TSTP Solution File: FLD051-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD051-4 : 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.BuvvJVlxrJ 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 22:39:28 EDT 2023
% Result : Unsatisfiable 125.66s 18.52s
% Output : Refutation 125.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : FLD051-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.BuvvJVlxrJ true
% 0.10/0.31 % Computer : n027.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Aug 28 00:58:51 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.10/0.32 % Python version: Python 3.6.8
% 0.10/0.32 % Running in FO mode
% 0.17/0.59 % Total configuration time : 435
% 0.17/0.59 % Estimated wc time : 1092
% 0.17/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.17/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.17/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.17/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.17/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.17/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.17/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.17/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 125.66/18.52 % Solved by fo/fo5.sh.
% 125.66/18.52 % done 18800 iterations in 17.787s
% 125.66/18.52 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 125.66/18.52 % SZS output start Refutation
% 125.66/18.52 thf(sum_type, type, sum: $i > $i > $i > $o).
% 125.66/18.52 thf(t_type, type, t: $i).
% 125.66/18.52 thf(b_type, type, b: $i).
% 125.66/18.52 thf(s_type, type, s: $i).
% 125.66/18.52 thf(a_type, type, a: $i).
% 125.66/18.52 thf(k_type, type, k: $i).
% 125.66/18.52 thf(d_type, type, d: $i).
% 125.66/18.52 thf(product_type, type, product: $i > $i > $i > $o).
% 125.66/18.52 thf(additive_identity_type, type, additive_identity: $i).
% 125.66/18.52 thf(multiply_type, type, multiply: $i > $i > $i).
% 125.66/18.52 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 125.66/18.52 thf(l_type, type, l: $i).
% 125.66/18.52 thf(c_type, type, c: $i).
% 125.66/18.52 thf(u_type, type, u: $i).
% 125.66/18.52 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 125.66/18.52 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 125.66/18.52 thf(defined_type, type, defined: $i > $o).
% 125.66/18.52 thf(different_identities, axiom,
% 125.66/18.52 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 125.66/18.52 thf(zip_derived_cl25, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [different_identities])).
% 125.66/18.52 thf(product_17, conjecture, (~( product @ b @ c @ l ))).
% 125.66/18.52 thf(zf_stmt_0, negated_conjecture, (product @ b @ c @ l),
% 125.66/18.52 inference('cnf.neg', [status(esa)], [product_17])).
% 125.66/18.52 thf(zip_derived_cl42, plain, ( (product @ b @ c @ l)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_0])).
% 125.66/18.52 thf(existence_of_identity_multiplication, axiom,
% 125.66/18.52 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 125.66/18.52 thf(zip_derived_cl7, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 125.66/18.52 thf(commutativity_multiplication, axiom,
% 125.66/18.52 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl80, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 125.66/18.52 thf(product_16, conjecture, (~( product @ a @ d @ k ))).
% 125.66/18.52 thf(zf_stmt_1, negated_conjecture, (product @ a @ d @ k),
% 125.66/18.52 inference('cnf.neg', [status(esa)], [product_16])).
% 125.66/18.52 thf(zip_derived_cl41, plain, ( (product @ a @ d @ k)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_1])).
% 125.66/18.52 thf(zip_derived_cl41, plain, ( (product @ a @ d @ k)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_1])).
% 125.66/18.52 thf(associativity_multiplication_2, axiom,
% 125.66/18.52 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 125.66/18.52 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 125.66/18.52 thf(zip_derived_cl6, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X3 @ X4 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X5)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 125.66/18.52 thf(zip_derived_cl141, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ a @ X1 @ X0)
% 125.66/18.52 | ~ (product @ d @ X2 @ X1)
% 125.66/18.52 | (product @ k @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl264, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ k @ X0 @ k) | ~ (product @ d @ X0 @ d))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl141])).
% 125.66/18.52 thf(zip_derived_cl266, plain,
% 125.66/18.52 ((~ (defined @ d) | (product @ k @ multiplicative_identity @ k))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl264])).
% 125.66/18.52 thf(d_is_defined, axiom, (defined @ d)).
% 125.66/18.52 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 125.66/18.52 inference('cnf', [status(esa)], [d_is_defined])).
% 125.66/18.52 thf(zip_derived_cl267, plain, ( (product @ k @ multiplicative_identity @ k)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl29])).
% 125.66/18.52 thf(existence_of_inverse_multiplication, axiom,
% 125.66/18.52 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 125.66/18.52 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 125.66/18.52 thf(zip_derived_cl8, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl182, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl80, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl141, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ a @ X1 @ X0)
% 125.66/18.52 | ~ (product @ d @ X2 @ X1)
% 125.66/18.52 | (product @ k @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl262, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ a)
% 125.66/18.52 | (product @ k @ X0 @ a)
% 125.66/18.52 | ~ (product @ d @ X0 @ multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl141])).
% 125.66/18.52 thf(a_is_defined, axiom, (defined @ a)).
% 125.66/18.52 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 125.66/18.52 inference('cnf', [status(esa)], [a_is_defined])).
% 125.66/18.52 thf(zip_derived_cl265, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ k @ X0 @ a)
% 125.66/18.52 | ~ (product @ d @ X0 @ multiplicative_identity))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl262, zip_derived_cl26])).
% 125.66/18.52 thf(zip_derived_cl2879, plain,
% 125.66/18.52 (( (sum @ additive_identity @ d @ additive_identity)
% 125.66/18.52 | ~ (defined @ d)
% 125.66/18.52 | (product @ k @ (multiplicative_inverse @ d) @ a))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl265])).
% 125.66/18.52 thf(not_sum_12, conjecture,
% 125.66/18.52 (sum @ additive_identity @ d @ additive_identity)).
% 125.66/18.52 thf(zf_stmt_2, negated_conjecture,
% 125.66/18.52 (~( sum @ additive_identity @ d @ additive_identity )),
% 125.66/18.52 inference('cnf.neg', [status(esa)], [not_sum_12])).
% 125.66/18.52 thf(zip_derived_cl37, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ d @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_2])).
% 125.66/18.52 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 125.66/18.52 inference('cnf', [status(esa)], [d_is_defined])).
% 125.66/18.52 thf(zip_derived_cl2924, plain,
% 125.66/18.52 ( (product @ k @ (multiplicative_inverse @ d) @ a)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl2879, zip_derived_cl37, zip_derived_cl29])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl2968, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ d) @ k @ a)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2924, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl6, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X3 @ X4 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X5)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 125.66/18.52 thf(zip_derived_cl149, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X1 @ X3 @ X1)
% 125.66/18.52 | (product @ X0 @ X3 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl3003, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ a @ X0 @ a) | ~ (product @ k @ X0 @ k))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2968, zip_derived_cl149])).
% 125.66/18.52 thf(zip_derived_cl3247, plain,
% 125.66/18.52 ( (product @ a @ multiplicative_identity @ a)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl267, zip_derived_cl3003])).
% 125.66/18.52 thf(totality_of_order_relation, axiom,
% 125.66/18.52 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 125.66/18.52 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 125.66/18.52 thf(zip_derived_cl22, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (less_or_equal @ X0 @ X1)
% 125.66/18.52 | (less_or_equal @ X1 @ X0)
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 125.66/18.52 thf(b_is_defined, axiom, (defined @ b)).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl561, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (less_or_equal @ X0 @ b)
% 125.66/18.52 | (less_or_equal @ b @ X0))),
% 125.66/18.52 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl18346, plain,
% 125.66/18.52 (( (less_or_equal @ b @ b) | ~ (defined @ b))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl561])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl18347, plain, ( (less_or_equal @ b @ b)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl18346, zip_derived_cl27])).
% 125.66/18.52 thf(antisymmetry_of_order_relation, axiom,
% 125.66/18.52 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 125.66/18.52 ( ~( less_or_equal @ Y @ X ) ))).
% 125.66/18.52 thf(zip_derived_cl20, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X1 @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 125.66/18.52 thf(zip_derived_cl18353, plain,
% 125.66/18.52 ((~ (less_or_equal @ b @ b) | (sum @ additive_identity @ b @ b))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18347, zip_derived_cl20])).
% 125.66/18.52 thf(zip_derived_cl18347, plain, ( (less_or_equal @ b @ b)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl18346, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl18356, plain, ( (sum @ additive_identity @ b @ b)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl18353, zip_derived_cl18347])).
% 125.66/18.52 thf(zip_derived_cl8, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 125.66/18.52 thf(existence_of_identity_addition, axiom,
% 125.66/18.52 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 125.66/18.52 thf(zip_derived_cl2, plain,
% 125.66/18.52 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 125.66/18.52 thf(zip_derived_cl2, plain,
% 125.66/18.52 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 125.66/18.52 thf(associativity_addition_1, axiom,
% 125.66/18.52 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 125.66/18.52 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 125.66/18.52 thf(zip_derived_cl0, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (sum @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (sum @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (sum @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (sum @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_addition_1])).
% 125.66/18.52 thf(zip_derived_cl46, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (sum @ X0 @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ X1 @ X1 @ X2)
% 125.66/18.52 | (sum @ X0 @ X2 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 125.66/18.52 thf(zip_derived_cl53, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ additive_identity)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl46])).
% 125.66/18.52 thf(well_definedness_of_additive_identity, axiom,
% 125.66/18.52 (defined @ additive_identity)).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl54, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl62, plain,
% 125.66/18.52 ((~ (defined @ additive_identity)
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @ additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl54])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl64, plain,
% 125.66/18.52 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl0, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (sum @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (sum @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (sum @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (sum @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_addition_1])).
% 125.66/18.52 thf(zip_derived_cl66, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (sum @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ additive_identity @ X1 @ X2)
% 125.66/18.52 | (sum @ additive_identity @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 125.66/18.52 thf(zip_derived_cl187, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | (sum @ additive_identity @ X1 @ additive_identity)
% 125.66/18.52 | ~ (sum @ additive_identity @ X0 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl66])).
% 125.66/18.52 thf(zip_derived_cl18371, plain,
% 125.66/18.52 (( (sum @ additive_identity @ b @ additive_identity)
% 125.66/18.52 | (product @ (multiplicative_inverse @ b) @ b @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | ~ (defined @ b))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18356, zip_derived_cl187])).
