TSTP Solution File: REL042-2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL042-2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.N7VWVyzDvF true
% Computer : n025.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 13:47:28 EDT 2023
% Result : Unsatisfiable 28.17s 4.61s
% Output : Refutation 28.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL042-2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.N7VWVyzDvF true
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 22:00:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 28.17/4.61 % Solved by fo/fo1_av.sh.
% 28.17/4.61 % done 1508 iterations in 3.855s
% 28.17/4.61 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 28.17/4.61 % SZS output start Refutation
% 28.17/4.61 thf(composition_type, type, composition: $i > $i > $i).
% 28.17/4.61 thf(meet_type, type, meet: $i > $i > $i).
% 28.17/4.61 thf(complement_type, type, complement: $i > $i).
% 28.17/4.61 thf(sk1_type, type, sk1: $i).
% 28.17/4.61 thf(converse_type, type, converse: $i > $i).
% 28.17/4.61 thf(top_type, type, top: $i).
% 28.17/4.61 thf(join_type, type, join: $i > $i > $i).
% 28.17/4.61 thf(zero_type, type, zero: $i).
% 28.17/4.61 thf(one_type, type, one: $i).
% 28.17/4.61 thf(composition_identity_6, axiom, (( composition @ A @ one ) = ( A ))).
% 28.17/4.61 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [composition_identity_6])).
% 28.17/4.61 thf(goals_17, conjecture,
% 28.17/4.61 (( meet @
% 28.17/4.61 ( composition @ sk1 @ A ) @ ( composition @ sk1 @ ( complement @ A ) ) ) !=
% 28.17/4.61 ( zero ))).
% 28.17/4.61 thf(zf_stmt_0, negated_conjecture,
% 28.17/4.61 (( meet @
% 28.17/4.61 ( composition @ sk1 @ A ) @ ( composition @ sk1 @ ( complement @ A ) ) ) =
% 28.17/4.61 ( zero )),
% 28.17/4.61 inference('cnf.neg', [status(esa)], [goals_17])).
% 28.17/4.61 thf(zip_derived_cl16, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((meet @ (composition @ sk1 @ X0) @
% 28.17/4.61 (composition @ sk1 @ (complement @ X0))) = (zero))),
% 28.17/4.61 inference('cnf', [status(esa)], [zf_stmt_0])).
% 28.17/4.61 thf(zip_derived_cl20, plain,
% 28.17/4.61 (((meet @ sk1 @ (composition @ sk1 @ (complement @ one))) = (zero))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl16])).
% 28.17/4.61 thf(converse_idempotence_8, axiom, (( converse @ ( converse @ A ) ) = ( A ))).
% 28.17/4.61 thf(zip_derived_cl7, plain,
% 28.17/4.61 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 28.17/4.61 thf(dedekind_law_14, axiom,
% 28.17/4.61 (( join @
% 28.17/4.61 ( meet @ ( composition @ A @ B ) @ C ) @
% 28.17/4.61 ( composition @
% 28.17/4.61 ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @
% 28.17/4.61 ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ) =
% 28.17/4.61 ( composition @
% 28.17/4.61 ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @
% 28.17/4.61 ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ))).
% 28.17/4.61 thf(zip_derived_cl13, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.17/4.61 ((join @ (meet @ (composition @ X0 @ X2) @ X1) @
% 28.17/4.61 (composition @ (meet @ X0 @ (composition @ X1 @ (converse @ X2))) @
% 28.17/4.61 (meet @ X2 @ (composition @ (converse @ X0) @ X1))))
% 28.17/4.61 = (composition @
% 28.17/4.61 (meet @ X0 @ (composition @ X1 @ (converse @ X2))) @
% 28.17/4.61 (meet @ X2 @ (composition @ (converse @ X0) @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [dedekind_law_14])).
% 28.17/4.61 thf(zip_derived_cl318, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.17/4.61 ((join @ (meet @ (composition @ (converse @ X0) @ X2) @ X1) @
% 28.17/4.61 (composition @
% 28.17/4.61 (meet @ (converse @ X0) @ (composition @ X1 @ (converse @ X2))) @
% 28.17/4.61 (meet @ X2 @ (composition @ X0 @ X1))))
% 28.17/4.61 = (composition @
% 28.17/4.61 (meet @ (converse @ X0) @ (composition @ X1 @ (converse @ X2))) @
% 28.17/4.61 (meet @ X2 @ (composition @ X0 @ X1))))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl13])).
