TSTP Solution File: REL044-2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL044-2 : 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.PUEEwxheow true
% Computer : n020.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 13:47:30 EDT 2023
% Result : Unsatisfiable 55.69s 8.57s
% Output : Refutation 55.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL044-2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.PUEEwxheow true
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 19:04:00 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 55.69/8.57 % Solved by fo/fo5.sh.
% 55.69/8.57 % done 3377 iterations in 7.796s
% 55.69/8.57 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 55.69/8.57 % SZS output start Refutation
% 55.69/8.57 thf(composition_type, type, composition: $i > $i > $i).
% 55.69/8.57 thf(meet_type, type, meet: $i > $i > $i).
% 55.69/8.57 thf(complement_type, type, complement: $i > $i).
% 55.69/8.57 thf(sk1_type, type, sk1: $i).
% 55.69/8.57 thf(converse_type, type, converse: $i > $i).
% 55.69/8.57 thf(sk3_type, type, sk3: $i).
% 55.69/8.57 thf(top_type, type, top: $i).
% 55.69/8.57 thf(join_type, type, join: $i > $i > $i).
% 55.69/8.57 thf(zero_type, type, zero: $i).
% 55.69/8.57 thf(sk2_type, type, sk2: $i).
% 55.69/8.57 thf(one_type, type, one: $i).
% 55.69/8.57 thf(def_top_12, axiom, (( top ) = ( join @ A @ ( complement @ A ) ))).
% 55.69/8.57 thf(zip_derived_cl11, plain,
% 55.69/8.57 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 55.69/8.57 inference('cnf', [status(esa)], [def_top_12])).
% 55.69/8.57 thf(converse_idempotence_8, axiom, (( converse @ ( converse @ A ) ) = ( A ))).
% 55.69/8.57 thf(zip_derived_cl7, plain,
% 55.69/8.57 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.57 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.57 thf(converse_additivity_9, axiom,
% 55.69/8.57 (( converse @ ( join @ A @ B ) ) =
% 55.69/8.57 ( join @ ( converse @ A ) @ ( converse @ B ) ))).
% 55.69/8.57 thf(zip_derived_cl8, plain,
% 55.69/8.57 (![X0 : $i, X1 : $i]:
% 55.69/8.57 ((converse @ (join @ X0 @ X1))
% 55.69/8.57 = (join @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.57 inference('cnf', [status(esa)], [converse_additivity_9])).
% 55.69/8.57 thf(zip_derived_cl26, plain,
% 55.69/8.57 (![X0 : $i, X1 : $i]:
% 55.69/8.57 ((converse @ (join @ (converse @ X0) @ X1))
% 55.69/8.57 = (join @ X0 @ (converse @ X1)))),
% 55.69/8.57 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 55.69/8.57 thf(zip_derived_cl79, plain,
% 55.69/8.57 (![X0 : $i]:
% 55.69/8.57 ((converse @ top)
% 55.69/8.57 = (join @ X0 @ (converse @ (complement @ (converse @ X0)))))),
% 55.69/8.57 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 55.69/8.57 thf(composition_identity_6, axiom, (( composition @ A @ one ) = ( A ))).
% 55.69/8.57 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 55.69/8.57 inference('cnf', [status(esa)], [composition_identity_6])).
% 55.69/8.57 thf(zip_derived_cl7, plain,
% 55.69/8.57 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.57 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.57 thf(converse_multiplicativity_10, axiom,
% 55.69/8.57 (( converse @ ( composition @ A @ B ) ) =
% 55.69/8.57 ( composition @ ( converse @ B ) @ ( converse @ A ) ))).
% 55.69/8.57 thf(zip_derived_cl9, plain,
% 55.69/8.57 (![X0 : $i, X1 : $i]:
% 55.69/8.57 ((converse @ (composition @ X1 @ X0))
% 55.69/8.57 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.57 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 55.69/8.57 thf(zip_derived_cl27, plain,
% 55.69/8.57 (![X0 : $i, X1 : $i]:
% 55.69/8.57 ((converse @ (composition @ (converse @ X0) @ X1))
% 55.69/8.57 = (composition @ (converse @ X1) @ X0))),
% 55.69/8.57 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 55.69/8.57 thf(zip_derived_cl213, plain,
% 55.69/8.57 (![X0 : $i]:
% 55.69/8.57 ((converse @ (converse @ X0)) = (composition @ (converse @ one) @ X0))),
% 55.69/8.57 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl27])).
% 55.69/8.57 thf(zip_derived_cl7, plain,
% 55.69/8.57 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.57 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl219, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl213, zip_derived_cl7])).
% 55.69/8.58 thf(zip_derived_cl219, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl213, zip_derived_cl7])).
% 55.69/8.58 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [composition_identity_6])).
% 55.69/8.58 thf(zip_derived_cl221, plain, (((one) = (converse @ one))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl219, zip_derived_cl5])).
% 55.69/8.58 thf(zip_derived_cl235, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (composition @ one @ X0))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl219, zip_derived_cl221])).
% 55.69/8.58 thf(converse_cancellativity_11, axiom,
% 55.69/8.58 (( join @
% 55.69/8.58 ( composition @
% 55.69/8.58 ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @
% 55.69/8.58 ( complement @ B ) ) =
% 55.69/8.58 ( complement @ B ))).
% 55.69/8.58 thf(zip_derived_cl10, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @
% 55.69/8.58 (composition @ (converse @ X1) @
% 55.69/8.58 (complement @ (composition @ X1 @ X0))) @
% 55.69/8.58 (complement @ X0)) = (complement @ X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 55.69/8.58 thf(zip_derived_cl532, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (composition @ (converse @ one) @ (complement @ X0)) @
% 55.69/8.58 (complement @ X0)) = (complement @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl235, zip_derived_cl10])).
% 55.69/8.58 thf(zip_derived_cl221, plain, (((one) = (converse @ one))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl219, zip_derived_cl5])).
