TSTP Solution File: FLD040-5 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD040-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.P4ZsIPzzU6 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 22:39:22 EDT 2023
% Result : Unsatisfiable 21.43s 3.72s
% Output : Refutation 21.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD040-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.P4ZsIPzzU6 true
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 00:30:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.21/0.36 % Running in FO mode
% 0.22/0.62 % Total configuration time : 435
% 0.22/0.62 % Estimated wc time : 1092
% 0.22/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 20.75/3.71 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 21.43/3.72 % Solved by fo/fo4.sh.
% 21.43/3.72 % done 5112 iterations in 2.854s
% 21.43/3.72 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 21.43/3.72 % SZS output start Refutation
% 21.43/3.72 thf(sum_type, type, sum: $i > $i > $i > $o).
% 21.43/3.72 thf(a_type, type, a: $i).
% 21.43/3.72 thf(add_type, type, add: $i > $i > $i).
% 21.43/3.72 thf(product_type, type, product: $i > $i > $i > $o).
% 21.43/3.72 thf(additive_identity_type, type, additive_identity: $i).
% 21.43/3.72 thf(multiply_type, type, multiply: $i > $i > $i).
% 21.43/3.72 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 21.43/3.72 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 21.43/3.72 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 21.43/3.72 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 21.43/3.72 thf(defined_type, type, defined: $i > $o).
% 21.43/3.72 thf(well_definedness_of_multiplicative_identity, axiom,
% 21.43/3.72 (defined @ multiplicative_identity)).
% 21.43/3.72 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 21.43/3.72 inference('cnf', [status(esa)],
% 21.43/3.72 [well_definedness_of_multiplicative_identity])).
% 21.43/3.72 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 21.43/3.72 inference('cnf', [status(esa)],
% 21.43/3.72 [well_definedness_of_multiplicative_identity])).
% 21.43/3.72 thf(totality_of_order_relation, axiom,
% 21.43/3.72 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 21.43/3.72 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 21.43/3.72 thf(zip_derived_cl22, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (less_or_equal @ X0 @ X1)
% 21.43/3.72 | (less_or_equal @ X1 @ X0)
% 21.43/3.72 | ~ (defined @ X0)
% 21.43/3.72 | ~ (defined @ X1))),
% 21.43/3.72 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 21.43/3.72 thf(zip_derived_cl76, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 (~ (defined @ X0)
% 21.43/3.72 | (less_or_equal @ X0 @ multiplicative_identity)
% 21.43/3.72 | (less_or_equal @ multiplicative_identity @ X0))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl22])).
% 21.43/3.72 thf(zip_derived_cl1838, plain,
% 21.43/3.72 (( (less_or_equal @ multiplicative_identity @ multiplicative_identity)
% 21.43/3.72 | (less_or_equal @ multiplicative_identity @ multiplicative_identity))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl76])).
% 21.43/3.72 thf(zip_derived_cl1843, plain,
% 21.43/3.72 ( (less_or_equal @ multiplicative_identity @ multiplicative_identity)),
% 21.43/3.72 inference('simplify', [status(thm)], [zip_derived_cl1838])).
% 21.43/3.72 thf(antisymmetry_of_order_relation, axiom,
% 21.43/3.72 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 21.43/3.72 ( ~( less_or_equal @ Y @ X ) ))).
% 21.43/3.72 thf(zip_derived_cl20, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (sum @ additive_identity @ X0 @ X1)
% 21.43/3.72 | ~ (less_or_equal @ X0 @ X1)
% 21.43/3.72 | ~ (less_or_equal @ X1 @ X0))),
% 21.43/3.72 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 21.43/3.72 thf(existence_of_identity_addition, axiom,
% 21.43/3.72 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 21.43/3.72 thf(zip_derived_cl2, plain,
% 21.43/3.72 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 21.43/3.72 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 21.43/3.72 thf(zip_derived_cl2, plain,
% 21.43/3.72 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 21.43/3.72 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 21.43/3.72 thf(associativity_addition_1, axiom,
% 21.43/3.72 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 21.43/3.72 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 21.43/3.72 thf(zip_derived_cl0, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2)
% 21.43/3.72 | ~ (sum @ X0 @ X3 @ X4)
% 21.43/3.72 | ~ (sum @ X3 @ X5 @ X1)
% 21.43/3.72 | ~ (sum @ X4 @ X5 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [associativity_addition_1])).
% 21.43/3.72 thf(zip_derived_cl36, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 (~ (sum @ X0 @ X1 @ X0)
% 21.43/3.72 | ~ (sum @ X1 @ X1 @ X2)
% 21.43/3.72 | (sum @ X0 @ X2 @ X0))),
% 21.43/3.72 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 21.43/3.72 thf(zip_derived_cl49, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 (~ (defined @ additive_identity)
% 21.43/3.72 | (sum @ additive_identity @ X0 @ additive_identity)
% 21.43/3.72 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl36])).
