TSTP Solution File: REL018-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL018-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.l9BBJ3KN0Y true
% Computer : n007.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 13:47:11 EDT 2023
% Result : Unsatisfiable 4.93s 1.33s
% Output : Refutation 4.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL018-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.l9BBJ3KN0Y true
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 22:43:11 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
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.21/0.67 % Total configuration time : 435
% 0.21/0.67 % Estimated wc time : 1092
% 0.21/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.97/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.97/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.97/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.97/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.97/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.97/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.97/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 4.93/1.33 % Solved by fo/fo4.sh.
% 4.93/1.33 % done 792 iterations in 0.549s
% 4.93/1.33 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 4.93/1.33 % SZS output start Refutation
% 4.93/1.33 thf(composition_type, type, composition: $i > $i > $i).
% 4.93/1.33 thf(meet_type, type, meet: $i > $i > $i).
% 4.93/1.33 thf(complement_type, type, complement: $i > $i).
% 4.93/1.33 thf(converse_type, type, converse: $i > $i).
% 4.93/1.33 thf(top_type, type, top: $i).
% 4.93/1.33 thf(join_type, type, join: $i > $i > $i).
% 4.93/1.33 thf(zero_type, type, zero: $i).
% 4.93/1.33 thf(sk1_type, type, sk1: $i).
% 4.93/1.33 thf(one_type, type, one: $i).
% 4.93/1.33 thf(composition_identity_6, axiom, (( composition @ A @ one ) = ( A ))).
% 4.93/1.33 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_identity_6])).
% 4.93/1.33 thf(converse_idempotence_8, axiom, (( converse @ ( converse @ A ) ) = ( A ))).
% 4.93/1.33 thf(zip_derived_cl7, plain,
% 4.93/1.33 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 4.93/1.33 thf(converse_multiplicativity_10, axiom,
% 4.93/1.33 (( converse @ ( composition @ A @ B ) ) =
% 4.93/1.33 ( composition @ ( converse @ B ) @ ( converse @ A ) ))).
% 4.93/1.33 thf(zip_derived_cl9, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((converse @ (composition @ X1 @ X0))
% 4.93/1.33 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 4.93/1.33 thf(zip_derived_cl21, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((converse @ (composition @ (converse @ X0) @ X1))
% 4.93/1.33 = (composition @ (converse @ X1) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 4.93/1.33 thf(zip_derived_cl636, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((converse @ (converse @ X0)) = (composition @ (converse @ one) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl21])).
% 4.93/1.33 thf(zip_derived_cl7, plain,
% 4.93/1.33 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 4.93/1.33 thf(zip_derived_cl643, plain,
% 4.93/1.33 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl636, zip_derived_cl7])).
% 4.93/1.33 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_identity_6])).
% 4.93/1.33 thf(composition_associativity_5, axiom,
% 4.93/1.33 (( composition @ A @ ( composition @ B @ C ) ) =
% 4.93/1.33 ( composition @ ( composition @ A @ B ) @ C ))).
% 4.93/1.33 thf(zip_derived_cl4, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((composition @ X0 @ (composition @ X1 @ X2))
% 4.93/1.33 = (composition @ (composition @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_associativity_5])).
% 4.93/1.33 thf(zip_derived_cl117, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((composition @ X0 @ (composition @ one @ X1))
% 4.93/1.33 = (composition @ X0 @ X1))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 4.93/1.33 thf(zip_derived_cl666, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ one @ X0) = (composition @ (converse @ one) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl643, zip_derived_cl117])).
% 4.93/1.33 thf(zip_derived_cl643, plain,
% 4.93/1.33 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl636, zip_derived_cl7])).
% 4.93/1.33 thf(zip_derived_cl674, plain,
% 4.93/1.33 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl666, zip_derived_cl643])).
% 4.93/1.33 thf(converse_cancellativity_11, axiom,
% 4.93/1.33 (( join @
% 4.93/1.33 ( composition @
% 4.93/1.33 ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @
% 4.93/1.33 ( complement @ B ) ) =
% 4.93/1.33 ( complement @ B ))).
% 4.93/1.33 thf(zip_derived_cl10, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @
% 4.93/1.33 (composition @ (converse @ X1) @
% 4.93/1.33 (complement @ (composition @ X1 @ X0))) @
% 4.93/1.33 (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 4.93/1.33 thf(zip_derived_cl680, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ (composition @ (converse @ one) @ (complement @ X0)) @
% 4.93/1.33 (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl674, zip_derived_cl10])).
