%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL050+4 : 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.yhETCKf88r 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 Oct 2 04:50:10 PM UTC 2025
% Result : Theorem 278.15s 40.32s
% Output : Refutation 278.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 15
% Syntax : Number of formulae : 294 ( 289 unt; 0 typ; 0 def)
% Number of atoms : 299 ( 298 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 1773 ( 9 ~; 3 |; 2 &;1759 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 351 ( 0 ^; 351 !; 0 ?; 351 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_type,type,
join: $i > $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(sk__type,type,
sk_: $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(goals,conjecture,
! [X0: $i] :
( ( ( join @ ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) @ ( complement @ ( composition @ X0 @ top ) ) )
= ( complement @ ( composition @ X0 @ top ) ) )
& ( ( join @ ( complement @ ( composition @ X0 @ top ) ) @ ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) )
= ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [X0: $i] :
( ( ( join @ ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) @ ( complement @ ( composition @ X0 @ top ) ) )
= ( complement @ ( composition @ X0 @ top ) ) )
& ( ( join @ ( complement @ ( composition @ X0 @ top ) ) @ ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) )
= ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) ) ),
inference('cnf.neg',[status(esa)],[goals]) ).
thf(zip_derived_cl16,plain,
( ( ( join @ ( composition @ ( complement @ ( composition @ sk_ @ top ) ) @ top ) @ ( complement @ ( composition @ sk_ @ top ) ) )
!= ( complement @ ( composition @ sk_ @ top ) ) )
| ( ( join @ ( complement @ ( composition @ sk_ @ top ) ) @ ( composition @ ( complement @ ( composition @ sk_ @ top ) ) @ top ) )
!= ( composition @ ( complement @ ( composition @ sk_ @ top ) ) @ top ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
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(zip_derived_cl19,plain,
( ( ( join @ ( complement @ ( composition @ sk_ @ top ) ) @ ( composition @ ( complement @ ( composition @ sk_ @ top ) ) @ top ) )
!= ( complement @ ( composition @ sk_ @ top ) ) )
| ( ( join @ ( complement @ ( composition @ sk_ @ top ) ) @ ( composition @ ( complement @ ( composition @ sk_ @ top ) ) @ top ) )
!= ( composition @ ( complement @ ( composition @ sk_ @ top ) ) @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl16,zip_derived_cl0]) ).
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_cl85,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ ( converse @ X0 ) @ X1 ) )
= ( composition @ ( converse @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
thf(zip_derived_cl1632,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl85]) ).
thf(zip_derived_cl7_001,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl1640,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1632,zip_derived_cl7]) ).
thf(zip_derived_cl5_002,plain,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[composition_identity]) ).
thf(composition_associativity,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[composition_associativity]) ).
thf(zip_derived_cl79,plain,
! [X0: $i,X1: $i] :
( ( composition @ X0 @ ( composition @ one @ X1 ) )
= ( composition @ X0 @ X1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl4]) ).
thf(zip_derived_cl1660,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1640,zip_derived_cl79]) ).
thf(zip_derived_cl1640_003,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1632,zip_derived_cl7]) ).
thf(zip_derived_cl1675,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl1660,zip_derived_cl1640]) ).
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_cl1682,plain,
! [X0: $i] :
( ( join @ ( composition @ ( converse @ one ) @ ( complement @ X0 ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1675,zip_derived_cl10]) ).
thf(zip_derived_cl1640_004,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1632,zip_derived_cl7]) ).
thf(zip_derived_cl1687,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1682,zip_derived_cl1640]) ).
thf(zip_derived_cl0_005,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
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(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_cl51,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_cl54,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl51]) ).
thf(zip_derived_cl1821,plain,
! [X0: $i] :
( X0
= ( join @ ( meet @ X0 @ ( complement @ X0 ) ) @ ( complement @ ( complement @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1687,zip_derived_cl54]) ).
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_cl1843,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1821,zip_derived_cl12]) ).
thf(zip_derived_cl1843_006,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1821,zip_derived_cl12]) ).
thf(zip_derived_cl54_007,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl51]) ).
thf(zip_derived_cl3564,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( join @ ( meet @ ( complement @ X0 ) @ zero ) @ ( complement @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1843,zip_derived_cl54]) ).
