TSTP Solution File: REL004-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL004-3 : 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.5jNChfTRQA true
% Computer : n009.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 13:47:01 EDT 2023
% Result : Unsatisfiable 0.56s 1.26s
% Output : Refutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL004-3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.5jNChfTRQA true
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 18:56:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.47/0.64 % Total configuration time : 435
% 0.47/0.64 % Estimated wc time : 1092
% 0.47/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.47/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.47/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.56/1.26 % Solved by fo/fo4.sh.
% 0.56/1.26 % done 407 iterations in 0.463s
% 0.56/1.26 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.56/1.26 % SZS output start Refutation
% 0.56/1.26 thf(composition_type, type, composition: $i > $i > $i).
% 0.56/1.26 thf(meet_type, type, meet: $i > $i > $i).
% 0.56/1.26 thf(complement_type, type, complement: $i > $i).
% 0.56/1.26 thf(sk1_type, type, sk1: $i).
% 0.56/1.26 thf(converse_type, type, converse: $i > $i).
% 0.56/1.26 thf(top_type, type, top: $i).
% 0.56/1.26 thf(join_type, type, join: $i > $i > $i).
% 0.56/1.26 thf(zero_type, type, zero: $i).
% 0.56/1.26 thf(one_type, type, one: $i).
% 0.56/1.26 thf(goals_17, conjecture,
% 0.56/1.26 (( converse @ ( complement @ sk1 ) ) = ( complement @ ( converse @ sk1 ) ))).
% 0.56/1.26 thf(zf_stmt_0, negated_conjecture,
% 0.56/1.26 (( converse @ ( complement @ sk1 ) ) != ( complement @ ( converse @ sk1 ) )),
% 0.56/1.26 inference('cnf.neg', [status(esa)], [goals_17])).
% 0.56/1.26 thf(zip_derived_cl16, plain,
% 0.56/1.26 (((converse @ (complement @ sk1)) != (complement @ (converse @ sk1)))),
% 0.56/1.26 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.56/1.26 thf(composition_identity_6, axiom, (( composition @ A @ one ) = ( A ))).
% 0.56/1.26 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [composition_identity_6])).
% 0.56/1.26 thf(converse_idempotence_8, axiom, (( converse @ ( converse @ A ) ) = ( A ))).
% 0.56/1.26 thf(zip_derived_cl7, plain,
% 0.56/1.26 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 0.56/1.26 thf(converse_multiplicativity_10, axiom,
% 0.56/1.26 (( converse @ ( composition @ A @ B ) ) =
% 0.56/1.26 ( composition @ ( converse @ B ) @ ( converse @ A ) ))).
% 0.56/1.26 thf(zip_derived_cl9, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((converse @ (composition @ X1 @ X0))
% 0.56/1.26 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 0.56/1.26 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 0.56/1.26 thf(zip_derived_cl34, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((converse @ (composition @ (converse @ X0) @ X1))
% 0.56/1.26 = (composition @ (converse @ X1) @ X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 0.56/1.26 thf(zip_derived_cl588, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((converse @ (converse @ X0)) = (composition @ (converse @ one) @ X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl34])).
% 0.56/1.26 thf(zip_derived_cl7, plain,
% 0.56/1.26 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 0.56/1.26 thf(zip_derived_cl595, plain,
% 0.56/1.26 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl588, zip_derived_cl7])).
% 0.56/1.26 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [composition_identity_6])).
% 0.56/1.26 thf(composition_associativity_5, axiom,
% 0.56/1.26 (( composition @ A @ ( composition @ B @ C ) ) =
% 0.56/1.26 ( composition @ ( composition @ A @ B ) @ C ))).
% 0.56/1.26 thf(zip_derived_cl4, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.26 ((composition @ X0 @ (composition @ X1 @ X2))
% 0.56/1.26 = (composition @ (composition @ X0 @ X1) @ X2))),
% 0.56/1.26 inference('cnf', [status(esa)], [composition_associativity_5])).
