TSTP Solution File: NUM061-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM061-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.iAG9V2BDDh true
% Computer : n014.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 12:39:07 EDT 2023
% Result : Unsatisfiable 31.67s 5.19s
% Output : Refutation 31.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM061-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.iAG9V2BDDh true
% 0.15/0.35 % Computer : n014.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
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 16:49:48 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox2/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
% 0.22/0.68 % Total configuration time : 435
% 0.22/0.68 % Estimated wc time : 1092
% 0.22/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 1.02/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 1.02/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 1.02/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.02/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.02/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.02/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 31.67/5.19 % Solved by fo/fo6_bce.sh.
% 31.67/5.19 % BCE start: 162
% 31.67/5.19 % BCE eliminated: 3
% 31.67/5.19 % PE start: 159
% 31.67/5.19 logic: eq
% 31.67/5.19 % PE eliminated: 27
% 31.67/5.19 % done 2158 iterations in 4.422s
% 31.67/5.19 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 31.67/5.19 % SZS output start Refutation
% 31.67/5.19 thf(universal_class_type, type, universal_class: $i).
% 31.67/5.19 thf(null_class_type, type, null_class: $i).
% 31.67/5.19 thf(domain_of_type, type, domain_of: $i > $i).
% 31.67/5.19 thf(member_type, type, member: $i > $i > $o).
% 31.67/5.19 thf(z_type, type, z: $i).
% 31.67/5.19 thf(second_type, type, second: $i > $i).
% 31.67/5.19 thf(unordered_pair_type, type, unordered_pair: $i > $i > $i).
% 31.67/5.19 thf(complement_type, type, complement: $i > $i).
% 31.67/5.19 thf(segment_type, type, segment: $i > $i > $i > $i).
% 31.67/5.19 thf(xr_type, type, xr: $i).
% 31.67/5.19 thf(singleton_type, type, singleton: $i > $i).
% 31.67/5.19 thf(u_type, type, u: $i).
% 31.67/5.19 thf(intersection_type, type, intersection: $i > $i > $i).
% 31.67/5.19 thf(subclass_type, type, subclass: $i > $i > $o).
% 31.67/5.19 thf(restrict_type, type, restrict: $i > $i > $i > $i).
% 31.67/5.19 thf(cross_product_type, type, cross_product: $i > $i > $i).
% 31.67/5.19 thf(y_type, type, y: $i).
% 31.67/5.19 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 31.67/5.19 thf(first_type, type, first: $i > $i).
% 31.67/5.19 thf(regular_type, type, regular: $i > $i).
% 31.67/5.19 thf(domain2, axiom,
% 31.67/5.19 (( ~( member @ Z @ universal_class ) ) |
% 31.67/5.19 ( ( restrict @ X @ ( singleton @ Z ) @ universal_class ) = ( null_class ) ) |
% 31.67/5.19 ( member @ Z @ ( domain_of @ X ) ))).
% 31.67/5.19 thf(zip_derived_cl30, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class)
% 31.67/5.19 | ((restrict @ X1 @ (singleton @ X0) @ universal_class)
% 31.67/5.19 = (null_class))
% 31.67/5.19 | (member @ X0 @ (domain_of @ X1)))),
% 31.67/5.19 inference('cnf', [status(esa)], [domain2])).
% 31.67/5.19 thf(prove_segments_property5_2, conjecture, (~( member @ u @ y ))).
% 31.67/5.19 thf(zf_stmt_0, negated_conjecture, (member @ u @ y),
% 31.67/5.19 inference('cnf.neg', [status(esa)], [prove_segments_property5_2])).
% 31.67/5.19 thf(zip_derived_cl159, plain, ( (member @ u @ y)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_0])).
% 31.67/5.19 thf(singleton_set, axiom, (( unordered_pair @ X @ X ) = ( singleton @ X ))).
% 31.67/5.19 thf(zip_derived_cl11, plain,
% 31.67/5.19 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 31.67/5.19 inference('cnf', [status(esa)], [singleton_set])).
% 31.67/5.19 thf(unordered_pair2, axiom,
% 31.67/5.19 (( ~( member @ X @ universal_class ) ) |
% 31.67/5.19 ( member @ X @ ( unordered_pair @ X @ Y ) ))).
% 31.67/5.19 thf(zip_derived_cl8, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class)
% 31.67/5.19 | (member @ X0 @ (unordered_pair @ X0 @ X1)))),
% 31.67/5.19 inference('cnf', [status(esa)], [unordered_pair2])).
% 31.67/5.19 thf(zip_derived_cl779, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class) | (member @ X0 @ (singleton @ X0)))),
% 31.67/5.19 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 31.67/5.19 thf(complement2, axiom,
% 31.67/5.19 (( ~( member @ Z @ universal_class ) ) |
% 31.67/5.19 ( member @ Z @ ( complement @ X ) ) | ( member @ Z @ X ))).
