TSTP Solution File: SEU343+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 11:58:23 EDT 2023
% Result : Theorem 6.91s 2.50s
% Output : Refutation 6.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 107
% Syntax : Number of formulae : 181 ( 45 unt; 35 typ; 0 def)
% Number of atoms : 415 ( 68 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 1525 ( 72 ~; 2 |; 158 &;1184 @)
% ( 3 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 2 con; 0-6 aty)
% Number of variables : 314 ( 0 ^; 284 !; 30 ?; 314 :)
% Comments :
%------------------------------------------------------------------------------
thf(element_type,type,
element: $i > $i > $o ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(boole_lattice_type,type,
boole_lattice: $i > $i ).
thf(join_type,type,
join: $i > $i > $i > $i ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(meet_type,type,
meet: $i > $i > $i > $i ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
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(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(strict_latt_str_type,type,
strict_latt_str: $i > $o ).
thf(latt_str_of_type,type,
latt_str_of: $i > $i > $i > $i ).
thf(latt_str_type,type,
latt_str: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(meet_semilatt_str_type,type,
meet_semilatt_str: $i > $o ).
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(join_semilatt_str_type,type,
join_semilatt_str: $i > $o ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(relation_type,type,
relation: $i > $o ).
thf(apply_binary_type,type,
apply_binary: $i > $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(apply_binary_as_element_type,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(subset_union2_type,type,
subset_union2: $i > $i > $i > $i ).
thf(the_L_meet_type,type,
the_L_meet: $i > $i ).
thf(the_L_join_type,type,
the_L_join: $i > $i ).
thf(subset_intersection2_type,type,
subset_intersection2: $i > $i > $i > $i ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(249,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(288,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(284,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(54,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattices) ).
thf(238,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(31,axiom,
? [A: $i] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(156,plain,
? [A: $i] : ( join_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(36,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(173,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(60,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(255,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)],[60]) ).
thf(37,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(175,plain,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(19,axiom,
? [A: $i] : ( latt_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(120,plain,
? [A: $i] : ( latt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(57,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(247,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)],[57]) ).
thf(26,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(142,plain,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(153,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(6,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(89,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(116,plain,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( ( join @ ( boole_lattice @ A ) @ B @ C )
= ( set_union2 @ B @ C ) )
& ( ( meet @ ( boole_lattice @ A ) @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( ( join @ ( boole_lattice @ A ) @ B @ C )
= ( set_union2 @ B @ C ) )
& ( ( meet @ ( boole_lattice @ A ) @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(74,plain,
~ ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( ( join @ ( boole_lattice @ A ) @ B @ C )
= ( set_union2 @ B @ C ) )
& ( ( meet @ ( boole_lattice @ A ) @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( strict_latt_str @ B )
& ( latt_str @ B ) )
=> ( ( B
= ( boole_lattice @ A ) )
<=> ( ( ( the_carrier @ B )
= ( powerset @ A ) )
& ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( ( apply_binary @ ( the_L_join @ B ) @ C @ D )
= ( subset_union2 @ A @ C @ D ) )
& ( ( apply_binary @ ( the_L_meet @ B ) @ C @ D )
= ( subset_intersection2 @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice3) ).
thf(206,plain,
! [A: $i,B: $i] :
( ( ( strict_latt_str @ B )
& ( latt_str @ B ) )
=> ( ( ( B
= ( boole_lattice @ A ) )
=> ( ( ( the_carrier @ B )
= ( powerset @ A ) )
& ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( ( apply_binary @ ( the_L_join @ B ) @ C @ D )
= ( subset_union2 @ A @ C @ D ) )
& ( ( apply_binary @ ( the_L_meet @ B ) @ C @ D )
= ( subset_intersection2 @ A @ C @ D ) ) ) ) ) ) )
& ( ( ( ( the_carrier @ B )
= ( powerset @ A ) )
& ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( ( apply_binary @ ( the_L_join @ B ) @ C @ D )
= ( subset_union2 @ A @ C @ D ) )
& ( ( apply_binary @ ( the_L_meet @ B ) @ C @ D )
= ( subset_intersection2 @ A @ C @ D ) ) ) ) ) )
=> ( B
= ( boole_lattice @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(233,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(85,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(275,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(24,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( apply_binary @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_binop_1) ).
