%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET114-7 : TPTP v9.2.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lzWxY89hyi true
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:51:37 PM UTC 2025
% Result : Unsatisfiable 0.57s 0.90s
% Output : Refutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET114-7 : TPTP v9.2.0. Bugfixed v7.3.0.
% 0.04/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lzWxY89hyi true
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 13:12:23 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Number of cores: 8
% 0.14/0.34 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.55/0.64 % Total configuration time : 435
% 0.55/0.64 % Estimated wc time : 1092
% 0.55/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.55/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.57/0.90 % Solved by fo/fo3_bce.sh.
% 0.57/0.90 % BCE start: 80
% 0.57/0.90 % BCE eliminated: 0
% 0.57/0.90 % PE start: 80
% 0.57/0.90 logic: eq
% 0.57/0.90 % PE eliminated: 7
% 0.57/0.90 % done 192 iterations in 0.157s
% 0.57/0.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.57/0.90 % SZS output start Refutation
% 0.57/0.90 thf(universal_class_type, type, universal_class: $i).
% 0.57/0.90 thf(null_class_type, type, null_class: $i).
% 0.57/0.90 thf(member_type, type, member: $i > $i > $o).
% 0.57/0.90 thf(second_type, type, second: $i > $i).
% 0.57/0.90 thf(unordered_pair_type, type, unordered_pair: $i > $i > $i).
% 0.57/0.90 thf(singleton_type, type, singleton: $i > $i).
% 0.57/0.90 thf(cross_product_type, type, cross_product: $i > $i > $i).
% 0.57/0.90 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 0.57/0.90 thf(x_type, type, x: $i).
% 0.57/0.90 thf(first_type, type, first: $i > $i).
% 0.57/0.90 thf(singleton_is_null_class, axiom,
% 0.57/0.90 (( member @ X @ universal_class ) | ( ( singleton @ X ) = ( null_class ) ))).
% 0.57/0.90 thf(zip_derived_cl54, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 ( (member @ X0 @ universal_class) | ((singleton @ X0) = (null_class)))),
% 0.57/0.90 inference('cnf', [status(esa)], [singleton_is_null_class])).
% 0.57/0.90 thf(prove_unique_1st_and_2nd_in_pair_of_non_sets2_1, conjecture,
% 0.57/0.90 (member @
% 0.57/0.90 ( ordered_pair @ ( first @ x ) @ ( second @ x ) ) @
% 0.57/0.90 ( cross_product @ universal_class @ universal_class ))).
% 0.57/0.90 thf(zf_stmt_0, negated_conjecture,
% 0.57/0.90 (~( member @
% 0.57/0.90 ( ordered_pair @ ( first @ x ) @ ( second @ x ) ) @
% 0.57/0.90 ( cross_product @ universal_class @ universal_class ) )),
% 0.57/0.90 inference('cnf.neg', [status(esa)],
% 0.57/0.90 [prove_unique_1st_and_2nd_in_pair_of_non_sets2_1])).
% 0.57/0.90 thf(zip_derived_cl79, plain,
% 0.57/0.90 (~ (member @ (ordered_pair @ (first @ x) @ (second @ x)) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))),
% 0.57/0.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.90 thf(ordered_pair, axiom,
% 0.57/0.90 (( unordered_pair @
% 0.57/0.90 ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) =
% 0.57/0.90 ( ordered_pair @ X @ Y ))).
% 0.57/0.90 thf(zip_derived_cl12, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i]:
% 0.57/0.90 ((unordered_pair @ (singleton @ X0) @
% 0.57/0.90 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 0.57/0.90 inference('cnf', [status(esa)], [ordered_pair])).
% 0.57/0.90 thf(zip_derived_cl488, plain,
% 0.57/0.90 (~ (member @
% 0.57/0.90 (unordered_pair @ (singleton @ (first @ x)) @
% 0.57/0.90 (unordered_pair @ (first @ x) @ (singleton @ (second @ x)))) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))),
% 0.57/0.90 inference('demod', [status(thm)], [zip_derived_cl79, zip_derived_cl12])).
% 0.57/0.90 thf(zip_derived_cl488, plain,
% 0.57/0.90 (~ (member @
% 0.57/0.90 (unordered_pair @ (singleton @ (first @ x)) @
% 0.57/0.90 (unordered_pair @ (first @ x) @ (singleton @ (second @ x)))) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))),
% 0.57/0.90 inference('demod', [status(thm)], [zip_derived_cl79, zip_derived_cl12])).
