TSTP Solution File: SEU343+1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qYntCEEnQM true
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:12:16 EDT 2023
% Result : Theorem 1.36s 1.37s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 42
% Syntax : Number of formulae : 178 ( 66 unt; 28 typ; 0 def)
% Number of atoms : 377 ( 91 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1847 ( 201 ~; 184 |; 22 &;1419 @)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 4 con; 0-6 aty)
% Number of variables : 200 ( 0 ^; 200 !; 0 ?; 200 :)
% Comments :
%------------------------------------------------------------------------------
thf(latt_str_type,type,
latt_str: $i > $o ).
thf(meet_type,type,
meet: $i > $i > $i > $i ).
thf(quasi_total_type,type,
quasi_total: $i > $i > $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(apply_binary_type,type,
apply_binary: $i > $i > $i > $i ).
thf(boole_lattice_type,type,
boole_lattice: $i > $i ).
thf(join_semilatt_str_type,type,
join_semilatt_str: $i > $o ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(the_L_join_type,type,
the_L_join: $i > $i ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(meet_semilatt_str_type,type,
meet_semilatt_str: $i > $o ).
thf(apply_binary_as_element_type,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(the_L_meet_type,type,
the_L_meet: $i > $i ).
thf(strict_latt_str_type,type,
strict_latt_str: $i > $o ).
thf(join_type,type,
join: $i > $i > $i > $i ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(sk__16_type,type,
sk__16: $i ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(subset_union2_type,type,
subset_union2: $i > $i > $i > $i ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(subset_intersection2_type,type,
subset_intersection2: $i > $i > $i > $i ).
thf(sk__18_type,type,
sk__18: $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(element_type,type,
element: $i > $i > $o ).
thf(sk__17_type,type,
sk__17: $i ).
thf(dt_l3_lattices,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ) ).
thf(zip_derived_cl26,plain,
! [X0: $i] :
( ( join_semilatt_str @ X0 )
| ~ ( latt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_l3_lattices]) ).
thf(dt_u2_lattices,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 ) ) ) ) ).
thf(zip_derived_cl31,plain,
! [X0: $i] :
( ( function @ ( the_L_join @ X0 ) )
| ~ ( join_semilatt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_u2_lattices]) ).
thf(zip_derived_cl492,plain,
! [X0: $i] :
( ~ ( latt_str @ X0 )
| ( function @ ( the_L_join @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl26,zip_derived_cl31]) ).
thf(zip_derived_cl25,plain,
! [X0: $i] :
( ( meet_semilatt_str @ X0 )
| ~ ( latt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_l3_lattices]) ).
thf(dt_u1_lattices,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 ) ) ) ) ).
thf(zip_derived_cl28,plain,
! [X0: $i] :
( ( function @ ( the_L_meet @ X0 ) )
| ~ ( meet_semilatt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_u1_lattices]) ).
thf(zip_derived_cl508,plain,
! [X0: $i] :
( ~ ( latt_str @ X0 )
| ( function @ ( the_L_meet @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl25,zip_derived_cl28]) ).
thf(redefinition_k4_subset_1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ) ).
thf(zip_derived_cl73,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( powerset @ X1 ) )
| ~ ( element @ X2 @ ( powerset @ X1 ) )
| ( ( subset_union2 @ X1 @ X0 @ X2 )
= ( set_union2 @ X0 @ X2 ) ) ),
inference(cnf,[status(esa)],[redefinition_k4_subset_1]) ).
thf(redefinition_k5_subset_1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ).
thf(zip_derived_cl74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( powerset @ X1 ) )
| ~ ( element @ X2 @ ( powerset @ X1 ) )
| ( ( subset_intersection2 @ X1 @ X0 @ X2 )
= ( set_intersection2 @ X0 @ X2 ) ) ),
inference(cnf,[status(esa)],[redefinition_k5_subset_1]) ).
thf(d1_lattice3,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 ) ) ) ) ) ) ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1
!= ( boole_lattice @ X0 ) )
| ~ ( element @ X2 @ ( powerset @ X0 ) )
| ( ( apply_binary @ ( the_L_join @ X1 ) @ X3 @ X2 )
= ( subset_union2 @ X0 @ X3 @ X2 ) )
| ~ ( element @ X3 @ ( powerset @ X0 ) )
| ~ ( latt_str @ X1 )
| ~ ( strict_latt_str @ X1 ) ),
inference(cnf,[status(esa)],[d1_lattice3]) ).