% 125.66/18.52 thf(not_sum_10, conjecture,
% 125.66/18.52 (sum @ additive_identity @ b @ additive_identity)).
% 125.66/18.52 thf(zf_stmt_3, negated_conjecture,
% 125.66/18.52 (~( sum @ additive_identity @ b @ additive_identity )),
% 125.66/18.52 inference('cnf.neg', [status(esa)], [not_sum_10])).
% 125.66/18.52 thf(zip_derived_cl35, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ b @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_3])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl18402, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ b) @ b @ multiplicative_identity)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl18371, zip_derived_cl35, zip_derived_cl27])).
% 125.66/18.52 thf(product_14, conjecture,
% 125.66/18.52 (~( product @ a @ ( multiplicative_inverse @ b ) @ s ))).
% 125.66/18.52 thf(zf_stmt_4, negated_conjecture,
% 125.66/18.52 (product @ a @ ( multiplicative_inverse @ b ) @ s),
% 125.66/18.52 inference('cnf.neg', [status(esa)], [product_14])).
% 125.66/18.52 thf(zip_derived_cl39, plain,
% 125.66/18.52 ( (product @ a @ (multiplicative_inverse @ b) @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_4])).
% 125.66/18.52 thf(zip_derived_cl6, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X3 @ X4 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X5)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 125.66/18.52 thf(zip_derived_cl140, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ a @ X1 @ X0)
% 125.66/18.52 | ~ (product @ (multiplicative_inverse @ b) @ X2 @ X1)
% 125.66/18.52 | (product @ s @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl18446, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ s @ b @ X0)
% 125.66/18.52 | ~ (product @ a @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18402, zip_derived_cl140])).
% 125.66/18.52 thf(zip_derived_cl18910, plain, ( (product @ s @ b @ a)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl3247, zip_derived_cl18446])).
% 125.66/18.52 thf(totality_of_multiplication, axiom,
% 125.66/18.52 (( product @ X @ Y @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 125.66/18.52 ( ~( defined @ Y ) ))).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(product_13, conjecture,
% 125.66/18.52 (~( product @ s @ ( multiplicative_inverse @ t ) @ u ))).
% 125.66/18.52 thf(zf_stmt_5, negated_conjecture,
% 125.66/18.52 (product @ s @ ( multiplicative_inverse @ t ) @ u),
% 125.66/18.52 inference('cnf.neg', [status(esa)], [product_13])).
% 125.66/18.52 thf(zip_derived_cl38, plain,
% 125.66/18.52 ( (product @ s @ (multiplicative_inverse @ t) @ u)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_5])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl85, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ t) @ s @ u)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl9])).
% 125.66/18.52 thf(associativity_multiplication_1, axiom,
% 125.66/18.52 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 125.66/18.52 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 125.66/18.52 thf(zip_derived_cl5, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (product @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 125.66/18.52 thf(zip_derived_cl95, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ u @ X1 @ X0)
% 125.66/18.52 | ~ (product @ s @ X1 @ X2)
% 125.66/18.52 | (product @ (multiplicative_inverse @ t) @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl1083, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ u)
% 125.66/18.52 | (product @ (multiplicative_inverse @ t) @ X1 @ (multiply @ u @ X0))
% 125.66/18.52 | ~ (product @ s @ X0 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl95])).
% 125.66/18.52 thf(u_is_defined, axiom, (defined @ u)).
% 125.66/18.52 thf(zip_derived_cl30, plain, ( (defined @ u)),
% 125.66/18.52 inference('cnf', [status(esa)], [u_is_defined])).
% 125.66/18.52 thf(zip_derived_cl1085, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (product @ (multiplicative_inverse @ t) @ X1 @ (multiply @ u @ X0))
% 125.66/18.52 | ~ (product @ s @ X0 @ X1))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl1083, zip_derived_cl30])).
% 125.66/18.52 thf(zip_derived_cl49419, plain,
% 125.66/18.52 (( (product @ (multiplicative_inverse @ t) @ a @ (multiply @ u @ b))
% 125.66/18.52 | ~ (defined @ b))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl18910, zip_derived_cl1085])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl49453, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ t) @ a @ (multiply @ u @ b))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl49419, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl59728, plain,
% 125.66/18.52 ( (product @ a @ (multiplicative_inverse @ t) @ (multiply @ u @ b))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl49453, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl2968, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ d) @ k @ a)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2924, zip_derived_cl9])).
% 125.66/18.52 thf(product_15, conjecture,
% 125.66/18.52 (~( product @ c @ ( multiplicative_inverse @ d ) @ t ))).
% 125.66/18.52 thf(zf_stmt_6, negated_conjecture,
% 125.66/18.52 (product @ c @ ( multiplicative_inverse @ d ) @ t),
% 125.66/18.52 inference('cnf.neg', [status(esa)], [product_15])).
% 125.66/18.52 thf(zip_derived_cl40, plain,
% 125.66/18.52 ( (product @ c @ (multiplicative_inverse @ d) @ t)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_6])).
% 125.66/18.52 thf(zip_derived_cl6, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X3 @ X4 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X5)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 125.66/18.52 thf(zip_derived_cl143, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ c @ X1 @ X0)
% 125.66/18.52 | ~ (product @ (multiplicative_inverse @ d) @ X2 @ X1)
% 125.66/18.52 | (product @ t @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl3007, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ t @ k @ X0) | ~ (product @ c @ a @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2968, zip_derived_cl143])).
% 125.66/18.52 thf(zip_derived_cl3402, plain,
% 125.66/18.52 ((~ (defined @ a)
% 125.66/18.52 | ~ (defined @ c)
% 125.66/18.52 | (product @ t @ k @ (multiply @ c @ a)))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl3007])).
% 125.66/18.52 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 125.66/18.52 inference('cnf', [status(esa)], [a_is_defined])).
% 125.66/18.52 thf(c_is_defined, axiom, (defined @ c)).
% 125.66/18.52 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 125.66/18.52 inference('cnf', [status(esa)], [c_is_defined])).
% 125.66/18.52 thf(zip_derived_cl3403, plain, ( (product @ t @ k @ (multiply @ c @ a))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl3402, zip_derived_cl26, zip_derived_cl28])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl456, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1)
% 125.66/18.52 | (product @ X0 @ X1 @ (multiply @ X1 @ X0)))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl8, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 125.66/18.52 thf(zip_derived_cl2, plain,
% 125.66/18.52 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 125.66/18.52 thf(zip_derived_cl66, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (sum @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ additive_identity @ X1 @ X2)
% 125.66/18.52 | (sum @ additive_identity @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 125.66/18.52 thf(zip_derived_cl157, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ additive_identity @ X0 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl66])).
% 125.66/18.52 thf(zip_derived_cl249, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl157])).
% 125.66/18.52 thf(zip_derived_cl258, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('simplify', [status(thm)], [zip_derived_cl249])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl39, plain,
% 125.66/18.52 ( (product @ a @ (multiplicative_inverse @ b) @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_4])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl81, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ b) @ a @ s)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl81, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ b) @ a @ s)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl7, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl5, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (product @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 125.66/18.52 thf(zip_derived_cl92, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (product @ X0 @ X2 @ X1)
% 125.66/18.52 | ~ (product @ X0 @ X2 @ X3)
% 125.66/18.52 | (product @ multiplicative_identity @ X3 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl1111, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ s)
% 125.66/18.52 | ~ (product @ (multiplicative_inverse @ b) @ a @ X0)
% 125.66/18.52 | ~ (defined @ (multiplicative_inverse @ b)))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl81, zip_derived_cl92])).
% 125.66/18.52 thf(well_definedness_of_multiplicative_inverse, axiom,
% 125.66/18.52 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 125.66/18.52 ( sum @ additive_identity @ X @ additive_identity ))).
% 125.66/18.52 thf(zip_derived_cl17, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (defined @ (multiplicative_inverse @ X0))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity))),
% 125.66/18.52 inference('cnf', [status(esa)],
% 125.66/18.52 [well_definedness_of_multiplicative_inverse])).
% 125.66/18.52 thf(zip_derived_cl35, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ b @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_3])).
% 125.66/18.52 thf(zip_derived_cl124, plain,
% 125.66/18.52 ((~ (defined @ b) | (defined @ (multiplicative_inverse @ b)))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl35])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl129, plain, ( (defined @ (multiplicative_inverse @ b))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl1146, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ s)
% 125.66/18.52 | ~ (product @ (multiplicative_inverse @ b) @ a @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl1111, zip_derived_cl129])).
% 125.66/18.52 thf(zip_derived_cl1336, plain,
% 125.66/18.52 ( (product @ multiplicative_identity @ s @ s)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl81, zip_derived_cl1146])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl1340, plain,
% 125.66/18.52 ( (product @ s @ multiplicative_identity @ s)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl1336, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl92, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (product @ X0 @ X2 @ X1)
% 125.66/18.52 | ~ (product @ X0 @ X2 @ X3)
% 125.66/18.52 | (product @ multiplicative_identity @ X3 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl1348, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ s)
% 125.66/18.52 | ~ (product @ s @ multiplicative_identity @ X0)
% 125.66/18.52 | ~ (defined @ s))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl1340, zip_derived_cl92])).
% 125.66/18.52 thf(s_is_defined, axiom, (defined @ s)).
% 125.66/18.52 thf(zip_derived_cl33, plain, ( (defined @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [s_is_defined])).
% 125.66/18.52 thf(zip_derived_cl1351, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ s)
% 125.66/18.52 | ~ (product @ s @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl1348, zip_derived_cl33])).
% 125.66/18.52 thf(zip_derived_cl1553, plain,
% 125.66/18.52 ((~ (defined @ multiplicative_identity)
% 125.66/18.52 | ~ (defined @ s)
% 125.66/18.52 | (product @ multiplicative_identity @
% 125.66/18.52 (multiply @ s @ multiplicative_identity) @ s))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl1351])).
