TSTP Solution File: FLD043-5 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD043-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aZm0Wn898x true
% Computer : n003.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 22:39:24 EDT 2023
% Result : Unsatisfiable 100.55s 15.05s
% Output : Refutation 101.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD043-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aZm0Wn898x true
% 0.15/0.37 % Computer : n003.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 : Sun Aug 27 23:39:10 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % 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
% 0.23/0.68 % Total configuration time : 435
% 0.23/0.68 % Estimated wc time : 1092
% 0.23/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.23/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.23/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.23/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.23/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.23/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.23/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.23/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 100.55/15.05 % Solved by fo/fo5.sh.
% 100.55/15.05 % done 19283 iterations in 14.243s
% 100.55/15.05 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 100.55/15.05 % SZS output start Refutation
% 100.55/15.05 thf(sum_type, type, sum: $i > $i > $i > $o).
% 100.55/15.05 thf(a_type, type, a: $i).
% 100.55/15.05 thf(add_type, type, add: $i > $i > $i).
% 100.55/15.05 thf(product_type, type, product: $i > $i > $i > $o).
% 100.55/15.05 thf(additive_identity_type, type, additive_identity: $i).
% 100.55/15.05 thf(multiply_type, type, multiply: $i > $i > $i).
% 100.55/15.05 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 100.55/15.05 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 100.55/15.05 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 100.55/15.05 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 100.55/15.05 thf(defined_type, type, defined: $i > $o).
% 100.55/15.05 thf(not_product_2, conjecture,
% 100.55/15.05 (product @ additive_identity @ a @ additive_identity)).
% 100.55/15.05 thf(zf_stmt_0, negated_conjecture,
% 100.55/15.05 (~( product @ additive_identity @ a @ additive_identity )),
% 100.55/15.05 inference('cnf.neg', [status(esa)], [not_product_2])).
% 100.55/15.05 thf(zip_derived_cl27, plain,
% 100.55/15.05 (~ (product @ additive_identity @ a @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [zf_stmt_0])).
% 100.55/15.05 thf(well_definedness_of_multiplication, axiom,
% 100.55/15.05 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 100.55/15.05 ( ~( defined @ Y ) ))).
% 100.55/15.05 thf(zip_derived_cl15, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (defined @ (multiply @ X0 @ X1))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 100.55/15.05 thf(totality_of_multiplication, axiom,
% 100.55/15.05 (( product @ X @ Y @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 100.55/15.05 ( ~( defined @ Y ) ))).
% 100.55/15.05 thf(zip_derived_cl19, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 100.55/15.05 thf(zip_derived_cl15, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (defined @ (multiply @ X0 @ X1))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 100.55/15.05 thf(zip_derived_cl19, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 100.55/15.05 thf(existence_of_identity_addition, axiom,
% 100.55/15.05 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 100.55/15.05 thf(zip_derived_cl2, plain,
% 100.55/15.05 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 100.55/15.05 thf(zip_derived_cl2, plain,
% 100.55/15.05 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 100.55/15.05 thf(associativity_addition_1, axiom,
% 100.55/15.05 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 100.55/15.05 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 100.55/15.05 thf(zip_derived_cl0, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X0 @ X3 @ X4)
% 100.55/15.05 | ~ (sum @ X3 @ X5 @ X1)
% 100.55/15.05 | ~ (sum @ X4 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_addition_1])).
% 100.55/15.05 thf(zip_derived_cl32, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (sum @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X1 @ X1 @ X0)
% 100.55/15.05 | (sum @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 100.55/15.05 thf(zip_derived_cl37, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (sum @ X0 @ additive_identity @ X0)
% 100.55/15.05 | ~ (sum @ X0 @ X0 @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl32])).
% 100.55/15.05 thf(zip_derived_cl42, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | (sum @ additive_identity @ additive_identity @ additive_identity)
% 100.55/15.05 | ~ (defined @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl37])).
% 100.55/15.05 thf(well_definedness_of_additive_identity, axiom,
% 100.55/15.05 (defined @ additive_identity)).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl45, plain,
% 100.55/15.05 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl42, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl45, plain,
% 100.55/15.05 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl42, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(existence_of_identity_multiplication, axiom,
% 100.55/15.05 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 100.55/15.05 thf(zip_derived_cl7, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 100.55/15.05 thf(commutativity_multiplication, axiom,
% 100.55/15.05 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl34, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl2, plain,
% 100.55/15.05 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 100.55/15.05 thf(commutativity_addition, axiom,
% 100.55/15.05 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 100.55/15.05 thf(zip_derived_cl4, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_addition])).
% 100.55/15.05 thf(zip_derived_cl52, plain,
% 100.55/15.05 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 100.55/15.05 thf(distributivity_2, axiom,
% 100.55/15.05 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 100.55/15.05 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 100.55/15.05 ( ~( sum @ C @ D @ B ) ))).
% 100.55/15.05 thf(zip_derived_cl11, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (product @ X3 @ X1 @ X5)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X6)
% 100.55/15.05 | ~ (sum @ X5 @ X6 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [distributivity_2])).
% 100.55/15.05 thf(zip_derived_cl205, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | ~ (sum @ X3 @ X2 @ X1)
% 100.55/15.05 | ~ (product @ additive_identity @ X4 @ X2)
% 100.55/15.05 | ~ (product @ X0 @ X4 @ X3)
% 100.55/15.05 | (product @ X0 @ X4 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl11])).
% 100.55/15.05 thf(zip_derived_cl7113, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ additive_identity @ X1 @ X2)
% 100.55/15.05 | ~ (product @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ X0 @ X0 @ X2)
% 100.55/15.05 | ~ (defined @ additive_identity))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl205])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl7115, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ additive_identity @ X1 @ X2)
% 100.55/15.05 | ~ (product @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ X0 @ X0 @ X2))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl7113, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7139, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ additive_identity)
% 100.55/15.05 | ~ (sum @ additive_identity @ additive_identity @ X0)
% 100.55/15.05 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl7115])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl7145, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (sum @ additive_identity @ additive_identity @ X0)
% 100.55/15.05 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl7139, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7155, plain,
% 100.55/15.05 ( (product @ additive_identity @ multiplicative_identity @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl7145])).
% 100.55/15.05 thf(distributivity_1, axiom,
% 100.55/15.05 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 100.55/15.05 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 100.55/15.05 ( ~( product @ Y @ Z @ D ) ))).
% 100.55/15.05 thf(zip_derived_cl10, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X3 @ X4 @ X5)
% 100.55/15.05 | ~ (product @ X5 @ X6 @ X2)
% 100.55/15.05 | ~ (product @ X3 @ X6 @ X0)
% 100.55/15.05 | ~ (product @ X4 @ X6 @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [distributivity_1])).
% 100.55/15.05 thf(zip_derived_cl138, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 100.55/15.05 (~ (product @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X3)
% 100.55/15.05 | ~ (sum @ X4 @ X2 @ X2)
% 100.55/15.05 | (sum @ X3 @ X0 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 100.55/15.05 thf(zip_derived_cl7174, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (sum @ X0 @ additive_identity @ additive_identity)
% 100.55/15.05 | ~ (sum @ X1 @ additive_identity @ additive_identity)
% 100.55/15.05 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7155, zip_derived_cl138])).
% 100.55/15.05 thf(zip_derived_cl9588, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (product @ additive_identity @ multiplicative_identity @ X0)
% 100.55/15.05 | (sum @ X0 @ additive_identity @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl7174])).
% 100.55/15.05 thf(zip_derived_cl9603, plain,
% 100.55/15.05 ((~ (defined @ multiplicative_identity)
% 100.55/15.05 | ~ (defined @ additive_identity)
% 100.55/15.05 | (sum @ (multiply @ additive_identity @ multiplicative_identity) @
% 100.55/15.05 additive_identity @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl9588])).
% 100.55/15.05 thf(well_definedness_of_multiplicative_identity, axiom,
% 100.55/15.05 (defined @ multiplicative_identity)).
% 100.55/15.05 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 100.55/15.05 inference('cnf', [status(esa)],
% 100.55/15.05 [well_definedness_of_multiplicative_identity])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl9612, plain,
% 100.55/15.05 ( (sum @ (multiply @ additive_identity @ multiplicative_identity) @
% 100.55/15.05 additive_identity @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl9603, zip_derived_cl16, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl4, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_addition])).
