%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET098-6 : 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.bCBH3CYoNh true
% Computer : n015.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 04:51:34 PM UTC 2025
% Result : Unsatisfiable 4.71s 1.32s
% Output : Refutation 4.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET098-6 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bCBH3CYoNh true
% 0.12/0.35 % Computer : n015.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Wed Oct 1 12:55:08 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % Running portfolio for 300 s
% 0.12/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35 % Number of cores: 8
% 0.12/0.36 % Python version: Python 3.6.8
% 0.12/0.36 % Running in FO mode
% 0.51/0.64 % Total configuration time : 435
% 0.51/0.64 % Estimated wc time : 1092
% 0.51/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.51/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.51/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.51/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.51/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.51/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 4.71/1.32 % Solved by fo/fo6_bce.sh.
% 4.71/1.32 % BCE start: 94
% 4.71/1.32 % BCE eliminated: 0
% 4.71/1.32 % PE start: 94
% 4.71/1.32 logic: eq
% 4.71/1.32 % PE eliminated: 16
% 4.71/1.32 % done 401 iterations in 0.568s
% 4.71/1.32 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.71/1.32 % SZS output start Refutation
% 4.71/1.32 thf(universal_class_type, type, universal_class: $i).
% 4.71/1.32 thf(null_class_type, type, null_class: $i).
% 4.71/1.32 thf(member_type, type, member: $i > $i > $o).
% 4.71/1.32 thf(x_type, type, x: $i).
% 4.71/1.32 thf(unordered_pair_type, type, unordered_pair: $i > $i > $i).
% 4.71/1.32 thf(complement_type, type, complement: $i > $i).
% 4.71/1.32 thf(singleton_type, type, singleton: $i > $i).
% 4.71/1.32 thf(intersection_type, type, intersection: $i > $i > $i).
% 4.71/1.32 thf(subclass_type, type, subclass: $i > $i > $o).
% 4.71/1.32 thf(not_subclass_element_type, type, not_subclass_element: $i > $i > $i).
% 4.71/1.32 thf(regular_type, type, regular: $i > $i).
% 4.71/1.32 thf(not_subclass_members1, axiom,
% 4.71/1.32 (( member @ ( not_subclass_element @ X @ Y ) @ X ) | ( subclass @ X @ Y ))).
% 4.71/1.32 thf(zip_derived_cl1, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 4.71/1.32 | (subclass @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [not_subclass_members1])).
% 4.71/1.32 thf(singleton_set, axiom, (( unordered_pair @ X @ X ) = ( singleton @ X ))).
% 4.71/1.32 thf(zip_derived_cl11, plain,
% 4.71/1.32 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 4.71/1.32 inference('cnf', [status(esa)], [singleton_set])).
% 4.71/1.32 thf(unordered_pair_member, axiom,
% 4.71/1.32 (( ~( member @ U @ ( unordered_pair @ X @ Y ) ) ) | ( ( U ) = ( X ) ) |
% 4.71/1.32 ( ( U ) = ( Y ) ))).
% 4.71/1.32 thf(zip_derived_cl7, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.71/1.32 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 4.71/1.32 | ((X0) = (X1))
% 4.71/1.32 | ((X0) = (X2)))),
% 4.71/1.32 inference('cnf', [status(esa)], [unordered_pair_member])).
% 4.71/1.32 thf(zip_derived_cl436, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ X1 @ (singleton @ X0)) | ((X1) = (X0)) | ((X1) = (X0)))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl7])).
% 4.71/1.32 thf(zip_derived_cl437, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 4.71/1.32 inference('simplify', [status(thm)], [zip_derived_cl436])).
% 4.71/1.32 thf(zip_derived_cl438, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 ( (subclass @ (singleton @ X0) @ X1)
% 4.71/1.32 | ((not_subclass_element @ (singleton @ X0) @ X1) = (X0)))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl437])).
