%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET071-6 : TPTP v9.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Is9VKE7VwV true
% Computer : n029.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 04:51:26 PM UTC 2025
% Result : Unsatisfiable 21.08s 3.65s
% Output : Refutation 21.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET071-6 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.03/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Is9VKE7VwV true
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Oct 1 13:23:38 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.22/0.37 % Running in FO mode
% 0.57/0.68 % Total configuration time : 435
% 0.57/0.68 % Estimated wc time : 1092
% 0.57/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.58/0.78 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.58/0.80 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.58/0.82 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.58/0.83 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.58/0.83 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.86 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 21.08/3.65 % Solved by fo/fo1_lcnf.sh.
% 21.08/3.65 % done 3554 iterations in 2.771s
% 21.08/3.65 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 21.08/3.65 % SZS output start Refutation
% 21.08/3.65 thf(universal_class_type, type, universal_class: $i).
% 21.08/3.65 thf(null_class_type, type, null_class: $i).
% 21.08/3.65 thf(member_type, type, member: $i > $i > $o).
% 21.08/3.65 thf(x_type, type, x: $i).
% 21.08/3.65 thf(unordered_pair_type, type, unordered_pair: $i > $i > $i).
% 21.08/3.65 thf(y_type, type, y: $i).
% 21.08/3.65 thf(singleton_type, type, singleton: $i > $i).
% 21.08/3.65 thf(subclass_type, type, subclass: $i > $i > $o).
% 21.08/3.65 thf(cross_product_type, type, cross_product: $i > $i > $i).
% 21.08/3.65 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 21.08/3.65 thf(regular_type, type, regular: $i > $i).
% 21.08/3.65 thf(regularity1, axiom,
% 21.08/3.65 (( ( X ) = ( null_class ) ) | ( member @ ( regular @ X ) @ X ))).
% 21.08/3.65 thf(zip_derived_cl65, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 (((((X0) = (null_class))) | (member @ (regular @ X0) @ X0)))),
% 21.08/3.65 inference('cnf', [status(esa)], [regularity1])).
% 21.08/3.65 thf(zip_derived_cl153, plain,
% 21.08/3.65 (![X0 : $i]: ( (((X0) = (null_class))) | (member @ (regular @ X0) @ X0))),
% 21.08/3.65 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl65])).
% 21.08/3.65 thf(zip_derived_cl154, plain,
% 21.08/3.65 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 21.08/3.65 inference('simplify nested equalities', [status(thm)],
% 21.08/3.65 [zip_derived_cl153])).
% 21.08/3.65 thf(unordered_pair_member, axiom,
% 21.08/3.65 (( ~( member @ U @ ( unordered_pair @ X @ Y ) ) ) | ( ( U ) = ( X ) ) |
% 21.08/3.65 ( ( U ) = ( Y ) ))).
% 21.08/3.65 thf(zip_derived_cl7, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.08/3.65 (((((~) @ (member @ X0 @ (unordered_pair @ X1 @ X2)))) |
% 21.08/3.65 (((X0) = (X1))) | (((X0) = (X2)))))),
% 21.08/3.65 inference('cnf', [status(esa)], [unordered_pair_member])).
% 21.08/3.65 thf(zip_derived_cl164, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.08/3.65 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 21.08/3.65 | (((X0) = (X1)))
% 21.08/3.65 | (((X0) = (X2))))),
% 21.08/3.65 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])).
% 21.08/3.65 thf(zip_derived_cl165, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.08/3.65 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 21.08/3.65 | ((X0) = (X1))
% 21.08/3.65 | ((X0) = (X2)))),
% 21.08/3.65 inference('simplify nested equalities', [status(thm)],
% 21.08/3.65 [zip_derived_cl164])).
% 21.08/3.65 thf(zip_derived_cl168, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 (((unordered_pair @ X1 @ X0) = (null_class))
% 21.08/3.65 | ((regular @ (unordered_pair @ X1 @ X0)) = (X1))
% 21.08/3.65 | ((regular @ (unordered_pair @ X1 @ X0)) = (X0)))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl165])).
% 21.08/3.65 thf(zip_derived_cl154, plain,
% 21.08/3.65 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 21.08/3.65 inference('simplify nested equalities', [status(thm)],
% 21.08/3.65 [zip_derived_cl153])).
