TSTP Solution File: FLD033-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD033-1 : 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.mWS1I24WOp true
% Computer : n012.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 22:39:19 EDT 2023
% Result : Unsatisfiable 174.73s 25.67s
% Output : Refutation 174.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD033-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.15/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.mWS1I24WOp true
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 00:11:40 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.36 % Number of cores: 8
% 0.22/0.36 % Python version: Python 3.6.8
% 0.22/0.36 % Running in FO mode
% 0.22/0.66 % Total configuration time : 435
% 0.22/0.66 % Estimated wc time : 1092
% 0.22/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 174.73/25.67 % Solved by fo/fo5.sh.
% 174.73/25.67 % done 27886 iterations in 24.851s
% 174.73/25.67 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 174.73/25.67 % SZS output start Refutation
% 174.73/25.67 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 174.73/25.67 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 174.73/25.67 thf(defined_type, type, defined: $i > $o).
% 174.73/25.67 thf(additive_identity_type, type, additive_identity: $i).
% 174.73/25.67 thf(multiply_type, type, multiply: $i > $i > $i).
% 174.73/25.67 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 174.73/25.67 thf(m_type, type, m: $i).
% 174.73/25.67 thf(equalish_type, type, equalish: $i > $i > $o).
% 174.73/25.67 thf(a_type, type, a: $i).
% 174.73/25.67 thf(m_not_equal_to_multiplicative_identity_5, conjecture,
% 174.73/25.67 (equalish @ m @ multiplicative_identity)).
% 174.73/25.67 thf(zf_stmt_0, negated_conjecture,
% 174.73/25.67 (~( equalish @ m @ multiplicative_identity )),
% 174.73/25.67 inference('cnf.neg', [status(esa)],
% 174.73/25.67 [m_not_equal_to_multiplicative_identity_5])).
% 174.73/25.67 thf(zip_derived_cl31, plain, (~ (equalish @ m @ multiplicative_identity)),
% 174.73/25.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 174.73/25.67 thf(existence_of_inverse_multiplication, axiom,
% 174.73/25.67 (( equalish @
% 174.73/25.67 ( multiply @ X @ ( multiplicative_inverse @ X ) ) @
% 174.73/25.67 multiplicative_identity ) |
% 174.73/25.67 ( ~( defined @ X ) ) | ( equalish @ X @ additive_identity ))).
% 174.73/25.67 thf(zip_derived_cl6, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 ( (equalish @ (multiply @ X0 @ (multiplicative_inverse @ X0)) @
% 174.73/25.67 multiplicative_identity)
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | (equalish @ X0 @ additive_identity))),
% 174.73/25.67 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 174.73/25.67 thf(compatibility_of_equality_and_multiplication, axiom,
% 174.73/25.67 (( equalish @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) |
% 174.73/25.67 ( ~( defined @ Z ) ) | ( ~( equalish @ X @ Y ) ))).
% 174.73/25.67 thf(zip_derived_cl24, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1))
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2))),
% 174.73/25.67 inference('cnf', [status(esa)],
% 174.73/25.67 [compatibility_of_equality_and_multiplication])).
% 174.73/25.67 thf(zip_derived_cl799, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ additive_identity)
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | (equalish @
% 174.73/25.67 (multiply @ (multiply @ X0 @ (multiplicative_inverse @ X0)) @ X1) @
% 174.73/25.67 (multiply @ multiplicative_identity @ X1)))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl24])).
% 174.73/25.67 thf(commutativity_multiplication, axiom,
% 174.73/25.67 (( equalish @ ( multiply @ X @ Y ) @ ( multiply @ Y @ X ) ) |
% 174.73/25.67 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 174.73/25.67 thf(zip_derived_cl7, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]:
% 174.73/25.67 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0))
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 174.73/25.67 thf(associativity_multiplication, axiom,
% 174.73/25.67 (( equalish @
% 174.73/25.67 ( multiply @ X @ ( multiply @ Y @ Z ) ) @
% 174.73/25.67 ( multiply @ ( multiply @ X @ Y ) @ Z ) ) |
% 174.73/25.67 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ) | ( ~( defined @ Z ) ))).
