%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM060-1 : TPTP v9.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.mnvtZazM01 true
% Computer : n010.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 Oct 2 04:45:50 PM UTC 2025
% Result : Unsatisfiable 142.92s 21.07s
% Output : Refutation 142.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : NUM060-1 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.11/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.mnvtZazM01 true
% 0.13/0.37 % Computer : n010.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Wed Oct 1 16:42:08 EDT 2025
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Running portfolio for 300 s
% 0.13/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % Number of cores: 8
% 0.13/0.37 % Python version: Python 3.6.8
% 0.13/0.37 % Running in FO mode
% 0.53/0.65 % Total configuration time : 435
% 0.53/0.65 % Estimated wc time : 1092
% 0.53/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 142.92/21.07 % Solved by fo/fo6_bce.sh.
% 142.92/21.07 % BCE start: 160
% 142.92/21.07 % BCE eliminated: 3
% 142.92/21.07 % PE start: 157
% 142.92/21.07 logic: eq
% 142.92/21.07 % PE eliminated: 27
% 142.92/21.07 % done 8664 iterations in 20.330s
% 142.92/21.07 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 142.92/21.07 % SZS output start Refutation
% 142.92/21.07 thf(universal_class_type, type, universal_class: $i).
% 142.92/21.07 thf(null_class_type, type, null_class: $i).
% 142.92/21.07 thf(domain_of_type, type, domain_of: $i > $i).
% 142.92/21.07 thf(member_type, type, member: $i > $i > $o).
% 142.92/21.07 thf(z_type, type, z: $i).
% 142.92/21.07 thf(second_type, type, second: $i > $i).
% 142.92/21.07 thf(unordered_pair_type, type, unordered_pair: $i > $i > $i).
% 142.92/21.07 thf(complement_type, type, complement: $i > $i).
% 142.92/21.07 thf(segment_type, type, segment: $i > $i > $i > $i).
% 142.92/21.07 thf(xr_type, type, xr: $i).
% 142.92/21.07 thf(singleton_type, type, singleton: $i > $i).
% 142.92/21.07 thf(u_type, type, u: $i).
% 142.92/21.07 thf(intersection_type, type, intersection: $i > $i > $i).
% 142.92/21.07 thf(flip_type, type, flip: $i > $i).
% 142.92/21.07 thf(rotate_type, type, rotate: $i > $i).
% 142.92/21.07 thf(subclass_type, type, subclass: $i > $i > $o).
% 142.92/21.07 thf(restrict_type, type, restrict: $i > $i > $i > $i).
% 142.92/21.07 thf(cross_product_type, type, cross_product: $i > $i > $i).
% 142.92/21.07 thf(y_type, type, y: $i).
% 142.92/21.07 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 142.92/21.07 thf(first_type, type, first: $i > $i).
% 142.92/21.07 thf(regular_type, type, regular: $i > $i).
% 142.92/21.07 thf(prove_segments_property4_2, conjecture,
% 142.92/21.07 (member @ u @ ( segment @ xr @ y @ z ))).
% 142.92/21.07 thf(zf_stmt_0, negated_conjecture,
% 142.92/21.07 (~( member @ u @ ( segment @ xr @ y @ z ) )),
% 142.92/21.07 inference('cnf.neg', [status(esa)], [prove_segments_property4_2])).
% 142.92/21.07 thf(zip_derived_cl159, plain, (~ (member @ u @ (segment @ xr @ y @ z))),
% 142.92/21.07 inference('cnf', [status(esa)], [zf_stmt_0])).
% 142.92/21.07 thf(cartesian_product3, axiom,
% 142.92/21.07 (( ~( member @ U @ X ) ) | ( ~( member @ V @ Y ) ) |
% 142.92/21.07 ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ))).
% 142.92/21.07 thf(zip_derived_cl15, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.07 (~ (member @ X0 @ X1)
% 142.92/21.07 | ~ (member @ X2 @ X3)
% 142.92/21.07 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 142.92/21.07 inference('cnf', [status(esa)], [cartesian_product3])).
% 142.92/21.07 thf(complement2, axiom,
% 142.92/21.07 (( ~( member @ Z @ universal_class ) ) |
% 142.92/21.07 ( member @ Z @ ( complement @ X ) ) | ( member @ Z @ X ))).
% 142.92/21.07 thf(zip_derived_cl24, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (~ (member @ X0 @ universal_class)
% 142.92/21.07 | (member @ X0 @ (complement @ X1))
% 142.92/21.07 | (member @ X0 @ X1))),
% 142.92/21.07 inference('cnf', [status(esa)], [complement2])).
% 142.92/21.07 thf(prove_segments_property4_1, conjecture,
% 142.92/21.07 (~( member @
% 142.92/21.07 ( ordered_pair @ u @ z ) @
% 142.92/21.07 ( intersection @ xr @ ( cross_product @ y @ universal_class ) ) ))).
% 142.92/21.07 thf(zf_stmt_1, negated_conjecture,
% 142.92/21.07 (member @
% 142.92/21.07 ( ordered_pair @ u @ z ) @
% 142.92/21.07 ( intersection @ xr @ ( cross_product @ y @ universal_class ) )),
% 142.92/21.07 inference('cnf.neg', [status(esa)], [prove_segments_property4_1])).
% 142.92/21.07 thf(zip_derived_cl158, plain,
% 142.92/21.07 ( (member @ (ordered_pair @ u @ z) @
% 142.92/21.07 (intersection @ xr @ (cross_product @ y @ universal_class)))),
% 142.92/21.07 inference('cnf', [status(esa)], [zf_stmt_1])).
% 142.92/21.07 thf(intersection2, axiom,
% 142.92/21.07 (( ~( member @ Z @ ( intersection @ X @ Y ) ) ) | ( member @ Z @ Y ))).
% 142.92/21.07 thf(zip_derived_cl21, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.07 (~ (member @ X0 @ (intersection @ X1 @ X2)) | (member @ X0 @ X2))),
% 142.92/21.07 inference('cnf', [status(esa)], [intersection2])).
% 142.92/21.07 thf(zip_derived_cl845, plain,
% 142.92/21.07 ( (member @ (ordered_pair @ u @ z) @
% 142.92/21.07 (cross_product @ y @ universal_class))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl21])).
% 142.92/21.07 thf(cartesian_product4, axiom,
% 142.92/21.07 (( ~( member @ Z @ ( cross_product @ X @ Y ) ) ) |
% 142.92/21.07 ( ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) = ( Z ) ))).
% 142.92/21.07 thf(zip_derived_cl16, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.07 (~ (member @ X0 @ (cross_product @ X1 @ X2))
% 142.92/21.07 | ((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0)))),
% 142.92/21.07 inference('cnf', [status(esa)], [cartesian_product4])).