% 21.08/3.65 thf(zip_derived_cl1676, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 (((regular @ (unordered_pair @ X0 @ X1)) = (X1))
% 21.08/3.65 | ((unordered_pair @ X0 @ X1) = (null_class))
% 21.08/3.65 | ((unordered_pair @ X0 @ X1) = (null_class))
% 21.08/3.65 | (member @ X0 @ (unordered_pair @ X0 @ X1)))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl168, zip_derived_cl154])).
% 21.08/3.65 thf(zip_derived_cl1709, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 ( (member @ X0 @ (unordered_pair @ X0 @ X1))
% 21.08/3.65 | ((unordered_pair @ X0 @ X1) = (null_class))
% 21.08/3.65 | ((regular @ (unordered_pair @ X0 @ X1)) = (X1)))),
% 21.08/3.65 inference('simplify', [status(thm)], [zip_derived_cl1676])).
% 21.08/3.65 thf(cartesian_product3, axiom,
% 21.08/3.65 (( ~( member @ U @ X ) ) | ( ~( member @ V @ Y ) ) |
% 21.08/3.65 ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ))).
% 21.08/3.65 thf(zip_derived_cl15, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.08/3.65 (((((~) @ (member @ X0 @ X1))) | (((~) @ (member @ X2 @ X3))) |
% 21.08/3.65 (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3))))),
% 21.08/3.65 inference('cnf', [status(esa)], [cartesian_product3])).
% 21.08/3.65 thf(zip_derived_cl326, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.08/3.65 (~ (member @ X0 @ X1)
% 21.08/3.65 | ~ (member @ X2 @ X3)
% 21.08/3.65 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 21.08/3.65 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl15])).
% 21.08/3.65 thf(singleton_set, axiom, (( unordered_pair @ X @ X ) = ( singleton @ X ))).
% 21.08/3.65 thf(zip_derived_cl11, plain,
% 21.08/3.65 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 21.08/3.65 inference('cnf', [status(esa)], [singleton_set])).
% 21.08/3.65 thf(zip_derived_cl165, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.08/3.65 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 21.08/3.65 | ((X0) = (X1))
% 21.08/3.65 | ((X0) = (X2)))),
% 21.08/3.65 inference('simplify nested equalities', [status(thm)],
% 21.08/3.65 [zip_derived_cl164])).
% 21.08/3.65 thf(zip_derived_cl169, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 (~ (member @ X1 @ (singleton @ X0)) | ((X1) = (X0)) | ((X1) = (X0)))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl165])).
% 21.08/3.65 thf(zip_derived_cl170, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 21.08/3.65 inference('simplify', [status(thm)], [zip_derived_cl169])).
% 21.08/3.65 thf(zip_derived_cl154, plain,
% 21.08/3.65 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 21.08/3.65 inference('simplify nested equalities', [status(thm)],
% 21.08/3.65 [zip_derived_cl153])).
% 21.08/3.65 thf(zip_derived_cl173, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 (((regular @ (singleton @ X0)) = (X0))
% 21.08/3.65 | ((singleton @ X0) = (null_class)))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl170, zip_derived_cl154])).
% 21.08/3.65 thf(zip_derived_cl154, plain,
% 21.08/3.65 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 21.08/3.65 inference('simplify nested equalities', [status(thm)],
% 21.08/3.65 [zip_derived_cl153])).
% 21.08/3.65 thf(class_elements_are_sets, axiom, (subclass @ X @ universal_class)).
% 21.08/3.65 thf(zip_derived_cl3, plain, (![X0 : $i]: (subclass @ X0 @ universal_class)),
% 21.08/3.65 inference('cnf', [status(esa)], [class_elements_are_sets])).
% 21.08/3.65 thf(subclass_members, axiom,
% 21.08/3.65 (( ~( subclass @ X @ Y ) ) | ( ~( member @ U @ X ) ) | ( member @ U @ Y ))).
% 21.08/3.65 thf(zip_derived_cl0, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.08/3.65 (((((~) @ (subclass @ X0 @ X1))) | (((~) @ (member @ X2 @ X0))) |
% 21.08/3.65 (member @ X2 @ X1)))),
% 21.08/3.65 inference('cnf', [status(esa)], [subclass_members])).
