TSTP Solution File: SET129-6 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET129-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.NgQh96huFE true
% Computer : n010.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 Aug 31 16:12:56 EDT 2023
% Result : Unsatisfiable 2.14s 1.04s
% Output : Refutation 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET129-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.NgQh96huFE true
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 15:46:35 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.20/0.67 % Total configuration time : 435
% 0.20/0.67 % Estimated wc time : 1092
% 0.20/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.20/0.80 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 2.14/1.04 % Solved by fo/fo6_bce.sh.
% 2.14/1.04 % BCE start: 96
% 2.14/1.04 % BCE eliminated: 0
% 2.14/1.04 % PE start: 96
% 2.14/1.04 logic: eq
% 2.14/1.04 % PE eliminated: 16
% 2.14/1.04 % done 394 iterations in 0.295s
% 2.14/1.04 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.14/1.04 % SZS output start Refutation
% 2.14/1.04 thf(universal_class_type, type, universal_class: $i).
% 2.14/1.04 thf(union_type, type, union: $i > $i > $i).
% 2.14/1.04 thf(null_class_type, type, null_class: $i).
% 2.14/1.04 thf(member_type, type, member: $i > $i > $o).
% 2.14/1.04 thf(z_type, type, z: $i).
% 2.14/1.04 thf(unordered_pair_type, type, unordered_pair: $i > $i > $i).
% 2.14/1.04 thf(complement_type, type, complement: $i > $i).
% 2.14/1.04 thf(set_builder_type, type, set_builder: $i > $i > $i).
% 2.14/1.04 thf(u_type, type, u: $i).
% 2.14/1.04 thf(singleton_type, type, singleton: $i > $i).
% 2.14/1.04 thf(intersection_type, type, intersection: $i > $i > $i).
% 2.14/1.04 thf(subclass_type, type, subclass: $i > $i > $o).
% 2.14/1.04 thf(y_type, type, y: $i).
% 2.14/1.04 thf(x_type, type, x: $i).
% 2.14/1.04 thf(regular_type, type, regular: $i > $i).
% 2.14/1.04 thf(complement2, axiom,
% 2.14/1.04 (( ~( member @ Z @ universal_class ) ) |
% 2.14/1.04 ( member @ Z @ ( complement @ X ) ) | ( member @ Z @ X ))).
% 2.14/1.04 thf(zip_derived_cl24, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X0 @ universal_class)
% 2.14/1.04 | (member @ X0 @ (complement @ X1))
% 2.14/1.04 | (member @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [complement2])).
% 2.14/1.04 thf(zip_derived_cl24, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X0 @ universal_class)
% 2.14/1.04 | (member @ X0 @ (complement @ X1))
% 2.14/1.04 | (member @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [complement2])).
% 2.14/1.04 thf(intersection3, axiom,
% 2.14/1.04 (( ~( member @ Z @ X ) ) | ( ~( member @ Z @ Y ) ) |
% 2.14/1.04 ( member @ Z @ ( intersection @ X @ Y ) ))).
% 2.14/1.04 thf(zip_derived_cl22, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.14/1.04 (~ (member @ X0 @ X1)
% 2.14/1.04 | ~ (member @ X0 @ X2)
% 2.14/1.04 | (member @ X0 @ (intersection @ X1 @ X2)))),
% 2.14/1.04 inference('cnf', [status(esa)], [intersection3])).
% 2.14/1.04 thf(zip_derived_cl24, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X0 @ universal_class)
% 2.14/1.04 | (member @ X0 @ (complement @ X1))
% 2.14/1.04 | (member @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [complement2])).
% 2.14/1.04 thf(zip_derived_cl24, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X0 @ universal_class)
% 2.14/1.04 | (member @ X0 @ (complement @ X1))
% 2.14/1.04 | (member @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [complement2])).
% 2.14/1.04 thf(zip_derived_cl22, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.14/1.04 (~ (member @ X0 @ X1)
% 2.14/1.04 | ~ (member @ X0 @ X2)
% 2.14/1.04 | (member @ X0 @ (intersection @ X1 @ X2)))),
% 2.14/1.04 inference('cnf', [status(esa)], [intersection3])).
