TSTP Solution File: FLD011-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD011-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.9JyMmwkLW1 true
% Computer : n028.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 22:39:08 EDT 2023
% Result : Unsatisfiable 187.01s 27.64s
% Output : Refutation 187.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD011-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.9JyMmwkLW1 true
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 00:00:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.19/0.65 % Total configuration time : 435
% 0.19/0.65 % Estimated wc time : 1092
% 0.19/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.19/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.19/0.72 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.19/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.19/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.19/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 187.01/27.64 % Solved by fo/fo13.sh.
% 187.01/27.64 % done 19178 iterations in 26.855s
% 187.01/27.64 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 187.01/27.64 % SZS output start Refutation
% 187.01/27.64 thf(sum_type, type, sum: $i > $i > $i > $o).
% 187.01/27.64 thf(a_type, type, a: $i).
% 187.01/27.64 thf(add_type, type, add: $i > $i > $i).
% 187.01/27.64 thf(product_type, type, product: $i > $i > $i > $o).
% 187.01/27.64 thf(additive_identity_type, type, additive_identity: $i).
% 187.01/27.64 thf(multiply_type, type, multiply: $i > $i > $i).
% 187.01/27.64 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 187.01/27.64 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 187.01/27.64 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 187.01/27.64 thf(defined_type, type, defined: $i > $o).
% 187.01/27.64 thf(well_definedness_of_multiplicative_inverse, axiom,
% 187.01/27.64 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 187.01/27.64 ( sum @ additive_identity @ X @ additive_identity ))).
% 187.01/27.64 thf(zip_derived_cl17, plain,
% 187.01/27.64 (![X0 : $i]:
% 187.01/27.64 ( (defined @ (multiplicative_inverse @ X0))
% 187.01/27.64 | ~ (defined @ X0)
% 187.01/27.64 | (sum @ additive_identity @ X0 @ additive_identity))),
% 187.01/27.64 inference('cnf', [status(esa)],
% 187.01/27.64 [well_definedness_of_multiplicative_inverse])).
% 187.01/27.64 thf(existence_of_inverse_multiplication, axiom,
% 187.01/27.64 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 187.01/27.64 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 187.01/27.64 thf(zip_derived_cl8, plain,
% 187.01/27.64 (![X0 : $i]:
% 187.01/27.64 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 187.01/27.64 multiplicative_identity)
% 187.01/27.64 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.64 | ~ (defined @ X0))),
% 187.01/27.64 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 187.01/27.64 thf(zip_derived_cl8, plain,
% 187.01/27.64 (![X0 : $i]:
% 187.01/27.64 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 187.01/27.64 multiplicative_identity)
% 187.01/27.64 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.64 | ~ (defined @ X0))),
% 187.01/27.64 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 187.01/27.64 thf(commutativity_multiplication, axiom,
% 187.01/27.64 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 187.01/27.64 thf(zip_derived_cl9, plain,
% 187.01/27.64 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.64 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.64 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 187.01/27.64 thf(zip_derived_cl49, plain,
% 187.01/27.64 (![X0 : $i]:
% 187.01/27.64 (~ (defined @ X0)
% 187.01/27.64 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.64 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 187.01/27.64 multiplicative_identity))),
% 187.01/27.64 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 187.01/27.64 thf(zip_derived_cl49, plain,
% 187.01/27.64 (![X0 : $i]:
% 187.01/27.64 (~ (defined @ X0)
% 187.01/27.64 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.64 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 187.01/27.64 multiplicative_identity))),
% 187.01/27.64 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 187.01/27.64 thf(existence_of_identity_multiplication, axiom,
% 187.01/27.64 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 187.01/27.64 thf(zip_derived_cl7, plain,
% 187.01/27.64 (![X0 : $i]:
% 187.01/27.65 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl9, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl34, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 187.01/27.65 thf(associativity_multiplication_1, axiom,
% 187.01/27.65 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 187.01/27.65 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 187.01/27.65 thf(zip_derived_cl5, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (product @ X0 @ X3 @ X4)
% 187.01/27.65 | ~ (product @ X3 @ X5 @ X1)
% 187.01/27.65 | ~ (product @ X4 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 187.01/27.65 thf(zip_derived_cl53, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (product @ X0 @ X2 @ X1)
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X3 @ X2)
% 187.01/27.65 | ~ (product @ X0 @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl5])).
% 187.01/27.65 thf(zip_derived_cl749, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (product @ X0 @ multiplicative_identity @ X1)
% 187.01/27.65 | ~ (product @ X0 @
% 187.01/27.65 (multiplicative_inverse @ multiplicative_identity) @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl53])).
% 187.01/27.65 thf(well_definedness_of_multiplicative_identity, axiom,
% 187.01/27.65 (defined @ multiplicative_identity)).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl765, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (product @ X0 @ multiplicative_identity @ X1)
% 187.01/27.65 | ~ (product @ X0 @
% 187.01/27.65 (multiplicative_inverse @ multiplicative_identity) @ X1))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl749, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl26902, plain,
% 187.01/27.65 (( (sum @ additive_identity @ multiplicative_identity @ additive_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | (product @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl765])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl26908, plain,
% 187.01/27.65 (( (sum @ additive_identity @ multiplicative_identity @ additive_identity)
% 187.01/27.65 | (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | (product @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl26902, zip_derived_cl16, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl26909, plain,
% 187.01/27.65 (( (product @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('simplify', [status(thm)], [zip_derived_cl26908])).
% 187.01/27.65 thf(totality_of_multiplication, axiom,
% 187.01/27.65 (( product @ X @ Y @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 187.01/27.65 ( ~( defined @ Y ) ))).
