%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL043+2 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.e0yeLkxMJL true
% Computer : n023.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 Oct 2 04:50:08 PM UTC 2025
% Result : Theorem 88.34s 13.29s
% Output : Refutation 88.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 280 ( 278 unt; 0 typ; 0 def)
% Number of atoms : 282 ( 281 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 1588 ( 3 ~; 0 |; 0 &;1583 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 365 ( 0 ^; 365 !; 0 ?; 365 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk__1_type,type,
sk__1: $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(sk__type,type,
sk_: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(top_type,type,
top: $i ).
thf(zero_type,type,
zero: $i ).
thf(composition_type,type,
composition: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(one_type,type,
one: $i ).
thf(maddux1_join_commutativity,axiom,
! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(maddux4_definiton_of_meet,axiom,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) ).
thf(zip_derived_cl3,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl158,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl3]) ).
thf(zip_derived_cl3_001,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl10777,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl158,zip_derived_cl3]) ).
thf(goals,conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( composition @ X0 @ ( converse @ X1 ) ) @ X2 )
= X2 )
=> ( ( join @ ( composition @ ( complement @ X2 ) @ X1 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( composition @ X0 @ ( converse @ X1 ) ) @ X2 )
= X2 )
=> ( ( join @ ( composition @ ( complement @ X2 ) @ X1 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ) ),
inference('cnf.neg',[status(esa)],[goals]) ).
thf(zip_derived_cl16,plain,
( ( join @ ( composition @ sk_ @ ( converse @ sk__1 ) ) @ sk__2 )
= sk__2 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(maddux3_a_kind_of_de_Morgan,axiom,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) ).
thf(zip_derived_cl2,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux3_a_kind_of_de_Morgan]) ).
thf(zip_derived_cl3_002,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl237,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(composition_identity,axiom,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ) ).
thf(zip_derived_cl5,plain,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[composition_identity]) ).
thf(converse_idempotence,axiom,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) ).
thf(zip_derived_cl7,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(converse_multiplicativity,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) ).
thf(zip_derived_cl9,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl40,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ ( converse @ X0 ) @ X1 ) )
= ( composition @ ( converse @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
thf(zip_derived_cl132,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl40]) ).
thf(zip_derived_cl7_003,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl138,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl132,zip_derived_cl7]) ).
thf(zip_derived_cl138_004,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl132,zip_derived_cl7]) ).
thf(zip_derived_cl5_005,plain,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[composition_identity]) ).
thf(zip_derived_cl140,plain,
( one
= ( converse @ one ) ),
inference('sup+',[status(thm)],[zip_derived_cl138,zip_derived_cl5]) ).
thf(zip_derived_cl210,plain,
! [X0: $i] :
( X0
= ( composition @ one @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl138,zip_derived_cl140]) ).
thf(converse_cancellativity,axiom,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X1 ) @ ( complement @ ( composition @ X1 @ X0 ) ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(cnf,[status(esa)],[converse_cancellativity]) ).
thf(zip_derived_cl278,plain,
! [X0: $i] :
( ( join @ ( composition @ ( converse @ one ) @ ( complement @ X0 ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl210,zip_derived_cl10]) ).
thf(zip_derived_cl140_006,plain,
( one
= ( converse @ one ) ),
inference('sup+',[status(thm)],[zip_derived_cl138,zip_derived_cl5]) ).
thf(zip_derived_cl210_007,plain,
! [X0: $i] :
( X0
= ( composition @ one @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl138,zip_derived_cl140]) ).
thf(zip_derived_cl279,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl278,zip_derived_cl140,zip_derived_cl210]) ).
thf(zip_derived_cl3_008,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl286,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl279,zip_derived_cl3]) ).
thf(def_zero,axiom,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ) ).
thf(zip_derived_cl12,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl237_009,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl246,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl12,zip_derived_cl237]) ).
thf(zip_derived_cl3_010,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl248,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl246,zip_derived_cl3]) ).
thf(zip_derived_cl0_011,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl404,plain,
! [X0: $i] :
( ( join @ ( meet @ X0 @ X0 ) @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl248,zip_derived_cl0]) ).