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_cl11_008,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl3_009,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_cl26,plain,
! [X0: $i] :
( ( meet @ X0 @ ( complement @ X0 ) )
= ( complement @ top ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl3]) ).
thf(zip_derived_cl12_010,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl29,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl3_011,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_cl48,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ ( complement @ X0 ) @ zero ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl29,zip_derived_cl3]) ).
thf(zip_derived_cl0_012,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl49,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl48,zip_derived_cl0]) ).
thf(zip_derived_cl413,plain,
( ( meet @ zero @ top )
= ( complement @ top ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl49]) ).
thf(zip_derived_cl29_013,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl419,plain,
( ( meet @ zero @ top )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl413,zip_derived_cl29]) ).
thf(zip_derived_cl51_014,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_cl421,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ ( complement @ zero ) @ top ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl419,zip_derived_cl51]) ).
thf(zip_derived_cl0_015,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl11_016,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl29_017,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl11_018,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl46,plain,
( top
= ( join @ top @ zero ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl29,zip_derived_cl11]) ).
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_cl50,plain,
! [X0: $i] :
( ( join @ top @ ( join @ zero @ X0 ) )
= ( join @ top @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl46,zip_derived_cl1]) ).
thf(zip_derived_cl67,plain,
( ( join @ top @ top )
= ( join @ top @ ( complement @ zero ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl50]) ).
thf(zip_derived_cl425,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl421,zip_derived_cl0,zip_derived_cl67]) ).
thf(zip_derived_cl50_019,plain,
! [X0: $i] :
( ( join @ top @ ( join @ zero @ X0 ) )
= ( join @ top @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl46,zip_derived_cl1]) ).
thf(zip_derived_cl477,plain,
( ( join @ top @ zero )
= ( join @ top @ ( complement @ ( join @ top @ top ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl425,zip_derived_cl50]) ).
thf(zip_derived_cl46_020,plain,
( top
= ( join @ top @ zero ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl29,zip_derived_cl11]) ).
thf(zip_derived_cl482,plain,
( top
= ( join @ top @ ( complement @ ( join @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl477,zip_derived_cl46]) ).
thf(zip_derived_cl11_021,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl1_022,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_cl33,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ X0 @ ( complement @ ( join @ X1 @ X0 ) ) ) )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).
thf(zip_derived_cl636,plain,
( ( join @ top @ top )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl482,zip_derived_cl33]) ).
thf(zip_derived_cl1_023,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_cl702,plain,
! [X0: $i] :
( ( join @ top @ ( join @ top @ X0 ) )
= ( join @ top @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl636,zip_derived_cl1]) ).
thf(zip_derived_cl11_024,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl67_025,plain,
( ( join @ top @ top )
= ( join @ top @ ( complement @ zero ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl50]) ).
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_cl69,plain,
! [X0: $i] :
( ( join @ top @ ( join @ ( complement @ zero ) @ X0 ) )
= ( join @ ( join @ top @ top ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl67,zip_derived_cl1]) ).
thf(zip_derived_cl1_027,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_cl70,plain,
! [X0: $i] :
( ( join @ top @ ( join @ ( complement @ zero ) @ X0 ) )
= ( join @ top @ ( join @ top @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl69,zip_derived_cl1]) ).
thf(zip_derived_cl168,plain,
( ( join @ top @ top )
= ( join @ top @ ( join @ top @ ( complement @ ( complement @ zero ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl70]) ).
thf(zip_derived_cl636_028,plain,
( ( join @ top @ top )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl482,zip_derived_cl33]) ).
thf(zip_derived_cl697,plain,
( top
= ( join @ top @ ( join @ top @ ( complement @ ( complement @ zero ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl168,zip_derived_cl636]) ).
thf(zip_derived_cl812,plain,
( top
= ( join @ top @ ( complement @ ( complement @ zero ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl702,zip_derived_cl697]) ).
thf(zip_derived_cl54_029,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl51]) ).
thf(zip_derived_cl1216,plain,
( ( complement @ zero )
= ( join @ ( meet @ ( complement @ zero ) @ top ) @ ( complement @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl812,zip_derived_cl54]) ).
thf(zip_derived_cl0_030,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl3_031,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_cl24,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl3]) ).
