%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM217-1 : 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.rNphCxnENu true
% Computer : n003.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 04:46:00 PM UTC 2025
% Result : Unsatisfiable 45.61s 7.18s
% Output : Refutation 45.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM217-1 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.04/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rNphCxnENu true
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 16:30:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.60/0.69 % Total configuration time : 435
% 0.60/0.69 % Estimated wc time : 1092
% 0.60/0.69 % Estimated cpu time (7 cpus) : 156.0
% 0.63/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.63/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.63/0.82 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.64/0.83 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.64/0.83 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.64/0.83 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.64/0.85 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.64/0.90 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 45.61/7.18 % Solved by fo/fo1_lcnf.sh.
% 45.61/7.18 % done 6411 iterations in 6.209s
% 45.61/7.18 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 45.61/7.18 % SZS output start Refutation
% 45.61/7.18 thf(universal_class_type, type, universal_class: $i).
% 45.61/7.18 thf(union_type, type, union: $i > $i > $i).
% 45.61/7.18 thf(null_class_type, type, null_class: $i).
% 45.61/7.18 thf(image_type, type, image: $i > $i > $i).
% 45.61/7.18 thf(domain_of_type, type, domain_of: $i > $i).
% 45.61/7.18 thf(member_type, type, member: $i > $i > $o).
% 45.61/7.18 thf(second_type, type, second: $i > $i).
% 45.61/7.18 thf(successor_relation_type, type, successor_relation: $i).
% 45.61/7.18 thf(unordered_pair_type, type, unordered_pair: $i > $i > $i).
% 45.61/7.18 thf(complement_type, type, complement: $i > $i).
% 45.61/7.18 thf(identity_relation_type, type, identity_relation: $i).
% 45.61/7.18 thf(apply_type, type, apply: $i > $i > $i).
% 45.61/7.18 thf(choice_type, type, choice: $i).
% 45.61/7.18 thf(recursion_equation_functions_type, type, recursion_equation_functions:
% 45.61/7.18 $i > $i).
% 45.61/7.18 thf(singleton_type, type, singleton: $i > $i).
% 45.61/7.18 thf(intersection_type, type, intersection: $i > $i > $i).
% 45.61/7.18 thf(rest_relation_type, type, rest_relation: $i).
% 45.61/7.18 thf(subclass_type, type, subclass: $i > $i > $o).
% 45.61/7.18 thf(restrict_type, type, restrict: $i > $i > $i > $i).
% 45.61/7.18 thf(cross_product_type, type, cross_product: $i > $i > $i).
% 45.61/7.18 thf(function_type, type, function: $i > $o).
% 45.61/7.18 thf(inverse_type, type, inverse: $i > $i).
% 45.61/7.18 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 45.61/7.18 thf(inductive_type, type, inductive: $i > $o).
% 45.61/7.18 thf(first_type, type, first: $i > $i).
% 45.61/7.18 thf(omega_type, type, omega: $i).
% 45.61/7.18 thf(symmetrization_of_type, type, symmetrization_of: $i > $i).
% 45.61/7.18 thf(not_subclass_element_type, type, not_subclass_element: $i > $i > $i).
% 45.61/7.18 thf(diagonalise_type, type, diagonalise: $i > $i).
% 45.61/7.18 thf(rest_of_type, type, rest_of: $i > $i).
% 45.61/7.18 thf(regular_type, type, regular: $i > $i).
% 45.61/7.18 thf(recursion_equation_functions1, axiom,
% 45.61/7.18 (( ~( member @ X @ ( recursion_equation_functions @ Z ) ) ) |
% 45.61/7.18 ( function @ Z ))).
% 45.61/7.18 thf(zip_derived_cl146, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (((((~) @ (member @ X0 @ (recursion_equation_functions @ X1)))) |
% 45.61/7.18 (function @ X1)))),
% 45.61/7.18 inference('cnf', [status(esa)], [recursion_equation_functions1])).
% 45.61/7.18 thf(zip_derived_cl242, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (member @ X0 @ (recursion_equation_functions @ X1))
% 45.61/7.18 | (function @ X1))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl146])).
% 45.61/7.18 thf(regularity1, axiom,
% 45.61/7.18 (( ( X ) = ( null_class ) ) | ( member @ ( regular @ X ) @ X ))).
% 45.61/7.18 thf(zip_derived_cl65, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (((((X0) = (null_class))) | (member @ (regular @ X0) @ X0)))),
% 45.61/7.18 inference('cnf', [status(esa)], [regularity1])).
% 45.61/7.18 thf(zip_derived_cl236, plain,
% 45.61/7.18 (![X0 : $i]: ( (((X0) = (null_class))) | (member @ (regular @ X0) @ X0))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl65])).
% 45.61/7.18 thf(zip_derived_cl237, plain,
% 45.61/7.18 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 45.61/7.18 inference('simplify nested equalities', [status(thm)],
% 45.61/7.18 [zip_derived_cl236])).
% 45.61/7.18 thf(zip_derived_cl245, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 ( (function @ X0)
% 45.61/7.18 | ((recursion_equation_functions @ X0) = (null_class)))),
% 45.61/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl242, zip_derived_cl237])).
% 45.61/7.18 thf(function1, axiom,
% 45.61/7.18 (( ~( function @ Xf ) ) |
% 45.61/7.18 ( subclass @ Xf @ ( cross_product @ universal_class @ universal_class ) ))).
% 45.61/7.18 thf(zip_derived_cl61, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (((((~) @ (function @ X0))) | (subclass @ X0 @
% 45.61/7.18 (cross_product @ universal_class @ universal_class))))),
% 45.61/7.18 inference('cnf', [status(esa)], [function1])).
% 45.61/7.18 thf(zip_derived_cl419, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (~ (function @ X0)
% 45.61/7.18 | (subclass @ X0 @
% 45.61/7.18 (cross_product @ universal_class @ universal_class)))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl61])).
% 45.61/7.18 thf(class_elements_are_sets, axiom, (subclass @ X @ universal_class)).
