TSTP Solution File: REL050-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL050-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g6SDHqDu8V true
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:47:33 EDT 2023
% Result : Unsatisfiable 37.73s 6.00s
% Output : Refutation 37.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL050-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g6SDHqDu8V true
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 00:20:59 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.16/0.34 % Running portfolio for 300 s
% 0.16/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.34 % Number of cores: 8
% 0.16/0.35 % Python version: Python 3.6.8
% 0.16/0.35 % Running in FO mode
% 0.20/0.65 % Total configuration time : 435
% 0.20/0.65 % Estimated wc time : 1092
% 0.20/0.65 % Estimated cpu time (7 cpus) : 156.0
% 1.15/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 1.15/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.15/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.15/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.15/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.15/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.15/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 37.73/6.00 % Solved by fo/fo5.sh.
% 37.73/6.00 % done 3598 iterations in 5.213s
% 37.73/6.00 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 37.73/6.00 % SZS output start Refutation
% 37.73/6.00 thf(composition_type, type, composition: $i > $i > $i).
% 37.73/6.00 thf(meet_type, type, meet: $i > $i > $i).
% 37.73/6.00 thf(complement_type, type, complement: $i > $i).
% 37.73/6.00 thf(converse_type, type, converse: $i > $i).
% 37.73/6.00 thf(top_type, type, top: $i).
% 37.73/6.00 thf(join_type, type, join: $i > $i > $i).
% 37.73/6.00 thf(zero_type, type, zero: $i).
% 37.73/6.00 thf(sk1_type, type, sk1: $i).
% 37.73/6.00 thf(one_type, type, one: $i).
% 37.73/6.00 thf(goals_14, conjecture,
% 37.73/6.00 (( complement @ ( composition @ sk1 @ top ) ) =
% 37.73/6.00 ( composition @ ( complement @ ( composition @ sk1 @ top ) ) @ top ))).
% 37.73/6.00 thf(zf_stmt_0, negated_conjecture,
% 37.73/6.00 (( complement @ ( composition @ sk1 @ top ) ) !=
% 37.73/6.00 ( composition @ ( complement @ ( composition @ sk1 @ top ) ) @ top )),
% 37.73/6.00 inference('cnf.neg', [status(esa)], [goals_14])).
% 37.73/6.00 thf(zip_derived_cl13, plain,
% 37.73/6.00 (((complement @ (composition @ sk1 @ top))
% 37.73/6.00 != (composition @ (complement @ (composition @ sk1 @ top)) @ top))),
% 37.73/6.00 inference('cnf', [status(esa)], [zf_stmt_0])).
% 37.73/6.00 thf(composition_identity_6, axiom, (( composition @ A @ one ) = ( A ))).
% 37.73/6.00 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_identity_6])).
% 37.73/6.00 thf(converse_idempotence_8, axiom, (( converse @ ( converse @ A ) ) = ( A ))).
% 37.73/6.00 thf(zip_derived_cl7, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 37.73/6.00 thf(converse_multiplicativity_10, axiom,
% 37.73/6.00 (( converse @ ( composition @ A @ B ) ) =
% 37.73/6.00 ( composition @ ( converse @ B ) @ ( converse @ A ) ))).
% 37.73/6.00 thf(zip_derived_cl9, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (composition @ X1 @ X0))
% 37.73/6.00 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 37.73/6.00 thf(zip_derived_cl20, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (composition @ (converse @ X0) @ X1))
% 37.73/6.00 = (composition @ (converse @ X1) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 37.73/6.00 thf(zip_derived_cl331, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((converse @ (converse @ X0)) = (composition @ (converse @ one) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl20])).
% 37.73/6.00 thf(zip_derived_cl7, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 37.73/6.00 thf(zip_derived_cl338, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl331, zip_derived_cl7])).
% 37.73/6.00 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_identity_6])).
% 37.73/6.00 thf(composition_associativity_5, axiom,
% 37.73/6.00 (( composition @ A @ ( composition @ B @ C ) ) =
% 37.73/6.00 ( composition @ ( composition @ A @ B ) @ C ))).
% 37.73/6.00 thf(zip_derived_cl4, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((composition @ X0 @ (composition @ X1 @ X2))
% 37.73/6.00 = (composition @ (composition @ X0 @ X1) @ X2))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_associativity_5])).
% 37.73/6.00 thf(zip_derived_cl70, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((composition @ X0 @ (composition @ one @ X1))
% 37.73/6.00 = (composition @ X0 @ X1))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 37.73/6.00 thf(zip_derived_cl359, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((composition @ one @ X0) = (composition @ (converse @ one) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl338, zip_derived_cl70])).
% 37.73/6.00 thf(zip_derived_cl338, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl331, zip_derived_cl7])).
% 37.73/6.00 thf(zip_derived_cl365, plain,
% 37.73/6.00 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl359, zip_derived_cl338])).
% 37.73/6.00 thf(converse_cancellativity_11, axiom,
% 37.73/6.00 (( join @
% 37.73/6.00 ( composition @
% 37.73/6.00 ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @
% 37.73/6.00 ( complement @ B ) ) =
% 37.73/6.00 ( complement @ B ))).