% 187.01/27.65 thf(zip_derived_cl19, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1))),
% 187.01/27.65 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 187.01/27.65 thf(zip_derived_cl8, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 187.01/27.65 thf(associativity_multiplication_2, axiom,
% 187.01/27.65 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 187.01/27.65 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 187.01/27.65 thf(zip_derived_cl6, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (product @ X3 @ X4 @ X0)
% 187.01/27.65 | ~ (product @ X4 @ X1 @ X5)
% 187.01/27.65 | ~ (product @ X3 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 187.01/27.65 thf(zip_derived_cl87, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | (product @ multiplicative_identity @ X2 @ X1)
% 187.01/27.65 | ~ (product @ X0 @ X2 @ X3)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ X0) @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 187.01/27.65 thf(zip_derived_cl1508, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ (multiplicative_inverse @ X1))
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | (sum @ additive_identity @ X1 @ additive_identity)
% 187.01/27.65 | (product @ multiplicative_identity @ X2 @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ X1) @ X0))
% 187.01/27.65 | ~ (product @ X1 @ X2 @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl87])).
% 187.01/27.65 thf(zip_derived_cl17, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (defined @ (multiplicative_inverse @ X0))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity))),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_inverse])).
% 187.01/27.65 thf(zip_derived_cl70358, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (product @ X1 @ X2 @ X0)
% 187.01/27.65 | (product @ multiplicative_identity @ X2 @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ X1) @ X0))
% 187.01/27.65 | (sum @ additive_identity @ X1 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | ~ (defined @ X0))),
% 187.01/27.65 inference('clc', [status(thm)], [zip_derived_cl1508, zip_derived_cl17])).
% 187.01/27.65 thf(zip_derived_cl70364, plain,
% 187.01/27.65 (( (sum @ additive_identity @ multiplicative_identity @ additive_identity)
% 187.01/27.65 | (product @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity))
% 187.01/27.65 | (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl26909, zip_derived_cl70358])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl70382, plain,
% 187.01/27.65 (( (sum @ additive_identity @ multiplicative_identity @ additive_identity)
% 187.01/27.65 | (product @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity))
% 187.01/27.65 | (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl70364, zip_derived_cl16, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl70383, plain,
% 187.01/27.65 (( (product @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity))
% 187.01/27.65 | (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('simplify', [status(thm)], [zip_derived_cl70382])).
% 187.01/27.65 thf(zip_derived_cl34, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl34, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 187.01/27.65 thf(existence_of_identity_addition, axiom,
% 187.01/27.65 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 187.01/27.65 thf(zip_derived_cl2, plain,
% 187.01/27.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 187.01/27.65 thf(commutativity_addition, axiom,
% 187.01/27.65 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 187.01/27.65 thf(zip_derived_cl4, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 187.01/27.65 thf(zip_derived_cl31, plain,
% 187.01/27.65 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl7, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 187.01/27.65 thf(distributivity_1, axiom,
% 187.01/27.65 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 187.01/27.65 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 187.01/27.65 ( ~( product @ Y @ Z @ D ) ))).
% 187.01/27.65 thf(zip_derived_cl10, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X3 @ X4 @ X5)
% 187.01/27.65 | ~ (product @ X5 @ X6 @ X2)
% 187.01/27.65 | ~ (product @ X3 @ X6 @ X0)
% 187.01/27.65 | ~ (product @ X4 @ X6 @ X1))),
% 187.01/27.65 inference('cnf', [status(esa)], [distributivity_1])).
% 187.01/27.65 thf(zip_derived_cl117, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X2 @ X1 @ X0)
% 187.01/27.65 | ~ (sum @ X4 @ X3 @ multiplicative_identity)
% 187.01/27.65 | ~ (product @ X4 @ X0 @ X2)
% 187.01/27.65 | ~ (product @ X3 @ X0 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl10])).
% 187.01/27.65 thf(zip_derived_cl1998, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ X2 @ X1 @ X0)
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X0 @ X2)
% 187.01/27.65 | ~ (product @ additive_identity @ X0 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl117])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl2000, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X2 @ X1 @ X0)
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X0 @ X2)
% 187.01/27.65 | ~ (product @ additive_identity @ X0 @ X1))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl1998, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl104233, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | (sum @ multiplicative_identity @ X0 @ multiplicative_identity)
% 187.01/27.65 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl2000])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl104348, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ multiplicative_identity @ X0 @ multiplicative_identity)
% 187.01/27.65 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl104233, zip_derived_cl16, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl105410, plain,
% 187.01/27.65 ((~ (defined @ additive_identity)
% 187.01/27.65 | (sum @ multiplicative_identity @ additive_identity @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl34, zip_derived_cl104348])).
% 187.01/27.65 thf(well_definedness_of_additive_identity, axiom,
% 187.01/27.65 (defined @ additive_identity)).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl105413, plain,
% 187.01/27.65 ( (sum @ multiplicative_identity @ additive_identity @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl105410, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl4, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 187.01/27.65 thf(zip_derived_cl105423, plain,
% 187.01/27.65 ( (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl105413, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl17, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (defined @ (multiplicative_inverse @ X0))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity))),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_inverse])).
% 187.01/27.65 thf(totality_of_addition, axiom,
% 187.01/27.65 (( sum @ X @ Y @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 187.01/27.65 ( ~( defined @ Y ) ))).
% 187.01/27.65 thf(zip_derived_cl18, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1))),
% 187.01/27.65 inference('cnf', [status(esa)], [totality_of_addition])).
% 187.01/27.65 thf(zip_derived_cl17, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (defined @ (multiplicative_inverse @ X0))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity))),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_inverse])).
% 187.01/27.65 thf(zip_derived_cl17, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (defined @ (multiplicative_inverse @ X0))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity))),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_inverse])).
% 187.01/27.65 thf(zip_derived_cl17, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (defined @ (multiplicative_inverse @ X0))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity))),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_inverse])).
% 187.01/27.65 thf(zip_derived_cl49, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl49, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl7, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl34, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 187.01/27.65 thf(not_product_3, conjecture,
% 187.01/27.65 (product @
% 187.01/27.65 multiplicative_identity @
% 187.01/27.65 ( multiplicative_inverse @ ( multiplicative_inverse @ a ) ) @ a)).
% 187.01/27.65 thf(zf_stmt_0, negated_conjecture,
% 187.01/27.65 (~( product @
% 187.01/27.65 multiplicative_identity @
% 187.01/27.65 ( multiplicative_inverse @ ( multiplicative_inverse @ a ) ) @ a )),
% 187.01/27.65 inference('cnf.neg', [status(esa)], [not_product_3])).
