%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL018+1 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.BsXku9dQxM true
% Computer : n004.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 04:50:00 PM UTC 2025
% Result : Theorem 4.72s 1.27s
% Output : Refutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 14
% Syntax : Number of formulae : 247 ( 245 unt; 0 typ; 0 def)
% Number of atoms : 249 ( 248 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 1234 ( 2 ~; 0 |; 0 &;1230 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 251 ( 0 ^; 251 !; 0 ?; 251 :)
% 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(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(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_cl176,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_cl191,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl12,zip_derived_cl176]) ).
thf(zip_derived_cl3_001,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl196,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl191,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(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_cl11_002,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl3_003,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_cl46,plain,
! [X0: $i] :
( ( meet @ X0 @ ( complement @ X0 ) )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl3]) ).
thf(zip_derived_cl12_004,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl49,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl3_005,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_cl53,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ ( complement @ X0 ) @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl49,zip_derived_cl3]) ).
thf(zip_derived_cl80,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl53]) ).
thf(zip_derived_cl300,plain,
( ( meet @ zero @ top )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl80]) ).
thf(zip_derived_cl49_006,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl308,plain,
( ( meet @ zero @ top )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl300,zip_derived_cl49]) ).
thf(zip_derived_cl176_007,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_cl313,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ ( complement @ zero ) @ top ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl308,zip_derived_cl176]) ).
thf(zip_derived_cl0_008,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl11_009,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl49_010,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,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_cl51,plain,
( top
= ( join @ top @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl49,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_cl54,plain,
! [X0: $i] :
( ( join @ top @ ( join @ zero @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl51,zip_derived_cl1]) ).
thf(zip_derived_cl161,plain,
( ( join @ top @ top )
= ( join @ top @ ( complement @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl54]) ).
thf(zip_derived_cl315,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl313,zip_derived_cl0,zip_derived_cl161]) ).
thf(zip_derived_cl315_012,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl313,zip_derived_cl0,zip_derived_cl161]) ).
thf(zip_derived_cl80_013,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl53]) ).
thf(zip_derived_cl319,plain,
( ( meet @ ( join @ top @ top ) @ top )
= ( complement @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl315,zip_derived_cl80]) ).
thf(zip_derived_cl176_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_cl330,plain,
( ( join @ top @ top )
= ( join @ ( complement @ zero ) @ ( complement @ ( join @ ( complement @ ( join @ top @ top ) ) @ top ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl319,zip_derived_cl176]) ).
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_cl315_016,plain,
( zero
= ( join @ zero @ ( complement @ ( join @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl313,zip_derived_cl0,zip_derived_cl161]) ).
thf(zip_derived_cl54_017,plain,
! [X0: $i] :
( ( join @ top @ ( join @ zero @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl51,zip_derived_cl1]) ).
thf(zip_derived_cl317,plain,
( ( join @ top @ zero )
= ( join @ top @ ( complement @ ( join @ top @ top ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl315,zip_derived_cl54]) ).
thf(zip_derived_cl51_018,plain,
( top
= ( join @ top @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl49,zip_derived_cl11]) ).
thf(zip_derived_cl322,plain,
( top
= ( join @ top @ ( complement @ ( join @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl317,zip_derived_cl51]) ).
thf(zip_derived_cl49_019,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl0_020,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl11_021,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl334,plain,
( ( join @ top @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl330,zip_derived_cl0,zip_derived_cl322,zip_derived_cl49,zip_derived_cl0,zip_derived_cl11]) ).
thf(zip_derived_cl49_022,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl337,plain,
( zero
= ( join @ zero @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl315,zip_derived_cl334,zip_derived_cl49]) ).
