TSTP Solution File: REL006+1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL006+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.HmG5NRPwVb 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 13:47:03 EDT 2023
% Result : Theorem 10.01s 2.17s
% Output : Refutation 10.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 22
% Syntax : Number of formulae : 236 ( 224 unt; 10 typ; 0 def)
% Number of atoms : 228 ( 227 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 1129 ( 2 ~; 0 |; 0 &;1125 @)
% ( 0 <=>; 2 =>; 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 : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 271 ( 0 ^; 271 !; 0 ?; 271 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk__type,type,
sk_: $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(converse_type,type,
converse: $i > $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(sk__1_type,type,
sk__1: $i ).
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_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_cl124,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl21]) ).
thf(zip_derived_cl7_001,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl130,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl124,zip_derived_cl7]) ).
thf(zip_derived_cl130_002,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl124,zip_derived_cl7]) ).
thf(zip_derived_cl5_003,plain,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[composition_identity]) ).
thf(zip_derived_cl132,plain,
( one
= ( converse @ one ) ),
inference('sup+',[status(thm)],[zip_derived_cl130,zip_derived_cl5]) ).
thf(zip_derived_cl136,plain,
! [X0: $i] :
( X0
= ( composition @ one @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl130,zip_derived_cl132]) ).
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_cl195,plain,
! [X0: $i] :
( ( join @ ( composition @ ( converse @ one ) @ ( complement @ X0 ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl136,zip_derived_cl10]) ).
thf(zip_derived_cl132_004,plain,
( one
= ( converse @ one ) ),
inference('sup+',[status(thm)],[zip_derived_cl130,zip_derived_cl5]) ).
thf(zip_derived_cl136_005,plain,
! [X0: $i] :
( X0
= ( composition @ one @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl130,zip_derived_cl132]) ).
thf(zip_derived_cl203,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl195,zip_derived_cl132,zip_derived_cl136]) ).
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(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_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_cl3503,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( join @ ( complement @ X0 ) @ ( complement @ ( complement @ X0 ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl203,zip_derived_cl31]) ).
thf(zip_derived_cl11_006,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl3528,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl3503,zip_derived_cl11]) ).
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_cl207,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_cl3823,plain,
! [X0: $i] :
( X0
= ( join @ ( meet @ X0 @ top ) @ ( complement @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3528,zip_derived_cl207]) ).
thf(zip_derived_cl11_007,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
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_cl172,plain,
! [X0: $i] :
( ( meet @ X0 @ ( complement @ X0 ) )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl3]) ).
thf(def_zero,axiom,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ) ).
thf(zip_derived_cl12,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl175,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl12]) ).
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_cl3835,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3823,zip_derived_cl175,zip_derived_cl0]) ).
thf(zip_derived_cl175_009,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl12]) ).
thf(zip_derived_cl3_010,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl232,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ ( complement @ X0 ) @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl175,zip_derived_cl3]) ).
thf(zip_derived_cl203_011,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl195,zip_derived_cl132,zip_derived_cl136]) ).
thf(zip_derived_cl3_012,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl3511,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl203,zip_derived_cl3]) ).
thf(zip_derived_cl207_013,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_cl3793,plain,
! [X0: $i] :
( X0
= ( join @ ( complement @ ( complement @ X0 ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3511,zip_derived_cl207]) ).
thf(zip_derived_cl0_014,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl11_015,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl175_016,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl12]) ).
thf(zip_derived_cl3802,plain,
! [X0: $i] :
( X0
= ( join @ ( complement @ ( complement @ X0 ) ) @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl3793,zip_derived_cl0,zip_derived_cl11,zip_derived_cl175]) ).
thf(zip_derived_cl232_017,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ ( complement @ X0 ) @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl175,zip_derived_cl3]) ).
thf(zip_derived_cl4678,plain,
! [X0: $i] :
( ( meet @ ( complement @ X0 ) @ top )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3802,zip_derived_cl232]) ).
thf(zip_derived_cl3835_018,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3823,zip_derived_cl175,zip_derived_cl0]) ).
thf(zip_derived_cl5020,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( join @ zero @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4678,zip_derived_cl3835]) ).
thf(zip_derived_cl5050,plain,
! [X0: $i] :
( ( complement @ ( join @ ( complement @ X0 ) @ zero ) )
= ( join @ zero @ ( meet @ X0 @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl232,zip_derived_cl5020]) ).
thf(zip_derived_cl232_019,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= ( complement @ ( join @ ( complement @ X0 ) @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl175,zip_derived_cl3]) ).
