TSTP Solution File: FLD038-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD038-1 : 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.t7sQBtu6WE true
% Computer : n032.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 22:39:21 EDT 2023
% Result : Unsatisfiable 42.71s 6.92s
% Output : Refutation 42.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD038-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.t7sQBtu6WE true
% 0.12/0.33 % Computer : n032.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 00:31:00 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in FO mode
% 0.19/0.59 % Total configuration time : 435
% 0.19/0.59 % Estimated wc time : 1092
% 0.19/0.59 % 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/fo13.sh running for 50s
% 0.19/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.19/0.71 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.19/0.72 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.19/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.19/0.73 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 42.71/6.92 % Solved by fo/fo5.sh.
% 42.71/6.92 % done 6345 iterations in 6.161s
% 42.71/6.92 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 42.71/6.92 % SZS output start Refutation
% 42.71/6.92 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 42.71/6.92 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 42.71/6.92 thf(defined_type, type, defined: $i > $o).
% 42.71/6.92 thf(additive_identity_type, type, additive_identity: $i).
% 42.71/6.92 thf(multiply_type, type, multiply: $i > $i > $i).
% 42.71/6.92 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 42.71/6.92 thf(b_type, type, b: $i).
% 42.71/6.92 thf(equalish_type, type, equalish: $i > $i > $o).
% 42.71/6.92 thf(a_type, type, a: $i).
% 42.71/6.92 thf(a_not_equal_to_b_5, conjecture, (equalish @ a @ b)).
% 42.71/6.92 thf(zf_stmt_0, negated_conjecture, (~( equalish @ a @ b )),
% 42.71/6.92 inference('cnf.neg', [status(esa)], [a_not_equal_to_b_5])).
% 42.71/6.92 thf(zip_derived_cl31, plain, (~ (equalish @ a @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [zf_stmt_0])).
% 42.71/6.92 thf(existence_of_inverse_multiplication, axiom,
% 42.71/6.92 (( equalish @
% 42.71/6.92 ( multiply @ X @ ( multiplicative_inverse @ X ) ) @
% 42.71/6.92 multiplicative_identity ) |
% 42.71/6.92 ( ~( defined @ X ) ) | ( equalish @ X @ additive_identity ))).
% 42.71/6.92 thf(zip_derived_cl6, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ (multiplicative_inverse @ X0)) @
% 42.71/6.92 multiplicative_identity)
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | (equalish @ X0 @ additive_identity))),
% 42.71/6.92 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 42.71/6.92 thf(compatibility_of_equality_and_multiplication, axiom,
% 42.71/6.92 (( equalish @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) |
% 42.71/6.92 ( ~( defined @ Z ) ) | ( ~( equalish @ X @ Y ) ))).
% 42.71/6.92 thf(zip_derived_cl24, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1))
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2))),
% 42.71/6.92 inference('cnf', [status(esa)],
% 42.71/6.92 [compatibility_of_equality_and_multiplication])).
% 42.71/6.92 thf(zip_derived_cl815, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ additive_identity)
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | (equalish @
% 42.71/6.92 (multiply @ (multiply @ X0 @ (multiplicative_inverse @ X0)) @ X1) @
% 42.71/6.92 (multiply @ multiplicative_identity @ X1)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl24])).
% 42.71/6.92 thf(commutativity_multiplication, axiom,
% 42.71/6.92 (( equalish @ ( multiply @ X @ Y ) @ ( multiply @ Y @ X ) ) |
% 42.71/6.92 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 42.71/6.92 thf(zip_derived_cl7, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 42.71/6.92 thf(zip_derived_cl24, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1))
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2))),
% 42.71/6.92 inference('cnf', [status(esa)],
% 42.71/6.92 [compatibility_of_equality_and_multiplication])).
% 42.71/6.92 thf(zip_derived_cl804, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 (~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X2)
% 42.71/6.92 | (equalish @ (multiply @ (multiply @ X0 @ X1) @ X2) @
% 42.71/6.92 (multiply @ (multiply @ X1 @ X0) @ X2)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl24])).
% 42.71/6.92 thf(associativity_multiplication, axiom,
% 42.71/6.92 (( equalish @
% 42.71/6.92 ( multiply @ X @ ( multiply @ Y @ Z ) ) @
% 42.71/6.92 ( multiply @ ( multiply @ X @ Y ) @ Z ) ) |
% 42.71/6.92 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ) | ( ~( defined @ Z ) ))).