% 21.43/3.72 thf(well_definedness_of_additive_identity, axiom,
% 21.43/3.72 (defined @ additive_identity)).
% 21.43/3.72 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 21.43/3.72 thf(zip_derived_cl56, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (sum @ additive_identity @ X0 @ additive_identity)
% 21.43/3.72 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl13])).
% 21.43/3.72 thf(zip_derived_cl63, plain,
% 21.43/3.72 ((~ (defined @ additive_identity)
% 21.43/3.72 | (sum @ additive_identity @ additive_identity @ additive_identity))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl56])).
% 21.43/3.72 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 21.43/3.72 thf(zip_derived_cl67, plain,
% 21.43/3.72 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl13])).
% 21.43/3.72 thf(zip_derived_cl0, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2)
% 21.43/3.72 | ~ (sum @ X0 @ X3 @ X4)
% 21.43/3.72 | ~ (sum @ X3 @ X5 @ X1)
% 21.43/3.72 | ~ (sum @ X4 @ X5 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [associativity_addition_1])).
% 21.43/3.72 thf(zip_derived_cl69, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 (~ (sum @ additive_identity @ X1 @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ X1 @ X2)
% 21.43/3.72 | (sum @ additive_identity @ X2 @ X0))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl0])).
% 21.43/3.72 thf(zip_derived_cl494, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (sum @ additive_identity @ X0 @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ X1 @ X0))),
% 21.43/3.72 inference('eq_fact', [status(thm)], [zip_derived_cl69])).
% 21.43/3.72 thf(zip_derived_cl502, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 (~ (less_or_equal @ X0 @ X1)
% 21.43/3.72 | ~ (less_or_equal @ X1 @ X0)
% 21.43/3.72 | (sum @ additive_identity @ X0 @ X0))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl494])).
% 21.43/3.72 thf(zip_derived_cl2647, plain,
% 21.43/3.72 (( (sum @ additive_identity @ multiplicative_identity @
% 21.43/3.72 multiplicative_identity)
% 21.43/3.72 | ~ (less_or_equal @ multiplicative_identity @ multiplicative_identity))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl1843, zip_derived_cl502])).
% 21.43/3.72 thf(zip_derived_cl1843, plain,
% 21.43/3.72 ( (less_or_equal @ multiplicative_identity @ multiplicative_identity)),
% 21.43/3.72 inference('simplify', [status(thm)], [zip_derived_cl1838])).
% 21.43/3.72 thf(zip_derived_cl2664, plain,
% 21.43/3.72 ( (sum @ additive_identity @ multiplicative_identity @
% 21.43/3.72 multiplicative_identity)),
% 21.43/3.72 inference('demod', [status(thm)],
% 21.43/3.72 [zip_derived_cl2647, zip_derived_cl1843])).
% 21.43/3.72 thf(existence_of_inverse_addition, axiom,
% 21.43/3.72 (( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) |
% 21.43/3.72 ( ~( defined @ X ) ))).
% 21.43/3.72 thf(zip_derived_cl3, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 21.43/3.72 | ~ (defined @ X0))),
% 21.43/3.72 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 21.43/3.72 thf(zip_derived_cl0, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2)
% 21.43/3.72 | ~ (sum @ X0 @ X3 @ X4)
% 21.43/3.72 | ~ (sum @ X3 @ X5 @ X1)
% 21.43/3.72 | ~ (sum @ X4 @ X5 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [associativity_addition_1])).
% 21.43/3.72 thf(zip_derived_cl33, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.43/3.72 (~ (defined @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ X2 @ X1)
% 21.43/3.72 | ~ (sum @ X0 @ X2 @ X3)
% 21.43/3.72 | (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 21.43/3.72 thf(zip_derived_cl959, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (sum @ (additive_inverse @ additive_identity) @ X0 @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ X1 @ X0)
% 21.43/3.72 | ~ (defined @ additive_identity))),
% 21.43/3.72 inference('eq_fact', [status(thm)], [zip_derived_cl33])).
% 21.43/3.72 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 21.43/3.72 thf(zip_derived_cl960, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (sum @ (additive_inverse @ additive_identity) @ X0 @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ X1 @ X0))),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl959, zip_derived_cl13])).
% 21.43/3.72 thf(zip_derived_cl2731, plain,
% 21.43/3.72 ( (sum @ (additive_inverse @ additive_identity) @
% 21.43/3.72 multiplicative_identity @ multiplicative_identity)),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl2664, zip_derived_cl960])).
% 21.43/3.72 thf(commutativity_addition, axiom,
% 21.43/3.72 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 21.43/3.72 thf(zip_derived_cl4, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [commutativity_addition])).
% 21.43/3.72 thf(zip_derived_cl2876, plain,
% 21.43/3.72 ( (sum @ multiplicative_identity @
% 21.43/3.72 (additive_inverse @ additive_identity) @ multiplicative_identity)),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl2731, zip_derived_cl4])).
