TSTP Solution File: FLD015-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD015-1 : 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.fD0e1A8pGP true
% Computer : n027.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 22:39:10 EDT 2023
% Result : Unsatisfiable 277.65s 40.81s
% Output : Refutation 277.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD015-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.fD0e1A8pGP true
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon Aug 28 01:03:06 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.16/0.35 % Running portfolio for 300 s
% 0.16/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.35 % Number of cores: 8
% 0.16/0.35 % Python version: Python 3.6.8
% 0.16/0.35 % Running in FO mode
% 0.20/0.64 % Total configuration time : 435
% 0.20/0.64 % Estimated wc time : 1092
% 0.20/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 277.65/40.81 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 277.65/40.81 % Solved by fo/fo5.sh.
% 277.65/40.81 % done 34704 iterations in 39.991s
% 277.65/40.81 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 277.65/40.81 % SZS output start Refutation
% 277.65/40.81 thf(defined_type, type, defined: $i > $o).
% 277.65/40.81 thf(additive_identity_type, type, additive_identity: $i).
% 277.65/40.81 thf(add_type, type, add: $i > $i > $i).
% 277.65/40.81 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 277.65/40.81 thf(b_type, type, b: $i).
% 277.65/40.81 thf(equalish_type, type, equalish: $i > $i > $o).
% 277.65/40.81 thf(a_type, type, a: $i).
% 277.65/40.81 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 277.65/40.81 thf(a_not_equal_to_b_4, conjecture, (equalish @ a @ b)).
% 277.65/40.81 thf(zf_stmt_0, negated_conjecture, (~( equalish @ a @ b )),
% 277.65/40.81 inference('cnf.neg', [status(esa)], [a_not_equal_to_b_4])).
% 277.65/40.81 thf(zip_derived_cl30, plain, (~ (equalish @ a @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [zf_stmt_0])).
% 277.65/40.81 thf(existence_of_inverse_addition, axiom,
% 277.65/40.81 (( equalish @ ( add @ X @ ( additive_inverse @ X ) ) @ additive_identity ) |
% 277.65/40.81 ( ~( defined @ X ) ))).
% 277.65/40.81 thf(zip_derived_cl2, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 ( (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ additive_identity)
% 277.65/40.81 | ~ (defined @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 277.65/40.81 thf(commutativity_addition, axiom,
% 277.65/40.81 (( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) ) | ( ~( defined @ X ) ) |
% 277.65/40.81 ( ~( defined @ Y ) ))).
% 277.65/40.81 thf(zip_derived_cl3, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [commutativity_addition])).
% 277.65/40.81 thf(transitivity_of_equality, axiom,
% 277.65/40.81 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 277.65/40.81 ( ~( equalish @ Y @ Z ) ))).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl99, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 (~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | ~ (equalish @ (add @ X1 @ X0) @ X2)
% 277.65/40.81 | (equalish @ (add @ X0 @ X1) @ X2))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl2370, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | (equalish @ (add @ (additive_inverse @ X0) @ X0) @
% 277.65/40.81 additive_identity)
% 277.65/40.81 | ~ (defined @ (additive_inverse @ X0))
% 277.65/40.81 | ~ (defined @ X0))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl99])).
% 277.65/40.81 thf(zip_derived_cl2395, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ (additive_inverse @ X0))
% 277.65/40.81 | (equalish @ (add @ (additive_inverse @ X0) @ X0) @
% 277.65/40.81 additive_identity)
% 277.65/40.81 | ~ (defined @ X0))),
% 277.65/40.81 inference('simplify', [status(thm)], [zip_derived_cl2370])).
% 277.65/40.81 thf(well_definedness_of_additive_inverse, axiom,
% 277.65/40.81 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 277.65/40.81 thf(zip_derived_cl11, plain,
% 277.65/40.81 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 277.65/40.81 thf(zip_derived_cl2450, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | (equalish @ (add @ (additive_inverse @ X0) @ X0) @
% 277.65/40.81 additive_identity))),
% 277.65/40.81 inference('clc', [status(thm)], [zip_derived_cl2395, zip_derived_cl11])).
% 277.65/40.81 thf(compatibility_of_equality_and_addition, axiom,
% 277.65/40.81 (( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) | ( ~( defined @ Z ) ) |
% 277.65/40.81 ( ~( equalish @ X @ Y ) ))).
