TSTP Solution File: FLD019-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD019-1 : 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.mr0XzA8kWg true
% Computer : n023.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 : Wed Aug 30 22:39:12 EDT 2023
% Result : Unsatisfiable 10.34s 2.10s
% Output : Refutation 10.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD019-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.mr0XzA8kWg true
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 00:13:40 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % Running portfolio for 300 s
% 0.12/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35 % Number of cores: 8
% 0.12/0.35 % Python version: Python 3.6.8
% 0.12/0.35 % Running in FO mode
% 0.43/0.63 % Total configuration time : 435
% 0.43/0.63 % Estimated wc time : 1092
% 0.43/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 10.34/2.10 % Solved by fo/fo5.sh.
% 10.34/2.10 % done 3063 iterations in 1.318s
% 10.34/2.10 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 10.34/2.10 % SZS output start Refutation
% 10.34/2.10 thf(defined_type, type, defined: $i > $o).
% 10.34/2.10 thf(additive_identity_type, type, additive_identity: $i).
% 10.34/2.10 thf(add_type, type, add: $i > $i > $i).
% 10.34/2.10 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 10.34/2.10 thf(equalish_type, type, equalish: $i > $i > $o).
% 10.34/2.10 thf(a_type, type, a: $i).
% 10.34/2.10 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 10.34/2.10 thf(a_not_equal_to_additive_identity_3, conjecture,
% 10.34/2.10 (equalish @ a @ additive_identity)).
% 10.34/2.10 thf(zf_stmt_0, negated_conjecture, (~( equalish @ a @ additive_identity )),
% 10.34/2.10 inference('cnf.neg', [status(esa)], [a_not_equal_to_additive_identity_3])).
% 10.34/2.10 thf(zip_derived_cl29, plain, (~ (equalish @ a @ additive_identity)),
% 10.34/2.10 inference('cnf', [status(esa)], [zf_stmt_0])).
% 10.34/2.10 thf(existence_of_identity_addition, axiom,
% 10.34/2.10 (( equalish @ ( add @ additive_identity @ X ) @ X ) | ( ~( defined @ X ) ))).
% 10.34/2.10 thf(zip_derived_cl1, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 10.34/2.10 thf(symmetry_of_equality, axiom,
% 10.34/2.10 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 10.34/2.10 thf(zip_derived_cl21, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 10.34/2.10 thf(zip_derived_cl33, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (defined @ X0) | (equalish @ X0 @ (add @ additive_identity @ X0)))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 10.34/2.10 thf(additive_inverse_equals_additive_identity_2, conjecture,
% 10.34/2.10 (~( equalish @ ( additive_inverse @ a ) @ additive_identity ))).
% 10.34/2.10 thf(zf_stmt_1, negated_conjecture,
% 10.34/2.10 (equalish @ ( additive_inverse @ a ) @ additive_identity),
% 10.34/2.10 inference('cnf.neg', [status(esa)],
% 10.34/2.10 [additive_inverse_equals_additive_identity_2])).
% 10.34/2.10 thf(zip_derived_cl28, plain,
% 10.34/2.10 ( (equalish @ (additive_inverse @ a) @ additive_identity)),
% 10.34/2.10 inference('cnf', [status(esa)], [zf_stmt_1])).
% 10.34/2.10 thf(transitivity_of_equality, axiom,
% 10.34/2.10 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 10.34/2.10 ( ~( equalish @ Y @ Z ) ))).
% 10.34/2.10 thf(zip_derived_cl22, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.34/2.10 ( (equalish @ X0 @ X1)
% 10.34/2.10 | ~ (equalish @ X0 @ X2)
% 10.34/2.10 | ~ (equalish @ X2 @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 10.34/2.10 thf(zip_derived_cl52, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (equalish @ additive_identity @ X0)
% 10.34/2.10 | (equalish @ (additive_inverse @ a) @ X0))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl22])).
% 10.34/2.10 thf(zip_derived_cl70, plain,
% 10.34/2.10 ((~ (defined @ additive_identity)
% 10.34/2.10 | (equalish @ (additive_inverse @ a) @
% 10.34/2.10 (add @ additive_identity @ additive_identity)))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl52])).