% 21.43/3.72 thf(zip_derived_cl4, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [commutativity_addition])).
% 21.43/3.72 thf(zip_derived_cl2, plain,
% 21.43/3.72 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 21.43/3.72 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 21.43/3.72 thf(zip_derived_cl152, plain,
% 21.43/3.72 (![X0 : $i]: ( (sum @ X0 @ additive_identity @ X0) | ~ (defined @ X0))),
% 21.43/3.72 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 21.43/3.72 thf(zip_derived_cl0, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2)
% 21.43/3.72 | ~ (sum @ X0 @ X3 @ X4)
% 21.43/3.72 | ~ (sum @ X3 @ X5 @ X1)
% 21.43/3.72 | ~ (sum @ X4 @ X5 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [associativity_addition_1])).
% 21.43/3.72 thf(zip_derived_cl165, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.43/3.72 (~ (defined @ X0)
% 21.43/3.72 | ~ (sum @ X0 @ X2 @ X1)
% 21.43/3.72 | ~ (sum @ additive_identity @ X2 @ X3)
% 21.43/3.72 | (sum @ X0 @ X3 @ X1))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl0])).
% 21.43/3.72 thf(zip_derived_cl5551, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (sum @ multiplicative_identity @ X0 @ multiplicative_identity)
% 21.43/3.72 | ~ (sum @ additive_identity @
% 21.43/3.72 (additive_inverse @ additive_identity) @ X0)
% 21.43/3.72 | ~ (defined @ multiplicative_identity))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl2876, zip_derived_cl165])).
% 21.43/3.72 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 21.43/3.72 inference('cnf', [status(esa)],
% 21.43/3.72 [well_definedness_of_multiplicative_identity])).
% 21.43/3.72 thf(zip_derived_cl5592, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (sum @ multiplicative_identity @ X0 @ multiplicative_identity)
% 21.43/3.72 | ~ (sum @ additive_identity @
% 21.43/3.72 (additive_inverse @ additive_identity) @ X0))),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl5551, zip_derived_cl16])).
% 21.43/3.72 thf(zip_derived_cl67, plain,
% 21.43/3.72 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl13])).
% 21.43/3.72 thf(zip_derived_cl960, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (sum @ (additive_inverse @ additive_identity) @ X0 @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ X1 @ X0))),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl959, zip_derived_cl13])).
% 21.43/3.72 thf(zip_derived_cl1081, plain,
% 21.43/3.72 ( (sum @ (additive_inverse @ additive_identity) @ additive_identity @
% 21.43/3.72 additive_identity)),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl960])).
% 21.43/3.72 thf(zip_derived_cl4, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [commutativity_addition])).
% 21.43/3.72 thf(zip_derived_cl1099, plain,
% 21.43/3.72 ( (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 21.43/3.72 additive_identity)),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl1081, zip_derived_cl4])).
% 21.43/3.72 thf(zip_derived_cl10240, plain,
% 21.43/3.72 ( (sum @ multiplicative_identity @ additive_identity @
% 21.43/3.72 multiplicative_identity)),
% 21.43/3.72 inference('sup+', [status(thm)], [zip_derived_cl5592, zip_derived_cl1099])).
% 21.43/3.72 thf(zip_derived_cl2, plain,
% 21.43/3.72 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 21.43/3.72 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 21.43/3.72 thf(zip_derived_cl0, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2)
% 21.43/3.72 | ~ (sum @ X0 @ X3 @ X4)
% 21.43/3.72 | ~ (sum @ X3 @ X5 @ X1)
% 21.43/3.72 | ~ (sum @ X4 @ X5 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [associativity_addition_1])).
% 21.43/3.72 thf(zip_derived_cl31, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.43/3.72 (~ (defined @ X0)
% 21.43/3.72 | ~ (sum @ X0 @ X2 @ X1)
% 21.43/3.72 | ~ (sum @ X0 @ X2 @ X3)
% 21.43/3.72 | (sum @ additive_identity @ X3 @ X1))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.43/3.72 thf(zip_derived_cl10310, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 21.43/3.72 | ~ (sum @ multiplicative_identity @ additive_identity @ X0)
% 21.43/3.72 | ~ (defined @ multiplicative_identity))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl10240, zip_derived_cl31])).
% 21.43/3.72 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 21.43/3.72 inference('cnf', [status(esa)],
% 21.43/3.72 [well_definedness_of_multiplicative_identity])).
% 21.43/3.72 thf(zip_derived_cl10338, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 21.43/3.72 | ~ (sum @ multiplicative_identity @ additive_identity @ X0))),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl10310, zip_derived_cl16])).
% 21.43/3.72 thf(totality_of_addition, axiom,
% 21.43/3.72 (( sum @ X @ Y @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 21.43/3.72 ( ~( defined @ Y ) ))).
