%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD012-4 : TPTP v9.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.1NukI1Ump2 true
% Computer : n024.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 : Thu Oct 2 04:33:09 PM UTC 2025
% Result : Unsatisfiable 171.85s 25.37s
% Output : Refutation 171.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : FLD012-4 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.08/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.1NukI1Ump2 true
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Oct 1 18:30:23 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in FO mode
% 0.55/0.69 % Total configuration time : 435
% 0.55/0.69 % Estimated wc time : 1092
% 0.55/0.69 % Estimated cpu time (7 cpus) : 156.0
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.59/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.59/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.59/0.85 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 171.85/25.37 % Solved by fo/fo5.sh.
% 171.85/25.37 % done 19569 iterations in 24.464s
% 171.85/25.37 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 171.85/25.37 % SZS output start Refutation
% 171.85/25.37 thf(sum_type, type, sum: $i > $i > $i > $o).
% 171.85/25.37 thf(b_type, type, b: $i).
% 171.85/25.37 thf(a_type, type, a: $i).
% 171.85/25.37 thf(v_type, type, v: $i).
% 171.85/25.37 thf(product_type, type, product: $i > $i > $i > $o).
% 171.85/25.37 thf(additive_identity_type, type, additive_identity: $i).
% 171.85/25.37 thf(multiply_type, type, multiply: $i > $i > $i).
% 171.85/25.37 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 171.85/25.37 thf(u_type, type, u: $i).
% 171.85/25.37 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 171.85/25.37 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 171.85/25.37 thf(defined_type, type, defined: $i > $o).
% 171.85/25.37 thf(existence_of_inverse_multiplication, axiom,
% 171.85/25.37 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 171.85/25.37 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 171.85/25.37 thf(zip_derived_cl8, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 171.85/25.37 multiplicative_identity)
% 171.85/25.37 | (sum @ additive_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 171.85/25.37 thf(commutativity_multiplication, axiom,
% 171.85/25.37 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 171.85/25.37 thf(zip_derived_cl9, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl193, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ X0)
% 171.85/25.37 | (sum @ additive_identity @ X0 @ additive_identity)
% 171.85/25.37 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 171.85/25.37 multiplicative_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 171.85/25.37 thf(existence_of_identity_multiplication, axiom,
% 171.85/25.37 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 171.85/25.37 thf(zip_derived_cl7, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl9, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl57, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 171.85/25.37 thf(product_7, conjecture, (~( product @ a @ b @ u ))).
% 171.85/25.37 thf(zf_stmt_0, negated_conjecture, (product @ a @ b @ u),
% 171.85/25.37 inference('cnf.neg', [status(esa)], [product_7])).
% 171.85/25.37 thf(zip_derived_cl32, plain, ( (product @ a @ b @ u)),
% 171.85/25.37 inference('cnf', [status(esa)], [zf_stmt_0])).
% 171.85/25.37 thf(associativity_multiplication_2, axiom,
% 171.85/25.37 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 171.85/25.37 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 171.85/25.37 thf(zip_derived_cl6, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (product @ X3 @ X4 @ X0)
% 171.85/25.37 | ~ (product @ X4 @ X1 @ X5)
% 171.85/25.37 | ~ (product @ X3 @ X5 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 171.85/25.37 thf(zip_derived_cl142, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 (~ (product @ a @ X1 @ X0)
% 171.85/25.37 | ~ (product @ b @ X2 @ X1)
% 171.85/25.37 | (product @ u @ X2 @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl6])).
% 171.85/25.37 thf(zip_derived_cl163, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ a)
% 171.85/25.37 | (product @ u @ X0 @ a)
% 171.85/25.37 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl142])).
% 171.85/25.37 thf(a_is_defined, axiom, (defined @ a)).
% 171.85/25.37 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 171.85/25.37 inference('cnf', [status(esa)], [a_is_defined])).
% 171.85/25.37 thf(zip_derived_cl165, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ u @ X0 @ a)
% 171.85/25.37 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl163, zip_derived_cl26])).
% 171.85/25.37 thf(zip_derived_cl2755, plain,
% 171.85/25.37 (( (sum @ additive_identity @ b @ additive_identity)
% 171.85/25.37 | ~ (defined @ b)
% 171.85/25.37 | (product @ u @ (multiplicative_inverse @ b) @ a))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl193, zip_derived_cl165])).
% 171.85/25.37 thf(not_sum_6, conjecture, (sum @ additive_identity @ b @ additive_identity)).
% 171.85/25.37 thf(zf_stmt_1, negated_conjecture,
% 171.85/25.37 (~( sum @ additive_identity @ b @ additive_identity )),
% 171.85/25.37 inference('cnf.neg', [status(esa)], [not_sum_6])).
% 171.85/25.37 thf(zip_derived_cl31, plain,
% 171.85/25.37 (~ (sum @ additive_identity @ b @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [zf_stmt_1])).
% 171.85/25.37 thf(b_is_defined, axiom, (defined @ b)).
% 171.85/25.37 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 171.85/25.37 inference('cnf', [status(esa)], [b_is_defined])).
% 171.85/25.37 thf(zip_derived_cl2798, plain,
% 171.85/25.37 ( (product @ u @ (multiplicative_inverse @ b) @ a)),
% 171.85/25.37 inference('demod', [status(thm)],
% 171.85/25.37 [zip_derived_cl2755, zip_derived_cl31, zip_derived_cl27])).
% 171.85/25.37 thf(zip_derived_cl9, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl2914, plain,
% 171.85/25.37 ( (product @ (multiplicative_inverse @ b) @ u @ a)),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl2798, zip_derived_cl9])).
% 171.85/25.37 thf(zip_derived_cl8, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 171.85/25.37 multiplicative_identity)
% 171.85/25.37 | (sum @ additive_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 171.85/25.37 thf(product_8, conjecture,
% 171.85/25.37 (~( product @
% 171.85/25.37 ( multiplicative_inverse @ a ) @ ( multiplicative_inverse @ b ) @ v ))).
% 171.85/25.37 thf(zf_stmt_2, negated_conjecture,
% 171.85/25.37 (product @
% 171.85/25.37 ( multiplicative_inverse @ a ) @ ( multiplicative_inverse @ b ) @ v),
% 171.85/25.37 inference('cnf.neg', [status(esa)], [product_8])).
% 171.85/25.37 thf(zip_derived_cl33, plain,
% 171.85/25.37 ( (product @ (multiplicative_inverse @ a) @
% 171.85/25.37 (multiplicative_inverse @ b) @ v)),
% 171.85/25.37 inference('cnf', [status(esa)], [zf_stmt_2])).
% 171.85/25.37 thf(zip_derived_cl6, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (product @ X3 @ X4 @ X0)
% 171.85/25.37 | ~ (product @ X4 @ X1 @ X5)
% 171.85/25.37 | ~ (product @ X3 @ X5 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 171.85/25.37 thf(zip_derived_cl140, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 (~ (product @ (multiplicative_inverse @ a) @ X1 @ X0)
% 171.85/25.37 | ~ (product @ (multiplicative_inverse @ b) @ X2 @ X1)
% 171.85/25.37 | (product @ v @ X2 @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl6])).
% 171.85/25.37 thf(zip_derived_cl350, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ a)
% 171.85/25.37 | (sum @ additive_identity @ a @ additive_identity)
% 171.85/25.37 | (product @ v @ X0 @ multiplicative_identity)
% 171.85/25.37 | ~ (product @ (multiplicative_inverse @ b) @ X0 @ a))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl140])).
% 171.85/25.37 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 171.85/25.37 inference('cnf', [status(esa)], [a_is_defined])).