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_cl449,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ X1 @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl24,zip_derived_cl3]) ).
thf(zip_derived_cl29_033,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl0_034,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1236,plain,
( ( complement @ zero )
= ( join @ zero @ ( meet @ top @ ( complement @ zero ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1216,zip_derived_cl449,zip_derived_cl29,zip_derived_cl0]) ).
thf(zip_derived_cl1687_035,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1682,zip_derived_cl1640]) ).
thf(zip_derived_cl3_036,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_cl1826,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1687,zip_derived_cl3]) ).
thf(zip_derived_cl29_037,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl3_038,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_cl45,plain,
! [X0: $i] :
( ( meet @ top @ X0 )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl29,zip_derived_cl3]) ).
thf(zip_derived_cl1966,plain,
! [X0: $i] :
( ( meet @ top @ ( complement @ X0 ) )
= ( complement @ ( join @ zero @ ( meet @ X0 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1826,zip_derived_cl45]) ).
thf(zip_derived_cl12_039,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl51_040,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_cl59,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X0 ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl12,zip_derived_cl51]) ).
thf(zip_derived_cl3_041,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_cl61,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl3]) ).
thf(zip_derived_cl2006,plain,
! [X0: $i] :
( ( meet @ top @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1966,zip_derived_cl61]) ).
thf(zip_derived_cl11_042,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl2574,plain,
( ( complement @ zero )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1236,zip_derived_cl2006,zip_derived_cl11]) ).
thf(zip_derived_cl3_043,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_cl2603,plain,
! [X0: $i] :
( ( meet @ X0 @ zero )
= ( complement @ ( join @ ( complement @ X0 ) @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2574,zip_derived_cl3]) ).
thf(zip_derived_cl11_044,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl11_045,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl1_046,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_cl36,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ ( complement @ X1 ) @ X0 ) )
= ( join @ top @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).
thf(zip_derived_cl853,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= ( join @ top @ ( complement @ ( complement @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl36]) ).
thf(zip_derived_cl1687_047,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1682,zip_derived_cl1640]) ).
thf(zip_derived_cl33_048,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ X0 @ ( complement @ ( join @ X1 @ X0 ) ) ) )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).
thf(zip_derived_cl1818,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( join @ ( complement @ X0 ) @ ( complement @ ( complement @ X0 ) ) ) )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl1687,zip_derived_cl33]) ).
thf(zip_derived_cl11_049,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl0_050,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1842,plain,
! [X0: $i] :
( ( join @ top @ ( complement @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1818,zip_derived_cl11,zip_derived_cl0]) ).
thf(zip_derived_cl1900,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl853,zip_derived_cl1842]) ).
thf(zip_derived_cl29_051,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl2627,plain,
! [X0: $i] :
( ( meet @ X0 @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl2603,zip_derived_cl1900,zip_derived_cl29]) ).
thf(zip_derived_cl3579,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( join @ zero @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3564,zip_derived_cl2627]) ).
thf(zip_derived_cl1843_052,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1821,zip_derived_cl12]) ).
thf(zip_derived_cl3593,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3579,zip_derived_cl1843]) ).
thf(zip_derived_cl3605,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1843,zip_derived_cl3593]) ).
thf(zip_derived_cl1900_053,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl853,zip_derived_cl1842]) ).
thf(zip_derived_cl7_054,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_cl44,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ ( converse @ X0 ) @ X1 ) )
= ( join @ X0 @ ( converse @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl1937,plain,
! [X0: $i] :
( ( converse @ top )
= ( join @ X0 @ ( converse @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1900,zip_derived_cl44]) ).
thf(zip_derived_cl702_055,plain,
! [X0: $i] :
( ( join @ top @ ( join @ top @ X0 ) )
= ( join @ top @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl636,zip_derived_cl1]) ).
thf(zip_derived_cl1_056,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_057,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl30,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X2 @ X1 ) )
= ( join @ X2 @ ( join @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl808,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= ( join @ top @ ( join @ X0 @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl702,zip_derived_cl30]) ).
thf(zip_derived_cl1900_058,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl853,zip_derived_cl1842]) ).
thf(zip_derived_cl1900_059,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl853,zip_derived_cl1842]) ).
thf(zip_derived_cl1920,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= top ),
inference(demod,[status(thm)],[zip_derived_cl808,zip_derived_cl1900,zip_derived_cl1900]) ).
thf(zip_derived_cl3144,plain,
( ( converse @ top )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl1937,zip_derived_cl1920]) ).
thf(zip_derived_cl29_060,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl10_061,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_cl124,plain,
! [X0: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ top ) ) ) @ zero )
= zero ),
inference('s_sup+',[status(thm)],[zip_derived_cl29,zip_derived_cl10]) ).