% 21.43/3.72 thf(zip_derived_cl18, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 21.43/3.72 | ~ (defined @ X0)
% 21.43/3.72 | ~ (defined @ X1))),
% 21.43/3.72 inference('cnf', [status(esa)], [totality_of_addition])).
% 21.43/3.72 thf(zip_derived_cl4, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [commutativity_addition])).
% 21.43/3.72 thf(zip_derived_cl602, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 (~ (defined @ X0)
% 21.43/3.72 | ~ (defined @ X1)
% 21.43/3.72 | (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 21.43/3.72 thf(zip_derived_cl18742, plain,
% 21.43/3.72 (( (sum @ additive_identity @
% 21.43/3.72 (add @ additive_identity @ multiplicative_identity) @
% 21.43/3.72 multiplicative_identity)
% 21.43/3.72 | ~ (defined @ additive_identity)
% 21.43/3.72 | ~ (defined @ multiplicative_identity))),
% 21.43/3.72 inference('sup+', [status(thm)], [zip_derived_cl10338, zip_derived_cl602])).
% 21.43/3.72 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 21.43/3.72 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 21.43/3.72 inference('cnf', [status(esa)],
% 21.43/3.72 [well_definedness_of_multiplicative_identity])).
% 21.43/3.72 thf(zip_derived_cl18851, plain,
% 21.43/3.72 ( (sum @ additive_identity @
% 21.43/3.72 (add @ additive_identity @ multiplicative_identity) @
% 21.43/3.72 multiplicative_identity)),
% 21.43/3.72 inference('demod', [status(thm)],
% 21.43/3.72 [zip_derived_cl18742, zip_derived_cl13, zip_derived_cl16])).
% 21.43/3.72 thf(zip_derived_cl67, plain,
% 21.43/3.72 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl13])).
% 21.43/3.72 thf(associativity_addition_2, axiom,
% 21.43/3.72 (( sum @ U @ Z @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 21.43/3.72 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ X @ V @ W ) ))).
% 21.43/3.72 thf(zip_derived_cl1, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2)
% 21.43/3.72 | ~ (sum @ X3 @ X4 @ X0)
% 21.43/3.72 | ~ (sum @ X4 @ X1 @ X5)
% 21.43/3.72 | ~ (sum @ X3 @ X5 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [associativity_addition_2])).
% 21.43/3.72 thf(zip_derived_cl99, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 (~ (sum @ additive_identity @ X1 @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ X2 @ X1)
% 21.43/3.72 | (sum @ additive_identity @ X2 @ X0))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl1])).
% 21.43/3.72 thf(zip_derived_cl19537, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 21.43/3.72 | ~ (sum @ additive_identity @ X0 @
% 21.43/3.72 (add @ additive_identity @ multiplicative_identity)))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl18851, zip_derived_cl99])).
% 21.43/3.72 thf(zip_derived_cl4, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [commutativity_addition])).
% 21.43/3.72 thf(zip_derived_cl20022, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 21.43/3.72 | ~ (sum @ X0 @ additive_identity @
% 21.43/3.72 (add @ additive_identity @ multiplicative_identity)))),
% 21.43/3.72 inference('sup+', [status(thm)], [zip_derived_cl19537, zip_derived_cl4])).
% 21.43/3.72 thf(zip_derived_cl18, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 21.43/3.72 | ~ (defined @ X0)
% 21.43/3.72 | ~ (defined @ X1))),
% 21.43/3.72 inference('cnf', [status(esa)], [totality_of_addition])).
% 21.43/3.72 thf(zip_derived_cl69, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 (~ (sum @ additive_identity @ X1 @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ X1 @ X2)
% 21.43/3.72 | (sum @ additive_identity @ X2 @ X0))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl0])).
% 21.43/3.72 thf(zip_derived_cl612, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 (~ (defined @ X0)
% 21.43/3.72 | ~ (defined @ additive_identity)
% 21.43/3.72 | (sum @ additive_identity @ X1 @ (add @ additive_identity @ X0))
% 21.43/3.72 | ~ (sum @ additive_identity @ X0 @ X1))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl69])).
% 21.43/3.72 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 21.43/3.72 thf(zip_derived_cl644, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 (~ (defined @ X0)
% 21.43/3.72 | (sum @ additive_identity @ X1 @ (add @ additive_identity @ X0))
% 21.43/3.72 | ~ (sum @ additive_identity @ X0 @ X1))),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl612, zip_derived_cl13])).
% 21.43/3.72 thf(zip_derived_cl21298, plain,
% 21.43/3.72 (( (sum @ additive_identity @ additive_identity @ multiplicative_identity)
% 21.43/3.72 | ~ (sum @ additive_identity @ multiplicative_identity @
% 21.43/3.72 additive_identity)
% 21.43/3.72 | ~ (defined @ multiplicative_identity))),
% 21.43/3.72 inference('sup+', [status(thm)], [zip_derived_cl20022, zip_derived_cl644])).