% 2.14/1.04 thf(zip_derived_cl24, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X0 @ universal_class)
% 2.14/1.04 | (member @ X0 @ (complement @ X1))
% 2.14/1.04 | (member @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [complement2])).
% 2.14/1.04 thf(zip_derived_cl24, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X0 @ universal_class)
% 2.14/1.04 | (member @ X0 @ (complement @ X1))
% 2.14/1.04 | (member @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [complement2])).
% 2.14/1.04 thf(zip_derived_cl22, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.14/1.04 (~ (member @ X0 @ X1)
% 2.14/1.04 | ~ (member @ X0 @ X2)
% 2.14/1.04 | (member @ X0 @ (intersection @ X1 @ X2)))),
% 2.14/1.04 inference('cnf', [status(esa)], [intersection3])).
% 2.14/1.04 thf(prove_members_of_built_triple_1, conjecture,
% 2.14/1.04 (~( member @
% 2.14/1.04 u @
% 2.14/1.04 ( set_builder @
% 2.14/1.04 x @ ( set_builder @ y @ ( set_builder @ z @ null_class ) ) ) ))).
% 2.14/1.04 thf(zf_stmt_0, negated_conjecture,
% 2.14/1.04 (member @
% 2.14/1.04 u @
% 2.14/1.04 ( set_builder @ x @ ( set_builder @ y @ ( set_builder @ z @ null_class ) ) )),
% 2.14/1.04 inference('cnf.neg', [status(esa)], [prove_members_of_built_triple_1])).
% 2.14/1.04 thf(zip_derived_cl92, plain,
% 2.14/1.04 ( (member @ u @
% 2.14/1.04 (set_builder @ x @ (set_builder @ y @ (set_builder @ z @ null_class))))),
% 2.14/1.04 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.14/1.04 thf(definition_of_set_builder, axiom,
% 2.14/1.04 (( union @ ( singleton @ X ) @ Y ) = ( set_builder @ X @ Y ))).
% 2.14/1.04 thf(zip_derived_cl91, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 ((union @ (singleton @ X0) @ X1) = (set_builder @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [definition_of_set_builder])).
% 2.14/1.04 thf(union, axiom,
% 2.14/1.04 (( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) =
% 2.14/1.04 ( union @ X @ Y ))).
% 2.14/1.04 thf(zip_derived_cl25, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 ((complement @ (intersection @ (complement @ X0) @ (complement @ X1)))
% 2.14/1.04 = (union @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [union])).
% 2.14/1.04 thf(complement1, axiom,
% 2.14/1.04 (( ~( member @ Z @ ( complement @ X ) ) ) | ( ~( member @ Z @ X ) ))).
% 2.14/1.04 thf(zip_derived_cl23, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [complement1])).
% 2.14/1.04 thf(zip_derived_cl537, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.14/1.04 (~ (member @ X2 @ (union @ X1 @ X0))
% 2.14/1.04 | ~ (member @ X2 @
% 2.14/1.04 (intersection @ (complement @ X1) @ (complement @ X0))))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl23])).
% 2.14/1.04 thf(zip_derived_cl583, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.14/1.04 (~ (member @ X2 @ (set_builder @ X1 @ X0))
% 2.14/1.04 | ~ (member @ X2 @
% 2.14/1.04 (intersection @ (complement @ (singleton @ X1)) @
% 2.14/1.04 (complement @ X0))))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl537])).
% 2.14/1.04 thf(zip_derived_cl609, plain,
% 2.14/1.04 (~ (member @ u @
% 2.14/1.04 (intersection @ (complement @ (singleton @ x)) @
% 2.14/1.04 (complement @ (set_builder @ y @ (set_builder @ z @ null_class)))))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl583])).
% 2.14/1.04 thf(zip_derived_cl654, plain,
% 2.14/1.04 ((~ (member @ u @
% 2.14/1.04 (complement @ (set_builder @ y @ (set_builder @ z @ null_class))))
% 2.14/1.04 | ~ (member @ u @ (complement @ (singleton @ x))))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl609])).
