TSTP Solution File: FLD032-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD032-1 : 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.d2S4Ry72AR true
% Computer : n011.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 22:39:18 EDT 2023
% Result : Unsatisfiable 18.82s 3.28s
% Output : Refutation 18.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD032-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.d2S4Ry72AR true
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 00:49:40 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.34 % Running portfolio for 300 s
% 0.19/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.35 % Number of cores: 8
% 0.19/0.35 % Python version: Python 3.6.8
% 0.19/0.35 % Running in FO mode
% 0.22/0.62 % Total configuration time : 435
% 0.22/0.62 % Estimated wc time : 1092
% 0.22/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.73 % /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/fo4.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 18.82/3.28 % Solved by fo/fo5.sh.
% 18.82/3.28 % done 4969 iterations in 2.492s
% 18.82/3.28 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 18.82/3.28 % SZS output start Refutation
% 18.82/3.28 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 18.82/3.28 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 18.82/3.28 thf(defined_type, type, defined: $i > $o).
% 18.82/3.28 thf(additive_identity_type, type, additive_identity: $i).
% 18.82/3.28 thf(multiply_type, type, multiply: $i > $i > $i).
% 18.82/3.28 thf(add_type, type, add: $i > $i > $i).
% 18.82/3.28 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 18.82/3.28 thf(equalish_type, type, equalish: $i > $i > $o).
% 18.82/3.28 thf(a_type, type, a: $i).
% 18.82/3.28 thf(a_not_equal_to_additive_identity_2, conjecture,
% 18.82/3.28 (equalish @ a @ additive_identity)).
% 18.82/3.28 thf(zf_stmt_0, negated_conjecture, (~( equalish @ a @ additive_identity )),
% 18.82/3.28 inference('cnf.neg', [status(esa)], [a_not_equal_to_additive_identity_2])).
% 18.82/3.28 thf(zip_derived_cl28, plain, (~ (equalish @ a @ additive_identity)),
% 18.82/3.28 inference('cnf', [status(esa)], [zf_stmt_0])).
% 18.82/3.28 thf(existence_of_inverse_multiplication, axiom,
% 18.82/3.28 (( equalish @
% 18.82/3.28 ( multiply @ X @ ( multiplicative_inverse @ X ) ) @
% 18.82/3.28 multiplicative_identity ) |
% 18.82/3.28 ( ~( defined @ X ) ) | ( equalish @ X @ additive_identity ))).
% 18.82/3.28 thf(zip_derived_cl6, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 ( (equalish @ (multiply @ X0 @ (multiplicative_inverse @ X0)) @
% 18.82/3.28 multiplicative_identity)
% 18.82/3.28 | ~ (defined @ X0)
% 18.82/3.28 | (equalish @ X0 @ additive_identity))),
% 18.82/3.28 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 18.82/3.28 thf(existence_of_identity_addition, axiom,
% 18.82/3.28 (( equalish @ ( add @ additive_identity @ X ) @ X ) | ( ~( defined @ X ) ))).
% 18.82/3.28 thf(zip_derived_cl1, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 18.82/3.28 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 18.82/3.28 thf(symmetry_of_equality, axiom,
% 18.82/3.28 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 18.82/3.28 thf(zip_derived_cl21, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 18.82/3.28 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 18.82/3.28 thf(zip_derived_cl59, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 (~ (defined @ X0) | (equalish @ X0 @ (add @ additive_identity @ X0)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 18.82/3.28 thf(multiplicative_inverses_equal, conjecture,
% 18.82/3.28 (~( equalish @ ( multiplicative_inverse @ a ) @ multiplicative_identity ))).
% 18.82/3.28 thf(zf_stmt_1, negated_conjecture,
% 18.82/3.28 (equalish @ ( multiplicative_inverse @ a ) @ multiplicative_identity),
% 18.82/3.28 inference('cnf.neg', [status(esa)], [multiplicative_inverses_equal])).
% 18.82/3.28 thf(zip_derived_cl29, plain,
% 18.82/3.28 ( (equalish @ (multiplicative_inverse @ a) @ multiplicative_identity)),
% 18.82/3.28 inference('cnf', [status(esa)], [zf_stmt_1])).
% 18.82/3.28 thf(transitivity_of_equality, axiom,
% 18.82/3.28 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 18.82/3.28 ( ~( equalish @ Y @ Z ) ))).