% 45.61/7.18 thf(zip_derived_cl3, plain, (![X0 : $i]: (subclass @ X0 @ universal_class)),
% 45.61/7.18 inference('cnf', [status(esa)], [class_elements_are_sets])).
% 45.61/7.18 thf(subclass_implies_equal, axiom,
% 45.61/7.18 (( ~( subclass @ X @ Y ) ) | ( ~( subclass @ Y @ X ) ) | ( ( X ) = ( Y ) ))).
% 45.61/7.18 thf(zip_derived_cl6, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (((((~) @ (subclass @ X0 @ X1))) | (((~) @ (subclass @ X1 @ X0))) |
% 45.61/7.18 (((X0) = (X1)))))),
% 45.61/7.18 inference('cnf', [status(esa)], [subclass_implies_equal])).
% 45.61/7.18 thf(zip_derived_cl205, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | (((X0) = (X1))))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])).
% 45.61/7.18 thf(zip_derived_cl206, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | ((X0) = (X1)))),
% 45.61/7.18 inference('simplify nested equalities', [status(thm)],
% 45.61/7.18 [zip_derived_cl205])).
% 45.61/7.18 thf(zip_derived_cl209, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (~ (subclass @ universal_class @ X0) | ((X0) = (universal_class)))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl206])).
% 45.61/7.18 thf(zip_derived_cl422, plain,
% 45.61/7.18 ((~ (function @ universal_class)
% 45.61/7.18 | ((cross_product @ universal_class @ universal_class)
% 45.61/7.18 = (universal_class)))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl419, zip_derived_cl209])).
% 45.61/7.18 thf(inductive1, axiom,
% 45.61/7.18 (( ~( inductive @ X ) ) | ( member @ null_class @ X ))).
% 45.61/7.18 thf(zip_derived_cl46, plain,
% 45.61/7.18 (![X0 : $i]: (((((~) @ (inductive @ X0))) | (member @ null_class @ X0)))),
% 45.61/7.18 inference('cnf', [status(esa)], [inductive1])).
% 45.61/7.18 thf(zip_derived_cl176, plain,
% 45.61/7.18 (![X0 : $i]: (~ (inductive @ X0) | (member @ null_class @ X0))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])).
% 45.61/7.18 thf(cartesian_product4, axiom,
% 45.61/7.18 (( ~( member @ Z @ ( cross_product @ X @ Y ) ) ) |
% 45.61/7.18 ( ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) = ( Z ) ))).
% 45.61/7.18 thf(zip_derived_cl16, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 (((((~) @ (member @ X0 @ (cross_product @ X1 @ X2)))) |
% 45.61/7.18 (((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0)))))),
% 45.61/7.18 inference('cnf', [status(esa)], [cartesian_product4])).
% 45.61/7.18 thf(zip_derived_cl443, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 (~ (member @ X0 @ (cross_product @ X1 @ X2))
% 45.61/7.18 | (((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0))))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl16])).
% 45.61/7.18 thf(zip_derived_cl444, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 (~ (member @ X0 @ (cross_product @ X1 @ X2))
% 45.61/7.18 | ((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0)))),
% 45.61/7.18 inference('simplify nested equalities', [status(thm)],
% 45.61/7.18 [zip_derived_cl443])).
% 45.61/7.18 thf(zip_derived_cl447, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (inductive @ (cross_product @ X1 @ X0))
% 45.61/7.18 | ((ordered_pair @ (first @ null_class) @ (second @ null_class))
% 45.61/7.18 = (null_class)))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl176, zip_derived_cl444])).
% 45.61/7.18 thf(zip_derived_cl1019, plain,
% 45.61/7.18 ((~ (function @ universal_class)
% 45.61/7.18 | ~ (inductive @ universal_class)
% 45.61/7.18 | ((ordered_pair @ (first @ null_class) @ (second @ null_class))
% 45.61/7.18 = (null_class)))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl422, zip_derived_cl447])).
% 45.61/7.18 thf(zip_derived_cl3, plain, (![X0 : $i]: (subclass @ X0 @ universal_class)),
% 45.61/7.18 inference('cnf', [status(esa)], [class_elements_are_sets])).
% 45.61/7.18 thf(inductive3, axiom,
% 45.61/7.18 (( ~( member @ null_class @ X ) ) |
% 45.61/7.18 ( ~( subclass @ ( image @ successor_relation @ X ) @ X ) ) |
% 45.61/7.18 ( inductive @ X ))).
% 45.61/7.18 thf(zip_derived_cl48, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (((((~) @ (member @ null_class @ X0))) |
% 45.61/7.18 (((~) @ (subclass @ (image @ successor_relation @ X0) @ X0))) |
% 45.61/7.18 (inductive @ X0)))),
% 45.61/7.18 inference('cnf', [status(esa)], [inductive3])).
% 45.61/7.18 thf(zip_derived_cl664, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (~ (member @ null_class @ X0)
% 45.61/7.18 | ~ (subclass @ (image @ successor_relation @ X0) @ X0)
% 45.61/7.18 | (inductive @ X0))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])).
% 45.61/7.18 thf(zip_derived_cl670, plain,
% 45.61/7.18 ((~ (member @ null_class @ universal_class)
% 45.61/7.18 | (inductive @ universal_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl664])).
% 45.61/7.18 thf(omega_is_inductive1, axiom, (inductive @ omega)).
% 45.61/7.18 thf(zip_derived_cl49, plain, ( (inductive @ omega)),
% 45.61/7.18 inference('cnf', [status(esa)], [omega_is_inductive1])).
% 45.61/7.18 thf(zip_derived_cl176, plain,
% 45.61/7.18 (![X0 : $i]: (~ (inductive @ X0) | (member @ null_class @ X0))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])).
% 45.61/7.18 thf(zip_derived_cl3, plain, (![X0 : $i]: (subclass @ X0 @ universal_class)),
% 45.61/7.18 inference('cnf', [status(esa)], [class_elements_are_sets])).