% 55.69/8.58 thf(zip_derived_cl235, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (composition @ one @ X0))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl219, zip_derived_cl221])).
% 55.69/8.58 thf(zip_derived_cl547, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl532, zip_derived_cl221, zip_derived_cl235])).
% 55.69/8.58 thf(zip_derived_cl11, plain,
% 55.69/8.58 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 55.69/8.58 inference('cnf', [status(esa)], [def_top_12])).
% 55.69/8.58 thf(maddux2_join_associativity_2, axiom,
% 55.69/8.58 (( join @ A @ ( join @ B @ C ) ) = ( join @ ( join @ A @ B ) @ C ))).
% 55.69/8.58 thf(zip_derived_cl1, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 55.69/8.58 thf(zip_derived_cl37, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 55.69/8.58 thf(zip_derived_cl1364, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (complement @ X0) @
% 55.69/8.58 (join @ (complement @ X0) @ (complement @ (complement @ X0))))
% 55.69/8.58 = (top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl547, zip_derived_cl37])).
% 55.69/8.58 thf(zip_derived_cl11, plain,
% 55.69/8.58 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 55.69/8.58 inference('cnf', [status(esa)], [def_top_12])).
% 55.69/8.58 thf(maddux1_join_commutativity_1, axiom,
% 55.69/8.58 (( join @ A @ B ) = ( join @ B @ A ))).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl1419, plain,
% 55.69/8.58 (![X0 : $i]: ((join @ top @ (complement @ X0)) = (top))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl1364, zip_derived_cl11, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl37, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 55.69/8.58 thf(zip_derived_cl1475, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1419, zip_derived_cl37])).
% 55.69/8.58 thf(zip_derived_cl11, plain,
% 55.69/8.58 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 55.69/8.58 inference('cnf', [status(esa)], [def_top_12])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl8, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (join @ X0 @ X1))
% 55.69/8.58 = (join @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_additivity_9])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl23, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @ (converse @ X0) @ (converse @ X1))
% 55.69/8.58 = (converse @ (join @ X1 @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl32, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @ (converse @ X1) @ X0)
% 55.69/8.58 = (converse @ (join @ (converse @ X0) @ X1)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl23])).
% 55.69/8.58 thf(zip_derived_cl363, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (converse @ (complement @ (converse @ X0))) @ X0)
% 55.69/8.58 = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl32])).
% 55.69/8.58 thf(zip_derived_cl1503, plain, (((top) = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1475, zip_derived_cl363])).
% 55.69/8.58 thf(zip_derived_cl1515, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((top) = (join @ X0 @ (converse @ (complement @ (converse @ X0)))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl79, zip_derived_cl1503])).
% 55.69/8.58 thf(goals_17, conjecture,
% 55.69/8.58 (( join @
% 55.69/8.58 ( composition @ ( complement @ sk1 ) @ sk2 ) @ ( complement @ sk3 ) ) !=
% 55.69/8.58 ( complement @ sk3 ))).
% 55.69/8.58 thf(zf_stmt_0, negated_conjecture,
% 55.69/8.58 (( join @
% 55.69/8.58 ( composition @ ( complement @ sk1 ) @ sk2 ) @ ( complement @ sk3 ) ) =
% 55.69/8.58 ( complement @ sk3 )),
% 55.69/8.58 inference('cnf.neg', [status(esa)], [goals_17])).
% 55.69/8.58 thf(zip_derived_cl16, plain,
% 55.69/8.58 (((join @ (composition @ (complement @ sk1) @ sk2) @ (complement @ sk3))
% 55.69/8.58 = (complement @ sk3))),
% 55.69/8.58 inference('cnf', [status(esa)], [zf_stmt_0])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl21, plain,
% 55.69/8.58 (((complement @ sk3)
% 55.69/8.58 = (join @ (complement @ sk3) @
% 55.69/8.58 (composition @ (complement @ sk1) @ sk2)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl1, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 55.69/8.58 thf(zip_derived_cl94, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (complement @ sk3) @
% 55.69/8.58 (join @ (composition @ (complement @ sk1) @ sk2) @ X0))
% 55.69/8.58 = (join @ (complement @ sk3) @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl1])).
% 55.69/8.58 thf(zip_derived_cl1723, plain,
% 55.69/8.58 (((join @ (complement @ sk3) @ top)
% 55.69/8.58 = (join @ (complement @ sk3) @
% 55.69/8.58 (converse @
% 55.69/8.58 (complement @
% 55.69/8.58 (converse @ (composition @ (complement @ sk1) @ sk2))))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1515, zip_derived_cl94])).
% 55.69/8.58 thf(zip_derived_cl1475, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1419, zip_derived_cl37])).
% 55.69/8.58 thf(zip_derived_cl1751, plain,
% 55.69/8.58 (((top)
% 55.69/8.58 = (join @ (complement @ sk3) @
% 55.69/8.58 (converse @
% 55.69/8.58 (complement @
% 55.69/8.58 (converse @ (composition @ (complement @ sk1) @ sk2))))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl1723, zip_derived_cl1475])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl8, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (join @ X0 @ X1))
% 55.69/8.58 = (join @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_additivity_9])).
% 55.69/8.58 thf(zip_derived_cl25, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (join @ X1 @ (converse @ X0)))
% 55.69/8.58 = (join @ (converse @ X1) @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 55.69/8.58 thf(zip_derived_cl2431, plain,
% 55.69/8.58 (((converse @ top)
% 55.69/8.58 = (join @ (converse @ (complement @ sk3)) @
% 55.69/8.58 (complement @ (converse @ (composition @ (complement @ sk1) @ sk2)))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1751, zip_derived_cl25])).
% 55.69/8.58 thf(zip_derived_cl1503, plain, (((top) = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1475, zip_derived_cl363])).
