TSTP Solution File: FLD026-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD026-3 : 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.SoejZ3JM8n true
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 22:39:15 EDT 2023
% Result : Unsatisfiable 45.42s 7.15s
% Output : Refutation 45.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : FLD026-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.SoejZ3JM8n true
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 00:37:12 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in FO mode
% 0.23/0.69 % Total configuration time : 435
% 0.23/0.69 % Estimated wc time : 1092
% 0.23/0.69 % Estimated cpu time (7 cpus) : 156.0
% 0.23/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 1.15/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.15/0.77 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.15/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.15/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.15/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.34/0.79 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 45.42/7.15 % Solved by fo/fo5.sh.
% 45.42/7.15 % done 10855 iterations in 6.331s
% 45.42/7.15 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 45.42/7.15 % SZS output start Refutation
% 45.42/7.15 thf(sum_type, type, sum: $i > $i > $i > $o).
% 45.42/7.15 thf(b_type, type, b: $i).
% 45.42/7.15 thf(a_type, type, a: $i).
% 45.42/7.15 thf(product_type, type, product: $i > $i > $i > $o).
% 45.42/7.15 thf(additive_identity_type, type, additive_identity: $i).
% 45.42/7.15 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 45.42/7.15 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 45.42/7.15 thf(defined_type, type, defined: $i > $o).
% 45.42/7.15 thf(not_sum_3, conjecture, (sum @ additive_identity @ a @ additive_identity)).
% 45.42/7.15 thf(zf_stmt_0, negated_conjecture,
% 45.42/7.15 (~( sum @ additive_identity @ a @ additive_identity )),
% 45.42/7.15 inference('cnf.neg', [status(esa)], [not_sum_3])).
% 45.42/7.15 thf(zip_derived_cl28, plain,
% 45.42/7.15 (~ (sum @ additive_identity @ a @ additive_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 45.42/7.15 thf(existence_of_inverse_multiplication, axiom,
% 45.42/7.15 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 45.42/7.15 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 45.42/7.15 thf(zip_derived_cl8, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 45.42/7.15 multiplicative_identity)
% 45.42/7.15 | (sum @ additive_identity @ X0 @ additive_identity)
% 45.42/7.15 | ~ (defined @ X0))),
% 45.42/7.15 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 45.42/7.15 thf(existence_of_identity_addition, axiom,
% 45.42/7.15 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 45.42/7.15 thf(zip_derived_cl2, plain,
% 45.42/7.15 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 45.42/7.15 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 45.42/7.15 thf(zip_derived_cl2, plain,
% 45.42/7.15 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 45.42/7.15 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 45.42/7.15 thf(zip_derived_cl2, plain,
% 45.42/7.15 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 45.42/7.15 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 45.42/7.15 thf(associativity_addition_1, axiom,
% 45.42/7.15 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 45.42/7.15 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 45.42/7.15 thf(zip_derived_cl0, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (sum @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (sum @ X0 @ X3 @ X4)
% 45.42/7.15 | ~ (sum @ X3 @ X5 @ X1)
% 45.42/7.15 | ~ (sum @ X4 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_addition_1])).
% 45.42/7.15 thf(zip_derived_cl33, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 (~ (sum @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (sum @ X1 @ X1 @ X0)
% 45.42/7.15 | (sum @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 45.42/7.15 thf(zip_derived_cl35, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (sum @ X0 @ additive_identity @ X0)
% 45.42/7.15 | ~ (sum @ X0 @ X0 @ additive_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl33])).
% 45.42/7.15 thf(zip_derived_cl38, plain,
% 45.42/7.15 ((~ (defined @ additive_identity)
% 45.42/7.15 | (sum @ additive_identity @ additive_identity @ additive_identity)
% 45.42/7.15 | ~ (defined @ additive_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl35])).
% 45.42/7.15 thf(well_definedness_of_additive_identity, axiom,
% 45.42/7.15 (defined @ additive_identity)).
% 45.42/7.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 45.42/7.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 45.42/7.15 thf(zip_derived_cl40, plain,
% 45.42/7.15 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl38, zip_derived_cl13, zip_derived_cl13])).
% 45.42/7.15 thf(zip_derived_cl0, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (sum @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (sum @ X0 @ X3 @ X4)
% 45.42/7.15 | ~ (sum @ X3 @ X5 @ X1)
% 45.42/7.15 | ~ (sum @ X4 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_addition_1])).
% 45.42/7.15 thf(zip_derived_cl42, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 (~ (sum @ additive_identity @ X1 @ X0)
% 45.42/7.15 | ~ (sum @ additive_identity @ X1 @ X2)
% 45.42/7.15 | (sum @ additive_identity @ X2 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl0])).
% 45.42/7.15 thf(zip_derived_cl46, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (sum @ additive_identity @ X1 @ X0)
% 45.42/7.15 | ~ (sum @ additive_identity @ X0 @ X1))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl42])).
