TSTP Solution File: SET018-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET018-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ioY3ESZxuA true
% Computer : n019.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 16:11:48 EDT 2023
% Result : Unsatisfiable 138.49s 20.53s
% Output : Refutation 138.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET018-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ioY3ESZxuA true
% 0.13/0.35 % Computer : n019.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 08:23:28 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
% 0.13/0.36 % Running in FO mode
% 0.22/0.66 % Total configuration time : 435
% 0.22/0.66 % Estimated wc time : 1092
% 0.22/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.22/0.79 % /export/starexec/sandbox/solver/bin/fo/fo17_bce.sh running for 50s
% 138.49/20.53 % Solved by fo/fo6_bce.sh.
% 138.49/20.53 % BCE start: 147
% 138.49/20.53 % BCE eliminated: 1
% 138.49/20.53 % PE start: 146
% 138.49/20.53 logic: eq
% 138.49/20.53 % PE eliminated: 11
% 138.49/20.53 % done 4857 iterations in 19.798s
% 138.49/20.53 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 138.49/20.53 % SZS output start Refutation
% 138.49/20.53 thf(singleton_set_type, type, singleton_set: $i > $i).
% 138.49/20.53 thf(non_ordered_pair_type, type, non_ordered_pair: $i > $i > $i).
% 138.49/20.53 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 138.49/20.53 thf(c_type, type, c: $i).
% 138.49/20.53 thf(member_type, type, member: $i > $i > $o).
% 138.49/20.53 thf(little_set_type, type, little_set: $i > $o).
% 138.49/20.53 thf(b_type, type, b: $i).
% 138.49/20.53 thf(a_type, type, a: $i).
% 138.49/20.53 thf(d_type, type, d: $i).
% 138.49/20.53 thf(ordered_pair, axiom,
% 138.49/20.53 (( ordered_pair @ X @ Y ) =
% 138.49/20.53 ( non_ordered_pair @ ( singleton_set @ X ) @ ( non_ordered_pair @ X @ Y ) ))).
% 138.49/20.53 thf(zip_derived_cl9, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 ((ordered_pair @ X0 @ X1)
% 138.49/20.53 = (non_ordered_pair @ (singleton_set @ X0) @
% 138.49/20.53 (non_ordered_pair @ X0 @ X1)))),
% 138.49/20.53 inference('cnf', [status(esa)], [ordered_pair])).
% 138.49/20.53 thf(non_ordered_pair3, axiom,
% 138.49/20.53 (( member @ U @ ( non_ordered_pair @ X @ Y ) ) | ( ~( little_set @ U ) ) |
% 138.49/20.53 ( ( U ) != ( Y ) ))).
% 138.49/20.53 thf(zip_derived_cl6, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 ( (member @ X0 @ (non_ordered_pair @ X1 @ X2))
% 138.49/20.53 | ~ (little_set @ X0)
% 138.49/20.53 | ((X0) != (X2)))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair3])).
% 138.49/20.53 thf(zip_derived_cl1051, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X1 @ X0)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl6])).
% 138.49/20.53 thf(zip_derived_cl4008, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ (non_ordered_pair @ X1 @ X0))
% 138.49/20.53 | (member @ (non_ordered_pair @ X1 @ X0) @ (ordered_pair @ X1 @ X0)))),
% 138.49/20.53 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1051])).
% 138.49/20.53 thf(non_ordered_pair4, axiom, (little_set @ ( non_ordered_pair @ X @ Y ))).
% 138.49/20.53 thf(zip_derived_cl7, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]: (little_set @ (non_ordered_pair @ X0 @ X1))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair4])).
% 138.49/20.53 thf(zip_derived_cl4010, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (member @ (non_ordered_pair @ X1 @ X0) @ (ordered_pair @ X1 @ X0))),
% 138.49/20.53 inference('demod', [status(thm)], [zip_derived_cl4008, zip_derived_cl7])).
% 138.49/20.53 thf(equal_ordered_pair, axiom,
% 138.49/20.53 (( ordered_pair @ a @ b ) = ( ordered_pair @ c @ d ))).
% 138.49/20.53 thf(zip_derived_cl145, plain,
% 138.49/20.53 (((ordered_pair @ a @ b) = (ordered_pair @ c @ d))),
% 138.49/20.53 inference('cnf', [status(esa)], [equal_ordered_pair])).
