TSTP Solution File: REL050+1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL050+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.XS4tKXtplY true
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:47:33 EDT 2023
% Result : Theorem 39.26s 6.26s
% Output : Refutation 39.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 23
% Syntax : Number of formulae : 264 ( 255 unt; 9 typ; 0 def)
% Number of atoms : 255 ( 254 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1387 ( 3 ~; 0 |; 0 &;1384 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 327 ( 0 ^; 327 !; 0 ?; 327 :)
% Comments :
%------------------------------------------------------------------------------
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(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] :
( ( complement @ ( composition @ X0 @ top ) )
= ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [X0: $i] :
( ( complement @ ( composition @ X0 @ top ) )
= ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) ),
inference('cnf.neg',[status(esa)],[goals]) ).
thf(zip_derived_cl13,plain,
( ( complement @ ( composition @ sk_ @ top ) )
!= ( composition @ ( complement @ ( composition @ sk_ @ top ) ) @ top ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
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_cl20,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_cl331,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl20]) ).
thf(zip_derived_cl7_001,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl338,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl331,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_cl70,plain,
! [X0: $i,X1: $i] :
( ( composition @ X0 @ ( composition @ one @ X1 ) )
= ( composition @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl4]) ).
thf(zip_derived_cl359,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl338,zip_derived_cl70]) ).
thf(zip_derived_cl338_003,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl331,zip_derived_cl7]) ).
thf(zip_derived_cl365,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl359,zip_derived_cl338]) ).
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_cl385,plain,
! [X0: $i] :
( ( join @ ( composition @ ( converse @ one ) @ ( complement @ X0 ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl365,zip_derived_cl10]) ).
thf(zip_derived_cl338_004,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl331,zip_derived_cl7]) ).
thf(zip_derived_cl5_005,plain,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[composition_identity]) ).
thf(zip_derived_cl360,plain,
( one
= ( converse @ one ) ),
inference('sup+',[status(thm)],[zip_derived_cl338,zip_derived_cl5]) ).
thf(zip_derived_cl365_006,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl359,zip_derived_cl338]) ).
thf(zip_derived_cl386,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl360,zip_derived_cl365]) ).
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_cl424,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl386,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(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_007,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_cl90,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_cl99,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl12,zip_derived_cl90]) ).
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_cl102,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl99,zip_derived_cl3]) ).
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_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_cl45,plain,
! [X0: $i] :
( ( meet @ X0 @ ( complement @ X0 ) )
= ( complement @ top ) ),
inference('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_cl48,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl12]) ).
thf(zip_derived_cl11_011,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl50,plain,
( top
= ( join @ top @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl48,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_cl55,plain,
! [X0: $i] :
( ( join @ top @ ( join @ zero @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl50,zip_derived_cl1]) ).
thf(zip_derived_cl202,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= ( join @ top @ ( meet @ X0 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl102,zip_derived_cl55]) ).
thf(zip_derived_cl457,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= ( join @ top @ ( complement @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl424,zip_derived_cl202]) ).
thf(zip_derived_cl11_012,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl48_013,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl45,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_cl52,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ ( complement @ X0 ) @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl48,zip_derived_cl3]) ).
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_cl53,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl0]) ).
thf(zip_derived_cl135,plain,
( ( meet @ zero @ top )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl53]) ).
thf(zip_derived_cl48_015,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl12]) ).
thf(zip_derived_cl141,plain,
( ( meet @ zero @ top )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl135,zip_derived_cl48]) ).
thf(zip_derived_cl90_016,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_cl144,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ ( complement @ zero ) @ top ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl141,zip_derived_cl90]) ).
thf(zip_derived_cl0_017,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl145,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ top @ ( complement @ zero ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl144,zip_derived_cl0]) ).
thf(zip_derived_cl11_018,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl55_019,plain,
! [X0: $i] :
( ( join @ top @ ( join @ zero @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl50,zip_derived_cl1]) ).
thf(zip_derived_cl201,plain,
( ( join @ top @ top )
= ( join @ top @ ( complement @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl55]) ).
thf(zip_derived_cl277,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl145,zip_derived_cl201]) ).
thf(zip_derived_cl53_020,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl0]) ).
thf(zip_derived_cl281,plain,
( ( meet @ ( join @ top @ top ) @ top )
= ( complement @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl277,zip_derived_cl53]) ).