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_cl379,plain,
! [X0: $i] :
( ( join @ zero @ ( join @ zero @ X0 ) )
= ( join @ zero @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl337,zip_derived_cl1]) ).
thf(zip_derived_cl660,plain,
! [X0: $i] :
( ( join @ zero @ X0 )
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl196,zip_derived_cl379]) ).
thf(zip_derived_cl196_024,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl191,zip_derived_cl3]) ).
thf(zip_derived_cl666,plain,
! [X0: $i] :
( ( join @ zero @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl660,zip_derived_cl196]) ).
thf(goals,conjecture,
! [X0: $i] :
( ( ( composition @ X0 @ top )
= X0 )
=> ( ( composition @ ( complement @ X0 ) @ top )
= ( complement @ X0 ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [X0: $i] :
( ( ( composition @ X0 @ top )
= X0 )
=> ( ( composition @ ( complement @ X0 ) @ top )
= ( complement @ X0 ) ) ),
inference('cnf.neg',[status(esa)],[goals]) ).
thf(zip_derived_cl13,plain,
( ( composition @ sk_ @ top )
= sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
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_cl251,plain,
( ( join @ ( composition @ ( converse @ sk_ ) @ ( complement @ sk_ ) ) @ ( complement @ top ) )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl13,zip_derived_cl10]) ).
thf(zip_derived_cl49_025,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl0_026,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl49_027,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl262,plain,
( ( join @ zero @ ( composition @ ( converse @ sk_ ) @ ( complement @ sk_ ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl251,zip_derived_cl49,zip_derived_cl0,zip_derived_cl49]) ).
thf(zip_derived_cl692,plain,
( ( composition @ ( converse @ sk_ ) @ ( complement @ sk_ ) )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl262]) ).
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_cl21,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_cl754,plain,
( ( converse @ zero )
= ( composition @ ( converse @ ( complement @ sk_ ) ) @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl692,zip_derived_cl21]) ).
thf(zip_derived_cl10_028,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_cl792,plain,
( ( join @ ( composition @ ( converse @ ( converse @ ( complement @ sk_ ) ) ) @ ( complement @ ( converse @ zero ) ) ) @ ( complement @ sk_ ) )
= ( complement @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl754,zip_derived_cl10]) ).
thf(zip_derived_cl7_029,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
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_cl794,plain,
( ( join @ ( complement @ sk_ ) @ ( composition @ ( complement @ sk_ ) @ ( complement @ ( converse @ zero ) ) ) )
= ( complement @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl792,zip_derived_cl7,zip_derived_cl0]) ).
thf(zip_derived_cl666_031,plain,
! [X0: $i] :
( ( join @ zero @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl660,zip_derived_cl196]) ).
thf(zip_derived_cl7_032,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_cl19,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_cl685,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( join @ ( converse @ zero ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl19]) ).
thf(zip_derived_cl7_033,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl698,plain,
! [X0: $i] :
( X0
= ( join @ ( converse @ zero ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl685,zip_derived_cl7]) ).
thf(zip_derived_cl666_034,plain,
! [X0: $i] :
( ( join @ zero @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl660,zip_derived_cl196]) ).
thf(zip_derived_cl0_035,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl677,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl0]) ).
thf(zip_derived_cl1010,plain,
( zero
= ( converse @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl698,zip_derived_cl677]) ).
thf(zip_derived_cl666_036,plain,
! [X0: $i] :
( ( join @ zero @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl660,zip_derived_cl196]) ).
thf(zip_derived_cl11_037,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl684,plain,
( top
= ( complement @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl11]) ).
thf(zip_derived_cl1031,plain,
( ( join @ ( complement @ sk_ ) @ ( composition @ ( complement @ sk_ ) @ top ) )
= ( complement @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl794,zip_derived_cl1010,zip_derived_cl684]) ).
thf(zip_derived_cl0_038,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl11_039,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl0_040,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1_041,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_cl32,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X1 @ X0 ) @ X2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1]) ).
thf(zip_derived_cl2411,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl32]) ).
thf(zip_derived_cl0_042,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl334_043,plain,
( ( join @ top @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl330,zip_derived_cl0,zip_derived_cl322,zip_derived_cl49,zip_derived_cl0,zip_derived_cl11]) ).
thf(zip_derived_cl1_044,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_cl342,plain,
! [X0: $i] :
( ( join @ top @ ( join @ top @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl334,zip_derived_cl1]) ).
thf(zip_derived_cl572,plain,
! [X0: $i] :
( ( join @ top @ ( join @ X0 @ top ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl342]) ).