% 277.65/40.81 thf(zip_derived_cl23, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2))),
% 277.65/40.81 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 277.65/40.81 thf(zip_derived_cl2458, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | (equalish @ (add @ (add @ (additive_inverse @ X0) @ X0) @ X1) @
% 277.65/40.81 (add @ additive_identity @ X1)))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl2450, zip_derived_cl23])).
% 277.65/40.81 thf(zip_derived_cl11, plain,
% 277.65/40.81 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 277.65/40.81 thf(well_definedness_of_addition, axiom,
% 277.65/40.81 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 277.65/40.81 ( ~( defined @ Y ) ))).
% 277.65/40.81 thf(zip_derived_cl9, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 277.65/40.81 thf(additive_inverse_equals_additive_inverse_3, conjecture,
% 277.65/40.81 (~( equalish @ ( additive_inverse @ a ) @ ( additive_inverse @ b ) ))).
% 277.65/40.81 thf(zf_stmt_1, negated_conjecture,
% 277.65/40.81 (equalish @ ( additive_inverse @ a ) @ ( additive_inverse @ b )),
% 277.65/40.81 inference('cnf.neg', [status(esa)],
% 277.65/40.81 [additive_inverse_equals_additive_inverse_3])).
% 277.65/40.81 thf(zip_derived_cl29, plain,
% 277.65/40.81 ( (equalish @ (additive_inverse @ a) @ (additive_inverse @ b))),
% 277.65/40.81 inference('cnf', [status(esa)], [zf_stmt_1])).
% 277.65/40.81 thf(symmetry_of_equality, axiom,
% 277.65/40.81 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 277.65/40.81 thf(zip_derived_cl21, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 277.65/40.81 thf(zip_derived_cl34, plain,
% 277.65/40.81 ( (equalish @ (additive_inverse @ b) @ (additive_inverse @ a))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl23, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2))),
% 277.65/40.81 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 277.65/40.81 thf(zip_derived_cl1064, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | (equalish @ (add @ (additive_inverse @ b) @ X0) @
% 277.65/40.81 (add @ (additive_inverse @ a) @ X0)))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl23])).
% 277.65/40.81 thf(zip_derived_cl11, plain,
% 277.65/40.81 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 277.65/40.81 thf(associativity_addition, axiom,
% 277.65/40.81 (( equalish @ ( add @ X @ ( add @ Y @ Z ) ) @ ( add @ ( add @ X @ Y ) @ Z ) ) |
% 277.65/40.81 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ) | ( ~( defined @ Z ) ))).
% 277.65/40.81 thf(zip_derived_cl0, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ (add @ X0 @ (add @ X1 @ X2)) @
% 277.65/40.81 (add @ (add @ X0 @ X1) @ X2))
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X2))),
% 277.65/40.81 inference('cnf', [status(esa)], [associativity_addition])).
% 277.65/40.81 thf(zip_derived_cl21, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 277.65/40.81 thf(zip_derived_cl33, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X2)
% 277.65/40.81 | (equalish @ (add @ (add @ X2 @ X1) @ X0) @
% 277.65/40.81 (add @ X2 @ (add @ X1 @ X0))))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl99, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 (~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | ~ (equalish @ (add @ X1 @ X0) @ X2)
% 277.65/40.81 | (equalish @ (add @ X0 @ X1) @ X2))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl2369, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 (~ (defined @ X2)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | (equalish @ (add @ X0 @ (add @ X2 @ X1)) @
% 277.65/40.81 (add @ X2 @ (add @ X1 @ X0)))
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ (add @ X2 @ X1)))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl99])).
% 277.65/40.81 thf(zip_derived_cl2394, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 (~ (defined @ (add @ X2 @ X1))
% 277.65/40.81 | (equalish @ (add @ X0 @ (add @ X2 @ X1)) @
% 277.65/40.81 (add @ X2 @ (add @ X1 @ X0)))
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X2))),
% 277.65/40.81 inference('simplify', [status(thm)], [zip_derived_cl2369])).
% 277.65/40.81 thf(zip_derived_cl9, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 277.65/40.81 thf(zip_derived_cl121580, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 (~ (defined @ X2)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | (equalish @ (add @ X0 @ (add @ X2 @ X1)) @
% 277.65/40.81 (add @ X2 @ (add @ X1 @ X0))))),
% 277.65/40.81 inference('clc', [status(thm)], [zip_derived_cl2394, zip_derived_cl9])).