% 45.42/7.15 thf(zip_derived_cl115, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 45.42/7.15 multiplicative_identity)
% 45.42/7.15 | (sum @ additive_identity @ additive_identity @ X0)
% 45.42/7.15 | ~ (defined @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl46])).
% 45.42/7.15 thf(zip_derived_cl121, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (sum @ additive_identity @ additive_identity @ X0)
% 45.42/7.15 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 45.42/7.15 multiplicative_identity)
% 45.42/7.15 | ~ (defined @ X0))),
% 45.42/7.15 inference('simplify', [status(thm)], [zip_derived_cl115])).
% 45.42/7.15 thf(existence_of_identity_multiplication, axiom,
% 45.42/7.15 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 45.42/7.15 thf(zip_derived_cl7, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 45.42/7.15 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 45.42/7.15 thf(commutativity_multiplication, axiom,
% 45.42/7.15 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 45.42/7.15 thf(zip_derived_cl9, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 45.42/7.15 thf(zip_derived_cl57, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl7, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 45.42/7.15 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 45.42/7.15 thf(associativity_multiplication_1, axiom,
% 45.42/7.15 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 45.42/7.15 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 45.42/7.15 thf(zip_derived_cl5, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (product @ X0 @ X3 @ X4)
% 45.42/7.15 | ~ (product @ X3 @ X5 @ X1)
% 45.42/7.15 | ~ (product @ X4 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 45.42/7.15 thf(zip_derived_cl106, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | ~ (product @ X0 @ X2 @ X1)
% 45.42/7.15 | ~ (product @ X0 @ X2 @ X3)
% 45.42/7.15 | (product @ multiplicative_identity @ X3 @ X1))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 45.42/7.15 thf(zip_derived_cl1753, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (product @ multiplicative_identity @ X1 @ X0)
% 45.42/7.15 | ~ (product @ X0 @ multiplicative_identity @ X1)
% 45.42/7.15 | ~ (defined @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl106])).
% 45.42/7.15 thf(zip_derived_cl1814, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 (~ (product @ X0 @ multiplicative_identity @ X1)
% 45.42/7.15 | (product @ multiplicative_identity @ X1 @ X0)
% 45.42/7.15 | ~ (defined @ X0))),
% 45.42/7.15 inference('simplify', [status(thm)], [zip_derived_cl1753])).
% 45.42/7.15 thf(zip_derived_cl2151, plain,
% 45.42/7.15 ((~ (defined @ multiplicative_identity)
% 45.42/7.15 | (sum @ additive_identity @ additive_identity @
% 45.42/7.15 multiplicative_identity)
% 45.42/7.15 | ~ (defined @ (multiplicative_inverse @ multiplicative_identity))
% 45.42/7.15 | (product @ multiplicative_identity @ multiplicative_identity @
% 45.42/7.15 (multiplicative_inverse @ multiplicative_identity)))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl121, zip_derived_cl1814])).
% 45.42/7.15 thf(well_definedness_of_multiplicative_identity, axiom,
% 45.42/7.15 (defined @ multiplicative_identity)).
% 45.42/7.15 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 45.42/7.15 inference('cnf', [status(esa)],
% 45.42/7.15 [well_definedness_of_multiplicative_identity])).
% 45.42/7.15 thf(different_identities, axiom,
% 45.42/7.15 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 45.42/7.15 thf(zip_derived_cl25, plain,
% 45.42/7.15 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [different_identities])).
% 45.42/7.15 thf(well_definedness_of_multiplicative_inverse, axiom,
% 45.42/7.15 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 45.42/7.15 ( sum @ additive_identity @ X @ additive_identity ))).
% 45.42/7.15 thf(zip_derived_cl17, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (defined @ (multiplicative_inverse @ X0))
% 45.42/7.15 | ~ (defined @ X0)
% 45.42/7.15 | (sum @ additive_identity @ X0 @ additive_identity))),
% 45.42/7.15 inference('cnf', [status(esa)],
% 45.42/7.15 [well_definedness_of_multiplicative_inverse])).
% 45.42/7.15 thf(zip_derived_cl46, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (sum @ additive_identity @ X1 @ X0)
% 45.42/7.15 | ~ (sum @ additive_identity @ X0 @ X1))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl42])).
% 45.42/7.15 thf(zip_derived_cl116, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (defined @ (multiplicative_inverse @ X0))
% 45.42/7.15 | (sum @ additive_identity @ additive_identity @ X0)
% 45.42/7.15 | ~ (defined @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl46])).
% 45.42/7.15 thf(zip_derived_cl122, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (sum @ additive_identity @ additive_identity @ X0)
% 45.42/7.15 | (defined @ (multiplicative_inverse @ X0))
% 45.42/7.15 | ~ (defined @ X0))),
% 45.42/7.15 inference('simplify', [status(thm)], [zip_derived_cl116])).