% 21.08/3.65 thf(zip_derived_cl94, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.08/3.65 (~ (subclass @ X0 @ X1) | ~ (member @ X2 @ X0) | (member @ X2 @ X1))),
% 21.08/3.65 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl0])).
% 21.08/3.65 thf(zip_derived_cl95, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl94])).
% 21.08/3.65 thf(zip_derived_cl155, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl95])).
% 21.08/3.65 thf(zip_derived_cl189, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 (((singleton @ X0) = (null_class))
% 21.08/3.65 | ((singleton @ X0) = (null_class))
% 21.08/3.65 | (member @ X0 @ universal_class))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl155])).
% 21.08/3.65 thf(zip_derived_cl191, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 ( (member @ X0 @ universal_class) | ((singleton @ X0) = (null_class)))),
% 21.08/3.65 inference('simplify', [status(thm)], [zip_derived_cl189])).
% 21.08/3.65 thf(prove_null_unordered_pair_3, conjecture, (member @ y @ universal_class)).
% 21.08/3.65 thf(zf_stmt_0, negated_conjecture, (~( member @ y @ universal_class )),
% 21.08/3.65 inference('cnf.neg', [status(esa)], [prove_null_unordered_pair_3])).
% 21.08/3.65 thf(zip_derived_cl93, plain, (~ (member @ y @ universal_class)),
% 21.08/3.65 inference('cnf', [status(esa)], [zf_stmt_0])).
% 21.08/3.65 thf(zip_derived_cl218, plain, (((singleton @ y) = (null_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl93])).
% 21.08/3.65 thf(zip_derived_cl191, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 ( (member @ X0 @ universal_class) | ((singleton @ X0) = (null_class)))),
% 21.08/3.65 inference('simplify', [status(thm)], [zip_derived_cl189])).
% 21.08/3.65 thf(prove_null_unordered_pair_2, conjecture, (member @ x @ universal_class)).
% 21.08/3.65 thf(zf_stmt_1, negated_conjecture, (~( member @ x @ universal_class )),
% 21.08/3.65 inference('cnf.neg', [status(esa)], [prove_null_unordered_pair_2])).
% 21.08/3.65 thf(zip_derived_cl92, plain, (~ (member @ x @ universal_class)),
% 21.08/3.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 21.08/3.65 thf(zip_derived_cl217, plain, (((singleton @ x) = (null_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl92])).
% 21.08/3.65 thf(ordered_pair, axiom,
% 21.08/3.65 (( unordered_pair @
% 21.08/3.65 ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) =
% 21.08/3.65 ( ordered_pair @ X @ Y ))).
% 21.08/3.65 thf(zip_derived_cl12, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 ((unordered_pair @ (singleton @ X0) @
% 21.08/3.65 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 21.08/3.65 inference('cnf', [status(esa)], [ordered_pair])).
% 21.08/3.65 thf(zip_derived_cl256, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 ((unordered_pair @ null_class @
% 21.08/3.65 (unordered_pair @ x @ (singleton @ X0))) = (ordered_pair @ x @ X0))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl12])).
% 21.08/3.65 thf(zip_derived_cl298, plain,
% 21.08/3.65 (((unordered_pair @ null_class @ (unordered_pair @ x @ null_class))
% 21.08/3.65 = (ordered_pair @ x @ y))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl256])).
% 21.08/3.65 thf(zip_derived_cl217, plain, (((singleton @ x) = (null_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl92])).
% 21.08/3.65 thf(zip_derived_cl256, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 ((unordered_pair @ null_class @
% 21.08/3.65 (unordered_pair @ x @ (singleton @ X0))) = (ordered_pair @ x @ X0))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl12])).
% 21.08/3.65 thf(zip_derived_cl297, plain,
% 21.08/3.65 (((unordered_pair @ null_class @ (unordered_pair @ x @ null_class))
% 21.08/3.65 = (ordered_pair @ x @ x))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl256])).
% 21.08/3.65 thf(zip_derived_cl308, plain,
% 21.08/3.65 (((ordered_pair @ x @ x) = (ordered_pair @ x @ y))),
% 21.08/3.65 inference('demod', [status(thm)], [zip_derived_cl298, zip_derived_cl297])).