% 174.73/25.67 thf(zip_derived_cl4, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ (multiply @ X0 @ (multiply @ X1 @ X2)) @
% 174.73/25.67 (multiply @ (multiply @ X0 @ X1) @ X2))
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | ~ (defined @ X2))),
% 174.73/25.67 inference('cnf', [status(esa)], [associativity_multiplication])).
% 174.73/25.67 thf(transitivity_of_equality, axiom,
% 174.73/25.67 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 174.73/25.67 ( ~( equalish @ Y @ Z ) ))).
% 174.73/25.67 thf(zip_derived_cl22, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2)
% 174.73/25.67 | ~ (equalish @ X2 @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 174.73/25.67 thf(zip_derived_cl178, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 174.73/25.67 (~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | ~ (defined @ X2)
% 174.73/25.67 | ~ (equalish @ (multiply @ (multiply @ X2 @ X1) @ X0) @ X3)
% 174.73/25.67 | (equalish @ (multiply @ X2 @ (multiply @ X1 @ X0)) @ X3))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl22])).
% 174.73/25.67 thf(zip_derived_cl3579, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 (~ (defined @ X2)
% 174.73/25.67 | ~ (defined @ (multiply @ X1 @ X0))
% 174.73/25.67 | (equalish @ (multiply @ X1 @ (multiply @ X0 @ X2)) @
% 174.73/25.67 (multiply @ X2 @ (multiply @ X1 @ X0)))
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X2))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl178])).
% 174.73/25.67 thf(zip_derived_cl3591, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 (~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | (equalish @ (multiply @ X1 @ (multiply @ X0 @ X2)) @
% 174.73/25.67 (multiply @ X2 @ (multiply @ X1 @ X0)))
% 174.73/25.67 | ~ (defined @ (multiply @ X1 @ X0))
% 174.73/25.67 | ~ (defined @ X2))),
% 174.73/25.67 inference('simplify', [status(thm)], [zip_derived_cl3579])).
% 174.73/25.67 thf(well_definedness_of_multiplication, axiom,
% 174.73/25.67 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 174.73/25.67 ( ~( defined @ Y ) ))).
% 174.73/25.67 thf(zip_derived_cl12, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]:
% 174.73/25.67 ( (defined @ (multiply @ X0 @ X1))
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 174.73/25.67 thf(zip_derived_cl197723, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 (~ (defined @ X2)
% 174.73/25.67 | (equalish @ (multiply @ X1 @ (multiply @ X0 @ X2)) @
% 174.73/25.67 (multiply @ X2 @ (multiply @ X1 @ X0)))
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | ~ (defined @ X0))),
% 174.73/25.67 inference('clc', [status(thm)], [zip_derived_cl3591, zip_derived_cl12])).
% 174.73/25.67 thf(zip_derived_cl12, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]:
% 174.73/25.67 ( (defined @ (multiply @ X0 @ X1))
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 174.73/25.67 thf(multiply_equals_a_4, conjecture,
% 174.73/25.67 (~( equalish @ ( multiply @ m @ a ) @ a ))).
% 174.73/25.67 thf(zf_stmt_1, negated_conjecture, (equalish @ ( multiply @ m @ a ) @ a),
% 174.73/25.67 inference('cnf.neg', [status(esa)], [multiply_equals_a_4])).
% 174.73/25.67 thf(zip_derived_cl30, plain, ( (equalish @ (multiply @ m @ a) @ a)),
% 174.73/25.67 inference('cnf', [status(esa)], [zf_stmt_1])).
% 174.73/25.67 thf(symmetry_of_equality, axiom,
% 174.73/25.67 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 174.73/25.67 thf(zip_derived_cl21, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 174.73/25.67 thf(zip_derived_cl36, plain, ( (equalish @ a @ (multiply @ m @ a))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl21])).
% 174.73/25.67 thf(zip_derived_cl24, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1))
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2))),
% 174.73/25.67 inference('cnf', [status(esa)],
% 174.73/25.67 [compatibility_of_equality_and_multiplication])).
% 174.73/25.67 thf(zip_derived_cl808, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 (~ (defined @ X0)
% 174.73/25.67 | (equalish @ (multiply @ a @ X0) @
% 174.73/25.67 (multiply @ (multiply @ m @ a) @ X0)))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl24])).