% 45.42/7.15 thf(zip_derived_cl25, plain,
% 45.42/7.15 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [different_identities])).
% 45.42/7.15 thf(zip_derived_cl205, plain,
% 45.42/7.15 ((~ (defined @ multiplicative_identity)
% 45.42/7.15 | (defined @ (multiplicative_inverse @ multiplicative_identity)))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl25])).
% 45.42/7.15 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 45.42/7.15 inference('cnf', [status(esa)],
% 45.42/7.15 [well_definedness_of_multiplicative_identity])).
% 45.42/7.15 thf(zip_derived_cl207, plain,
% 45.42/7.15 ( (defined @ (multiplicative_inverse @ multiplicative_identity))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl205, zip_derived_cl16])).
% 45.42/7.15 thf(zip_derived_cl2159, plain,
% 45.42/7.15 ( (product @ multiplicative_identity @ multiplicative_identity @
% 45.42/7.15 (multiplicative_inverse @ multiplicative_identity))),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl2151, zip_derived_cl16, zip_derived_cl25,
% 45.42/7.15 zip_derived_cl207])).
% 45.42/7.15 thf(zip_derived_cl57, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl7, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 45.42/7.15 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 45.42/7.15 thf(product_4, conjecture, (~( product @ multiplicative_identity @ a @ b ))).
% 45.42/7.15 thf(zf_stmt_1, negated_conjecture,
% 45.42/7.15 (product @ multiplicative_identity @ a @ b),
% 45.42/7.15 inference('cnf.neg', [status(esa)], [product_4])).
% 45.42/7.15 thf(zip_derived_cl29, plain, ( (product @ multiplicative_identity @ a @ b)),
% 45.42/7.15 inference('cnf', [status(esa)], [zf_stmt_1])).
% 45.42/7.15 thf(associativity_multiplication_2, axiom,
% 45.42/7.15 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 45.42/7.15 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 45.42/7.15 thf(zip_derived_cl6, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (product @ X3 @ X4 @ X0)
% 45.42/7.15 | ~ (product @ X4 @ X1 @ X5)
% 45.42/7.15 | ~ (product @ X3 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 45.42/7.15 thf(zip_derived_cl169, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 (~ (product @ multiplicative_identity @ X1 @ X0)
% 45.42/7.15 | ~ (product @ a @ X2 @ X1)
% 45.42/7.15 | (product @ b @ X2 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl6])).
% 45.42/7.15 thf(zip_derived_cl289, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (product @ b @ X1 @ X0)
% 45.42/7.15 | ~ (product @ a @ X1 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl169])).
% 45.42/7.15 thf(zip_derived_cl342, plain,
% 45.42/7.15 ((~ (defined @ a)
% 45.42/7.15 | (product @ b @ multiplicative_identity @ a)
% 45.42/7.15 | ~ (defined @ a))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl289])).
% 45.42/7.15 thf(a_is_defined, axiom, (defined @ a)).
% 45.42/7.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 45.42/7.15 inference('cnf', [status(esa)], [a_is_defined])).
% 45.42/7.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 45.42/7.15 inference('cnf', [status(esa)], [a_is_defined])).
% 45.42/7.15 thf(zip_derived_cl344, plain, ( (product @ b @ multiplicative_identity @ a)),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl342, zip_derived_cl26, zip_derived_cl26])).
% 45.42/7.15 thf(zip_derived_cl29, plain, ( (product @ multiplicative_identity @ a @ b)),
% 45.42/7.15 inference('cnf', [status(esa)], [zf_stmt_1])).
% 45.42/7.15 thf(zip_derived_cl9, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 45.42/7.15 thf(zip_derived_cl58, plain, ( (product @ a @ multiplicative_identity @ b)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl57, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl29, plain, ( (product @ multiplicative_identity @ a @ b)),
% 45.42/7.15 inference('cnf', [status(esa)], [zf_stmt_1])).
% 45.42/7.15 thf(zip_derived_cl5, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (product @ X0 @ X3 @ X4)
% 45.42/7.15 | ~ (product @ X3 @ X5 @ X1)
% 45.42/7.15 | ~ (product @ X4 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 45.42/7.15 thf(zip_derived_cl107, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 (~ (product @ b @ X1 @ X0)
% 45.42/7.15 | ~ (product @ a @ X1 @ X2)
% 45.42/7.15 | (product @ multiplicative_identity @ X2 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl5])).
% 45.42/7.15 thf(zip_derived_cl133, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ b)
% 45.42/7.15 | (product @ multiplicative_identity @ X0 @ b)
% 45.42/7.15 | ~ (product @ a @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl107])).
% 45.42/7.15 thf(b_is_defined, axiom, (defined @ b)).
% 45.42/7.15 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 45.42/7.15 inference('cnf', [status(esa)], [b_is_defined])).