thf(zip_derived_cl90_021,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_cl294,plain,
( ( join @ top @ top )
= ( join @ ( complement @ zero ) @ ( complement @ ( join @ ( complement @ ( join @ top @ top ) ) @ top ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl281,zip_derived_cl90]) ).
thf(zip_derived_cl0_022,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl277_023,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl145,zip_derived_cl201]) ).
thf(zip_derived_cl55_024,plain,
! [X0: $i] :
( ( join @ top @ ( join @ zero @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl50,zip_derived_cl1]) ).
thf(zip_derived_cl279,plain,
( ( join @ top @ zero )
= ( join @ top @ ( complement @ ( join @ top @ top ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl277,zip_derived_cl55]) ).
thf(zip_derived_cl50_025,plain,
( top
= ( join @ top @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl48,zip_derived_cl11]) ).
thf(zip_derived_cl284,plain,
( top
= ( join @ top @ ( complement @ ( join @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl279,zip_derived_cl50]) ).
thf(zip_derived_cl48_026,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl12]) ).
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_cl11_028,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl298,plain,
( ( join @ top @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl294,zip_derived_cl0,zip_derived_cl284,zip_derived_cl48,zip_derived_cl0,zip_derived_cl11]) ).
thf(zip_derived_cl1_029,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_030,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_cl1080,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= ( join @ top @ ( join @ top @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl298,zip_derived_cl27]) ).
thf(zip_derived_cl1223,plain,
! [X0: $i] :
( ( join @ ( complement @ ( complement @ X0 ) ) @ top )
= ( join @ top @ ( join @ top @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl457,zip_derived_cl1080]) ).
thf(zip_derived_cl1080_031,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= ( join @ top @ ( join @ top @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl298,zip_derived_cl27]) ).
thf(zip_derived_cl1236,plain,
! [X0: $i] :
( ( join @ ( complement @ ( complement @ X0 ) ) @ top )
= ( join @ X0 @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl1223,zip_derived_cl1080]) ).
thf(zip_derived_cl0_032,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1258,plain,
! [X0: $i] :
( ( join @ top @ ( complement @ ( complement @ X0 ) ) )
= ( join @ X0 @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1236,zip_derived_cl0]) ).
thf(zip_derived_cl386_033,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl360,zip_derived_cl365]) ).
thf(zip_derived_cl11_034,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl1_035,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_cl1380,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( join @ ( complement @ X0 ) @ ( complement @ ( complement @ X0 ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl386,zip_derived_cl30]) ).
thf(zip_derived_cl11_036,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl0_037,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1427,plain,
! [X0: $i] :
( ( join @ top @ ( complement @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1380,zip_derived_cl11,zip_derived_cl0]) ).
thf(zip_derived_cl1465,plain,
! [X0: $i] :
( top
= ( join @ X0 @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl1258,zip_derived_cl1427]) ).
thf(zip_derived_cl365_038,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl359,zip_derived_cl338]) ).
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_cl383,plain,
! [X0: $i,X1: $i] :
( ( composition @ ( join @ one @ X1 ) @ X0 )
= ( join @ X0 @ ( composition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl365,zip_derived_cl6]) ).
thf(zip_derived_cl17299,plain,
! [X0: $i] :
( ( composition @ top @ X0 )
= ( join @ X0 @ ( composition @ top @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1465,zip_derived_cl383]) ).
thf(zip_derived_cl7_039,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl9_040,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl21,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ ( converse @ X0 ) ) )
= ( composition @ X0 @ ( converse @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
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_041,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl16,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_cl390,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( composition @ X1 @ ( converse @ X0 ) ) @ ( converse @ X2 ) )
= ( converse @ ( join @ X2 @ ( composition @ X0 @ ( converse @ X1 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl21,zip_derived_cl16]) ).
thf(zip_derived_cl18649,plain,
! [X0: $i] :
( ( join @ ( composition @ X0 @ ( converse @ top ) ) @ ( converse @ ( converse @ X0 ) ) )
= ( converse @ ( composition @ top @ ( converse @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl17299,zip_derived_cl390]) ).
thf(zip_derived_cl457_042,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= ( join @ top @ ( complement @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl424,zip_derived_cl202]) ).