% 21.43/3.72 thf(different_identities, axiom,
% 21.43/3.72 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 21.43/3.72 thf(zip_derived_cl25, plain,
% 21.43/3.72 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [different_identities])).
% 21.43/3.72 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 21.43/3.72 inference('cnf', [status(esa)],
% 21.43/3.72 [well_definedness_of_multiplicative_identity])).
% 21.43/3.72 thf(zip_derived_cl21353, plain,
% 21.43/3.72 (~ (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 21.43/3.72 inference('demod', [status(thm)],
% 21.43/3.72 [zip_derived_cl21298, zip_derived_cl25, zip_derived_cl16])).
% 21.43/3.72 thf(totality_of_multiplication, axiom,
% 21.43/3.72 (( product @ X @ Y @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 21.43/3.72 ( ~( defined @ Y ) ))).
% 21.43/3.72 thf(zip_derived_cl19, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 21.43/3.72 | ~ (defined @ X0)
% 21.43/3.72 | ~ (defined @ X1))),
% 21.43/3.72 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 21.43/3.72 thf(a_is_defined, axiom, (defined @ a)).
% 21.43/3.72 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 21.43/3.72 inference('cnf', [status(esa)], [a_is_defined])).
% 21.43/3.72 thf(existence_of_inverse_multiplication, axiom,
% 21.43/3.72 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 21.43/3.72 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 21.43/3.72 thf(zip_derived_cl8, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 21.43/3.72 multiplicative_identity)
% 21.43/3.72 | (sum @ additive_identity @ X0 @ additive_identity)
% 21.43/3.72 | ~ (defined @ X0))),
% 21.43/3.72 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 21.43/3.72 thf(zip_derived_cl186, plain,
% 21.43/3.72 (( (sum @ additive_identity @ a @ additive_identity)
% 21.43/3.72 | (product @ (multiplicative_inverse @ a) @ a @
% 21.43/3.72 multiplicative_identity))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl8])).
% 21.43/3.72 thf(not_sum_2, conjecture, (sum @ additive_identity @ a @ additive_identity)).
% 21.43/3.72 thf(zf_stmt_0, negated_conjecture,
% 21.43/3.72 (~( sum @ additive_identity @ a @ additive_identity )),
% 21.43/3.72 inference('cnf.neg', [status(esa)], [not_sum_2])).
% 21.43/3.72 thf(zip_derived_cl27, plain,
% 21.43/3.72 (~ (sum @ additive_identity @ a @ additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [zf_stmt_0])).
% 21.43/3.72 thf(zip_derived_cl189, plain,
% 21.43/3.72 ( (product @ (multiplicative_inverse @ a) @ a @ multiplicative_identity)),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl186, zip_derived_cl27])).
% 21.43/3.72 thf(zip_derived_cl2, plain,
% 21.43/3.72 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 21.43/3.72 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 21.43/3.72 thf(zip_derived_cl152, plain,
% 21.43/3.72 (![X0 : $i]: ( (sum @ X0 @ additive_identity @ X0) | ~ (defined @ X0))),
% 21.43/3.72 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 21.43/3.72 thf(sum_3, conjecture,
% 21.43/3.72 (~( sum @
% 21.43/3.72 additive_identity @ ( multiplicative_inverse @ a ) @ additive_identity ))).
% 21.43/3.72 thf(zf_stmt_1, negated_conjecture,
% 21.43/3.72 (sum @
% 21.43/3.72 additive_identity @ ( multiplicative_inverse @ a ) @ additive_identity),
% 21.43/3.72 inference('cnf.neg', [status(esa)], [sum_3])).
% 21.43/3.72 thf(zip_derived_cl28, plain,
% 21.43/3.72 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 21.43/3.72 additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [zf_stmt_1])).
% 21.43/3.72 thf(zip_derived_cl1, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2)
% 21.43/3.72 | ~ (sum @ X3 @ X4 @ X0)
% 21.43/3.72 | ~ (sum @ X4 @ X1 @ X5)
% 21.43/3.72 | ~ (sum @ X3 @ X5 @ X2))),
% 21.43/3.72 inference('cnf', [status(esa)], [associativity_addition_2])).
% 21.43/3.72 thf(zip_derived_cl101, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 (~ (sum @ additive_identity @ X1 @ X0)
% 21.43/3.72 | ~ (sum @ (multiplicative_inverse @ a) @ X2 @ X1)
% 21.43/3.72 | (sum @ additive_identity @ X2 @ X0))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl1])).
% 21.43/3.72 thf(zip_derived_cl174, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 (~ (defined @ (multiplicative_inverse @ a))
% 21.43/3.72 | (sum @ additive_identity @ additive_identity @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl101])).