% 4.93/1.33 thf(zip_derived_cl643, plain,
% 4.93/1.33 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl636, zip_derived_cl7])).
% 4.93/1.33 thf(zip_derived_cl683, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl680, zip_derived_cl643])).
% 4.93/1.33 thf(maddux3_a_kind_of_de_Morgan_3, axiom,
% 4.93/1.33 (( A ) =
% 4.93/1.33 ( join @
% 4.93/1.33 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @
% 4.93/1.33 ( complement @ ( join @ ( complement @ A ) @ B ) ) ))).
% 4.93/1.33 thf(zip_derived_cl2, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 4.93/1.33 thf(maddux4_definiton_of_meet_4, axiom,
% 4.93/1.33 (( meet @ A @ B ) =
% 4.93/1.33 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ))).
% 4.93/1.33 thf(zip_derived_cl3, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 4.93/1.33 thf(zip_derived_cl176, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @ (meet @ X0 @ X1) @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ X1))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl707, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @ (meet @ X0 @ (complement @ X0)) @
% 4.93/1.33 (complement @ (complement @ X0))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl683, zip_derived_cl176])).
% 4.93/1.33 thf(def_zero_13, axiom, (( zero ) = ( meet @ A @ ( complement @ A ) ))).
% 4.93/1.33 thf(zip_derived_cl12, plain,
% 4.93/1.33 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_zero_13])).
% 4.93/1.33 thf(zip_derived_cl737, plain,
% 4.93/1.33 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl707, zip_derived_cl12])).
% 4.93/1.33 thf(def_top_12, axiom, (( top ) = ( join @ A @ ( complement @ A ) ))).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl3, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 4.93/1.33 thf(zip_derived_cl46, plain,
% 4.93/1.33 (![X0 : $i]: ((meet @ X0 @ (complement @ X0)) = (complement @ top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl12, plain,
% 4.93/1.33 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_zero_13])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl683, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl680, zip_derived_cl643])).
% 4.93/1.33 thf(zip_derived_cl715, plain,
% 4.93/1.33 (((join @ (complement @ top) @ zero) = (complement @ top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl683])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl729, plain, (((join @ zero @ zero) = (zero))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl715, zip_derived_cl49, zip_derived_cl49])).
% 4.93/1.33 thf(maddux2_join_associativity_2, axiom,
% 4.93/1.33 (( join @ A @ ( join @ B @ C ) ) = ( join @ ( join @ A @ B ) @ C ))).
% 4.93/1.33 thf(zip_derived_cl1, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 4.93/1.33 thf(zip_derived_cl823, plain,
% 4.93/1.33 (![X0 : $i]: ((join @ zero @ (join @ zero @ X0)) = (join @ zero @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl729, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl3069, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ zero @ X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl737, zip_derived_cl823])).
% 4.93/1.33 thf(zip_derived_cl737, plain,
% 4.93/1.33 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl707, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl3084, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl3069, zip_derived_cl737])).
% 4.93/1.33 thf(goals_14, conjecture, (( composition @ sk1 @ top ) != ( sk1 ))).
% 4.93/1.33 thf(zf_stmt_0, negated_conjecture, (( composition @ sk1 @ top ) = ( sk1 )),
% 4.93/1.33 inference('cnf.neg', [status(esa)], [goals_14])).
% 4.93/1.33 thf(zip_derived_cl13, plain, (((composition @ sk1 @ top) = (sk1))),
% 4.93/1.33 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.93/1.33 thf(zip_derived_cl10, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @
% 4.93/1.33 (composition @ (converse @ X1) @
% 4.93/1.33 (complement @ (composition @ X1 @ X0))) @
% 4.93/1.33 (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 4.93/1.33 thf(zip_derived_cl251, plain,
% 4.93/1.33 (((join @ (composition @ (converse @ sk1) @ (complement @ sk1)) @
% 4.93/1.33 (complement @ top)) = (complement @ top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl10])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(maddux1_join_commutativity_1, axiom,
% 4.93/1.33 (( join @ A @ B ) = ( join @ B @ A ))).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl262, plain,
% 4.93/1.33 (((join @ zero @ (composition @ (converse @ sk1) @ (complement @ sk1)))
% 4.93/1.33 = (zero))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl251, zip_derived_cl49, zip_derived_cl0,
% 4.93/1.33 zip_derived_cl49])).
% 4.93/1.33 thf(zip_derived_cl3318, plain,
% 4.93/1.33 (((composition @ (converse @ sk1) @ (complement @ sk1)) = (zero))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3084, zip_derived_cl262])).
