TSTP Solution File: FLD041-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD041-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.vVsouZrSki true
% Computer : n005.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 22:39:23 EDT 2023
% Result : Unsatisfiable 132.07s 20.02s
% Output : Refutation 132.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : FLD041-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.vVsouZrSki true
% 0.13/0.36 % Computer : n005.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Aug 28 00:15:23 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.20/0.59 % Total configuration time : 435
% 0.20/0.59 % Estimated wc time : 1092
% 0.20/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 132.07/20.02 % Solved by fo/fo5.sh.
% 132.07/20.02 % done 18452 iterations in 19.236s
% 132.07/20.02 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 132.07/20.02 % SZS output start Refutation
% 132.07/20.02 thf(sum_type, type, sum: $i > $i > $i > $o).
% 132.07/20.02 thf(b_type, type, b: $i).
% 132.07/20.02 thf(a_type, type, a: $i).
% 132.07/20.02 thf(product_type, type, product: $i > $i > $i > $o).
% 132.07/20.02 thf(additive_identity_type, type, additive_identity: $i).
% 132.07/20.02 thf(multiply_type, type, multiply: $i > $i > $i).
% 132.07/20.02 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 132.07/20.02 thf(c_type, type, c: $i).
% 132.07/20.02 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 132.07/20.02 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 132.07/20.02 thf(defined_type, type, defined: $i > $o).
% 132.07/20.02 thf(different_identities, axiom,
% 132.07/20.02 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 132.07/20.02 thf(zip_derived_cl25, plain,
% 132.07/20.02 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [different_identities])).
% 132.07/20.02 thf(totality_of_multiplication, axiom,
% 132.07/20.02 (( product @ X @ Y @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 132.07/20.02 ( ~( defined @ Y ) ))).
% 132.07/20.02 thf(zip_derived_cl19, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 132.07/20.02 | ~ (defined @ X0)
% 132.07/20.02 | ~ (defined @ X1))),
% 132.07/20.02 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 132.07/20.02 thf(well_definedness_of_multiplication, axiom,
% 132.07/20.02 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 132.07/20.02 ( ~( defined @ Y ) ))).
% 132.07/20.02 thf(zip_derived_cl15, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i]:
% 132.07/20.02 ( (defined @ (multiply @ X0 @ X1))
% 132.07/20.02 | ~ (defined @ X0)
% 132.07/20.02 | ~ (defined @ X1))),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 132.07/20.02 thf(zip_derived_cl19, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 132.07/20.02 | ~ (defined @ X0)
% 132.07/20.02 | ~ (defined @ X1))),
% 132.07/20.02 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 132.07/20.02 thf(existence_of_identity_addition, axiom,
% 132.07/20.02 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 132.07/20.02 thf(zip_derived_cl2, plain,
% 132.07/20.02 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 132.07/20.02 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 132.07/20.02 thf(zip_derived_cl2, plain,
% 132.07/20.02 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 132.07/20.02 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 132.07/20.02 thf(zip_derived_cl2, plain,
% 132.07/20.02 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 132.07/20.02 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 132.07/20.02 thf(associativity_addition_1, axiom,
% 132.07/20.02 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 132.07/20.02 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 132.07/20.02 thf(zip_derived_cl0, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 132.07/20.02 ( (sum @ X0 @ X1 @ X2)
% 132.07/20.02 | ~ (sum @ X0 @ X3 @ X4)
% 132.07/20.02 | ~ (sum @ X3 @ X5 @ X1)
% 132.07/20.02 | ~ (sum @ X4 @ X5 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [associativity_addition_1])).
% 132.07/20.02 thf(zip_derived_cl36, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 (~ (sum @ X0 @ X1 @ X0)
% 132.07/20.02 | ~ (sum @ X1 @ X1 @ X2)
% 132.07/20.02 | (sum @ X0 @ X2 @ X0))),
% 132.07/20.02 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 132.07/20.02 thf(zip_derived_cl45, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (defined @ additive_identity)
% 132.07/20.02 | (sum @ additive_identity @ X0 @ additive_identity)
% 132.07/20.02 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl36])).
% 132.07/20.02 thf(well_definedness_of_additive_identity, axiom,
% 132.07/20.02 (defined @ additive_identity)).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl46, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (sum @ additive_identity @ X0 @ additive_identity)
% 132.07/20.02 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl13])).
% 132.07/20.02 thf(zip_derived_cl47, plain,
% 132.07/20.02 ((~ (defined @ additive_identity)
% 132.07/20.02 | (sum @ additive_identity @ additive_identity @ additive_identity))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl46])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl49, plain,
% 132.07/20.02 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl13])).