% 277.65/40.81 thf(zip_derived_cl11, plain,
% 277.65/40.81 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 277.65/40.81 thf(zip_derived_cl9, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 277.65/40.81 thf(totality_of_order_relation, axiom,
% 277.65/40.81 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 277.65/40.81 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 277.65/40.81 thf(zip_derived_cl17, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 ( (less_or_equal @ X0 @ X1)
% 277.65/40.81 | (less_or_equal @ X1 @ X0)
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 277.65/40.81 thf(b_is_defined, axiom, (defined @ b)).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl778, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | (less_or_equal @ X0 @ b)
% 277.65/40.81 | (less_or_equal @ b @ X0))),
% 277.65/40.81 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl28])).
% 277.65/40.81 thf(zip_derived_cl4420, plain,
% 277.65/40.81 (( (less_or_equal @ b @ b) | ~ (defined @ b))),
% 277.65/40.81 inference('eq_fact', [status(thm)], [zip_derived_cl778])).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl4421, plain, ( (less_or_equal @ b @ b)),
% 277.65/40.81 inference('demod', [status(thm)], [zip_derived_cl4420, zip_derived_cl28])).
% 277.65/40.81 thf(antisymmetry_of_order_relation, axiom,
% 277.65/40.81 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 277.65/40.81 ( ~( less_or_equal @ Y @ X ) ))).
% 277.65/40.81 thf(zip_derived_cl15, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (less_or_equal @ X0 @ X1)
% 277.65/40.81 | ~ (less_or_equal @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 277.65/40.81 thf(zip_derived_cl4433, plain,
% 277.65/40.81 ((~ (less_or_equal @ b @ b) | (equalish @ b @ b))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl4421, zip_derived_cl15])).
% 277.65/40.81 thf(zip_derived_cl4421, plain, ( (less_or_equal @ b @ b)),
% 277.65/40.81 inference('demod', [status(thm)], [zip_derived_cl4420, zip_derived_cl28])).
% 277.65/40.81 thf(zip_derived_cl4436, plain, ( (equalish @ b @ b)),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl4433, zip_derived_cl4421])).
% 277.65/40.81 thf(zip_derived_cl23, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2))),
% 277.65/40.81 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 277.65/40.81 thf(zip_derived_cl4462, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0) | (equalish @ (add @ b @ X0) @ (add @ b @ X0)))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl4436, zip_derived_cl23])).
% 277.65/40.81 thf(zip_derived_cl33, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X2)
% 277.65/40.81 | (equalish @ (add @ (add @ X2 @ X1) @ X0) @
% 277.65/40.81 (add @ X2 @ (add @ X1 @ X0))))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl2, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 ( (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ additive_identity)
% 277.65/40.81 | ~ (defined @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 277.65/40.81 thf(zip_derived_cl21, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 277.65/40.81 thf(zip_derived_cl65, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | (equalish @ additive_identity @
% 277.65/40.81 (add @ X0 @ (additive_inverse @ X0))))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl23, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2))),
% 277.65/40.81 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 277.65/40.81 thf(zip_derived_cl1044, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | (equalish @ (add @ additive_identity @ X1) @
% 277.65/40.81 (add @ (add @ X0 @ (additive_inverse @ X0)) @ X1)))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl23])).
% 277.65/40.81 thf(zip_derived_cl17, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 ( (less_or_equal @ X0 @ X1)
% 277.65/40.81 | (less_or_equal @ X1 @ X0)
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 277.65/40.81 thf(a_is_defined, axiom, (defined @ a)).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl777, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | (less_or_equal @ X0 @ a)
% 277.65/40.81 | (less_or_equal @ a @ X0))),
% 277.65/40.81 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl2955, plain,
% 277.65/40.81 (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 277.65/40.81 inference('eq_fact', [status(thm)], [zip_derived_cl777])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl2956, plain, ( (less_or_equal @ a @ a)),
% 277.65/40.81 inference('demod', [status(thm)], [zip_derived_cl2955, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl15, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (less_or_equal @ X0 @ X1)
% 277.65/40.81 | ~ (less_or_equal @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 277.65/40.81 thf(zip_derived_cl2967, plain,
% 277.65/40.81 ((~ (less_or_equal @ a @ a) | (equalish @ a @ a))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl2956, zip_derived_cl15])).