% 0.57/0.90 thf(existence_of_1st_and_2nd_2, axiom,
% 0.57/0.90 (( member @
% 0.57/0.90 ( ordered_pair @ ( first @ X ) @ ( second @ X ) ) @
% 0.57/0.90 ( cross_product @ universal_class @ universal_class ) ) |
% 0.57/0.90 ( ( first @ X ) = ( X ) ))).
% 0.57/0.90 thf(zip_derived_cl72, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 ( (member @ (ordered_pair @ (first @ X0) @ (second @ X0)) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))
% 0.57/0.90 | ((first @ X0) = (X0)))),
% 0.57/0.90 inference('cnf', [status(esa)], [existence_of_1st_and_2nd_2])).
% 0.57/0.90 thf(zip_derived_cl12, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i]:
% 0.57/0.90 ((unordered_pair @ (singleton @ X0) @
% 0.57/0.90 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 0.57/0.90 inference('cnf', [status(esa)], [ordered_pair])).
% 0.57/0.90 thf(zip_derived_cl803, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 ( (member @
% 0.57/0.90 (unordered_pair @ (singleton @ (first @ X0)) @
% 0.57/0.90 (unordered_pair @ (first @ X0) @ (singleton @ (second @ X0)))) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))
% 0.57/0.90 | ((first @ X0) = (X0)))),
% 0.57/0.90 inference('demod', [status(thm)], [zip_derived_cl72, zip_derived_cl12])).
% 0.57/0.90 thf(zip_derived_cl909, plain, (((first @ x) = (x))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl488, zip_derived_cl803])).
% 0.57/0.90 thf(zip_derived_cl909, plain, (((first @ x) = (x))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl488, zip_derived_cl803])).
% 0.57/0.90 thf(zip_derived_cl930, plain,
% 0.57/0.90 (~ (member @
% 0.57/0.90 (unordered_pair @ (singleton @ x) @
% 0.57/0.90 (unordered_pair @ x @ (singleton @ (second @ x)))) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))),
% 0.57/0.90 inference('demod', [status(thm)],
% 0.57/0.90 [zip_derived_cl488, zip_derived_cl909, zip_derived_cl909])).
% 0.57/0.90 thf(cartesian_product3, axiom,
% 0.57/0.90 (( ~( member @ U @ X ) ) | ( ~( member @ V @ Y ) ) |
% 0.57/0.90 ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ))).
% 0.57/0.90 thf(zip_derived_cl15, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.90 (~ (member @ X0 @ X1)
% 0.57/0.90 | ~ (member @ X2 @ X3)
% 0.57/0.90 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 0.57/0.90 inference('cnf', [status(esa)], [cartesian_product3])).
% 0.57/0.90 thf(zip_derived_cl12, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i]:
% 0.57/0.90 ((unordered_pair @ (singleton @ X0) @
% 0.57/0.90 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 0.57/0.90 inference('cnf', [status(esa)], [ordered_pair])).
% 0.57/0.90 thf(zip_derived_cl539, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.90 (~ (member @ X0 @ X1)
% 0.57/0.90 | ~ (member @ X2 @ X3)
% 0.57/0.90 | (member @
% 0.57/0.90 (unordered_pair @ (singleton @ X0) @
% 0.57/0.90 (unordered_pair @ X0 @ (singleton @ X2))) @
% 0.57/0.90 (cross_product @ X1 @ X3)))),
% 0.57/0.90 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl12])).
% 0.57/0.90 thf(zip_derived_cl974, plain,
% 0.57/0.90 ((~ (member @ (second @ x) @ universal_class)
% 0.57/0.90 | ~ (member @ x @ universal_class))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl930, zip_derived_cl539])).
% 0.57/0.90 thf(zip_derived_cl54, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 ( (member @ X0 @ universal_class) | ((singleton @ X0) = (null_class)))),
% 0.57/0.90 inference('cnf', [status(esa)], [singleton_is_null_class])).
% 0.57/0.90 thf(zip_derived_cl990, plain,
% 0.57/0.90 ((~ (member @ x @ universal_class)
% 0.57/0.90 | ((singleton @ (second @ x)) = (null_class)))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl54])).