% 132.07/20.02 thf(existence_of_identity_multiplication, axiom,
% 132.07/20.02 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 132.07/20.02 thf(zip_derived_cl7, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 132.07/20.02 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 132.07/20.02 thf(commutativity_multiplication, axiom,
% 132.07/20.02 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 132.07/20.02 thf(zip_derived_cl9, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 132.07/20.02 thf(zip_derived_cl55, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 132.07/20.02 thf(zip_derived_cl2, plain,
% 132.07/20.02 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 132.07/20.02 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 132.07/20.02 thf(commutativity_addition, axiom,
% 132.07/20.02 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 132.07/20.02 thf(zip_derived_cl4, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [commutativity_addition])).
% 132.07/20.02 thf(zip_derived_cl50, plain,
% 132.07/20.02 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 132.07/20.02 thf(distributivity_2, axiom,
% 132.07/20.02 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 132.07/20.02 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 132.07/20.02 ( ~( sum @ C @ D @ B ) ))).
% 132.07/20.02 thf(zip_derived_cl11, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2)
% 132.07/20.02 | ~ (sum @ X3 @ X4 @ X0)
% 132.07/20.02 | ~ (product @ X3 @ X1 @ X5)
% 132.07/20.02 | ~ (product @ X4 @ X1 @ X6)
% 132.07/20.02 | ~ (sum @ X5 @ X6 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [distributivity_2])).
% 132.07/20.02 thf(zip_derived_cl296, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 132.07/20.02 (~ (defined @ X0)
% 132.07/20.02 | ~ (sum @ X3 @ X2 @ X1)
% 132.07/20.02 | ~ (product @ additive_identity @ X4 @ X2)
% 132.07/20.02 | ~ (product @ X0 @ X4 @ X3)
% 132.07/20.02 | (product @ X0 @ X4 @ X1))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl11])).
% 132.07/20.02 thf(zip_derived_cl7115, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 ( (product @ additive_identity @ X1 @ X2)
% 132.07/20.02 | ~ (product @ additive_identity @ X1 @ X0)
% 132.07/20.02 | ~ (sum @ X0 @ X0 @ X2)
% 132.07/20.02 | ~ (defined @ additive_identity))),
% 132.07/20.02 inference('eq_fact', [status(thm)], [zip_derived_cl296])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl7117, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 ( (product @ additive_identity @ X1 @ X2)
% 132.07/20.02 | ~ (product @ additive_identity @ X1 @ X0)
% 132.07/20.02 | ~ (sum @ X0 @ X0 @ X2))),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl7115, zip_derived_cl13])).
% 132.07/20.02 thf(zip_derived_cl7123, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (defined @ additive_identity)
% 132.07/20.02 | ~ (sum @ additive_identity @ additive_identity @ X0)
% 132.07/20.02 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl7117])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl7127, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (sum @ additive_identity @ additive_identity @ X0)
% 132.07/20.02 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl7123, zip_derived_cl13])).
% 132.07/20.02 thf(zip_derived_cl7136, plain,
% 132.07/20.02 ( (product @ additive_identity @ multiplicative_identity @
% 132.07/20.02 additive_identity)),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl7127])).
% 132.07/20.02 thf(zip_derived_cl9, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 132.07/20.02 thf(zip_derived_cl7153, plain,
% 132.07/20.02 ( (product @ multiplicative_identity @ additive_identity @
% 132.07/20.02 additive_identity)),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7136, zip_derived_cl9])).
% 132.07/20.02 thf(distributivity_1, axiom,
% 132.07/20.02 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 132.07/20.02 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 132.07/20.02 ( ~( product @ Y @ Z @ D ) ))).
% 132.07/20.02 thf(zip_derived_cl10, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 132.07/20.02 ( (sum @ X0 @ X1 @ X2)
% 132.07/20.02 | ~ (sum @ X3 @ X4 @ X5)
% 132.07/20.02 | ~ (product @ X5 @ X6 @ X2)
% 132.07/20.02 | ~ (product @ X3 @ X6 @ X0)
% 132.07/20.02 | ~ (product @ X4 @ X6 @ X1))),
% 132.07/20.02 inference('cnf', [status(esa)], [distributivity_1])).
% 132.07/20.02 thf(zip_derived_cl253, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 132.07/20.02 (~ (product @ X2 @ X1 @ X0)
% 132.07/20.02 | ~ (product @ X4 @ X1 @ X3)
% 132.07/20.02 | ~ (sum @ X4 @ X2 @ X2)
% 132.07/20.02 | (sum @ X3 @ X0 @ X0))),
% 132.07/20.02 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 132.07/20.02 thf(zip_derived_cl7172, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i]:
% 132.07/20.02 ( (sum @ X0 @ additive_identity @ additive_identity)
% 132.07/20.02 | ~ (sum @ X1 @ multiplicative_identity @ multiplicative_identity)
% 132.07/20.02 | ~ (product @ X1 @ additive_identity @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7153, zip_derived_cl253])).