% 21.43/3.72 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 21.43/3.72 inference('cnf', [status(esa)], [a_is_defined])).
% 21.43/3.72 thf(well_definedness_of_multiplicative_inverse, axiom,
% 21.43/3.72 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 21.43/3.72 ( sum @ additive_identity @ X @ additive_identity ))).
% 21.43/3.72 thf(zip_derived_cl17, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (defined @ (multiplicative_inverse @ X0))
% 21.43/3.72 | ~ (defined @ X0)
% 21.43/3.72 | (sum @ additive_identity @ X0 @ additive_identity))),
% 21.43/3.72 inference('cnf', [status(esa)],
% 21.43/3.72 [well_definedness_of_multiplicative_inverse])).
% 21.43/3.72 thf(zip_derived_cl40, plain,
% 21.43/3.72 (( (sum @ additive_identity @ a @ additive_identity)
% 21.43/3.72 | (defined @ (multiplicative_inverse @ a)))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl17])).
% 21.43/3.72 thf(zip_derived_cl27, plain,
% 21.43/3.72 (~ (sum @ additive_identity @ a @ additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [zf_stmt_0])).
% 21.43/3.72 thf(zip_derived_cl42, plain, ( (defined @ (multiplicative_inverse @ a))),
% 21.43/3.72 inference('clc', [status(thm)], [zip_derived_cl40, zip_derived_cl27])).
% 21.43/3.72 thf(zip_derived_cl181, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 ( (sum @ additive_identity @ additive_identity @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0))),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl174, zip_derived_cl42])).
% 21.43/3.72 thf(zip_derived_cl201, plain,
% 21.43/3.72 ((~ (defined @ (multiplicative_inverse @ a))
% 21.43/3.72 | (sum @ additive_identity @ additive_identity @
% 21.43/3.72 (multiplicative_inverse @ a)))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl181])).
% 21.43/3.72 thf(zip_derived_cl42, plain, ( (defined @ (multiplicative_inverse @ a))),
% 21.43/3.72 inference('clc', [status(thm)], [zip_derived_cl40, zip_derived_cl27])).
% 21.43/3.72 thf(zip_derived_cl205, plain,
% 21.43/3.72 ( (sum @ additive_identity @ additive_identity @
% 21.43/3.72 (multiplicative_inverse @ a))),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl201, zip_derived_cl42])).
% 21.43/3.72 thf(zip_derived_cl494, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (sum @ additive_identity @ X0 @ X0)
% 21.43/3.72 | ~ (sum @ additive_identity @ X1 @ X0))),
% 21.43/3.72 inference('eq_fact', [status(thm)], [zip_derived_cl69])).
% 21.43/3.72 thf(zip_derived_cl506, plain,
% 21.43/3.72 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 21.43/3.72 (multiplicative_inverse @ a))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl205, zip_derived_cl494])).
% 21.43/3.72 thf(distributivity_1, axiom,
% 21.43/3.72 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 21.43/3.72 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 21.43/3.72 ( ~( product @ Y @ Z @ D ) ))).
% 21.43/3.72 thf(zip_derived_cl10, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 21.43/3.72 ( (sum @ X0 @ X1 @ X2)
% 21.43/3.72 | ~ (sum @ X3 @ X4 @ X5)
% 21.43/3.72 | ~ (product @ X5 @ X6 @ X2)
% 21.43/3.72 | ~ (product @ X3 @ X6 @ X0)
% 21.43/3.72 | ~ (product @ X4 @ X6 @ X1))),
% 21.43/3.72 inference('cnf', [status(esa)], [distributivity_1])).
% 21.43/3.72 thf(zip_derived_cl547, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.43/3.72 (~ (product @ (multiplicative_inverse @ a) @ X1 @ X0)
% 21.43/3.72 | ~ (product @ additive_identity @ X1 @ X2)
% 21.43/3.72 | ~ (product @ (multiplicative_inverse @ a) @ X1 @ X3)
% 21.43/3.72 | (sum @ X2 @ X0 @ X3))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl506, zip_derived_cl10])).
% 21.43/3.72 thf(zip_derived_cl16099, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.72 ( (sum @ X2 @ X0 @ X0)
% 21.43/3.72 | ~ (product @ (multiplicative_inverse @ a) @ X1 @ X0)
% 21.43/3.72 | ~ (product @ additive_identity @ X1 @ X2))),
% 21.43/3.72 inference('eq_fact', [status(thm)], [zip_derived_cl547])).
% 21.43/3.72 thf(zip_derived_cl24978, plain,
% 21.43/3.72 (![X0 : $i]:
% 21.43/3.72 (~ (product @ additive_identity @ a @ X0)
% 21.43/3.72 | (sum @ X0 @ multiplicative_identity @ multiplicative_identity))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl16099])).
