TSTP Solution File: LAT036-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LAT036-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.BDuN46NuNN true
% Computer : n012.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 06:45:43 EDT 2023
% Result : Unsatisfiable 57.59s 8.95s
% Output : Refutation 57.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT036-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.BDuN46NuNN true
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 08:27:41 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in FO mode
% 0.22/0.66 % Total configuration time : 435
% 0.22/0.66 % Estimated wc time : 1092
% 0.22/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 57.59/8.95 % Solved by fo/fo3_bce.sh.
% 57.59/8.95 % BCE start: 24
% 57.59/8.95 % BCE eliminated: 0
% 57.59/8.95 % PE start: 24
% 57.59/8.95 logic: eq
% 57.59/8.95 % PE eliminated: 0
% 57.59/8.95 % done 2095 iterations in 8.197s
% 57.59/8.95 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 57.59/8.95 % SZS output start Refutation
% 57.59/8.95 thf(n0_type, type, n0: $i).
% 57.59/8.95 thf(k_type, type, k: $i > $i).
% 57.59/8.95 thf(n1_type, type, n1: $i).
% 57.59/8.95 thf(cc_type, type, cc: $i).
% 57.59/8.95 thf(join_type, type, join: $i > $i > $i).
% 57.59/8.95 thf(meet_type, type, meet: $i > $i > $i).
% 57.59/8.95 thf(bb_type, type, bb: $i).
% 57.59/8.95 thf(aa_type, type, aa: $i).
% 57.59/8.95 thf(lhs2, axiom,
% 57.59/8.95 (( join @ ( k @ ( k @ ( k @ bb ) ) ) @ ( join @ aa @ ( k @ aa ) ) ) =
% 57.59/8.95 ( join @ aa @ ( k @ aa ) ))).
% 57.59/8.95 thf(zip_derived_cl20, plain,
% 57.59/8.95 (((join @ (k @ (k @ (k @ bb))) @ (join @ aa @ (k @ aa)))
% 57.59/8.95 = (join @ aa @ (k @ aa)))),
% 57.59/8.95 inference('cnf', [status(esa)], [lhs2])).
% 57.59/8.95 thf(absorption1, axiom, (( meet @ X @ ( join @ X @ Y ) ) = ( X ))).
% 57.59/8.95 thf(zip_derived_cl2, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((meet @ X0 @ (join @ X0 @ X1)) = (X0))),
% 57.59/8.95 inference('cnf', [status(esa)], [absorption1])).
% 57.59/8.95 thf(zip_derived_cl34, plain,
% 57.59/8.95 (((meet @ (k @ (k @ (k @ bb))) @ (join @ aa @ (k @ aa)))
% 57.59/8.95 = (k @ (k @ (k @ bb))))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl2])).
% 57.59/8.95 thf(x_meet_0, axiom, (( meet @ X @ n0 ) = ( n0 ))).
% 57.59/8.95 thf(zip_derived_cl10, plain, (![X0 : $i]: ((meet @ X0 @ n0) = (n0))),
% 57.59/8.95 inference('cnf', [status(esa)], [x_meet_0])).
% 57.59/8.95 thf(commutativity_of_meet, axiom, (( meet @ X @ Y ) = ( meet @ Y @ X ))).
% 57.59/8.95 thf(zip_derived_cl4, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 57.59/8.95 thf(zip_derived_cl26, plain, (![X0 : $i]: ((n0) = (meet @ n0 @ X0))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl4])).
% 57.59/8.95 thf(modular, axiom,
% 57.59/8.95 (( ( meet @ X @ Z ) != ( X ) ) |
% 57.59/8.95 ( ( meet @ Z @ ( join @ X @ Y ) ) = ( join @ X @ ( meet @ Y @ Z ) ) ))).
% 57.59/8.95 thf(zip_derived_cl14, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 57.59/8.95 (((meet @ X0 @ X1) != (X0))
% 57.59/8.95 | ((meet @ X1 @ (join @ X0 @ X2)) = (join @ X0 @ (meet @ X2 @ X1))))),
% 57.59/8.95 inference('cnf', [status(esa)], [modular])).
% 57.59/8.95 thf(zip_derived_cl189, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 (((meet @ X0 @ (join @ X1 @ n0)) = (join @ X1 @ n0))
% 57.59/8.95 | ((meet @ X1 @ X0) != (X1)))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl14])).