thf(zip_derived_cl1427_043,plain,
! [X0: $i] :
( ( join @ top @ ( complement @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1380,zip_derived_cl11,zip_derived_cl0]) ).
thf(zip_derived_cl1464,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= top ),
inference(demod,[status(thm)],[zip_derived_cl457,zip_derived_cl1427]) ).
thf(zip_derived_cl7_044,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl8_045,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_additivity]) ).
thf(zip_derived_cl18,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X1 @ ( converse @ X0 ) ) )
= ( join @ ( converse @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl1504,plain,
! [X0: $i] :
( ( converse @ top )
= ( join @ ( converse @ top ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1464,zip_derived_cl18]) ).
thf(zip_derived_cl30_046,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_cl1811,plain,
( ( converse @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1504,zip_derived_cl30]) ).
thf(zip_derived_cl7_047,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl0_048,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1811_049,plain,
( ( converse @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1504,zip_derived_cl30]) ).
thf(zip_derived_cl9_050,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl1842,plain,
! [X0: $i] :
( ( converse @ ( composition @ X0 @ top ) )
= ( composition @ top @ ( converse @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1811,zip_derived_cl9]) ).
thf(zip_derived_cl7_051,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl2674,plain,
! [X0: $i] :
( ( converse @ ( composition @ top @ ( converse @ X0 ) ) )
= ( composition @ X0 @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1842,zip_derived_cl7]) ).
thf(zip_derived_cl18706,plain,
! [X0: $i] :
( ( join @ X0 @ ( composition @ X0 @ top ) )
= ( composition @ X0 @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl18649,zip_derived_cl1811,zip_derived_cl7,zip_derived_cl0,zip_derived_cl2674]) ).
thf(zip_derived_cl12_052,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl3_053,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_cl10_054,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_cl79,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( composition @ ( converse @ X2 ) @ ( complement @ ( composition @ X2 @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) ) ) ) @ ( meet @ X1 @ X0 ) )
= ( complement @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl10]) ).
thf(zip_derived_cl3_055,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_cl86,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( composition @ ( converse @ X2 ) @ ( complement @ ( composition @ X2 @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) ) ) ) @ ( meet @ X1 @ X0 ) )
= ( meet @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl79,zip_derived_cl3]) ).
thf(zip_derived_cl4476,plain,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X1 ) @ ( complement @ ( composition @ X1 @ ( join @ ( complement @ X0 ) @ ( complement @ ( complement @ X0 ) ) ) ) ) ) @ zero )
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl12,zip_derived_cl86]) ).
thf(zip_derived_cl424_056,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl386,zip_derived_cl3]) ).
thf(zip_derived_cl424_057,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl386,zip_derived_cl3]) ).
thf(zip_derived_cl386_058,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl360,zip_derived_cl365]) ).
thf(zip_derived_cl90_059,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_cl423,plain,
! [X0: $i] :
( X0
= ( join @ ( meet @ X0 @ ( complement @ X0 ) ) @ ( complement @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl386,zip_derived_cl90]) ).
thf(zip_derived_cl12_060,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl441,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl423,zip_derived_cl12]) ).
thf(zip_derived_cl53_061,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl0]) ).
thf(zip_derived_cl482,plain,
! [X0: $i] :
( ( meet @ ( complement @ X0 ) @ top )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl441,zip_derived_cl53]) ).
thf(zip_derived_cl496,plain,
! [X0: $i] :
( ( meet @ ( meet @ X0 @ X0 ) @ top )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl424,zip_derived_cl482]) ).
thf(zip_derived_cl1465_062,plain,
! [X0: $i] :
( top
= ( join @ X0 @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl1258,zip_derived_cl1427]) ).
thf(zip_derived_cl90_063,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_cl1518,plain,
! [X0: $i] :
( X0
= ( join @ ( meet @ X0 @ top ) @ ( complement @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1465,zip_derived_cl90]) ).
thf(zip_derived_cl48_064,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl12]) ).
thf(zip_derived_cl0_065,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1528,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1518,zip_derived_cl48,zip_derived_cl0]) ).
thf(zip_derived_cl2076,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl496,zip_derived_cl1528]) ).
thf(zip_derived_cl441_066,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl423,zip_derived_cl12]) ).
