%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET066-6 : 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.lsQV1MVuRE true
% Computer : n016.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 04:51:25 PM UTC 2025
% Result : Unsatisfiable 255.14s 37.03s
% Output : Refutation 255.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SET066-6 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.04/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.lsQV1MVuRE true
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 1 12:57:53 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.33 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.33 % Running in FO mode
% 0.49/0.62 % Total configuration time : 435
% 0.49/0.62 % Estimated wc time : 1092
% 0.49/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.52/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.52/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo17_bce.sh running for 50s
% 3.71/1.09 % /export/starexec/sandbox2/solver/bin/fo/fo8.sh running for 50s
% 255.14/37.03 % Solved by fo/fo8.sh.
% 255.14/37.03 % done 11386 iterations in 35.895s
% 255.14/37.03 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 255.14/37.03 % SZS output start Refutation
% 255.14/37.03 thf(universal_class_type, type, universal_class: $i).
% 255.14/37.03 thf(null_class_type, type, null_class: $i).
% 255.14/37.03 thf(member_type, type, member: $i > $i > $o).
% 255.14/37.03 thf(x_type, type, x: $i).
% 255.14/37.03 thf(unordered_pair_type, type, unordered_pair: $i > $i > $i).
% 255.14/37.03 thf(y_type, type, y: $i).
% 255.14/37.03 thf(singleton_type, type, singleton: $i > $i).
% 255.14/37.03 thf(subclass_type, type, subclass: $i > $i > $o).
% 255.14/37.03 thf(not_subclass_element_type, type, not_subclass_element: $i > $i > $i).
% 255.14/37.03 thf(regular_type, type, regular: $i > $i).
% 255.14/37.03 thf(singleton_set, axiom, (( unordered_pair @ X @ X ) = ( singleton @ X ))).
% 255.14/37.03 thf(zip_derived_cl11, plain,
% 255.14/37.03 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 255.14/37.03 inference('cnf', [status(esa)], [singleton_set])).
% 255.14/37.03 thf(zip_derived_cl11, plain,
% 255.14/37.03 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 255.14/37.03 inference('cnf', [status(esa)], [singleton_set])).
% 255.14/37.03 thf(regularity1, axiom,
% 255.14/37.03 (( ( X ) = ( null_class ) ) | ( member @ ( regular @ X ) @ X ))).
% 255.14/37.03 thf(zip_derived_cl65, plain,
% 255.14/37.03 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 255.14/37.03 inference('cnf', [status(esa)], [regularity1])).
% 255.14/37.03 thf(unordered_pair_member, axiom,
% 255.14/37.03 (( ~( member @ U @ ( unordered_pair @ X @ Y ) ) ) | ( ( U ) = ( X ) ) |
% 255.14/37.03 ( ( U ) = ( Y ) ))).
% 255.14/37.03 thf(zip_derived_cl7, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 255.14/37.03 | ((X0) = (X1))
% 255.14/37.03 | ((X0) = (X2)))),
% 255.14/37.03 inference('cnf', [status(esa)], [unordered_pair_member])).
% 255.14/37.03 thf(zip_derived_cl180, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (((unordered_pair @ X1 @ X0) = (null_class))
% 255.14/37.03 | ((regular @ (unordered_pair @ X1 @ X0)) = (X1))
% 255.14/37.03 | ((regular @ (unordered_pair @ X1 @ X0)) = (X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl7])).
% 255.14/37.03 thf(zip_derived_cl65, plain,
% 255.14/37.03 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 255.14/37.03 inference('cnf', [status(esa)], [regularity1])).
% 255.14/37.03 thf(class_elements_are_sets, axiom, (subclass @ X @ universal_class)).
% 255.14/37.03 thf(zip_derived_cl3, plain, (![X0 : $i]: (subclass @ X0 @ universal_class)),
% 255.14/37.03 inference('cnf', [status(esa)], [class_elements_are_sets])).
% 255.14/37.03 thf(subclass_members, axiom,
% 255.14/37.03 (( ~( subclass @ X @ Y ) ) | ( ~( member @ U @ X ) ) | ( member @ U @ Y ))).
% 255.14/37.03 thf(zip_derived_cl0, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (subclass @ X0 @ X1) | ~ (member @ X2 @ X0) | (member @ X2 @ X1))),
% 255.14/37.03 inference('cnf', [status(esa)], [subclass_members])).
% 255.14/37.03 thf(zip_derived_cl93, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 255.14/37.03 thf(zip_derived_cl175, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl93])).
