%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD007-1 : 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.Qaj5jvKYts true
% Computer : n007.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 04:33:07 PM UTC 2025
% Result : Unsatisfiable 123.39s 18.46s
% Output : Refutation 123.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : FLD007-1 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.08/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Qaj5jvKYts true
% 0.14/0.37 % Computer : n007.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Oct 1 18:29:38 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % Running portfolio for 300 s
% 0.14/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % Number of cores: 8
% 0.14/0.38 % Python version: Python 3.6.8
% 0.14/0.38 % Running in FO mode
% 0.54/0.64 % Total configuration time : 435
% 0.54/0.64 % Estimated wc time : 1092
% 0.54/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 123.39/18.46 % Solved by fo/fo5.sh.
% 123.39/18.46 % done 14566 iterations in 17.660s
% 123.39/18.46 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 123.39/18.46 % SZS output start Refutation
% 123.39/18.46 thf(defined_type, type, defined: $i > $o).
% 123.39/18.46 thf(additive_identity_type, type, additive_identity: $i).
% 123.39/18.46 thf(add_type, type, add: $i > $i > $i).
% 123.39/18.46 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 123.39/18.46 thf(equalish_type, type, equalish: $i > $i > $o).
% 123.39/18.46 thf(a_type, type, a: $i).
% 123.39/18.46 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 123.39/18.46 thf(well_definedness_of_additive_inverse, axiom,
% 123.39/18.46 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 123.39/18.46 thf(zip_derived_cl11, plain,
% 123.39/18.46 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 123.39/18.46 thf(zip_derived_cl11, plain,
% 123.39/18.46 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 123.39/18.46 thf(zip_derived_cl11, plain,
% 123.39/18.46 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 123.39/18.46 thf(existence_of_inverse_addition, axiom,
% 123.39/18.46 (( equalish @ ( add @ X @ ( additive_inverse @ X ) ) @ additive_identity ) |
% 123.39/18.46 ( ~( defined @ X ) ))).
% 123.39/18.46 thf(zip_derived_cl2, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 ( (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ additive_identity)
% 123.39/18.46 | ~ (defined @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 123.39/18.46 thf(compatibility_of_equality_and_addition, axiom,
% 123.39/18.46 (( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) | ( ~( defined @ Z ) ) |
% 123.39/18.46 ( ~( equalish @ X @ Y ) ))).
% 123.39/18.46 thf(zip_derived_cl23, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 123.39/18.46 | ~ (defined @ X1)
% 123.39/18.46 | ~ (equalish @ X0 @ X2))),
% 123.39/18.46 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 123.39/18.46 thf(zip_derived_cl105, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | ~ (defined @ X1)
% 123.39/18.46 | (equalish @ (add @ (add @ X0 @ (additive_inverse @ X0)) @ X1) @
% 123.39/18.46 (add @ additive_identity @ X1)))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl23])).
% 123.39/18.46 thf(associativity_addition, axiom,
% 123.39/18.46 (( equalish @ ( add @ X @ ( add @ Y @ Z ) ) @ ( add @ ( add @ X @ Y ) @ Z ) ) |
% 123.39/18.46 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ) | ( ~( defined @ Z ) ))).
% 123.39/18.46 thf(zip_derived_cl0, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 ( (equalish @ (add @ X0 @ (add @ X1 @ X2)) @
% 123.39/18.46 (add @ (add @ X0 @ X1) @ X2))
% 123.39/18.46 | ~ (defined @ X0)
% 123.39/18.46 | ~ (defined @ X1)
% 123.39/18.46 | ~ (defined @ X2))),
% 123.39/18.46 inference('cnf', [status(esa)], [associativity_addition])).
% 123.39/18.46 thf(commutativity_addition, axiom,
% 123.39/18.46 (( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) ) | ( ~( defined @ X ) ) |
% 123.39/18.46 ( ~( defined @ Y ) ))).
% 123.39/18.46 thf(zip_derived_cl3, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 123.39/18.46 | ~ (defined @ X0)
% 123.39/18.46 | ~ (defined @ X1))),
% 123.39/18.46 inference('cnf', [status(esa)], [commutativity_addition])).
% 123.39/18.46 thf(transitivity_of_equality, axiom,
% 123.39/18.46 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 123.39/18.46 ( ~( equalish @ Y @ Z ) ))).