% 10.34/2.10 thf(well_definedness_of_additive_identity, axiom,
% 10.34/2.10 (defined @ additive_identity)).
% 10.34/2.10 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 10.34/2.10 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 10.34/2.10 thf(zip_derived_cl77, plain,
% 10.34/2.10 ( (equalish @ (additive_inverse @ a) @
% 10.34/2.10 (add @ additive_identity @ additive_identity))),
% 10.34/2.10 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl10])).
% 10.34/2.10 thf(zip_derived_cl21, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 10.34/2.10 thf(zip_derived_cl141, plain,
% 10.34/2.10 ( (equalish @ (add @ additive_identity @ additive_identity) @
% 10.34/2.10 (additive_inverse @ a))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl21])).
% 10.34/2.10 thf(compatibility_of_equality_and_addition, axiom,
% 10.34/2.10 (( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) | ( ~( defined @ Z ) ) |
% 10.34/2.10 ( ~( equalish @ X @ Y ) ))).
% 10.34/2.10 thf(zip_derived_cl23, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.34/2.10 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 10.34/2.10 | ~ (defined @ X1)
% 10.34/2.10 | ~ (equalish @ X0 @ X2))),
% 10.34/2.10 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 10.34/2.10 thf(zip_derived_cl616, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | (equalish @
% 10.34/2.10 (add @ (add @ additive_identity @ additive_identity) @ X0) @
% 10.34/2.10 (add @ (additive_inverse @ a) @ X0)))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl23])).
% 10.34/2.10 thf(associativity_addition, axiom,
% 10.34/2.10 (( equalish @ ( add @ X @ ( add @ Y @ Z ) ) @ ( add @ ( add @ X @ Y ) @ Z ) ) |
% 10.34/2.10 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ) | ( ~( defined @ Z ) ))).
% 10.34/2.10 thf(zip_derived_cl0, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.34/2.10 ( (equalish @ (add @ X0 @ (add @ X1 @ X2)) @
% 10.34/2.10 (add @ (add @ X0 @ X1) @ X2))
% 10.34/2.10 | ~ (defined @ X0)
% 10.34/2.10 | ~ (defined @ X1)
% 10.34/2.10 | ~ (defined @ X2))),
% 10.34/2.10 inference('cnf', [status(esa)], [associativity_addition])).
% 10.34/2.10 thf(zip_derived_cl33, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (defined @ X0) | (equalish @ X0 @ (add @ additive_identity @ X0)))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 10.34/2.10 thf(zip_derived_cl22, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.34/2.10 ( (equalish @ X0 @ X1)
% 10.34/2.10 | ~ (equalish @ X0 @ X2)
% 10.34/2.10 | ~ (equalish @ X2 @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 10.34/2.10 thf(zip_derived_cl45, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | ~ (equalish @ (add @ additive_identity @ X0) @ X1)
% 10.34/2.10 | (equalish @ X0 @ X1))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl22])).
% 10.34/2.10 thf(zip_derived_cl85, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | ~ (defined @ X1)
% 10.34/2.10 | ~ (defined @ additive_identity)
% 10.34/2.10 | (equalish @ (add @ X1 @ X0) @
% 10.34/2.10 (add @ (add @ additive_identity @ X1) @ X0))
% 10.34/2.10 | ~ (defined @ (add @ X1 @ X0)))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl45])).
% 10.34/2.10 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 10.34/2.10 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 10.34/2.10 thf(zip_derived_cl88, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | ~ (defined @ X1)
% 10.34/2.10 | (equalish @ (add @ X1 @ X0) @
% 10.34/2.10 (add @ (add @ additive_identity @ X1) @ X0))
% 10.34/2.10 | ~ (defined @ (add @ X1 @ X0)))),
% 10.34/2.10 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl10])).
% 10.34/2.10 thf(well_definedness_of_addition, axiom,
% 10.34/2.10 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 10.34/2.10 ( ~( defined @ Y ) ))).