% 55.69/8.58 thf(zip_derived_cl2442, plain,
% 55.69/8.58 (((top)
% 55.69/8.58 = (join @ (converse @ (complement @ sk3)) @
% 55.69/8.58 (complement @ (converse @ (composition @ (complement @ sk1) @ sk2)))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl2431, zip_derived_cl1503])).
% 55.69/8.58 thf(zip_derived_cl547, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl532, zip_derived_cl221, zip_derived_cl235])).
% 55.69/8.58 thf(maddux3_a_kind_of_de_Morgan_3, axiom,
% 55.69/8.58 (( A ) =
% 55.69/8.58 ( join @
% 55.69/8.58 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @
% 55.69/8.58 ( complement @ ( join @ ( complement @ A ) @ B ) ) ))).
% 55.69/8.58 thf(zip_derived_cl2, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 55.69/8.58 thf(maddux4_definiton_of_meet_4, axiom,
% 55.69/8.58 (( meet @ A @ B ) =
% 55.69/8.58 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ))).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl142, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ X1) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ X1))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl564, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ (complement @ X0)) @
% 55.69/8.58 (complement @ (complement @ X0))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl547, zip_derived_cl142])).
% 55.69/8.58 thf(def_zero_13, axiom, (( zero ) = ( meet @ A @ ( complement @ A ) ))).
% 55.69/8.58 thf(zip_derived_cl12, plain,
% 55.69/8.58 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 55.69/8.58 inference('cnf', [status(esa)], [def_zero_13])).
% 55.69/8.58 thf(zip_derived_cl583, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl564, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl11, plain,
% 55.69/8.58 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 55.69/8.58 inference('cnf', [status(esa)], [def_top_12])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl101, plain,
% 55.69/8.58 (![X0 : $i]: ((meet @ X0 @ (complement @ X0)) = (complement @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl12, plain,
% 55.69/8.58 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 55.69/8.58 inference('cnf', [status(esa)], [def_zero_13])).
% 55.69/8.58 thf(zip_derived_cl104, plain, (((zero) = (complement @ top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl129, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((meet @ X0 @ top) = (complement @ (join @ (complement @ X0) @ zero)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl104, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl130, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((meet @ X0 @ top) = (complement @ (join @ zero @ (complement @ X0))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl129, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl1075, plain,
% 55.69/8.58 (![X0 : $i]: ((meet @ (complement @ X0) @ top) = (complement @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl583, zip_derived_cl130])).
% 55.69/8.58 thf(zip_derived_cl1475, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1419, zip_derived_cl37])).
% 55.69/8.58 thf(zip_derived_cl142, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ X1) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ X1))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl1495, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (join @ (meet @ X0 @ top) @ (complement @ top)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1475, zip_derived_cl142])).
% 55.69/8.58 thf(zip_derived_cl104, plain, (((zero) = (complement @ top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl1509, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ top)))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl1495, zip_derived_cl104, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl1943, plain,
% 55.69/8.58 (![X0 : $i]: ((complement @ X0) = (join @ zero @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1075, zip_derived_cl1509])).
% 55.69/8.58 thf(zip_derived_cl583, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl564, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl363, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (converse @ (complement @ (converse @ X0))) @ X0)
% 55.69/8.58 = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl32])).
% 55.69/8.58 thf(zip_derived_cl1503, plain, (((top) = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1475, zip_derived_cl363])).
% 55.69/8.58 thf(zip_derived_cl1520, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (converse @ (complement @ (converse @ X0))) @ X0) = (top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl363, zip_derived_cl1503])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl142, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ X1) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ X1))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl145, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ X1) @
% 55.69/8.58 (complement @ (join @ X1 @ (complement @ X0)))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl142])).
% 55.69/8.58 thf(zip_derived_cl6642, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @
% 55.69/8.58 (meet @ X0 @
% 55.69/8.58 (converse @ (complement @ (converse @ (complement @ X0))))) @
% 55.69/8.58 (complement @ top)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1520, zip_derived_cl145])).
% 55.69/8.58 thf(zip_derived_cl104, plain, (((zero) = (complement @ top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl583, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl564, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl2152, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl583, zip_derived_cl2018])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl2357, plain, (![X0 : $i]: ((join @ X0 @ zero) = (X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2152, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl6687, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (meet @ X0 @
% 55.69/8.58 (converse @ (complement @ (converse @ (complement @ X0))))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl6642, zip_derived_cl104, zip_derived_cl2357])).
% 55.69/8.58 thf(zip_derived_cl8436, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((complement @ X0)
% 55.69/8.58 = (meet @ (complement @ X0) @
% 55.69/8.58 (converse @ (complement @ (converse @ X0)))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2018, zip_derived_cl6687])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl142, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ X1) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ X1))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl150, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ (complement @ X1) @ (complement @ X0))
% 55.69/8.58 = (join @
% 55.69/8.58 (meet @ (join @ (complement @ X1) @ (complement @ X0)) @ X2) @
% 55.69/8.58 (complement @ (join @ (meet @ X1 @ X0) @ X2))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl142])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl95, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((meet @ (join @ (complement @ X1) @ (complement @ X0)) @ X2)
% 55.69/8.58 = (complement @ (join @ (meet @ X1 @ X0) @ (complement @ X2))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl7209, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ (complement @ X1) @ (complement @ X0))
% 55.69/8.58 = (join @ (complement @ (join @ (meet @ X1 @ X0) @ X2)) @
% 55.69/8.58 (complement @ (join @ (meet @ X1 @ X0) @ (complement @ X2)))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl150, zip_derived_cl95, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl24538, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @ (complement @ (complement @ X0)) @
% 55.69/8.58 (complement @ (converse @ (complement @ (converse @ X0)))))
% 55.69/8.58 = (join @
% 55.69/8.58 (complement @
% 55.69/8.58 (join @
% 55.69/8.58 (meet @ (complement @ X0) @
% 55.69/8.58 (converse @ (complement @ (converse @ X0)))) @
% 55.69/8.58 X1)) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ (complement @ X1)))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl8436, zip_derived_cl7209])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl8436, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((complement @ X0)
% 55.69/8.58 = (meet @ (complement @ X0) @
% 55.69/8.58 (converse @ (complement @ (converse @ X0)))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2018, zip_derived_cl6687])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl142, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ X1) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ X1))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl24614, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ X0 @
% 55.69/8.58 (complement @ (converse @ (complement @ (converse @ X0))))) = (
% 55.69/8.58 X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl24538, zip_derived_cl2018, zip_derived_cl8436,
% 55.69/8.58 zip_derived_cl3, zip_derived_cl0, zip_derived_cl142])).