thf(zip_derived_cl575,plain,
! [X0: $i] :
( ( join @ ( complement @ ( complement @ X0 ) ) @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl286,zip_derived_cl404]) ).
thf(def_top,axiom,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl3_012,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl160,plain,
! [X0: $i] :
( ( meet @ X0 @ ( complement @ X0 ) )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl3]) ).
thf(zip_derived_cl12_013,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl163,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl12]) ).
thf(zip_derived_cl3_014,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl232,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ ( complement @ X0 ) @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl163,zip_derived_cl3]) ).
thf(zip_derived_cl3545,plain,
! [X0: $i] :
( ( meet @ ( complement @ X0 ) @ top )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl575,zip_derived_cl232]) ).
thf(zip_derived_cl237_015,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl3567,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( join @ ( complement @ X0 ) @ ( complement @ ( join @ ( complement @ ( complement @ X0 ) ) @ top ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3545,zip_derived_cl237]) ).
thf(zip_derived_cl279_016,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl278,zip_derived_cl140,zip_derived_cl210]) ).
thf(zip_derived_cl11_017,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(maddux2_join_associativity,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) ).
thf(zip_derived_cl1,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl30,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ X0 @ ( complement @ ( join @ X1 @ X0 ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).
thf(zip_derived_cl1330,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( join @ ( complement @ X0 ) @ ( complement @ ( complement @ X0 ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl279,zip_derived_cl30]) ).
thf(zip_derived_cl11_018,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl1380,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1330,zip_derived_cl11]) ).
thf(zip_derived_cl0_019,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1454,plain,
! [X0: $i] :
( ( join @ top @ ( complement @ X0 ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1380,zip_derived_cl0]) ).
thf(zip_derived_cl30_020,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ X0 @ ( complement @ ( join @ X1 @ X0 ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).
thf(zip_derived_cl1473,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1454,zip_derived_cl30]) ).
thf(zip_derived_cl163_021,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl12]) ).
thf(zip_derived_cl3581,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( join @ ( complement @ X0 ) @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl3567,zip_derived_cl1473,zip_derived_cl163]) ).
thf(zip_derived_cl575_022,plain,
! [X0: $i] :
( ( join @ ( complement @ ( complement @ X0 ) ) @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl286,zip_derived_cl404]) ).
thf(zip_derived_cl3805,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl279_023,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl278,zip_derived_cl140,zip_derived_cl210]) ).
thf(zip_derived_cl3829,plain,
! [X0: $i] :
( ( join @ ( complement @ ( complement @ X0 ) ) @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3805,zip_derived_cl279]) ).
thf(zip_derived_cl3805_024,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl3805_025,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl3852,plain,
! [X0: $i] :
( ( join @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl3829,zip_derived_cl3805,zip_derived_cl3805]) ).
thf(zip_derived_cl1_026,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl0_027,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl27,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X2 @ X1 ) )
= ( join @ X2 @ ( join @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl3863,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( join @ X1 @ X0 ) )
= ( join @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3852,zip_derived_cl27]) ).
thf(zip_derived_cl5760,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) @ X0 )
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl237,zip_derived_cl3863]) ).
thf(zip_derived_cl0_028,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl237_029,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl5816,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl5760,zip_derived_cl0,zip_derived_cl237]) ).
thf(zip_derived_cl3863_030,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( join @ X1 @ X0 ) )
= ( join @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3852,zip_derived_cl27]) ).
thf(zip_derived_cl5972,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) @ X0 )
= ( join @ X0 @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5816,zip_derived_cl3863]) ).
thf(zip_derived_cl5816_031,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl5760,zip_derived_cl0,zip_derived_cl237]) ).
thf(zip_derived_cl6052,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl5972,zip_derived_cl5816]) ).
thf(zip_derived_cl3_032,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl6692,plain,
! [X0: $i,X1: $i] :
( ( meet @ ( join @ ( complement @ ( complement @ X0 ) ) @ X1 ) @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6052,zip_derived_cl3]) ).
thf(zip_derived_cl3805_033,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl3805_034,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl6774,plain,
! [X0: $i,X1: $i] :
( ( meet @ ( join @ X0 @ X1 ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl6692,zip_derived_cl3805,zip_derived_cl3805]) ).
