TSTP Solution File: FLD047-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD047-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xUf6QQzI4K true
% Computer : n015.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 22:39:26 EDT 2023
% Result : Unsatisfiable 83.55s 12.61s
% Output : Refutation 83.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : FLD047-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.15/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xUf6QQzI4K true
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Aug 28 00:09:39 EDT 2023
% 0.22/0.37 % CPUTime :
% 0.22/0.37 % Running portfolio for 300 s
% 0.22/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.37 % Number of cores: 8
% 0.22/0.38 % Python version: Python 3.6.8
% 0.22/0.38 % Running in FO mode
% 0.23/0.68 % Total configuration time : 435
% 0.23/0.68 % Estimated wc time : 1092
% 0.23/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.65/0.76 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.65/0.77 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.65/0.79 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.65/0.80 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.65/0.80 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.65/0.81 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.83/0.81 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 83.55/12.61 % Solved by fo/fo5.sh.
% 83.55/12.61 % done 17118 iterations in 11.761s
% 83.55/12.61 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 83.55/12.61 % SZS output start Refutation
% 83.55/12.61 thf(sum_type, type, sum: $i > $i > $i > $o).
% 83.55/12.61 thf(b_type, type, b: $i).
% 83.55/12.61 thf(a_type, type, a: $i).
% 83.55/12.61 thf(t_type, type, t: $i).
% 83.55/12.61 thf(u_type, type, u: $i).
% 83.55/12.61 thf(product_type, type, product: $i > $i > $i > $o).
% 83.55/12.61 thf(additive_identity_type, type, additive_identity: $i).
% 83.55/12.61 thf(multiply_type, type, multiply: $i > $i > $i).
% 83.55/12.61 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 83.55/12.61 thf(c_type, type, c: $i).
% 83.55/12.61 thf(s_type, type, s: $i).
% 83.55/12.61 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 83.55/12.61 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 83.55/12.61 thf(defined_type, type, defined: $i > $o).
% 83.55/12.61 thf(different_identities, axiom,
% 83.55/12.61 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 83.55/12.61 thf(zip_derived_cl25, plain,
% 83.55/12.61 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 83.55/12.61 inference('cnf', [status(esa)], [different_identities])).
% 83.55/12.61 thf(product_10, conjecture, (~( product @ a @ c @ s ))).
% 83.55/12.61 thf(zf_stmt_0, negated_conjecture, (product @ a @ c @ s),
% 83.55/12.61 inference('cnf.neg', [status(esa)], [product_10])).
% 83.55/12.61 thf(zip_derived_cl35, plain, ( (product @ a @ c @ s)),
% 83.55/12.61 inference('cnf', [status(esa)], [zf_stmt_0])).
% 83.55/12.61 thf(existence_of_inverse_multiplication, axiom,
% 83.55/12.61 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 83.55/12.61 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 83.55/12.61 thf(zip_derived_cl8, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 83.55/12.61 multiplicative_identity)
% 83.55/12.61 | (sum @ additive_identity @ X0 @ additive_identity)
% 83.55/12.61 | ~ (defined @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 83.55/12.61 thf(commutativity_multiplication, axiom,
% 83.55/12.61 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 83.55/12.61 thf(zip_derived_cl9, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.61 thf(zip_derived_cl185, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 (~ (defined @ X0)
% 83.55/12.61 | (sum @ additive_identity @ X0 @ additive_identity)
% 83.55/12.61 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 83.55/12.61 multiplicative_identity))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 83.55/12.61 thf(existence_of_identity_multiplication, axiom,
% 83.55/12.61 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 83.55/12.61 thf(zip_derived_cl7, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 83.55/12.61 thf(zip_derived_cl9, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.61 thf(zip_derived_cl51, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 83.55/12.61 thf(product_11, conjecture, (~( product @ b @ c @ t ))).
% 83.55/12.61 thf(zf_stmt_1, negated_conjecture, (product @ b @ c @ t),
% 83.55/12.61 inference('cnf.neg', [status(esa)], [product_11])).
% 83.55/12.61 thf(zip_derived_cl36, plain, ( (product @ b @ c @ t)),
% 83.55/12.61 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.55/12.61 thf(zip_derived_cl9, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.61 thf(zip_derived_cl54, plain, ( (product @ c @ b @ t)),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl9])).
% 83.55/12.61 thf(associativity_multiplication_2, axiom,
% 83.55/12.61 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 83.55/12.61 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 83.55/12.61 thf(zip_derived_cl6, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2)
% 83.55/12.61 | ~ (product @ X3 @ X4 @ X0)
% 83.55/12.61 | ~ (product @ X4 @ X1 @ X5)
% 83.55/12.61 | ~ (product @ X3 @ X5 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 83.55/12.61 thf(zip_derived_cl154, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 (~ (product @ c @ X1 @ X0)
% 83.55/12.61 | ~ (product @ b @ X2 @ X1)
% 83.55/12.61 | (product @ t @ X2 @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl6])).
% 83.55/12.61 thf(zip_derived_cl342, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 (~ (defined @ c)
% 83.55/12.61 | (product @ t @ X0 @ c)
% 83.55/12.61 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl154])).
% 83.55/12.61 thf(c_is_defined, axiom, (defined @ c)).
% 83.55/12.61 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 83.55/12.61 inference('cnf', [status(esa)], [c_is_defined])).
% 83.55/12.61 thf(zip_derived_cl345, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 ( (product @ t @ X0 @ c)
% 83.55/12.61 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 83.55/12.61 inference('demod', [status(thm)], [zip_derived_cl342, zip_derived_cl28])).
% 83.55/12.61 thf(zip_derived_cl2644, plain,
% 83.55/12.61 (( (sum @ additive_identity @ b @ additive_identity)
% 83.55/12.61 | ~ (defined @ b)
% 83.55/12.61 | (product @ t @ (multiplicative_inverse @ b) @ c))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl345])).
% 83.55/12.61 thf(not_sum_7, conjecture, (sum @ additive_identity @ b @ additive_identity)).
% 83.55/12.61 thf(zf_stmt_2, negated_conjecture,
% 83.55/12.61 (~( sum @ additive_identity @ b @ additive_identity )),
% 83.55/12.61 inference('cnf.neg', [status(esa)], [not_sum_7])).
% 83.55/12.61 thf(zip_derived_cl32, plain,
% 83.55/12.61 (~ (sum @ additive_identity @ b @ additive_identity)),
% 83.55/12.61 inference('cnf', [status(esa)], [zf_stmt_2])).
% 83.55/12.61 thf(b_is_defined, axiom, (defined @ b)).
% 83.55/12.61 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 83.55/12.61 inference('cnf', [status(esa)], [b_is_defined])).
% 83.55/12.61 thf(zip_derived_cl2682, plain,
% 83.55/12.61 ( (product @ t @ (multiplicative_inverse @ b) @ c)),
% 83.55/12.61 inference('demod', [status(thm)],
% 83.55/12.61 [zip_derived_cl2644, zip_derived_cl32, zip_derived_cl27])).