% 142.92/21.07 thf(zip_derived_cl850, plain,
% 142.92/21.07 (((ordered_pair @ (first @ (ordered_pair @ u @ z)) @
% 142.92/21.07 (second @ (ordered_pair @ u @ z))) = (ordered_pair @ u @ z))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl845, zip_derived_cl16])).
% 142.92/21.07 thf(singleton_set, axiom, (( unordered_pair @ X @ X ) = ( singleton @ X ))).
% 142.92/21.07 thf(zip_derived_cl11, plain,
% 142.92/21.07 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 142.92/21.07 inference('cnf', [status(esa)], [singleton_set])).
% 142.92/21.07 thf(unordered_pair2, axiom,
% 142.92/21.07 (( ~( member @ X @ universal_class ) ) |
% 142.92/21.07 ( member @ X @ ( unordered_pair @ X @ Y ) ))).
% 142.92/21.07 thf(zip_derived_cl8, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (~ (member @ X0 @ universal_class)
% 142.92/21.07 | (member @ X0 @ (unordered_pair @ X0 @ X1)))),
% 142.92/21.07 inference('cnf', [status(esa)], [unordered_pair2])).
% 142.92/21.07 thf(zip_derived_cl773, plain,
% 142.92/21.07 (![X0 : $i]:
% 142.92/21.07 (~ (member @ X0 @ universal_class) | (member @ X0 @ (singleton @ X0)))),
% 142.92/21.07 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 142.92/21.07 thf(zip_derived_cl845, plain,
% 142.92/21.07 ( (member @ (ordered_pair @ u @ z) @
% 142.92/21.07 (cross_product @ y @ universal_class))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl21])).
% 142.92/21.07 thf(cartesian_product2, axiom,
% 142.92/21.07 (( ~( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) |
% 142.92/21.07 ( member @ V @ Y ))).
% 142.92/21.07 thf(zip_derived_cl14, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.07 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 142.92/21.07 | (member @ X1 @ X3))),
% 142.92/21.07 inference('cnf', [status(esa)], [cartesian_product2])).
% 142.92/21.07 thf(zip_derived_cl852, plain, ( (member @ z @ universal_class)),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl845, zip_derived_cl14])).
% 142.92/21.07 thf(zip_derived_cl15, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.07 (~ (member @ X0 @ X1)
% 142.92/21.07 | ~ (member @ X2 @ X3)
% 142.92/21.07 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 142.92/21.07 inference('cnf', [status(esa)], [cartesian_product3])).
% 142.92/21.07 thf(zip_derived_cl850, plain,
% 142.92/21.07 (((ordered_pair @ (first @ (ordered_pair @ u @ z)) @
% 142.92/21.07 (second @ (ordered_pair @ u @ z))) = (ordered_pair @ u @ z))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl845, zip_derived_cl16])).
% 142.92/21.07 thf(cartesian_product1, axiom,
% 142.92/21.07 (( ~( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) |
% 142.92/21.07 ( member @ U @ X ))).
% 142.92/21.07 thf(zip_derived_cl13, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.07 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 142.92/21.07 | (member @ X0 @ X2))),
% 142.92/21.07 inference('cnf', [status(esa)], [cartesian_product1])).
% 142.92/21.07 thf(zip_derived_cl867, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (~ (member @ (ordered_pair @ u @ z) @ (cross_product @ X1 @ X0))
% 142.92/21.07 | (member @ (first @ (ordered_pair @ u @ z)) @ X1))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl850, zip_derived_cl13])).
% 142.92/21.07 thf(zip_derived_cl1059, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (~ (member @ z @ X0)
% 142.92/21.07 | ~ (member @ u @ X1)
% 142.92/21.07 | (member @ (first @ (ordered_pair @ u @ z)) @ X1))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl867])).
% 142.92/21.07 thf(zip_derived_cl1175, plain,
% 142.92/21.07 (![X0 : $i]:
% 142.92/21.07 (~ (member @ u @ X0)
% 142.92/21.07 | (member @ (first @ (ordered_pair @ u @ z)) @ X0))),
% 142.92/21.07 inference('s_sup-', [status(thm)],
% 142.92/21.07 [zip_derived_cl852, zip_derived_cl1059])).
% 142.92/21.07 thf(zip_derived_cl11, plain,
% 142.92/21.07 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 142.92/21.07 inference('cnf', [status(esa)], [singleton_set])).
% 142.92/21.07 thf(unordered_pair_member, axiom,
% 142.92/21.07 (( ~( member @ U @ ( unordered_pair @ X @ Y ) ) ) | ( ( U ) = ( X ) ) |
% 142.92/21.07 ( ( U ) = ( Y ) ))).
% 142.92/21.07 thf(zip_derived_cl7, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.07 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 142.92/21.07 | ((X0) = (X1))
% 142.92/21.07 | ((X0) = (X2)))),
% 142.92/21.07 inference('cnf', [status(esa)], [unordered_pair_member])).
% 142.92/21.07 thf(zip_derived_cl769, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (~ (member @ X1 @ (singleton @ X0)) | ((X1) = (X0)) | ((X1) = (X0)))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl7])).
% 142.92/21.07 thf(zip_derived_cl770, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 142.92/21.07 inference('simplify', [status(thm)], [zip_derived_cl769])).
% 142.92/21.07 thf(zip_derived_cl1182, plain,
% 142.92/21.07 (![X0 : $i]:
% 142.92/21.07 (~ (member @ u @ (singleton @ X0))
% 142.92/21.07 | ((first @ (ordered_pair @ u @ z)) = (X0)))),
% 142.92/21.07 inference('s_sup-', [status(thm)],
% 142.92/21.07 [zip_derived_cl1175, zip_derived_cl770])).
% 142.92/21.07 thf(zip_derived_cl1226, plain,
% 142.92/21.07 ((~ (member @ u @ universal_class)
% 142.92/21.07 | ((first @ (ordered_pair @ u @ z)) = (u)))),
% 142.92/21.07 inference('s_sup-', [status(thm)],
% 142.92/21.07 [zip_derived_cl773, zip_derived_cl1182])).
% 142.92/21.07 thf(zip_derived_cl845, plain,
% 142.92/21.07 ( (member @ (ordered_pair @ u @ z) @
% 142.92/21.07 (cross_product @ y @ universal_class))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl21])).
% 142.92/21.07 thf(zip_derived_cl13, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.07 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 142.92/21.07 | (member @ X0 @ X2))),
% 142.92/21.07 inference('cnf', [status(esa)], [cartesian_product1])).
% 142.92/21.07 thf(zip_derived_cl851, plain, ( (member @ u @ y)),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl845, zip_derived_cl13])).
% 142.92/21.07 thf(class_elements_are_sets, axiom, (subclass @ X @ universal_class)).