% 4.71/1.32 thf(not_subclass_members2, axiom,
% 4.71/1.32 (( ~( member @ ( not_subclass_element @ X @ Y ) @ Y ) ) |
% 4.71/1.32 ( subclass @ X @ Y ))).
% 4.71/1.32 thf(zip_derived_cl2, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ (not_subclass_element @ X0 @ X1) @ X1)
% 4.71/1.32 | (subclass @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [not_subclass_members2])).
% 4.71/1.32 thf(zip_derived_cl1169, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 ( (subclass @ (singleton @ X0) @ X1)
% 4.71/1.32 | ~ (member @ X0 @ X1)
% 4.71/1.32 | (subclass @ (singleton @ X0) @ X1))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl438, zip_derived_cl2])).
% 4.71/1.32 thf(zip_derived_cl1183, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ X0 @ X1) | (subclass @ (singleton @ X0) @ X1))),
% 4.71/1.32 inference('simplify', [status(thm)], [zip_derived_cl1169])).
% 4.71/1.32 thf(complement2, axiom,
% 4.71/1.32 (( ~( member @ Z @ universal_class ) ) |
% 4.71/1.32 ( member @ Z @ ( complement @ X ) ) | ( member @ Z @ X ))).
% 4.71/1.32 thf(zip_derived_cl24, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ X0 @ universal_class)
% 4.71/1.32 | (member @ X0 @ (complement @ X1))
% 4.71/1.32 | (member @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [complement2])).
% 4.71/1.32 thf(zip_derived_cl1, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 4.71/1.32 | (subclass @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [not_subclass_members1])).
% 4.71/1.32 thf(zip_derived_cl1, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 4.71/1.32 | (subclass @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [not_subclass_members1])).
% 4.71/1.32 thf(intersection2, axiom,
% 4.71/1.32 (( ~( member @ Z @ ( intersection @ X @ Y ) ) ) | ( member @ Z @ Y ))).
% 4.71/1.32 thf(zip_derived_cl21, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.71/1.32 (~ (member @ X0 @ (intersection @ X1 @ X2)) | (member @ X0 @ X2))),
% 4.71/1.32 inference('cnf', [status(esa)], [intersection2])).
% 4.71/1.32 thf(zip_derived_cl520, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.71/1.32 ( (subclass @ (intersection @ X1 @ X0) @ X2)
% 4.71/1.32 | (member @
% 4.71/1.32 (not_subclass_element @ (intersection @ X1 @ X0) @ X2) @ X0))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 4.71/1.32 thf(prove_corollary_1_to_number_of_elements_in_class_1, conjecture,
% 4.71/1.32 (member @
% 4.71/1.32 ( not_subclass_element @
% 4.71/1.32 ( intersection @
% 4.71/1.32 ( complement @
% 4.71/1.32 ( singleton @ ( not_subclass_element @ x @ null_class ) ) ) @
% 4.71/1.32 x ) @
% 4.71/1.32 null_class ) @
% 4.71/1.32 x)).
% 4.71/1.32 thf(zf_stmt_0, negated_conjecture,
% 4.71/1.32 (~( member @
% 4.71/1.32 ( not_subclass_element @
% 4.71/1.32 ( intersection @
% 4.71/1.32 ( complement @
% 4.71/1.32 ( singleton @ ( not_subclass_element @ x @ null_class ) ) ) @
% 4.71/1.32 x ) @
% 4.71/1.32 null_class ) @
% 4.71/1.32 x )),
% 4.71/1.32 inference('cnf.neg', [status(esa)],
% 4.71/1.32 [prove_corollary_1_to_number_of_elements_in_class_1])).
% 4.71/1.32 thf(zip_derived_cl91, plain,
% 4.71/1.32 (~ (member @
% 4.71/1.32 (not_subclass_element @
% 4.71/1.32 (intersection @
% 4.71/1.32 (complement @ (singleton @ (not_subclass_element @ x @ null_class))) @
% 4.71/1.32 x) @
% 4.71/1.32 null_class) @
% 4.71/1.32 x)),
% 4.71/1.32 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.71/1.32 thf(zip_derived_cl1990, plain,
% 4.71/1.32 ( (subclass @
% 4.71/1.32 (intersection @
% 4.71/1.32 (complement @ (singleton @ (not_subclass_element @ x @ null_class))) @
% 4.71/1.32 x) @
% 4.71/1.32 null_class)),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl520, zip_derived_cl91])).
