TSTP Solution File: LAT219-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LAT219-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lTXiSUu1co true
% Computer : n023.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 06:46:13 EDT 2023
% Result : Unsatisfiable 255.77s 37.33s
% Output : Refutation 255.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT219-1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lTXiSUu1co true
% 0.13/0.34 % Computer : n023.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 09:25:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.52/0.66 % Total configuration time : 435
% 0.52/0.66 % Estimated wc time : 1092
% 0.52/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 255.77/37.33 % Solved by fo/fo4.sh.
% 255.77/37.33 % done 13437 iterations in 36.547s
% 255.77/37.33 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 255.77/37.33 % SZS output start Refutation
% 255.77/37.33 thf(b_type, type, b: $i).
% 255.77/37.33 thf(one_type, type, one: $i).
% 255.77/37.33 thf(join_type, type, join: $i > $i > $i).
% 255.77/37.33 thf(a_type, type, a: $i).
% 255.77/37.33 thf(zero_type, type, zero: $i).
% 255.77/37.33 thf(meet_type, type, meet: $i > $i > $i).
% 255.77/37.33 thf(complement_type, type, complement: $i > $i).
% 255.77/37.33 thf(complement_join, axiom, (( join @ X @ ( complement @ X ) ) = ( one ))).
% 255.77/37.33 thf(zip_derived_cl8, plain,
% 255.77/37.33 (![X0 : $i]: ((join @ X0 @ (complement @ X0)) = (one))),
% 255.77/37.33 inference('cnf', [status(esa)], [complement_join])).
% 255.77/37.33 thf(zip_derived_cl8, plain,
% 255.77/37.33 (![X0 : $i]: ((join @ X0 @ (complement @ X0)) = (one))),
% 255.77/37.33 inference('cnf', [status(esa)], [complement_join])).
% 255.77/37.33 thf(prove_distributivity_hypothesis, axiom, (( meet @ b @ a ) = ( a ))).
% 255.77/37.33 thf(zip_derived_cl12, plain, (((meet @ b @ a) = (a))),
% 255.77/37.33 inference('cnf', [status(esa)], [prove_distributivity_hypothesis])).
% 255.77/37.33 thf(absorption2, axiom, (( join @ X @ ( meet @ X @ Y ) ) = ( X ))).
% 255.77/37.33 thf(zip_derived_cl3, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X0 @ X1)) = (X0))),
% 255.77/37.33 inference('cnf', [status(esa)], [absorption2])).
% 255.77/37.33 thf(zip_derived_cl29, plain, (((join @ b @ a) = (b))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl3])).
% 255.77/37.33 thf(associativity_of_join, axiom,
% 255.77/37.33 (( join @ ( join @ X @ Y ) @ Z ) = ( join @ X @ ( join @ Y @ Z ) ))).
% 255.77/37.33 thf(zip_derived_cl7, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ (join @ X0 @ X1) @ X2) = (join @ X0 @ (join @ X1 @ X2)))),
% 255.77/37.33 inference('cnf', [status(esa)], [associativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl180, plain,
% 255.77/37.33 (![X0 : $i]: ((join @ b @ X0) = (join @ b @ (join @ a @ X0)))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl7])).
% 255.77/37.33 thf(zip_derived_cl520, plain,
% 255.77/37.33 (((join @ b @ (complement @ a)) = (join @ b @ one))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl180])).
% 255.77/37.33 thf(zip_derived_cl8, plain,
% 255.77/37.33 (![X0 : $i]: ((join @ X0 @ (complement @ X0)) = (one))),
% 255.77/37.33 inference('cnf', [status(esa)], [complement_join])).
% 255.77/37.33 thf(absorption1, axiom, (( meet @ X @ ( join @ X @ Y ) ) = ( X ))).
% 255.77/37.33 thf(zip_derived_cl2, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((meet @ X0 @ (join @ X0 @ X1)) = (X0))),
% 255.77/37.33 inference('cnf', [status(esa)], [absorption1])).
% 255.77/37.33 thf(zip_derived_cl15, plain, (![X0 : $i]: ((meet @ X0 @ one) = (X0))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl2])).
% 255.77/37.33 thf(commutativity_of_meet, axiom, (( meet @ X @ Y ) = ( meet @ Y @ X ))).
% 255.77/37.33 thf(zip_derived_cl4, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 255.77/37.33 thf(zip_derived_cl18, plain, (![X0 : $i]: ((X0) = (meet @ one @ X0))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl4])).