% 0.56/1.26 thf(zip_derived_cl165, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((composition @ X0 @ (composition @ one @ X1))
% 0.56/1.26 = (composition @ X0 @ X1))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 0.56/1.26 thf(zip_derived_cl614, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((composition @ one @ X0) = (composition @ (converse @ one) @ X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl595, zip_derived_cl165])).
% 0.56/1.26 thf(zip_derived_cl595, plain,
% 0.56/1.26 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl588, zip_derived_cl7])).
% 0.56/1.26 thf(zip_derived_cl627, plain,
% 0.56/1.26 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl614, zip_derived_cl595])).
% 0.56/1.26 thf(converse_cancellativity_11, axiom,
% 0.56/1.26 (( join @
% 0.56/1.26 ( composition @
% 0.56/1.26 ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @
% 0.56/1.26 ( complement @ B ) ) =
% 0.56/1.26 ( complement @ B ))).
% 0.56/1.26 thf(zip_derived_cl10, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @
% 0.56/1.26 (composition @ (converse @ X1) @
% 0.56/1.26 (complement @ (composition @ X1 @ X0))) @
% 0.56/1.26 (complement @ X0)) = (complement @ X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 0.56/1.26 thf(zip_derived_cl662, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ (composition @ (converse @ one) @ (complement @ X0)) @
% 0.56/1.26 (complement @ X0)) = (complement @ X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl627, zip_derived_cl10])).
% 0.56/1.26 thf(zip_derived_cl595, plain,
% 0.56/1.26 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl588, zip_derived_cl7])).
% 0.56/1.26 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [composition_identity_6])).
% 0.56/1.26 thf(zip_derived_cl615, plain, (((one) = (converse @ one))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl595, zip_derived_cl5])).
% 0.56/1.26 thf(zip_derived_cl627, plain,
% 0.56/1.26 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl614, zip_derived_cl595])).
% 0.56/1.26 thf(zip_derived_cl669, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl662, zip_derived_cl615, zip_derived_cl627])).
% 0.56/1.26 thf(maddux4_definiton_of_meet_4, axiom,
% 0.56/1.26 (( meet @ A @ B ) =
% 0.56/1.26 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ))).
% 0.56/1.26 thf(zip_derived_cl3, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((meet @ X0 @ X1)
% 0.56/1.26 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 0.56/1.26 thf(zip_derived_cl684, plain,
% 0.56/1.26 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl669, zip_derived_cl3])).
% 0.56/1.26 thf(def_top_12, axiom, (( top ) = ( join @ A @ ( complement @ A ) ))).
% 0.56/1.26 thf(zip_derived_cl11, plain,
% 0.56/1.26 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 0.56/1.26 inference('cnf', [status(esa)], [def_top_12])).
% 0.56/1.26 thf(zip_derived_cl3, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((meet @ X0 @ X1)
% 0.56/1.26 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 0.56/1.26 thf(zip_derived_cl64, plain,
% 0.56/1.26 (![X0 : $i]: ((meet @ X0 @ (complement @ X0)) = (complement @ top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 0.56/1.26 thf(def_zero_13, axiom, (( zero ) = ( meet @ A @ ( complement @ A ) ))).
% 0.56/1.26 thf(zip_derived_cl12, plain,
% 0.56/1.26 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 0.56/1.26 inference('cnf', [status(esa)], [def_zero_13])).
% 0.56/1.26 thf(zip_derived_cl67, plain, (((zero) = (complement @ top))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl12])).
% 0.56/1.26 thf(zip_derived_cl3, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((meet @ X0 @ X1)
% 0.56/1.26 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 0.56/1.26 thf(zip_derived_cl71, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((meet @ X0 @ top) = (complement @ (join @ (complement @ X0) @ zero)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl67, zip_derived_cl3])).