% 4.71/1.32 thf(zip_derived_cl1, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 4.71/1.32 | (subclass @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [not_subclass_members1])).
% 4.71/1.32 thf(regularity1, axiom,
% 4.71/1.32 (( ( X ) = ( null_class ) ) | ( member @ ( regular @ X ) @ X ))).
% 4.71/1.32 thf(zip_derived_cl65, plain,
% 4.71/1.32 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 4.71/1.32 inference('cnf', [status(esa)], [regularity1])).
% 4.71/1.32 thf(class_elements_are_sets, axiom, (subclass @ X @ universal_class)).
% 4.71/1.32 thf(zip_derived_cl3, plain, (![X0 : $i]: (subclass @ X0 @ universal_class)),
% 4.71/1.32 inference('cnf', [status(esa)], [class_elements_are_sets])).
% 4.71/1.32 thf(subclass_members, axiom,
% 4.71/1.32 (( ~( subclass @ X @ Y ) ) | ( ~( member @ U @ X ) ) | ( member @ U @ Y ))).
% 4.71/1.32 thf(zip_derived_cl0, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.71/1.32 (~ (subclass @ X0 @ X1) | ~ (member @ X2 @ X0) | (member @ X2 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [subclass_members])).
% 4.71/1.32 thf(zip_derived_cl421, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 4.71/1.32 thf(zip_derived_cl454, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl421])).
% 4.71/1.32 thf(zip_derived_cl65, plain,
% 4.71/1.32 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 4.71/1.32 inference('cnf', [status(esa)], [regularity1])).
% 4.71/1.32 thf(complement1, axiom,
% 4.71/1.32 (( ~( member @ Z @ ( complement @ X ) ) ) | ( ~( member @ Z @ X ) ))).
% 4.71/1.32 thf(zip_derived_cl23, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [complement1])).
% 4.71/1.32 thf(zip_derived_cl457, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 (((complement @ X0) = (null_class))
% 4.71/1.32 | ~ (member @ (regular @ (complement @ X0)) @ X0))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl23])).
% 4.71/1.32 thf(zip_derived_cl496, plain,
% 4.71/1.32 ((((complement @ universal_class) = (null_class))
% 4.71/1.32 | ((complement @ universal_class) = (null_class)))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl454, zip_derived_cl457])).
% 4.71/1.32 thf(zip_derived_cl499, plain,
% 4.71/1.32 (((complement @ universal_class) = (null_class))),
% 4.71/1.32 inference('simplify', [status(thm)], [zip_derived_cl496])).
% 4.71/1.32 thf(zip_derived_cl23, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [complement1])).
% 4.71/1.32 thf(zip_derived_cl508, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 (~ (member @ X0 @ null_class) | ~ (member @ X0 @ universal_class))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl499, zip_derived_cl23])).
% 4.71/1.32 thf(zip_derived_cl421, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 4.71/1.32 thf(zip_derived_cl512, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 4.71/1.32 inference('clc', [status(thm)], [zip_derived_cl508, zip_derived_cl421])).
% 4.71/1.32 thf(zip_derived_cl513, plain, (![X0 : $i]: (subclass @ null_class @ X0)),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl512])).
% 4.71/1.32 thf(subclass_implies_equal, axiom,
% 4.71/1.32 (( ~( subclass @ X @ Y ) ) | ( ~( subclass @ Y @ X ) ) | ( ( X ) = ( Y ) ))).
% 4.71/1.32 thf(zip_derived_cl6, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | ((X0) = (X1)))),
% 4.71/1.32 inference('cnf', [status(esa)], [subclass_implies_equal])).