% 100.55/15.05 thf(zip_derived_cl9618, plain,
% 100.55/15.05 ( (sum @ additive_identity @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity) @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl9612, zip_derived_cl4])).
% 100.55/15.05 thf(well_definedness_of_multiplicative_inverse, axiom,
% 100.55/15.05 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 100.55/15.05 ( sum @ additive_identity @ X @ additive_identity ))).
% 100.55/15.05 thf(zip_derived_cl17, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (defined @ (multiplicative_inverse @ X0))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | (sum @ additive_identity @ X0 @ additive_identity))),
% 100.55/15.05 inference('cnf', [status(esa)],
% 100.55/15.05 [well_definedness_of_multiplicative_inverse])).
% 100.55/15.05 thf(totality_of_order_relation, axiom,
% 100.55/15.05 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 100.55/15.05 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 100.55/15.05 thf(zip_derived_cl22, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (less_or_equal @ X0 @ X1)
% 100.55/15.05 | (less_or_equal @ X1 @ X0)
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 100.55/15.05 thf(a_is_defined, axiom, (defined @ a)).
% 100.55/15.05 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 100.55/15.05 inference('cnf', [status(esa)], [a_is_defined])).
% 100.55/15.05 thf(zip_derived_cl173, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (less_or_equal @ X0 @ a)
% 100.55/15.05 | (less_or_equal @ a @ X0))),
% 100.55/15.05 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl26])).
% 100.55/15.05 thf(zip_derived_cl5163, plain,
% 100.55/15.05 (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl173])).
% 100.55/15.05 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 100.55/15.05 inference('cnf', [status(esa)], [a_is_defined])).
% 100.55/15.05 thf(zip_derived_cl5164, plain, ( (less_or_equal @ a @ a)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl5163, zip_derived_cl26])).
% 100.55/15.05 thf(antisymmetry_of_order_relation, axiom,
% 100.55/15.05 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 100.55/15.05 ( ~( less_or_equal @ Y @ X ) ))).
% 100.55/15.05 thf(zip_derived_cl20, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @ X1)
% 100.55/15.05 | ~ (less_or_equal @ X0 @ X1)
% 100.55/15.05 | ~ (less_or_equal @ X1 @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 100.55/15.05 thf(zip_derived_cl5184, plain,
% 100.55/15.05 ((~ (less_or_equal @ a @ a) | (sum @ additive_identity @ a @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl5164, zip_derived_cl20])).
% 100.55/15.05 thf(zip_derived_cl5164, plain, ( (less_or_equal @ a @ a)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl5163, zip_derived_cl26])).
% 100.55/15.05 thf(zip_derived_cl5187, plain, ( (sum @ additive_identity @ a @ a)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl5184, zip_derived_cl5164])).
% 100.55/15.05 thf(zip_derived_cl45, plain,
% 100.55/15.05 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl42, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl0, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X0 @ X3 @ X4)
% 100.55/15.05 | ~ (sum @ X3 @ X5 @ X1)
% 100.55/15.05 | ~ (sum @ X4 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_addition_1])).
% 100.55/15.05 thf(zip_derived_cl48, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (sum @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ additive_identity @ X1 @ X2)
% 100.55/15.05 | (sum @ additive_identity @ X2 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 100.55/15.05 thf(zip_derived_cl5204, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @ a)
% 100.55/15.05 | ~ (sum @ additive_identity @ a @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl5187, zip_derived_cl48])).
% 100.55/15.05 thf(zip_derived_cl5292, plain,
% 100.55/15.05 ((~ (defined @ a)
% 100.55/15.05 | (defined @ (multiplicative_inverse @ a))
% 100.55/15.05 | (sum @ additive_identity @ additive_identity @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl5204])).
% 100.55/15.05 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 100.55/15.05 inference('cnf', [status(esa)], [a_is_defined])).
% 100.55/15.05 thf(zip_derived_cl5298, plain,
% 100.55/15.05 (( (defined @ (multiplicative_inverse @ a))
% 100.55/15.05 | (sum @ additive_identity @ additive_identity @ a))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl5292, zip_derived_cl26])).
% 100.55/15.05 thf(zip_derived_cl7145, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (sum @ additive_identity @ additive_identity @ X0)
% 100.55/15.05 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl7139, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7160, plain,
% 100.55/15.05 (( (defined @ (multiplicative_inverse @ a))
% 100.55/15.05 | (product @ additive_identity @ multiplicative_identity @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl5298, zip_derived_cl7145])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl7380, plain,
% 100.55/15.05 (( (defined @ (multiplicative_inverse @ a))
% 100.55/15.05 | (product @ multiplicative_identity @ additive_identity @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7160, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl19, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 100.55/15.05 thf(zip_derived_cl15, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (defined @ (multiply @ X0 @ X1))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 100.55/15.05 thf(zip_derived_cl52, plain,
% 100.55/15.05 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 100.55/15.05 thf(zip_derived_cl19, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 100.55/15.05 thf(zip_derived_cl7155, plain,
% 100.55/15.05 ( (product @ additive_identity @ multiplicative_identity @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl7145])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl7169, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7155, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl22, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (less_or_equal @ X0 @ X1)
% 100.55/15.05 | (less_or_equal @ X1 @ X0)
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 100.55/15.05 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 100.55/15.05 inference('cnf', [status(esa)],
% 100.55/15.05 [well_definedness_of_multiplicative_identity])).
% 100.55/15.05 thf(zip_derived_cl170, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (less_or_equal @ X0 @ multiplicative_identity)
% 100.55/15.05 | (less_or_equal @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl16])).
% 100.55/15.05 thf(zip_derived_cl365, plain,
% 100.55/15.05 (( (less_or_equal @ multiplicative_identity @ multiplicative_identity)
% 100.55/15.05 | ~ (defined @ multiplicative_identity))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl170])).
% 100.55/15.05 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 100.55/15.05 inference('cnf', [status(esa)],
% 100.55/15.05 [well_definedness_of_multiplicative_identity])).
% 100.55/15.05 thf(zip_derived_cl366, plain,
% 100.55/15.05 ( (less_or_equal @ multiplicative_identity @ multiplicative_identity)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl365, zip_derived_cl16])).
% 100.55/15.05 thf(zip_derived_cl20, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @ X1)
% 100.55/15.05 | ~ (less_or_equal @ X0 @ X1)
% 100.55/15.05 | ~ (less_or_equal @ X1 @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 100.55/15.05 thf(zip_derived_cl370, plain,
% 100.55/15.05 ((~ (less_or_equal @ multiplicative_identity @ multiplicative_identity)
% 100.55/15.05 | (sum @ additive_identity @ multiplicative_identity @
% 100.55/15.05 multiplicative_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl366, zip_derived_cl20])).
% 100.55/15.05 thf(zip_derived_cl366, plain,
% 100.55/15.05 ( (less_or_equal @ multiplicative_identity @ multiplicative_identity)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl365, zip_derived_cl16])).
% 100.55/15.05 thf(zip_derived_cl372, plain,
% 100.55/15.05 ( (sum @ additive_identity @ multiplicative_identity @
% 100.55/15.05 multiplicative_identity)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl370, zip_derived_cl366])).
% 100.55/15.05 thf(zip_derived_cl11, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (product @ X3 @ X1 @ X5)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X6)
% 100.55/15.05 | ~ (sum @ X5 @ X6 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [distributivity_2])).
% 100.55/15.05 thf(zip_derived_cl375, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (sum @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ X3 @ X1)
% 100.55/15.05 | ~ (product @ additive_identity @ X3 @ X2)
% 100.55/15.05 | (product @ multiplicative_identity @ X3 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl372, zip_derived_cl11])).
% 100.55/15.05 thf(zip_derived_cl13492, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (product @ multiplicative_identity @ additive_identity @ X0)
% 100.55/15.05 | ~ (product @ additive_identity @ additive_identity @ X1)
% 100.55/15.05 | ~ (sum @ X1 @ additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7169, zip_derived_cl375])).
% 100.55/15.05 thf(zip_derived_cl13533, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ additive_identity)
% 100.55/15.05 | ~ (defined @ additive_identity)
% 100.55/15.05 | ~ (sum @ (multiply @ additive_identity @ additive_identity) @
% 100.55/15.05 additive_identity @ X0)
% 100.55/15.05 | (product @ multiplicative_identity @ additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl13492])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl13535, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (sum @ (multiply @ additive_identity @ additive_identity) @
% 100.55/15.05 additive_identity @ X0)
% 100.55/15.05 | (product @ multiplicative_identity @ additive_identity @ X0))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl13533, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl13644, plain,
% 100.55/15.05 ((~ (defined @ (multiply @ additive_identity @ additive_identity))
% 100.55/15.05 | (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 (multiply @ additive_identity @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl13535])).