% 45.42/7.15 thf(zip_derived_cl134, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ multiplicative_identity @ X0 @ b)
% 45.42/7.15 | ~ (product @ a @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl133, zip_derived_cl27])).
% 45.42/7.15 thf(zip_derived_cl136, plain, ( (product @ multiplicative_identity @ b @ b)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl134])).
% 45.42/7.15 thf(zip_derived_cl9, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 45.42/7.15 thf(zip_derived_cl139, plain, ( (product @ b @ multiplicative_identity @ b)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl5, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (product @ X0 @ X3 @ X4)
% 45.42/7.15 | ~ (product @ X3 @ X5 @ X1)
% 45.42/7.15 | ~ (product @ X4 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 45.42/7.15 thf(zip_derived_cl140, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 (~ (product @ b @ X1 @ X0)
% 45.42/7.15 | ~ (product @ multiplicative_identity @ X1 @ X2)
% 45.42/7.15 | (product @ b @ X2 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl5])).
% 45.42/7.15 thf(zip_derived_cl353, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ b @ X0 @ a)
% 45.42/7.15 | ~ (product @ multiplicative_identity @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl344, zip_derived_cl140])).
% 45.42/7.15 thf(zip_derived_cl2173, plain,
% 45.42/7.15 ( (product @ b @ (multiplicative_inverse @ multiplicative_identity) @ a)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl2159, zip_derived_cl353])).
% 45.42/7.15 thf(zip_derived_cl40, plain,
% 45.42/7.15 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl38, zip_derived_cl13, zip_derived_cl13])).
% 45.42/7.15 thf(zip_derived_cl57, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl57, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl40, plain,
% 45.42/7.15 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl38, zip_derived_cl13, zip_derived_cl13])).
% 45.42/7.15 thf(distributivity_2, axiom,
% 45.42/7.15 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 45.42/7.15 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 45.42/7.15 ( ~( sum @ C @ D @ B ) ))).
% 45.42/7.15 thf(zip_derived_cl11, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (sum @ X3 @ X4 @ X0)
% 45.42/7.15 | ~ (product @ X3 @ X1 @ X5)
% 45.42/7.15 | ~ (product @ X4 @ X1 @ X6)
% 45.42/7.15 | ~ (sum @ X5 @ X6 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [distributivity_2])).
% 45.42/7.15 thf(zip_derived_cl262, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 45.42/7.15 (~ (sum @ X2 @ X1 @ X0)
% 45.42/7.15 | ~ (product @ additive_identity @ X3 @ X1)
% 45.42/7.15 | ~ (product @ additive_identity @ X3 @ X2)
% 45.42/7.15 | (product @ additive_identity @ X3 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl11])).
% 45.42/7.15 thf(zip_derived_cl5710, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 (~ (defined @ additive_identity)
% 45.42/7.15 | (product @ additive_identity @ multiplicative_identity @ X0)
% 45.42/7.15 | ~ (product @ additive_identity @ multiplicative_identity @ X1)
% 45.42/7.15 | ~ (sum @ X1 @ additive_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl262])).
% 45.42/7.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 45.42/7.15 thf(zip_derived_cl5716, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 ( (product @ additive_identity @ multiplicative_identity @ X0)
% 45.42/7.15 | ~ (product @ additive_identity @ multiplicative_identity @ X1)
% 45.42/7.15 | ~ (sum @ X1 @ additive_identity @ X0))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl5710, zip_derived_cl13])).
% 45.42/7.15 thf(zip_derived_cl5991, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ additive_identity)
% 45.42/7.15 | ~ (sum @ additive_identity @ additive_identity @ X0)
% 45.42/7.15 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl5716])).
% 45.42/7.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 45.42/7.15 thf(zip_derived_cl5994, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (sum @ additive_identity @ additive_identity @ X0)
% 45.42/7.15 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl5991, zip_derived_cl13])).
% 45.42/7.15 thf(zip_derived_cl6002, plain,
% 45.42/7.15 ( (product @ additive_identity @ multiplicative_identity @
% 45.42/7.15 additive_identity)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl5994])).
% 45.42/7.15 thf(zip_derived_cl2159, plain,
% 45.42/7.15 ( (product @ multiplicative_identity @ multiplicative_identity @
% 45.42/7.15 (multiplicative_inverse @ multiplicative_identity))),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl2151, zip_derived_cl16, zip_derived_cl25,
% 45.42/7.15 zip_derived_cl207])).
% 45.42/7.15 thf(zip_derived_cl57, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl5, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (product @ X0 @ X3 @ X4)
% 45.42/7.15 | ~ (product @ X3 @ X5 @ X1)
% 45.42/7.15 | ~ (product @ X4 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 45.42/7.15 thf(zip_derived_cl105, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | ~ (product @ X0 @ X2 @ X1)
% 45.42/7.15 | ~ (product @ multiplicative_identity @ X2 @ X3)
% 45.42/7.15 | (product @ X0 @ X3 @ X1))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl5])).