% 10.34/2.10 thf(zip_derived_cl9, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 10.34/2.10 thf(zip_derived_cl2130, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 ( (equalish @ (add @ X1 @ X0) @
% 10.34/2.10 (add @ (add @ additive_identity @ X1) @ X0))
% 10.34/2.10 | ~ (defined @ X1)
% 10.34/2.10 | ~ (defined @ X0))),
% 10.34/2.10 inference('clc', [status(thm)], [zip_derived_cl88, zip_derived_cl9])).
% 10.34/2.10 thf(totality_of_order_relation, axiom,
% 10.34/2.10 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 10.34/2.10 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 10.34/2.10 thf(zip_derived_cl17, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 ( (less_or_equal @ X0 @ X1)
% 10.34/2.10 | (less_or_equal @ X1 @ X0)
% 10.34/2.10 | ~ (defined @ X0)
% 10.34/2.10 | ~ (defined @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 10.34/2.10 thf(a_is_defined, axiom, (defined @ a)).
% 10.34/2.10 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 10.34/2.10 inference('cnf', [status(esa)], [a_is_defined])).
% 10.34/2.10 thf(zip_derived_cl468, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | (less_or_equal @ X0 @ a)
% 10.34/2.10 | (less_or_equal @ a @ X0))),
% 10.34/2.10 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl27])).
% 10.34/2.10 thf(zip_derived_cl7286, plain,
% 10.34/2.10 (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 10.34/2.10 inference('eq_fact', [status(thm)], [zip_derived_cl468])).
% 10.34/2.10 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 10.34/2.10 inference('cnf', [status(esa)], [a_is_defined])).
% 10.34/2.10 thf(zip_derived_cl7287, plain, ( (less_or_equal @ a @ a)),
% 10.34/2.10 inference('demod', [status(thm)], [zip_derived_cl7286, zip_derived_cl27])).
% 10.34/2.10 thf(antisymmetry_of_order_relation, axiom,
% 10.34/2.10 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 10.34/2.10 ( ~( less_or_equal @ Y @ X ) ))).
% 10.34/2.10 thf(zip_derived_cl15, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 ( (equalish @ X0 @ X1)
% 10.34/2.10 | ~ (less_or_equal @ X0 @ X1)
% 10.34/2.10 | ~ (less_or_equal @ X1 @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 10.34/2.10 thf(zip_derived_cl7306, plain,
% 10.34/2.10 ((~ (less_or_equal @ a @ a) | (equalish @ a @ a))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl7287, zip_derived_cl15])).
% 10.34/2.10 thf(zip_derived_cl7287, plain, ( (less_or_equal @ a @ a)),
% 10.34/2.10 inference('demod', [status(thm)], [zip_derived_cl7286, zip_derived_cl27])).
% 10.34/2.10 thf(zip_derived_cl7310, plain, ( (equalish @ a @ a)),
% 10.34/2.10 inference('demod', [status(thm)],
% 10.34/2.10 [zip_derived_cl7306, zip_derived_cl7287])).
% 10.34/2.10 thf(zip_derived_cl1, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 10.34/2.10 thf(zip_derived_cl22, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.34/2.10 ( (equalish @ X0 @ X1)
% 10.34/2.10 | ~ (equalish @ X0 @ X2)
% 10.34/2.10 | ~ (equalish @ X2 @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 10.34/2.10 thf(zip_derived_cl47, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | ~ (equalish @ X0 @ X1)
% 10.34/2.10 | (equalish @ (add @ additive_identity @ X0) @ X1))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 10.34/2.10 thf(zip_derived_cl7312, plain,
% 10.34/2.10 (( (equalish @ (add @ additive_identity @ a) @ a) | ~ (defined @ a))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl7310, zip_derived_cl47])).
% 10.34/2.10 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 10.34/2.10 inference('cnf', [status(esa)], [a_is_defined])).
% 10.34/2.10 thf(zip_derived_cl7321, plain,
% 10.34/2.10 ( (equalish @ (add @ additive_identity @ a) @ a)),
% 10.34/2.10 inference('demod', [status(thm)], [zip_derived_cl7312, zip_derived_cl27])).