% 100.55/15.05 thf(zip_derived_cl13657, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | ~ (defined @ additive_identity)
% 100.55/15.05 | (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 (multiply @ additive_identity @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl13644])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl13658, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 (multiply @ additive_identity @ additive_identity))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl13657, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7169, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7155, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl7, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 100.55/15.05 thf(associativity_multiplication_1, axiom,
% 100.55/15.05 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 100.55/15.05 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 100.55/15.05 thf(zip_derived_cl5, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (product @ X0 @ X3 @ X4)
% 100.55/15.05 | ~ (product @ X3 @ X5 @ X1)
% 100.55/15.05 | ~ (product @ X4 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 100.55/15.05 thf(zip_derived_cl111, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | ~ (product @ X0 @ X2 @ X1)
% 100.55/15.05 | ~ (product @ X0 @ X2 @ X3)
% 100.55/15.05 | (product @ multiplicative_identity @ X3 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 100.55/15.05 thf(zip_derived_cl7193, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ additive_identity @ X0)
% 100.55/15.05 | ~ (defined @ multiplicative_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7169, zip_derived_cl111])).
% 100.55/15.05 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 100.55/15.05 inference('cnf', [status(esa)],
% 100.55/15.05 [well_definedness_of_multiplicative_identity])).
% 100.55/15.05 thf(zip_derived_cl7206, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ additive_identity @ X0))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl7193, zip_derived_cl16])).
% 100.55/15.05 thf(zip_derived_cl13681, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @
% 100.55/15.05 (multiply @ additive_identity @ additive_identity) @ additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl13658, zip_derived_cl7206])).
% 100.55/15.05 thf(zip_derived_cl7169, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7155, zip_derived_cl9])).
% 100.55/15.05 thf(associativity_multiplication_2, axiom,
% 100.55/15.05 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 100.55/15.05 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 100.55/15.05 thf(zip_derived_cl6, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (product @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X5)
% 100.55/15.05 | ~ (product @ X3 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 100.55/15.05 thf(zip_derived_cl7190, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (product @ multiplicative_identity @ X1 @ X0)
% 100.55/15.05 | ~ (product @ additive_identity @ X2 @ X1)
% 100.55/15.05 | (product @ additive_identity @ X2 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7169, zip_derived_cl6])).
% 100.55/15.05 thf(zip_derived_cl13746, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ additive_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (product @ additive_identity @ X0 @
% 100.55/15.05 (multiply @ additive_identity @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl13681, zip_derived_cl7190])).
% 100.55/15.05 thf(zip_derived_cl13790, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | ~ (defined @ additive_identity)
% 100.55/15.05 | (product @ additive_identity @ additive_identity @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl13746])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl13793, plain,
% 100.55/15.05 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl13790, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7155, plain,
% 100.55/15.05 ( (product @ additive_identity @ multiplicative_identity @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl7145])).
% 100.55/15.05 thf(zip_derived_cl5, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (product @ X0 @ X3 @ X4)
% 100.55/15.05 | ~ (product @ X3 @ X5 @ X1)
% 100.55/15.05 | ~ (product @ X4 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 100.55/15.05 thf(zip_derived_cl7167, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (product @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ X1 @ X2)
% 100.55/15.05 | (product @ additive_identity @ X2 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7155, zip_derived_cl5])).
% 100.55/15.05 thf(zip_derived_cl13818, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ additive_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl13793, zip_derived_cl7167])).
% 100.55/15.05 thf(zip_derived_cl14457, plain,
% 100.55/15.05 (( (defined @ (multiplicative_inverse @ a))
% 100.55/15.05 | (product @ additive_identity @ a @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl7380, zip_derived_cl13818])).
% 100.55/15.05 thf(zip_derived_cl27, plain,
% 100.55/15.05 (~ (product @ additive_identity @ a @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [zf_stmt_0])).
% 100.55/15.05 thf(zip_derived_cl15238, plain, ( (defined @ (multiplicative_inverse @ a))),
% 100.55/15.05 inference('clc', [status(thm)], [zip_derived_cl14457, zip_derived_cl27])).
% 100.55/15.05 thf(zip_derived_cl22, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (less_or_equal @ X0 @ X1)
% 100.55/15.05 | (less_or_equal @ X1 @ X0)
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 100.55/15.05 thf(zip_derived_cl15239, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (less_or_equal @ X0 @ (multiplicative_inverse @ a))
% 100.55/15.05 | (less_or_equal @ (multiplicative_inverse @ a) @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl15238, zip_derived_cl22])).
% 100.55/15.05 thf(zip_derived_cl15508, plain,
% 100.55/15.05 (( (less_or_equal @ (multiplicative_inverse @ a) @
% 100.55/15.05 (multiplicative_inverse @ a))
% 100.55/15.05 | ~ (defined @ (multiplicative_inverse @ a)))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl15239])).
% 100.55/15.05 thf(zip_derived_cl15238, plain, ( (defined @ (multiplicative_inverse @ a))),
% 100.55/15.05 inference('clc', [status(thm)], [zip_derived_cl14457, zip_derived_cl27])).
% 100.55/15.05 thf(zip_derived_cl15509, plain,
% 100.55/15.05 ( (less_or_equal @ (multiplicative_inverse @ a) @
% 100.55/15.05 (multiplicative_inverse @ a))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl15508, zip_derived_cl15238])).
% 100.55/15.05 thf(zip_derived_cl20, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @ X1)
% 100.55/15.05 | ~ (less_or_equal @ X0 @ X1)
% 100.55/15.05 | ~ (less_or_equal @ X1 @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 100.55/15.05 thf(zip_derived_cl15524, plain,
% 100.55/15.05 ((~ (less_or_equal @ (multiplicative_inverse @ a) @
% 100.55/15.05 (multiplicative_inverse @ a))
% 100.55/15.05 | (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 100.55/15.05 (multiplicative_inverse @ a)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl15509, zip_derived_cl20])).
% 100.55/15.05 thf(zip_derived_cl15509, plain,
% 100.55/15.05 ( (less_or_equal @ (multiplicative_inverse @ a) @
% 100.55/15.05 (multiplicative_inverse @ a))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl15508, zip_derived_cl15238])).
% 100.55/15.05 thf(zip_derived_cl15529, plain,
% 100.55/15.05 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 100.55/15.05 (multiplicative_inverse @ a))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl15524, zip_derived_cl15509])).
% 100.55/15.05 thf(zip_derived_cl4, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_addition])).
% 100.55/15.05 thf(zip_derived_cl15536, plain,
% 100.55/15.05 ( (sum @ (multiplicative_inverse @ a) @ additive_identity @
% 100.55/15.05 (multiplicative_inverse @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl15529, zip_derived_cl4])).
% 100.55/15.05 thf(associativity_addition_2, axiom,
% 100.55/15.05 (( sum @ U @ Z @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 100.55/15.05 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ X @ V @ W ) ))).
% 100.55/15.05 thf(zip_derived_cl1, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (sum @ X4 @ X1 @ X5)
% 100.55/15.05 | ~ (sum @ X3 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_addition_2])).
% 100.55/15.05 thf(zip_derived_cl71, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (sum @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ X1 @ X3 @ X1)
% 100.55/15.05 | (sum @ X0 @ X3 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl1])).
% 100.55/15.05 thf(zip_derived_cl15661, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ (multiplicative_inverse @ a) @ X0 @
% 100.55/15.05 (multiplicative_inverse @ a))
% 100.55/15.05 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl15536, zip_derived_cl71])).
% 100.55/15.05 thf(zip_derived_cl15860, plain,
% 100.55/15.05 ( (sum @ (multiplicative_inverse @ a) @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity) @
% 100.55/15.05 (multiplicative_inverse @ a))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl9618, zip_derived_cl15661])).
% 100.55/15.05 thf(well_definedness_of_additive_inverse, axiom,
% 100.55/15.05 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 100.55/15.05 thf(zip_derived_cl14, plain,
% 100.55/15.05 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 100.55/15.05 thf(zip_derived_cl14, plain,
% 100.55/15.05 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 100.55/15.05 thf(zip_derived_cl2, plain,
% 100.55/15.05 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 100.55/15.05 thf(existence_of_inverse_addition, axiom,
% 100.55/15.05 (( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) |
% 100.55/15.05 ( ~( defined @ X ) ))).