% 255.77/37.33 thf(zip_derived_cl3, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X0 @ X1)) = (X0))),
% 255.77/37.33 inference('cnf', [status(esa)], [absorption2])).
% 255.77/37.33 thf(zip_derived_cl33, plain, (![X0 : $i]: ((join @ one @ X0) = (one))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl3])).
% 255.77/37.33 thf(commutativity_of_join, axiom, (( join @ X @ Y ) = ( join @ Y @ X ))).
% 255.77/37.33 thf(zip_derived_cl5, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl154, plain, (![X0 : $i]: ((join @ X0 @ one) = (one))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl5])).
% 255.77/37.33 thf(zip_derived_cl528, plain, (((join @ b @ (complement @ a)) = (one))),
% 255.77/37.33 inference('demod', [status(thm)], [zip_derived_cl520, zip_derived_cl154])).
% 255.77/37.33 thf(equation_H2, axiom,
% 255.77/37.33 (( meet @ X @ ( join @ Y @ ( meet @ X @ Z ) ) ) =
% 255.77/37.33 ( meet @
% 255.77/37.33 X @
% 255.77/37.33 ( join @
% 255.77/37.33 Y @
% 255.77/37.33 ( meet @
% 255.77/37.33 Z @ ( join @ ( meet @ X @ ( join @ Y @ Z ) ) @ ( meet @ Y @ Z ) ) ) ) ))).
% 255.77/37.33 thf(zip_derived_cl11, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((meet @ X0 @ (join @ X1 @ (meet @ X0 @ X2)))
% 255.77/37.33 = (meet @ X0 @
% 255.77/37.33 (join @ X1 @
% 255.77/37.33 (meet @ X2 @
% 255.77/37.33 (join @ (meet @ X0 @ (join @ X1 @ X2)) @ (meet @ X1 @ X2))))))),
% 255.77/37.33 inference('cnf', [status(esa)], [equation_H2])).
% 255.77/37.33 thf(zip_derived_cl5, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl332, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((meet @ X0 @ (join @ X1 @ (meet @ X0 @ X2)))
% 255.77/37.33 = (meet @ X0 @
% 255.77/37.33 (join @ X1 @
% 255.77/37.33 (meet @ X2 @
% 255.77/37.33 (join @ (meet @ X1 @ X2) @ (meet @ X0 @ (join @ X1 @ X2)))))))),
% 255.77/37.33 inference('demod', [status(thm)], [zip_derived_cl11, zip_derived_cl5])).
% 255.77/37.33 thf(zip_derived_cl540, plain,
% 255.77/37.33 (![X0 : $i]:
% 255.77/37.33 ((meet @ X0 @ (join @ b @ (meet @ X0 @ (complement @ a))))
% 255.77/37.33 = (meet @ X0 @
% 255.77/37.33 (join @ b @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (join @ (meet @ b @ (complement @ a)) @ (meet @ X0 @ one))))))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl528, zip_derived_cl332])).
% 255.77/37.33 thf(zip_derived_cl15, plain, (![X0 : $i]: ((meet @ X0 @ one) = (X0))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl2])).
% 255.77/37.33 thf(zip_derived_cl547, plain,
% 255.77/37.33 (![X0 : $i]:
% 255.77/37.33 ((meet @ X0 @ (join @ b @ (meet @ X0 @ (complement @ a))))
% 255.77/37.33 = (meet @ X0 @
% 255.77/37.33 (join @ b @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (join @ (meet @ b @ (complement @ a)) @ X0)))))),
% 255.77/37.33 inference('demod', [status(thm)], [zip_derived_cl540, zip_derived_cl15])).
% 255.77/37.33 thf(zip_derived_cl31558, plain,
% 255.77/37.33 (((meet @ (complement @ (meet @ b @ (complement @ a))) @
% 255.77/37.33 (join @ b @
% 255.77/37.33 (meet @ (complement @ (meet @ b @ (complement @ a))) @
% 255.77/37.33 (complement @ a))))
% 255.77/37.33 = (meet @ (complement @ (meet @ b @ (complement @ a))) @
% 255.77/37.33 (join @ b @ (meet @ (complement @ a) @ one))))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl547])).
% 255.77/37.33 thf(zip_derived_cl4, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 255.77/37.33 thf(zip_derived_cl15, plain, (![X0 : $i]: ((meet @ X0 @ one) = (X0))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl2])).