% 132.07/20.02 thf(zip_derived_cl8173, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (defined @ multiplicative_identity)
% 132.07/20.02 | ~ (product @ additive_identity @ additive_identity @ X0)
% 132.07/20.02 | (sum @ X0 @ additive_identity @ additive_identity))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl7172])).
% 132.07/20.02 thf(well_definedness_of_multiplicative_identity, axiom,
% 132.07/20.02 (defined @ multiplicative_identity)).
% 132.07/20.02 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 132.07/20.02 inference('cnf', [status(esa)],
% 132.07/20.02 [well_definedness_of_multiplicative_identity])).
% 132.07/20.02 thf(zip_derived_cl8175, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (product @ additive_identity @ additive_identity @ X0)
% 132.07/20.02 | (sum @ X0 @ additive_identity @ additive_identity))),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl8173, zip_derived_cl16])).
% 132.07/20.02 thf(zip_derived_cl8177, plain,
% 132.07/20.02 ((~ (defined @ additive_identity)
% 132.07/20.02 | ~ (defined @ additive_identity)
% 132.07/20.02 | (sum @ (multiply @ additive_identity @ additive_identity) @
% 132.07/20.02 additive_identity @ additive_identity))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl8175])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl8178, plain,
% 132.07/20.02 ( (sum @ (multiply @ additive_identity @ additive_identity) @
% 132.07/20.02 additive_identity @ additive_identity)),
% 132.07/20.02 inference('demod', [status(thm)],
% 132.07/20.02 [zip_derived_cl8177, zip_derived_cl13, zip_derived_cl13])).
% 132.07/20.02 thf(zip_derived_cl50, plain,
% 132.07/20.02 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 132.07/20.02 thf(zip_derived_cl2, plain,
% 132.07/20.02 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 132.07/20.02 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 132.07/20.02 thf(zip_derived_cl0, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 132.07/20.02 ( (sum @ X0 @ X1 @ X2)
% 132.07/20.02 | ~ (sum @ X0 @ X3 @ X4)
% 132.07/20.02 | ~ (sum @ X3 @ X5 @ X1)
% 132.07/20.02 | ~ (sum @ X4 @ X5 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [associativity_addition_1])).
% 132.07/20.02 thf(zip_derived_cl44, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 132.07/20.02 (~ (defined @ X0)
% 132.07/20.02 | ~ (sum @ X0 @ X2 @ X1)
% 132.07/20.02 | ~ (sum @ X0 @ X2 @ X3)
% 132.07/20.02 | (sum @ additive_identity @ X3 @ X1))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 132.07/20.02 thf(zip_derived_cl785, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i]:
% 132.07/20.02 (~ (defined @ X0)
% 132.07/20.02 | (sum @ additive_identity @ X1 @ X0)
% 132.07/20.02 | ~ (sum @ X0 @ additive_identity @ X1)
% 132.07/20.02 | ~ (defined @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl44])).
% 132.07/20.02 thf(zip_derived_cl819, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i]:
% 132.07/20.02 (~ (sum @ X0 @ additive_identity @ X1)
% 132.07/20.02 | (sum @ additive_identity @ X1 @ X0)
% 132.07/20.02 | ~ (defined @ X0))),
% 132.07/20.02 inference('simplify', [status(thm)], [zip_derived_cl785])).
% 132.07/20.02 thf(zip_derived_cl8194, plain,
% 132.07/20.02 ((~ (defined @ (multiply @ additive_identity @ additive_identity))
% 132.07/20.02 | (sum @ additive_identity @ additive_identity @
% 132.07/20.02 (multiply @ additive_identity @ additive_identity)))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl8178, zip_derived_cl819])).
% 132.07/20.02 thf(zip_derived_cl8423, plain,
% 132.07/20.02 ((~ (defined @ additive_identity)
% 132.07/20.02 | ~ (defined @ additive_identity)
% 132.07/20.02 | (sum @ additive_identity @ additive_identity @
% 132.07/20.02 (multiply @ additive_identity @ additive_identity)))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl8194])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl8424, plain,
% 132.07/20.02 ( (sum @ additive_identity @ additive_identity @
% 132.07/20.02 (multiply @ additive_identity @ additive_identity))),
% 132.07/20.02 inference('demod', [status(thm)],
% 132.07/20.02 [zip_derived_cl8423, zip_derived_cl13, zip_derived_cl13])).
% 132.07/20.02 thf(zip_derived_cl7127, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (sum @ additive_identity @ additive_identity @ X0)
% 132.07/20.02 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl7123, zip_derived_cl13])).
% 132.07/20.02 thf(zip_derived_cl8543, plain,
% 132.07/20.02 ( (product @ additive_identity @ multiplicative_identity @
% 132.07/20.02 (multiply @ additive_identity @ additive_identity))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl8424, zip_derived_cl7127])).
