TSTP Solution File: REL004-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL004-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.gZRYbsUpxP true
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:47:00 EDT 2023
% Result : Unsatisfiable 15.16s 2.74s
% Output : Refutation 15.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL004-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.gZRYbsUpxP true
% 0.10/0.32 % Computer : n027.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Aug 25 20:51:34 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Running portfolio for 300 s
% 0.10/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.32 % Number of cores: 8
% 0.10/0.32 % Python version: Python 3.6.8
% 0.10/0.32 % Running in FO mode
% 0.16/0.56 % Total configuration time : 435
% 0.16/0.56 % Estimated wc time : 1092
% 0.16/0.56 % Estimated cpu time (7 cpus) : 156.0
% 0.16/0.63 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.16/0.64 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.16/0.65 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.16/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.16/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.16/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.16/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 15.16/2.74 % Solved by fo/fo1_av.sh.
% 15.16/2.74 % done 809 iterations in 2.053s
% 15.16/2.74 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 15.16/2.74 % SZS output start Refutation
% 15.16/2.74 thf(composition_type, type, composition: $i > $i > $i).
% 15.16/2.74 thf(meet_type, type, meet: $i > $i > $i).
% 15.16/2.74 thf(complement_type, type, complement: $i > $i).
% 15.16/2.74 thf(converse_type, type, converse: $i > $i).
% 15.16/2.74 thf(top_type, type, top: $i).
% 15.16/2.74 thf(join_type, type, join: $i > $i > $i).
% 15.16/2.74 thf(zero_type, type, zero: $i).
% 15.16/2.74 thf(sk1_type, type, sk1: $i).
% 15.16/2.74 thf(one_type, type, one: $i).
% 15.16/2.74 thf(goals_14, conjecture,
% 15.16/2.74 (( converse @ ( complement @ sk1 ) ) = ( complement @ ( converse @ sk1 ) ))).
% 15.16/2.74 thf(zf_stmt_0, negated_conjecture,
% 15.16/2.74 (( converse @ ( complement @ sk1 ) ) != ( complement @ ( converse @ sk1 ) )),
% 15.16/2.74 inference('cnf.neg', [status(esa)], [goals_14])).
% 15.16/2.74 thf(zip_derived_cl13, plain,
% 15.16/2.74 (((converse @ (complement @ sk1)) != (complement @ (converse @ sk1)))),
% 15.16/2.74 inference('cnf', [status(esa)], [zf_stmt_0])).
% 15.16/2.74 thf(def_zero_13, axiom, (( zero ) = ( meet @ A @ ( complement @ A ) ))).
% 15.16/2.74 thf(zip_derived_cl12, plain,
% 15.16/2.74 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 15.16/2.74 inference('cnf', [status(esa)], [def_zero_13])).
% 15.16/2.74 thf(maddux3_a_kind_of_de_Morgan_3, axiom,
% 15.16/2.74 (( A ) =
% 15.16/2.74 ( join @
% 15.16/2.74 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @
% 15.16/2.74 ( complement @ ( join @ ( complement @ A ) @ B ) ) ))).
% 15.16/2.74 thf(zip_derived_cl2, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @
% 15.16/2.74 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 15.16/2.74 (complement @ (join @ (complement @ X0) @ X1))))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 15.16/2.74 thf(maddux4_definiton_of_meet_4, axiom,
% 15.16/2.74 (( meet @ A @ B ) =
% 15.16/2.74 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ))).
% 15.16/2.74 thf(zip_derived_cl3, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((meet @ X0 @ X1)
% 15.16/2.74 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 15.16/2.74 thf(maddux1_join_commutativity_1, axiom,
% 15.16/2.74 (( join @ A @ B ) = ( join @ B @ A ))).