thf(zip_derived_cl988,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( strict_latt_str @ ( boole_lattice @ X0 ) )
| ~ ( latt_str @ ( boole_lattice @ X0 ) )
| ~ ( element @ X1 @ ( powerset @ X0 ) )
| ( ( apply_binary @ ( the_L_join @ ( boole_lattice @ X0 ) ) @ X1 @ X2 )
= ( subset_union2 @ X0 @ X1 @ X2 ) )
| ~ ( element @ X2 @ ( powerset @ X0 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl10]) ).
thf(dt_k1_lattice3,axiom,
! [A: $i] :
( ( latt_str @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) ) ) ).
thf(zip_derived_cl16,plain,
! [X0: $i] : ( strict_latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl17,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl989,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X1 @ ( powerset @ X0 ) )
| ( ( apply_binary @ ( the_L_join @ ( boole_lattice @ X0 ) ) @ X1 @ X2 )
= ( subset_union2 @ X0 @ X1 @ X2 ) )
| ~ ( element @ X2 @ ( powerset @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl988,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl9,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1
!= ( boole_lattice @ X0 ) )
| ~ ( element @ X2 @ ( powerset @ X0 ) )
| ( ( apply_binary @ ( the_L_meet @ X1 ) @ X3 @ X2 )
= ( subset_intersection2 @ X0 @ X3 @ X2 ) )
| ~ ( element @ X3 @ ( powerset @ X0 ) )
| ~ ( latt_str @ X1 )
| ~ ( strict_latt_str @ X1 ) ),
inference(cnf,[status(esa)],[d1_lattice3]) ).
thf(zip_derived_cl976,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( strict_latt_str @ ( boole_lattice @ X0 ) )
| ~ ( latt_str @ ( boole_lattice @ X0 ) )
| ~ ( element @ X1 @ ( powerset @ X0 ) )
| ( ( apply_binary @ ( the_L_meet @ ( boole_lattice @ X0 ) ) @ X1 @ X2 )
= ( subset_intersection2 @ X0 @ X1 @ X2 ) )
| ~ ( element @ X2 @ ( powerset @ X0 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl16_001,plain,
! [X0: $i] : ( strict_latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl17_002,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl977,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X1 @ ( powerset @ X0 ) )
| ( ( apply_binary @ ( the_L_meet @ ( boole_lattice @ X0 ) ) @ X1 @ X2 )
= ( subset_intersection2 @ X0 @ X1 @ X2 ) )
| ~ ( element @ X2 @ ( powerset @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl976,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl11,plain,
! [X0: $i,X1: $i] :
( ( X1
!= ( boole_lattice @ X0 ) )
| ( ( the_carrier @ X1 )
= ( powerset @ X0 ) )
| ~ ( latt_str @ X1 )
| ~ ( strict_latt_str @ X1 ) ),
inference(cnf,[status(esa)],[d1_lattice3]) ).
thf(zip_derived_cl951,plain,
! [X0: $i] :
( ~ ( strict_latt_str @ ( boole_lattice @ X0 ) )
| ~ ( latt_str @ ( boole_lattice @ X0 ) )
| ( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl16_003,plain,
! [X0: $i] : ( strict_latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl17_004,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl952,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl26_005,plain,
! [X0: $i] :
( ( join_semilatt_str @ X0 )
| ~ ( latt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_l3_lattices]) ).
thf(d1_lattices,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 ) ) ) ) ) ).
thf(zip_derived_cl12,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ( ( join @ X1 @ X0 @ X2 )
= ( apply_binary_as_element @ ( the_carrier @ X1 ) @ ( the_carrier @ X1 ) @ ( the_carrier @ X1 ) @ ( the_L_join @ X1 ) @ X0 @ X2 ) )
| ~ ( element @ X2 @ ( the_carrier @ X1 ) )
| ~ ( join_semilatt_str @ X1 )
| ( empty_carrier @ X1 ) ),
inference(cnf,[status(esa)],[d1_lattices]) ).
