TSTP Solution File: REL013-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL013-1 : 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.2lni6prIDW true
% Computer : n024.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 13:47:08 EDT 2023
% Result : Unsatisfiable 1.37s 1.16s
% Output : Refutation 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : REL013-1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.2lni6prIDW true
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 22:49:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.22/0.66 % Total configuration time : 435
% 0.22/0.66 % Estimated wc time : 1092
% 0.22/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.99/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.99/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.99/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.99/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.99/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.99/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.99/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.37/1.16 % Solved by fo/fo1_av.sh.
% 1.37/1.16 % done 360 iterations in 0.377s
% 1.37/1.16 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.37/1.16 % SZS output start Refutation
% 1.37/1.16 thf(composition_type, type, composition: $i > $i > $i).
% 1.37/1.16 thf(meet_type, type, meet: $i > $i > $i).
% 1.37/1.16 thf(complement_type, type, complement: $i > $i).
% 1.37/1.16 thf(converse_type, type, converse: $i > $i).
% 1.37/1.16 thf(top_type, type, top: $i).
% 1.37/1.16 thf(join_type, type, join: $i > $i > $i).
% 1.37/1.16 thf(zero_type, type, zero: $i).
% 1.37/1.16 thf(sk1_type, type, sk1: $i).
% 1.37/1.16 thf(one_type, type, one: $i).
% 1.37/1.16 thf(goals_14, conjecture,
% 1.37/1.16 (~( ( ( composition @ zero @ sk1 ) != ( zero ) ) |
% 1.37/1.16 ( ( composition @ sk1 @ zero ) != ( zero ) ) ))).
% 1.37/1.16 thf(zf_stmt_0, negated_conjecture,
% 1.37/1.16 (( ( composition @ zero @ sk1 ) != ( zero ) ) |
% 1.37/1.16 ( ( composition @ sk1 @ zero ) != ( zero ) )),
% 1.37/1.16 inference('cnf.neg', [status(esa)], [goals_14])).
% 1.37/1.16 thf(zip_derived_cl13, plain,
% 1.37/1.16 ((((composition @ zero @ sk1) != (zero))
% 1.37/1.16 | ((composition @ sk1 @ zero) != (zero)))),
% 1.37/1.16 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.37/1.16 thf(zip_derived_cl15, plain,
% 1.37/1.16 ((((composition @ zero @ sk1) != (zero)))
% 1.37/1.16 <= (~ (((composition @ zero @ sk1) = (zero))))),
% 1.37/1.16 inference('split', [status(esa)], [zip_derived_cl13])).
% 1.37/1.16 thf(composition_identity_6, axiom, (( composition @ A @ one ) = ( A ))).
% 1.37/1.16 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [composition_identity_6])).
% 1.37/1.16 thf(converse_idempotence_8, axiom, (( converse @ ( converse @ A ) ) = ( A ))).
% 1.37/1.16 thf(zip_derived_cl7, plain,
% 1.37/1.16 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 1.37/1.16 thf(converse_multiplicativity_10, axiom,
% 1.37/1.16 (( converse @ ( composition @ A @ B ) ) =
% 1.37/1.16 ( composition @ ( converse @ B ) @ ( converse @ A ) ))).
% 1.37/1.16 thf(zip_derived_cl9, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((converse @ (composition @ X1 @ X0))
% 1.37/1.16 = (composition @ (converse @ X0) @ (converse @ X1)))),
% 1.37/1.16 inference('cnf', [status(esa)], [converse_multiplicativity_10])).
% 1.37/1.16 thf(zip_derived_cl51, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((converse @ (composition @ (converse @ X0) @ X1))
% 1.37/1.16 = (composition @ (converse @ X1) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 1.37/1.16 thf(zip_derived_cl60, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((converse @ (converse @ X0)) = (composition @ (converse @ one) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl51])).
% 1.37/1.16 thf(zip_derived_cl7, plain,
% 1.37/1.16 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 1.37/1.16 thf(zip_derived_cl65, plain,
% 1.37/1.16 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl7])).
% 1.37/1.16 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [composition_identity_6])).
% 1.37/1.16 thf(composition_associativity_5, axiom,
% 1.37/1.16 (( composition @ A @ ( composition @ B @ C ) ) =
% 1.37/1.16 ( composition @ ( composition @ A @ B ) @ C ))).
