TSTP Solution File: FLD024-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD024-1 : 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.5qSPMJocwj true
% Computer : n010.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 22:39:14 EDT 2023
% Result : Unsatisfiable 16.10s 2.97s
% Output : Refutation 16.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD024-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.5qSPMJocwj true
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 23:54:19 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.22/0.36 % Running in FO mode
% 0.22/0.67 % Total configuration time : 435
% 0.22/0.67 % Estimated wc time : 1092
% 0.22/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.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/fo1_av.sh running for 75s
% 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
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 16.10/2.97 % Solved by fo/fo5.sh.
% 16.10/2.97 % done 4131 iterations in 2.164s
% 16.10/2.97 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 16.10/2.97 % SZS output start Refutation
% 16.10/2.97 thf(defined_type, type, defined: $i > $o).
% 16.10/2.97 thf(additive_identity_type, type, additive_identity: $i).
% 16.10/2.97 thf(add_type, type, add: $i > $i > $i).
% 16.10/2.97 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 16.10/2.97 thf(b_type, type, b: $i).
% 16.10/2.97 thf(equalish_type, type, equalish: $i > $i > $o).
% 16.10/2.97 thf(a_type, type, a: $i).
% 16.10/2.97 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 16.10/2.97 thf(a_not_equal_to_b_4, conjecture, (equalish @ a @ b)).
% 16.10/2.97 thf(zf_stmt_0, negated_conjecture, (~( equalish @ a @ b )),
% 16.10/2.97 inference('cnf.neg', [status(esa)], [a_not_equal_to_b_4])).
% 16.10/2.97 thf(zip_derived_cl30, plain, (~ (equalish @ a @ b)),
% 16.10/2.97 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.10/2.97 thf(existence_of_inverse_addition, axiom,
% 16.10/2.97 (( equalish @ ( add @ X @ ( additive_inverse @ X ) ) @ additive_identity ) |
% 16.10/2.97 ( ~( defined @ X ) ))).
% 16.10/2.97 thf(zip_derived_cl2, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 ( (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ additive_identity)
% 16.10/2.97 | ~ (defined @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 16.10/2.97 thf(compatibility_of_equality_and_addition, axiom,
% 16.10/2.97 (( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) | ( ~( defined @ Z ) ) |
% 16.10/2.97 ( ~( equalish @ X @ Y ) ))).
% 16.10/2.97 thf(zip_derived_cl23, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2))),
% 16.10/2.97 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 16.10/2.97 thf(zip_derived_cl623, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 (~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | (equalish @ (add @ (add @ X0 @ (additive_inverse @ X0)) @ X1) @
% 16.10/2.97 (add @ additive_identity @ X1)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl23])).
% 16.10/2.97 thf(well_definedness_of_additive_inverse, axiom,
% 16.10/2.97 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 16.10/2.97 thf(zip_derived_cl11, plain,
% 16.10/2.97 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 16.10/2.97 thf(commutativity_addition, axiom,
% 16.10/2.97 (( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) ) | ( ~( defined @ X ) ) |
% 16.10/2.97 ( ~( defined @ Y ) ))).
% 16.10/2.97 thf(zip_derived_cl3, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 16.10/2.97 | ~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [commutativity_addition])).
% 16.10/2.97 thf(zip_derived_cl23, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2))),
% 16.10/2.97 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 16.10/2.97 thf(zip_derived_cl611, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 (~ (defined @ X1)
% 16.10/2.97 | ~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X2)
% 16.10/2.97 | (equalish @ (add @ (add @ X0 @ X1) @ X2) @
% 16.10/2.97 (add @ (add @ X1 @ X0) @ X2)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl23])).
% 16.10/2.97 thf(zip_derived_cl11, plain,
% 16.10/2.97 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 16.10/2.97 thf(well_definedness_of_addition, axiom,
% 16.10/2.97 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 16.10/2.97 ( ~( defined @ Y ) ))).