% 28.17/4.61 thf(zip_derived_cl16937, plain,
% 28.17/4.61 (((join @
% 28.17/4.61 (meet @ (composition @ (converse @ sk1) @ sk1) @ (complement @ one)) @
% 28.17/4.61 (composition @
% 28.17/4.61 (meet @ (converse @ sk1) @
% 28.17/4.61 (composition @ (complement @ one) @ (converse @ sk1))) @
% 28.17/4.61 zero))
% 28.17/4.61 = (composition @
% 28.17/4.61 (meet @ (converse @ sk1) @
% 28.17/4.61 (composition @ (complement @ one) @ (converse @ sk1))) @
% 28.17/4.61 zero))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl318])).
% 28.17/4.61 thf(maddux1_join_commutativity_1, axiom,
% 28.17/4.61 (( join @ A @ B ) = ( join @ B @ A ))).
% 28.17/4.61 thf(zip_derived_cl0, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 28.17/4.61 thf(maddux4_definiton_of_meet_4, axiom,
% 28.17/4.61 (( meet @ A @ B ) =
% 28.17/4.61 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ))).
% 28.17/4.61 thf(zip_derived_cl3, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((meet @ X0 @ X1)
% 28.17/4.61 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 28.17/4.61 thf(zip_derived_cl132, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((meet @ X0 @ X1)
% 28.17/4.61 = (complement @ (join @ (complement @ X1) @ (complement @ X0))))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl3, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((meet @ X0 @ X1)
% 28.17/4.61 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 28.17/4.61 thf(zip_derived_cl5521, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((meet @ X0 @ X1) = (meet @ X1 @ X0))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl7, plain,
% 28.17/4.61 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 28.17/4.61 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [composition_identity_6])).
% 28.17/4.61 thf(zip_derived_cl7, plain,
% 28.17/4.61 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 28.17/4.61 thf(converse_multiplicativity_10, axiom,
% 28.17/4.61 (( converse @ ( composition @ A @ B ) ) =
% 28.17/4.61 ( composition @ ( converse @ B ) @ ( converse @ A ) ))).
% 28.17/4.61 thf(zip_derived_cl9, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((converse @ (composition @ X1 @ X0))
% 28.17/4.61 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 28.17/4.61 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 28.17/4.61 thf(zip_derived_cl64, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((converse @ (composition @ (converse @ X0) @ X1))
% 28.17/4.61 = (composition @ (converse @ X1) @ X0))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 28.17/4.61 thf(zip_derived_cl200, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((converse @ (converse @ X0)) = (composition @ (converse @ one) @ X0))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl64])).
% 28.17/4.61 thf(zip_derived_cl7, plain,
% 28.17/4.61 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 28.17/4.61 thf(zip_derived_cl207, plain,
% 28.17/4.61 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl7])).
% 28.17/4.61 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [composition_identity_6])).
% 28.17/4.61 thf(composition_associativity_5, axiom,
% 28.17/4.61 (( composition @ A @ ( composition @ B @ C ) ) =
% 28.17/4.61 ( composition @ ( composition @ A @ B ) @ C ))).
% 28.17/4.61 thf(zip_derived_cl4, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.17/4.61 ((composition @ X0 @ (composition @ X1 @ X2))
% 28.17/4.61 = (composition @ (composition @ X0 @ X1) @ X2))),
% 28.17/4.61 inference('cnf', [status(esa)], [composition_associativity_5])).
% 28.17/4.61 thf(zip_derived_cl34, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((composition @ X0 @ (composition @ one @ X1))
% 28.17/4.61 = (composition @ X0 @ X1))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 28.17/4.61 thf(zip_derived_cl216, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((composition @ one @ X0) = (composition @ (converse @ one) @ X0))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl207, zip_derived_cl34])).
% 28.17/4.61 thf(zip_derived_cl207, plain,
% 28.17/4.61 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl7])).