% 55.69/8.58 thf(zip_derived_cl26, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (join @ (converse @ X0) @ X1))
% 55.69/8.58 = (join @ X0 @ (converse @ X1)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 55.69/8.58 thf(zip_derived_cl24693, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((converse @ (converse @ X0))
% 55.69/8.58 = (join @ X0 @
% 55.69/8.58 (converse @
% 55.69/8.58 (complement @
% 55.69/8.58 (converse @ (complement @ (converse @ (converse @ X0))))))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl24614, zip_derived_cl26])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl24798, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ X0 @
% 55.69/8.58 (converse @ (complement @ (converse @ (complement @ X0))))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl24693, zip_derived_cl7, zip_derived_cl7])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl547, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl532, zip_derived_cl221, zip_derived_cl235])).
% 55.69/8.58 thf(zip_derived_cl2159, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (complement @ (complement @ X0)) @ X0)
% 55.69/8.58 = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2018, zip_derived_cl547])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl2174, plain, (![X0 : $i]: ((join @ X0 @ X0) = (X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl2159, zip_derived_cl2018, zip_derived_cl2018])).
% 55.69/8.58 thf(zip_derived_cl142, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ X1) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ X1))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl1, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 55.69/8.58 thf(zip_derived_cl143, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ (meet @ X0 @ X2) @
% 55.69/8.58 (join @ (complement @ (join @ (complement @ X0) @ X2)) @ X1))
% 55.69/8.58 = (join @ X0 @ X1))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl142, zip_derived_cl1])).
% 55.69/8.58 thf(zip_derived_cl6364, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @ (meet @ X1 @ X0) @
% 55.69/8.58 (complement @ (join @ (complement @ X1) @ X0)))
% 55.69/8.58 = (join @ X1 @ (complement @ (join @ (complement @ X1) @ X0))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2174, zip_derived_cl143])).
% 55.69/8.58 thf(zip_derived_cl142, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ X1) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ X1))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl6432, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X1) = (join @ X1 @ (complement @ (join @ (complement @ X1) @ X0))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl6364, zip_derived_cl142])).
% 55.69/8.58 thf(zip_derived_cl6908, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((complement @ X0)
% 55.69/8.58 = (join @ (complement @ X0) @ (complement @ (join @ X0 @ X1))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2018, zip_derived_cl6432])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl99, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X1) @ (complement @ X0))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl11890, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ (join @ X0 @ X1) @ X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl6908, zip_derived_cl99])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl12066, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((meet @ (join @ X0 @ X1) @ X0) = (X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl11890, zip_derived_cl2018])).
% 55.69/8.58 thf(zip_derived_cl12089, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((meet @ (join @ X1 @ X0) @ X0) = (X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl12066])).
% 55.69/8.58 thf(zip_derived_cl25531, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((meet @ X0 @
% 55.69/8.58 (converse @ (complement @ (converse @ (complement @ X0)))))
% 55.69/8.58 = (converse @ (complement @ (converse @ (complement @ X0)))))),
% 55.69/8.58 inference('sup+', [status(thm)],
% 55.69/8.58 [zip_derived_cl24798, zip_derived_cl12089])).
% 55.69/8.58 thf(zip_derived_cl6687, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (meet @ X0 @
% 55.69/8.58 (converse @ (complement @ (converse @ (complement @ X0))))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl6642, zip_derived_cl104, zip_derived_cl2357])).
% 55.69/8.58 thf(zip_derived_cl25622, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((X0) = (converse @ (complement @ (converse @ (complement @ X0)))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl25531, zip_derived_cl6687])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl25673, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((converse @ X0) = (complement @ (converse @ (complement @ X0))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl25622, zip_derived_cl7])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl26031, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((converse @ (complement @ X0)) = (complement @ (converse @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)],
% 55.69/8.58 [zip_derived_cl25673, zip_derived_cl2018])).
% 55.69/8.58 thf(zip_derived_cl26096, plain,
% 55.69/8.58 (((top)
% 55.69/8.58 = (join @ (complement @ (converse @ sk3)) @
% 55.69/8.58 (complement @ (converse @ (composition @ (complement @ sk1) @ sk2)))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl2442, zip_derived_cl26031])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl27239, plain,
% 55.69/8.58 (((meet @ (converse @ sk3) @
% 55.69/8.58 (converse @ (composition @ (complement @ sk1) @ sk2)))
% 55.69/8.58 = (complement @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl26096, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl104, plain, (((zero) = (complement @ top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl27275, plain,
% 55.69/8.58 (((meet @ (converse @ sk3) @
% 55.69/8.58 (converse @ (composition @ (complement @ sk1) @ sk2))) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl27239, zip_derived_cl104])).
% 55.69/8.58 thf(zip_derived_cl9, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (composition @ X1 @ X0))
% 55.69/8.58 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 55.69/8.58 thf(dedekind_law_14, axiom,
% 55.69/8.58 (( join @
% 55.69/8.58 ( meet @ ( composition @ A @ B ) @ C ) @
% 55.69/8.58 ( composition @
% 55.69/8.58 ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @
% 55.69/8.58 ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ) =
% 55.69/8.58 ( composition @
% 55.69/8.58 ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @
% 55.69/8.58 ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ))).