% 142.92/21.07 thf(zip_derived_cl3, plain, (![X0 : $i]: (subclass @ X0 @ universal_class)),
% 142.92/21.07 inference('cnf', [status(esa)], [class_elements_are_sets])).
% 142.92/21.07 thf(subclass_members, axiom,
% 142.92/21.07 (( ~( subclass @ X @ Y ) ) | ( ~( member @ U @ X ) ) | ( member @ U @ Y ))).
% 142.92/21.07 thf(zip_derived_cl0, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.07 (~ (subclass @ X0 @ X1) | ~ (member @ X2 @ X0) | (member @ X2 @ X1))),
% 142.92/21.07 inference('cnf', [status(esa)], [subclass_members])).
% 142.92/21.07 thf(zip_derived_cl744, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 142.92/21.07 thf(zip_derived_cl853, plain, ( (member @ u @ universal_class)),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl851, zip_derived_cl744])).
% 142.92/21.07 thf(zip_derived_cl1227, plain, (((first @ (ordered_pair @ u @ z)) = (u))),
% 142.92/21.07 inference('demod', [status(thm)], [zip_derived_cl1226, zip_derived_cl853])).
% 142.92/21.07 thf(zip_derived_cl1228, plain,
% 142.92/21.07 (((ordered_pair @ u @ (second @ (ordered_pair @ u @ z)))
% 142.92/21.07 = (ordered_pair @ u @ z))),
% 142.92/21.07 inference('demod', [status(thm)], [zip_derived_cl850, zip_derived_cl1227])).
% 142.92/21.07 thf(rotate3, axiom,
% 142.92/21.07 (( ~( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) |
% 142.92/21.07 ( ~( member @
% 142.92/21.07 ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @
% 142.92/21.07 ( cross_product @
% 142.92/21.07 ( cross_product @ universal_class @ universal_class ) @
% 142.92/21.07 universal_class ) ) ) |
% 142.92/21.07 ( member @
% 142.92/21.07 ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ))).
% 142.92/21.07 thf(zip_derived_cl33, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.07 (~ (member @ (ordered_pair @ (ordered_pair @ X0 @ X1) @ X2) @ X3)
% 142.92/21.07 | ~ (member @ (ordered_pair @ (ordered_pair @ X2 @ X0) @ X1) @
% 142.92/21.07 (cross_product @
% 142.92/21.07 (cross_product @ universal_class @ universal_class) @
% 142.92/21.07 universal_class))
% 142.92/21.07 | (member @ (ordered_pair @ (ordered_pair @ X2 @ X0) @ X1) @
% 142.92/21.07 (rotate @ X3)))),
% 142.92/21.07 inference('cnf', [status(esa)], [rotate3])).
% 142.92/21.07 thf(zip_derived_cl1261, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (~ (member @
% 142.92/21.07 (ordered_pair @
% 142.92/21.07 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ X1) @ u) @
% 142.92/21.07 X0)
% 142.92/21.07 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.07 (cross_product @
% 142.92/21.07 (cross_product @ universal_class @ universal_class) @
% 142.92/21.07 universal_class))
% 142.92/21.07 | (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.07 (rotate @ X0)))),
% 142.92/21.07 inference('s_sup+', [status(thm)], [zip_derived_cl1228, zip_derived_cl33])).
% 142.92/21.07 thf(zip_derived_cl1741, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 ( (member @
% 142.92/21.07 (ordered_pair @
% 142.92/21.07 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ X1) @ u) @
% 142.92/21.07 X0)
% 142.92/21.07 | ~ (member @
% 142.92/21.07 (ordered_pair @
% 142.92/21.07 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ X1) @ u) @
% 142.92/21.07 universal_class)
% 142.92/21.07 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.07 (cross_product @
% 142.92/21.07 (cross_product @ universal_class @ universal_class) @
% 142.92/21.07 universal_class))
% 142.92/21.07 | (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.07 (rotate @ (complement @ X0))))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl1261])).
% 142.92/21.07 thf(ordered_pair, axiom,
% 142.92/21.07 (( unordered_pair @
% 142.92/21.07 ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) =
% 142.92/21.07 ( ordered_pair @ X @ Y ))).
% 142.92/21.07 thf(zip_derived_cl12, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 ((unordered_pair @ (singleton @ X0) @
% 142.92/21.07 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 142.92/21.07 inference('cnf', [status(esa)], [ordered_pair])).
% 142.92/21.07 thf(unordered_pairs_in_universal, axiom,
% 142.92/21.07 (member @ ( unordered_pair @ X @ Y ) @ universal_class)).
% 142.92/21.07 thf(zip_derived_cl10, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (member @ (unordered_pair @ X0 @ X1) @ universal_class)),
% 142.92/21.07 inference('cnf', [status(esa)], [unordered_pairs_in_universal])).
% 142.92/21.07 thf(zip_derived_cl788, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (member @ (ordered_pair @ X1 @ X0) @ universal_class)),
% 142.92/21.07 inference('s_sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl10])).
% 142.92/21.07 thf(zip_derived_cl1758, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 ( (member @
% 142.92/21.07 (ordered_pair @
% 142.92/21.07 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ X1) @ u) @
% 142.92/21.07 X0)
% 142.92/21.07 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.07 (cross_product @
% 142.92/21.07 (cross_product @ universal_class @ universal_class) @
% 142.92/21.07 universal_class))
% 142.92/21.07 | (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.07 (rotate @ (complement @ X0))))),
% 142.92/21.07 inference('demod', [status(thm)], [zip_derived_cl1741, zip_derived_cl788])).
% 142.92/21.07 thf(zip_derived_cl853, plain, ( (member @ u @ universal_class)),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl851, zip_derived_cl744])).
% 142.92/21.07 thf(zip_derived_cl773, plain,
% 142.92/21.07 (![X0 : $i]:
% 142.92/21.07 (~ (member @ X0 @ universal_class) | (member @ X0 @ (singleton @ X0)))),
% 142.92/21.07 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 142.92/21.07 thf(zip_derived_cl15, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.07 (~ (member @ X0 @ X1)
% 142.92/21.07 | ~ (member @ X2 @ X3)
% 142.92/21.07 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 142.92/21.07 inference('cnf', [status(esa)], [cartesian_product3])).
% 142.92/21.07 thf(zip_derived_cl1228, plain,
% 142.92/21.07 (((ordered_pair @ u @ (second @ (ordered_pair @ u @ z)))
% 142.92/21.07 = (ordered_pair @ u @ z))),
% 142.92/21.07 inference('demod', [status(thm)], [zip_derived_cl850, zip_derived_cl1227])).
% 142.92/21.07 thf(zip_derived_cl14, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.07 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 142.92/21.07 | (member @ X1 @ X3))),
% 142.92/21.07 inference('cnf', [status(esa)], [cartesian_product2])).