% 28.17/4.61 thf(zip_derived_cl220, plain,
% 28.17/4.61 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl216, zip_derived_cl207])).
% 28.17/4.61 thf(composition_distributivity_7, axiom,
% 28.17/4.61 (( composition @ ( join @ A @ B ) @ C ) =
% 28.17/4.61 ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ))).
% 28.17/4.61 thf(zip_derived_cl6, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.17/4.61 ((composition @ (join @ X0 @ X2) @ X1)
% 28.17/4.61 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 28.17/4.61 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 28.17/4.61 thf(zip_derived_cl282, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((composition @ (join @ one @ X1) @ X0)
% 28.17/4.61 = (join @ X0 @ (composition @ X1 @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl220, zip_derived_cl6])).
% 28.17/4.61 thf(def_top_12, axiom, (( top ) = ( join @ A @ ( complement @ A ) ))).
% 28.17/4.61 thf(zip_derived_cl11, plain,
% 28.17/4.61 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 28.17/4.61 inference('cnf', [status(esa)], [def_top_12])).
% 28.17/4.61 thf(zip_derived_cl3, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((meet @ X0 @ X1)
% 28.17/4.61 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 28.17/4.61 thf(zip_derived_cl134, plain,
% 28.17/4.61 (![X0 : $i]: ((meet @ X0 @ (complement @ X0)) = (complement @ top))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 28.17/4.61 thf(def_zero_13, axiom, (( zero ) = ( meet @ A @ ( complement @ A ) ))).
% 28.17/4.61 thf(zip_derived_cl12, plain,
% 28.17/4.61 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 28.17/4.61 inference('cnf', [status(esa)], [def_zero_13])).
% 28.17/4.61 thf(zip_derived_cl137, plain, (((zero) = (complement @ top))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl12])).
% 28.17/4.61 thf(converse_cancellativity_11, axiom,
% 28.17/4.61 (( join @
% 28.17/4.61 ( composition @
% 28.17/4.61 ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @
% 28.17/4.61 ( complement @ B ) ) =
% 28.17/4.61 ( complement @ B ))).
% 28.17/4.61 thf(zip_derived_cl10, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((join @
% 28.17/4.61 (composition @ (converse @ X1) @
% 28.17/4.61 (complement @ (composition @ X1 @ X0))) @
% 28.17/4.61 (complement @ X0)) = (complement @ X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 28.17/4.61 thf(zip_derived_cl268, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((join @
% 28.17/4.61 (composition @ (converse @ X0) @
% 28.17/4.61 (complement @ (composition @ X0 @ top))) @
% 28.17/4.61 zero) = (zero))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl137, zip_derived_cl10])).
% 28.17/4.61 thf(zip_derived_cl12912, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((join @
% 28.17/4.61 (composition @ (converse @ (join @ one @ X0)) @
% 28.17/4.61 (complement @ (join @ top @ (composition @ X0 @ top)))) @
% 28.17/4.61 zero) = (zero))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl282, zip_derived_cl268])).
% 28.17/4.61 thf(zip_derived_cl207, plain,
% 28.17/4.61 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl7])).
% 28.17/4.61 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [composition_identity_6])).
% 28.17/4.61 thf(zip_derived_cl217, plain, (((one) = (converse @ one))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl207, zip_derived_cl5])).
% 28.17/4.61 thf(converse_additivity_9, axiom,
% 28.17/4.61 (( converse @ ( join @ A @ B ) ) =
% 28.17/4.61 ( join @ ( converse @ A ) @ ( converse @ B ) ))).
% 28.17/4.61 thf(zip_derived_cl8, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((converse @ (join @ X0 @ X1))
% 28.17/4.61 = (join @ (converse @ X0) @ (converse @ X1)))),
% 28.17/4.61 inference('cnf', [status(esa)], [converse_additivity_9])).
% 28.17/4.61 thf(zip_derived_cl242, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((converse @ (join @ one @ X0)) = (join @ one @ (converse @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl8])).
% 28.17/4.61 thf(zip_derived_cl220, plain,
% 28.17/4.61 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl216, zip_derived_cl207])).