% 37.73/6.00 thf(zip_derived_cl10, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @
% 37.73/6.00 (composition @ (converse @ X1) @
% 37.73/6.00 (complement @ (composition @ X1 @ X0))) @
% 37.73/6.00 (complement @ X0)) = (complement @ X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 37.73/6.00 thf(zip_derived_cl385, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (composition @ (converse @ one) @ (complement @ X0)) @
% 37.73/6.00 (complement @ X0)) = (complement @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl365, zip_derived_cl10])).
% 37.73/6.00 thf(zip_derived_cl338, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl331, zip_derived_cl7])).
% 37.73/6.00 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_identity_6])).
% 37.73/6.00 thf(zip_derived_cl360, plain, (((one) = (converse @ one))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl338, zip_derived_cl5])).
% 37.73/6.00 thf(zip_derived_cl365, plain,
% 37.73/6.00 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl359, zip_derived_cl338])).
% 37.73/6.00 thf(zip_derived_cl386, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl385, zip_derived_cl360, zip_derived_cl365])).
% 37.73/6.00 thf(maddux4_definiton_of_meet_4, axiom,
% 37.73/6.00 (( meet @ A @ B ) =
% 37.73/6.00 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ))).
% 37.73/6.00 thf(zip_derived_cl3, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((meet @ X0 @ X1)
% 37.73/6.00 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 37.73/6.00 thf(zip_derived_cl424, plain,
% 37.73/6.00 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl3])).
% 37.73/6.00 thf(def_zero_13, axiom, (( zero ) = ( meet @ A @ ( complement @ A ) ))).
% 37.73/6.00 thf(zip_derived_cl12, plain,
% 37.73/6.00 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_zero_13])).
% 37.73/6.00 thf(maddux3_a_kind_of_de_Morgan_3, axiom,
% 37.73/6.00 (( A ) =
% 37.73/6.00 ( join @
% 37.73/6.00 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @
% 37.73/6.00 ( complement @ ( join @ ( complement @ A ) @ B ) ) ))).
% 37.73/6.00 thf(zip_derived_cl2, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ X1))))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 37.73/6.00 thf(zip_derived_cl3, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((meet @ X0 @ X1)
% 37.73/6.00 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 37.73/6.00 thf(zip_derived_cl90, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @ (meet @ X0 @ X1) @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ X1))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl99, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @ zero @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ (complement @ X0)))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl90])).
% 37.73/6.00 thf(zip_derived_cl3, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((meet @ X0 @ X1)
% 37.73/6.00 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 37.73/6.00 thf(zip_derived_cl102, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl3])).
% 37.73/6.00 thf(def_top_12, axiom, (( top ) = ( join @ A @ ( complement @ A ) ))).
% 37.73/6.00 thf(zip_derived_cl11, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_top_12])).
% 37.73/6.00 thf(zip_derived_cl3, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((meet @ X0 @ X1)
% 37.73/6.00 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 37.73/6.00 thf(zip_derived_cl45, plain,
% 37.73/6.00 (![X0 : $i]: ((meet @ X0 @ (complement @ X0)) = (complement @ top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl12, plain,
% 37.73/6.00 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_zero_13])).
% 37.73/6.00 thf(zip_derived_cl48, plain, (((zero) = (complement @ top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl11, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_top_12])).
% 37.73/6.00 thf(zip_derived_cl50, plain, (((top) = (join @ top @ zero))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl11])).
% 37.73/6.00 thf(maddux2_join_associativity_2, axiom,
% 37.73/6.00 (( join @ A @ ( join @ B @ C ) ) = ( join @ ( join @ A @ B ) @ C ))).
% 37.73/6.00 thf(zip_derived_cl1, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 37.73/6.00 thf(zip_derived_cl55, plain,
% 37.73/6.00 (![X0 : $i]: ((join @ top @ (join @ zero @ X0)) = (join @ top @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1])).
% 37.73/6.00 thf(zip_derived_cl202, plain,
% 37.73/6.00 (![X0 : $i]: ((join @ top @ X0) = (join @ top @ (meet @ X0 @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl55])).
% 37.73/6.00 thf(zip_derived_cl457, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ top @ X0) = (join @ top @ (complement @ (complement @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl424, zip_derived_cl202])).
% 37.73/6.00 thf(zip_derived_cl11, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_top_12])).
% 37.73/6.00 thf(zip_derived_cl48, plain, (((zero) = (complement @ top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl3, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((meet @ X0 @ X1)
% 37.73/6.00 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 37.73/6.00 thf(zip_derived_cl52, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((meet @ X0 @ top) = (complement @ (join @ (complement @ X0) @ zero)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl3])).
% 37.73/6.00 thf(maddux1_join_commutativity_1, axiom,
% 37.73/6.00 (( join @ A @ B ) = ( join @ B @ A ))).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl53, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((meet @ X0 @ top) = (complement @ (join @ zero @ (complement @ X0))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl135, plain, (((meet @ zero @ top) = (complement @ top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl53])).
% 37.73/6.00 thf(zip_derived_cl48, plain, (((zero) = (complement @ top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl141, plain, (((meet @ zero @ top) = (zero))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl135, zip_derived_cl48])).