% 123.39/18.46 thf(zip_derived_cl22, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 ( (equalish @ X0 @ X1)
% 123.39/18.46 | ~ (equalish @ X0 @ X2)
% 123.39/18.46 | ~ (equalish @ X2 @ X1))),
% 123.39/18.46 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 123.39/18.46 thf(zip_derived_cl67, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 (~ (defined @ X1)
% 123.39/18.46 | ~ (defined @ X0)
% 123.39/18.46 | ~ (equalish @ (add @ X1 @ X0) @ X2)
% 123.39/18.46 | (equalish @ (add @ X0 @ X1) @ X2))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 123.39/18.46 thf(zip_derived_cl1670, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | ~ (defined @ X1)
% 123.39/18.46 | ~ (defined @ X2)
% 123.39/18.46 | (equalish @ (add @ (add @ X1 @ X0) @ X2) @
% 123.39/18.46 (add @ (add @ X2 @ X1) @ X0))
% 123.39/18.46 | ~ (defined @ (add @ X1 @ X0))
% 123.39/18.46 | ~ (defined @ X2))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl67])).
% 123.39/18.46 thf(zip_derived_cl1687, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 (~ (defined @ (add @ X1 @ X0))
% 123.39/18.46 | (equalish @ (add @ (add @ X1 @ X0) @ X2) @
% 123.39/18.46 (add @ (add @ X2 @ X1) @ X0))
% 123.39/18.46 | ~ (defined @ X2)
% 123.39/18.46 | ~ (defined @ X1)
% 123.39/18.46 | ~ (defined @ X0))),
% 123.39/18.46 inference('simplify', [status(thm)], [zip_derived_cl1670])).
% 123.39/18.46 thf(well_definedness_of_addition, axiom,
% 123.39/18.46 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 123.39/18.46 ( ~( defined @ Y ) ))).
% 123.39/18.46 thf(zip_derived_cl9, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 123.39/18.46 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 123.39/18.46 thf(zip_derived_cl96258, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | ~ (defined @ X1)
% 123.39/18.46 | ~ (defined @ X2)
% 123.39/18.46 | (equalish @ (add @ (add @ X1 @ X0) @ X2) @
% 123.39/18.46 (add @ (add @ X2 @ X1) @ X0)))),
% 123.39/18.46 inference('clc', [status(thm)], [zip_derived_cl1687, zip_derived_cl9])).
% 123.39/18.46 thf(zip_derived_cl2, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 ( (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ additive_identity)
% 123.39/18.46 | ~ (defined @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 123.39/18.46 thf(symmetry_of_equality, axiom,
% 123.39/18.46 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 123.39/18.46 thf(zip_derived_cl21, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 123.39/18.46 thf(zip_derived_cl32, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | (equalish @ additive_identity @
% 123.39/18.46 (add @ X0 @ (additive_inverse @ X0))))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl21])).
% 123.39/18.46 thf(zip_derived_cl23, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 123.39/18.46 | ~ (defined @ X1)
% 123.39/18.46 | ~ (equalish @ X0 @ X2))),
% 123.39/18.46 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 123.39/18.46 thf(zip_derived_cl107, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | ~ (defined @ X1)
% 123.39/18.46 | (equalish @ (add @ additive_identity @ X1) @
% 123.39/18.46 (add @ (add @ X0 @ (additive_inverse @ X0)) @ X1)))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl23])).
% 123.39/18.46 thf(totality_of_order_relation, axiom,
% 123.39/18.46 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 123.39/18.46 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 123.39/18.46 thf(zip_derived_cl17, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 ( (less_or_equal @ X0 @ X1)
% 123.39/18.46 | (less_or_equal @ X1 @ X0)
% 123.39/18.46 | ~ (defined @ X0)
% 123.39/18.46 | ~ (defined @ X1))),
% 123.39/18.46 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 123.39/18.46 thf(a_is_defined, axiom, (defined @ a)).
% 123.39/18.46 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 123.39/18.46 inference('cnf', [status(esa)], [a_is_defined])).
% 123.39/18.46 thf(zip_derived_cl185, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | (less_or_equal @ X0 @ a)
% 123.39/18.46 | (less_or_equal @ a @ X0))),
% 123.39/18.46 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl27])).
% 123.39/18.46 thf(zip_derived_cl2077, plain,
% 123.39/18.46 (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 123.39/18.46 inference('eq_fact', [status(thm)], [zip_derived_cl185])).
% 123.39/18.46 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 123.39/18.46 inference('cnf', [status(esa)], [a_is_defined])).
% 123.39/18.46 thf(zip_derived_cl2078, plain, ( (less_or_equal @ a @ a)),
% 123.39/18.46 inference('demod', [status(thm)], [zip_derived_cl2077, zip_derived_cl27])).