% 42.71/6.92 thf(zip_derived_cl4, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ (multiply @ X1 @ X2)) @
% 42.71/6.92 (multiply @ (multiply @ X0 @ X1) @ X2))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ X2))),
% 42.71/6.92 inference('cnf', [status(esa)], [associativity_multiplication])).
% 42.71/6.92 thf(well_definedness_of_multiplication, axiom,
% 42.71/6.92 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 42.71/6.92 ( ~( defined @ Y ) ))).
% 42.71/6.92 thf(zip_derived_cl12, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (defined @ (multiply @ X0 @ X1))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 42.71/6.92 thf(zip_derived_cl804, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 (~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X2)
% 42.71/6.92 | (equalish @ (multiply @ (multiply @ X0 @ X1) @ X2) @
% 42.71/6.92 (multiply @ (multiply @ X1 @ X0) @ X2)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl24])).
% 42.71/6.92 thf(zip_derived_cl12, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (defined @ (multiply @ X0 @ X1))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 42.71/6.92 thf(zip_derived_cl7, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 42.71/6.92 thf(multiplicative_identity_equals_multiply_4, conjecture,
% 42.71/6.92 (~( equalish @
% 42.71/6.92 multiplicative_identity @
% 42.71/6.92 ( multiply @ b @ ( multiplicative_inverse @ a ) ) ))).
% 42.71/6.92 thf(zf_stmt_1, negated_conjecture,
% 42.71/6.92 (equalish @
% 42.71/6.92 multiplicative_identity @
% 42.71/6.92 ( multiply @ b @ ( multiplicative_inverse @ a ) )),
% 42.71/6.92 inference('cnf.neg', [status(esa)],
% 42.71/6.92 [multiplicative_identity_equals_multiply_4])).
% 42.71/6.92 thf(zip_derived_cl30, plain,
% 42.71/6.92 ( (equalish @ multiplicative_identity @
% 42.71/6.92 (multiply @ b @ (multiplicative_inverse @ a)))),
% 42.71/6.92 inference('cnf', [status(esa)], [zf_stmt_1])).
% 42.71/6.92 thf(transitivity_of_equality, axiom,
% 42.71/6.92 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 42.71/6.92 ( ~( equalish @ Y @ Z ) ))).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl52, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @ (multiply @ b @ (multiplicative_inverse @ a)) @ X0)
% 42.71/6.92 | (equalish @ multiplicative_identity @ X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl257, plain,
% 42.71/6.92 ((~ (defined @ (multiplicative_inverse @ a))
% 42.71/6.92 | ~ (defined @ b)
% 42.71/6.92 | (equalish @ multiplicative_identity @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ b)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl52])).
% 42.71/6.92 thf(well_definedness_of_multiplicative_inverse, axiom,
% 42.71/6.92 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 42.71/6.92 ( equalish @ X @ additive_identity ))).
% 42.71/6.92 thf(zip_derived_cl14, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 ( (defined @ (multiplicative_inverse @ X0))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | (equalish @ X0 @ additive_identity))),
% 42.71/6.92 inference('cnf', [status(esa)],
% 42.71/6.92 [well_definedness_of_multiplicative_inverse])).
% 42.71/6.92 thf(a_not_equal_to_additive_identity_3, conjecture,
% 42.71/6.92 (equalish @ a @ additive_identity)).
% 42.71/6.92 thf(zf_stmt_2, negated_conjecture, (~( equalish @ a @ additive_identity )),
% 42.71/6.92 inference('cnf.neg', [status(esa)], [a_not_equal_to_additive_identity_3])).
% 42.71/6.92 thf(zip_derived_cl29, plain, (~ (equalish @ a @ additive_identity)),
% 42.71/6.92 inference('cnf', [status(esa)], [zf_stmt_2])).
% 42.71/6.92 thf(zip_derived_cl32, plain,
% 42.71/6.92 ((~ (defined @ a) | (defined @ (multiplicative_inverse @ a)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl29])).
% 42.71/6.92 thf(a_is_defined, axiom, (defined @ a)).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 42.71/6.92 thf(b_is_defined, axiom, (defined @ b)).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl262, plain,
% 42.71/6.92 ( (equalish @ multiplicative_identity @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ b))),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl257, zip_derived_cl33, zip_derived_cl28])).