% 174.73/25.67 thf(zip_derived_cl6, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 ( (equalish @ (multiply @ X0 @ (multiplicative_inverse @ X0)) @
% 174.73/25.67 multiplicative_identity)
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | (equalish @ X0 @ additive_identity))),
% 174.73/25.67 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 174.73/25.67 thf(zip_derived_cl21, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 174.73/25.67 thf(zip_derived_cl217, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ additive_identity)
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | (equalish @ multiplicative_identity @
% 174.73/25.67 (multiply @ X0 @ (multiplicative_inverse @ X0))))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 174.73/25.67 thf(zip_derived_cl22, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2)
% 174.73/25.67 | ~ (equalish @ X2 @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 174.73/25.67 thf(zip_derived_cl4195, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]:
% 174.73/25.67 (~ (defined @ X0)
% 174.73/25.67 | (equalish @ X0 @ additive_identity)
% 174.73/25.67 | ~ (equalish @ (multiply @ X0 @ (multiplicative_inverse @ X0)) @ X1)
% 174.73/25.67 | (equalish @ multiplicative_identity @ X1))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl217, zip_derived_cl22])).
% 174.73/25.67 thf(zip_derived_cl232455, plain,
% 174.73/25.67 ((~ (defined @ (multiplicative_inverse @ a))
% 174.73/25.67 | (equalish @ multiplicative_identity @
% 174.73/25.67 (multiply @ (multiply @ m @ a) @ (multiplicative_inverse @ a)))
% 174.73/25.67 | (equalish @ a @ additive_identity)
% 174.73/25.67 | ~ (defined @ a))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl808, zip_derived_cl4195])).
% 174.73/25.67 thf(well_definedness_of_multiplicative_inverse, axiom,
% 174.73/25.67 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 174.73/25.67 ( equalish @ X @ additive_identity ))).
% 174.73/25.67 thf(zip_derived_cl14, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 ( (defined @ (multiplicative_inverse @ X0))
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | (equalish @ X0 @ additive_identity))),
% 174.73/25.67 inference('cnf', [status(esa)],
% 174.73/25.67 [well_definedness_of_multiplicative_inverse])).
% 174.73/25.67 thf(a_not_equal_to_additive_identity_3, conjecture,
% 174.73/25.67 (equalish @ a @ additive_identity)).
% 174.73/25.67 thf(zf_stmt_2, negated_conjecture, (~( equalish @ a @ additive_identity )),
% 174.73/25.67 inference('cnf.neg', [status(esa)], [a_not_equal_to_additive_identity_3])).
% 174.73/25.67 thf(zip_derived_cl29, plain, (~ (equalish @ a @ additive_identity)),
% 174.73/25.67 inference('cnf', [status(esa)], [zf_stmt_2])).
% 174.73/25.67 thf(zip_derived_cl32, plain,
% 174.73/25.67 ((~ (defined @ a) | (defined @ (multiplicative_inverse @ a)))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl29])).
% 174.73/25.67 thf(a_is_defined, axiom, (defined @ a)).
% 174.73/25.67 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 174.73/25.67 inference('cnf', [status(esa)], [a_is_defined])).
% 174.73/25.67 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 174.73/25.67 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 174.73/25.67 thf(zip_derived_cl29, plain, (~ (equalish @ a @ additive_identity)),
% 174.73/25.67 inference('cnf', [status(esa)], [zf_stmt_2])).
% 174.73/25.67 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 174.73/25.67 inference('cnf', [status(esa)], [a_is_defined])).
% 174.73/25.67 thf(zip_derived_cl232620, plain,
% 174.73/25.67 ( (equalish @ multiplicative_identity @
% 174.73/25.67 (multiply @ (multiply @ m @ a) @ (multiplicative_inverse @ a)))),
% 174.73/25.67 inference('demod', [status(thm)],
% 174.73/25.67 [zip_derived_cl232455, zip_derived_cl33, zip_derived_cl29,
% 174.73/25.67 zip_derived_cl27])).
% 174.73/25.67 thf(zip_derived_cl21, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 174.73/25.67 thf(zip_derived_cl233800, plain,
% 174.73/25.67 ( (equalish @
% 174.73/25.67 (multiply @ (multiply @ m @ a) @ (multiplicative_inverse @ a)) @
% 174.73/25.67 multiplicative_identity)),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl232620, zip_derived_cl21])).