% 15.16/2.74 thf(zip_derived_cl0, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 15.16/2.74 thf(zip_derived_cl71, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @ (complement @ (join @ (complement @ X0) @ X1)) @
% 15.16/2.74 (meet @ X0 @ X1)))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl2, zip_derived_cl3, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl71, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @ (complement @ (join @ (complement @ X0) @ X1)) @
% 15.16/2.74 (meet @ X0 @ X1)))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl2, zip_derived_cl3, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl73, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @ (complement @ X0) @ X1)
% 15.16/2.74 = (join @ (complement @ X0) @
% 15.16/2.74 (meet @ (join @ (complement @ X0) @ X1) @ (meet @ X0 @ X1))))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl71, zip_derived_cl71])).
% 15.16/2.74 thf(zip_derived_cl1614, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((join @ (complement @ X0) @ (complement @ X0))
% 15.16/2.74 = (join @ (complement @ X0) @
% 15.16/2.74 (meet @ (join @ (complement @ X0) @ (complement @ X0)) @ zero)))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl73])).
% 15.16/2.74 thf(composition_identity_6, axiom, (( composition @ A @ one ) = ( A ))).
% 15.16/2.74 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 15.16/2.74 inference('cnf', [status(esa)], [composition_identity_6])).
% 15.16/2.74 thf(converse_idempotence_8, axiom, (( converse @ ( converse @ A ) ) = ( A ))).
% 15.16/2.74 thf(zip_derived_cl7, plain,
% 15.16/2.74 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 15.16/2.74 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 15.16/2.74 thf(converse_multiplicativity_10, axiom,
% 15.16/2.74 (( converse @ ( composition @ A @ B ) ) =
% 15.16/2.74 ( composition @ ( converse @ B ) @ ( converse @ A ) ))).
% 15.16/2.74 thf(zip_derived_cl9, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((converse @ (composition @ X1 @ X0))
% 15.16/2.74 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 15.16/2.74 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 15.16/2.74 thf(zip_derived_cl49, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((converse @ (composition @ (converse @ X0) @ X1))
% 15.16/2.74 = (composition @ (converse @ X1) @ X0))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 15.16/2.74 thf(zip_derived_cl229, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((converse @ (converse @ X0)) = (composition @ (converse @ one) @ X0))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl49])).
% 15.16/2.74 thf(zip_derived_cl7, plain,
% 15.16/2.74 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 15.16/2.74 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 15.16/2.74 thf(zip_derived_cl236, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl229, zip_derived_cl7])).
% 15.16/2.74 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 15.16/2.74 inference('cnf', [status(esa)], [composition_identity_6])).
% 15.16/2.74 thf(composition_associativity_5, axiom,
% 15.16/2.74 (( composition @ A @ ( composition @ B @ C ) ) =
% 15.16/2.74 ( composition @ ( composition @ A @ B ) @ C ))).
% 15.16/2.74 thf(zip_derived_cl4, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.16/2.74 ((composition @ X0 @ (composition @ X1 @ X2))
% 15.16/2.74 = (composition @ (composition @ X0 @ X1) @ X2))),
% 15.16/2.74 inference('cnf', [status(esa)], [composition_associativity_5])).
% 15.16/2.74 thf(zip_derived_cl33, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((composition @ X0 @ (composition @ one @ X1))
% 15.16/2.74 = (composition @ X0 @ X1))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 15.16/2.74 thf(zip_derived_cl247, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((composition @ one @ X0) = (composition @ (converse @ one) @ X0))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl236, zip_derived_cl33])).
% 15.16/2.74 thf(zip_derived_cl236, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl229, zip_derived_cl7])).
% 15.16/2.74 thf(zip_derived_cl253, plain,
% 15.16/2.74 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl247, zip_derived_cl236])).
% 15.16/2.74 thf(converse_cancellativity_11, axiom,
% 15.16/2.74 (( join @
% 15.16/2.74 ( composition @
% 15.16/2.74 ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @
% 15.16/2.74 ( complement @ B ) ) =
% 15.16/2.74 ( complement @ B ))).
% 15.16/2.74 thf(zip_derived_cl10, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @
% 15.16/2.74 (composition @ (converse @ X1) @
% 15.16/2.74 (complement @ (composition @ X1 @ X0))) @
% 15.16/2.74 (complement @ X0)) = (complement @ X0))),
% 15.16/2.74 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 15.16/2.74 thf(zip_derived_cl277, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((join @ (composition @ (converse @ one) @ (complement @ X0)) @
% 15.16/2.74 (complement @ X0)) = (complement @ X0))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl253, zip_derived_cl10])).