% 123.39/18.46 thf(antisymmetry_of_order_relation, axiom,
% 123.39/18.46 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 123.39/18.46 ( ~( less_or_equal @ Y @ X ) ))).
% 123.39/18.46 thf(zip_derived_cl15, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 ( (equalish @ X0 @ X1)
% 123.39/18.46 | ~ (less_or_equal @ X0 @ X1)
% 123.39/18.46 | ~ (less_or_equal @ X1 @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 123.39/18.46 thf(zip_derived_cl2097, plain,
% 123.39/18.46 ((~ (less_or_equal @ a @ a) | (equalish @ a @ a))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl2078, zip_derived_cl15])).
% 123.39/18.46 thf(zip_derived_cl2078, plain, ( (less_or_equal @ a @ a)),
% 123.39/18.46 inference('demod', [status(thm)], [zip_derived_cl2077, zip_derived_cl27])).
% 123.39/18.46 thf(zip_derived_cl2103, plain, ( (equalish @ a @ a)),
% 123.39/18.46 inference('demod', [status(thm)],
% 123.39/18.46 [zip_derived_cl2097, zip_derived_cl2078])).
% 123.39/18.46 thf(existence_of_identity_addition, axiom,
% 123.39/18.46 (( equalish @ ( add @ additive_identity @ X ) @ X ) | ( ~( defined @ X ) ))).
% 123.39/18.46 thf(zip_derived_cl1, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 123.39/18.46 thf(zip_derived_cl22, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 ( (equalish @ X0 @ X1)
% 123.39/18.46 | ~ (equalish @ X0 @ X2)
% 123.39/18.46 | ~ (equalish @ X2 @ X1))),
% 123.39/18.46 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 123.39/18.46 thf(zip_derived_cl45, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | ~ (equalish @ X0 @ X1)
% 123.39/18.46 | (equalish @ (add @ additive_identity @ X0) @ X1))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 123.39/18.46 thf(zip_derived_cl2107, plain,
% 123.39/18.46 (( (equalish @ (add @ additive_identity @ a) @ a) | ~ (defined @ a))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl2103, zip_derived_cl45])).
% 123.39/18.46 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 123.39/18.46 inference('cnf', [status(esa)], [a_is_defined])).
% 123.39/18.46 thf(zip_derived_cl2117, plain,
% 123.39/18.46 ( (equalish @ (add @ additive_identity @ a) @ a)),
% 123.39/18.46 inference('demod', [status(thm)], [zip_derived_cl2107, zip_derived_cl27])).
% 123.39/18.46 thf(zip_derived_cl21, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 123.39/18.46 thf(zip_derived_cl2127, plain,
% 123.39/18.46 ( (equalish @ a @ (add @ additive_identity @ a))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl2117, zip_derived_cl21])).
% 123.39/18.46 thf(zip_derived_cl22, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 ( (equalish @ X0 @ X1)
% 123.39/18.46 | ~ (equalish @ X0 @ X2)
% 123.39/18.46 | ~ (equalish @ X2 @ X1))),
% 123.39/18.46 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 123.39/18.46 thf(zip_derived_cl2240, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 (~ (equalish @ (add @ additive_identity @ a) @ X0)
% 123.39/18.46 | (equalish @ a @ X0))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl2127, zip_derived_cl22])).
% 123.39/18.46 thf(zip_derived_cl3113, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 (~ (defined @ a)
% 123.39/18.46 | ~ (defined @ X0)
% 123.39/18.46 | (equalish @ a @ (add @ (add @ X0 @ (additive_inverse @ X0)) @ a)))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl107, zip_derived_cl2240])).
% 123.39/18.46 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 123.39/18.46 inference('cnf', [status(esa)], [a_is_defined])).
% 123.39/18.46 thf(zip_derived_cl3122, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | (equalish @ a @ (add @ (add @ X0 @ (additive_inverse @ X0)) @ a)))),
% 123.39/18.46 inference('demod', [status(thm)], [zip_derived_cl3113, zip_derived_cl27])).
% 123.39/18.46 thf(zip_derived_cl22, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 ( (equalish @ X0 @ X1)
% 123.39/18.46 | ~ (equalish @ X0 @ X2)
% 123.39/18.46 | ~ (equalish @ X2 @ X1))),
% 123.39/18.46 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 123.39/18.46 thf(zip_derived_cl109014, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | ~ (equalish @ (add @ (add @ X0 @ (additive_inverse @ X0)) @ a) @ X1)
% 123.39/18.46 | (equalish @ a @ X1))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl3122, zip_derived_cl22])).