thf(zip_derived_cl3240,plain,
( ( join @ ( composition @ top @ ( complement @ ( composition @ top @ top ) ) ) @ zero )
= zero ),
inference('s_sup+',[status(thm)],[zip_derived_cl3144,zip_derived_cl124]) ).
thf(zip_derived_cl0_062,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl3328,plain,
( ( join @ zero @ ( composition @ top @ ( complement @ ( composition @ top @ top ) ) ) )
= zero ),
inference('s_sup+',[status(thm)],[zip_derived_cl3240,zip_derived_cl0]) ).
thf(zip_derived_cl3985,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference('s_sup+',[status(thm)],[zip_derived_cl3605,zip_derived_cl3328]) ).
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_cl4047,plain,
! [X0: $i] :
( ( composition @ ( join @ top @ X0 ) @ ( complement @ ( composition @ top @ top ) ) )
= ( join @ zero @ ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3985,zip_derived_cl6]) ).
thf(zip_derived_cl1920_063,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= top ),
inference(demod,[status(thm)],[zip_derived_cl808,zip_derived_cl1900,zip_derived_cl1900]) ).
thf(zip_derived_cl3985_064,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference('s_sup+',[status(thm)],[zip_derived_cl3605,zip_derived_cl3328]) ).
thf(zip_derived_cl3605_065,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1843,zip_derived_cl3593]) ).
thf(zip_derived_cl4087,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4047,zip_derived_cl1920,zip_derived_cl3985,zip_derived_cl3605]) ).
thf(zip_derived_cl1675_066,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl1660,zip_derived_cl1640]) ).
thf(zip_derived_cl4163,plain,
( zero
= ( complement @ ( composition @ top @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4087,zip_derived_cl1675]) ).
thf(zip_derived_cl3593_067,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3579,zip_derived_cl1843]) ).
thf(zip_derived_cl4297,plain,
( ( composition @ top @ top )
= ( complement @ zero ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4163,zip_derived_cl3593]) ).
thf(zip_derived_cl2574_068,plain,
( ( complement @ zero )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1236,zip_derived_cl2006,zip_derived_cl11]) ).
thf(zip_derived_cl4323,plain,
( ( composition @ top @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl4297,zip_derived_cl2574]) ).
thf(zip_derived_cl4_069,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[composition_associativity]) ).
thf(zip_derived_cl3144_070,plain,
( ( converse @ top )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl1937,zip_derived_cl1920]) ).
thf(zip_derived_cl11_071,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl24_072,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl3]) ).
thf(zip_derived_cl452,plain,
! [X0: $i] :
( ( meet @ ( complement @ X0 ) @ X0 )
= ( complement @ top ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl24]) ).
thf(zip_derived_cl29_073,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl465,plain,
! [X0: $i] :
( ( meet @ ( complement @ X0 ) @ X0 )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl452,zip_derived_cl29]) ).
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_cl518,plain,
! [X0: $i,X1: $i] :
( ( join @ ( meet @ ( composition @ ( complement @ ( composition @ X0 @ ( converse @ X1 ) ) ) @ X1 ) @ X0 ) @ ( composition @ zero @ ( meet @ X1 @ ( composition @ ( converse @ ( complement @ ( composition @ X0 @ ( converse @ X1 ) ) ) ) @ X0 ) ) ) )
= ( composition @ zero @ ( meet @ X1 @ ( composition @ ( converse @ ( complement @ ( composition @ X0 @ ( converse @ X1 ) ) ) ) @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl465,zip_derived_cl13]) ).
thf(zip_derived_cl449_074,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ X1 @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl24,zip_derived_cl3]) ).
thf(zip_derived_cl530,plain,
! [X0: $i,X1: $i] :
( ( join @ ( meet @ X0 @ ( composition @ ( complement @ ( composition @ X0 @ ( converse @ X1 ) ) ) @ X1 ) ) @ ( composition @ zero @ ( meet @ X1 @ ( composition @ ( converse @ ( complement @ ( composition @ X0 @ ( converse @ X1 ) ) ) ) @ X0 ) ) ) )
= ( composition @ zero @ ( meet @ X1 @ ( composition @ ( converse @ ( complement @ ( composition @ X0 @ ( converse @ X1 ) ) ) ) @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl518,zip_derived_cl449]) ).