% 15.16/2.74 thf(zip_derived_cl236, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl229, zip_derived_cl7])).
% 15.16/2.74 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 15.16/2.74 inference('cnf', [status(esa)], [composition_identity_6])).
% 15.16/2.74 thf(zip_derived_cl248, plain, (((one) = (converse @ one))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl236, zip_derived_cl5])).
% 15.16/2.74 thf(zip_derived_cl253, plain,
% 15.16/2.74 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl247, zip_derived_cl236])).
% 15.16/2.74 thf(zip_derived_cl278, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl277, zip_derived_cl248, zip_derived_cl253])).
% 15.16/2.74 thf(zip_derived_cl278, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl277, zip_derived_cl248, zip_derived_cl253])).
% 15.16/2.74 thf(zip_derived_cl278, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl277, zip_derived_cl248, zip_derived_cl253])).
% 15.16/2.74 thf(zip_derived_cl71, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @ (complement @ (join @ (complement @ X0) @ X1)) @
% 15.16/2.74 (meet @ X0 @ X1)))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl2, zip_derived_cl3, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl351, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @ (complement @ (complement @ X0)) @
% 15.16/2.74 (meet @ X0 @ (complement @ X0))))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl278, zip_derived_cl71])).
% 15.16/2.74 thf(zip_derived_cl12, plain,
% 15.16/2.74 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 15.16/2.74 inference('cnf', [status(esa)], [def_zero_13])).
% 15.16/2.74 thf(zip_derived_cl0, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 15.16/2.74 thf(zip_derived_cl357, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl351, zip_derived_cl12, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl357, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl351, zip_derived_cl12, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl0, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 15.16/2.74 thf(def_top_12, axiom, (( top ) = ( join @ A @ ( complement @ A ) ))).
% 15.16/2.74 thf(zip_derived_cl11, plain,
% 15.16/2.74 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 15.16/2.74 inference('cnf', [status(esa)], [def_top_12])).
% 15.16/2.74 thf(maddux2_join_associativity_2, axiom,
% 15.16/2.74 (( join @ A @ ( join @ B @ C ) ) = ( join @ ( join @ A @ B ) @ C ))).
% 15.16/2.74 thf(zip_derived_cl1, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.16/2.74 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 15.16/2.74 thf(zip_derived_cl26, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @ X1 @ (join @ (complement @ X1) @ X0)) = (join @ top @ X0))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 15.16/2.74 thf(zip_derived_cl278, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl277, zip_derived_cl248, zip_derived_cl253])).
% 15.16/2.74 thf(zip_derived_cl11, plain,
% 15.16/2.74 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 15.16/2.74 inference('cnf', [status(esa)], [def_top_12])).
% 15.16/2.74 thf(zip_derived_cl1, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.16/2.74 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 15.16/2.74 thf(zip_derived_cl23, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 15.16/2.74 thf(zip_derived_cl488, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((join @ (complement @ X0) @
% 15.16/2.74 (join @ (complement @ X0) @ (complement @ (complement @ X0))))
% 15.16/2.74 = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl278, zip_derived_cl23])).
% 15.16/2.74 thf(zip_derived_cl11, plain,
% 15.16/2.74 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 15.16/2.74 inference('cnf', [status(esa)], [def_top_12])).
% 15.16/2.74 thf(zip_derived_cl0, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 15.16/2.74 thf(zip_derived_cl506, plain,
% 15.16/2.74 (![X0 : $i]: ((join @ top @ (complement @ X0)) = (top))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl488, zip_derived_cl11, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl23, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 15.16/2.74 thf(zip_derived_cl525, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl506, zip_derived_cl23])).
% 15.16/2.74 thf(zip_derived_cl0, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 15.16/2.74 thf(zip_derived_cl529, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl525, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl588, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @ X1 @ (join @ (complement @ X1) @ X0)) = (top))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl529])).