% 0.56/1.26 thf(zip_derived_cl822, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((meet @ (complement @ X0) @ top)
% 0.56/1.26 = (complement @ (join @ (meet @ X0 @ X0) @ zero)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl684, zip_derived_cl71])).
% 0.56/1.26 thf(zip_derived_cl12, plain,
% 0.56/1.26 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 0.56/1.26 inference('cnf', [status(esa)], [def_zero_13])).
% 0.56/1.26 thf(maddux3_a_kind_of_de_Morgan_3, axiom,
% 0.56/1.26 (( A ) =
% 0.56/1.26 ( join @
% 0.56/1.26 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @
% 0.56/1.26 ( complement @ ( join @ ( complement @ A ) @ B ) ) ))).
% 0.56/1.26 thf(zip_derived_cl2, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 0.56/1.26 thf(zip_derived_cl3, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((meet @ X0 @ X1)
% 0.56/1.26 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 0.56/1.26 thf(zip_derived_cl57, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @ (meet @ X0 @ X1) @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ X1))))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 0.56/1.26 thf(zip_derived_cl191, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @ zero @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ (complement @ X0)))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl57])).
% 0.56/1.26 thf(zip_derived_cl3, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((meet @ X0 @ X1)
% 0.56/1.26 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 0.56/1.26 thf(zip_derived_cl194, plain,
% 0.56/1.26 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl191, zip_derived_cl3])).
% 0.56/1.26 thf(maddux1_join_commutativity_1, axiom,
% 0.56/1.26 (( join @ A @ B ) = ( join @ B @ A ))).
% 0.56/1.26 thf(zip_derived_cl0, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 0.56/1.26 thf(zip_derived_cl402, plain,
% 0.56/1.26 (![X0 : $i]: ((join @ (meet @ X0 @ X0) @ zero) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 0.56/1.26 thf(zip_derived_cl842, plain,
% 0.56/1.26 (![X0 : $i]: ((meet @ (complement @ X0) @ top) = (complement @ X0))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl822, zip_derived_cl402])).
% 0.56/1.26 thf(zip_derived_cl57, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @ (meet @ X0 @ X1) @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ X1))))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 0.56/1.26 thf(zip_derived_cl1035, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((complement @ X0)
% 0.56/1.26 = (join @ (complement @ X0) @
% 0.56/1.26 (complement @ (join @ (complement @ (complement @ X0)) @ top))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl842, zip_derived_cl57])).
% 0.56/1.26 thf(zip_derived_cl669, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl662, zip_derived_cl615, zip_derived_cl627])).
% 0.56/1.26 thf(zip_derived_cl11, plain,
% 0.56/1.26 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 0.56/1.26 inference('cnf', [status(esa)], [def_top_12])).
% 0.56/1.26 thf(maddux2_join_associativity_2, axiom,
% 0.56/1.26 (( join @ A @ ( join @ B @ C ) ) = ( join @ ( join @ A @ B ) @ C ))).
% 0.56/1.26 thf(zip_derived_cl1, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.26 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 0.56/1.26 thf(zip_derived_cl22, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 0.56/1.26 thf(zip_derived_cl752, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ (complement @ X0) @
% 0.56/1.26 (join @ (complement @ X0) @ (complement @ (complement @ X0))))
% 0.56/1.26 = (top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl669, zip_derived_cl22])).
% 0.56/1.26 thf(zip_derived_cl11, plain,
% 0.56/1.26 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 0.56/1.26 inference('cnf', [status(esa)], [def_top_12])).
% 0.56/1.26 thf(zip_derived_cl777, plain,
% 0.56/1.26 (![X0 : $i]: ((join @ (complement @ X0) @ top) = (top))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl752, zip_derived_cl11])).
% 0.56/1.26 thf(zip_derived_cl0, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 0.56/1.26 thf(zip_derived_cl864, plain,
% 0.56/1.26 (![X0 : $i]: ((join @ top @ (complement @ X0)) = (top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl777, zip_derived_cl0])).