% 123.39/18.46 thf(zip_derived_cl109147, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 (~ (defined @ a)
% 123.39/18.46 | ~ (defined @ X0)
% 123.39/18.46 | ~ (defined @ (additive_inverse @ X0))
% 123.39/18.46 | (equalish @ a @ (add @ (add @ a @ X0) @ (additive_inverse @ X0)))
% 123.39/18.46 | ~ (defined @ X0))),
% 123.39/18.46 inference('sup-', [status(thm)],
% 123.39/18.46 [zip_derived_cl96258, zip_derived_cl109014])).
% 123.39/18.46 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 123.39/18.46 inference('cnf', [status(esa)], [a_is_defined])).
% 123.39/18.46 thf(zip_derived_cl109172, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | ~ (defined @ (additive_inverse @ X0))
% 123.39/18.46 | (equalish @ a @ (add @ (add @ a @ X0) @ (additive_inverse @ X0)))
% 123.39/18.46 | ~ (defined @ X0))),
% 123.39/18.46 inference('demod', [status(thm)],
% 123.39/18.46 [zip_derived_cl109147, zip_derived_cl27])).
% 123.39/18.46 thf(zip_derived_cl109173, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 ( (equalish @ a @ (add @ (add @ a @ X0) @ (additive_inverse @ X0)))
% 123.39/18.46 | ~ (defined @ (additive_inverse @ X0))
% 123.39/18.46 | ~ (defined @ X0))),
% 123.39/18.46 inference('simplify', [status(thm)], [zip_derived_cl109172])).
% 123.39/18.46 thf(zip_derived_cl11, plain,
% 123.39/18.46 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 123.39/18.46 thf(zip_derived_cl114297, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | (equalish @ a @ (add @ (add @ a @ X0) @ (additive_inverse @ X0))))),
% 123.39/18.46 inference('clc', [status(thm)], [zip_derived_cl109173, zip_derived_cl11])).
% 123.39/18.46 thf(zip_derived_cl22, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 ( (equalish @ X0 @ X1)
% 123.39/18.46 | ~ (equalish @ X0 @ X2)
% 123.39/18.46 | ~ (equalish @ X2 @ X1))),
% 123.39/18.46 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 123.39/18.46 thf(zip_derived_cl114308, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | ~ (equalish @ (add @ (add @ a @ X0) @ (additive_inverse @ X0)) @ X1)
% 123.39/18.46 | (equalish @ a @ X1))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl114297, zip_derived_cl22])).
% 123.39/18.46 thf(zip_derived_cl114444, plain,
% 123.39/18.46 ((~ (defined @ (additive_inverse @ (additive_inverse @ a)))
% 123.39/18.46 | ~ (defined @ a)
% 123.39/18.46 | (equalish @ a @
% 123.39/18.46 (add @ additive_identity @
% 123.39/18.46 (additive_inverse @ (additive_inverse @ a))))
% 123.39/18.46 | ~ (defined @ (additive_inverse @ a)))),
% 123.39/18.46 inference('sup-', [status(thm)],
% 123.39/18.46 [zip_derived_cl105, zip_derived_cl114308])).
% 123.39/18.46 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 123.39/18.46 inference('cnf', [status(esa)], [a_is_defined])).
% 123.39/18.46 thf(zip_derived_cl114458, plain,
% 123.39/18.46 ((~ (defined @ (additive_inverse @ (additive_inverse @ a)))
% 123.39/18.46 | (equalish @ a @
% 123.39/18.46 (add @ additive_identity @
% 123.39/18.46 (additive_inverse @ (additive_inverse @ a))))
% 123.39/18.46 | ~ (defined @ (additive_inverse @ a)))),
% 123.39/18.46 inference('demod', [status(thm)],
% 123.39/18.46 [zip_derived_cl114444, zip_derived_cl27])).
% 123.39/18.46 thf(zip_derived_cl11, plain,
% 123.39/18.46 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 123.39/18.46 thf(zip_derived_cl114466, plain,
% 123.39/18.46 ((~ (defined @ (additive_inverse @ a))
% 123.39/18.46 | (equalish @ a @
% 123.39/18.46 (add @ additive_identity @
% 123.39/18.46 (additive_inverse @ (additive_inverse @ a)))))),
% 123.39/18.46 inference('clc', [status(thm)], [zip_derived_cl114458, zip_derived_cl11])).
