%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD060-2 : TPTP v9.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Kgrq1z0TMt true
% Computer : n024.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 04:33:21 PM UTC 2025
% Result : Unsatisfiable 26.15s 4.25s
% Output : Refutation 26.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : FLD060-2 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.00/0.09 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Kgrq1z0TMt true
% 0.07/0.28 % Computer : n024.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Wed Oct 1 18:26:08 EDT 2025
% 0.07/0.28 % CPUTime :
% 0.07/0.28 % Running portfolio for 300 s
% 0.07/0.28 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.28 % Number of cores: 8
% 0.10/0.28 % Python version: Python 3.6.8
% 0.10/0.28 % Running in FO mode
% 0.11/0.57 % Total configuration time : 435
% 0.11/0.57 % Estimated wc time : 1092
% 0.11/0.57 % Estimated cpu time (7 cpus) : 156.0
% 0.75/0.61 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.75/0.61 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 1.01/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 1.01/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.01/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.01/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.01/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 26.15/4.25 % Solved by fo/fo5.sh.
% 26.15/4.25 % done 6771 iterations in 3.566s
% 26.15/4.25 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 26.15/4.25 % SZS output start Refutation
% 26.15/4.25 thf(defined_type, type, defined: $i > $o).
% 26.15/4.25 thf(v_type, type, v: $i).
% 26.15/4.25 thf(add_type, type, add: $i > $i > $i).
% 26.15/4.25 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 26.15/4.25 thf(b_type, type, b: $i).
% 26.15/4.25 thf(u_type, type, u: $i).
% 26.15/4.25 thf(equalish_type, type, equalish: $i > $i > $o).
% 26.15/4.25 thf(a_type, type, a: $i).
% 26.15/4.25 thf(not_less_or_equal_8, conjecture, (less_or_equal @ u @ v)).
% 26.15/4.25 thf(zf_stmt_0, negated_conjecture, (~( less_or_equal @ u @ v )),
% 26.15/4.25 inference('cnf.neg', [status(esa)], [not_less_or_equal_8])).
% 26.15/4.25 thf(zip_derived_cl34, plain, (~ (less_or_equal @ u @ v)),
% 26.15/4.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 26.15/4.25 thf(totality_of_order_relation, axiom,
% 26.15/4.25 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 26.15/4.25 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 26.15/4.25 thf(zip_derived_cl17, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | (less_or_equal @ X1 @ X0)
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (defined @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 26.15/4.25 thf(zip_derived_cl865, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0) | ~ (defined @ X0) | (less_or_equal @ X0 @ X0))),
% 26.15/4.25 inference('eq_fact', [status(thm)], [zip_derived_cl17])).
% 26.15/4.25 thf(zip_derived_cl869, plain,
% 26.15/4.25 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 26.15/4.25 inference('simplify', [status(thm)], [zip_derived_cl865])).
% 26.15/4.25 thf(add_equals_v_6, conjecture, (~( equalish @ ( add @ b @ b ) @ v ))).
% 26.15/4.25 thf(zf_stmt_1, negated_conjecture, (equalish @ ( add @ b @ b ) @ v),
% 26.15/4.25 inference('cnf.neg', [status(esa)], [add_equals_v_6])).
% 26.15/4.25 thf(zip_derived_cl32, plain, ( (equalish @ (add @ b @ b) @ v)),
% 26.15/4.25 inference('cnf', [status(esa)], [zf_stmt_1])).
% 26.15/4.25 thf(symmetry_of_equality, axiom,
% 26.15/4.25 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 26.15/4.25 thf(zip_derived_cl21, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 26.15/4.25 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 26.15/4.25 thf(zip_derived_cl37, plain, ( (equalish @ v @ (add @ b @ b))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl21])).
% 26.15/4.25 thf(compatibility_of_equality_and_order_relation, axiom,
% 26.15/4.25 (( less_or_equal @ Y @ Z ) | ( ~( less_or_equal @ X @ Z ) ) |
% 26.15/4.25 ( ~( equalish @ X @ Y ) ))).