% 1.37/1.16 thf(zip_derived_cl4, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.16 ((composition @ X0 @ (composition @ X1 @ X2))
% 1.37/1.16 = (composition @ (composition @ X0 @ X1) @ X2))),
% 1.37/1.16 inference('cnf', [status(esa)], [composition_associativity_5])).
% 1.37/1.16 thf(zip_derived_cl30, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((composition @ X0 @ (composition @ one @ X1))
% 1.37/1.16 = (composition @ X0 @ X1))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 1.37/1.16 thf(zip_derived_cl72, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((composition @ one @ X0) = (composition @ (converse @ one) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl65, zip_derived_cl30])).
% 1.37/1.16 thf(zip_derived_cl65, plain,
% 1.37/1.16 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl7])).
% 1.37/1.16 thf(zip_derived_cl76, plain, (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl72, zip_derived_cl65])).
% 1.37/1.16 thf(converse_cancellativity_11, axiom,
% 1.37/1.16 (( join @
% 1.37/1.16 ( composition @
% 1.37/1.16 ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @
% 1.37/1.16 ( complement @ B ) ) =
% 1.37/1.16 ( complement @ B ))).
% 1.37/1.16 thf(zip_derived_cl10, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((join @
% 1.37/1.16 (composition @ (converse @ X1) @
% 1.37/1.16 (complement @ (composition @ X1 @ X0))) @
% 1.37/1.16 (complement @ X0)) = (complement @ X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 1.37/1.16 thf(zip_derived_cl223, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((join @ (composition @ (converse @ one) @ (complement @ X0)) @
% 1.37/1.16 (complement @ X0)) = (complement @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl10])).
% 1.37/1.16 thf(zip_derived_cl65, plain,
% 1.37/1.16 (![X0 : $i]: ((X0) = (composition @ (converse @ one) @ X0))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl7])).
% 1.37/1.16 thf(zip_derived_cl5, plain, (![X0 : $i]: ((composition @ X0 @ one) = (X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [composition_identity_6])).
% 1.37/1.16 thf(zip_derived_cl73, plain, (((one) = (converse @ one))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl65, zip_derived_cl5])).
% 1.37/1.16 thf(zip_derived_cl76, plain, (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl72, zip_derived_cl65])).
% 1.37/1.16 thf(zip_derived_cl232, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 1.37/1.16 inference('demod', [status(thm)],
% 1.37/1.16 [zip_derived_cl223, zip_derived_cl73, zip_derived_cl76])).
% 1.37/1.16 thf(maddux4_definiton_of_meet_4, axiom,
% 1.37/1.16 (( meet @ A @ B ) =
% 1.37/1.16 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ))).
% 1.37/1.16 thf(zip_derived_cl3, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((meet @ X0 @ X1)
% 1.37/1.16 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 1.37/1.16 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 1.37/1.16 thf(zip_derived_cl242, plain,
% 1.37/1.16 (![X0 : $i]: ((meet @ X0 @ X0) = (complement @ (complement @ X0)))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl232, zip_derived_cl3])).
% 1.37/1.16 thf(def_zero_13, axiom, (( zero ) = ( meet @ A @ ( complement @ A ) ))).
% 1.37/1.16 thf(zip_derived_cl12, plain,
% 1.37/1.16 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 1.37/1.16 inference('cnf', [status(esa)], [def_zero_13])).
% 1.37/1.16 thf(maddux3_a_kind_of_de_Morgan_3, axiom,
% 1.37/1.16 (( A ) =
% 1.37/1.16 ( join @
% 1.37/1.16 ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @
% 1.37/1.16 ( complement @ ( join @ ( complement @ A ) @ B ) ) ))).
% 1.37/1.16 thf(zip_derived_cl2, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((X0)
% 1.37/1.16 = (join @
% 1.37/1.16 (complement @ (join @ (complement @ X0) @ (complement @ X1))) @
% 1.37/1.16 (complement @ (join @ (complement @ X0) @ X1))))),
% 1.37/1.16 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan_3])).
% 1.37/1.16 thf(zip_derived_cl3, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((meet @ X0 @ X1)
% 1.37/1.16 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 1.37/1.16 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 1.37/1.16 thf(zip_derived_cl107, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((X0)
% 1.37/1.16 = (join @ (meet @ X0 @ X1) @
% 1.37/1.16 (complement @ (join @ (complement @ X0) @ X1))))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl3])).