% 18.82/3.28 thf(zip_derived_cl22, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.82/3.28 ( (equalish @ X0 @ X1)
% 18.82/3.28 | ~ (equalish @ X0 @ X2)
% 18.82/3.28 | ~ (equalish @ X2 @ X1))),
% 18.82/3.28 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 18.82/3.28 thf(zip_derived_cl49, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 (~ (equalish @ multiplicative_identity @ X0)
% 18.82/3.28 | (equalish @ (multiplicative_inverse @ a) @ X0))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl22])).
% 18.82/3.28 thf(zip_derived_cl73, plain,
% 18.82/3.28 ((~ (defined @ multiplicative_identity)
% 18.82/3.28 | (equalish @ (multiplicative_inverse @ a) @
% 18.82/3.28 (add @ additive_identity @ multiplicative_identity)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl49])).
% 18.82/3.28 thf(well_definedness_of_multiplicative_identity, axiom,
% 18.82/3.28 (defined @ multiplicative_identity)).
% 18.82/3.28 thf(zip_derived_cl13, plain, ( (defined @ multiplicative_identity)),
% 18.82/3.28 inference('cnf', [status(esa)],
% 18.82/3.28 [well_definedness_of_multiplicative_identity])).
% 18.82/3.28 thf(zip_derived_cl75, plain,
% 18.82/3.28 ( (equalish @ (multiplicative_inverse @ a) @
% 18.82/3.28 (add @ additive_identity @ multiplicative_identity))),
% 18.82/3.28 inference('demod', [status(thm)], [zip_derived_cl73, zip_derived_cl13])).
% 18.82/3.28 thf(zip_derived_cl21, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 18.82/3.28 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 18.82/3.28 thf(zip_derived_cl93, plain,
% 18.82/3.28 ( (equalish @ (add @ additive_identity @ multiplicative_identity) @
% 18.82/3.28 (multiplicative_inverse @ a))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl21])).
% 18.82/3.28 thf(compatibility_of_equality_and_multiplication, axiom,
% 18.82/3.28 (( equalish @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) |
% 18.82/3.28 ( ~( defined @ Z ) ) | ( ~( equalish @ X @ Y ) ))).
% 18.82/3.28 thf(zip_derived_cl24, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.82/3.28 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1))
% 18.82/3.28 | ~ (defined @ X1)
% 18.82/3.28 | ~ (equalish @ X0 @ X2))),
% 18.82/3.28 inference('cnf', [status(esa)],
% 18.82/3.28 [compatibility_of_equality_and_multiplication])).
% 18.82/3.28 thf(zip_derived_cl844, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 (~ (defined @ X0)
% 18.82/3.28 | (equalish @
% 18.82/3.28 (multiply @
% 18.82/3.28 (add @ additive_identity @ multiplicative_identity) @ X0) @
% 18.82/3.28 (multiply @ (multiplicative_inverse @ a) @ X0)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl24])).
% 18.82/3.28 thf(zip_derived_cl59, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 (~ (defined @ X0) | (equalish @ X0 @ (add @ additive_identity @ X0)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 18.82/3.28 thf(zip_derived_cl24, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.82/3.28 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1))
% 18.82/3.28 | ~ (defined @ X1)
% 18.82/3.28 | ~ (equalish @ X0 @ X2))),
% 18.82/3.28 inference('cnf', [status(esa)],
% 18.82/3.28 [compatibility_of_equality_and_multiplication])).
% 18.82/3.28 thf(zip_derived_cl825, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]:
% 18.82/3.28 (~ (defined @ X0)
% 18.82/3.28 | ~ (defined @ X1)
% 18.82/3.28 | (equalish @ (multiply @ X0 @ X1) @
% 18.82/3.28 (multiply @ (add @ additive_identity @ X0) @ X1)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl24])).
% 18.82/3.28 thf(totality_of_order_relation, axiom,
% 18.82/3.28 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 18.82/3.28 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 18.82/3.28 thf(zip_derived_cl17, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]:
% 18.82/3.28 ( (less_or_equal @ X0 @ X1)
% 18.82/3.28 | (less_or_equal @ X1 @ X0)
% 18.82/3.28 | ~ (defined @ X0)
% 18.82/3.28 | ~ (defined @ X1))),
% 18.82/3.28 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 18.82/3.28 thf(a_is_defined, axiom, (defined @ a)).