% 255.14/37.03 thf(zip_derived_cl2514, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (((regular @ (unordered_pair @ X0 @ X1)) = (X1))
% 255.14/37.03 | ((unordered_pair @ X0 @ X1) = (null_class))
% 255.14/37.03 | ((unordered_pair @ X0 @ X1) = (null_class))
% 255.14/37.03 | (member @ X0 @ universal_class))),
% 255.14/37.03 inference('s_sup+', [status(thm)], [zip_derived_cl180, zip_derived_cl175])).
% 255.14/37.03 thf(zip_derived_cl2544, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (member @ X0 @ universal_class)
% 255.14/37.03 | ((unordered_pair @ X0 @ X1) = (null_class))
% 255.14/37.03 | ((regular @ (unordered_pair @ X0 @ X1)) = (X1)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2514])).
% 255.14/37.03 thf(zip_derived_cl175, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl93])).
% 255.14/37.03 thf(zip_derived_cl18940, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (((unordered_pair @ X1 @ X0) = (null_class))
% 255.14/37.03 | (member @ X1 @ universal_class)
% 255.14/37.03 | ((unordered_pair @ X1 @ X0) = (null_class))
% 255.14/37.03 | (member @ X0 @ universal_class))),
% 255.14/37.03 inference('s_sup+', [status(thm)],
% 255.14/37.03 [zip_derived_cl2544, zip_derived_cl175])).
% 255.14/37.03 thf(zip_derived_cl18996, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ X1 @ universal_class)
% 255.14/37.03 | ((unordered_pair @ X1 @ X0) = (null_class)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl18940])).
% 255.14/37.03 thf(prove_commutativity_of_unordered_pair_1, conjecture,
% 255.14/37.03 (( unordered_pair @ x @ y ) = ( unordered_pair @ y @ x ))).
% 255.14/37.03 thf(zf_stmt_0, negated_conjecture,
% 255.14/37.03 (( unordered_pair @ x @ y ) != ( unordered_pair @ y @ x )),
% 255.14/37.03 inference('cnf.neg', [status(esa)],
% 255.14/37.03 [prove_commutativity_of_unordered_pair_1])).
% 255.14/37.03 thf(zip_derived_cl91, plain,
% 255.14/37.03 (((unordered_pair @ x @ y) != (unordered_pair @ y @ x))),
% 255.14/37.03 inference('cnf', [status(esa)], [zf_stmt_0])).
% 255.14/37.03 thf(zip_derived_cl19225, plain,
% 255.14/37.03 (( (member @ y @ universal_class)
% 255.14/37.03 | (member @ x @ universal_class)
% 255.14/37.03 | ((unordered_pair @ x @ y) != (null_class)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl18996, zip_derived_cl91])).
% 255.14/37.03 thf(zip_derived_cl18996, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ X1 @ universal_class)
% 255.14/37.03 | ((unordered_pair @ X1 @ X0) = (null_class)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl18940])).
% 255.14/37.03 thf(zip_derived_cl19381, plain,
% 255.14/37.03 (( (member @ x @ universal_class) | (member @ y @ universal_class))),
% 255.14/37.03 inference('clc', [status(thm)],
% 255.14/37.03 [zip_derived_cl19225, zip_derived_cl18996])).
% 255.14/37.03 thf(unordered_pair2, axiom,
% 255.14/37.03 (( ~( member @ X @ universal_class ) ) |
% 255.14/37.03 ( member @ X @ ( unordered_pair @ X @ Y ) ))).
% 255.14/37.03 thf(zip_derived_cl8, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ X0 @ (unordered_pair @ X0 @ X1)))),
% 255.14/37.03 inference('cnf', [status(esa)], [unordered_pair2])).
% 255.14/37.03 thf(zip_derived_cl19423, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | (member @ y @ (unordered_pair @ y @ X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl19381, zip_derived_cl8])).
% 255.14/37.03 thf(zip_derived_cl19473, plain,
% 255.14/37.03 (( (member @ x @ universal_class) | (member @ y @ (singleton @ y)))),
% 255.14/37.03 inference('s_sup+', [status(thm)],
% 255.14/37.03 [zip_derived_cl11, zip_derived_cl19423])).
% 255.14/37.03 thf(not_subclass_members1, axiom,
% 255.14/37.03 (( member @ ( not_subclass_element @ X @ Y ) @ X ) | ( subclass @ X @ Y ))).