% 45.42/7.15 thf(zip_derived_cl2166, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 ( (product @ X1 @
% 45.42/7.15 (multiplicative_inverse @ multiplicative_identity) @ X0)
% 45.42/7.15 | ~ (product @ X1 @ multiplicative_identity @ X0)
% 45.42/7.15 | ~ (defined @ X1))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl2159, zip_derived_cl105])).
% 45.42/7.15 thf(zip_derived_cl6023, plain,
% 45.42/7.15 ((~ (defined @ additive_identity)
% 45.42/7.15 | (product @ additive_identity @
% 45.42/7.15 (multiplicative_inverse @ multiplicative_identity) @
% 45.42/7.15 additive_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl6002, zip_derived_cl2166])).
% 45.42/7.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 45.42/7.15 thf(zip_derived_cl6038, plain,
% 45.42/7.15 ( (product @ additive_identity @
% 45.42/7.15 (multiplicative_inverse @ multiplicative_identity) @ additive_identity)),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl6023, zip_derived_cl13])).
% 45.42/7.15 thf(distributivity_1, axiom,
% 45.42/7.15 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 45.42/7.15 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 45.42/7.15 ( ~( product @ Y @ Z @ D ) ))).
% 45.42/7.15 thf(zip_derived_cl10, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 45.42/7.15 ( (sum @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (sum @ X3 @ X4 @ X5)
% 45.42/7.15 | ~ (product @ X5 @ X6 @ X2)
% 45.42/7.15 | ~ (product @ X3 @ X6 @ X0)
% 45.42/7.15 | ~ (product @ X4 @ X6 @ X1))),
% 45.42/7.15 inference('cnf', [status(esa)], [distributivity_1])).
% 45.42/7.15 thf(zip_derived_cl228, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 45.42/7.15 (~ (product @ X2 @ X1 @ X0)
% 45.42/7.15 | ~ (product @ X4 @ X1 @ X3)
% 45.42/7.15 | ~ (sum @ X4 @ X2 @ X2)
% 45.42/7.15 | (sum @ X3 @ X0 @ X0))),
% 45.42/7.15 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 45.42/7.15 thf(zip_derived_cl6155, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 ( (sum @ X0 @ additive_identity @ additive_identity)
% 45.42/7.15 | ~ (sum @ X1 @ additive_identity @ additive_identity)
% 45.42/7.15 | ~ (product @ X1 @
% 45.42/7.15 (multiplicative_inverse @ multiplicative_identity) @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl6038, zip_derived_cl228])).
% 45.42/7.15 thf(zip_derived_cl10567, plain,
% 45.42/7.15 ((~ (sum @ b @ additive_identity @ additive_identity)
% 45.42/7.15 | (sum @ a @ additive_identity @ additive_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl2173, zip_derived_cl6155])).
% 45.42/7.15 thf(zip_derived_cl8, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 45.42/7.15 multiplicative_identity)
% 45.42/7.15 | (sum @ additive_identity @ X0 @ additive_identity)
% 45.42/7.15 | ~ (defined @ X0))),
% 45.42/7.15 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 45.42/7.15 thf(zip_derived_cl9, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 45.42/7.15 thf(zip_derived_cl98, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (sum @ additive_identity @ X0 @ additive_identity)
% 45.42/7.15 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 45.42/7.15 multiplicative_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl98, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (sum @ additive_identity @ X0 @ additive_identity)
% 45.42/7.15 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 45.42/7.15 multiplicative_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl289, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (product @ b @ X1 @ X0)
% 45.42/7.15 | ~ (product @ a @ X1 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl169])).
% 45.42/7.15 thf(zip_derived_cl1351, plain,
% 45.42/7.15 (( (sum @ additive_identity @ a @ additive_identity)
% 45.42/7.15 | ~ (defined @ a)
% 45.42/7.15 | (product @ b @ (multiplicative_inverse @ a) @
% 45.42/7.15 multiplicative_identity)
% 45.42/7.15 | ~ (defined @ multiplicative_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl289])).
% 45.42/7.15 thf(zip_derived_cl28, plain,
% 45.42/7.15 (~ (sum @ additive_identity @ a @ additive_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 45.42/7.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 45.42/7.15 inference('cnf', [status(esa)], [a_is_defined])).
% 45.42/7.15 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 45.42/7.15 inference('cnf', [status(esa)],
% 45.42/7.15 [well_definedness_of_multiplicative_identity])).
% 45.42/7.15 thf(zip_derived_cl1364, plain,
% 45.42/7.15 ( (product @ b @ (multiplicative_inverse @ a) @ multiplicative_identity)),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl1351, zip_derived_cl28, zip_derived_cl26,
% 45.42/7.15 zip_derived_cl16])).
% 45.42/7.15 thf(zip_derived_cl136, plain, ( (product @ multiplicative_identity @ b @ b)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl134])).