% 125.66/18.52 thf(well_definedness_of_multiplicative_identity, axiom,
% 125.66/18.52 (defined @ multiplicative_identity)).
% 125.66/18.52 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)],
% 125.66/18.52 [well_definedness_of_multiplicative_identity])).
% 125.66/18.52 thf(zip_derived_cl33, plain, ( (defined @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [s_is_defined])).
% 125.66/18.52 thf(zip_derived_cl1556, plain,
% 125.66/18.52 ( (product @ multiplicative_identity @
% 125.66/18.52 (multiply @ s @ multiplicative_identity) @ s)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl1553, zip_derived_cl16, zip_derived_cl33])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl1620, plain,
% 125.66/18.52 ( (product @ (multiply @ s @ multiplicative_identity) @
% 125.66/18.52 multiplicative_identity @ s)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl1556, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl80, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl95, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ u @ X1 @ X0)
% 125.66/18.52 | ~ (product @ s @ X1 @ X2)
% 125.66/18.52 | (product @ (multiplicative_inverse @ t) @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl1084, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ u)
% 125.66/18.52 | (product @ (multiplicative_inverse @ t) @ X0 @ u)
% 125.66/18.52 | ~ (product @ s @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl95])).
% 125.66/18.52 thf(zip_derived_cl30, plain, ( (defined @ u)),
% 125.66/18.52 inference('cnf', [status(esa)], [u_is_defined])).
% 125.66/18.52 thf(zip_derived_cl1086, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ (multiplicative_inverse @ t) @ X0 @ u)
% 125.66/18.52 | ~ (product @ s @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl1084, zip_derived_cl30])).
% 125.66/18.52 thf(zip_derived_cl1087, plain,
% 125.66/18.52 ((~ (defined @ multiplicative_identity)
% 125.66/18.52 | ~ (defined @ s)
% 125.66/18.52 | (product @ (multiplicative_inverse @ t) @
% 125.66/18.52 (multiply @ s @ multiplicative_identity) @ u))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl1086])).
% 125.66/18.52 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)],
% 125.66/18.52 [well_definedness_of_multiplicative_identity])).
% 125.66/18.52 thf(zip_derived_cl33, plain, ( (defined @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [s_is_defined])).
% 125.66/18.52 thf(zip_derived_cl1089, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ t) @
% 125.66/18.52 (multiply @ s @ multiplicative_identity) @ u)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl1087, zip_derived_cl16, zip_derived_cl33])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl1732, plain,
% 125.66/18.52 ( (product @ (multiply @ s @ multiplicative_identity) @
% 125.66/18.52 (multiplicative_inverse @ t) @ u)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl1089, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl6, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X3 @ X4 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X5)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 125.66/18.52 thf(zip_derived_cl2115, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ (multiply @ s @ multiplicative_identity) @ X1 @ X0)
% 125.66/18.52 | ~ (product @ (multiplicative_inverse @ t) @ X2 @ X1)
% 125.66/18.52 | (product @ u @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl1732, zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl109185, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ u @ X0 @ s)
% 125.66/18.52 | ~ (product @ (multiplicative_inverse @ t) @ X0 @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl1620, zip_derived_cl2115])).
% 125.66/18.52 thf(zip_derived_cl109204, plain,
% 125.66/18.52 ((~ (defined @ t)
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @ t)
% 125.66/18.52 | (product @ u @ t @ s))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl258, zip_derived_cl109185])).
% 125.66/18.52 thf(t_is_defined, axiom, (defined @ t)).
% 125.66/18.52 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 125.66/18.52 inference('cnf', [status(esa)], [t_is_defined])).
% 125.66/18.52 thf(zip_derived_cl109211, plain,
% 125.66/18.52 (( (sum @ additive_identity @ additive_identity @ t)
% 125.66/18.52 | (product @ u @ t @ s))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl109204, zip_derived_cl34])).
% 125.66/18.52 thf(zip_derived_cl80, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl2, plain,
% 125.66/18.52 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 125.66/18.52 thf(commutativity_addition, axiom,
% 125.66/18.52 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 125.66/18.52 thf(zip_derived_cl4, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_addition])).
% 125.66/18.52 thf(zip_derived_cl76, plain,
% 125.66/18.52 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 125.66/18.52 thf(distributivity_2, axiom,
% 125.66/18.52 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 125.66/18.52 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 125.66/18.52 ( ~( sum @ C @ D @ B ) ))).
% 125.66/18.52 thf(zip_derived_cl11, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (sum @ X3 @ X4 @ X0)
% 125.66/18.52 | ~ (product @ X3 @ X1 @ X5)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X6)
% 125.66/18.52 | ~ (sum @ X5 @ X6 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [distributivity_2])).
% 125.66/18.52 thf(zip_derived_cl289, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (sum @ X3 @ X2 @ X1)
% 125.66/18.52 | ~ (product @ additive_identity @ X4 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X4 @ X3)
% 125.66/18.52 | (product @ X0 @ X4 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl11])).
% 125.66/18.52 thf(zip_derived_cl6145, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ additive_identity @ X1 @ X2)
% 125.66/18.52 | ~ (product @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ X0 @ X0 @ X2)
% 125.66/18.52 | ~ (defined @ additive_identity))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl289])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl6147, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ additive_identity @ X1 @ X2)
% 125.66/18.52 | ~ (product @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ X0 @ X0 @ X2))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl6145, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl6276, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ additive_identity)
% 125.66/18.52 | ~ (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl6147])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl6280, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl6276, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl109603, plain,
% 125.66/18.52 (( (product @ u @ t @ s)
% 125.66/18.52 | (product @ additive_identity @ multiplicative_identity @ t))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl109211, zip_derived_cl6280])).
% 125.66/18.52 thf(zip_derived_cl64, plain,
% 125.66/18.52 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl6280, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl6276, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl6289, plain,
% 125.66/18.52 ( (product @ additive_identity @ multiplicative_identity @
% 125.66/18.52 additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl6280])).
% 125.66/18.52 thf(well_definedness_of_multiplication, axiom,
% 125.66/18.52 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 125.66/18.52 ( ~( defined @ Y ) ))).
% 125.66/18.52 thf(zip_derived_cl15, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (defined @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl76, plain,
% 125.66/18.52 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 125.66/18.52 thf(zip_derived_cl258, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('simplify', [status(thm)], [zip_derived_cl249])).
% 125.66/18.52 thf(zip_derived_cl6289, plain,
% 125.66/18.52 ( (product @ additive_identity @ multiplicative_identity @
% 125.66/18.52 additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl6280])).
% 125.66/18.52 thf(distributivity_1, axiom,
% 125.66/18.52 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 125.66/18.52 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 125.66/18.52 ( ~( product @ Y @ Z @ D ) ))).
% 125.66/18.52 thf(zip_derived_cl10, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 125.66/18.52 ( (sum @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (sum @ X3 @ X4 @ X5)
% 125.66/18.52 | ~ (product @ X5 @ X6 @ X2)
% 125.66/18.52 | ~ (product @ X3 @ X6 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X6 @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [distributivity_1])).
% 125.66/18.52 thf(zip_derived_cl241, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (product @ X4 @ X1 @ X3)
% 125.66/18.52 | ~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ X2 @ X4 @ X2)
% 125.66/18.52 | (sum @ X0 @ X3 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 125.66/18.52 thf(zip_derived_cl6307, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (sum @ X0 @ additive_identity @ X0)
% 125.66/18.52 | ~ (sum @ X1 @ additive_identity @ X1)
% 125.66/18.52 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl6289, zip_derived_cl241])).
% 125.66/18.52 thf(zip_derived_cl8376, plain,
% 125.66/18.52 ((~ (defined @ multiplicative_identity)
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | ~ (sum @ (multiplicative_inverse @ multiplicative_identity) @
% 125.66/18.52 additive_identity @
% 125.66/18.52 (multiplicative_inverse @ multiplicative_identity))
% 125.66/18.52 | (sum @ multiplicative_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl258, zip_derived_cl6307])).
% 125.66/18.52 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)],
% 125.66/18.52 [well_definedness_of_multiplicative_identity])).
% 125.66/18.52 thf(zip_derived_cl25, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [different_identities])).
% 125.66/18.52 thf(zip_derived_cl8437, plain,
% 125.66/18.52 ((~ (sum @ (multiplicative_inverse @ multiplicative_identity) @
% 125.66/18.52 additive_identity @
% 125.66/18.52 (multiplicative_inverse @ multiplicative_identity))
% 125.66/18.52 | (sum @ multiplicative_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl8376, zip_derived_cl16, zip_derived_cl25])).
% 125.66/18.52 thf(zip_derived_cl8589, plain,
% 125.66/18.52 ((~ (defined @ (multiplicative_inverse @ multiplicative_identity))
% 125.66/18.52 | (sum @ multiplicative_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl8437])).
% 125.66/18.52 thf(zip_derived_cl17, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (defined @ (multiplicative_inverse @ X0))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity))),
% 125.66/18.52 inference('cnf', [status(esa)],
% 125.66/18.52 [well_definedness_of_multiplicative_inverse])).
% 125.66/18.52 thf(zip_derived_cl157, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ additive_identity @ X0 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl66])).
% 125.66/18.52 thf(zip_derived_cl250, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (defined @ (multiplicative_inverse @ X0))
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl157])).
% 125.66/18.52 thf(zip_derived_cl259, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (defined @ (multiplicative_inverse @ X0))
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('simplify', [status(thm)], [zip_derived_cl250])).
% 125.66/18.52 thf(zip_derived_cl25, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [different_identities])).
% 125.66/18.52 thf(zip_derived_cl1787, plain,
% 125.66/18.52 ((~ (defined @ multiplicative_identity)
% 125.66/18.52 | (defined @ (multiplicative_inverse @ multiplicative_identity)))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl259, zip_derived_cl25])).
% 125.66/18.52 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)],
% 125.66/18.52 [well_definedness_of_multiplicative_identity])).
% 125.66/18.52 thf(zip_derived_cl1802, plain,
% 125.66/18.52 ( (defined @ (multiplicative_inverse @ multiplicative_identity))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl1787, zip_derived_cl16])).