% 171.85/25.37 thf(zip_derived_cl353, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (sum @ additive_identity @ a @ additive_identity)
% 171.85/25.37 | (product @ v @ X0 @ multiplicative_identity)
% 171.85/25.37 | ~ (product @ (multiplicative_inverse @ b) @ X0 @ a))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl350, zip_derived_cl26])).
% 171.85/25.37 thf(not_sum_5, conjecture, (sum @ additive_identity @ a @ additive_identity)).
% 171.85/25.37 thf(zf_stmt_3, negated_conjecture,
% 171.85/25.37 (~( sum @ additive_identity @ a @ additive_identity )),
% 171.85/25.37 inference('cnf.neg', [status(esa)], [not_sum_5])).
% 171.85/25.37 thf(zip_derived_cl30, plain,
% 171.85/25.37 (~ (sum @ additive_identity @ a @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [zf_stmt_3])).
% 171.85/25.37 thf(zip_derived_cl424, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (product @ (multiplicative_inverse @ b) @ X0 @ a)
% 171.85/25.37 | (product @ v @ X0 @ multiplicative_identity))),
% 171.85/25.37 inference('clc', [status(thm)], [zip_derived_cl353, zip_derived_cl30])).
% 171.85/25.37 thf(zip_derived_cl3017, plain,
% 171.85/25.37 ( (product @ v @ u @ multiplicative_identity)),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl2914, zip_derived_cl424])).
% 171.85/25.37 thf(zip_derived_cl9, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl3023, plain,
% 171.85/25.37 ( (product @ u @ v @ multiplicative_identity)),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl3017, zip_derived_cl9])).
% 171.85/25.37 thf(zip_derived_cl7, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl8, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 171.85/25.37 multiplicative_identity)
% 171.85/25.37 | (sum @ additive_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 171.85/25.37 thf(associativity_multiplication_1, axiom,
% 171.85/25.37 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 171.85/25.37 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 171.85/25.37 thf(zip_derived_cl5, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (product @ X0 @ X3 @ X4)
% 171.85/25.37 | ~ (product @ X3 @ X5 @ X1)
% 171.85/25.37 | ~ (product @ X4 @ X5 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 171.85/25.37 thf(zip_derived_cl191, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 171.85/25.37 (~ (defined @ X0)
% 171.85/25.37 | (sum @ additive_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (product @ multiplicative_identity @ X2 @ X1)
% 171.85/25.37 | ~ (product @ X0 @ X2 @ X3)
% 171.85/25.37 | (product @ (multiplicative_inverse @ X0) @ X3 @ X1))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl5])).
% 171.85/25.37 thf(zip_derived_cl2616, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 (~ (defined @ X0)
% 171.85/25.37 | (product @ (multiplicative_inverse @ X2) @ X1 @ X0)
% 171.85/25.37 | ~ (product @ X2 @ X0 @ X1)
% 171.85/25.37 | (sum @ additive_identity @ X2 @ additive_identity)
% 171.85/25.37 | ~ (defined @ X2))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl191])).
% 171.85/25.37 thf(zip_derived_cl111401, plain,
% 171.85/25.37 ((~ (defined @ u)
% 171.85/25.37 | (sum @ additive_identity @ u @ additive_identity)
% 171.85/25.37 | (product @ (multiplicative_inverse @ u) @ multiplicative_identity @
% 171.85/25.37 v)
% 171.85/25.37 | ~ (defined @ v))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl3023, zip_derived_cl2616])).
% 171.85/25.37 thf(u_is_defined, axiom, (defined @ u)).
% 171.85/25.37 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 171.85/25.37 inference('cnf', [status(esa)], [u_is_defined])).
% 171.85/25.37 thf(v_is_defined, axiom, (defined @ v)).
% 171.85/25.37 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 171.85/25.37 inference('cnf', [status(esa)], [v_is_defined])).
% 171.85/25.37 thf(zip_derived_cl112328, plain,
% 171.85/25.37 (( (sum @ additive_identity @ u @ additive_identity)
% 171.85/25.37 | (product @ (multiplicative_inverse @ u) @ multiplicative_identity @
% 171.85/25.37 v))),
% 171.85/25.37 inference('demod', [status(thm)],
% 171.85/25.37 [zip_derived_cl111401, zip_derived_cl28, zip_derived_cl29])).
% 171.85/25.37 thf(zip_derived_cl9, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl130810, plain,
% 171.85/25.37 (( (sum @ additive_identity @ u @ additive_identity)
% 171.85/25.37 | (product @ multiplicative_identity @ (multiplicative_inverse @ u) @
% 171.85/25.37 v))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl112328, zip_derived_cl9])).
% 171.85/25.37 thf(not_product_9, conjecture,
% 171.85/25.37 (product @ multiplicative_identity @ ( multiplicative_inverse @ u ) @ v)).
% 171.85/25.37 thf(zf_stmt_4, negated_conjecture,
% 171.85/25.37 (~( product @ multiplicative_identity @ ( multiplicative_inverse @ u ) @ v )),
% 171.85/25.37 inference('cnf.neg', [status(esa)], [not_product_9])).
% 171.85/25.37 thf(zip_derived_cl34, plain,
% 171.85/25.37 (~ (product @ multiplicative_identity @ (multiplicative_inverse @ u) @ v)),
% 171.85/25.37 inference('cnf', [status(esa)], [zf_stmt_4])).
% 171.85/25.37 thf(zip_derived_cl136372, plain,
% 171.85/25.37 ( (sum @ additive_identity @ u @ additive_identity)),
% 171.85/25.37 inference('clc', [status(thm)], [zip_derived_cl130810, zip_derived_cl34])).
% 171.85/25.37 thf(totality_of_order_relation, axiom,
% 171.85/25.37 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 171.85/25.37 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 171.85/25.37 thf(zip_derived_cl22, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (less_or_equal @ X0 @ X1)
% 171.85/25.37 | (less_or_equal @ X1 @ X0)
% 171.85/25.37 | ~ (defined @ X0)
% 171.85/25.37 | ~ (defined @ X1))),
% 171.85/25.37 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 171.85/25.37 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 171.85/25.37 inference('cnf', [status(esa)], [u_is_defined])).
% 171.85/25.37 thf(zip_derived_cl527, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ X0)
% 171.85/25.37 | (less_or_equal @ X0 @ u)
% 171.85/25.37 | (less_or_equal @ u @ X0))),
% 171.85/25.37 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl28])).
% 171.85/25.37 thf(zip_derived_cl14232, plain,
% 171.85/25.37 (( (less_or_equal @ u @ u) | ~ (defined @ u))),
% 171.85/25.37 inference('eq_fact', [status(thm)], [zip_derived_cl527])).
% 171.85/25.37 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 171.85/25.37 inference('cnf', [status(esa)], [u_is_defined])).
% 171.85/25.37 thf(zip_derived_cl14233, plain, ( (less_or_equal @ u @ u)),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl14232, zip_derived_cl28])).
% 171.85/25.37 thf(antisymmetry_of_order_relation, axiom,
% 171.85/25.37 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 171.85/25.37 ( ~( less_or_equal @ Y @ X ) ))).
% 171.85/25.37 thf(zip_derived_cl20, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (sum @ additive_identity @ X0 @ X1)
% 171.85/25.37 | ~ (less_or_equal @ X0 @ X1)
% 171.85/25.37 | ~ (less_or_equal @ X1 @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 171.85/25.37 thf(zip_derived_cl14239, plain,
% 171.85/25.37 ((~ (less_or_equal @ u @ u) | (sum @ additive_identity @ u @ u))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl14233, zip_derived_cl20])).
% 171.85/25.37 thf(zip_derived_cl14233, plain, ( (less_or_equal @ u @ u)),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl14232, zip_derived_cl28])).