% 1.37/1.16 thf(zip_derived_cl187, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((X0)
% 1.37/1.16 = (join @ zero @
% 1.37/1.16 (complement @ (join @ (complement @ X0) @ (complement @ X0)))))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl107])).
% 1.37/1.16 thf(zip_derived_cl3, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((meet @ X0 @ X1)
% 1.37/1.16 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 1.37/1.16 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 1.37/1.16 thf(zip_derived_cl190, plain,
% 1.37/1.16 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl187, zip_derived_cl3])).
% 1.37/1.16 thf(def_top_12, axiom, (( top ) = ( join @ A @ ( complement @ A ) ))).
% 1.37/1.16 thf(zip_derived_cl11, plain,
% 1.37/1.16 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 1.37/1.16 inference('cnf', [status(esa)], [def_top_12])).
% 1.37/1.16 thf(zip_derived_cl3, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((meet @ X0 @ X1)
% 1.37/1.16 = (complement @ (join @ (complement @ X0) @ (complement @ X1))))),
% 1.37/1.16 inference('cnf', [status(esa)], [maddux4_definiton_of_meet_4])).
% 1.37/1.16 thf(zip_derived_cl114, plain,
% 1.37/1.16 (![X0 : $i]: ((meet @ X0 @ (complement @ X0)) = (complement @ top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 1.37/1.16 thf(zip_derived_cl12, plain,
% 1.37/1.16 (![X0 : $i]: ((zero) = (meet @ X0 @ (complement @ X0)))),
% 1.37/1.16 inference('cnf', [status(esa)], [def_zero_13])).
% 1.37/1.16 thf(zip_derived_cl117, plain, (((zero) = (complement @ top))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl114, zip_derived_cl12])).
% 1.37/1.16 thf(zip_derived_cl232, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 1.37/1.16 inference('demod', [status(thm)],
% 1.37/1.16 [zip_derived_cl223, zip_derived_cl73, zip_derived_cl76])).
% 1.37/1.16 thf(zip_derived_cl244, plain, (((join @ zero @ zero) = (zero))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl117, zip_derived_cl232])).
% 1.37/1.16 thf(maddux2_join_associativity_2, axiom,
% 1.37/1.16 (( join @ A @ ( join @ B @ C ) ) = ( join @ ( join @ A @ B ) @ C ))).
% 1.37/1.16 thf(zip_derived_cl1, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.16 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 1.37/1.16 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 1.37/1.16 thf(zip_derived_cl250, plain,
% 1.37/1.16 (![X0 : $i]: ((join @ zero @ (join @ zero @ X0)) = (join @ zero @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl244, zip_derived_cl1])).
% 1.37/1.16 thf(zip_derived_cl258, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl190, zip_derived_cl250])).
% 1.37/1.16 thf(zip_derived_cl190, plain,
% 1.37/1.16 (![X0 : $i]: ((X0) = (join @ zero @ (meet @ X0 @ X0)))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl187, zip_derived_cl3])).
% 1.37/1.16 thf(zip_derived_cl271, plain, (![X0 : $i]: ((X0) = (meet @ X0 @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl190])).
% 1.37/1.16 thf(zip_derived_cl374, plain,
% 1.37/1.16 (![X0 : $i]: ((X0) = (complement @ (complement @ X0)))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl242, zip_derived_cl271])).
% 1.37/1.16 thf(zip_derived_cl232, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((join @ (complement @ X0) @ (complement @ X0)) = (complement @ X0))),
% 1.37/1.16 inference('demod', [status(thm)],
% 1.37/1.16 [zip_derived_cl223, zip_derived_cl73, zip_derived_cl76])).
% 1.37/1.16 thf(zip_derived_cl380, plain, (![X0 : $i]: ((join @ X0 @ X0) = (X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl374, zip_derived_cl232])).
% 1.37/1.16 thf(zip_derived_cl11, plain,
% 1.37/1.16 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 1.37/1.16 inference('cnf', [status(esa)], [def_top_12])).