% 2.14/1.04 thf(zip_derived_cl656, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ x))
% 2.14/1.04 | ~ (member @ u @ universal_class)
% 2.14/1.04 | ~ (member @ u @
% 2.14/1.04 (complement @ (set_builder @ y @ (set_builder @ z @ null_class)))))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl654])).
% 2.14/1.04 thf(zip_derived_cl92, plain,
% 2.14/1.04 ( (member @ u @
% 2.14/1.04 (set_builder @ x @ (set_builder @ y @ (set_builder @ z @ null_class))))),
% 2.14/1.04 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.14/1.04 thf(class_elements_are_sets, axiom, (subclass @ X @ universal_class)).
% 2.14/1.04 thf(zip_derived_cl3, plain, (![X0 : $i]: (subclass @ X0 @ universal_class)),
% 2.14/1.04 inference('cnf', [status(esa)], [class_elements_are_sets])).
% 2.14/1.04 thf(subclass_members, axiom,
% 2.14/1.04 (( ~( subclass @ X @ Y ) ) | ( ~( member @ U @ X ) ) | ( member @ U @ Y ))).
% 2.14/1.04 thf(zip_derived_cl0, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.14/1.04 (~ (subclass @ X0 @ X1) | ~ (member @ X2 @ X0) | (member @ X2 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [subclass_members])).
% 2.14/1.04 thf(zip_derived_cl426, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 2.14/1.04 thf(zip_derived_cl430, plain, ( (member @ u @ universal_class)),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl426])).
% 2.14/1.04 thf(zip_derived_cl658, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ x))
% 2.14/1.04 | ~ (member @ u @
% 2.14/1.04 (complement @ (set_builder @ y @ (set_builder @ z @ null_class)))))),
% 2.14/1.04 inference('demod', [status(thm)], [zip_derived_cl656, zip_derived_cl430])).
% 2.14/1.04 thf(zip_derived_cl659, plain,
% 2.14/1.04 (( (member @ u @ (set_builder @ y @ (set_builder @ z @ null_class)))
% 2.14/1.04 | ~ (member @ u @ universal_class)
% 2.14/1.04 | (member @ u @ (singleton @ x)))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl658])).
% 2.14/1.04 thf(zip_derived_cl430, plain, ( (member @ u @ universal_class)),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl426])).
% 2.14/1.04 thf(zip_derived_cl660, plain,
% 2.14/1.04 (( (member @ u @ (set_builder @ y @ (set_builder @ z @ null_class)))
% 2.14/1.04 | (member @ u @ (singleton @ x)))),
% 2.14/1.04 inference('demod', [status(thm)], [zip_derived_cl659, zip_derived_cl430])).
% 2.14/1.04 thf(zip_derived_cl583, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.14/1.04 (~ (member @ X2 @ (set_builder @ X1 @ X0))
% 2.14/1.04 | ~ (member @ X2 @
% 2.14/1.04 (intersection @ (complement @ (singleton @ X1)) @
% 2.14/1.04 (complement @ X0))))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl537])).
% 2.14/1.04 thf(zip_derived_cl677, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ x))
% 2.14/1.04 | ~ (member @ u @
% 2.14/1.04 (intersection @ (complement @ (singleton @ y)) @
% 2.14/1.04 (complement @ (set_builder @ z @ null_class)))))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl660, zip_derived_cl583])).
% 2.14/1.04 thf(zip_derived_cl743, plain,
% 2.14/1.04 ((~ (member @ u @ (complement @ (set_builder @ z @ null_class)))
% 2.14/1.04 | ~ (member @ u @ (complement @ (singleton @ y)))
% 2.14/1.04 | (member @ u @ (singleton @ x)))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl677])).
% 2.14/1.04 thf(zip_derived_cl745, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ y))
% 2.14/1.04 | ~ (member @ u @ universal_class)
% 2.14/1.04 | ~ (member @ u @ (complement @ (set_builder @ z @ null_class)))
% 2.14/1.04 | (member @ u @ (singleton @ x)))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl743])).