% 21.43/3.72 thf(zip_derived_cl24982, plain,
% 21.43/3.72 ((~ (defined @ a)
% 21.43/3.72 | ~ (defined @ additive_identity)
% 21.43/3.72 | (sum @ (multiply @ additive_identity @ a) @
% 21.43/3.72 multiplicative_identity @ multiplicative_identity))),
% 21.43/3.72 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl24978])).
% 21.43/3.72 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 21.43/3.72 inference('cnf', [status(esa)], [a_is_defined])).
% 21.43/3.72 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 21.43/3.72 thf(zip_derived_cl24983, plain,
% 21.43/3.72 ( (sum @ (multiply @ additive_identity @ a) @ multiplicative_identity @
% 21.43/3.72 multiplicative_identity)),
% 21.43/3.72 inference('demod', [status(thm)],
% 21.43/3.72 [zip_derived_cl24982, zip_derived_cl26, zip_derived_cl13])).
% 21.43/3.72 thf(zip_derived_cl19, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i]:
% 21.43/3.72 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 21.43/3.72 | ~ (defined @ X0)
% 21.43/3.72 | ~ (defined @ X1))),
% 21.43/3.72 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 21.43/3.72 thf(zip_derived_cl189, plain,
% 21.43/3.72 ( (product @ (multiplicative_inverse @ a) @ a @ multiplicative_identity)),
% 21.43/3.72 inference('demod', [status(thm)], [zip_derived_cl186, zip_derived_cl27])).
% 21.43/3.72 thf(zip_derived_cl28, plain,
% 21.43/3.72 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 21.43/3.72 additive_identity)),
% 21.43/3.72 inference('cnf', [status(esa)], [zf_stmt_1])).
% 21.43/3.72 thf(distributivity_2, axiom,
% 21.43/3.72 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 21.43/3.72 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 21.43/3.72 ( ~( sum @ C @ D @ B ) ))).
% 21.43/3.72 thf(zip_derived_cl11, plain,
% 21.43/3.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 21.43/3.72 ( (product @ X0 @ X1 @ X2)
% 21.43/3.72 | ~ (sum @ X3 @ X4 @ X0)
% 21.43/3.72 | ~ (product @ X3 @ X1 @ X5)
% 21.43/3.72 | ~ (product @ X4 @ X1 @ X6)
% 21.43/3.73 | ~ (sum @ X5 @ X6 @ X2))),
% 21.43/3.73 inference('cnf', [status(esa)], [distributivity_2])).
% 21.43/3.73 thf(zip_derived_cl409, plain,
% 21.43/3.73 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.43/3.73 (~ (sum @ X2 @ X1 @ X0)
% 21.43/3.73 | ~ (product @ (multiplicative_inverse @ a) @ X3 @ X1)
% 21.43/3.73 | ~ (product @ additive_identity @ X3 @ X2)
% 21.43/3.73 | (product @ additive_identity @ X3 @ X0))),
% 21.43/3.73 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl11])).
% 21.43/3.73 thf(zip_derived_cl11834, plain,
% 21.43/3.73 (![X0 : $i, X1 : $i]:
% 21.43/3.73 ( (product @ additive_identity @ a @ X0)
% 21.43/3.73 | ~ (product @ additive_identity @ a @ X1)
% 21.43/3.73 | ~ (sum @ X1 @ multiplicative_identity @ X0))),
% 21.43/3.73 inference('sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl409])).
% 21.43/3.73 thf(zip_derived_cl13534, plain,
% 21.43/3.73 (![X0 : $i]:
% 21.43/3.73 (~ (defined @ a)
% 21.43/3.73 | ~ (defined @ additive_identity)
% 21.43/3.73 | ~ (sum @ (multiply @ additive_identity @ a) @
% 21.43/3.73 multiplicative_identity @ X0)
% 21.43/3.73 | (product @ additive_identity @ a @ X0))),
% 21.43/3.73 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl11834])).
% 21.43/3.73 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 21.43/3.73 inference('cnf', [status(esa)], [a_is_defined])).
% 21.43/3.73 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 21.43/3.73 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 21.43/3.73 thf(zip_derived_cl13536, plain,
% 21.43/3.73 (![X0 : $i]:
% 21.43/3.73 (~ (sum @ (multiply @ additive_identity @ a) @
% 21.43/3.73 multiplicative_identity @ X0)
% 21.43/3.73 | (product @ additive_identity @ a @ X0))),
% 21.43/3.73 inference('demod', [status(thm)],
% 21.43/3.73 [zip_derived_cl13534, zip_derived_cl26, zip_derived_cl13])).
% 21.43/3.73 thf(zip_derived_cl25291, plain,
% 21.43/3.73 ( (product @ additive_identity @ a @ multiplicative_identity)),
% 21.43/3.73 inference('sup-', [status(thm)],
% 21.43/3.73 [zip_derived_cl24983, zip_derived_cl13536])).