thf(zip_derived_cl8479,plain,
( ( meet @ sk__2 @ ( composition @ sk_ @ ( converse @ sk__1 ) ) )
= ( composition @ sk_ @ ( converse @ sk__1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl16,zip_derived_cl6774]) ).
thf(zip_derived_cl3805_035,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl237_036,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl11_037,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl0_038,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1_039,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl31,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X1 @ X0 ) @ X2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1]) ).
thf(zip_derived_cl1628,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl31]) ).
thf(zip_derived_cl0_040,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl11_041,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl16_042,plain,
( ( join @ ( composition @ sk_ @ ( converse @ sk__1 ) ) @ sk__2 )
= sk__2 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_043,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl35,plain,
! [X0: $i] :
( ( join @ ( composition @ sk_ @ ( converse @ sk__1 ) ) @ ( join @ sk__2 @ X0 ) )
= ( join @ sk__2 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl16,zip_derived_cl1]) ).
thf(zip_derived_cl199,plain,
( ( join @ ( composition @ sk_ @ ( converse @ sk__1 ) ) @ top )
= ( join @ sk__2 @ ( complement @ sk__2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl35]) ).
thf(zip_derived_cl11_044,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl202,plain,
( ( join @ ( composition @ sk_ @ ( converse @ sk__1 ) ) @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl199,zip_derived_cl11]) ).
thf(zip_derived_cl1_045,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl207,plain,
! [X0: $i] :
( ( join @ ( composition @ sk_ @ ( converse @ sk__1 ) ) @ ( join @ top @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl202,zip_derived_cl1]) ).
thf(zip_derived_cl457,plain,
! [X0: $i] :
( ( join @ ( composition @ sk_ @ ( converse @ sk__1 ) ) @ ( join @ X0 @ top ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl207]) ).
thf(zip_derived_cl1473_046,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1454,zip_derived_cl30]) ).
thf(zip_derived_cl1473_047,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1454,zip_derived_cl30]) ).
thf(zip_derived_cl1570,plain,
! [X0: $i] :
( top
= ( join @ top @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl457,zip_derived_cl1473,zip_derived_cl1473]) ).
thf(zip_derived_cl1663,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1628,zip_derived_cl1570]) ).
thf(zip_derived_cl1750,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( meet @ X0 @ X1 ) ) @ X0 )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl237,zip_derived_cl1663]) ).
thf(zip_derived_cl3_048,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl3268,plain,
! [X0: $i,X1: $i] :
( ( meet @ ( meet @ ( complement @ X0 ) @ X1 ) @ X0 )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1750,zip_derived_cl3]) ).
thf(zip_derived_cl163_049,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl12]) ).
thf(zip_derived_cl3296,plain,
! [X0: $i,X1: $i] :
( ( meet @ ( meet @ ( complement @ X0 ) @ X1 ) @ X0 )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl3268,zip_derived_cl163]) ).
thf(zip_derived_cl5283,plain,
! [X0: $i,X1: $i] :
( ( meet @ ( meet @ X0 @ X1 ) @ ( complement @ X0 ) )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl3805,zip_derived_cl3296]) ).
thf(zip_derived_cl8885,plain,
( ( meet @ ( composition @ sk_ @ ( converse @ sk__1 ) ) @ ( complement @ sk__2 ) )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl8479,zip_derived_cl5283]) ).
thf(zip_derived_cl10911,plain,
( ( meet @ ( complement @ sk__2 ) @ ( composition @ sk_ @ ( converse @ sk__1 ) ) )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl10777,zip_derived_cl8885]) ).
thf(zip_derived_cl7_050,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(dedekind_law,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) )
= ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X2 ) @ X1 ) @ ( composition @ ( meet @ X0 @ ( composition @ X1 @ ( converse @ X2 ) ) ) @ ( meet @ X2 @ ( composition @ ( converse @ X0 ) @ X1 ) ) ) )
= ( composition @ ( meet @ X0 @ ( composition @ X1 @ ( converse @ X2 ) ) ) @ ( meet @ X2 @ ( composition @ ( converse @ X0 ) @ X1 ) ) ) ),
inference(cnf,[status(esa)],[dedekind_law]) ).