thf(zip_derived_cl3835_020,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ X0 @ top ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3823,zip_derived_cl175,zip_derived_cl0]) ).
thf(zip_derived_cl5053,plain,
! [X0: $i] :
( ( meet @ X0 @ top )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl5050,zip_derived_cl232,zip_derived_cl3835]) ).
thf(zip_derived_cl5148,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3835,zip_derived_cl5053]) ).
thf(goals,conjecture,
! [X0: $i,X1: $i] :
( ( ( meet @ ( converse @ X0 ) @ X1 )
= zero )
=> ( ( meet @ X0 @ ( converse @ X1 ) )
= zero ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( ( meet @ ( converse @ X0 ) @ X1 )
= zero )
=> ( ( meet @ X0 @ ( converse @ X1 ) )
= zero ) ),
inference('cnf.neg',[status(esa)],[goals]) ).
thf(zip_derived_cl13,plain,
( ( meet @ ( converse @ sk_ ) @ sk__1 )
= zero ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl207_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_cl216,plain,
( ( converse @ sk_ )
= ( join @ zero @ ( complement @ ( join @ ( complement @ ( converse @ sk_ ) ) @ sk__1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl13,zip_derived_cl207]) ).
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_cl218,plain,
( ( converse @ sk_ )
= ( join @ zero @ ( complement @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl216,zip_derived_cl0]) ).
thf(zip_derived_cl5186,plain,
( ( converse @ sk_ )
= ( complement @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5148,zip_derived_cl218]) ).
thf(zip_derived_cl5148_023,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3835,zip_derived_cl5053]) ).
thf(zip_derived_cl203_024,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl195,zip_derived_cl132,zip_derived_cl136]) ).
thf(zip_derived_cl207_025,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_cl3507,plain,
! [X0: $i] :
( X0
= ( join @ ( meet @ X0 @ ( complement @ X0 ) ) @ ( complement @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl203,zip_derived_cl207]) ).
thf(zip_derived_cl12_026,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl3530,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3507,zip_derived_cl12]) ).
thf(zip_derived_cl5187,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5148,zip_derived_cl3530]) ).
thf(zip_derived_cl5869,plain,
( ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) )
= ( complement @ ( converse @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5186,zip_derived_cl5187]) ).
thf(zip_derived_cl3530_027,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3507,zip_derived_cl12]) ).
thf(zip_derived_cl0_028,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl11_029,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl31_030,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_cl1025,plain,
! [X0: $i] :
( ( join @ X0 @ ( join @ ( complement @ X0 ) @ ( complement @ top ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl31]) ).
thf(zip_derived_cl175_031,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl12]) ).
thf(zip_derived_cl1073,plain,
! [X0: $i] :
( ( join @ X0 @ ( join @ ( complement @ X0 ) @ zero ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1025,zip_derived_cl175]) ).
thf(zip_derived_cl1393,plain,
! [X0: $i] :
( ( join @ X0 @ ( join @ zero @ ( complement @ X0 ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1073]) ).
thf(zip_derived_cl4157,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ X0 )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl3530,zip_derived_cl1393]) ).
thf(zip_derived_cl1_032,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_033,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_cl4182,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ top )
= ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4157,zip_derived_cl28]) ).
thf(zip_derived_cl3528_034,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl3503,zip_derived_cl11]) ).
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_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_cl218_038,plain,
( ( converse @ sk_ )
= ( join @ zero @ ( complement @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl216,zip_derived_cl0]) ).
thf(zip_derived_cl1_039,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl219,plain,
! [X0: $i] :
( ( join @ zero @ ( join @ ( complement @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) ) @ X0 ) )
= ( join @ ( converse @ sk_ ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl218,zip_derived_cl1]) ).
thf(zip_derived_cl221,plain,
! [X0: $i] :
( ( join @ zero @ ( join @ X0 @ ( complement @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) ) ) )
= ( join @ ( converse @ sk_ ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl219]) ).
thf(zip_derived_cl307,plain,
( ( join @ zero @ top )
= ( join @ ( converse @ sk_ ) @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl221]) ).
thf(zip_derived_cl175_040,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl12]) ).
thf(zip_derived_cl11_041,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl228,plain,
( top
= ( join @ top @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl175,zip_derived_cl11]) ).
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_cl234,plain,
( ( join @ zero @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl228,zip_derived_cl0]) ).
thf(zip_derived_cl311,plain,
( top
= ( join @ ( converse @ sk_ ) @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl307,zip_derived_cl234]) ).
thf(zip_derived_cl7_043,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_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_cl315,plain,
( ( converse @ top )
= ( join @ sk_ @ ( converse @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl311,zip_derived_cl20]) ).