% 57.59/8.95 thf(x_join_0, axiom, (( join @ X @ n0 ) = ( X ))).
% 57.59/8.95 thf(zip_derived_cl11, plain, (![X0 : $i]: ((join @ X0 @ n0) = (X0))),
% 57.59/8.95 inference('cnf', [status(esa)], [x_join_0])).
% 57.59/8.95 thf(zip_derived_cl11, plain, (![X0 : $i]: ((join @ X0 @ n0) = (X0))),
% 57.59/8.95 inference('cnf', [status(esa)], [x_join_0])).
% 57.59/8.95 thf(zip_derived_cl197, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 (((meet @ X0 @ X1) = (X1)) | ((meet @ X1 @ X0) != (X1)))),
% 57.59/8.95 inference('demod', [status(thm)],
% 57.59/8.95 [zip_derived_cl189, zip_derived_cl11, zip_derived_cl11])).
% 57.59/8.95 thf(zip_derived_cl444, plain,
% 57.59/8.95 ((((k @ (k @ (k @ bb))) != (k @ (k @ (k @ bb))))
% 57.59/8.95 | ((meet @ (join @ aa @ (k @ aa)) @ (k @ (k @ (k @ bb))))
% 57.59/8.95 = (k @ (k @ (k @ bb)))))),
% 57.59/8.95 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl197])).
% 57.59/8.95 thf(zip_derived_cl457, plain,
% 57.59/8.95 (((meet @ (join @ aa @ (k @ aa)) @ (k @ (k @ (k @ bb))))
% 57.59/8.95 = (k @ (k @ (k @ bb))))),
% 57.59/8.95 inference('simplify', [status(thm)], [zip_derived_cl444])).
% 57.59/8.95 thf(lhs1, axiom,
% 57.59/8.95 (( join @ ( k @ ( k @ aa ) ) @ ( join @ aa @ ( k @ aa ) ) ) =
% 57.59/8.95 ( join @ aa @ ( k @ aa ) ))).
% 57.59/8.95 thf(zip_derived_cl19, plain,
% 57.59/8.95 (((join @ (k @ (k @ aa)) @ (join @ aa @ (k @ aa)))
% 57.59/8.95 = (join @ aa @ (k @ aa)))),
% 57.59/8.95 inference('cnf', [status(esa)], [lhs1])).
% 57.59/8.95 thf(zip_derived_cl2, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((meet @ X0 @ (join @ X0 @ X1)) = (X0))),
% 57.59/8.95 inference('cnf', [status(esa)], [absorption1])).
% 57.59/8.95 thf(zip_derived_cl33, plain,
% 57.59/8.95 (((meet @ (k @ (k @ aa)) @ (join @ aa @ (k @ aa))) = (k @ (k @ aa)))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 57.59/8.95 thf(zip_derived_cl197, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 (((meet @ X0 @ X1) = (X1)) | ((meet @ X1 @ X0) != (X1)))),
% 57.59/8.95 inference('demod', [status(thm)],
% 57.59/8.95 [zip_derived_cl189, zip_derived_cl11, zip_derived_cl11])).
% 57.59/8.95 thf(zip_derived_cl443, plain,
% 57.59/8.95 ((((k @ (k @ aa)) != (k @ (k @ aa)))
% 57.59/8.95 | ((meet @ (join @ aa @ (k @ aa)) @ (k @ (k @ aa))) = (k @ (k @ aa))))),
% 57.59/8.95 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl197])).
% 57.59/8.95 thf(zip_derived_cl456, plain,
% 57.59/8.95 (((meet @ (join @ aa @ (k @ aa)) @ (k @ (k @ aa))) = (k @ (k @ aa)))),
% 57.59/8.95 inference('simplify', [status(thm)], [zip_derived_cl443])).
% 57.59/8.95 thf(dist_meet, axiom,
% 57.59/8.95 (( meet @ X @ ( join @ Y @ Z ) ) =
% 57.59/8.95 ( join @ ( meet @ X @ Y ) @ ( meet @ X @ Z ) ))).
% 57.59/8.95 thf(zip_derived_cl9, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 57.59/8.95 ((meet @ X0 @ (join @ X1 @ X2))
% 57.59/8.95 = (join @ (meet @ X0 @ X1) @ (meet @ X0 @ X2)))),
% 57.59/8.95 inference('cnf', [status(esa)], [dist_meet])).