% 142.92/21.07 thf(zip_derived_cl1248, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (~ (member @ (ordered_pair @ u @ z) @ (cross_product @ X1 @ X0))
% 142.92/21.07 | (member @ (second @ (ordered_pair @ u @ z)) @ X0))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl1228, zip_derived_cl14])).
% 142.92/21.07 thf(zip_derived_cl1500, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (~ (member @ z @ X0)
% 142.92/21.07 | ~ (member @ u @ X1)
% 142.92/21.07 | (member @ (second @ (ordered_pair @ u @ z)) @ X0))),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl1248])).
% 142.92/21.07 thf(zip_derived_cl1865, plain,
% 142.92/21.07 (![X0 : $i]:
% 142.92/21.07 (~ (member @ z @ universal_class)
% 142.92/21.07 | ~ (member @ u @ X0)
% 142.92/21.07 | (member @ (second @ (ordered_pair @ u @ z)) @ (singleton @ z)))),
% 142.92/21.07 inference('s_sup-', [status(thm)],
% 142.92/21.07 [zip_derived_cl773, zip_derived_cl1500])).
% 142.92/21.07 thf(zip_derived_cl852, plain, ( (member @ z @ universal_class)),
% 142.92/21.07 inference('s_sup-', [status(thm)], [zip_derived_cl845, zip_derived_cl14])).
% 142.92/21.07 thf(zip_derived_cl1883, plain,
% 142.92/21.07 (![X0 : $i]:
% 142.92/21.07 (~ (member @ u @ X0)
% 142.92/21.07 | (member @ (second @ (ordered_pair @ u @ z)) @ (singleton @ z)))),
% 142.92/21.07 inference('demod', [status(thm)], [zip_derived_cl1865, zip_derived_cl852])).
% 142.92/21.07 thf(zip_derived_cl1957, plain,
% 142.92/21.07 ( (member @ (second @ (ordered_pair @ u @ z)) @ (singleton @ z))),
% 142.92/21.07 inference('s_sup-', [status(thm)],
% 142.92/21.07 [zip_derived_cl853, zip_derived_cl1883])).
% 142.92/21.07 thf(zip_derived_cl770, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 142.92/21.07 inference('simplify', [status(thm)], [zip_derived_cl769])).
% 142.92/21.07 thf(zip_derived_cl1972, plain, (((second @ (ordered_pair @ u @ z)) = (z))),
% 142.92/21.07 inference('s_sup-', [status(thm)],
% 142.92/21.07 [zip_derived_cl1957, zip_derived_cl770])).
% 142.92/21.07 thf(zip_derived_cl2202, plain,
% 142.92/21.07 (![X0 : $i, X1 : $i]:
% 142.92/21.07 ( (member @ (ordered_pair @ (ordered_pair @ z @ X1) @ u) @ X0)
% 142.92/21.07 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.07 (cross_product @
% 142.92/21.07 (cross_product @ universal_class @ universal_class) @
% 142.92/21.07 universal_class))
% 142.92/21.07 | (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.07 (rotate @ (complement @ X0))))),
% 142.92/21.07 inference('demod', [status(thm)],
% 142.92/21.07 [zip_derived_cl1758, zip_derived_cl1972])).
% 142.92/21.08 thf(zip_derived_cl11, plain,
% 142.92/21.08 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 142.92/21.08 inference('cnf', [status(esa)], [singleton_set])).
% 142.92/21.08 thf(zip_derived_cl8, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ universal_class)
% 142.92/21.08 | (member @ X0 @ (unordered_pair @ X0 @ X1)))),
% 142.92/21.08 inference('cnf', [status(esa)], [unordered_pair2])).
% 142.92/21.08 thf(zip_derived_cl851, plain, ( (member @ u @ y)),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl845, zip_derived_cl13])).
% 142.92/21.08 thf(zip_derived_cl1228, plain,
% 142.92/21.08 (((ordered_pair @ u @ (second @ (ordered_pair @ u @ z)))
% 142.92/21.08 = (ordered_pair @ u @ z))),
% 142.92/21.08 inference('demod', [status(thm)], [zip_derived_cl850, zip_derived_cl1227])).
% 142.92/21.08 thf(zip_derived_cl15, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.08 (~ (member @ X0 @ X1)
% 142.92/21.08 | ~ (member @ X2 @ X3)
% 142.92/21.08 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 142.92/21.08 inference('cnf', [status(esa)], [cartesian_product3])).
% 142.92/21.08 thf(zip_derived_cl1259, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ u @ X1)
% 142.92/21.08 | ~ (member @ (second @ (ordered_pair @ u @ z)) @ X0)
% 142.92/21.08 | (member @ (ordered_pair @ u @ z) @ (cross_product @ X1 @ X0)))),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl1228, zip_derived_cl15])).
% 142.92/21.08 thf(zip_derived_cl1689, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ (second @ (ordered_pair @ u @ z)) @ X0)
% 142.92/21.08 | (member @ (ordered_pair @ u @ z) @ (cross_product @ y @ X0)))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl851, zip_derived_cl1259])).
% 142.92/21.08 thf(zip_derived_cl1836, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ (second @ (ordered_pair @ u @ z)) @ universal_class)
% 142.92/21.08 | (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ y @
% 142.92/21.08 (unordered_pair @ (second @ (ordered_pair @ u @ z)) @ X0))))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl1689])).
% 142.92/21.08 thf(zip_derived_cl845, plain,
% 142.92/21.08 ( (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ y @ universal_class))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl21])).
% 142.92/21.08 thf(zip_derived_cl1248, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ u @ z) @ (cross_product @ X1 @ X0))
% 142.92/21.08 | (member @ (second @ (ordered_pair @ u @ z)) @ X0))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl1228, zip_derived_cl14])).
% 142.92/21.08 thf(zip_derived_cl1501, plain,
% 142.92/21.08 ( (member @ (second @ (ordered_pair @ u @ z)) @ universal_class)),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl845, zip_derived_cl1248])).
% 142.92/21.08 thf(zip_derived_cl1855, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ y @
% 142.92/21.08 (unordered_pair @ (second @ (ordered_pair @ u @ z)) @ X0)))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl1836, zip_derived_cl1501])).
% 142.92/21.08 thf(zip_derived_cl1972, plain, (((second @ (ordered_pair @ u @ z)) = (z))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl1957, zip_derived_cl770])).
% 142.92/21.08 thf(zip_derived_cl2295, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ y @ (unordered_pair @ z @ X0)))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl1855, zip_derived_cl1972])).
% 142.92/21.08 thf(zip_derived_cl2300, plain,
% 142.92/21.08 ( (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ y @ (singleton @ z)))),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl2295])).