% 255.77/37.33 thf(zip_derived_cl528, plain, (((join @ b @ (complement @ a)) = (one))),
% 255.77/37.33 inference('demod', [status(thm)], [zip_derived_cl520, zip_derived_cl154])).
% 255.77/37.33 thf(zip_derived_cl15, plain, (![X0 : $i]: ((meet @ X0 @ one) = (X0))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl2])).
% 255.77/37.33 thf(zip_derived_cl31639, plain,
% 255.77/37.33 (((meet @ (complement @ (meet @ b @ (complement @ a))) @
% 255.77/37.33 (join @ b @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (complement @ (meet @ b @ (complement @ a))))))
% 255.77/37.33 = (complement @ (meet @ b @ (complement @ a))))),
% 255.77/37.33 inference('demod', [status(thm)],
% 255.77/37.33 [zip_derived_cl31558, zip_derived_cl4, zip_derived_cl15,
% 255.77/37.33 zip_derived_cl528, zip_derived_cl15])).
% 255.77/37.33 thf(zip_derived_cl4, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 255.77/37.33 thf(zip_derived_cl3, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X0 @ X1)) = (X0))),
% 255.77/37.33 inference('cnf', [status(esa)], [absorption2])).
% 255.77/37.33 thf(zip_derived_cl24, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X1 @ X0)) = (X0))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 255.77/37.33 thf(zip_derived_cl7, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ (join @ X0 @ X1) @ X2) = (join @ X0 @ (join @ X1 @ X2)))),
% 255.77/37.33 inference('cnf', [status(esa)], [associativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl489, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ X1 @ X0)
% 255.77/37.33 = (join @ X1 @ (join @ X0 @ (meet @ X2 @ (join @ X1 @ X0)))))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl7])).
% 255.77/37.33 thf(zip_derived_cl33056, plain,
% 255.77/37.33 (((join @ b @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (complement @ (meet @ b @ (complement @ a)))))
% 255.77/37.33 = (join @ b @
% 255.77/37.33 (join @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (complement @ (meet @ b @ (complement @ a)))) @
% 255.77/37.33 (complement @ (meet @ b @ (complement @ a))))))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl31639, zip_derived_cl489])).
% 255.77/37.33 thf(zip_derived_cl5, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl24, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X1 @ X0)) = (X0))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 255.77/37.33 thf(zip_derived_cl33226, plain,
% 255.77/37.33 (((join @ b @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (complement @ (meet @ b @ (complement @ a)))))
% 255.77/37.33 = (join @ b @ (complement @ (meet @ b @ (complement @ a)))))),
% 255.77/37.33 inference('demod', [status(thm)],
% 255.77/37.33 [zip_derived_cl33056, zip_derived_cl5, zip_derived_cl24])).
% 255.77/37.33 thf(zip_derived_cl5, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl5, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl29, plain, (((join @ b @ a) = (b))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl3])).
% 255.77/37.33 thf(zip_derived_cl5, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl44, plain, (((b) = (join @ a @ b))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl5])).
% 255.77/37.33 thf(zip_derived_cl7, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ (join @ X0 @ X1) @ X2) = (join @ X0 @ (join @ X1 @ X2)))),
% 255.77/37.33 inference('cnf', [status(esa)], [associativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl181, plain,
% 255.77/37.33 (![X0 : $i]: ((join @ b @ X0) = (join @ a @ (join @ b @ X0)))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl7])).
% 255.77/37.33 thf(zip_derived_cl2, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((meet @ X0 @ (join @ X0 @ X1)) = (X0))),
% 255.77/37.33 inference('cnf', [status(esa)], [absorption1])).
% 255.77/37.33 thf(zip_derived_cl713, plain,
% 255.77/37.33 (![X0 : $i]: ((meet @ a @ (join @ b @ X0)) = (a))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl2])).
% 255.77/37.33 thf(zip_derived_cl755, plain,
% 255.77/37.33 (![X0 : $i]: ((meet @ a @ (join @ X0 @ b)) = (a))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl713])).
% 255.77/37.33 thf(zip_derived_cl24, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X1 @ X0)) = (X0))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 255.77/37.33 thf(zip_derived_cl830, plain,
% 255.77/37.33 (![X0 : $i]: ((join @ (join @ X0 @ b) @ a) = (join @ X0 @ b))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl755, zip_derived_cl24])).
% 255.77/37.33 thf(zip_derived_cl5641, plain,
% 255.77/37.33 (![X0 : $i]: ((join @ (join @ b @ X0) @ a) = (join @ X0 @ b))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl830])).