% 21.43/3.73 thf(zip_derived_cl24978, plain,
% 21.43/3.73 (![X0 : $i]:
% 21.43/3.73 (~ (product @ additive_identity @ a @ X0)
% 21.43/3.73 | (sum @ X0 @ multiplicative_identity @ multiplicative_identity))),
% 21.43/3.73 inference('sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl16099])).
% 21.43/3.73 thf(zip_derived_cl25316, plain,
% 21.43/3.73 ( (sum @ multiplicative_identity @ multiplicative_identity @
% 21.43/3.73 multiplicative_identity)),
% 21.43/3.73 inference('sup-', [status(thm)],
% 21.43/3.73 [zip_derived_cl25291, zip_derived_cl24978])).
% 21.43/3.73 thf(zip_derived_cl4, plain,
% 21.43/3.73 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.43/3.73 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 21.43/3.73 inference('cnf', [status(esa)], [commutativity_addition])).
% 21.43/3.73 thf(zip_derived_cl3, plain,
% 21.43/3.73 (![X0 : $i]:
% 21.43/3.73 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 21.43/3.73 | ~ (defined @ X0))),
% 21.43/3.73 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 21.43/3.73 thf(zip_derived_cl3, plain,
% 21.43/3.73 (![X0 : $i]:
% 21.43/3.73 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 21.43/3.73 | ~ (defined @ X0))),
% 21.43/3.73 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 21.43/3.73 thf(zip_derived_cl1, plain,
% 21.43/3.73 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 21.43/3.73 ( (sum @ X0 @ X1 @ X2)
% 21.43/3.73 | ~ (sum @ X3 @ X4 @ X0)
% 21.43/3.73 | ~ (sum @ X4 @ X1 @ X5)
% 21.43/3.73 | ~ (sum @ X3 @ X5 @ X2))),
% 21.43/3.73 inference('cnf', [status(esa)], [associativity_addition_2])).
% 21.43/3.73 thf(zip_derived_cl102, plain,
% 21.43/3.73 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.43/3.73 (~ (defined @ X0)
% 21.43/3.73 | ~ (sum @ (additive_inverse @ X0) @ X2 @ X1)
% 21.43/3.73 | ~ (sum @ X0 @ X3 @ X2)
% 21.43/3.73 | (sum @ additive_identity @ X3 @ X1))),
% 21.43/3.73 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 21.43/3.73 thf(zip_derived_cl3603, plain,
% 21.43/3.73 (![X0 : $i, X1 : $i]:
% 21.43/3.73 (~ (defined @ X0)
% 21.43/3.73 | (sum @ additive_identity @ X1 @ additive_identity)
% 21.43/3.73 | ~ (sum @ X0 @ X1 @ X0)
% 21.43/3.73 | ~ (defined @ X0))),
% 21.43/3.73 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl102])).
% 21.43/3.73 thf(zip_derived_cl3608, plain,
% 21.43/3.73 (![X0 : $i, X1 : $i]:
% 21.43/3.73 (~ (sum @ X0 @ X1 @ X0)
% 21.43/3.73 | (sum @ additive_identity @ X1 @ additive_identity)
% 21.43/3.73 | ~ (defined @ X0))),
% 21.43/3.73 inference('simplify', [status(thm)], [zip_derived_cl3603])).
% 21.43/3.73 thf(zip_derived_cl8056, plain,
% 21.43/3.73 (![X0 : $i, X1 : $i]:
% 21.43/3.73 (~ (sum @ X1 @ X0 @ X0)
% 21.43/3.73 | ~ (defined @ X0)
% 21.43/3.73 | (sum @ additive_identity @ X1 @ additive_identity))),
% 21.43/3.73 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl3608])).
% 21.43/3.73 thf(zip_derived_cl25667, plain,
% 21.43/3.73 (( (sum @ additive_identity @ multiplicative_identity @ additive_identity)
% 21.43/3.73 | ~ (defined @ multiplicative_identity))),
% 21.43/3.73 inference('sup-', [status(thm)],
% 21.43/3.73 [zip_derived_cl25316, zip_derived_cl8056])).
% 21.43/3.73 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 21.43/3.73 inference('cnf', [status(esa)],
% 21.43/3.73 [well_definedness_of_multiplicative_identity])).
% 21.43/3.73 thf(zip_derived_cl25700, plain,
% 21.43/3.73 ( (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 21.43/3.73 inference('demod', [status(thm)], [zip_derived_cl25667, zip_derived_cl16])).
% 21.43/3.73 thf(zip_derived_cl25848, plain, ($false),
% 21.43/3.73 inference('demod', [status(thm)],
% 21.43/3.73 [zip_derived_cl21353, zip_derived_cl25700])).
% 21.43/3.73
% 21.43/3.73 % SZS output end Refutation
% 21.43/3.73
% 21.43/3.73
% 21.43/3.73 % Terminating...
% 21.89/3.89 % Runner terminated.
% 21.89/3.89 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------