $i > $o ).
thf(61,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(301,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(65,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(317,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(23,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_lattice2) ).
thf(173,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_join @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function )
& ( A @ the_L_join @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice2) ).
thf(159,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_join @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function )
& ( A @ the_L_join @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(82,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(409,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(89,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(441,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(138,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(70,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ meet ) ) )
= ( C @ ( B @ ( A @ the_L_meet @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattices) ).
thf(333,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ meet ) ) )
= ( C @ ( B @ ( A @ the_L_meet @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(41,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(234,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(217,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(46,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(247,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(269,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(25,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(184,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(344,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( C @ ( B @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(325,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( C @ ( B @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_intersection2 ) ) )
= ( B @ ( C @ ( A @ subset_intersection2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(261,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_intersection2 ) ) )
= ( B @ ( C @ ( A @ subset_intersection2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(66,axiom,
? [A: $i] :
( ( A @ strict_latt_str )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(321,plain,
? [A: $i] :
( ( A @ strict_latt_str )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(121,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(348,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(34,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(211,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ strict_latt_str )
=> ( A
= ( A @ the_L_meet @ ( A @ the_L_join @ ( A @ the_carrier @ latt_str_of ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(253,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ strict_latt_str )
=> ( A
= ( A @ the_L_meet @ ( A @ the_L_join @ ( A @ the_carrier @ latt_str_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(147,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(221,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) )
= ( F @ ( E @ ( D @ apply_binary ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) )
= ( F @ ( E @ ( D @ apply_binary ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(312,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_union2 ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(206,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_union2 ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(424,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(27,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(192,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( A @ boole_lattice @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_lattice @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ ( A @ boole_lattice @ meet ) ) )
= ( C @ ( B @ set_intersection2 ) ) )
& ( ( C @ ( B @ ( A @ boole_lattice @ join ) ) )
= ( C @ ( B @ set_union2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).
thf(429,plain,
! [A: $i,B: $i] :
( ( A @ boole_lattice @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_lattice @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ ( A @ boole_lattice @ meet ) ) )
= ( C @ ( B @ set_intersection2 ) ) )
& ( ( C @ ( B @ ( A @ boole_lattice @ join ) ) )
= ( C @ ( B @ set_union2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_intersection2 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(275,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_intersection2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(29,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(197,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
thf(435,plain,
! [A: $i] :
( ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(339,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(256,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(109,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(328,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( C @ ( B @ ( A @ meet ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(266,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( C @ ( B @ ( A @ meet ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,axiom,
? [A: $i] : ( A @ meet_semilatt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(237,plain,
? [A: $i] : ( A @ meet_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ latt_str )
& ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(105,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ latt_str )
& ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(244,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(84,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_semilattstr )
<=> ? [B: $i] :
( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_lattices) ).
thf(412,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ? [B: $i] :
( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
& ( A @ the_carrier @ ( B @ element ) ) )
=> ( A @ lower_bounded_semilattstr ) )
& ( ( A @ lower_bounded_semilattstr )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(22,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice2) ).
thf(166,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(264,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(57,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(279,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(24,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(180,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19,axiom,
? [A: $i] : ( A @ join_semilatt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(149,plain,
? [A: $i] : ( A @ join_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(204,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(259,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(81,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(406,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
thf(303,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(208,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(5,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(103,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( B @ ( C @ ( A @ meet_commut ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(330,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( B @ ( C @ ( A @ meet_commut ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(13,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(130,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(223,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(80,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_semilattstr )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B
= ( A @ bottom_of_semilattstr ) )
<=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattices) ).
thf(394,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_semilattstr )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
=> ( B
= ( A @ bottom_of_semilattstr ) ) )
& ( ( B
= ( A @ bottom_of_semilattstr ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(60,axiom,
? [A: $i] : ( A @ latt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(299,plain,
? [A: $i] : ( A @ latt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lattice3) ).
thf(374,plain,
! [A: $i] :
( ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(10,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(123,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(194,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_intersection2 ) ) )
= ( C @ ( B @ set_intersection2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_intersection2 ) ) )
= ( C @ ( B @ set_intersection2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str )
& ~ ( C @ ( B @ ( A @ latt_str_of ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str )
& ~ ( C @ ( B @ ( A @ latt_str_of ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(47,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= ( C @ ( B @ ( A @ the_L_join @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattices) ).
thf(250,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= ( C @ ( B @ ( A @ the_L_join @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ boole_lattice @ latt_str )
& ( A @ boole_lattice @ strict_latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
thf(368,plain,
! [A: $i] :
( ( A @ boole_lattice @ latt_str )
& ( A @ boole_lattice @ strict_latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ strict_latt_str ) )
=> ( ( B
= ( A @ boole_lattice ) )
<=> ( ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( B @ the_L_meet @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_intersection2 ) ) ) )
& ( ( D @ ( C @ ( B @ the_L_join @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_union2 ) ) ) ) ) ) )
& ( ( B @ the_carrier )
= ( A @ powerset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice3) ).
thf(351,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ strict_latt_str ) )
=> ( ( ( ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( B @ the_L_meet @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_intersection2 ) ) ) )
& ( ( D @ ( C @ ( B @ the_L_join @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_union2 ) ) ) ) ) ) )
& ( ( B @ the_carrier )
= ( A @ powerset ) ) )
=> ( B
= ( A @ boole_lattice ) ) )
& ( ( B
= ( A @ boole_lattice ) )
=> ( ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( B @ the_L_meet @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_intersection2 ) ) ) )
& ( ( D @ ( C @ ( B @ the_L_join @ apply_binary ) ) )
= ( D @ ( C @ ( A @ subset_union2 ) ) ) ) ) ) )
& ( ( B @ the_carrier )
= ( A @ powerset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_join @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function )
& ( A @ the_L_join @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lattice2) ).