% 187.01/27.65 thf(zip_derived_cl28, plain,
% 187.01/27.65 (~ (product @ multiplicative_identity @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a)) @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_0])).
% 187.01/27.65 thf(zip_derived_cl5, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (product @ X0 @ X3 @ X4)
% 187.01/27.65 | ~ (product @ X3 @ X5 @ X1)
% 187.01/27.65 | ~ (product @ X4 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 187.01/27.65 thf(zip_derived_cl51, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (product @ multiplicative_identity @ X1 @ X0)
% 187.01/27.65 | ~ (product @ X1 @ X2 @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a)))
% 187.01/27.65 | ~ (product @ X0 @ X2 @ a))),
% 187.01/27.65 inference('s_sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl5])).
% 187.01/27.65 thf(zip_derived_cl61, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X0 @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a)))
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X0 @ a))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl51])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl64, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (product @ multiplicative_identity @ X0 @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a)))
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X0 @ a))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl66, plain,
% 187.01/27.65 ((~ (defined @ a)
% 187.01/27.65 | ~ (product @ multiplicative_identity @ a @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl64])).
% 187.01/27.65 thf(a_is_defined, axiom, (defined @ a)).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl67, plain,
% 187.01/27.65 (~ (product @ multiplicative_identity @ a @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl9, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl69, plain,
% 187.01/27.65 (~ (product @ a @ multiplicative_identity @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('s_sup+', [status(thm)], [zip_derived_cl67, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl5, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (product @ X0 @ X3 @ X4)
% 187.01/27.65 | ~ (product @ X3 @ X5 @ X1)
% 187.01/27.65 | ~ (product @ X4 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 187.01/27.65 thf(zip_derived_cl70, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (product @ a @ X1 @ X0)
% 187.01/27.65 | ~ (product @ X1 @ X2 @ multiplicative_identity)
% 187.01/27.65 | ~ (product @ X0 @ X2 @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('s_sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl5])).
% 187.01/27.65 thf(zip_derived_cl121, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ a @ additive_identity)
% 187.01/27.65 | ~ (defined @ a)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @ X0 @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X0 @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl70])).
% 187.01/27.65 thf(not_sum_2, conjecture, (sum @ additive_identity @ a @ additive_identity)).
% 187.01/27.65 thf(zf_stmt_1, negated_conjecture,
% 187.01/27.65 (~( sum @ additive_identity @ a @ additive_identity )),
% 187.01/27.65 inference('cnf.neg', [status(esa)], [not_sum_2])).
% 187.01/27.65 thf(zip_derived_cl27, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ a @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl124, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (product @ (multiplicative_inverse @ a) @ X0 @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X0 @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl121, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl131, plain,
% 187.01/27.65 (( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | ~ (defined @ (multiplicative_inverse @ a))
% 187.01/27.65 | ~ (product @ multiplicative_identity @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a)) @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl124])).
% 187.01/27.65 thf(zip_derived_cl134, plain,
% 187.01/27.65 (( (sum @ additive_identity @ a @ additive_identity)
% 187.01/27.65 | ~ (defined @ a)
% 187.01/27.65 | (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | ~ (product @ multiplicative_identity @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a)) @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl131])).
% 187.01/27.65 thf(zip_derived_cl27, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ a @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl135, plain,
% 187.01/27.65 (( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | ~ (product @ multiplicative_identity @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a)) @
% 187.01/27.65 (multiplicative_inverse @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl134, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl7, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl151, plain,
% 187.01/27.65 (( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | ~ (defined @ (multiplicative_inverse @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('s_sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl7])).
% 187.01/27.65 thf(zip_derived_cl164, plain,
% 187.01/27.65 (( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | ~ (defined @ (multiplicative_inverse @ a))
% 187.01/27.65 | (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl151])).
% 187.01/27.65 thf(zip_derived_cl165, plain,
% 187.01/27.65 ((~ (defined @ (multiplicative_inverse @ a))
% 187.01/27.65 | (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('simplify', [status(thm)], [zip_derived_cl164])).
% 187.01/27.65 thf(zip_derived_cl199, plain,
% 187.01/27.65 (( (sum @ additive_identity @ a @ additive_identity)
% 187.01/27.65 | ~ (defined @ a)
% 187.01/27.65 | (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl165])).
% 187.01/27.65 thf(zip_derived_cl27, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ a @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl200, plain,
% 187.01/27.65 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl199, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl2, plain,
% 187.01/27.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 187.01/27.65 thf(associativity_addition_1, axiom,
% 187.01/27.65 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 187.01/27.65 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 187.01/27.65 thf(zip_derived_cl0, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X4)
% 187.01/27.65 | ~ (sum @ X3 @ X5 @ X1)
% 187.01/27.65 | ~ (sum @ X4 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_addition_1])).
% 187.01/27.65 thf(zip_derived_cl29, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 187.01/27.65 thf(zip_derived_cl235, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ additive_identity)
% 187.01/27.65 | (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl200, zip_derived_cl29])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl242, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl235, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl285, plain,
% 187.01/27.65 ((~ (defined @ (multiplicative_inverse @ a))
% 187.01/27.65 | ~ (defined @ additive_identity)
% 187.01/27.65 | (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl242])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl288, plain,
% 187.01/27.65 ((~ (defined @ (multiplicative_inverse @ a))
% 187.01/27.65 | (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl285, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl448, plain,
% 187.01/27.65 (( (sum @ additive_identity @ a @ additive_identity)
% 187.01/27.65 | ~ (defined @ a)
% 187.01/27.65 | (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl288])).
% 187.01/27.65 thf(zip_derived_cl27, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ a @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl449, plain,
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl448, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl200, plain,
% 187.01/27.65 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl199, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl242, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl235, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl287, plain,
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl200, zip_derived_cl242])).
% 187.01/27.65 thf(zip_derived_cl18, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1))),
% 187.01/27.65 inference('cnf', [status(esa)], [totality_of_addition])).