% 174.73/25.67 thf(zip_derived_cl7, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]:
% 174.73/25.67 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0))
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 174.73/25.67 thf(zip_derived_cl22, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2)
% 174.73/25.67 | ~ (equalish @ X2 @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 174.73/25.67 thf(zip_derived_cl252, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 (~ (defined @ X1)
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (equalish @ (multiply @ X1 @ X0) @ X2)
% 174.73/25.67 | (equalish @ (multiply @ X0 @ X1) @ X2))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl22])).
% 174.73/25.67 thf(zip_derived_cl234605, plain,
% 174.73/25.67 (( (equalish @
% 174.73/25.67 (multiply @ (multiplicative_inverse @ a) @ (multiply @ m @ a)) @
% 174.73/25.67 multiplicative_identity)
% 174.73/25.67 | ~ (defined @ (multiplicative_inverse @ a))
% 174.73/25.67 | ~ (defined @ (multiply @ m @ a)))),
% 174.73/25.67 inference('sup-', [status(thm)],
% 174.73/25.67 [zip_derived_cl233800, zip_derived_cl252])).
% 174.73/25.67 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 174.73/25.67 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 174.73/25.67 thf(zip_derived_cl234608, plain,
% 174.73/25.67 (( (equalish @
% 174.73/25.67 (multiply @ (multiplicative_inverse @ a) @ (multiply @ m @ a)) @
% 174.73/25.67 multiplicative_identity)
% 174.73/25.67 | ~ (defined @ (multiply @ m @ a)))),
% 174.73/25.67 inference('demod', [status(thm)],
% 174.73/25.67 [zip_derived_cl234605, zip_derived_cl33])).
% 174.73/25.67 thf(zip_derived_cl235765, plain,
% 174.73/25.67 ((~ (defined @ a)
% 174.73/25.67 | ~ (defined @ m)
% 174.73/25.67 | (equalish @
% 174.73/25.67 (multiply @ (multiplicative_inverse @ a) @ (multiply @ m @ a)) @
% 174.73/25.67 multiplicative_identity))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl234608])).
% 174.73/25.67 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 174.73/25.67 inference('cnf', [status(esa)], [a_is_defined])).
% 174.73/25.67 thf(m_is_defined, axiom, (defined @ m)).
% 174.73/25.67 thf(zip_derived_cl28, plain, ( (defined @ m)),
% 174.73/25.67 inference('cnf', [status(esa)], [m_is_defined])).
% 174.73/25.67 thf(zip_derived_cl235766, plain,
% 174.73/25.67 ( (equalish @
% 174.73/25.67 (multiply @ (multiplicative_inverse @ a) @ (multiply @ m @ a)) @
% 174.73/25.67 multiplicative_identity)),
% 174.73/25.67 inference('demod', [status(thm)],
% 174.73/25.67 [zip_derived_cl235765, zip_derived_cl27, zip_derived_cl28])).
% 174.73/25.67 thf(zip_derived_cl21, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 174.73/25.67 thf(zip_derived_cl235772, plain,
% 174.73/25.67 ( (equalish @ multiplicative_identity @
% 174.73/25.67 (multiply @ (multiplicative_inverse @ a) @ (multiply @ m @ a)))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl235766, zip_derived_cl21])).
% 174.73/25.67 thf(zip_derived_cl22, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2)
% 174.73/25.67 | ~ (equalish @ X2 @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 174.73/25.67 thf(zip_derived_cl235788, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 (~ (equalish @
% 174.73/25.67 (multiply @ (multiplicative_inverse @ a) @ (multiply @ m @ a)) @
% 174.73/25.67 X0)
% 174.73/25.67 | (equalish @ multiplicative_identity @ X0))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl235772, zip_derived_cl22])).
% 174.73/25.67 thf(zip_derived_cl246977, plain,
% 174.73/25.67 ((~ (defined @ m)
% 174.73/25.67 | ~ (defined @ (multiplicative_inverse @ a))
% 174.73/25.67 | ~ (defined @ a)
% 174.73/25.67 | (equalish @ multiplicative_identity @
% 174.73/25.67 (multiply @ a @ (multiply @ (multiplicative_inverse @ a) @ m))))),
% 174.73/25.67 inference('sup-', [status(thm)],
% 174.73/25.67 [zip_derived_cl197723, zip_derived_cl235788])).