thf(zip_derived_cl4163_075,plain,
( zero
= ( complement @ ( composition @ top @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4087,zip_derived_cl1675]) ).
thf(zip_derived_cl10_076,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_cl4308,plain,
( ( join @ ( composition @ ( converse @ top ) @ zero ) @ ( complement @ top ) )
= ( complement @ top ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4163,zip_derived_cl10]) ).
thf(zip_derived_cl3144_077,plain,
( ( converse @ top )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl1937,zip_derived_cl1920]) ).
thf(zip_derived_cl29_078,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl0_079,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl3605_080,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1843,zip_derived_cl3593]) ).
thf(zip_derived_cl29_081,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl4332,plain,
( ( composition @ top @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl4308,zip_derived_cl3144,zip_derived_cl29,zip_derived_cl0,zip_derived_cl3605,zip_derived_cl29]) ).
thf(zip_derived_cl9_082,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl10_083,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_cl128,plain,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ ( converse @ X0 ) ) @ ( complement @ ( converse @ ( composition @ X1 @ X0 ) ) ) ) @ ( complement @ ( converse @ X1 ) ) )
= ( complement @ ( converse @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl10]) ).
thf(zip_derived_cl7_084,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl0_085,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl130,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_cl128,zip_derived_cl7,zip_derived_cl0]) ).
thf(zip_derived_cl4444,plain,
( ( join @ ( complement @ ( converse @ top ) ) @ ( composition @ zero @ ( complement @ ( converse @ zero ) ) ) )
= ( complement @ ( converse @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4332,zip_derived_cl130]) ).
thf(zip_derived_cl3144_086,plain,
( ( converse @ top )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl1937,zip_derived_cl1920]) ).
thf(zip_derived_cl29_087,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl3605_088,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1843,zip_derived_cl3593]) ).
thf(zip_derived_cl3144_089,plain,
( ( converse @ top )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl1937,zip_derived_cl1920]) ).
thf(zip_derived_cl29_090,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl4481,plain,
( ( composition @ zero @ ( complement @ ( converse @ zero ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl4444,zip_derived_cl3144,zip_derived_cl29,zip_derived_cl3605,zip_derived_cl3144,zip_derived_cl29]) ).
thf(zip_derived_cl3605_091,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1843,zip_derived_cl3593]) ).
thf(zip_derived_cl7_092,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl8_093,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_additivity]) ).
thf(zip_derived_cl43,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X1 @ ( converse @ X0 ) ) )
= ( join @ ( converse @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl3984,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( join @ ( converse @ zero ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3605,zip_derived_cl43]) ).
thf(zip_derived_cl7_094,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl3991,plain,
! [X0: $i] :
( X0
= ( join @ ( converse @ zero ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3984,zip_derived_cl7]) ).
thf(zip_derived_cl11_095,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl6070,plain,
( top
= ( complement @ ( converse @ zero ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3991,zip_derived_cl11]) ).
thf(zip_derived_cl6093,plain,
( ( composition @ zero @ top )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl4481,zip_derived_cl6070]) ).
thf(zip_derived_cl7_096,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl13_097,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_cl151,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ ( converse @ X0 ) @ X2 ) @ X1 ) @ ( composition @ ( meet @ ( converse @ X0 ) @ ( composition @ X1 @ ( converse @ X2 ) ) ) @ ( meet @ X2 @ ( composition @ X0 @ X1 ) ) ) )
= ( composition @ ( meet @ ( converse @ X0 ) @ ( composition @ X1 @ ( converse @ X2 ) ) ) @ ( meet @ X2 @ ( composition @ X0 @ X1 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl13]) ).
thf(zip_derived_cl6303,plain,
! [X0: $i] :
( ( join @ ( meet @ ( composition @ ( converse @ zero ) @ X0 ) @ top ) @ ( composition @ ( meet @ ( converse @ zero ) @ ( composition @ top @ ( converse @ X0 ) ) ) @ ( meet @ X0 @ zero ) ) )
= ( composition @ ( meet @ ( converse @ zero ) @ ( composition @ top @ ( converse @ X0 ) ) ) @ ( meet @ X0 @ zero ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl6093,zip_derived_cl151]) ).
thf(zip_derived_cl3991_098,plain,
! [X0: $i] :
( X0
= ( join @ ( converse @ zero ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3984,zip_derived_cl7]) ).