% 83.55/12.61 thf(zip_derived_cl9, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.61 thf(zip_derived_cl2699, plain,
% 83.55/12.61 ( (product @ (multiplicative_inverse @ b) @ t @ c)),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl2682, zip_derived_cl9])).
% 83.55/12.61 thf(product_9, conjecture,
% 83.55/12.61 (~( product @ a @ ( multiplicative_inverse @ b ) @ u ))).
% 83.55/12.61 thf(zf_stmt_3, negated_conjecture,
% 83.55/12.61 (product @ a @ ( multiplicative_inverse @ b ) @ u),
% 83.55/12.61 inference('cnf.neg', [status(esa)], [product_9])).
% 83.55/12.61 thf(zip_derived_cl34, plain,
% 83.55/12.61 ( (product @ a @ (multiplicative_inverse @ b) @ u)),
% 83.55/12.61 inference('cnf', [status(esa)], [zf_stmt_3])).
% 83.55/12.61 thf(zip_derived_cl6, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2)
% 83.55/12.61 | ~ (product @ X3 @ X4 @ X0)
% 83.55/12.61 | ~ (product @ X4 @ X1 @ X5)
% 83.55/12.61 | ~ (product @ X3 @ X5 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 83.55/12.61 thf(zip_derived_cl150, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 (~ (product @ a @ X1 @ X0)
% 83.55/12.61 | ~ (product @ (multiplicative_inverse @ b) @ X2 @ X1)
% 83.55/12.61 | (product @ u @ X2 @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl6])).
% 83.55/12.61 thf(zip_derived_cl2741, plain,
% 83.55/12.61 (![X0 : $i]: ( (product @ u @ t @ X0) | ~ (product @ a @ c @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl2699, zip_derived_cl150])).
% 83.55/12.61 thf(zip_derived_cl2905, plain, ( (product @ u @ t @ s)),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl2741])).
% 83.55/12.61 thf(zip_derived_cl9, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.61 thf(zip_derived_cl2909, plain, ( (product @ t @ u @ s)),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl2905, zip_derived_cl9])).
% 83.55/12.61 thf(zip_derived_cl7, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 83.55/12.61 thf(zip_derived_cl8, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 83.55/12.61 multiplicative_identity)
% 83.55/12.61 | (sum @ additive_identity @ X0 @ additive_identity)
% 83.55/12.61 | ~ (defined @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 83.55/12.61 thf(associativity_multiplication_1, axiom,
% 83.55/12.61 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 83.55/12.61 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 83.55/12.61 thf(zip_derived_cl5, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2)
% 83.55/12.61 | ~ (product @ X0 @ X3 @ X4)
% 83.55/12.61 | ~ (product @ X3 @ X5 @ X1)
% 83.55/12.61 | ~ (product @ X4 @ X5 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 83.55/12.61 thf(zip_derived_cl183, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.55/12.61 (~ (defined @ X0)
% 83.55/12.61 | (sum @ additive_identity @ X0 @ additive_identity)
% 83.55/12.61 | ~ (product @ multiplicative_identity @ X2 @ X1)
% 83.55/12.61 | ~ (product @ X0 @ X2 @ X3)
% 83.55/12.61 | (product @ (multiplicative_inverse @ X0) @ X3 @ X1))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl5])).
% 83.55/12.61 thf(zip_derived_cl2490, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 (~ (defined @ X0)
% 83.55/12.61 | (product @ (multiplicative_inverse @ X2) @ X1 @ X0)
% 83.55/12.61 | ~ (product @ X2 @ X0 @ X1)
% 83.55/12.61 | (sum @ additive_identity @ X2 @ additive_identity)
% 83.55/12.61 | ~ (defined @ X2))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl183])).
% 83.55/12.61 thf(zip_derived_cl131469, plain,
% 83.55/12.61 ((~ (defined @ t)
% 83.55/12.61 | (sum @ additive_identity @ t @ additive_identity)
% 83.55/12.61 | (product @ (multiplicative_inverse @ t) @ s @ u)
% 83.55/12.61 | ~ (defined @ u))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl2909, zip_derived_cl2490])).
% 83.55/12.61 thf(t_is_defined, axiom, (defined @ t)).
% 83.55/12.61 thf(zip_derived_cl31, plain, ( (defined @ t)),
% 83.55/12.61 inference('cnf', [status(esa)], [t_is_defined])).
% 83.55/12.61 thf(u_is_defined, axiom, (defined @ u)).
% 83.55/12.61 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 83.55/12.61 inference('cnf', [status(esa)], [u_is_defined])).
% 83.55/12.61 thf(zip_derived_cl132310, plain,
% 83.55/12.61 (( (sum @ additive_identity @ t @ additive_identity)
% 83.55/12.61 | (product @ (multiplicative_inverse @ t) @ s @ u))),
% 83.55/12.61 inference('demod', [status(thm)],
% 83.55/12.61 [zip_derived_cl131469, zip_derived_cl31, zip_derived_cl29])).
% 83.55/12.61 thf(zip_derived_cl9, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.61 thf(zip_derived_cl133315, plain,
% 83.55/12.61 (( (sum @ additive_identity @ t @ additive_identity)
% 83.55/12.61 | (product @ s @ (multiplicative_inverse @ t) @ u))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl132310, zip_derived_cl9])).
% 83.55/12.61 thf(not_product_12, conjecture,
% 83.55/12.61 (product @ s @ ( multiplicative_inverse @ t ) @ u)).
% 83.55/12.61 thf(zf_stmt_4, negated_conjecture,
% 83.55/12.61 (~( product @ s @ ( multiplicative_inverse @ t ) @ u )),
% 83.55/12.61 inference('cnf.neg', [status(esa)], [not_product_12])).
% 83.55/12.61 thf(zip_derived_cl37, plain,
% 83.55/12.61 (~ (product @ s @ (multiplicative_inverse @ t) @ u)),
% 83.55/12.61 inference('cnf', [status(esa)], [zf_stmt_4])).
% 83.55/12.61 thf(zip_derived_cl133466, plain,
% 83.55/12.61 ( (sum @ additive_identity @ t @ additive_identity)),
% 83.55/12.61 inference('clc', [status(thm)], [zip_derived_cl133315, zip_derived_cl37])).
% 83.55/12.61 thf(totality_of_order_relation, axiom,
% 83.55/12.61 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 83.55/12.61 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 83.55/12.61 thf(zip_derived_cl22, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i]:
% 83.55/12.61 ( (less_or_equal @ X0 @ X1)
% 83.55/12.61 | (less_or_equal @ X1 @ X0)
% 83.55/12.61 | ~ (defined @ X0)
% 83.55/12.61 | ~ (defined @ X1))),
% 83.55/12.61 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 83.55/12.61 thf(zip_derived_cl31, plain, ( (defined @ t)),
% 83.55/12.61 inference('cnf', [status(esa)], [t_is_defined])).