% 171.85/25.37 thf(zip_derived_cl14242, plain, ( (sum @ additive_identity @ u @ u)),
% 171.85/25.37 inference('demod', [status(thm)],
% 171.85/25.37 [zip_derived_cl14239, zip_derived_cl14233])).
% 171.85/25.37 thf(existence_of_identity_addition, axiom,
% 171.85/25.37 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 171.85/25.37 thf(zip_derived_cl2, plain,
% 171.85/25.37 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 171.85/25.37 thf(zip_derived_cl2, plain,
% 171.85/25.37 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 171.85/25.37 thf(associativity_addition_1, axiom,
% 171.85/25.37 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 171.85/25.37 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 171.85/25.37 thf(zip_derived_cl0, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.37 ( (sum @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (sum @ X0 @ X3 @ X4)
% 171.85/25.37 | ~ (sum @ X3 @ X5 @ X1)
% 171.85/25.37 | ~ (sum @ X4 @ X5 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [associativity_addition_1])).
% 171.85/25.37 thf(zip_derived_cl37, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 (~ (sum @ X0 @ X1 @ X0)
% 171.85/25.37 | ~ (sum @ X1 @ X1 @ X2)
% 171.85/25.37 | (sum @ X0 @ X2 @ X0))),
% 171.85/25.37 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 171.85/25.37 thf(zip_derived_cl44, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ additive_identity)
% 171.85/25.37 | (sum @ additive_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl37])).
% 171.85/25.37 thf(well_definedness_of_additive_identity, axiom,
% 171.85/25.37 (defined @ additive_identity)).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl45, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (sum @ additive_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl44, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl46, plain,
% 171.85/25.37 ((~ (defined @ additive_identity)
% 171.85/25.37 | (sum @ additive_identity @ additive_identity @ additive_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl45])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl48, plain,
% 171.85/25.37 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl0, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.37 ( (sum @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (sum @ X0 @ X3 @ X4)
% 171.85/25.37 | ~ (sum @ X3 @ X5 @ X1)
% 171.85/25.37 | ~ (sum @ X4 @ X5 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [associativity_addition_1])).
% 171.85/25.37 thf(zip_derived_cl50, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 (~ (sum @ additive_identity @ X1 @ X0)
% 171.85/25.37 | ~ (sum @ additive_identity @ X1 @ X2)
% 171.85/25.37 | (sum @ additive_identity @ X2 @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl0])).
% 171.85/25.37 thf(zip_derived_cl14259, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (sum @ additive_identity @ X0 @ u)
% 171.85/25.37 | ~ (sum @ additive_identity @ u @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl14242, zip_derived_cl50])).
% 171.85/25.37 thf(zip_derived_cl136483, plain,
% 171.85/25.37 ( (sum @ additive_identity @ additive_identity @ u)),
% 171.85/25.37 inference('sup-', [status(thm)],
% 171.85/25.37 [zip_derived_cl136372, zip_derived_cl14259])).
% 171.85/25.37 thf(zip_derived_cl57, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 171.85/25.37 thf(zip_derived_cl57, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 171.85/25.37 thf(zip_derived_cl48, plain,
% 171.85/25.37 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl13])).
% 171.85/25.37 thf(distributivity_2, axiom,
% 171.85/25.37 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 171.85/25.37 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 171.85/25.37 ( ~( sum @ C @ D @ B ) ))).
% 171.85/25.37 thf(zip_derived_cl11, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (sum @ X3 @ X4 @ X0)
% 171.85/25.37 | ~ (product @ X3 @ X1 @ X5)
% 171.85/25.37 | ~ (product @ X4 @ X1 @ X6)
% 171.85/25.37 | ~ (sum @ X5 @ X6 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [distributivity_2])).
% 171.85/25.37 thf(zip_derived_cl284, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 171.85/25.37 (~ (sum @ X2 @ X1 @ X0)
% 171.85/25.37 | ~ (product @ additive_identity @ X3 @ X1)
% 171.85/25.37 | ~ (product @ additive_identity @ X3 @ X2)
% 171.85/25.37 | (product @ additive_identity @ X3 @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl11])).
% 171.85/25.37 thf(zip_derived_cl5373, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 (~ (defined @ additive_identity)
% 171.85/25.37 | (product @ additive_identity @ multiplicative_identity @ X0)
% 171.85/25.37 | ~ (product @ additive_identity @ multiplicative_identity @ X1)
% 171.85/25.37 | ~ (sum @ X1 @ additive_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl284])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl5378, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (product @ additive_identity @ multiplicative_identity @ X0)
% 171.85/25.37 | ~ (product @ additive_identity @ multiplicative_identity @ X1)
% 171.85/25.37 | ~ (sum @ X1 @ additive_identity @ X0))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl5373, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl5843, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ additive_identity)
% 171.85/25.37 | ~ (sum @ additive_identity @ additive_identity @ X0)
% 171.85/25.37 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl5378])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl5846, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (sum @ additive_identity @ additive_identity @ X0)
% 171.85/25.37 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl5843, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl137478, plain,
% 171.85/25.37 ( (product @ additive_identity @ multiplicative_identity @ u)),
% 171.85/25.37 inference('sup-', [status(thm)],
% 171.85/25.37 [zip_derived_cl136483, zip_derived_cl5846])).
% 171.85/25.37 thf(well_definedness_of_multiplication, axiom,
% 171.85/25.37 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 171.85/25.37 ( ~( defined @ Y ) ))).
% 171.85/25.37 thf(zip_derived_cl15, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (defined @ (multiply @ X0 @ X1))
% 171.85/25.37 | ~ (defined @ X0)
% 171.85/25.37 | ~ (defined @ X1))),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 171.85/25.37 thf(totality_of_multiplication, axiom,
% 171.85/25.37 (( product @ X @ Y @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 171.85/25.37 ( ~( defined @ Y ) ))).
% 171.85/25.37 thf(zip_derived_cl19, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 171.85/25.37 | ~ (defined @ X0)
% 171.85/25.37 | ~ (defined @ X1))),
% 171.85/25.37 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 171.85/25.37 thf(zip_derived_cl57, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 171.85/25.37 thf(zip_derived_cl2, plain,
% 171.85/25.37 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 171.85/25.37 thf(zip_derived_cl57, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 171.85/25.37 thf(zip_derived_cl57, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 171.85/25.37 thf(zip_derived_cl5, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (product @ X0 @ X3 @ X4)
% 171.85/25.37 | ~ (product @ X3 @ X5 @ X1)
% 171.85/25.37 | ~ (product @ X4 @ X5 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 171.85/25.37 thf(zip_derived_cl99, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 171.85/25.37 (~ (defined @ X0)
% 171.85/25.37 | ~ (product @ X0 @ X2 @ X1)
% 171.85/25.37 | ~ (product @ multiplicative_identity @ X2 @ X3)
% 171.85/25.37 | (product @ X0 @ X3 @ X1))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl5])).
% 171.85/25.37 thf(zip_derived_cl1399, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (product @ multiplicative_identity @ X0 @ X0)
% 171.85/25.37 | ~ (product @ multiplicative_identity @ X1 @ X0)
% 171.85/25.37 | ~ (defined @ multiplicative_identity))),
% 171.85/25.37 inference('eq_fact', [status(thm)], [zip_derived_cl99])).
% 171.85/25.37 thf(well_definedness_of_multiplicative_identity, axiom,
% 171.85/25.37 (defined @ multiplicative_identity)).
% 171.85/25.37 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 171.85/25.37 inference('cnf', [status(esa)],
% 171.85/25.37 [well_definedness_of_multiplicative_identity])).
% 171.85/25.37 thf(zip_derived_cl1401, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (product @ multiplicative_identity @ X0 @ X0)
% 171.85/25.37 | ~ (product @ multiplicative_identity @ X1 @ X0))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl1399, zip_derived_cl16])).