% 125.66/18.52 thf(zip_derived_cl8590, plain,
% 125.66/18.52 ( (sum @ multiplicative_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl8589, zip_derived_cl1802])).
% 125.66/18.52 thf(zip_derived_cl4, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_addition])).
% 125.66/18.52 thf(zip_derived_cl8594, plain,
% 125.66/18.52 ( (sum @ additive_identity @ multiplicative_identity @
% 125.66/18.52 multiplicative_identity)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8590, zip_derived_cl4])).
% 125.66/18.52 thf(zip_derived_cl6289, plain,
% 125.66/18.52 ( (product @ additive_identity @ multiplicative_identity @
% 125.66/18.52 additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl6280])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl6301, plain,
% 125.66/18.52 ( (product @ multiplicative_identity @ additive_identity @
% 125.66/18.52 additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl6289, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl10, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 125.66/18.52 ( (sum @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (sum @ X3 @ X4 @ X5)
% 125.66/18.52 | ~ (product @ X5 @ X6 @ X2)
% 125.66/18.52 | ~ (product @ X3 @ X6 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X6 @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [distributivity_1])).
% 125.66/18.52 thf(zip_derived_cl242, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X3)
% 125.66/18.52 | ~ (sum @ X4 @ X2 @ X2)
% 125.66/18.52 | (sum @ X3 @ X0 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 125.66/18.52 thf(zip_derived_cl6321, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (sum @ X0 @ additive_identity @ additive_identity)
% 125.66/18.52 | ~ (sum @ X1 @ multiplicative_identity @ multiplicative_identity)
% 125.66/18.52 | ~ (product @ X1 @ additive_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl6301, zip_derived_cl242])).
% 125.66/18.52 thf(zip_derived_cl12499, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (product @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (sum @ X0 @ additive_identity @ additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8594, zip_derived_cl6321])).
% 125.66/18.52 thf(zip_derived_cl12505, plain,
% 125.66/18.52 ((~ (defined @ additive_identity)
% 125.66/18.52 | ~ (defined @ additive_identity)
% 125.66/18.52 | (sum @ (multiply @ additive_identity @ additive_identity) @
% 125.66/18.52 additive_identity @ additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl12499])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl12507, plain,
% 125.66/18.52 ( (sum @ (multiply @ additive_identity @ additive_identity) @
% 125.66/18.52 additive_identity @ additive_identity)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl12505, zip_derived_cl13, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl76, plain,
% 125.66/18.52 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 125.66/18.52 thf(zip_derived_cl2, plain,
% 125.66/18.52 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 125.66/18.52 thf(zip_derived_cl0, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (sum @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (sum @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (sum @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (sum @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_addition_1])).
% 125.66/18.52 thf(zip_derived_cl52, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (sum @ X0 @ X2 @ X1)
% 125.66/18.52 | ~ (sum @ X0 @ X2 @ X3)
% 125.66/18.52 | (sum @ additive_identity @ X3 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 125.66/18.52 thf(zip_derived_cl764, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ X0 @ additive_identity @ X1)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl52])).
% 125.66/18.52 thf(zip_derived_cl784, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (sum @ X0 @ additive_identity @ X1)
% 125.66/18.52 | (sum @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('simplify', [status(thm)], [zip_derived_cl764])).
% 125.66/18.52 thf(zip_derived_cl12613, plain,
% 125.66/18.52 ((~ (defined @ (multiply @ additive_identity @ additive_identity))
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @
% 125.66/18.52 (multiply @ additive_identity @ additive_identity)))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl12507, zip_derived_cl784])).
% 125.66/18.52 thf(zip_derived_cl13078, plain,
% 125.66/18.52 ((~ (defined @ additive_identity)
% 125.66/18.52 | ~ (defined @ additive_identity)
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @
% 125.66/18.52 (multiply @ additive_identity @ additive_identity)))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl12613])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl13079, plain,
% 125.66/18.52 ( (sum @ additive_identity @ additive_identity @
% 125.66/18.52 (multiply @ additive_identity @ additive_identity))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl13078, zip_derived_cl13, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl6280, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl6276, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl13135, plain,
% 125.66/18.52 ( (product @ additive_identity @ multiplicative_identity @
% 125.66/18.52 (multiply @ additive_identity @ additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl13079, zip_derived_cl6280])).
% 125.66/18.52 thf(zip_derived_cl6289, plain,
% 125.66/18.52 ( (product @ additive_identity @ multiplicative_identity @
% 125.66/18.52 additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl6280])).
% 125.66/18.52 thf(zip_derived_cl92, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (product @ X0 @ X2 @ X1)
% 125.66/18.52 | ~ (product @ X0 @ X2 @ X3)
% 125.66/18.52 | (product @ multiplicative_identity @ X3 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl6303, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 125.66/18.52 | ~ (defined @ additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl6289, zip_derived_cl92])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl6314, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl6303, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl13796, plain,
% 125.66/18.52 ( (product @ multiplicative_identity @
% 125.66/18.52 (multiply @ additive_identity @ additive_identity) @ additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl13135, zip_derived_cl6314])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl13830, plain,
% 125.66/18.52 ( (product @ (multiply @ additive_identity @ additive_identity) @
% 125.66/18.52 multiplicative_identity @ additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl13796, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl5, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (product @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 125.66/18.52 thf(zip_derived_cl454, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1)
% 125.66/18.52 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | (product @ X1 @ X4 @ X2))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl13911, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 125.66/18.52 | ~ (defined @ additive_identity)
% 125.66/18.52 | ~ (defined @ additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl13830, zip_derived_cl454])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 125.66/18.52 thf(zip_derived_cl13915, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl13911, zip_derived_cl13, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl14008, plain,
% 125.66/18.52 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl6289, zip_derived_cl13915])).
% 125.66/18.52 thf(zip_derived_cl5, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (product @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 125.66/18.52 thf(zip_derived_cl14018, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (product @ additive_identity @ X1 @ X2)
% 125.66/18.52 | (product @ additive_identity @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl14008, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl16698, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ additive_identity @ X0 @ X0)
% 125.66/18.52 | ~ (product @ additive_identity @ X1 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl14018])).
% 125.66/18.52 thf(zip_derived_cl110571, plain,
% 125.66/18.52 (( (product @ u @ t @ s) | (product @ additive_identity @ t @ t))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl109603, zip_derived_cl16698])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl111294, plain,
% 125.66/18.52 (( (product @ u @ t @ s) | (product @ t @ additive_identity @ t))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl110571, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl80, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl42, plain, ( (product @ b @ c @ l)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_0])).
% 125.66/18.52 thf(zip_derived_cl42, plain, ( (product @ b @ c @ l)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_0])).
% 125.66/18.52 thf(zip_derived_cl6, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X3 @ X4 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X5)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 125.66/18.52 thf(zip_derived_cl142, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ b @ X1 @ X0)
% 125.66/18.52 | ~ (product @ c @ X2 @ X1)
% 125.66/18.52 | (product @ l @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl312, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ l @ X0 @ l) | ~ (product @ c @ X0 @ c))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl142])).
% 125.66/18.52 thf(zip_derived_cl314, plain,
% 125.66/18.52 ((~ (defined @ c) | (product @ l @ multiplicative_identity @ l))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl312])).
% 125.66/18.52 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 125.66/18.52 inference('cnf', [status(esa)], [c_is_defined])).
% 125.66/18.52 thf(zip_derived_cl315, plain, ( (product @ l @ multiplicative_identity @ l)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl314, zip_derived_cl28])).
% 125.66/18.52 thf(zip_derived_cl182, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl80, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl42, plain, ( (product @ b @ c @ l)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_0])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl83, plain, ( (product @ c @ b @ l)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl6, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X3 @ X4 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X5)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 125.66/18.52 thf(zip_derived_cl144, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ c @ X1 @ X0)
% 125.66/18.52 | ~ (product @ b @ X2 @ X1)
% 125.66/18.52 | (product @ l @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl344, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ c)
% 125.66/18.52 | (product @ l @ X0 @ c)
% 125.66/18.52 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl144])).
% 125.66/18.52 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 125.66/18.52 inference('cnf', [status(esa)], [c_is_defined])).
% 125.66/18.52 thf(zip_derived_cl347, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ l @ X0 @ c)
% 125.66/18.52 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl344, zip_derived_cl28])).
% 125.66/18.52 thf(zip_derived_cl2874, plain,
% 125.66/18.52 (( (sum @ additive_identity @ b @ additive_identity)
% 125.66/18.52 | ~ (defined @ b)
% 125.66/18.52 | (product @ l @ (multiplicative_inverse @ b) @ c))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl347])).
% 125.66/18.52 thf(zip_derived_cl35, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ b @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_3])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl2919, plain,
% 125.66/18.52 ( (product @ l @ (multiplicative_inverse @ b) @ c)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl2874, zip_derived_cl35, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl2946, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ b) @ l @ c)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2919, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl149, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X1 @ X3 @ X1)
% 125.66/18.52 | (product @ X0 @ X3 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl2982, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ c @ X0 @ c) | ~ (product @ l @ X0 @ l))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2946, zip_derived_cl149])).
% 125.66/18.52 thf(zip_derived_cl3065, plain,
% 125.66/18.52 ( (product @ c @ multiplicative_identity @ c)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl315, zip_derived_cl2982])).
% 125.66/18.52 thf(zip_derived_cl22, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (less_or_equal @ X0 @ X1)
% 125.66/18.52 | (less_or_equal @ X1 @ X0)
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 125.66/18.52 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 125.66/18.52 inference('cnf', [status(esa)], [d_is_defined])).
% 125.66/18.52 thf(zip_derived_cl563, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (less_or_equal @ X0 @ d)
% 125.66/18.52 | (less_or_equal @ d @ X0))),
% 125.66/18.52 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl29])).
% 125.66/18.52 thf(zip_derived_cl18608, plain,
% 125.66/18.52 (( (less_or_equal @ d @ d) | ~ (defined @ d))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl563])).
% 125.66/18.52 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 125.66/18.52 inference('cnf', [status(esa)], [d_is_defined])).