% 42.71/6.92 thf(zip_derived_cl30, plain,
% 42.71/6.92 ( (equalish @ multiplicative_identity @
% 42.71/6.92 (multiply @ b @ (multiplicative_inverse @ a)))),
% 42.71/6.92 inference('cnf', [status(esa)], [zf_stmt_1])).
% 42.71/6.92 thf(symmetry_of_equality, axiom,
% 42.71/6.92 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl36, plain,
% 42.71/6.92 ( (equalish @ (multiply @ b @ (multiplicative_inverse @ a)) @
% 42.71/6.92 multiplicative_identity)),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl52, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @ (multiply @ b @ (multiplicative_inverse @ a)) @ X0)
% 42.71/6.92 | (equalish @ multiplicative_identity @ X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl74, plain,
% 42.71/6.92 ( (equalish @ multiplicative_identity @ multiplicative_identity)),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl52])).
% 42.71/6.92 thf(existence_of_identity_multiplication, axiom,
% 42.71/6.92 (( equalish @ ( multiply @ multiplicative_identity @ X ) @ X ) |
% 42.71/6.92 ( ~( defined @ X ) ))).
% 42.71/6.92 thf(zip_derived_cl5, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ multiplicative_identity @ X0) @ X0)
% 42.71/6.92 | ~ (defined @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl50, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | ~ (equalish @ X0 @ X1)
% 42.71/6.92 | (equalish @ (multiply @ multiplicative_identity @ X0) @ X1))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl97, plain,
% 42.71/6.92 (( (equalish @
% 42.71/6.92 (multiply @ multiplicative_identity @ multiplicative_identity) @
% 42.71/6.92 multiplicative_identity)
% 42.71/6.92 | ~ (defined @ multiplicative_identity))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl50])).
% 42.71/6.92 thf(well_definedness_of_multiplicative_identity, axiom,
% 42.71/6.92 (defined @ multiplicative_identity)).
% 42.71/6.92 thf(zip_derived_cl13, plain, ( (defined @ multiplicative_identity)),
% 42.71/6.92 inference('cnf', [status(esa)],
% 42.71/6.92 [well_definedness_of_multiplicative_identity])).
% 42.71/6.92 thf(zip_derived_cl101, plain,
% 42.71/6.92 ( (equalish @
% 42.71/6.92 (multiply @ multiplicative_identity @ multiplicative_identity) @
% 42.71/6.92 multiplicative_identity)),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl97, zip_derived_cl13])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl109, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @ multiplicative_identity @ X0)
% 42.71/6.92 | (equalish @
% 42.71/6.92 (multiply @ multiplicative_identity @ multiplicative_identity) @
% 42.71/6.92 X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl101, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl282, plain,
% 42.71/6.92 ( (equalish @
% 42.71/6.92 (multiply @ multiplicative_identity @ multiplicative_identity) @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ b))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl262, zip_derived_cl109])).
% 42.71/6.92 thf(zip_derived_cl24, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1))
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2))),
% 42.71/6.92 inference('cnf', [status(esa)],
% 42.71/6.92 [compatibility_of_equality_and_multiplication])).
% 42.71/6.92 thf(zip_derived_cl812, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | (equalish @
% 42.71/6.92 (multiply @
% 42.71/6.92 (multiply @ multiplicative_identity @ multiplicative_identity) @
% 42.71/6.92 X0) @
% 42.71/6.92 (multiply @ (multiply @ (multiplicative_inverse @ a) @ b) @ X0)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl282, zip_derived_cl24])).
% 42.71/6.92 thf(zip_derived_cl4, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ (multiply @ X1 @ X2)) @
% 42.71/6.92 (multiply @ (multiply @ X0 @ X1) @ X2))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ X2))),
% 42.71/6.92 inference('cnf', [status(esa)], [associativity_multiplication])).
% 42.71/6.92 thf(zip_derived_cl5, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ multiplicative_identity @ X0) @ X0)
% 42.71/6.92 | ~ (defined @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl44, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | (equalish @ X0 @ (multiply @ multiplicative_identity @ X0)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl63, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | ~ (equalish @ (multiply @ multiplicative_identity @ X0) @ X1)
% 42.71/6.92 | (equalish @ X0 @ X1))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl179, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ multiplicative_identity)
% 42.71/6.92 | (equalish @ (multiply @ X1 @ X0) @
% 42.71/6.92 (multiply @ (multiply @ multiplicative_identity @ X1) @ X0))
% 42.71/6.92 | ~ (defined @ (multiply @ X1 @ X0)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl63])).