% 83.55/12.61 thf(zip_derived_cl571, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 (~ (defined @ X0)
% 83.55/12.61 | (less_or_equal @ X0 @ t)
% 83.55/12.61 | (less_or_equal @ t @ X0))),
% 83.55/12.61 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl31])).
% 83.55/12.61 thf(zip_derived_cl16748, plain,
% 83.55/12.61 (( (less_or_equal @ t @ t) | ~ (defined @ t))),
% 83.55/12.61 inference('eq_fact', [status(thm)], [zip_derived_cl571])).
% 83.55/12.61 thf(zip_derived_cl31, plain, ( (defined @ t)),
% 83.55/12.61 inference('cnf', [status(esa)], [t_is_defined])).
% 83.55/12.61 thf(zip_derived_cl16749, plain, ( (less_or_equal @ t @ t)),
% 83.55/12.61 inference('demod', [status(thm)], [zip_derived_cl16748, zip_derived_cl31])).
% 83.55/12.61 thf(antisymmetry_of_order_relation, axiom,
% 83.55/12.61 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 83.55/12.61 ( ~( less_or_equal @ Y @ X ) ))).
% 83.55/12.61 thf(zip_derived_cl20, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i]:
% 83.55/12.61 ( (sum @ additive_identity @ X0 @ X1)
% 83.55/12.61 | ~ (less_or_equal @ X0 @ X1)
% 83.55/12.61 | ~ (less_or_equal @ X1 @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 83.55/12.61 thf(zip_derived_cl16756, plain,
% 83.55/12.61 ((~ (less_or_equal @ t @ t) | (sum @ additive_identity @ t @ t))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl16749, zip_derived_cl20])).
% 83.55/12.61 thf(zip_derived_cl16749, plain, ( (less_or_equal @ t @ t)),
% 83.55/12.61 inference('demod', [status(thm)], [zip_derived_cl16748, zip_derived_cl31])).
% 83.55/12.61 thf(zip_derived_cl16759, plain, ( (sum @ additive_identity @ t @ t)),
% 83.55/12.61 inference('demod', [status(thm)],
% 83.55/12.61 [zip_derived_cl16756, zip_derived_cl16749])).
% 83.55/12.61 thf(existence_of_identity_addition, axiom,
% 83.55/12.61 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 83.55/12.61 thf(zip_derived_cl2, plain,
% 83.55/12.61 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 83.55/12.61 thf(zip_derived_cl2, plain,
% 83.55/12.61 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 83.55/12.61 thf(associativity_addition_1, axiom,
% 83.55/12.61 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 83.55/12.61 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 83.55/12.61 thf(zip_derived_cl0, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.61 ( (sum @ X0 @ X1 @ X2)
% 83.55/12.61 | ~ (sum @ X0 @ X3 @ X4)
% 83.55/12.61 | ~ (sum @ X3 @ X5 @ X1)
% 83.55/12.61 | ~ (sum @ X4 @ X5 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [associativity_addition_1])).
% 83.55/12.61 thf(zip_derived_cl40, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 (~ (sum @ X0 @ X1 @ X0)
% 83.55/12.61 | ~ (sum @ X1 @ X1 @ X2)
% 83.55/12.61 | (sum @ X0 @ X2 @ X0))),
% 83.55/12.61 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 83.55/12.61 thf(zip_derived_cl47, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 (~ (defined @ additive_identity)
% 83.55/12.61 | (sum @ additive_identity @ X0 @ additive_identity)
% 83.55/12.61 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl40])).
% 83.55/12.61 thf(well_definedness_of_additive_identity, axiom,
% 83.55/12.61 (defined @ additive_identity)).
% 83.55/12.61 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.61 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.61 thf(zip_derived_cl48, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 ( (sum @ additive_identity @ X0 @ additive_identity)
% 83.55/12.61 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 83.55/12.61 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl13])).
% 83.55/12.61 thf(zip_derived_cl63, plain,
% 83.55/12.61 ((~ (defined @ additive_identity)
% 83.55/12.61 | (sum @ additive_identity @ additive_identity @ additive_identity))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl48])).
% 83.55/12.61 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.61 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.61 thf(zip_derived_cl65, plain,
% 83.55/12.61 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 83.55/12.61 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl13])).
% 83.55/12.61 thf(zip_derived_cl0, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.61 ( (sum @ X0 @ X1 @ X2)
% 83.55/12.61 | ~ (sum @ X0 @ X3 @ X4)
% 83.55/12.61 | ~ (sum @ X3 @ X5 @ X1)
% 83.55/12.61 | ~ (sum @ X4 @ X5 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [associativity_addition_1])).
% 83.55/12.61 thf(zip_derived_cl66, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 (~ (sum @ additive_identity @ X1 @ X0)
% 83.55/12.61 | ~ (sum @ additive_identity @ X1 @ X2)
% 83.55/12.61 | (sum @ additive_identity @ X2 @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 83.55/12.61 thf(zip_derived_cl16784, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 ( (sum @ additive_identity @ X0 @ t)
% 83.55/12.61 | ~ (sum @ additive_identity @ t @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl16759, zip_derived_cl66])).
% 83.55/12.61 thf(zip_derived_cl133591, plain,
% 83.55/12.61 ( (sum @ additive_identity @ additive_identity @ t)),
% 83.55/12.61 inference('sup-', [status(thm)],
% 83.55/12.61 [zip_derived_cl133466, zip_derived_cl16784])).
% 83.55/12.61 thf(zip_derived_cl65, plain,
% 83.55/12.61 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 83.55/12.61 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl13])).
% 83.55/12.61 thf(zip_derived_cl51, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 83.55/12.61 thf(zip_derived_cl2, plain,
% 83.55/12.61 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 83.55/12.61 thf(commutativity_addition, axiom,
% 83.55/12.61 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 83.55/12.61 thf(zip_derived_cl4, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [commutativity_addition])).
% 83.55/12.61 thf(zip_derived_cl49, plain,
% 83.55/12.61 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 83.55/12.61 thf(distributivity_2, axiom,
% 83.55/12.61 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 83.55/12.61 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 83.55/12.61 ( ~( sum @ C @ D @ B ) ))).
% 83.55/12.61 thf(zip_derived_cl11, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ X2)
% 83.55/12.61 | ~ (sum @ X3 @ X4 @ X0)
% 83.55/12.61 | ~ (product @ X3 @ X1 @ X5)
% 83.55/12.61 | ~ (product @ X4 @ X1 @ X6)
% 83.55/12.61 | ~ (sum @ X5 @ X6 @ X2))),
% 83.55/12.61 inference('cnf', [status(esa)], [distributivity_2])).