thf(zip_derived_cl1826_099,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1687,zip_derived_cl3]) ).
thf(zip_derived_cl3579_100,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( join @ zero @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3564,zip_derived_cl2627]) ).
thf(zip_derived_cl3596,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1826,zip_derived_cl3579]) ).
thf(zip_derived_cl61_101,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl3]) ).
thf(zip_derived_cl3599,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl3596,zip_derived_cl61]) ).
thf(zip_derived_cl51_102,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_cl3718,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ ( complement @ ( join @ ( complement @ X0 ) @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3599,zip_derived_cl51]) ).
thf(zip_derived_cl0_103,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl11_104,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl29_105,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl3758,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl3718,zip_derived_cl0,zip_derived_cl11,zip_derived_cl29]) ).
thf(zip_derived_cl6074,plain,
( ( converse @ zero )
= zero ),
inference('s_sup+',[status(thm)],[zip_derived_cl3991,zip_derived_cl3758]) ).
thf(zip_derived_cl49_106,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl48,zip_derived_cl0]) ).
thf(zip_derived_cl3579_107,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( join @ zero @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3564,zip_derived_cl2627]) ).
thf(zip_derived_cl3583,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl49,zip_derived_cl3579]) ).
thf(zip_derived_cl3593_108,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3579,zip_derived_cl1843]) ).
thf(zip_derived_cl5290,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl3583,zip_derived_cl3593]) ).
thf(zip_derived_cl6074_109,plain,
( ( converse @ zero )
= zero ),
inference('s_sup+',[status(thm)],[zip_derived_cl3991,zip_derived_cl3758]) ).
thf(zip_derived_cl2574_110,plain,
( ( complement @ zero )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1236,zip_derived_cl2006,zip_derived_cl11]) ).
thf(zip_derived_cl3_111,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_cl2576,plain,
! [X0: $i] :
( ( meet @ zero @ X0 )
= ( complement @ ( join @ top @ ( complement @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2574,zip_derived_cl3]) ).
thf(zip_derived_cl1920_112,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= top ),
inference(demod,[status(thm)],[zip_derived_cl808,zip_derived_cl1900,zip_derived_cl1900]) ).
thf(zip_derived_cl29_113,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl12]) ).
thf(zip_derived_cl2612,plain,
! [X0: $i] :
( ( meet @ zero @ X0 )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl2576,zip_derived_cl1920,zip_derived_cl29]) ).
thf(zip_derived_cl2627_114,plain,
! [X0: $i] :
( ( meet @ X0 @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl2603,zip_derived_cl1900,zip_derived_cl29]) ).
thf(zip_derived_cl4087_115,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4047,zip_derived_cl1920,zip_derived_cl3985,zip_derived_cl3605]) ).
thf(zip_derived_cl4_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[composition_associativity]) ).
thf(zip_derived_cl6_117,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_cl106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( composition @ ( join @ X3 @ ( composition @ X2 @ X1 ) ) @ X0 )
= ( join @ ( composition @ X3 @ X0 ) @ ( composition @ X2 @ ( composition @ X1 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4,zip_derived_cl6]) ).
thf(zip_derived_cl4137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X2 @ ( composition @ X1 @ X0 ) ) @ ( complement @ ( composition @ top @ top ) ) )
= ( join @ ( composition @ X2 @ ( complement @ ( composition @ top @ top ) ) ) @ ( composition @ X1 @ zero ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4087,zip_derived_cl106]) ).
thf(zip_derived_cl4087_118,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4047,zip_derived_cl1920,zip_derived_cl3985,zip_derived_cl3605]) ).
thf(zip_derived_cl4087_119,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4047,zip_derived_cl1920,zip_derived_cl3985,zip_derived_cl3605]) ).
thf(zip_derived_cl3605_120,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1843,zip_derived_cl3593]) ).
thf(zip_derived_cl4193,plain,
! [X1: $i] :
( zero
= ( composition @ X1 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl4137,zip_derived_cl4087,zip_derived_cl4087,zip_derived_cl3605]) ).
thf(zip_derived_cl3758_121,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl3718,zip_derived_cl0,zip_derived_cl11,zip_derived_cl29]) ).
thf(zip_derived_cl6074_122,plain,
( ( converse @ zero )
= zero ),
inference('s_sup+',[status(thm)],[zip_derived_cl3991,zip_derived_cl3758]) ).