thf(zip_derived_cl490,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( latt_str @ X0 )
| ( empty_carrier @ X0 )
| ~ ( element @ X2 @ ( the_carrier @ X0 ) )
| ( ( join @ X0 @ X1 @ X2 )
= ( apply_binary_as_element @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) @ ( the_L_join @ X0 ) @ X1 @ X2 ) )
| ~ ( element @ X1 @ ( the_carrier @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl1136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( boole_lattice @ X0 ) @ X2 @ X1 )
= ( apply_binary_as_element @ ( the_carrier @ ( boole_lattice @ X0 ) ) @ ( the_carrier @ ( boole_lattice @ X0 ) ) @ ( powerset @ X0 ) @ ( the_L_join @ ( boole_lattice @ X0 ) ) @ X2 @ X1 ) )
| ~ ( element @ X2 @ ( the_carrier @ ( boole_lattice @ X0 ) ) )
| ~ ( element @ X1 @ ( the_carrier @ ( boole_lattice @ X0 ) ) )
| ( empty_carrier @ ( boole_lattice @ X0 ) )
| ~ ( latt_str @ ( boole_lattice @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl952,zip_derived_cl490]) ).
thf(zip_derived_cl952_006,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_007,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_008,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_009,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(fc1_lattice3,axiom,
! [A: $i] :
( ( strict_latt_str @ ( boole_lattice @ A ) )
& ~ ( empty_carrier @ ( boole_lattice @ A ) ) ) ).
thf(zip_derived_cl40,plain,
! [X0: $i] :
~ ( empty_carrier @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[fc1_lattice3]) ).
thf(zip_derived_cl17_010,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl1139,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( boole_lattice @ X0 ) @ X2 @ X1 )
= ( apply_binary_as_element @ ( powerset @ X0 ) @ ( powerset @ X0 ) @ ( powerset @ X0 ) @ ( the_L_join @ ( boole_lattice @ X0 ) ) @ X2 @ X1 ) )
| ~ ( element @ X2 @ ( powerset @ X0 ) )
| ~ ( element @ X1 @ ( powerset @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1136,zip_derived_cl952,zip_derived_cl952,zip_derived_cl952,zip_derived_cl952,zip_derived_cl40,zip_derived_cl17]) ).
thf(redefinition_k2_binop_1,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 ) ) ) ).
thf(zip_derived_cl72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( element @ X0 @ X1 )
| ~ ( relation_of2 @ X2 @ ( cartesian_product2 @ X1 @ X3 ) @ X4 )
| ~ ( quasi_total @ X2 @ ( cartesian_product2 @ X1 @ X3 ) @ X4 )
| ~ ( function @ X2 )
| ( empty @ X3 )
| ( empty @ X1 )
| ~ ( element @ X5 @ X3 )
| ( ( apply_binary_as_element @ X1 @ X3 @ X4 @ X2 @ X0 @ X5 )
= ( apply_binary @ X2 @ X0 @ X5 ) ) ),
inference(cnf,[status(esa)],[redefinition_k2_binop_1]) ).
thf(zip_derived_cl3743,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( boole_lattice @ X2 ) @ X1 @ X0 )
= ( apply_binary @ ( the_L_join @ ( boole_lattice @ X2 ) ) @ X1 @ X0 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ( empty @ ( powerset @ X2 ) )
| ( empty @ ( powerset @ X2 ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ X2 ) ) )
| ~ ( quasi_total @ ( the_L_join @ ( boole_lattice @ X2 ) ) @ ( cartesian_product2 @ ( powerset @ X2 ) @ ( powerset @ X2 ) ) @ ( powerset @ X2 ) )
| ~ ( relation_of2 @ ( the_L_join @ ( boole_lattice @ X2 ) ) @ ( cartesian_product2 @ ( powerset @ X2 ) @ ( powerset @ X2 ) ) @ ( powerset @ X2 ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1139,zip_derived_cl72]) ).
thf(fc1_subset_1,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ) ).
thf(zip_derived_cl43,plain,
! [X0: $i] :
~ ( empty @ ( powerset @ X0 ) ),
inference(cnf,[status(esa)],[fc1_subset_1]) ).