% 31.67/5.19 thf(zip_derived_cl24, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class)
% 31.67/5.19 | (member @ X0 @ (complement @ X1))
% 31.67/5.19 | (member @ X0 @ X1))),
% 31.67/5.19 inference('cnf', [status(esa)], [complement2])).
% 31.67/5.19 thf(zip_derived_cl24, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class)
% 31.67/5.19 | (member @ X0 @ (complement @ X1))
% 31.67/5.19 | (member @ X0 @ X1))),
% 31.67/5.19 inference('cnf', [status(esa)], [complement2])).
% 31.67/5.19 thf(cartesian_product3, axiom,
% 31.67/5.19 (( ~( member @ U @ X ) ) | ( ~( member @ V @ Y ) ) |
% 31.67/5.19 ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ))).
% 31.67/5.19 thf(zip_derived_cl15, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ X0 @ X1)
% 31.67/5.19 | ~ (member @ X2 @ X3)
% 31.67/5.19 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 31.67/5.19 inference('cnf', [status(esa)], [cartesian_product3])).
% 31.67/5.19 thf(prove_segments_property5_3, conjecture,
% 31.67/5.19 (~( member @ z @ universal_class ))).
% 31.67/5.19 thf(zf_stmt_1, negated_conjecture, (member @ z @ universal_class),
% 31.67/5.19 inference('cnf.neg', [status(esa)], [prove_segments_property5_3])).
% 31.67/5.19 thf(zip_derived_cl160, plain, ( (member @ z @ universal_class)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_1])).
% 31.67/5.19 thf(zip_derived_cl159, plain, ( (member @ u @ y)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_0])).
% 31.67/5.19 thf(class_elements_are_sets, axiom, (subclass @ X @ universal_class)).
% 31.67/5.19 thf(zip_derived_cl3, plain, (![X0 : $i]: (subclass @ X0 @ universal_class)),
% 31.67/5.19 inference('cnf', [status(esa)], [class_elements_are_sets])).
% 31.67/5.19 thf(subclass_members, axiom,
% 31.67/5.19 (( ~( subclass @ X @ Y ) ) | ( ~( member @ U @ X ) ) | ( member @ U @ Y ))).
% 31.67/5.19 thf(zip_derived_cl0, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 (~ (subclass @ X0 @ X1) | ~ (member @ X2 @ X0) | (member @ X2 @ X1))),
% 31.67/5.19 inference('cnf', [status(esa)], [subclass_members])).
% 31.67/5.19 thf(zip_derived_cl751, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 31.67/5.19 thf(zip_derived_cl755, plain, ( (member @ u @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl15, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ X0 @ X1)
% 31.67/5.19 | ~ (member @ X2 @ X3)
% 31.67/5.19 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 31.67/5.19 inference('cnf', [status(esa)], [cartesian_product3])).
% 31.67/5.19 thf(cartesian_product4, axiom,
% 31.67/5.19 (( ~( member @ Z @ ( cross_product @ X @ Y ) ) ) |
% 31.67/5.19 ( ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) = ( Z ) ))).
% 31.67/5.19 thf(zip_derived_cl16, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 (~ (member @ X0 @ (cross_product @ X1 @ X2))
% 31.67/5.19 | ((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0)))),
% 31.67/5.19 inference('cnf', [status(esa)], [cartesian_product4])).
% 31.67/5.19 thf(zip_derived_cl816, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ X2 @ X0)
% 31.67/5.19 | ~ (member @ X3 @ X1)
% 31.67/5.19 | ((ordered_pair @ (first @ (ordered_pair @ X3 @ X2)) @
% 31.67/5.19 (second @ (ordered_pair @ X3 @ X2))) = (ordered_pair @ X3 @ X2)))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl16])).
% 31.67/5.19 thf(zip_derived_cl1929, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X1 @ X0)
% 31.67/5.19 | ((ordered_pair @ (first @ (ordered_pair @ X1 @ u)) @
% 31.67/5.19 (second @ (ordered_pair @ X1 @ u))) = (ordered_pair @ X1 @ u)))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl755, zip_derived_cl816])).
% 31.67/5.19 thf(zip_derived_cl2057, plain,
% 31.67/5.19 (((ordered_pair @ (first @ (ordered_pair @ z @ u)) @
% 31.67/5.19 (second @ (ordered_pair @ z @ u))) = (ordered_pair @ z @ u))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl160, zip_derived_cl1929])).
% 31.67/5.19 thf(cartesian_product1, axiom,
% 31.67/5.19 (( ~( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) |
% 31.67/5.19 ( member @ U @ X ))).
% 31.67/5.19 thf(zip_derived_cl13, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 31.67/5.19 | (member @ X0 @ X2))),
% 31.67/5.19 inference('cnf', [status(esa)], [cartesian_product1])).
% 31.67/5.19 thf(zip_derived_cl2208, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ (ordered_pair @ z @ u) @ (cross_product @ X1 @ X0))
% 31.67/5.19 | (member @ (first @ (ordered_pair @ z @ u)) @ X1))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl2057, zip_derived_cl13])).