% 42.71/6.92 thf(zip_derived_cl13, plain, ( (defined @ multiplicative_identity)),
% 42.71/6.92 inference('cnf', [status(esa)],
% 42.71/6.92 [well_definedness_of_multiplicative_identity])).
% 42.71/6.92 thf(zip_derived_cl180, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | (equalish @ (multiply @ X1 @ X0) @
% 42.71/6.92 (multiply @ (multiply @ multiplicative_identity @ X1) @ X0))
% 42.71/6.92 | ~ (defined @ (multiply @ X1 @ X0)))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl179, zip_derived_cl13])).
% 42.71/6.92 thf(zip_derived_cl12, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (defined @ (multiply @ X0 @ X1))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 42.71/6.92 thf(zip_derived_cl4376, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X1 @ X0) @
% 42.71/6.92 (multiply @ (multiply @ multiplicative_identity @ X1) @ X0))
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ X0))),
% 42.71/6.92 inference('clc', [status(thm)], [zip_derived_cl180, zip_derived_cl12])).
% 42.71/6.92 thf(totality_of_order_relation, axiom,
% 42.71/6.92 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 42.71/6.92 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 42.71/6.92 thf(zip_derived_cl17, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (less_or_equal @ X0 @ X1)
% 42.71/6.92 | (less_or_equal @ X1 @ X0)
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl517, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | (less_or_equal @ X0 @ a)
% 42.71/6.92 | (less_or_equal @ a @ X0))),
% 42.71/6.92 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl8789, plain,
% 42.71/6.92 (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 42.71/6.92 inference('eq_fact', [status(thm)], [zip_derived_cl517])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl8790, plain, ( (less_or_equal @ a @ a)),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl8789, zip_derived_cl27])).
% 42.71/6.92 thf(antisymmetry_of_order_relation, axiom,
% 42.71/6.92 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 42.71/6.92 ( ~( less_or_equal @ Y @ X ) ))).
% 42.71/6.92 thf(zip_derived_cl15, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (less_or_equal @ X0 @ X1)
% 42.71/6.92 | ~ (less_or_equal @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 42.71/6.92 thf(zip_derived_cl8805, plain,
% 42.71/6.92 ((~ (less_or_equal @ a @ a) | (equalish @ a @ a))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl8790, zip_derived_cl15])).
% 42.71/6.92 thf(zip_derived_cl8790, plain, ( (less_or_equal @ a @ a)),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl8789, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl8809, plain, ( (equalish @ a @ a)),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl8805, zip_derived_cl8790])).
% 42.71/6.92 thf(zip_derived_cl50, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | ~ (equalish @ X0 @ X1)
% 42.71/6.92 | (equalish @ (multiply @ multiplicative_identity @ X0) @ X1))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl8812, plain,
% 42.71/6.92 (( (equalish @ (multiply @ multiplicative_identity @ a) @ a)
% 42.71/6.92 | ~ (defined @ a))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl8809, zip_derived_cl50])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl8820, plain,
% 42.71/6.92 ( (equalish @ (multiply @ multiplicative_identity @ a) @ a)),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl8812, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl8825, plain,
% 42.71/6.92 ( (equalish @ a @ (multiply @ multiplicative_identity @ a))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl8820, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl8838, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @ (multiply @ multiplicative_identity @ a) @ X0)
% 42.71/6.92 | (equalish @ a @ X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl8825, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl9196, plain,
% 42.71/6.92 ((~ (defined @ a)
% 42.71/6.92 | ~ (defined @ multiplicative_identity)
% 42.71/6.92 | (equalish @ a @
% 42.71/6.92 (multiply @
% 42.71/6.92 (multiply @ multiplicative_identity @ multiplicative_identity) @ a)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl4376, zip_derived_cl8838])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl13, plain, ( (defined @ multiplicative_identity)),
% 42.71/6.92 inference('cnf', [status(esa)],
% 42.71/6.92 [well_definedness_of_multiplicative_identity])).