% 171.85/25.37 thf(zip_derived_cl1408, plain,
% 171.85/25.37 ((~ (defined @ multiplicative_identity)
% 171.85/25.37 | (product @ multiplicative_identity @ multiplicative_identity @
% 171.85/25.37 multiplicative_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl1401])).
% 171.85/25.37 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 171.85/25.37 inference('cnf', [status(esa)],
% 171.85/25.37 [well_definedness_of_multiplicative_identity])).
% 171.85/25.37 thf(zip_derived_cl1417, plain,
% 171.85/25.37 ( (product @ multiplicative_identity @ multiplicative_identity @
% 171.85/25.37 multiplicative_identity)),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl1408, zip_derived_cl16])).
% 171.85/25.37 thf(distributivity_1, axiom,
% 171.85/25.37 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 171.85/25.37 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 171.85/25.37 ( ~( product @ Y @ Z @ D ) ))).
% 171.85/25.37 thf(zip_derived_cl10, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 171.85/25.37 ( (sum @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (sum @ X3 @ X4 @ X5)
% 171.85/25.37 | ~ (product @ X5 @ X6 @ X2)
% 171.85/25.37 | ~ (product @ X3 @ X6 @ X0)
% 171.85/25.37 | ~ (product @ X4 @ X6 @ X1))),
% 171.85/25.37 inference('cnf', [status(esa)], [distributivity_1])).
% 171.85/25.37 thf(zip_derived_cl247, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 171.85/25.37 (~ (product @ X2 @ X1 @ X0)
% 171.85/25.37 | ~ (product @ X4 @ X1 @ X3)
% 171.85/25.37 | ~ (sum @ X4 @ X2 @ X2)
% 171.85/25.37 | (sum @ X3 @ X0 @ X0))),
% 171.85/25.37 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 171.85/25.37 thf(zip_derived_cl4552, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (sum @ X0 @ multiplicative_identity @ multiplicative_identity)
% 171.85/25.37 | ~ (sum @ X1 @ multiplicative_identity @ multiplicative_identity)
% 171.85/25.37 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl1417, zip_derived_cl247])).
% 171.85/25.37 thf(zip_derived_cl4658, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (defined @ multiplicative_identity)
% 171.85/25.37 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 171.85/25.37 | (sum @ X0 @ multiplicative_identity @ multiplicative_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4552])).
% 171.85/25.37 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 171.85/25.37 inference('cnf', [status(esa)],
% 171.85/25.37 [well_definedness_of_multiplicative_identity])).
% 171.85/25.37 thf(zip_derived_cl4660, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (product @ additive_identity @ multiplicative_identity @ X0)
% 171.85/25.37 | (sum @ X0 @ multiplicative_identity @ multiplicative_identity))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl4658, zip_derived_cl16])).
% 171.85/25.37 thf(zip_derived_cl4662, plain,
% 171.85/25.37 ((~ (defined @ additive_identity)
% 171.85/25.37 | (sum @ additive_identity @ multiplicative_identity @
% 171.85/25.37 multiplicative_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl4660])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl4664, plain,
% 171.85/25.37 ( (sum @ additive_identity @ multiplicative_identity @
% 171.85/25.37 multiplicative_identity)),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl4662, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl48, plain,
% 171.85/25.37 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl5846, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (sum @ additive_identity @ additive_identity @ X0)
% 171.85/25.37 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl5843, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl5854, plain,
% 171.85/25.37 ( (product @ additive_identity @ multiplicative_identity @
% 171.85/25.37 additive_identity)),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl5846])).
% 171.85/25.37 thf(zip_derived_cl9, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl5864, plain,
% 171.85/25.37 ( (product @ multiplicative_identity @ additive_identity @
% 171.85/25.37 additive_identity)),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl5854, zip_derived_cl9])).
% 171.85/25.37 thf(zip_derived_cl247, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 171.85/25.37 (~ (product @ X2 @ X1 @ X0)
% 171.85/25.37 | ~ (product @ X4 @ X1 @ X3)
% 171.85/25.37 | ~ (sum @ X4 @ X2 @ X2)
% 171.85/25.37 | (sum @ X3 @ X0 @ X0))),
% 171.85/25.37 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 171.85/25.37 thf(zip_derived_cl5893, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (sum @ X0 @ additive_identity @ additive_identity)
% 171.85/25.37 | ~ (sum @ X1 @ multiplicative_identity @ multiplicative_identity)
% 171.85/25.37 | ~ (product @ X1 @ additive_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl5864, zip_derived_cl247])).
% 171.85/25.37 thf(zip_derived_cl8003, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (product @ additive_identity @ additive_identity @ X0)
% 171.85/25.37 | (sum @ X0 @ additive_identity @ additive_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl4664, zip_derived_cl5893])).
% 171.85/25.37 thf(zip_derived_cl8008, plain,
% 171.85/25.37 ((~ (defined @ additive_identity)
% 171.85/25.37 | ~ (defined @ additive_identity)
% 171.85/25.37 | (sum @ (multiply @ additive_identity @ additive_identity) @
% 171.85/25.37 additive_identity @ additive_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl8003])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl8009, plain,
% 171.85/25.37 ( (sum @ (multiply @ additive_identity @ additive_identity) @
% 171.85/25.37 additive_identity @ additive_identity)),
% 171.85/25.37 inference('demod', [status(thm)],
% 171.85/25.37 [zip_derived_cl8008, zip_derived_cl13, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl2, plain,
% 171.85/25.37 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 171.85/25.37 thf(commutativity_addition, axiom,
% 171.85/25.37 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 171.85/25.37 thf(zip_derived_cl4, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [commutativity_addition])).
% 171.85/25.37 thf(zip_derived_cl54, plain,
% 171.85/25.37 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 171.85/25.37 thf(zip_derived_cl2, plain,
% 171.85/25.37 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 171.85/25.37 thf(zip_derived_cl0, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.37 ( (sum @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (sum @ X0 @ X3 @ X4)
% 171.85/25.37 | ~ (sum @ X3 @ X5 @ X1)
% 171.85/25.37 | ~ (sum @ X4 @ X5 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [associativity_addition_1])).
% 171.85/25.37 thf(zip_derived_cl43, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 171.85/25.37 (~ (defined @ X0)
% 171.85/25.37 | ~ (sum @ X0 @ X2 @ X1)
% 171.85/25.37 | ~ (sum @ X0 @ X2 @ X3)
% 171.85/25.37 | (sum @ additive_identity @ X3 @ X1))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 171.85/25.37 thf(zip_derived_cl705, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 (~ (defined @ X0)
% 171.85/25.37 | (sum @ additive_identity @ X1 @ X0)
% 171.85/25.37 | ~ (sum @ X0 @ additive_identity @ X1)
% 171.85/25.37 | ~ (defined @ X0))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl43])).
% 171.85/25.37 thf(zip_derived_cl725, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 (~ (sum @ X0 @ additive_identity @ X1)
% 171.85/25.37 | (sum @ additive_identity @ X1 @ X0)
% 171.85/25.37 | ~ (defined @ X0))),
% 171.85/25.37 inference('simplify', [status(thm)], [zip_derived_cl705])).
% 171.85/25.37 thf(zip_derived_cl8035, plain,
% 171.85/25.37 ((~ (defined @ (multiply @ additive_identity @ additive_identity))
% 171.85/25.37 | (sum @ additive_identity @ additive_identity @
% 171.85/25.37 (multiply @ additive_identity @ additive_identity)))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl8009, zip_derived_cl725])).