% 31.67/5.19 thf(zip_derived_cl8073, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ u @ X0)
% 31.67/5.19 | ~ (member @ z @ X1)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ z @ u)) @ X1))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl2208])).
% 31.67/5.19 thf(zip_derived_cl8087, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 ( (member @ u @ X0)
% 31.67/5.19 | ~ (member @ u @ universal_class)
% 31.67/5.19 | ~ (member @ z @ X1)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ z @ u)) @ X1))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl8073])).
% 31.67/5.19 thf(zip_derived_cl755, plain, ( (member @ u @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl8098, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 ( (member @ u @ X0)
% 31.67/5.19 | ~ (member @ z @ X1)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ z @ u)) @ X1))),
% 31.67/5.19 inference('demod', [status(thm)], [zip_derived_cl8087, zip_derived_cl755])).
% 31.67/5.19 thf(zip_derived_cl8073, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ u @ X0)
% 31.67/5.19 | ~ (member @ z @ X1)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ z @ u)) @ X1))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl2208])).
% 31.67/5.19 thf(zip_derived_cl8645, plain,
% 31.67/5.19 (![X1 : $i]:
% 31.67/5.19 ( (member @ (first @ (ordered_pair @ z @ u)) @ X1)
% 31.67/5.19 | ~ (member @ z @ X1))),
% 31.67/5.19 inference('clc', [status(thm)], [zip_derived_cl8098, zip_derived_cl8073])).
% 31.67/5.19 thf(complement1, axiom,
% 31.67/5.19 (( ~( member @ Z @ ( complement @ X ) ) ) | ( ~( member @ Z @ X ) ))).
% 31.67/5.19 thf(zip_derived_cl23, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 31.67/5.19 inference('cnf', [status(esa)], [complement1])).
% 31.67/5.19 thf(zip_derived_cl8682, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ z @ (complement @ X0))
% 31.67/5.19 | ~ (member @ (first @ (ordered_pair @ z @ u)) @ X0))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl8645, zip_derived_cl23])).
% 31.67/5.19 thf(zip_derived_cl8821, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 ( (member @ z @ X0)
% 31.67/5.19 | ~ (member @ z @ universal_class)
% 31.67/5.19 | ~ (member @ (first @ (ordered_pair @ z @ u)) @ X0))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl8682])).
% 31.67/5.19 thf(zip_derived_cl160, plain, ( (member @ z @ universal_class)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_1])).
% 31.67/5.19 thf(zip_derived_cl8826, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 ( (member @ z @ X0)
% 31.67/5.19 | ~ (member @ (first @ (ordered_pair @ z @ u)) @ X0))),
% 31.67/5.19 inference('demod', [status(thm)], [zip_derived_cl8821, zip_derived_cl160])).
% 31.67/5.19 thf(zip_derived_cl8848, plain,
% 31.67/5.19 ((~ (member @ (first @ (ordered_pair @ z @ u)) @ universal_class)
% 31.67/5.19 | (member @ z @ (singleton @ (first @ (ordered_pair @ z @ u)))))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl779, zip_derived_cl8826])).
% 31.67/5.19 thf(zip_derived_cl160, plain, ( (member @ z @ universal_class)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_1])).
% 31.67/5.19 thf(zip_derived_cl8645, plain,
% 31.67/5.19 (![X1 : $i]:
% 31.67/5.19 ( (member @ (first @ (ordered_pair @ z @ u)) @ X1)
% 31.67/5.19 | ~ (member @ z @ X1))),
% 31.67/5.19 inference('clc', [status(thm)], [zip_derived_cl8098, zip_derived_cl8073])).
% 31.67/5.19 thf(zip_derived_cl751, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 31.67/5.19 thf(zip_derived_cl8647, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ z @ X0)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ z @ u)) @ universal_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl8645, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl8777, plain,
% 31.67/5.19 ( (member @ (first @ (ordered_pair @ z @ u)) @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl160, zip_derived_cl8647])).
% 31.67/5.19 thf(zip_derived_cl8869, plain,
% 31.67/5.19 ( (member @ z @ (singleton @ (first @ (ordered_pair @ z @ u))))),
% 31.67/5.19 inference('demod', [status(thm)],
% 31.67/5.19 [zip_derived_cl8848, zip_derived_cl8777])).
% 31.67/5.19 thf(zip_derived_cl779, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class) | (member @ X0 @ (singleton @ X0)))),
% 31.67/5.19 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 31.67/5.19 thf(zip_derived_cl8645, plain,
% 31.67/5.19 (![X1 : $i]:
% 31.67/5.19 ( (member @ (first @ (ordered_pair @ z @ u)) @ X1)
% 31.67/5.19 | ~ (member @ z @ X1))),
% 31.67/5.19 inference('clc', [status(thm)], [zip_derived_cl8098, zip_derived_cl8073])).
% 31.67/5.19 thf(zip_derived_cl11, plain,
% 31.67/5.19 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 31.67/5.19 inference('cnf', [status(esa)], [singleton_set])).