thf(zip_derived_cl355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X2 @ ( converse @ X0 ) ) @ X1 ) @ ( composition @ ( meet @ X2 @ ( composition @ X1 @ X0 ) ) @ ( meet @ ( converse @ X0 ) @ ( composition @ ( converse @ X2 ) @ X1 ) ) ) )
= ( composition @ ( meet @ X2 @ ( composition @ X1 @ ( converse @ ( converse @ X0 ) ) ) ) @ ( meet @ ( converse @ X0 ) @ ( composition @ ( converse @ X2 ) @ X1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl13]) ).
thf(zip_derived_cl7_051,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl377,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X2 @ ( converse @ X0 ) ) @ X1 ) @ ( composition @ ( meet @ X2 @ ( composition @ X1 @ X0 ) ) @ ( meet @ ( converse @ X0 ) @ ( composition @ ( converse @ X2 ) @ X1 ) ) ) )
= ( composition @ ( meet @ X2 @ ( composition @ X1 @ X0 ) ) @ ( meet @ ( converse @ X0 ) @ ( composition @ ( converse @ X2 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl355,zip_derived_cl7]) ).
thf(zip_derived_cl36553,plain,
( ( join @ ( meet @ ( composition @ ( complement @ sk__2 ) @ ( converse @ ( converse @ sk__1 ) ) ) @ sk_ ) @ ( composition @ zero @ ( meet @ ( converse @ ( converse @ sk__1 ) ) @ ( composition @ ( converse @ ( complement @ sk__2 ) ) @ sk_ ) ) ) )
= ( composition @ ( meet @ ( complement @ sk__2 ) @ ( composition @ sk_ @ ( converse @ sk__1 ) ) ) @ ( meet @ ( converse @ ( converse @ sk__1 ) ) @ ( composition @ ( converse @ ( complement @ sk__2 ) ) @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10911,zip_derived_cl377]) ).
thf(zip_derived_cl7_052,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl10777_053,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl158,zip_derived_cl3]) ).
thf(zip_derived_cl7_054,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl3805_055,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl11_056,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl7_057,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(converse_additivity,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_additivity]) ).
thf(zip_derived_cl0_058,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl23,plain,
! [X0: $i,X1: $i] :
( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ ( join @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8,zip_derived_cl0]) ).
thf(zip_derived_cl46,plain,
! [X0: $i,X1: $i] :
( ( join @ ( converse @ X1 ) @ X0 )
= ( converse @ ( join @ ( converse @ X0 ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl23]) ).
thf(zip_derived_cl880,plain,
! [X0: $i] :
( ( join @ ( converse @ ( complement @ ( converse @ X0 ) ) ) @ X0 )
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl46]) ).
thf(zip_derived_cl1473_059,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1454,zip_derived_cl30]) ).
thf(zip_derived_cl880_060,plain,
! [X0: $i] :
( ( join @ ( converse @ ( complement @ ( converse @ X0 ) ) ) @ X0 )
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl46]) ).
thf(zip_derived_cl1497,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1473,zip_derived_cl880]) ).
thf(zip_derived_cl1522,plain,
! [X0: $i] :
( ( join @ ( converse @ ( complement @ ( converse @ X0 ) ) ) @ X0 )
= top ),
inference(demod,[status(thm)],[zip_derived_cl880,zip_derived_cl1497]) ).
thf(zip_derived_cl0_061,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl237_062,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl240,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl237]) ).
thf(zip_derived_cl19052,plain,
! [X0: $i] :
( X0
= ( join @ ( meet @ X0 @ ( converse @ ( complement @ ( converse @ ( complement @ X0 ) ) ) ) ) @ ( complement @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl240]) ).
thf(zip_derived_cl163_063,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl12]) ).
thf(zip_derived_cl575_064,plain,
! [X0: $i] :
( ( join @ ( complement @ ( complement @ X0 ) ) @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl286,zip_derived_cl404]) ).