% 45.42/7.15 thf(zip_derived_cl5, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (product @ X0 @ X3 @ X4)
% 45.42/7.15 | ~ (product @ X3 @ X5 @ X1)
% 45.42/7.15 | ~ (product @ X4 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 45.42/7.15 thf(zip_derived_cl138, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 (~ (product @ b @ X1 @ X0)
% 45.42/7.15 | ~ (product @ b @ X1 @ X2)
% 45.42/7.15 | (product @ multiplicative_identity @ X2 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl5])).
% 45.42/7.15 thf(zip_derived_cl194, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 ( (product @ multiplicative_identity @ X0 @ X0)
% 45.42/7.15 | ~ (product @ b @ X1 @ X0))),
% 45.42/7.15 inference('eq_fact', [status(thm)], [zip_derived_cl138])).
% 45.42/7.15 thf(zip_derived_cl1379, plain,
% 45.42/7.15 ( (product @ multiplicative_identity @ multiplicative_identity @
% 45.42/7.15 multiplicative_identity)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl1364, zip_derived_cl194])).
% 45.42/7.15 thf(zip_derived_cl344, plain, ( (product @ b @ multiplicative_identity @ a)),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl342, zip_derived_cl26, zip_derived_cl26])).
% 45.42/7.15 thf(zip_derived_cl9, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 45.42/7.15 thf(zip_derived_cl348, plain, ( (product @ multiplicative_identity @ b @ a)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl344, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl6, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (product @ X3 @ X4 @ X0)
% 45.42/7.15 | ~ (product @ X4 @ X1 @ X5)
% 45.42/7.15 | ~ (product @ X3 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 45.42/7.15 thf(zip_derived_cl357, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 (~ (product @ multiplicative_identity @ X1 @ X0)
% 45.42/7.15 | ~ (product @ b @ X2 @ X1)
% 45.42/7.15 | (product @ a @ X2 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl6])).
% 45.42/7.15 thf(zip_derived_cl8100, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ a @ X0 @ multiplicative_identity)
% 45.42/7.15 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl1379, zip_derived_cl357])).
% 45.42/7.15 thf(zip_derived_cl8158, plain,
% 45.42/7.15 (( (sum @ additive_identity @ b @ additive_identity)
% 45.42/7.15 | ~ (defined @ b)
% 45.42/7.15 | (product @ a @ (multiplicative_inverse @ b) @
% 45.42/7.15 multiplicative_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl8100])).
% 45.42/7.15 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 45.42/7.15 inference('cnf', [status(esa)], [b_is_defined])).
% 45.42/7.15 thf(zip_derived_cl8161, plain,
% 45.42/7.15 (( (sum @ additive_identity @ b @ additive_identity)
% 45.42/7.15 | (product @ a @ (multiplicative_inverse @ b) @
% 45.42/7.15 multiplicative_identity))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl8158, zip_derived_cl27])).
% 45.42/7.15 thf(zip_derived_cl57, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl169, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 (~ (product @ multiplicative_identity @ X1 @ X0)
% 45.42/7.15 | ~ (product @ a @ X2 @ X1)
% 45.42/7.15 | (product @ b @ X2 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl6])).
% 45.42/7.15 thf(zip_derived_cl288, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ multiplicative_identity)
% 45.42/7.15 | (product @ b @ X0 @ multiplicative_identity)
% 45.42/7.15 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl169])).
% 45.42/7.15 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 45.42/7.15 inference('cnf', [status(esa)],
% 45.42/7.15 [well_definedness_of_multiplicative_identity])).
% 45.42/7.15 thf(zip_derived_cl292, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ b @ X0 @ multiplicative_identity)
% 45.42/7.15 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl288, zip_derived_cl16])).
% 45.42/7.15 thf(zip_derived_cl12493, plain,
% 45.42/7.15 (( (sum @ additive_identity @ b @ additive_identity)
% 45.42/7.15 | (product @ b @ (multiplicative_inverse @ b) @
% 45.42/7.15 multiplicative_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl8161, zip_derived_cl292])).
% 45.42/7.15 thf(zip_derived_cl57, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl1364, plain,
% 45.42/7.15 ( (product @ b @ (multiplicative_inverse @ a) @ multiplicative_identity)),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl1351, zip_derived_cl28, zip_derived_cl26,
% 45.42/7.15 zip_derived_cl16])).
% 45.42/7.15 thf(zip_derived_cl9, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 45.42/7.15 thf(zip_derived_cl1373, plain,
% 45.42/7.15 ( (product @ (multiplicative_inverse @ a) @ b @ multiplicative_identity)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl1364, zip_derived_cl9])).