% 16.10/2.97 thf(zip_derived_cl9, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 16.10/2.97 thf(zip_derived_cl11, plain,
% 16.10/2.97 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 16.10/2.97 thf(existence_of_identity_addition, axiom,
% 16.10/2.97 (( equalish @ ( add @ additive_identity @ X ) @ X ) | ( ~( defined @ X ) ))).
% 16.10/2.97 thf(zip_derived_cl1, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 16.10/2.97 thf(symmetry_of_equality, axiom,
% 16.10/2.97 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 16.10/2.97 thf(zip_derived_cl21, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 16.10/2.97 thf(zip_derived_cl32, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (defined @ X0) | (equalish @ X0 @ (add @ additive_identity @ X0)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 16.10/2.97 thf(additive_identity_equals_add_3, conjecture,
% 16.10/2.97 (~( equalish @ additive_identity @ ( add @ b @ ( additive_inverse @ a ) ) ))).
% 16.10/2.97 thf(zf_stmt_1, negated_conjecture,
% 16.10/2.97 (equalish @ additive_identity @ ( add @ b @ ( additive_inverse @ a ) )),
% 16.10/2.97 inference('cnf.neg', [status(esa)], [additive_identity_equals_add_3])).
% 16.10/2.97 thf(zip_derived_cl29, plain,
% 16.10/2.97 ( (equalish @ additive_identity @ (add @ b @ (additive_inverse @ a)))),
% 16.10/2.97 inference('cnf', [status(esa)], [zf_stmt_1])).
% 16.10/2.97 thf(zip_derived_cl21, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 16.10/2.97 thf(zip_derived_cl34, plain,
% 16.10/2.97 ( (equalish @ (add @ b @ (additive_inverse @ a)) @ additive_identity)),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl21])).
% 16.10/2.97 thf(transitivity_of_equality, axiom,
% 16.10/2.97 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 16.10/2.97 ( ~( equalish @ Y @ Z ) ))).
% 16.10/2.97 thf(zip_derived_cl22, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2)
% 16.10/2.97 | ~ (equalish @ X2 @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.10/2.97 thf(zip_derived_cl49, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (equalish @ additive_identity @ X0)
% 16.10/2.97 | (equalish @ (add @ b @ (additive_inverse @ a)) @ X0))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl22])).
% 16.10/2.97 thf(zip_derived_cl55, plain,
% 16.10/2.97 ((~ (defined @ additive_identity)
% 16.10/2.97 | (equalish @ (add @ b @ (additive_inverse @ a)) @
% 16.10/2.97 (add @ additive_identity @ additive_identity)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl49])).
% 16.10/2.97 thf(well_definedness_of_additive_identity, axiom,
% 16.10/2.97 (defined @ additive_identity)).
% 16.10/2.97 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 16.10/2.97 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 16.10/2.97 thf(zip_derived_cl60, plain,
% 16.10/2.97 ( (equalish @ (add @ b @ (additive_inverse @ a)) @
% 16.10/2.97 (add @ additive_identity @ additive_identity))),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl10])).
% 16.10/2.97 thf(zip_derived_cl21, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 16.10/2.97 thf(zip_derived_cl63, plain,
% 16.10/2.97 ( (equalish @ (add @ additive_identity @ additive_identity) @
% 16.10/2.97 (add @ b @ (additive_inverse @ a)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl21])).
% 16.10/2.97 thf(zip_derived_cl23, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2))),
% 16.10/2.97 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 16.10/2.97 thf(zip_derived_cl614, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (defined @ X0)
% 16.10/2.97 | (equalish @
% 16.10/2.97 (add @ (add @ additive_identity @ additive_identity) @ X0) @
% 16.10/2.97 (add @ (add @ b @ (additive_inverse @ a)) @ X0)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl23])).
% 16.10/2.97 thf(associativity_addition, axiom,
% 16.10/2.97 (( equalish @ ( add @ X @ ( add @ Y @ Z ) ) @ ( add @ ( add @ X @ Y ) @ Z ) ) |
% 16.10/2.97 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ) | ( ~( defined @ Z ) ))).