% 255.14/37.03 thf(zip_derived_cl1, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 255.14/37.03 | (subclass @ X0 @ X1))),
% 255.14/37.03 inference('cnf', [status(esa)], [not_subclass_members1])).
% 255.14/37.03 thf(zip_derived_cl7, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 255.14/37.03 | ((X0) = (X1))
% 255.14/37.03 | ((X0) = (X2)))),
% 255.14/37.03 inference('cnf', [status(esa)], [unordered_pair_member])).
% 255.14/37.03 thf(zip_derived_cl107, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ X1 @ X0) @ X2)
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X1 @ X0) @ X2) = (X1))
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X1 @ X0) @ X2) = (X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 255.14/37.03 thf(not_subclass_members2, axiom,
% 255.14/37.03 (( ~( member @ ( not_subclass_element @ X @ Y ) @ Y ) ) |
% 255.14/37.03 ( subclass @ X @ Y ))).
% 255.14/37.03 thf(zip_derived_cl2, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ (not_subclass_element @ X0 @ X1) @ X1)
% 255.14/37.03 | (subclass @ X0 @ X1))),
% 255.14/37.03 inference('cnf', [status(esa)], [not_subclass_members2])).
% 255.14/37.03 thf(zip_derived_cl2185, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (((not_subclass_element @ (unordered_pair @ X2 @ X0) @ X1) = (X2))
% 255.14/37.03 | (subclass @ (unordered_pair @ X2 @ X0) @ X1)
% 255.14/37.03 | ~ (member @ X0 @ X1)
% 255.14/37.03 | (subclass @ (unordered_pair @ X2 @ X0) @ X1))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl107, zip_derived_cl2])).
% 255.14/37.03 thf(zip_derived_cl2209, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1)
% 255.14/37.03 | (subclass @ (unordered_pair @ X2 @ X0) @ X1)
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X2 @ X0) @ X1) = (X2)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2185])).
% 255.14/37.03 thf(zip_derived_cl144493, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ y) @ (singleton @ y))
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X0 @ y) @
% 255.14/37.03 (singleton @ y)) = (X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl19473, zip_derived_cl2209])).
% 255.14/37.03 thf(zip_derived_cl1, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 255.14/37.03 | (subclass @ X0 @ X1))),
% 255.14/37.03 inference('cnf', [status(esa)], [not_subclass_members1])).
% 255.14/37.03 thf(zip_derived_cl93, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 255.14/37.03 thf(zip_derived_cl100, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ X0 @ X1)
% 255.14/37.03 | (member @ (not_subclass_element @ X0 @ X1) @ universal_class))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl93])).
% 255.14/37.03 thf(zip_derived_cl145221, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ X0 @ y) @ (singleton @ y))
% 255.14/37.03 | (member @ x @ universal_class)
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ y) @ (singleton @ y))
% 255.14/37.03 | (member @ X0 @ universal_class))),
% 255.14/37.03 inference('s_sup+', [status(thm)],
% 255.14/37.03 [zip_derived_cl144493, zip_derived_cl100])).
% 255.14/37.03 thf(zip_derived_cl145245, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ x @ universal_class)
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ y) @ (singleton @ y)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl145221])).
% 255.14/37.03 thf(zip_derived_cl19381, plain,
% 255.14/37.03 (( (member @ x @ universal_class) | (member @ y @ universal_class))),
% 255.14/37.03 inference('clc', [status(thm)],
% 255.14/37.03 [zip_derived_cl19225, zip_derived_cl18996])).
% 255.14/37.03 thf(unordered_pair3, axiom,
% 255.14/37.03 (( ~( member @ Y @ universal_class ) ) |
% 255.14/37.03 ( member @ Y @ ( unordered_pair @ X @ Y ) ))).
% 255.14/37.03 thf(zip_derived_cl9, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ X0 @ (unordered_pair @ X1 @ X0)))),
% 255.14/37.03 inference('cnf', [status(esa)], [unordered_pair3])).
% 255.14/37.03 thf(zip_derived_cl19424, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | (member @ y @ (unordered_pair @ X0 @ y)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl19381, zip_derived_cl9])).
% 255.14/37.03 thf(zip_derived_cl1, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (member @ (not_subclass_element @ X0 @ X1) @ X0)
% 255.14/37.03 | (subclass @ X0 @ X1))),
% 255.14/37.03 inference('cnf', [status(esa)], [not_subclass_members1])).
% 255.14/37.03 thf(zip_derived_cl11, plain,
% 255.14/37.03 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 255.14/37.03 inference('cnf', [status(esa)], [singleton_set])).