% 26.15/4.25 thf(zip_derived_cl25, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X2 @ X1)
% 26.15/4.25 | ~ (equalish @ X2 @ X0))),
% 26.15/4.25 inference('cnf', [status(esa)],
% 26.15/4.25 [compatibility_of_equality_and_order_relation])).
% 26.15/4.25 thf(zip_derived_cl1321, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (less_or_equal @ v @ X0) | (less_or_equal @ (add @ b @ b) @ X0))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl25])).
% 26.15/4.25 thf(zip_derived_cl1496, plain,
% 26.15/4.25 ((~ (defined @ v) | (less_or_equal @ (add @ b @ b) @ v))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl869, zip_derived_cl1321])).
% 26.15/4.25 thf(v_is_defined, axiom, (defined @ v)).
% 26.15/4.25 thf(zip_derived_cl30, plain, ( (defined @ v)),
% 26.15/4.25 inference('cnf', [status(esa)], [v_is_defined])).
% 26.15/4.25 thf(zip_derived_cl1500, plain, ( (less_or_equal @ (add @ b @ b) @ v)),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl1496, zip_derived_cl30])).
% 26.15/4.25 thf(zip_derived_cl32, plain, ( (equalish @ (add @ b @ b) @ v)),
% 26.15/4.25 inference('cnf', [status(esa)], [zf_stmt_1])).
% 26.15/4.25 thf(zip_derived_cl25, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X2 @ X1)
% 26.15/4.25 | ~ (equalish @ X2 @ X0))),
% 26.15/4.25 inference('cnf', [status(esa)],
% 26.15/4.25 [compatibility_of_equality_and_order_relation])).
% 26.15/4.25 thf(zip_derived_cl1286, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (less_or_equal @ (add @ b @ b) @ X0) | (less_or_equal @ v @ X0))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl25])).
% 26.15/4.25 thf(zip_derived_cl1504, plain, ( (less_or_equal @ v @ v)),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl1500, zip_derived_cl1286])).
% 26.15/4.25 thf(zip_derived_cl17, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | (less_or_equal @ X1 @ X0)
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (defined @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 26.15/4.25 thf(u_is_defined, axiom, (defined @ u)).
% 26.15/4.25 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 26.15/4.25 inference('cnf', [status(esa)], [u_is_defined])).
% 26.15/4.25 thf(zip_derived_cl833, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0)
% 26.15/4.25 | (less_or_equal @ X0 @ u)
% 26.15/4.25 | (less_or_equal @ u @ X0))),
% 26.15/4.25 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl29])).
% 26.15/4.25 thf(zip_derived_cl1321, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (less_or_equal @ v @ X0) | (less_or_equal @ (add @ b @ b) @ X0))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl25])).
% 26.15/4.25 thf(zip_derived_cl2818, plain,
% 26.15/4.25 (( (less_or_equal @ u @ v)
% 26.15/4.25 | ~ (defined @ v)
% 26.15/4.25 | (less_or_equal @ (add @ b @ b) @ u))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl833, zip_derived_cl1321])).
% 26.15/4.25 thf(zip_derived_cl34, plain, (~ (less_or_equal @ u @ v)),
% 26.15/4.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 26.15/4.25 thf(zip_derived_cl30, plain, ( (defined @ v)),
% 26.15/4.25 inference('cnf', [status(esa)], [v_is_defined])).
% 26.15/4.25 thf(zip_derived_cl2850, plain, ( (less_or_equal @ (add @ b @ b) @ u)),
% 26.15/4.25 inference('demod', [status(thm)],
% 26.15/4.25 [zip_derived_cl2818, zip_derived_cl34, zip_derived_cl30])).
% 26.15/4.25 thf(antisymmetry_of_order_relation, axiom,
% 26.15/4.25 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 26.15/4.25 ( ~( less_or_equal @ Y @ X ) ))).