thf(114,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_join @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function )
& ( A @ the_L_join @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_intersection2 ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(346,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_intersection2 ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(35,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(214,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(59,axiom,
? [A: $i] :
( ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).
thf(287,plain,
? [A: $i] :
( ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ latt_str_of ) ) )
= ( F @ ( E @ ( D @ latt_str_of ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ latt_str_of ) ) )
= ( F @ ( E @ ( D @ latt_str_of ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(64,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(315,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(83,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( A @ bottom_of_semilattstr @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(410,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( A @ bottom_of_semilattstr @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(273,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( B @ ( C @ ( A @ subset_union2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(341,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( B @ ( C @ ( A @ subset_union2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(3,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ apply_binary ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_binop_1) ).
thf(94,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ apply_binary ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
thf(283,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(239,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(242,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(86,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(427,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_union2 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(200,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_union2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ boole_lattice @ bottom_of_semilattstr )
= empty_set )
& ( A @ boole_lattice @ lower_bounded_semilattstr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice3) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ boole_lattice @ bottom_of_semilattstr )
= empty_set )
& ( A @ boole_lattice @ lower_bounded_semilattstr ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(90,plain,
~ ! [A: $i] :
( ( ( A @ boole_lattice @ bottom_of_semilattstr )
= empty_set )
& ( A @ boole_lattice @ lower_bounded_semilattstr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,axiom,
? [A: $i] :
( ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(227,plain,
? [A: $i] :
( ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet_commut ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(232,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet_commut ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(474,plain,
$false,
inference(e,[status(thm)],[301,317,173,159,409,441,138,333,234,217,247,269,184,125,344,325,261,321,121,348,211,253,147,221,132,312,206,424,192,429,275,197,435,97,339,256,109,328,266,128,237,105,244,412,166,264,279,180,149,204,259,406,303,208,103,330,130,223,394,135,299,374,123,194,336,143,250,368,351,186,114,346,214,287,151,315,410,273,341,94,283,239,242,427,200,90,227,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU345+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.62 % Computer : n002.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Sat Sep 26 09:19:20 UTC 2026
% 0.15/0.62 % CPUTime :
% 0.15/0.62 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/1.37 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.73 % [INFO] Parsing done (353ms).
% 1.49/1.76 % [INFO] Running in sequential loop mode.
% 2.40/2.29 % [INFO] eprover registered as external prover.
% 2.57/2.31 % [INFO] Scanning for conjecture ...
% 2.70/2.48 % [INFO] Found a conjecture (or negated_conjecture) and 101 axioms. Running axiom selection ...
% 2.97/2.63 % [INFO] Axiom selection finished. Selected 87 axioms (removed 14 axioms).
% 3.29/2.88 % [INFO] Problem is first-order (TPTP FOF).
% 3.46/2.90 % [INFO] Type checking passed.
% 3.46/2.91 % [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 ...
% 9.00/5.32 % External prover 'e' found a proof!
% 9.00/5.32 % [INFO] Killing All external provers ...
% 9.00/5.32 % Time passed: 4488ms (effective reasoning time: 3544ms)
% 9.00/5.32 % 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)>
% 9.00/5.32 % Axioms used in derivation (87): redefinition_k4_subset_1, redefinition_k2_binop_1, d1_lattices, redefinition_m2_relset_1, idempotence_k3_xboole_0, t1_boole, redefinition_k5_subset_1, d13_lattices, fc1_xboole_0, d16_lattices, existence_l1_lattices, d5_tarski, t1_subset, fc4_subset_1, existence_l3_lattices, dt_k5_lattices, fc4_lattice2, t2_boole, dt_k4_subset_1, fc2_lattice2, dt_m2_relset_1, idempotence_k5_subset_1, commutativity_k3_xboole_0, fc3_lattice2, dt_k2_binop_1, fc2_xboole_0, rc3_lattices, dt_l1_lattices, t6_boole, rc2_subset_1, existence_l2_lattices, commutativity_k2_xboole_0, fc3_subset_1, t5_subset, existence_m1_relset_1, commutativity_k5_subset_1, dt_l3_lattices, fc2_subset_1, fc2_lattice3, fc1_lattice3, dt_l2_lattices, t4_subset, fc3_xboole_0, t7_boole, rc3_struct_0, commutativity_k4_lattices, fc1_subset_1, fc5_lattice2, rc1_subset_1, cc1_lattices, t3_subset, cc1_relset_1, rc9_lattices, dt_u1_lattices, existence_m1_subset_1, commutativity_k2_tarski, commutativity_k4_subset_1, dt_k5_subset_1, existence_m2_relset_1, fc1_struct_0, dt_k4_lattices, reflexivity_r1_tarski, t2_xboole_1, d2_lattices, dt_g3_lattices, rc6_lattices, free_g3_lattices, dt_k1_lattices, dt_k1_lattice3, abstractness_v3_lattices, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, d1_lattice3, idempotence_k2_xboole_0, t1_lattice3, existence_l1_struct_0, dt_k2_lattices, dt_u2_lattices, idempotence_k4_subset_1, d1_binop_1, rc2_xboole_0, fc3_lattices, antisymmetry_r2_hidden, cc2_lattices, redefinition_k4_lattices
% 9.00/5.32 % No. of inferences in proof: 178
% 9.00/5.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4488 ms resp. 3544 ms w/o parsing
% 9.53/5.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.53/5.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------