% 42.71/6.92 thf(zip_derived_cl9204, plain,
% 42.71/6.92 ( (equalish @ a @
% 42.71/6.92 (multiply @
% 42.71/6.92 (multiply @ multiplicative_identity @ multiplicative_identity) @ a))),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl9196, zip_derived_cl27, zip_derived_cl13])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl9672, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @
% 42.71/6.92 (multiply @
% 42.71/6.92 (multiply @ multiplicative_identity @ multiplicative_identity) @
% 42.71/6.92 a) @
% 42.71/6.92 X0)
% 42.71/6.92 | (equalish @ a @ X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl9204, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl26258, plain,
% 42.71/6.92 ((~ (defined @ a)
% 42.71/6.92 | (equalish @ a @
% 42.71/6.92 (multiply @ (multiply @ (multiplicative_inverse @ a) @ b) @ a)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl812, zip_derived_cl9672])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl26276, plain,
% 42.71/6.92 ( (equalish @ a @
% 42.71/6.92 (multiply @ (multiply @ (multiplicative_inverse @ a) @ b) @ a))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl26258, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl26503, plain,
% 42.71/6.92 ( (equalish @
% 42.71/6.92 (multiply @ (multiply @ (multiplicative_inverse @ a) @ b) @ a) @ a)),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl26276, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl4, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ (multiply @ X1 @ X2)) @
% 42.71/6.92 (multiply @ (multiply @ X0 @ X1) @ X2))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ X2))),
% 42.71/6.92 inference('cnf', [status(esa)], [associativity_multiplication])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl178, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ X2)
% 42.71/6.92 | ~ (equalish @ (multiply @ (multiply @ X2 @ X1) @ X0) @ X3)
% 42.71/6.92 | (equalish @ (multiply @ X2 @ (multiply @ X1 @ X0)) @ X3))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl26716, plain,
% 42.71/6.92 (( (equalish @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ (multiply @ b @ a)) @ a)
% 42.71/6.92 | ~ (defined @ (multiplicative_inverse @ a))
% 42.71/6.92 | ~ (defined @ b)
% 42.71/6.92 | ~ (defined @ a))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl26503, zip_derived_cl178])).
% 42.71/6.92 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl26718, plain,
% 42.71/6.92 ( (equalish @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ (multiply @ b @ a)) @ a)),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl26716, zip_derived_cl33, zip_derived_cl28,
% 42.71/6.92 zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl7, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0))
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl253, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 (~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (equalish @ (multiply @ X1 @ X0) @ X2)
% 42.71/6.92 | (equalish @ (multiply @ X0 @ X1) @ X2))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl26797, plain,
% 42.71/6.92 (( (equalish @
% 42.71/6.92 (multiply @ (multiply @ b @ a) @ (multiplicative_inverse @ a)) @ a)
% 42.71/6.92 | ~ (defined @ (multiply @ b @ a))
% 42.71/6.92 | ~ (defined @ (multiplicative_inverse @ a)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl26718, zip_derived_cl253])).
% 42.71/6.92 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl26798, plain,
% 42.71/6.92 (( (equalish @
% 42.71/6.92 (multiply @ (multiply @ b @ a) @ (multiplicative_inverse @ a)) @ a)
% 42.71/6.92 | ~ (defined @ (multiply @ b @ a)))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl26797, zip_derived_cl33])).
% 42.71/6.92 thf(zip_derived_cl28724, plain,
% 42.71/6.92 ((~ (defined @ a)
% 42.71/6.92 | ~ (defined @ b)
% 42.71/6.92 | (equalish @
% 42.71/6.92 (multiply @ (multiply @ b @ a) @ (multiplicative_inverse @ a)) @ a))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl26798])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl28725, plain,
% 42.71/6.92 ( (equalish @
% 42.71/6.92 (multiply @ (multiply @ b @ a) @ (multiplicative_inverse @ a)) @ a)),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl28724, zip_derived_cl27, zip_derived_cl28])).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl28729, plain,
% 42.71/6.92 ( (equalish @ a @
% 42.71/6.92 (multiply @ (multiply @ b @ a) @ (multiplicative_inverse @ a)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl28725, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl28742, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @
% 42.71/6.92 (multiply @ (multiply @ b @ a) @ (multiplicative_inverse @ a)) @
% 42.71/6.92 X0)
% 42.71/6.92 | (equalish @ a @ X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl28729, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl32739, plain,
% 42.71/6.92 ((~ (defined @ (multiplicative_inverse @ a))
% 42.71/6.92 | ~ (defined @ b)
% 42.71/6.92 | ~ (defined @ a)
% 42.71/6.92 | (equalish @ a @
% 42.71/6.92 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ a))))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl804, zip_derived_cl28742])).