% 26.15/4.25 thf(zip_derived_cl15, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]:
% 26.15/4.25 ( (equalish @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X1 @ X0))),
% 26.15/4.25 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 26.15/4.25 thf(zip_derived_cl2870, plain,
% 26.15/4.25 ((~ (less_or_equal @ u @ (add @ b @ b)) | (equalish @ (add @ b @ b) @ u))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl2850, zip_derived_cl15])).
% 26.15/4.25 thf(less_or_equal_7, conjecture, (~( less_or_equal @ a @ b ))).
% 26.15/4.25 thf(zf_stmt_2, negated_conjecture, (less_or_equal @ a @ b),
% 26.15/4.25 inference('cnf.neg', [status(esa)], [less_or_equal_7])).
% 26.15/4.25 thf(zip_derived_cl33, plain, ( (less_or_equal @ a @ b)),
% 26.15/4.25 inference('cnf', [status(esa)], [zf_stmt_2])).
% 26.15/4.25 thf(compatibility_of_order_relation_and_addition, axiom,
% 26.15/4.25 (( less_or_equal @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) |
% 26.15/4.25 ( ~( defined @ Z ) ) | ( ~( less_or_equal @ X @ Y ) ))).
% 26.15/4.25 thf(zip_derived_cl18, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (less_or_equal @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 26.15/4.25 | ~ (defined @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X0 @ X2))),
% 26.15/4.25 inference('cnf', [status(esa)],
% 26.15/4.25 [compatibility_of_order_relation_and_addition])).
% 26.15/4.25 thf(zip_derived_cl922, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0) | (less_or_equal @ (add @ a @ X0) @ (add @ b @ X0)))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl18])).
% 26.15/4.25 thf(zip_derived_cl17, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | (less_or_equal @ X1 @ X0)
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (defined @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 26.15/4.25 thf(a_is_defined, axiom, (defined @ a)).
% 26.15/4.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 26.15/4.25 inference('cnf', [status(esa)], [a_is_defined])).
% 26.15/4.25 thf(zip_derived_cl831, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0)
% 26.15/4.25 | (less_or_equal @ X0 @ a)
% 26.15/4.25 | (less_or_equal @ a @ X0))),
% 26.15/4.25 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl27])).
% 26.15/4.25 thf(zip_derived_cl1001, plain,
% 26.15/4.25 (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 26.15/4.25 inference('eq_fact', [status(thm)], [zip_derived_cl831])).
% 26.15/4.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 26.15/4.25 inference('cnf', [status(esa)], [a_is_defined])).
% 26.15/4.25 thf(zip_derived_cl1002, plain, ( (less_or_equal @ a @ a)),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl1001, zip_derived_cl27])).
% 26.15/4.25 thf(zip_derived_cl18, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (less_or_equal @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 26.15/4.25 | ~ (defined @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X0 @ X2))),
% 26.15/4.25 inference('cnf', [status(esa)],
% 26.15/4.25 [compatibility_of_order_relation_and_addition])).
% 26.15/4.25 thf(zip_derived_cl1009, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0) | (less_or_equal @ (add @ a @ X0) @ (add @ a @ X0)))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl1002, zip_derived_cl18])).
% 26.15/4.25 thf(zip_derived_cl17, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | (less_or_equal @ X1 @ X0)
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (defined @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 26.15/4.25 thf(b_is_defined, axiom, (defined @ b)).
% 26.15/4.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 26.15/4.25 inference('cnf', [status(esa)], [b_is_defined])).
% 26.15/4.25 thf(zip_derived_cl832, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0)
% 26.15/4.25 | (less_or_equal @ X0 @ b)
% 26.15/4.25 | (less_or_equal @ b @ X0))),
% 26.15/4.25 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl28])).
% 26.15/4.25 thf(zip_derived_cl2058, plain,
% 26.15/4.25 (( (less_or_equal @ b @ b) | ~ (defined @ b))),
% 26.15/4.25 inference('eq_fact', [status(thm)], [zip_derived_cl832])).
% 26.15/4.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 26.15/4.25 inference('cnf', [status(esa)], [b_is_defined])).