% 0.57/0.90 thf(zip_derived_cl1000, plain,
% 0.57/0.90 ((((singleton @ x) = (null_class))
% 0.57/0.90 | ((singleton @ (second @ x)) = (null_class)))),
% 0.57/0.90 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl990])).
% 0.57/0.90 thf(existence_of_1st_and_2nd_5, axiom,
% 0.57/0.90 (( ( ordered_pair @ ( first @ X ) @ ( second @ X ) ) = ( X ) ) |
% 0.57/0.90 ( ( second @ X ) = ( X ) ))).
% 0.57/0.90 thf(zip_derived_cl75, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 (((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0))
% 0.57/0.90 | ((second @ X0) = (X0)))),
% 0.57/0.90 inference('cnf', [status(esa)], [existence_of_1st_and_2nd_5])).
% 0.57/0.90 thf(ordered_pair_is_set, axiom,
% 0.57/0.90 (member @ ( ordered_pair @ X @ Y ) @ universal_class)).
% 0.57/0.90 thf(zip_derived_cl63, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i]:
% 0.57/0.90 (member @ (ordered_pair @ X0 @ X1) @ universal_class)),
% 0.57/0.90 inference('cnf', [status(esa)], [ordered_pair_is_set])).
% 0.57/0.90 thf(corollary_to_set_in_its_singleton, axiom,
% 0.57/0.90 (( ~( member @ X @ universal_class ) ) |
% 0.57/0.90 ( ( singleton @ X ) != ( null_class ) ))).
% 0.57/0.90 thf(zip_derived_cl51, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 (~ (member @ X0 @ universal_class)
% 0.57/0.90 | ((singleton @ X0) != (null_class)))),
% 0.57/0.90 inference('cnf', [status(esa)], [corollary_to_set_in_its_singleton])).
% 0.57/0.90 thf(zip_derived_cl329, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i]:
% 0.57/0.90 ((singleton @ (ordered_pair @ X1 @ X0)) != (null_class))),
% 0.57/0.90 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl51])).
% 0.57/0.90 thf(zip_derived_cl466, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 (((singleton @ X0) != (null_class)) | ((second @ X0) = (X0)))),
% 0.57/0.90 inference('sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl329])).
% 0.57/0.90 thf(prove_unique_2nd_in_pair_of_non_sets, conjecture,
% 0.57/0.90 (( second @ x ) = ( x ))).
% 0.57/0.90 thf(zf_stmt_1, negated_conjecture, (( second @ x ) != ( x )),
% 0.57/0.90 inference('cnf.neg', [status(esa)], [prove_unique_2nd_in_pair_of_non_sets])).
% 0.57/0.90 thf(zip_derived_cl78, plain, (((second @ x) != (x))),
% 0.57/0.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.57/0.90 thf(zip_derived_cl474, plain,
% 0.57/0.90 ((((x) != (x)) | ((singleton @ x) != (null_class)))),
% 0.57/0.90 inference('sup-', [status(thm)], [zip_derived_cl466, zip_derived_cl78])).
% 0.57/0.90 thf(zip_derived_cl477, plain, (((singleton @ x) != (null_class))),
% 0.57/0.90 inference('simplify', [status(thm)], [zip_derived_cl474])).
% 0.57/0.90 thf(zip_derived_cl1001, plain, (((singleton @ (second @ x)) = (null_class))),
% 0.57/0.90 inference('simplify_reflect-', [status(thm)],
% 0.57/0.90 [zip_derived_cl1000, zip_derived_cl477])).
% 0.57/0.90 thf(existence_of_1st_and_2nd_3, axiom,
% 0.57/0.90 (( member @
% 0.57/0.90 ( ordered_pair @ ( first @ X ) @ ( second @ X ) ) @
% 0.57/0.90 ( cross_product @ universal_class @ universal_class ) ) |
% 0.57/0.90 ( ( second @ X ) = ( X ) ))).
% 0.57/0.90 thf(zip_derived_cl73, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 ( (member @ (ordered_pair @ (first @ X0) @ (second @ X0)) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))
% 0.57/0.90 | ((second @ X0) = (X0)))),
% 0.57/0.90 inference('cnf', [status(esa)], [existence_of_1st_and_2nd_3])).