% 37.73/6.00 thf(zip_derived_cl90, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @ (meet @ X0 @ X1) @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ X1))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl144, plain,
% 37.73/6.00 (((zero)
% 37.73/6.00 = (join @ zero @ (complement @ (join @ (complement @ zero) @ top))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl141, zip_derived_cl90])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl145, plain,
% 37.73/6.00 (((zero)
% 37.73/6.00 = (join @ zero @ (complement @ (join @ top @ (complement @ zero)))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl144, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl11, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_top_12])).
% 37.73/6.00 thf(zip_derived_cl55, plain,
% 37.73/6.00 (![X0 : $i]: ((join @ top @ (join @ zero @ X0)) = (join @ top @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1])).
% 37.73/6.00 thf(zip_derived_cl201, plain,
% 37.73/6.00 (((join @ top @ top) = (join @ top @ (complement @ zero)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl55])).
% 37.73/6.00 thf(zip_derived_cl277, plain,
% 37.73/6.00 (((zero) = (join @ zero @ (complement @ (join @ top @ top))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl145, zip_derived_cl201])).
% 37.73/6.00 thf(zip_derived_cl53, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((meet @ X0 @ top) = (complement @ (join @ zero @ (complement @ X0))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl281, plain,
% 37.73/6.00 (((meet @ (join @ top @ top) @ top) = (complement @ zero))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl277, zip_derived_cl53])).
% 37.73/6.00 thf(zip_derived_cl90, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @ (meet @ X0 @ X1) @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ X1))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl294, plain,
% 37.73/6.00 (((join @ top @ top)
% 37.73/6.00 = (join @ (complement @ zero) @
% 37.73/6.00 (complement @ (join @ (complement @ (join @ top @ top)) @ top))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl281, zip_derived_cl90])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl277, plain,
% 37.73/6.00 (((zero) = (join @ zero @ (complement @ (join @ top @ top))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl145, zip_derived_cl201])).
% 37.73/6.00 thf(zip_derived_cl55, plain,
% 37.73/6.00 (![X0 : $i]: ((join @ top @ (join @ zero @ X0)) = (join @ top @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1])).
% 37.73/6.00 thf(zip_derived_cl279, plain,
% 37.73/6.00 (((join @ top @ zero) = (join @ top @ (complement @ (join @ top @ top))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl277, zip_derived_cl55])).
% 37.73/6.00 thf(zip_derived_cl50, plain, (((top) = (join @ top @ zero))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl11])).
% 37.73/6.00 thf(zip_derived_cl284, plain,
% 37.73/6.00 (((top) = (join @ top @ (complement @ (join @ top @ top))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl279, zip_derived_cl50])).
% 37.73/6.00 thf(zip_derived_cl48, plain, (((zero) = (complement @ top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl11, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_top_12])).
% 37.73/6.00 thf(zip_derived_cl298, plain, (((join @ top @ top) = (top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl294, zip_derived_cl0, zip_derived_cl284,
% 37.73/6.00 zip_derived_cl48, zip_derived_cl0, zip_derived_cl11])).
% 37.73/6.00 thf(zip_derived_cl1, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl27, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @ X0 @ (join @ X2 @ X1)) = (join @ X2 @ (join @ X1 @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl1080, plain,
% 37.73/6.00 (![X0 : $i]: ((join @ X0 @ top) = (join @ top @ (join @ top @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl298, zip_derived_cl27])).
% 37.73/6.00 thf(zip_derived_cl1223, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (complement @ (complement @ X0)) @ top)
% 37.73/6.00 = (join @ top @ (join @ top @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl457, zip_derived_cl1080])).
% 37.73/6.00 thf(zip_derived_cl1080, plain,
% 37.73/6.00 (![X0 : $i]: ((join @ X0 @ top) = (join @ top @ (join @ top @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl298, zip_derived_cl27])).
% 37.73/6.00 thf(zip_derived_cl1236, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (complement @ (complement @ X0)) @ top) = (join @ X0 @ top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl1223, zip_derived_cl1080])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl1258, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ top @ (complement @ (complement @ X0))) = (join @ X0 @ top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1236, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl386, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl385, zip_derived_cl360, zip_derived_cl365])).
% 37.73/6.00 thf(zip_derived_cl11, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_top_12])).
% 37.73/6.00 thf(zip_derived_cl1, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 37.73/6.00 thf(zip_derived_cl30, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 37.73/6.00 thf(zip_derived_cl1380, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (complement @ X0) @
% 37.73/6.00 (join @ (complement @ X0) @ (complement @ (complement @ X0))))
% 37.73/6.00 = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl30])).
% 37.73/6.00 thf(zip_derived_cl11, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_top_12])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl1427, plain,
% 37.73/6.00 (![X0 : $i]: ((join @ top @ (complement @ X0)) = (top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl1380, zip_derived_cl11, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl1465, plain, (![X0 : $i]: ((top) = (join @ X0 @ top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl1258, zip_derived_cl1427])).
% 37.73/6.00 thf(zip_derived_cl365, plain,
% 37.73/6.00 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl359, zip_derived_cl338])).
% 37.73/6.00 thf(composition_distributivity_7, axiom,
% 37.73/6.00 (( composition @ ( join @ A @ B ) @ C ) =
% 37.73/6.00 ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ))).