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_cl0_046,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl17,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_cl27,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( converse @ X1 ) )
= ( converse @ ( join @ X1 @ ( converse @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl17]) ).
thf(zip_derived_cl625,plain,
( ( join @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) @ ( converse @ sk_ ) )
= ( converse @ ( converse @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl315,zip_derived_cl27]) ).
thf(zip_derived_cl7_047,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl648,plain,
( ( join @ ( join @ sk__1 @ ( complement @ ( converse @ sk_ ) ) ) @ ( converse @ sk_ ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl625,zip_derived_cl7]) ).
thf(zip_derived_cl1_048,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_cl681,plain,
( ( join @ sk__1 @ ( join @ ( complement @ ( converse @ sk_ ) ) @ ( converse @ sk_ ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl648,zip_derived_cl1]) ).
thf(zip_derived_cl11_049,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl7_050,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl17_051,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_cl26,plain,
! [X0: $i,X1: $i] :
( ( join @ ( converse @ X1 ) @ X0 )
= ( converse @ ( join @ ( converse @ X0 ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl17]) ).
thf(zip_derived_cl444,plain,
! [X0: $i] :
( ( join @ ( converse @ ( complement @ ( converse @ X0 ) ) ) @ X0 )
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl26]) ).
thf(zip_derived_cl20_052,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_cl494,plain,
! [X0: $i] :
( ( converse @ ( converse @ top ) )
= ( join @ ( complement @ ( converse @ X0 ) ) @ ( converse @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl444,zip_derived_cl20]) ).
thf(zip_derived_cl7_053,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl511,plain,
! [X0: $i] :
( top
= ( join @ ( complement @ ( converse @ X0 ) ) @ ( converse @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl494,zip_derived_cl7]) ).
thf(zip_derived_cl682,plain,
( ( join @ sk__1 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl681,zip_derived_cl511]) ).
thf(zip_derived_cl1_054,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_cl685,plain,
! [X0: $i] :
( ( join @ sk__1 @ ( join @ top @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl682,zip_derived_cl1]) ).
thf(zip_derived_cl687,plain,
! [X0: $i] :
( ( join @ sk__1 @ ( join @ X0 @ top ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl685]) ).
thf(zip_derived_cl3820,plain,
! [X0: $i] :
( ( join @ sk__1 @ top )
= ( join @ top @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3528,zip_derived_cl687]) ).
thf(zip_derived_cl682_055,plain,
( ( join @ sk__1 @ top )
= top ),
inference(demod,[status(thm)],[zip_derived_cl681,zip_derived_cl511]) ).
thf(zip_derived_cl3832,plain,
! [X0: $i] :
( top
= ( join @ top @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3820,zip_derived_cl682]) ).
thf(zip_derived_cl31_056,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_cl3882,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl3832,zip_derived_cl31]) ).
thf(zip_derived_cl4212,plain,
! [X0: $i,X1: $i] :
( top
= ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4182,zip_derived_cl3882]) ).
thf(zip_derived_cl5889,plain,
( top
= ( join @ ( complement @ sk__1 ) @ ( complement @ ( converse @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5869,zip_derived_cl4212]) ).
thf(zip_derived_cl3_057,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_cl6059,plain,
( ( meet @ sk__1 @ ( converse @ sk_ ) )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl5889,zip_derived_cl3]) ).
thf(zip_derived_cl175_058,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl12]) ).
thf(zip_derived_cl6067,plain,
( ( meet @ sk__1 @ ( converse @ sk_ ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl6059,zip_derived_cl175]) ).
thf(zip_derived_cl207_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_cl6069,plain,
( sk__1
= ( join @ zero @ ( complement @ ( join @ ( complement @ sk__1 ) @ ( converse @ sk_ ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6067,zip_derived_cl207]) ).
thf(zip_derived_cl5148_060,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3835,zip_derived_cl5053]) ).
thf(zip_derived_cl7027,plain,
( ( complement @ ( join @ ( complement @ sk__1 ) @ ( converse @ sk_ ) ) )
= sk__1 ),
inference('sup+',[status(thm)],[zip_derived_cl6069,zip_derived_cl5148]) ).
thf(zip_derived_cl5187_061,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5148,zip_derived_cl3530]) ).
thf(zip_derived_cl7041,plain,
( ( join @ ( complement @ sk__1 ) @ ( converse @ sk_ ) )
= ( complement @ sk__1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7027,zip_derived_cl5187]) ).
thf(zip_derived_cl7_062,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl8_063,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_cl7278,plain,
( ( converse @ ( complement @ sk__1 ) )
= ( join @ ( converse @ ( complement @ sk__1 ) ) @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl7041,zip_derived_cl19]) ).