% 100.55/15.05 thf(zip_derived_cl3, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 100.55/15.05 | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 100.55/15.05 thf(zip_derived_cl4, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_addition])).
% 100.55/15.05 thf(zip_derived_cl55, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 100.55/15.05 thf(zip_derived_cl48, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (sum @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ additive_identity @ X1 @ X2)
% 100.55/15.05 | (sum @ additive_identity @ X2 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 100.55/15.05 thf(zip_derived_cl231, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ additive_identity)
% 100.55/15.05 | (sum @ additive_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (sum @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity) @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl48])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl233, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (sum @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity) @ X0))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl231, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl330, plain,
% 100.55/15.05 ((~ (defined @ (additive_inverse @ additive_identity))
% 100.55/15.05 | (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 100.55/15.05 additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl233])).
% 100.55/15.05 thf(zip_derived_cl334, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 100.55/15.05 additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl330])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl335, plain,
% 100.55/15.05 ( (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl334, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl15661, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ (multiplicative_inverse @ a) @ X0 @
% 100.55/15.05 (multiplicative_inverse @ a))
% 100.55/15.05 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl15536, zip_derived_cl71])).
% 100.55/15.05 thf(zip_derived_cl15856, plain,
% 100.55/15.05 ( (sum @ (multiplicative_inverse @ a) @
% 100.55/15.05 (additive_inverse @ additive_identity) @ (multiplicative_inverse @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl335, zip_derived_cl15661])).
% 100.55/15.05 thf(zip_derived_cl2, plain,
% 100.55/15.05 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 100.55/15.05 thf(zip_derived_cl3, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 100.55/15.05 | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 100.55/15.05 thf(zip_derived_cl0, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X0 @ X3 @ X4)
% 100.55/15.05 | ~ (sum @ X3 @ X5 @ X1)
% 100.55/15.05 | ~ (sum @ X4 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_addition_1])).
% 100.55/15.05 thf(zip_derived_cl30, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | ~ (sum @ additive_identity @ X2 @ X1)
% 100.55/15.05 | ~ (sum @ X0 @ X2 @ X3)
% 100.55/15.05 | (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 100.55/15.05 thf(zip_derived_cl387, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (sum @ (additive_inverse @ X2) @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ X2 @ X0 @ X1)
% 100.55/15.05 | ~ (defined @ X2))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl30])).
% 100.55/15.05 thf(zip_derived_cl16280, plain,
% 100.55/15.05 ((~ (defined @ (multiplicative_inverse @ a))
% 100.55/15.05 | (sum @ (additive_inverse @ (multiplicative_inverse @ a)) @
% 100.55/15.05 (multiplicative_inverse @ a) @
% 100.55/15.05 (additive_inverse @ additive_identity))
% 100.55/15.05 | ~ (defined @ (additive_inverse @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl15856, zip_derived_cl387])).
% 100.55/15.05 thf(zip_derived_cl15238, plain, ( (defined @ (multiplicative_inverse @ a))),
% 100.55/15.05 inference('clc', [status(thm)], [zip_derived_cl14457, zip_derived_cl27])).
% 100.55/15.05 thf(zip_derived_cl16301, plain,
% 100.55/15.05 (( (sum @ (additive_inverse @ (multiplicative_inverse @ a)) @
% 100.55/15.05 (multiplicative_inverse @ a) @ (additive_inverse @ additive_identity))
% 100.55/15.05 | ~ (defined @ (additive_inverse @ additive_identity)))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl16280, zip_derived_cl15238])).
% 100.55/15.05 thf(zip_derived_cl18372, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | (sum @ (additive_inverse @ (multiplicative_inverse @ a)) @
% 100.55/15.05 (multiplicative_inverse @ a) @
% 100.55/15.05 (additive_inverse @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl16301])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl18373, plain,
% 100.55/15.05 ( (sum @ (additive_inverse @ (multiplicative_inverse @ a)) @
% 100.55/15.05 (multiplicative_inverse @ a) @ (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl18372, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl3, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 100.55/15.05 | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 100.55/15.05 thf(zip_derived_cl1, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (sum @ X4 @ X1 @ X5)
% 100.55/15.05 | ~ (sum @ X3 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_addition_2])).
% 100.55/15.05 thf(zip_derived_cl68, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | ~ (sum @ (additive_inverse @ X0) @ X2 @ X1)
% 100.55/15.05 | ~ (sum @ X0 @ X3 @ X2)
% 100.55/15.05 | (sum @ additive_identity @ X3 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 100.55/15.05 thf(zip_derived_cl22813, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @
% 100.55/15.05 (additive_inverse @ additive_identity))
% 100.55/15.05 | ~ (sum @ (multiplicative_inverse @ a) @ X0 @
% 100.55/15.05 (multiplicative_inverse @ a))
% 100.55/15.05 | ~ (defined @ (multiplicative_inverse @ a)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl18373, zip_derived_cl68])).
% 100.55/15.05 thf(zip_derived_cl15238, plain, ( (defined @ (multiplicative_inverse @ a))),
% 100.55/15.05 inference('clc', [status(thm)], [zip_derived_cl14457, zip_derived_cl27])).
% 100.55/15.05 thf(zip_derived_cl22830, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @
% 100.55/15.05 (additive_inverse @ additive_identity))
% 100.55/15.05 | ~ (sum @ (multiplicative_inverse @ a) @ X0 @
% 100.55/15.05 (multiplicative_inverse @ a)))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl22813, zip_derived_cl15238])).
% 100.55/15.05 thf(zip_derived_cl22839, plain,
% 100.55/15.05 ( (sum @ additive_identity @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity) @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl15860, zip_derived_cl22830])).
% 100.55/15.05 thf(zip_derived_cl2, plain,
% 100.55/15.05 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 100.55/15.05 thf(zip_derived_cl48, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (sum @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ additive_identity @ X1 @ X2)
% 100.55/15.05 | (sum @ additive_identity @ X2 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 100.55/15.05 thf(zip_derived_cl74, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (sum @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ additive_identity @ X0 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl48])).
% 100.55/15.05 thf(zip_derived_cl24557, plain,
% 100.55/15.05 (( (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity))
% 100.55/15.05 | ~ (defined @ (multiply @ additive_identity @ multiplicative_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl22839, zip_derived_cl74])).
% 100.55/15.05 thf(zip_derived_cl41518, plain,
% 100.55/15.05 ((~ (defined @ multiplicative_identity)
% 100.55/15.05 | ~ (defined @ additive_identity)
% 100.55/15.05 | (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl24557])).
% 100.55/15.05 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 100.55/15.05 inference('cnf', [status(esa)],
% 100.55/15.05 [well_definedness_of_multiplicative_identity])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl41519, plain,
% 100.55/15.05 ( (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl41518, zip_derived_cl16, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl13793, plain,
% 100.55/15.05 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl13790, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl14, plain,
% 100.55/15.05 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 100.55/15.05 thf(zip_derived_cl335, plain,
% 100.55/15.05 ( (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl334, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl74, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (sum @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ additive_identity @ X0 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl48])).
% 100.55/15.05 thf(zip_derived_cl790, plain,
% 100.55/15.05 (( (sum @ additive_identity @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))
% 100.55/15.05 | ~ (defined @ (additive_inverse @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl335, zip_derived_cl74])).
% 100.55/15.05 thf(zip_derived_cl807, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | (sum @ additive_identity @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl790])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl808, plain,
% 100.55/15.05 ( (sum @ additive_identity @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl807, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7145, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (sum @ additive_identity @ additive_identity @ X0)
% 100.55/15.05 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl7139, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7156, plain,
% 100.55/15.05 ( (product @ additive_identity @ multiplicative_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl808, zip_derived_cl7145])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl7251, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7156, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl7190, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (product @ multiplicative_identity @ X1 @ X0)
% 100.55/15.05 | ~ (product @ additive_identity @ X2 @ X1)
% 100.55/15.05 | (product @ additive_identity @ X2 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7169, zip_derived_cl6])).
% 100.55/15.05 thf(zip_derived_cl8093, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ additive_identity @ X0 @
% 100.55/15.05 (additive_inverse @ additive_identity))
% 100.55/15.05 | ~ (product @ additive_identity @ X0 @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7251, zip_derived_cl7190])).