% 142.92/21.08 thf(zip_derived_cl158, plain,
% 142.92/21.08 ( (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (intersection @ xr @ (cross_product @ y @ universal_class)))),
% 142.92/21.08 inference('cnf', [status(esa)], [zf_stmt_1])).
% 142.92/21.08 thf(intersection1, axiom,
% 142.92/21.08 (( ~( member @ Z @ ( intersection @ X @ Y ) ) ) | ( member @ Z @ X ))).
% 142.92/21.08 thf(zip_derived_cl20, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.08 (~ (member @ X0 @ (intersection @ X1 @ X2)) | (member @ X0 @ X1))),
% 142.92/21.08 inference('cnf', [status(esa)], [intersection1])).
% 142.92/21.08 thf(zip_derived_cl838, plain, ( (member @ (ordered_pair @ u @ z) @ xr)),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl20])).
% 142.92/21.08 thf(intersection3, axiom,
% 142.92/21.08 (( ~( member @ Z @ X ) ) | ( ~( member @ Z @ Y ) ) |
% 142.92/21.08 ( member @ Z @ ( intersection @ X @ Y ) ))).
% 142.92/21.08 thf(zip_derived_cl22, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.08 (~ (member @ X0 @ X1)
% 142.92/21.08 | ~ (member @ X0 @ X2)
% 142.92/21.08 | (member @ X0 @ (intersection @ X1 @ X2)))),
% 142.92/21.08 inference('cnf', [status(esa)], [intersection3])).
% 142.92/21.08 thf(zip_derived_cl773, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ X0 @ universal_class) | (member @ X0 @ (singleton @ X0)))),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 142.92/21.08 thf(zip_derived_cl1259, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ u @ X1)
% 142.92/21.08 | ~ (member @ (second @ (ordered_pair @ u @ z)) @ X0)
% 142.92/21.08 | (member @ (ordered_pair @ u @ z) @ (cross_product @ X1 @ X0)))),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl1228, zip_derived_cl15])).
% 142.92/21.08 thf(zip_derived_cl1673, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ u @ universal_class)
% 142.92/21.08 | ~ (member @ (second @ (ordered_pair @ u @ z)) @ X0)
% 142.92/21.08 | (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ (singleton @ u) @ X0)))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl773, zip_derived_cl1259])).
% 142.92/21.08 thf(zip_derived_cl853, plain, ( (member @ u @ universal_class)),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl851, zip_derived_cl744])).
% 142.92/21.08 thf(zip_derived_cl1692, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ (second @ (ordered_pair @ u @ z)) @ X0)
% 142.92/21.08 | (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ (singleton @ u) @ X0)))),
% 142.92/21.08 inference('demod', [status(thm)], [zip_derived_cl1673, zip_derived_cl853])).
% 142.92/21.08 thf(zip_derived_cl1972, plain, (((second @ (ordered_pair @ u @ z)) = (z))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl1957, zip_derived_cl770])).
% 142.92/21.08 thf(zip_derived_cl2057, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ z @ X0)
% 142.92/21.08 | (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ (singleton @ u) @ X0)))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl1692, zip_derived_cl1972])).
% 142.92/21.08 thf(zip_derived_cl853, plain, ( (member @ u @ universal_class)),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl851, zip_derived_cl744])).
% 142.92/21.08 thf(domain2, axiom,
% 142.92/21.08 (( ~( member @ Z @ universal_class ) ) |
% 142.92/21.08 ( ( restrict @ X @ ( singleton @ Z ) @ universal_class ) = ( null_class ) ) |
% 142.92/21.08 ( member @ Z @ ( domain_of @ X ) ))).
% 142.92/21.08 thf(zip_derived_cl30, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ universal_class)
% 142.92/21.08 | ((restrict @ X1 @ (singleton @ X0) @ universal_class)
% 142.92/21.08 = (null_class))
% 142.92/21.08 | (member @ X0 @ (domain_of @ X1)))),
% 142.92/21.08 inference('cnf', [status(esa)], [domain2])).
% 142.92/21.08 thf(restriction1, axiom,
% 142.92/21.08 (( intersection @ Xr @ ( cross_product @ X @ Y ) ) =
% 142.92/21.08 ( restrict @ Xr @ X @ Y ))).
% 142.92/21.08 thf(zip_derived_cl27, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.08 ((intersection @ X0 @ (cross_product @ X1 @ X2))
% 142.92/21.08 = (restrict @ X0 @ X1 @ X2))),
% 142.92/21.08 inference('cnf', [status(esa)], [restriction1])).
% 142.92/21.08 thf(zip_derived_cl22, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.08 (~ (member @ X0 @ X1)
% 142.92/21.08 | ~ (member @ X0 @ X2)
% 142.92/21.08 | (member @ X0 @ (intersection @ X1 @ X2)))),
% 142.92/21.08 inference('cnf', [status(esa)], [intersection3])).
% 142.92/21.08 thf(zip_derived_cl905, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.08 (~ (member @ X3 @ X2)
% 142.92/21.08 | ~ (member @ X3 @ (cross_product @ X1 @ X0))
% 142.92/21.08 | (member @ X3 @ (restrict @ X2 @ X1 @ X0)))),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl22])).
% 142.92/21.08 thf(zip_derived_cl4057, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.08 ( (member @ X0 @ (domain_of @ X1))
% 142.92/21.08 | ~ (member @ X0 @ universal_class)
% 142.92/21.08 | ~ (member @ X2 @ X1)
% 142.92/21.08 | ~ (member @ X2 @
% 142.92/21.08 (cross_product @ (singleton @ X0) @ universal_class))
% 142.92/21.08 | (member @ X2 @ null_class))),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl905])).
% 142.92/21.08 thf(regularity1, axiom,
% 142.92/21.08 (( ( X ) = ( null_class ) ) | ( member @ ( regular @ X ) @ X ))).
% 142.92/21.08 thf(zip_derived_cl65, plain,
% 142.92/21.08 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 142.92/21.08 inference('cnf', [status(esa)], [regularity1])).
% 142.92/21.08 thf(zip_derived_cl744, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 142.92/21.08 thf(zip_derived_cl1062, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl744])).
% 142.92/21.08 thf(zip_derived_cl65, plain,
% 142.92/21.08 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 142.92/21.08 inference('cnf', [status(esa)], [regularity1])).
% 142.92/21.08 thf(complement1, axiom,
% 142.92/21.08 (( ~( member @ Z @ ( complement @ X ) ) ) | ( ~( member @ Z @ X ) ))).
% 142.92/21.08 thf(zip_derived_cl23, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 142.92/21.08 inference('cnf', [status(esa)], [complement1])).
% 142.92/21.08 thf(zip_derived_cl1068, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (((complement @ X0) = (null_class))
% 142.92/21.08 | ~ (member @ (regular @ (complement @ X0)) @ X0))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl23])).