% 42.71/6.92 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl32748, plain,
% 42.71/6.92 ( (equalish @ a @
% 42.71/6.92 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ a)))),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl32739, zip_derived_cl33, zip_derived_cl28,
% 42.71/6.92 zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl32792, plain,
% 42.71/6.92 ( (equalish @
% 42.71/6.92 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ a)) @ a)),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl32748, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl253, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 (~ (defined @ X1)
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (equalish @ (multiply @ X1 @ X0) @ X2)
% 42.71/6.92 | (equalish @ (multiply @ X0 @ X1) @ X2))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl32825, plain,
% 42.71/6.92 (( (equalish @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ (multiply @ a @ b)) @ a)
% 42.71/6.92 | ~ (defined @ (multiplicative_inverse @ a))
% 42.71/6.92 | ~ (defined @ (multiply @ a @ b)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl32792, zip_derived_cl253])).
% 42.71/6.92 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl32827, plain,
% 42.71/6.92 (( (equalish @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ (multiply @ a @ b)) @ a)
% 42.71/6.92 | ~ (defined @ (multiply @ a @ b)))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl32825, zip_derived_cl33])).
% 42.71/6.92 thf(zip_derived_cl32898, plain,
% 42.71/6.92 ((~ (defined @ b)
% 42.71/6.92 | ~ (defined @ a)
% 42.71/6.92 | (equalish @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ (multiply @ a @ b)) @ a))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl32827])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl32899, plain,
% 42.71/6.92 ( (equalish @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ (multiply @ a @ b)) @ a)),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl32898, zip_derived_cl28, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl32903, plain,
% 42.71/6.92 ( (equalish @ a @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ (multiply @ a @ b)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl32899, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl32914, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @
% 42.71/6.92 (multiply @ (multiplicative_inverse @ a) @ (multiply @ a @ b)) @
% 42.71/6.92 X0)
% 42.71/6.92 | (equalish @ a @ X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl32903, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl34510, plain,
% 42.71/6.92 ((~ (defined @ b)
% 42.71/6.92 | ~ (defined @ a)
% 42.71/6.92 | ~ (defined @ (multiplicative_inverse @ a))
% 42.71/6.92 | (equalish @ a @
% 42.71/6.92 (multiply @ (multiply @ (multiplicative_inverse @ a) @ a) @ b)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl32914])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl34518, plain,
% 42.71/6.92 ( (equalish @ a @
% 42.71/6.92 (multiply @ (multiply @ (multiplicative_inverse @ a) @ a) @ b))),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl34510, zip_derived_cl28, zip_derived_cl27,
% 42.71/6.92 zip_derived_cl33])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl34547, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @
% 42.71/6.92 (multiply @ (multiply @ (multiplicative_inverse @ a) @ a) @ b) @
% 42.71/6.92 X0)
% 42.71/6.92 | (equalish @ a @ X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl34518, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl34919, plain,
% 42.71/6.92 ((~ (defined @ b)
% 42.71/6.92 | ~ (defined @ (multiplicative_inverse @ a))
% 42.71/6.92 | ~ (defined @ a)
% 42.71/6.92 | (equalish @ a @
% 42.71/6.92 (multiply @ (multiply @ a @ (multiplicative_inverse @ a)) @ b)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl804, zip_derived_cl34547])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl34928, plain,
% 42.71/6.92 ( (equalish @ a @
% 42.71/6.92 (multiply @ (multiply @ a @ (multiplicative_inverse @ a)) @ b))),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl34919, zip_derived_cl28, zip_derived_cl33,
% 42.71/6.92 zip_derived_cl27])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl34933, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @
% 42.71/6.92 (multiply @ (multiply @ a @ (multiplicative_inverse @ a)) @ b) @
% 42.71/6.92 X0)
% 42.71/6.92 | (equalish @ a @ X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl34928, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl35587, plain,
% 42.71/6.92 ((~ (defined @ b)
% 42.71/6.92 | ~ (defined @ a)
% 42.71/6.92 | (equalish @ a @ additive_identity)
% 42.71/6.92 | (equalish @ a @ (multiply @ multiplicative_identity @ b)))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl815, zip_derived_cl34933])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 42.71/6.92 inference('cnf', [status(esa)], [a_is_defined])).
% 42.71/6.92 thf(zip_derived_cl29, plain, (~ (equalish @ a @ additive_identity)),
% 42.71/6.92 inference('cnf', [status(esa)], [zf_stmt_2])).