% 125.66/18.52 thf(zip_derived_cl18609, plain, ( (less_or_equal @ d @ d)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl18608, zip_derived_cl29])).
% 125.66/18.52 thf(zip_derived_cl20, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X1 @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 125.66/18.52 thf(zip_derived_cl18615, plain,
% 125.66/18.52 ((~ (less_or_equal @ d @ d) | (sum @ additive_identity @ d @ d))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18609, zip_derived_cl20])).
% 125.66/18.52 thf(zip_derived_cl18609, plain, ( (less_or_equal @ d @ d)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl18608, zip_derived_cl29])).
% 125.66/18.52 thf(zip_derived_cl18618, plain, ( (sum @ additive_identity @ d @ d)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl18615, zip_derived_cl18609])).
% 125.66/18.52 thf(zip_derived_cl187, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | (sum @ additive_identity @ X1 @ additive_identity)
% 125.66/18.52 | ~ (sum @ additive_identity @ X0 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl66])).
% 125.66/18.52 thf(zip_derived_cl18633, plain,
% 125.66/18.52 (( (sum @ additive_identity @ d @ additive_identity)
% 125.66/18.52 | (product @ (multiplicative_inverse @ d) @ d @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | ~ (defined @ d))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18618, zip_derived_cl187])).
% 125.66/18.52 thf(zip_derived_cl37, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ d @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_2])).
% 125.66/18.52 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 125.66/18.52 inference('cnf', [status(esa)], [d_is_defined])).
% 125.66/18.52 thf(zip_derived_cl18664, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ d) @ d @ multiplicative_identity)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl18633, zip_derived_cl37, zip_derived_cl29])).
% 125.66/18.52 thf(zip_derived_cl143, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ c @ X1 @ X0)
% 125.66/18.52 | ~ (product @ (multiplicative_inverse @ d) @ X2 @ X1)
% 125.66/18.52 | (product @ t @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl18730, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ t @ d @ X0)
% 125.66/18.52 | ~ (product @ c @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18664, zip_derived_cl143])).
% 125.66/18.52 thf(zip_derived_cl19362, plain, ( (product @ t @ d @ c)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl3065, zip_derived_cl18730])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl19368, plain, ( (product @ d @ t @ c)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19362, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl149, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X1 @ X3 @ X1)
% 125.66/18.52 | (product @ X0 @ X3 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl19387, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ c @ X0 @ c) | ~ (product @ t @ X0 @ t))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19368, zip_derived_cl149])).
% 125.66/18.52 thf(zip_derived_cl111748, plain,
% 125.66/18.52 (( (product @ u @ t @ s) | (product @ c @ additive_identity @ c))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl111294, zip_derived_cl19387])).
% 125.66/18.52 thf(zip_derived_cl22, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (less_or_equal @ X0 @ X1)
% 125.66/18.52 | (less_or_equal @ X1 @ X0)
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 125.66/18.52 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 125.66/18.52 inference('cnf', [status(esa)], [c_is_defined])).
% 125.66/18.52 thf(zip_derived_cl562, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (less_or_equal @ X0 @ c)
% 125.66/18.52 | (less_or_equal @ c @ X0))),
% 125.66/18.52 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl28])).
% 125.66/18.52 thf(zip_derived_cl18489, plain,
% 125.66/18.52 (( (less_or_equal @ c @ c) | ~ (defined @ c))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl562])).
% 125.66/18.52 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 125.66/18.52 inference('cnf', [status(esa)], [c_is_defined])).
% 125.66/18.52 thf(zip_derived_cl18490, plain, ( (less_or_equal @ c @ c)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl18489, zip_derived_cl28])).
% 125.66/18.52 thf(zip_derived_cl20, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X1 @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 125.66/18.52 thf(zip_derived_cl18496, plain,
% 125.66/18.52 ((~ (less_or_equal @ c @ c) | (sum @ additive_identity @ c @ c))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18490, zip_derived_cl20])).
% 125.66/18.52 thf(zip_derived_cl18490, plain, ( (less_or_equal @ c @ c)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl18489, zip_derived_cl28])).
% 125.66/18.52 thf(zip_derived_cl18499, plain, ( (sum @ additive_identity @ c @ c)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl18496, zip_derived_cl18490])).
% 125.66/18.52 thf(zip_derived_cl187, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | (sum @ additive_identity @ X1 @ additive_identity)
% 125.66/18.52 | ~ (sum @ additive_identity @ X0 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl66])).
% 125.66/18.52 thf(zip_derived_cl18514, plain,
% 125.66/18.52 (( (sum @ additive_identity @ c @ additive_identity)
% 125.66/18.52 | (product @ (multiplicative_inverse @ c) @ c @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | ~ (defined @ c))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18499, zip_derived_cl187])).
% 125.66/18.52 thf(not_sum_11, conjecture,
% 125.66/18.52 (sum @ additive_identity @ c @ additive_identity)).
% 125.66/18.52 thf(zf_stmt_7, negated_conjecture,
% 125.66/18.52 (~( sum @ additive_identity @ c @ additive_identity )),
% 125.66/18.52 inference('cnf.neg', [status(esa)], [not_sum_11])).
% 125.66/18.52 thf(zip_derived_cl36, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ c @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_7])).
% 125.66/18.52 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 125.66/18.52 inference('cnf', [status(esa)], [c_is_defined])).
% 125.66/18.52 thf(zip_derived_cl18545, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ c) @ c @ multiplicative_identity)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl18514, zip_derived_cl36, zip_derived_cl28])).
% 125.66/18.52 thf(zip_derived_cl149, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X1 @ X3 @ X1)
% 125.66/18.52 | (product @ X0 @ X3 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl18580, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ multiplicative_identity)
% 125.66/18.52 | ~ (product @ c @ X0 @ c))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18545, zip_derived_cl149])).
% 125.66/18.52 thf(zip_derived_cl111886, plain,
% 125.66/18.52 (( (product @ u @ t @ s)
% 125.66/18.52 | (product @ multiplicative_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl111748, zip_derived_cl18580])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl112868, plain,
% 125.66/18.52 (( (product @ u @ t @ s)
% 125.66/18.52 | (product @ additive_identity @ multiplicative_identity @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl111886, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl64, plain,
% 125.66/18.52 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl6289, plain,
% 125.66/18.52 ( (product @ additive_identity @ multiplicative_identity @
% 125.66/18.52 additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl6280])).
% 125.66/18.52 thf(zip_derived_cl242, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X4 @ X1 @ X3)
% 125.66/18.52 | ~ (sum @ X4 @ X2 @ X2)
% 125.66/18.52 | (sum @ X3 @ X0 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 125.66/18.52 thf(zip_derived_cl6305, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (sum @ X0 @ additive_identity @ additive_identity)
% 125.66/18.52 | ~ (sum @ X1 @ additive_identity @ additive_identity)
% 125.66/18.52 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl6289, zip_derived_cl242])).
% 125.66/18.52 thf(zip_derived_cl6570, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (product @ additive_identity @ multiplicative_identity @ X0)
% 125.66/18.52 | (sum @ X0 @ additive_identity @ additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl6305])).
% 125.66/18.52 thf(zip_derived_cl113495, plain,
% 125.66/18.52 (( (product @ u @ t @ s)
% 125.66/18.52 | (sum @ multiplicative_identity @ additive_identity @
% 125.66/18.52 additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl112868, zip_derived_cl6570])).
% 125.66/18.52 thf(zip_derived_cl8590, plain,
% 125.66/18.52 ( (sum @ multiplicative_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl8589, zip_derived_cl1802])).
% 125.66/18.52 thf(zip_derived_cl52, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (sum @ X0 @ X2 @ X1)
% 125.66/18.52 | ~ (sum @ X0 @ X2 @ X3)
% 125.66/18.52 | (sum @ additive_identity @ X3 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 125.66/18.52 thf(zip_derived_cl8601, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 125.66/18.52 | ~ (sum @ multiplicative_identity @ additive_identity @ X0)
% 125.66/18.52 | ~ (defined @ multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8590, zip_derived_cl52])).
% 125.66/18.52 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)],
% 125.66/18.52 [well_definedness_of_multiplicative_identity])).
% 125.66/18.52 thf(zip_derived_cl8610, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 125.66/18.52 | ~ (sum @ multiplicative_identity @ additive_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl8601, zip_derived_cl16])).
% 125.66/18.52 thf(zip_derived_cl113606, plain,
% 125.66/18.52 (( (product @ u @ t @ s)
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl113495, zip_derived_cl8610])).
% 125.66/18.52 thf(zip_derived_cl25, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [different_identities])).
% 125.66/18.52 thf(zip_derived_cl114259, plain, ( (product @ u @ t @ s)),
% 125.66/18.52 inference('clc', [status(thm)], [zip_derived_cl113606, zip_derived_cl25])).
% 125.66/18.52 thf(zip_derived_cl95, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ u @ X1 @ X0)
% 125.66/18.52 | ~ (product @ s @ X1 @ X2)
% 125.66/18.52 | (product @ (multiplicative_inverse @ t) @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl114279, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ (multiplicative_inverse @ t) @ X0 @ s)
% 125.66/18.52 | ~ (product @ s @ t @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl114259, zip_derived_cl95])).
% 125.66/18.52 thf(zip_derived_cl115028, plain,
% 125.66/18.52 ((~ (defined @ t)
% 125.66/18.52 | ~ (defined @ s)
% 125.66/18.52 | (product @ (multiplicative_inverse @ t) @ (multiply @ s @ t) @ s))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl114279])).
% 125.66/18.52 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 125.66/18.52 inference('cnf', [status(esa)], [t_is_defined])).
% 125.66/18.52 thf(zip_derived_cl33, plain, ( (defined @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [s_is_defined])).
% 125.66/18.52 thf(zip_derived_cl115030, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ t) @ (multiply @ s @ t) @ s)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl115028, zip_derived_cl34, zip_derived_cl33])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl117665, plain,
% 125.66/18.52 ( (product @ (multiply @ s @ t) @ (multiplicative_inverse @ t) @ s)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl115030, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl454, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1)
% 125.66/18.52 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | (product @ X1 @ X4 @ X2))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl120157, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ s @ X0 @ s)
% 125.66/18.52 | ~ (product @ t @ (multiplicative_inverse @ t) @ X0)
% 125.66/18.52 | ~ (defined @ s)
% 125.66/18.52 | ~ (defined @ t))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl117665, zip_derived_cl454])).