% 0.56/1.26 thf(zip_derived_cl22, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 0.56/1.26 thf(zip_derived_cl888, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl864, zip_derived_cl22])).
% 0.56/1.26 thf(zip_derived_cl67, plain, (((zero) = (complement @ top))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl12])).
% 0.56/1.26 thf(zip_derived_cl1045, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ X0) = (join @ (complement @ X0) @ zero))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl1035, zip_derived_cl888, zip_derived_cl67])).
% 0.56/1.26 thf(zip_derived_cl684, plain,
% 0.56/1.26 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl669, zip_derived_cl3])).
% 0.56/1.26 thf(zip_derived_cl402, plain,
% 0.56/1.26 (![X0 : $i]: ((join @ (meet @ X0 @ X0) @ zero) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 0.56/1.26 thf(zip_derived_cl831, plain,
% 0.56/1.26 (![X0 : $i]: ((join @ (complement @ (complement @ X0)) @ zero) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl684, zip_derived_cl402])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl11, plain,
% 0.56/1.26 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 0.56/1.26 inference('cnf', [status(esa)], [def_top_12])).
% 0.56/1.26 thf(zip_derived_cl7, plain,
% 0.56/1.26 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 0.56/1.26 thf(converse_additivity_9, axiom,
% 0.56/1.26 (( converse @ ( join @ A @ B ) ) =
% 0.56/1.26 ( join @ ( converse @ A ) @ ( converse @ B ) ))).
% 0.56/1.26 thf(zip_derived_cl8, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((converse @ (join @ X0 @ X1))
% 0.56/1.26 = (join @ (converse @ X0) @ (converse @ X1)))),
% 0.56/1.26 inference('cnf', [status(esa)], [converse_additivity_9])).
% 0.56/1.26 thf(zip_derived_cl33, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((converse @ (join @ (converse @ X0) @ X1))
% 0.56/1.26 = (join @ X0 @ (converse @ X1)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 0.56/1.26 thf(zip_derived_cl120, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((converse @ top)
% 0.56/1.26 = (join @ X0 @ (converse @ (complement @ (converse @ X0)))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl33])).
% 0.56/1.26 thf(zip_derived_cl888, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl864, zip_derived_cl22])).
% 0.56/1.26 thf(zip_derived_cl0, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 0.56/1.26 thf(zip_derived_cl895, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl888, zip_derived_cl0])).
% 0.56/1.26 thf(zip_derived_cl120, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((converse @ top)
% 0.56/1.26 = (join @ X0 @ (converse @ (complement @ (converse @ X0)))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl33])).
% 0.56/1.26 thf(zip_derived_cl926, plain, (((converse @ top) = (top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl895, zip_derived_cl120])).
% 0.56/1.26 thf(zip_derived_cl935, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((top) = (join @ X0 @ (converse @ (complement @ (converse @ X0)))))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl120, zip_derived_cl926])).
% 0.56/1.26 thf(zip_derived_cl57, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @ (meet @ X0 @ X1) @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ X1))))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 0.56/1.26 thf(zip_derived_cl1989, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @
% 0.56/1.26 (meet @ X0 @
% 0.56/1.26 (converse @ (complement @ (converse @ (complement @ X0))))) @
% 0.56/1.26 (complement @ top)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl935, zip_derived_cl57])).
% 0.56/1.26 thf(zip_derived_cl67, plain, (((zero) = (complement @ top))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl12])).
% 0.56/1.26 thf(zip_derived_cl831, plain,
% 0.56/1.26 (![X0 : $i]: ((join @ (complement @ (complement @ X0)) @ zero) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl684, zip_derived_cl402])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl1454, plain, (![X0 : $i]: ((join @ X0 @ zero) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl831, zip_derived_cl1407])).
% 0.56/1.26 thf(zip_derived_cl2022, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (meet @ X0 @
% 0.56/1.26 (converse @ (complement @ (converse @ (complement @ X0))))))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl1989, zip_derived_cl67, zip_derived_cl1454])).