% 132.07/20.02 thf(zip_derived_cl7136, plain,
% 132.07/20.02 ( (product @ additive_identity @ multiplicative_identity @
% 132.07/20.02 additive_identity)),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl7127])).
% 132.07/20.02 thf(zip_derived_cl7, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 132.07/20.02 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 132.07/20.02 thf(associativity_multiplication_1, axiom,
% 132.07/20.02 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 132.07/20.02 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 132.07/20.02 thf(zip_derived_cl5, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2)
% 132.07/20.02 | ~ (product @ X0 @ X3 @ X4)
% 132.07/20.02 | ~ (product @ X3 @ X5 @ X1)
% 132.07/20.02 | ~ (product @ X4 @ X5 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 132.07/20.02 thf(zip_derived_cl102, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 132.07/20.02 (~ (defined @ X0)
% 132.07/20.02 | ~ (product @ X0 @ X2 @ X1)
% 132.07/20.02 | ~ (product @ X0 @ X2 @ X3)
% 132.07/20.02 | (product @ multiplicative_identity @ X3 @ X1))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 132.07/20.02 thf(zip_derived_cl7158, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 132.07/20.02 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 132.07/20.02 | ~ (defined @ additive_identity))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7136, zip_derived_cl102])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl7166, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 132.07/20.02 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl7158, zip_derived_cl13])).
% 132.07/20.02 thf(zip_derived_cl9032, plain,
% 132.07/20.02 ( (product @ multiplicative_identity @
% 132.07/20.02 (multiply @ additive_identity @ additive_identity) @ additive_identity)),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl8543, zip_derived_cl7166])).
% 132.07/20.02 thf(zip_derived_cl7153, plain,
% 132.07/20.02 ( (product @ multiplicative_identity @ additive_identity @
% 132.07/20.02 additive_identity)),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7136, zip_derived_cl9])).
% 132.07/20.02 thf(associativity_multiplication_2, axiom,
% 132.07/20.02 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 132.07/20.02 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 132.07/20.02 thf(zip_derived_cl6, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2)
% 132.07/20.02 | ~ (product @ X3 @ X4 @ X0)
% 132.07/20.02 | ~ (product @ X4 @ X1 @ X5)
% 132.07/20.02 | ~ (product @ X3 @ X5 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 132.07/20.02 thf(zip_derived_cl7168, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 (~ (product @ multiplicative_identity @ X1 @ X0)
% 132.07/20.02 | ~ (product @ additive_identity @ X2 @ X1)
% 132.07/20.02 | (product @ additive_identity @ X2 @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7153, zip_derived_cl6])).
% 132.07/20.02 thf(zip_derived_cl11166, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (product @ additive_identity @ X0 @ additive_identity)
% 132.07/20.02 | ~ (product @ additive_identity @ X0 @
% 132.07/20.02 (multiply @ additive_identity @ additive_identity)))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl9032, zip_derived_cl7168])).
% 132.07/20.02 thf(zip_derived_cl11508, plain,
% 132.07/20.02 ((~ (defined @ additive_identity)
% 132.07/20.02 | ~ (defined @ additive_identity)
% 132.07/20.02 | (product @ additive_identity @ additive_identity @ additive_identity))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl11166])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 132.07/20.02 thf(zip_derived_cl11510, plain,
% 132.07/20.02 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 132.07/20.02 inference('demod', [status(thm)],
% 132.07/20.02 [zip_derived_cl11508, zip_derived_cl13, zip_derived_cl13])).
% 132.07/20.02 thf(sum_7, conjecture,
% 132.07/20.02 (~( sum @ additive_identity @ c @ additive_identity ))).
% 132.07/20.02 thf(zf_stmt_0, negated_conjecture,
% 132.07/20.02 (sum @ additive_identity @ c @ additive_identity),
% 132.07/20.02 inference('cnf.neg', [status(esa)], [sum_7])).
% 132.07/20.02 thf(zip_derived_cl32, plain,
% 132.07/20.02 ( (sum @ additive_identity @ c @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 132.07/20.02 thf(zip_derived_cl2, plain,
% 132.07/20.02 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 132.07/20.02 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 132.07/20.02 thf(zip_derived_cl49, plain,
% 132.07/20.02 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl13])).
% 132.07/20.02 thf(zip_derived_cl0, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 132.07/20.02 ( (sum @ X0 @ X1 @ X2)
% 132.07/20.02 | ~ (sum @ X0 @ X3 @ X4)
% 132.07/20.02 | ~ (sum @ X3 @ X5 @ X1)
% 132.07/20.02 | ~ (sum @ X4 @ X5 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [associativity_addition_1])).
% 132.07/20.02 thf(zip_derived_cl59, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 (~ (sum @ additive_identity @ X1 @ X0)
% 132.07/20.02 | ~ (sum @ additive_identity @ X1 @ X2)
% 132.07/20.02 | (sum @ additive_identity @ X2 @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl0])).