% 4.93/1.33 thf(zip_derived_cl21, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((converse @ (composition @ (converse @ X0) @ X1))
% 4.93/1.33 = (composition @ (converse @ X1) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 4.93/1.33 thf(zip_derived_cl3724, plain,
% 4.93/1.33 (((converse @ zero)
% 4.93/1.33 = (composition @ (converse @ (complement @ sk1)) @ sk1))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3318, zip_derived_cl21])).
% 4.93/1.33 thf(zip_derived_cl3084, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl3069, zip_derived_cl737])).
% 4.93/1.33 thf(zip_derived_cl683, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl680, zip_derived_cl643])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl1, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 4.93/1.33 thf(zip_derived_cl13, plain, (((composition @ sk1 @ top) = (sk1))),
% 4.93/1.33 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.93/1.33 thf(composition_distributivity_7, axiom,
% 4.93/1.33 (( composition @ ( join @ A @ B ) @ C ) =
% 4.93/1.33 ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ))).
% 4.93/1.33 thf(zip_derived_cl6, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((composition @ (join @ X0 @ X2) @ X1)
% 4.93/1.33 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 4.93/1.33 thf(zip_derived_cl135, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ X0 @ sk1) @ top)
% 4.93/1.33 = (join @ (composition @ X0 @ top) @ sk1))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl6])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl142, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ X0 @ sk1) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ X0 @ top)))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl135, zip_derived_cl0])).
% 4.93/1.33 thf(zip_derived_cl156, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((composition @ (join @ X1 @ (join @ X0 @ sk1)) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ (join @ X1 @ X0) @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl142])).
% 4.93/1.33 thf(zip_derived_cl407, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((composition @ (join @ X1 @ (join @ sk1 @ X0)) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ (join @ X1 @ X0) @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl156])).
% 4.93/1.33 thf(zip_derived_cl429, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ X0 @ top) @ top)
% 4.93/1.33 = (join @ sk1 @
% 4.93/1.33 (composition @ (join @ X0 @ (complement @ sk1)) @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl407])).
% 4.93/1.33 thf(zip_derived_cl924, plain,
% 4.93/1.33 (((composition @ (join @ (complement @ sk1) @ top) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ (complement @ sk1) @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl683, zip_derived_cl429])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl13, plain, (((composition @ sk1 @ top) = (sk1))),
% 4.93/1.33 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.93/1.33 thf(zip_derived_cl6, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((composition @ (join @ X0 @ X2) @ X1)
% 4.93/1.33 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 4.93/1.33 thf(zip_derived_cl140, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ sk1 @ X0) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ X0 @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl6])).
% 4.93/1.33 thf(zip_derived_cl149, plain,
% 4.93/1.33 (((composition @ top @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ (complement @ sk1) @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl140])).
% 4.93/1.33 thf(zip_derived_cl928, plain,
% 4.93/1.33 (((composition @ (join @ (complement @ sk1) @ top) @ top)
% 4.93/1.33 = (composition @ top @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl924, zip_derived_cl149])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl156, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((composition @ (join @ X1 @ (join @ X0 @ sk1)) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ (join @ X1 @ X0) @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl142])).
% 4.93/1.33 thf(zip_derived_cl403, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((composition @ (join @ (join @ X1 @ sk1) @ X0) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ (join @ X0 @ X1) @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl156])).
% 4.93/1.33 thf(zip_derived_cl1, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 4.93/1.33 thf(zip_derived_cl410, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((composition @ (join @ X1 @ (join @ sk1 @ X0)) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ (join @ X0 @ X1) @ top)))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl485, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ X0 @ top) @ top)
% 4.93/1.33 = (join @ sk1 @
% 4.93/1.33 (composition @ (join @ (complement @ sk1) @ X0) @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl410])).
% 4.93/1.33 thf(zip_derived_cl959, plain,
% 4.93/1.33 (((composition @ (join @ top @ top) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ top @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl928, zip_derived_cl485])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl3, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 4.93/1.33 thf(zip_derived_cl53, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((meet @ X0 @ top) = (complement @ (join @ (complement @ X0) @ zero)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl80, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((meet @ X0 @ top) = (complement @ (join @ zero @ (complement @ X0))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl53])).
% 4.93/1.33 thf(zip_derived_cl342, plain, (((meet @ zero @ top) = (complement @ top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl80])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl350, plain, (((meet @ zero @ top) = (zero))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl342, zip_derived_cl49])).