% 45.61/7.18 thf(subclass_members, axiom,
% 45.61/7.18 (( ~( subclass @ X @ Y ) ) | ( ~( member @ U @ X ) ) | ( member @ U @ Y ))).
% 45.61/7.18 thf(zip_derived_cl0, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 (((((~) @ (subclass @ X0 @ X1))) | (((~) @ (member @ X2 @ X0))) |
% 45.61/7.18 (member @ X2 @ X1)))),
% 45.61/7.18 inference('cnf', [status(esa)], [subclass_members])).
% 45.61/7.18 thf(zip_derived_cl159, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 (~ (subclass @ X0 @ X1) | ~ (member @ X2 @ X0) | (member @ X2 @ X1))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl0])).
% 45.61/7.18 thf(zip_derived_cl160, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl159])).
% 45.61/7.18 thf(zip_derived_cl177, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (~ (inductive @ X0) | (member @ null_class @ universal_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl176, zip_derived_cl160])).
% 45.61/7.18 thf(zip_derived_cl179, plain, ( (member @ null_class @ universal_class)),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl177])).
% 45.61/7.18 thf(zip_derived_cl673, plain, ( (inductive @ universal_class)),
% 45.61/7.18 inference('demod', [status(thm)], [zip_derived_cl670, zip_derived_cl179])).
% 45.61/7.18 thf(zip_derived_cl1021, plain,
% 45.61/7.18 ((~ (function @ universal_class)
% 45.61/7.18 | ((ordered_pair @ (first @ null_class) @ (second @ null_class))
% 45.61/7.18 = (null_class)))),
% 45.61/7.18 inference('demod', [status(thm)], [zip_derived_cl1019, zip_derived_cl673])).
% 45.61/7.18 thf(ordered_pair, axiom,
% 45.61/7.18 (( unordered_pair @
% 45.61/7.18 ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) =
% 45.61/7.18 ( ordered_pair @ X @ Y ))).
% 45.61/7.18 thf(zip_derived_cl12, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 ((unordered_pair @ (singleton @ X0) @
% 45.61/7.18 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 45.61/7.18 inference('cnf', [status(esa)], [ordered_pair])).
% 45.61/7.18 thf(unordered_pair2, axiom,
% 45.61/7.18 (( ~( member @ X @ universal_class ) ) |
% 45.61/7.18 ( member @ X @ ( unordered_pair @ X @ Y ) ))).
% 45.61/7.18 thf(zip_derived_cl8, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (((((~) @ (member @ X0 @ universal_class))) | (member @ X0 @
% 45.61/7.18 (unordered_pair @ X0 @ X1))))),
% 45.61/7.18 inference('cnf', [status(esa)], [unordered_pair2])).
% 45.61/7.18 thf(zip_derived_cl254, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (member @ X0 @ universal_class)
% 45.61/7.18 | (member @ X0 @ (unordered_pair @ X0 @ X1)))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl8])).
% 45.61/7.18 thf(zip_derived_cl283, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (member @ (singleton @ X1) @ universal_class)
% 45.61/7.18 | (member @ (singleton @ X1) @ (ordered_pair @ X1 @ X0)))),
% 45.61/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl254])).
% 45.61/7.18 thf(singleton_set, axiom, (( unordered_pair @ X @ X ) = ( singleton @ X ))).
% 45.61/7.18 thf(zip_derived_cl11, plain,
% 45.61/7.18 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 45.61/7.18 inference('cnf', [status(esa)], [singleton_set])).
% 45.61/7.18 thf(unordered_pairs_in_universal, axiom,
% 45.61/7.18 (member @ ( unordered_pair @ X @ Y ) @ universal_class)).
% 45.61/7.18 thf(zip_derived_cl10, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (member @ (unordered_pair @ X0 @ X1) @ universal_class)),
% 45.61/7.18 inference('cnf', [status(esa)], [unordered_pairs_in_universal])).
% 45.61/7.18 thf(zip_derived_cl171, plain,
% 45.61/7.18 (![X0 : $i]: (member @ (singleton @ X0) @ universal_class)),
% 45.61/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl10])).
% 45.61/7.18 thf(zip_derived_cl288, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (member @ (singleton @ X1) @ (ordered_pair @ X1 @ X0))),
% 45.61/7.18 inference('demod', [status(thm)], [zip_derived_cl283, zip_derived_cl171])).
% 45.61/7.18 thf(zip_derived_cl1818, plain,
% 45.61/7.18 ((~ (function @ universal_class)
% 45.61/7.18 | (member @ (singleton @ (first @ null_class)) @ null_class))),
% 45.61/7.18 inference('s_sup+', [status(thm)],
% 45.61/7.18 [zip_derived_cl1021, zip_derived_cl288])).
% 45.61/7.18 thf(zip_derived_cl237, plain,
% 45.61/7.18 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 45.61/7.18 inference('simplify nested equalities', [status(thm)],
% 45.61/7.18 [zip_derived_cl236])).
% 45.61/7.18 thf(zip_derived_cl160, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl159])).
% 45.61/7.18 thf(zip_derived_cl238, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl237, zip_derived_cl160])).
% 45.61/7.18 thf(zip_derived_cl237, plain,
% 45.61/7.18 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 45.61/7.18 inference('simplify nested equalities', [status(thm)],
% 45.61/7.18 [zip_derived_cl236])).
% 45.61/7.18 thf(complement1, axiom,
% 45.61/7.18 (( ~( member @ Z @ ( complement @ X ) ) ) | ( ~( member @ Z @ X ) ))).
% 45.61/7.18 thf(zip_derived_cl23, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (((((~) @ (member @ X0 @ (complement @ X1)))) |
% 45.61/7.18 (((~) @ (member @ X0 @ X1)))))),
% 45.61/7.18 inference('cnf', [status(esa)], [complement1])).
% 45.61/7.18 thf(zip_derived_cl326, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])).
% 45.61/7.18 thf(zip_derived_cl329, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (((complement @ X0) = (null_class))
% 45.61/7.18 | ~ (member @ (regular @ (complement @ X0)) @ X0))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl237, zip_derived_cl326])).