% 132.07/20.02 thf(zip_derived_cl115, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i]:
% 132.07/20.02 (~ (defined @ X0)
% 132.07/20.02 | (sum @ additive_identity @ X1 @ X0)
% 132.07/20.02 | ~ (sum @ additive_identity @ X0 @ X1))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl59])).
% 132.07/20.02 thf(zip_derived_cl211, plain,
% 132.07/20.02 (( (sum @ additive_identity @ additive_identity @ c) | ~ (defined @ c))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl115])).
% 132.07/20.02 thf(c_is_defined, axiom, (defined @ c)).
% 132.07/20.02 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 132.07/20.02 inference('cnf', [status(esa)], [c_is_defined])).
% 132.07/20.02 thf(zip_derived_cl220, plain,
% 132.07/20.02 ( (sum @ additive_identity @ additive_identity @ c)),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl211, zip_derived_cl28])).
% 132.07/20.02 thf(zip_derived_cl7127, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (sum @ additive_identity @ additive_identity @ X0)
% 132.07/20.02 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl7123, zip_derived_cl13])).
% 132.07/20.02 thf(zip_derived_cl7145, plain,
% 132.07/20.02 ( (product @ additive_identity @ multiplicative_identity @ c)),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl220, zip_derived_cl7127])).
% 132.07/20.02 thf(zip_derived_cl9, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 132.07/20.02 thf(zip_derived_cl7185, plain,
% 132.07/20.02 ( (product @ multiplicative_identity @ additive_identity @ c)),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7145, zip_derived_cl9])).
% 132.07/20.02 thf(zip_derived_cl6, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2)
% 132.07/20.02 | ~ (product @ X3 @ X4 @ X0)
% 132.07/20.02 | ~ (product @ X4 @ X1 @ X5)
% 132.07/20.02 | ~ (product @ X3 @ X5 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 132.07/20.02 thf(zip_derived_cl153, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 132.07/20.02 (~ (product @ X2 @ X1 @ X0)
% 132.07/20.02 | ~ (product @ X1 @ X3 @ X1)
% 132.07/20.02 | (product @ X0 @ X3 @ X0))),
% 132.07/20.02 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 132.07/20.02 thf(zip_derived_cl7203, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (product @ c @ X0 @ c)
% 132.07/20.02 | ~ (product @ additive_identity @ X0 @ additive_identity))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7185, zip_derived_cl153])).
% 132.07/20.02 thf(zip_derived_cl11537, plain, ( (product @ c @ additive_identity @ c)),
% 132.07/20.02 inference('sup-', [status(thm)],
% 132.07/20.02 [zip_derived_cl11510, zip_derived_cl7203])).
% 132.07/20.02 thf(existence_of_inverse_multiplication, axiom,
% 132.07/20.02 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 132.07/20.02 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 132.07/20.02 thf(zip_derived_cl8, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 132.07/20.02 multiplicative_identity)
% 132.07/20.02 | (sum @ additive_identity @ X0 @ additive_identity)
% 132.07/20.02 | ~ (defined @ X0))),
% 132.07/20.02 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 132.07/20.02 thf(zip_derived_cl9, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 132.07/20.02 thf(zip_derived_cl194, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (defined @ X0)
% 132.07/20.02 | (sum @ additive_identity @ X0 @ additive_identity)
% 132.07/20.02 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 132.07/20.02 multiplicative_identity))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 132.07/20.02 thf(zip_derived_cl55, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 132.07/20.02 thf(product_6, conjecture, (~( product @ a @ b @ c ))).
% 132.07/20.02 thf(zf_stmt_1, negated_conjecture, (product @ a @ b @ c),
% 132.07/20.02 inference('cnf.neg', [status(esa)], [product_6])).
% 132.07/20.02 thf(zip_derived_cl31, plain, ( (product @ a @ b @ c)),
% 132.07/20.02 inference('cnf', [status(esa)], [zf_stmt_1])).
% 132.07/20.02 thf(zip_derived_cl6, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2)
% 132.07/20.02 | ~ (product @ X3 @ X4 @ X0)
% 132.07/20.02 | ~ (product @ X4 @ X1 @ X5)
% 132.07/20.02 | ~ (product @ X3 @ X5 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 132.07/20.02 thf(zip_derived_cl149, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 (~ (product @ a @ X1 @ X0)
% 132.07/20.02 | ~ (product @ b @ X2 @ X1)
% 132.07/20.02 | (product @ c @ X2 @ X0))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl6])).
% 132.07/20.02 thf(zip_derived_cl2663, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 (~ (defined @ a)
% 132.07/20.02 | (product @ c @ X0 @ a)
% 132.07/20.02 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl149])).
% 132.07/20.02 thf(a_is_defined, axiom, (defined @ a)).
% 132.07/20.02 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 132.07/20.02 inference('cnf', [status(esa)], [a_is_defined])).