% 171.85/25.37 thf(zip_derived_cl33763, plain,
% 171.85/25.37 ((~ (defined @ additive_identity)
% 171.85/25.37 | ~ (defined @ additive_identity)
% 171.85/25.37 | (sum @ additive_identity @ additive_identity @
% 171.85/25.37 (multiply @ additive_identity @ additive_identity)))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl8035])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl33764, plain,
% 171.85/25.37 ( (sum @ additive_identity @ additive_identity @
% 171.85/25.37 (multiply @ additive_identity @ additive_identity))),
% 171.85/25.37 inference('demod', [status(thm)],
% 171.85/25.37 [zip_derived_cl33763, zip_derived_cl13, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl5846, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 (~ (sum @ additive_identity @ additive_identity @ X0)
% 171.85/25.37 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl5843, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl33832, plain,
% 171.85/25.37 ( (product @ additive_identity @ multiplicative_identity @
% 171.85/25.37 (multiply @ additive_identity @ additive_identity))),
% 171.85/25.37 inference('sup-', [status(thm)],
% 171.85/25.37 [zip_derived_cl33764, zip_derived_cl5846])).
% 171.85/25.37 thf(zip_derived_cl5854, plain,
% 171.85/25.37 ( (product @ additive_identity @ multiplicative_identity @
% 171.85/25.37 additive_identity)),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl5846])).
% 171.85/25.37 thf(zip_derived_cl7, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 171.85/25.37 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl5, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (product @ X0 @ X3 @ X4)
% 171.85/25.37 | ~ (product @ X3 @ X5 @ X1)
% 171.85/25.37 | ~ (product @ X4 @ X5 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 171.85/25.37 thf(zip_derived_cl100, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 171.85/25.37 (~ (defined @ X0)
% 171.85/25.37 | ~ (product @ X0 @ X2 @ X1)
% 171.85/25.37 | ~ (product @ X0 @ X2 @ X3)
% 171.85/25.37 | (product @ multiplicative_identity @ X3 @ X1))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 171.85/25.37 thf(zip_derived_cl5869, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 171.85/25.37 | ~ (defined @ additive_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl5854, zip_derived_cl100])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl5886, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('demod', [status(thm)], [zip_derived_cl5869, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl33896, plain,
% 171.85/25.37 ( (product @ multiplicative_identity @
% 171.85/25.37 (multiply @ additive_identity @ additive_identity) @ additive_identity)),
% 171.85/25.37 inference('sup-', [status(thm)],
% 171.85/25.37 [zip_derived_cl33832, zip_derived_cl5886])).
% 171.85/25.37 thf(zip_derived_cl9, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.37 thf(zip_derived_cl34006, plain,
% 171.85/25.37 ( (product @ (multiply @ additive_identity @ additive_identity) @
% 171.85/25.37 multiplicative_identity @ additive_identity)),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl33896, zip_derived_cl9])).
% 171.85/25.37 thf(zip_derived_cl19, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 171.85/25.37 | ~ (defined @ X0)
% 171.85/25.37 | ~ (defined @ X1))),
% 171.85/25.37 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 171.85/25.37 thf(zip_derived_cl5, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.37 ( (product @ X0 @ X1 @ X2)
% 171.85/25.37 | ~ (product @ X0 @ X3 @ X4)
% 171.85/25.37 | ~ (product @ X3 @ X5 @ X1)
% 171.85/25.37 | ~ (product @ X4 @ X5 @ X2))),
% 171.85/25.37 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 171.85/25.37 thf(zip_derived_cl425, plain,
% 171.85/25.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 171.85/25.37 (~ (defined @ X0)
% 171.85/25.37 | ~ (defined @ X1)
% 171.85/25.37 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 171.85/25.37 | ~ (product @ X0 @ X3 @ X4)
% 171.85/25.37 | (product @ X1 @ X4 @ X2))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 171.85/25.37 thf(zip_derived_cl34235, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ additive_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 171.85/25.37 | ~ (defined @ additive_identity)
% 171.85/25.37 | ~ (defined @ additive_identity))),
% 171.85/25.37 inference('sup-', [status(thm)], [zip_derived_cl34006, zip_derived_cl425])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.37 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.37 thf(zip_derived_cl34239, plain,
% 171.85/25.37 (![X0 : $i]:
% 171.85/25.37 ( (product @ additive_identity @ X0 @ additive_identity)
% 171.85/25.37 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 171.85/25.37 inference('demod', [status(thm)],
% 171.85/25.37 [zip_derived_cl34235, zip_derived_cl13, zip_derived_cl13])).
% 171.85/25.37 thf(zip_derived_cl138210, plain,
% 171.85/25.37 ( (product @ additive_identity @ u @ additive_identity)),
% 171.85/25.37 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl137478, zip_derived_cl34239])).
% 171.85/25.38 thf(zip_derived_cl19, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 171.85/25.38 | ~ (defined @ X0)
% 171.85/25.38 | ~ (defined @ X1))),
% 171.85/25.38 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 171.85/25.38 thf(zip_derived_cl19, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 171.85/25.38 | ~ (defined @ X0)
% 171.85/25.38 | ~ (defined @ X1))),
% 171.85/25.38 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 171.85/25.38 thf(zip_derived_cl3023, plain,
% 171.85/25.38 ( (product @ u @ v @ multiplicative_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl3017, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl57, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl32, plain, ( (product @ a @ b @ u)),
% 171.85/25.38 inference('cnf', [status(esa)], [zf_stmt_0])).
% 171.85/25.38 thf(zip_derived_cl142, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 (~ (product @ a @ X1 @ X0)
% 171.85/25.38 | ~ (product @ b @ X2 @ X1)
% 171.85/25.38 | (product @ u @ X2 @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl6])).
% 171.85/25.38 thf(zip_derived_cl164, plain,
% 171.85/25.38 (![X0 : $i]: ( (product @ u @ X0 @ u) | ~ (product @ b @ X0 @ b))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl142])).
% 171.85/25.38 thf(zip_derived_cl166, plain,
% 171.85/25.38 ((~ (defined @ b) | (product @ u @ multiplicative_identity @ u))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl164])).
% 171.85/25.38 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 171.85/25.38 inference('cnf', [status(esa)], [b_is_defined])).
% 171.85/25.38 thf(zip_derived_cl167, plain, ( (product @ u @ multiplicative_identity @ u)),
% 171.85/25.38 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl27])).
% 171.85/25.38 thf(zip_derived_cl9, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.38 thf(zip_derived_cl170, plain, ( (product @ multiplicative_identity @ u @ u)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl5, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2)
% 171.85/25.38 | ~ (product @ X0 @ X3 @ X4)
% 171.85/25.38 | ~ (product @ X3 @ X5 @ X1)
% 171.85/25.38 | ~ (product @ X4 @ X5 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 171.85/25.38 thf(zip_derived_cl173, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 (~ (product @ u @ X1 @ X0)
% 171.85/25.38 | ~ (product @ u @ X1 @ X2)
% 171.85/25.38 | (product @ multiplicative_identity @ X2 @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl170, zip_derived_cl5])).
% 171.85/25.38 thf(zip_derived_cl3045, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ multiplicative_identity @ X0 @ multiplicative_identity)
% 171.85/25.38 | ~ (product @ u @ v @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl3023, zip_derived_cl173])).
% 171.85/25.38 thf(zip_derived_cl4303, plain,
% 171.85/25.38 ((~ (defined @ v)
% 171.85/25.38 | ~ (defined @ u)
% 171.85/25.38 | (product @ multiplicative_identity @ (multiply @ u @ v) @
% 171.85/25.38 multiplicative_identity))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl3045])).
% 171.85/25.38 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 171.85/25.38 inference('cnf', [status(esa)], [v_is_defined])).
% 171.85/25.38 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 171.85/25.38 inference('cnf', [status(esa)], [u_is_defined])).