% 83.55/12.61 thf(zip_derived_cl282, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 83.55/12.61 (~ (defined @ X0)
% 83.55/12.61 | ~ (sum @ X3 @ X2 @ X1)
% 83.55/12.61 | ~ (product @ additive_identity @ X4 @ X2)
% 83.55/12.61 | ~ (product @ X0 @ X4 @ X3)
% 83.55/12.61 | (product @ X0 @ X4 @ X1))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl11])).
% 83.55/12.61 thf(zip_derived_cl5475, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 ( (product @ additive_identity @ X1 @ X2)
% 83.55/12.61 | ~ (product @ additive_identity @ X1 @ X0)
% 83.55/12.61 | ~ (sum @ X0 @ X0 @ X2)
% 83.55/12.61 | ~ (defined @ additive_identity))),
% 83.55/12.61 inference('eq_fact', [status(thm)], [zip_derived_cl282])).
% 83.55/12.61 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.61 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.61 thf(zip_derived_cl5477, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 ( (product @ additive_identity @ X1 @ X2)
% 83.55/12.61 | ~ (product @ additive_identity @ X1 @ X0)
% 83.55/12.61 | ~ (sum @ X0 @ X0 @ X2))),
% 83.55/12.61 inference('demod', [status(thm)], [zip_derived_cl5475, zip_derived_cl13])).
% 83.55/12.61 thf(zip_derived_cl5489, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 (~ (defined @ additive_identity)
% 83.55/12.61 | ~ (sum @ additive_identity @ additive_identity @ X0)
% 83.55/12.61 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl5477])).
% 83.55/12.61 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.61 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.61 thf(zip_derived_cl5493, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 (~ (sum @ additive_identity @ additive_identity @ X0)
% 83.55/12.61 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 83.55/12.61 inference('demod', [status(thm)], [zip_derived_cl5489, zip_derived_cl13])).
% 83.55/12.61 thf(zip_derived_cl5502, plain,
% 83.55/12.61 ( (product @ additive_identity @ multiplicative_identity @
% 83.55/12.61 additive_identity)),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl5493])).
% 83.55/12.61 thf(well_definedness_of_multiplication, axiom,
% 83.55/12.61 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 83.55/12.61 ( ~( defined @ Y ) ))).
% 83.55/12.61 thf(zip_derived_cl15, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i]:
% 83.55/12.61 ( (defined @ (multiply @ X0 @ X1))
% 83.55/12.61 | ~ (defined @ X0)
% 83.55/12.61 | ~ (defined @ X1))),
% 83.55/12.61 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 83.55/12.61 thf(totality_of_multiplication, axiom,
% 83.55/12.61 (( product @ X @ Y @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 83.55/12.61 ( ~( defined @ Y ) ))).
% 83.55/12.61 thf(zip_derived_cl19, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i]:
% 83.55/12.61 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 83.55/12.61 | ~ (defined @ X0)
% 83.55/12.61 | ~ (defined @ X1))),
% 83.55/12.61 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 83.55/12.61 thf(zip_derived_cl49, plain,
% 83.55/12.61 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 83.55/12.61 thf(zip_derived_cl8, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.61 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 83.55/12.61 multiplicative_identity)
% 83.55/12.61 | (sum @ additive_identity @ X0 @ additive_identity)
% 83.55/12.61 | ~ (defined @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 83.55/12.61 thf(zip_derived_cl2, plain,
% 83.55/12.61 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 83.55/12.61 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 83.55/12.61 thf(zip_derived_cl66, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.61 (~ (sum @ additive_identity @ X1 @ X0)
% 83.55/12.61 | ~ (sum @ additive_identity @ X1 @ X2)
% 83.55/12.61 | (sum @ additive_identity @ X2 @ X0))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 83.55/12.61 thf(zip_derived_cl114, plain,
% 83.55/12.61 (![X0 : $i, X1 : $i]:
% 83.55/12.61 (~ (defined @ X0)
% 83.55/12.61 | (sum @ additive_identity @ X1 @ X0)
% 83.55/12.61 | ~ (sum @ additive_identity @ X0 @ X1))),
% 83.55/12.61 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl66])).
% 83.55/12.61 thf(zip_derived_cl206, plain,
% 83.55/12.61 (![X0 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 83.55/12.62 multiplicative_identity)
% 83.55/12.62 | (sum @ additive_identity @ additive_identity @ X0)
% 83.55/12.62 | ~ (defined @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl114])).
% 83.55/12.62 thf(zip_derived_cl215, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (sum @ additive_identity @ additive_identity @ X0)
% 83.55/12.62 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 83.55/12.62 multiplicative_identity)
% 83.55/12.62 | ~ (defined @ X0))),
% 83.55/12.62 inference('simplify', [status(thm)], [zip_derived_cl206])).
% 83.55/12.62 thf(zip_derived_cl5502, plain,
% 83.55/12.62 ( (product @ additive_identity @ multiplicative_identity @
% 83.55/12.62 additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl5493])).
% 83.55/12.62 thf(distributivity_1, axiom,
% 83.55/12.62 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 83.55/12.62 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 83.55/12.62 ( ~( product @ Y @ Z @ D ) ))).
% 83.55/12.62 thf(zip_derived_cl10, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 83.55/12.62 ( (sum @ X0 @ X1 @ X2)
% 83.55/12.62 | ~ (sum @ X3 @ X4 @ X5)
% 83.55/12.62 | ~ (product @ X5 @ X6 @ X2)
% 83.55/12.62 | ~ (product @ X3 @ X6 @ X0)
% 83.55/12.62 | ~ (product @ X4 @ X6 @ X1))),
% 83.55/12.62 inference('cnf', [status(esa)], [distributivity_1])).
% 83.55/12.62 thf(zip_derived_cl244, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 83.55/12.62 (~ (product @ X4 @ X1 @ X3)
% 83.55/12.62 | ~ (product @ X2 @ X1 @ X0)
% 83.55/12.62 | ~ (sum @ X2 @ X4 @ X2)
% 83.55/12.62 | (sum @ X0 @ X3 @ X0))),
% 83.55/12.62 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 83.55/12.62 thf(zip_derived_cl5519, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 ( (sum @ X0 @ additive_identity @ X0)
% 83.55/12.62 | ~ (sum @ X1 @ additive_identity @ X1)
% 83.55/12.62 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl5502, zip_derived_cl244])).
% 83.55/12.62 thf(zip_derived_cl7066, plain,
% 83.55/12.62 ((~ (defined @ multiplicative_identity)
% 83.55/12.62 | (sum @ additive_identity @ additive_identity @
% 83.55/12.62 multiplicative_identity)
% 83.55/12.62 | ~ (sum @ (multiplicative_inverse @ multiplicative_identity) @
% 83.55/12.62 additive_identity @
% 83.55/12.62 (multiplicative_inverse @ multiplicative_identity))
% 83.55/12.62 | (sum @ multiplicative_identity @ additive_identity @
% 83.55/12.62 multiplicative_identity))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl215, zip_derived_cl5519])).