% 55.69/8.58 thf(zip_derived_cl13, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ (meet @ (composition @ X0 @ X2) @ X1) @
% 55.69/8.58 (composition @ (meet @ X0 @ (composition @ X1 @ (converse @ X2))) @
% 55.69/8.58 (meet @ X2 @ (composition @ (converse @ X0) @ X1))))
% 55.69/8.58 = (composition @
% 55.69/8.58 (meet @ X0 @ (composition @ X1 @ (converse @ X2))) @
% 55.69/8.58 (meet @ X2 @ (composition @ (converse @ X0) @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [dedekind_law_14])).
% 55.69/8.58 thf(zip_derived_cl617, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ (meet @ (composition @ X0 @ X2) @ (converse @ X1)) @
% 55.69/8.58 (composition @
% 55.69/8.58 (meet @ X0 @ (composition @ (converse @ X1) @ (converse @ X2))) @
% 55.69/8.58 (meet @ X2 @ (converse @ (composition @ X1 @ X0)))))
% 55.69/8.58 = (composition @
% 55.69/8.58 (meet @ X0 @ (composition @ (converse @ X1) @ (converse @ X2))) @
% 55.69/8.58 (meet @ X2 @ (composition @ (converse @ X0) @ (converse @ X1)))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl13])).
% 55.69/8.58 thf(zip_derived_cl9, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (composition @ X1 @ X0))
% 55.69/8.58 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 55.69/8.58 thf(zip_derived_cl9, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (composition @ X1 @ X0))
% 55.69/8.58 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 55.69/8.58 thf(zip_derived_cl9, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (composition @ X1 @ X0))
% 55.69/8.58 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 55.69/8.58 thf(zip_derived_cl645, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ (meet @ (composition @ X0 @ X2) @ (converse @ X1)) @
% 55.69/8.58 (composition @ (meet @ X0 @ (converse @ (composition @ X2 @ X1))) @
% 55.69/8.58 (meet @ X2 @ (converse @ (composition @ X1 @ X0)))))
% 55.69/8.58 = (composition @
% 55.69/8.58 (meet @ X0 @ (converse @ (composition @ X2 @ X1))) @
% 55.69/8.58 (meet @ X2 @ (converse @ (composition @ X1 @ X0)))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl617, zip_derived_cl9, zip_derived_cl9,
% 55.69/8.58 zip_derived_cl9])).
% 55.69/8.58 thf(zip_derived_cl33151, plain,
% 55.69/8.58 (((join @
% 55.69/8.58 (meet @ (composition @ (converse @ sk3) @ (complement @ sk1)) @
% 55.69/8.58 (converse @ sk2)) @
% 55.69/8.58 (composition @ zero @
% 55.69/8.58 (meet @ (complement @ sk1) @
% 55.69/8.58 (converse @ (composition @ sk2 @ (converse @ sk3))))))
% 55.69/8.58 = (composition @
% 55.69/8.58 (meet @ (converse @ sk3) @
% 55.69/8.58 (converse @ (composition @ (complement @ sk1) @ sk2))) @
% 55.69/8.58 (meet @ (complement @ sk1) @
% 55.69/8.58 (converse @ (composition @ sk2 @ (converse @ sk3))))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl27275, zip_derived_cl645])).
% 55.69/8.58 thf(zip_derived_cl99, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X1) @ (complement @ X0))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl6089, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((meet @ X0 @ X1) = (meet @ X1 @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl99, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl9, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (composition @ X1 @ X0))
% 55.69/8.58 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 55.69/8.58 thf(zip_derived_cl28, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (composition @ X1 @ (converse @ X0)))
% 55.69/8.58 = (composition @ X0 @ (converse @ X1)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 55.69/8.58 thf(zip_derived_cl2152, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl583, zip_derived_cl2018])).
% 55.69/8.58 thf(zip_derived_cl1515, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((top) = (join @ X0 @ (converse @ (complement @ (converse @ X0)))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl79, zip_derived_cl1503])).
% 55.69/8.58 thf(zip_derived_cl2376, plain,
% 55.69/8.58 (((top) = (converse @ (complement @ (converse @ zero))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2152, zip_derived_cl1515])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl2552, plain,
% 55.69/8.58 (((converse @ top) = (complement @ (converse @ zero)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2376, zip_derived_cl7])).
% 55.69/8.58 thf(zip_derived_cl1503, plain, (((top) = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1475, zip_derived_cl363])).
% 55.69/8.58 thf(zip_derived_cl2587, plain, (((top) = (complement @ (converse @ zero)))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl2552, zip_derived_cl1503])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl2623, plain, (((converse @ zero) = (complement @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2587, zip_derived_cl2018])).
% 55.69/8.58 thf(zip_derived_cl104, plain, (((zero) = (complement @ top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl2636, plain, (((converse @ zero) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2623, zip_derived_cl104])).
% 55.69/8.58 thf(zip_derived_cl27, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (composition @ (converse @ X0) @ X1))
% 55.69/8.58 = (composition @ (converse @ X1) @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 55.69/8.58 thf(zip_derived_cl2665, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((converse @ (composition @ zero @ X0))
% 55.69/8.58 = (composition @ (converse @ X0) @ zero))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2636, zip_derived_cl27])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl6128, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((converse @ (composition @ (converse @ X0) @ zero))
% 55.69/8.58 = (composition @ zero @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2665, zip_derived_cl7])).
% 55.69/8.58 thf(zip_derived_cl1515, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((top) = (join @ X0 @ (converse @ (complement @ (converse @ X0)))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl79, zip_derived_cl1503])).
% 55.69/8.58 thf(zip_derived_cl235, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (composition @ one @ X0))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl219, zip_derived_cl221])).
% 55.69/8.58 thf(composition_distributivity_7, axiom,
% 55.69/8.58 (( composition @ ( join @ A @ B ) @ C ) =
% 55.69/8.58 ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ))).