% 125.66/18.52 thf(zip_derived_cl33, plain, ( (defined @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [s_is_defined])).
% 125.66/18.52 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 125.66/18.52 inference('cnf', [status(esa)], [t_is_defined])).
% 125.66/18.52 thf(zip_derived_cl120162, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ s @ X0 @ s)
% 125.66/18.52 | ~ (product @ t @ (multiplicative_inverse @ t) @ X0))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl120157, zip_derived_cl33, zip_derived_cl34])).
% 125.66/18.52 thf(zip_derived_cl120165, plain,
% 125.66/18.52 ((~ (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | ~ (defined @ t)
% 125.66/18.52 | (product @ s @ (multiply @ (multiplicative_inverse @ t) @ t) @ s))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl456, zip_derived_cl120162])).
% 125.66/18.52 thf(zip_derived_cl17, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (defined @ (multiplicative_inverse @ X0))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity))),
% 125.66/18.52 inference('cnf', [status(esa)],
% 125.66/18.52 [well_definedness_of_multiplicative_inverse])).
% 125.66/18.52 thf(zip_derived_cl22, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (less_or_equal @ X0 @ X1)
% 125.66/18.52 | (less_or_equal @ X1 @ X0)
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 125.66/18.52 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 125.66/18.52 inference('cnf', [status(esa)], [t_is_defined])).
% 125.66/18.52 thf(zip_derived_cl568, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (less_or_equal @ X0 @ t)
% 125.66/18.52 | (less_or_equal @ t @ X0))),
% 125.66/18.52 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl34])).
% 125.66/18.52 thf(zip_derived_cl19213, plain,
% 125.66/18.52 (( (less_or_equal @ t @ t) | ~ (defined @ t))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl568])).
% 125.66/18.52 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 125.66/18.52 inference('cnf', [status(esa)], [t_is_defined])).
% 125.66/18.52 thf(zip_derived_cl19214, plain, ( (less_or_equal @ t @ t)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl19213, zip_derived_cl34])).
% 125.66/18.52 thf(zip_derived_cl20, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X1 @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 125.66/18.52 thf(zip_derived_cl19220, plain,
% 125.66/18.52 ((~ (less_or_equal @ t @ t) | (sum @ additive_identity @ t @ t))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19214, zip_derived_cl20])).
% 125.66/18.52 thf(zip_derived_cl19214, plain, ( (less_or_equal @ t @ t)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl19213, zip_derived_cl34])).
% 125.66/18.52 thf(zip_derived_cl19223, plain, ( (sum @ additive_identity @ t @ t)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl19220, zip_derived_cl19214])).
% 125.66/18.52 thf(zip_derived_cl66, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (sum @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ additive_identity @ X1 @ X2)
% 125.66/18.52 | (sum @ additive_identity @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 125.66/18.52 thf(zip_derived_cl19249, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ t)
% 125.66/18.52 | ~ (sum @ additive_identity @ t @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19223, zip_derived_cl66])).
% 125.66/18.52 thf(zip_derived_cl20754, plain,
% 125.66/18.52 ((~ (defined @ t)
% 125.66/18.52 | (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @ t))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl19249])).
% 125.66/18.52 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 125.66/18.52 inference('cnf', [status(esa)], [t_is_defined])).
% 125.66/18.52 thf(zip_derived_cl20761, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @ t))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl20754, zip_derived_cl34])).
% 125.66/18.52 thf(zip_derived_cl14008, plain,
% 125.66/18.52 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl6289, zip_derived_cl13915])).
% 125.66/18.52 thf(zip_derived_cl6147, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ additive_identity @ X1 @ X2)
% 125.66/18.52 | ~ (product @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ X0 @ X0 @ X2))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl6145, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl14038, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (product @ additive_identity @ additive_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl14008, zip_derived_cl6147])).
% 125.66/18.52 thf(zip_derived_cl22652, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (product @ additive_identity @ additive_identity @ t))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl20761, zip_derived_cl14038])).
% 125.66/18.52 thf(zip_derived_cl16698, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ additive_identity @ X0 @ X0)
% 125.66/18.52 | ~ (product @ additive_identity @ X1 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl14018])).
% 125.66/18.52 thf(zip_derived_cl24407, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (product @ additive_identity @ t @ t))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl22652, zip_derived_cl16698])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl28822, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (product @ t @ additive_identity @ t))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl24407, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl19387, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ c @ X0 @ c) | ~ (product @ t @ X0 @ t))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19368, zip_derived_cl149])).
% 125.66/18.52 thf(zip_derived_cl30020, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (product @ c @ additive_identity @ c))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl28822, zip_derived_cl19387])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl182, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl80, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl142, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ b @ X1 @ X0)
% 125.66/18.52 | ~ (product @ c @ X2 @ X1)
% 125.66/18.52 | (product @ l @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl311, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ b)
% 125.66/18.52 | (product @ l @ X0 @ b)
% 125.66/18.52 | ~ (product @ c @ X0 @ multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl142])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl313, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ l @ X0 @ b)
% 125.66/18.52 | ~ (product @ c @ X0 @ multiplicative_identity))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl311, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl2876, plain,
% 125.66/18.52 (( (sum @ additive_identity @ c @ additive_identity)
% 125.66/18.52 | ~ (defined @ c)
% 125.66/18.52 | (product @ l @ (multiplicative_inverse @ c) @ b))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl313])).
% 125.66/18.52 thf(zip_derived_cl36, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ c @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_7])).
% 125.66/18.52 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 125.66/18.52 inference('cnf', [status(esa)], [c_is_defined])).
% 125.66/18.52 thf(zip_derived_cl2921, plain,
% 125.66/18.52 ( (product @ l @ (multiplicative_inverse @ c) @ b)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl2876, zip_derived_cl36, zip_derived_cl28])).
% 125.66/18.52 thf(zip_derived_cl83, plain, ( (product @ c @ b @ l)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl5, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (product @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 125.66/18.52 thf(zip_derived_cl100, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ l @ X1 @ X0)
% 125.66/18.52 | ~ (product @ b @ X1 @ X2)
% 125.66/18.52 | (product @ c @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl2962, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ c @ X0 @ b)
% 125.66/18.52 | ~ (product @ b @ (multiplicative_inverse @ c) @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl2921, zip_derived_cl100])).
% 125.66/18.52 thf(zip_derived_cl3864, plain,
% 125.66/18.52 ((~ (defined @ (multiplicative_inverse @ c))
% 125.66/18.52 | ~ (defined @ b)
% 125.66/18.52 | (product @ c @ (multiply @ b @ (multiplicative_inverse @ c)) @ b))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl2962])).
% 125.66/18.52 thf(zip_derived_cl17, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (defined @ (multiplicative_inverse @ X0))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity))),
% 125.66/18.52 inference('cnf', [status(esa)],
% 125.66/18.52 [well_definedness_of_multiplicative_inverse])).
% 125.66/18.52 thf(zip_derived_cl36, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ c @ additive_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_7])).
% 125.66/18.52 thf(zip_derived_cl125, plain,
% 125.66/18.52 ((~ (defined @ c) | (defined @ (multiplicative_inverse @ c)))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl36])).
% 125.66/18.52 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 125.66/18.52 inference('cnf', [status(esa)], [c_is_defined])).
% 125.66/18.52 thf(zip_derived_cl130, plain, ( (defined @ (multiplicative_inverse @ c))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl125, zip_derived_cl28])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl3865, plain,
% 125.66/18.52 ( (product @ c @ (multiply @ b @ (multiplicative_inverse @ c)) @ b)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl3864, zip_derived_cl130, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl3974, plain,
% 125.66/18.52 ( (product @ (multiply @ b @ (multiplicative_inverse @ c)) @ c @ b)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl3865, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl149, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X1 @ X3 @ X1)
% 125.66/18.52 | (product @ X0 @ X3 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl4161, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ b @ X0 @ b) | ~ (product @ c @ X0 @ c))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl3974, zip_derived_cl149])).
% 125.66/18.52 thf(zip_derived_cl30295, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (product @ b @ additive_identity @ b))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl30020, zip_derived_cl4161])).
% 125.66/18.52 thf(zip_derived_cl18402, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ b) @ b @ multiplicative_identity)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl18371, zip_derived_cl35, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl149, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X1 @ X3 @ X1)
% 125.66/18.52 | (product @ X0 @ X3 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl18437, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ multiplicative_identity)
% 125.66/18.52 | ~ (product @ b @ X0 @ b))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18402, zip_derived_cl149])).
% 125.66/18.52 thf(zip_derived_cl86140, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (product @ multiplicative_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl30295, zip_derived_cl18437])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl86209, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (product @ additive_identity @ multiplicative_identity @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl86140, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl6570, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (product @ additive_identity @ multiplicative_identity @ X0)
% 125.66/18.52 | (sum @ X0 @ additive_identity @ additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl6305])).
% 125.66/18.52 thf(zip_derived_cl86719, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (sum @ multiplicative_identity @ additive_identity @
% 125.66/18.52 additive_identity))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl86209, zip_derived_cl6570])).
% 125.66/18.52 thf(zip_derived_cl8610, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 125.66/18.52 | ~ (sum @ multiplicative_identity @ additive_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl8601, zip_derived_cl16])).
% 125.66/18.52 thf(zip_derived_cl87247, plain,
% 125.66/18.52 (( (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | (sum @ additive_identity @ additive_identity @
% 125.66/18.52 multiplicative_identity))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl86719, zip_derived_cl8610])).
% 125.66/18.52 thf(zip_derived_cl25, plain,
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 125.66/18.52 inference('cnf', [status(esa)], [different_identities])).
% 125.66/18.52 thf(zip_derived_cl87516, plain, ( (defined @ (multiplicative_inverse @ t))),
% 125.66/18.52 inference('clc', [status(thm)], [zip_derived_cl87247, zip_derived_cl25])).