% 0.57/0.90 thf(zip_derived_cl12, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i]:
% 0.57/0.90 ((unordered_pair @ (singleton @ X0) @
% 0.57/0.90 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 0.57/0.90 inference('cnf', [status(esa)], [ordered_pair])).
% 0.57/0.90 thf(zip_derived_cl1280, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 ( (member @
% 0.57/0.90 (unordered_pair @ (singleton @ (first @ X0)) @
% 0.57/0.90 (unordered_pair @ (first @ X0) @ (singleton @ (second @ X0)))) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))
% 0.57/0.90 | ((second @ X0) = (X0)))),
% 0.57/0.90 inference('demod', [status(thm)], [zip_derived_cl73, zip_derived_cl12])).
% 0.57/0.90 thf(zip_derived_cl1312, plain,
% 0.57/0.90 (( (member @
% 0.57/0.90 (unordered_pair @ (singleton @ (first @ x)) @
% 0.57/0.90 (unordered_pair @ (first @ x) @ null_class)) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))
% 0.57/0.90 | ((second @ x) = (x)))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl1001, zip_derived_cl1280])).
% 0.57/0.90 thf(zip_derived_cl909, plain, (((first @ x) = (x))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl488, zip_derived_cl803])).
% 0.57/0.90 thf(zip_derived_cl909, plain, (((first @ x) = (x))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl488, zip_derived_cl803])).
% 0.57/0.90 thf(commutativity_of_unordered_pair, axiom,
% 0.57/0.90 (( unordered_pair @ X @ Y ) = ( unordered_pair @ Y @ X ))).
% 0.57/0.90 thf(zip_derived_cl36, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i]:
% 0.57/0.90 ((unordered_pair @ X1 @ X0) = (unordered_pair @ X0 @ X1))),
% 0.57/0.90 inference('cnf', [status(esa)], [commutativity_of_unordered_pair])).
% 0.57/0.90 thf(zip_derived_cl909, plain, (((first @ x) = (x))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl488, zip_derived_cl803])).
% 0.57/0.90 thf(zip_derived_cl75, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 (((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0))
% 0.57/0.90 | ((second @ X0) = (X0)))),
% 0.57/0.90 inference('cnf', [status(esa)], [existence_of_1st_and_2nd_5])).
% 0.57/0.90 thf(zip_derived_cl932, plain,
% 0.57/0.90 ((((ordered_pair @ x @ (second @ x)) = (x)) | ((second @ x) = (x)))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl909, zip_derived_cl75])).
% 0.57/0.90 thf(zip_derived_cl78, plain, (((second @ x) != (x))),
% 0.57/0.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.57/0.90 thf(zip_derived_cl938, plain, (((ordered_pair @ x @ (second @ x)) = (x))),
% 0.57/0.90 inference('simplify_reflect-', [status(thm)],
% 0.57/0.90 [zip_derived_cl932, zip_derived_cl78])).
% 0.57/0.90 thf(property_1_of_ordered_pair, axiom,
% 0.57/0.90 (( ( unordered_pair @
% 0.57/0.90 ( singleton @ X ) @ ( unordered_pair @ X @ null_class ) ) =
% 0.57/0.90 ( ordered_pair @ X @ Y ) ) |
% 0.57/0.90 ( member @ Y @ universal_class ))).
% 0.57/0.90 thf(zip_derived_cl66, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i]:
% 0.57/0.90 (((unordered_pair @ (singleton @ X0) @
% 0.57/0.90 (unordered_pair @ X0 @ null_class)) = (ordered_pair @ X0 @ X1))
% 0.57/0.90 | (member @ X1 @ universal_class))),
% 0.57/0.90 inference('cnf', [status(esa)], [property_1_of_ordered_pair])).
% 0.57/0.90 thf(zip_derived_cl1076, plain,
% 0.57/0.90 ((((unordered_pair @ (singleton @ x) @ (unordered_pair @ x @ null_class))
% 0.57/0.90 = (x))
% 0.57/0.90 | (member @ (second @ x) @ universal_class))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl66])).
% 0.57/0.90 thf(zip_derived_cl36, plain,
% 0.57/0.90 (![X0 : $i, X1 : $i]:
% 0.57/0.90 ((unordered_pair @ X1 @ X0) = (unordered_pair @ X0 @ X1))),
% 0.57/0.90 inference('cnf', [status(esa)], [commutativity_of_unordered_pair])).