% 26.15/4.25 thf(zip_derived_cl2059, plain, ( (less_or_equal @ b @ b)),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl2058, zip_derived_cl28])).
% 26.15/4.25 thf(zip_derived_cl15, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]:
% 26.15/4.25 ( (equalish @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X1 @ X0))),
% 26.15/4.25 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 26.15/4.25 thf(zip_derived_cl2069, plain,
% 26.15/4.25 ((~ (less_or_equal @ b @ b) | (equalish @ b @ b))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl2059, zip_derived_cl15])).
% 26.15/4.25 thf(zip_derived_cl2059, plain, ( (less_or_equal @ b @ b)),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl2058, zip_derived_cl28])).
% 26.15/4.25 thf(zip_derived_cl2073, plain, ( (equalish @ b @ b)),
% 26.15/4.25 inference('demod', [status(thm)],
% 26.15/4.25 [zip_derived_cl2069, zip_derived_cl2059])).
% 26.15/4.25 thf(compatibility_of_equality_and_addition, axiom,
% 26.15/4.25 (( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) | ( ~( defined @ Z ) ) |
% 26.15/4.25 ( ~( equalish @ X @ Y ) ))).
% 26.15/4.25 thf(zip_derived_cl23, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 26.15/4.25 | ~ (defined @ X1)
% 26.15/4.25 | ~ (equalish @ X0 @ X2))),
% 26.15/4.25 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 26.15/4.25 thf(zip_derived_cl2080, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0) | (equalish @ (add @ b @ X0) @ (add @ b @ X0)))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl2073, zip_derived_cl23])).
% 26.15/4.25 thf(commutativity_addition, axiom,
% 26.15/4.25 (( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) ) | ( ~( defined @ X ) ) |
% 26.15/4.25 ( ~( defined @ Y ) ))).
% 26.15/4.25 thf(zip_derived_cl3, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]:
% 26.15/4.25 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (defined @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [commutativity_addition])).
% 26.15/4.25 thf(transitivity_of_equality, axiom,
% 26.15/4.25 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 26.15/4.25 ( ~( equalish @ Y @ Z ) ))).
% 26.15/4.25 thf(zip_derived_cl22, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (equalish @ X0 @ X1)
% 26.15/4.25 | ~ (equalish @ X0 @ X2)
% 26.15/4.25 | ~ (equalish @ X2 @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 26.15/4.25 thf(zip_derived_cl170, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 (~ (defined @ X1)
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (equalish @ (add @ X1 @ X0) @ X2)
% 26.15/4.25 | (equalish @ (add @ X0 @ X1) @ X2))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 26.15/4.25 thf(zip_derived_cl9436, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0)
% 26.15/4.25 | (equalish @ (add @ X0 @ b) @ (add @ b @ X0))
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (defined @ b))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl2080, zip_derived_cl170])).
% 26.15/4.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 26.15/4.25 inference('cnf', [status(esa)], [b_is_defined])).
% 26.15/4.25 thf(zip_derived_cl9441, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0)
% 26.15/4.25 | (equalish @ (add @ X0 @ b) @ (add @ b @ X0))
% 26.15/4.25 | ~ (defined @ X0))),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl9436, zip_derived_cl28])).
% 26.15/4.25 thf(zip_derived_cl9442, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 ( (equalish @ (add @ X0 @ b) @ (add @ b @ X0)) | ~ (defined @ X0))),
% 26.15/4.25 inference('simplify', [status(thm)], [zip_derived_cl9441])).
% 26.15/4.25 thf(zip_derived_cl1002, plain, ( (less_or_equal @ a @ a)),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl1001, zip_derived_cl27])).
% 26.15/4.25 thf(zip_derived_cl15, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]:
% 26.15/4.25 ( (equalish @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X1 @ X0))),
% 26.15/4.25 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 26.15/4.25 thf(zip_derived_cl1007, plain,
% 26.15/4.25 ((~ (less_or_equal @ a @ a) | (equalish @ a @ a))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl1002, zip_derived_cl15])).