% 16.10/2.97 thf(zip_derived_cl0, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ (add @ X0 @ (add @ X1 @ X2)) @
% 16.10/2.97 (add @ (add @ X0 @ X1) @ X2))
% 16.10/2.97 | ~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | ~ (defined @ X2))),
% 16.10/2.97 inference('cnf', [status(esa)], [associativity_addition])).
% 16.10/2.97 thf(zip_derived_cl32, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (defined @ X0) | (equalish @ X0 @ (add @ additive_identity @ X0)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 16.10/2.97 thf(zip_derived_cl22, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2)
% 16.10/2.97 | ~ (equalish @ X2 @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.10/2.97 thf(zip_derived_cl44, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 (~ (defined @ X0)
% 16.10/2.97 | ~ (equalish @ (add @ additive_identity @ X0) @ X1)
% 16.10/2.97 | (equalish @ X0 @ X1))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl22])).
% 16.10/2.97 thf(zip_derived_cl78, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 (~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | ~ (defined @ additive_identity)
% 16.10/2.97 | (equalish @ (add @ X1 @ X0) @
% 16.10/2.97 (add @ (add @ additive_identity @ X1) @ X0))
% 16.10/2.97 | ~ (defined @ (add @ X1 @ X0)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl44])).
% 16.10/2.97 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 16.10/2.97 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 16.10/2.97 thf(zip_derived_cl82, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 (~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | (equalish @ (add @ X1 @ X0) @
% 16.10/2.97 (add @ (add @ additive_identity @ X1) @ X0))
% 16.10/2.97 | ~ (defined @ (add @ X1 @ X0)))),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl10])).
% 16.10/2.97 thf(zip_derived_cl9, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 16.10/2.97 thf(zip_derived_cl2162, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 ( (equalish @ (add @ X1 @ X0) @
% 16.10/2.97 (add @ (add @ additive_identity @ X1) @ X0))
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | ~ (defined @ X0))),
% 16.10/2.97 inference('clc', [status(thm)], [zip_derived_cl82, zip_derived_cl9])).
% 16.10/2.97 thf(totality_of_order_relation, axiom,
% 16.10/2.97 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 16.10/2.97 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 16.10/2.97 thf(zip_derived_cl17, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 ( (less_or_equal @ X0 @ X1)
% 16.10/2.97 | (less_or_equal @ X1 @ X0)
% 16.10/2.97 | ~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 16.10/2.97 thf(a_is_defined, axiom, (defined @ a)).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl464, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (defined @ X0)
% 16.10/2.97 | (less_or_equal @ X0 @ a)
% 16.10/2.97 | (less_or_equal @ a @ X0))),
% 16.10/2.97 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl5497, plain,
% 16.10/2.97 (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 16.10/2.97 inference('eq_fact', [status(thm)], [zip_derived_cl464])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl5498, plain, ( (less_or_equal @ a @ a)),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl5497, zip_derived_cl27])).
% 16.10/2.97 thf(antisymmetry_of_order_relation, axiom,
% 16.10/2.97 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 16.10/2.97 ( ~( less_or_equal @ Y @ X ) ))).
% 16.10/2.97 thf(zip_derived_cl15, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (less_or_equal @ X0 @ X1)
% 16.10/2.97 | ~ (less_or_equal @ X1 @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 16.10/2.97 thf(zip_derived_cl5509, plain,
% 16.10/2.97 ((~ (less_or_equal @ a @ a) | (equalish @ a @ a))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl5498, zip_derived_cl15])).
% 16.10/2.97 thf(zip_derived_cl5498, plain, ( (less_or_equal @ a @ a)),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl5497, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl5513, plain, ( (equalish @ a @ a)),
% 16.10/2.97 inference('demod', [status(thm)],
% 16.10/2.97 [zip_derived_cl5509, zip_derived_cl5498])).