% 55.69/8.58 thf(zip_derived_cl6, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((composition @ (join @ X0 @ X2) @ X1)
% 55.69/8.58 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 55.69/8.58 thf(zip_derived_cl336, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((composition @ (join @ X1 @ one) @ X0)
% 55.69/8.58 = (join @ (composition @ X1 @ X0) @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl235, zip_derived_cl6])).
% 55.69/8.58 thf(zip_derived_cl1751, plain,
% 55.69/8.58 (((top)
% 55.69/8.58 = (join @ (complement @ sk3) @
% 55.69/8.58 (converse @
% 55.69/8.58 (complement @
% 55.69/8.58 (converse @ (composition @ (complement @ sk1) @ sk2))))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl1723, zip_derived_cl1475])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl23, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @ (converse @ X0) @ (converse @ X1))
% 55.69/8.58 = (converse @ (join @ X1 @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl33, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @ X0 @ (converse @ X1))
% 55.69/8.58 = (converse @ (join @ X1 @ (converse @ X0))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl23])).
% 55.69/8.58 thf(zip_derived_cl2432, plain,
% 55.69/8.58 (((join @
% 55.69/8.58 (complement @ (converse @ (composition @ (complement @ sk1) @ sk2))) @
% 55.69/8.58 (converse @ (complement @ sk3))) = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1751, zip_derived_cl33])).
% 55.69/8.58 thf(zip_derived_cl1503, plain, (((top) = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1475, zip_derived_cl363])).
% 55.69/8.58 thf(zip_derived_cl2443, plain,
% 55.69/8.58 (((join @
% 55.69/8.58 (complement @ (converse @ (composition @ (complement @ sk1) @ sk2))) @
% 55.69/8.58 (converse @ (complement @ sk3))) = (top))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl2432, zip_derived_cl1503])).
% 55.69/8.58 thf(zip_derived_cl25, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (join @ X1 @ (converse @ X0)))
% 55.69/8.58 = (join @ (converse @ X1) @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 55.69/8.58 thf(zip_derived_cl9, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (composition @ X1 @ X0))
% 55.69/8.58 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 55.69/8.58 thf(zip_derived_cl49, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((converse @ (composition @ X2 @ (join @ X1 @ (converse @ X0))))
% 55.69/8.58 = (composition @ (join @ (converse @ X1) @ X0) @ (converse @ X2)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl9])).
% 55.69/8.58 thf(zip_derived_cl2943, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((converse @ (composition @ X0 @ top))
% 55.69/8.58 = (composition @
% 55.69/8.58 (join @
% 55.69/8.58 (converse @
% 55.69/8.58 (complement @
% 55.69/8.58 (converse @ (composition @ (complement @ sk1) @ sk2)))) @
% 55.69/8.58 (complement @ sk3)) @
% 55.69/8.58 (converse @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2443, zip_derived_cl49])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl1751, plain,
% 55.69/8.58 (((top)
% 55.69/8.58 = (join @ (complement @ sk3) @
% 55.69/8.58 (converse @
% 55.69/8.58 (complement @
% 55.69/8.58 (converse @ (composition @ (complement @ sk1) @ sk2))))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl1723, zip_derived_cl1475])).
% 55.69/8.58 thf(zip_derived_cl2953, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((converse @ (composition @ X0 @ top))
% 55.69/8.58 = (composition @ top @ (converse @ X0)))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl2943, zip_derived_cl0, zip_derived_cl1751])).
% 55.69/8.58 thf(zip_derived_cl13733, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((converse @ (join @ (composition @ X0 @ top) @ top))
% 55.69/8.58 = (composition @ top @ (converse @ (join @ X0 @ one))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl336, zip_derived_cl2953])).
% 55.69/8.58 thf(zip_derived_cl1475, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1419, zip_derived_cl37])).
% 55.69/8.58 thf(zip_derived_cl1503, plain, (((top) = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1475, zip_derived_cl363])).
% 55.69/8.58 thf(zip_derived_cl221, plain, (((one) = (converse @ one))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl219, zip_derived_cl5])).
% 55.69/8.58 thf(zip_derived_cl23, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @ (converse @ X0) @ (converse @ X1))
% 55.69/8.58 = (converse @ (join @ X1 @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl239, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ one @ (converse @ X0)) = (converse @ (join @ X0 @ one)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl23])).
% 55.69/8.58 thf(zip_derived_cl13811, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((top) = (composition @ top @ (join @ one @ (converse @ X0))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl13733, zip_derived_cl1475, zip_derived_cl1503,
% 55.69/8.58 zip_derived_cl239])).
% 55.69/8.58 thf(zip_derived_cl20127, plain, (((top) = (composition @ top @ top))),
% 55.69/8.58 inference('sup+', [status(thm)],
% 55.69/8.58 [zip_derived_cl1515, zip_derived_cl13811])).
% 55.69/8.58 thf(zip_derived_cl10, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((join @
% 55.69/8.58 (composition @ (converse @ X1) @
% 55.69/8.58 (complement @ (composition @ X1 @ X0))) @
% 55.69/8.58 (complement @ X0)) = (complement @ X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 55.69/8.58 thf(zip_derived_cl20204, plain,
% 55.69/8.58 (((join @ (composition @ (converse @ top) @ (complement @ top)) @
% 55.69/8.58 (complement @ top)) = (complement @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl20127, zip_derived_cl10])).
% 55.69/8.58 thf(zip_derived_cl1503, plain, (((top) = (converse @ top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1475, zip_derived_cl363])).
% 55.69/8.58 thf(zip_derived_cl104, plain, (((zero) = (complement @ top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl104, plain, (((zero) = (complement @ top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl2357, plain, (![X0 : $i]: ((join @ X0 @ zero) = (X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2152, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl104, plain, (((zero) = (complement @ top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl20220, plain, (((composition @ top @ zero) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl20204, zip_derived_cl1503, zip_derived_cl104,
% 55.69/8.58 zip_derived_cl104, zip_derived_cl2357, zip_derived_cl104])).