% 125.66/18.52 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 125.66/18.52 inference('cnf', [status(esa)], [t_is_defined])).
% 125.66/18.52 thf(zip_derived_cl120171, plain,
% 125.66/18.52 ( (product @ s @ (multiply @ (multiplicative_inverse @ t) @ t) @ s)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl120165, zip_derived_cl87516, zip_derived_cl34])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl19, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 125.66/18.52 thf(zip_derived_cl18402, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ b) @ b @ multiplicative_identity)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl18371, zip_derived_cl35, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl39, plain,
% 125.66/18.52 ( (product @ a @ (multiplicative_inverse @ b) @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_4])).
% 125.66/18.52 thf(zip_derived_cl5, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (product @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 125.66/18.52 thf(zip_derived_cl96, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ s @ X1 @ X0)
% 125.66/18.52 | ~ (product @ (multiplicative_inverse @ b) @ X1 @ X2)
% 125.66/18.52 | (product @ a @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl18444, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ a @ multiplicative_identity @ X0)
% 125.66/18.52 | ~ (product @ s @ b @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18402, zip_derived_cl96])).
% 125.66/18.52 thf(zip_derived_cl18903, plain,
% 125.66/18.52 ((~ (defined @ b)
% 125.66/18.52 | ~ (defined @ s)
% 125.66/18.52 | (product @ a @ multiplicative_identity @ (multiply @ s @ b)))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl18444])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl33, plain, ( (defined @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [s_is_defined])).
% 125.66/18.52 thf(zip_derived_cl18905, plain,
% 125.66/18.52 ( (product @ a @ multiplicative_identity @ (multiply @ s @ b))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl18903, zip_derived_cl27, zip_derived_cl33])).
% 125.66/18.52 thf(zip_derived_cl80, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl41, plain, ( (product @ a @ d @ k)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_1])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl82, plain, ( (product @ d @ a @ k)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl5, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (product @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 125.66/18.52 thf(zip_derived_cl101, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (product @ k @ X1 @ X0)
% 125.66/18.52 | ~ (product @ a @ X1 @ X2)
% 125.66/18.52 | (product @ d @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl208, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ k)
% 125.66/18.52 | (product @ d @ X0 @ k)
% 125.66/18.52 | ~ (product @ a @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl101])).
% 125.66/18.52 thf(k_is_defined, axiom, (defined @ k)).
% 125.66/18.52 thf(zip_derived_cl31, plain, ( (defined @ k)),
% 125.66/18.52 inference('cnf', [status(esa)], [k_is_defined])).
% 125.66/18.52 thf(zip_derived_cl209, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ d @ X0 @ k)
% 125.66/18.52 | ~ (product @ a @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl208, zip_derived_cl31])).
% 125.66/18.52 thf(zip_derived_cl24166, plain, ( (product @ d @ (multiply @ s @ b) @ k)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18905, zip_derived_cl209])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl24177, plain, ( (product @ (multiply @ s @ b) @ d @ k)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl24166, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl454, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1)
% 125.66/18.52 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | (product @ X1 @ X4 @ X2))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl24219, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ s @ X0 @ k)
% 125.66/18.52 | ~ (product @ b @ d @ X0)
% 125.66/18.52 | ~ (defined @ s)
% 125.66/18.52 | ~ (defined @ b))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl24177, zip_derived_cl454])).
% 125.66/18.52 thf(zip_derived_cl33, plain, ( (defined @ s)),
% 125.66/18.52 inference('cnf', [status(esa)], [s_is_defined])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl24221, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ s @ X0 @ k) | ~ (product @ b @ d @ X0))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl24219, zip_derived_cl33, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl24268, plain,
% 125.66/18.52 ((~ (defined @ d)
% 125.66/18.52 | ~ (defined @ b)
% 125.66/18.52 | (product @ s @ (multiply @ b @ d) @ k))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl24221])).
% 125.66/18.52 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 125.66/18.52 inference('cnf', [status(esa)], [d_is_defined])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl24270, plain, ( (product @ s @ (multiply @ b @ d) @ k)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl24268, zip_derived_cl29, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl24296, plain, ( (product @ (multiply @ b @ d) @ s @ k)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl24270, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl149, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (product @ X2 @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X1 @ X3 @ X1)
% 125.66/18.52 | (product @ X0 @ X3 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 125.66/18.52 thf(zip_derived_cl24363, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ k @ X0 @ k) | ~ (product @ s @ X0 @ s))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl24296, zip_derived_cl149])).
% 125.66/18.52 thf(zip_derived_cl121396, plain,
% 125.66/18.52 ( (product @ k @ (multiply @ (multiplicative_inverse @ t) @ t) @ k)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl120171, zip_derived_cl24363])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl123387, plain,
% 125.66/18.52 ( (product @ (multiply @ (multiplicative_inverse @ t) @ t) @ k @ k)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl121396, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl454, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1)
% 125.66/18.52 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | (product @ X1 @ X4 @ X2))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl125367, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ (multiplicative_inverse @ t) @ X0 @ k)
% 125.66/18.52 | ~ (product @ t @ k @ X0)
% 125.66/18.52 | ~ (defined @ (multiplicative_inverse @ t))
% 125.66/18.52 | ~ (defined @ t))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl123387, zip_derived_cl454])).
% 125.66/18.52 thf(zip_derived_cl87516, plain, ( (defined @ (multiplicative_inverse @ t))),
% 125.66/18.52 inference('clc', [status(thm)], [zip_derived_cl87247, zip_derived_cl25])).
% 125.66/18.52 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 125.66/18.52 inference('cnf', [status(esa)], [t_is_defined])).
% 125.66/18.52 thf(zip_derived_cl125373, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ (multiplicative_inverse @ t) @ X0 @ k)
% 125.66/18.52 | ~ (product @ t @ k @ X0))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl125367, zip_derived_cl87516, zip_derived_cl34])).
% 125.66/18.52 thf(zip_derived_cl125377, plain,
% 125.66/18.52 ( (product @ (multiplicative_inverse @ t) @ (multiply @ c @ a) @ k)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl3403, zip_derived_cl125373])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl126180, plain,
% 125.66/18.52 ( (product @ (multiply @ c @ a) @ (multiplicative_inverse @ t) @ k)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl125377, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl454, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1)
% 125.66/18.52 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | (product @ X1 @ X4 @ X2))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl127417, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ c @ X0 @ k)
% 125.66/18.52 | ~ (product @ a @ (multiplicative_inverse @ t) @ X0)
% 125.66/18.52 | ~ (defined @ c)
% 125.66/18.52 | ~ (defined @ a))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl126180, zip_derived_cl454])).
% 125.66/18.52 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 125.66/18.52 inference('cnf', [status(esa)], [c_is_defined])).
% 125.66/18.52 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 125.66/18.52 inference('cnf', [status(esa)], [a_is_defined])).
% 125.66/18.52 thf(zip_derived_cl127422, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ c @ X0 @ k)
% 125.66/18.52 | ~ (product @ a @ (multiplicative_inverse @ t) @ X0))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl127417, zip_derived_cl28, zip_derived_cl26])).
% 125.66/18.52 thf(zip_derived_cl127426, plain, ( (product @ c @ (multiply @ u @ b) @ k)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl59728, zip_derived_cl127422])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl127432, plain, ( (product @ (multiply @ u @ b) @ c @ k)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl127426, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl454, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1)
% 125.66/18.52 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | (product @ X1 @ X4 @ X2))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl127559, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ u @ X0 @ k)
% 125.66/18.52 | ~ (product @ b @ c @ X0)
% 125.66/18.52 | ~ (defined @ u)
% 125.66/18.52 | ~ (defined @ b))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl127432, zip_derived_cl454])).
% 125.66/18.52 thf(zip_derived_cl30, plain, ( (defined @ u)),
% 125.66/18.52 inference('cnf', [status(esa)], [u_is_defined])).
% 125.66/18.52 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 125.66/18.52 inference('cnf', [status(esa)], [b_is_defined])).
% 125.66/18.52 thf(zip_derived_cl127564, plain,
% 125.66/18.52 (![X0 : $i]: ( (product @ u @ X0 @ k) | ~ (product @ b @ c @ X0))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl127559, zip_derived_cl30, zip_derived_cl27])).
% 125.66/18.52 thf(zip_derived_cl127571, plain, ( (product @ u @ l @ k)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl127564])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl127576, plain, ( (product @ l @ u @ k)),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl127571, zip_derived_cl9])).
% 125.66/18.52 thf(zip_derived_cl7, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl8, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 125.66/18.52 multiplicative_identity)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (defined @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 125.66/18.52 thf(zip_derived_cl5, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2)
% 125.66/18.52 | ~ (product @ X0 @ X3 @ X4)
% 125.66/18.52 | ~ (product @ X3 @ X5 @ X1)
% 125.66/18.52 | ~ (product @ X4 @ X5 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 125.66/18.52 thf(zip_derived_cl180, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (sum @ additive_identity @ X0 @ additive_identity)
% 125.66/18.52 | ~ (product @ multiplicative_identity @ X2 @ X1)
% 125.66/18.52 | ~ (product @ X0 @ X2 @ X3)
% 125.66/18.52 | (product @ (multiplicative_inverse @ X0) @ X3 @ X1))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl5])).
% 125.66/18.52 thf(zip_derived_cl2701, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (product @ (multiplicative_inverse @ X2) @ X1 @ X0)
% 125.66/18.52 | ~ (product @ X2 @ X0 @ X1)
% 125.66/18.52 | (sum @ additive_identity @ X2 @ additive_identity)
% 125.66/18.52 | ~ (defined @ X2))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl180])).
% 125.66/18.52 thf(zip_derived_cl145484, plain,
% 125.66/18.52 ((~ (defined @ l)
% 125.66/18.52 | (sum @ additive_identity @ l @ additive_identity)
% 125.66/18.52 | (product @ (multiplicative_inverse @ l) @ k @ u)
% 125.66/18.52 | ~ (defined @ u))),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl127576, zip_derived_cl2701])).