% 4.71/1.32 thf(zip_derived_cl516, plain,
% 4.71/1.32 (![X0 : $i]: (~ (subclass @ X0 @ null_class) | ((null_class) = (X0)))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl513, zip_derived_cl6])).
% 4.71/1.32 thf(zip_derived_cl2022, plain,
% 4.71/1.32 (((null_class)
% 4.71/1.32 = (intersection @
% 4.71/1.32 (complement @ (singleton @ (not_subclass_element @ x @ null_class))) @
% 4.71/1.32 x))),
% 4.71/1.32 inference('s_sup-', [status(thm)],
% 4.71/1.32 [zip_derived_cl1990, zip_derived_cl516])).
% 4.71/1.32 thf(intersection3, axiom,
% 4.71/1.32 (( ~( member @ Z @ X ) ) | ( ~( member @ Z @ Y ) ) |
% 4.71/1.32 ( member @ Z @ ( intersection @ X @ Y ) ))).
% 4.71/1.32 thf(zip_derived_cl22, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.71/1.32 (~ (member @ X0 @ X1)
% 4.71/1.32 | ~ (member @ X0 @ X2)
% 4.71/1.32 | (member @ X0 @ (intersection @ X1 @ X2)))),
% 4.71/1.32 inference('cnf', [status(esa)], [intersection3])).
% 4.71/1.32 thf(zip_derived_cl2030, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 (~ (member @ X0 @
% 4.71/1.32 (complement @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class))))
% 4.71/1.32 | ~ (member @ X0 @ x)
% 4.71/1.32 | (member @ X0 @ null_class))),
% 4.71/1.32 inference('s_sup+', [status(thm)], [zip_derived_cl2022, zip_derived_cl22])).
% 4.71/1.32 thf(zip_derived_cl512, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 4.71/1.32 inference('clc', [status(thm)], [zip_derived_cl508, zip_derived_cl421])).
% 4.71/1.32 thf(zip_derived_cl2040, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 (~ (member @ X0 @
% 4.71/1.32 (complement @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class))))
% 4.71/1.32 | ~ (member @ X0 @ x))),
% 4.71/1.32 inference('demod', [status(thm)], [zip_derived_cl2030, zip_derived_cl512])).
% 4.71/1.32 thf(zip_derived_cl2075, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 ( (subclass @ x @ X0)
% 4.71/1.32 | ~ (member @ (not_subclass_element @ x @ X0) @
% 4.71/1.32 (complement @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class)))))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl2040])).
% 4.71/1.32 thf(zip_derived_cl2114, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 ( (member @ (not_subclass_element @ x @ X0) @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class)))
% 4.71/1.32 | ~ (member @ (not_subclass_element @ x @ X0) @ universal_class)
% 4.71/1.32 | (subclass @ x @ X0))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl2075])).
% 4.71/1.32 thf(zip_derived_cl1, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 4.71/1.32 | (subclass @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [not_subclass_members1])).
% 4.71/1.32 thf(zip_derived_cl421, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 4.71/1.32 thf(zip_derived_cl425, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 ( (subclass @ X0 @ X1)
% 4.71/1.32 | (member @ (not_subclass_element @ X0 @ X1) @ universal_class))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl421])).
% 4.71/1.32 thf(zip_derived_cl2387, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 ( (subclass @ x @ X0)
% 4.71/1.32 | (member @ (not_subclass_element @ x @ X0) @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class))))),
% 4.71/1.32 inference('clc', [status(thm)], [zip_derived_cl2114, zip_derived_cl425])).
% 4.71/1.32 thf(zip_derived_cl2, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ (not_subclass_element @ X0 @ X1) @ X1)
% 4.71/1.32 | (subclass @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [not_subclass_members2])).
% 4.71/1.32 thf(zip_derived_cl2392, plain,
% 4.71/1.32 (( (subclass @ x @ (singleton @ (not_subclass_element @ x @ null_class)))
% 4.71/1.32 | (subclass @ x @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class))))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl2387, zip_derived_cl2])).