% 83.55/12.62 thf(well_definedness_of_multiplicative_identity, axiom,
% 83.55/12.62 (defined @ multiplicative_identity)).
% 83.55/12.62 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 83.55/12.62 inference('cnf', [status(esa)],
% 83.55/12.62 [well_definedness_of_multiplicative_identity])).
% 83.55/12.62 thf(zip_derived_cl25, plain,
% 83.55/12.62 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [different_identities])).
% 83.55/12.62 thf(zip_derived_cl7114, plain,
% 83.55/12.62 ((~ (sum @ (multiplicative_inverse @ multiplicative_identity) @
% 83.55/12.62 additive_identity @
% 83.55/12.62 (multiplicative_inverse @ multiplicative_identity))
% 83.55/12.62 | (sum @ multiplicative_identity @ additive_identity @
% 83.55/12.62 multiplicative_identity))),
% 83.55/12.62 inference('demod', [status(thm)],
% 83.55/12.62 [zip_derived_cl7066, zip_derived_cl16, zip_derived_cl25])).
% 83.55/12.62 thf(zip_derived_cl7118, plain,
% 83.55/12.62 ((~ (defined @ (multiplicative_inverse @ multiplicative_identity))
% 83.55/12.62 | (sum @ multiplicative_identity @ additive_identity @
% 83.55/12.62 multiplicative_identity))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl7114])).
% 83.55/12.62 thf(well_definedness_of_multiplicative_inverse, axiom,
% 83.55/12.62 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 83.55/12.62 ( sum @ additive_identity @ X @ additive_identity ))).
% 83.55/12.62 thf(zip_derived_cl17, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (defined @ (multiplicative_inverse @ X0))
% 83.55/12.62 | ~ (defined @ X0)
% 83.55/12.62 | (sum @ additive_identity @ X0 @ additive_identity))),
% 83.55/12.62 inference('cnf', [status(esa)],
% 83.55/12.62 [well_definedness_of_multiplicative_inverse])).
% 83.55/12.62 thf(zip_derived_cl114, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | (sum @ additive_identity @ X1 @ X0)
% 83.55/12.62 | ~ (sum @ additive_identity @ X0 @ X1))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl66])).
% 83.55/12.62 thf(zip_derived_cl207, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | (defined @ (multiplicative_inverse @ X0))
% 83.55/12.62 | (sum @ additive_identity @ additive_identity @ X0)
% 83.55/12.62 | ~ (defined @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl114])).
% 83.55/12.62 thf(zip_derived_cl216, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (sum @ additive_identity @ additive_identity @ X0)
% 83.55/12.62 | (defined @ (multiplicative_inverse @ X0))
% 83.55/12.62 | ~ (defined @ X0))),
% 83.55/12.62 inference('simplify', [status(thm)], [zip_derived_cl207])).
% 83.55/12.62 thf(zip_derived_cl25, plain,
% 83.55/12.62 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [different_identities])).
% 83.55/12.62 thf(zip_derived_cl2058, plain,
% 83.55/12.62 ((~ (defined @ multiplicative_identity)
% 83.55/12.62 | (defined @ (multiplicative_inverse @ multiplicative_identity)))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl216, zip_derived_cl25])).
% 83.55/12.62 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 83.55/12.62 inference('cnf', [status(esa)],
% 83.55/12.62 [well_definedness_of_multiplicative_identity])).
% 83.55/12.62 thf(zip_derived_cl2073, plain,
% 83.55/12.62 ( (defined @ (multiplicative_inverse @ multiplicative_identity))),
% 83.55/12.62 inference('demod', [status(thm)], [zip_derived_cl2058, zip_derived_cl16])).
% 83.55/12.62 thf(zip_derived_cl7119, plain,
% 83.55/12.62 ( (sum @ multiplicative_identity @ additive_identity @
% 83.55/12.62 multiplicative_identity)),
% 83.55/12.62 inference('demod', [status(thm)],
% 83.55/12.62 [zip_derived_cl7118, zip_derived_cl2073])).
% 83.55/12.62 thf(zip_derived_cl4, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.62 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [commutativity_addition])).
% 83.55/12.62 thf(zip_derived_cl7123, plain,
% 83.55/12.62 ( (sum @ additive_identity @ multiplicative_identity @
% 83.55/12.62 multiplicative_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl7119, zip_derived_cl4])).
% 83.55/12.62 thf(zip_derived_cl5502, plain,
% 83.55/12.62 ( (product @ additive_identity @ multiplicative_identity @
% 83.55/12.62 additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl5493])).
% 83.55/12.62 thf(zip_derived_cl9, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.62 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.62 thf(zip_derived_cl5513, plain,
% 83.55/12.62 ( (product @ multiplicative_identity @ additive_identity @
% 83.55/12.62 additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl5502, zip_derived_cl9])).
% 83.55/12.62 thf(zip_derived_cl10, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 83.55/12.62 ( (sum @ X0 @ X1 @ X2)
% 83.55/12.62 | ~ (sum @ X3 @ X4 @ X5)
% 83.55/12.62 | ~ (product @ X5 @ X6 @ X2)
% 83.55/12.62 | ~ (product @ X3 @ X6 @ X0)
% 83.55/12.62 | ~ (product @ X4 @ X6 @ X1))),
% 83.55/12.62 inference('cnf', [status(esa)], [distributivity_1])).
% 83.55/12.62 thf(zip_derived_cl245, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 83.55/12.62 (~ (product @ X2 @ X1 @ X0)
% 83.55/12.62 | ~ (product @ X4 @ X1 @ X3)
% 83.55/12.62 | ~ (sum @ X4 @ X2 @ X2)
% 83.55/12.62 | (sum @ X3 @ X0 @ X0))),
% 83.55/12.62 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 83.55/12.62 thf(zip_derived_cl5532, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 ( (sum @ X0 @ additive_identity @ additive_identity)
% 83.55/12.62 | ~ (sum @ X1 @ multiplicative_identity @ multiplicative_identity)
% 83.55/12.62 | ~ (product @ X1 @ additive_identity @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl5513, zip_derived_cl245])).
% 83.55/12.62 thf(zip_derived_cl7411, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 (~ (product @ additive_identity @ additive_identity @ X0)
% 83.55/12.62 | (sum @ X0 @ additive_identity @ additive_identity))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl7123, zip_derived_cl5532])).
% 83.55/12.62 thf(zip_derived_cl7416, plain,
% 83.55/12.62 ((~ (defined @ additive_identity)
% 83.55/12.62 | ~ (defined @ additive_identity)
% 83.55/12.62 | (sum @ (multiply @ additive_identity @ additive_identity) @
% 83.55/12.62 additive_identity @ additive_identity))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl7411])).