% 31.67/5.19 thf(unordered_pair_member, axiom,
% 31.67/5.19 (( ~( member @ U @ ( unordered_pair @ X @ Y ) ) ) | ( ( U ) = ( X ) ) |
% 31.67/5.19 ( ( U ) = ( Y ) ))).
% 31.67/5.19 thf(zip_derived_cl7, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 31.67/5.19 | ((X0) = (X1))
% 31.67/5.19 | ((X0) = (X2)))),
% 31.67/5.19 inference('cnf', [status(esa)], [unordered_pair_member])).
% 31.67/5.19 thf(zip_derived_cl774, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X1 @ (singleton @ X0)) | ((X1) = (X0)) | ((X1) = (X0)))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl7])).
% 31.67/5.19 thf(zip_derived_cl775, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 31.67/5.19 inference('simplify', [status(thm)], [zip_derived_cl774])).
% 31.67/5.19 thf(zip_derived_cl8672, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ z @ (singleton @ X0))
% 31.67/5.19 | ((first @ (ordered_pair @ z @ u)) = (X0)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl8645, zip_derived_cl775])).
% 31.67/5.19 thf(zip_derived_cl8888, plain,
% 31.67/5.19 ((~ (member @ z @ universal_class)
% 31.67/5.19 | ((first @ (ordered_pair @ z @ u)) = (z)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl779, zip_derived_cl8672])).
% 31.67/5.19 thf(zip_derived_cl160, plain, ( (member @ z @ universal_class)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_1])).
% 31.67/5.19 thf(zip_derived_cl8895, plain, (((first @ (ordered_pair @ z @ u)) = (z))),
% 31.67/5.19 inference('demod', [status(thm)], [zip_derived_cl8888, zip_derived_cl160])).
% 31.67/5.19 thf(zip_derived_cl9079, plain, ( (member @ z @ (singleton @ z))),
% 31.67/5.19 inference('demod', [status(thm)],
% 31.67/5.19 [zip_derived_cl8869, zip_derived_cl8895])).
% 31.67/5.19 thf(zip_derived_cl15, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ X0 @ X1)
% 31.67/5.19 | ~ (member @ X2 @ X3)
% 31.67/5.19 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 31.67/5.19 inference('cnf', [status(esa)], [cartesian_product3])).
% 31.67/5.19 thf(prove_segments_property5_1, conjecture,
% 31.67/5.19 (~( member @ ( ordered_pair @ u @ z ) @ xr ))).
% 31.67/5.19 thf(zf_stmt_2, negated_conjecture, (member @ ( ordered_pair @ u @ z ) @ xr),
% 31.67/5.19 inference('cnf.neg', [status(esa)], [prove_segments_property5_1])).
% 31.67/5.19 thf(zip_derived_cl158, plain, ( (member @ (ordered_pair @ u @ z) @ xr)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_2])).
% 31.67/5.19 thf(intersection3, axiom,
% 31.67/5.19 (( ~( member @ Z @ X ) ) | ( ~( member @ Z @ Y ) ) |
% 31.67/5.19 ( member @ Z @ ( intersection @ X @ Y ) ))).
% 31.67/5.19 thf(zip_derived_cl22, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 (~ (member @ X0 @ X1)
% 31.67/5.19 | ~ (member @ X0 @ X2)
% 31.67/5.19 | (member @ X0 @ (intersection @ X1 @ X2)))),
% 31.67/5.19 inference('cnf', [status(esa)], [intersection3])).
% 31.67/5.19 thf(zip_derived_cl779, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class) | (member @ X0 @ (singleton @ X0)))),
% 31.67/5.19 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 31.67/5.19 thf(zip_derived_cl24, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class)
% 31.67/5.19 | (member @ X0 @ (complement @ X1))
% 31.67/5.19 | (member @ X0 @ X1))),
% 31.67/5.19 inference('cnf', [status(esa)], [complement2])).
% 31.67/5.19 thf(zip_derived_cl24, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class)
% 31.67/5.19 | (member @ X0 @ (complement @ X1))
% 31.67/5.19 | (member @ X0 @ X1))),
% 31.67/5.19 inference('cnf', [status(esa)], [complement2])).
% 31.67/5.19 thf(zip_derived_cl15, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ X0 @ X1)
% 31.67/5.19 | ~ (member @ X2 @ X3)
% 31.67/5.19 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 31.67/5.19 inference('cnf', [status(esa)], [cartesian_product3])).
% 31.67/5.19 thf(zip_derived_cl755, plain, ( (member @ u @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl160, plain, ( (member @ z @ universal_class)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_1])).
% 31.67/5.19 thf(zip_derived_cl816, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ X2 @ X0)
% 31.67/5.19 | ~ (member @ X3 @ X1)
% 31.67/5.19 | ((ordered_pair @ (first @ (ordered_pair @ X3 @ X2)) @
% 31.67/5.19 (second @ (ordered_pair @ X3 @ X2))) = (ordered_pair @ X3 @ X2)))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl16])).