% 15.16/2.74 thf(zip_derived_cl601, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @ X0 @ (join @ X1 @ (complement @ X0))) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl588])).
% 15.16/2.74 thf(zip_derived_cl937, plain,
% 15.16/2.74 (![X0 : $i]: ((join @ (complement @ X0) @ X0) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl601])).
% 15.16/2.74 thf(zip_derived_cl1, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.16/2.74 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 15.16/2.74 thf(zip_derived_cl951, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @ (complement @ X1) @ (join @ X1 @ X0)) = (join @ top @ X0))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl937, zip_derived_cl1])).
% 15.16/2.74 thf(zip_derived_cl529, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl525, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl967, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @ (complement @ X1) @ (join @ X1 @ X0)) = (top))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl951, zip_derived_cl529])).
% 15.16/2.74 thf(zip_derived_cl1300, plain,
% 15.16/2.74 (![X0 : $i]: ((join @ (complement @ zero) @ X0) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl967])).
% 15.16/2.74 thf(zip_derived_cl0, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 15.16/2.74 thf(zip_derived_cl3, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((meet @ X0 @ X1)
% 15.16/2.74 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 15.16/2.74 thf(zip_derived_cl55, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((meet @ X0 @ X1)
% 15.16/2.74 = (complement @ (join @ (complement @ X1) @ (complement @ X0))))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 15.16/2.74 thf(zip_derived_cl1411, plain,
% 15.16/2.74 (![X0 : $i]: ((meet @ X0 @ zero) = (complement @ top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl1300, zip_derived_cl55])).
% 15.16/2.74 thf(zip_derived_cl11, plain,
% 15.16/2.74 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 15.16/2.74 inference('cnf', [status(esa)], [def_top_12])).
% 15.16/2.74 thf(zip_derived_cl3, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((meet @ X0 @ X1)
% 15.16/2.74 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 15.16/2.74 thf(zip_derived_cl57, plain,
% 15.16/2.74 (![X0 : $i]: ((meet @ X0 @ (complement @ X0)) = (complement @ top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 15.16/2.74 thf(zip_derived_cl12, plain,
% 15.16/2.74 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 15.16/2.74 inference('cnf', [status(esa)], [def_zero_13])).
% 15.16/2.74 thf(zip_derived_cl60, plain, (((zero) = (complement @ top))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl12])).
% 15.16/2.74 thf(zip_derived_cl1425, plain, (![X0 : $i]: ((meet @ X0 @ zero) = (zero))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl1411, zip_derived_cl60])).
% 15.16/2.74 thf(zip_derived_cl0, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 15.16/2.74 thf(zip_derived_cl1647, plain,
% 15.16/2.74 (![X0 : $i]: ((complement @ X0) = (join @ zero @ (complement @ X0)))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl1614, zip_derived_cl278, zip_derived_cl278,
% 15.16/2.74 zip_derived_cl1425, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl357, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl351, zip_derived_cl12, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl1686, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 15.16/2.74 inference('s_sup+', [status(thm)],
% 15.16/2.74 [zip_derived_cl1647, zip_derived_cl357])).
% 15.16/2.74 thf(zip_derived_cl937, plain,
% 15.16/2.74 (![X0 : $i]: ((join @ (complement @ X0) @ X0) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl601])).
% 15.16/2.74 thf(zip_derived_cl7, plain,
% 15.16/2.74 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 15.16/2.74 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 15.16/2.74 thf(converse_additivity_9, axiom,
% 15.16/2.74 (( converse @ ( join @ A @ B ) ) =
% 15.16/2.74 ( join @ ( converse @ A ) @ ( converse @ B ) ))).
% 15.16/2.74 thf(zip_derived_cl8, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((converse @ (join @ X0 @ X1))
% 15.16/2.74 = (join @ (converse @ X0) @ (converse @ X1)))),
% 15.16/2.74 inference('cnf', [status(esa)], [converse_additivity_9])).