% 55.69/8.58 thf(zip_derived_cl6, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((composition @ (join @ X0 @ X2) @ X1)
% 55.69/8.58 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 55.69/8.58 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 55.69/8.58 thf(zip_derived_cl20237, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((composition @ (join @ top @ X0) @ zero)
% 55.69/8.58 = (join @ zero @ (composition @ X0 @ zero)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl20220, zip_derived_cl6])).
% 55.69/8.58 thf(zip_derived_cl1475, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1419, zip_derived_cl37])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl1488, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1475, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl20220, plain, (((composition @ top @ zero) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl20204, zip_derived_cl1503, zip_derived_cl104,
% 55.69/8.58 zip_derived_cl104, zip_derived_cl2357, zip_derived_cl104])).
% 55.69/8.58 thf(zip_derived_cl2152, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl583, zip_derived_cl2018])).
% 55.69/8.58 thf(zip_derived_cl20257, plain,
% 55.69/8.58 (![X0 : $i]: ((zero) = (composition @ X0 @ zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl20237, zip_derived_cl1488, zip_derived_cl20220,
% 55.69/8.58 zip_derived_cl2152])).
% 55.69/8.58 thf(zip_derived_cl2636, plain, (((converse @ zero) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2623, zip_derived_cl104])).
% 55.69/8.58 thf(zip_derived_cl20846, plain,
% 55.69/8.58 (![X0 : $i]: ((zero) = (composition @ zero @ X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl6128, zip_derived_cl20257, zip_derived_cl2636])).
% 55.69/8.58 thf(zip_derived_cl2357, plain, (![X0 : $i]: ((join @ X0 @ zero) = (X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2152, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl27275, plain,
% 55.69/8.58 (((meet @ (converse @ sk3) @
% 55.69/8.58 (converse @ (composition @ (complement @ sk1) @ sk2))) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl27239, zip_derived_cl104])).
% 55.69/8.58 thf(zip_derived_cl28, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((converse @ (composition @ X1 @ (converse @ X0)))
% 55.69/8.58 = (composition @ X0 @ (converse @ X1)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 55.69/8.58 thf(zip_derived_cl20846, plain,
% 55.69/8.58 (![X0 : $i]: ((zero) = (composition @ zero @ X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl6128, zip_derived_cl20257, zip_derived_cl2636])).
% 55.69/8.58 thf(zip_derived_cl33319, plain,
% 55.69/8.58 (((meet @ (converse @ sk2) @
% 55.69/8.58 (composition @ (converse @ sk3) @ (complement @ sk1))) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl33151, zip_derived_cl6089, zip_derived_cl28,
% 55.69/8.58 zip_derived_cl20846, zip_derived_cl2357, zip_derived_cl27275,
% 55.69/8.58 zip_derived_cl28, zip_derived_cl20846])).
% 55.69/8.58 thf(zip_derived_cl13, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.69/8.58 ((join @ (meet @ (composition @ X0 @ X2) @ X1) @
% 55.69/8.58 (composition @ (meet @ X0 @ (composition @ X1 @ (converse @ X2))) @
% 55.69/8.58 (meet @ X2 @ (composition @ (converse @ X0) @ X1))))
% 55.69/8.58 = (composition @
% 55.69/8.58 (meet @ X0 @ (composition @ X1 @ (converse @ X2))) @
% 55.69/8.58 (meet @ X2 @ (composition @ (converse @ X0) @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [dedekind_law_14])).
% 55.69/8.58 thf(zip_derived_cl41603, plain,
% 55.69/8.58 (((join @
% 55.69/8.58 (meet @ (composition @ sk3 @ (converse @ sk2)) @ (complement @ sk1)) @
% 55.69/8.58 (composition @
% 55.69/8.58 (meet @ sk3 @
% 55.69/8.58 (composition @ (complement @ sk1) @ (converse @ (converse @ sk2)))) @
% 55.69/8.58 zero))
% 55.69/8.58 = (composition @
% 55.69/8.58 (meet @ sk3 @
% 55.69/8.58 (composition @ (complement @ sk1) @ (converse @ (converse @ sk2)))) @
% 55.69/8.58 (meet @ (converse @ sk2) @
% 55.69/8.58 (composition @ (converse @ sk3) @ (complement @ sk1)))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl33319, zip_derived_cl13])).
% 55.69/8.58 thf(zip_derived_cl6089, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((meet @ X0 @ X1) = (meet @ X1 @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl99, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl11, plain,
% 55.69/8.58 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 55.69/8.58 inference('cnf', [status(esa)], [def_top_12])).
% 55.69/8.58 thf(zip_derived_cl94, plain,
% 55.69/8.58 (![X0 : $i]:
% 55.69/8.58 ((join @ (complement @ sk3) @
% 55.69/8.58 (join @ (composition @ (complement @ sk1) @ sk2) @ X0))
% 55.69/8.58 = (join @ (complement @ sk3) @ X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl1])).
% 55.69/8.58 thf(zip_derived_cl120, plain,
% 55.69/8.58 (((join @ (complement @ sk3) @ top)
% 55.69/8.58 = (join @ (complement @ sk3) @
% 55.69/8.58 (complement @ (composition @ (complement @ sk1) @ sk2))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl94])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl123, plain,
% 55.69/8.58 (((join @ top @ (complement @ sk3))
% 55.69/8.58 = (join @ (complement @ sk3) @
% 55.69/8.58 (complement @ (composition @ (complement @ sk1) @ sk2))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl120, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl3, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((meet @ X0 @ X1)
% 55.69/8.58 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 55.69/8.58 thf(zip_derived_cl305, plain,
% 55.69/8.58 (((meet @ sk3 @ (composition @ (complement @ sk1) @ sk2))
% 55.69/8.58 = (complement @ (join @ top @ (complement @ sk3))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl123, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl1419, plain,
% 55.69/8.58 (![X0 : $i]: ((join @ top @ (complement @ X0)) = (top))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl1364, zip_derived_cl11, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl104, plain, (((zero) = (complement @ top))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 55.69/8.58 thf(zip_derived_cl1462, plain,
% 55.69/8.58 (((meet @ sk3 @ (composition @ (complement @ sk1) @ sk2)) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl305, zip_derived_cl1419, zip_derived_cl104])).