% 26.15/4.25 thf(zip_derived_cl1002, plain, ( (less_or_equal @ a @ a)),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl1001, zip_derived_cl27])).
% 26.15/4.25 thf(zip_derived_cl1010, plain, ( (equalish @ a @ a)),
% 26.15/4.25 inference('demod', [status(thm)],
% 26.15/4.25 [zip_derived_cl1007, zip_derived_cl1002])).
% 26.15/4.25 thf(zip_derived_cl23, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 26.15/4.25 | ~ (defined @ X1)
% 26.15/4.25 | ~ (equalish @ X0 @ X2))),
% 26.15/4.25 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 26.15/4.25 thf(zip_derived_cl1092, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0) | (equalish @ (add @ a @ X0) @ (add @ a @ X0)))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl1010, zip_derived_cl23])).
% 26.15/4.25 thf(zip_derived_cl170, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 (~ (defined @ X1)
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (equalish @ (add @ X1 @ X0) @ X2)
% 26.15/4.25 | (equalish @ (add @ X0 @ X1) @ X2))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 26.15/4.25 thf(zip_derived_cl7247, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0)
% 26.15/4.25 | (equalish @ (add @ X0 @ a) @ (add @ a @ X0))
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (defined @ a))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl1092, zip_derived_cl170])).
% 26.15/4.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 26.15/4.25 inference('cnf', [status(esa)], [a_is_defined])).
% 26.15/4.25 thf(zip_derived_cl7252, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0)
% 26.15/4.25 | (equalish @ (add @ X0 @ a) @ (add @ a @ X0))
% 26.15/4.25 | ~ (defined @ X0))),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl7247, zip_derived_cl27])).
% 26.15/4.25 thf(zip_derived_cl7253, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 ( (equalish @ (add @ X0 @ a) @ (add @ a @ X0)) | ~ (defined @ X0))),
% 26.15/4.25 inference('simplify', [status(thm)], [zip_derived_cl7252])).
% 26.15/4.25 thf(zip_derived_cl22, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (equalish @ X0 @ X1)
% 26.15/4.25 | ~ (equalish @ X0 @ X2)
% 26.15/4.25 | ~ (equalish @ X2 @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 26.15/4.25 thf(zip_derived_cl12290, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i]:
% 26.15/4.25 (~ (defined @ X0)
% 26.15/4.25 | ~ (equalish @ (add @ a @ X0) @ X1)
% 26.15/4.25 | (equalish @ (add @ X0 @ a) @ X1))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl7253, zip_derived_cl22])).
% 26.15/4.25 thf(zip_derived_cl15215, plain,
% 26.15/4.25 ((~ (defined @ a)
% 26.15/4.25 | (equalish @ (add @ b @ a) @ (add @ b @ a))
% 26.15/4.25 | ~ (defined @ b))),
% 26.15/4.25 inference('sup-', [status(thm)],
% 26.15/4.25 [zip_derived_cl9442, zip_derived_cl12290])).
% 26.15/4.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 26.15/4.25 inference('cnf', [status(esa)], [a_is_defined])).
% 26.15/4.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 26.15/4.25 inference('cnf', [status(esa)], [b_is_defined])).
% 26.15/4.25 thf(zip_derived_cl15225, plain,
% 26.15/4.25 ( (equalish @ (add @ b @ a) @ (add @ b @ a))),
% 26.15/4.25 inference('demod', [status(thm)],
% 26.15/4.25 [zip_derived_cl15215, zip_derived_cl27, zip_derived_cl28])).
% 26.15/4.25 thf(zip_derived_cl170, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 (~ (defined @ X1)
% 26.15/4.25 | ~ (defined @ X0)
% 26.15/4.25 | ~ (equalish @ (add @ X1 @ X0) @ X2)
% 26.15/4.25 | (equalish @ (add @ X0 @ X1) @ X2))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 26.15/4.25 thf(zip_derived_cl15279, plain,
% 26.15/4.25 (( (equalish @ (add @ a @ b) @ (add @ b @ a))
% 26.15/4.25 | ~ (defined @ a)
% 26.15/4.25 | ~ (defined @ b))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl15225, zip_derived_cl170])).