thf(zip_derived_cl2612_123,plain,
! [X0: $i] :
( ( meet @ zero @ X0 )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl2576,zip_derived_cl1920,zip_derived_cl29]) ).
thf(zip_derived_cl2627_124,plain,
! [X0: $i] :
( ( meet @ X0 @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl2603,zip_derived_cl1900,zip_derived_cl29]) ).
thf(zip_derived_cl4193_125,plain,
! [X1: $i] :
( zero
= ( composition @ X1 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl4137,zip_derived_cl4087,zip_derived_cl4087,zip_derived_cl3605]) ).
thf(zip_derived_cl6349,plain,
! [X0: $i] :
( ( composition @ zero @ X0 )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl6303,zip_derived_cl6074,zip_derived_cl5290,zip_derived_cl6074,zip_derived_cl2612,zip_derived_cl2627,zip_derived_cl4193,zip_derived_cl3758,zip_derived_cl6074,zip_derived_cl2612,zip_derived_cl2627,zip_derived_cl4193]) ).
thf(zip_derived_cl3758_126,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl3718,zip_derived_cl0,zip_derived_cl11,zip_derived_cl29]) ).
thf(zip_derived_cl6349_127,plain,
! [X0: $i] :
( ( composition @ zero @ X0 )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl6303,zip_derived_cl6074,zip_derived_cl5290,zip_derived_cl6074,zip_derived_cl2612,zip_derived_cl2627,zip_derived_cl4193,zip_derived_cl3758,zip_derived_cl6074,zip_derived_cl2612,zip_derived_cl2627,zip_derived_cl4193]) ).
thf(zip_derived_cl8986,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ ( composition @ ( complement @ ( composition @ X0 @ ( converse @ X1 ) ) ) @ X1 ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl530,zip_derived_cl6349,zip_derived_cl3758,zip_derived_cl6349]) ).
thf(zip_derived_cl51_128,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_cl54_129,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ X1 @ ( complement @ X0 ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl51]) ).
thf(zip_derived_cl1211,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X0 ) @ X1 )
= ( join @ ( meet @ ( join @ ( complement @ X0 ) @ X1 ) @ ( meet @ X0 @ X1 ) ) @ ( complement @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl51,zip_derived_cl54]) ).
thf(zip_derived_cl449_130,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ X1 @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl24,zip_derived_cl3]) ).
thf(zip_derived_cl0_131,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1233,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X0 ) @ X1 )
= ( join @ ( complement @ X0 ) @ ( meet @ ( meet @ X0 @ X1 ) @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1211,zip_derived_cl449,zip_derived_cl0]) ).
thf(zip_derived_cl63105,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X1 ) @ ( composition @ ( complement @ ( composition @ X1 @ ( converse @ X0 ) ) ) @ X0 ) )
= ( join @ ( complement @ X1 ) @ ( meet @ zero @ ( join @ ( complement @ X1 ) @ ( composition @ ( complement @ ( composition @ X1 @ ( converse @ X0 ) ) ) @ X0 ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl8986,zip_derived_cl1233]) ).
thf(zip_derived_cl2612_132,plain,
! [X0: $i] :
( ( meet @ zero @ X0 )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl2576,zip_derived_cl1920,zip_derived_cl29]) ).
thf(zip_derived_cl3758_133,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl3718,zip_derived_cl0,zip_derived_cl11,zip_derived_cl29]) ).
thf(zip_derived_cl63188,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X1 ) @ ( composition @ ( complement @ ( composition @ X1 @ ( converse @ X0 ) ) ) @ X0 ) )
= ( complement @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl63105,zip_derived_cl2612,zip_derived_cl3758]) ).
thf(zip_derived_cl63369,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) )
= ( complement @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3144,zip_derived_cl63188]) ).
thf(zip_derived_cl63526,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( composition @ X1 @ X0 ) ) @ ( composition @ ( complement @ ( composition @ X1 @ ( composition @ X0 @ top ) ) ) @ top ) )
= ( complement @ ( composition @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4,zip_derived_cl63369]) ).
thf(zip_derived_cl64218,plain,
! [X0: $i] :
( ( join @ ( complement @ ( composition @ X0 @ top ) ) @ ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) )
= ( complement @ ( composition @ X0 @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4323,zip_derived_cl63526]) ).