% 255.77/37.33 thf(zip_derived_cl36998, plain,
% 255.77/37.33 (((join @ (join @ b @ (complement @ (meet @ b @ (complement @ a)))) @ a)
% 255.77/37.33 = (join @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (complement @ (meet @ b @ (complement @ a)))) @
% 255.77/37.33 b))),
% 255.77/37.33 inference('sup+', [status(thm)],
% 255.77/37.33 [zip_derived_cl33226, zip_derived_cl5641])).
% 255.77/37.33 thf(zip_derived_cl5641, plain,
% 255.77/37.33 (![X0 : $i]: ((join @ (join @ b @ X0) @ a) = (join @ X0 @ b))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl830])).
% 255.77/37.33 thf(zip_derived_cl5, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl37143, plain,
% 255.77/37.33 (((join @ b @ (complement @ (meet @ b @ (complement @ a))))
% 255.77/37.33 = (join @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (complement @ (meet @ b @ (complement @ a)))) @
% 255.77/37.33 b))),
% 255.77/37.33 inference('demod', [status(thm)],
% 255.77/37.33 [zip_derived_cl36998, zip_derived_cl5641, zip_derived_cl5])).
% 255.77/37.33 thf(zip_derived_cl24, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X1 @ X0)) = (X0))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 255.77/37.33 thf(zip_derived_cl7, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ (join @ X0 @ X1) @ X2) = (join @ X0 @ (join @ X1 @ X2)))),
% 255.77/37.33 inference('cnf', [status(esa)], [associativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl486, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ X0 @ X1) = (join @ X0 @ (join @ (meet @ X2 @ X0) @ X1)))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl7])).
% 255.77/37.33 thf(zip_derived_cl62549, plain,
% 255.77/37.33 (((join @ (complement @ (meet @ b @ (complement @ a))) @ b)
% 255.77/37.33 = (join @ (complement @ (meet @ b @ (complement @ a))) @
% 255.77/37.33 (join @ b @ (complement @ (meet @ b @ (complement @ a))))))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl37143, zip_derived_cl486])).
% 255.77/37.33 thf(zip_derived_cl5, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl62774, plain,
% 255.77/37.33 (((join @ b @ (complement @ (meet @ b @ (complement @ a))))
% 255.77/37.33 = (join @ (complement @ (meet @ b @ (complement @ a))) @
% 255.77/37.33 (join @ b @ (complement @ (meet @ b @ (complement @ a))))))),
% 255.77/37.33 inference('demod', [status(thm)], [zip_derived_cl62549, zip_derived_cl5])).
% 255.77/37.33 thf(zip_derived_cl8, plain,
% 255.77/37.33 (![X0 : $i]: ((join @ X0 @ (complement @ X0)) = (one))),
% 255.77/37.33 inference('cnf', [status(esa)], [complement_join])).
% 255.77/37.33 thf(zip_derived_cl7, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ (join @ X0 @ X1) @ X2) = (join @ X0 @ (join @ X1 @ X2)))),
% 255.77/37.33 inference('cnf', [status(esa)], [associativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl175, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]:
% 255.77/37.33 ((join @ one @ X0) = (join @ X1 @ (join @ (complement @ X1) @ X0)))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl7])).
% 255.77/37.33 thf(zip_derived_cl33, plain, (![X0 : $i]: ((join @ one @ X0) = (one))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl3])).
% 255.77/37.33 thf(zip_derived_cl183, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]:
% 255.77/37.33 ((one) = (join @ X1 @ (join @ (complement @ X1) @ X0)))),
% 255.77/37.33 inference('demod', [status(thm)], [zip_derived_cl175, zip_derived_cl33])).
% 255.77/37.33 thf(zip_derived_cl141029, plain,
% 255.77/37.33 (((one)
% 255.77/37.33 = (join @ (meet @ b @ (complement @ a)) @
% 255.77/37.33 (join @ b @ (complement @ (meet @ b @ (complement @ a))))))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl62774, zip_derived_cl183])).
% 255.77/37.33 thf(zip_derived_cl3, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X0 @ X1)) = (X0))),
% 255.77/37.33 inference('cnf', [status(esa)], [absorption2])).