% 28.17/4.61 thf(zip_derived_cl10, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((join @
% 28.17/4.61 (composition @ (converse @ X1) @
% 28.17/4.61 (complement @ (composition @ X1 @ X0))) @
% 28.17/4.61 (complement @ X0)) = (complement @ X0))),
% 28.17/4.61 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 28.17/4.61 thf(zip_derived_cl284, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((join @ (composition @ (converse @ one) @ (complement @ X0)) @
% 28.17/4.61 (complement @ X0)) = (complement @ X0))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl220, zip_derived_cl10])).
% 28.17/4.61 thf(zip_derived_cl217, plain, (((one) = (converse @ one))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl207, zip_derived_cl5])).
% 28.17/4.61 thf(zip_derived_cl220, plain,
% 28.17/4.61 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl216, zip_derived_cl207])).
% 28.17/4.61 thf(zip_derived_cl285, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl284, zip_derived_cl217, zip_derived_cl220])).
% 28.17/4.61 thf(zip_derived_cl11, plain,
% 28.17/4.61 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 28.17/4.61 inference('cnf', [status(esa)], [def_top_12])).
% 28.17/4.61 thf(maddux2_join_associativity_2, axiom,
% 28.17/4.61 (( join @ A @ ( join @ B @ C ) ) = ( join @ ( join @ A @ B ) @ C ))).
% 28.17/4.61 thf(zip_derived_cl1, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.17/4.61 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 28.17/4.61 thf(zip_derived_cl25, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 28.17/4.61 thf(zip_derived_cl818, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((join @ (complement @ X0) @
% 28.17/4.61 (join @ (complement @ X0) @ (complement @ (complement @ X0))))
% 28.17/4.61 = (top))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl285, zip_derived_cl25])).
% 28.17/4.61 thf(zip_derived_cl11, plain,
% 28.17/4.61 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 28.17/4.61 inference('cnf', [status(esa)], [def_top_12])).
% 28.17/4.61 thf(zip_derived_cl0, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 28.17/4.61 thf(zip_derived_cl846, plain,
% 28.17/4.61 (![X0 : $i]: ((join @ top @ (complement @ X0)) = (top))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl818, zip_derived_cl11, zip_derived_cl0])).
% 28.17/4.61 thf(zip_derived_cl25, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 28.17/4.61 thf(zip_derived_cl875, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl846, zip_derived_cl25])).
% 28.17/4.61 thf(zip_derived_cl0, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 28.17/4.61 thf(zip_derived_cl880, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl875, zip_derived_cl0])).
% 28.17/4.61 thf(zip_derived_cl137, plain, (((zero) = (complement @ top))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl12])).
% 28.17/4.61 thf(zip_derived_cl282, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((composition @ (join @ one @ X1) @ X0)
% 28.17/4.61 = (join @ X0 @ (composition @ X1 @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl220, zip_derived_cl6])).
% 28.17/4.61 thf(zip_derived_cl12, plain,
% 28.17/4.61 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 28.17/4.61 inference('cnf', [status(esa)], [def_zero_13])).
% 28.17/4.61 thf(maddux3_a_kind_of_de_Morgan_3, axiom,
% 28.17/4.61 (( A ) =
% 28.17/4.61 ( join @
% 28.17/4.61 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @
% 28.17/4.61 ( complement @ ( join @ ( complement @ A ) @ B ) ) ))).
% 28.17/4.61 thf(zip_derived_cl2, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((X0)
% 28.17/4.61 = (join @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 28.17/4.61 thf(zip_derived_cl3, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((meet @ X0 @ X1)
% 28.17/4.61 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 28.17/4.61 thf(zip_derived_cl126, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((X0)
% 28.17/4.61 = (join @ (meet @ X0 @ X1) @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ X1))))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl230, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((X0)
% 28.17/4.61 = (join @ zero @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ (complement @ X0)))))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl126])).
% 28.17/4.61 thf(zip_derived_cl3, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((meet @ X0 @ X1)
% 28.17/4.61 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 28.17/4.61 thf(zip_derived_cl237, plain,
% 28.17/4.61 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl230, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl285, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl284, zip_derived_cl217, zip_derived_cl220])).