% 123.39/18.46 thf(zip_derived_cl114467, plain,
% 123.39/18.46 ((~ (defined @ a)
% 123.39/18.46 | (equalish @ a @
% 123.39/18.46 (add @ additive_identity @
% 123.39/18.46 (additive_inverse @ (additive_inverse @ a)))))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl114466])).
% 123.39/18.46 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 123.39/18.46 inference('cnf', [status(esa)], [a_is_defined])).
% 123.39/18.46 thf(zip_derived_cl114468, plain,
% 123.39/18.46 ( (equalish @ a @
% 123.39/18.46 (add @ additive_identity @ (additive_inverse @ (additive_inverse @ a))))),
% 123.39/18.46 inference('demod', [status(thm)],
% 123.39/18.46 [zip_derived_cl114467, zip_derived_cl27])).
% 123.39/18.46 thf(zip_derived_cl21, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 123.39/18.46 thf(zip_derived_cl114478, plain,
% 123.39/18.46 ( (equalish @
% 123.39/18.46 (add @ additive_identity @ (additive_inverse @ (additive_inverse @ a))) @
% 123.39/18.46 a)),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl114468, zip_derived_cl21])).
% 123.39/18.46 thf(zip_derived_cl1, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 123.39/18.46 thf(zip_derived_cl21, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 123.39/18.46 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 123.39/18.46 thf(zip_derived_cl30, plain,
% 123.39/18.46 (![X0 : $i]:
% 123.39/18.46 (~ (defined @ X0) | (equalish @ X0 @ (add @ additive_identity @ X0)))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 123.39/18.46 thf(zip_derived_cl22, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 123.39/18.46 ( (equalish @ X0 @ X1)
% 123.39/18.46 | ~ (equalish @ X0 @ X2)
% 123.39/18.46 | ~ (equalish @ X2 @ X1))),
% 123.39/18.46 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 123.39/18.46 thf(zip_derived_cl42, plain,
% 123.39/18.46 (![X0 : $i, X1 : $i]:
% 123.39/18.46 (~ (defined @ X0)
% 123.39/18.46 | ~ (equalish @ (add @ additive_identity @ X0) @ X1)
% 123.39/18.46 | (equalish @ X0 @ X1))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl22])).
% 123.39/18.46 thf(zip_derived_cl114594, plain,
% 123.39/18.46 (( (equalish @ (additive_inverse @ (additive_inverse @ a)) @ a)
% 123.39/18.46 | ~ (defined @ (additive_inverse @ (additive_inverse @ a))))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl114478, zip_derived_cl42])).
% 123.39/18.46 thf(additive_inverse_not_equal_to_a_2, conjecture,
% 123.39/18.46 (equalish @ ( additive_inverse @ ( additive_inverse @ a ) ) @ a)).
% 123.39/18.46 thf(zf_stmt_0, negated_conjecture,
% 123.39/18.46 (~( equalish @ ( additive_inverse @ ( additive_inverse @ a ) ) @ a )),
% 123.39/18.46 inference('cnf.neg', [status(esa)], [additive_inverse_not_equal_to_a_2])).
% 123.39/18.46 thf(zip_derived_cl28, plain,
% 123.39/18.46 (~ (equalish @ (additive_inverse @ (additive_inverse @ a)) @ a)),
% 123.39/18.46 inference('cnf', [status(esa)], [zf_stmt_0])).
% 123.39/18.46 thf(zip_derived_cl114599, plain,
% 123.39/18.46 (~ (defined @ (additive_inverse @ (additive_inverse @ a)))),
% 123.39/18.46 inference('clc', [status(thm)], [zip_derived_cl114594, zip_derived_cl28])).
% 123.39/18.46 thf(zip_derived_cl114600, plain, (~ (defined @ (additive_inverse @ a))),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl114599])).
% 123.39/18.46 thf(zip_derived_cl114601, plain, (~ (defined @ a)),
% 123.39/18.46 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl114600])).
% 123.39/18.46 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 123.39/18.46 inference('cnf', [status(esa)], [a_is_defined])).
% 123.39/18.46 thf(zip_derived_cl114602, plain, ($false),
% 123.39/18.46 inference('demod', [status(thm)],
% 123.39/18.46 [zip_derived_cl114601, zip_derived_cl27])).
% 123.39/18.46
% 123.39/18.46 % SZS output end Refutation
% 123.39/18.46
% 123.39/18.46
% 123.39/18.46 % Terminating...
% 123.80/18.64 % Runner terminated.
% 123.80/18.64 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------