% 255.14/37.03 thf(zip_derived_cl7, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 255.14/37.03 | ((X0) = (X1))
% 255.14/37.03 | ((X0) = (X2)))),
% 255.14/37.03 inference('cnf', [status(esa)], [unordered_pair_member])).
% 255.14/37.03 thf(zip_derived_cl108, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X1 @ (singleton @ X0)) | ((X1) = (X0)) | ((X1) = (X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl7])).
% 255.14/37.03 thf(zip_derived_cl109, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl108])).
% 255.14/37.03 thf(zip_derived_cl110, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ (singleton @ X0) @ X1)
% 255.14/37.03 | ((not_subclass_element @ (singleton @ X0) @ X1) = (X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl109])).
% 255.14/37.03 thf(zip_derived_cl2, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ (not_subclass_element @ X0 @ X1) @ X1)
% 255.14/37.03 | (subclass @ X0 @ X1))),
% 255.14/37.03 inference('cnf', [status(esa)], [not_subclass_members2])).
% 255.14/37.03 thf(zip_derived_cl2224, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ (singleton @ X0) @ X1)
% 255.14/37.03 | ~ (member @ X0 @ X1)
% 255.14/37.03 | (subclass @ (singleton @ X0) @ X1))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl2])).
% 255.14/37.03 thf(zip_derived_cl2230, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1) | (subclass @ (singleton @ X0) @ X1))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2224])).
% 255.14/37.03 thf(zip_derived_cl19614, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | (subclass @ (singleton @ y) @ (unordered_pair @ X0 @ y)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl19424, zip_derived_cl2230])).
% 255.14/37.03 thf(subclass_implies_equal, axiom,
% 255.14/37.03 (( ~( subclass @ X @ Y ) ) | ( ~( subclass @ Y @ X ) ) | ( ( X ) = ( Y ) ))).
% 255.14/37.03 thf(zip_derived_cl6, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | ((X0) = (X1)))),
% 255.14/37.03 inference('cnf', [status(esa)], [subclass_implies_equal])).
% 255.14/37.03 thf(zip_derived_cl19784, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | ~ (subclass @ (unordered_pair @ X0 @ y) @ (singleton @ y))
% 255.14/37.03 | ((singleton @ y) = (unordered_pair @ X0 @ y)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl19614, zip_derived_cl6])).
% 255.14/37.03 thf(zip_derived_cl146824, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ x @ universal_class)
% 255.14/37.03 | ((singleton @ y) = (unordered_pair @ X0 @ y)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl145245, zip_derived_cl19784])).
% 255.14/37.03 thf(zip_derived_cl146842, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 (((singleton @ y) = (unordered_pair @ X0 @ y))
% 255.14/37.03 | (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ x @ universal_class))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl146824])).
% 255.14/37.03 thf(zip_derived_cl19473, plain,
% 255.14/37.03 (( (member @ x @ universal_class) | (member @ y @ (singleton @ y)))),
% 255.14/37.03 inference('s_sup+', [status(thm)],
% 255.14/37.03 [zip_derived_cl11, zip_derived_cl19423])).
% 255.14/37.03 thf(zip_derived_cl107, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ X1 @ X0) @ X2)
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X1 @ X0) @ X2) = (X1))
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X1 @ X0) @ X2) = (X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 255.14/37.03 thf(zip_derived_cl2, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ (not_subclass_element @ X0 @ X1) @ X1)
% 255.14/37.03 | (subclass @ X0 @ X1))),
% 255.14/37.03 inference('cnf', [status(esa)], [not_subclass_members2])).
% 255.14/37.03 thf(zip_derived_cl2181, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (((not_subclass_element @ (unordered_pair @ X0 @ X2) @ X1) = (X2))
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ X2) @ X1)
% 255.14/37.03 | ~ (member @ X0 @ X1)
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ X2) @ X1))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl107, zip_derived_cl2])).
% 255.14/37.03 thf(zip_derived_cl2205, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1)
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ X2) @ X1)
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X0 @ X2) @ X1) = (X2)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2181])).
% 255.14/37.03 thf(zip_derived_cl131119, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | (subclass @ (unordered_pair @ y @ X0) @ (singleton @ y))
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ y @ X0) @
% 255.14/37.03 (singleton @ y)) = (X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl19473, zip_derived_cl2205])).
