TSTP Solution File: SET020-6 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET020-6 : 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.Me6caeVjtf true
% Computer : n022.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 16:11:51 EDT 2023
% Result : Unsatisfiable 1.40s 0.84s
% Output : Refutation 1.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET020-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.15/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Me6caeVjtf true
% 0.15/0.36 % Computer : n022.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 : Sat Aug 26 10:13:25 EDT 2023
% 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
% 0.15/0.37 % Running in FO mode
% 0.22/0.67 % Total configuration time : 435
% 0.22/0.68 % Estimated wc time : 1092
% 0.22/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.79 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.40/0.84 % Solved by fo/fo3_bce.sh.
% 1.40/0.84 % BCE start: 55
% 1.40/0.84 % BCE eliminated: 4
% 1.40/0.84 % PE start: 51
% 1.40/0.84 logic: eq
% 1.40/0.84 % PE eliminated: 12
% 1.40/0.84 % done 130 iterations in 0.073s
% 1.40/0.84 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.40/0.84 % SZS output start Refutation
% 1.40/0.84 thf(universal_class_type, type, universal_class: $i).
% 1.40/0.84 thf(member_type, type, member: $i > $i > $o).
% 1.40/0.84 thf(second_type, type, second: $i > $i).
% 1.40/0.84 thf(u_type, type, u: $i).
% 1.40/0.84 thf(unordered_pair_type, type, unordered_pair: $i > $i > $i).
% 1.40/0.84 thf(v_type, type, v: $i).
% 1.40/0.84 thf(singleton_type, type, singleton: $i > $i).
% 1.40/0.84 thf(cross_product_type, type, cross_product: $i > $i > $i).
% 1.40/0.84 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 1.40/0.84 thf(first_type, type, first: $i > $i).
% 1.40/0.84 thf(singleton_set, axiom, (( unordered_pair @ X @ X ) = ( singleton @ X ))).
% 1.40/0.84 thf(zip_derived_cl11, plain,
% 1.40/0.84 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 1.40/0.84 inference('cnf', [status(esa)], [singleton_set])).
% 1.40/0.84 thf(unordered_pair2, axiom,
% 1.40/0.84 (( ~( member @ X @ universal_class ) ) |
% 1.40/0.84 ( member @ X @ ( unordered_pair @ X @ Y ) ))).
% 1.40/0.84 thf(zip_derived_cl8, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 (~ (member @ X0 @ universal_class)
% 1.40/0.84 | (member @ X0 @ (unordered_pair @ X0 @ X1)))),
% 1.40/0.84 inference('cnf', [status(esa)], [unordered_pair2])).
% 1.40/0.84 thf(zip_derived_cl280, plain,
% 1.40/0.84 (![X0 : $i]:
% 1.40/0.84 ( (member @ X0 @ (singleton @ X0)) | ~ (member @ X0 @ universal_class))),
% 1.40/0.84 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 1.40/0.84 thf(cartesian_product2, axiom,
% 1.40/0.84 (( ~( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) |
% 1.40/0.84 ( member @ V @ Y ))).
% 1.40/0.84 thf(zip_derived_cl14, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.40/0.84 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 1.40/0.84 | (member @ X1 @ X3))),
% 1.40/0.84 inference('cnf', [status(esa)], [cartesian_product2])).
% 1.40/0.84 thf(prove_unique_1st_and_2nd_in_pair_of_sets1_1, conjecture,
% 1.40/0.84 (~( member @
% 1.40/0.84 ( ordered_pair @ u @ v ) @
% 1.40/0.84 ( cross_product @ universal_class @ universal_class ) ))).
% 1.40/0.84 thf(zf_stmt_0, negated_conjecture,
% 1.40/0.84 (member @
% 1.40/0.84 ( ordered_pair @ u @ v ) @
% 1.40/0.84 ( cross_product @ universal_class @ universal_class )),
% 1.40/0.84 inference('cnf.neg', [status(esa)],
% 1.40/0.84 [prove_unique_1st_and_2nd_in_pair_of_sets1_1])).