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(zip_derived_cl21_045,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_cl729,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl21]) ).
thf(zip_derived_cl7_046,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl736,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl729,zip_derived_cl7]) ).
thf(zip_derived_cl5_047,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_cl117,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_cl905,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl736,zip_derived_cl117]) ).
thf(zip_derived_cl736_048,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl729,zip_derived_cl7]) ).
thf(zip_derived_cl914,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl905,zip_derived_cl736]) ).
thf(zip_derived_cl10_049,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_cl921,plain,
! [X0: $i] :
( ( join @ ( composition @ ( converse @ one ) @ ( complement @ X0 ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl914,zip_derived_cl10]) ).
thf(zip_derived_cl736_050,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl729,zip_derived_cl7]) ).
thf(zip_derived_cl925,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl921,zip_derived_cl736]) ).
thf(zip_derived_cl176_051,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_cl1072,plain,
! [X0: $i] :
( X0
= ( join @ ( meet @ X0 @ ( complement @ X0 ) ) @ ( complement @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl925,zip_derived_cl176]) ).
thf(zip_derived_cl12_052,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl666_053,plain,
! [X0: $i] :
( ( join @ zero @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl660,zip_derived_cl196]) ).
thf(zip_derived_cl1086,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1072,zip_derived_cl12,zip_derived_cl666]) ).
thf(zip_derived_cl925_054,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl921,zip_derived_cl736]) ).
thf(zip_derived_cl1097,plain,
! [X0: $i] :
( ( join @ ( complement @ ( complement @ X0 ) ) @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1086,zip_derived_cl925]) ).
thf(zip_derived_cl1086_055,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1072,zip_derived_cl12,zip_derived_cl666]) ).
thf(zip_derived_cl1086_056,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1072,zip_derived_cl12,zip_derived_cl666]) ).
thf(zip_derived_cl1106,plain,
! [X0: $i] :
( ( join @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl1097,zip_derived_cl1086,zip_derived_cl1086]) ).
thf(zip_derived_cl11_057,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl1_058,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl31,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ X0 @ ( complement @ ( join @ X1 @ X0 ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).
thf(zip_derived_cl2103,plain,
! [X0: $i] :
( ( join @ X0 @ ( join @ X0 @ ( complement @ X0 ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1106,zip_derived_cl31]) ).
thf(zip_derived_cl11_059,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl2151,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl2103,zip_derived_cl11]) ).
thf(zip_derived_cl2151_060,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl2103,zip_derived_cl11]) ).
thf(zip_derived_cl2239,plain,
! [X0: $i] :
( top
= ( join @ top @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl572,zip_derived_cl2151,zip_derived_cl2151]) ).
thf(zip_derived_cl2449,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl2411,zip_derived_cl2239]) ).
thf(zip_derived_cl3286,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X0 ) @ ( join @ X1 @ X0 ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl2449]) ).
thf(zip_derived_cl3868,plain,
( ( join @ ( complement @ ( composition @ ( complement @ sk_ ) @ top ) ) @ ( complement @ sk_ ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1031,zip_derived_cl3286]) ).
thf(zip_derived_cl176_061,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_cl4065,plain,
( ( composition @ ( complement @ sk_ ) @ top )
= ( join @ ( meet @ ( composition @ ( complement @ sk_ ) @ top ) @ ( complement @ sk_ ) ) @ ( complement @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3868,zip_derived_cl176]) ).
thf(zip_derived_cl49_062,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl677_063,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl0]) ).
thf(zip_derived_cl4080,plain,
( ( composition @ ( complement @ sk_ ) @ top )
= ( meet @ ( composition @ ( complement @ sk_ ) @ top ) @ ( complement @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4065,zip_derived_cl49,zip_derived_cl677]) ).
thf(zip_derived_cl0_064,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl3_065,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_cl44,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl3]) ).
thf(zip_derived_cl3_066,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl4016,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl44,zip_derived_cl3]) ).