% 57.59/8.95 thf(zip_derived_cl463, plain,
% 57.59/8.95 (![X0 : $i]:
% 57.59/8.95 ((meet @ (join @ aa @ (k @ aa)) @ (join @ (k @ (k @ aa)) @ X0))
% 57.59/8.95 = (join @ (k @ (k @ aa)) @ (meet @ (join @ aa @ (k @ aa)) @ X0)))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl456, zip_derived_cl9])).
% 57.59/8.95 thf(zip_derived_cl37439, plain,
% 57.59/8.95 (((meet @ (join @ aa @ (k @ aa)) @
% 57.59/8.95 (join @ (k @ (k @ aa)) @ (k @ (k @ (k @ bb)))))
% 57.59/8.95 = (join @ (k @ (k @ aa)) @ (k @ (k @ (k @ bb)))))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl457, zip_derived_cl463])).
% 57.59/8.95 thf(k_on_meet, axiom,
% 57.59/8.95 (( k @ ( meet @ U @ V ) ) = ( join @ ( k @ U ) @ ( k @ V ) ))).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(commutativity_of_join, axiom, (( join @ X @ Y ) = ( join @ Y @ X ))).
% 57.59/8.95 thf(zip_derived_cl5, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_join])).
% 57.59/8.95 thf(zip_derived_cl98, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((join @ (k @ X0) @ (k @ X1)) = (k @ (meet @ X1 @ X0)))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl5])).
% 57.59/8.95 thf(zip_derived_cl4, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 57.59/8.95 thf(zip_derived_cl4, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 57.59/8.95 thf(zip_derived_cl98, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((join @ (k @ X0) @ (k @ X1)) = (k @ (meet @ X1 @ X0)))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl5])).
% 57.59/8.95 thf(zip_derived_cl4, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 57.59/8.95 thf(zip_derived_cl37483, plain,
% 57.59/8.95 (((meet @ (k @ (meet @ (k @ aa) @ (k @ (k @ bb)))) @
% 57.59/8.95 (join @ aa @ (k @ aa))) = (k @ (meet @ (k @ aa) @ (k @ (k @ bb)))))),
% 57.59/8.95 inference('demod', [status(thm)],
% 57.59/8.95 [zip_derived_cl37439, zip_derived_cl98, zip_derived_cl4,
% 57.59/8.95 zip_derived_cl4, zip_derived_cl98, zip_derived_cl4])).
% 57.59/8.95 thf(x_meet_1, axiom, (( meet @ X @ n1 ) = ( X ))).
% 57.59/8.95 thf(zip_derived_cl12, plain, (![X0 : $i]: ((meet @ X0 @ n1) = (X0))),
% 57.59/8.95 inference('cnf', [status(esa)], [x_meet_1])).
% 57.59/8.95 thf(zip_derived_cl4, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 57.59/8.95 thf(zip_derived_cl27, plain, (![X0 : $i]: ((X0) = (meet @ n1 @ X0))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl4])).
% 57.59/8.95 thf(zip_derived_cl14, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 57.59/8.95 (((meet @ X0 @ X1) != (X0))
% 57.59/8.95 | ((meet @ X1 @ (join @ X0 @ X2)) = (join @ X0 @ (meet @ X2 @ X1))))),
% 57.59/8.95 inference('cnf', [status(esa)], [modular])).
% 57.59/8.95 thf(zip_derived_cl190, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 (((meet @ X0 @ (join @ X1 @ n1)) = (join @ X1 @ X0))
% 57.59/8.95 | ((meet @ X1 @ X0) != (X1)))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl14])).
% 57.59/8.95 thf(x_join_1, axiom, (( join @ X @ n1 ) = ( n1 ))).
% 57.59/8.95 thf(zip_derived_cl13, plain, (![X0 : $i]: ((join @ X0 @ n1) = (n1))),
% 57.59/8.95 inference('cnf', [status(esa)], [x_join_1])).
% 57.59/8.95 thf(zip_derived_cl12, plain, (![X0 : $i]: ((meet @ X0 @ n1) = (X0))),
% 57.59/8.95 inference('cnf', [status(esa)], [x_meet_1])).