thf(zip_derived_cl3805_065,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl3822,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl575,zip_derived_cl3805]) ).
thf(zip_derived_cl19137,plain,
! [X0: $i] :
( X0
= ( meet @ X0 @ ( converse @ ( complement @ ( converse @ ( complement @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl19052,zip_derived_cl163,zip_derived_cl3822]) ).
thf(zip_derived_cl19341,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( meet @ ( complement @ X0 ) @ ( converse @ ( complement @ ( converse @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3805,zip_derived_cl19137]) ).
thf(zip_derived_cl3_066,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl237_067,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl244,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( complement @ X1 ) @ ( complement @ X0 ) )
= ( join @ ( meet @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) @ X2 ) @ ( complement @ ( join @ ( meet @ X1 @ X0 ) @ X2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl237]) ).
thf(zip_derived_cl3_068,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl3_069,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl153,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( meet @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) @ X2 )
= ( complement @ ( join @ ( meet @ X1 @ X0 ) @ ( complement @ X2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl3]) ).
thf(zip_derived_cl0_070,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl19689,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( complement @ X1 ) @ ( complement @ X0 ) )
= ( join @ ( complement @ ( join @ ( meet @ X1 @ X0 ) @ X2 ) ) @ ( complement @ ( join @ ( meet @ X1 @ X0 ) @ ( complement @ X2 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl244,zip_derived_cl153,zip_derived_cl0]) ).
thf(zip_derived_cl26874,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( complement @ X0 ) ) @ ( complement @ ( converse @ ( complement @ ( converse @ X0 ) ) ) ) )
= ( join @ ( complement @ ( join @ ( meet @ ( complement @ X0 ) @ ( converse @ ( complement @ ( converse @ X0 ) ) ) ) @ X1 ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl19341,zip_derived_cl19689]) ).
thf(zip_derived_cl3805_071,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl19341_072,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( meet @ ( complement @ X0 ) @ ( converse @ ( complement @ ( converse @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3805,zip_derived_cl19137]) ).
thf(zip_derived_cl3_073,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl0_074,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl237_075,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl26944,plain,
! [X0: $i] :
( ( join @ X0 @ ( complement @ ( converse @ ( complement @ ( converse @ X0 ) ) ) ) )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl26874,zip_derived_cl3805,zip_derived_cl19341,zip_derived_cl3,zip_derived_cl0,zip_derived_cl237]) ).
thf(zip_derived_cl7_076,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl8_077,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_additivity]) ).
thf(zip_derived_cl26,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ ( converse @ X0 ) @ X1 ) )
= ( join @ X0 @ ( converse @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl27764,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( join @ X0 @ ( converse @ ( complement @ ( converse @ ( complement @ ( converse @ ( converse @ X0 ) ) ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl26944,zip_derived_cl26]) ).
thf(zip_derived_cl7_078,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl7_079,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl27861,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ ( converse @ ( complement @ ( converse @ ( complement @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl27764,zip_derived_cl7,zip_derived_cl7]) ).
thf(zip_derived_cl0_080,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl5816_081,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl5760,zip_derived_cl0,zip_derived_cl237]) ).
thf(zip_derived_cl5997,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl5816]) ).
thf(zip_derived_cl3863_082,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( join @ X1 @ X0 ) )
= ( join @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3852,zip_derived_cl27]) ).
thf(zip_derived_cl6565,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) @ X0 )
= ( join @ X0 @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5997,zip_derived_cl3863]) ).
thf(zip_derived_cl5997_083,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl5816]) ).
thf(zip_derived_cl6636,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl6565,zip_derived_cl5997]) ).
thf(zip_derived_cl3_084,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl8074,plain,
! [X0: $i,X1: $i] :
( ( meet @ ( join @ X1 @ ( complement @ ( complement @ X0 ) ) ) @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6636,zip_derived_cl3]) ).
thf(zip_derived_cl3805_085,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl3805_086,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl8153,plain,
! [X0: $i,X1: $i] :
( ( meet @ ( join @ X1 @ X0 ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl8074,zip_derived_cl3805,zip_derived_cl3805]) ).