% 83.55/12.62 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.62 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.62 thf(zip_derived_cl7417, plain,
% 83.55/12.62 ( (sum @ (multiply @ additive_identity @ additive_identity) @
% 83.55/12.62 additive_identity @ additive_identity)),
% 83.55/12.62 inference('demod', [status(thm)],
% 83.55/12.62 [zip_derived_cl7416, zip_derived_cl13, zip_derived_cl13])).
% 83.55/12.62 thf(zip_derived_cl49, plain,
% 83.55/12.62 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 83.55/12.62 thf(zip_derived_cl2, plain,
% 83.55/12.62 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 83.55/12.62 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 83.55/12.62 thf(zip_derived_cl0, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.62 ( (sum @ X0 @ X1 @ X2)
% 83.55/12.62 | ~ (sum @ X0 @ X3 @ X4)
% 83.55/12.62 | ~ (sum @ X3 @ X5 @ X1)
% 83.55/12.62 | ~ (sum @ X4 @ X5 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [associativity_addition_1])).
% 83.55/12.62 thf(zip_derived_cl46, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | ~ (sum @ X0 @ X2 @ X1)
% 83.55/12.62 | ~ (sum @ X0 @ X2 @ X3)
% 83.55/12.62 | (sum @ additive_identity @ X3 @ X1))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 83.55/12.62 thf(zip_derived_cl752, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | (sum @ additive_identity @ X1 @ X0)
% 83.55/12.62 | ~ (sum @ X0 @ additive_identity @ X1)
% 83.55/12.62 | ~ (defined @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl46])).
% 83.55/12.62 thf(zip_derived_cl773, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 (~ (sum @ X0 @ additive_identity @ X1)
% 83.55/12.62 | (sum @ additive_identity @ X1 @ X0)
% 83.55/12.62 | ~ (defined @ X0))),
% 83.55/12.62 inference('simplify', [status(thm)], [zip_derived_cl752])).
% 83.55/12.62 thf(zip_derived_cl7462, plain,
% 83.55/12.62 ((~ (defined @ (multiply @ additive_identity @ additive_identity))
% 83.55/12.62 | (sum @ additive_identity @ additive_identity @
% 83.55/12.62 (multiply @ additive_identity @ additive_identity)))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl7417, zip_derived_cl773])).
% 83.55/12.62 thf(zip_derived_cl7624, plain,
% 83.55/12.62 ((~ (defined @ additive_identity)
% 83.55/12.62 | ~ (defined @ additive_identity)
% 83.55/12.62 | (sum @ additive_identity @ additive_identity @
% 83.55/12.62 (multiply @ additive_identity @ additive_identity)))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl7462])).
% 83.55/12.62 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.62 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.62 thf(zip_derived_cl7625, plain,
% 83.55/12.62 ( (sum @ additive_identity @ additive_identity @
% 83.55/12.62 (multiply @ additive_identity @ additive_identity))),
% 83.55/12.62 inference('demod', [status(thm)],
% 83.55/12.62 [zip_derived_cl7624, zip_derived_cl13, zip_derived_cl13])).
% 83.55/12.62 thf(zip_derived_cl5493, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 (~ (sum @ additive_identity @ additive_identity @ X0)
% 83.55/12.62 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 83.55/12.62 inference('demod', [status(thm)], [zip_derived_cl5489, zip_derived_cl13])).
% 83.55/12.62 thf(zip_derived_cl7673, plain,
% 83.55/12.62 ( (product @ additive_identity @ multiplicative_identity @
% 83.55/12.62 (multiply @ additive_identity @ additive_identity))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl7625, zip_derived_cl5493])).
% 83.55/12.62 thf(zip_derived_cl5502, plain,
% 83.55/12.62 ( (product @ additive_identity @ multiplicative_identity @
% 83.55/12.62 additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl5493])).
% 83.55/12.62 thf(zip_derived_cl7, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 83.55/12.62 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 83.55/12.62 thf(zip_derived_cl5, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.62 ( (product @ X0 @ X1 @ X2)
% 83.55/12.62 | ~ (product @ X0 @ X3 @ X4)
% 83.55/12.62 | ~ (product @ X3 @ X5 @ X1)
% 83.55/12.62 | ~ (product @ X4 @ X5 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 83.55/12.62 thf(zip_derived_cl95, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | ~ (product @ X0 @ X2 @ X1)
% 83.55/12.62 | ~ (product @ X0 @ X2 @ X3)
% 83.55/12.62 | (product @ multiplicative_identity @ X3 @ X1))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 83.55/12.62 thf(zip_derived_cl5517, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 83.55/12.62 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 83.55/12.62 | ~ (defined @ additive_identity))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl5502, zip_derived_cl95])).
% 83.55/12.62 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.62 thf(zip_derived_cl5526, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 83.55/12.62 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 83.55/12.62 inference('demod', [status(thm)], [zip_derived_cl5517, zip_derived_cl13])).
% 83.55/12.62 thf(zip_derived_cl9139, plain,
% 83.55/12.62 ( (product @ multiplicative_identity @
% 83.55/12.62 (multiply @ additive_identity @ additive_identity) @ additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl7673, zip_derived_cl5526])).
% 83.55/12.62 thf(zip_derived_cl9, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.62 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.62 thf(zip_derived_cl9270, plain,
% 83.55/12.62 ( (product @ (multiply @ additive_identity @ additive_identity) @
% 83.55/12.62 multiplicative_identity @ additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl9139, zip_derived_cl9])).
% 83.55/12.62 thf(zip_derived_cl19, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 83.55/12.62 | ~ (defined @ X0)
% 83.55/12.62 | ~ (defined @ X1))),
% 83.55/12.62 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 83.55/12.62 thf(zip_derived_cl5, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.62 ( (product @ X0 @ X1 @ X2)
% 83.55/12.62 | ~ (product @ X0 @ X3 @ X4)
% 83.55/12.62 | ~ (product @ X3 @ X5 @ X1)
% 83.55/12.62 | ~ (product @ X4 @ X5 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 83.55/12.62 thf(zip_derived_cl446, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | ~ (defined @ X1)
% 83.55/12.62 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 83.55/12.62 | ~ (product @ X0 @ X3 @ X4)
% 83.55/12.62 | (product @ X1 @ X4 @ X2))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 83.55/12.62 thf(zip_derived_cl9577, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (product @ additive_identity @ X0 @ additive_identity)
% 83.55/12.62 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 83.55/12.62 | ~ (defined @ additive_identity)
% 83.55/12.62 | ~ (defined @ additive_identity))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl9270, zip_derived_cl446])).
% 83.55/12.62 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.62 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 83.55/12.62 thf(zip_derived_cl9648, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (product @ additive_identity @ X0 @ additive_identity)
% 83.55/12.62 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 83.55/12.62 inference('demod', [status(thm)],
% 83.55/12.62 [zip_derived_cl9577, zip_derived_cl13, zip_derived_cl13])).
% 83.55/12.62 thf(zip_derived_cl9722, plain,
% 83.55/12.62 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl5502, zip_derived_cl9648])).