% 4.71/1.32 thf(zip_derived_cl2394, plain,
% 4.71/1.32 ( (subclass @ x @ (singleton @ (not_subclass_element @ x @ null_class)))),
% 4.71/1.32 inference('simplify', [status(thm)], [zip_derived_cl2392])).
% 4.71/1.32 thf(zip_derived_cl6, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | ((X0) = (X1)))),
% 4.71/1.32 inference('cnf', [status(esa)], [subclass_implies_equal])).
% 4.71/1.32 thf(zip_derived_cl2397, plain,
% 4.71/1.32 ((~ (subclass @ (singleton @ (not_subclass_element @ x @ null_class)) @ x)
% 4.71/1.32 | ((x) = (singleton @ (not_subclass_element @ x @ null_class))))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl2394, zip_derived_cl6])).
% 4.71/1.32 thf(prove_corollary_1_to_number_of_elements_in_class_2, conjecture,
% 4.71/1.32 (( singleton @ ( not_subclass_element @ x @ null_class ) ) = ( x ))).
% 4.71/1.32 thf(zf_stmt_1, negated_conjecture,
% 4.71/1.32 (( singleton @ ( not_subclass_element @ x @ null_class ) ) != ( x )),
% 4.71/1.32 inference('cnf.neg', [status(esa)],
% 4.71/1.32 [prove_corollary_1_to_number_of_elements_in_class_2])).
% 4.71/1.32 thf(zip_derived_cl92, plain,
% 4.71/1.32 (((singleton @ (not_subclass_element @ x @ null_class)) != (x))),
% 4.71/1.32 inference('cnf', [status(esa)], [zf_stmt_1])).
% 4.71/1.32 thf(zip_derived_cl2399, plain,
% 4.71/1.32 (~ (subclass @ (singleton @ (not_subclass_element @ x @ null_class)) @ x)),
% 4.71/1.32 inference('simplify_reflect-', [status(thm)],
% 4.71/1.32 [zip_derived_cl2397, zip_derived_cl92])).
% 4.71/1.32 thf(zip_derived_cl2400, plain,
% 4.71/1.32 (~ (member @ (not_subclass_element @ x @ null_class) @ x)),
% 4.71/1.32 inference('s_sup-', [status(thm)],
% 4.71/1.32 [zip_derived_cl1183, zip_derived_cl2399])).
% 4.71/1.32 thf(zip_derived_cl454, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl421])).
% 4.71/1.32 thf(zip_derived_cl24, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (~ (member @ X0 @ universal_class)
% 4.71/1.32 | (member @ X0 @ (complement @ X1))
% 4.71/1.32 | (member @ X0 @ X1))),
% 4.71/1.32 inference('cnf', [status(esa)], [complement2])).
% 4.71/1.32 thf(zip_derived_cl65, plain,
% 4.71/1.32 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 4.71/1.32 inference('cnf', [status(esa)], [regularity1])).
% 4.71/1.32 thf(zip_derived_cl2040, plain,
% 4.71/1.32 (![X0 : $i]:
% 4.71/1.32 (~ (member @ X0 @
% 4.71/1.32 (complement @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class))))
% 4.71/1.32 | ~ (member @ X0 @ x))),
% 4.71/1.32 inference('demod', [status(thm)], [zip_derived_cl2030, zip_derived_cl512])).
% 4.71/1.32 thf(zip_derived_cl2078, plain,
% 4.71/1.32 ((((x) = (null_class))
% 4.71/1.32 | ~ (member @ (regular @ x) @
% 4.71/1.32 (complement @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class)))))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl2040])).
% 4.71/1.32 thf(prove_corollary_1_to_number_of_elements_in_class_3, conjecture,
% 4.71/1.32 (( x ) = ( null_class ))).
% 4.71/1.32 thf(zf_stmt_2, negated_conjecture, (( x ) != ( null_class )),
% 4.71/1.32 inference('cnf.neg', [status(esa)],
% 4.71/1.32 [prove_corollary_1_to_number_of_elements_in_class_3])).