% 132.07/20.02 thf(zip_derived_cl2666, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (product @ c @ X0 @ a)
% 132.07/20.02 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 132.07/20.02 inference('demod', [status(thm)], [zip_derived_cl2663, zip_derived_cl26])).
% 132.07/20.02 thf(zip_derived_cl4499, plain,
% 132.07/20.02 (( (sum @ additive_identity @ b @ additive_identity)
% 132.07/20.02 | ~ (defined @ b)
% 132.07/20.02 | (product @ c @ (multiplicative_inverse @ b) @ a))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl2666])).
% 132.07/20.02 thf(not_sum_5, conjecture, (sum @ additive_identity @ b @ additive_identity)).
% 132.07/20.02 thf(zf_stmt_2, negated_conjecture,
% 132.07/20.02 (~( sum @ additive_identity @ b @ additive_identity )),
% 132.07/20.02 inference('cnf.neg', [status(esa)], [not_sum_5])).
% 132.07/20.02 thf(zip_derived_cl30, plain,
% 132.07/20.02 (~ (sum @ additive_identity @ b @ additive_identity)),
% 132.07/20.02 inference('cnf', [status(esa)], [zf_stmt_2])).
% 132.07/20.02 thf(b_is_defined, axiom, (defined @ b)).
% 132.07/20.02 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 132.07/20.02 inference('cnf', [status(esa)], [b_is_defined])).
% 132.07/20.02 thf(zip_derived_cl4500, plain,
% 132.07/20.02 ( (product @ c @ (multiplicative_inverse @ b) @ a)),
% 132.07/20.02 inference('demod', [status(thm)],
% 132.07/20.02 [zip_derived_cl4499, zip_derived_cl30, zip_derived_cl27])).
% 132.07/20.02 thf(zip_derived_cl9, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.02 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 132.07/20.02 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 132.07/20.02 thf(zip_derived_cl4503, plain,
% 132.07/20.02 ( (product @ (multiplicative_inverse @ b) @ c @ a)),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl4500, zip_derived_cl9])).
% 132.07/20.02 thf(zip_derived_cl153, plain,
% 132.07/20.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 132.07/20.02 (~ (product @ X2 @ X1 @ X0)
% 132.07/20.02 | ~ (product @ X1 @ X3 @ X1)
% 132.07/20.02 | (product @ X0 @ X3 @ X0))),
% 132.07/20.02 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 132.07/20.02 thf(zip_derived_cl4514, plain,
% 132.07/20.02 (![X0 : $i]: ( (product @ a @ X0 @ a) | ~ (product @ c @ X0 @ c))),
% 132.07/20.02 inference('sup-', [status(thm)], [zip_derived_cl4503, zip_derived_cl153])).
% 132.07/20.02 thf(zip_derived_cl11561, plain, ( (product @ a @ additive_identity @ a)),
% 132.07/20.02 inference('sup-', [status(thm)],
% 132.07/20.02 [zip_derived_cl11537, zip_derived_cl4514])).
% 132.07/20.02 thf(zip_derived_cl8, plain,
% 132.07/20.02 (![X0 : $i]:
% 132.07/20.02 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 132.07/20.02 multiplicative_identity)
% 132.07/20.02 | (sum @ additive_identity @ X0 @ additive_identity)
% 132.07/20.03 | ~ (defined @ X0))),
% 132.07/20.03 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 132.07/20.03 thf(zip_derived_cl153, plain,
% 132.07/20.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 132.07/20.03 (~ (product @ X2 @ X1 @ X0)
% 132.07/20.03 | ~ (product @ X1 @ X3 @ X1)
% 132.07/20.03 | (product @ X0 @ X3 @ X0))),
% 132.07/20.03 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 132.07/20.03 thf(zip_derived_cl2806, plain,
% 132.07/20.03 (![X0 : $i, X1 : $i]:
% 132.07/20.03 (~ (defined @ X0)
% 132.07/20.03 | (sum @ additive_identity @ X0 @ additive_identity)
% 132.07/20.03 | (product @ multiplicative_identity @ X1 @ multiplicative_identity)
% 132.07/20.03 | ~ (product @ X0 @ X1 @ X0))),
% 132.07/20.03 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl153])).
% 132.07/20.03 thf(zip_derived_cl133214, plain,
% 132.07/20.03 (( (product @ multiplicative_identity @ additive_identity @
% 132.07/20.03 multiplicative_identity)
% 132.07/20.03 | (sum @ additive_identity @ a @ additive_identity)
% 132.07/20.03 | ~ (defined @ a))),
% 132.07/20.03 inference('sup-', [status(thm)],
% 132.07/20.03 [zip_derived_cl11561, zip_derived_cl2806])).
% 132.07/20.03 thf(not_sum_4, conjecture, (sum @ additive_identity @ a @ additive_identity)).