% 21.08/3.65 thf(cartesian_product2, axiom,
% 21.08/3.65 (( ~( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) |
% 21.08/3.65 ( member @ V @ Y ))).
% 21.08/3.65 thf(zip_derived_cl14, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.08/3.65 (((((~) @ (member @ (ordered_pair @ X0 @ X1) @
% 21.08/3.65 (cross_product @ X2 @ X3)))) |
% 21.08/3.65 (member @ X1 @ X3)))),
% 21.08/3.65 inference('cnf', [status(esa)], [cartesian_product2])).
% 21.08/3.65 thf(zip_derived_cl312, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.08/3.65 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 21.08/3.65 | (member @ X1 @ X3))),
% 21.08/3.65 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl14])).
% 21.08/3.65 thf(zip_derived_cl317, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 (~ (member @ (ordered_pair @ x @ x) @ (cross_product @ X1 @ X0))
% 21.08/3.65 | (member @ y @ X0))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl308, zip_derived_cl312])).
% 21.08/3.65 thf(zip_derived_cl335, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 (~ (member @ x @ X0) | ~ (member @ x @ X1) | (member @ y @ X0))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl326, zip_derived_cl317])).
% 21.08/3.65 thf(zip_derived_cl340, plain,
% 21.08/3.65 (![X0 : $i]: ( (member @ y @ X0) | ~ (member @ x @ X0))),
% 21.08/3.65 inference('condensation', [status(thm)], [zip_derived_cl335])).
% 21.08/3.65 thf(zip_derived_cl95, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl94])).
% 21.08/3.65 thf(zip_derived_cl341, plain,
% 21.08/3.65 (![X0 : $i]: (~ (member @ x @ X0) | (member @ y @ universal_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl340, zip_derived_cl95])).
% 21.08/3.65 thf(zip_derived_cl93, plain, (~ (member @ y @ universal_class)),
% 21.08/3.65 inference('cnf', [status(esa)], [zf_stmt_0])).
% 21.08/3.65 thf(zip_derived_cl360, plain, (![X0 : $i]: ~ (member @ x @ X0)),
% 21.08/3.65 inference('clc', [status(thm)], [zip_derived_cl341, zip_derived_cl93])).
% 21.08/3.65 thf(zip_derived_cl14315, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 (((regular @ (unordered_pair @ x @ X0)) = (X0))
% 21.08/3.65 | ((unordered_pair @ x @ X0) = (null_class)))),
% 21.08/3.65 inference('s_sup-', [status(thm)],
% 21.08/3.65 [zip_derived_cl1709, zip_derived_cl360])).
% 21.08/3.65 thf(zip_derived_cl155, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl95])).
% 21.08/3.65 thf(zip_derived_cl14960, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 (((unordered_pair @ x @ X0) = (null_class))
% 21.08/3.65 | ((unordered_pair @ x @ X0) = (null_class))
% 21.08/3.65 | (member @ X0 @ universal_class))),
% 21.08/3.65 inference('s_sup+', [status(thm)],
% 21.08/3.65 [zip_derived_cl14315, zip_derived_cl155])).
% 21.08/3.65 thf(zip_derived_cl14981, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 ( (member @ X0 @ universal_class)
% 21.08/3.65 | ((unordered_pair @ x @ X0) = (null_class)))),
% 21.08/3.65 inference('simplify', [status(thm)], [zip_derived_cl14960])).
% 21.08/3.65 thf(zip_derived_cl218, plain, (((singleton @ y) = (null_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl93])).
% 21.08/3.65 thf(zip_derived_cl12, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 ((unordered_pair @ (singleton @ X0) @
% 21.08/3.65 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 21.08/3.65 inference('cnf', [status(esa)], [ordered_pair])).
% 21.08/3.65 thf(zip_derived_cl255, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 ((unordered_pair @ (singleton @ X0) @
% 21.08/3.65 (unordered_pair @ X0 @ null_class)) = (ordered_pair @ X0 @ y))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl12])).
% 21.08/3.65 thf(zip_derived_cl217, plain, (((singleton @ x) = (null_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl92])).