% 57.59/8.95 thf(zip_derived_cl198, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 (((X0) = (join @ X1 @ X0)) | ((meet @ X1 @ X0) != (X1)))),
% 57.59/8.95 inference('demod', [status(thm)],
% 57.59/8.95 [zip_derived_cl190, zip_derived_cl13, zip_derived_cl12])).
% 57.59/8.95 thf(rhs, conjecture,
% 57.59/8.95 (( join @
% 57.59/8.95 ( k @ ( k @ ( join @ aa @ ( k @ bb ) ) ) ) @
% 57.59/8.95 ( join @ ( meet @ aa @ ( k @ ( meet @ bb @ cc ) ) ) @ ( k @ aa ) ) ) =
% 57.59/8.95 ( join @ ( meet @ aa @ ( k @ ( meet @ bb @ cc ) ) ) @ ( k @ aa ) ))).
% 57.59/8.95 thf(zf_stmt_0, negated_conjecture,
% 57.59/8.95 (( join @
% 57.59/8.95 ( k @ ( k @ ( join @ aa @ ( k @ bb ) ) ) ) @
% 57.59/8.95 ( join @ ( meet @ aa @ ( k @ ( meet @ bb @ cc ) ) ) @ ( k @ aa ) ) ) !=
% 57.59/8.95 ( join @ ( meet @ aa @ ( k @ ( meet @ bb @ cc ) ) ) @ ( k @ aa ) )),
% 57.59/8.95 inference('cnf.neg', [status(esa)], [rhs])).
% 57.59/8.95 thf(zip_derived_cl23, plain,
% 57.59/8.95 (((join @ (k @ (k @ (join @ aa @ (k @ bb)))) @
% 57.59/8.95 (join @ (meet @ aa @ (k @ (meet @ bb @ cc))) @ (k @ aa)))
% 57.59/8.95 != (join @ (meet @ aa @ (k @ (meet @ bb @ cc))) @ (k @ aa)))),
% 57.59/8.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 57.59/8.95 thf(zip_derived_cl5, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_join])).
% 57.59/8.95 thf(zip_derived_cl5, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_join])).
% 57.59/8.95 thf(zip_derived_cl47, plain,
% 57.59/8.95 (((join @ (k @ (k @ (join @ aa @ (k @ bb)))) @
% 57.59/8.95 (join @ (k @ aa) @ (meet @ aa @ (k @ (meet @ bb @ cc)))))
% 57.59/8.95 != (join @ (k @ aa) @ (meet @ aa @ (k @ (meet @ bb @ cc)))))),
% 57.59/8.95 inference('demod', [status(thm)],
% 57.59/8.95 [zip_derived_cl23, zip_derived_cl5, zip_derived_cl5])).
% 57.59/8.95 thf(k_on_join, axiom,
% 57.59/8.95 (( k @ ( join @ U @ V ) ) = ( meet @ ( k @ U ) @ ( k @ V ) ))).
% 57.59/8.95 thf(zip_derived_cl15, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (join @ X0 @ X1)) = (meet @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_join])).
% 57.59/8.95 thf(dist_join, axiom,
% 57.59/8.95 (( join @ X @ ( meet @ Y @ Z ) ) =
% 57.59/8.95 ( meet @ ( join @ X @ Y ) @ ( join @ X @ Z ) ))).
% 57.59/8.95 thf(zip_derived_cl8, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 57.59/8.95 ((join @ X0 @ (meet @ X1 @ X2))
% 57.59/8.95 = (meet @ (join @ X0 @ X1) @ (join @ X0 @ X2)))),
% 57.59/8.95 inference('cnf', [status(esa)], [dist_join])).
% 57.59/8.95 thf(zip_derived_cl5, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_join])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl4, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 57.59/8.95 thf(zip_derived_cl8, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 57.59/8.95 ((join @ X0 @ (meet @ X1 @ X2))
% 57.59/8.95 = (meet @ (join @ X0 @ X1) @ (join @ X0 @ X2)))),
% 57.59/8.95 inference('cnf', [status(esa)], [dist_join])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(associativity_of_meet, axiom,
% 57.59/8.95 (( meet @ ( meet @ X @ Y ) @ Z ) = ( meet @ X @ ( meet @ Y @ Z ) ))).