% 132.07/20.03 thf(zf_stmt_3, negated_conjecture,
% 132.07/20.03 (~( sum @ additive_identity @ a @ additive_identity )),
% 132.07/20.03 inference('cnf.neg', [status(esa)], [not_sum_4])).
% 132.07/20.03 thf(zip_derived_cl29, plain,
% 132.07/20.03 (~ (sum @ additive_identity @ a @ additive_identity)),
% 132.07/20.03 inference('cnf', [status(esa)], [zf_stmt_3])).
% 132.07/20.03 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 132.07/20.03 inference('cnf', [status(esa)], [a_is_defined])).
% 132.07/20.03 thf(zip_derived_cl133317, plain,
% 132.07/20.03 ( (product @ multiplicative_identity @ additive_identity @
% 132.07/20.03 multiplicative_identity)),
% 132.07/20.03 inference('demod', [status(thm)],
% 132.07/20.03 [zip_derived_cl133214, zip_derived_cl29, zip_derived_cl26])).
% 132.07/20.03 thf(zip_derived_cl9, plain,
% 132.07/20.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.03 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 132.07/20.03 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 132.07/20.03 thf(zip_derived_cl133382, plain,
% 132.07/20.03 ( (product @ additive_identity @ multiplicative_identity @
% 132.07/20.03 multiplicative_identity)),
% 132.07/20.03 inference('sup-', [status(thm)], [zip_derived_cl133317, zip_derived_cl9])).
% 132.07/20.03 thf(zip_derived_cl49, plain,
% 132.07/20.03 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 132.07/20.03 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl13])).
% 132.07/20.03 thf(zip_derived_cl7136, plain,
% 132.07/20.03 ( (product @ additive_identity @ multiplicative_identity @
% 132.07/20.03 additive_identity)),
% 132.07/20.03 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl7127])).
% 132.07/20.03 thf(zip_derived_cl253, plain,
% 132.07/20.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 132.07/20.03 (~ (product @ X2 @ X1 @ X0)
% 132.07/20.03 | ~ (product @ X4 @ X1 @ X3)
% 132.07/20.03 | ~ (sum @ X4 @ X2 @ X2)
% 132.07/20.03 | (sum @ X3 @ X0 @ X0))),
% 132.07/20.03 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 132.07/20.03 thf(zip_derived_cl7156, plain,
% 132.07/20.03 (![X0 : $i, X1 : $i]:
% 132.07/20.03 ( (sum @ X0 @ additive_identity @ additive_identity)
% 132.07/20.03 | ~ (sum @ X1 @ additive_identity @ additive_identity)
% 132.07/20.03 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 132.07/20.03 inference('sup-', [status(thm)], [zip_derived_cl7136, zip_derived_cl253])).
% 132.07/20.03 thf(zip_derived_cl7391, plain,
% 132.07/20.03 (![X0 : $i]:
% 132.07/20.03 (~ (product @ additive_identity @ multiplicative_identity @ X0)
% 132.07/20.03 | (sum @ X0 @ additive_identity @ additive_identity))),
% 132.07/20.03 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl7156])).
% 132.07/20.03 thf(zip_derived_cl133546, plain,
% 132.07/20.03 ( (sum @ multiplicative_identity @ additive_identity @ additive_identity)),
% 132.07/20.03 inference('sup-', [status(thm)],
% 132.07/20.03 [zip_derived_cl133382, zip_derived_cl7391])).
% 132.07/20.03 thf(totality_of_order_relation, axiom,
% 132.07/20.03 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 132.07/20.03 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 132.07/20.03 thf(zip_derived_cl22, plain,
% 132.07/20.03 (![X0 : $i, X1 : $i]:
% 132.07/20.03 ( (less_or_equal @ X0 @ X1)
% 132.07/20.03 | (less_or_equal @ X1 @ X0)
% 132.07/20.03 | ~ (defined @ X0)
% 132.07/20.03 | ~ (defined @ X1))),
% 132.07/20.03 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 132.07/20.03 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 132.07/20.03 inference('cnf', [status(esa)],
% 132.07/20.03 [well_definedness_of_multiplicative_identity])).
% 132.07/20.03 thf(zip_derived_cl554, plain,
% 132.07/20.03 (![X0 : $i]:
% 132.07/20.03 (~ (defined @ X0)
% 132.07/20.03 | (less_or_equal @ X0 @ multiplicative_identity)
% 132.07/20.03 | (less_or_equal @ multiplicative_identity @ X0))),
% 132.07/20.03 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl16])).
% 132.07/20.03 thf(zip_derived_cl16183, plain,
% 132.07/20.03 (( (less_or_equal @ multiplicative_identity @ multiplicative_identity)
% 132.07/20.03 | ~ (defined @ multiplicative_identity))),
% 132.07/20.03 inference('eq_fact', [status(thm)], [zip_derived_cl554])).