thf(zip_derived_cl64218_134,plain,
! [X0: $i] :
( ( join @ ( complement @ ( composition @ X0 @ top ) ) @ ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) )
= ( complement @ ( composition @ X0 @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4323,zip_derived_cl63526]) ).
thf(zip_derived_cl64308,plain,
( ( ( complement @ ( composition @ sk_ @ top ) )
!= ( complement @ ( composition @ sk_ @ top ) ) )
| ( ( complement @ ( composition @ sk_ @ top ) )
!= ( composition @ ( complement @ ( composition @ sk_ @ top ) ) @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl19,zip_derived_cl64218,zip_derived_cl64218]) ).
thf(zip_derived_cl64309,plain,
( ( complement @ ( composition @ sk_ @ top ) )
!= ( composition @ ( complement @ ( composition @ sk_ @ top ) ) @ top ) ),
inference(simplify,[status(thm)],[zip_derived_cl64308]) ).
thf(zip_derived_cl1900_135,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl853,zip_derived_cl1842]) ).
thf(zip_derived_cl1675_136,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl1660,zip_derived_cl1640]) ).
thf(zip_derived_cl6_137,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_cl1680,plain,
! [X0: $i,X1: $i] :
( ( composition @ ( join @ one @ X1 ) @ X0 )
= ( join @ X0 @ ( composition @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1675,zip_derived_cl6]) ).
thf(zip_derived_cl79294,plain,
! [X0: $i] :
( ( composition @ top @ X0 )
= ( join @ X0 @ ( composition @ top @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1900,zip_derived_cl1680]) ).
thf(zip_derived_cl44_138,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ ( converse @ X0 ) @ X1 ) )
= ( join @ X0 @ ( converse @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl80171,plain,
! [X0: $i] :
( ( converse @ ( composition @ top @ ( converse @ X0 ) ) )
= ( join @ X0 @ ( converse @ ( composition @ top @ ( converse @ X0 ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl79294,zip_derived_cl44]) ).
thf(zip_derived_cl7_139,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl9_140,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl86,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ ( converse @ X0 ) ) )
= ( composition @ X0 @ ( converse @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
thf(zip_derived_cl3144_141,plain,
( ( converse @ top )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl1937,zip_derived_cl1920]) ).
thf(zip_derived_cl86_142,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ ( converse @ X0 ) ) )
= ( composition @ X0 @ ( converse @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
thf(zip_derived_cl3144_143,plain,
( ( converse @ top )
= top ),
inference('s_sup+',[status(thm)],[zip_derived_cl1937,zip_derived_cl1920]) ).
thf(zip_derived_cl80265,plain,
! [X0: $i] :
( ( composition @ X0 @ top )
= ( join @ X0 @ ( composition @ X0 @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl80171,zip_derived_cl86,zip_derived_cl3144,zip_derived_cl86,zip_derived_cl3144]) ).
thf(zip_derived_cl64218_144,plain,
! [X0: $i] :
( ( join @ ( complement @ ( composition @ X0 @ top ) ) @ ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) )
= ( complement @ ( composition @ X0 @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4323,zip_derived_cl63526]) ).
thf(zip_derived_cl81060,plain,
! [X0: $i] :
( ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top )
= ( complement @ ( composition @ X0 @ top ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl80265,zip_derived_cl64218]) ).
thf(zip_derived_cl81234,plain,
( ( complement @ ( composition @ sk_ @ top ) )
!= ( complement @ ( composition @ sk_ @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl64309,zip_derived_cl81060]) ).
thf(zip_derived_cl81235,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl81234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL050+4 : 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.yhETCKf88r true
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 1 12:23:38 EDT 2025
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in FO mode
% 0.55/0.65 % Total configuration time : 435
% 0.55/0.65 % Estimated wc time : 1092
% 0.55/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 278.15/40.32 % Solved by fo/fo6_bce.sh.
% 278.15/40.32 % BCE start: 17
% 278.15/40.32 % BCE eliminated: 0
% 278.15/40.32 % PE start: 17
% 278.15/40.32 logic: eq
% 278.15/40.32 % PE eliminated: 0
% 278.15/40.32 % done 2188 iterations in 39.582s
% 278.15/40.32 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 278.15/40.32 % SZS output start Refutation
% See solution above
% 278.15/40.33
% 278.15/40.33
% 278.15/40.33 % Terminating...
% 278.55/40.45 % Runner terminated.
% 278.55/40.46 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------