% 0.57/0.90 thf(zip_derived_cl1001, plain, (((singleton @ (second @ x)) = (null_class))),
% 0.57/0.90 inference('simplify_reflect-', [status(thm)],
% 0.57/0.90 [zip_derived_cl1000, zip_derived_cl477])).
% 0.57/0.90 thf(set_in_its_singleton, axiom,
% 0.57/0.90 (( ~( member @ X @ universal_class ) ) | ( member @ X @ ( singleton @ X ) ))).
% 0.57/0.90 thf(zip_derived_cl50, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 (~ (member @ X0 @ universal_class) | (member @ X0 @ (singleton @ X0)))),
% 0.57/0.90 inference('cnf', [status(esa)], [set_in_its_singleton])).
% 0.57/0.90 thf(zip_derived_cl1009, plain,
% 0.57/0.90 (( (member @ (second @ x) @ null_class)
% 0.57/0.90 | ~ (member @ (second @ x) @ universal_class))),
% 0.57/0.90 inference('sup+', [status(thm)], [zip_derived_cl1001, zip_derived_cl50])).
% 0.57/0.90 thf(existence_of_null_class, axiom, (~( member @ Z @ null_class ))).
% 0.57/0.90 thf(zip_derived_cl31, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 0.57/0.90 inference('cnf', [status(esa)], [existence_of_null_class])).
% 0.57/0.90 thf(zip_derived_cl1066, plain, (~ (member @ (second @ x) @ universal_class)),
% 0.57/0.90 inference('clc', [status(thm)], [zip_derived_cl1009, zip_derived_cl31])).
% 0.57/0.90 thf(zip_derived_cl1079, plain,
% 0.57/0.90 (((unordered_pair @ (singleton @ x) @ (unordered_pair @ null_class @ x))
% 0.57/0.90 = (x))),
% 0.57/0.90 inference('demod', [status(thm)],
% 0.57/0.90 [zip_derived_cl1076, zip_derived_cl36, zip_derived_cl1066])).
% 0.57/0.90 thf(zip_derived_cl75, plain,
% 0.57/0.90 (![X0 : $i]:
% 0.57/0.90 (((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0))
% 0.57/0.90 | ((second @ X0) = (X0)))),
% 0.57/0.90 inference('cnf', [status(esa)], [existence_of_1st_and_2nd_5])).
% 0.57/0.90 thf(zip_derived_cl79, plain,
% 0.57/0.90 (~ (member @ (ordered_pair @ (first @ x) @ (second @ x)) @
% 0.57/0.90 (cross_product @ universal_class @ universal_class))),
% 0.57/0.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.90 thf(zip_derived_cl469, plain,
% 0.57/0.90 ((~ (member @ x @ (cross_product @ universal_class @ universal_class))
% 0.57/0.90 | ((second @ x) = (x)))),
% 0.57/0.90 inference('sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl79])).
% 0.57/0.90 thf(zip_derived_cl78, plain, (((second @ x) != (x))),
% 0.57/0.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.57/0.90 thf(zip_derived_cl471, plain,
% 0.57/0.90 (~ (member @ x @ (cross_product @ universal_class @ universal_class))),
% 0.57/0.90 inference('simplify_reflect-', [status(thm)],
% 0.57/0.90 [zip_derived_cl469, zip_derived_cl78])).
% 0.57/0.90 thf(zip_derived_cl1322, plain, (((second @ x) = (x))),
% 0.57/0.90 inference('demod', [status(thm)],
% 0.57/0.90 [zip_derived_cl1312, zip_derived_cl909, zip_derived_cl909,
% 0.57/0.90 zip_derived_cl36, zip_derived_cl1079, zip_derived_cl471])).
% 0.57/0.90 thf(zip_derived_cl78, plain, (((second @ x) != (x))),
% 0.57/0.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.57/0.90 thf(zip_derived_cl1323, plain, ($false),
% 0.57/0.90 inference('simplify_reflect-', [status(thm)],
% 0.57/0.90 [zip_derived_cl1322, zip_derived_cl78])).
% 0.57/0.90
% 0.57/0.90 % SZS output end Refutation
% 0.57/0.90
% 0.57/0.90
% 0.57/0.90 % Terminating...
% 0.60/0.96 % Runner terminated.
% 0.60/0.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------