% 1.37/1.16 thf(zip_derived_cl1, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.16 ((join @ X0 @ (join @ X1 @ X2)) = (join @ (join @ X0 @ X1) @ X2))),
% 1.37/1.16 inference('cnf', [status(esa)], [maddux2_join_associativity_2])).
% 1.37/1.16 thf(zip_derived_cl27, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 1.37/1.16 thf(zip_derived_cl592, plain,
% 1.37/1.16 (![X0 : $i]: ((join @ X0 @ (join @ X0 @ (complement @ X0))) = (top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl380, zip_derived_cl27])).
% 1.37/1.16 thf(zip_derived_cl11, plain,
% 1.37/1.16 (![X0 : $i]: ((top) = (join @ X0 @ (complement @ X0)))),
% 1.37/1.16 inference('cnf', [status(esa)], [def_top_12])).
% 1.37/1.16 thf(zip_derived_cl613, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl592, zip_derived_cl11])).
% 1.37/1.16 thf(maddux1_join_commutativity_1, axiom,
% 1.37/1.16 (( join @ A @ B ) = ( join @ B @ A ))).
% 1.37/1.16 thf(zip_derived_cl0, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 1.37/1.16 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 1.37/1.16 thf(zip_derived_cl635, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl613, zip_derived_cl0])).
% 1.37/1.16 thf(zip_derived_cl76, plain, (![X0 : $i]: ((composition @ one @ X0) = (X0))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl72, zip_derived_cl65])).
% 1.37/1.16 thf(composition_distributivity_7, axiom,
% 1.37/1.16 (( composition @ ( join @ A @ B ) @ C ) =
% 1.37/1.16 ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ))).
% 1.37/1.16 thf(zip_derived_cl6, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.16 ((composition @ (join @ X0 @ X2) @ X1)
% 1.37/1.16 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 1.37/1.16 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 1.37/1.16 thf(zip_derived_cl129, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((composition @ (join @ X1 @ one) @ X0)
% 1.37/1.16 = (join @ (composition @ X1 @ X0) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl6])).
% 1.37/1.16 thf(zip_derived_cl669, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((composition @ top @ X0) = (join @ (composition @ top @ X0) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl635, zip_derived_cl129])).
% 1.37/1.16 thf(zip_derived_cl613, plain, (![X0 : $i]: ((join @ X0 @ top) = (top))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl592, zip_derived_cl11])).
% 1.37/1.16 thf(zip_derived_cl2861, plain, (((composition @ top @ top) = (top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl669, zip_derived_cl613])).
% 1.37/1.16 thf(zip_derived_cl10, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((join @
% 1.37/1.16 (composition @ (converse @ X1) @
% 1.37/1.16 (complement @ (composition @ X1 @ X0))) @
% 1.37/1.16 (complement @ X0)) = (complement @ X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [converse_cancellativity_11])).
% 1.37/1.16 thf(zip_derived_cl2878, plain,
% 1.37/1.16 (((join @ (composition @ (converse @ top) @ (complement @ top)) @
% 1.37/1.16 (complement @ top)) = (complement @ top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl2861, zip_derived_cl10])).
% 1.37/1.16 thf(zip_derived_cl635, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl613, zip_derived_cl0])).
% 1.37/1.16 thf(zip_derived_cl7, plain,
% 1.37/1.16 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 1.37/1.16 thf(converse_additivity_9, axiom,
% 1.37/1.16 (( converse @ ( join @ A @ B ) ) =
% 1.37/1.16 ( join @ ( converse @ A ) @ ( converse @ B ) ))).
% 1.37/1.16 thf(zip_derived_cl8, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((converse @ (join @ X0 @ X1))
% 1.37/1.16 = (join @ (converse @ X0) @ (converse @ X1)))),
% 1.37/1.16 inference('cnf', [status(esa)], [converse_additivity_9])).
% 1.37/1.16 thf(zip_derived_cl48, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((converse @ (join @ X1 @ (converse @ X0)))
% 1.37/1.16 = (join @ (converse @ X1) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 1.37/1.16 thf(zip_derived_cl847, plain,
% 1.37/1.16 (![X0 : $i]: ((converse @ top) = (join @ (converse @ top) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl635, zip_derived_cl48])).