% 125.66/18.52 thf(l_is_defined, axiom, (defined @ l)).
% 125.66/18.52 thf(zip_derived_cl32, plain, ( (defined @ l)),
% 125.66/18.52 inference('cnf', [status(esa)], [l_is_defined])).
% 125.66/18.52 thf(zip_derived_cl30, plain, ( (defined @ u)),
% 125.66/18.52 inference('cnf', [status(esa)], [u_is_defined])).
% 125.66/18.52 thf(zip_derived_cl146677, plain,
% 125.66/18.52 (( (sum @ additive_identity @ l @ additive_identity)
% 125.66/18.52 | (product @ (multiplicative_inverse @ l) @ k @ u))),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl145484, zip_derived_cl32, zip_derived_cl30])).
% 125.66/18.52 thf(zip_derived_cl9, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.52 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.52 thf(zip_derived_cl149613, plain,
% 125.66/18.52 (( (sum @ additive_identity @ l @ additive_identity)
% 125.66/18.52 | (product @ k @ (multiplicative_inverse @ l) @ u))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl146677, zip_derived_cl9])).
% 125.66/18.52 thf(not_product_18, conjecture,
% 125.66/18.52 (product @ k @ ( multiplicative_inverse @ l ) @ u)).
% 125.66/18.52 thf(zf_stmt_8, negated_conjecture,
% 125.66/18.52 (~( product @ k @ ( multiplicative_inverse @ l ) @ u )),
% 125.66/18.52 inference('cnf.neg', [status(esa)], [not_product_18])).
% 125.66/18.52 thf(zip_derived_cl43, plain,
% 125.66/18.52 (~ (product @ k @ (multiplicative_inverse @ l) @ u)),
% 125.66/18.52 inference('cnf', [status(esa)], [zf_stmt_8])).
% 125.66/18.52 thf(zip_derived_cl151704, plain,
% 125.66/18.52 ( (sum @ additive_identity @ l @ additive_identity)),
% 125.66/18.52 inference('clc', [status(thm)], [zip_derived_cl149613, zip_derived_cl43])).
% 125.66/18.52 thf(zip_derived_cl22, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (less_or_equal @ X0 @ X1)
% 125.66/18.52 | (less_or_equal @ X1 @ X0)
% 125.66/18.52 | ~ (defined @ X0)
% 125.66/18.52 | ~ (defined @ X1))),
% 125.66/18.52 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 125.66/18.52 thf(zip_derived_cl32, plain, ( (defined @ l)),
% 125.66/18.52 inference('cnf', [status(esa)], [l_is_defined])).
% 125.66/18.52 thf(zip_derived_cl566, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (defined @ X0)
% 125.66/18.52 | (less_or_equal @ X0 @ l)
% 125.66/18.52 | (less_or_equal @ l @ X0))),
% 125.66/18.52 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl32])).
% 125.66/18.52 thf(zip_derived_cl18995, plain,
% 125.66/18.52 (( (less_or_equal @ l @ l) | ~ (defined @ l))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl566])).
% 125.66/18.52 thf(zip_derived_cl32, plain, ( (defined @ l)),
% 125.66/18.52 inference('cnf', [status(esa)], [l_is_defined])).
% 125.66/18.52 thf(zip_derived_cl18996, plain, ( (less_or_equal @ l @ l)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl18995, zip_derived_cl32])).
% 125.66/18.52 thf(zip_derived_cl20, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X0 @ X1)
% 125.66/18.52 | ~ (less_or_equal @ X1 @ X0))),
% 125.66/18.52 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 125.66/18.52 thf(zip_derived_cl19002, plain,
% 125.66/18.52 ((~ (less_or_equal @ l @ l) | (sum @ additive_identity @ l @ l))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl18996, zip_derived_cl20])).
% 125.66/18.52 thf(zip_derived_cl18996, plain, ( (less_or_equal @ l @ l)),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl18995, zip_derived_cl32])).
% 125.66/18.52 thf(zip_derived_cl19005, plain, ( (sum @ additive_identity @ l @ l)),
% 125.66/18.52 inference('demod', [status(thm)],
% 125.66/18.52 [zip_derived_cl19002, zip_derived_cl18996])).
% 125.66/18.52 thf(zip_derived_cl66, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.52 (~ (sum @ additive_identity @ X1 @ X0)
% 125.66/18.52 | ~ (sum @ additive_identity @ X1 @ X2)
% 125.66/18.52 | (sum @ additive_identity @ X2 @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 125.66/18.52 thf(zip_derived_cl19031, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 ( (sum @ additive_identity @ X0 @ l)
% 125.66/18.52 | ~ (sum @ additive_identity @ l @ X0))),
% 125.66/18.52 inference('sup-', [status(thm)], [zip_derived_cl19005, zip_derived_cl66])).
% 125.66/18.52 thf(zip_derived_cl151817, plain,
% 125.66/18.52 ( (sum @ additive_identity @ additive_identity @ l)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl151704, zip_derived_cl19031])).
% 125.66/18.52 thf(zip_derived_cl6280, plain,
% 125.66/18.52 (![X0 : $i]:
% 125.66/18.52 (~ (sum @ additive_identity @ additive_identity @ X0)
% 125.66/18.52 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 125.66/18.52 inference('demod', [status(thm)], [zip_derived_cl6276, zip_derived_cl13])).
% 125.66/18.52 thf(zip_derived_cl153113, plain,
% 125.66/18.52 ( (product @ additive_identity @ multiplicative_identity @ l)),
% 125.66/18.52 inference('sup-', [status(thm)],
% 125.66/18.52 [zip_derived_cl151817, zip_derived_cl6280])).
% 125.66/18.52 thf(zip_derived_cl16698, plain,
% 125.66/18.52 (![X0 : $i, X1 : $i]:
% 125.66/18.52 ( (product @ additive_identity @ X0 @ X0)
% 125.66/18.52 | ~ (product @ additive_identity @ X1 @ X0))),
% 125.66/18.52 inference('eq_fact', [status(thm)], [zip_derived_cl14018])).
% 125.66/18.53 thf(zip_derived_cl155195, plain, ( (product @ additive_identity @ l @ l)),
% 125.66/18.53 inference('sup-', [status(thm)],
% 125.66/18.53 [zip_derived_cl153113, zip_derived_cl16698])).
% 125.66/18.53 thf(zip_derived_cl9, plain,
% 125.66/18.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.53 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.53 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.53 thf(zip_derived_cl158246, plain, ( (product @ l @ additive_identity @ l)),
% 125.66/18.53 inference('sup-', [status(thm)], [zip_derived_cl155195, zip_derived_cl9])).
% 125.66/18.53 thf(zip_derived_cl2982, plain,
% 125.66/18.53 (![X0 : $i]: ( (product @ c @ X0 @ c) | ~ (product @ l @ X0 @ l))),
% 125.66/18.53 inference('sup-', [status(thm)], [zip_derived_cl2946, zip_derived_cl149])).
% 125.66/18.53 thf(zip_derived_cl158465, plain, ( (product @ c @ additive_identity @ c)),
% 125.66/18.53 inference('sup-', [status(thm)],
% 125.66/18.53 [zip_derived_cl158246, zip_derived_cl2982])).
% 125.66/18.53 thf(zip_derived_cl18580, plain,
% 125.66/18.53 (![X0 : $i]:
% 125.66/18.53 ( (product @ multiplicative_identity @ X0 @ multiplicative_identity)
% 125.66/18.53 | ~ (product @ c @ X0 @ c))),
% 125.66/18.53 inference('sup-', [status(thm)], [zip_derived_cl18545, zip_derived_cl149])).
% 125.66/18.53 thf(zip_derived_cl161117, plain,
% 125.66/18.53 ( (product @ multiplicative_identity @ additive_identity @
% 125.66/18.53 multiplicative_identity)),
% 125.66/18.53 inference('sup-', [status(thm)],
% 125.66/18.53 [zip_derived_cl158465, zip_derived_cl18580])).
% 125.66/18.53 thf(zip_derived_cl9, plain,
% 125.66/18.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 125.66/18.53 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 125.66/18.53 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 125.66/18.53 thf(zip_derived_cl161973, plain,
% 125.66/18.53 ( (product @ additive_identity @ multiplicative_identity @
% 125.66/18.53 multiplicative_identity)),
% 125.66/18.53 inference('sup-', [status(thm)], [zip_derived_cl161117, zip_derived_cl9])).
% 125.66/18.53 thf(zip_derived_cl6570, plain,
% 125.66/18.53 (![X0 : $i]:
% 125.66/18.53 (~ (product @ additive_identity @ multiplicative_identity @ X0)
% 125.66/18.53 | (sum @ X0 @ additive_identity @ additive_identity))),
% 125.66/18.53 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl6305])).
% 125.66/18.53 thf(zip_derived_cl162437, plain,
% 125.66/18.53 ( (sum @ multiplicative_identity @ additive_identity @ additive_identity)),
% 125.66/18.53 inference('sup-', [status(thm)],
% 125.66/18.53 [zip_derived_cl161973, zip_derived_cl6570])).
% 125.66/18.53 thf(zip_derived_cl8610, plain,
% 125.66/18.53 (![X0 : $i]:
% 125.66/18.53 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 125.66/18.53 | ~ (sum @ multiplicative_identity @ additive_identity @ X0))),
% 125.66/18.53 inference('demod', [status(thm)], [zip_derived_cl8601, zip_derived_cl16])).
% 125.66/18.53 thf(zip_derived_cl162851, plain,
% 125.66/18.53 ( (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 125.66/18.53 inference('sup-', [status(thm)],
% 125.66/18.53 [zip_derived_cl162437, zip_derived_cl8610])).
% 125.66/18.53 thf(zip_derived_cl163283, plain, ($false),
% 125.66/18.53 inference('demod', [status(thm)],
% 125.66/18.53 [zip_derived_cl25, zip_derived_cl162851])).
% 125.66/18.53
% 125.66/18.53 % SZS output end Refutation
% 125.66/18.53
% 125.66/18.53
% 125.66/18.53 % Terminating...
% 126.15/18.64 % Runner terminated.
% 126.15/18.64 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------