thf(zip_derived_cl43_011,plain,
! [X0: $i] :
~ ( empty @ ( powerset @ X0 ) ),
inference(cnf,[status(esa)],[fc1_subset_1]) ).
thf(zip_derived_cl952_012,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl26_013,plain,
! [X0: $i] :
( ( join_semilatt_str @ X0 )
| ~ ( latt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_l3_lattices]) ).
thf(zip_derived_cl32,plain,
! [X0: $i] :
( ( quasi_total @ ( the_L_join @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) )
| ~ ( join_semilatt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_u2_lattices]) ).
thf(zip_derived_cl493,plain,
! [X0: $i] :
( ~ ( latt_str @ X0 )
| ( quasi_total @ ( the_L_join @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl26,zip_derived_cl32]) ).
thf(zip_derived_cl1006,plain,
! [X0: $i] :
( ( quasi_total @ ( the_L_join @ ( boole_lattice @ X0 ) ) @ ( cartesian_product2 @ ( the_carrier @ ( boole_lattice @ X0 ) ) @ ( the_carrier @ ( boole_lattice @ X0 ) ) ) @ ( powerset @ X0 ) )
| ~ ( latt_str @ ( boole_lattice @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl952,zip_derived_cl493]) ).
thf(zip_derived_cl952_014,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_015,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl17_016,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl1009,plain,
! [X0: $i] : ( quasi_total @ ( the_L_join @ ( boole_lattice @ X0 ) ) @ ( cartesian_product2 @ ( powerset @ X0 ) @ ( powerset @ X0 ) ) @ ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1006,zip_derived_cl952,zip_derived_cl952,zip_derived_cl17]) ).
thf(zip_derived_cl952_017,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl26_018,plain,
! [X0: $i] :
( ( join_semilatt_str @ X0 )
| ~ ( latt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_l3_lattices]) ).
thf(zip_derived_cl33,plain,
! [X0: $i] :
( ( relation_of2_as_subset @ ( the_L_join @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) )
| ~ ( join_semilatt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_u2_lattices]) ).
thf(redefinition_m2_relset_1,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) ).
thf(zip_derived_cl75,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_of2 @ X0 @ X1 @ X2 )
| ~ ( relation_of2_as_subset @ X0 @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[redefinition_m2_relset_1]) ).
thf(zip_derived_cl475,plain,
! [X0: $i] :
( ~ ( join_semilatt_str @ X0 )
| ( relation_of2 @ ( the_L_join @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl33,zip_derived_cl75]) ).
thf(zip_derived_cl494,plain,
! [X0: $i] :
( ~ ( latt_str @ X0 )
| ( relation_of2 @ ( the_L_join @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl26,zip_derived_cl475]) ).
thf(zip_derived_cl1014,plain,
! [X0: $i] :
( ( relation_of2 @ ( the_L_join @ ( boole_lattice @ X0 ) ) @ ( cartesian_product2 @ ( the_carrier @ ( boole_lattice @ X0 ) ) @ ( the_carrier @ ( boole_lattice @ X0 ) ) ) @ ( powerset @ X0 ) )
| ~ ( latt_str @ ( boole_lattice @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl952,zip_derived_cl494]) ).
thf(zip_derived_cl952_019,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_020,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl17_021,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl1017,plain,
! [X0: $i] : ( relation_of2 @ ( the_L_join @ ( boole_lattice @ X0 ) ) @ ( cartesian_product2 @ ( powerset @ X0 ) @ ( powerset @ X0 ) ) @ ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1014,zip_derived_cl952,zip_derived_cl952,zip_derived_cl17]) ).
thf(zip_derived_cl3746,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( boole_lattice @ X2 ) @ X1 @ X0 )
= ( apply_binary @ ( the_L_join @ ( boole_lattice @ X2 ) ) @ X1 @ X0 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ X2 ) ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3743,zip_derived_cl43,zip_derived_cl43,zip_derived_cl1009,zip_derived_cl1017]) ).
thf(zip_derived_cl3747,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( function @ ( the_L_join @ ( boole_lattice @ X2 ) ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ( ( join @ ( boole_lattice @ X2 ) @ X1 @ X0 )
= ( apply_binary @ ( the_L_join @ ( boole_lattice @ X2 ) ) @ X1 @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3746]) ).