% 1.40/0.84 thf(zip_derived_cl54, plain,
% 1.40/0.84 ( (member @ (ordered_pair @ u @ v) @
% 1.40/0.84 (cross_product @ universal_class @ universal_class))),
% 1.40/0.84 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.40/0.84 thf(zip_derived_cl285, plain, ( (member @ v @ universal_class)),
% 1.40/0.84 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl54])).
% 1.40/0.84 thf(zip_derived_cl54, plain,
% 1.40/0.84 ( (member @ (ordered_pair @ u @ v) @
% 1.40/0.84 (cross_product @ universal_class @ universal_class))),
% 1.40/0.84 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.40/0.84 thf(cartesian_product4, axiom,
% 1.40/0.84 (( ~( member @ Z @ ( cross_product @ X @ Y ) ) ) |
% 1.40/0.84 ( ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) = ( Z ) ))).
% 1.40/0.84 thf(zip_derived_cl16, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.40/0.84 (~ (member @ X0 @ (cross_product @ X1 @ X2))
% 1.40/0.84 | ((ordered_pair @ (first @ X0) @ (second @ X0)) = (X0)))),
% 1.40/0.84 inference('cnf', [status(esa)], [cartesian_product4])).
% 1.40/0.84 thf(zip_derived_cl303, plain,
% 1.40/0.84 (((ordered_pair @ (first @ (ordered_pair @ u @ v)) @
% 1.40/0.84 (second @ (ordered_pair @ u @ v))) = (ordered_pair @ u @ v))),
% 1.40/0.84 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl16])).
% 1.40/0.84 thf(ordered_pair, axiom,
% 1.40/0.84 (( unordered_pair @
% 1.40/0.84 ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) =
% 1.40/0.84 ( ordered_pair @ X @ Y ))).
% 1.40/0.84 thf(zip_derived_cl12, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 ((unordered_pair @ (singleton @ X0) @
% 1.40/0.84 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 1.40/0.84 inference('cnf', [status(esa)], [ordered_pair])).
% 1.40/0.84 thf(zip_derived_cl12, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 ((unordered_pair @ (singleton @ X0) @
% 1.40/0.84 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 1.40/0.84 inference('cnf', [status(esa)], [ordered_pair])).
% 1.40/0.84 thf(zip_derived_cl12, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 ((unordered_pair @ (singleton @ X0) @
% 1.40/0.84 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 1.40/0.84 inference('cnf', [status(esa)], [ordered_pair])).
% 1.40/0.84 thf(zip_derived_cl12, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 ((unordered_pair @ (singleton @ X0) @
% 1.40/0.84 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 1.40/0.84 inference('cnf', [status(esa)], [ordered_pair])).
% 1.40/0.84 thf(zip_derived_cl321, plain,
% 1.40/0.84 (((unordered_pair @
% 1.40/0.84 (singleton @
% 1.40/0.84 (first @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v))))) @
% 1.40/0.84 (unordered_pair @
% 1.40/0.84 (first @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v)))) @
% 1.40/0.84 (singleton @
% 1.40/0.84 (second @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v)))))))
% 1.40/0.84 = (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v))))),
% 1.40/0.84 inference('demod', [status(thm)],
% 1.40/0.84 [zip_derived_cl303, zip_derived_cl12, zip_derived_cl12,
% 1.40/0.84 zip_derived_cl12, zip_derived_cl12])).
% 1.40/0.84 thf(cartesian_product1, axiom,
% 1.40/0.84 (( ~( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) |
% 1.40/0.84 ( member @ U @ X ))).
% 1.40/0.84 thf(zip_derived_cl13, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.40/0.84 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 1.40/0.84 | (member @ X0 @ X2))),
% 1.40/0.84 inference('cnf', [status(esa)], [cartesian_product1])).
% 1.40/0.84 thf(zip_derived_cl12, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 ((unordered_pair @ (singleton @ X0) @
% 1.40/0.84 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 1.40/0.84 inference('cnf', [status(esa)], [ordered_pair])).