% 45.61/7.18 thf(zip_derived_cl716, plain,
% 45.61/7.18 ((((complement @ universal_class) = (null_class))
% 45.61/7.18 | ((complement @ universal_class) = (null_class)))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl238, zip_derived_cl329])).
% 45.61/7.18 thf(zip_derived_cl720, plain,
% 45.61/7.18 (((complement @ universal_class) = (null_class))),
% 45.61/7.18 inference('simplify', [status(thm)], [zip_derived_cl716])).
% 45.61/7.18 thf(zip_derived_cl326, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])).
% 45.61/7.18 thf(zip_derived_cl723, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (~ (member @ X0 @ null_class) | ~ (member @ X0 @ universal_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl720, zip_derived_cl326])).
% 45.61/7.18 thf(zip_derived_cl160, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl159])).
% 45.61/7.18 thf(zip_derived_cl765, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 45.61/7.18 inference('clc', [status(thm)], [zip_derived_cl723, zip_derived_cl160])).
% 45.61/7.18 thf(zip_derived_cl1834, plain, (~ (function @ universal_class)),
% 45.61/7.18 inference('clc', [status(thm)], [zip_derived_cl1818, zip_derived_cl765])).
% 45.61/7.18 thf(zip_derived_cl1837, plain,
% 45.61/7.18 (((recursion_equation_functions @ universal_class) = (null_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)],
% 45.61/7.18 [zip_derived_cl245, zip_derived_cl1834])).
% 45.61/7.18 thf(intersection1, axiom,
% 45.61/7.18 (( ~( member @ Z @ ( intersection @ X @ Y ) ) ) | ( member @ Z @ X ))).
% 45.61/7.18 thf(zip_derived_cl20, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 (((((~) @ (member @ X0 @ (intersection @ X1 @ X2)))) | (member @
% 45.61/7.18 X0 @ X1)))),
% 45.61/7.18 inference('cnf', [status(esa)], [intersection1])).
% 45.61/7.18 thf(zip_derived_cl376, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 (~ (member @ X0 @ (intersection @ X1 @ X2)) | (member @ X0 @ X1))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])).
% 45.61/7.18 thf(not_subclass_members1, axiom,
% 45.61/7.18 (( member @ ( not_subclass_element @ X @ Y ) @ X ) | ( subclass @ X @ Y ))).
% 45.61/7.18 thf(zip_derived_cl1, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (((member @ (not_subclass_element @ X0 @ X1) @ X0) | (subclass @
% 45.61/7.18 X0 @ X1)))),
% 45.61/7.18 inference('cnf', [status(esa)], [not_subclass_members1])).
% 45.61/7.18 thf(zip_derived_cl168, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 45.61/7.18 | (subclass @ X0 @ X1))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1])).
% 45.61/7.18 thf(zip_derived_cl377, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 ( (member @ (not_subclass_element @ (intersection @ X1 @ X0) @ X2) @
% 45.61/7.18 X1)
% 45.61/7.18 | (subclass @ (intersection @ X1 @ X0) @ X2))),
% 45.61/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl376, zip_derived_cl168])).
% 45.61/7.18 thf(zip_derived_cl765, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 45.61/7.18 inference('clc', [status(thm)], [zip_derived_cl723, zip_derived_cl160])).
% 45.61/7.18 thf(zip_derived_cl3199, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]: (subclass @ (intersection @ null_class @ X1) @ X0)),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl377, zip_derived_cl765])).
% 45.61/7.18 thf(zip_derived_cl168, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 45.61/7.18 | (subclass @ X0 @ X1))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1])).
% 45.61/7.18 thf(zip_derived_cl765, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 45.61/7.18 inference('clc', [status(thm)], [zip_derived_cl723, zip_derived_cl160])).
% 45.61/7.18 thf(zip_derived_cl766, plain, (![X0 : $i]: (subclass @ null_class @ X0)),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl168, zip_derived_cl765])).
% 45.61/7.18 thf(zip_derived_cl206, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | ((X0) = (X1)))),
% 45.61/7.18 inference('simplify nested equalities', [status(thm)],
% 45.61/7.18 [zip_derived_cl205])).
% 45.61/7.18 thf(zip_derived_cl770, plain,
% 45.61/7.18 (![X0 : $i]: (~ (subclass @ X0 @ null_class) | ((null_class) = (X0)))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl766, zip_derived_cl206])).
% 45.61/7.18 thf(zip_derived_cl3251, plain,
% 45.61/7.18 (![X0 : $i]: ((null_class) = (intersection @ null_class @ X0))),
% 45.61/7.18 inference('s_sup-', [status(thm)],
% 45.61/7.18 [zip_derived_cl3199, zip_derived_cl770])).
% 45.61/7.18 thf(diagonalisation, axiom,
% 45.61/7.18 (( complement @ ( domain_of @ ( intersection @ Xr @ identity_relation ) ) ) =
% 45.61/7.18 ( diagonalise @ Xr ))).
% 45.61/7.18 thf(zip_derived_cl75, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 ((complement @ (domain_of @ (intersection @ X0 @ identity_relation)))
% 45.61/7.18 = (diagonalise @ X0))),
% 45.61/7.18 inference('cnf', [status(esa)], [diagonalisation])).
% 45.61/7.18 thf(zip_derived_cl3288, plain,
% 45.61/7.18 (((complement @ (domain_of @ null_class)) = (diagonalise @ null_class))),
% 45.61/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl3251, zip_derived_cl75])).
% 45.61/7.18 thf(zip_derived_cl237, plain,
% 45.61/7.18 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 45.61/7.18 inference('simplify nested equalities', [status(thm)],
% 45.61/7.18 [zip_derived_cl236])).
% 45.61/7.18 thf(zip_derived_cl3251, plain,
% 45.61/7.18 (![X0 : $i]: ((null_class) = (intersection @ null_class @ X0))),
% 45.61/7.18 inference('s_sup-', [status(thm)],
% 45.61/7.18 [zip_derived_cl3199, zip_derived_cl770])).