% 174.73/25.67 thf(zip_derived_cl28, plain, ( (defined @ m)),
% 174.73/25.67 inference('cnf', [status(esa)], [m_is_defined])).
% 174.73/25.67 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 174.73/25.67 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 174.73/25.67 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 174.73/25.67 inference('cnf', [status(esa)], [a_is_defined])).
% 174.73/25.67 thf(zip_derived_cl246989, plain,
% 174.73/25.67 ( (equalish @ multiplicative_identity @
% 174.73/25.67 (multiply @ a @ (multiply @ (multiplicative_inverse @ a) @ m)))),
% 174.73/25.67 inference('demod', [status(thm)],
% 174.73/25.67 [zip_derived_cl246977, zip_derived_cl28, zip_derived_cl33,
% 174.73/25.67 zip_derived_cl27])).
% 174.73/25.67 thf(zip_derived_cl21, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 174.73/25.67 thf(zip_derived_cl246997, plain,
% 174.73/25.67 ( (equalish @
% 174.73/25.67 (multiply @ a @ (multiply @ (multiplicative_inverse @ a) @ m)) @
% 174.73/25.67 multiplicative_identity)),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl246989, zip_derived_cl21])).
% 174.73/25.67 thf(zip_derived_cl4, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ (multiply @ X0 @ (multiply @ X1 @ X2)) @
% 174.73/25.67 (multiply @ (multiply @ X0 @ X1) @ X2))
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | ~ (defined @ X2))),
% 174.73/25.67 inference('cnf', [status(esa)], [associativity_multiplication])).
% 174.73/25.67 thf(zip_derived_cl21, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 174.73/25.67 thf(zip_derived_cl177, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 (~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | ~ (defined @ X2)
% 174.73/25.67 | (equalish @ (multiply @ (multiply @ X2 @ X1) @ X0) @
% 174.73/25.67 (multiply @ X2 @ (multiply @ X1 @ X0))))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl21])).
% 174.73/25.67 thf(zip_derived_cl22, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2)
% 174.73/25.67 | ~ (equalish @ X2 @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 174.73/25.67 thf(zip_derived_cl3516, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 174.73/25.67 (~ (defined @ X2)
% 174.73/25.67 | ~ (defined @ X1)
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (equalish @ (multiply @ X2 @ (multiply @ X1 @ X0)) @ X3)
% 174.73/25.67 | (equalish @ (multiply @ (multiply @ X2 @ X1) @ X0) @ X3))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl177, zip_derived_cl22])).
% 174.73/25.67 thf(zip_derived_cl247283, plain,
% 174.73/25.67 (( (equalish @
% 174.73/25.67 (multiply @ (multiply @ a @ (multiplicative_inverse @ a)) @ m) @
% 174.73/25.67 multiplicative_identity)
% 174.73/25.67 | ~ (defined @ m)
% 174.73/25.67 | ~ (defined @ (multiplicative_inverse @ a))
% 174.73/25.67 | ~ (defined @ a))),
% 174.73/25.67 inference('sup-', [status(thm)],
% 174.73/25.67 [zip_derived_cl246997, zip_derived_cl3516])).
% 174.73/25.67 thf(zip_derived_cl28, plain, ( (defined @ m)),
% 174.73/25.67 inference('cnf', [status(esa)], [m_is_defined])).
% 174.73/25.67 thf(zip_derived_cl33, plain, ( (defined @ (multiplicative_inverse @ a))),
% 174.73/25.67 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 174.73/25.67 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 174.73/25.67 inference('cnf', [status(esa)], [a_is_defined])).
% 174.73/25.67 thf(zip_derived_cl247286, plain,
% 174.73/25.67 ( (equalish @
% 174.73/25.67 (multiply @ (multiply @ a @ (multiplicative_inverse @ a)) @ m) @
% 174.73/25.67 multiplicative_identity)),
% 174.73/25.67 inference('demod', [status(thm)],
% 174.73/25.67 [zip_derived_cl247283, zip_derived_cl28, zip_derived_cl33,
% 174.73/25.67 zip_derived_cl27])).
% 174.73/25.67 thf(zip_derived_cl21, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 174.73/25.67 thf(zip_derived_cl247292, plain,
% 174.73/25.67 ( (equalish @ multiplicative_identity @
% 174.73/25.67 (multiply @ (multiply @ a @ (multiplicative_inverse @ a)) @ m))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl247286, zip_derived_cl21])).