% 4.93/1.33 thf(zip_derived_cl176, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @ (meet @ X0 @ X1) @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ X1))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl355, plain,
% 4.93/1.33 (((zero)
% 4.93/1.33 = (join @ zero @ (complement @ (join @ (complement @ zero) @ top))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl350, zip_derived_cl176])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl51, plain, (((top) = (join @ top @ zero))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl11])).
% 4.93/1.33 thf(zip_derived_cl1, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 4.93/1.33 thf(zip_derived_cl54, plain,
% 4.93/1.33 (![X0 : $i]: ((join @ top @ (join @ zero @ X0)) = (join @ top @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl161, plain,
% 4.93/1.33 (((join @ top @ top) = (join @ top @ (complement @ zero)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl54])).
% 4.93/1.33 thf(zip_derived_cl357, plain,
% 4.93/1.33 (((zero) = (join @ zero @ (complement @ (join @ top @ top))))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl355, zip_derived_cl0, zip_derived_cl161])).
% 4.93/1.33 thf(zip_derived_cl80, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((meet @ X0 @ top) = (complement @ (join @ zero @ (complement @ X0))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl53])).
% 4.93/1.33 thf(zip_derived_cl361, plain,
% 4.93/1.33 (((meet @ (join @ top @ top) @ top) = (complement @ zero))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl80])).
% 4.93/1.33 thf(zip_derived_cl737, plain,
% 4.93/1.33 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl707, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl3, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 4.93/1.33 thf(zip_derived_cl50, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((meet @ top @ X0) = (complement @ (join @ zero @ (complement @ X0))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl884, plain,
% 4.93/1.33 (![X0 : $i]: ((meet @ top @ (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl737, zip_derived_cl50])).
% 4.93/1.33 thf(zip_derived_cl176, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @ (meet @ X0 @ X1) @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ X1))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl894, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((top)
% 4.93/1.33 = (join @ (complement @ X0) @
% 4.93/1.33 (complement @ (join @ (complement @ top) @ (complement @ X0)))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl884, zip_derived_cl176])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl80, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((meet @ X0 @ top) = (complement @ (join @ zero @ (complement @ X0))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl53])).
% 4.93/1.33 thf(zip_derived_cl910, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ (complement @ X0) @ (meet @ X0 @ top)))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl894, zip_derived_cl49, zip_derived_cl80])).
% 4.93/1.33 thf(zip_derived_cl1107, plain,
% 4.93/1.33 (((top)
% 4.93/1.33 = (join @ (complement @ (join @ top @ top)) @ (complement @ zero)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl361, zip_derived_cl910])).
% 4.93/1.33 thf(zip_derived_cl3, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 4.93/1.33 thf(zip_derived_cl1255, plain,
% 4.93/1.33 (((meet @ (join @ top @ top) @ zero) = (complement @ top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl1107, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl1259, plain,
% 4.93/1.33 (((meet @ (join @ top @ top) @ zero) = (zero))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl1255, zip_derived_cl49])).
% 4.93/1.33 thf(zip_derived_cl176, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @ (meet @ X0 @ X1) @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ X1))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl1260, plain,
% 4.93/1.33 (((join @ top @ top)
% 4.93/1.33 = (join @ zero @
% 4.93/1.33 (complement @ (join @ (complement @ (join @ top @ top)) @ zero))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl1259, zip_derived_cl176])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl357, plain,
% 4.93/1.33 (((zero) = (join @ zero @ (complement @ (join @ top @ top))))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl355, zip_derived_cl0, zip_derived_cl161])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl1263, plain, (((join @ top @ top) = (top))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl1260, zip_derived_cl0, zip_derived_cl357,
% 4.93/1.33 zip_derived_cl11])).
% 4.93/1.33 thf(zip_derived_cl1272, plain,
% 4.93/1.33 (((composition @ top @ top) = (join @ sk1 @ (composition @ top @ top)))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl959, zip_derived_cl1263])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl1, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 4.93/1.33 thf(zip_derived_cl31, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_identity_6])).
% 4.93/1.33 thf(zip_derived_cl674, plain,
% 4.93/1.33 (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl666, zip_derived_cl643])).
% 4.93/1.33 thf(zip_derived_cl140, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ sk1 @ X0) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ X0 @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl6])).
% 4.93/1.33 thf(zip_derived_cl4, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((composition @ X0 @ (composition @ X1 @ X2))
% 4.93/1.33 = (composition @ (composition @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_associativity_5])).
% 4.93/1.33 thf(zip_derived_cl144, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((composition @ (join @ sk1 @ X0) @ (composition @ top @ X1))
% 4.93/1.33 = (composition @ (join @ sk1 @ (composition @ X0 @ top)) @ X1))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl140, zip_derived_cl4])).