thf(zip_derived_cl4234,plain,
( ( composition @ ( complement @ sk_ ) @ top )
= ( meet @ ( complement @ sk_ ) @ ( composition @ ( complement @ sk_ ) @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4080,zip_derived_cl4016]) ).
thf(zip_derived_cl176_067,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl4659,plain,
( ( complement @ sk_ )
= ( join @ ( composition @ ( complement @ sk_ ) @ top ) @ ( complement @ ( join @ ( complement @ ( complement @ sk_ ) ) @ ( composition @ ( complement @ sk_ ) @ top ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4234,zip_derived_cl176]) ).
thf(zip_derived_cl1086_068,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1072,zip_derived_cl12,zip_derived_cl666]) ).
thf(zip_derived_cl11_069,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl13_070,plain,
( ( composition @ sk_ @ top )
= sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
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_cl140,plain,
! [X0: $i] :
( ( composition @ ( join @ sk_ @ X0 ) @ top )
= ( join @ sk_ @ ( composition @ X0 @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl13,zip_derived_cl6]) ).
thf(zip_derived_cl149,plain,
( ( composition @ top @ top )
= ( join @ sk_ @ ( composition @ ( complement @ sk_ ) @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl140]) ).
thf(zip_derived_cl149_071,plain,
( ( composition @ top @ top )
= ( join @ sk_ @ ( composition @ ( complement @ sk_ ) @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl140]) ).
thf(zip_derived_cl31_072,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_cl2134,plain,
( ( join @ sk_ @ ( join @ ( composition @ ( complement @ sk_ ) @ top ) @ ( complement @ ( composition @ top @ top ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl149,zip_derived_cl31]) ).
thf(zip_derived_cl1106_073,plain,
! [X0: $i] :
( ( join @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl1097,zip_derived_cl1086,zip_derived_cl1086]) ).
thf(zip_derived_cl149_074,plain,
( ( composition @ top @ top )
= ( join @ sk_ @ ( composition @ ( complement @ sk_ ) @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl140]) ).
thf(zip_derived_cl1_075,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_cl232,plain,
! [X0: $i] :
( ( join @ sk_ @ ( join @ ( composition @ ( complement @ sk_ ) @ top ) @ X0 ) )
= ( join @ ( composition @ top @ top ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl149,zip_derived_cl1]) ).
thf(zip_derived_cl1218,plain,
( ( join @ sk_ @ ( composition @ ( complement @ sk_ ) @ top ) )
= ( join @ ( composition @ top @ top ) @ ( composition @ ( complement @ sk_ ) @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1106,zip_derived_cl232]) ).
thf(zip_derived_cl149_076,plain,
( ( composition @ top @ top )
= ( join @ sk_ @ ( composition @ ( complement @ sk_ ) @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl140]) ).
thf(zip_derived_cl1240,plain,
( ( composition @ top @ top )
= ( join @ ( composition @ top @ top ) @ ( composition @ ( complement @ sk_ ) @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1218,zip_derived_cl149]) ).
thf(zip_derived_cl6_077,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_cl1360,plain,
( ( composition @ ( join @ top @ ( complement @ sk_ ) ) @ top )
= ( composition @ top @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1240,zip_derived_cl6]) ).
thf(zip_derived_cl0_078,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1361,plain,
( ( composition @ ( join @ ( complement @ sk_ ) @ top ) @ top )
= ( composition @ top @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl1360,zip_derived_cl0]) ).
thf(zip_derived_cl10_079,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_cl1365,plain,
( ( join @ ( composition @ ( converse @ ( join @ ( complement @ sk_ ) @ top ) ) @ ( complement @ ( composition @ top @ top ) ) ) @ ( complement @ top ) )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1361,zip_derived_cl10]) ).
thf(zip_derived_cl49_080,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl677_081,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl0]) ).
thf(zip_derived_cl49_082,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl1371,plain,
( ( composition @ ( converse @ ( join @ ( complement @ sk_ ) @ top ) ) @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl1365,zip_derived_cl49,zip_derived_cl677,zip_derived_cl49]) ).