% 28.17/4.61 thf(zip_derived_cl3, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((meet @ X0 @ X1)
% 28.17/4.61 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 28.17/4.61 thf(zip_derived_cl360, plain,
% 28.17/4.61 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl285, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl360, plain,
% 28.17/4.61 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl285, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl2, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((X0)
% 28.17/4.61 = (join @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 28.17/4.61 thf(zip_derived_cl2, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((X0)
% 28.17/4.61 = (join @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 28.17/4.61 thf(zip_derived_cl84, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((join @ (complement @ X0) @ (complement @ X1))
% 28.17/4.61 = (join @ (complement @ X0) @
% 28.17/4.61 (complement @
% 28.17/4.61 (join @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 28.17/4.61 (join @ (complement @ X0) @ X1)))))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl2])).
% 28.17/4.61 thf(zip_derived_cl0, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 28.17/4.61 thf(zip_derived_cl1, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.17/4.61 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 28.17/4.61 thf(zip_derived_cl85, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((join @ (complement @ X0) @ (complement @ X1))
% 28.17/4.61 = (join @ (complement @ X0) @
% 28.17/4.61 (complement @
% 28.17/4.61 (join @ (complement @ X0) @
% 28.17/4.61 (join @ X1 @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ (complement @ X1))))))))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl84, zip_derived_cl0, zip_derived_cl1])).
% 28.17/4.61 thf(zip_derived_cl3, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((meet @ X0 @ X1)
% 28.17/4.61 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 28.17/4.61 thf(zip_derived_cl1728, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((join @ (complement @ X0) @ (complement @ X1))
% 28.17/4.61 = (join @ (complement @ X0) @
% 28.17/4.61 (complement @
% 28.17/4.61 (join @ (complement @ X0) @ (join @ X1 @ (meet @ X0 @ X1))))))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl1746, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((join @ (complement @ X0) @ (complement @ X0))
% 28.17/4.61 = (join @ (complement @ X0) @
% 28.17/4.61 (complement @
% 28.17/4.61 (join @ (complement @ X0) @
% 28.17/4.61 (join @ X0 @ (complement @ (complement @ X0)))))))),
% 28.17/4.61 inference('s_sup+', [status(thm)],
% 28.17/4.61 [zip_derived_cl360, zip_derived_cl1728])).
% 28.17/4.61 thf(zip_derived_cl285, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl284, zip_derived_cl217, zip_derived_cl220])).
% 28.17/4.61 thf(zip_derived_cl1, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.17/4.61 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 28.17/4.61 thf(zip_derived_cl0, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 28.17/4.61 thf(zip_derived_cl22, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.17/4.61 ((join @ X0 @ (join @ X2 @ X1)) = (join @ X2 @ (join @ X1 @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 28.17/4.61 thf(zip_derived_cl0, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 28.17/4.61 thf(zip_derived_cl11, plain,
% 28.17/4.61 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 28.17/4.61 inference('cnf', [status(esa)], [def_top_12])).
% 28.17/4.61 thf(zip_derived_cl875, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl846, zip_derived_cl25])).
% 28.17/4.61 thf(zip_derived_cl137, plain, (((zero) = (complement @ top))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl12])).
% 28.17/4.61 thf(zip_derived_cl0, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 28.17/4.61 thf(zip_derived_cl1766, plain,
% 28.17/4.61 (![X0 : $i]: ((complement @ X0) = (join @ zero @ (complement @ X0)))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl1746, zip_derived_cl285, zip_derived_cl22,
% 28.17/4.61 zip_derived_cl0, zip_derived_cl11, zip_derived_cl875,
% 28.17/4.61 zip_derived_cl137, zip_derived_cl0])).
% 28.17/4.61 thf(zip_derived_cl2086, plain,
% 28.17/4.61 (![X0 : $i]: ((meet @ X0 @ X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)],
% 28.17/4.61 [zip_derived_cl360, zip_derived_cl1766])).
% 28.17/4.61 thf(zip_derived_cl237, plain,
% 28.17/4.61 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl230, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl2089, plain, (![X0 : $i]: ((meet @ X0 @ X0) = (X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl2086, zip_derived_cl237])).