thf(137,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( apply_binary @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( subset_union2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(252,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( subset_union2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(9,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(97,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,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(109,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,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(124,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)],[21]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_union2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(193,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_union2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(23,axiom,
? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(134,plain,
? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(244,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(63,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
thf(266,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(166,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)],[34]) ).
thf(28,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(148,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,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(161,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)],[33]) ).
thf(39,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(180,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(191,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(70,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(286,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)],[70]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(291,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(118,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(281,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(259,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(41,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(187,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)],[41]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(230,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(271,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(11,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(103,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,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(140,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(91,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,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(198,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)],[45]) ).
thf(67,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( meet @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_meet @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattices) ).
thf(278,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( meet @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_meet @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(55,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(241,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)],[55]) ).
thf(29,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(150,plain,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(62,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(263,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(47,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(203,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(12,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(104,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,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(158,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(16,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(114,plain,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(35,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(171,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(235,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
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(82,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(183,plain,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(65,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(273,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(13,axiom,
? [A: $i] : ( meet_semilatt_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(107,plain,
? [A: $i] : ( meet_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(73,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(294,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(3,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(79,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)],[3]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(195,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(8,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(94,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)],[8]) ).
thf(22,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(131,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( element @ ( apply_binary_as_element @ A @ B @ C @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(178,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( element @ ( apply_binary_as_element @ A @ B @ C @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,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(111,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)],[15]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( ( apply_binary_as_element @ A @ B @ C @ D @ E @ F )
= ( apply_binary @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(227,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( ( apply_binary_as_element @ A @ B @ C @ D @ E @ F )
= ( apply_binary @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(122,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(49,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(222,plain,
! [A: $i] :
( ( strict_latt_str @ ( boole_lattice @ A ) )
& ( latt_str @ ( boole_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(10,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(100,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(348,plain,
$false,
inference(e,[status(thm)],[249,288,284,238,156,173,255,175,120,247,142,153,89,116,74,206,233,85,201,275,137,252,97,109,124,193,134,244,266,166,148,161,180,191,286,291,118,281,259,187,230,271,103,140,91,198,278,241,150,263,203,104,158,114,171,235,82,146,183,273,107,294,79,195,94,131,178,111,227,122,222,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n009.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 13:25:04 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.83/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.02 % [INFO] Parsing done (170ms).
% 1.45/1.03 % [INFO] Running in sequential loop mode.
% 1.89/1.23 % [INFO] eprover registered as external prover.
% 1.89/1.23 % [INFO] cvc4 registered as external prover.
% 1.95/1.23 % [INFO] Scanning for conjecture ...
% 1.95/1.31 % [INFO] Found a conjecture and 85 axioms. Running axiom selection ...
% 2.18/1.37 % [INFO] Axiom selection finished. Selected 71 axioms (removed 14 axioms).
% 2.44/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.44/1.45 % [INFO] Type checking passed.
% 2.44/1.45 % [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 ...
% 6.91/2.50 % External prover 'e' found a proof!
% 6.91/2.50 % [INFO] Killing All external provers ...
% 6.91/2.50 % Time passed: 1974ms (effective reasoning time: 1469ms)
% 6.91/2.50 % 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)>
% 6.91/2.50 % Axioms used in derivation (71): rc1_subset_1, redefinition_k4_subset_1, redefinition_k2_binop_1, idempotence_k2_xboole_0, d1_lattices, redefinition_m2_relset_1, idempotence_k3_xboole_0, t1_boole, redefinition_k5_subset_1, fc1_xboole_0, existence_l1_lattices, d5_tarski, t1_subset, fc4_subset_1, existence_l3_lattices, t2_boole, dt_k4_subset_1, dt_m2_relset_1, idempotence_k5_subset_1, commutativity_k3_xboole_0, 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, fc1_lattice3, dt_l2_lattices, t4_subset, fc3_xboole_0, t7_boole, rc3_struct_0, fc1_subset_1, t3_subset, cc1_relset_1, 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, reflexivity_r1_tarski, 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, 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
% 6.91/2.50 % No. of inferences in proof: 146
% 6.91/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1974 ms resp. 1469 ms w/o parsing
% 6.91/2.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.91/2.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------