thf(zip_derived_cl2082,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl2076,zip_derived_cl441]) ).
thf(zip_derived_cl2087,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl424,zip_derived_cl2082]) ).
thf(zip_derived_cl2087_067,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl424,zip_derived_cl2082]) ).
thf(zip_derived_cl11_068,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl2210,plain,
! [X0: $i] :
( top
= ( join @ ( complement @ X0 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl2087,zip_derived_cl11]) ).
thf(zip_derived_cl2082_069,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl2076,zip_derived_cl441]) ).
thf(zip_derived_cl90_070,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_cl2095,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ ( complement @ ( join @ ( complement @ X0 ) @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2082,zip_derived_cl90]) ).
thf(zip_derived_cl0_071,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl11_072,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl48_073,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl12]) ).
thf(zip_derived_cl2104,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl2095,zip_derived_cl0,zip_derived_cl11,zip_derived_cl48]) ).
thf(zip_derived_cl12_074,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl4536,plain,
! [X1: $i] :
( ( composition @ ( converse @ X1 ) @ ( complement @ ( composition @ X1 @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl4476,zip_derived_cl2087,zip_derived_cl2210,zip_derived_cl2104,zip_derived_cl12]) ).
thf(zip_derived_cl20_075,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_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_cl328,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( composition @ ( composition @ ( converse @ X1 ) @ X0 ) @ ( complement @ ( composition @ ( composition @ ( converse @ X0 ) @ X1 ) @ X2 ) ) ) @ ( complement @ X2 ) )
= ( complement @ X2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl20,zip_derived_cl10]) ).
thf(zip_derived_cl4_077,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_cl4_078,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_cl0_079,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl344,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( complement @ X2 ) @ ( composition @ ( converse @ X1 ) @ ( composition @ X0 @ ( complement @ ( composition @ ( converse @ X0 ) @ ( composition @ X1 @ X2 ) ) ) ) ) )
= ( complement @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl328,zip_derived_cl4,zip_derived_cl4,zip_derived_cl0]) ).
thf(zip_derived_cl17043,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( complement @ ( composition @ X0 @ top ) ) ) @ ( composition @ ( converse @ ( converse @ X0 ) ) @ ( composition @ X1 @ ( complement @ ( composition @ ( converse @ X1 ) @ zero ) ) ) ) )
= ( complement @ ( complement @ ( composition @ X0 @ top ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4536,zip_derived_cl344]) ).
thf(zip_derived_cl2087_080,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl424,zip_derived_cl2082]) ).
thf(zip_derived_cl7_081,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl1811_082,plain,
( ( converse @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1504,zip_derived_cl30]) ).
thf(zip_derived_cl4536_083,plain,
! [X1: $i] :
( ( composition @ ( converse @ X1 ) @ ( complement @ ( composition @ X1 @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl4476,zip_derived_cl2087,zip_derived_cl2210,zip_derived_cl2104,zip_derived_cl12]) ).
thf(zip_derived_cl4789,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl1811,zip_derived_cl4536]) ).
thf(zip_derived_cl6_084,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_cl4819,plain,
! [X0: $i] :
( ( composition @ ( join @ top @ X0 ) @ ( complement @ ( composition @ top @ top ) ) )
= ( join @ zero @ ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4789,zip_derived_cl6]) ).
thf(zip_derived_cl1464_085,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= top ),
inference(demod,[status(thm)],[zip_derived_cl457,zip_derived_cl1427]) ).
thf(zip_derived_cl4789_086,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl1811,zip_derived_cl4536]) ).
thf(zip_derived_cl102_087,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl99,zip_derived_cl3]) ).
thf(zip_derived_cl2082_088,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl2076,zip_derived_cl441]) ).
thf(zip_derived_cl2086,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl102,zip_derived_cl2082]) ).
thf(zip_derived_cl4828,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4819,zip_derived_cl1464,zip_derived_cl4789,zip_derived_cl2086]) ).
thf(zip_derived_cl4_089,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_cl4846,plain,
! [X0: $i,X1: $i] :
( ( composition @ X1 @ ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl4828,zip_derived_cl4]) ).
thf(zip_derived_cl4828_090,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4819,zip_derived_cl1464,zip_derived_cl4789,zip_derived_cl2086]) ).