% 55.69/8.58 thf(zip_derived_cl20846, plain,
% 55.69/8.58 (![X0 : $i]: ((zero) = (composition @ zero @ X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl6128, zip_derived_cl20257, zip_derived_cl2636])).
% 55.69/8.58 thf(zip_derived_cl2357, plain, (![X0 : $i]: ((join @ X0 @ zero) = (X0))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl2152, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl7, plain,
% 55.69/8.58 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 55.69/8.58 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 55.69/8.58 thf(zip_derived_cl1462, plain,
% 55.69/8.58 (((meet @ sk3 @ (composition @ (complement @ sk1) @ sk2)) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl305, zip_derived_cl1419, zip_derived_cl104])).
% 55.69/8.58 thf(zip_derived_cl33319, plain,
% 55.69/8.58 (((meet @ (converse @ sk2) @
% 55.69/8.58 (composition @ (converse @ sk3) @ (complement @ sk1))) = (zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl33151, zip_derived_cl6089, zip_derived_cl28,
% 55.69/8.58 zip_derived_cl20846, zip_derived_cl2357, zip_derived_cl27275,
% 55.69/8.58 zip_derived_cl28, zip_derived_cl20846])).
% 55.69/8.58 thf(zip_derived_cl20846, plain,
% 55.69/8.58 (![X0 : $i]: ((zero) = (composition @ zero @ X0))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl6128, zip_derived_cl20257, zip_derived_cl2636])).
% 55.69/8.58 thf(zip_derived_cl41621, plain,
% 55.69/8.58 (((meet @ (complement @ sk1) @ (composition @ sk3 @ (converse @ sk2)))
% 55.69/8.58 = (zero))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl41603, zip_derived_cl6089, zip_derived_cl7,
% 55.69/8.58 zip_derived_cl1462, zip_derived_cl20846, zip_derived_cl2357,
% 55.69/8.58 zip_derived_cl7, zip_derived_cl1462, zip_derived_cl33319,
% 55.69/8.58 zip_derived_cl20846])).
% 55.69/8.58 thf(zip_derived_cl142, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]:
% 55.69/8.58 ((X0)
% 55.69/8.58 = (join @ (meet @ X0 @ X1) @
% 55.69/8.58 (complement @ (join @ (complement @ X0) @ X1))))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 55.69/8.58 thf(zip_derived_cl41624, plain,
% 55.69/8.58 (((complement @ sk1)
% 55.69/8.58 = (join @ zero @
% 55.69/8.58 (complement @
% 55.69/8.58 (join @ (complement @ (complement @ sk1)) @
% 55.69/8.58 (composition @ sk3 @ (converse @ sk2))))))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl41621, zip_derived_cl142])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl2152, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl583, zip_derived_cl2018])).
% 55.69/8.58 thf(zip_derived_cl41653, plain,
% 55.69/8.58 (((complement @ sk1)
% 55.69/8.58 = (complement @ (join @ sk1 @ (composition @ sk3 @ (converse @ sk2)))))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl41624, zip_derived_cl2018, zip_derived_cl2152])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl42141, plain,
% 55.69/8.58 (((join @ sk1 @ (composition @ sk3 @ (converse @ sk2)))
% 55.69/8.58 = (complement @ (complement @ sk1)))),
% 55.69/8.58 inference('sup+', [status(thm)],
% 55.69/8.58 [zip_derived_cl41653, zip_derived_cl2018])).
% 55.69/8.58 thf(zip_derived_cl2018, plain,
% 55.69/8.58 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 55.69/8.58 inference('sup+', [status(thm)], [zip_derived_cl1943, zip_derived_cl583])).
% 55.69/8.58 thf(zip_derived_cl42207, plain,
% 55.69/8.58 (((join @ sk1 @ (composition @ sk3 @ (converse @ sk2))) = (sk1))),
% 55.69/8.58 inference('demod', [status(thm)],
% 55.69/8.58 [zip_derived_cl42141, zip_derived_cl2018])).
% 55.69/8.58 thf(goals_18, conjecture,
% 55.69/8.58 (( join @ ( composition @ sk3 @ ( converse @ sk2 ) ) @ sk1 ) = ( sk1 ))).
% 55.69/8.58 thf(zf_stmt_1, negated_conjecture,
% 55.69/8.58 (( join @ ( composition @ sk3 @ ( converse @ sk2 ) ) @ sk1 ) != ( sk1 )),
% 55.69/8.58 inference('cnf.neg', [status(esa)], [goals_18])).
% 55.69/8.58 thf(zip_derived_cl17, plain,
% 55.69/8.58 (((join @ (composition @ sk3 @ (converse @ sk2)) @ sk1) != (sk1))),
% 55.69/8.58 inference('cnf', [status(esa)], [zf_stmt_1])).
% 55.69/8.58 thf(zip_derived_cl0, plain,
% 55.69/8.58 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 55.69/8.58 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 55.69/8.58 thf(zip_derived_cl20, plain,
% 55.69/8.58 (((join @ sk1 @ (composition @ sk3 @ (converse @ sk2))) != (sk1))),
% 55.69/8.58 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl0])).
% 55.69/8.58 thf(zip_derived_cl42208, plain, ($false),
% 55.69/8.58 inference('simplify_reflect-', [status(thm)],
% 55.69/8.58 [zip_derived_cl42207, zip_derived_cl20])).
% 55.69/8.58
% 55.69/8.58 % SZS output end Refutation
% 55.69/8.58
% 55.69/8.58
% 55.69/8.58 % Terminating...
% 56.31/8.69 % Runner terminated.
% 56.31/8.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------