% 0.56/1.26 thf(zip_derived_cl2133, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((complement @ X0)
% 0.56/1.26 = (meet @ (complement @ X0) @
% 0.56/1.26 (converse @ (complement @ (converse @ X0)))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1407, zip_derived_cl2022])).
% 0.56/1.26 thf(zip_derived_cl2, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 0.56/1.26 thf(zip_derived_cl2, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 0.56/1.26 thf(zip_derived_cl54, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @ (complement @ X0) @ (complement @ X1))
% 0.56/1.26 = (join @ (complement @ X0) @
% 0.56/1.26 (complement @
% 0.56/1.26 (join @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 0.56/1.26 (join @ (complement @ X0) @ X1)))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl2])).
% 0.56/1.26 thf(zip_derived_cl0, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 0.56/1.26 thf(zip_derived_cl1, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.26 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 0.56/1.26 thf(zip_derived_cl55, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @ (complement @ X0) @ (complement @ X1))
% 0.56/1.26 = (join @ (complement @ X0) @
% 0.56/1.26 (complement @
% 0.56/1.26 (join @ (complement @ X0) @
% 0.56/1.26 (join @ X1 @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ (complement @ X1))))))))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl54, zip_derived_cl0, zip_derived_cl1])).
% 0.56/1.26 thf(zip_derived_cl3, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((meet @ X0 @ X1)
% 0.56/1.26 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 0.56/1.26 thf(zip_derived_cl2830, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @ (complement @ X0) @ (complement @ X1))
% 0.56/1.26 = (join @ (complement @ X0) @
% 0.56/1.26 (complement @
% 0.56/1.26 (join @ (complement @ X0) @ (join @ X1 @ (meet @ X0 @ X1))))))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl3])).
% 0.56/1.26 thf(zip_derived_cl2857, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ (complement @ (complement @ X0)) @
% 0.56/1.26 (complement @ (converse @ (complement @ (converse @ X0)))))
% 0.56/1.26 = (join @ (complement @ (complement @ X0)) @
% 0.56/1.26 (complement @
% 0.56/1.26 (join @ (complement @ (complement @ X0)) @
% 0.56/1.26 (join @ (converse @ (complement @ (converse @ X0))) @
% 0.56/1.26 (complement @ X0))))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl2133, zip_derived_cl2830])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl0, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 0.56/1.26 thf(zip_derived_cl11, plain,
% 0.56/1.26 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 0.56/1.26 inference('cnf', [status(esa)], [def_top_12])).
% 0.56/1.26 thf(zip_derived_cl1, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.26 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 0.56/1.26 thf(zip_derived_cl25, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @ X1 @ (join @ (complement @ X1) @ X0)) = (join @ top @ X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 0.56/1.26 thf(zip_derived_cl895, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl888, zip_derived_cl0])).
% 0.56/1.26 thf(zip_derived_cl964, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @ X1 @ (join @ (complement @ X1) @ X0)) = (top))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl895])).
% 0.56/1.26 thf(zip_derived_cl67, plain, (((zero) = (complement @ top))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl12])).
% 0.56/1.26 thf(zip_derived_cl1454, plain, (![X0 : $i]: ((join @ X0 @ zero) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl831, zip_derived_cl1407])).
% 0.56/1.26 thf(zip_derived_cl2883, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ X0 @
% 0.56/1.26 (complement @ (converse @ (complement @ (converse @ X0))))) = (
% 0.56/1.26 X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl2857, zip_derived_cl1407, zip_derived_cl1407,
% 0.56/1.26 zip_derived_cl1407, zip_derived_cl0, zip_derived_cl964,
% 0.56/1.26 zip_derived_cl67, zip_derived_cl1454])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl669, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl662, zip_derived_cl615, zip_derived_cl627])).