% 2.14/1.04 thf(zip_derived_cl430, plain, ( (member @ u @ universal_class)),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl426])).
% 2.14/1.04 thf(zip_derived_cl747, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ y))
% 2.14/1.04 | ~ (member @ u @ (complement @ (set_builder @ z @ null_class)))
% 2.14/1.04 | (member @ u @ (singleton @ x)))),
% 2.14/1.04 inference('demod', [status(thm)], [zip_derived_cl745, zip_derived_cl430])).
% 2.14/1.04 thf(zip_derived_cl748, plain,
% 2.14/1.04 (( (member @ u @ (set_builder @ z @ null_class))
% 2.14/1.04 | ~ (member @ u @ universal_class)
% 2.14/1.04 | (member @ u @ (singleton @ y))
% 2.14/1.04 | (member @ u @ (singleton @ x)))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl747])).
% 2.14/1.04 thf(zip_derived_cl430, plain, ( (member @ u @ universal_class)),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl426])).
% 2.14/1.04 thf(zip_derived_cl749, plain,
% 2.14/1.04 (( (member @ u @ (set_builder @ z @ null_class))
% 2.14/1.04 | (member @ u @ (singleton @ y))
% 2.14/1.04 | (member @ u @ (singleton @ x)))),
% 2.14/1.04 inference('demod', [status(thm)], [zip_derived_cl748, zip_derived_cl430])).
% 2.14/1.04 thf(zip_derived_cl583, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.14/1.04 (~ (member @ X2 @ (set_builder @ X1 @ X0))
% 2.14/1.04 | ~ (member @ X2 @
% 2.14/1.04 (intersection @ (complement @ (singleton @ X1)) @
% 2.14/1.04 (complement @ X0))))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl537])).
% 2.14/1.04 thf(zip_derived_cl758, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ x))
% 2.14/1.04 | (member @ u @ (singleton @ y))
% 2.14/1.04 | ~ (member @ u @
% 2.14/1.04 (intersection @ (complement @ (singleton @ z)) @
% 2.14/1.04 (complement @ null_class))))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl749, zip_derived_cl583])).
% 2.14/1.04 thf(zip_derived_cl1122, plain,
% 2.14/1.04 ((~ (member @ u @ (complement @ null_class))
% 2.14/1.04 | ~ (member @ u @ (complement @ (singleton @ z)))
% 2.14/1.04 | (member @ u @ (singleton @ x))
% 2.14/1.04 | (member @ u @ (singleton @ y)))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl758])).
% 2.14/1.04 thf(zip_derived_cl1565, plain,
% 2.14/1.04 (( (member @ u @ null_class)
% 2.14/1.04 | ~ (member @ u @ universal_class)
% 2.14/1.04 | ~ (member @ u @ (complement @ (singleton @ z)))
% 2.14/1.04 | (member @ u @ (singleton @ x))
% 2.14/1.04 | (member @ u @ (singleton @ y)))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl1122])).
% 2.14/1.04 thf(regularity1, axiom,
% 2.14/1.04 (( ( X ) = ( null_class ) ) | ( member @ ( regular @ X ) @ X ))).
% 2.14/1.04 thf(zip_derived_cl65, plain,
% 2.14/1.04 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 2.14/1.04 inference('cnf', [status(esa)], [regularity1])).
% 2.14/1.04 thf(zip_derived_cl426, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 2.14/1.04 thf(zip_derived_cl443, plain,
% 2.14/1.04 (![X0 : $i]:
% 2.14/1.04 (((X0) = (null_class)) | (member @ (regular @ X0) @ universal_class))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl426])).
% 2.14/1.04 thf(zip_derived_cl65, plain,
% 2.14/1.04 (![X0 : $i]: (((X0) = (null_class)) | (member @ (regular @ X0) @ X0))),
% 2.14/1.04 inference('cnf', [status(esa)], [regularity1])).
% 2.14/1.04 thf(zip_derived_cl23, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [complement1])).