thf(zip_derived_cl952_022,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl25_023,plain,
! [X0: $i] :
( ( meet_semilatt_str @ X0 )
| ~ ( latt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_l3_lattices]) ).
thf(d2_lattices,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 ) ) ) ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ( ( meet @ X1 @ X0 @ X2 )
= ( apply_binary_as_element @ ( the_carrier @ X1 ) @ ( the_carrier @ X1 ) @ ( the_carrier @ X1 ) @ ( the_L_meet @ X1 ) @ X0 @ X2 ) )
| ~ ( element @ X2 @ ( the_carrier @ X1 ) )
| ~ ( meet_semilatt_str @ X1 )
| ( empty_carrier @ X1 ) ),
inference(cnf,[status(esa)],[d2_lattices]) ).
thf(zip_derived_cl506,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( latt_str @ X0 )
| ( empty_carrier @ X0 )
| ~ ( element @ X2 @ ( the_carrier @ X0 ) )
| ( ( meet @ X0 @ X1 @ X2 )
= ( apply_binary_as_element @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) @ ( the_L_meet @ X0 ) @ X1 @ X2 ) )
| ~ ( element @ X1 @ ( the_carrier @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl25,zip_derived_cl13]) ).
thf(zip_derived_cl1163,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( meet @ ( boole_lattice @ X0 ) @ X2 @ X1 )
= ( apply_binary_as_element @ ( the_carrier @ ( boole_lattice @ X0 ) ) @ ( the_carrier @ ( boole_lattice @ X0 ) ) @ ( powerset @ X0 ) @ ( the_L_meet @ ( boole_lattice @ X0 ) ) @ X2 @ X1 ) )
| ~ ( element @ X2 @ ( the_carrier @ ( boole_lattice @ X0 ) ) )
| ~ ( element @ X1 @ ( the_carrier @ ( boole_lattice @ X0 ) ) )
| ( empty_carrier @ ( boole_lattice @ X0 ) )
| ~ ( latt_str @ ( boole_lattice @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl952,zip_derived_cl506]) ).
thf(zip_derived_cl952_024,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_025,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_026,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_027,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl40_028,plain,
! [X0: $i] :
~ ( empty_carrier @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[fc1_lattice3]) ).
thf(zip_derived_cl17_029,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl1166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( meet @ ( boole_lattice @ X0 ) @ X2 @ X1 )
= ( apply_binary_as_element @ ( powerset @ X0 ) @ ( powerset @ X0 ) @ ( powerset @ X0 ) @ ( the_L_meet @ ( boole_lattice @ X0 ) ) @ X2 @ X1 ) )
| ~ ( element @ X2 @ ( powerset @ X0 ) )
| ~ ( element @ X1 @ ( powerset @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1163,zip_derived_cl952,zip_derived_cl952,zip_derived_cl952,zip_derived_cl952,zip_derived_cl40,zip_derived_cl17]) ).
thf(zip_derived_cl72_030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( element @ X0 @ X1 )
| ~ ( relation_of2 @ X2 @ ( cartesian_product2 @ X1 @ X3 ) @ X4 )
| ~ ( quasi_total @ X2 @ ( cartesian_product2 @ X1 @ X3 ) @ X4 )
| ~ ( function @ X2 )
| ( empty @ X3 )
| ( empty @ X1 )
| ~ ( element @ X5 @ X3 )
| ( ( apply_binary_as_element @ X1 @ X3 @ X4 @ X2 @ X0 @ X5 )
= ( apply_binary @ X2 @ X0 @ X5 ) ) ),
inference(cnf,[status(esa)],[redefinition_k2_binop_1]) ).
thf(zip_derived_cl3907,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( meet @ ( boole_lattice @ X2 ) @ X1 @ X0 )
= ( apply_binary @ ( the_L_meet @ ( boole_lattice @ X2 ) ) @ X1 @ X0 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ( empty @ ( powerset @ X2 ) )
| ( empty @ ( powerset @ X2 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ X2 ) ) )
| ~ ( quasi_total @ ( the_L_meet @ ( boole_lattice @ X2 ) ) @ ( cartesian_product2 @ ( powerset @ X2 ) @ ( powerset @ X2 ) ) @ ( powerset @ X2 ) )
| ~ ( relation_of2 @ ( the_L_meet @ ( boole_lattice @ X2 ) ) @ ( cartesian_product2 @ ( powerset @ X2 ) @ ( powerset @ X2 ) ) @ ( powerset @ X2 ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1166,zip_derived_cl72]) ).