% 45.61/7.18 thf(restriction1, axiom,
% 45.61/7.18 (( intersection @ Xr @ ( cross_product @ X @ Y ) ) =
% 45.61/7.18 ( restrict @ Xr @ X @ Y ))).
% 45.61/7.18 thf(zip_derived_cl27, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 ((intersection @ X0 @ (cross_product @ X1 @ X2))
% 45.61/7.18 = (restrict @ X0 @ X1 @ X2))),
% 45.61/7.18 inference('cnf', [status(esa)], [restriction1])).
% 45.61/7.18 thf(zip_derived_cl3284, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]: ((null_class) = (restrict @ null_class @ X1 @ X0))),
% 45.61/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl3251, zip_derived_cl27])).
% 45.61/7.18 thf(domain1, axiom,
% 45.61/7.18 (( ( restrict @ X @ ( singleton @ Z ) @ universal_class ) != ( null_class ) ) |
% 45.61/7.18 ( ~( member @ Z @ ( domain_of @ X ) ) ))).
% 45.61/7.18 thf(zip_derived_cl29, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (((((restrict @ X0 @ (singleton @ X1) @ universal_class) !=
% 45.61/7.18 (null_class))) |
% 45.61/7.18 (((~) @ (member @ X1 @ (domain_of @ X0))))))),
% 45.61/7.18 inference('cnf', [status(esa)], [domain1])).
% 45.61/7.18 thf(zip_derived_cl616, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 ( (((restrict @ X0 @ (singleton @ X1) @ universal_class) !=
% 45.61/7.18 (null_class)))
% 45.61/7.18 | ~ (member @ X1 @ (domain_of @ X0)))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])).
% 45.61/7.18 thf(zip_derived_cl617, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (((restrict @ X0 @ (singleton @ X1) @ universal_class) != (null_class))
% 45.61/7.18 | ~ (member @ X1 @ (domain_of @ X0)))),
% 45.61/7.18 inference('simplify nested equalities', [status(thm)],
% 45.61/7.18 [zip_derived_cl616])).
% 45.61/7.18 thf(zip_derived_cl3417, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (((null_class) != (null_class))
% 45.61/7.18 | ~ (member @ X0 @ (domain_of @ null_class)))),
% 45.61/7.18 inference('s_sup-', [status(thm)],
% 45.61/7.18 [zip_derived_cl3284, zip_derived_cl617])).
% 45.61/7.18 thf(zip_derived_cl3421, plain,
% 45.61/7.18 (![X0 : $i]: ~ (member @ X0 @ (domain_of @ null_class))),
% 45.61/7.18 inference('simplify', [status(thm)], [zip_derived_cl3417])).
% 45.61/7.18 thf(zip_derived_cl3428, plain, (((domain_of @ null_class) = (null_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)],
% 45.61/7.18 [zip_derived_cl237, zip_derived_cl3421])).
% 45.61/7.18 thf(zip_derived_cl3433, plain,
% 45.61/7.18 (((complement @ null_class) = (diagonalise @ null_class))),
% 45.61/7.18 inference('demod', [status(thm)],
% 45.61/7.18 [zip_derived_cl3288, zip_derived_cl3428])).
% 45.61/7.18 thf(zip_derived_cl720, plain,
% 45.61/7.18 (((complement @ universal_class) = (null_class))),
% 45.61/7.18 inference('simplify', [status(thm)], [zip_derived_cl716])).
% 45.61/7.18 thf(union, axiom,
% 45.61/7.18 (( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) =
% 45.61/7.18 ( union @ X @ Y ))).
% 45.61/7.18 thf(zip_derived_cl25, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 ((complement @ (intersection @ (complement @ X0) @ (complement @ X1)))
% 45.61/7.18 = (union @ X0 @ X1))),
% 45.61/7.18 inference('cnf', [status(esa)], [union])).
% 45.61/7.18 thf(zip_derived_cl724, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 ((complement @ (intersection @ null_class @ (complement @ X0)))
% 45.61/7.18 = (union @ universal_class @ X0))),
% 45.61/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl720, zip_derived_cl25])).
% 45.61/7.18 thf(zip_derived_cl3251, plain,
% 45.61/7.18 (![X0 : $i]: ((null_class) = (intersection @ null_class @ X0))),
% 45.61/7.18 inference('s_sup-', [status(thm)],
% 45.61/7.18 [zip_derived_cl3199, zip_derived_cl770])).
% 45.61/7.18 thf(zip_derived_cl3257, plain,
% 45.61/7.18 (![X0 : $i]: ((complement @ null_class) = (union @ universal_class @ X0))),
% 45.61/7.18 inference('demod', [status(thm)], [zip_derived_cl724, zip_derived_cl3251])).
% 45.61/7.18 thf(zip_derived_cl3433, plain,
% 45.61/7.18 (((complement @ null_class) = (diagonalise @ null_class))),
% 45.61/7.18 inference('demod', [status(thm)],
% 45.61/7.18 [zip_derived_cl3288, zip_derived_cl3428])).
% 45.61/7.18 thf(zip_derived_cl3600, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 ((diagonalise @ null_class) = (union @ universal_class @ X0))),
% 45.61/7.18 inference('demod', [status(thm)],
% 45.61/7.18 [zip_derived_cl3257, zip_derived_cl3433])).
% 45.61/7.18 thf(symmetrization, axiom,
% 45.61/7.18 (( union @ X @ ( inverse @ X ) ) = ( symmetrization_of @ X ))).
% 45.61/7.18 thf(zip_derived_cl112, plain,
% 45.61/7.18 (![X0 : $i]: ((union @ X0 @ (inverse @ X0)) = (symmetrization_of @ X0))),
% 45.61/7.18 inference('cnf', [status(esa)], [symmetrization])).
% 45.61/7.18 thf(zip_derived_cl3613, plain,
% 45.61/7.18 (((diagonalise @ null_class) = (symmetrization_of @ universal_class))),
% 45.61/7.18 inference('s_sup+', [status(thm)],
% 45.61/7.18 [zip_derived_cl3600, zip_derived_cl112])).