% 21.08/3.65 thf(zip_derived_cl12, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i]:
% 21.08/3.65 ((unordered_pair @ (singleton @ X0) @
% 21.08/3.65 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 21.08/3.65 inference('cnf', [status(esa)], [ordered_pair])).
% 21.08/3.65 thf(zip_derived_cl254, plain,
% 21.08/3.65 (![X0 : $i]:
% 21.08/3.65 ((unordered_pair @ (singleton @ X0) @
% 21.08/3.65 (unordered_pair @ X0 @ null_class)) = (ordered_pair @ X0 @ x))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl12])).
% 21.08/3.65 thf(zip_derived_cl592, plain,
% 21.08/3.65 (![X0 : $i]: ((ordered_pair @ X0 @ x) = (ordered_pair @ X0 @ y))),
% 21.08/3.65 inference('demod', [status(thm)], [zip_derived_cl255, zip_derived_cl254])).
% 21.08/3.65 thf(zip_derived_cl326, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.08/3.65 (~ (member @ X0 @ X1)
% 21.08/3.65 | ~ (member @ X2 @ X3)
% 21.08/3.65 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 21.08/3.65 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl15])).
% 21.08/3.65 thf(zip_derived_cl597, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.08/3.65 (~ (member @ X0 @ X2)
% 21.08/3.65 | ~ (member @ y @ X1)
% 21.08/3.65 | (member @ (ordered_pair @ X0 @ x) @ (cross_product @ X2 @ X1)))),
% 21.08/3.65 inference('s_sup+', [status(thm)], [zip_derived_cl592, zip_derived_cl326])).
% 21.08/3.65 thf(zip_derived_cl312, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.08/3.65 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 21.08/3.65 | (member @ X1 @ X3))),
% 21.08/3.65 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl14])).
% 21.08/3.65 thf(zip_derived_cl1150, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.08/3.65 (~ (member @ y @ X0) | ~ (member @ X2 @ X1) | (member @ x @ X0))),
% 21.08/3.65 inference('s_sup-', [status(thm)], [zip_derived_cl597, zip_derived_cl312])).
% 21.08/3.65 thf(zip_derived_cl360, plain, (![X0 : $i]: ~ (member @ x @ X0)),
% 21.08/3.65 inference('clc', [status(thm)], [zip_derived_cl341, zip_derived_cl93])).
% 21.08/3.65 thf(zip_derived_cl1160, plain,
% 21.08/3.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.08/3.65 (~ (member @ y @ X0) | ~ (member @ X2 @ X1))),
% 21.08/3.65 inference('demod', [status(thm)], [zip_derived_cl1150, zip_derived_cl360])).
% 21.08/3.65 thf(zip_derived_cl1165, plain, (![X0 : $i]: ~ (member @ y @ X0)),
% 21.08/3.65 inference('condensation', [status(thm)], [zip_derived_cl1160])).
% 21.08/3.65 thf(zip_derived_cl15026, plain, (((unordered_pair @ x @ y) = (null_class))),
% 21.08/3.65 inference('s_sup-', [status(thm)],
% 21.08/3.65 [zip_derived_cl14981, zip_derived_cl1165])).
% 21.08/3.65 thf(prove_null_unordered_pair_1, conjecture,
% 21.08/3.65 (( unordered_pair @ x @ y ) = ( null_class ))).
% 21.08/3.65 thf(zf_stmt_2, negated_conjecture,
% 21.08/3.65 (( unordered_pair @ x @ y ) != ( null_class )),
% 21.08/3.65 inference('cnf.neg', [status(esa)], [prove_null_unordered_pair_1])).
% 21.08/3.65 thf(zip_derived_cl91, plain, (((unordered_pair @ x @ y) != (null_class))),
% 21.08/3.65 inference('cnf', [status(esa)], [zf_stmt_2])).
% 21.08/3.65 thf(zip_derived_cl15033, plain, ($false),
% 21.08/3.65 inference('simplify_reflect-', [status(thm)],
% 21.08/3.65 [zip_derived_cl15026, zip_derived_cl91])).
% 21.08/3.65
% 21.08/3.65 % SZS output end Refutation
% 21.08/3.65
% 21.08/3.65
% 21.08/3.65 % Terminating...
% 21.40/3.70 % Runner terminated.
% 21.40/3.71 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------