% 57.59/8.95 thf(zip_derived_cl6, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 57.59/8.95 ((meet @ (meet @ X0 @ X1) @ X2) = (meet @ X0 @ (meet @ X1 @ X2)))),
% 57.59/8.95 inference('cnf', [status(esa)], [associativity_of_meet])).
% 57.59/8.95 thf(zip_derived_cl8, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 57.59/8.95 ((join @ X0 @ (meet @ X1 @ X2))
% 57.59/8.95 = (meet @ (join @ X0 @ X1) @ (join @ X0 @ X2)))),
% 57.59/8.95 inference('cnf', [status(esa)], [dist_join])).
% 57.59/8.95 thf(zip_derived_cl5, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((join @ X1 @ X0) = (join @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_join])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl4, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]: ((meet @ X1 @ X0) = (meet @ X0 @ X1))),
% 57.59/8.95 inference('cnf', [status(esa)], [commutativity_of_meet])).
% 57.59/8.95 thf(zip_derived_cl249, plain,
% 57.59/8.95 (((meet @
% 57.59/8.95 (k @
% 57.59/8.95 (meet @ (k @ aa) @
% 57.59/8.95 (meet @ (k @ (k @ bb)) @ (meet @ aa @ (meet @ bb @ cc))))) @
% 57.59/8.95 (join @ (k @ (meet @ (k @ aa) @ (k @ (k @ bb)))) @
% 57.59/8.95 (join @ aa @ (k @ aa))))
% 57.59/8.95 != (meet @ (k @ (meet @ aa @ (meet @ bb @ cc))) @
% 57.59/8.95 (join @ aa @ (k @ aa))))),
% 57.59/8.95 inference('demod', [status(thm)],
% 57.59/8.95 [zip_derived_cl47, zip_derived_cl15, zip_derived_cl8,
% 57.59/8.95 zip_derived_cl5, zip_derived_cl16, zip_derived_cl4,
% 57.59/8.95 zip_derived_cl8, zip_derived_cl16, zip_derived_cl6,
% 57.59/8.95 zip_derived_cl8, zip_derived_cl5, zip_derived_cl16,
% 57.59/8.95 zip_derived_cl4])).
% 57.59/8.95 thf(zip_derived_cl537, plain,
% 57.59/8.95 ((((meet @
% 57.59/8.95 (k @
% 57.59/8.95 (meet @ (k @ aa) @
% 57.59/8.95 (meet @ (k @ (k @ bb)) @ (meet @ aa @ (meet @ bb @ cc))))) @
% 57.59/8.95 (join @ aa @ (k @ aa)))
% 57.59/8.95 != (meet @ (k @ (meet @ aa @ (meet @ bb @ cc))) @
% 57.59/8.95 (join @ aa @ (k @ aa))))
% 57.59/8.95 | ((meet @ (k @ (meet @ (k @ aa) @ (k @ (k @ bb)))) @
% 57.59/8.95 (join @ aa @ (k @ aa))) != (k @ (meet @ (k @ aa) @ (k @ (k @ bb))))))),
% 57.59/8.95 inference('sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl249])).
% 57.59/8.95 thf(lhs4, axiom,
% 57.59/8.95 (( join @
% 57.59/8.95 ( k @ ( k @ ( k @ bb ) ) ) @
% 57.59/8.95 ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) ) =
% 57.59/8.95 ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ))).
% 57.59/8.95 thf(zip_derived_cl22, plain,
% 57.59/8.95 (((join @ (k @ (k @ (k @ bb))) @
% 57.59/8.95 (join @ (k @ aa) @ (join @ (k @ bb) @ (k @ cc))))
% 57.59/8.95 = (join @ (k @ aa) @ (join @ (k @ bb) @ (k @ cc))))),
% 57.59/8.95 inference('cnf', [status(esa)], [lhs4])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl95, plain,
% 57.59/8.95 (((k @ (meet @ (k @ (k @ bb)) @ (meet @ aa @ (meet @ bb @ cc))))
% 57.59/8.95 = (k @ (meet @ aa @ (meet @ bb @ cc))))),
% 57.59/8.95 inference('demod', [status(thm)],
% 57.59/8.95 [zip_derived_cl22, zip_derived_cl16, zip_derived_cl16,
% 57.59/8.95 zip_derived_cl16, zip_derived_cl16, zip_derived_cl16])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl255, plain,
% 57.59/8.95 (![X0 : $i]:
% 57.59/8.95 ((k @
% 57.59/8.95 (meet @ X0 @
% 57.59/8.95 (meet @ (k @ (k @ bb)) @ (meet @ aa @ (meet @ bb @ cc)))))
% 57.59/8.95 = (join @ (k @ X0) @ (k @ (meet @ aa @ (meet @ bb @ cc)))))),
% 57.59/8.95 inference('sup+', [status(thm)], [zip_derived_cl95, zip_derived_cl16])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl257, plain,
% 57.59/8.95 (![X0 : $i]:
% 57.59/8.95 ((k @
% 57.59/8.95 (meet @ X0 @
% 57.59/8.95 (meet @ (k @ (k @ bb)) @ (meet @ aa @ (meet @ bb @ cc)))))
% 57.59/8.95 = (k @ (meet @ X0 @ (meet @ aa @ (meet @ bb @ cc)))))),
% 57.59/8.95 inference('demod', [status(thm)], [zip_derived_cl255, zip_derived_cl16])).