% 255.14/37.03 thf(zip_derived_cl100, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ X0 @ X1)
% 255.14/37.03 | (member @ (not_subclass_element @ X0 @ X1) @ universal_class))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl93])).
% 255.14/37.03 thf(zip_derived_cl131871, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ y @ X0) @ (singleton @ y))
% 255.14/37.03 | (member @ x @ universal_class)
% 255.14/37.03 | (subclass @ (unordered_pair @ y @ X0) @ (singleton @ y))
% 255.14/37.03 | (member @ X0 @ universal_class))),
% 255.14/37.03 inference('s_sup+', [status(thm)],
% 255.14/37.03 [zip_derived_cl131119, zip_derived_cl100])).
% 255.14/37.03 thf(zip_derived_cl131890, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ x @ universal_class)
% 255.14/37.03 | (subclass @ (unordered_pair @ y @ X0) @ (singleton @ y)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl131871])).
% 255.14/37.03 thf(zip_derived_cl19423, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | (member @ y @ (unordered_pair @ y @ X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl19381, zip_derived_cl8])).
% 255.14/37.03 thf(zip_derived_cl2230, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1) | (subclass @ (singleton @ X0) @ X1))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2224])).
% 255.14/37.03 thf(zip_derived_cl19445, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | (subclass @ (singleton @ y) @ (unordered_pair @ y @ X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl19423, zip_derived_cl2230])).
% 255.14/37.03 thf(zip_derived_cl6, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | ((X0) = (X1)))),
% 255.14/37.03 inference('cnf', [status(esa)], [subclass_implies_equal])).
% 255.14/37.03 thf(zip_derived_cl19695, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | ~ (subclass @ (unordered_pair @ y @ X0) @ (singleton @ y))
% 255.14/37.03 | ((singleton @ y) = (unordered_pair @ y @ X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl19445, zip_derived_cl6])).
% 255.14/37.03 thf(zip_derived_cl132942, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ x @ universal_class)
% 255.14/37.03 | (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ x @ universal_class)
% 255.14/37.03 | ((singleton @ y) = (unordered_pair @ y @ X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl131890, zip_derived_cl19695])).
% 255.14/37.03 thf(zip_derived_cl132958, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 (((singleton @ y) = (unordered_pair @ y @ X0))
% 255.14/37.03 | (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ x @ universal_class))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl132942])).
% 255.14/37.03 thf(zip_derived_cl91, plain,
% 255.14/37.03 (((unordered_pair @ x @ y) != (unordered_pair @ y @ x))),
% 255.14/37.03 inference('cnf', [status(esa)], [zf_stmt_0])).
% 255.14/37.03 thf(zip_derived_cl133427, plain,
% 255.14/37.03 (( (member @ x @ universal_class)
% 255.14/37.03 | (member @ x @ universal_class)
% 255.14/37.03 | ((unordered_pair @ x @ y) != (singleton @ y)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl132958, zip_derived_cl91])).
% 255.14/37.03 thf(zip_derived_cl133780, plain,
% 255.14/37.03 ((((unordered_pair @ x @ y) != (singleton @ y))
% 255.14/37.03 | (member @ x @ universal_class))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl133427])).
% 255.14/37.03 thf(zip_derived_cl147306, plain,
% 255.14/37.03 (( (member @ x @ universal_class)
% 255.14/37.03 | (member @ x @ universal_class)
% 255.14/37.03 | ((singleton @ y) != (singleton @ y))
% 255.14/37.03 | (member @ x @ universal_class))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl146842, zip_derived_cl133780])).
% 255.14/37.03 thf(zip_derived_cl147726, plain, ( (member @ x @ universal_class)),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl147306])).
% 255.14/37.03 thf(zip_derived_cl8, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ X0 @ (unordered_pair @ X0 @ X1)))),
% 255.14/37.03 inference('cnf', [status(esa)], [unordered_pair2])).
% 255.14/37.03 thf(zip_derived_cl147886, plain,
% 255.14/37.03 (![X0 : $i]: (member @ x @ (unordered_pair @ x @ X0))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147726, zip_derived_cl8])).
% 255.14/37.03 thf(zip_derived_cl147986, plain, ( (member @ x @ (singleton @ x))),
% 255.14/37.03 inference('s_sup+', [status(thm)],
% 255.14/37.03 [zip_derived_cl11, zip_derived_cl147886])).
% 255.14/37.03 thf(zip_derived_cl2209, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1)
% 255.14/37.03 | (subclass @ (unordered_pair @ X2 @ X0) @ X1)
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X2 @ X0) @ X1) = (X2)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2185])).