% 31.67/5.19 thf(zip_derived_cl1931, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X1 @ X0)
% 31.67/5.19 | ((ordered_pair @ (first @ (ordered_pair @ X1 @ z)) @
% 31.67/5.19 (second @ (ordered_pair @ X1 @ z))) = (ordered_pair @ X1 @ z)))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl160, zip_derived_cl816])).
% 31.67/5.19 thf(zip_derived_cl2166, plain,
% 31.67/5.19 (((ordered_pair @ (first @ (ordered_pair @ u @ z)) @
% 31.67/5.19 (second @ (ordered_pair @ u @ z))) = (ordered_pair @ u @ z))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl755, zip_derived_cl1931])).
% 31.67/5.19 thf(zip_derived_cl13, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 31.67/5.19 | (member @ X0 @ X2))),
% 31.67/5.19 inference('cnf', [status(esa)], [cartesian_product1])).
% 31.67/5.19 thf(zip_derived_cl2388, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ (ordered_pair @ u @ z) @ (cross_product @ X1 @ X0))
% 31.67/5.19 | (member @ (first @ (ordered_pair @ u @ z)) @ X1))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl2166, zip_derived_cl13])).
% 31.67/5.19 thf(zip_derived_cl3804, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ z @ X0)
% 31.67/5.19 | ~ (member @ u @ X1)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ u @ z)) @ X1))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl2388])).
% 31.67/5.19 thf(zip_derived_cl3819, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 ( (member @ z @ X0)
% 31.67/5.19 | ~ (member @ z @ universal_class)
% 31.67/5.19 | ~ (member @ u @ X1)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ u @ z)) @ X1))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl3804])).
% 31.67/5.19 thf(zip_derived_cl160, plain, ( (member @ z @ universal_class)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_1])).
% 31.67/5.19 thf(zip_derived_cl3828, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 ( (member @ z @ X0)
% 31.67/5.19 | ~ (member @ u @ X1)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ u @ z)) @ X1))),
% 31.67/5.19 inference('demod', [status(thm)], [zip_derived_cl3819, zip_derived_cl160])).
% 31.67/5.19 thf(zip_derived_cl3804, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ z @ X0)
% 31.67/5.19 | ~ (member @ u @ X1)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ u @ z)) @ X1))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl2388])).
% 31.67/5.19 thf(zip_derived_cl3830, plain,
% 31.67/5.19 (![X1 : $i]:
% 31.67/5.19 ( (member @ (first @ (ordered_pair @ u @ z)) @ X1)
% 31.67/5.19 | ~ (member @ u @ X1))),
% 31.67/5.19 inference('clc', [status(thm)], [zip_derived_cl3828, zip_derived_cl3804])).
% 31.67/5.19 thf(zip_derived_cl23, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 31.67/5.19 inference('cnf', [status(esa)], [complement1])).
% 31.67/5.19 thf(zip_derived_cl3847, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ u @ (complement @ X0))
% 31.67/5.19 | ~ (member @ (first @ (ordered_pair @ u @ z)) @ X0))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl3830, zip_derived_cl23])).
% 31.67/5.19 thf(zip_derived_cl3917, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 ( (member @ u @ X0)
% 31.67/5.19 | ~ (member @ u @ universal_class)
% 31.67/5.19 | ~ (member @ (first @ (ordered_pair @ u @ z)) @ X0))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl3847])).
% 31.67/5.19 thf(zip_derived_cl755, plain, ( (member @ u @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl3922, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 ( (member @ u @ X0)
% 31.67/5.19 | ~ (member @ (first @ (ordered_pair @ u @ z)) @ X0))),
% 31.67/5.19 inference('demod', [status(thm)], [zip_derived_cl3917, zip_derived_cl755])).
% 31.67/5.19 thf(zip_derived_cl3938, plain,
% 31.67/5.19 ((~ (member @ (first @ (ordered_pair @ u @ z)) @ universal_class)
% 31.67/5.19 | (member @ u @ (singleton @ (first @ (ordered_pair @ u @ z)))))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl779, zip_derived_cl3922])).
% 31.67/5.19 thf(zip_derived_cl755, plain, ( (member @ u @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl3830, plain,
% 31.67/5.19 (![X1 : $i]:
% 31.67/5.19 ( (member @ (first @ (ordered_pair @ u @ z)) @ X1)
% 31.67/5.19 | ~ (member @ u @ X1))),
% 31.67/5.19 inference('clc', [status(thm)], [zip_derived_cl3828, zip_derived_cl3804])).
% 31.67/5.19 thf(zip_derived_cl751, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 31.67/5.19 thf(zip_derived_cl3832, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ u @ X0)
% 31.67/5.19 | (member @ (first @ (ordered_pair @ u @ z)) @ universal_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl3830, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl3903, plain,
% 31.67/5.19 ( (member @ (first @ (ordered_pair @ u @ z)) @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl755, zip_derived_cl3832])).