% 10.34/2.10 thf(zip_derived_cl21, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 10.34/2.10 thf(zip_derived_cl7330, plain,
% 10.34/2.10 ( (equalish @ a @ (add @ additive_identity @ a))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl7321, zip_derived_cl21])).
% 10.34/2.10 thf(zip_derived_cl22, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.34/2.10 ( (equalish @ X0 @ X1)
% 10.34/2.10 | ~ (equalish @ X0 @ X2)
% 10.34/2.10 | ~ (equalish @ X2 @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 10.34/2.10 thf(zip_derived_cl7421, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (equalish @ (add @ additive_identity @ a) @ X0)
% 10.34/2.10 | (equalish @ a @ X0))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl7330, zip_derived_cl22])).
% 10.34/2.10 thf(zip_derived_cl7449, plain,
% 10.34/2.10 ((~ (defined @ a)
% 10.34/2.10 | ~ (defined @ additive_identity)
% 10.34/2.10 | (equalish @ a @
% 10.34/2.10 (add @ (add @ additive_identity @ additive_identity) @ a)))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl2130, zip_derived_cl7421])).
% 10.34/2.10 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 10.34/2.10 inference('cnf', [status(esa)], [a_is_defined])).
% 10.34/2.10 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 10.34/2.10 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 10.34/2.10 thf(zip_derived_cl7454, plain,
% 10.34/2.10 ( (equalish @ a @
% 10.34/2.10 (add @ (add @ additive_identity @ additive_identity) @ a))),
% 10.34/2.10 inference('demod', [status(thm)],
% 10.34/2.10 [zip_derived_cl7449, zip_derived_cl27, zip_derived_cl10])).
% 10.34/2.10 thf(zip_derived_cl22, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.34/2.10 ( (equalish @ X0 @ X1)
% 10.34/2.10 | ~ (equalish @ X0 @ X2)
% 10.34/2.10 | ~ (equalish @ X2 @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 10.34/2.10 thf(zip_derived_cl8133, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (equalish @
% 10.34/2.10 (add @ (add @ additive_identity @ additive_identity) @ a) @ X0)
% 10.34/2.10 | (equalish @ a @ X0))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl7454, zip_derived_cl22])).
% 10.34/2.10 thf(zip_derived_cl12721, plain,
% 10.34/2.10 ((~ (defined @ a) | (equalish @ a @ (add @ (additive_inverse @ a) @ a)))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl616, zip_derived_cl8133])).
% 10.34/2.10 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 10.34/2.10 inference('cnf', [status(esa)], [a_is_defined])).
% 10.34/2.10 thf(zip_derived_cl12729, plain,
% 10.34/2.10 ( (equalish @ a @ (add @ (additive_inverse @ a) @ a))),
% 10.34/2.10 inference('demod', [status(thm)], [zip_derived_cl12721, zip_derived_cl27])).
% 10.34/2.10 thf(zip_derived_cl21, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 10.34/2.10 thf(zip_derived_cl12751, plain,
% 10.34/2.10 ( (equalish @ (add @ (additive_inverse @ a) @ a) @ a)),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl12729, zip_derived_cl21])).
% 10.34/2.10 thf(commutativity_addition, axiom,
% 10.34/2.10 (( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) ) | ( ~( defined @ X ) ) |
% 10.34/2.10 ( ~( defined @ Y ) ))).
% 10.34/2.10 thf(zip_derived_cl3, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 10.34/2.10 | ~ (defined @ X0)
% 10.34/2.10 | ~ (defined @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [commutativity_addition])).
% 10.34/2.10 thf(existence_of_inverse_addition, axiom,
% 10.34/2.10 (( equalish @ ( add @ X @ ( additive_inverse @ X ) ) @ additive_identity ) |
% 10.34/2.10 ( ~( defined @ X ) ))).