% 187.01/27.65 thf(zip_derived_cl17, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (defined @ (multiplicative_inverse @ X0))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity))),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_inverse])).
% 187.01/27.65 thf(zip_derived_cl2, plain,
% 187.01/27.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 187.01/27.65 thf(zip_derived_cl242, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl235, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl286, plain,
% 187.01/27.65 ((~ (defined @ (multiplicative_inverse @ a))
% 187.01/27.65 | (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl242])).
% 187.01/27.65 thf(zip_derived_cl297, plain,
% 187.01/27.65 (( (sum @ additive_identity @ a @ additive_identity)
% 187.01/27.65 | ~ (defined @ a)
% 187.01/27.65 | (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl286])).
% 187.01/27.65 thf(zip_derived_cl27, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ a @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl298, plain,
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (multiplicative_inverse @ a))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl297, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl29, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 187.01/27.65 thf(zip_derived_cl304, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ additive_identity)
% 187.01/27.65 | (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl29])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl306, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl304, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl307, plain,
% 187.01/27.65 ((~ (defined @ additive_identity)
% 187.01/27.65 | ~ (defined @ additive_identity)
% 187.01/27.65 | (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 (add @ additive_identity @ additive_identity)))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl306])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl312, plain,
% 187.01/27.65 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 (add @ additive_identity @ additive_identity))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl307, zip_derived_cl13, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl242, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl235, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl380, plain,
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ additive_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl312, zip_derived_cl242])).
% 187.01/27.65 thf(zip_derived_cl29, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 187.01/27.65 thf(zip_derived_cl387, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ additive_identity)
% 187.01/27.65 | (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ additive_identity) @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl380, zip_derived_cl29])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl392, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ additive_identity) @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl387, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl506, plain,
% 187.01/27.65 ( (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ additive_identity) @ additive_identity)),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl287, zip_derived_cl392])).
% 187.01/27.65 thf(zip_derived_cl4, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 187.01/27.65 thf(zip_derived_cl526, plain,
% 187.01/27.65 ( (sum @ (add @ additive_identity @ additive_identity) @
% 187.01/27.65 additive_identity @ additive_identity)),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl506, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl18, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1))),
% 187.01/27.65 inference('cnf', [status(esa)], [totality_of_addition])).
% 187.01/27.65 thf(zip_derived_cl0, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X4)
% 187.01/27.65 | ~ (sum @ X3 @ X5 @ X1)
% 187.01/27.65 | ~ (sum @ X4 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_addition_1])).
% 187.01/27.65 thf(zip_derived_cl57, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | (sum @ X1 @ X3 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X4 @ X3)
% 187.01/27.65 | ~ (sum @ (add @ X1 @ X0) @ X4 @ X2))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl0])).
% 187.01/27.65 thf(zip_derived_cl916, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ additive_identity)
% 187.01/27.65 | ~ (defined @ additive_identity)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl526, zip_derived_cl57])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl920, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl916, zip_derived_cl13, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl939, plain,
% 187.01/27.65 ( (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)) @
% 187.01/27.65 additive_identity)),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl449, zip_derived_cl920])).
% 187.01/27.65 thf(zip_derived_cl29, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 187.01/27.65 thf(zip_derived_cl949, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ additive_identity)
% 187.01/27.65 | (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)) @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl939, zip_derived_cl29])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl955, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)) @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl949, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl31, plain,
% 187.01/27.65 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl0, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X4)
% 187.01/27.65 | ~ (sum @ X3 @ X5 @ X1)
% 187.01/27.65 | ~ (sum @ X4 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_addition_1])).
% 187.01/27.65 thf(zip_derived_cl36, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ additive_identity @ X3 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl0])).
% 187.01/27.65 thf(zip_derived_cl1161, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (defined @ additive_identity)
% 187.01/27.65 | ~ (sum @ additive_identity @ X1 @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)))
% 187.01/27.65 | ~ (sum @ additive_identity @ X1 @ X0))),
% 187.01/27.65 inference('s_sup+', [status(thm)], [zip_derived_cl955, zip_derived_cl36])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl1183, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ X1 @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)))
% 187.01/27.65 | ~ (sum @ additive_identity @ X1 @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl1161, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl105617, plain,
% 187.01/27.65 (( (sum @ additive_identity @ additive_identity @ multiplicative_identity)
% 187.01/27.65 | ~ (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a))))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl105423, zip_derived_cl1183])).
% 187.01/27.65 thf(different_identities, axiom,
% 187.01/27.65 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 187.01/27.65 thf(zip_derived_cl25, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [different_identities])).
% 187.01/27.65 thf(zip_derived_cl105690, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl105617, zip_derived_cl25])).
% 187.01/27.65 thf(zip_derived_cl449, plain,
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl448, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl2, plain,
% 187.01/27.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 187.01/27.65 thf(associativity_addition_2, axiom,
% 187.01/27.65 (( sum @ U @ Z @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 187.01/27.65 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ X @ V @ W ) ))).
% 187.01/27.65 thf(zip_derived_cl1, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X3 @ X4 @ X0)
% 187.01/27.65 | ~ (sum @ X4 @ X1 @ X5)
% 187.01/27.65 | ~ (sum @ X3 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_addition_2])).
% 187.01/27.65 thf(zip_derived_cl40, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ X0 @ X2 @ X3)
% 187.01/27.65 | ~ (sum @ additive_identity @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 187.01/27.65 thf(zip_derived_cl465, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ X1 @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)))
% 187.01/27.65 | ~ (sum @ X0 @ X1 @ additive_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl449, zip_derived_cl40])).
% 187.01/27.65 thf(zip_derived_cl106046, plain,
% 187.01/27.65 ((~ (defined @ additive_identity)
% 187.01/27.65 | ~ (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl105690, zip_derived_cl465])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl106093, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl106046, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl106216, plain,
% 187.01/27.65 ( (product @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl70383, zip_derived_cl106093])).