% 174.73/25.67 thf(zip_derived_cl22, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2)
% 174.73/25.67 | ~ (equalish @ X2 @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 174.73/25.67 thf(zip_derived_cl247308, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 (~ (equalish @
% 174.73/25.67 (multiply @ (multiply @ a @ (multiplicative_inverse @ a)) @ m) @
% 174.73/25.67 X0)
% 174.73/25.67 | (equalish @ multiplicative_identity @ X0))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl247292, zip_derived_cl22])).
% 174.73/25.67 thf(zip_derived_cl253747, plain,
% 174.73/25.67 ((~ (defined @ m)
% 174.73/25.67 | ~ (defined @ a)
% 174.73/25.67 | (equalish @ a @ additive_identity)
% 174.73/25.67 | (equalish @ multiplicative_identity @
% 174.73/25.67 (multiply @ multiplicative_identity @ m)))),
% 174.73/25.67 inference('sup-', [status(thm)],
% 174.73/25.67 [zip_derived_cl799, zip_derived_cl247308])).
% 174.73/25.67 thf(zip_derived_cl28, plain, ( (defined @ m)),
% 174.73/25.67 inference('cnf', [status(esa)], [m_is_defined])).
% 174.73/25.67 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 174.73/25.67 inference('cnf', [status(esa)], [a_is_defined])).
% 174.73/25.67 thf(zip_derived_cl29, plain, (~ (equalish @ a @ additive_identity)),
% 174.73/25.67 inference('cnf', [status(esa)], [zf_stmt_2])).
% 174.73/25.67 thf(zip_derived_cl253759, plain,
% 174.73/25.67 ( (equalish @ multiplicative_identity @
% 174.73/25.67 (multiply @ multiplicative_identity @ m))),
% 174.73/25.67 inference('demod', [status(thm)],
% 174.73/25.67 [zip_derived_cl253747, zip_derived_cl28, zip_derived_cl27,
% 174.73/25.67 zip_derived_cl29])).
% 174.73/25.67 thf(zip_derived_cl21, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 174.73/25.67 thf(zip_derived_cl253766, plain,
% 174.73/25.67 ( (equalish @ (multiply @ multiplicative_identity @ m) @
% 174.73/25.67 multiplicative_identity)),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl253759, zip_derived_cl21])).
% 174.73/25.67 thf(totality_of_order_relation, axiom,
% 174.73/25.67 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 174.73/25.67 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 174.73/25.67 thf(zip_derived_cl17, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]:
% 174.73/25.67 ( (less_or_equal @ X0 @ X1)
% 174.73/25.67 | (less_or_equal @ X1 @ X0)
% 174.73/25.67 | ~ (defined @ X0)
% 174.73/25.67 | ~ (defined @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 174.73/25.67 thf(zip_derived_cl28, plain, ( (defined @ m)),
% 174.73/25.67 inference('cnf', [status(esa)], [m_is_defined])).
% 174.73/25.67 thf(zip_derived_cl505, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 (~ (defined @ X0)
% 174.73/25.67 | (less_or_equal @ X0 @ m)
% 174.73/25.67 | (less_or_equal @ m @ X0))),
% 174.73/25.67 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl28])).
% 174.73/25.67 thf(zip_derived_cl8407, plain,
% 174.73/25.67 (( (less_or_equal @ m @ m) | ~ (defined @ m))),
% 174.73/25.67 inference('eq_fact', [status(thm)], [zip_derived_cl505])).
% 174.73/25.67 thf(zip_derived_cl28, plain, ( (defined @ m)),
% 174.73/25.67 inference('cnf', [status(esa)], [m_is_defined])).
% 174.73/25.67 thf(zip_derived_cl8408, plain, ( (less_or_equal @ m @ m)),
% 174.73/25.67 inference('demod', [status(thm)], [zip_derived_cl8407, zip_derived_cl28])).
% 174.73/25.67 thf(antisymmetry_of_order_relation, axiom,
% 174.73/25.67 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 174.73/25.67 ( ~( less_or_equal @ Y @ X ) ))).