% 171.85/25.38 thf(zip_derived_cl4305, plain,
% 171.85/25.38 ( (product @ multiplicative_identity @ (multiply @ u @ v) @
% 171.85/25.38 multiplicative_identity)),
% 171.85/25.38 inference('demod', [status(thm)],
% 171.85/25.38 [zip_derived_cl4303, zip_derived_cl29, zip_derived_cl28])).
% 171.85/25.38 thf(zip_derived_cl5854, plain,
% 171.85/25.38 ( (product @ additive_identity @ multiplicative_identity @
% 171.85/25.38 additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl5846])).
% 171.85/25.38 thf(zip_derived_cl6, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2)
% 171.85/25.38 | ~ (product @ X3 @ X4 @ X0)
% 171.85/25.38 | ~ (product @ X4 @ X1 @ X5)
% 171.85/25.38 | ~ (product @ X3 @ X5 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 171.85/25.38 thf(zip_derived_cl146, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 171.85/25.38 (~ (product @ X2 @ X1 @ X0)
% 171.85/25.38 | ~ (product @ X1 @ X3 @ X1)
% 171.85/25.38 | (product @ X0 @ X3 @ X0))),
% 171.85/25.38 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 171.85/25.38 thf(zip_derived_cl5866, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ additive_identity @ X0 @ additive_identity)
% 171.85/25.38 | ~ (product @ multiplicative_identity @ X0 @ multiplicative_identity))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl5854, zip_derived_cl146])).
% 171.85/25.38 thf(zip_derived_cl5932, plain,
% 171.85/25.38 ( (product @ additive_identity @ (multiply @ u @ v) @ additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl4305, zip_derived_cl5866])).
% 171.85/25.38 thf(zip_derived_cl9, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.38 thf(zip_derived_cl6043, plain,
% 171.85/25.38 ( (product @ (multiply @ u @ v) @ additive_identity @ additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl5932, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl425, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 171.85/25.38 (~ (defined @ X0)
% 171.85/25.38 | ~ (defined @ X1)
% 171.85/25.38 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 171.85/25.38 | ~ (product @ X0 @ X3 @ X4)
% 171.85/25.38 | (product @ X1 @ X4 @ X2))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 171.85/25.38 thf(zip_derived_cl8757, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ u @ X0 @ additive_identity)
% 171.85/25.38 | ~ (product @ v @ additive_identity @ X0)
% 171.85/25.38 | ~ (defined @ u)
% 171.85/25.38 | ~ (defined @ v))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl6043, zip_derived_cl425])).
% 171.85/25.38 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 171.85/25.38 inference('cnf', [status(esa)], [u_is_defined])).
% 171.85/25.38 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 171.85/25.38 inference('cnf', [status(esa)], [v_is_defined])).
% 171.85/25.38 thf(zip_derived_cl8813, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ u @ X0 @ additive_identity)
% 171.85/25.38 | ~ (product @ v @ additive_identity @ X0))),
% 171.85/25.38 inference('demod', [status(thm)],
% 171.85/25.38 [zip_derived_cl8757, zip_derived_cl28, zip_derived_cl29])).
% 171.85/25.38 thf(zip_derived_cl8869, plain,
% 171.85/25.38 ((~ (defined @ additive_identity)
% 171.85/25.38 | ~ (defined @ v)
% 171.85/25.38 | (product @ u @ (multiply @ v @ additive_identity) @
% 171.85/25.38 additive_identity))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl8813])).
% 171.85/25.38 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.38 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.38 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 171.85/25.38 inference('cnf', [status(esa)], [v_is_defined])).
% 171.85/25.38 thf(zip_derived_cl8870, plain,
% 171.85/25.38 ( (product @ u @ (multiply @ v @ additive_identity) @ additive_identity)),
% 171.85/25.38 inference('demod', [status(thm)],
% 171.85/25.38 [zip_derived_cl8869, zip_derived_cl13, zip_derived_cl29])).
% 171.85/25.38 thf(zip_derived_cl9, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.38 thf(zip_derived_cl9252, plain,
% 171.85/25.38 ( (product @ (multiply @ v @ additive_identity) @ u @ additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl8870, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl425, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 171.85/25.38 (~ (defined @ X0)
% 171.85/25.38 | ~ (defined @ X1)
% 171.85/25.38 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 171.85/25.38 | ~ (product @ X0 @ X3 @ X4)
% 171.85/25.38 | (product @ X1 @ X4 @ X2))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 171.85/25.38 thf(zip_derived_cl10290, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ v @ X0 @ additive_identity)
% 171.85/25.38 | ~ (product @ additive_identity @ u @ X0)
% 171.85/25.38 | ~ (defined @ v)
% 171.85/25.38 | ~ (defined @ additive_identity))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl9252, zip_derived_cl425])).
% 171.85/25.38 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 171.85/25.38 inference('cnf', [status(esa)], [v_is_defined])).
% 171.85/25.38 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 171.85/25.38 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 171.85/25.38 thf(zip_derived_cl10292, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ v @ X0 @ additive_identity)
% 171.85/25.38 | ~ (product @ additive_identity @ u @ X0))),
% 171.85/25.38 inference('demod', [status(thm)],
% 171.85/25.38 [zip_derived_cl10290, zip_derived_cl29, zip_derived_cl13])).
% 171.85/25.38 thf(zip_derived_cl138665, plain,
% 171.85/25.38 ( (product @ v @ additive_identity @ additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl138210, zip_derived_cl10292])).
% 171.85/25.38 thf(zip_derived_cl9, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.38 thf(zip_derived_cl138880, plain,
% 171.85/25.38 ( (product @ additive_identity @ v @ additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl138665, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl136483, plain,
% 171.85/25.38 ( (sum @ additive_identity @ additive_identity @ u)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl136372, zip_derived_cl14259])).
% 171.85/25.38 thf(zip_derived_cl11, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2)
% 171.85/25.38 | ~ (sum @ X3 @ X4 @ X0)
% 171.85/25.38 | ~ (product @ X3 @ X1 @ X5)
% 171.85/25.38 | ~ (product @ X4 @ X1 @ X6)
% 171.85/25.38 | ~ (sum @ X5 @ X6 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [distributivity_2])).
% 171.85/25.38 thf(zip_derived_cl290, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 171.85/25.38 (~ (sum @ X2 @ X1 @ X0)
% 171.85/25.38 | ~ (product @ X1 @ X3 @ X1)
% 171.85/25.38 | ~ (product @ X2 @ X3 @ X2)
% 171.85/25.38 | (product @ X0 @ X3 @ X0))),
% 171.85/25.38 inference('eq_fact', [status(thm)], [zip_derived_cl11])).
% 171.85/25.38 thf(zip_derived_cl137354, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ u @ X0 @ u)
% 171.85/25.38 | ~ (product @ additive_identity @ X0 @ additive_identity)
% 171.85/25.38 | ~ (product @ additive_identity @ X0 @ additive_identity))),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl136483, zip_derived_cl290])).
% 171.85/25.38 thf(zip_derived_cl137501, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 (~ (product @ additive_identity @ X0 @ additive_identity)
% 171.85/25.38 | (product @ u @ X0 @ u))),
% 171.85/25.38 inference('simplify', [status(thm)], [zip_derived_cl137354])).
% 171.85/25.38 thf(zip_derived_cl164302, plain, ( (product @ u @ v @ u)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl138880, zip_derived_cl137501])).
% 171.85/25.38 thf(zip_derived_cl19, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 171.85/25.38 | ~ (defined @ X0)
% 171.85/25.38 | ~ (defined @ X1))),
% 171.85/25.38 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 171.85/25.38 thf(zip_derived_cl167, plain, ( (product @ u @ multiplicative_identity @ u)),
% 171.85/25.38 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl27])).