% 16.10/2.97 thf(zip_derived_cl1, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 16.10/2.97 thf(zip_derived_cl22, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2)
% 16.10/2.97 | ~ (equalish @ X2 @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.10/2.97 thf(zip_derived_cl46, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 (~ (defined @ X0)
% 16.10/2.97 | ~ (equalish @ X0 @ X1)
% 16.10/2.97 | (equalish @ (add @ additive_identity @ X0) @ X1))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 16.10/2.97 thf(zip_derived_cl5515, plain,
% 16.10/2.97 (( (equalish @ (add @ additive_identity @ a) @ a) | ~ (defined @ a))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl5513, zip_derived_cl46])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl5524, plain,
% 16.10/2.97 ( (equalish @ (add @ additive_identity @ a) @ a)),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl5515, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl21, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 16.10/2.97 thf(zip_derived_cl5532, plain,
% 16.10/2.97 ( (equalish @ a @ (add @ additive_identity @ a))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl5524, zip_derived_cl21])).
% 16.10/2.97 thf(zip_derived_cl22, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2)
% 16.10/2.97 | ~ (equalish @ X2 @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.10/2.97 thf(zip_derived_cl5691, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (equalish @ (add @ additive_identity @ a) @ X0)
% 16.10/2.97 | (equalish @ a @ X0))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl5532, zip_derived_cl22])).
% 16.10/2.97 thf(zip_derived_cl5905, plain,
% 16.10/2.97 ((~ (defined @ a)
% 16.10/2.97 | ~ (defined @ additive_identity)
% 16.10/2.97 | (equalish @ a @
% 16.10/2.97 (add @ (add @ additive_identity @ additive_identity) @ a)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl2162, zip_derived_cl5691])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 16.10/2.97 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 16.10/2.97 thf(zip_derived_cl5909, plain,
% 16.10/2.97 ( (equalish @ a @
% 16.10/2.97 (add @ (add @ additive_identity @ additive_identity) @ a))),
% 16.10/2.97 inference('demod', [status(thm)],
% 16.10/2.97 [zip_derived_cl5905, zip_derived_cl27, zip_derived_cl10])).
% 16.10/2.97 thf(zip_derived_cl22, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2)
% 16.10/2.97 | ~ (equalish @ X2 @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.10/2.97 thf(zip_derived_cl6414, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (equalish @
% 16.10/2.97 (add @ (add @ additive_identity @ additive_identity) @ a) @ X0)
% 16.10/2.97 | (equalish @ a @ X0))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl5909, zip_derived_cl22])).
% 16.10/2.97 thf(zip_derived_cl10282, plain,
% 16.10/2.97 ((~ (defined @ a)
% 16.10/2.97 | (equalish @ a @ (add @ (add @ b @ (additive_inverse @ a)) @ a)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl614, zip_derived_cl6414])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl10290, plain,
% 16.10/2.97 ( (equalish @ a @ (add @ (add @ b @ (additive_inverse @ a)) @ a))),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl10282, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl21, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 16.10/2.97 thf(zip_derived_cl10342, plain,
% 16.10/2.97 ( (equalish @ (add @ (add @ b @ (additive_inverse @ a)) @ a) @ a)),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl10290, zip_derived_cl21])).
% 16.10/2.97 thf(zip_derived_cl0, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ (add @ X0 @ (add @ X1 @ X2)) @
% 16.10/2.97 (add @ (add @ X0 @ X1) @ X2))
% 16.10/2.97 | ~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | ~ (defined @ X2))),
% 16.10/2.97 inference('cnf', [status(esa)], [associativity_addition])).
% 16.10/2.97 thf(zip_derived_cl22, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2)
% 16.10/2.97 | ~ (equalish @ X2 @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.10/2.97 thf(zip_derived_cl47, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.10/2.97 (~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1)
% 16.10/2.97 | ~ (defined @ X2)
% 16.10/2.97 | ~ (equalish @ (add @ (add @ X2 @ X1) @ X0) @ X3)
% 16.10/2.97 | (equalish @ (add @ X2 @ (add @ X1 @ X0)) @ X3))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl22])).