% 1.37/1.16 thf(zip_derived_cl27, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((join @ X1 @ (join @ X0 @ (complement @ (join @ X1 @ X0)))) = (top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 1.37/1.16 thf(zip_derived_cl1262, plain, (((converse @ top) = (top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl27])).
% 1.37/1.16 thf(zip_derived_cl117, plain, (((zero) = (complement @ top))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl114, zip_derived_cl12])).
% 1.37/1.16 thf(zip_derived_cl117, plain, (((zero) = (complement @ top))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl114, zip_derived_cl12])).
% 1.37/1.16 thf(zip_derived_cl669, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((composition @ top @ X0) = (join @ (composition @ top @ X0) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl635, zip_derived_cl129])).
% 1.37/1.16 thf(zip_derived_cl117, plain, (((zero) = (complement @ top))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl114, zip_derived_cl12])).
% 1.37/1.16 thf(zip_derived_cl2884, plain, (((composition @ top @ zero) = (zero))),
% 1.37/1.16 inference('demod', [status(thm)],
% 1.37/1.16 [zip_derived_cl2878, zip_derived_cl1262, zip_derived_cl117,
% 1.37/1.16 zip_derived_cl117, zip_derived_cl669, zip_derived_cl117])).
% 1.37/1.16 thf(zip_derived_cl6, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.37/1.16 ((composition @ (join @ X0 @ X2) @ X1)
% 1.37/1.16 = (join @ (composition @ X0 @ X1) @ (composition @ X2 @ X1)))),
% 1.37/1.16 inference('cnf', [status(esa)], [composition_distributivity_7])).
% 1.37/1.16 thf(zip_derived_cl2934, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((composition @ (join @ top @ X0) @ zero)
% 1.37/1.16 = (join @ zero @ (composition @ X0 @ zero)))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl2884, zip_derived_cl6])).
% 1.37/1.16 thf(zip_derived_cl635, plain, (![X0 : $i]: ((join @ top @ X0) = (top))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl613, zip_derived_cl0])).
% 1.37/1.16 thf(zip_derived_cl2884, plain, (((composition @ top @ zero) = (zero))),
% 1.37/1.16 inference('demod', [status(thm)],
% 1.37/1.16 [zip_derived_cl2878, zip_derived_cl1262, zip_derived_cl117,
% 1.37/1.16 zip_derived_cl117, zip_derived_cl669, zip_derived_cl117])).
% 1.37/1.16 thf(zip_derived_cl258, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl190, zip_derived_cl250])).
% 1.37/1.16 thf(zip_derived_cl2943, plain,
% 1.37/1.16 (![X0 : $i]: ((zero) = (composition @ X0 @ zero))),
% 1.37/1.16 inference('demod', [status(thm)],
% 1.37/1.16 [zip_derived_cl2934, zip_derived_cl635, zip_derived_cl2884,
% 1.37/1.16 zip_derived_cl258])).
% 1.37/1.16 thf(zip_derived_cl14, plain,
% 1.37/1.16 ((((composition @ sk1 @ zero) != (zero)))
% 1.37/1.16 <= (~ (((composition @ sk1 @ zero) = (zero))))),
% 1.37/1.16 inference('split', [status(esa)], [zip_derived_cl13])).
% 1.37/1.16 thf(zip_derived_cl2976, plain,
% 1.37/1.16 ((((zero) != (zero))) <= (~ (((composition @ sk1 @ zero) = (zero))))),
% 1.37/1.16 inference('s_sup-', [status(thm)], [zip_derived_cl2943, zip_derived_cl14])).
% 1.37/1.16 thf('0', plain, ((((composition @ sk1 @ zero) = (zero)))),
% 1.37/1.16 inference('simplify', [status(thm)], [zip_derived_cl2976])).
% 1.37/1.16 thf('1', plain,
% 1.37/1.16 (~ (((composition @ zero @ sk1) = (zero))) |
% 1.37/1.16 ~ (((composition @ sk1 @ zero) = (zero)))),
% 1.37/1.16 inference('split', [status(esa)], [zip_derived_cl13])).
% 1.37/1.16 thf('2', plain, (~ (((composition @ zero @ sk1) = (zero)))),
% 1.37/1.16 inference('sat_resolution*', [status(thm)], ['0', '1'])).
% 1.37/1.16 thf(zip_derived_cl2992, plain, (((composition @ zero @ sk1) != (zero))),
% 1.37/1.16 inference('simpl_trail', [status(thm)], [zip_derived_cl15, '2'])).