thf(zip_derived_cl28938,plain,
! [X0: $i] :
( ( meet @ X0 @ ( converse @ ( complement @ ( converse @ ( complement @ X0 ) ) ) ) )
= ( converse @ ( complement @ ( converse @ ( complement @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl27861,zip_derived_cl8153]) ).
thf(zip_derived_cl19137_087,plain,
! [X0: $i] :
( X0
= ( meet @ X0 @ ( converse @ ( complement @ ( converse @ ( complement @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl19052,zip_derived_cl163,zip_derived_cl3822]) ).
thf(zip_derived_cl29026,plain,
! [X0: $i] :
( X0
= ( converse @ ( complement @ ( converse @ ( complement @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl28938,zip_derived_cl19137]) ).
thf(zip_derived_cl7_088,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl29553,plain,
! [X0: $i] :
( ( converse @ X0 )
= ( complement @ ( converse @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl29026,zip_derived_cl7]) ).
thf(zip_derived_cl3805_089,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl29745,plain,
! [X0: $i] :
( ( complement @ ( converse @ X0 ) )
= ( converse @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl29553,zip_derived_cl3805]) ).
thf(zip_derived_cl279_090,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl278,zip_derived_cl140,zip_derived_cl210]) ).
thf(zip_derived_cl237_091,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl285,plain,
! [X0: $i] :
( X0
= ( join @ ( meet @ X0 @ ( complement @ X0 ) ) @ ( complement @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl279,zip_derived_cl237]) ).
thf(zip_derived_cl12_092,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl295,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl285,zip_derived_cl12]) ).
thf(zip_derived_cl3805_093,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl3821,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl295,zip_derived_cl3805]) ).
thf(zip_derived_cl11_094,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl26_095,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ ( converse @ X0 ) @ X1 ) )
= ( join @ X0 @ ( converse @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl80,plain,
! [X0: $i] :
( ( converse @ top )
= ( join @ X0 @ ( converse @ ( complement @ ( converse @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl26]) ).
thf(zip_derived_cl1497_096,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1473,zip_derived_cl880]) ).
thf(zip_derived_cl1513,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( converse @ ( complement @ ( converse @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl80,zip_derived_cl1497]) ).
thf(zip_derived_cl4024,plain,
( top
= ( converse @ ( complement @ ( converse @ zero ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3821,zip_derived_cl1513]) ).
thf(zip_derived_cl7_097,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl4064,plain,
( ( converse @ top )
= ( complement @ ( converse @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4024,zip_derived_cl7]) ).
thf(zip_derived_cl1497_098,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1473,zip_derived_cl880]) ).
thf(zip_derived_cl4100,plain,
( top
= ( complement @ ( converse @ zero ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4064,zip_derived_cl1497]) ).
thf(zip_derived_cl3805_099,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl4146,plain,
( ( complement @ top )
= ( converse @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl4100,zip_derived_cl3805]) ).
thf(zip_derived_cl163_100,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl12]) ).
thf(zip_derived_cl4160,plain,
( zero
= ( converse @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl4146,zip_derived_cl163]) ).
thf(zip_derived_cl40_101,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ ( converse @ X0 ) @ X1 ) )
= ( composition @ ( converse @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
thf(zip_derived_cl4175,plain,
! [X0: $i] :
( ( converse @ ( composition @ zero @ X0 ) )
= ( composition @ ( converse @ X0 ) @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl4160,zip_derived_cl40]) ).
thf(zip_derived_cl7_102,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl4961,plain,
! [X0: $i] :
( ( converse @ ( composition @ ( converse @ X0 ) @ zero ) )
= ( composition @ zero @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl4175,zip_derived_cl7]) ).
thf(zip_derived_cl1497_103,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1473,zip_derived_cl880]) ).
thf(zip_derived_cl1497_104,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1473,zip_derived_cl880]) ).
thf(zip_derived_cl9_105,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl1529,plain,
! [X0: $i] :
( ( converse @ ( composition @ X0 @ top ) )
= ( composition @ top @ ( converse @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1497,zip_derived_cl9]) ).