% 37.73/6.00 thf(zip_derived_cl6, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((composition @ (join @ X0 @ X2) @ X1)
% 37.73/6.00 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 37.73/6.00 thf(zip_derived_cl383, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((composition @ (join @ one @ X1) @ X0)
% 37.73/6.00 = (join @ X0 @ (composition @ X1 @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl365, zip_derived_cl6])).
% 37.73/6.00 thf(zip_derived_cl17299, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((composition @ top @ X0) = (join @ X0 @ (composition @ top @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1465, zip_derived_cl383])).
% 37.73/6.00 thf(zip_derived_cl7, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 37.73/6.00 thf(zip_derived_cl9, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (composition @ X1 @ X0))
% 37.73/6.00 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 37.73/6.00 thf(zip_derived_cl21, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (composition @ X1 @ (converse @ X0)))
% 37.73/6.00 = (composition @ X0 @ (converse @ X1)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 37.73/6.00 thf(converse_additivity_9, axiom,
% 37.73/6.00 (( converse @ ( join @ A @ B ) ) =
% 37.73/6.00 ( join @ ( converse @ A ) @ ( converse @ B ) ))).
% 37.73/6.00 thf(zip_derived_cl8, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (join @ X0 @ X1))
% 37.73/6.00 = (join @ (converse @ X0) @ (converse @ X1)))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_additivity_9])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl16, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @ (converse @ X0) @ (converse @ X1))
% 37.73/6.00 = (converse @ (join @ X1 @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl390, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @ (composition @ X1 @ (converse @ X0)) @ (converse @ X2))
% 37.73/6.00 = (converse @ (join @ X2 @ (composition @ X0 @ (converse @ X1)))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl16])).
% 37.73/6.00 thf(zip_derived_cl18649, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (composition @ X0 @ (converse @ top)) @
% 37.73/6.00 (converse @ (converse @ X0)))
% 37.73/6.00 = (converse @ (composition @ top @ (converse @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl17299, zip_derived_cl390])).
% 37.73/6.00 thf(zip_derived_cl457, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ top @ X0) = (join @ top @ (complement @ (complement @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl424, zip_derived_cl202])).
% 37.73/6.00 thf(zip_derived_cl1427, plain,
% 37.73/6.00 (![X0 : $i]: ((join @ top @ (complement @ X0)) = (top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl1380, zip_derived_cl11, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl1464, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl457, zip_derived_cl1427])).
% 37.73/6.00 thf(zip_derived_cl7, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 37.73/6.00 thf(zip_derived_cl8, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (join @ X0 @ X1))
% 37.73/6.00 = (join @ (converse @ X0) @ (converse @ X1)))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_additivity_9])).
% 37.73/6.00 thf(zip_derived_cl18, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (join @ X1 @ (converse @ X0)))
% 37.73/6.00 = (join @ (converse @ X1) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 37.73/6.00 thf(zip_derived_cl1504, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ top) = (join @ (converse @ top) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1464, zip_derived_cl18])).
% 37.73/6.00 thf(zip_derived_cl30, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 37.73/6.00 thf(zip_derived_cl1811, plain, (((converse @ top) = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1504, zip_derived_cl30])).
% 37.73/6.00 thf(zip_derived_cl7, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl1811, plain, (((converse @ top) = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1504, zip_derived_cl30])).
% 37.73/6.00 thf(zip_derived_cl9, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (composition @ X1 @ X0))
% 37.73/6.00 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 37.73/6.00 thf(zip_derived_cl1842, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((converse @ (composition @ X0 @ top))
% 37.73/6.00 = (composition @ top @ (converse @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1811, zip_derived_cl9])).
% 37.73/6.00 thf(zip_derived_cl7, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 37.73/6.00 thf(zip_derived_cl2674, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((converse @ (composition @ top @ (converse @ X0)))
% 37.73/6.00 = (composition @ X0 @ top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1842, zip_derived_cl7])).
% 37.73/6.00 thf(zip_derived_cl18706, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ X0 @ (composition @ X0 @ top)) = (composition @ X0 @ top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl18649, zip_derived_cl1811, zip_derived_cl7,
% 37.73/6.00 zip_derived_cl0, zip_derived_cl2674])).
% 37.73/6.00 thf(zip_derived_cl12, plain,
% 37.73/6.00 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_zero_13])).
% 37.73/6.00 thf(zip_derived_cl3, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((meet @ X0 @ X1)
% 37.73/6.00 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 37.73/6.00 thf(zip_derived_cl10, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @
% 37.73/6.00 (composition @ (converse @ X1) @
% 37.73/6.00 (complement @ (composition @ X1 @ X0))) @
% 37.73/6.00 (complement @ X0)) = (complement @ X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 37.73/6.00 thf(zip_derived_cl79, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @
% 37.73/6.00 (composition @ (converse @ X2) @
% 37.73/6.00 (complement @
% 37.73/6.00 (composition @ X2 @ (join @ (complement @ X1) @ (complement @ X0))))) @
% 37.73/6.00 (meet @ X1 @ X0))
% 37.73/6.00 = (complement @ (join @ (complement @ X1) @ (complement @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl10])).