% 45.61/7.18 thf(zip_derived_cl3627, plain,
% 45.61/7.18 (((complement @ null_class) = (symmetrization_of @ universal_class))),
% 45.61/7.18 inference('demod', [status(thm)],
% 45.61/7.18 [zip_derived_cl3433, zip_derived_cl3613])).
% 45.61/7.18 thf(zip_derived_cl179, plain, ( (member @ null_class @ universal_class)),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl177])).
% 45.61/7.18 thf(rest_relation1, axiom,
% 45.61/7.18 (subclass @
% 45.61/7.18 rest_relation @ ( cross_product @ universal_class @ universal_class ))).
% 45.61/7.18 thf(zip_derived_cl143, plain,
% 45.61/7.18 ( (subclass @ rest_relation @
% 45.61/7.18 (cross_product @ universal_class @ universal_class))),
% 45.61/7.18 inference('cnf', [status(esa)], [rest_relation1])).
% 45.61/7.18 thf(zip_derived_cl159, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.18 (~ (subclass @ X0 @ X1) | ~ (member @ X2 @ X0) | (member @ X2 @ X1))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl0])).
% 45.61/7.18 thf(zip_derived_cl193, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (~ (member @ X0 @ rest_relation)
% 45.61/7.18 | (member @ X0 @ (cross_product @ universal_class @ universal_class)))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl159])).
% 45.61/7.18 thf(cartesian_product2, axiom,
% 45.61/7.18 (( ~( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) |
% 45.61/7.18 ( member @ V @ Y ))).
% 45.61/7.18 thf(zip_derived_cl14, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 45.61/7.18 (((((~) @ (member @ (ordered_pair @ X0 @ X1) @
% 45.61/7.18 (cross_product @ X2 @ X3)))) |
% 45.61/7.18 (member @ X1 @ X3)))),
% 45.61/7.18 inference('cnf', [status(esa)], [cartesian_product2])).
% 45.61/7.18 thf(zip_derived_cl360, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 45.61/7.18 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 45.61/7.18 | (member @ X1 @ X3))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl14])).
% 45.61/7.18 thf(zip_derived_cl1209, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (~ (member @ (ordered_pair @ X1 @ X0) @ rest_relation)
% 45.61/7.18 | (member @ X0 @ universal_class))),
% 45.61/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl193, zip_derived_cl360])).
% 45.61/7.18 thf(rest_relation3, axiom,
% 45.61/7.18 (( ~( member @ X @ universal_class ) ) |
% 45.61/7.18 ( member @ ( ordered_pair @ X @ ( rest_of @ X ) ) @ rest_relation ))).
% 45.61/7.18 thf(zip_derived_cl145, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (((((~) @ (member @ X0 @ universal_class))) | (member @
% 45.61/7.18 (ordered_pair @ X0 @ (rest_of @ X0)) @ rest_relation)))),
% 45.61/7.18 inference('cnf', [status(esa)], [rest_relation3])).
% 45.61/7.18 thf(zip_derived_cl606, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 (~ (member @ X0 @ universal_class)
% 45.61/7.18 | (member @ (ordered_pair @ X0 @ (rest_of @ X0)) @ rest_relation))),
% 45.61/7.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl145])).
% 45.61/7.18 thf(zip_derived_cl1619, plain,
% 45.61/7.18 (![X0 : $i]:
% 45.61/7.18 ( (member @ (rest_of @ X0) @ universal_class)
% 45.61/7.18 | ~ (member @ X0 @ universal_class))),
% 45.61/7.18 inference('s_sup+', [status(thm)],
% 45.61/7.18 [zip_derived_cl1209, zip_derived_cl606])).
% 45.61/7.18 thf(complement2, axiom,
% 45.61/7.18 (( ~( member @ Z @ universal_class ) ) |
% 45.61/7.18 ( member @ Z @ ( complement @ X ) ) | ( member @ Z @ X ))).
% 45.61/7.18 thf(zip_derived_cl24, plain,
% 45.61/7.18 (![X0 : $i, X1 : $i]:
% 45.61/7.18 (((((~) @ (member @ X0 @ universal_class))) |
% 45.61/7.18 (member @ X0 @ (complement @ X1)) | (member @ X0 @ X1)))),
% 45.61/7.18 inference('cnf', [status(esa)], [complement2])).
% 45.61/7.19 thf(zip_derived_cl546, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 (~ (member @ X0 @ universal_class)
% 45.61/7.19 | (member @ X0 @ (complement @ X1))
% 45.61/7.19 | (member @ X0 @ X1))),
% 45.61/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])).
% 45.61/7.19 thf(zip_derived_cl1627, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 (~ (member @ X0 @ universal_class)
% 45.61/7.19 | (member @ (rest_of @ X0) @ (complement @ X1))
% 45.61/7.19 | (member @ (rest_of @ X0) @ X1))),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl1619, zip_derived_cl546])).
% 45.61/7.19 thf(zip_derived_cl31167, plain,
% 45.61/7.19 (![X0 : $i]:
% 45.61/7.19 ( (member @ (rest_of @ null_class) @ (complement @ X0))
% 45.61/7.19 | (member @ (rest_of @ null_class) @ X0))),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl179, zip_derived_cl1627])).
% 45.61/7.19 thf(zip_derived_cl31221, plain,
% 45.61/7.19 (( (member @ (rest_of @ null_class) @
% 45.61/7.19 (symmetrization_of @ universal_class))
% 45.61/7.19 | (member @ (rest_of @ null_class) @ null_class))),
% 45.61/7.19 inference('s_sup+', [status(thm)],
% 45.61/7.19 [zip_derived_cl3627, zip_derived_cl31167])).
% 45.61/7.19 thf(zip_derived_cl765, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 45.61/7.19 inference('clc', [status(thm)], [zip_derived_cl723, zip_derived_cl160])).