% 26.15/4.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 26.15/4.25 inference('cnf', [status(esa)], [a_is_defined])).
% 26.15/4.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 26.15/4.25 inference('cnf', [status(esa)], [b_is_defined])).
% 26.15/4.25 thf(zip_derived_cl15280, plain,
% 26.15/4.25 ( (equalish @ (add @ a @ b) @ (add @ b @ a))),
% 26.15/4.25 inference('demod', [status(thm)],
% 26.15/4.25 [zip_derived_cl15279, zip_derived_cl27, zip_derived_cl28])).
% 26.15/4.25 thf(zip_derived_cl25, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X2 @ X1)
% 26.15/4.25 | ~ (equalish @ X2 @ X0))),
% 26.15/4.25 inference('cnf', [status(esa)],
% 26.15/4.25 [compatibility_of_equality_and_order_relation])).
% 26.15/4.25 thf(zip_derived_cl15289, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (less_or_equal @ (add @ a @ b) @ X0)
% 26.15/4.25 | (less_or_equal @ (add @ b @ a) @ X0))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl15280, zip_derived_cl25])).
% 26.15/4.25 thf(zip_derived_cl15413, plain,
% 26.15/4.25 ((~ (defined @ b) | (less_or_equal @ (add @ b @ a) @ (add @ a @ b)))),
% 26.15/4.25 inference('sup-', [status(thm)],
% 26.15/4.25 [zip_derived_cl1009, zip_derived_cl15289])).
% 26.15/4.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 26.15/4.25 inference('cnf', [status(esa)], [b_is_defined])).
% 26.15/4.25 thf(zip_derived_cl15420, plain,
% 26.15/4.25 ( (less_or_equal @ (add @ b @ a) @ (add @ a @ b))),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl15413, zip_derived_cl28])).
% 26.15/4.25 thf(zip_derived_cl922, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (defined @ X0) | (less_or_equal @ (add @ a @ X0) @ (add @ b @ X0)))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl18])).
% 26.15/4.25 thf(add_equals_u_5, conjecture, (~( equalish @ ( add @ a @ a ) @ u ))).
% 26.15/4.25 thf(zf_stmt_3, negated_conjecture, (equalish @ ( add @ a @ a ) @ u),
% 26.15/4.25 inference('cnf.neg', [status(esa)], [add_equals_u_5])).
% 26.15/4.25 thf(zip_derived_cl31, plain, ( (equalish @ (add @ a @ a) @ u)),
% 26.15/4.25 inference('cnf', [status(esa)], [zf_stmt_3])).
% 26.15/4.25 thf(zip_derived_cl25, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X2 @ X1)
% 26.15/4.25 | ~ (equalish @ X2 @ X0))),
% 26.15/4.25 inference('cnf', [status(esa)],
% 26.15/4.25 [compatibility_of_equality_and_order_relation])).
% 26.15/4.25 thf(zip_derived_cl1283, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (less_or_equal @ (add @ a @ a) @ X0) | (less_or_equal @ u @ X0))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl25])).
% 26.15/4.25 thf(zip_derived_cl37898, plain,
% 26.15/4.25 ((~ (defined @ a) | (less_or_equal @ u @ (add @ b @ a)))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl922, zip_derived_cl1283])).
% 26.15/4.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 26.15/4.25 inference('cnf', [status(esa)], [a_is_defined])).
% 26.15/4.25 thf(zip_derived_cl37928, plain, ( (less_or_equal @ u @ (add @ b @ a))),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl37898, zip_derived_cl27])).
% 26.15/4.25 thf(transitivity_of_order_relation, axiom,
% 26.15/4.25 (( less_or_equal @ X @ Z ) | ( ~( less_or_equal @ X @ Y ) ) |
% 26.15/4.25 ( ~( less_or_equal @ Y @ Z ) ))).