% 57.59/8.95 thf(lhs3, axiom,
% 57.59/8.95 (( join @
% 57.59/8.95 ( k @ ( k @ aa ) ) @
% 57.59/8.95 ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) ) =
% 57.59/8.95 ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ))).
% 57.59/8.95 thf(zip_derived_cl21, plain,
% 57.59/8.95 (((join @ (k @ (k @ aa)) @
% 57.59/8.95 (join @ (k @ aa) @ (join @ (k @ bb) @ (k @ cc))))
% 57.59/8.95 = (join @ (k @ aa) @ (join @ (k @ bb) @ (k @ cc))))),
% 57.59/8.95 inference('cnf', [status(esa)], [lhs3])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl16, plain,
% 57.59/8.95 (![X0 : $i, X1 : $i]:
% 57.59/8.95 ((k @ (meet @ X0 @ X1)) = (join @ (k @ X0) @ (k @ X1)))),
% 57.59/8.95 inference('cnf', [status(esa)], [k_on_meet])).
% 57.59/8.95 thf(zip_derived_cl94, plain,
% 57.59/8.95 (((k @ (meet @ (k @ aa) @ (meet @ aa @ (meet @ bb @ cc))))
% 57.59/8.95 = (k @ (meet @ aa @ (meet @ bb @ cc))))),
% 57.59/8.95 inference('demod', [status(thm)],
% 57.59/8.95 [zip_derived_cl21, zip_derived_cl16, zip_derived_cl16,
% 57.59/8.95 zip_derived_cl16, zip_derived_cl16, zip_derived_cl16])).
% 57.59/8.95 thf(zip_derived_cl19146, plain,
% 57.59/8.95 ((((meet @ (k @ (meet @ aa @ (meet @ bb @ cc))) @ (join @ aa @ (k @ aa)))
% 57.59/8.95 != (meet @ (k @ (meet @ aa @ (meet @ bb @ cc))) @
% 57.59/8.95 (join @ aa @ (k @ aa))))
% 57.59/8.95 | ((meet @ (k @ (meet @ (k @ aa) @ (k @ (k @ bb)))) @
% 57.59/8.95 (join @ aa @ (k @ aa))) != (k @ (meet @ (k @ aa) @ (k @ (k @ bb))))))),
% 57.59/8.95 inference('demod', [status(thm)],
% 57.59/8.95 [zip_derived_cl537, zip_derived_cl257, zip_derived_cl94])).
% 57.59/8.95 thf(zip_derived_cl19147, plain,
% 57.59/8.95 (((meet @ (k @ (meet @ (k @ aa) @ (k @ (k @ bb)))) @
% 57.59/8.95 (join @ aa @ (k @ aa))) != (k @ (meet @ (k @ aa) @ (k @ (k @ bb)))))),
% 57.59/8.95 inference('simplify', [status(thm)], [zip_derived_cl19146])).
% 57.59/8.95 thf(zip_derived_cl37484, plain, ($false),
% 57.59/8.95 inference('simplify_reflect-', [status(thm)],
% 57.59/8.95 [zip_derived_cl37483, zip_derived_cl19147])).
% 57.59/8.95
% 57.59/8.95 % SZS output end Refutation
% 57.59/8.95
% 57.59/8.95
% 57.59/8.95 % Terminating...
% 58.28/9.00 % Runner terminated.
% 58.32/9.02 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------