% 100.55/15.05 thf(zip_derived_cl13825, plain,
% 100.55/15.05 ( (product @ additive_identity @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl13793, zip_derived_cl8093])).
% 100.55/15.05 thf(zip_derived_cl13793, plain,
% 100.55/15.05 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl13790, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7251, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7156, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl34, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl5, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (product @ X0 @ X3 @ X4)
% 100.55/15.05 | ~ (product @ X3 @ X5 @ X1)
% 100.55/15.05 | ~ (product @ X4 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 100.55/15.05 thf(zip_derived_cl110, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | ~ (product @ X0 @ X2 @ X1)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ X2 @ X3)
% 100.55/15.05 | (product @ X0 @ X3 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl5])).
% 100.55/15.05 thf(zip_derived_cl7282, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (product @ X1 @ (additive_inverse @ additive_identity) @ X0)
% 100.55/15.05 | ~ (product @ X1 @ additive_identity @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7251, zip_derived_cl110])).
% 100.55/15.05 thf(zip_derived_cl13809, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | (product @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity) @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl13793, zip_derived_cl7282])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl13839, plain,
% 100.55/15.05 ( (product @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity) @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl13809, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl13881, plain,
% 100.55/15.05 ( (product @ (additive_inverse @ additive_identity) @
% 100.55/15.05 additive_identity @ additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl13839, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl808, plain,
% 100.55/15.05 ( (sum @ additive_identity @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl807, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl48, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (sum @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ additive_identity @ X1 @ X2)
% 100.55/15.05 | (sum @ additive_identity @ X2 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 100.55/15.05 thf(zip_derived_cl77, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @ X0)
% 100.55/15.05 | ~ (sum @ additive_identity @ X1 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl48])).
% 100.55/15.05 thf(zip_derived_cl818, plain,
% 100.55/15.05 ( (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl808, zip_derived_cl77])).
% 100.55/15.05 thf(zip_derived_cl4, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_addition])).
% 100.55/15.05 thf(zip_derived_cl889, plain,
% 100.55/15.05 ( (sum @ (additive_inverse @ additive_identity) @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl818, zip_derived_cl4])).
% 100.55/15.05 thf(zip_derived_cl11, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (product @ X3 @ X1 @ X5)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X6)
% 100.55/15.05 | ~ (sum @ X5 @ X6 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [distributivity_2])).
% 100.55/15.05 thf(zip_derived_cl907, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (sum @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (product @ additive_identity @ X3 @ X1)
% 100.55/15.05 | ~ (product @ (additive_inverse @ additive_identity) @ X3 @ X2)
% 100.55/15.05 | (product @ (additive_inverse @ additive_identity) @ X3 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl889, zip_derived_cl11])).
% 100.55/15.05 thf(zip_derived_cl39533, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (product @ (additive_inverse @ additive_identity) @
% 100.55/15.05 additive_identity @ X0)
% 100.55/15.05 | ~ (product @ additive_identity @ additive_identity @ X1)
% 100.55/15.05 | ~ (sum @ additive_identity @ X1 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl13881, zip_derived_cl907])).
% 100.55/15.05 thf(zip_derived_cl39556, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (sum @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity) @ X0)
% 100.55/15.05 | (product @ (additive_inverse @ additive_identity) @
% 100.55/15.05 additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl13825, zip_derived_cl39533])).
% 100.55/15.05 thf(zip_derived_cl41602, plain,
% 100.55/15.05 ( (product @ (additive_inverse @ additive_identity) @
% 100.55/15.05 additive_identity @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl41519, zip_derived_cl39556])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl41875, plain,
% 100.55/15.05 ( (product @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity) @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl41602, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl372, plain,
% 100.55/15.05 ( (sum @ additive_identity @ multiplicative_identity @
% 100.55/15.05 multiplicative_identity)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl370, zip_derived_cl366])).
% 100.55/15.05 thf(existence_of_inverse_multiplication, axiom,
% 100.55/15.05 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 100.55/15.05 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 100.55/15.05 thf(zip_derived_cl8, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 100.55/15.05 multiplicative_identity)
% 100.55/15.05 | (sum @ additive_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 100.55/15.05 thf(zip_derived_cl52, plain,
% 100.55/15.05 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 100.55/15.05 thf(zip_derived_cl0, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X0 @ X3 @ X4)
% 100.55/15.05 | ~ (sum @ X3 @ X5 @ X1)
% 100.55/15.05 | ~ (sum @ X4 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_addition_1])).
% 100.55/15.05 thf(zip_derived_cl62, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | ~ (sum @ X0 @ X2 @ X1)
% 100.55/15.05 | ~ (sum @ additive_identity @ X2 @ X3)
% 100.55/15.05 | (sum @ X0 @ X3 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 100.55/15.05 thf(zip_derived_cl503, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 100.55/15.05 multiplicative_identity)
% 100.55/15.05 | (sum @ X2 @ additive_identity @ X1)
% 100.55/15.05 | ~ (sum @ X2 @ X0 @ X1)
% 100.55/15.05 | ~ (defined @ X2))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl62])).
% 100.55/15.05 thf(zip_derived_cl19025, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | (sum @ additive_identity @ additive_identity @
% 100.55/15.05 multiplicative_identity)
% 100.55/15.05 | (product @ (multiplicative_inverse @ multiplicative_identity) @
% 100.55/15.05 multiplicative_identity @ multiplicative_identity)
% 100.55/15.05 | ~ (defined @ multiplicative_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl372, zip_derived_cl503])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(different_identities, axiom,
% 100.55/15.05 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 100.55/15.05 thf(zip_derived_cl25, plain,
% 100.55/15.05 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [different_identities])).
% 100.55/15.05 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 100.55/15.05 inference('cnf', [status(esa)],
% 100.55/15.05 [well_definedness_of_multiplicative_identity])).
% 100.55/15.05 thf(zip_derived_cl19168, plain,
% 100.55/15.05 ( (product @ (multiplicative_inverse @ multiplicative_identity) @
% 100.55/15.05 multiplicative_identity @ multiplicative_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl19025, zip_derived_cl13, zip_derived_cl25,
% 100.55/15.05 zip_derived_cl16])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl19314, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @
% 100.55/15.05 (multiplicative_inverse @ multiplicative_identity) @
% 100.55/15.05 multiplicative_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl19168, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl7155, plain,
% 100.55/15.05 ( (product @ additive_identity @ multiplicative_identity @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl7145])).
% 100.55/15.05 thf(zip_derived_cl6, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (product @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X5)
% 100.55/15.05 | ~ (product @ X3 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 100.55/15.05 thf(zip_derived_cl122, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (product @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (product @ X1 @ X3 @ X1)
% 100.55/15.05 | (product @ X0 @ X3 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 100.55/15.05 thf(zip_derived_cl7173, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ additive_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ X0 @ multiplicative_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7155, zip_derived_cl122])).
% 100.55/15.05 thf(zip_derived_cl19354, plain,
% 100.55/15.05 ( (product @ additive_identity @
% 100.55/15.05 (multiplicative_inverse @ multiplicative_identity) @ additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl19314, zip_derived_cl7173])).
% 100.55/15.05 thf(zip_derived_cl7251, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7156, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl122, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (product @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (product @ X1 @ X3 @ X1)
% 100.55/15.05 | (product @ X0 @ X3 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 100.55/15.05 thf(zip_derived_cl7276, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ (additive_inverse @ additive_identity) @ X0 @
% 100.55/15.05 (additive_inverse @ additive_identity))
% 100.55/15.05 | ~ (product @ additive_identity @ X0 @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7251, zip_derived_cl122])).
% 100.55/15.05 thf(zip_derived_cl19668, plain,
% 100.55/15.05 ( (product @ (additive_inverse @ additive_identity) @
% 100.55/15.05 (multiplicative_inverse @ multiplicative_identity) @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl19354, zip_derived_cl7276])).
% 100.55/15.05 thf(zip_derived_cl13839, plain,
% 100.55/15.05 ( (product @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity) @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl13809, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl6, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (product @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X5)
% 100.55/15.05 | ~ (product @ X3 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 100.55/15.05 thf(zip_derived_cl13880, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (product @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (product @ (additive_inverse @ additive_identity) @ X2 @ X1)
% 100.55/15.05 | (product @ additive_identity @ X2 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl13839, zip_derived_cl6])).