% 187.01/27.65 thf(zip_derived_cl7, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl8, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 187.01/27.65 thf(zip_derived_cl5, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (product @ X0 @ X3 @ X4)
% 187.01/27.65 | ~ (product @ X3 @ X5 @ X1)
% 187.01/27.65 | ~ (product @ X4 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 187.01/27.65 thf(zip_derived_cl56, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | (product @ (multiplicative_inverse @ X0) @ X2 @ X1)
% 187.01/27.65 | ~ (product @ X0 @ X3 @ X2)
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl5])).
% 187.01/27.65 thf(zip_derived_cl877, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | (sum @ additive_identity @ X1 @ additive_identity)
% 187.01/27.65 | (product @ (multiplicative_inverse @ X1) @ X2 @ X0)
% 187.01/27.65 | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl56])).
% 187.01/27.65 thf(zip_derived_cl123427, plain,
% 187.01/27.65 ((~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | (product @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl106216, zip_derived_cl877])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl106093, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl106046, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl123494, plain,
% 187.01/27.65 ( (product @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity) @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl123427, zip_derived_cl16, zip_derived_cl16,
% 187.01/27.65 zip_derived_cl106093])).
% 187.01/27.65 thf(zip_derived_cl9, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl137622, plain,
% 187.01/27.65 ( (product @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity) @
% 187.01/27.65 (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl123494, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl49, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl49, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl10, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X3 @ X4 @ X5)
% 187.01/27.65 | ~ (product @ X5 @ X6 @ X2)
% 187.01/27.65 | ~ (product @ X3 @ X6 @ X0)
% 187.01/27.65 | ~ (product @ X4 @ X6 @ X1))),
% 187.01/27.65 inference('cnf', [status(esa)], [distributivity_1])).
% 187.01/27.65 thf(zip_derived_cl116, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ X2 @ X1 @ multiplicative_identity)
% 187.01/27.65 | ~ (sum @ X4 @ X3 @ X0)
% 187.01/27.65 | ~ (product @ X4 @ (multiplicative_inverse @ X0) @ X2)
% 187.01/27.65 | ~ (product @ X3 @ (multiplicative_inverse @ X0) @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl10])).
% 187.01/27.65 thf(zip_derived_cl1968, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ multiplicative_identity @ X1 @ multiplicative_identity)
% 187.01/27.65 | ~ (sum @ X0 @ X2 @ X0)
% 187.01/27.65 | ~ (product @ X2 @ (multiplicative_inverse @ X0) @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl116])).
% 187.01/27.65 thf(zip_derived_cl1975, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (product @ X2 @ (multiplicative_inverse @ X0) @ X1)
% 187.01/27.65 | ~ (sum @ X0 @ X2 @ X0)
% 187.01/27.65 | (sum @ multiplicative_identity @ X1 @ multiplicative_identity)
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity))),
% 187.01/27.65 inference('simplify', [status(thm)], [zip_derived_cl1968])).
% 187.01/27.65 thf(zip_derived_cl144054, plain,
% 187.01/27.65 ((~ (sum @ multiplicative_identity @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity) @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | (sum @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl137622, zip_derived_cl1975])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl106093, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl106046, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl144066, plain,
% 187.01/27.65 ((~ (sum @ multiplicative_identity @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity) @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | (sum @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl144054, zip_derived_cl16, zip_derived_cl106093])).
% 187.01/27.65 thf(zip_derived_cl105413, plain,
% 187.01/27.65 ( (sum @ multiplicative_identity @ additive_identity @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl105410, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl18, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1))),
% 187.01/27.65 inference('cnf', [status(esa)], [totality_of_addition])).
% 187.01/27.65 thf(zip_derived_cl4, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 187.01/27.65 thf(zip_derived_cl59, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 187.01/27.65 thf(existence_of_inverse_addition, axiom,
% 187.01/27.65 (( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) |
% 187.01/27.65 ( ~( defined @ X ) ))).
% 187.01/27.65 thf(zip_derived_cl3, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 187.01/27.65 thf(zip_derived_cl1, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X3 @ X4 @ X0)
% 187.01/27.65 | ~ (sum @ X4 @ X1 @ X5)
% 187.01/27.65 | ~ (sum @ X3 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_addition_2])).
% 187.01/27.65 thf(zip_derived_cl41, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ X0 @ X2 @ X3)
% 187.01/27.65 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 187.01/27.65 thf(zip_derived_cl1047, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (defined @ X1)
% 187.01/27.65 | ~ (defined @ (additive_inverse @ X0))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X2 @
% 187.01/27.65 (add @ X1 @ (additive_inverse @ X0)))
% 187.01/27.65 | ~ (sum @ X0 @ X2 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl41])).
% 187.01/27.65 thf(well_definedness_of_additive_inverse, axiom,
% 187.01/27.65 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 187.01/27.65 thf(zip_derived_cl14, plain,
% 187.01/27.65 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 187.01/27.65 thf(zip_derived_cl37430, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (sum @ X0 @ X2 @ X1)
% 187.01/27.65 | (sum @ additive_identity @ X2 @
% 187.01/27.65 (add @ X1 @ (additive_inverse @ X0)))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1))),
% 187.01/27.65 inference('clc', [status(thm)], [zip_derived_cl1047, zip_derived_cl14])).
% 187.01/27.65 thf(zip_derived_cl105435, plain,
% 187.01/27.65 (( (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (add @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ multiplicative_identity)))
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl105413, zip_derived_cl37430])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl105516, plain,
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (add @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ multiplicative_identity)))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl105435, zip_derived_cl16, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl105423, plain,
% 187.01/27.65 ( (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl105413, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl955, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)) @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl949, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl31, plain,
% 187.01/27.65 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl1, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X3 @ X4 @ X0)
% 187.01/27.65 | ~ (sum @ X4 @ X1 @ X5)
% 187.01/27.65 | ~ (sum @ X3 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_addition_2])).
% 187.01/27.65 thf(zip_derived_cl39, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ additive_identity @ X2 @ X3)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl1])).