% 45.61/7.19 thf(zip_derived_cl31233, plain,
% 45.61/7.19 ( (member @ (rest_of @ null_class) @
% 45.61/7.19 (symmetrization_of @ universal_class))),
% 45.61/7.19 inference('demod', [status(thm)],
% 45.61/7.19 [zip_derived_cl31221, zip_derived_cl765])).
% 45.61/7.19 thf(zip_derived_cl160, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 45.61/7.19 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl159])).
% 45.61/7.19 thf(zip_derived_cl31236, plain,
% 45.61/7.19 ( (member @ (rest_of @ null_class) @ universal_class)),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl31233, zip_derived_cl160])).
% 45.61/7.19 thf(choice2, axiom,
% 45.61/7.19 (( ~( member @ Y @ universal_class ) ) | ( ( Y ) = ( null_class ) ) |
% 45.61/7.19 ( member @ ( apply @ choice @ Y ) @ Y ))).
% 45.61/7.19 thf(zip_derived_cl69, plain,
% 45.61/7.19 (![X0 : $i]:
% 45.61/7.19 (((((~) @ (member @ X0 @ universal_class))) |
% 45.61/7.19 (((X0) = (null_class))) | (member @ (apply @ choice @ X0) @ X0)))),
% 45.61/7.19 inference('cnf', [status(esa)], [choice2])).
% 45.61/7.19 thf(zip_derived_cl679, plain,
% 45.61/7.19 (![X0 : $i]:
% 45.61/7.19 (~ (member @ X0 @ universal_class)
% 45.61/7.19 | (((X0) = (null_class)))
% 45.61/7.19 | (member @ (apply @ choice @ X0) @ X0))),
% 45.61/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl69])).
% 45.61/7.19 thf(zip_derived_cl680, plain,
% 45.61/7.19 (![X0 : $i]:
% 45.61/7.19 (~ (member @ X0 @ universal_class)
% 45.61/7.19 | ((X0) = (null_class))
% 45.61/7.19 | (member @ (apply @ choice @ X0) @ X0))),
% 45.61/7.19 inference('simplify nested equalities', [status(thm)],
% 45.61/7.19 [zip_derived_cl679])).
% 45.61/7.19 thf(zip_derived_cl31251, plain,
% 45.61/7.19 ((((rest_of @ null_class) = (null_class))
% 45.61/7.19 | (member @ (apply @ choice @ (rest_of @ null_class)) @
% 45.61/7.19 (rest_of @ null_class)))),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl31236, zip_derived_cl680])).
% 45.61/7.19 thf(prove_corollary_2_to_rest_defn_1, conjecture,
% 45.61/7.19 (( rest_of @ null_class ) = ( null_class ))).
% 45.61/7.19 thf(zf_stmt_0, negated_conjecture,
% 45.61/7.19 (( rest_of @ null_class ) != ( null_class )),
% 45.61/7.19 inference('cnf.neg', [status(esa)], [prove_corollary_2_to_rest_defn_1])).
% 45.61/7.19 thf(zip_derived_cl158, plain, (((rest_of @ null_class) != (null_class))),
% 45.61/7.19 inference('cnf', [status(esa)], [zf_stmt_0])).
% 45.61/7.19 thf(zip_derived_cl31257, plain,
% 45.61/7.19 ( (member @ (apply @ choice @ (rest_of @ null_class)) @
% 45.61/7.19 (rest_of @ null_class))),
% 45.61/7.19 inference('simplify_reflect-', [status(thm)],
% 45.61/7.19 [zip_derived_cl31251, zip_derived_cl158])).
% 45.61/7.19 thf(rest_of1, axiom,
% 45.61/7.19 (subclass @
% 45.61/7.19 ( rest_of @ X ) @ ( cross_product @ universal_class @ universal_class ))).
% 45.61/7.19 thf(zip_derived_cl139, plain,
% 45.61/7.19 (![X0 : $i]:
% 45.61/7.19 (subclass @ (rest_of @ X0) @
% 45.61/7.19 (cross_product @ universal_class @ universal_class))),
% 45.61/7.19 inference('cnf', [status(esa)], [rest_of1])).
% 45.61/7.19 thf(zip_derived_cl159, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.19 (~ (subclass @ X0 @ X1) | ~ (member @ X2 @ X0) | (member @ X2 @ X1))),
% 45.61/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl0])).
% 45.61/7.19 thf(zip_derived_cl221, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 (~ (member @ X1 @ (rest_of @ X0))
% 45.61/7.19 | (member @ X1 @ (cross_product @ universal_class @ universal_class)))),
% 45.61/7.19 inference('s_sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl159])).
% 45.61/7.19 thf(zip_derived_cl31262, plain,
% 45.61/7.19 ( (member @ (apply @ choice @ (rest_of @ null_class)) @
% 45.61/7.19 (cross_product @ universal_class @ universal_class))),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl31257, zip_derived_cl221])).
% 45.61/7.19 thf(zip_derived_cl444, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.19 (~ (member @ X0 @ (cross_product @ X1 @ X2))
% 45.61/7.19 | ((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0)))),
% 45.61/7.19 inference('simplify nested equalities', [status(thm)],
% 45.61/7.19 [zip_derived_cl443])).
% 45.61/7.19 thf(zip_derived_cl31285, plain,
% 45.61/7.19 (((ordered_pair @ (first @ (apply @ choice @ (rest_of @ null_class))) @
% 45.61/7.19 (second @ (apply @ choice @ (rest_of @ null_class))))
% 45.61/7.19 = (apply @ choice @ (rest_of @ null_class)))),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl31262, zip_derived_cl444])).
% 45.61/7.19 thf(rest_of2, axiom,
% 45.61/7.19 (( ~( member @ ( ordered_pair @ U @ V ) @ ( rest_of @ X ) ) ) |
% 45.61/7.19 ( member @ U @ ( domain_of @ X ) ))).