% 16.10/2.97 thf(zip_derived_cl10389, plain,
% 16.10/2.97 (( (equalish @ (add @ b @ (add @ (additive_inverse @ a) @ a)) @ a)
% 16.10/2.97 | ~ (defined @ b)
% 16.10/2.97 | ~ (defined @ (additive_inverse @ a))
% 16.10/2.97 | ~ (defined @ a))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl10342, zip_derived_cl47])).
% 16.10/2.97 thf(b_is_defined, axiom, (defined @ b)).
% 16.10/2.97 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 16.10/2.97 inference('cnf', [status(esa)], [b_is_defined])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl10391, plain,
% 16.10/2.97 (( (equalish @ (add @ b @ (add @ (additive_inverse @ a) @ a)) @ a)
% 16.10/2.97 | ~ (defined @ (additive_inverse @ a)))),
% 16.10/2.97 inference('demod', [status(thm)],
% 16.10/2.97 [zip_derived_cl10389, zip_derived_cl28, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl10511, plain,
% 16.10/2.97 ((~ (defined @ a)
% 16.10/2.97 | (equalish @ (add @ b @ (add @ (additive_inverse @ a) @ a)) @ a))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl10391])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl10512, plain,
% 16.10/2.97 ( (equalish @ (add @ b @ (add @ (additive_inverse @ a) @ a)) @ a)),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl10511, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl3, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 16.10/2.97 | ~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [commutativity_addition])).
% 16.10/2.97 thf(zip_derived_cl22, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2)
% 16.10/2.97 | ~ (equalish @ X2 @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.10/2.97 thf(zip_derived_cl106, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 (~ (defined @ X1)
% 16.10/2.97 | ~ (defined @ X0)
% 16.10/2.97 | ~ (equalish @ (add @ X1 @ X0) @ X2)
% 16.10/2.97 | (equalish @ (add @ X0 @ X1) @ X2))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 16.10/2.97 thf(zip_derived_cl10589, plain,
% 16.10/2.97 (( (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a)
% 16.10/2.97 | ~ (defined @ (add @ (additive_inverse @ a) @ a))
% 16.10/2.97 | ~ (defined @ b))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl10512, zip_derived_cl106])).
% 16.10/2.97 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 16.10/2.97 inference('cnf', [status(esa)], [b_is_defined])).
% 16.10/2.97 thf(zip_derived_cl10591, plain,
% 16.10/2.97 (( (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a)
% 16.10/2.97 | ~ (defined @ (add @ (additive_inverse @ a) @ a)))),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl10589, zip_derived_cl28])).
% 16.10/2.97 thf(zip_derived_cl20249, plain,
% 16.10/2.97 ((~ (defined @ a)
% 16.10/2.97 | ~ (defined @ (additive_inverse @ a))
% 16.10/2.97 | (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl10591])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl20250, plain,
% 16.10/2.97 ((~ (defined @ (additive_inverse @ a))
% 16.10/2.97 | (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a))),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl20249, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl20251, plain,
% 16.10/2.97 ((~ (defined @ a)
% 16.10/2.97 | (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl20250])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl20252, plain,
% 16.10/2.97 ( (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a)),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl20251, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl21, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 16.10/2.97 thf(zip_derived_cl20257, plain,
% 16.10/2.97 ( (equalish @ a @ (add @ (add @ (additive_inverse @ a) @ a) @ b))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl20252, zip_derived_cl21])).
% 16.10/2.97 thf(zip_derived_cl22, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2)
% 16.10/2.97 | ~ (equalish @ X2 @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.10/2.97 thf(zip_derived_cl20293, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ X0)
% 16.10/2.97 | (equalish @ a @ X0))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl20257, zip_derived_cl22])).
% 16.10/2.97 thf(zip_derived_cl20568, plain,
% 16.10/2.97 ((~ (defined @ b)
% 16.10/2.97 | ~ (defined @ (additive_inverse @ a))
% 16.10/2.97 | ~ (defined @ a)
% 16.10/2.97 | (equalish @ a @ (add @ (add @ a @ (additive_inverse @ a)) @ b)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl611, zip_derived_cl20293])).