thf(zip_derived_cl7_106,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl2555,plain,
! [X0: $i] :
( ( converse @ ( composition @ top @ ( converse @ X0 ) ) )
= ( composition @ X0 @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1529,zip_derived_cl7]) ).
thf(zip_derived_cl8980,plain,
( ( converse @ ( composition @ top @ top ) )
= ( composition @ top @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1497,zip_derived_cl2555]) ).
thf(zip_derived_cl9_107,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl10_108,plain,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X1 ) @ ( complement @ ( composition @ X1 @ X0 ) ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(cnf,[status(esa)],[converse_cancellativity]) ).
thf(zip_derived_cl185,plain,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ ( converse @ X0 ) ) @ ( complement @ ( converse @ ( composition @ X1 @ X0 ) ) ) ) @ ( complement @ ( converse @ X1 ) ) )
= ( complement @ ( converse @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl10]) ).
thf(zip_derived_cl7_109,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl0_110,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl192,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( converse @ X1 ) ) @ ( composition @ X0 @ ( complement @ ( converse @ ( composition @ X1 @ X0 ) ) ) ) )
= ( complement @ ( converse @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl185,zip_derived_cl7,zip_derived_cl0]) ).
thf(zip_derived_cl16784,plain,
( ( join @ ( complement @ ( converse @ top ) ) @ ( composition @ top @ ( complement @ ( composition @ top @ top ) ) ) )
= ( complement @ ( converse @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8980,zip_derived_cl192]) ).
thf(zip_derived_cl1497_111,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1473,zip_derived_cl880]) ).
thf(zip_derived_cl163_112,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl12]) ).
thf(zip_derived_cl3821_113,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl295,zip_derived_cl3805]) ).
thf(zip_derived_cl1497_114,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1473,zip_derived_cl880]) ).
thf(zip_derived_cl163_115,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl12]) ).
thf(zip_derived_cl16856,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl16784,zip_derived_cl1497,zip_derived_cl163,zip_derived_cl3821,zip_derived_cl1497,zip_derived_cl163]) ).
thf(zip_derived_cl16856_116,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl16784,zip_derived_cl1497,zip_derived_cl163,zip_derived_cl3821,zip_derived_cl1497,zip_derived_cl163]) ).
thf(zip_derived_cl210_117,plain,
! [X0: $i] :
( X0
= ( composition @ one @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl138,zip_derived_cl140]) ).
thf(composition_distributivity,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) ).
thf(zip_derived_cl6,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X2 ) @ X1 )
= ( join @ ( composition @ X0 @ X1 ) @ ( composition @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[composition_distributivity]) ).
thf(zip_derived_cl276,plain,
! [X0: $i,X1: $i] :
( ( composition @ ( join @ one @ X1 ) @ X0 )
= ( join @ X0 @ ( composition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl210,zip_derived_cl6]) ).
thf(zip_derived_cl20624,plain,
( ( composition @ ( join @ one @ top ) @ ( complement @ ( composition @ top @ top ) ) )
= ( join @ ( complement @ ( composition @ top @ top ) ) @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl16856,zip_derived_cl276]) ).
thf(zip_derived_cl1473_118,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1454,zip_derived_cl30]) ).
thf(zip_derived_cl16856_119,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl16784,zip_derived_cl1497,zip_derived_cl163,zip_derived_cl3821,zip_derived_cl1497,zip_derived_cl163]) ).
thf(zip_derived_cl3822_120,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl575,zip_derived_cl3805]) ).
thf(zip_derived_cl20639,plain,
( zero
= ( complement @ ( composition @ top @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl20624,zip_derived_cl1473,zip_derived_cl16856,zip_derived_cl3822]) ).
thf(zip_derived_cl20678,plain,
( ( composition @ top @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl16856,zip_derived_cl20639]) ).
thf(zip_derived_cl6_121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X2 ) @ X1 )
= ( join @ ( composition @ X0 @ X1 ) @ ( composition @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[composition_distributivity]) ).
thf(zip_derived_cl20874,plain,
! [X0: $i] :
( ( composition @ ( join @ X0 @ top ) @ zero )
= ( join @ ( composition @ X0 @ zero ) @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl20678,zip_derived_cl6]) ).