% 0.56/1.26 thf(zip_derived_cl1461, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ (complement @ (complement @ X0)) @ X0)
% 0.56/1.26 = (complement @ (complement @ X0)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1407, zip_derived_cl669])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl1478, plain, (![X0 : $i]: ((join @ X0 @ X0) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl1461, zip_derived_cl1407, zip_derived_cl1407])).
% 0.56/1.26 thf(zip_derived_cl1, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.26 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 0.56/1.26 thf(zip_derived_cl0, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 0.56/1.26 thf(zip_derived_cl19, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.26 ((join @ X0 @ (join @ X2 @ X1)) = (join @ X2 @ (join @ X1 @ X0)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 0.56/1.26 thf(zip_derived_cl1554, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X0 @ (join @ X1 @ X0)) = (join @ X1 @ X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1478, zip_derived_cl19])).
% 0.56/1.26 thf(zip_derived_cl2962, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ (complement @ (converse @ (complement @ (converse @ X0)))) @
% 0.56/1.26 X0)
% 0.56/1.26 = (join @ X0 @
% 0.56/1.26 (complement @ (converse @ (complement @ (converse @ X0))))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl2883, zip_derived_cl1554])).
% 0.56/1.26 thf(zip_derived_cl2883, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ X0 @
% 0.56/1.26 (complement @ (converse @ (complement @ (converse @ X0))))) = (
% 0.56/1.26 X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl2857, zip_derived_cl1407, zip_derived_cl1407,
% 0.56/1.26 zip_derived_cl1407, zip_derived_cl0, zip_derived_cl964,
% 0.56/1.26 zip_derived_cl67, zip_derived_cl1454])).
% 0.56/1.26 thf(zip_derived_cl2998, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ (complement @ (converse @ (complement @ (converse @ X0)))) @
% 0.56/1.26 X0) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl2962, zip_derived_cl2883])).
% 0.56/1.26 thf(zip_derived_cl3, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((meet @ X0 @ X1)
% 0.56/1.26 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 0.56/1.26 thf(zip_derived_cl3183, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((meet @ (converse @ (complement @ (converse @ (complement @ X0)))) @
% 0.56/1.26 X0) = (complement @ (complement @ X0)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl2998, zip_derived_cl3])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl3212, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((meet @ (converse @ (complement @ (converse @ (complement @ X0)))) @
% 0.56/1.26 X0) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl3183, zip_derived_cl1407])).
% 0.56/1.26 thf(zip_derived_cl57, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @ (meet @ X0 @ X1) @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ X1))))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 0.56/1.26 thf(zip_derived_cl1478, plain, (![X0 : $i]: ((join @ X0 @ X0) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl1461, zip_derived_cl1407, zip_derived_cl1407])).
% 0.56/1.26 thf(zip_derived_cl1, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.26 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 0.56/1.26 thf(zip_derived_cl1552, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X0 @ (join @ X0 @ X1)) = (join @ X0 @ X1))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1478, zip_derived_cl1])).
% 0.56/1.26 thf(zip_derived_cl2438, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @ (meet @ X0 @ X1) @ X0)
% 0.56/1.26 = (join @ (meet @ X0 @ X1) @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ X1))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl1552])).
% 0.56/1.26 thf(zip_derived_cl0, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 0.56/1.26 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 0.56/1.26 thf(zip_derived_cl57, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @ (meet @ X0 @ X1) @
% 0.56/1.26 (complement @ (join @ (complement @ X0) @ X1))))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 0.56/1.26 thf(zip_derived_cl2467, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X0 @ X1)) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl2438, zip_derived_cl0, zip_derived_cl57])).
% 0.56/1.26 thf(zip_derived_cl1554, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X0 @ (join @ X1 @ X0)) = (join @ X1 @ X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1478, zip_derived_cl19])).
% 0.56/1.26 thf(zip_derived_cl2723, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((join @ (meet @ X0 @ X1) @ X0) = (join @ X0 @ (meet @ X0 @ X1)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl2467, zip_derived_cl1554])).