% 187.01/27.65 thf(zip_derived_cl1162, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (defined @ additive_identity)
% 187.01/27.65 | ~ (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)) @ X1)
% 187.01/27.65 | ~ (sum @ additive_identity @ X1 @ X0))),
% 187.01/27.65 inference('s_sup+', [status(thm)], [zip_derived_cl955, zip_derived_cl39])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl1184, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)) @ X1)
% 187.01/27.65 | ~ (sum @ additive_identity @ X1 @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl1162, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl105618, plain,
% 187.01/27.65 (( (sum @ additive_identity @ additive_identity @ multiplicative_identity)
% 187.01/27.65 | ~ (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl105423, zip_derived_cl1184])).
% 187.01/27.65 thf(zip_derived_cl25, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [different_identities])).
% 187.01/27.65 thf(zip_derived_cl105691, plain,
% 187.01/27.65 (~ (sum @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)) @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl105618, zip_derived_cl25])).
% 187.01/27.65 thf(zip_derived_cl4, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 187.01/27.65 thf(zip_derived_cl107019, plain,
% 187.01/27.65 (~ (sum @ (add @ additive_identity @ (multiplicative_inverse @ a)) @
% 187.01/27.65 additive_identity @ multiplicative_identity)),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl105691, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl449, plain,
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (add @ additive_identity @ (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl448, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl1, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X3 @ X4 @ X0)
% 187.01/27.65 | ~ (sum @ X4 @ X1 @ X5)
% 187.01/27.65 | ~ (sum @ X3 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_addition_2])).
% 187.01/27.65 thf(zip_derived_cl459, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ (add @ additive_identity @ (multiplicative_inverse @ a)) @
% 187.01/27.65 X1 @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ additive_identity @ X2 @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl449, zip_derived_cl1])).
% 187.01/27.65 thf(zip_derived_cl108154, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (sum @ additive_identity @ additive_identity @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ X0 @ multiplicative_identity))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl107019, zip_derived_cl459])).
% 187.01/27.65 thf(zip_derived_cl133805, plain,
% 187.01/27.65 (~ (sum @ additive_identity @
% 187.01/27.65 (add @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ multiplicative_identity)) @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl105516, zip_derived_cl108154])).
% 187.01/27.65 thf(zip_derived_cl2, plain,
% 187.01/27.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 187.01/27.65 thf(zip_derived_cl3, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 187.01/27.65 thf(zip_derived_cl4, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 187.01/27.65 thf(zip_derived_cl32, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl0, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X4)
% 187.01/27.65 | ~ (sum @ X3 @ X5 @ X1)
% 187.01/27.65 | ~ (sum @ X4 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_addition_1])).
% 187.01/27.65 thf(zip_derived_cl42, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X2)
% 187.01/27.65 | ~ (sum @ additive_identity @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl0])).
% 187.01/27.65 thf(zip_derived_cl491, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | (sum @ X1 @ X2 @ X0)
% 187.01/27.65 | ~ (sum @ (additive_inverse @ X1) @ X0 @ X2))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl42])).
% 187.01/27.65 thf(zip_derived_cl133891, plain,
% 187.01/27.65 ((~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (defined @ additive_identity)
% 187.01/27.65 | ~ (sum @ (additive_inverse @ additive_identity) @
% 187.01/27.65 multiplicative_identity @
% 187.01/27.65 (add @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ multiplicative_identity))))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl133805, zip_derived_cl491])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl133953, plain,
% 187.01/27.65 (~ (sum @ (additive_inverse @ additive_identity) @
% 187.01/27.65 multiplicative_identity @
% 187.01/27.65 (add @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ multiplicative_identity)))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl133891, zip_derived_cl16, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl4, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 187.01/27.65 thf(zip_derived_cl141931, plain,
% 187.01/27.65 (~ (sum @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ additive_identity) @
% 187.01/27.65 (add @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ multiplicative_identity)))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl133953, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl32, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl39, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ X2 @ X1)
% 187.01/27.65 | ~ (sum @ additive_identity @ X2 @ X3)
% 187.01/27.65 | ~ (sum @ X0 @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl1])).
% 187.01/27.65 thf(zip_derived_cl354, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 (~ (defined @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ (additive_inverse @ additive_identity) @ X1)
% 187.01/27.65 | ~ (sum @ X0 @ additive_identity @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl39])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl362, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ X0 @ (additive_inverse @ additive_identity) @ X1)
% 187.01/27.65 | ~ (sum @ X0 @ additive_identity @ X1))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl354, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl146382, plain,
% 187.01/27.65 ((~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (sum @ multiplicative_identity @ additive_identity @
% 187.01/27.65 (add @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ multiplicative_identity))))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl141931, zip_derived_cl362])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl146395, plain,
% 187.01/27.65 (~ (sum @ multiplicative_identity @ additive_identity @
% 187.01/27.65 (add @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ multiplicative_identity)))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl146382, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl4, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 187.01/27.65 thf(zip_derived_cl146398, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 (add @ multiplicative_identity @
% 187.01/27.65 (additive_inverse @ multiplicative_identity)))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl146395, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl37430, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (sum @ X0 @ X2 @ X1)
% 187.01/27.65 | (sum @ additive_identity @ X2 @
% 187.01/27.65 (add @ X1 @ (additive_inverse @ X0)))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1))),
% 187.01/27.65 inference('clc', [status(thm)], [zip_derived_cl1047, zip_derived_cl14])).
% 187.01/27.65 thf(zip_derived_cl146489, plain,
% 187.01/27.65 ((~ (sum @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl146398, zip_derived_cl37430])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl146502, plain,
% 187.01/27.65 (~ (sum @ multiplicative_identity @ multiplicative_identity @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl146489, zip_derived_cl16, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl146513, plain,
% 187.01/27.65 (~ (sum @ multiplicative_identity @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity) @
% 187.01/27.65 multiplicative_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl144066, zip_derived_cl146502])).
% 187.01/27.65 thf(zip_derived_cl298, plain,
% 187.01/27.65 ( (sum @ additive_identity @ additive_identity @
% 187.01/27.65 (multiplicative_inverse @ a))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl297, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl306, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @ X0)
% 187.01/27.65 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl304, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl311, plain,
% 187.01/27.65 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 (multiplicative_inverse @ a))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl306])).