thf(zip_derived_cl43_031,plain,
! [X0: $i] :
~ ( empty @ ( powerset @ X0 ) ),
inference(cnf,[status(esa)],[fc1_subset_1]) ).
thf(zip_derived_cl43_032,plain,
! [X0: $i] :
~ ( empty @ ( powerset @ X0 ) ),
inference(cnf,[status(esa)],[fc1_subset_1]) ).
thf(zip_derived_cl952_033,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl25_034,plain,
! [X0: $i] :
( ( meet_semilatt_str @ X0 )
| ~ ( latt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_l3_lattices]) ).
thf(zip_derived_cl29,plain,
! [X0: $i] :
( ( quasi_total @ ( the_L_meet @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) )
| ~ ( meet_semilatt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_u1_lattices]) ).
thf(zip_derived_cl509,plain,
! [X0: $i] :
( ~ ( latt_str @ X0 )
| ( quasi_total @ ( the_L_meet @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl25,zip_derived_cl29]) ).
thf(zip_derived_cl1032,plain,
! [X0: $i] :
( ( quasi_total @ ( the_L_meet @ ( boole_lattice @ X0 ) ) @ ( cartesian_product2 @ ( the_carrier @ ( boole_lattice @ X0 ) ) @ ( the_carrier @ ( boole_lattice @ X0 ) ) ) @ ( powerset @ X0 ) )
| ~ ( latt_str @ ( boole_lattice @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl952,zip_derived_cl509]) ).
thf(zip_derived_cl952_035,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_036,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl17_037,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl1035,plain,
! [X0: $i] : ( quasi_total @ ( the_L_meet @ ( boole_lattice @ X0 ) ) @ ( cartesian_product2 @ ( powerset @ X0 ) @ ( powerset @ X0 ) ) @ ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1032,zip_derived_cl952,zip_derived_cl952,zip_derived_cl17]) ).
thf(zip_derived_cl952_038,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl25_039,plain,
! [X0: $i] :
( ( meet_semilatt_str @ X0 )
| ~ ( latt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_l3_lattices]) ).
thf(zip_derived_cl30,plain,
! [X0: $i] :
( ( relation_of2_as_subset @ ( the_L_meet @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) )
| ~ ( meet_semilatt_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_u1_lattices]) ).
thf(zip_derived_cl75_040,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_of2 @ X0 @ X1 @ X2 )
| ~ ( relation_of2_as_subset @ X0 @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[redefinition_m2_relset_1]) ).
thf(zip_derived_cl474,plain,
! [X0: $i] :
( ~ ( meet_semilatt_str @ X0 )
| ( relation_of2 @ ( the_L_meet @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl30,zip_derived_cl75]) ).
thf(zip_derived_cl510,plain,
! [X0: $i] :
( ~ ( latt_str @ X0 )
| ( relation_of2 @ ( the_L_meet @ X0 ) @ ( cartesian_product2 @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) ) @ ( the_carrier @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl25,zip_derived_cl474]) ).
thf(zip_derived_cl1041,plain,
! [X0: $i] :
( ( relation_of2 @ ( the_L_meet @ ( boole_lattice @ X0 ) ) @ ( cartesian_product2 @ ( the_carrier @ ( boole_lattice @ X0 ) ) @ ( the_carrier @ ( boole_lattice @ X0 ) ) ) @ ( powerset @ X0 ) )
| ~ ( latt_str @ ( boole_lattice @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl952,zip_derived_cl510]) ).
thf(zip_derived_cl952_041,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl952_042,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl17_043,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl1044,plain,
! [X0: $i] : ( relation_of2 @ ( the_L_meet @ ( boole_lattice @ X0 ) ) @ ( cartesian_product2 @ ( powerset @ X0 ) @ ( powerset @ X0 ) ) @ ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1041,zip_derived_cl952,zip_derived_cl952,zip_derived_cl17]) ).