% 26.15/4.25 thf(zip_derived_cl16, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X0 @ X2)
% 26.15/4.25 | ~ (less_or_equal @ X2 @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 26.15/4.25 thf(zip_derived_cl37956, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (less_or_equal @ (add @ b @ a) @ X0) | (less_or_equal @ u @ X0))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl37928, zip_derived_cl16])).
% 26.15/4.25 thf(zip_derived_cl38091, plain, ( (less_or_equal @ u @ (add @ a @ b))),
% 26.15/4.25 inference('sup-', [status(thm)],
% 26.15/4.25 [zip_derived_cl15420, zip_derived_cl37956])).
% 26.15/4.25 thf(zip_derived_cl16, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X0 @ X2)
% 26.15/4.25 | ~ (less_or_equal @ X2 @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 26.15/4.25 thf(zip_derived_cl38116, plain,
% 26.15/4.25 (![X0 : $i]:
% 26.15/4.25 (~ (less_or_equal @ (add @ a @ b) @ X0) | (less_or_equal @ u @ X0))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl38091, zip_derived_cl16])).
% 26.15/4.25 thf(zip_derived_cl38290, plain,
% 26.15/4.25 ((~ (defined @ b) | (less_or_equal @ u @ (add @ b @ b)))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl922, zip_derived_cl38116])).
% 26.15/4.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 26.15/4.25 inference('cnf', [status(esa)], [b_is_defined])).
% 26.15/4.25 thf(zip_derived_cl38306, plain, ( (less_or_equal @ u @ (add @ b @ b))),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl38290, zip_derived_cl28])).
% 26.15/4.25 thf(zip_derived_cl38760, plain, ( (equalish @ (add @ b @ b) @ u)),
% 26.15/4.25 inference('demod', [status(thm)],
% 26.15/4.25 [zip_derived_cl2870, zip_derived_cl38306])).
% 26.15/4.25 thf(zip_derived_cl37, plain, ( (equalish @ v @ (add @ b @ b))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl21])).
% 26.15/4.25 thf(zip_derived_cl22, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (equalish @ X0 @ X1)
% 26.15/4.25 | ~ (equalish @ X0 @ X2)
% 26.15/4.25 | ~ (equalish @ X2 @ X1))),
% 26.15/4.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 26.15/4.25 thf(zip_derived_cl63, plain,
% 26.15/4.25 (![X0 : $i]: (~ (equalish @ (add @ b @ b) @ X0) | (equalish @ v @ X0))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl22])).
% 26.15/4.25 thf(zip_derived_cl38828, plain, ( (equalish @ v @ u)),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl38760, zip_derived_cl63])).
% 26.15/4.25 thf(zip_derived_cl25, plain,
% 26.15/4.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.15/4.25 ( (less_or_equal @ X0 @ X1)
% 26.15/4.25 | ~ (less_or_equal @ X2 @ X1)
% 26.15/4.25 | ~ (equalish @ X2 @ X0))),
% 26.15/4.25 inference('cnf', [status(esa)],
% 26.15/4.25 [compatibility_of_equality_and_order_relation])).
% 26.15/4.25 thf(zip_derived_cl38842, plain,
% 26.15/4.25 (![X0 : $i]: (~ (less_or_equal @ v @ X0) | (less_or_equal @ u @ X0))),
% 26.15/4.25 inference('sup-', [status(thm)], [zip_derived_cl38828, zip_derived_cl25])).
% 26.15/4.25 thf(zip_derived_cl39830, plain, ( (less_or_equal @ u @ v)),
% 26.15/4.25 inference('sup-', [status(thm)],
% 26.15/4.25 [zip_derived_cl1504, zip_derived_cl38842])).
% 26.15/4.25 thf(zip_derived_cl39840, plain, ($false),
% 26.15/4.25 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl39830])).
% 26.15/4.25
% 26.15/4.25 % SZS output end Refutation
% 26.15/4.25
% 26.15/4.25
% 26.15/4.25 % Terminating...
% 26.25/4.29 % Runner terminated.
% 26.25/4.31 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------