% 138.49/20.53 thf(zip_derived_cl9, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 ((ordered_pair @ X0 @ X1)
% 138.49/20.53 = (non_ordered_pair @ (singleton_set @ X0) @
% 138.49/20.53 (non_ordered_pair @ X0 @ X1)))),
% 138.49/20.53 inference('cnf', [status(esa)], [ordered_pair])).
% 138.49/20.53 thf(non_ordered_pair1, axiom,
% 138.49/20.53 (( ~( member @ U @ ( non_ordered_pair @ X @ Y ) ) ) | ( ( U ) = ( X ) ) |
% 138.49/20.53 ( ( U ) = ( Y ) ))).
% 138.49/20.53 thf(zip_derived_cl4, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 (~ (member @ X0 @ (non_ordered_pair @ X1 @ X2))
% 138.49/20.53 | ((X0) = (X1))
% 138.49/20.53 | ((X0) = (X2)))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair1])).
% 138.49/20.53 thf(zip_derived_cl1058, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 (~ (member @ X2 @ (ordered_pair @ X1 @ X0))
% 138.49/20.53 | ((X2) = (singleton_set @ X1))
% 138.49/20.53 | ((X2) = (non_ordered_pair @ X1 @ X0)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl4])).
% 138.49/20.53 thf(zip_derived_cl4055, plain,
% 138.49/20.53 (![X0 : $i]:
% 138.49/20.53 (~ (member @ X0 @ (ordered_pair @ a @ b))
% 138.49/20.53 | ((X0) = (singleton_set @ c))
% 138.49/20.53 | ((X0) = (non_ordered_pair @ c @ d)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl145, zip_derived_cl1058])).
% 138.49/20.53 thf(zip_derived_cl38875, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ b) = (singleton_set @ c))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ c @ d)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl4010, zip_derived_cl4055])).
% 138.49/20.53 thf(singleton_set, axiom,
% 138.49/20.53 (( singleton_set @ X ) = ( non_ordered_pair @ X @ X ))).
% 138.49/20.53 thf(zip_derived_cl8, plain,
% 138.49/20.53 (![X0 : $i]: ((singleton_set @ X0) = (non_ordered_pair @ X0 @ X0))),
% 138.49/20.53 inference('cnf', [status(esa)], [singleton_set])).
% 138.49/20.53 thf(zip_derived_cl39819, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ b) = (non_ordered_pair @ c @ d))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ c @ c)))),
% 138.49/20.53 inference('s_sup+', [status(thm)], [zip_derived_cl38875, zip_derived_cl8])).
% 138.49/20.53 thf(zip_derived_cl145, plain,
% 138.49/20.53 (((ordered_pair @ a @ b) = (ordered_pair @ c @ d))),
% 138.49/20.53 inference('cnf', [status(esa)], [equal_ordered_pair])).
% 138.49/20.53 thf(zip_derived_cl4010, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (member @ (non_ordered_pair @ X1 @ X0) @ (ordered_pair @ X1 @ X0))),
% 138.49/20.53 inference('demod', [status(thm)], [zip_derived_cl4008, zip_derived_cl7])).
% 138.49/20.53 thf(zip_derived_cl13267, plain,
% 138.49/20.53 ( (member @ (non_ordered_pair @ c @ d) @ (ordered_pair @ a @ b))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl145, zip_derived_cl4010])).
% 138.49/20.53 thf(zip_derived_cl1058, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 (~ (member @ X2 @ (ordered_pair @ X1 @ X0))
% 138.49/20.53 | ((X2) = (singleton_set @ X1))
% 138.49/20.53 | ((X2) = (non_ordered_pair @ X1 @ X0)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl4])).
% 138.49/20.53 thf(zip_derived_cl38774, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ d) = (singleton_set @ a))
% 138.49/20.53 | ((non_ordered_pair @ c @ d) = (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl13267, zip_derived_cl1058])).
% 138.49/20.53 thf(zip_derived_cl8, plain,
% 138.49/20.53 (![X0 : $i]: ((singleton_set @ X0) = (non_ordered_pair @ X0 @ X0))),
% 138.49/20.53 inference('cnf', [status(esa)], [singleton_set])).
% 138.49/20.53 thf(zip_derived_cl38777, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ d) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((non_ordered_pair @ c @ d) = (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('demod', [status(thm)], [zip_derived_cl38774, zip_derived_cl8])).
% 138.49/20.53 thf(zip_derived_cl1051, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X1 @ X0)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl6])).