thf(zip_derived_cl3910,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( meet @ ( boole_lattice @ X2 ) @ X1 @ X0 )
= ( apply_binary @ ( the_L_meet @ ( boole_lattice @ X2 ) ) @ X1 @ X0 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ X2 ) ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3907,zip_derived_cl43,zip_derived_cl43,zip_derived_cl1035,zip_derived_cl1044]) ).
thf(zip_derived_cl3911,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( function @ ( the_L_meet @ ( boole_lattice @ X2 ) ) )
| ~ ( element @ X1 @ ( powerset @ X2 ) )
| ~ ( element @ X0 @ ( powerset @ X2 ) )
| ( ( meet @ ( boole_lattice @ X2 ) @ X1 @ X0 )
= ( apply_binary @ ( the_L_meet @ ( boole_lattice @ X2 ) ) @ X1 @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3910]) ).
thf(t1_lattice3,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 ) ) ) ) ) ).
thf(zf_stmt_0,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('cnf.neg',[status(esa)],[t1_lattice3]) ).
thf(zip_derived_cl84,plain,
( ( ( join @ ( boole_lattice @ sk__16 ) @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) )
| ( ( meet @ ( boole_lattice @ sk__16 ) @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3915,plain,
( ( ( apply_binary @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) )
| ~ ( element @ sk__18 @ ( powerset @ sk__16 ) )
| ~ ( element @ sk__17 @ ( powerset @ sk__16 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ( ( join @ ( boole_lattice @ sk__16 ) @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3911,zip_derived_cl84]) ).
thf(zip_derived_cl85,plain,
element @ sk__18 @ ( the_carrier @ ( boole_lattice @ sk__16 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl952_044,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl954,plain,
element @ sk__18 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl85,zip_derived_cl952]) ).
thf(zip_derived_cl83,plain,
element @ sk__17 @ ( the_carrier @ ( boole_lattice @ sk__16 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl952_045,plain,
! [X0: $i] :
( ( the_carrier @ ( boole_lattice @ X0 ) )
= ( powerset @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl951,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl953,plain,
element @ sk__17 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl83,zip_derived_cl952]) ).
thf(zip_derived_cl3919,plain,
( ( ( apply_binary @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ( ( join @ ( boole_lattice @ sk__16 ) @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3915,zip_derived_cl954,zip_derived_cl953]) ).
thf(zip_derived_cl3920,plain,
( ( ( apply_binary @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) )
| ~ ( element @ sk__18 @ ( powerset @ sk__16 ) )
| ~ ( element @ sk__17 @ ( powerset @ sk__16 ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ( ( apply_binary @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3747,zip_derived_cl3919]) ).
thf(zip_derived_cl954_046,plain,
element @ sk__18 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl85,zip_derived_cl952]) ).
thf(zip_derived_cl953_047,plain,
element @ sk__17 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl83,zip_derived_cl952]) ).
thf(zip_derived_cl3921,plain,
( ( ( apply_binary @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ( ( apply_binary @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3920,zip_derived_cl954,zip_derived_cl953]) ).
thf(zip_derived_cl3922,plain,
( ( ( subset_intersection2 @ sk__16 @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) )
| ~ ( element @ sk__18 @ ( powerset @ sk__16 ) )
| ~ ( element @ sk__17 @ ( powerset @ sk__16 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ( ( apply_binary @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl977,zip_derived_cl3921]) ).
thf(zip_derived_cl954_048,plain,
element @ sk__18 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl85,zip_derived_cl952]) ).
thf(zip_derived_cl953_049,plain,
element @ sk__17 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl83,zip_derived_cl952]) ).
thf(zip_derived_cl3923,plain,
( ( ( subset_intersection2 @ sk__16 @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ( ( apply_binary @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3922,zip_derived_cl954,zip_derived_cl953]) ).
thf(zip_derived_cl3924,plain,
( ( ( subset_union2 @ sk__16 @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) )
| ~ ( element @ sk__18 @ ( powerset @ sk__16 ) )
| ~ ( element @ sk__17 @ ( powerset @ sk__16 ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ( ( subset_intersection2 @ sk__16 @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl989,zip_derived_cl3923]) ).