% 31.67/5.19 thf(zip_derived_cl3957, plain,
% 31.67/5.19 ( (member @ u @ (singleton @ (first @ (ordered_pair @ u @ z))))),
% 31.67/5.19 inference('demod', [status(thm)],
% 31.67/5.19 [zip_derived_cl3938, zip_derived_cl3903])).
% 31.67/5.19 thf(zip_derived_cl779, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class) | (member @ X0 @ (singleton @ X0)))),
% 31.67/5.19 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 31.67/5.19 thf(zip_derived_cl3830, plain,
% 31.67/5.19 (![X1 : $i]:
% 31.67/5.19 ( (member @ (first @ (ordered_pair @ u @ z)) @ X1)
% 31.67/5.19 | ~ (member @ u @ X1))),
% 31.67/5.19 inference('clc', [status(thm)], [zip_derived_cl3828, zip_derived_cl3804])).
% 31.67/5.19 thf(zip_derived_cl775, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 31.67/5.19 inference('simplify', [status(thm)], [zip_derived_cl774])).
% 31.67/5.19 thf(zip_derived_cl3840, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ u @ (singleton @ X0))
% 31.67/5.19 | ((first @ (ordered_pair @ u @ z)) = (X0)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl3830, zip_derived_cl775])).
% 31.67/5.19 thf(zip_derived_cl3925, plain,
% 31.67/5.19 ((~ (member @ u @ universal_class)
% 31.67/5.19 | ((first @ (ordered_pair @ u @ z)) = (u)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl779, zip_derived_cl3840])).
% 31.67/5.19 thf(zip_derived_cl755, plain, ( (member @ u @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl3933, plain, (((first @ (ordered_pair @ u @ z)) = (u))),
% 31.67/5.19 inference('demod', [status(thm)], [zip_derived_cl3925, zip_derived_cl755])).
% 31.67/5.19 thf(zip_derived_cl4068, plain, ( (member @ u @ (singleton @ u))),
% 31.67/5.19 inference('demod', [status(thm)],
% 31.67/5.19 [zip_derived_cl3957, zip_derived_cl3933])).
% 31.67/5.19 thf(zip_derived_cl160, plain, ( (member @ z @ universal_class)),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_1])).
% 31.67/5.19 thf(zip_derived_cl15, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ X0 @ X1)
% 31.67/5.19 | ~ (member @ X2 @ X3)
% 31.67/5.19 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 31.67/5.19 inference('cnf', [status(esa)], [cartesian_product3])).
% 31.67/5.19 thf(zip_derived_cl755, plain, ( (member @ u @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl30, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class)
% 31.67/5.19 | ((restrict @ X1 @ (singleton @ X0) @ universal_class)
% 31.67/5.19 = (null_class))
% 31.67/5.19 | (member @ X0 @ (domain_of @ X1)))),
% 31.67/5.19 inference('cnf', [status(esa)], [domain2])).
% 31.67/5.19 thf(restriction1, axiom,
% 31.67/5.19 (( intersection @ Xr @ ( cross_product @ X @ Y ) ) =
% 31.67/5.19 ( restrict @ Xr @ X @ Y ))).
% 31.67/5.19 thf(zip_derived_cl27, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 ((intersection @ X0 @ (cross_product @ X1 @ X2))
% 31.67/5.19 = (restrict @ X0 @ X1 @ X2))),
% 31.67/5.19 inference('cnf', [status(esa)], [restriction1])).
% 31.67/5.19 thf(zip_derived_cl22, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 (~ (member @ X0 @ X1)
% 31.67/5.19 | ~ (member @ X0 @ X2)
% 31.67/5.19 | (member @ X0 @ (intersection @ X1 @ X2)))),
% 31.67/5.19 inference('cnf', [status(esa)], [intersection3])).
% 31.67/5.19 thf(zip_derived_cl895, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.67/5.19 (~ (member @ X3 @ X2)
% 31.67/5.19 | ~ (member @ X3 @ (cross_product @ X1 @ X0))
% 31.67/5.19 | (member @ X3 @ (restrict @ X2 @ X1 @ X0)))),
% 31.67/5.19 inference('s_sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl22])).
% 31.67/5.19 thf(zip_derived_cl12047, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 ( (member @ X0 @ (domain_of @ X1))
% 31.67/5.19 | ~ (member @ X0 @ universal_class)
% 31.67/5.19 | ~ (member @ X2 @ X1)
% 31.67/5.19 | ~ (member @ X2 @
% 31.67/5.19 (cross_product @ (singleton @ X0) @ universal_class))
% 31.67/5.19 | (member @ X2 @ null_class))),
% 31.67/5.19 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl895])).
% 31.67/5.19 thf(regularity1, axiom,
% 31.67/5.19 (( ( X ) = ( null_class ) ) | ( member @ ( regular @ X ) @ X ))).
% 31.67/5.19 thf(zip_derived_cl65, plain,
% 31.67/5.19 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 31.67/5.19 inference('cnf', [status(esa)], [regularity1])).