% 2.14/1.04 thf(zip_derived_cl446, plain,
% 2.14/1.04 (![X0 : $i]:
% 2.14/1.04 (((complement @ X0) = (null_class))
% 2.14/1.04 | ~ (member @ (regular @ (complement @ X0)) @ X0))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl23])).
% 2.14/1.04 thf(zip_derived_cl459, plain,
% 2.14/1.04 ((((complement @ universal_class) = (null_class))
% 2.14/1.04 | ((complement @ universal_class) = (null_class)))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl443, zip_derived_cl446])).
% 2.14/1.04 thf(zip_derived_cl460, plain,
% 2.14/1.04 (((complement @ universal_class) = (null_class))),
% 2.14/1.04 inference('simplify', [status(thm)], [zip_derived_cl459])).
% 2.14/1.04 thf(zip_derived_cl23, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X0 @ (complement @ X1)) | ~ (member @ X0 @ X1))),
% 2.14/1.04 inference('cnf', [status(esa)], [complement1])).
% 2.14/1.04 thf(zip_derived_cl471, plain,
% 2.14/1.04 (![X0 : $i]:
% 2.14/1.04 (~ (member @ X0 @ null_class) | ~ (member @ X0 @ universal_class))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl460, zip_derived_cl23])).
% 2.14/1.04 thf(zip_derived_cl426, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X1 @ X0) | (member @ X1 @ universal_class))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 2.14/1.04 thf(zip_derived_cl473, plain, (![X0 : $i]: ~ (member @ X0 @ null_class)),
% 2.14/1.04 inference('clc', [status(thm)], [zip_derived_cl471, zip_derived_cl426])).
% 2.14/1.04 thf(zip_derived_cl430, plain, ( (member @ u @ universal_class)),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl426])).
% 2.14/1.04 thf(zip_derived_cl1566, plain,
% 2.14/1.04 ((~ (member @ u @ (complement @ (singleton @ z)))
% 2.14/1.04 | (member @ u @ (singleton @ x))
% 2.14/1.04 | (member @ u @ (singleton @ y)))),
% 2.14/1.04 inference('demod', [status(thm)],
% 2.14/1.04 [zip_derived_cl1565, zip_derived_cl473, zip_derived_cl430])).
% 2.14/1.04 thf(zip_derived_cl1567, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ z))
% 2.14/1.04 | ~ (member @ u @ universal_class)
% 2.14/1.04 | (member @ u @ (singleton @ x))
% 2.14/1.04 | (member @ u @ (singleton @ y)))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl1566])).
% 2.14/1.04 thf(zip_derived_cl430, plain, ( (member @ u @ universal_class)),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl426])).
% 2.14/1.04 thf(zip_derived_cl1569, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ z))
% 2.14/1.04 | (member @ u @ (singleton @ x))
% 2.14/1.04 | (member @ u @ (singleton @ y)))),
% 2.14/1.04 inference('demod', [status(thm)], [zip_derived_cl1567, zip_derived_cl430])).
% 2.14/1.04 thf(singleton_set, axiom, (( unordered_pair @ X @ X ) = ( singleton @ X ))).
% 2.14/1.04 thf(zip_derived_cl11, plain,
% 2.14/1.04 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 2.14/1.04 inference('cnf', [status(esa)], [singleton_set])).
% 2.14/1.04 thf(unordered_pair_member, axiom,
% 2.14/1.04 (( ~( member @ U @ ( unordered_pair @ X @ Y ) ) ) | ( ( U ) = ( X ) ) |
% 2.14/1.04 ( ( U ) = ( Y ) ))).
% 2.14/1.04 thf(zip_derived_cl7, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.14/1.04 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 2.14/1.04 | ((X0) = (X1))
% 2.14/1.04 | ((X0) = (X2)))),
% 2.14/1.04 inference('cnf', [status(esa)], [unordered_pair_member])).
% 2.14/1.04 thf(zip_derived_cl438, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (~ (member @ X1 @ (singleton @ X0)) | ((X1) = (X0)) | ((X1) = (X0)))),
% 2.14/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl7])).