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_cl4212_065,plain,
! [X0: $i,X1: $i] :
( top
= ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4182,zip_derived_cl3882]) ).
thf(zip_derived_cl5450,plain,
! [X0: $i,X1: $i] :
( top
= ( join @ ( complement @ X0 ) @ ( join @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl4212]) ).
thf(zip_derived_cl7408,plain,
( top
= ( join @ ( complement @ sk_ ) @ ( converse @ ( complement @ sk__1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7278,zip_derived_cl5450]) ).
thf(zip_derived_cl27_066,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( converse @ X1 ) )
= ( converse @ ( join @ X1 @ ( converse @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl17]) ).
thf(zip_derived_cl7746,plain,
( ( join @ ( complement @ sk__1 ) @ ( converse @ ( complement @ sk_ ) ) )
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl7408,zip_derived_cl27]) ).
thf(zip_derived_cl3882_067,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl3832,zip_derived_cl31]) ).
thf(zip_derived_cl444_068,plain,
! [X0: $i] :
( ( join @ ( converse @ ( complement @ ( converse @ X0 ) ) ) @ X0 )
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl26]) ).
thf(zip_derived_cl3927,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl3882,zip_derived_cl444]) ).
thf(zip_derived_cl7763,plain,
( ( join @ ( complement @ sk__1 ) @ ( converse @ ( complement @ sk_ ) ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl7746,zip_derived_cl3927]) ).
thf(zip_derived_cl207_069,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_cl8125,plain,
( sk__1
= ( join @ ( meet @ sk__1 @ ( converse @ ( complement @ sk_ ) ) ) @ ( complement @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7763,zip_derived_cl207]) ).
thf(zip_derived_cl175_070,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl12]) ).
thf(zip_derived_cl5148_071,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3835,zip_derived_cl5053]) ).
thf(zip_derived_cl0_072,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl5157,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl5148,zip_derived_cl0]) ).
thf(zip_derived_cl8142,plain,
( sk__1
= ( meet @ sk__1 @ ( converse @ ( complement @ sk_ ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8125,zip_derived_cl175,zip_derived_cl5157]) ).
thf(zip_derived_cl0_073,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl3_074,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_cl170,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_075,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_cl9611,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl170,zip_derived_cl3]) ).
thf(zip_derived_cl207_076,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_cl4212_077,plain,
! [X0: $i,X1: $i] :
( top
= ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4182,zip_derived_cl3882]) ).
thf(zip_derived_cl207_078,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_cl5448,plain,
! [X0: $i,X1: $i] :
( X1
= ( join @ ( meet @ X1 @ ( join @ X1 @ X0 ) ) @ ( complement @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4212,zip_derived_cl207]) ).
thf(zip_derived_cl175_079,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl12]) ).
thf(zip_derived_cl5157_080,plain,
! [X0: $i] :
( ( join @ X0 @ zero )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl5148,zip_derived_cl0]) ).
thf(zip_derived_cl5506,plain,
! [X0: $i,X1: $i] :
( X1
= ( meet @ X1 @ ( join @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5448,zip_derived_cl175,zip_derived_cl5157]) ).
thf(zip_derived_cl5528,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ ( meet @ X0 @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl207,zip_derived_cl5506]) ).
thf(zip_derived_cl9731,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ ( meet @ X1 @ X0 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl9611,zip_derived_cl5528]) ).
thf(zip_derived_cl9817,plain,
( ( meet @ ( converse @ ( complement @ sk_ ) ) @ sk__1 )
= ( meet @ sk__1 @ ( converse @ ( complement @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8142,zip_derived_cl9731]) ).
thf(zip_derived_cl8142_081,plain,
( sk__1
= ( meet @ sk__1 @ ( converse @ ( complement @ sk_ ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8125,zip_derived_cl175,zip_derived_cl5157]) ).
thf(zip_derived_cl9837,plain,
( ( meet @ ( converse @ ( complement @ sk_ ) ) @ sk__1 )
= sk__1 ),
inference(demod,[status(thm)],[zip_derived_cl9817,zip_derived_cl8142]) ).
thf(zip_derived_cl207_082,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_cl5187_083,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5148,zip_derived_cl3530]) ).