% 277.65/40.81 thf(zip_derived_cl2956, plain, ( (less_or_equal @ a @ a)),
% 277.65/40.81 inference('demod', [status(thm)], [zip_derived_cl2955, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl2970, plain, ( (equalish @ a @ a)),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl2967, zip_derived_cl2956])).
% 277.65/40.81 thf(existence_of_identity_addition, axiom,
% 277.65/40.81 (( equalish @ ( add @ additive_identity @ X ) @ X ) | ( ~( defined @ X ) ))).
% 277.65/40.81 thf(zip_derived_cl1, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl46, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (equalish @ X0 @ X1)
% 277.65/40.81 | (equalish @ (add @ additive_identity @ X0) @ X1))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl2981, plain,
% 277.65/40.81 (( (equalish @ (add @ additive_identity @ a) @ a) | ~ (defined @ a))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl2970, zip_derived_cl46])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl2991, plain,
% 277.65/40.81 ( (equalish @ (add @ additive_identity @ a) @ a)),
% 277.65/40.81 inference('demod', [status(thm)], [zip_derived_cl2981, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl21, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 277.65/40.81 thf(zip_derived_cl3029, plain,
% 277.65/40.81 ( (equalish @ a @ (add @ additive_identity @ a))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl2991, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl3121, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (equalish @ (add @ additive_identity @ a) @ X0)
% 277.65/40.81 | (equalish @ a @ X0))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl3029, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl35430, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ a)
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | (equalish @ a @ (add @ (add @ X0 @ (additive_inverse @ X0)) @ a)))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl1044, zip_derived_cl3121])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl35456, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | (equalish @ a @ (add @ (add @ X0 @ (additive_inverse @ X0)) @ a)))),
% 277.65/40.81 inference('demod', [status(thm)], [zip_derived_cl35430, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl280528, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (equalish @ (add @ (add @ X0 @ (additive_inverse @ X0)) @ a) @ X1)
% 277.65/40.81 | (equalish @ a @ X1))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl35456, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl280655, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ (additive_inverse @ X0))
% 277.65/40.81 | ~ (defined @ a)
% 277.65/40.81 | (equalish @ a @ (add @ X0 @ (add @ (additive_inverse @ X0) @ a)))
% 277.65/40.81 | ~ (defined @ X0))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl280528])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl280684, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ (additive_inverse @ X0))
% 277.65/40.81 | (equalish @ a @ (add @ X0 @ (add @ (additive_inverse @ X0) @ a)))
% 277.65/40.81 | ~ (defined @ X0))),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl280655, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl280685, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 ( (equalish @ a @ (add @ X0 @ (add @ (additive_inverse @ X0) @ a)))
% 277.65/40.81 | ~ (defined @ (additive_inverse @ X0))
% 277.65/40.81 | ~ (defined @ X0))),
% 277.65/40.81 inference('simplify', [status(thm)], [zip_derived_cl280684])).
% 277.65/40.81 thf(zip_derived_cl11, plain,
% 277.65/40.81 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 277.65/40.81 thf(zip_derived_cl280822, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | (equalish @ a @ (add @ X0 @ (add @ (additive_inverse @ X0) @ a))))),
% 277.65/40.81 inference('clc', [status(thm)], [zip_derived_cl280685, zip_derived_cl11])).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl280838, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (equalish @ (add @ X0 @ (add @ (additive_inverse @ X0) @ a)) @ X1)
% 277.65/40.81 | (equalish @ a @ X1))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl280822, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl281099, plain,
% 277.65/40.81 ((~ (defined @ (add @ (additive_inverse @ b) @ a))
% 277.65/40.81 | (equalish @ a @ (add @ b @ (add @ (additive_inverse @ b) @ a)))
% 277.65/40.81 | ~ (defined @ b))),
% 277.65/40.81 inference('sup-', [status(thm)],
% 277.65/40.81 [zip_derived_cl4462, zip_derived_cl280838])).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl281173, plain,
% 277.65/40.81 ((~ (defined @ (add @ (additive_inverse @ b) @ a))
% 277.65/40.81 | (equalish @ a @ (add @ b @ (add @ (additive_inverse @ b) @ a))))),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl281099, zip_derived_cl28])).