% 255.77/37.33 thf(zip_derived_cl7, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ (join @ X0 @ X1) @ X2) = (join @ X0 @ (join @ X1 @ X2)))),
% 255.77/37.33 inference('cnf', [status(esa)], [associativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl174, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ X0 @ X1) = (join @ X0 @ (join @ (meet @ X0 @ X2) @ X1)))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl7])).
% 255.77/37.33 thf(zip_derived_cl147425, plain,
% 255.77/37.33 (((join @ b @ (join @ b @ (complement @ (meet @ b @ (complement @ a)))))
% 255.77/37.33 = (join @ b @ one))),
% 255.77/37.33 inference('sup+', [status(thm)],
% 255.77/37.33 [zip_derived_cl141029, zip_derived_cl174])).
% 255.77/37.33 thf(zip_derived_cl154, plain, (![X0 : $i]: ((join @ X0 @ one) = (one))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl5])).
% 255.77/37.33 thf(zip_derived_cl147901, plain,
% 255.77/37.33 (((join @ b @ (join @ b @ (complement @ (meet @ b @ (complement @ a)))))
% 255.77/37.33 = (one))),
% 255.77/37.33 inference('demod', [status(thm)],
% 255.77/37.33 [zip_derived_cl147425, zip_derived_cl154])).
% 255.77/37.33 thf(idempotence_of_join, axiom, (( join @ X @ X ) = ( X ))).
% 255.77/37.33 thf(zip_derived_cl1, plain, (![X0 : $i]: ((join @ X0 @ X0) = (X0))),
% 255.77/37.33 inference('cnf', [status(esa)], [idempotence_of_join])).
% 255.77/37.33 thf(zip_derived_cl7, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((join @ (join @ X0 @ X1) @ X2) = (join @ X0 @ (join @ X1 @ X2)))),
% 255.77/37.33 inference('cnf', [status(esa)], [associativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl171, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ X1) = (join @ X0 @ (join @ X0 @ X1)))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 255.77/37.33 thf(zip_derived_cl151608, plain,
% 255.77/37.33 (((join @ b @ (complement @ (meet @ b @ (complement @ a)))) = (one))),
% 255.77/37.33 inference('sup+', [status(thm)],
% 255.77/37.33 [zip_derived_cl147901, zip_derived_cl171])).
% 255.77/37.33 thf(zip_derived_cl33226, plain,
% 255.77/37.33 (((join @ b @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (complement @ (meet @ b @ (complement @ a)))))
% 255.77/37.33 = (join @ b @ (complement @ (meet @ b @ (complement @ a)))))),
% 255.77/37.33 inference('demod', [status(thm)],
% 255.77/37.33 [zip_derived_cl33056, zip_derived_cl5, zip_derived_cl24])).
% 255.77/37.33 thf(zip_derived_cl3, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X0 @ (meet @ X0 @ X1)) = (X0))),
% 255.77/37.33 inference('cnf', [status(esa)], [absorption2])).
% 255.77/37.33 thf(meet_join_complement, axiom,
% 255.77/37.33 (( ( meet @ X @ Y ) != ( zero ) ) | ( ( join @ X @ Y ) != ( one ) ) |
% 255.77/37.33 ( ( complement @ X ) = ( Y ) ))).
% 255.77/37.33 thf(zip_derived_cl10, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]:
% 255.77/37.33 (((meet @ X0 @ X1) != (zero))
% 255.77/37.33 | ((join @ X0 @ X1) != (one))
% 255.77/37.33 | ((complement @ X0) = (X1)))),
% 255.77/37.33 inference('cnf', [status(esa)], [meet_join_complement])).
% 255.77/37.33 thf(prove_distributivity, conjecture,
% 255.77/37.33 (( join @ ( complement @ b ) @ ( complement @ a ) ) = ( complement @ a ))).
% 255.77/37.33 thf(zf_stmt_0, negated_conjecture,
% 255.77/37.33 (( join @ ( complement @ b ) @ ( complement @ a ) ) != ( complement @ a )),
% 255.77/37.33 inference('cnf.neg', [status(esa)], [prove_distributivity])).
% 255.77/37.33 thf(zip_derived_cl13, plain,
% 255.77/37.33 (((join @ (complement @ b) @ (complement @ a)) != (complement @ a))),
% 255.77/37.33 inference('cnf', [status(esa)], [zf_stmt_0])).
% 255.77/37.33 thf(zip_derived_cl5, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 255.77/37.33 inference('cnf', [status(esa)], [commutativity_of_join])).