thf(zip_derived_cl4865,plain,
! [X1: $i] :
( ( composition @ X1 @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl4846,zip_derived_cl4828]) ).
thf(zip_derived_cl424_091,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl386,zip_derived_cl3]) ).
thf(zip_derived_cl482_092,plain,
! [X0: $i] :
( ( meet @ ( complement @ X0 ) @ top )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl441,zip_derived_cl53]) ).
thf(zip_derived_cl424_093,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl386,zip_derived_cl3]) ).
thf(zip_derived_cl48_094,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl12]) ).
thf(zip_derived_cl3_095,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_cl49,plain,
! [X0: $i] :
( ( meet @ top @ X0 )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl48,zip_derived_cl3]) ).
thf(zip_derived_cl446,plain,
! [X0: $i] :
( ( meet @ top @ ( complement @ X0 ) )
= ( complement @ ( join @ zero @ ( meet @ X0 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl424,zip_derived_cl49]) ).
thf(zip_derived_cl102_096,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl99,zip_derived_cl3]) ).
thf(zip_derived_cl460,plain,
! [X0: $i] :
( ( meet @ top @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl446,zip_derived_cl102]) ).
thf(zip_derived_cl90_097,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_cl464,plain,
! [X0: $i] :
( top
= ( join @ ( complement @ X0 ) @ ( complement @ ( join @ ( complement @ top ) @ ( complement @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl460,zip_derived_cl90]) ).
thf(zip_derived_cl48_098,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl12]) ).
thf(zip_derived_cl53_099,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl0]) ).
thf(zip_derived_cl476,plain,
! [X0: $i] :
( top
= ( join @ ( complement @ X0 ) @ ( meet @ X0 @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl464,zip_derived_cl48,zip_derived_cl53]) ).
thf(zip_derived_cl506,plain,
! [X0: $i] :
( top
= ( join @ ( complement @ ( complement @ X0 ) ) @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl482,zip_derived_cl476]) ).
thf(zip_derived_cl536,plain,
! [X0: $i] :
( top
= ( join @ ( complement @ ( complement @ ( complement @ X0 ) ) ) @ ( meet @ X0 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl424,zip_derived_cl506]) ).
thf(zip_derived_cl30_100,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_cl1385,plain,
! [X0: $i] :
( ( join @ ( complement @ ( complement @ ( complement @ X0 ) ) ) @ ( join @ ( meet @ X0 @ X0 ) @ ( complement @ top ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl536,zip_derived_cl30]) ).
thf(zip_derived_cl48_101,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl12]) ).
thf(zip_derived_cl0_102,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl102_103,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl99,zip_derived_cl3]) ).
thf(zip_derived_cl0_104,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1432,plain,
! [X0: $i] :
( ( join @ X0 @ ( complement @ ( complement @ ( complement @ X0 ) ) ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1385,zip_derived_cl48,zip_derived_cl0,zip_derived_cl102,zip_derived_cl0]) ).
thf(zip_derived_cl441_105,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl423,zip_derived_cl12]) ).
thf(zip_derived_cl1612,plain,
( ( complement @ zero )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1432,zip_derived_cl441]) ).
thf(zip_derived_cl4_106,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_107,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_cl108,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('sup+',[status(thm)],[zip_derived_cl4,zip_derived_cl6]) ).
thf(zip_derived_cl2087_108,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl424,zip_derived_cl2082]) ).
thf(zip_derived_cl17133,plain,
! [X0: $i,X1: $i] :
( ( composition @ ( join @ X0 @ ( composition @ X0 @ X1 ) ) @ top )
= ( composition @ X0 @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl17043,zip_derived_cl2087,zip_derived_cl7,zip_derived_cl4865,zip_derived_cl1612,zip_derived_cl108,zip_derived_cl2087]) ).
thf(zip_derived_cl36381,plain,
! [X0: $i] :
( ( composition @ ( composition @ X0 @ top ) @ top )
= ( composition @ X0 @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl18706,zip_derived_cl17133]) ).
thf(zip_derived_cl4536_109,plain,
! [X1: $i] :
( ( composition @ ( converse @ X1 ) @ ( complement @ ( composition @ X1 @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl4476,zip_derived_cl2087,zip_derived_cl2210,zip_derived_cl2104,zip_derived_cl12]) ).