% 100.55/15.05 thf(zip_derived_cl38618, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ additive_identity @
% 100.55/15.05 (multiplicative_inverse @ multiplicative_identity) @ X0)
% 100.55/15.05 | ~ (product @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity) @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl19668, zip_derived_cl13880])).
% 100.55/15.05 thf(zip_derived_cl42153, plain,
% 100.55/15.05 ( (product @ additive_identity @
% 100.55/15.05 (multiplicative_inverse @ multiplicative_identity) @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl41875, zip_derived_cl38618])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl45646, plain,
% 100.55/15.05 ( (product @ (multiplicative_inverse @ multiplicative_identity) @
% 100.55/15.05 additive_identity @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl42153, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl19314, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @
% 100.55/15.05 (multiplicative_inverse @ multiplicative_identity) @
% 100.55/15.05 multiplicative_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl19168, zip_derived_cl9])).
% 100.55/15.05 thf(well_definedness_of_addition, axiom,
% 100.55/15.05 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 100.55/15.05 ( ~( defined @ Y ) ))).
% 100.55/15.05 thf(zip_derived_cl12, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 100.55/15.05 thf(zip_derived_cl34, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 100.55/15.05 thf(totality_of_addition, axiom,
% 100.55/15.05 (( sum @ X @ Y @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 100.55/15.05 ( ~( defined @ Y ) ))).
% 100.55/15.05 thf(zip_derived_cl18, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [totality_of_addition])).
% 100.55/15.05 thf(zip_derived_cl5204, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @ a)
% 100.55/15.05 | ~ (sum @ additive_identity @ a @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl5187, zip_derived_cl48])).
% 100.55/15.05 thf(zip_derived_cl5289, plain,
% 100.55/15.05 ((~ (defined @ a)
% 100.55/15.05 | ~ (defined @ additive_identity)
% 100.55/15.05 | (sum @ additive_identity @ (add @ additive_identity @ a) @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl5204])).
% 100.55/15.05 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 100.55/15.05 inference('cnf', [status(esa)], [a_is_defined])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl5295, plain,
% 100.55/15.05 ( (sum @ additive_identity @ (add @ additive_identity @ a) @ a)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl5289, zip_derived_cl26, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl11, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (sum @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (product @ X3 @ X1 @ X5)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X6)
% 100.55/15.05 | ~ (sum @ X5 @ X6 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [distributivity_2])).
% 100.55/15.05 thf(zip_derived_cl213, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (sum @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (product @ X1 @ X3 @ X1)
% 100.55/15.05 | ~ (product @ X2 @ X3 @ X2)
% 100.55/15.05 | (product @ X0 @ X3 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl11])).
% 100.55/15.05 thf(zip_derived_cl7836, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ a @ X0 @ a)
% 100.55/15.05 | ~ (product @ additive_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (product @ (add @ additive_identity @ a) @ X0 @
% 100.55/15.05 (add @ additive_identity @ a)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl5295, zip_derived_cl213])).
% 100.55/15.05 thf(zip_derived_cl12619, plain,
% 100.55/15.05 ((~ (defined @ (add @ additive_identity @ a))
% 100.55/15.05 | ~ (product @ additive_identity @ multiplicative_identity @
% 100.55/15.05 additive_identity)
% 100.55/15.05 | (product @ a @ multiplicative_identity @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl7836])).
% 100.55/15.05 thf(zip_derived_cl7155, plain,
% 100.55/15.05 ( (product @ additive_identity @ multiplicative_identity @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl7145])).
% 100.55/15.05 thf(zip_derived_cl12621, plain,
% 100.55/15.05 ((~ (defined @ (add @ additive_identity @ a))
% 100.55/15.05 | (product @ a @ multiplicative_identity @ a))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl12619, zip_derived_cl7155])).
% 100.55/15.05 thf(zip_derived_cl12623, plain,
% 100.55/15.05 ((~ (defined @ a)
% 100.55/15.05 | ~ (defined @ additive_identity)
% 100.55/15.05 | (product @ a @ multiplicative_identity @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl12621])).
% 100.55/15.05 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 100.55/15.05 inference('cnf', [status(esa)], [a_is_defined])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl12624, plain,
% 100.55/15.05 ( (product @ a @ multiplicative_identity @ a)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl12623, zip_derived_cl26, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl122, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (product @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (product @ X1 @ X3 @ X1)
% 100.55/15.05 | (product @ X0 @ X3 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 100.55/15.05 thf(zip_derived_cl12631, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ a @ X0 @ a)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ X0 @ multiplicative_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl12624, zip_derived_cl122])).
% 100.55/15.05 thf(zip_derived_cl19357, plain,
% 100.55/15.05 ( (product @ a @ (multiplicative_inverse @ multiplicative_identity) @ a)),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl19314, zip_derived_cl12631])).
% 100.55/15.05 thf(zip_derived_cl5, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (product @ X0 @ X3 @ X4)
% 100.55/15.05 | ~ (product @ X3 @ X5 @ X1)
% 100.55/15.05 | ~ (product @ X4 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 100.55/15.05 thf(zip_derived_cl19727, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (product @ a @ X1 @ X0)
% 100.55/15.05 | ~ (product @ (multiplicative_inverse @ multiplicative_identity) @
% 100.55/15.05 X1 @ X2)
% 100.55/15.05 | (product @ a @ X2 @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl19357, zip_derived_cl5])).
% 100.55/15.05 thf(zip_derived_cl123732, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ a @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity) @ X0)
% 100.55/15.05 | ~ (product @ a @ additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl45646, zip_derived_cl19727])).
% 100.55/15.05 thf(zip_derived_cl123771, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | ~ (defined @ a)
% 100.55/15.05 | (product @ a @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity) @
% 100.55/15.05 (multiply @ a @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl123732])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 100.55/15.05 inference('cnf', [status(esa)], [a_is_defined])).
% 100.55/15.05 thf(zip_derived_cl123773, plain,
% 100.55/15.05 ( (product @ a @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity) @
% 100.55/15.05 (multiply @ a @ additive_identity))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl123771, zip_derived_cl13, zip_derived_cl26])).
% 100.55/15.05 thf(zip_derived_cl19, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 100.55/15.05 | ~ (defined @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 100.55/15.05 thf(zip_derived_cl7155, plain,
% 100.55/15.05 ( (product @ additive_identity @ multiplicative_identity @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl7145])).
% 100.55/15.05 thf(zip_derived_cl111, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | ~ (product @ X0 @ X2 @ X1)
% 100.55/15.05 | ~ (product @ X0 @ X2 @ X3)
% 100.55/15.05 | (product @ multiplicative_identity @ X3 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 100.55/15.05 thf(zip_derived_cl7172, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 100.55/15.05 | ~ (defined @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7155, zip_derived_cl111])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl7184, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl7172, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7345, plain,
% 100.55/15.05 ((~ (defined @ multiplicative_identity)
% 100.55/15.05 | ~ (defined @ additive_identity)
% 100.55/15.05 | (product @ multiplicative_identity @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity) @
% 100.55/15.05 additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl7184])).
% 100.55/15.05 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 100.55/15.05 inference('cnf', [status(esa)],
% 100.55/15.05 [well_definedness_of_multiplicative_identity])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl7350, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity) @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl7345, zip_derived_cl16, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl110, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | ~ (product @ X0 @ X2 @ X1)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ X2 @ X3)
% 100.55/15.05 | (product @ X0 @ X3 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl5])).
% 100.55/15.05 thf(zip_derived_cl7774, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (product @ X1 @ additive_identity @ X0)
% 100.55/15.05 | ~ (product @ X1 @
% 100.55/15.05 (multiply @ additive_identity @ multiplicative_identity) @ X0)
% 100.55/15.05 | ~ (defined @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7350, zip_derived_cl110])).
% 100.55/15.05 thf(zip_derived_cl123789, plain,
% 100.55/15.05 ((~ (defined @ a)
% 100.55/15.05 | (product @ a @ additive_identity @
% 100.55/15.05 (multiply @ a @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl123773, zip_derived_cl7774])).
% 100.55/15.05 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 100.55/15.05 inference('cnf', [status(esa)], [a_is_defined])).