thf(zip_derived_cl1086_083,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1072,zip_derived_cl12,zip_derived_cl666]) ).
thf(zip_derived_cl11_084,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl1094,plain,
! [X0: $i] :
( top
= ( join @ ( complement @ X0 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1086,zip_derived_cl11]) ).
thf(zip_derived_cl677_085,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl0]) ).
thf(zip_derived_cl754_086,plain,
( ( converse @ zero )
= ( composition @ ( converse @ ( complement @ sk_ ) ) @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl692,zip_derived_cl21]) ).
thf(zip_derived_cl1010_087,plain,
( zero
= ( converse @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl698,zip_derived_cl677]) ).
thf(zip_derived_cl1030,plain,
( zero
= ( composition @ ( converse @ ( complement @ sk_ ) ) @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl754,zip_derived_cl1010]) ).
thf(zip_derived_cl6_088,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_cl1053,plain,
! [X0: $i] :
( ( composition @ ( join @ ( converse @ ( complement @ sk_ ) ) @ X0 ) @ sk_ )
= ( join @ zero @ ( composition @ X0 @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1030,zip_derived_cl6]) ).
thf(zip_derived_cl666_089,plain,
! [X0: $i] :
( ( join @ zero @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl660,zip_derived_cl196]) ).
thf(zip_derived_cl1057,plain,
! [X0: $i] :
( ( composition @ ( join @ ( converse @ ( complement @ sk_ ) ) @ X0 ) @ sk_ )
= ( composition @ X0 @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl1053,zip_derived_cl666]) ).
thf(zip_derived_cl1544,plain,
( ( composition @ ( converse @ ( complement @ sk_ ) ) @ sk_ )
= ( composition @ zero @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl677,zip_derived_cl1057]) ).
thf(zip_derived_cl1030_090,plain,
( zero
= ( composition @ ( converse @ ( complement @ sk_ ) ) @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl754,zip_derived_cl1010]) ).
thf(zip_derived_cl1548,plain,
( zero
= ( composition @ zero @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl1544,zip_derived_cl1030]) ).
thf(zip_derived_cl1010_091,plain,
( zero
= ( converse @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl698,zip_derived_cl677]) ).
thf(zip_derived_cl21_092,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_cl1038,plain,
! [X0: $i] :
( ( converse @ ( composition @ zero @ X0 ) )
= ( composition @ ( converse @ X0 ) @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl1010,zip_derived_cl21]) ).
thf(zip_derived_cl1862,plain,
( ( converse @ zero )
= ( composition @ ( converse @ sk_ ) @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl1548,zip_derived_cl1038]) ).
thf(zip_derived_cl1010_093,plain,
( zero
= ( converse @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl698,zip_derived_cl677]) ).
thf(zip_derived_cl1869,plain,
( zero
= ( composition @ ( converse @ sk_ ) @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl1862,zip_derived_cl1010]) ).
thf(zip_derived_cl10_094,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_cl1895,plain,
( ( join @ ( composition @ ( converse @ ( converse @ sk_ ) ) @ ( complement @ zero ) ) @ ( complement @ zero ) )
= ( complement @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl1869,zip_derived_cl10]) ).
thf(zip_derived_cl7_095,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl684_096,plain,
( top
= ( complement @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl11]) ).
thf(zip_derived_cl13_097,plain,
( ( composition @ sk_ @ top )
= sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl684_098,plain,
( top
= ( complement @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl11]) ).
thf(zip_derived_cl684_099,plain,
( top
= ( complement @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl11]) ).
thf(zip_derived_cl1900,plain,
( ( join @ sk_ @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1895,zip_derived_cl7,zip_derived_cl684,zip_derived_cl13,zip_derived_cl684,zip_derived_cl684]) ).
thf(zip_derived_cl1_100,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_101,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl28,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_cl1905,plain,
! [X0: $i] :
( ( join @ top @ ( join @ X0 @ sk_ ) )
= ( join @ X0 @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1900,zip_derived_cl28]) ).