% 28.17/4.61 thf(zip_derived_cl2124, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl237, zip_derived_cl2089])).
% 28.17/4.61 thf(zip_derived_cl2089, plain, (![X0 : $i]: ((meet @ X0 @ X0) = (X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl2086, zip_derived_cl237])).
% 28.17/4.61 thf(zip_derived_cl126, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((X0)
% 28.17/4.61 = (join @ (meet @ X0 @ X1) @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ X1))))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl2129, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((X0) = (join @ X0 @ (complement @ (join @ (complement @ X0) @ X0))))),
% 28.17/4.61 inference('s_sup+', [status(thm)],
% 28.17/4.61 [zip_derived_cl2089, zip_derived_cl126])).
% 28.17/4.61 thf(zip_derived_cl0, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 28.17/4.61 thf(zip_derived_cl11, plain,
% 28.17/4.61 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 28.17/4.61 inference('cnf', [status(esa)], [def_top_12])).
% 28.17/4.61 thf(zip_derived_cl137, plain, (((zero) = (complement @ top))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl12])).
% 28.17/4.61 thf(zip_derived_cl2139, plain, (![X0 : $i]: ((X0) = (join @ X0 @ zero))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl2129, zip_derived_cl0, zip_derived_cl11,
% 28.17/4.61 zip_derived_cl137])).
% 28.17/4.61 thf(zip_derived_cl12984, plain,
% 28.17/4.61 (![X0 : $i]: ((composition @ (converse @ X0) @ zero) = (zero))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl12912, zip_derived_cl242, zip_derived_cl880,
% 28.17/4.61 zip_derived_cl137, zip_derived_cl282, zip_derived_cl2124,
% 28.17/4.61 zip_derived_cl2139])).
% 28.17/4.61 thf(zip_derived_cl13360, plain,
% 28.17/4.61 (![X0 : $i]: ((composition @ X0 @ zero) = (zero))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl12984])).
% 28.17/4.61 thf(zip_derived_cl2139, plain, (![X0 : $i]: ((X0) = (join @ X0 @ zero))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl2129, zip_derived_cl0, zip_derived_cl11,
% 28.17/4.61 zip_derived_cl137])).
% 28.17/4.61 thf(zip_derived_cl13360, plain,
% 28.17/4.61 (![X0 : $i]: ((composition @ X0 @ zero) = (zero))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl12984])).
% 28.17/4.61 thf(zip_derived_cl17074, plain,
% 28.17/4.61 (((meet @ (complement @ one) @ (composition @ (converse @ sk1) @ sk1))
% 28.17/4.61 = (zero))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl16937, zip_derived_cl5521, zip_derived_cl13360,
% 28.17/4.61 zip_derived_cl2139, zip_derived_cl13360])).
% 28.17/4.61 thf(zip_derived_cl126, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((X0)
% 28.17/4.61 = (join @ (meet @ X0 @ X1) @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ X1))))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl17129, plain,
% 28.17/4.61 (((complement @ one)
% 28.17/4.61 = (join @ zero @
% 28.17/4.61 (complement @
% 28.17/4.61 (join @ (complement @ (complement @ one)) @
% 28.17/4.61 (composition @ (converse @ sk1) @ sk1)))))),
% 28.17/4.61 inference('s_sup+', [status(thm)],
% 28.17/4.61 [zip_derived_cl17074, zip_derived_cl126])).
% 28.17/4.61 thf(zip_derived_cl1766, plain,
% 28.17/4.61 (![X0 : $i]: ((complement @ X0) = (join @ zero @ (complement @ X0)))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl1746, zip_derived_cl285, zip_derived_cl22,
% 28.17/4.61 zip_derived_cl0, zip_derived_cl11, zip_derived_cl875,
% 28.17/4.61 zip_derived_cl137, zip_derived_cl0])).
% 28.17/4.61 thf(zip_derived_cl285, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl284, zip_derived_cl217, zip_derived_cl220])).