% 4.93/1.33 thf(zip_derived_cl681, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ sk1 @ one) @ (composition @ top @ X0))
% 4.93/1.33 = (composition @ (join @ sk1 @ top) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl674, zip_derived_cl144])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl1272, plain,
% 4.93/1.33 (((composition @ top @ top) = (join @ sk1 @ (composition @ top @ top)))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl959, zip_derived_cl1263])).
% 4.93/1.33 thf(zip_derived_cl1, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 4.93/1.33 thf(zip_derived_cl1280, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ sk1 @ (join @ (composition @ top @ top) @ X0))
% 4.93/1.33 = (join @ (composition @ top @ top) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl1272, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl1326, plain,
% 4.93/1.33 (((join @ sk1 @ top)
% 4.93/1.33 = (join @ (composition @ top @ top) @
% 4.93/1.33 (complement @ (composition @ top @ top))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1280])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl1329, plain, (((join @ sk1 @ top) = (top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl1326, zip_derived_cl11])).
% 4.93/1.33 thf(zip_derived_cl1338, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ sk1 @ one) @ (composition @ top @ X0))
% 4.93/1.33 = (composition @ top @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl681, zip_derived_cl1329])).
% 4.93/1.33 thf(zip_derived_cl2449, plain,
% 4.93/1.33 (((composition @ (join @ sk1 @ one) @ top) = (composition @ top @ one))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl1338])).
% 4.93/1.33 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_identity_6])).
% 4.93/1.33 thf(zip_derived_cl2450, plain,
% 4.93/1.33 (((composition @ (join @ sk1 @ one) @ top) = (top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl2449, zip_derived_cl5])).
% 4.93/1.33 thf(zip_derived_cl6, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((composition @ (join @ X0 @ X2) @ X1)
% 4.93/1.33 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 4.93/1.33 thf(zip_derived_cl2456, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ (join @ sk1 @ one) @ X0) @ top)
% 4.93/1.33 = (join @ top @ (composition @ X0 @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl2450, zip_derived_cl6])).
% 4.93/1.33 thf(zip_derived_cl1, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 4.93/1.33 thf(zip_derived_cl140, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ sk1 @ X0) @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ X0 @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl6])).
% 4.93/1.33 thf(zip_derived_cl12, plain,
% 4.93/1.33 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_zero_13])).
% 4.93/1.33 thf(zip_derived_cl176, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @ (meet @ X0 @ X1) @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ X1))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl191, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @ zero @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ (complement @ X0)))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl176])).
% 4.93/1.33 thf(zip_derived_cl3, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 4.93/1.33 thf(zip_derived_cl196, plain,
% 4.93/1.33 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl191, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl54, plain,
% 4.93/1.33 (![X0 : $i]: ((join @ top @ (join @ zero @ X0)) = (join @ top @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl232, plain,
% 4.93/1.33 (![X0 : $i]: ((join @ top @ X0) = (join @ top @ (meet @ X0 @ X0)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl54])).
% 4.93/1.33 thf(zip_derived_cl683, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl680, zip_derived_cl643])).
% 4.93/1.33 thf(zip_derived_cl3, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 4.93/1.33 thf(zip_derived_cl708, plain,
% 4.93/1.33 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl683, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl871, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ top @ X0) = (join @ top @ (complement @ (complement @ X0))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl232, zip_derived_cl708])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl1837, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ (complement @ (complement @ X0)) @ top) = (join @ top @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl871, zip_derived_cl0])).
% 4.93/1.33 thf(zip_derived_cl683, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl680, zip_derived_cl643])).
% 4.93/1.33 thf(zip_derived_cl31, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl1992, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ (complement @ X0) @
% 4.93/1.33 (join @ (complement @ X0) @ (complement @ (complement @ X0))))
% 4.93/1.33 = (top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl683, zip_derived_cl31])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl2063, plain,
% 4.93/1.33 (![X0 : $i]: ((join @ (complement @ X0) @ top) = (top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl1992, zip_derived_cl11])).
% 4.93/1.33 thf(zip_derived_cl2161, plain, (![X0 : $i]: ((top) = (join @ top @ X0))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl1837, zip_derived_cl2063])).
% 4.93/1.33 thf(zip_derived_cl2462, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((join @ sk1 @ (composition @ (join @ one @ X0) @ top)) = (top))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl2456, zip_derived_cl1, zip_derived_cl140,
% 4.93/1.33 zip_derived_cl2161])).