% 255.14/37.03 thf(zip_derived_cl148145, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ X0 @ x) @ (singleton @ x))
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X0 @ x) @
% 255.14/37.03 (singleton @ x)) = (X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147986, zip_derived_cl2209])).
% 255.14/37.03 thf(zip_derived_cl100, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ X0 @ X1)
% 255.14/37.03 | (member @ (not_subclass_element @ X0 @ X1) @ universal_class))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl93])).
% 255.14/37.03 thf(zip_derived_cl159864, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ X0 @ x) @ (singleton @ x))
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ x) @ (singleton @ x))
% 255.14/37.03 | (member @ X0 @ universal_class))),
% 255.14/37.03 inference('s_sup+', [status(thm)],
% 255.14/37.03 [zip_derived_cl148145, zip_derived_cl100])).
% 255.14/37.03 thf(zip_derived_cl159889, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ X0 @ universal_class)
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ x) @ (singleton @ x)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl159864])).
% 255.14/37.03 thf(zip_derived_cl147726, plain, ( (member @ x @ universal_class)),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl147306])).
% 255.14/37.03 thf(zip_derived_cl9, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ X0 @ (unordered_pair @ X1 @ X0)))),
% 255.14/37.03 inference('cnf', [status(esa)], [unordered_pair3])).
% 255.14/37.03 thf(zip_derived_cl147887, plain,
% 255.14/37.03 (![X0 : $i]: (member @ x @ (unordered_pair @ X0 @ x))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147726, zip_derived_cl9])).
% 255.14/37.03 thf(zip_derived_cl2230, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1) | (subclass @ (singleton @ X0) @ X1))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2224])).
% 255.14/37.03 thf(zip_derived_cl148246, plain,
% 255.14/37.03 (![X0 : $i]: (subclass @ (singleton @ x) @ (unordered_pair @ X0 @ x))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147887, zip_derived_cl2230])).
% 255.14/37.03 thf(zip_derived_cl6, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | ((X0) = (X1)))),
% 255.14/37.03 inference('cnf', [status(esa)], [subclass_implies_equal])).
% 255.14/37.03 thf(zip_derived_cl148424, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 (~ (subclass @ (unordered_pair @ X0 @ x) @ (singleton @ x))
% 255.14/37.03 | ((singleton @ x) = (unordered_pair @ X0 @ x)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl148246, zip_derived_cl6])).
% 255.14/37.03 thf(zip_derived_cl160567, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ X0 @ universal_class)
% 255.14/37.03 | ((singleton @ x) = (unordered_pair @ X0 @ x)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl159889, zip_derived_cl148424])).
% 255.14/37.03 thf(zip_derived_cl91, plain,
% 255.14/37.03 (((unordered_pair @ x @ y) != (unordered_pair @ y @ x))),
% 255.14/37.03 inference('cnf', [status(esa)], [zf_stmt_0])).
% 255.14/37.03 thf(zip_derived_cl161036, plain,
% 255.14/37.03 (( (member @ y @ universal_class)
% 255.14/37.03 | ((unordered_pair @ x @ y) != (singleton @ x)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl160567, zip_derived_cl91])).
% 255.14/37.03 thf(zip_derived_cl147986, plain, ( (member @ x @ (singleton @ x))),
% 255.14/37.03 inference('s_sup+', [status(thm)],
% 255.14/37.03 [zip_derived_cl11, zip_derived_cl147886])).
% 255.14/37.03 thf(zip_derived_cl2205, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1)
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ X2) @ X1)
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X0 @ X2) @ X1) = (X2)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2181])).
% 255.14/37.03 thf(zip_derived_cl148144, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ x @ X0) @ (singleton @ x))
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ x @ X0) @
% 255.14/37.03 (singleton @ x)) = (X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147986, zip_derived_cl2205])).
% 255.14/37.03 thf(zip_derived_cl100, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ X0 @ X1)
% 255.14/37.03 | (member @ (not_subclass_element @ X0 @ X1) @ universal_class))),
% 255.14/37.03 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl93])).
% 255.14/37.03 thf(zip_derived_cl157938, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ x @ X0) @ (singleton @ x))
% 255.14/37.03 | (subclass @ (unordered_pair @ x @ X0) @ (singleton @ x))
% 255.14/37.03 | (member @ X0 @ universal_class))),
% 255.14/37.03 inference('s_sup+', [status(thm)],
% 255.14/37.03 [zip_derived_cl148144, zip_derived_cl100])).