thf(zip_derived_cl1473_122,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1454,zip_derived_cl30]) ).
thf(zip_derived_cl20678_123,plain,
( ( composition @ top @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl16856,zip_derived_cl20639]) ).
thf(zip_derived_cl3822_124,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl575,zip_derived_cl3805]) ).
thf(zip_derived_cl20897,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl20874,zip_derived_cl1473,zip_derived_cl20678,zip_derived_cl3822]) ).
thf(zip_derived_cl4160_125,plain,
( zero
= ( converse @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl4146,zip_derived_cl163]) ).
thf(zip_derived_cl20921,plain,
! [X0: $i] :
( zero
= ( composition @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl4961,zip_derived_cl20897,zip_derived_cl4160]) ).
thf(zip_derived_cl3822_126,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl575,zip_derived_cl3805]) ).
thf(zip_derived_cl10911_127,plain,
( ( meet @ ( complement @ sk__2 ) @ ( composition @ sk_ @ ( converse @ sk__1 ) ) )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl10777,zip_derived_cl8885]) ).
thf(zip_derived_cl7_128,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl29745_129,plain,
! [X0: $i] :
( ( complement @ ( converse @ X0 ) )
= ( converse @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl29553,zip_derived_cl3805]) ).
thf(zip_derived_cl20921_130,plain,
! [X0: $i] :
( zero
= ( composition @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl4961,zip_derived_cl20897,zip_derived_cl4160]) ).
thf(zip_derived_cl36789,plain,
( ( meet @ sk_ @ ( composition @ ( complement @ sk__2 ) @ sk__1 ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl36553,zip_derived_cl7,zip_derived_cl10777,zip_derived_cl7,zip_derived_cl29745,zip_derived_cl20921,zip_derived_cl3822,zip_derived_cl10911,zip_derived_cl7,zip_derived_cl29745,zip_derived_cl20921]) ).
thf(zip_derived_cl240_131,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl237]) ).
thf(zip_derived_cl36896,plain,
( sk_
= ( join @ zero @ ( complement @ ( join @ ( composition @ ( complement @ sk__2 ) @ sk__1 ) @ ( complement @ sk_ ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl36789,zip_derived_cl240]) ).
thf(zip_derived_cl0_132,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl3821_133,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl295,zip_derived_cl3805]) ).
thf(zip_derived_cl36924,plain,
( sk_
= ( complement @ ( join @ ( complement @ sk_ ) @ ( composition @ ( complement @ sk__2 ) @ sk__1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl36896,zip_derived_cl0,zip_derived_cl3821]) ).
thf(zip_derived_cl3805_134,plain,
! [X0: $i] :
( ( complement @ ( complement @ X0 ) )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3581,zip_derived_cl575]) ).
thf(zip_derived_cl38065,plain,
( ( complement @ sk_ )
= ( join @ ( complement @ sk_ ) @ ( composition @ ( complement @ sk__2 ) @ sk__1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl36924,zip_derived_cl3805]) ).
thf(zip_derived_cl17,plain,
( ( join @ ( composition @ ( complement @ sk__2 ) @ sk__1 ) @ ( complement @ sk_ ) )
!= ( complement @ sk_ ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_135,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl20,plain,
( ( join @ ( complement @ sk_ ) @ ( composition @ ( complement @ sk__2 ) @ sk__1 ) )
!= ( complement @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl17,zip_derived_cl0]) ).
thf(zip_derived_cl38122,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl38065,zip_derived_cl20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL043+2 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.e0yeLkxMJL true
% 0.14/0.35 % Computer : n023.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 Oct 1 12:23:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.55/0.67 % Total configuration time : 435
% 0.55/0.67 % Estimated wc time : 1092
% 0.55/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.83 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 88.34/13.29 % Solved by fo/fo4.sh.
% 88.34/13.29 % done 2890 iterations in 12.391s
% 88.34/13.29 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 88.34/13.29 % SZS output start Refutation
% See solution above
% 88.34/13.29
% 88.34/13.29
% 88.34/13.29 % Terminating...
% 88.52/13.33 % Runner terminated.
% 88.52/13.35 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------