% 42.71/6.92 thf(zip_derived_cl35597, plain,
% 42.71/6.92 ( (equalish @ a @ (multiply @ multiplicative_identity @ b))),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl35587, zip_derived_cl28, zip_derived_cl27,
% 42.71/6.92 zip_derived_cl29])).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl35601, plain,
% 42.71/6.92 ( (equalish @ (multiply @ multiplicative_identity @ b) @ a)),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl35597, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl17, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (less_or_equal @ X0 @ X1)
% 42.71/6.92 | (less_or_equal @ X1 @ X0)
% 42.71/6.92 | ~ (defined @ X0)
% 42.71/6.92 | ~ (defined @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl518, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | (less_or_equal @ X0 @ b)
% 42.71/6.92 | (less_or_equal @ b @ X0))),
% 42.71/6.92 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl28])).
% 42.71/6.92 thf(zip_derived_cl8922, plain,
% 42.71/6.92 (( (less_or_equal @ b @ b) | ~ (defined @ b))),
% 42.71/6.92 inference('eq_fact', [status(thm)], [zip_derived_cl518])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl8923, plain, ( (less_or_equal @ b @ b)),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl8922, zip_derived_cl28])).
% 42.71/6.92 thf(zip_derived_cl15, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (less_or_equal @ X0 @ X1)
% 42.71/6.92 | ~ (less_or_equal @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 42.71/6.92 thf(zip_derived_cl8938, plain,
% 42.71/6.92 ((~ (less_or_equal @ b @ b) | (equalish @ b @ b))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl8923, zip_derived_cl15])).
% 42.71/6.92 thf(zip_derived_cl8923, plain, ( (less_or_equal @ b @ b)),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl8922, zip_derived_cl28])).
% 42.71/6.92 thf(zip_derived_cl8942, plain, ( (equalish @ b @ b)),
% 42.71/6.92 inference('demod', [status(thm)],
% 42.71/6.92 [zip_derived_cl8938, zip_derived_cl8923])).
% 42.71/6.92 thf(zip_derived_cl50, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]:
% 42.71/6.92 (~ (defined @ X0)
% 42.71/6.92 | ~ (equalish @ X0 @ X1)
% 42.71/6.92 | (equalish @ (multiply @ multiplicative_identity @ X0) @ X1))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl8945, plain,
% 42.71/6.92 (( (equalish @ (multiply @ multiplicative_identity @ b) @ b)
% 42.71/6.92 | ~ (defined @ b))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl8942, zip_derived_cl50])).
% 42.71/6.92 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 42.71/6.92 inference('cnf', [status(esa)], [b_is_defined])).
% 42.71/6.92 thf(zip_derived_cl8953, plain,
% 42.71/6.92 ( (equalish @ (multiply @ multiplicative_identity @ b) @ b)),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl8945, zip_derived_cl28])).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl9071, plain,
% 42.71/6.92 ( (equalish @ b @ (multiply @ multiplicative_identity @ b))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl8953, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl22, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 42.71/6.92 ( (equalish @ X0 @ X1)
% 42.71/6.92 | ~ (equalish @ X0 @ X2)
% 42.71/6.92 | ~ (equalish @ X2 @ X1))),
% 42.71/6.92 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 42.71/6.92 thf(zip_derived_cl9084, plain,
% 42.71/6.92 (![X0 : $i]:
% 42.71/6.92 (~ (equalish @ (multiply @ multiplicative_identity @ b) @ X0)
% 42.71/6.92 | (equalish @ b @ X0))),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl9071, zip_derived_cl22])).
% 42.71/6.92 thf(zip_derived_cl35641, plain, ( (equalish @ b @ a)),
% 42.71/6.92 inference('sup-', [status(thm)],
% 42.71/6.92 [zip_derived_cl35601, zip_derived_cl9084])).
% 42.71/6.92 thf(zip_derived_cl21, plain,
% 42.71/6.92 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 42.71/6.92 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 42.71/6.92 thf(zip_derived_cl35656, plain, ( (equalish @ a @ b)),
% 42.71/6.92 inference('sup-', [status(thm)], [zip_derived_cl35641, zip_derived_cl21])).
% 42.71/6.92 thf(zip_derived_cl35682, plain, ($false),
% 42.71/6.92 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl35656])).
% 42.71/6.92
% 42.71/6.92 % SZS output end Refutation
% 42.71/6.92
% 42.71/6.92
% 42.71/6.93 % Terminating...
% 43.43/7.04 % Runner terminated.
% 43.43/7.06 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------