% 255.14/37.03 thf(zip_derived_cl157962, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ X0 @ universal_class)
% 255.14/37.03 | (subclass @ (unordered_pair @ x @ X0) @ (singleton @ x)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl157938])).
% 255.14/37.03 thf(zip_derived_cl147886, plain,
% 255.14/37.03 (![X0 : $i]: (member @ x @ (unordered_pair @ x @ X0))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147726, zip_derived_cl8])).
% 255.14/37.03 thf(zip_derived_cl2230, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1) | (subclass @ (singleton @ X0) @ X1))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2224])).
% 255.14/37.03 thf(zip_derived_cl147940, plain,
% 255.14/37.03 (![X0 : $i]: (subclass @ (singleton @ x) @ (unordered_pair @ x @ X0))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147886, zip_derived_cl2230])).
% 255.14/37.03 thf(zip_derived_cl6, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | ((X0) = (X1)))),
% 255.14/37.03 inference('cnf', [status(esa)], [subclass_implies_equal])).
% 255.14/37.03 thf(zip_derived_cl148395, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 (~ (subclass @ (unordered_pair @ x @ X0) @ (singleton @ x))
% 255.14/37.03 | ((singleton @ x) = (unordered_pair @ x @ X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147940, zip_derived_cl6])).
% 255.14/37.03 thf(zip_derived_cl158890, plain,
% 255.14/37.03 (![X0 : $i]:
% 255.14/37.03 ( (member @ X0 @ universal_class)
% 255.14/37.03 | ((singleton @ x) = (unordered_pair @ x @ X0)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl157962, zip_derived_cl148395])).
% 255.14/37.03 thf(zip_derived_cl161369, plain, ( (member @ y @ universal_class)),
% 255.14/37.03 inference('clc', [status(thm)],
% 255.14/37.03 [zip_derived_cl161036, zip_derived_cl158890])).
% 255.14/37.03 thf(zip_derived_cl9, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ X0 @ (unordered_pair @ X1 @ X0)))),
% 255.14/37.03 inference('cnf', [status(esa)], [unordered_pair3])).
% 255.14/37.03 thf(zip_derived_cl161458, plain,
% 255.14/37.03 (![X0 : $i]: (member @ y @ (unordered_pair @ X0 @ y))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl161369, zip_derived_cl9])).
% 255.14/37.03 thf(zip_derived_cl147886, plain,
% 255.14/37.03 (![X0 : $i]: (member @ x @ (unordered_pair @ x @ X0))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147726, zip_derived_cl8])).
% 255.14/37.03 thf(zip_derived_cl2209, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1)
% 255.14/37.03 | (subclass @ (unordered_pair @ X2 @ X0) @ X1)
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X2 @ X0) @ X1) = (X2)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2185])).
% 255.14/37.03 thf(zip_derived_cl147939, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ X1 @ x) @ (unordered_pair @ x @ X0))
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X1 @ x) @
% 255.14/37.03 (unordered_pair @ x @ X0)) = (X1)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147886, zip_derived_cl2209])).
% 255.14/37.03 thf(zip_derived_cl2, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ (not_subclass_element @ X0 @ X1) @ X1)
% 255.14/37.03 | (subclass @ X0 @ X1))),
% 255.14/37.03 inference('cnf', [status(esa)], [not_subclass_members2])).
% 255.14/37.03 thf(zip_derived_cl180818, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ X0 @ x) @ (unordered_pair @ x @ X1))
% 255.14/37.03 | ~ (member @ X0 @ (unordered_pair @ x @ X1))
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ x) @ (unordered_pair @ x @ X1)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147939, zip_derived_cl2])).
% 255.14/37.03 thf(zip_derived_cl180876, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ (unordered_pair @ x @ X1))
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ x) @ (unordered_pair @ x @ X1)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl180818])).
% 255.14/37.03 thf(zip_derived_cl180948, plain,
% 255.14/37.03 ( (subclass @ (unordered_pair @ y @ x) @ (unordered_pair @ x @ y))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl161458, zip_derived_cl180876])).
% 255.14/37.03 thf(zip_derived_cl6, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (subclass @ X0 @ X1) | ~ (subclass @ X1 @ X0) | ((X0) = (X1)))),
% 255.14/37.03 inference('cnf', [status(esa)], [subclass_implies_equal])).