% 1.37/1.16 thf(zip_derived_cl258, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl190, zip_derived_cl250])).
% 1.37/1.16 thf(zip_derived_cl48, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((converse @ (join @ X1 @ (converse @ X0)))
% 1.37/1.16 = (join @ (converse @ X1) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 1.37/1.16 thf(zip_derived_cl848, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((converse @ (converse @ X0)) = (join @ (converse @ zero) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl48])).
% 1.37/1.16 thf(zip_derived_cl7, plain,
% 1.37/1.16 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 1.37/1.16 thf(zip_derived_cl862, plain,
% 1.37/1.16 (![X0 : $i]: ((X0) = (join @ (converse @ zero) @ X0))),
% 1.37/1.16 inference('demod', [status(thm)], [zip_derived_cl848, zip_derived_cl7])).
% 1.37/1.16 thf(zip_derived_cl258, plain, (![X0 : $i]: ((join @ zero @ X0) = (X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl190, zip_derived_cl250])).
% 1.37/1.16 thf(zip_derived_cl0, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 1.37/1.16 inference('cnf', [status(esa)], [maddux1_join_commutativity_1])).
% 1.37/1.16 thf(zip_derived_cl265, plain, (![X0 : $i]: ((join @ X0 @ zero) = (X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl0])).
% 1.37/1.16 thf(zip_derived_cl889, plain, (((zero) = (converse @ zero))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl862, zip_derived_cl265])).
% 1.37/1.16 thf(zip_derived_cl51, plain,
% 1.37/1.16 (![X0 : $i, X1 : $i]:
% 1.37/1.16 ((converse @ (composition @ (converse @ X0) @ X1))
% 1.37/1.16 = (composition @ (converse @ X1) @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 1.37/1.16 thf(zip_derived_cl913, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((converse @ (composition @ zero @ X0))
% 1.37/1.16 = (composition @ (converse @ X0) @ zero))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl889, zip_derived_cl51])).
% 1.37/1.16 thf(zip_derived_cl7, plain,
% 1.37/1.16 (![X0 : $i]: ((converse @ (converse @ X0)) = (X0))),
% 1.37/1.16 inference('cnf', [status(esa)], [converse_idempotence_8])).
% 1.37/1.16 thf(zip_derived_cl950, plain,
% 1.37/1.16 (![X0 : $i]:
% 1.37/1.16 ((converse @ (composition @ (converse @ X0) @ zero))
% 1.37/1.16 = (composition @ zero @ X0))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl913, zip_derived_cl7])).
% 1.37/1.16 thf(zip_derived_cl2943, plain,
% 1.37/1.16 (![X0 : $i]: ((zero) = (composition @ X0 @ zero))),
% 1.37/1.16 inference('demod', [status(thm)],
% 1.37/1.16 [zip_derived_cl2934, zip_derived_cl635, zip_derived_cl2884,
% 1.37/1.16 zip_derived_cl258])).
% 1.37/1.16 thf(zip_derived_cl889, plain, (((zero) = (converse @ zero))),
% 1.37/1.16 inference('s_sup+', [status(thm)], [zip_derived_cl862, zip_derived_cl265])).
% 1.37/1.16 thf(zip_derived_cl2952, plain,
% 1.37/1.16 (![X0 : $i]: ((zero) = (composition @ zero @ X0))),
% 1.37/1.16 inference('demod', [status(thm)],
% 1.37/1.16 [zip_derived_cl950, zip_derived_cl2943, zip_derived_cl889])).
% 1.37/1.16 thf(zip_derived_cl3067, plain, (((zero) != (zero))),
% 1.37/1.16 inference('demod', [status(thm)],
% 1.37/1.16 [zip_derived_cl2992, zip_derived_cl2952])).
% 1.37/1.16 thf(zip_derived_cl3068, plain, ($false),
% 1.37/1.16 inference('simplify', [status(thm)], [zip_derived_cl3067])).
% 1.37/1.16
% 1.37/1.16 % SZS output end Refutation
% 1.37/1.16
% 1.37/1.16
% 1.37/1.16 % Terminating...
% 1.78/1.27 % Runner terminated.
% 1.78/1.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------