% 187.01/27.65 thf(zip_derived_cl4, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 187.01/27.65 thf(zip_derived_cl339, plain,
% 187.01/27.65 ( (sum @ (multiplicative_inverse @ a) @ additive_identity @
% 187.01/27.65 (multiplicative_inverse @ a))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl311, zip_derived_cl4])).
% 187.01/27.65 thf(zip_derived_cl8, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 187.01/27.65 multiplicative_identity)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0))),
% 187.01/27.65 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 187.01/27.65 thf(zip_derived_cl10, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 187.01/27.65 ( (sum @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X3 @ X4 @ X5)
% 187.01/27.65 | ~ (product @ X5 @ X6 @ X2)
% 187.01/27.65 | ~ (product @ X3 @ X6 @ X0)
% 187.01/27.65 | ~ (product @ X4 @ X6 @ X1))),
% 187.01/27.65 inference('cnf', [status(esa)], [distributivity_1])).
% 187.01/27.65 thf(zip_derived_cl118, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | (sum @ X2 @ X1 @ multiplicative_identity)
% 187.01/27.65 | ~ (sum @ X4 @ X3 @ (multiplicative_inverse @ X0))
% 187.01/27.65 | ~ (product @ X4 @ X0 @ X2)
% 187.01/27.65 | ~ (product @ X3 @ X0 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl10])).
% 187.01/27.65 thf(zip_derived_cl2091, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 (~ (defined @ a)
% 187.01/27.65 | (sum @ additive_identity @ a @ additive_identity)
% 187.01/27.65 | (sum @ X1 @ X0 @ multiplicative_identity)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @ a @ X1)
% 187.01/27.65 | ~ (product @ additive_identity @ a @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl339, zip_derived_cl118])).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl27, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ a @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 187.01/27.65 thf(zip_derived_cl2102, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (sum @ X1 @ X0 @ multiplicative_identity)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @ a @ X1)
% 187.01/27.65 | ~ (product @ additive_identity @ a @ X0))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl2091, zip_derived_cl26, zip_derived_cl27])).
% 187.01/27.65 thf(zip_derived_cl146549, plain,
% 187.01/27.65 ((~ (product @ (multiplicative_inverse @ a) @ a @ multiplicative_identity)
% 187.01/27.65 | ~ (product @ additive_identity @ a @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity)))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl146513, zip_derived_cl2102])).
% 187.01/27.65 thf(zip_derived_cl147599, plain,
% 187.01/27.65 ((~ (defined @ a)
% 187.01/27.65 | (sum @ additive_identity @ a @ additive_identity)
% 187.01/27.65 | ~ (product @ additive_identity @ a @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity)))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl8, zip_derived_cl146549])).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl27, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ a @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 187.01/27.65 thf(zip_derived_cl147600, plain,
% 187.01/27.65 (~ (product @ additive_identity @ a @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl147599, zip_derived_cl26, zip_derived_cl27])).
% 187.01/27.65 thf(zip_derived_cl9, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl147603, plain,
% 187.01/27.65 (~ (product @ a @ additive_identity @
% 187.01/27.65 (multiply @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl147600, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl19, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1))),
% 187.01/27.65 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 187.01/27.65 thf(zip_derived_cl9, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl90, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | (product @ X0 @ X1 @ (multiply @ X1 @ X0)))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl49, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 187.01/27.65 multiplicative_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl5, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (product @ X0 @ X3 @ X4)
% 187.01/27.65 | ~ (product @ X3 @ X5 @ X1)
% 187.01/27.65 | ~ (product @ X4 @ X5 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 187.01/27.65 thf(zip_derived_cl54, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 ( (sum @ additive_identity @ X0 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (product @ X0 @ X2 @ X1)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ X0) @ X3 @ X2)
% 187.01/27.65 | ~ (product @ multiplicative_identity @ X3 @ X1))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl5])).
% 187.01/27.65 thf(zip_derived_cl1720, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | (sum @ additive_identity @ X1 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | (product @ X1 @ X2 @ (multiply @ X0 @ multiplicative_identity))
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ X1) @ X0 @ X2))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl54])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl1763, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X1 @ additive_identity)
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | (product @ X1 @ X2 @ (multiply @ X0 @ multiplicative_identity))
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ X1) @ X0 @ X2))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl1720, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl147661, plain,
% 187.01/27.65 ((~ (defined @ (multiplicative_inverse @ multiplicative_identity))
% 187.01/27.65 | (sum @ additive_identity @ a @ additive_identity)
% 187.01/27.65 | ~ (defined @ a)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @
% 187.01/27.65 (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('s_sup+', [status(thm)],
% 187.01/27.65 [zip_derived_cl147603, zip_derived_cl1763])).
% 187.01/27.65 thf(zip_derived_cl27, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ a @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl147674, plain,
% 187.01/27.65 ((~ (defined @ (multiplicative_inverse @ multiplicative_identity))
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @
% 187.01/27.65 (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl147661, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl147756, plain,
% 187.01/27.65 (( (sum @ additive_identity @ multiplicative_identity @ additive_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @
% 187.01/27.65 (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 additive_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl17, zip_derived_cl147674])).
% 187.01/27.65 thf(zip_derived_cl106093, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl106046, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl147757, plain,
% 187.01/27.65 (~ (product @ (multiplicative_inverse @ a) @
% 187.01/27.65 (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl147756, zip_derived_cl106093, zip_derived_cl16])).
% 187.01/27.65 thf(zip_derived_cl17, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 ( (defined @ (multiplicative_inverse @ X0))
% 187.01/27.65 | ~ (defined @ X0)
% 187.01/27.65 | (sum @ additive_identity @ X0 @ additive_identity))),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_inverse])).
% 187.01/27.65 thf(zip_derived_cl34, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl311, plain,
% 187.01/27.65 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 (multiplicative_inverse @ a))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl306])).