% 138.49/20.53 thf(zip_derived_cl38786, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ d) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | ~ (little_set @ d)
% 138.49/20.53 | (member @ d @ (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl38777, zip_derived_cl1051])).
% 138.49/20.53 thf(d_little_set, axiom, (little_set @ d)).
% 138.49/20.53 thf(zip_derived_cl144, plain, ( (little_set @ d)),
% 138.49/20.53 inference('cnf', [status(esa)], [d_little_set])).
% 138.49/20.53 thf(zip_derived_cl38808, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ d) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | (member @ d @ (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl38786, zip_derived_cl144])).
% 138.49/20.53 thf(zip_derived_cl4, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 (~ (member @ X0 @ (non_ordered_pair @ X1 @ X2))
% 138.49/20.53 | ((X0) = (X1))
% 138.49/20.53 | ((X0) = (X2)))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair1])).
% 138.49/20.53 thf(zip_derived_cl82486, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ d) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((d) = (a))
% 138.49/20.53 | ((d) = (b)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl38808, zip_derived_cl4])).
% 138.49/20.53 thf(prove_second_components_equal, conjecture, (( b ) = ( d ))).
% 138.49/20.53 thf(zf_stmt_0, negated_conjecture, (( b ) != ( d )),
% 138.49/20.53 inference('cnf.neg', [status(esa)], [prove_second_components_equal])).
% 138.49/20.53 thf(zip_derived_cl146, plain, (((b) != (d))),
% 138.49/20.53 inference('cnf', [status(esa)], [zf_stmt_0])).
% 138.49/20.53 thf(zip_derived_cl82491, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ d) = (non_ordered_pair @ a @ a)) | ((d) = (a)))),
% 138.49/20.53 inference('simplify_reflect-', [status(thm)],
% 138.49/20.53 [zip_derived_cl82486, zip_derived_cl146])).
% 138.49/20.53 thf(zip_derived_cl1051, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X1 @ X0)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl6])).
% 138.49/20.53 thf(zip_derived_cl82500, plain,
% 138.49/20.53 ((((d) = (a))
% 138.49/20.53 | ~ (little_set @ d)
% 138.49/20.53 | (member @ d @ (non_ordered_pair @ a @ a)))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl82491, zip_derived_cl1051])).
% 138.49/20.53 thf(zip_derived_cl144, plain, ( (little_set @ d)),
% 138.49/20.53 inference('cnf', [status(esa)], [d_little_set])).
% 138.49/20.53 thf(zip_derived_cl82531, plain,
% 138.49/20.53 ((((d) = (a)) | (member @ d @ (non_ordered_pair @ a @ a)))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl82500, zip_derived_cl144])).
% 138.49/20.53 thf(zip_derived_cl8, plain,
% 138.49/20.53 (![X0 : $i]: ((singleton_set @ X0) = (non_ordered_pair @ X0 @ X0))),
% 138.49/20.53 inference('cnf', [status(esa)], [singleton_set])).
% 138.49/20.53 thf(zip_derived_cl8, plain,
% 138.49/20.53 (![X0 : $i]: ((singleton_set @ X0) = (non_ordered_pair @ X0 @ X0))),
% 138.49/20.53 inference('cnf', [status(esa)], [singleton_set])).
% 138.49/20.53 thf(zip_derived_cl4, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 (~ (member @ X0 @ (non_ordered_pair @ X1 @ X2))
% 138.49/20.53 | ((X0) = (X1))
% 138.49/20.53 | ((X0) = (X2)))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair1])).
% 138.49/20.53 thf(zip_derived_cl1029, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (member @ X1 @ (singleton_set @ X0))
% 138.49/20.53 | ((X1) = (X0))
% 138.49/20.53 | ((X1) = (X0)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl4])).
% 138.49/20.53 thf(zip_derived_cl1030, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (((X1) = (X0)) | ~ (member @ X1 @ (singleton_set @ X0)))),
% 138.49/20.53 inference('simplify', [status(thm)], [zip_derived_cl1029])).
% 138.49/20.53 thf(zip_derived_cl1034, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (((X1) = (X0)) | ~ (member @ X1 @ (non_ordered_pair @ X0 @ X0)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl1030])).
% 138.49/20.53 thf(zip_derived_cl84396, plain, (((d) = (a))),
% 138.49/20.53 inference('clc', [status(thm)], [zip_derived_cl82531, zip_derived_cl1034])).