% 37.73/6.00 thf(zip_derived_cl3, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((meet @ X0 @ X1)
% 37.73/6.00 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 37.73/6.00 thf(zip_derived_cl86, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @
% 37.73/6.00 (composition @ (converse @ X2) @
% 37.73/6.00 (complement @
% 37.73/6.00 (composition @ X2 @ (join @ (complement @ X1) @ (complement @ X0))))) @
% 37.73/6.00 (meet @ X1 @ X0)) = (meet @ X1 @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl79, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl4476, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @
% 37.73/6.00 (composition @ (converse @ X1) @
% 37.73/6.00 (complement @
% 37.73/6.00 (composition @ X1 @
% 37.73/6.00 (join @ (complement @ X0) @ (complement @ (complement @ X0)))))) @
% 37.73/6.00 zero) = (meet @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl86])).
% 37.73/6.00 thf(zip_derived_cl424, plain,
% 37.73/6.00 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl424, plain,
% 37.73/6.00 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl386, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl385, zip_derived_cl360, zip_derived_cl365])).
% 37.73/6.00 thf(zip_derived_cl90, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @ (meet @ X0 @ X1) @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ X1))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl423, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @ (meet @ X0 @ (complement @ X0)) @
% 37.73/6.00 (complement @ (complement @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl90])).
% 37.73/6.00 thf(zip_derived_cl12, plain,
% 37.73/6.00 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_zero_13])).
% 37.73/6.00 thf(zip_derived_cl441, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl423, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl53, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((meet @ X0 @ top) = (complement @ (join @ zero @ (complement @ X0))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl482, plain,
% 37.73/6.00 (![X0 : $i]: ((meet @ (complement @ X0) @ top) = (complement @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl441, zip_derived_cl53])).
% 37.73/6.00 thf(zip_derived_cl496, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((meet @ (meet @ X0 @ X0) @ top) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl424, zip_derived_cl482])).
% 37.73/6.00 thf(zip_derived_cl1465, plain, (![X0 : $i]: ((top) = (join @ X0 @ top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl1258, zip_derived_cl1427])).
% 37.73/6.00 thf(zip_derived_cl90, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @ (meet @ X0 @ X1) @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ X1))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl1518, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ (meet @ X0 @ top) @ (complement @ top)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1465, zip_derived_cl90])).
% 37.73/6.00 thf(zip_derived_cl48, plain, (((zero) = (complement @ top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl1528, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ top)))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl1518, zip_derived_cl48, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl2076, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((meet @ X0 @ X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl496, zip_derived_cl1528])).
% 37.73/6.00 thf(zip_derived_cl441, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl423, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl2082, plain, (![X0 : $i]: ((meet @ X0 @ X0) = (X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2076, zip_derived_cl441])).
% 37.73/6.00 thf(zip_derived_cl2087, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl424, zip_derived_cl2082])).
% 37.73/6.00 thf(zip_derived_cl2087, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl424, zip_derived_cl2082])).
% 37.73/6.00 thf(zip_derived_cl11, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_top_12])).
% 37.73/6.00 thf(zip_derived_cl2210, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ (complement @ X0) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl2087, zip_derived_cl11])).
% 37.73/6.00 thf(zip_derived_cl2082, plain, (![X0 : $i]: ((meet @ X0 @ X0) = (X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2076, zip_derived_cl441])).
% 37.73/6.00 thf(zip_derived_cl90, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @ (meet @ X0 @ X1) @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ X1))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl2095, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((X0) = (join @ X0 @ (complement @ (join @ (complement @ X0) @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl2082, zip_derived_cl90])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl11, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_top_12])).
% 37.73/6.00 thf(zip_derived_cl48, plain, (((zero) = (complement @ top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl2104, plain, (![X0 : $i]: ((X0) = (join @ X0 @ zero))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl2095, zip_derived_cl0, zip_derived_cl11,
% 37.73/6.00 zip_derived_cl48])).
% 37.73/6.00 thf(zip_derived_cl12, plain,
% 37.73/6.00 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 37.73/6.00 inference('cnf', [status(esa)], [def_zero_13])).
% 37.73/6.00 thf(zip_derived_cl4536, plain,
% 37.73/6.00 (![X1 : $i]:
% 37.73/6.00 ((composition @ (converse @ X1) @
% 37.73/6.00 (complement @ (composition @ X1 @ top))) = (zero))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl4476, zip_derived_cl2087, zip_derived_cl2210,
% 37.73/6.00 zip_derived_cl2104, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl20, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (composition @ (converse @ X0) @ X1))
% 37.73/6.00 = (composition @ (converse @ X1) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 37.73/6.00 thf(zip_derived_cl10, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @
% 37.73/6.00 (composition @ (converse @ X1) @
% 37.73/6.00 (complement @ (composition @ X1 @ X0))) @
% 37.73/6.00 (complement @ X0)) = (complement @ X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 37.73/6.00 thf(zip_derived_cl328, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @
% 37.73/6.00 (composition @ (composition @ (converse @ X1) @ X0) @
% 37.73/6.00 (complement @
% 37.73/6.00 (composition @ (composition @ (converse @ X0) @ X1) @ X2))) @
% 37.73/6.00 (complement @ X2)) = (complement @ X2))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl10])).
% 37.73/6.00 thf(zip_derived_cl4, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((composition @ X0 @ (composition @ X1 @ X2))
% 37.73/6.00 = (composition @ (composition @ X0 @ X1) @ X2))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_associativity_5])).