% 1.40/0.84 thf(zip_derived_cl313, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.40/0.84 (~ (member @
% 1.40/0.84 (unordered_pair @ (singleton @ X0) @
% 1.40/0.84 (unordered_pair @ X0 @ (singleton @ X1))) @
% 1.40/0.84 (cross_product @ X2 @ X3))
% 1.40/0.84 | (member @ X0 @ X2))),
% 1.40/0.84 inference('demod', [status(thm)], [zip_derived_cl13, zip_derived_cl12])).
% 1.40/0.84 thf(zip_derived_cl442, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 (~ (member @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v))) @
% 1.40/0.84 (cross_product @ X1 @ X0))
% 1.40/0.84 | (member @
% 1.40/0.84 (first @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v)))) @
% 1.40/0.84 X1))),
% 1.40/0.84 inference('sup-', [status(thm)], [zip_derived_cl321, zip_derived_cl313])).
% 1.40/0.84 thf(cartesian_product3, axiom,
% 1.40/0.84 (( ~( member @ U @ X ) ) | ( ~( member @ V @ Y ) ) |
% 1.40/0.84 ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ))).
% 1.40/0.84 thf(zip_derived_cl15, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.40/0.84 (~ (member @ X0 @ X1)
% 1.40/0.84 | ~ (member @ X2 @ X3)
% 1.40/0.84 | (member @ (ordered_pair @ X0 @ X2) @ (cross_product @ X1 @ X3)))),
% 1.40/0.84 inference('cnf', [status(esa)], [cartesian_product3])).
% 1.40/0.84 thf(zip_derived_cl12, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 ((unordered_pair @ (singleton @ X0) @
% 1.40/0.84 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 1.40/0.84 inference('cnf', [status(esa)], [ordered_pair])).
% 1.40/0.84 thf(zip_derived_cl336, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.40/0.84 (~ (member @ X0 @ X1)
% 1.40/0.84 | ~ (member @ X2 @ X3)
% 1.40/0.84 | (member @
% 1.40/0.84 (unordered_pair @ (singleton @ X0) @
% 1.40/0.84 (unordered_pair @ X0 @ (singleton @ X2))) @
% 1.40/0.84 (cross_product @ X1 @ X3)))),
% 1.40/0.84 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl12])).
% 1.40/0.84 thf(zip_derived_cl463, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 ( (member @
% 1.40/0.84 (first @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v)))) @
% 1.40/0.84 X1)
% 1.40/0.84 | ~ (member @ v @ X0)
% 1.40/0.84 | ~ (member @ u @ X1))),
% 1.40/0.84 inference('sup+', [status(thm)], [zip_derived_cl442, zip_derived_cl336])).
% 1.40/0.84 thf(zip_derived_cl472, plain,
% 1.40/0.84 (![X0 : $i]:
% 1.40/0.84 (~ (member @ u @ X0)
% 1.40/0.84 | (member @
% 1.40/0.84 (first @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v)))) @
% 1.40/0.84 X0))),
% 1.40/0.84 inference('sup-', [status(thm)], [zip_derived_cl285, zip_derived_cl463])).
% 1.40/0.84 thf(zip_derived_cl11, plain,
% 1.40/0.84 (![X0 : $i]: ((unordered_pair @ X0 @ X0) = (singleton @ X0))),
% 1.40/0.84 inference('cnf', [status(esa)], [singleton_set])).
% 1.40/0.84 thf(unordered_pair_member, axiom,
% 1.40/0.84 (( ~( member @ U @ ( unordered_pair @ X @ Y ) ) ) | ( ( U ) = ( X ) ) |
% 1.40/0.84 ( ( U ) = ( Y ) ))).
% 1.40/0.84 thf(zip_derived_cl7, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.40/0.84 (~ (member @ X0 @ (unordered_pair @ X1 @ X2))
% 1.40/0.84 | ((X0) = (X1))
% 1.40/0.84 | ((X0) = (X2)))),
% 1.40/0.84 inference('cnf', [status(esa)], [unordered_pair_member])).