% 45.61/7.19 thf(zip_derived_cl140, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.19 (((((~) @ (member @ (ordered_pair @ X0 @ X1) @ (rest_of @ X2)))) |
% 45.61/7.19 (member @ X0 @ (domain_of @ X2))))),
% 45.61/7.19 inference('cnf', [status(esa)], [rest_of2])).
% 45.61/7.19 thf(zip_derived_cl632, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.19 (~ (member @ (ordered_pair @ X0 @ X1) @ (rest_of @ X2))
% 45.61/7.19 | (member @ X0 @ (domain_of @ X2)))),
% 45.61/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl140])).
% 45.61/7.19 thf(zip_derived_cl33367, plain,
% 45.61/7.19 (![X0 : $i]:
% 45.61/7.19 (~ (member @ (apply @ choice @ (rest_of @ null_class)) @
% 45.61/7.19 (rest_of @ X0))
% 45.61/7.19 | (member @ (first @ (apply @ choice @ (rest_of @ null_class))) @
% 45.61/7.19 (domain_of @ X0)))),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl31285, zip_derived_cl632])).
% 45.61/7.19 thf(zip_derived_cl376, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.19 (~ (member @ X0 @ (intersection @ X1 @ X2)) | (member @ X0 @ X1))),
% 45.61/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])).
% 45.61/7.19 thf(zip_derived_cl237, plain,
% 45.61/7.19 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 45.61/7.19 inference('simplify nested equalities', [status(thm)],
% 45.61/7.19 [zip_derived_cl236])).
% 45.61/7.19 thf(zip_derived_cl379, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 ( (member @ (regular @ (intersection @ X1 @ X0)) @ X1)
% 45.61/7.19 | ((intersection @ X1 @ X0) = (null_class)))),
% 45.61/7.19 inference('s_sup+', [status(thm)], [zip_derived_cl376, zip_derived_cl237])).
% 45.61/7.19 thf(zip_derived_cl242, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 (~ (member @ X0 @ (recursion_equation_functions @ X1))
% 45.61/7.19 | (function @ X1))),
% 45.61/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl146])).
% 45.61/7.19 thf(zip_derived_cl3373, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 (((intersection @ (recursion_equation_functions @ X0) @ X1)
% 45.61/7.19 = (null_class))
% 45.61/7.19 | (function @ X0))),
% 45.61/7.19 inference('s_sup-', [status(thm)], [zip_derived_cl379, zip_derived_cl242])).
% 45.61/7.19 thf(zip_derived_cl27, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.19 ((intersection @ X0 @ (cross_product @ X1 @ X2))
% 45.61/7.19 = (restrict @ X0 @ X1 @ X2))),
% 45.61/7.19 inference('cnf', [status(esa)], [restriction1])).
% 45.61/7.19 thf(zip_derived_cl5237, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.61/7.19 ( (function @ X2)
% 45.61/7.19 | ((null_class)
% 45.61/7.19 = (restrict @ (recursion_equation_functions @ X2) @ X1 @ X0)))),
% 45.61/7.19 inference('s_sup+', [status(thm)], [zip_derived_cl3373, zip_derived_cl27])).
% 45.61/7.19 thf(zip_derived_cl617, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 (((restrict @ X0 @ (singleton @ X1) @ universal_class) != (null_class))
% 45.61/7.19 | ~ (member @ X1 @ (domain_of @ X0)))),
% 45.61/7.19 inference('simplify nested equalities', [status(thm)],
% 45.61/7.19 [zip_derived_cl616])).
% 45.61/7.19 thf(zip_derived_cl15739, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 ( (function @ X1)
% 45.61/7.19 | ((null_class) != (null_class))
% 45.61/7.19 | ~ (member @ X0 @ (domain_of @ (recursion_equation_functions @ X1))))),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl5237, zip_derived_cl617])).
% 45.61/7.19 thf(zip_derived_cl15781, plain,
% 45.61/7.19 (![X0 : $i, X1 : $i]:
% 45.61/7.19 (~ (member @ X0 @ (domain_of @ (recursion_equation_functions @ X1)))
% 45.61/7.19 | (function @ X1))),
% 45.61/7.19 inference('simplify', [status(thm)], [zip_derived_cl15739])).
% 45.61/7.19 thf(zip_derived_cl36198, plain,
% 45.61/7.19 (![X0 : $i]:
% 45.61/7.19 (~ (member @ (apply @ choice @ (rest_of @ null_class)) @
% 45.61/7.19 (rest_of @ (recursion_equation_functions @ X0)))
% 45.61/7.19 | (function @ X0))),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl33367, zip_derived_cl15781])).
% 45.61/7.19 thf(zip_derived_cl36215, plain,
% 45.61/7.19 ((~ (member @ (apply @ choice @ (rest_of @ null_class)) @
% 45.61/7.19 (rest_of @ null_class))
% 45.61/7.19 | (function @ universal_class))),
% 45.61/7.19 inference('s_sup-', [status(thm)],
% 45.61/7.19 [zip_derived_cl1837, zip_derived_cl36198])).
% 45.61/7.19 thf(zip_derived_cl31257, plain,
% 45.61/7.19 ( (member @ (apply @ choice @ (rest_of @ null_class)) @
% 45.61/7.19 (rest_of @ null_class))),
% 45.61/7.19 inference('simplify_reflect-', [status(thm)],
% 45.61/7.19 [zip_derived_cl31251, zip_derived_cl158])).
% 45.61/7.19 thf(zip_derived_cl1834, plain, (~ (function @ universal_class)),
% 45.61/7.19 inference('clc', [status(thm)], [zip_derived_cl1818, zip_derived_cl765])).
% 45.61/7.19 thf(zip_derived_cl36224, plain, ($false),
% 45.61/7.19 inference('demod', [status(thm)],
% 45.61/7.19 [zip_derived_cl36215, zip_derived_cl31257, zip_derived_cl1834])).
% 45.61/7.19
% 45.61/7.19 % SZS output end Refutation
% 45.61/7.19
% 45.61/7.19
% 45.61/7.19 % Terminating...
% 45.61/7.23 % Runner terminated.
% 45.61/7.24 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------