% 45.42/7.15 thf(zip_derived_cl6, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 45.42/7.15 ( (product @ X0 @ X1 @ X2)
% 45.42/7.15 | ~ (product @ X3 @ X4 @ X0)
% 45.42/7.15 | ~ (product @ X4 @ X1 @ X5)
% 45.42/7.15 | ~ (product @ X3 @ X5 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 45.42/7.15 thf(zip_derived_cl1435, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 (~ (product @ (multiplicative_inverse @ a) @ X1 @ X0)
% 45.42/7.15 | ~ (product @ b @ X2 @ X1)
% 45.42/7.15 | (product @ multiplicative_identity @ X2 @ X0))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl1373, zip_derived_cl6])).
% 45.42/7.15 thf(zip_derived_cl63684, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ (multiplicative_inverse @ a))
% 45.42/7.15 | (product @ multiplicative_identity @ X0 @
% 45.42/7.15 (multiplicative_inverse @ a))
% 45.42/7.15 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl1435])).
% 45.42/7.15 thf(zip_derived_cl17, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (defined @ (multiplicative_inverse @ X0))
% 45.42/7.15 | ~ (defined @ X0)
% 45.42/7.15 | (sum @ additive_identity @ X0 @ additive_identity))),
% 45.42/7.15 inference('cnf', [status(esa)],
% 45.42/7.15 [well_definedness_of_multiplicative_inverse])).
% 45.42/7.15 thf(zip_derived_cl28, plain,
% 45.42/7.15 (~ (sum @ additive_identity @ a @ additive_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 45.42/7.15 thf(zip_derived_cl68, plain,
% 45.42/7.15 ((~ (defined @ a) | (defined @ (multiplicative_inverse @ a)))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl28])).
% 45.42/7.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 45.42/7.15 inference('cnf', [status(esa)], [a_is_defined])).
% 45.42/7.15 thf(zip_derived_cl71, plain, ( (defined @ (multiplicative_inverse @ a))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl26])).
% 45.42/7.15 thf(zip_derived_cl63722, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ multiplicative_identity @ X0 @
% 45.42/7.15 (multiplicative_inverse @ a))
% 45.42/7.15 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl63684, zip_derived_cl71])).
% 45.42/7.15 thf(zip_derived_cl66022, plain,
% 45.42/7.15 (( (sum @ additive_identity @ b @ additive_identity)
% 45.42/7.15 | (product @ multiplicative_identity @ (multiplicative_inverse @ b) @
% 45.42/7.15 (multiplicative_inverse @ a)))),
% 45.42/7.15 inference('sup-', [status(thm)],
% 45.42/7.15 [zip_derived_cl12493, zip_derived_cl63722])).
% 45.42/7.15 thf(zip_derived_cl7, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 45.42/7.15 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 45.42/7.15 thf(zip_derived_cl106, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | ~ (product @ X0 @ X2 @ X1)
% 45.42/7.15 | ~ (product @ X0 @ X2 @ X3)
% 45.42/7.15 | (product @ multiplicative_identity @ X3 @ X1))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 45.42/7.15 thf(zip_derived_cl1755, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (product @ multiplicative_identity @ X1 @ X0)
% 45.42/7.15 | ~ (product @ multiplicative_identity @ X0 @ X1)
% 45.42/7.15 | ~ (defined @ multiplicative_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl106])).
% 45.42/7.15 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 45.42/7.15 inference('cnf', [status(esa)],
% 45.42/7.15 [well_definedness_of_multiplicative_identity])).
% 45.42/7.15 thf(zip_derived_cl1816, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (product @ multiplicative_identity @ X1 @ X0)
% 45.42/7.15 | ~ (product @ multiplicative_identity @ X0 @ X1))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl1755, zip_derived_cl16])).
% 45.42/7.15 thf(zip_derived_cl72375, plain,
% 45.42/7.15 (( (sum @ additive_identity @ b @ additive_identity)
% 45.42/7.15 | (product @ multiplicative_identity @ (multiplicative_inverse @ a) @
% 45.42/7.15 (multiplicative_inverse @ b))
% 45.42/7.15 | ~ (defined @ (multiplicative_inverse @ b)))),
% 45.42/7.15 inference('sup-', [status(thm)],
% 45.42/7.15 [zip_derived_cl66022, zip_derived_cl1816])).
% 45.42/7.15 thf(zip_derived_cl17, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 ( (defined @ (multiplicative_inverse @ X0))
% 45.42/7.15 | ~ (defined @ X0)
% 45.42/7.15 | (sum @ additive_identity @ X0 @ additive_identity))),
% 45.42/7.15 inference('cnf', [status(esa)],
% 45.42/7.15 [well_definedness_of_multiplicative_inverse])).
% 45.42/7.15 thf(commutativity_addition, axiom,
% 45.42/7.15 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 45.42/7.15 thf(zip_derived_cl4, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_addition])).
% 45.42/7.15 thf(zip_derived_cl64, plain,
% 45.42/7.15 (![X0 : $i]:
% 45.42/7.15 (~ (defined @ X0)
% 45.42/7.15 | (defined @ (multiplicative_inverse @ X0))
% 45.42/7.15 | (sum @ X0 @ additive_identity @ additive_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl4])).