% 142.92/21.08 thf(zip_derived_cl2993, plain,
% 142.92/21.08 ((((complement @ universal_class) = (null_class))
% 142.92/21.08 | ((complement @ universal_class) = (null_class)))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl1062, zip_derived_cl1068])).
% 142.92/21.08 thf(zip_derived_cl2996, plain,
% 142.92/21.08 (((complement @ universal_class) = (null_class))),
% 142.92/21.08 inference('simplify', [status(thm)], [zip_derived_cl2993])).
% 142.92/21.08 thf(zip_derived_cl23, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 142.92/21.08 inference('cnf', [status(esa)], [complement1])).
% 142.92/21.08 thf(zip_derived_cl3000, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ X0 @ null_class) | ~ (member @ X0 @ universal_class))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl2996, zip_derived_cl23])).
% 142.92/21.08 thf(zip_derived_cl744, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 142.92/21.08 thf(zip_derived_cl3032, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 142.92/21.08 inference('clc', [status(thm)], [zip_derived_cl3000, zip_derived_cl744])).
% 142.92/21.08 thf(zip_derived_cl4059, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.08 ( (member @ X0 @ (domain_of @ X1))
% 142.92/21.08 | ~ (member @ X0 @ universal_class)
% 142.92/21.08 | ~ (member @ X2 @ X1)
% 142.92/21.08 | ~ (member @ X2 @
% 142.92/21.08 (cross_product @ (singleton @ X0) @ universal_class)))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl4057, zip_derived_cl3032])).
% 142.92/21.08 thf(zip_derived_cl4201, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 ( (member @ u @ (domain_of @ X0))
% 142.92/21.08 | ~ (member @ X1 @ X0)
% 142.92/21.08 | ~ (member @ X1 @
% 142.92/21.08 (cross_product @ (singleton @ u) @ universal_class)))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl853, zip_derived_cl4059])).
% 142.92/21.08 thf(zip_derived_cl34803, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ z @ universal_class)
% 142.92/21.08 | (member @ u @ (domain_of @ X0))
% 142.92/21.08 | ~ (member @ (ordered_pair @ u @ z) @ X0))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl2057, zip_derived_cl4201])).
% 142.92/21.08 thf(zip_derived_cl852, plain, ( (member @ z @ universal_class)),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl845, zip_derived_cl14])).
% 142.92/21.08 thf(zip_derived_cl34807, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 ( (member @ u @ (domain_of @ X0))
% 142.92/21.08 | ~ (member @ (ordered_pair @ u @ z) @ X0))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl34803, zip_derived_cl852])).
% 142.92/21.08 thf(zip_derived_cl15, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.08 (~ (member @ X0 @ X1)
% 142.92/21.08 | ~ (member @ X2 @ X3)
% 142.92/21.08 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 142.92/21.08 inference('cnf', [status(esa)], [cartesian_product3])).
% 142.92/21.08 thf(zip_derived_cl24, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ universal_class)
% 142.92/21.08 | (member @ X0 @ (complement @ X1))
% 142.92/21.08 | (member @ X0 @ X1))),
% 142.92/21.08 inference('cnf', [status(esa)], [complement2])).
% 142.92/21.08 thf(zip_derived_cl1228, plain,
% 142.92/21.08 (((ordered_pair @ u @ (second @ (ordered_pair @ u @ z)))
% 142.92/21.08 = (ordered_pair @ u @ z))),
% 142.92/21.08 inference('demod', [status(thm)], [zip_derived_cl850, zip_derived_cl1227])).
% 142.92/21.08 thf(flip3, axiom,
% 142.92/21.08 (( ~( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) |
% 142.92/21.08 ( ~( member @
% 142.92/21.08 ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @
% 142.92/21.08 ( cross_product @
% 142.92/21.08 ( cross_product @ universal_class @ universal_class ) @
% 142.92/21.08 universal_class ) ) ) |
% 142.92/21.08 ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ))).
% 142.92/21.08 thf(zip_derived_cl36, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ X0 @ X1) @ X2) @ X3)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ X1 @ X0) @ X2) @
% 142.92/21.08 (cross_product @
% 142.92/21.08 (cross_product @ universal_class @ universal_class) @
% 142.92/21.08 universal_class))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ X1 @ X0) @ X2) @
% 142.92/21.08 (flip @ X3)))),
% 142.92/21.08 inference('cnf', [status(esa)], [flip3])).
% 142.92/21.08 thf(zip_derived_cl1262, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @
% 142.92/21.08 (ordered_pair @
% 142.92/21.08 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ u) @ X1) @
% 142.92/21.08 X0)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (cross_product @
% 142.92/21.08 (cross_product @ universal_class @ universal_class) @
% 142.92/21.08 universal_class))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (flip @ X0)))),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl1228, zip_derived_cl36])).
% 142.92/21.08 thf(zip_derived_cl1775, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 ( (member @
% 142.92/21.08 (ordered_pair @
% 142.92/21.08 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ u) @ X1) @
% 142.92/21.08 X0)
% 142.92/21.08 | ~ (member @
% 142.92/21.08 (ordered_pair @
% 142.92/21.08 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ u) @ X1) @
% 142.92/21.08 universal_class)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (cross_product @
% 142.92/21.08 (cross_product @ universal_class @ universal_class) @
% 142.92/21.08 universal_class))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (flip @ (complement @ X0))))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl1262])).
% 142.92/21.08 thf(zip_derived_cl788, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (member @ (ordered_pair @ X1 @ X0) @ universal_class)),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl10])).
% 142.92/21.08 thf(zip_derived_cl1795, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 ( (member @
% 142.92/21.08 (ordered_pair @
% 142.92/21.08 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ u) @ X1) @
% 142.92/21.08 X0)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (cross_product @
% 142.92/21.08 (cross_product @ universal_class @ universal_class) @
% 142.92/21.08 universal_class))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (flip @ (complement @ X0))))),
% 142.92/21.08 inference('demod', [status(thm)], [zip_derived_cl1775, zip_derived_cl788])).
% 142.92/21.08 thf(zip_derived_cl1972, plain, (((second @ (ordered_pair @ u @ z)) = (z))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl1957, zip_derived_cl770])).
% 142.92/21.08 thf(zip_derived_cl2231, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 ( (member @ (ordered_pair @ (ordered_pair @ z @ u) @ X1) @ X0)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (cross_product @
% 142.92/21.08 (cross_product @ universal_class @ universal_class) @
% 142.92/21.08 universal_class))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (flip @ (complement @ X0))))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl1795, zip_derived_cl1972])).
% 142.92/21.08 thf(zip_derived_cl788, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (member @ (ordered_pair @ X1 @ X0) @ universal_class)),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl10])).