% 15.16/2.74 thf(zip_derived_cl18, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((converse @ (join @ X1 @ (converse @ X0)))
% 15.16/2.74 = (join @ (converse @ X1) @ X0))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 15.16/2.74 thf(zip_derived_cl961, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((converse @ top)
% 15.16/2.74 = (join @ (converse @ (complement @ (converse @ X0))) @ X0))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl937, zip_derived_cl18])).
% 15.16/2.74 thf(zip_derived_cl529, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl525, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl11, plain,
% 15.16/2.74 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 15.16/2.74 inference('cnf', [status(esa)], [def_top_12])).
% 15.16/2.74 thf(zip_derived_cl7, plain,
% 15.16/2.74 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 15.16/2.74 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 15.16/2.74 thf(zip_derived_cl8, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((converse @ (join @ X0 @ X1))
% 15.16/2.74 = (join @ (converse @ X0) @ (converse @ X1)))),
% 15.16/2.74 inference('cnf', [status(esa)], [converse_additivity_9])).
% 15.16/2.74 thf(zip_derived_cl19, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((converse @ (join @ (converse @ X0) @ X1))
% 15.16/2.74 = (join @ X0 @ (converse @ X1)))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 15.16/2.74 thf(zip_derived_cl147, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((converse @ top)
% 15.16/2.74 = (join @ X0 @ (converse @ (complement @ (converse @ X0)))))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl19])).
% 15.16/2.74 thf(zip_derived_cl559, plain, (((converse @ top) = (top))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl529, zip_derived_cl147])).
% 15.16/2.74 thf(zip_derived_cl974, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((top) = (join @ (converse @ (complement @ (converse @ X0))) @ X0))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl961, zip_derived_cl559])).
% 15.16/2.74 thf(zip_derived_cl0, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 15.16/2.74 thf(zip_derived_cl71, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @ (complement @ (join @ (complement @ X0) @ X1)) @
% 15.16/2.74 (meet @ X0 @ X1)))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl2, zip_derived_cl3, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl78, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @ (complement @ (join @ X1 @ (complement @ X0))) @
% 15.16/2.74 (meet @ X0 @ X1)))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl71])).
% 15.16/2.74 thf(zip_derived_cl2073, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @ (complement @ top) @
% 15.16/2.74 (meet @ X0 @
% 15.16/2.74 (converse @ (complement @ (converse @ (complement @ X0)))))))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl78])).
% 15.16/2.74 thf(zip_derived_cl60, plain, (((zero) = (complement @ top))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl12])).
% 15.16/2.74 thf(zip_derived_cl357, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl351, zip_derived_cl12, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl1686, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 15.16/2.74 inference('s_sup+', [status(thm)],
% 15.16/2.74 [zip_derived_cl1647, zip_derived_cl357])).
% 15.16/2.74 thf(zip_derived_cl1694, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl357, zip_derived_cl1686])).
% 15.16/2.74 thf(zip_derived_cl2094, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (meet @ X0 @
% 15.16/2.74 (converse @ (complement @ (converse @ (complement @ X0))))))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl2073, zip_derived_cl60, zip_derived_cl1694])).
% 15.16/2.74 thf(zip_derived_cl3669, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((complement @ X0)
% 15.16/2.74 = (meet @ (complement @ X0) @
% 15.16/2.74 (converse @ (complement @ (converse @ X0)))))),
% 15.16/2.74 inference('s_sup+', [status(thm)],
% 15.16/2.74 [zip_derived_cl1686, zip_derived_cl2094])).
% 15.16/2.74 thf(zip_derived_cl3, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((meet @ X0 @ X1)
% 15.16/2.74 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 15.16/2.74 thf(zip_derived_cl71, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @ (complement @ (join @ (complement @ X0) @ X1)) @
% 15.16/2.74 (meet @ X0 @ X1)))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl2, zip_derived_cl3, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl82, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.16/2.74 ((join @ (complement @ X1) @ (complement @ X0))
% 15.16/2.74 = (join @ (complement @ (join @ (meet @ X1 @ X0) @ X2)) @
% 15.16/2.74 (meet @ (join @ (complement @ X1) @ (complement @ X0)) @ X2)))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl71])).