% 83.55/12.62 thf(zip_derived_cl5477, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.62 ( (product @ additive_identity @ X1 @ X2)
% 83.55/12.62 | ~ (product @ additive_identity @ X1 @ X0)
% 83.55/12.62 | ~ (sum @ X0 @ X0 @ X2))),
% 83.55/12.62 inference('demod', [status(thm)], [zip_derived_cl5475, zip_derived_cl13])).
% 83.55/12.62 thf(zip_derived_cl9747, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 (~ (sum @ additive_identity @ additive_identity @ X0)
% 83.55/12.62 | (product @ additive_identity @ additive_identity @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl9722, zip_derived_cl5477])).
% 83.55/12.62 thf(zip_derived_cl134508, plain,
% 83.55/12.62 ( (product @ additive_identity @ additive_identity @ t)),
% 83.55/12.62 inference('sup-', [status(thm)],
% 83.55/12.62 [zip_derived_cl133591, zip_derived_cl9747])).
% 83.55/12.62 thf(zip_derived_cl9722, plain,
% 83.55/12.62 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl5502, zip_derived_cl9648])).
% 83.55/12.62 thf(zip_derived_cl5, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.62 ( (product @ X0 @ X1 @ X2)
% 83.55/12.62 | ~ (product @ X0 @ X3 @ X4)
% 83.55/12.62 | ~ (product @ X3 @ X5 @ X1)
% 83.55/12.62 | ~ (product @ X4 @ X5 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 83.55/12.62 thf(zip_derived_cl9729, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.62 (~ (product @ additive_identity @ X1 @ X0)
% 83.55/12.62 | ~ (product @ additive_identity @ X1 @ X2)
% 83.55/12.62 | (product @ additive_identity @ X2 @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl9722, zip_derived_cl5])).
% 83.55/12.62 thf(zip_derived_cl13873, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 ( (product @ additive_identity @ X0 @ X0)
% 83.55/12.62 | ~ (product @ additive_identity @ X1 @ X0))),
% 83.55/12.62 inference('eq_fact', [status(thm)], [zip_derived_cl9729])).
% 83.55/12.62 thf(zip_derived_cl135871, plain, ( (product @ additive_identity @ t @ t)),
% 83.55/12.62 inference('sup-', [status(thm)],
% 83.55/12.62 [zip_derived_cl134508, zip_derived_cl13873])).
% 83.55/12.62 thf(zip_derived_cl9, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.62 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.62 thf(zip_derived_cl136515, plain, ( (product @ t @ additive_identity @ t)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl135871, zip_derived_cl9])).
% 83.55/12.62 thf(zip_derived_cl2699, plain,
% 83.55/12.62 ( (product @ (multiplicative_inverse @ b) @ t @ c)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl2682, zip_derived_cl9])).
% 83.55/12.62 thf(zip_derived_cl6, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 83.55/12.62 ( (product @ X0 @ X1 @ X2)
% 83.55/12.62 | ~ (product @ X3 @ X4 @ X0)
% 83.55/12.62 | ~ (product @ X4 @ X1 @ X5)
% 83.55/12.62 | ~ (product @ X3 @ X5 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 83.55/12.62 thf(zip_derived_cl157, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.55/12.62 (~ (product @ X2 @ X1 @ X0)
% 83.55/12.62 | ~ (product @ X1 @ X3 @ X1)
% 83.55/12.62 | (product @ X0 @ X3 @ X0))),
% 83.55/12.62 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 83.55/12.62 thf(zip_derived_cl2736, plain,
% 83.55/12.62 (![X0 : $i]: ( (product @ c @ X0 @ c) | ~ (product @ t @ X0 @ t))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl2699, zip_derived_cl157])).
% 83.55/12.62 thf(zip_derived_cl138361, plain, ( (product @ c @ additive_identity @ c)),
% 83.55/12.62 inference('sup-', [status(thm)],
% 83.55/12.62 [zip_derived_cl136515, zip_derived_cl2736])).
% 83.55/12.62 thf(zip_derived_cl22, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 ( (less_or_equal @ X0 @ X1)
% 83.55/12.62 | (less_or_equal @ X1 @ X0)
% 83.55/12.62 | ~ (defined @ X0)
% 83.55/12.62 | ~ (defined @ X1))),
% 83.55/12.62 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 83.55/12.62 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 83.55/12.62 inference('cnf', [status(esa)], [c_is_defined])).
% 83.55/12.62 thf(zip_derived_cl568, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | (less_or_equal @ X0 @ c)
% 83.55/12.62 | (less_or_equal @ c @ X0))),
% 83.55/12.62 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl28])).
% 83.55/12.62 thf(zip_derived_cl16399, plain,
% 83.55/12.62 (( (less_or_equal @ c @ c) | ~ (defined @ c))),
% 83.55/12.62 inference('eq_fact', [status(thm)], [zip_derived_cl568])).
% 83.55/12.62 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 83.55/12.62 inference('cnf', [status(esa)], [c_is_defined])).
% 83.55/12.62 thf(zip_derived_cl16400, plain, ( (less_or_equal @ c @ c)),
% 83.55/12.62 inference('demod', [status(thm)], [zip_derived_cl16399, zip_derived_cl28])).
% 83.55/12.62 thf(zip_derived_cl20, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 ( (sum @ additive_identity @ X0 @ X1)
% 83.55/12.62 | ~ (less_or_equal @ X0 @ X1)
% 83.55/12.62 | ~ (less_or_equal @ X1 @ X0))),
% 83.55/12.62 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 83.55/12.62 thf(zip_derived_cl16406, plain,
% 83.55/12.62 ((~ (less_or_equal @ c @ c) | (sum @ additive_identity @ c @ c))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl16400, zip_derived_cl20])).
% 83.55/12.62 thf(zip_derived_cl16400, plain, ( (less_or_equal @ c @ c)),
% 83.55/12.62 inference('demod', [status(thm)], [zip_derived_cl16399, zip_derived_cl28])).
% 83.55/12.62 thf(zip_derived_cl16409, plain, ( (sum @ additive_identity @ c @ c)),
% 83.55/12.62 inference('demod', [status(thm)],
% 83.55/12.62 [zip_derived_cl16406, zip_derived_cl16400])).
% 83.55/12.62 thf(zip_derived_cl8, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 83.55/12.62 multiplicative_identity)
% 83.55/12.62 | (sum @ additive_identity @ X0 @ additive_identity)
% 83.55/12.62 | ~ (defined @ X0))),
% 83.55/12.62 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 83.55/12.62 thf(zip_derived_cl66, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.62 (~ (sum @ additive_identity @ X1 @ X0)
% 83.55/12.62 | ~ (sum @ additive_identity @ X1 @ X2)
% 83.55/12.62 | (sum @ additive_identity @ X2 @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 83.55/12.62 thf(zip_derived_cl190, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 83.55/12.62 multiplicative_identity)
% 83.55/12.62 | (sum @ additive_identity @ X1 @ additive_identity)
% 83.55/12.62 | ~ (sum @ additive_identity @ X0 @ X1))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl66])).