thf(zip_derived_cl203_084,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl195,zip_derived_cl132,zip_derived_cl136]) ).
thf(zip_derived_cl5561,plain,
! [X0: $i] :
( ( join @ ( complement @ ( complement @ X0 ) ) @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5187,zip_derived_cl203]) ).
thf(zip_derived_cl5187_085,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5148,zip_derived_cl3530]) ).
thf(zip_derived_cl5187_086,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5148,zip_derived_cl3530]) ).
thf(zip_derived_cl5576,plain,
! [X0: $i] :
( ( join @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl5561,zip_derived_cl5187,zip_derived_cl5187]) ).
thf(zip_derived_cl1_087,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_cl5781,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( join @ X0 @ X1 ) )
= ( join @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5576,zip_derived_cl1]) ).
thf(zip_derived_cl8805,plain,
! [X0: $i,X1: $i] :
( ( join @ ( meet @ X0 @ X1 ) @ X0 )
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl207,zip_derived_cl5781]) ).
thf(zip_derived_cl0_088,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl207_089,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_cl8852,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( meet @ X0 @ X1 ) )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl8805,zip_derived_cl0,zip_derived_cl207]) ).
thf(zip_derived_cl20_090,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_cl8931,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( converse @ X0 ) )
= ( join @ X0 @ ( converse @ ( meet @ ( converse @ X0 ) @ X1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8852,zip_derived_cl20]) ).
thf(zip_derived_cl7_091,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl8964,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ X0 @ ( converse @ ( meet @ ( converse @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8931,zip_derived_cl7]) ).
thf(zip_derived_cl9916,plain,
( ( complement @ sk_ )
= ( join @ ( complement @ sk_ ) @ ( converse @ sk__1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9837,zip_derived_cl8964]) ).
thf(zip_derived_cl5450_092,plain,
! [X0: $i,X1: $i] :
( top
= ( join @ ( complement @ X0 ) @ ( join @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl4212]) ).
thf(zip_derived_cl10432,plain,
( top
= ( join @ ( complement @ ( converse @ sk__1 ) ) @ ( complement @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9916,zip_derived_cl5450]) ).
thf(zip_derived_cl3_093,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_cl12_094,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl167,plain,
! [X0: $i,X1: $i] :
( zero
= ( meet @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) @ ( meet @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl12]) ).
thf(zip_derived_cl11426,plain,
( zero
= ( meet @ top @ ( meet @ ( converse @ sk__1 ) @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10432,zip_derived_cl167]) ).
thf(zip_derived_cl9611_095,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl170,zip_derived_cl3]) ).
thf(zip_derived_cl175_096,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl12]) ).
thf(zip_derived_cl3_097,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_cl226,plain,
! [X0: $i] :
( ( meet @ top @ X0 )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl175,zip_derived_cl3]) ).
thf(zip_derived_cl5020_098,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( join @ zero @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4678,zip_derived_cl3835]) ).
thf(zip_derived_cl5033,plain,
! [X0: $i] :
( ( meet @ top @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl226,zip_derived_cl5020]) ).
thf(zip_derived_cl5187_099,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5148,zip_derived_cl3530]) ).
thf(zip_derived_cl5556,plain,
! [X0: $i] :
( ( meet @ top @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl5033,zip_derived_cl5187]) ).
thf(zip_derived_cl11444,plain,
( zero
= ( meet @ sk_ @ ( converse @ sk__1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl11426,zip_derived_cl9611,zip_derived_cl5556]) ).
thf(zip_derived_cl14,plain,
( ( meet @ sk_ @ ( converse @ sk__1 ) )
!= zero ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl11445,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl11444,zip_derived_cl14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL006+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.HmG5NRPwVb true
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.21/0.35 % WCLimit : 300
% 0.21/0.35 % DateTime : Fri Aug 25 20:40:19 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.35 % Running portfolio for 300 s
% 0.21/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.35 % Number of cores: 8
% 0.21/0.35 % Python version: Python 3.6.8
% 0.21/0.36 % Running in FO mode
% 0.22/0.64 % Total configuration time : 435
% 0.22/0.64 % Estimated wc time : 1092
% 0.22/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 10.01/2.17 % Solved by fo/fo4.sh.
% 10.01/2.17 % done 1491 iterations in 1.384s
% 10.01/2.17 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 10.01/2.17 % SZS output start Refutation
% See solution above
% 10.01/2.17
% 10.01/2.17
% 10.01/2.17 % Terminating...
% 10.99/2.25 % Runner terminated.
% 10.99/2.26 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------