% 16.10/2.97 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 16.10/2.97 inference('cnf', [status(esa)], [b_is_defined])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl20576, plain,
% 16.10/2.97 ((~ (defined @ (additive_inverse @ a))
% 16.10/2.97 | (equalish @ a @ (add @ (add @ a @ (additive_inverse @ a)) @ b)))),
% 16.10/2.97 inference('demod', [status(thm)],
% 16.10/2.97 [zip_derived_cl20568, zip_derived_cl28, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl20758, plain,
% 16.10/2.97 ((~ (defined @ a)
% 16.10/2.97 | (equalish @ a @ (add @ (add @ a @ (additive_inverse @ a)) @ b)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl20576])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl20759, plain,
% 16.10/2.97 ( (equalish @ a @ (add @ (add @ a @ (additive_inverse @ a)) @ b))),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl20758, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl22, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (equalish @ X0 @ X2)
% 16.10/2.97 | ~ (equalish @ X2 @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.10/2.97 thf(zip_derived_cl20765, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (equalish @ (add @ (add @ a @ (additive_inverse @ a)) @ b) @ X0)
% 16.10/2.97 | (equalish @ a @ X0))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl20759, zip_derived_cl22])).
% 16.10/2.97 thf(zip_derived_cl21274, plain,
% 16.10/2.97 ((~ (defined @ b)
% 16.10/2.97 | ~ (defined @ a)
% 16.10/2.97 | (equalish @ a @ (add @ additive_identity @ b)))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl623, zip_derived_cl20765])).
% 16.10/2.97 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 16.10/2.97 inference('cnf', [status(esa)], [b_is_defined])).
% 16.10/2.97 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 16.10/2.97 inference('cnf', [status(esa)], [a_is_defined])).
% 16.10/2.97 thf(zip_derived_cl21283, plain,
% 16.10/2.97 ( (equalish @ a @ (add @ additive_identity @ b))),
% 16.10/2.97 inference('demod', [status(thm)],
% 16.10/2.97 [zip_derived_cl21274, zip_derived_cl28, zip_derived_cl27])).
% 16.10/2.97 thf(zip_derived_cl21, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 16.10/2.97 thf(zip_derived_cl21288, plain,
% 16.10/2.97 ( (equalish @ (add @ additive_identity @ b) @ a)),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl21283, zip_derived_cl21])).
% 16.10/2.97 thf(zip_derived_cl17, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 ( (less_or_equal @ X0 @ X1)
% 16.10/2.97 | (less_or_equal @ X1 @ X0)
% 16.10/2.97 | ~ (defined @ X0)
% 16.10/2.97 | ~ (defined @ X1))),
% 16.10/2.97 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 16.10/2.97 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 16.10/2.97 inference('cnf', [status(esa)], [b_is_defined])).
% 16.10/2.97 thf(zip_derived_cl465, plain,
% 16.10/2.97 (![X0 : $i]:
% 16.10/2.97 (~ (defined @ X0)
% 16.10/2.97 | (less_or_equal @ X0 @ b)
% 16.10/2.97 | (less_or_equal @ b @ X0))),
% 16.10/2.97 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl28])).
% 16.10/2.97 thf(zip_derived_cl5655, plain,
% 16.10/2.97 (( (less_or_equal @ b @ b) | ~ (defined @ b))),
% 16.10/2.97 inference('eq_fact', [status(thm)], [zip_derived_cl465])).
% 16.10/2.97 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 16.10/2.97 inference('cnf', [status(esa)], [b_is_defined])).
% 16.10/2.97 thf(zip_derived_cl5656, plain, ( (less_or_equal @ b @ b)),
% 16.10/2.97 inference('demod', [status(thm)], [zip_derived_cl5655, zip_derived_cl28])).
% 16.10/2.97 thf(zip_derived_cl15, plain,
% 16.10/2.97 (![X0 : $i, X1 : $i]:
% 16.10/2.97 ( (equalish @ X0 @ X1)
% 16.10/2.97 | ~ (less_or_equal @ X0 @ X1)
% 16.10/2.97 | ~ (less_or_equal @ X1 @ X0))),
% 16.10/2.97 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 16.10/2.97 thf(zip_derived_cl5667, plain,
% 16.10/2.97 ((~ (less_or_equal @ b @ b) | (equalish @ b @ b))),
% 16.10/2.97 inference('sup-', [status(thm)], [zip_derived_cl5656, zip_derived_cl15])).