% 1.40/0.84 thf(zip_derived_cl268, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 (~ (member @ X1 @ (singleton @ X0)) | ((X1) = (X0)) | ((X1) = (X0)))),
% 1.40/0.84 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl7])).
% 1.40/0.84 thf(zip_derived_cl269, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 (((X1) = (X0)) | ~ (member @ X1 @ (singleton @ X0)))),
% 1.40/0.84 inference('simplify', [status(thm)], [zip_derived_cl268])).
% 1.40/0.84 thf(zip_derived_cl509, plain,
% 1.40/0.84 (![X0 : $i]:
% 1.40/0.84 (~ (member @ u @ (singleton @ X0))
% 1.40/0.84 | ((first @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v))))
% 1.40/0.84 = (X0)))),
% 1.40/0.84 inference('sup-', [status(thm)], [zip_derived_cl472, zip_derived_cl269])).
% 1.40/0.84 thf(zip_derived_cl523, plain,
% 1.40/0.84 ((~ (member @ u @ universal_class)
% 1.40/0.84 | ((first @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v))))
% 1.40/0.84 = (u)))),
% 1.40/0.84 inference('sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl509])).
% 1.40/0.84 thf(zip_derived_cl13, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.40/0.84 (~ (member @ (ordered_pair @ X0 @ X1) @ (cross_product @ X2 @ X3))
% 1.40/0.84 | (member @ X0 @ X2))),
% 1.40/0.84 inference('cnf', [status(esa)], [cartesian_product1])).
% 1.40/0.84 thf(zip_derived_cl54, plain,
% 1.40/0.84 ( (member @ (ordered_pair @ u @ v) @
% 1.40/0.84 (cross_product @ universal_class @ universal_class))),
% 1.40/0.84 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.40/0.84 thf(zip_derived_cl271, plain, ( (member @ u @ universal_class)),
% 1.40/0.84 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl54])).
% 1.40/0.84 thf(zip_derived_cl524, plain,
% 1.40/0.84 (((first @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v))))
% 1.40/0.84 = (u))),
% 1.40/0.84 inference('demod', [status(thm)], [zip_derived_cl523, zip_derived_cl271])).
% 1.40/0.84 thf(prove_unique_1st_and_2nd_in_pair_of_sets1_2, conjecture,
% 1.40/0.84 (( first @ ( ordered_pair @ u @ v ) ) = ( u ))).
% 1.40/0.84 thf(zf_stmt_1, negated_conjecture,
% 1.40/0.84 (( first @ ( ordered_pair @ u @ v ) ) != ( u )),
% 1.40/0.84 inference('cnf.neg', [status(esa)],
% 1.40/0.84 [prove_unique_1st_and_2nd_in_pair_of_sets1_2])).
% 1.40/0.84 thf(zip_derived_cl53, plain, (((first @ (ordered_pair @ u @ v)) != (u))),
% 1.40/0.84 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.40/0.84 thf(zip_derived_cl12, plain,
% 1.40/0.84 (![X0 : $i, X1 : $i]:
% 1.40/0.84 ((unordered_pair @ (singleton @ X0) @
% 1.40/0.84 (unordered_pair @ X0 @ (singleton @ X1))) = (ordered_pair @ X0 @ X1))),
% 1.40/0.84 inference('cnf', [status(esa)], [ordered_pair])).
% 1.40/0.84 thf(zip_derived_cl316, plain,
% 1.40/0.84 (((first @
% 1.40/0.84 (unordered_pair @ (singleton @ u) @
% 1.40/0.84 (unordered_pair @ u @ (singleton @ v))))
% 1.40/0.84 != (u))),
% 1.40/0.84 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl12])).
% 1.40/0.84 thf(zip_derived_cl525, plain, ($false),
% 1.40/0.84 inference('simplify_reflect-', [status(thm)],
% 1.40/0.84 [zip_derived_cl524, zip_derived_cl316])).
% 1.40/0.84
% 1.40/0.84 % SZS output end Refutation
% 1.40/0.84
% 1.40/0.84
% 1.40/0.84 % Terminating...
% 1.40/0.87 % Runner terminated.
% 1.40/0.89 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------