% 277.65/40.81 thf(zip_derived_cl286572, plain,
% 277.65/40.81 ((~ (defined @ a)
% 277.65/40.81 | ~ (defined @ (additive_inverse @ b))
% 277.65/40.81 | (equalish @ a @ (add @ b @ (add @ (additive_inverse @ b) @ a))))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl281173])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl286573, plain,
% 277.65/40.81 ((~ (defined @ (additive_inverse @ b))
% 277.65/40.81 | (equalish @ a @ (add @ b @ (add @ (additive_inverse @ b) @ a))))),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl286572, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl286876, plain,
% 277.65/40.81 ((~ (defined @ b)
% 277.65/40.81 | (equalish @ a @ (add @ b @ (add @ (additive_inverse @ b) @ a))))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl286573])).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl286877, plain,
% 277.65/40.81 ( (equalish @ a @ (add @ b @ (add @ (additive_inverse @ b) @ a)))),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl286876, zip_derived_cl28])).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl286893, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (equalish @ (add @ b @ (add @ (additive_inverse @ b) @ a)) @ X0)
% 277.65/40.81 | (equalish @ a @ X0))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl286877, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl287034, plain,
% 277.65/40.81 ((~ (defined @ b)
% 277.65/40.81 | ~ (defined @ a)
% 277.65/40.81 | ~ (defined @ (additive_inverse @ b))
% 277.65/40.81 | (equalish @ a @ (add @ (additive_inverse @ b) @ (add @ a @ b))))),
% 277.65/40.81 inference('sup-', [status(thm)],
% 277.65/40.81 [zip_derived_cl121580, zip_derived_cl286893])).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl287063, plain,
% 277.65/40.81 ((~ (defined @ (additive_inverse @ b))
% 277.65/40.81 | (equalish @ a @ (add @ (additive_inverse @ b) @ (add @ a @ b))))),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl287034, zip_derived_cl28, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl287073, plain,
% 277.65/40.81 ((~ (defined @ b)
% 277.65/40.81 | (equalish @ a @ (add @ (additive_inverse @ b) @ (add @ a @ b))))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl287063])).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl287074, plain,
% 277.65/40.81 ( (equalish @ a @ (add @ (additive_inverse @ b) @ (add @ a @ b)))),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl287073, zip_derived_cl28])).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl288181, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (equalish @ (add @ (additive_inverse @ b) @ (add @ a @ b)) @ X0)
% 277.65/40.81 | (equalish @ a @ X0))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl287074, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl288327, plain,
% 277.65/40.81 ((~ (defined @ (add @ a @ b))
% 277.65/40.81 | (equalish @ a @ (add @ (additive_inverse @ a) @ (add @ a @ b))))),
% 277.65/40.81 inference('sup-', [status(thm)],
% 277.65/40.81 [zip_derived_cl1064, zip_derived_cl288181])).
% 277.65/40.81 thf(zip_derived_cl288346, plain,
% 277.65/40.81 ((~ (defined @ b)
% 277.65/40.81 | ~ (defined @ a)
% 277.65/40.81 | (equalish @ a @ (add @ (additive_inverse @ a) @ (add @ a @ b))))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl288327])).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl288347, plain,
% 277.65/40.81 ( (equalish @ a @ (add @ (additive_inverse @ a) @ (add @ a @ b)))),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl288346, zip_derived_cl28, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl21, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 277.65/40.81 thf(zip_derived_cl288362, plain,
% 277.65/40.81 ( (equalish @ (add @ (additive_inverse @ a) @ (add @ a @ b)) @ a)),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl288347, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl33, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X2)
% 277.65/40.81 | (equalish @ (add @ (add @ X2 @ X1) @ X0) @
% 277.65/40.81 (add @ X2 @ (add @ X1 @ X0))))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl48, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 277.65/40.81 (~ (defined @ X2)
% 277.65/40.81 | ~ (defined @ X1)
% 277.65/40.81 | ~ (defined @ X0)
% 277.65/40.81 | ~ (equalish @ (add @ X2 @ (add @ X1 @ X0)) @ X3)
% 277.65/40.81 | (equalish @ (add @ (add @ X2 @ X1) @ X0) @ X3))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl288476, plain,
% 277.65/40.81 (( (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a)
% 277.65/40.81 | ~ (defined @ b)
% 277.65/40.81 | ~ (defined @ a)
% 277.65/40.81 | ~ (defined @ (additive_inverse @ a)))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl288362, zip_derived_cl48])).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl288477, plain,
% 277.65/40.81 (( (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a)
% 277.65/40.81 | ~ (defined @ (additive_inverse @ a)))),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl288476, zip_derived_cl28, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl288478, plain,
% 277.65/40.81 ((~ (defined @ a)
% 277.65/40.81 | (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl288477])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl288479, plain,
% 277.65/40.81 ( (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ a)),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl288478, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl21, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 277.65/40.81 thf(zip_derived_cl288494, plain,
% 277.65/40.81 ( (equalish @ a @ (add @ (add @ (additive_inverse @ a) @ a) @ b))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl288479, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl288744, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (equalish @ (add @ (add @ (additive_inverse @ a) @ a) @ b) @ X0)
% 277.65/40.81 | (equalish @ a @ X0))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl288494, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl290488, plain,
% 277.65/40.81 ((~ (defined @ b)
% 277.65/40.81 | ~ (defined @ a)
% 277.65/40.81 | (equalish @ a @ (add @ additive_identity @ b)))),
% 277.65/40.81 inference('sup-', [status(thm)],
% 277.65/40.81 [zip_derived_cl2458, zip_derived_cl288744])).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 277.65/40.81 inference('cnf', [status(esa)], [a_is_defined])).