% 171.85/25.38 thf(zip_derived_cl173, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 (~ (product @ u @ X1 @ X0)
% 171.85/25.38 | ~ (product @ u @ X1 @ X2)
% 171.85/25.38 | (product @ multiplicative_identity @ X2 @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl170, zip_derived_cl5])).
% 171.85/25.38 thf(zip_derived_cl301, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ multiplicative_identity @ X0 @ u)
% 171.85/25.38 | ~ (product @ u @ multiplicative_identity @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl173])).
% 171.85/25.38 thf(zip_derived_cl442, plain,
% 171.85/25.38 ((~ (defined @ multiplicative_identity)
% 171.85/25.38 | ~ (defined @ u)
% 171.85/25.38 | (product @ multiplicative_identity @
% 171.85/25.38 (multiply @ u @ multiplicative_identity) @ u))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl301])).
% 171.85/25.38 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 171.85/25.38 inference('cnf', [status(esa)],
% 171.85/25.38 [well_definedness_of_multiplicative_identity])).
% 171.85/25.38 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 171.85/25.38 inference('cnf', [status(esa)], [u_is_defined])).
% 171.85/25.38 thf(zip_derived_cl456, plain,
% 171.85/25.38 ( (product @ multiplicative_identity @
% 171.85/25.38 (multiply @ u @ multiplicative_identity) @ u)),
% 171.85/25.38 inference('demod', [status(thm)],
% 171.85/25.38 [zip_derived_cl442, zip_derived_cl16, zip_derived_cl28])).
% 171.85/25.38 thf(zip_derived_cl3017, plain,
% 171.85/25.38 ( (product @ v @ u @ multiplicative_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl2914, zip_derived_cl424])).
% 171.85/25.38 thf(zip_derived_cl57, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl33, plain,
% 171.85/25.38 ( (product @ (multiplicative_inverse @ a) @
% 171.85/25.38 (multiplicative_inverse @ b) @ v)),
% 171.85/25.38 inference('cnf', [status(esa)], [zf_stmt_2])).
% 171.85/25.38 thf(zip_derived_cl140, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 (~ (product @ (multiplicative_inverse @ a) @ X1 @ X0)
% 171.85/25.38 | ~ (product @ (multiplicative_inverse @ b) @ X2 @ X1)
% 171.85/25.38 | (product @ v @ X2 @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl6])).
% 171.85/25.38 thf(zip_derived_cl351, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ v @ X0 @ v)
% 171.85/25.38 | ~ (product @ (multiplicative_inverse @ b) @ X0 @
% 171.85/25.38 (multiplicative_inverse @ b)))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl140])).
% 171.85/25.38 thf(zip_derived_cl354, plain,
% 171.85/25.38 ((~ (defined @ (multiplicative_inverse @ b))
% 171.85/25.38 | (product @ v @ multiplicative_identity @ v))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl351])).
% 171.85/25.38 thf(well_definedness_of_multiplicative_inverse, axiom,
% 171.85/25.38 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 171.85/25.38 ( sum @ additive_identity @ X @ additive_identity ))).
% 171.85/25.38 thf(zip_derived_cl17, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (defined @ (multiplicative_inverse @ X0))
% 171.85/25.38 | ~ (defined @ X0)
% 171.85/25.38 | (sum @ additive_identity @ X0 @ additive_identity))),
% 171.85/25.38 inference('cnf', [status(esa)],
% 171.85/25.38 [well_definedness_of_multiplicative_inverse])).
% 171.85/25.38 thf(zip_derived_cl31, plain,
% 171.85/25.38 (~ (sum @ additive_identity @ b @ additive_identity)),
% 171.85/25.38 inference('cnf', [status(esa)], [zf_stmt_1])).
% 171.85/25.38 thf(zip_derived_cl91, plain,
% 171.85/25.38 ((~ (defined @ b) | (defined @ (multiplicative_inverse @ b)))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl31])).
% 171.85/25.38 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 171.85/25.38 inference('cnf', [status(esa)], [b_is_defined])).
% 171.85/25.38 thf(zip_derived_cl95, plain, ( (defined @ (multiplicative_inverse @ b))),
% 171.85/25.38 inference('demod', [status(thm)], [zip_derived_cl91, zip_derived_cl27])).
% 171.85/25.38 thf(zip_derived_cl355, plain, ( (product @ v @ multiplicative_identity @ v)),
% 171.85/25.38 inference('demod', [status(thm)], [zip_derived_cl354, zip_derived_cl95])).
% 171.85/25.38 thf(zip_derived_cl6, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2)
% 171.85/25.38 | ~ (product @ X3 @ X4 @ X0)
% 171.85/25.38 | ~ (product @ X4 @ X1 @ X5)
% 171.85/25.38 | ~ (product @ X3 @ X5 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 171.85/25.38 thf(zip_derived_cl357, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 (~ (product @ v @ X1 @ X0)
% 171.85/25.38 | ~ (product @ multiplicative_identity @ X2 @ X1)
% 171.85/25.38 | (product @ v @ X2 @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl355, zip_derived_cl6])).
% 171.85/25.38 thf(zip_derived_cl3029, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ v @ X0 @ multiplicative_identity)
% 171.85/25.38 | ~ (product @ multiplicative_identity @ X0 @ u))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl3017, zip_derived_cl357])).
% 171.85/25.38 thf(zip_derived_cl4062, plain,
% 171.85/25.38 ( (product @ v @ (multiply @ u @ multiplicative_identity) @
% 171.85/25.38 multiplicative_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl456, zip_derived_cl3029])).
% 171.85/25.38 thf(zip_derived_cl9, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.38 thf(zip_derived_cl4720, plain,
% 171.85/25.38 ( (product @ (multiply @ u @ multiplicative_identity) @ v @
% 171.85/25.38 multiplicative_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl4062, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl456, plain,
% 171.85/25.38 ( (product @ multiplicative_identity @
% 171.85/25.38 (multiply @ u @ multiplicative_identity) @ u)),
% 171.85/25.38 inference('demod', [status(thm)],
% 171.85/25.38 [zip_derived_cl442, zip_derived_cl16, zip_derived_cl28])).
% 171.85/25.38 thf(zip_derived_cl5, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2)
% 171.85/25.38 | ~ (product @ X0 @ X3 @ X4)
% 171.85/25.38 | ~ (product @ X3 @ X5 @ X1)
% 171.85/25.38 | ~ (product @ X4 @ X5 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 171.85/25.38 thf(zip_derived_cl493, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 (~ (product @ u @ X1 @ X0)
% 171.85/25.38 | ~ (product @ (multiply @ u @ multiplicative_identity) @ X1 @ X2)
% 171.85/25.38 | (product @ multiplicative_identity @ X2 @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl456, zip_derived_cl5])).
% 171.85/25.38 thf(zip_derived_cl12340, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ multiplicative_identity @ multiplicative_identity @ X0)
% 171.85/25.38 | ~ (product @ u @ v @ X0))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl4720, zip_derived_cl493])).
% 171.85/25.38 thf(zip_derived_cl164576, plain,
% 171.85/25.38 ( (product @ multiplicative_identity @ multiplicative_identity @ u)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl164302, zip_derived_cl12340])).
% 171.85/25.38 thf(zip_derived_cl1417, plain,
% 171.85/25.38 ( (product @ multiplicative_identity @ multiplicative_identity @
% 171.85/25.38 multiplicative_identity)),
% 171.85/25.38 inference('demod', [status(thm)], [zip_derived_cl1408, zip_derived_cl16])).