% 255.77/37.33 thf(zip_derived_cl38, plain,
% 255.77/37.33 (((join @ (complement @ a) @ (complement @ b)) != (complement @ a))),
% 255.77/37.33 inference('demod', [status(thm)], [zip_derived_cl13, zip_derived_cl5])).
% 255.77/37.33 thf(zip_derived_cl50, plain,
% 255.77/37.33 (![X0 : $i]:
% 255.77/37.33 (((join @ (complement @ a) @ X0) != (complement @ a))
% 255.77/37.33 | ((join @ b @ X0) != (one))
% 255.77/37.33 | ((meet @ b @ X0) != (zero)))),
% 255.77/37.33 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl38])).
% 255.77/37.33 thf(zip_derived_cl71, plain,
% 255.77/37.33 (![X0 : $i]:
% 255.77/37.33 (((complement @ a) != (complement @ a))
% 255.77/37.33 | ((meet @ b @ (meet @ (complement @ a) @ X0)) != (zero))
% 255.77/37.33 | ((join @ b @ (meet @ (complement @ a) @ X0)) != (one)))),
% 255.77/37.33 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl50])).
% 255.77/37.33 thf(zip_derived_cl76, plain,
% 255.77/37.33 (![X0 : $i]:
% 255.77/37.33 (((join @ b @ (meet @ (complement @ a) @ X0)) != (one))
% 255.77/37.33 | ((meet @ b @ (meet @ (complement @ a) @ X0)) != (zero)))),
% 255.77/37.33 inference('simplify', [status(thm)], [zip_derived_cl71])).
% 255.77/37.33 thf(zip_derived_cl37011, plain,
% 255.77/37.33 ((((join @ b @ (complement @ (meet @ b @ (complement @ a)))) != (one))
% 255.77/37.33 | ((meet @ b @
% 255.77/37.33 (meet @ (complement @ a) @
% 255.77/37.33 (complement @ (meet @ b @ (complement @ a)))))
% 255.77/37.33 != (zero)))),
% 255.77/37.33 inference('sup-', [status(thm)], [zip_derived_cl33226, zip_derived_cl76])).
% 255.77/37.33 thf(complement_meet, axiom, (( meet @ X @ ( complement @ X ) ) = ( zero ))).
% 255.77/37.33 thf(zip_derived_cl9, plain,
% 255.77/37.33 (![X0 : $i]: ((meet @ X0 @ (complement @ X0)) = (zero))),
% 255.77/37.33 inference('cnf', [status(esa)], [complement_meet])).
% 255.77/37.33 thf(associativity_of_meet, axiom,
% 255.77/37.33 (( meet @ ( meet @ X @ Y ) @ Z ) = ( meet @ X @ ( meet @ Y @ Z ) ))).
% 255.77/37.33 thf(zip_derived_cl6, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.77/37.33 ((meet @ (meet @ X0 @ X1) @ X2) = (meet @ X0 @ (meet @ X1 @ X2)))),
% 255.77/37.33 inference('cnf', [status(esa)], [associativity_of_meet])).
% 255.77/37.33 thf(zip_derived_cl101, plain,
% 255.77/37.33 (![X0 : $i, X1 : $i]:
% 255.77/37.33 ((zero) = (meet @ X1 @ (meet @ X0 @ (complement @ (meet @ X1 @ X0)))))),
% 255.77/37.33 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl6])).
% 255.77/37.33 thf(zip_derived_cl37149, plain,
% 255.77/37.33 ((((join @ b @ (complement @ (meet @ b @ (complement @ a)))) != (one))
% 255.77/37.33 | ((zero) != (zero)))),
% 255.77/37.33 inference('demod', [status(thm)],
% 255.77/37.33 [zip_derived_cl37011, zip_derived_cl101])).
% 255.77/37.33 thf(zip_derived_cl37150, plain,
% 255.77/37.33 (((join @ b @ (complement @ (meet @ b @ (complement @ a)))) != (one))),
% 255.77/37.33 inference('simplify', [status(thm)], [zip_derived_cl37149])).
% 255.77/37.33 thf(zip_derived_cl152054, plain, ($false),
% 255.77/37.33 inference('simplify_reflect-', [status(thm)],
% 255.77/37.33 [zip_derived_cl151608, zip_derived_cl37150])).
% 255.77/37.33
% 255.77/37.33 % SZS output end Refutation
% 255.77/37.33
% 255.77/37.33
% 255.77/37.33 % Terminating...
% 255.92/37.42 % Runner terminated.
% 255.92/37.44 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------