% 4.93/1.33 thf(zip_derived_cl2489, plain,
% 4.93/1.33 (((join @ sk1 @ (composition @ top @ top)) = (top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl2462])).
% 4.93/1.33 thf(zip_derived_cl2506, plain, (((composition @ top @ top) = (top))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl1272, zip_derived_cl2489])).
% 4.93/1.33 thf(zip_derived_cl10, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @
% 4.93/1.33 (composition @ (converse @ X1) @
% 4.93/1.33 (complement @ (composition @ X1 @ X0))) @
% 4.93/1.33 (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 4.93/1.33 thf(zip_derived_cl2543, plain,
% 4.93/1.33 (((join @ (composition @ (converse @ top) @ (complement @ top)) @
% 4.93/1.33 (complement @ top)) = (complement @ top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl2506, zip_derived_cl10])).
% 4.93/1.33 thf(zip_derived_cl2161, plain, (![X0 : $i]: ((top) = (join @ top @ X0))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl1837, zip_derived_cl2063])).
% 4.93/1.33 thf(zip_derived_cl7, plain,
% 4.93/1.33 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 4.93/1.33 thf(converse_additivity_9, axiom,
% 4.93/1.33 (( converse @ ( join @ A @ B ) ) =
% 4.93/1.33 ( join @ ( converse @ A ) @ ( converse @ B ) ))).
% 4.93/1.33 thf(zip_derived_cl8, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((converse @ (join @ X0 @ X1))
% 4.93/1.33 = (join @ (converse @ X0) @ (converse @ X1)))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_additivity_9])).
% 4.93/1.33 thf(zip_derived_cl19, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((converse @ (join @ X1 @ (converse @ X0)))
% 4.93/1.33 = (join @ (converse @ X1) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 4.93/1.33 thf(zip_derived_cl2212, plain,
% 4.93/1.33 (![X0 : $i]: ((converse @ top) = (join @ (converse @ top) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl2161, zip_derived_cl19])).
% 4.93/1.33 thf(zip_derived_cl31, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl2381, plain, (((converse @ top) = (top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl2212, zip_derived_cl31])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl2551, plain,
% 4.93/1.33 (((join @ zero @ (composition @ top @ zero)) = (zero))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl2543, zip_derived_cl2381, zip_derived_cl49,
% 4.93/1.33 zip_derived_cl49, zip_derived_cl0, zip_derived_cl49])).
% 4.93/1.33 thf(zip_derived_cl3320, plain, (((composition @ top @ zero) = (zero))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3084, zip_derived_cl2551])).
% 4.93/1.33 thf(zip_derived_cl6, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((composition @ (join @ X0 @ X2) @ X1)
% 4.93/1.33 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 4.93/1.33 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 4.93/1.33 thf(zip_derived_cl3390, plain,
% 4.93/1.33 (![X0 : $i]:
% 4.93/1.33 ((composition @ (join @ top @ X0) @ zero)
% 4.93/1.33 = (join @ zero @ (composition @ X0 @ zero)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3320, zip_derived_cl6])).
% 4.93/1.33 thf(zip_derived_cl2161, plain, (![X0 : $i]: ((top) = (join @ top @ X0))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl1837, zip_derived_cl2063])).
% 4.93/1.33 thf(zip_derived_cl3320, plain, (((composition @ top @ zero) = (zero))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3084, zip_derived_cl2551])).
% 4.93/1.33 thf(zip_derived_cl3084, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl3069, zip_derived_cl737])).
% 4.93/1.33 thf(zip_derived_cl3398, plain,
% 4.93/1.33 (![X0 : $i]: ((zero) = (composition @ X0 @ zero))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl3390, zip_derived_cl2161, zip_derived_cl3320,
% 4.93/1.33 zip_derived_cl3084])).
% 4.93/1.33 thf(zip_derived_cl21, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((converse @ (composition @ (converse @ X0) @ X1))
% 4.93/1.33 = (composition @ (converse @ X1) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 4.93/1.33 thf(zip_derived_cl3410, plain,
% 4.93/1.33 (![X0 : $i]: ((converse @ zero) = (composition @ (converse @ zero) @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3398, zip_derived_cl21])).
% 4.93/1.33 thf(zip_derived_cl3398, plain,
% 4.93/1.33 (![X0 : $i]: ((zero) = (composition @ X0 @ zero))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl3390, zip_derived_cl2161, zip_derived_cl3320,
% 4.93/1.33 zip_derived_cl3084])).