% 28.17/4.61 thf(zip_derived_cl126, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]:
% 28.17/4.61 ((X0)
% 28.17/4.61 = (join @ (meet @ X0 @ X1) @
% 28.17/4.61 (complement @ (join @ (complement @ X0) @ X1))))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 28.17/4.61 thf(zip_derived_cl359, plain,
% 28.17/4.61 (![X0 : $i]:
% 28.17/4.61 ((X0)
% 28.17/4.61 = (join @ (meet @ X0 @ (complement @ X0)) @
% 28.17/4.61 (complement @ (complement @ X0))))),
% 28.17/4.61 inference('s_sup+', [status(thm)], [zip_derived_cl285, zip_derived_cl126])).
% 28.17/4.61 thf(zip_derived_cl12, plain,
% 28.17/4.61 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 28.17/4.61 inference('cnf', [status(esa)], [def_zero_13])).
% 28.17/4.61 thf(zip_derived_cl365, plain,
% 28.17/4.61 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl359, zip_derived_cl12])).
% 28.17/4.61 thf(zip_derived_cl2084, plain,
% 28.17/4.61 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)],
% 28.17/4.61 [zip_derived_cl1766, zip_derived_cl365])).
% 28.17/4.61 thf(zip_derived_cl2124, plain, (![X0 : $i]: ((X0) = (join @ zero @ X0))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl237, zip_derived_cl2089])).
% 28.17/4.61 thf(zip_derived_cl17152, plain,
% 28.17/4.61 (((complement @ one)
% 28.17/4.61 = (complement @ (join @ one @ (composition @ (converse @ sk1) @ sk1))))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl17129, zip_derived_cl2084, zip_derived_cl2124])).
% 28.17/4.61 thf(zip_derived_cl2084, plain,
% 28.17/4.61 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)],
% 28.17/4.61 [zip_derived_cl1766, zip_derived_cl365])).
% 28.17/4.61 thf(zip_derived_cl17421, plain,
% 28.17/4.61 (((join @ one @ (composition @ (converse @ sk1) @ sk1))
% 28.17/4.61 = (complement @ (complement @ one)))),
% 28.17/4.61 inference('s_sup+', [status(thm)],
% 28.17/4.61 [zip_derived_cl17152, zip_derived_cl2084])).
% 28.17/4.61 thf(zip_derived_cl2084, plain,
% 28.17/4.61 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 28.17/4.61 inference('s_sup+', [status(thm)],
% 28.17/4.61 [zip_derived_cl1766, zip_derived_cl365])).
% 28.17/4.61 thf(zip_derived_cl17450, plain,
% 28.17/4.61 (((join @ one @ (composition @ (converse @ sk1) @ sk1)) = (one))),
% 28.17/4.61 inference('demod', [status(thm)],
% 28.17/4.61 [zip_derived_cl17421, zip_derived_cl2084])).
% 28.17/4.61 thf(goals_18, conjecture,
% 28.17/4.61 (( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one ) = ( one ))).
% 28.17/4.61 thf(zf_stmt_1, negated_conjecture,
% 28.17/4.61 (( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one ) != ( one )),
% 28.17/4.61 inference('cnf.neg', [status(esa)], [goals_18])).
% 28.17/4.61 thf(zip_derived_cl17, plain,
% 28.17/4.61 (((join @ (composition @ (converse @ sk1) @ sk1) @ one) != (one))),
% 28.17/4.61 inference('cnf', [status(esa)], [zf_stmt_1])).
% 28.17/4.61 thf(zip_derived_cl0, plain,
% 28.17/4.61 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 28.17/4.61 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 28.17/4.61 thf(zip_derived_cl21, plain,
% 28.17/4.61 (((join @ one @ (composition @ (converse @ sk1) @ sk1)) != (one))),
% 28.17/4.61 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl0])).
% 28.17/4.61 thf(zip_derived_cl17451, plain, ($false),
% 28.17/4.61 inference('simplify_reflect-', [status(thm)],
% 28.17/4.61 [zip_derived_cl17450, zip_derived_cl21])).
% 28.17/4.61
% 28.17/4.61 % SZS output end Refutation
% 28.17/4.61
% 28.17/4.61
% 28.17/4.61 % Terminating...
% 28.46/4.68 % Runner terminated.
% 28.46/4.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------