% 138.49/20.53 thf(zip_derived_cl84446, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ b) = (non_ordered_pair @ c @ a))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ c @ c)))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl39819, zip_derived_cl84396])).
% 138.49/20.53 thf(non_ordered_pair2, axiom,
% 138.49/20.53 (( member @ U @ ( non_ordered_pair @ X @ Y ) ) | ( ~( little_set @ U ) ) |
% 138.49/20.53 ( ( U ) != ( X ) ))).
% 138.49/20.53 thf(zip_derived_cl5, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 ( (member @ X0 @ (non_ordered_pair @ X1 @ X2))
% 138.49/20.53 | ~ (little_set @ X0)
% 138.49/20.53 | ((X0) != (X1)))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair2])).
% 138.49/20.53 thf(zip_derived_cl1045, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X0 @ X1)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl5])).
% 138.49/20.53 thf(zip_derived_cl8, plain,
% 138.49/20.53 (![X0 : $i]: ((singleton_set @ X0) = (non_ordered_pair @ X0 @ X0))),
% 138.49/20.53 inference('cnf', [status(esa)], [singleton_set])).
% 138.49/20.53 thf(zip_derived_cl9, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 ((ordered_pair @ X0 @ X1)
% 138.49/20.53 = (non_ordered_pair @ (singleton_set @ X0) @
% 138.49/20.53 (non_ordered_pair @ X0 @ X1)))),
% 138.49/20.53 inference('cnf', [status(esa)], [ordered_pair])).
% 138.49/20.53 thf(zip_derived_cl1045, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X0 @ X1)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl5])).
% 138.49/20.53 thf(zip_derived_cl2165, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ (singleton_set @ X1))
% 138.49/20.53 | (member @ (singleton_set @ X1) @ (ordered_pair @ X1 @ X0)))),
% 138.49/20.53 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1045])).
% 138.49/20.53 thf(zip_derived_cl8, plain,
% 138.49/20.53 (![X0 : $i]: ((singleton_set @ X0) = (non_ordered_pair @ X0 @ X0))),
% 138.49/20.53 inference('cnf', [status(esa)], [singleton_set])).
% 138.49/20.53 thf(zip_derived_cl7, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]: (little_set @ (non_ordered_pair @ X0 @ X1))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair4])).
% 138.49/20.53 thf(zip_derived_cl1056, plain,
% 138.49/20.53 (![X0 : $i]: (little_set @ (singleton_set @ X0))),
% 138.49/20.53 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl7])).
% 138.49/20.53 thf(zip_derived_cl2167, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (member @ (singleton_set @ X1) @ (ordered_pair @ X1 @ X0))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl2165, zip_derived_cl1056])).
% 138.49/20.53 thf(zip_derived_cl2586, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (member @ (non_ordered_pair @ X0 @ X0) @ (ordered_pair @ X0 @ X1))),
% 138.49/20.53 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl2167])).
% 138.49/20.53 thf(zip_derived_cl4055, plain,
% 138.49/20.53 (![X0 : $i]:
% 138.49/20.53 (~ (member @ X0 @ (ordered_pair @ a @ b))
% 138.49/20.53 | ((X0) = (singleton_set @ c))
% 138.49/20.53 | ((X0) = (non_ordered_pair @ c @ d)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl145, zip_derived_cl1058])).
% 138.49/20.53 thf(zip_derived_cl38874, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ a) = (singleton_set @ c))
% 138.49/20.53 | ((non_ordered_pair @ a @ a) = (non_ordered_pair @ c @ d)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl2586, zip_derived_cl4055])).
% 138.49/20.53 thf(zip_derived_cl84396, plain, (((d) = (a))),
% 138.49/20.53 inference('clc', [status(thm)], [zip_derived_cl82531, zip_derived_cl1034])).
% 138.49/20.53 thf(zip_derived_cl84438, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ a) = (singleton_set @ c))
% 138.49/20.53 | ((non_ordered_pair @ a @ a) = (non_ordered_pair @ c @ a)))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl38874, zip_derived_cl84396])).
% 138.49/20.53 thf(zip_derived_cl1030, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (((X1) = (X0)) | ~ (member @ X1 @ (singleton_set @ X0)))),
% 138.49/20.53 inference('simplify', [status(thm)], [zip_derived_cl1029])).