% 37.73/6.00 thf(zip_derived_cl4, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((composition @ X0 @ (composition @ X1 @ X2))
% 37.73/6.00 = (composition @ (composition @ X0 @ X1) @ X2))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_associativity_5])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl344, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @ (complement @ X2) @
% 37.73/6.00 (composition @ (converse @ X1) @
% 37.73/6.00 (composition @ X0 @
% 37.73/6.00 (complement @
% 37.73/6.00 (composition @ (converse @ X0) @ (composition @ X1 @ X2))))))
% 37.73/6.00 = (complement @ X2))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl328, zip_derived_cl4, zip_derived_cl4,
% 37.73/6.00 zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl17043, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @ (complement @ (complement @ (composition @ X0 @ top))) @
% 37.73/6.00 (composition @ (converse @ (converse @ X0)) @
% 37.73/6.00 (composition @ X1 @
% 37.73/6.00 (complement @ (composition @ (converse @ X1) @ zero)))))
% 37.73/6.00 = (complement @ (complement @ (composition @ X0 @ top))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl4536, zip_derived_cl344])).
% 37.73/6.00 thf(zip_derived_cl2087, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl424, zip_derived_cl2082])).
% 37.73/6.00 thf(zip_derived_cl7, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 37.73/6.00 thf(zip_derived_cl1811, plain, (((converse @ top) = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1504, zip_derived_cl30])).
% 37.73/6.00 thf(zip_derived_cl4536, plain,
% 37.73/6.00 (![X1 : $i]:
% 37.73/6.00 ((composition @ (converse @ X1) @
% 37.73/6.00 (complement @ (composition @ X1 @ top))) = (zero))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl4476, zip_derived_cl2087, zip_derived_cl2210,
% 37.73/6.00 zip_derived_cl2104, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl4789, plain,
% 37.73/6.00 (((composition @ top @ (complement @ (composition @ top @ top))) = (zero))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1811, zip_derived_cl4536])).
% 37.73/6.00 thf(zip_derived_cl6, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((composition @ (join @ X0 @ X2) @ X1)
% 37.73/6.00 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 37.73/6.00 thf(zip_derived_cl4819, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((composition @ (join @ top @ X0) @
% 37.73/6.00 (complement @ (composition @ top @ top)))
% 37.73/6.00 = (join @ zero @
% 37.73/6.00 (composition @ X0 @ (complement @ (composition @ top @ top)))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl4789, zip_derived_cl6])).
% 37.73/6.00 thf(zip_derived_cl1464, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl457, zip_derived_cl1427])).
% 37.73/6.00 thf(zip_derived_cl4789, plain,
% 37.73/6.00 (((composition @ top @ (complement @ (composition @ top @ top))) = (zero))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1811, zip_derived_cl4536])).
% 37.73/6.00 thf(zip_derived_cl102, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl2082, plain, (![X0 : $i]: ((meet @ X0 @ X0) = (X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2076, zip_derived_cl441])).
% 37.73/6.00 thf(zip_derived_cl2086, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl102, zip_derived_cl2082])).
% 37.73/6.00 thf(zip_derived_cl4828, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((zero)
% 37.73/6.00 = (composition @ X0 @ (complement @ (composition @ top @ top))))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl4819, zip_derived_cl1464, zip_derived_cl4789,
% 37.73/6.00 zip_derived_cl2086])).
% 37.73/6.00 thf(zip_derived_cl4, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((composition @ X0 @ (composition @ X1 @ X2))
% 37.73/6.00 = (composition @ (composition @ X0 @ X1) @ X2))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_associativity_5])).
% 37.73/6.00 thf(zip_derived_cl4846, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((composition @ X1 @
% 37.73/6.00 (composition @ X0 @ (complement @ (composition @ top @ top))))
% 37.73/6.00 = (zero))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl4828, zip_derived_cl4])).
% 37.73/6.00 thf(zip_derived_cl4828, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((zero)
% 37.73/6.00 = (composition @ X0 @ (complement @ (composition @ top @ top))))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl4819, zip_derived_cl1464, zip_derived_cl4789,
% 37.73/6.00 zip_derived_cl2086])).
% 37.73/6.00 thf(zip_derived_cl4865, plain,
% 37.73/6.00 (![X1 : $i]: ((composition @ X1 @ zero) = (zero))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl4846, zip_derived_cl4828])).
% 37.73/6.00 thf(zip_derived_cl424, plain,
% 37.73/6.00 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl482, plain,
% 37.73/6.00 (![X0 : $i]: ((meet @ (complement @ X0) @ top) = (complement @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl441, zip_derived_cl53])).
% 37.73/6.00 thf(zip_derived_cl424, plain,
% 37.73/6.00 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl48, plain, (((zero) = (complement @ top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl3, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((meet @ X0 @ X1)
% 37.73/6.00 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 37.73/6.00 thf(zip_derived_cl49, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((meet @ top @ X0) = (complement @ (join @ zero @ (complement @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl446, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((meet @ top @ (complement @ X0))
% 37.73/6.00 = (complement @ (join @ zero @ (meet @ X0 @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl424, zip_derived_cl49])).