% 15.16/2.74 thf(zip_derived_cl3, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((meet @ X0 @ X1)
% 15.16/2.74 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 15.16/2.74 thf(zip_derived_cl3, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((meet @ X0 @ X1)
% 15.16/2.74 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 15.16/2.74 thf(zip_derived_cl51, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.16/2.74 ((meet @ (join @ (complement @ X1) @ (complement @ X0)) @ X2)
% 15.16/2.74 = (complement @ (join @ (meet @ X1 @ X0) @ (complement @ X2))))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 15.16/2.74 thf(zip_derived_cl2147, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.16/2.74 ((join @ (complement @ X1) @ (complement @ X0))
% 15.16/2.74 = (join @ (complement @ (join @ (meet @ X1 @ X0) @ X2)) @
% 15.16/2.74 (complement @ (join @ (meet @ X1 @ X0) @ (complement @ X2)))))),
% 15.16/2.74 inference('demod', [status(thm)], [zip_derived_cl82, zip_derived_cl51])).
% 15.16/2.74 thf(zip_derived_cl4756, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((join @ (complement @ (complement @ X0)) @
% 15.16/2.74 (complement @ (converse @ (complement @ (converse @ X0)))))
% 15.16/2.74 = (join @ (complement @ (join @ (complement @ X0) @ X1)) @
% 15.16/2.74 (complement @ (join @ (complement @ X0) @ (complement @ X1)))))),
% 15.16/2.74 inference('s_sup+', [status(thm)],
% 15.16/2.74 [zip_derived_cl3669, zip_derived_cl2147])).
% 15.16/2.74 thf(zip_derived_cl1686, plain,
% 15.16/2.74 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 15.16/2.74 inference('s_sup+', [status(thm)],
% 15.16/2.74 [zip_derived_cl1647, zip_derived_cl357])).
% 15.16/2.74 thf(zip_derived_cl3, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((meet @ X0 @ X1)
% 15.16/2.74 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 15.16/2.74 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 15.16/2.74 thf(zip_derived_cl71, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((X0)
% 15.16/2.74 = (join @ (complement @ (join @ (complement @ X0) @ X1)) @
% 15.16/2.74 (meet @ X0 @ X1)))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl2, zip_derived_cl3, zip_derived_cl0])).
% 15.16/2.74 thf(zip_derived_cl4796, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((join @ X0 @
% 15.16/2.74 (complement @ (converse @ (complement @ (converse @ X0))))) = (
% 15.16/2.74 X0))),
% 15.16/2.74 inference('demod', [status(thm)],
% 15.16/2.74 [zip_derived_cl4756, zip_derived_cl1686, zip_derived_cl3,
% 15.16/2.74 zip_derived_cl71])).
% 15.16/2.74 thf(zip_derived_cl19, plain,
% 15.16/2.74 (![X0 : $i, X1 : $i]:
% 15.16/2.74 ((converse @ (join @ (converse @ X0) @ X1))
% 15.16/2.74 = (join @ X0 @ (converse @ X1)))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 15.16/2.74 thf(zip_derived_cl6204, plain,
% 15.16/2.74 (![X0 : $i]:
% 15.16/2.74 ((converse @ (converse @ X0))
% 15.16/2.74 = (join @ X0 @
% 15.16/2.74 (converse @
% 15.16/2.74 (complement @
% 15.16/2.74 (converse @ (complement @ (converse @ (converse @ X0))))))))),
% 15.16/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl4796, zip_derived_cl19])).
% 15.16/2.74 thf(zip_derived_cl7, plain,
% 15.42/2.74 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 15.42/2.74 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 15.42/2.74 thf(zip_derived_cl7, plain,
% 15.42/2.74 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 15.42/2.74 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 15.42/2.74 thf(zip_derived_cl6255, plain,
% 15.42/2.74 (![X0 : $i]:
% 15.42/2.74 ((X0)
% 15.42/2.74 = (join @ X0 @
% 15.42/2.74 (converse @ (complement @ (converse @ (complement @ X0))))))),
% 15.42/2.74 inference('demod', [status(thm)],
% 15.42/2.74 [zip_derived_cl6204, zip_derived_cl7, zip_derived_cl7])).