% 31.67/5.19 thf(zip_derived_cl751, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 31.67/5.19 thf(zip_derived_cl932, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl65, plain,
% 31.67/5.19 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 31.67/5.19 inference('cnf', [status(esa)], [regularity1])).
% 31.67/5.19 thf(zip_derived_cl23, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 31.67/5.19 inference('cnf', [status(esa)], [complement1])).
% 31.67/5.19 thf(zip_derived_cl938, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (((complement @ X0) = (null_class))
% 31.67/5.19 | ~ (member @ (regular @ (complement @ X0)) @ X0))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl23])).
% 31.67/5.19 thf(zip_derived_cl983, plain,
% 31.67/5.19 ((((complement @ universal_class) = (null_class))
% 31.67/5.19 | ((complement @ universal_class) = (null_class)))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl932, zip_derived_cl938])).
% 31.67/5.19 thf(zip_derived_cl985, plain,
% 31.67/5.19 (((complement @ universal_class) = (null_class))),
% 31.67/5.19 inference('simplify', [status(thm)], [zip_derived_cl983])).
% 31.67/5.19 thf(zip_derived_cl23, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 31.67/5.19 inference('cnf', [status(esa)], [complement1])).
% 31.67/5.19 thf(zip_derived_cl986, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ X0 @ null_class) | ~ (member @ X0 @ universal_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl985, zip_derived_cl23])).
% 31.67/5.19 thf(zip_derived_cl751, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 31.67/5.19 thf(zip_derived_cl991, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 31.67/5.19 inference('clc', [status(thm)], [zip_derived_cl986, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl12051, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 ( (member @ X0 @ (domain_of @ X1))
% 31.67/5.19 | ~ (member @ X0 @ universal_class)
% 31.67/5.19 | ~ (member @ X2 @ X1)
% 31.67/5.19 | ~ (member @ X2 @
% 31.67/5.19 (cross_product @ (singleton @ X0) @ universal_class)))),
% 31.67/5.19 inference('demod', [status(thm)],
% 31.67/5.19 [zip_derived_cl12047, zip_derived_cl991])).
% 31.67/5.19 thf(zip_derived_cl12158, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 ( (member @ u @ (domain_of @ X0))
% 31.67/5.19 | ~ (member @ X1 @ X0)
% 31.67/5.19 | ~ (member @ X1 @
% 31.67/5.19 (cross_product @ (singleton @ u) @ universal_class)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl755, zip_derived_cl12051])).
% 31.67/5.19 thf(zip_derived_cl13770, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 (~ (member @ X0 @ universal_class)
% 31.67/5.19 | ~ (member @ X1 @ (singleton @ u))
% 31.67/5.19 | (member @ u @ (domain_of @ X2))
% 31.67/5.19 | ~ (member @ (ordered_pair @ X1 @ X0) @ X2))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl15, zip_derived_cl12158])).
% 31.67/5.19 thf(zip_derived_cl14041, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ X0 @ (singleton @ u))
% 31.67/5.19 | (member @ u @ (domain_of @ X1))
% 31.67/5.19 | ~ (member @ (ordered_pair @ X0 @ z) @ X1))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl160, zip_derived_cl13770])).
% 31.67/5.19 thf(zip_derived_cl14179, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 ( (member @ u @ (domain_of @ X0))
% 31.67/5.19 | ~ (member @ (ordered_pair @ u @ z) @ X0))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl4068, zip_derived_cl14041])).
% 31.67/5.19 thf(domain1, axiom,
% 31.67/5.19 (( ( restrict @ X @ ( singleton @ Z ) @ universal_class ) != ( null_class ) ) |
% 31.67/5.19 ( ~( member @ Z @ ( domain_of @ X ) ) ))).
% 31.67/5.19 thf(zip_derived_cl29, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (((restrict @ X0 @ (singleton @ X1) @ universal_class) != (null_class))
% 31.67/5.19 | ~ (member @ X1 @ (domain_of @ X0)))),
% 31.67/5.19 inference('cnf', [status(esa)], [domain1])).
% 31.67/5.19 thf(zip_derived_cl14273, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ (ordered_pair @ u @ z) @ X0)
% 31.67/5.19 | ((restrict @ X0 @ (singleton @ u) @ universal_class)
% 31.67/5.19 != (null_class)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl14179, zip_derived_cl29])).
% 31.67/5.19 thf(zip_derived_cl14295, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ (ordered_pair @ u @ z) @ X0)
% 31.67/5.19 | ~ (member @ (ordered_pair @ u @ z) @ X1)
% 31.67/5.19 | ((restrict @ (intersection @ X1 @ X0) @ (singleton @ u) @
% 31.67/5.19 universal_class) != (null_class)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl22, zip_derived_cl14273])).