% 83.55/12.62 thf(zip_derived_cl16424, plain,
% 83.55/12.62 (( (sum @ additive_identity @ c @ additive_identity)
% 83.55/12.62 | (product @ (multiplicative_inverse @ c) @ c @
% 83.55/12.62 multiplicative_identity)
% 83.55/12.62 | ~ (defined @ c))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl16409, zip_derived_cl190])).
% 83.55/12.62 thf(not_sum_8, conjecture, (sum @ additive_identity @ c @ additive_identity)).
% 83.55/12.62 thf(zf_stmt_5, negated_conjecture,
% 83.55/12.62 (~( sum @ additive_identity @ c @ additive_identity )),
% 83.55/12.62 inference('cnf.neg', [status(esa)], [not_sum_8])).
% 83.55/12.62 thf(zip_derived_cl33, plain,
% 83.55/12.62 (~ (sum @ additive_identity @ c @ additive_identity)),
% 83.55/12.62 inference('cnf', [status(esa)], [zf_stmt_5])).
% 83.55/12.62 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 83.55/12.62 inference('cnf', [status(esa)], [c_is_defined])).
% 83.55/12.62 thf(zip_derived_cl16454, plain,
% 83.55/12.62 ( (product @ (multiplicative_inverse @ c) @ c @ multiplicative_identity)),
% 83.55/12.62 inference('demod', [status(thm)],
% 83.55/12.62 [zip_derived_cl16424, zip_derived_cl33, zip_derived_cl28])).
% 83.55/12.62 thf(zip_derived_cl157, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.55/12.62 (~ (product @ X2 @ X1 @ X0)
% 83.55/12.62 | ~ (product @ X1 @ X3 @ X1)
% 83.55/12.62 | (product @ X0 @ X3 @ X0))),
% 83.55/12.62 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 83.55/12.62 thf(zip_derived_cl16485, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (product @ multiplicative_identity @ X0 @ multiplicative_identity)
% 83.55/12.62 | ~ (product @ c @ X0 @ c))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl16454, zip_derived_cl157])).
% 83.55/12.62 thf(zip_derived_cl138679, plain,
% 83.55/12.62 ( (product @ multiplicative_identity @ additive_identity @
% 83.55/12.62 multiplicative_identity)),
% 83.55/12.62 inference('sup-', [status(thm)],
% 83.55/12.62 [zip_derived_cl138361, zip_derived_cl16485])).
% 83.55/12.62 thf(zip_derived_cl9, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.55/12.62 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 83.55/12.62 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 83.55/12.62 thf(zip_derived_cl139642, plain,
% 83.55/12.62 ( (product @ additive_identity @ multiplicative_identity @
% 83.55/12.62 multiplicative_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl138679, zip_derived_cl9])).
% 83.55/12.62 thf(zip_derived_cl65, plain,
% 83.55/12.62 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 83.55/12.62 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl13])).
% 83.55/12.62 thf(zip_derived_cl5502, plain,
% 83.55/12.62 ( (product @ additive_identity @ multiplicative_identity @
% 83.55/12.62 additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl5493])).
% 83.55/12.62 thf(zip_derived_cl245, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 83.55/12.62 (~ (product @ X2 @ X1 @ X0)
% 83.55/12.62 | ~ (product @ X4 @ X1 @ X3)
% 83.55/12.62 | ~ (sum @ X4 @ X2 @ X2)
% 83.55/12.62 | (sum @ X3 @ X0 @ X0))),
% 83.55/12.62 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 83.55/12.62 thf(zip_derived_cl5516, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i]:
% 83.55/12.62 ( (sum @ X0 @ additive_identity @ additive_identity)
% 83.55/12.62 | ~ (sum @ X1 @ additive_identity @ additive_identity)
% 83.55/12.62 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl5502, zip_derived_cl245])).
% 83.55/12.62 thf(zip_derived_cl5676, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 (~ (product @ additive_identity @ multiplicative_identity @ X0)
% 83.55/12.62 | (sum @ X0 @ additive_identity @ additive_identity))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl5516])).
% 83.55/12.62 thf(zip_derived_cl140211, plain,
% 83.55/12.62 ( (sum @ multiplicative_identity @ additive_identity @ additive_identity)),
% 83.55/12.62 inference('sup-', [status(thm)],
% 83.55/12.62 [zip_derived_cl139642, zip_derived_cl5676])).
% 83.55/12.62 thf(zip_derived_cl7119, plain,
% 83.55/12.62 ( (sum @ multiplicative_identity @ additive_identity @
% 83.55/12.62 multiplicative_identity)),
% 83.55/12.62 inference('demod', [status(thm)],
% 83.55/12.62 [zip_derived_cl7118, zip_derived_cl2073])).
% 83.55/12.62 thf(zip_derived_cl46, plain,
% 83.55/12.62 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.55/12.62 (~ (defined @ X0)
% 83.55/12.62 | ~ (sum @ X0 @ X2 @ X1)
% 83.55/12.62 | ~ (sum @ X0 @ X2 @ X3)
% 83.55/12.62 | (sum @ additive_identity @ X3 @ X1))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 83.55/12.62 thf(zip_derived_cl7130, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 83.55/12.62 | ~ (sum @ multiplicative_identity @ additive_identity @ X0)
% 83.55/12.62 | ~ (defined @ multiplicative_identity))),
% 83.55/12.62 inference('sup-', [status(thm)], [zip_derived_cl7119, zip_derived_cl46])).
% 83.55/12.62 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 83.55/12.62 inference('cnf', [status(esa)],
% 83.55/12.62 [well_definedness_of_multiplicative_identity])).
% 83.55/12.62 thf(zip_derived_cl7137, plain,
% 83.55/12.62 (![X0 : $i]:
% 83.55/12.62 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 83.55/12.62 | ~ (sum @ multiplicative_identity @ additive_identity @ X0))),
% 83.55/12.62 inference('demod', [status(thm)], [zip_derived_cl7130, zip_derived_cl16])).
% 83.55/12.62 thf(zip_derived_cl140766, plain,
% 83.55/12.62 ( (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 83.55/12.62 inference('sup-', [status(thm)],
% 83.55/12.62 [zip_derived_cl140211, zip_derived_cl7137])).
% 83.55/12.62 thf(zip_derived_cl141128, plain, ($false),
% 83.55/12.62 inference('demod', [status(thm)],
% 83.55/12.62 [zip_derived_cl25, zip_derived_cl140766])).
% 83.55/12.62
% 83.55/12.62 % SZS output end Refutation
% 83.55/12.62
% 83.55/12.62
% 83.55/12.62 % Terminating...
% 84.30/12.74 % Runner terminated.
% 84.30/12.75 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------