% 37.73/6.00 thf(zip_derived_cl102, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl460, plain,
% 37.73/6.00 (![X0 : $i]: ((meet @ top @ (complement @ X0)) = (complement @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl446, zip_derived_cl102])).
% 37.73/6.00 thf(zip_derived_cl90, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((X0)
% 37.73/6.00 = (join @ (meet @ X0 @ X1) @
% 37.73/6.00 (complement @ (join @ (complement @ X0) @ X1))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl464, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((top)
% 37.73/6.00 = (join @ (complement @ X0) @
% 37.73/6.00 (complement @ (join @ (complement @ top) @ (complement @ X0)))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl460, zip_derived_cl90])).
% 37.73/6.00 thf(zip_derived_cl48, plain, (((zero) = (complement @ top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl53, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((meet @ X0 @ top) = (complement @ (join @ zero @ (complement @ X0))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl476, plain,
% 37.73/6.00 (![X0 : $i]: ((top) = (join @ (complement @ X0) @ (meet @ X0 @ top)))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl464, zip_derived_cl48, zip_derived_cl53])).
% 37.73/6.00 thf(zip_derived_cl506, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((top) = (join @ (complement @ (complement @ X0)) @ (complement @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl482, zip_derived_cl476])).
% 37.73/6.00 thf(zip_derived_cl536, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((top)
% 37.73/6.00 = (join @ (complement @ (complement @ (complement @ X0))) @
% 37.73/6.00 (meet @ X0 @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl424, zip_derived_cl506])).
% 37.73/6.00 thf(zip_derived_cl30, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 37.73/6.00 thf(zip_derived_cl1385, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (complement @ (complement @ (complement @ X0))) @
% 37.73/6.00 (join @ (meet @ X0 @ X0) @ (complement @ top))) = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl536, zip_derived_cl30])).
% 37.73/6.00 thf(zip_derived_cl48, plain, (((zero) = (complement @ top))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl102, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl3])).
% 37.73/6.00 thf(zip_derived_cl0, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 37.73/6.00 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 37.73/6.00 thf(zip_derived_cl1432, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ X0 @ (complement @ (complement @ (complement @ X0)))) = (top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl1385, zip_derived_cl48, zip_derived_cl0,
% 37.73/6.00 zip_derived_cl102, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl441, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl423, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl1612, plain, (((complement @ zero) = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1432, zip_derived_cl441])).
% 37.73/6.00 thf(zip_derived_cl4, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((composition @ X0 @ (composition @ X1 @ X2))
% 37.73/6.00 = (composition @ (composition @ X0 @ X1) @ X2))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_associativity_5])).
% 37.73/6.00 thf(zip_derived_cl6, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((composition @ (join @ X0 @ X2) @ X1)
% 37.73/6.00 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 37.73/6.00 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 37.73/6.00 thf(zip_derived_cl108, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.73/6.00 ((composition @ (join @ X3 @ (composition @ X2 @ X1)) @ X0)
% 37.73/6.00 = (join @ (composition @ X3 @ X0) @
% 37.73/6.00 (composition @ X2 @ (composition @ X1 @ X0))))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl6])).
% 37.73/6.00 thf(zip_derived_cl2087, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl424, zip_derived_cl2082])).
% 37.73/6.00 thf(zip_derived_cl17133, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((composition @ (join @ X0 @ (composition @ X0 @ X1)) @ top)
% 37.73/6.00 = (composition @ X0 @ top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl17043, zip_derived_cl2087, zip_derived_cl7,
% 37.73/6.00 zip_derived_cl4865, zip_derived_cl1612, zip_derived_cl108,
% 37.73/6.00 zip_derived_cl2087])).
% 37.73/6.00 thf(zip_derived_cl36381, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((composition @ (composition @ X0 @ top) @ top)
% 37.73/6.00 = (composition @ X0 @ top))),
% 37.73/6.00 inference('sup+', [status(thm)],
% 37.73/6.00 [zip_derived_cl18706, zip_derived_cl17133])).
% 37.73/6.00 thf(zip_derived_cl4536, plain,
% 37.73/6.00 (![X1 : $i]:
% 37.73/6.00 ((composition @ (converse @ X1) @
% 37.73/6.00 (complement @ (composition @ X1 @ top))) = (zero))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl4476, zip_derived_cl2087, zip_derived_cl2210,
% 37.73/6.00 zip_derived_cl2104, zip_derived_cl12])).
% 37.73/6.00 thf(zip_derived_cl20, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (composition @ (converse @ X0) @ X1))
% 37.73/6.00 = (composition @ (converse @ X1) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 37.73/6.00 thf(zip_derived_cl4757, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((converse @ zero)
% 37.73/6.00 = (composition @
% 37.73/6.00 (converse @ (complement @ (composition @ X0 @ top))) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl4536, zip_derived_cl20])).
% 37.73/6.00 thf(zip_derived_cl2086, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl102, zip_derived_cl2082])).
% 37.73/6.00 thf(zip_derived_cl18, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((converse @ (join @ X1 @ (converse @ X0)))
% 37.73/6.00 = (join @ (converse @ X1) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 37.73/6.00 thf(zip_derived_cl2335, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((converse @ (converse @ X0)) = (join @ (converse @ zero) @ X0))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl2086, zip_derived_cl18])).