% 255.14/37.03 thf(zip_derived_cl180969, plain,
% 255.14/37.03 ((~ (subclass @ (unordered_pair @ x @ y) @ (unordered_pair @ y @ x))
% 255.14/37.03 | ((unordered_pair @ y @ x) = (unordered_pair @ x @ y)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl180948, zip_derived_cl6])).
% 255.14/37.03 thf(zip_derived_cl91, plain,
% 255.14/37.03 (((unordered_pair @ x @ y) != (unordered_pair @ y @ x))),
% 255.14/37.03 inference('cnf', [status(esa)], [zf_stmt_0])).
% 255.14/37.03 thf(zip_derived_cl180988, plain,
% 255.14/37.03 (~ (subclass @ (unordered_pair @ x @ y) @ (unordered_pair @ y @ x))),
% 255.14/37.03 inference('simplify_reflect-', [status(thm)],
% 255.14/37.03 [zip_derived_cl180969, zip_derived_cl91])).
% 255.14/37.03 thf(zip_derived_cl161369, plain, ( (member @ y @ universal_class)),
% 255.14/37.03 inference('clc', [status(thm)],
% 255.14/37.03 [zip_derived_cl161036, zip_derived_cl158890])).
% 255.14/37.03 thf(zip_derived_cl8, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ universal_class)
% 255.14/37.03 | (member @ X0 @ (unordered_pair @ X0 @ X1)))),
% 255.14/37.03 inference('cnf', [status(esa)], [unordered_pair2])).
% 255.14/37.03 thf(zip_derived_cl161457, plain,
% 255.14/37.03 (![X0 : $i]: (member @ y @ (unordered_pair @ y @ X0))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl161369, zip_derived_cl8])).
% 255.14/37.03 thf(zip_derived_cl147887, plain,
% 255.14/37.03 (![X0 : $i]: (member @ x @ (unordered_pair @ X0 @ x))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147726, zip_derived_cl9])).
% 255.14/37.03 thf(zip_derived_cl2205, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 255.14/37.03 (~ (member @ X0 @ X1)
% 255.14/37.03 | (subclass @ (unordered_pair @ X0 @ X2) @ X1)
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ X0 @ X2) @ X1) = (X2)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl2181])).
% 255.14/37.03 thf(zip_derived_cl148244, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ x @ X1) @ (unordered_pair @ X0 @ x))
% 255.14/37.03 | ((not_subclass_element @ (unordered_pair @ x @ X1) @
% 255.14/37.03 (unordered_pair @ X0 @ x)) = (X1)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl147887, zip_derived_cl2205])).
% 255.14/37.03 thf(zip_derived_cl2, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ (not_subclass_element @ X0 @ X1) @ X1)
% 255.14/37.03 | (subclass @ X0 @ X1))),
% 255.14/37.03 inference('cnf', [status(esa)], [not_subclass_members2])).
% 255.14/37.03 thf(zip_derived_cl198843, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 ( (subclass @ (unordered_pair @ x @ X0) @ (unordered_pair @ X1 @ x))
% 255.14/37.03 | ~ (member @ X0 @ (unordered_pair @ X1 @ x))
% 255.14/37.03 | (subclass @ (unordered_pair @ x @ X0) @ (unordered_pair @ X1 @ x)))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl148244, zip_derived_cl2])).
% 255.14/37.03 thf(zip_derived_cl198902, plain,
% 255.14/37.03 (![X0 : $i, X1 : $i]:
% 255.14/37.03 (~ (member @ X0 @ (unordered_pair @ X1 @ x))
% 255.14/37.03 | (subclass @ (unordered_pair @ x @ X0) @ (unordered_pair @ X1 @ x)))),
% 255.14/37.03 inference('simplify', [status(thm)], [zip_derived_cl198843])).
% 255.14/37.03 thf(zip_derived_cl199060, plain,
% 255.14/37.03 ( (subclass @ (unordered_pair @ x @ y) @ (unordered_pair @ y @ x))),
% 255.14/37.03 inference('s_sup-', [status(thm)],
% 255.14/37.03 [zip_derived_cl161457, zip_derived_cl198902])).
% 255.14/37.03 thf(zip_derived_cl199078, plain, ($false),
% 255.14/37.03 inference('demod', [status(thm)],
% 255.14/37.03 [zip_derived_cl180988, zip_derived_cl199060])).
% 255.14/37.03
% 255.14/37.03 % SZS output end Refutation
% 255.14/37.03
% 255.14/37.03
% 255.14/37.03 % Terminating...
% 255.23/37.10 % Runner terminated.
% 255.23/37.12 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------