% 15.42/2.74 thf(zip_derived_cl0, plain,
% 15.42/2.74 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 15.42/2.74 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 15.42/2.74 thf(zip_derived_cl71, plain,
% 15.42/2.74 (![X0 : $i, X1 : $i]:
% 15.42/2.74 ((X0)
% 15.42/2.74 = (join @ (complement @ (join @ (complement @ X0) @ X1)) @
% 15.42/2.74 (meet @ X0 @ X1)))),
% 15.42/2.74 inference('demod', [status(thm)],
% 15.42/2.74 [zip_derived_cl2, zip_derived_cl3, zip_derived_cl0])).
% 15.42/2.74 thf(zip_derived_cl588, plain,
% 15.42/2.74 (![X0 : $i, X1 : $i]:
% 15.42/2.74 ((join @ X1 @ (join @ (complement @ X1) @ X0)) = (top))),
% 15.42/2.74 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl529])).
% 15.42/2.74 thf(zip_derived_cl610, plain,
% 15.42/2.74 (![X0 : $i, X1 : $i]:
% 15.42/2.74 ((join @ (join @ (complement @ X0) @ X1) @ X0) = (top))),
% 15.42/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl71, zip_derived_cl588])).
% 15.42/2.74 thf(zip_derived_cl78, plain,
% 15.42/2.74 (![X0 : $i, X1 : $i]:
% 15.42/2.74 ((X0)
% 15.42/2.74 = (join @ (complement @ (join @ X1 @ (complement @ X0))) @
% 15.42/2.74 (meet @ X0 @ X1)))),
% 15.42/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl71])).
% 15.42/2.74 thf(zip_derived_cl2070, plain,
% 15.42/2.74 (![X0 : $i, X1 : $i]:
% 15.42/2.74 ((X1)
% 15.42/2.74 = (join @ (complement @ top) @
% 15.42/2.74 (meet @ X1 @ (join @ (complement @ (complement @ X1)) @ X0))))),
% 15.42/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl610, zip_derived_cl78])).
% 15.42/2.74 thf(zip_derived_cl60, plain, (((zero) = (complement @ top))),
% 15.42/2.74 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl12])).
% 15.42/2.74 thf(zip_derived_cl1686, plain,
% 15.42/2.74 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 15.42/2.74 inference('s_sup+', [status(thm)],
% 15.42/2.74 [zip_derived_cl1647, zip_derived_cl357])).
% 15.42/2.74 thf(zip_derived_cl1694, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 15.42/2.74 inference('demod', [status(thm)], [zip_derived_cl357, zip_derived_cl1686])).
% 15.42/2.74 thf(zip_derived_cl2091, plain,
% 15.42/2.74 (![X0 : $i, X1 : $i]: ((X1) = (meet @ X1 @ (join @ X1 @ X0)))),
% 15.42/2.74 inference('demod', [status(thm)],
% 15.42/2.74 [zip_derived_cl2070, zip_derived_cl60, zip_derived_cl1686,
% 15.42/2.74 zip_derived_cl1694])).
% 15.42/2.74 thf(zip_derived_cl2316, plain,
% 15.42/2.74 (![X0 : $i, X1 : $i]: ((X0) = (meet @ X0 @ (join @ X1 @ X0)))),
% 15.42/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2091])).
% 15.42/2.74 thf(zip_derived_cl6455, plain,
% 15.42/2.74 (![X0 : $i]:
% 15.42/2.74 ((converse @ (complement @ (converse @ (complement @ X0))))
% 15.42/2.74 = (meet @
% 15.42/2.74 (converse @ (complement @ (converse @ (complement @ X0)))) @ X0))),
% 15.42/2.74 inference('s_sup+', [status(thm)],
% 15.42/2.74 [zip_derived_cl6255, zip_derived_cl2316])).