% 138.49/20.53 thf(zip_derived_cl84992, plain,
% 138.49/20.53 (![X0 : $i]:
% 138.49/20.53 (((non_ordered_pair @ a @ a) = (non_ordered_pair @ c @ a))
% 138.49/20.53 | ((X0) = (c))
% 138.49/20.53 | ~ (member @ X0 @ (non_ordered_pair @ a @ a)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl84438, zip_derived_cl1030])).
% 138.49/20.53 thf(zip_derived_cl100701, plain,
% 138.49/20.53 ((~ (little_set @ a)
% 138.49/20.53 | ((non_ordered_pair @ a @ a) = (non_ordered_pair @ c @ a))
% 138.49/20.53 | ((a) = (c)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl1045, zip_derived_cl84992])).
% 138.49/20.53 thf(a_little_set, axiom, (little_set @ a)).
% 138.49/20.53 thf(zip_derived_cl141, plain, ( (little_set @ a)),
% 138.49/20.53 inference('cnf', [status(esa)], [a_little_set])).
% 138.49/20.53 thf(zip_derived_cl100842, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ a) = (non_ordered_pair @ c @ a)) | ((a) = (c)))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl100701, zip_derived_cl141])).
% 138.49/20.53 thf(zip_derived_cl100988, plain,
% 138.49/20.53 (((non_ordered_pair @ a @ a) = (non_ordered_pair @ c @ a))),
% 138.49/20.53 inference('condensation', [status(thm)], [zip_derived_cl100842])).
% 138.49/20.53 thf(zip_derived_cl100993, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ b) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ c @ c)))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl84446, zip_derived_cl100988])).
% 138.49/20.53 thf(zip_derived_cl1045, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X0 @ X1)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl5])).
% 138.49/20.53 thf(zip_derived_cl1045, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X0 @ X1)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl5])).
% 138.49/20.53 thf(zip_derived_cl82491, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ d) = (non_ordered_pair @ a @ a)) | ((d) = (a)))),
% 138.49/20.53 inference('simplify_reflect-', [status(thm)],
% 138.49/20.53 [zip_derived_cl82486, zip_derived_cl146])).
% 138.49/20.53 thf(zip_derived_cl4, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 (~ (member @ X0 @ (non_ordered_pair @ X1 @ X2))
% 138.49/20.53 | ((X0) = (X1))
% 138.49/20.53 | ((X0) = (X2)))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair1])).
% 138.49/20.53 thf(zip_derived_cl82492, plain,
% 138.49/20.53 (![X0 : $i]:
% 138.49/20.53 (((d) = (a))
% 138.49/20.53 | ~ (member @ X0 @ (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((X0) = (c))
% 138.49/20.53 | ((X0) = (d)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl82491, zip_derived_cl4])).
% 138.49/20.53 thf(zip_derived_cl82550, plain,
% 138.49/20.53 ((~ (little_set @ a) | ((d) = (a)) | ((a) = (c)) | ((a) = (d)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl1045, zip_derived_cl82492])).
% 138.49/20.53 thf(zip_derived_cl141, plain, ( (little_set @ a)),
% 138.49/20.53 inference('cnf', [status(esa)], [a_little_set])).
% 138.49/20.53 thf(zip_derived_cl82691, plain, ((((d) = (a)) | ((a) = (c)) | ((a) = (d)))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl82550, zip_derived_cl141])).
% 138.49/20.53 thf(zip_derived_cl82692, plain, ((((a) = (c)) | ((d) = (a)))),
% 138.49/20.53 inference('simplify', [status(thm)], [zip_derived_cl82691])).
% 138.49/20.53 thf(zip_derived_cl145, plain,
% 138.49/20.53 (((ordered_pair @ a @ b) = (ordered_pair @ c @ d))),
% 138.49/20.53 inference('cnf', [status(esa)], [equal_ordered_pair])).
% 138.49/20.53 thf(zip_derived_cl2167, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (member @ (singleton_set @ X1) @ (ordered_pair @ X1 @ X0))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl2165, zip_derived_cl1056])).
% 138.49/20.53 thf(zip_derived_cl2585, plain,
% 138.49/20.53 ( (member @ (singleton_set @ c) @ (ordered_pair @ a @ b))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl145, zip_derived_cl2167])).
% 138.49/20.53 thf(zip_derived_cl8, plain,
% 138.49/20.53 (![X0 : $i]: ((singleton_set @ X0) = (non_ordered_pair @ X0 @ X0))),
% 138.49/20.53 inference('cnf', [status(esa)], [singleton_set])).