% 4.93/1.33 thf(zip_derived_cl3562, plain, (((zero) = (converse @ zero))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3410, zip_derived_cl3398])).
% 4.93/1.33 thf(zip_derived_cl3729, plain,
% 4.93/1.33 (((zero) = (composition @ (converse @ (complement @ sk1)) @ sk1))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl3724, zip_derived_cl3562])).
% 4.93/1.33 thf(zip_derived_cl10, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @
% 4.93/1.33 (composition @ (converse @ X1) @
% 4.93/1.33 (complement @ (composition @ X1 @ X0))) @
% 4.93/1.33 (complement @ X0)) = (complement @ X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 4.93/1.33 thf(zip_derived_cl3818, plain,
% 4.93/1.33 (((join @
% 4.93/1.33 (composition @ (converse @ (converse @ (complement @ sk1))) @
% 4.93/1.33 (complement @ zero)) @
% 4.93/1.33 (complement @ sk1)) = (complement @ sk1))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3729, zip_derived_cl10])).
% 4.93/1.33 thf(zip_derived_cl7, plain,
% 4.93/1.33 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 4.93/1.33 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 4.93/1.33 thf(zip_derived_cl3084, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl3069, zip_derived_cl737])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl3305, plain, (((top) = (complement @ zero))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3084, zip_derived_cl11])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl3823, plain,
% 4.93/1.33 (((join @ (complement @ sk1) @ (composition @ (complement @ sk1) @ top))
% 4.93/1.33 = (complement @ sk1))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl3818, zip_derived_cl7, zip_derived_cl3305,
% 4.93/1.33 zip_derived_cl0])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl11, plain,
% 4.93/1.33 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 4.93/1.33 inference('cnf', [status(esa)], [def_top_12])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl1, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 4.93/1.33 thf(zip_derived_cl32, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X1 @ X0) @ X2))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl2305, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @ (complement @ X1) @ (join @ X1 @ X0)) = (join @ top @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl32])).
% 4.93/1.33 thf(zip_derived_cl2161, plain, (![X0 : $i]: ((top) = (join @ top @ X0))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl1837, zip_derived_cl2063])).
% 4.93/1.33 thf(zip_derived_cl2346, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @ (complement @ X1) @ (join @ X1 @ X0)) = (top))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl2305, zip_derived_cl2161])).
% 4.93/1.33 thf(zip_derived_cl4382, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((join @ (complement @ X0) @ (join @ X1 @ X0)) = (top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2346])).
% 4.93/1.33 thf(zip_derived_cl4793, plain,
% 4.93/1.33 (((join @ (complement @ (composition @ (complement @ sk1) @ top)) @
% 4.93/1.33 (complement @ sk1)) = (top))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3823, zip_derived_cl4382])).
% 4.93/1.33 thf(zip_derived_cl176, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @ (meet @ X0 @ X1) @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ X1))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl4858, plain,
% 4.93/1.33 (((composition @ (complement @ sk1) @ top)
% 4.93/1.33 = (join @
% 4.93/1.33 (meet @ (composition @ (complement @ sk1) @ top) @
% 4.93/1.33 (complement @ sk1)) @
% 4.93/1.33 (complement @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl4793, zip_derived_cl176])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl3, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 4.93/1.33 thf(zip_derived_cl44, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X1) @ (complement @ X0))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl3, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((meet @ X0 @ X1)
% 4.93/1.33 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 4.93/1.33 thf(zip_derived_cl4025, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((meet @ X0 @ X1) = (meet @ X1 @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl823, plain,
% 4.93/1.33 (![X0 : $i]: ((join @ zero @ (join @ zero @ X0)) = (join @ zero @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl729, zip_derived_cl1])).
% 4.93/1.33 thf(zip_derived_cl1, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 4.93/1.33 thf(zip_derived_cl0, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 4.93/1.33 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 4.93/1.33 thf(zip_derived_cl28, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.93/1.33 ((join @ X0 @ (join @ X2 @ X1)) = (join @ X2 @ (join @ X1 @ X0)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 4.93/1.33 thf(zip_derived_cl3050, plain,
% 4.93/1.33 (![X0 : $i]: ((join @ X0 @ (join @ zero @ zero)) = (join @ zero @ X0))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl823, zip_derived_cl28])).
% 4.93/1.33 thf(zip_derived_cl729, plain, (((join @ zero @ zero) = (zero))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl715, zip_derived_cl49, zip_derived_cl49])).
% 4.93/1.33 thf(zip_derived_cl3095, plain,
% 4.93/1.33 (![X0 : $i]: ((join @ X0 @ zero) = (join @ zero @ X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl3050, zip_derived_cl729])).