% 4.71/1.32 thf(zip_derived_cl93, plain, (((x) != (null_class))),
% 4.71/1.32 inference('cnf', [status(esa)], [zf_stmt_2])).
% 4.71/1.32 thf(zip_derived_cl2081, plain,
% 4.71/1.32 (~ (member @ (regular @ x) @
% 4.71/1.32 (complement @ (singleton @ (not_subclass_element @ x @ null_class))))),
% 4.71/1.32 inference('simplify_reflect-', [status(thm)],
% 4.71/1.32 [zip_derived_cl2078, zip_derived_cl93])).
% 4.71/1.32 thf(zip_derived_cl2083, plain,
% 4.71/1.32 (( (member @ (regular @ x) @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class)))
% 4.71/1.32 | ~ (member @ (regular @ x) @ universal_class))),
% 4.71/1.32 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl2081])).
% 4.71/1.32 thf(zip_derived_cl2231, plain,
% 4.71/1.32 ((((x) = (null_class))
% 4.71/1.32 | (member @ (regular @ x) @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class))))),
% 4.71/1.32 inference('s_sup-', [status(thm)],
% 4.71/1.32 [zip_derived_cl454, zip_derived_cl2083])).
% 4.71/1.32 thf(zip_derived_cl93, plain, (((x) != (null_class))),
% 4.71/1.32 inference('cnf', [status(esa)], [zf_stmt_2])).
% 4.71/1.32 thf(zip_derived_cl2232, plain,
% 4.71/1.32 ( (member @ (regular @ x) @
% 4.71/1.32 (singleton @ (not_subclass_element @ x @ null_class)))),
% 4.71/1.32 inference('simplify_reflect-', [status(thm)],
% 4.71/1.32 [zip_derived_cl2231, zip_derived_cl93])).
% 4.71/1.32 thf(zip_derived_cl437, plain,
% 4.71/1.32 (![X0 : $i, X1 : $i]:
% 4.71/1.32 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 4.71/1.32 inference('simplify', [status(thm)], [zip_derived_cl436])).
% 4.71/1.32 thf(zip_derived_cl2235, plain,
% 4.71/1.32 (((regular @ x) = (not_subclass_element @ x @ null_class))),
% 4.71/1.32 inference('s_sup-', [status(thm)],
% 4.71/1.32 [zip_derived_cl2232, zip_derived_cl437])).
% 4.71/1.32 thf(zip_derived_cl65, plain,
% 4.71/1.32 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 4.71/1.32 inference('cnf', [status(esa)], [regularity1])).
% 4.71/1.32 thf(zip_derived_cl2241, plain,
% 4.71/1.32 ((((x) = (null_class))
% 4.71/1.32 | (member @ (not_subclass_element @ x @ null_class) @ x))),
% 4.71/1.32 inference('s_sup+', [status(thm)], [zip_derived_cl2235, zip_derived_cl65])).
% 4.71/1.32 thf(zip_derived_cl93, plain, (((x) != (null_class))),
% 4.71/1.32 inference('cnf', [status(esa)], [zf_stmt_2])).
% 4.71/1.32 thf(zip_derived_cl2245, plain,
% 4.71/1.32 ( (member @ (not_subclass_element @ x @ null_class) @ x)),
% 4.71/1.32 inference('simplify_reflect-', [status(thm)],
% 4.71/1.32 [zip_derived_cl2241, zip_derived_cl93])).
% 4.71/1.32 thf(zip_derived_cl2402, plain, ($false),
% 4.71/1.32 inference('demod', [status(thm)],
% 4.71/1.32 [zip_derived_cl2400, zip_derived_cl2245])).
% 4.71/1.32
% 4.71/1.32 % SZS output end Refutation
% 4.71/1.32
% 4.71/1.32
% 4.71/1.32 % Terminating...
% 5.33/1.36 % Runner terminated.
% 5.33/1.38 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------