% 138.49/20.53 thf(zip_derived_cl2588, plain,
% 138.49/20.53 ( (member @ (non_ordered_pair @ c @ c) @ (ordered_pair @ a @ b))),
% 138.49/20.53 inference('demod', [status(thm)], [zip_derived_cl2585, zip_derived_cl8])).
% 138.49/20.53 thf(zip_derived_cl1058, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 (~ (member @ X2 @ (ordered_pair @ X1 @ X0))
% 138.49/20.53 | ((X2) = (singleton_set @ X1))
% 138.49/20.53 | ((X2) = (non_ordered_pair @ X1 @ X0)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl4])).
% 138.49/20.53 thf(zip_derived_cl4023, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ c) = (singleton_set @ a))
% 138.49/20.53 | ((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl2588, zip_derived_cl1058])).
% 138.49/20.53 thf(zip_derived_cl8, plain,
% 138.49/20.53 (![X0 : $i]: ((singleton_set @ X0) = (non_ordered_pair @ X0 @ X0))),
% 138.49/20.53 inference('cnf', [status(esa)], [singleton_set])).
% 138.49/20.53 thf(zip_derived_cl4056, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('demod', [status(thm)], [zip_derived_cl4023, zip_derived_cl8])).
% 138.49/20.53 thf(zip_derived_cl1045, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X0 @ X1)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl5])).
% 138.49/20.53 thf(zip_derived_cl4066, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | ~ (little_set @ c)
% 138.49/20.53 | (member @ c @ (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl4056, zip_derived_cl1045])).
% 138.49/20.53 thf(c_little_set, axiom, (little_set @ c)).
% 138.49/20.53 thf(zip_derived_cl143, plain, ( (little_set @ c)),
% 138.49/20.53 inference('cnf', [status(esa)], [c_little_set])).
% 138.49/20.53 thf(zip_derived_cl4082, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | (member @ c @ (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('demod', [status(thm)], [zip_derived_cl4066, zip_derived_cl143])).
% 138.49/20.53 thf(zip_derived_cl4, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 (~ (member @ X0 @ (non_ordered_pair @ X1 @ X2))
% 138.49/20.53 | ((X0) = (X1))
% 138.49/20.53 | ((X0) = (X2)))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair1])).
% 138.49/20.53 thf(zip_derived_cl5161, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((c) = (a))
% 138.49/20.53 | ((c) = (b)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl4082, zip_derived_cl4])).
% 138.49/20.53 thf(zip_derived_cl5167, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a)) | ((c) = (b)))),
% 138.49/20.53 inference('condensation', [status(thm)], [zip_derived_cl5161])).
% 138.49/20.53 thf(zip_derived_cl1045, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X0 @ X1)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl5])).
% 138.49/20.53 thf(zip_derived_cl5171, plain,
% 138.49/20.53 ((((c) = (b))
% 138.49/20.53 | ~ (little_set @ c)
% 138.49/20.53 | (member @ c @ (non_ordered_pair @ a @ a)))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl5167, zip_derived_cl1045])).
% 138.49/20.53 thf(zip_derived_cl143, plain, ( (little_set @ c)),
% 138.49/20.53 inference('cnf', [status(esa)], [c_little_set])).
% 138.49/20.53 thf(zip_derived_cl5194, plain,
% 138.49/20.53 ((((c) = (b)) | (member @ c @ (non_ordered_pair @ a @ a)))),
% 138.49/20.53 inference('demod', [status(thm)], [zip_derived_cl5171, zip_derived_cl143])).
% 138.49/20.53 thf(zip_derived_cl1034, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (((X1) = (X0)) | ~ (member @ X1 @ (non_ordered_pair @ X0 @ X0)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl1030])).
% 138.49/20.53 thf(zip_derived_cl6141, plain, ((((c) = (b)) | ((c) = (a)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl5194, zip_derived_cl1034])).
% 138.49/20.53 thf(zip_derived_cl38875, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ b) = (singleton_set @ c))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ c @ d)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl4010, zip_derived_cl4055])).
% 138.49/20.53 thf(zip_derived_cl39911, plain,
% 138.49/20.53 ((((c) = (a))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (singleton_set @ b))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ d)))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl6141, zip_derived_cl38875])).