% 4.93/1.33 thf(zip_derived_cl3084, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl3069, zip_derived_cl737])).
% 4.93/1.33 thf(zip_derived_cl3622, plain, (![X0 : $i]: ((join @ X0 @ zero) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl3095, zip_derived_cl3084])).
% 4.93/1.33 thf(zip_derived_cl4868, plain,
% 4.93/1.33 (((composition @ (complement @ sk1) @ top)
% 4.93/1.33 = (meet @ (complement @ sk1) @
% 4.93/1.33 (composition @ (complement @ sk1) @ top)))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl4858, zip_derived_cl4025, zip_derived_cl49,
% 4.93/1.33 zip_derived_cl3622])).
% 4.93/1.33 thf(zip_derived_cl176, plain,
% 4.93/1.33 (![X0 : $i, X1 : $i]:
% 4.93/1.33 ((X0)
% 4.93/1.33 = (join @ (meet @ X0 @ X1) @
% 4.93/1.33 (complement @ (join @ (complement @ X0) @ X1))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 4.93/1.33 thf(zip_derived_cl4955, plain,
% 4.93/1.33 (((complement @ sk1)
% 4.93/1.33 = (join @ (composition @ (complement @ sk1) @ top) @
% 4.93/1.33 (complement @
% 4.93/1.33 (join @ (complement @ (complement @ sk1)) @
% 4.93/1.33 (composition @ (complement @ sk1) @ top)))))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl4868, zip_derived_cl176])).
% 4.93/1.33 thf(zip_derived_cl3084, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl3069, zip_derived_cl737])).
% 4.93/1.33 thf(zip_derived_cl737, plain,
% 4.93/1.33 (![X0 : $i]: ((X0) = (join @ zero @ (complement @ (complement @ X0))))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl707, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl3315, plain,
% 4.93/1.33 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl3084, zip_derived_cl737])).
% 4.93/1.33 thf(zip_derived_cl149, plain,
% 4.93/1.33 (((composition @ top @ top)
% 4.93/1.33 = (join @ sk1 @ (composition @ (complement @ sk1) @ top)))),
% 4.93/1.33 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl140])).
% 4.93/1.33 thf(zip_derived_cl2506, plain, (((composition @ top @ top) = (top))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl1272, zip_derived_cl2489])).
% 4.93/1.33 thf(zip_derived_cl2529, plain,
% 4.93/1.33 (((top) = (join @ sk1 @ (composition @ (complement @ sk1) @ top)))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl149, zip_derived_cl2506])).
% 4.93/1.33 thf(zip_derived_cl49, plain, (((zero) = (complement @ top))),
% 4.93/1.33 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 4.93/1.33 thf(zip_derived_cl3622, plain, (![X0 : $i]: ((join @ X0 @ zero) = (X0))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl3095, zip_derived_cl3084])).
% 4.93/1.33 thf(zip_derived_cl4956, plain,
% 4.93/1.33 (((complement @ sk1) = (composition @ (complement @ sk1) @ top))),
% 4.93/1.33 inference('demod', [status(thm)],
% 4.93/1.33 [zip_derived_cl4955, zip_derived_cl3315, zip_derived_cl2529,
% 4.93/1.33 zip_derived_cl49, zip_derived_cl3622])).
% 4.93/1.33 thf(goals_15, conjecture,
% 4.93/1.33 (( composition @ ( complement @ sk1 ) @ top ) = ( complement @ sk1 ))).
% 4.93/1.33 thf(zf_stmt_1, negated_conjecture,
% 4.93/1.33 (( composition @ ( complement @ sk1 ) @ top ) != ( complement @ sk1 )),
% 4.93/1.33 inference('cnf.neg', [status(esa)], [goals_15])).
% 4.93/1.33 thf(zip_derived_cl14, plain,
% 4.93/1.33 (((composition @ (complement @ sk1) @ top) != (complement @ sk1))),
% 4.93/1.33 inference('cnf', [status(esa)], [zf_stmt_1])).
% 4.93/1.33 thf(zip_derived_cl4957, plain, ($false),
% 4.93/1.33 inference('simplify_reflect-', [status(thm)],
% 4.93/1.33 [zip_derived_cl4956, zip_derived_cl14])).
% 4.93/1.33
% 4.93/1.33 % SZS output end Refutation
% 4.93/1.33
% 4.93/1.33
% 4.93/1.33 % Terminating...
% 4.93/1.36 % Runner terminated.
% 4.93/1.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------