% 45.42/7.15 thf(zip_derived_cl10567, plain,
% 45.42/7.15 ((~ (sum @ b @ additive_identity @ additive_identity)
% 45.42/7.15 | (sum @ a @ additive_identity @ additive_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl2173, zip_derived_cl6155])).
% 45.42/7.15 thf(zip_derived_cl10586, plain,
% 45.42/7.15 (( (defined @ (multiplicative_inverse @ b))
% 45.42/7.15 | ~ (defined @ b)
% 45.42/7.15 | (sum @ a @ additive_identity @ additive_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl10567])).
% 45.42/7.15 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 45.42/7.15 inference('cnf', [status(esa)], [b_is_defined])).
% 45.42/7.15 thf(zip_derived_cl10587, plain,
% 45.42/7.15 (( (defined @ (multiplicative_inverse @ b))
% 45.42/7.15 | (sum @ a @ additive_identity @ additive_identity))),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl10586, zip_derived_cl27])).
% 45.42/7.15 thf(zip_derived_cl4, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_addition])).
% 45.42/7.15 thf(zip_derived_cl10591, plain,
% 45.42/7.15 (( (defined @ (multiplicative_inverse @ b))
% 45.42/7.15 | (sum @ additive_identity @ a @ additive_identity))),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl10587, zip_derived_cl4])).
% 45.42/7.15 thf(zip_derived_cl28, plain,
% 45.42/7.15 (~ (sum @ additive_identity @ a @ additive_identity)),
% 45.42/7.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 45.42/7.15 thf(zip_derived_cl10607, plain, ( (defined @ (multiplicative_inverse @ b))),
% 45.42/7.15 inference('clc', [status(thm)], [zip_derived_cl10591, zip_derived_cl28])).
% 45.42/7.15 thf(zip_derived_cl72390, plain,
% 45.42/7.15 (( (sum @ additive_identity @ b @ additive_identity)
% 45.42/7.15 | (product @ multiplicative_identity @ (multiplicative_inverse @ a) @
% 45.42/7.15 (multiplicative_inverse @ b)))),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl72375, zip_derived_cl10607])).
% 45.42/7.15 thf(not_product_5, conjecture,
% 45.42/7.15 (product @
% 45.42/7.15 multiplicative_identity @ ( multiplicative_inverse @ a ) @
% 45.42/7.15 ( multiplicative_inverse @ b ))).
% 45.42/7.15 thf(zf_stmt_2, negated_conjecture,
% 45.42/7.15 (~( product @
% 45.42/7.15 multiplicative_identity @ ( multiplicative_inverse @ a ) @
% 45.42/7.15 ( multiplicative_inverse @ b ) )),
% 45.42/7.15 inference('cnf.neg', [status(esa)], [not_product_5])).
% 45.42/7.15 thf(zip_derived_cl30, plain,
% 45.42/7.15 (~ (product @ multiplicative_identity @ (multiplicative_inverse @ a) @
% 45.42/7.15 (multiplicative_inverse @ b))),
% 45.42/7.15 inference('cnf', [status(esa)], [zf_stmt_2])).
% 45.42/7.15 thf(zip_derived_cl73959, plain,
% 45.42/7.15 ( (sum @ additive_identity @ b @ additive_identity)),
% 45.42/7.15 inference('clc', [status(thm)], [zip_derived_cl72390, zip_derived_cl30])).
% 45.42/7.15 thf(zip_derived_cl4, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_addition])).
% 45.42/7.15 thf(zip_derived_cl73963, plain,
% 45.42/7.15 ( (sum @ b @ additive_identity @ additive_identity)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl73959, zip_derived_cl4])).
% 45.42/7.15 thf(zip_derived_cl74154, plain,
% 45.42/7.15 ( (sum @ a @ additive_identity @ additive_identity)),
% 45.42/7.15 inference('demod', [status(thm)],
% 45.42/7.15 [zip_derived_cl10567, zip_derived_cl73963])).
% 45.42/7.15 thf(zip_derived_cl4, plain,
% 45.42/7.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 45.42/7.15 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 45.42/7.15 inference('cnf', [status(esa)], [commutativity_addition])).
% 45.42/7.15 thf(zip_derived_cl74910, plain,
% 45.42/7.15 ( (sum @ additive_identity @ a @ additive_identity)),
% 45.42/7.15 inference('sup-', [status(thm)], [zip_derived_cl74154, zip_derived_cl4])).
% 45.42/7.15 thf(zip_derived_cl75545, plain, ($false),
% 45.42/7.15 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl74910])).
% 45.42/7.15
% 45.42/7.15 % SZS output end Refutation
% 45.42/7.15
% 45.42/7.15
% 45.42/7.16 % Terminating...
% 45.42/7.25 % Runner terminated.
% 45.42/7.25 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------