% 37.73/6.00 thf(zip_derived_cl7, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 37.73/6.00 thf(zip_derived_cl2344, plain,
% 37.73/6.00 (![X0 : $i]: ((X0) = (join @ (converse @ zero) @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl2335, zip_derived_cl7])).
% 37.73/6.00 thf(zip_derived_cl2104, plain, (![X0 : $i]: ((X0) = (join @ X0 @ zero))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl2095, zip_derived_cl0, zip_derived_cl11,
% 37.73/6.00 zip_derived_cl48])).
% 37.73/6.00 thf(zip_derived_cl2577, plain, (((converse @ zero) = (zero))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl2344, zip_derived_cl2104])).
% 37.73/6.00 thf(zip_derived_cl4813, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((zero)
% 37.73/6.00 = (composition @
% 37.73/6.00 (converse @ (complement @ (composition @ X0 @ top))) @ X0))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl4757, zip_derived_cl2577])).
% 37.73/6.00 thf(zip_derived_cl36530, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((zero)
% 37.73/6.00 = (composition @
% 37.73/6.00 (converse @ (complement @ (composition @ X0 @ top))) @
% 37.73/6.00 (composition @ X0 @ top)))),
% 37.73/6.00 inference('sup+', [status(thm)],
% 37.73/6.00 [zip_derived_cl36381, zip_derived_cl4813])).
% 37.73/6.00 thf(zip_derived_cl10, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @
% 37.73/6.00 (composition @ (converse @ X1) @
% 37.73/6.00 (complement @ (composition @ X1 @ X0))) @
% 37.73/6.00 (complement @ X0)) = (complement @ X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 37.73/6.00 thf(zip_derived_cl37510, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @
% 37.73/6.00 (composition @
% 37.73/6.00 (converse @ (converse @ (complement @ (composition @ X0 @ top)))) @
% 37.73/6.00 (complement @ zero)) @
% 37.73/6.00 (complement @ (composition @ X0 @ top)))
% 37.73/6.00 = (complement @ (composition @ X0 @ top)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl36530, zip_derived_cl10])).
% 37.73/6.00 thf(zip_derived_cl7, plain,
% 37.73/6.00 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 37.73/6.00 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 37.73/6.00 thf(zip_derived_cl1612, plain, (((complement @ zero) = (top))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1432, zip_derived_cl441])).
% 37.73/6.00 thf(zip_derived_cl18706, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ X0 @ (composition @ X0 @ top)) = (composition @ X0 @ top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl18649, zip_derived_cl1811, zip_derived_cl7,
% 37.73/6.00 zip_derived_cl0, zip_derived_cl2674])).
% 37.73/6.00 thf(zip_derived_cl2086, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl102, zip_derived_cl2082])).
% 37.73/6.00 thf(zip_derived_cl27, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.73/6.00 ((join @ X0 @ (join @ X2 @ X1)) = (join @ X2 @ (join @ X1 @ X0)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 37.73/6.00 thf(zip_derived_cl2326, plain,
% 37.73/6.00 (![X0 : $i, X1 : $i]:
% 37.73/6.00 ((join @ X1 @ X0) = (join @ zero @ (join @ X0 @ X1)))),
% 37.73/6.00 inference('sup+', [status(thm)], [zip_derived_cl2086, zip_derived_cl27])).
% 37.73/6.00 thf(zip_derived_cl20053, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (composition @ X0 @ top) @ X0)
% 37.73/6.00 = (join @ zero @ (composition @ X0 @ top)))),
% 37.73/6.00 inference('sup+', [status(thm)],
% 37.73/6.00 [zip_derived_cl18706, zip_derived_cl2326])).
% 37.73/6.00 thf(zip_derived_cl2086, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl102, zip_derived_cl2082])).
% 37.73/6.00 thf(zip_derived_cl20128, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((join @ (composition @ X0 @ top) @ X0) = (composition @ X0 @ top))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl20053, zip_derived_cl2086])).
% 37.73/6.00 thf(zip_derived_cl37609, plain,
% 37.73/6.00 (![X0 : $i]:
% 37.73/6.00 ((composition @ (complement @ (composition @ X0 @ top)) @ top)
% 37.73/6.00 = (complement @ (composition @ X0 @ top)))),
% 37.73/6.00 inference('demod', [status(thm)],
% 37.73/6.00 [zip_derived_cl37510, zip_derived_cl7, zip_derived_cl1612,
% 37.73/6.00 zip_derived_cl20128])).
% 37.73/6.00 thf(zip_derived_cl37642, plain,
% 37.73/6.00 (((complement @ (composition @ sk1 @ top))
% 37.73/6.00 != (complement @ (composition @ sk1 @ top)))),
% 37.73/6.00 inference('demod', [status(thm)], [zip_derived_cl13, zip_derived_cl37609])).
% 37.73/6.00 thf(zip_derived_cl37643, plain, ($false),
% 37.73/6.00 inference('simplify', [status(thm)], [zip_derived_cl37642])).
% 37.73/6.00
% 37.73/6.00 % SZS output end Refutation
% 37.73/6.00
% 37.73/6.00
% 37.73/6.00 % Terminating...
% 37.73/6.08 % Runner terminated.
% 37.73/6.08 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------