% 100.55/15.05 thf(zip_derived_cl123799, plain,
% 100.55/15.05 ( (product @ a @ additive_identity @ (multiply @ a @ additive_identity))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl123789, zip_derived_cl26])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl123802, plain,
% 100.55/15.05 ( (product @ additive_identity @ a @ (multiply @ a @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl123799, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl372, plain,
% 100.55/15.05 ( (sum @ additive_identity @ multiplicative_identity @
% 100.55/15.05 multiplicative_identity)),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl370, zip_derived_cl366])).
% 100.55/15.05 thf(zip_derived_cl12624, plain,
% 100.55/15.05 ( (product @ a @ multiplicative_identity @ a)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl12623, zip_derived_cl26, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl12627, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @ a @ a)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl12624, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl138, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 100.55/15.05 (~ (product @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X3)
% 100.55/15.05 | ~ (sum @ X4 @ X2 @ X2)
% 100.55/15.05 | (sum @ X3 @ X0 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 100.55/15.05 thf(zip_derived_cl12651, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 ( (sum @ X0 @ a @ a)
% 100.55/15.05 | ~ (sum @ X1 @ multiplicative_identity @ multiplicative_identity)
% 100.55/15.05 | ~ (product @ X1 @ a @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl12627, zip_derived_cl138])).
% 100.55/15.05 thf(zip_derived_cl169413, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (product @ additive_identity @ a @ X0) | (sum @ X0 @ a @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl372, zip_derived_cl12651])).
% 100.55/15.05 thf(zip_derived_cl169434, plain,
% 100.55/15.05 ( (sum @ (multiply @ a @ additive_identity) @ a @ a)),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl123802, zip_derived_cl169413])).
% 100.55/15.05 thf(zip_derived_cl4, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_addition])).
% 100.55/15.05 thf(zip_derived_cl169454, plain,
% 100.55/15.05 ( (sum @ a @ (multiply @ a @ additive_identity) @ a)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl169434, zip_derived_cl4])).
% 100.55/15.05 thf(zip_derived_cl5187, plain, ( (sum @ additive_identity @ a @ a)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl5184, zip_derived_cl5164])).
% 100.55/15.05 thf(zip_derived_cl4, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_addition])).
% 100.55/15.05 thf(zip_derived_cl5192, plain, ( (sum @ a @ additive_identity @ a)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl5187, zip_derived_cl4])).
% 100.55/15.05 thf(zip_derived_cl387, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (sum @ (additive_inverse @ X2) @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ X2 @ X0 @ X1)
% 100.55/15.05 | ~ (defined @ X2))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl30])).
% 100.55/15.05 thf(zip_derived_cl14020, plain,
% 100.55/15.05 ((~ (defined @ a)
% 100.55/15.05 | (sum @ (additive_inverse @ a) @ a @ additive_identity)
% 100.55/15.05 | ~ (defined @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl5192, zip_derived_cl387])).
% 100.55/15.05 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 100.55/15.05 inference('cnf', [status(esa)], [a_is_defined])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl14132, plain,
% 100.55/15.05 ( (sum @ (additive_inverse @ a) @ a @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl14020, zip_derived_cl26, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl71, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (sum @ X2 @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ X1 @ X3 @ X1)
% 100.55/15.05 | (sum @ X0 @ X3 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl1])).
% 100.55/15.05 thf(zip_derived_cl14519, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (sum @ additive_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (sum @ a @ X0 @ a))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl14132, zip_derived_cl71])).
% 100.55/15.05 thf(zip_derived_cl169665, plain,
% 100.55/15.05 ( (sum @ additive_identity @ (multiply @ a @ additive_identity) @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl169454, zip_derived_cl14519])).
% 100.55/15.05 thf(zip_derived_cl74, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | (sum @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ additive_identity @ X0 @ X1))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl48])).
% 100.55/15.05 thf(zip_derived_cl169839, plain,
% 100.55/15.05 (( (sum @ additive_identity @ additive_identity @
% 100.55/15.05 (multiply @ a @ additive_identity))
% 100.55/15.05 | ~ (defined @ (multiply @ a @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl169665, zip_derived_cl74])).
% 100.55/15.05 thf(zip_derived_cl173910, plain,
% 100.55/15.05 ((~ (defined @ additive_identity)
% 100.55/15.05 | ~ (defined @ a)
% 100.55/15.05 | (sum @ additive_identity @ additive_identity @
% 100.55/15.05 (multiply @ a @ additive_identity)))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl169839])).
% 100.55/15.05 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 100.55/15.05 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 100.55/15.05 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 100.55/15.05 inference('cnf', [status(esa)], [a_is_defined])).
% 100.55/15.05 thf(zip_derived_cl173911, plain,
% 100.55/15.05 ( (sum @ additive_identity @ additive_identity @
% 100.55/15.05 (multiply @ a @ additive_identity))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl173910, zip_derived_cl13, zip_derived_cl26])).
% 100.55/15.05 thf(zip_derived_cl13793, plain,
% 100.55/15.05 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl13790, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl7115, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ additive_identity @ X1 @ X2)
% 100.55/15.05 | ~ (product @ additive_identity @ X1 @ X0)
% 100.55/15.05 | ~ (sum @ X0 @ X0 @ X2))),
% 100.55/15.05 inference('demod', [status(thm)], [zip_derived_cl7113, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl13817, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 (~ (sum @ additive_identity @ additive_identity @ X0)
% 100.55/15.05 | (product @ additive_identity @ additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl13793, zip_derived_cl7115])).
% 100.55/15.05 thf(zip_derived_cl174085, plain,
% 100.55/15.05 ( (product @ additive_identity @ additive_identity @
% 100.55/15.05 (multiply @ a @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl173911, zip_derived_cl13817])).
% 100.55/15.05 thf(zip_derived_cl13793, plain,
% 100.55/15.05 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl13790, zip_derived_cl13, zip_derived_cl13])).
% 100.55/15.05 thf(zip_derived_cl5, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (product @ X0 @ X3 @ X4)
% 100.55/15.05 | ~ (product @ X3 @ X5 @ X1)
% 100.55/15.05 | ~ (product @ X4 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 100.55/15.05 thf(zip_derived_cl115, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 (~ (product @ X0 @ X1 @ X0)
% 100.55/15.05 | ~ (product @ X1 @ X1 @ X2)
% 100.55/15.05 | (product @ X0 @ X2 @ X0))),
% 100.55/15.05 inference('eq_fact', [status(thm)], [zip_derived_cl5])).
% 100.55/15.05 thf(zip_derived_cl13799, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ additive_identity @ X0 @ additive_identity)
% 100.55/15.05 | ~ (product @ additive_identity @ additive_identity @ X0))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl13793, zip_derived_cl115])).
% 100.55/15.05 thf(zip_derived_cl174533, plain,
% 100.55/15.05 ( (product @ additive_identity @ (multiply @ a @ additive_identity) @
% 100.55/15.05 additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl174085, zip_derived_cl13799])).
% 100.55/15.05 thf(zip_derived_cl123799, plain,
% 100.55/15.05 ( (product @ a @ additive_identity @ (multiply @ a @ additive_identity))),
% 100.55/15.05 inference('demod', [status(thm)],
% 100.55/15.05 [zip_derived_cl123789, zip_derived_cl26])).
% 100.55/15.05 thf(zip_derived_cl19354, plain,
% 100.55/15.05 ( (product @ additive_identity @
% 100.55/15.05 (multiplicative_inverse @ multiplicative_identity) @ additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)],
% 100.55/15.05 [zip_derived_cl19314, zip_derived_cl7173])).
% 100.55/15.05 thf(zip_derived_cl9, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl19641, plain,
% 100.55/15.05 ( (product @ (multiplicative_inverse @ multiplicative_identity) @
% 100.55/15.05 additive_identity @ additive_identity)),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl19354, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl7251, plain,
% 100.55/15.05 ( (product @ multiplicative_identity @ additive_identity @
% 100.55/15.05 (additive_inverse @ additive_identity))),
% 100.55/15.05 inference('sup-', [status(thm)], [zip_derived_cl7156, zip_derived_cl9])).