% 174.73/25.67 thf(zip_derived_cl15, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ X1)
% 174.73/25.67 | ~ (less_or_equal @ X0 @ X1)
% 174.73/25.67 | ~ (less_or_equal @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 174.73/25.67 thf(zip_derived_cl8422, plain,
% 174.73/25.67 ((~ (less_or_equal @ m @ m) | (equalish @ m @ m))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl8408, zip_derived_cl15])).
% 174.73/25.67 thf(zip_derived_cl8408, plain, ( (less_or_equal @ m @ m)),
% 174.73/25.67 inference('demod', [status(thm)], [zip_derived_cl8407, zip_derived_cl28])).
% 174.73/25.67 thf(zip_derived_cl8426, plain, ( (equalish @ m @ m)),
% 174.73/25.67 inference('demod', [status(thm)],
% 174.73/25.67 [zip_derived_cl8422, zip_derived_cl8408])).
% 174.73/25.67 thf(existence_of_identity_multiplication, axiom,
% 174.73/25.67 (( equalish @ ( multiply @ multiplicative_identity @ X ) @ X ) |
% 174.73/25.67 ( ~( defined @ X ) ))).
% 174.73/25.67 thf(zip_derived_cl5, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 ( (equalish @ (multiply @ multiplicative_identity @ X0) @ X0)
% 174.73/25.67 | ~ (defined @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 174.73/25.67 thf(zip_derived_cl22, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2)
% 174.73/25.67 | ~ (equalish @ X2 @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 174.73/25.67 thf(zip_derived_cl50, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]:
% 174.73/25.67 (~ (defined @ X0)
% 174.73/25.67 | ~ (equalish @ X0 @ X1)
% 174.73/25.67 | (equalish @ (multiply @ multiplicative_identity @ X0) @ X1))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl22])).
% 174.73/25.67 thf(zip_derived_cl8429, plain,
% 174.73/25.67 (( (equalish @ (multiply @ multiplicative_identity @ m) @ m)
% 174.73/25.67 | ~ (defined @ m))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl8426, zip_derived_cl50])).
% 174.73/25.67 thf(zip_derived_cl28, plain, ( (defined @ m)),
% 174.73/25.67 inference('cnf', [status(esa)], [m_is_defined])).
% 174.73/25.67 thf(zip_derived_cl8437, plain,
% 174.73/25.67 ( (equalish @ (multiply @ multiplicative_identity @ m) @ m)),
% 174.73/25.67 inference('demod', [status(thm)], [zip_derived_cl8429, zip_derived_cl28])).
% 174.73/25.67 thf(zip_derived_cl21, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 174.73/25.67 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 174.73/25.67 thf(zip_derived_cl8442, plain,
% 174.73/25.67 ( (equalish @ m @ (multiply @ multiplicative_identity @ m))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl8437, zip_derived_cl21])).
% 174.73/25.67 thf(zip_derived_cl22, plain,
% 174.73/25.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 174.73/25.67 ( (equalish @ X0 @ X1)
% 174.73/25.67 | ~ (equalish @ X0 @ X2)
% 174.73/25.67 | ~ (equalish @ X2 @ X1))),
% 174.73/25.67 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 174.73/25.67 thf(zip_derived_cl8455, plain,
% 174.73/25.67 (![X0 : $i]:
% 174.73/25.67 (~ (equalish @ (multiply @ multiplicative_identity @ m) @ X0)
% 174.73/25.67 | (equalish @ m @ X0))),
% 174.73/25.67 inference('sup-', [status(thm)], [zip_derived_cl8442, zip_derived_cl22])).
% 174.73/25.67 thf(zip_derived_cl253846, plain, ( (equalish @ m @ multiplicative_identity)),
% 174.73/25.67 inference('sup-', [status(thm)],
% 174.73/25.67 [zip_derived_cl253766, zip_derived_cl8455])).
% 174.73/25.67 thf(zip_derived_cl253863, plain, ($false),
% 174.73/25.67 inference('demod', [status(thm)],
% 174.73/25.67 [zip_derived_cl31, zip_derived_cl253846])).
% 174.73/25.67
% 174.73/25.67 % SZS output end Refutation
% 174.73/25.67
% 174.73/25.67
% 174.73/25.67 % Terminating...
% 175.39/25.75 % Runner terminated.
% 175.39/25.76 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------