% 277.65/40.81 thf(zip_derived_cl290513, plain,
% 277.65/40.81 ( (equalish @ a @ (add @ additive_identity @ b))),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl290488, zip_derived_cl28, zip_derived_cl27])).
% 277.65/40.81 thf(zip_derived_cl21, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 277.65/40.81 thf(zip_derived_cl290532, plain,
% 277.65/40.81 ( (equalish @ (add @ additive_identity @ b) @ a)),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl290513, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl4436, plain, ( (equalish @ b @ b)),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl4433, zip_derived_cl4421])).
% 277.65/40.81 thf(zip_derived_cl46, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]:
% 277.65/40.81 (~ (defined @ X0)
% 277.65/40.81 | ~ (equalish @ X0 @ X1)
% 277.65/40.81 | (equalish @ (add @ additive_identity @ X0) @ X1))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl4455, plain,
% 277.65/40.81 (( (equalish @ (add @ additive_identity @ b) @ b) | ~ (defined @ b))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl4436, zip_derived_cl46])).
% 277.65/40.81 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 277.65/40.81 inference('cnf', [status(esa)], [b_is_defined])).
% 277.65/40.81 thf(zip_derived_cl4465, plain,
% 277.65/40.81 ( (equalish @ (add @ additive_identity @ b) @ b)),
% 277.65/40.81 inference('demod', [status(thm)], [zip_derived_cl4455, zip_derived_cl28])).
% 277.65/40.81 thf(zip_derived_cl21, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 277.65/40.81 thf(zip_derived_cl4504, plain,
% 277.65/40.81 ( (equalish @ b @ (add @ additive_identity @ b))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl4465, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl22, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 277.65/40.81 ( (equalish @ X0 @ X1)
% 277.65/40.81 | ~ (equalish @ X0 @ X2)
% 277.65/40.81 | ~ (equalish @ X2 @ X1))),
% 277.65/40.81 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 277.65/40.81 thf(zip_derived_cl4605, plain,
% 277.65/40.81 (![X0 : $i]:
% 277.65/40.81 (~ (equalish @ (add @ additive_identity @ b) @ X0)
% 277.65/40.81 | (equalish @ b @ X0))),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl4504, zip_derived_cl22])).
% 277.65/40.81 thf(zip_derived_cl290656, plain, ( (equalish @ b @ a)),
% 277.65/40.81 inference('sup-', [status(thm)],
% 277.65/40.81 [zip_derived_cl290532, zip_derived_cl4605])).
% 277.65/40.81 thf(zip_derived_cl21, plain,
% 277.65/40.81 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 277.65/40.81 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 277.65/40.81 thf(zip_derived_cl290685, plain, ( (equalish @ a @ b)),
% 277.65/40.81 inference('sup-', [status(thm)], [zip_derived_cl290656, zip_derived_cl21])).
% 277.65/40.81 thf(zip_derived_cl291000, plain, ($false),
% 277.65/40.81 inference('demod', [status(thm)],
% 277.65/40.81 [zip_derived_cl30, zip_derived_cl290685])).
% 277.65/40.81
% 277.65/40.81 % SZS output end Refutation
% 277.65/40.81
% 277.65/40.81
% 277.65/40.82 % Terminating...
% 277.83/40.94 % Runner terminated.
% 277.83/40.96 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------