% 31.67/5.19 thf(zip_derived_cl14889, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ (ordered_pair @ u @ z) @ X0)
% 31.67/5.19 | ((restrict @ (intersection @ X0 @ xr) @ (singleton @ u) @
% 31.67/5.19 universal_class) != (null_class)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl158, zip_derived_cl14295])).
% 31.67/5.19 thf(zip_derived_cl15516, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ z @ X0)
% 31.67/5.19 | ~ (member @ u @ X1)
% 31.67/5.19 | ((restrict @ (intersection @ (cross_product @ X1 @ X0) @ xr) @
% 31.67/5.19 (singleton @ u) @ universal_class) != (null_class)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl15, zip_derived_cl14889])).
% 31.67/5.19 thf(restriction2, axiom,
% 31.67/5.19 (( intersection @ ( cross_product @ X @ Y ) @ Xr ) =
% 31.67/5.19 ( restrict @ Xr @ X @ Y ))).
% 31.67/5.19 thf(zip_derived_cl28, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 ((intersection @ (cross_product @ X1 @ X2) @ X0)
% 31.67/5.19 = (restrict @ X0 @ X1 @ X2))),
% 31.67/5.19 inference('cnf', [status(esa)], [restriction2])).
% 31.67/5.19 thf(zip_derived_cl15533, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i]:
% 31.67/5.19 (~ (member @ z @ X0)
% 31.67/5.19 | ~ (member @ u @ X1)
% 31.67/5.19 | ((restrict @ (restrict @ xr @ X1 @ X0) @ (singleton @ u) @
% 31.67/5.19 universal_class) != (null_class)))),
% 31.67/5.19 inference('demod', [status(thm)], [zip_derived_cl15516, zip_derived_cl28])).
% 31.67/5.19 thf(zip_derived_cl16419, plain,
% 31.67/5.19 (![X0 : $i]:
% 31.67/5.19 (~ (member @ u @ X0)
% 31.67/5.19 | ((restrict @ (restrict @ xr @ X0 @ (singleton @ z)) @
% 31.67/5.19 (singleton @ u) @ universal_class) != (null_class)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl9079, zip_derived_cl15533])).
% 31.67/5.19 thf(zip_derived_cl18369, plain,
% 31.67/5.19 (((restrict @ (restrict @ xr @ y @ (singleton @ z)) @ (singleton @ u) @
% 31.67/5.19 universal_class) != (null_class))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl159, zip_derived_cl16419])).
% 31.67/5.19 thf(zip_derived_cl21069, plain,
% 31.67/5.19 (( (member @ u @ (domain_of @ (restrict @ xr @ y @ (singleton @ z))))
% 31.67/5.19 | ~ (member @ u @ universal_class)
% 31.67/5.19 | ((null_class) != (null_class)))),
% 31.67/5.19 inference('s_sup-', [status(thm)],
% 31.67/5.19 [zip_derived_cl30, zip_derived_cl18369])).
% 31.67/5.19 thf(segment, axiom,
% 31.67/5.19 (( segment @ Xr @ Y @ Z ) =
% 31.67/5.19 ( domain_of @ ( restrict @ Xr @ Y @ ( singleton @ Z ) ) ))).
% 31.67/5.19 thf(zip_derived_cl121, plain,
% 31.67/5.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.67/5.19 ((segment @ X0 @ X1 @ X2)
% 31.67/5.19 = (domain_of @ (restrict @ X0 @ X1 @ (singleton @ X2))))),
% 31.67/5.19 inference('cnf', [status(esa)], [segment])).
% 31.67/5.19 thf(prove_segments_property5_4, conjecture,
% 31.67/5.19 (member @ u @ ( segment @ xr @ y @ z ))).
% 31.67/5.19 thf(zf_stmt_3, negated_conjecture,
% 31.67/5.19 (~( member @ u @ ( segment @ xr @ y @ z ) )),
% 31.67/5.19 inference('cnf.neg', [status(esa)], [prove_segments_property5_4])).
% 31.67/5.19 thf(zip_derived_cl161, plain, (~ (member @ u @ (segment @ xr @ y @ z))),
% 31.67/5.19 inference('cnf', [status(esa)], [zf_stmt_3])).
% 31.67/5.19 thf(zip_derived_cl755, plain, ( (member @ u @ universal_class)),
% 31.67/5.19 inference('s_sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl751])).
% 31.67/5.19 thf(zip_derived_cl21072, plain, (((null_class) != (null_class))),
% 31.67/5.19 inference('demod', [status(thm)],
% 31.67/5.19 [zip_derived_cl21069, zip_derived_cl121, zip_derived_cl161,
% 31.67/5.19 zip_derived_cl755])).
% 31.67/5.19 thf(zip_derived_cl21073, plain, ($false),
% 31.67/5.19 inference('simplify', [status(thm)], [zip_derived_cl21072])).
% 31.67/5.19
% 31.67/5.19 % SZS output end Refutation
% 31.67/5.19
% 31.67/5.19
% 31.67/5.19 % Terminating...
% 32.32/5.29 % Runner terminated.
% 32.32/5.31 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------