thf(zip_derived_cl20_110,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_cl4757,plain,
! [X0: $i] :
( ( converse @ zero )
= ( composition @ ( converse @ ( complement @ ( composition @ X0 @ top ) ) ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl4536,zip_derived_cl20]) ).
thf(zip_derived_cl2086_111,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl102,zip_derived_cl2082]) ).
thf(zip_derived_cl18_112,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X1 @ ( converse @ X0 ) ) )
= ( join @ ( converse @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl2335,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( join @ ( converse @ zero ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl2086,zip_derived_cl18]) ).
thf(zip_derived_cl7_113,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl2344,plain,
! [X0: $i] :
( X0
= ( join @ ( converse @ zero ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2335,zip_derived_cl7]) ).
thf(zip_derived_cl2104_114,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl2095,zip_derived_cl0,zip_derived_cl11,zip_derived_cl48]) ).
thf(zip_derived_cl2577,plain,
( ( converse @ zero )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl2344,zip_derived_cl2104]) ).
thf(zip_derived_cl4813,plain,
! [X0: $i] :
( zero
= ( composition @ ( converse @ ( complement @ ( composition @ X0 @ top ) ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl4757,zip_derived_cl2577]) ).
thf(zip_derived_cl36530,plain,
! [X0: $i] :
( zero
= ( composition @ ( converse @ ( complement @ ( composition @ X0 @ top ) ) ) @ ( composition @ X0 @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl36381,zip_derived_cl4813]) ).
thf(zip_derived_cl10_115,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_cl37510,plain,
! [X0: $i] :
( ( join @ ( composition @ ( converse @ ( converse @ ( complement @ ( composition @ X0 @ top ) ) ) ) @ ( complement @ zero ) ) @ ( complement @ ( composition @ X0 @ top ) ) )
= ( complement @ ( composition @ X0 @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl36530,zip_derived_cl10]) ).
thf(zip_derived_cl7_116,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl1612_117,plain,
( ( complement @ zero )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1432,zip_derived_cl441]) ).
thf(zip_derived_cl18706_118,plain,
! [X0: $i] :
( ( join @ X0 @ ( composition @ X0 @ top ) )
= ( composition @ X0 @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl18649,zip_derived_cl1811,zip_derived_cl7,zip_derived_cl0,zip_derived_cl2674]) ).
thf(zip_derived_cl2086_119,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl102,zip_derived_cl2082]) ).
thf(zip_derived_cl27_120,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_cl2326,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ zero @ ( join @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2086,zip_derived_cl27]) ).
thf(zip_derived_cl20053,plain,
! [X0: $i] :
( ( join @ ( composition @ X0 @ top ) @ X0 )
= ( join @ zero @ ( composition @ X0 @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl18706,zip_derived_cl2326]) ).
thf(zip_derived_cl2086_121,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl102,zip_derived_cl2082]) ).
thf(zip_derived_cl20128,plain,
! [X0: $i] :
( ( join @ ( composition @ X0 @ top ) @ X0 )
= ( composition @ X0 @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl20053,zip_derived_cl2086]) ).
thf(zip_derived_cl37609,plain,
! [X0: $i] :
( ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top )
= ( complement @ ( composition @ X0 @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl37510,zip_derived_cl7,zip_derived_cl1612,zip_derived_cl20128]) ).
thf(zip_derived_cl37642,plain,
( ( complement @ ( composition @ sk_ @ top ) )
!= ( complement @ ( composition @ sk_ @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl13,zip_derived_cl37609]) ).
thf(zip_derived_cl37643,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl37642]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL050+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.XS4tKXtplY true
% 0.17/0.36 % Computer : n027.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Fri Aug 25 19:31:04 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.21/0.36 % Running portfolio for 300 s
% 0.21/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.36 % Number of cores: 8
% 0.21/0.36 % Python version: Python 3.6.8
% 0.21/0.36 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 39.26/6.26 % Solved by fo/fo5.sh.
% 39.26/6.26 % done 3598 iterations in 5.463s
% 39.26/6.26 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 39.26/6.26 % SZS output start Refutation
% See solution above
% 39.26/6.26
% 39.26/6.26
% 39.26/6.26 % Terminating...
% 39.53/6.41 % Runner terminated.
% 39.53/6.41 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------