% 132.07/20.03 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 132.07/20.03 inference('cnf', [status(esa)],
% 132.07/20.03 [well_definedness_of_multiplicative_identity])).
% 132.07/20.03 thf(zip_derived_cl16184, plain,
% 132.07/20.03 ( (less_or_equal @ multiplicative_identity @ multiplicative_identity)),
% 132.07/20.03 inference('demod', [status(thm)], [zip_derived_cl16183, zip_derived_cl16])).
% 132.07/20.03 thf(antisymmetry_of_order_relation, axiom,
% 132.07/20.03 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 132.07/20.03 ( ~( less_or_equal @ Y @ X ) ))).
% 132.07/20.03 thf(zip_derived_cl20, plain,
% 132.07/20.03 (![X0 : $i, X1 : $i]:
% 132.07/20.03 ( (sum @ additive_identity @ X0 @ X1)
% 132.07/20.03 | ~ (less_or_equal @ X0 @ X1)
% 132.07/20.03 | ~ (less_or_equal @ X1 @ X0))),
% 132.07/20.03 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 132.07/20.03 thf(zip_derived_cl16190, plain,
% 132.07/20.03 ((~ (less_or_equal @ multiplicative_identity @ multiplicative_identity)
% 132.07/20.03 | (sum @ additive_identity @ multiplicative_identity @
% 132.07/20.03 multiplicative_identity))),
% 132.07/20.03 inference('sup-', [status(thm)], [zip_derived_cl16184, zip_derived_cl20])).
% 132.07/20.03 thf(zip_derived_cl16184, plain,
% 132.07/20.03 ( (less_or_equal @ multiplicative_identity @ multiplicative_identity)),
% 132.07/20.03 inference('demod', [status(thm)], [zip_derived_cl16183, zip_derived_cl16])).
% 132.07/20.03 thf(zip_derived_cl16193, plain,
% 132.07/20.03 ( (sum @ additive_identity @ multiplicative_identity @
% 132.07/20.03 multiplicative_identity)),
% 132.07/20.03 inference('demod', [status(thm)],
% 132.07/20.03 [zip_derived_cl16190, zip_derived_cl16184])).
% 132.07/20.03 thf(zip_derived_cl4, plain,
% 132.07/20.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 132.07/20.03 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 132.07/20.03 inference('cnf', [status(esa)], [commutativity_addition])).
% 132.07/20.03 thf(zip_derived_cl16198, plain,
% 132.07/20.03 ( (sum @ multiplicative_identity @ additive_identity @
% 132.07/20.03 multiplicative_identity)),
% 132.07/20.03 inference('sup-', [status(thm)], [zip_derived_cl16193, zip_derived_cl4])).
% 132.07/20.03 thf(zip_derived_cl44, plain,
% 132.07/20.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 132.07/20.03 (~ (defined @ X0)
% 132.07/20.03 | ~ (sum @ X0 @ X2 @ X1)
% 132.07/20.03 | ~ (sum @ X0 @ X2 @ X3)
% 132.07/20.03 | (sum @ additive_identity @ X3 @ X1))),
% 132.07/20.03 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 132.07/20.03 thf(zip_derived_cl16267, plain,
% 132.07/20.03 (![X0 : $i]:
% 132.07/20.03 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 132.07/20.03 | ~ (sum @ multiplicative_identity @ additive_identity @ X0)
% 132.07/20.03 | ~ (defined @ multiplicative_identity))),
% 132.07/20.03 inference('sup-', [status(thm)], [zip_derived_cl16198, zip_derived_cl44])).
% 132.07/20.03 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 132.07/20.03 inference('cnf', [status(esa)],
% 132.07/20.03 [well_definedness_of_multiplicative_identity])).
% 132.07/20.03 thf(zip_derived_cl16278, plain,
% 132.07/20.03 (![X0 : $i]:
% 132.07/20.03 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 132.07/20.03 | ~ (sum @ multiplicative_identity @ additive_identity @ X0))),
% 132.07/20.03 inference('demod', [status(thm)], [zip_derived_cl16267, zip_derived_cl16])).
% 132.07/20.03 thf(zip_derived_cl133731, plain,
% 132.07/20.03 ( (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 132.07/20.03 inference('sup-', [status(thm)],
% 132.07/20.03 [zip_derived_cl133546, zip_derived_cl16278])).
% 132.07/20.03 thf(zip_derived_cl134372, plain, ($false),
% 132.07/20.03 inference('demod', [status(thm)],
% 132.07/20.03 [zip_derived_cl25, zip_derived_cl133731])).
% 132.07/20.03
% 132.07/20.03 % SZS output end Refutation
% 132.07/20.03
% 132.07/20.03
% 132.07/20.03 % Terminating...
% 132.66/20.12 % Runner terminated.
% 132.66/20.14 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------