% 10.34/2.10 thf(zip_derived_cl2, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 ( (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ additive_identity)
% 10.34/2.10 | ~ (defined @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 10.34/2.10 thf(zip_derived_cl21, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 10.34/2.10 thf(zip_derived_cl67, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | (equalish @ additive_identity @
% 10.34/2.10 (add @ X0 @ (additive_inverse @ X0))))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl21])).
% 10.34/2.10 thf(zip_derived_cl22, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.34/2.10 ( (equalish @ X0 @ X1)
% 10.34/2.10 | ~ (equalish @ X0 @ X2)
% 10.34/2.10 | ~ (equalish @ X2 @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 10.34/2.10 thf(zip_derived_cl1710, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | ~ (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ X1)
% 10.34/2.10 | (equalish @ additive_identity @ X1))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl22])).
% 10.34/2.10 thf(zip_derived_cl1849, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (defined @ (additive_inverse @ X0))
% 10.34/2.10 | ~ (defined @ X0)
% 10.34/2.10 | (equalish @ additive_identity @
% 10.34/2.10 (add @ (additive_inverse @ X0) @ X0))
% 10.34/2.10 | ~ (defined @ X0))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1710])).
% 10.34/2.10 thf(zip_derived_cl1857, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 ( (equalish @ additive_identity @ (add @ (additive_inverse @ X0) @ X0))
% 10.34/2.10 | ~ (defined @ X0)
% 10.34/2.10 | ~ (defined @ (additive_inverse @ X0)))),
% 10.34/2.10 inference('simplify', [status(thm)], [zip_derived_cl1849])).
% 10.34/2.10 thf(well_definedness_of_additive_inverse, axiom,
% 10.34/2.10 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 10.34/2.10 thf(zip_derived_cl11, plain,
% 10.34/2.10 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 10.34/2.10 thf(zip_derived_cl3697, plain,
% 10.34/2.10 (![X0 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | (equalish @ additive_identity @
% 10.34/2.10 (add @ (additive_inverse @ X0) @ X0)))),
% 10.34/2.10 inference('clc', [status(thm)], [zip_derived_cl1857, zip_derived_cl11])).
% 10.34/2.10 thf(zip_derived_cl22, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.34/2.10 ( (equalish @ X0 @ X1)
% 10.34/2.10 | ~ (equalish @ X0 @ X2)
% 10.34/2.10 | ~ (equalish @ X2 @ X1))),
% 10.34/2.10 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 10.34/2.10 thf(zip_derived_cl3703, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]:
% 10.34/2.10 (~ (defined @ X0)
% 10.34/2.10 | ~ (equalish @ (add @ (additive_inverse @ X0) @ X0) @ X1)
% 10.34/2.10 | (equalish @ additive_identity @ X1))),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl3697, zip_derived_cl22])).
% 10.34/2.10 thf(zip_derived_cl12780, plain,
% 10.34/2.10 (( (equalish @ additive_identity @ a) | ~ (defined @ a))),
% 10.34/2.10 inference('sup-', [status(thm)],
% 10.34/2.10 [zip_derived_cl12751, zip_derived_cl3703])).
% 10.34/2.10 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 10.34/2.10 inference('cnf', [status(esa)], [a_is_defined])).
% 10.34/2.10 thf(zip_derived_cl12782, plain, ( (equalish @ additive_identity @ a)),
% 10.34/2.10 inference('demod', [status(thm)], [zip_derived_cl12780, zip_derived_cl27])).
% 10.34/2.10 thf(zip_derived_cl21, plain,
% 10.34/2.10 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 10.34/2.10 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 10.34/2.10 thf(zip_derived_cl12787, plain, ( (equalish @ a @ additive_identity)),
% 10.34/2.10 inference('sup-', [status(thm)], [zip_derived_cl12782, zip_derived_cl21])).
% 10.34/2.10 thf(zip_derived_cl12821, plain, ($false),
% 10.34/2.10 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl12787])).
% 10.34/2.10
% 10.34/2.10 % SZS output end Refutation
% 10.34/2.10
% 10.34/2.10
% 10.34/2.10 % Terminating...
% 10.78/2.16 % Runner terminated.
% 10.78/2.18 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------