% 100.55/15.05 thf(zip_derived_cl7, plain,
% 100.55/15.05 (![X0 : $i]:
% 100.55/15.05 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 100.55/15.05 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 100.55/15.05 thf(zip_derived_cl6, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.55/15.05 ( (product @ X0 @ X1 @ X2)
% 100.55/15.05 | ~ (product @ X3 @ X4 @ X0)
% 100.55/15.05 | ~ (product @ X4 @ X1 @ X5)
% 100.55/15.05 | ~ (product @ X3 @ X5 @ X2))),
% 100.55/15.05 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 100.55/15.05 thf(zip_derived_cl118, plain,
% 100.55/15.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.55/15.05 (~ (defined @ X0)
% 100.55/15.05 | ~ (product @ multiplicative_identity @ X2 @ X1)
% 101.17/15.06 | ~ (product @ X0 @ X3 @ X2)
% 101.17/15.06 | (product @ X0 @ X3 @ X1))),
% 101.17/15.06 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl6])).
% 101.17/15.06 thf(zip_derived_cl7284, plain,
% 101.17/15.06 (![X0 : $i, X1 : $i]:
% 101.17/15.06 ( (product @ X1 @ X0 @ (additive_inverse @ additive_identity))
% 101.17/15.06 | ~ (product @ X1 @ X0 @ additive_identity)
% 101.17/15.06 | ~ (defined @ X1))),
% 101.17/15.06 inference('sup-', [status(thm)], [zip_derived_cl7251, zip_derived_cl118])).
% 101.17/15.06 thf(zip_derived_cl19787, plain,
% 101.17/15.06 ((~ (defined @ (multiplicative_inverse @ multiplicative_identity))
% 101.17/15.06 | (product @ (multiplicative_inverse @ multiplicative_identity) @
% 101.17/15.06 additive_identity @ (additive_inverse @ additive_identity)))),
% 101.17/15.06 inference('sup-', [status(thm)],
% 101.17/15.06 [zip_derived_cl19641, zip_derived_cl7284])).
% 101.17/15.06 thf(zip_derived_cl17, plain,
% 101.17/15.06 (![X0 : $i]:
% 101.17/15.06 ( (defined @ (multiplicative_inverse @ X0))
% 101.17/15.06 | ~ (defined @ X0)
% 101.17/15.06 | (sum @ additive_identity @ X0 @ additive_identity))),
% 101.17/15.06 inference('cnf', [status(esa)],
% 101.17/15.06 [well_definedness_of_multiplicative_inverse])).
% 101.17/15.06 thf(zip_derived_cl372, plain,
% 101.17/15.06 ( (sum @ additive_identity @ multiplicative_identity @
% 101.17/15.06 multiplicative_identity)),
% 101.17/15.06 inference('demod', [status(thm)], [zip_derived_cl370, zip_derived_cl366])).
% 101.17/15.06 thf(zip_derived_cl48, plain,
% 101.17/15.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.17/15.06 (~ (sum @ additive_identity @ X1 @ X0)
% 101.17/15.06 | ~ (sum @ additive_identity @ X1 @ X2)
% 101.17/15.06 | (sum @ additive_identity @ X2 @ X0))),
% 101.17/15.06 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 101.17/15.06 thf(zip_derived_cl379, plain,
% 101.17/15.06 (![X0 : $i]:
% 101.17/15.06 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 101.17/15.06 | ~ (sum @ additive_identity @ multiplicative_identity @ X0))),
% 101.17/15.06 inference('sup-', [status(thm)], [zip_derived_cl372, zip_derived_cl48])).
% 101.17/15.06 thf(zip_derived_cl417, plain,
% 101.17/15.06 ((~ (defined @ multiplicative_identity)
% 101.17/15.06 | (defined @ (multiplicative_inverse @ multiplicative_identity))
% 101.17/15.06 | (sum @ additive_identity @ additive_identity @
% 101.17/15.06 multiplicative_identity))),
% 101.17/15.06 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl379])).
% 101.17/15.06 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 101.17/15.06 inference('cnf', [status(esa)],
% 101.17/15.06 [well_definedness_of_multiplicative_identity])).
% 101.17/15.06 thf(zip_derived_cl422, plain,
% 101.17/15.06 (( (defined @ (multiplicative_inverse @ multiplicative_identity))
% 101.17/15.06 | (sum @ additive_identity @ additive_identity @
% 101.17/15.06 multiplicative_identity))),
% 101.17/15.06 inference('demod', [status(thm)], [zip_derived_cl417, zip_derived_cl16])).
% 101.17/15.06 thf(zip_derived_cl25, plain,
% 101.17/15.06 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 101.17/15.06 inference('cnf', [status(esa)], [different_identities])).
% 101.17/15.06 thf(zip_derived_cl430, plain,
% 101.17/15.06 ( (defined @ (multiplicative_inverse @ multiplicative_identity))),
% 101.17/15.06 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl25])).
% 101.17/15.06 thf(zip_derived_cl19794, plain,
% 101.17/15.06 ( (product @ (multiplicative_inverse @ multiplicative_identity) @
% 101.17/15.06 additive_identity @ (additive_inverse @ additive_identity))),
% 101.17/15.06 inference('demod', [status(thm)],
% 101.17/15.06 [zip_derived_cl19787, zip_derived_cl430])).
% 101.17/15.06 thf(zip_derived_cl19727, plain,
% 101.17/15.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.17/15.06 (~ (product @ a @ X1 @ X0)
% 101.17/15.06 | ~ (product @ (multiplicative_inverse @ multiplicative_identity) @
% 101.17/15.06 X1 @ X2)
% 101.17/15.06 | (product @ a @ X2 @ X0))),
% 101.17/15.06 inference('sup-', [status(thm)], [zip_derived_cl19357, zip_derived_cl5])).
% 101.17/15.06 thf(zip_derived_cl123729, plain,
% 101.17/15.06 (![X0 : $i]:
% 101.17/15.06 ( (product @ a @ (additive_inverse @ additive_identity) @ X0)
% 101.17/15.06 | ~ (product @ a @ additive_identity @ X0))),
% 101.17/15.06 inference('sup-', [status(thm)],
% 101.17/15.06 [zip_derived_cl19794, zip_derived_cl19727])).
% 101.17/15.06 thf(zip_derived_cl123823, plain,
% 101.17/15.06 ( (product @ a @ (additive_inverse @ additive_identity) @
% 101.17/15.06 (multiply @ a @ additive_identity))),
% 101.17/15.06 inference('sup-', [status(thm)],
% 101.17/15.06 [zip_derived_cl123799, zip_derived_cl123729])).
% 101.17/15.06 thf(zip_derived_cl9, plain,
% 101.17/15.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.17/15.06 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 101.17/15.06 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 101.17/15.06 thf(zip_derived_cl124106, plain,
% 101.17/15.06 ( (product @ (additive_inverse @ additive_identity) @ a @
% 101.17/15.06 (multiply @ a @ additive_identity))),
% 101.17/15.06 inference('sup-', [status(thm)], [zip_derived_cl123823, zip_derived_cl9])).
% 101.17/15.06 thf(zip_derived_cl13880, plain,
% 101.17/15.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 101.17/15.06 (~ (product @ additive_identity @ X1 @ X0)
% 101.17/15.06 | ~ (product @ (additive_inverse @ additive_identity) @ X2 @ X1)
% 101.17/15.06 | (product @ additive_identity @ X2 @ X0))),
% 101.17/15.06 inference('sup-', [status(thm)], [zip_derived_cl13839, zip_derived_cl6])).
% 101.17/15.06 thf(zip_derived_cl124460, plain,
% 101.17/15.06 (![X0 : $i]:
% 101.17/15.06 ( (product @ additive_identity @ a @ X0)
% 101.17/15.06 | ~ (product @ additive_identity @
% 101.17/15.06 (multiply @ a @ additive_identity) @ X0))),
% 101.17/15.06 inference('sup-', [status(thm)],
% 101.17/15.06 [zip_derived_cl124106, zip_derived_cl13880])).
% 101.17/15.06 thf(zip_derived_cl174930, plain,
% 101.17/15.06 ( (product @ additive_identity @ a @ additive_identity)),
% 101.17/15.06 inference('sup-', [status(thm)],
% 101.17/15.06 [zip_derived_cl174533, zip_derived_cl124460])).
% 101.17/15.06 thf(zip_derived_cl174952, plain, ($false),
% 101.17/15.06 inference('demod', [status(thm)],
% 101.17/15.06 [zip_derived_cl27, zip_derived_cl174930])).
% 101.17/15.06
% 101.17/15.06 % SZS output end Refutation
% 101.17/15.06
% 101.17/15.06
% 101.17/15.06 % Terminating...
% 101.36/15.14 % Runner terminated.
% 101.38/15.16 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------