% 2.14/1.04 thf(zip_derived_cl439, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 2.14/1.04 inference('simplify', [status(thm)], [zip_derived_cl438])).
% 2.14/1.04 thf(zip_derived_cl1572, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ y))
% 2.14/1.04 | (member @ u @ (singleton @ x))
% 2.14/1.04 | ((u) = (z)))),
% 2.14/1.04 inference('s_sup-', [status(thm)],
% 2.14/1.04 [zip_derived_cl1569, zip_derived_cl439])).
% 2.14/1.04 thf(prove_members_of_built_triple_4, conjecture, (( u ) = ( z ))).
% 2.14/1.04 thf(zf_stmt_1, negated_conjecture, (( u ) != ( z )),
% 2.14/1.04 inference('cnf.neg', [status(esa)], [prove_members_of_built_triple_4])).
% 2.14/1.04 thf(zip_derived_cl95, plain, (((u) != (z))),
% 2.14/1.04 inference('cnf', [status(esa)], [zf_stmt_1])).
% 2.14/1.04 thf(zip_derived_cl1577, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ y)) | (member @ u @ (singleton @ x)))),
% 2.14/1.04 inference('simplify_reflect-', [status(thm)],
% 2.14/1.04 [zip_derived_cl1572, zip_derived_cl95])).
% 2.14/1.04 thf(zip_derived_cl439, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 2.14/1.04 inference('simplify', [status(thm)], [zip_derived_cl438])).
% 2.14/1.04 thf(zip_derived_cl1579, plain,
% 2.14/1.04 (( (member @ u @ (singleton @ x)) | ((u) = (y)))),
% 2.14/1.04 inference('s_sup-', [status(thm)],
% 2.14/1.04 [zip_derived_cl1577, zip_derived_cl439])).
% 2.14/1.04 thf(prove_members_of_built_triple_3, conjecture, (( u ) = ( y ))).
% 2.14/1.04 thf(zf_stmt_2, negated_conjecture, (( u ) != ( y )),
% 2.14/1.04 inference('cnf.neg', [status(esa)], [prove_members_of_built_triple_3])).
% 2.14/1.04 thf(zip_derived_cl94, plain, (((u) != (y))),
% 2.14/1.04 inference('cnf', [status(esa)], [zf_stmt_2])).
% 2.14/1.04 thf(zip_derived_cl1584, plain, ( (member @ u @ (singleton @ x))),
% 2.14/1.04 inference('simplify_reflect-', [status(thm)],
% 2.14/1.04 [zip_derived_cl1579, zip_derived_cl94])).
% 2.14/1.04 thf(zip_derived_cl439, plain,
% 2.14/1.04 (![X0 : $i, X1 : $i]:
% 2.14/1.04 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 2.14/1.04 inference('simplify', [status(thm)], [zip_derived_cl438])).
% 2.14/1.04 thf(zip_derived_cl1586, plain, (((u) = (x))),
% 2.14/1.04 inference('s_sup-', [status(thm)],
% 2.14/1.04 [zip_derived_cl1584, zip_derived_cl439])).
% 2.14/1.04 thf(prove_members_of_built_triple_2, conjecture, (( u ) = ( x ))).
% 2.14/1.04 thf(zf_stmt_3, negated_conjecture, (( u ) != ( x )),
% 2.14/1.04 inference('cnf.neg', [status(esa)], [prove_members_of_built_triple_2])).
% 2.14/1.04 thf(zip_derived_cl93, plain, (((u) != (x))),
% 2.14/1.04 inference('cnf', [status(esa)], [zf_stmt_3])).
% 2.14/1.04 thf(zip_derived_cl1590, plain, ($false),
% 2.14/1.04 inference('simplify_reflect-', [status(thm)],
% 2.14/1.04 [zip_derived_cl1586, zip_derived_cl93])).
% 2.14/1.04
% 2.14/1.04 % SZS output end Refutation
% 2.14/1.04
% 2.14/1.04
% 2.14/1.04 % Terminating...
% 2.31/1.12 % Runner terminated.
% 2.31/1.13 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------