% 142.92/21.08 thf(zip_derived_cl15, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.08 (~ (member @ X0 @ X1)
% 142.92/21.08 | ~ (member @ X2 @ X3)
% 142.92/21.08 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 142.92/21.08 inference('cnf', [status(esa)], [cartesian_product3])).
% 142.92/21.08 thf(zip_derived_cl1228, plain,
% 142.92/21.08 (((ordered_pair @ u @ (second @ (ordered_pair @ u @ z)))
% 142.92/21.08 = (ordered_pair @ u @ z))),
% 142.92/21.08 inference('demod', [status(thm)], [zip_derived_cl850, zip_derived_cl1227])).
% 142.92/21.08 thf(flip2, axiom,
% 142.92/21.08 (( ~( member @
% 142.92/21.08 ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) ) |
% 142.92/21.08 ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ))).
% 142.92/21.08 thf(zip_derived_cl35, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ X0 @ X1) @ X2) @
% 142.92/21.08 (flip @ X3))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ X1 @ X0) @ X2) @ X3))),
% 142.92/21.08 inference('cnf', [status(esa)], [flip2])).
% 142.92/21.08 thf(zip_derived_cl1252, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (flip @ X0))
% 142.92/21.08 | (member @
% 142.92/21.08 (ordered_pair @
% 142.92/21.08 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ u) @ X1) @
% 142.92/21.08 X0))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl1228, zip_derived_cl35])).
% 142.92/21.08 thf(zip_derived_cl23, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 142.92/21.08 inference('cnf', [status(esa)], [complement1])).
% 142.92/21.08 thf(zip_derived_cl1596, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (flip @ (complement @ X0)))
% 142.92/21.08 | ~ (member @
% 142.92/21.08 (ordered_pair @
% 142.92/21.08 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ u) @ X1) @
% 142.92/21.08 X0))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl1252, zip_derived_cl23])).
% 142.92/21.08 thf(zip_derived_cl1972, plain, (((second @ (ordered_pair @ u @ z)) = (z))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl1957, zip_derived_cl770])).
% 142.92/21.08 thf(zip_derived_cl2003, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (flip @ (complement @ X0)))
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ z @ u) @ X1) @ X0))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl1596, zip_derived_cl1972])).
% 142.92/21.08 thf(zip_derived_cl2382, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.08 (~ (member @ X2 @ X0)
% 142.92/21.08 | ~ (member @ (ordered_pair @ z @ u) @ X1)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X2) @
% 142.92/21.08 (flip @ (complement @ (cross_product @ X1 @ X0)))))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl2003])).
% 142.92/21.08 thf(zip_derived_cl2464, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X1 @ X0)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (flip @ (complement @ (cross_product @ universal_class @ X0)))))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl788, zip_derived_cl2382])).
% 142.92/21.08 thf(zip_derived_cl2484, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (cross_product @
% 142.92/21.08 (cross_product @ universal_class @ universal_class) @
% 142.92/21.08 universal_class))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ z @ u) @ X1) @
% 142.92/21.08 (cross_product @ universal_class @ X0))
% 142.92/21.08 | ~ (member @ X1 @ X0))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl2231, zip_derived_cl2464])).
% 142.92/21.08 thf(zip_derived_cl4025, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ universal_class)
% 142.92/21.08 | ~ (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ universal_class @ universal_class))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ z @ u) @ X0) @
% 142.92/21.08 (cross_product @ universal_class @ X1))
% 142.92/21.08 | ~ (member @ X0 @ X1))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl2484])).
% 142.92/21.08 thf(zip_derived_cl1501, plain,
% 142.92/21.08 ( (member @ (second @ (ordered_pair @ u @ z)) @ universal_class)),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl845, zip_derived_cl1248])).
% 142.92/21.08 thf(zip_derived_cl853, plain, ( (member @ u @ universal_class)),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl851, zip_derived_cl744])).
% 142.92/21.08 thf(zip_derived_cl1259, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ u @ X1)
% 142.92/21.08 | ~ (member @ (second @ (ordered_pair @ u @ z)) @ X0)
% 142.92/21.08 | (member @ (ordered_pair @ u @ z) @ (cross_product @ X1 @ X0)))),
% 142.92/21.08 inference('s_sup+', [status(thm)], [zip_derived_cl1228, zip_derived_cl15])).
% 142.92/21.08 thf(zip_derived_cl1688, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ (second @ (ordered_pair @ u @ z)) @ X0)
% 142.92/21.08 | (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ universal_class @ X0)))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl853, zip_derived_cl1259])).
% 142.92/21.08 thf(zip_derived_cl1713, plain,
% 142.92/21.08 ( (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ universal_class @ universal_class))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl1501, zip_derived_cl1688])).
% 142.92/21.08 thf(zip_derived_cl4028, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ universal_class)
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ z @ u) @ X0) @
% 142.92/21.08 (cross_product @ universal_class @ X1))
% 142.92/21.08 | ~ (member @ X0 @ X1))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl4025, zip_derived_cl1713])).
% 142.92/21.08 thf(zip_derived_cl744, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 142.92/21.08 thf(zip_derived_cl28695, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ X1)
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ z @ u) @ X0) @
% 142.92/21.08 (cross_product @ universal_class @ X1)))),
% 142.92/21.08 inference('clc', [status(thm)], [zip_derived_cl4028, zip_derived_cl744])).
% 142.92/21.08 thf(zip_derived_cl1228, plain,
% 142.92/21.08 (((ordered_pair @ u @ (second @ (ordered_pair @ u @ z)))
% 142.92/21.08 = (ordered_pair @ u @ z))),
% 142.92/21.08 inference('demod', [status(thm)], [zip_derived_cl850, zip_derived_cl1227])).
% 142.92/21.08 thf(rotate2, axiom,
% 142.92/21.08 (( ~( member @
% 142.92/21.08 ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) ) |
% 142.92/21.08 ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ))).
% 142.92/21.08 thf(zip_derived_cl32, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ X0 @ X1) @ X2) @
% 142.92/21.08 (rotate @ X3))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ X1 @ X2) @ X0) @ X3))),
% 142.92/21.08 inference('cnf', [status(esa)], [rotate2])).
% 142.92/21.08 thf(zip_derived_cl1251, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (rotate @ X0))
% 142.92/21.08 | (member @
% 142.92/21.08 (ordered_pair @
% 142.92/21.08 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ X1) @ u) @
% 142.92/21.08 X0))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl1228, zip_derived_cl32])).
% 142.92/21.08 thf(zip_derived_cl23, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 142.92/21.08 inference('cnf', [status(esa)], [complement1])).
% 142.92/21.08 thf(zip_derived_cl1514, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (rotate @ (complement @ X0)))
% 142.92/21.08 | ~ (member @
% 142.92/21.08 (ordered_pair @
% 142.92/21.08 (ordered_pair @ (second @ (ordered_pair @ u @ z)) @ X1) @ u) @
% 142.92/21.08 X0))),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl1251, zip_derived_cl23])).