% 138.49/20.53 thf(zip_derived_cl8, plain,
% 138.49/20.53 (![X0 : $i]: ((singleton_set @ X0) = (non_ordered_pair @ X0 @ X0))),
% 138.49/20.53 inference('cnf', [status(esa)], [singleton_set])).
% 138.49/20.53 thf(zip_derived_cl39934, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ d))
% 138.49/20.53 | ((c) = (a))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ b)))),
% 138.49/20.53 inference('s_sup+', [status(thm)], [zip_derived_cl39911, zip_derived_cl8])).
% 138.49/20.53 thf(zip_derived_cl82871, plain,
% 138.49/20.53 ((((a) = (c))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ a))
% 138.49/20.53 | ((c) = (a))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ b)))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl82692, zip_derived_cl39934])).
% 138.49/20.53 thf(zip_derived_cl82881, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ b))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ a))
% 138.49/20.53 | ((a) = (c)))),
% 138.49/20.53 inference('simplify', [status(thm)], [zip_derived_cl82871])).
% 138.49/20.53 thf(zip_derived_cl1034, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (((X1) = (X0)) | ~ (member @ X1 @ (non_ordered_pair @ X0 @ X0)))),
% 138.49/20.53 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl1030])).
% 138.49/20.53 thf(zip_derived_cl85538, plain,
% 138.49/20.53 (![X0 : $i]:
% 138.49/20.53 (((a) = (c))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ a))
% 138.49/20.53 | ((X0) = (b))
% 138.49/20.53 | ~ (member @ X0 @ (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl82881, zip_derived_cl1034])).
% 138.49/20.53 thf(zip_derived_cl104548, plain,
% 138.49/20.53 ((~ (little_set @ a)
% 138.49/20.53 | ((a) = (c))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ a))
% 138.49/20.53 | ((a) = (b)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl1045, zip_derived_cl85538])).
% 138.49/20.53 thf(zip_derived_cl141, plain, ( (little_set @ a)),
% 138.49/20.53 inference('cnf', [status(esa)], [a_little_set])).
% 138.49/20.53 thf(zip_derived_cl104690, plain,
% 138.49/20.53 ((((a) = (c))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ a))
% 138.49/20.53 | ((a) = (b)))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl104548, zip_derived_cl141])).
% 138.49/20.53 thf(zip_derived_cl146, plain, (((b) != (d))),
% 138.49/20.53 inference('cnf', [status(esa)], [zf_stmt_0])).
% 138.49/20.53 thf(zip_derived_cl84396, plain, (((d) = (a))),
% 138.49/20.53 inference('clc', [status(thm)], [zip_derived_cl82531, zip_derived_cl1034])).
% 138.49/20.53 thf(zip_derived_cl84399, plain, (((b) != (a))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl146, zip_derived_cl84396])).
% 138.49/20.53 thf(zip_derived_cl104691, plain,
% 138.49/20.53 ((((a) = (c)) | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ b @ a)))),
% 138.49/20.53 inference('simplify_reflect-', [status(thm)],
% 138.49/20.53 [zip_derived_cl104690, zip_derived_cl84399])).
% 138.49/20.53 thf(zip_derived_cl6141, plain, ((((c) = (b)) | ((c) = (a)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl5194, zip_derived_cl1034])).
% 138.49/20.53 thf(zip_derived_cl100988, plain,
% 138.49/20.53 (((non_ordered_pair @ a @ a) = (non_ordered_pair @ c @ a))),
% 138.49/20.53 inference('condensation', [status(thm)], [zip_derived_cl100842])).
% 138.49/20.53 thf(zip_derived_cl101036, plain,
% 138.49/20.53 ((((c) = (a)) | ((non_ordered_pair @ a @ a) = (non_ordered_pair @ b @ a)))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl6141, zip_derived_cl100988])).
% 138.49/20.53 thf(zip_derived_cl104873, plain,
% 138.49/20.53 ((((a) = (c))
% 138.49/20.53 | ((c) = (a))
% 138.49/20.53 | ((non_ordered_pair @ a @ a) = (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl104691, zip_derived_cl101036])).
% 138.49/20.53 thf(zip_derived_cl104884, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ a) = (non_ordered_pair @ a @ b)) | ((a) = (c)))),
% 138.49/20.53 inference('simplify', [status(thm)], [zip_derived_cl104873])).
% 138.49/20.53 thf(zip_derived_cl4056, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ b)))),
% 138.49/20.53 inference('demod', [status(thm)], [zip_derived_cl4023, zip_derived_cl8])).