thf(zip_derived_cl954_050,plain,
element @ sk__18 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl85,zip_derived_cl952]) ).
thf(zip_derived_cl953_051,plain,
element @ sk__17 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl83,zip_derived_cl952]) ).
thf(zip_derived_cl3925,plain,
( ( ( subset_union2 @ sk__16 @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ( ( subset_intersection2 @ sk__16 @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3924,zip_derived_cl954,zip_derived_cl953]) ).
thf(zip_derived_cl3926,plain,
( ( ( set_intersection2 @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) )
| ~ ( element @ sk__18 @ ( powerset @ sk__16 ) )
| ~ ( element @ sk__17 @ ( powerset @ sk__16 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ( ( subset_union2 @ sk__16 @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl3925]) ).
thf(zip_derived_cl954_052,plain,
element @ sk__18 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl85,zip_derived_cl952]) ).
thf(zip_derived_cl953_053,plain,
element @ sk__17 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl83,zip_derived_cl952]) ).
thf(zip_derived_cl3928,plain,
( ( ( set_intersection2 @ sk__17 @ sk__18 )
!= ( set_intersection2 @ sk__17 @ sk__18 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ( ( subset_union2 @ sk__16 @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3926,zip_derived_cl954,zip_derived_cl953]) ).
thf(zip_derived_cl3929,plain,
( ( ( subset_union2 @ sk__16 @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3928]) ).
thf(zip_derived_cl3932,plain,
( ( ( set_union2 @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) )
| ~ ( element @ sk__18 @ ( powerset @ sk__16 ) )
| ~ ( element @ sk__17 @ ( powerset @ sk__16 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl3929]) ).
thf(zip_derived_cl954_054,plain,
element @ sk__18 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl85,zip_derived_cl952]) ).
thf(zip_derived_cl953_055,plain,
element @ sk__17 @ ( powerset @ sk__16 ),
inference(demod,[status(thm)],[zip_derived_cl83,zip_derived_cl952]) ).
thf(zip_derived_cl3934,plain,
( ( ( set_union2 @ sk__17 @ sk__18 )
!= ( set_union2 @ sk__17 @ sk__18 ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3932,zip_derived_cl954,zip_derived_cl953]) ).
thf(zip_derived_cl3935,plain,
( ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) )
| ~ ( function @ ( the_L_meet @ ( boole_lattice @ sk__16 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3934]) ).
thf(zip_derived_cl3939,plain,
( ~ ( latt_str @ ( boole_lattice @ sk__16 ) )
| ~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl508,zip_derived_cl3935]) ).
thf(zip_derived_cl17_056,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl3940,plain,
~ ( function @ ( the_L_join @ ( boole_lattice @ sk__16 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3939,zip_derived_cl17]) ).
thf(zip_derived_cl3943,plain,
~ ( latt_str @ ( boole_lattice @ sk__16 ) ),
inference('sup-',[status(thm)],[zip_derived_cl492,zip_derived_cl3940]) ).
thf(zip_derived_cl17_057,plain,
! [X0: $i] : ( latt_str @ ( boole_lattice @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_lattice3]) ).
thf(zip_derived_cl3944,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl3943,zip_derived_cl17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qYntCEEnQM true
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 20:52:39 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.35 % Running portfolio for 300 s
% 0.21/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.36 % Number of cores: 8
% 0.21/0.36 % Python version: Python 3.6.8
% 0.21/0.36 % Running in FO mode
% 0.21/0.63 % Total configuration time : 435
% 0.21/0.63 % Estimated wc time : 1092
% 0.21/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.36/1.37 % Solved by fo/fo3_bce.sh.
% 1.36/1.37 % BCE start: 86
% 1.36/1.37 % BCE eliminated: 3
% 1.36/1.37 % PE start: 83
% 1.36/1.37 logic: eq
% 1.36/1.37 % PE eliminated: -15
% 1.36/1.37 % done 653 iterations in 0.605s
% 1.36/1.37 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.36/1.37 % SZS output start Refutation
% See solution above
% 1.36/1.37
% 1.36/1.37
% 1.36/1.37 % Terminating...
% 1.36/1.48 % Runner terminated.
% 1.36/1.49 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------