% 142.92/21.08 thf(zip_derived_cl1972, plain, (((second @ (ordered_pair @ u @ z)) = (z))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl1957, zip_derived_cl770])).
% 142.92/21.08 thf(zip_derived_cl2001, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ X1) @
% 142.92/21.08 (rotate @ (complement @ X0)))
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ z @ X1) @ u) @ X0))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl1514, zip_derived_cl1972])).
% 142.92/21.08 thf(zip_derived_cl28715, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ u @ X0)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ u) @
% 142.92/21.08 (rotate @ (complement @ (cross_product @ universal_class @ X0)))))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl28695, zip_derived_cl2001])).
% 142.92/21.08 thf(zip_derived_cl34837, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ u @ z) @ X0)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ u) @
% 142.92/21.08 (rotate @
% 142.92/21.08 (complement @
% 142.92/21.08 (cross_product @ universal_class @ (domain_of @ X0))))))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl34807, zip_derived_cl28715])).
% 142.92/21.08 thf(zip_derived_cl35828, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ u @ z) @ X0)
% 142.92/21.08 | ~ (member @ (ordered_pair @ u @ z) @ X1)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ u) @
% 142.92/21.08 (rotate @
% 142.92/21.08 (complement @
% 142.92/21.08 (cross_product @ universal_class @
% 142.92/21.08 (domain_of @ (intersection @ X1 @ X0)))))))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl22, zip_derived_cl34837])).
% 142.92/21.08 thf(zip_derived_cl89444, plain,
% 142.92/21.08 (![X0 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ u @ z) @ X0)
% 142.92/21.08 | ~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ u) @
% 142.92/21.08 (rotate @
% 142.92/21.08 (complement @
% 142.92/21.08 (cross_product @ universal_class @
% 142.92/21.08 (domain_of @ (intersection @ X0 @ xr)))))))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl838, zip_derived_cl35828])).
% 142.92/21.08 thf(zip_derived_cl90016, plain,
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ u) @
% 142.92/21.08 (rotate @
% 142.92/21.08 (complement @
% 142.92/21.08 (cross_product @ universal_class @
% 142.92/21.08 (domain_of @
% 142.92/21.08 (intersection @ (cross_product @ y @ (singleton @ z)) @ xr))))))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl2300, zip_derived_cl89444])).
% 142.92/21.08 thf(restriction2, axiom,
% 142.92/21.08 (( intersection @ ( cross_product @ X @ Y ) @ Xr ) =
% 142.92/21.08 ( restrict @ Xr @ X @ Y ))).
% 142.92/21.08 thf(zip_derived_cl28, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.08 ((intersection @ (cross_product @ X1 @ X2) @ X0)
% 142.92/21.08 = (restrict @ X0 @ X1 @ X2))),
% 142.92/21.08 inference('cnf', [status(esa)], [restriction2])).
% 142.92/21.08 thf(segment, axiom,
% 142.92/21.08 (( segment @ Xr @ Y @ Z ) =
% 142.92/21.08 ( domain_of @ ( restrict @ Xr @ Y @ ( singleton @ Z ) ) ))).
% 142.92/21.08 thf(zip_derived_cl121, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 142.92/21.08 ((segment @ X0 @ X1 @ X2)
% 142.92/21.08 = (domain_of @ (restrict @ X0 @ X1 @ (singleton @ X2))))),
% 142.92/21.08 inference('cnf', [status(esa)], [segment])).
% 142.92/21.08 thf(zip_derived_cl90056, plain,
% 142.92/21.08 (~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ u) @
% 142.92/21.08 (rotate @
% 142.92/21.08 (complement @
% 142.92/21.08 (cross_product @ universal_class @ (segment @ xr @ y @ z)))))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl90016, zip_derived_cl28, zip_derived_cl121])).
% 142.92/21.08 thf(zip_derived_cl94256, plain,
% 142.92/21.08 ((~ (member @ (ordered_pair @ (ordered_pair @ u @ z) @ u) @
% 142.92/21.08 (cross_product @
% 142.92/21.08 (cross_product @ universal_class @ universal_class) @
% 142.92/21.08 universal_class))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ z @ u) @ u) @
% 142.92/21.08 (cross_product @ universal_class @ (segment @ xr @ y @ z))))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl2202, zip_derived_cl90056])).
% 142.92/21.08 thf(zip_derived_cl94257, plain,
% 142.92/21.08 ((~ (member @ u @ universal_class)
% 142.92/21.08 | ~ (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ universal_class @ universal_class))
% 142.92/21.08 | (member @ (ordered_pair @ (ordered_pair @ z @ u) @ u) @
% 142.92/21.08 (cross_product @ universal_class @ (segment @ xr @ y @ z))))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl15, zip_derived_cl94256])).
% 142.92/21.08 thf(zip_derived_cl853, plain, ( (member @ u @ universal_class)),
% 142.92/21.08 inference('s_sup-', [status(thm)], [zip_derived_cl851, zip_derived_cl744])).
% 142.92/21.08 thf(zip_derived_cl1713, plain,
% 142.92/21.08 ( (member @ (ordered_pair @ u @ z) @
% 142.92/21.08 (cross_product @ universal_class @ universal_class))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl1501, zip_derived_cl1688])).
% 142.92/21.08 thf(zip_derived_cl94258, plain,
% 142.92/21.08 ( (member @ (ordered_pair @ (ordered_pair @ z @ u) @ u) @
% 142.92/21.08 (cross_product @ universal_class @ (segment @ xr @ y @ z)))),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl94257, zip_derived_cl853, zip_derived_cl1713])).
% 142.92/21.08 thf(zip_derived_cl14, plain,
% 142.92/21.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 142.92/21.08 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 142.92/21.08 | (member @ X1 @ X3))),
% 142.92/21.08 inference('cnf', [status(esa)], [cartesian_product2])).
% 142.92/21.08 thf(zip_derived_cl94291, plain, ( (member @ u @ (segment @ xr @ y @ z))),
% 142.92/21.08 inference('s_sup-', [status(thm)],
% 142.92/21.08 [zip_derived_cl94258, zip_derived_cl14])).
% 142.92/21.08 thf(zip_derived_cl94310, plain, ($false),
% 142.92/21.08 inference('demod', [status(thm)],
% 142.92/21.08 [zip_derived_cl159, zip_derived_cl94291])).
% 142.92/21.08
% 142.92/21.08 % SZS output end Refutation
% 142.92/21.08
% 142.92/21.08
% 142.92/21.08 % Terminating...
% 143.82/21.19 % Runner terminated.
% 143.82/21.22 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------