thf(zip_derived_cl2032,plain,
( ( join @ top @ top )
= ( join @ ( complement @ sk_ ) @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1094,zip_derived_cl1905]) ).
thf(zip_derived_cl1106_102,plain,
! [X0: $i] :
( ( join @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl1097,zip_derived_cl1086,zip_derived_cl1086]) ).
thf(zip_derived_cl2036,plain,
( top
= ( join @ ( complement @ sk_ ) @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl2032,zip_derived_cl1106]) ).
thf(zip_derived_cl2060,plain,
( ( composition @ ( converse @ top ) @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl1371,zip_derived_cl2036]) ).
thf(zip_derived_cl2151_103,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl2103,zip_derived_cl11]) ).
thf(zip_derived_cl7_104,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl8_105,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_additivity]) ).
thf(zip_derived_cl20,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ ( converse @ X0 ) @ X1 ) )
= ( join @ X0 @ ( converse @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl2253,plain,
! [X0: $i] :
( ( converse @ top )
= ( join @ X0 @ ( converse @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2151,zip_derived_cl20]) ).
thf(zip_derived_cl1094_106,plain,
! [X0: $i] :
( top
= ( join @ ( complement @ X0 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1086,zip_derived_cl11]) ).
thf(zip_derived_cl2500,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl2253,zip_derived_cl1094]) ).
thf(zip_derived_cl2534,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl2060,zip_derived_cl2500]) ).
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_cl2621,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_cl2534,zip_derived_cl6]) ).
thf(zip_derived_cl2239_108,plain,
! [X0: $i] :
( top
= ( join @ top @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl572,zip_derived_cl2151,zip_derived_cl2151]) ).
thf(zip_derived_cl2534_109,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl2060,zip_derived_cl2500]) ).
thf(zip_derived_cl666_110,plain,
! [X0: $i] :
( ( join @ zero @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl660,zip_derived_cl196]) ).
thf(zip_derived_cl2626,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2621,zip_derived_cl2239,zip_derived_cl2534,zip_derived_cl666]) ).
thf(zip_derived_cl914_111,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl905,zip_derived_cl736]) ).
thf(zip_derived_cl2860,plain,
( zero
= ( complement @ ( composition @ top @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2626,zip_derived_cl914]) ).
thf(zip_derived_cl677_112,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl0]) ).
thf(zip_derived_cl149_113,plain,
( ( composition @ top @ top )
= ( join @ sk_ @ ( composition @ ( complement @ sk_ ) @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl140]) ).
thf(zip_derived_cl2878,plain,
( ( composition @ top @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl2134,zip_derived_cl2860,zip_derived_cl677,zip_derived_cl149]) ).
thf(zip_derived_cl2901,plain,
( top
= ( join @ sk_ @ ( composition @ ( complement @ sk_ ) @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl149,zip_derived_cl2878]) ).
thf(zip_derived_cl49_114,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl46,zip_derived_cl12]) ).
thf(zip_derived_cl677_115,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl666,zip_derived_cl0]) ).
thf(zip_derived_cl4661,plain,
( ( complement @ sk_ )
= ( composition @ ( complement @ sk_ ) @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl4659,zip_derived_cl1086,zip_derived_cl2901,zip_derived_cl49,zip_derived_cl677]) ).
thf(zip_derived_cl14,plain,
( ( composition @ ( complement @ sk_ ) @ top )
!= ( complement @ sk_ ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4662,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl4661,zip_derived_cl14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL018+1 : TPTP v9.2.0. Released v4.0.0.
% 0.04/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.BsXku9dQxM true
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 12:22:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.56/0.64 % Total configuration time : 435
% 0.56/0.64 % Estimated wc time : 1092
% 0.56/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 4.72/1.27 % Solved by fo/fo4.sh.
% 4.72/1.27 % done 713 iterations in 0.485s
% 4.72/1.27 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.72/1.27 % SZS output start Refutation
% See solution above
% 4.72/1.27
% 4.72/1.27
% 4.72/1.27 % Terminating...
% 5.13/1.36 % Runner terminated.
% 5.13/1.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------