% 0.56/1.26 thf(zip_derived_cl2467, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X0 @ X1)) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl2438, zip_derived_cl0, zip_derived_cl57])).
% 0.56/1.26 thf(zip_derived_cl2754, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]: ((join @ (meet @ X0 @ X1) @ X0) = (X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl2723, zip_derived_cl2467])).
% 0.56/1.26 thf(zip_derived_cl3716, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ X0 @
% 0.56/1.26 (converse @ (complement @ (converse @ (complement @ X0)))))
% 0.56/1.26 = (converse @ (complement @ (converse @ (complement @ X0)))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl3212, zip_derived_cl2754])).
% 0.56/1.26 thf(zip_derived_cl2883, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((join @ X0 @
% 0.56/1.26 (complement @ (converse @ (complement @ (converse @ X0))))) = (
% 0.56/1.26 X0))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl2857, zip_derived_cl1407, zip_derived_cl1407,
% 0.56/1.26 zip_derived_cl1407, zip_derived_cl0, zip_derived_cl964,
% 0.56/1.26 zip_derived_cl67, zip_derived_cl1454])).
% 0.56/1.26 thf(zip_derived_cl33, plain,
% 0.56/1.26 (![X0 : $i, X1 : $i]:
% 0.56/1.26 ((converse @ (join @ (converse @ X0) @ X1))
% 0.56/1.26 = (join @ X0 @ (converse @ X1)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 0.56/1.26 thf(zip_derived_cl2974, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((converse @ (converse @ X0))
% 0.56/1.26 = (join @ X0 @
% 0.56/1.26 (converse @
% 0.56/1.26 (complement @
% 0.56/1.26 (converse @ (complement @ (converse @ (converse @ X0))))))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl2883, zip_derived_cl33])).
% 0.56/1.26 thf(zip_derived_cl7, plain,
% 0.56/1.26 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 0.56/1.26 thf(zip_derived_cl7, plain,
% 0.56/1.26 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 0.56/1.26 thf(zip_derived_cl3005, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((X0)
% 0.56/1.26 = (join @ X0 @
% 0.56/1.26 (converse @ (complement @ (converse @ (complement @ X0))))))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl2974, zip_derived_cl7, zip_derived_cl7])).
% 0.56/1.26 thf(zip_derived_cl3733, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((X0) = (converse @ (complement @ (converse @ (complement @ X0)))))),
% 0.56/1.26 inference('demod', [status(thm)],
% 0.56/1.26 [zip_derived_cl3716, zip_derived_cl3005])).
% 0.56/1.26 thf(zip_derived_cl7, plain,
% 0.56/1.26 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 0.56/1.26 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 0.56/1.26 thf(zip_derived_cl3744, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((converse @ X0) = (complement @ (converse @ (complement @ X0))))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl3733, zip_derived_cl7])).
% 0.56/1.26 thf(zip_derived_cl1407, plain,
% 0.56/1.26 (![X0 : $i]: ((complement @ (complement @ X0)) = (X0))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl831])).
% 0.56/1.26 thf(zip_derived_cl3817, plain,
% 0.56/1.26 (![X0 : $i]:
% 0.56/1.26 ((complement @ (converse @ X0)) = (converse @ (complement @ X0)))),
% 0.56/1.26 inference('sup+', [status(thm)], [zip_derived_cl3744, zip_derived_cl1407])).
% 0.56/1.26 thf(zip_derived_cl3854, plain,
% 0.56/1.26 (((complement @ (converse @ sk1)) != (complement @ (converse @ sk1)))),
% 0.56/1.26 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl3817])).
% 0.56/1.26 thf(zip_derived_cl3855, plain, ($false),
% 0.56/1.26 inference('simplify', [status(thm)], [zip_derived_cl3854])).
% 0.56/1.26
% 0.56/1.26 % SZS output end Refutation
% 0.56/1.26
% 0.56/1.26
% 0.56/1.26 % Terminating...
% 5.03/1.36 % Runner terminated.
% 5.03/1.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------