% 15.42/2.74 thf(zip_derived_cl4796, plain,
% 15.42/2.74 (![X0 : $i]:
% 15.42/2.74 ((join @ X0 @
% 15.42/2.74 (complement @ (converse @ (complement @ (converse @ X0))))) = (
% 15.42/2.74 X0))),
% 15.42/2.74 inference('demod', [status(thm)],
% 15.42/2.74 [zip_derived_cl4756, zip_derived_cl1686, zip_derived_cl3,
% 15.42/2.74 zip_derived_cl71])).
% 15.42/2.74 thf(zip_derived_cl55, plain,
% 15.42/2.74 (![X0 : $i, X1 : $i]:
% 15.42/2.74 ((meet @ X0 @ X1)
% 15.42/2.74 = (complement @ (join @ (complement @ X1) @ (complement @ X0))))),
% 15.42/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 15.42/2.74 thf(zip_derived_cl6194, plain,
% 15.42/2.74 (![X0 : $i]:
% 15.42/2.74 ((meet @ (converse @ (complement @ (converse @ (complement @ X0)))) @
% 15.42/2.74 X0) = (complement @ (complement @ X0)))),
% 15.42/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl4796, zip_derived_cl55])).
% 15.42/2.74 thf(zip_derived_cl1686, plain,
% 15.42/2.74 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 15.42/2.74 inference('s_sup+', [status(thm)],
% 15.42/2.74 [zip_derived_cl1647, zip_derived_cl357])).
% 15.42/2.74 thf(zip_derived_cl6245, plain,
% 15.42/2.74 (![X0 : $i]:
% 15.42/2.74 ((meet @ (converse @ (complement @ (converse @ (complement @ X0)))) @
% 15.42/2.74 X0) = (X0))),
% 15.42/2.74 inference('demod', [status(thm)],
% 15.42/2.74 [zip_derived_cl6194, zip_derived_cl1686])).
% 15.42/2.74 thf(zip_derived_cl6501, plain,
% 15.42/2.74 (![X0 : $i]:
% 15.42/2.74 ((converse @ (complement @ (converse @ (complement @ X0)))) = (X0))),
% 15.42/2.74 inference('demod', [status(thm)],
% 15.42/2.74 [zip_derived_cl6455, zip_derived_cl6245])).
% 15.42/2.74 thf(zip_derived_cl7, plain,
% 15.42/2.74 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 15.42/2.74 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 15.42/2.74 thf(zip_derived_cl6523, plain,
% 15.42/2.74 (![X0 : $i]:
% 15.42/2.74 ((converse @ X0) = (complement @ (converse @ (complement @ X0))))),
% 15.42/2.74 inference('s_sup+', [status(thm)], [zip_derived_cl6501, zip_derived_cl7])).
% 15.42/2.74 thf(zip_derived_cl1686, plain,
% 15.42/2.74 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 15.42/2.74 inference('s_sup+', [status(thm)],
% 15.42/2.74 [zip_derived_cl1647, zip_derived_cl357])).
% 15.42/2.74 thf(zip_derived_cl6844, plain,
% 15.42/2.74 (![X0 : $i]:
% 15.42/2.74 ((converse @ (complement @ X0)) = (complement @ (converse @ X0)))),
% 15.42/2.74 inference('s_sup+', [status(thm)],
% 15.42/2.74 [zip_derived_cl6523, zip_derived_cl1686])).
% 15.42/2.74 thf(zip_derived_cl6883, plain,
% 15.42/2.74 (((complement @ (converse @ sk1)) != (complement @ (converse @ sk1)))),
% 15.42/2.74 inference('demod', [status(thm)], [zip_derived_cl13, zip_derived_cl6844])).
% 15.42/2.74 thf(zip_derived_cl6884, plain, ($false),
% 15.42/2.74 inference('simplify', [status(thm)], [zip_derived_cl6883])).
% 15.42/2.74
% 15.42/2.74 % SZS output end Refutation
% 15.42/2.74
% 15.42/2.74
% 15.42/2.74 % Terminating...
% 15.42/2.84 % Runner terminated.
% 15.42/2.84 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------