% 16.28/2.97 thf(zip_derived_cl5656, plain, ( (less_or_equal @ b @ b)),
% 16.28/2.97 inference('demod', [status(thm)], [zip_derived_cl5655, zip_derived_cl28])).
% 16.28/2.97 thf(zip_derived_cl5671, plain, ( (equalish @ b @ b)),
% 16.28/2.97 inference('demod', [status(thm)],
% 16.28/2.97 [zip_derived_cl5667, zip_derived_cl5656])).
% 16.28/2.97 thf(zip_derived_cl46, plain,
% 16.28/2.97 (![X0 : $i, X1 : $i]:
% 16.28/2.97 (~ (defined @ X0)
% 16.28/2.97 | ~ (equalish @ X0 @ X1)
% 16.28/2.97 | (equalish @ (add @ additive_identity @ X0) @ X1))),
% 16.28/2.97 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 16.28/2.97 thf(zip_derived_cl5673, plain,
% 16.28/2.97 (( (equalish @ (add @ additive_identity @ b) @ b) | ~ (defined @ b))),
% 16.28/2.97 inference('sup-', [status(thm)], [zip_derived_cl5671, zip_derived_cl46])).
% 16.28/2.97 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 16.28/2.97 inference('cnf', [status(esa)], [b_is_defined])).
% 16.28/2.97 thf(zip_derived_cl5682, plain,
% 16.28/2.97 ( (equalish @ (add @ additive_identity @ b) @ b)),
% 16.28/2.97 inference('demod', [status(thm)], [zip_derived_cl5673, zip_derived_cl28])).
% 16.28/2.97 thf(zip_derived_cl21, plain,
% 16.28/2.97 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 16.28/2.97 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 16.28/2.97 thf(zip_derived_cl5814, plain,
% 16.28/2.97 ( (equalish @ b @ (add @ additive_identity @ b))),
% 16.28/2.97 inference('sup-', [status(thm)], [zip_derived_cl5682, zip_derived_cl21])).
% 16.28/2.97 thf(zip_derived_cl22, plain,
% 16.28/2.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.28/2.97 ( (equalish @ X0 @ X1)
% 16.28/2.97 | ~ (equalish @ X0 @ X2)
% 16.28/2.97 | ~ (equalish @ X2 @ X1))),
% 16.28/2.97 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 16.28/2.97 thf(zip_derived_cl5841, plain,
% 16.28/2.97 (![X0 : $i]:
% 16.28/2.97 (~ (equalish @ (add @ additive_identity @ b) @ X0)
% 16.28/2.97 | (equalish @ b @ X0))),
% 16.28/2.97 inference('sup-', [status(thm)], [zip_derived_cl5814, zip_derived_cl22])).
% 16.28/2.97 thf(zip_derived_cl21336, plain, ( (equalish @ b @ a)),
% 16.28/2.97 inference('sup-', [status(thm)],
% 16.28/2.97 [zip_derived_cl21288, zip_derived_cl5841])).
% 16.28/2.97 thf(zip_derived_cl21, plain,
% 16.28/2.97 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 16.28/2.97 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 16.28/2.97 thf(zip_derived_cl21346, plain, ( (equalish @ a @ b)),
% 16.28/2.97 inference('sup-', [status(thm)], [zip_derived_cl21336, zip_derived_cl21])).
% 16.28/2.97 thf(zip_derived_cl21378, plain, ($false),
% 16.28/2.97 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl21346])).
% 16.28/2.97
% 16.28/2.97 % SZS output end Refutation
% 16.28/2.97
% 16.28/2.97
% 16.28/2.97 % Terminating...
% 16.80/3.10 % Runner terminated.
% 16.80/3.11 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------