% 138.49/20.53 thf(zip_derived_cl4079, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ b) != (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a)))),
% 138.49/20.53 inference('eq_fact', [status(thm)], [zip_derived_cl4056])).
% 138.49/20.53 thf(zip_derived_cl104958, plain,
% 138.49/20.53 ((((a) = (c))
% 138.49/20.53 | ((non_ordered_pair @ a @ a) != (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl104884, zip_derived_cl4079])).
% 138.49/20.53 thf(zip_derived_cl104985, plain,
% 138.49/20.53 ((((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a)) | ((a) = (c)))),
% 138.49/20.53 inference('simplify', [status(thm)], [zip_derived_cl104958])).
% 138.49/20.53 thf(zip_derived_cl105767, plain,
% 138.49/20.53 (((non_ordered_pair @ c @ c) = (non_ordered_pair @ a @ a))),
% 138.49/20.53 inference('condensation', [status(thm)], [zip_derived_cl104985])).
% 138.49/20.53 thf(zip_derived_cl105770, plain,
% 138.49/20.53 ((((non_ordered_pair @ a @ b) = (non_ordered_pair @ a @ a))
% 138.49/20.53 | ((non_ordered_pair @ a @ b) = (non_ordered_pair @ a @ a)))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl100993, zip_derived_cl105767])).
% 138.49/20.53 thf(zip_derived_cl105771, plain,
% 138.49/20.53 (((non_ordered_pair @ a @ b) = (non_ordered_pair @ a @ a))),
% 138.49/20.53 inference('simplify', [status(thm)], [zip_derived_cl105770])).
% 138.49/20.53 thf(zip_derived_cl1051, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i]:
% 138.49/20.53 (~ (little_set @ X0) | (member @ X0 @ (non_ordered_pair @ X1 @ X0)))),
% 138.49/20.53 inference('eq_res', [status(thm)], [zip_derived_cl6])).
% 138.49/20.53 thf(zip_derived_cl105950, plain,
% 138.49/20.53 ((~ (little_set @ b) | (member @ b @ (non_ordered_pair @ a @ a)))),
% 138.49/20.53 inference('s_sup+', [status(thm)],
% 138.49/20.53 [zip_derived_cl105771, zip_derived_cl1051])).
% 138.49/20.53 thf(b_little_set, axiom, (little_set @ b)).
% 138.49/20.53 thf(zip_derived_cl142, plain, ( (little_set @ b)),
% 138.49/20.53 inference('cnf', [status(esa)], [b_little_set])).
% 138.49/20.53 thf(zip_derived_cl105976, plain,
% 138.49/20.53 ( (member @ b @ (non_ordered_pair @ a @ a))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl105950, zip_derived_cl142])).
% 138.49/20.53 thf(zip_derived_cl4, plain,
% 138.49/20.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 138.49/20.53 (~ (member @ X0 @ (non_ordered_pair @ X1 @ X2))
% 138.49/20.53 | ((X0) = (X1))
% 138.49/20.53 | ((X0) = (X2)))),
% 138.49/20.53 inference('cnf', [status(esa)], [non_ordered_pair1])).
% 138.49/20.53 thf(zip_derived_cl106900, plain, ((((b) = (a)) | ((b) = (a)))),
% 138.49/20.53 inference('s_sup-', [status(thm)],
% 138.49/20.53 [zip_derived_cl105976, zip_derived_cl4])).
% 138.49/20.53 thf(zip_derived_cl106909, plain, (((b) = (a))),
% 138.49/20.53 inference('simplify', [status(thm)], [zip_derived_cl106900])).
% 138.49/20.53 thf(zip_derived_cl84399, plain, (((b) != (a))),
% 138.49/20.53 inference('demod', [status(thm)],
% 138.49/20.53 [zip_derived_cl146, zip_derived_cl84396])).
% 138.49/20.53 thf(zip_derived_cl106910, plain, ($false),
% 138.49/20.53 inference('simplify_reflect-', [status(thm)],
% 138.49/20.53 [zip_derived_cl106909, zip_derived_cl84399])).
% 138.49/20.53
% 138.49/20.53 % SZS output end Refutation
% 138.49/20.53
% 138.49/20.53
% 138.49/20.53 % Terminating...
% 138.90/20.60 % Runner terminated.
% 138.90/20.61 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------