% 171.85/25.38 thf(zip_derived_cl10, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 171.85/25.38 ( (sum @ X0 @ X1 @ X2)
% 171.85/25.38 | ~ (sum @ X3 @ X4 @ X5)
% 171.85/25.38 | ~ (product @ X5 @ X6 @ X2)
% 171.85/25.38 | ~ (product @ X3 @ X6 @ X0)
% 171.85/25.38 | ~ (product @ X4 @ X6 @ X1))),
% 171.85/25.38 inference('cnf', [status(esa)], [distributivity_1])).
% 171.85/25.38 thf(zip_derived_cl1421, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 171.85/25.38 (~ (product @ X1 @ multiplicative_identity @ X0)
% 171.85/25.38 | ~ (product @ X3 @ multiplicative_identity @ X2)
% 171.85/25.38 | ~ (sum @ X3 @ X1 @ multiplicative_identity)
% 171.85/25.38 | (sum @ X2 @ X0 @ multiplicative_identity))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl1417, zip_derived_cl10])).
% 171.85/25.38 thf(zip_derived_cl55631, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i]:
% 171.85/25.38 ( (sum @ X0 @ X0 @ multiplicative_identity)
% 171.85/25.38 | ~ (sum @ X1 @ X1 @ multiplicative_identity)
% 171.85/25.38 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 171.85/25.38 inference('eq_fact', [status(thm)], [zip_derived_cl1421])).
% 171.85/25.38 thf(zip_derived_cl166269, plain,
% 171.85/25.38 ((~ (sum @ multiplicative_identity @ multiplicative_identity @
% 171.85/25.38 multiplicative_identity)
% 171.85/25.38 | (sum @ u @ u @ multiplicative_identity))),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl164576, zip_derived_cl55631])).
% 171.85/25.38 thf(zip_derived_cl137478, plain,
% 171.85/25.38 ( (product @ additive_identity @ multiplicative_identity @ u)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl136483, zip_derived_cl5846])).
% 171.85/25.38 thf(zip_derived_cl5886, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 171.85/25.38 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 171.85/25.38 inference('demod', [status(thm)], [zip_derived_cl5869, zip_derived_cl13])).
% 171.85/25.38 thf(zip_derived_cl138202, plain,
% 171.85/25.38 ( (product @ multiplicative_identity @ u @ additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl137478, zip_derived_cl5886])).
% 171.85/25.38 thf(zip_derived_cl9, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.38 thf(zip_derived_cl138549, plain,
% 171.85/25.38 ( (product @ u @ multiplicative_identity @ additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl138202, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl55631, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i]:
% 171.85/25.38 ( (sum @ X0 @ X0 @ multiplicative_identity)
% 171.85/25.38 | ~ (sum @ X1 @ X1 @ multiplicative_identity)
% 171.85/25.38 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 171.85/25.38 inference('eq_fact', [status(thm)], [zip_derived_cl1421])).
% 171.85/25.38 thf(zip_derived_cl138774, plain,
% 171.85/25.38 ((~ (sum @ u @ u @ multiplicative_identity)
% 171.85/25.38 | (sum @ additive_identity @ additive_identity @
% 171.85/25.38 multiplicative_identity))),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl138549, zip_derived_cl55631])).
% 171.85/25.38 thf(different_identities, axiom,
% 171.85/25.38 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 171.85/25.38 thf(zip_derived_cl25, plain,
% 171.85/25.38 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 171.85/25.38 inference('cnf', [status(esa)], [different_identities])).
% 171.85/25.38 thf(zip_derived_cl142365, plain, (~ (sum @ u @ u @ multiplicative_identity)),
% 171.85/25.38 inference('clc', [status(thm)], [zip_derived_cl138774, zip_derived_cl25])).
% 171.85/25.38 thf(zip_derived_cl166350, plain,
% 171.85/25.38 (~ (sum @ multiplicative_identity @ multiplicative_identity @
% 171.85/25.38 multiplicative_identity)),
% 171.85/25.38 inference('demod', [status(thm)],
% 171.85/25.38 [zip_derived_cl166269, zip_derived_cl142365])).
% 171.85/25.38 thf(zip_derived_cl5854, plain,
% 171.85/25.38 ( (product @ additive_identity @ multiplicative_identity @
% 171.85/25.38 additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl5846])).
% 171.85/25.38 thf(zip_derived_cl34239, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ additive_identity @ X0 @ additive_identity)
% 171.85/25.38 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 171.85/25.38 inference('demod', [status(thm)],
% 171.85/25.38 [zip_derived_cl34235, zip_derived_cl13, zip_derived_cl13])).
% 171.85/25.38 thf(zip_derived_cl34243, plain,
% 171.85/25.38 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl5854, zip_derived_cl34239])).
% 171.85/25.38 thf(zip_derived_cl137501, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 (~ (product @ additive_identity @ X0 @ additive_identity)
% 171.85/25.38 | (product @ u @ X0 @ u))),
% 171.85/25.38 inference('simplify', [status(thm)], [zip_derived_cl137354])).
% 171.85/25.38 thf(zip_derived_cl164276, plain, ( (product @ u @ additive_identity @ u)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl34243, zip_derived_cl137501])).
% 171.85/25.38 thf(zip_derived_cl3017, plain,
% 171.85/25.38 ( (product @ v @ u @ multiplicative_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl2914, zip_derived_cl424])).
% 171.85/25.38 thf(zip_derived_cl146, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 171.85/25.38 (~ (product @ X2 @ X1 @ X0)
% 171.85/25.38 | ~ (product @ X1 @ X3 @ X1)
% 171.85/25.38 | (product @ X0 @ X3 @ X0))),
% 171.85/25.38 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 171.85/25.38 thf(zip_derived_cl3025, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 ( (product @ multiplicative_identity @ X0 @ multiplicative_identity)
% 171.85/25.38 | ~ (product @ u @ X0 @ u))),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl3017, zip_derived_cl146])).
% 171.85/25.38 thf(zip_derived_cl164419, plain,
% 171.85/25.38 ( (product @ multiplicative_identity @ additive_identity @
% 171.85/25.38 multiplicative_identity)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl164276, zip_derived_cl3025])).
% 171.85/25.38 thf(zip_derived_cl9, plain,
% 171.85/25.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 171.85/25.38 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 171.85/25.38 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 171.85/25.38 thf(zip_derived_cl164763, plain,
% 171.85/25.38 ( (product @ additive_identity @ multiplicative_identity @
% 171.85/25.38 multiplicative_identity)),
% 171.85/25.38 inference('sup-', [status(thm)], [zip_derived_cl164419, zip_derived_cl9])).
% 171.85/25.38 thf(zip_derived_cl4660, plain,
% 171.85/25.38 (![X0 : $i]:
% 171.85/25.38 (~ (product @ additive_identity @ multiplicative_identity @ X0)
% 171.85/25.38 | (sum @ X0 @ multiplicative_identity @ multiplicative_identity))),
% 171.85/25.38 inference('demod', [status(thm)], [zip_derived_cl4658, zip_derived_cl16])).
% 171.85/25.38 thf(zip_derived_cl166795, plain,
% 171.85/25.38 ( (sum @ multiplicative_identity @ multiplicative_identity @
% 171.85/25.38 multiplicative_identity)),
% 171.85/25.38 inference('sup-', [status(thm)],
% 171.85/25.38 [zip_derived_cl164763, zip_derived_cl4660])).
% 171.85/25.38 thf(zip_derived_cl169109, plain, ($false),
% 171.85/25.38 inference('demod', [status(thm)],
% 171.85/25.38 [zip_derived_cl166350, zip_derived_cl166795])).
% 171.85/25.38
% 171.85/25.38 % SZS output end Refutation
% 171.85/25.38
% 171.85/25.38
% 171.85/25.38 % Terminating...
% 172.51/25.46 % Runner terminated.
% 172.51/25.47 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------