% 187.01/27.65 thf(zip_derived_cl34, plain,
% 187.01/27.65 (![X0 : $i]:
% 187.01/27.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl200, plain,
% 187.01/27.65 ( (sum @ additive_identity @ (multiplicative_inverse @ a) @
% 187.01/27.65 additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl199, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(distributivity_2, axiom,
% 187.01/27.65 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 187.01/27.65 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 187.01/27.65 ( ~( sum @ C @ D @ B ) ))).
% 187.01/27.65 thf(zip_derived_cl11, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2)
% 187.01/27.65 | ~ (sum @ X3 @ X4 @ X0)
% 187.01/27.65 | ~ (product @ X3 @ X1 @ X5)
% 187.01/27.65 | ~ (product @ X4 @ X1 @ X6)
% 187.01/27.65 | ~ (sum @ X5 @ X6 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [distributivity_2])).
% 187.01/27.65 thf(zip_derived_cl203, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 187.01/27.65 ( (product @ additive_identity @ X1 @ X0)
% 187.01/27.65 | ~ (product @ additive_identity @ X1 @ X2)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @ X1 @ X3)
% 187.01/27.65 | ~ (sum @ X2 @ X3 @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl200, zip_derived_cl11])).
% 187.01/27.65 thf(zip_derived_cl3549, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 (~ (defined @ additive_identity)
% 187.01/27.65 | (product @ additive_identity @ multiplicative_identity @ X0)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @
% 187.01/27.65 multiplicative_identity @ X1)
% 187.01/27.65 | ~ (sum @ additive_identity @ X1 @ X0))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl203])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl3553, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i]:
% 187.01/27.65 ( (product @ additive_identity @ multiplicative_identity @ X0)
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @
% 187.01/27.65 multiplicative_identity @ X1)
% 187.01/27.65 | ~ (sum @ additive_identity @ X1 @ X0))),
% 187.01/27.65 inference('demod', [status(thm)], [zip_derived_cl3549, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl206920, plain,
% 187.01/27.65 (( (product @ additive_identity @ multiplicative_identity @
% 187.01/27.65 (multiplicative_inverse @ a))
% 187.01/27.65 | ~ (product @ (multiplicative_inverse @ a) @
% 187.01/27.65 multiplicative_identity @ (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl311, zip_derived_cl3553])).
% 187.01/27.65 thf(zip_derived_cl209118, plain,
% 187.01/27.65 ((~ (defined @ (multiplicative_inverse @ a))
% 187.01/27.65 | (product @ additive_identity @ multiplicative_identity @
% 187.01/27.65 (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl34, zip_derived_cl206920])).
% 187.01/27.65 thf(zip_derived_cl230794, plain,
% 187.01/27.65 (( (sum @ additive_identity @ a @ additive_identity)
% 187.01/27.65 | ~ (defined @ a)
% 187.01/27.65 | (product @ additive_identity @ multiplicative_identity @
% 187.01/27.65 (multiplicative_inverse @ a)))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl17, zip_derived_cl209118])).
% 187.01/27.65 thf(zip_derived_cl27, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ a @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 187.01/27.65 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 187.01/27.65 inference('cnf', [status(esa)], [a_is_defined])).
% 187.01/27.65 thf(zip_derived_cl230795, plain,
% 187.01/27.65 ( (product @ additive_identity @ multiplicative_identity @
% 187.01/27.65 (multiplicative_inverse @ a))),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl230794, zip_derived_cl27, zip_derived_cl26])).
% 187.01/27.65 thf(zip_derived_cl9, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl230801, plain,
% 187.01/27.65 ( (product @ multiplicative_identity @ additive_identity @
% 187.01/27.65 (multiplicative_inverse @ a))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl230795, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl877, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 (~ (defined @ X0)
% 187.01/27.65 | ~ (defined @ X1)
% 187.01/27.65 | (sum @ additive_identity @ X1 @ additive_identity)
% 187.01/27.65 | (product @ (multiplicative_inverse @ X1) @ X2 @ X0)
% 187.01/27.65 | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl56])).
% 187.01/27.65 thf(zip_derived_cl231103, plain,
% 187.01/27.65 ((~ (defined @ additive_identity)
% 187.01/27.65 | ~ (defined @ multiplicative_identity)
% 187.01/27.65 | (sum @ additive_identity @ multiplicative_identity @
% 187.01/27.65 additive_identity)
% 187.01/27.65 | (product @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 (multiplicative_inverse @ a) @ additive_identity))),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl230801, zip_derived_cl877])).
% 187.01/27.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 187.01/27.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 187.01/27.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 187.01/27.65 inference('cnf', [status(esa)],
% 187.01/27.65 [well_definedness_of_multiplicative_identity])).
% 187.01/27.65 thf(zip_derived_cl106093, plain,
% 187.01/27.65 (~ (sum @ additive_identity @ multiplicative_identity @ additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl106046, zip_derived_cl13])).
% 187.01/27.65 thf(zip_derived_cl231158, plain,
% 187.01/27.65 ( (product @ (multiplicative_inverse @ multiplicative_identity) @
% 187.01/27.65 (multiplicative_inverse @ a) @ additive_identity)),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl231103, zip_derived_cl13, zip_derived_cl16,
% 187.01/27.65 zip_derived_cl106093])).
% 187.01/27.65 thf(zip_derived_cl9, plain,
% 187.01/27.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 187.01/27.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 187.01/27.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 187.01/27.65 thf(zip_derived_cl231293, plain,
% 187.01/27.65 ( (product @ (multiplicative_inverse @ a) @
% 187.01/27.65 (multiplicative_inverse @ multiplicative_identity) @ additive_identity)),
% 187.01/27.65 inference('s_sup-', [status(thm)],
% 187.01/27.65 [zip_derived_cl231158, zip_derived_cl9])).
% 187.01/27.65 thf(zip_derived_cl231445, plain, ($false),
% 187.01/27.65 inference('demod', [status(thm)],
% 187.01/27.65 [zip_derived_cl147757, zip_derived_cl231293])).
% 187.01/27.65
% 187.01/27.65 % SZS output end Refutation
% 187.01/27.65
% 187.01/27.65
% 187.01/27.65 % Terminating...
% 187.71/27.71 % Runner terminated.
% 187.71/27.72 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------