% 18.82/3.28 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 18.82/3.28 inference('cnf', [status(esa)], [a_is_defined])).
% 18.82/3.28 thf(zip_derived_cl551, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 (~ (defined @ X0)
% 18.82/3.28 | (less_or_equal @ X0 @ a)
% 18.82/3.28 | (less_or_equal @ a @ X0))),
% 18.82/3.28 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl27])).
% 18.82/3.28 thf(zip_derived_cl10054, plain,
% 18.82/3.28 (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 18.82/3.28 inference('eq_fact', [status(thm)], [zip_derived_cl551])).
% 18.82/3.28 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 18.82/3.28 inference('cnf', [status(esa)], [a_is_defined])).
% 18.82/3.28 thf(zip_derived_cl10055, plain, ( (less_or_equal @ a @ a)),
% 18.82/3.28 inference('demod', [status(thm)], [zip_derived_cl10054, zip_derived_cl27])).
% 18.82/3.28 thf(antisymmetry_of_order_relation, axiom,
% 18.82/3.28 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 18.82/3.28 ( ~( less_or_equal @ Y @ X ) ))).
% 18.82/3.28 thf(zip_derived_cl15, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]:
% 18.82/3.28 ( (equalish @ X0 @ X1)
% 18.82/3.28 | ~ (less_or_equal @ X0 @ X1)
% 18.82/3.28 | ~ (less_or_equal @ X1 @ X0))),
% 18.82/3.28 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 18.82/3.28 thf(zip_derived_cl10079, plain,
% 18.82/3.28 ((~ (less_or_equal @ a @ a) | (equalish @ a @ a))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl10055, zip_derived_cl15])).
% 18.82/3.28 thf(zip_derived_cl10055, plain, ( (less_or_equal @ a @ a)),
% 18.82/3.28 inference('demod', [status(thm)], [zip_derived_cl10054, zip_derived_cl27])).
% 18.82/3.28 thf(zip_derived_cl10083, plain, ( (equalish @ a @ a)),
% 18.82/3.28 inference('demod', [status(thm)],
% 18.82/3.28 [zip_derived_cl10079, zip_derived_cl10055])).
% 18.82/3.28 thf(existence_of_identity_multiplication, axiom,
% 18.82/3.28 (( equalish @ ( multiply @ multiplicative_identity @ X ) @ X ) |
% 18.82/3.28 ( ~( defined @ X ) ))).
% 18.82/3.28 thf(zip_derived_cl5, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 ( (equalish @ (multiply @ multiplicative_identity @ X0) @ X0)
% 18.82/3.28 | ~ (defined @ X0))),
% 18.82/3.28 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 18.82/3.28 thf(zip_derived_cl22, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.82/3.28 ( (equalish @ X0 @ X1)
% 18.82/3.28 | ~ (equalish @ X0 @ X2)
% 18.82/3.28 | ~ (equalish @ X2 @ X1))),
% 18.82/3.28 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 18.82/3.28 thf(zip_derived_cl62, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]:
% 18.82/3.28 (~ (defined @ X0)
% 18.82/3.28 | ~ (equalish @ X0 @ X1)
% 18.82/3.28 | (equalish @ (multiply @ multiplicative_identity @ X0) @ X1))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl22])).
% 18.82/3.28 thf(zip_derived_cl10087, plain,
% 18.82/3.28 (( (equalish @ (multiply @ multiplicative_identity @ a) @ a)
% 18.82/3.28 | ~ (defined @ a))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl10083, zip_derived_cl62])).
% 18.82/3.28 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 18.82/3.28 inference('cnf', [status(esa)], [a_is_defined])).
% 18.82/3.28 thf(zip_derived_cl10097, plain,
% 18.82/3.28 ( (equalish @ (multiply @ multiplicative_identity @ a) @ a)),
% 18.82/3.28 inference('demod', [status(thm)], [zip_derived_cl10087, zip_derived_cl27])).
% 18.82/3.28 thf(zip_derived_cl21, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 18.82/3.28 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 18.82/3.28 thf(zip_derived_cl10150, plain,
% 18.82/3.28 ( (equalish @ a @ (multiply @ multiplicative_identity @ a))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl10097, zip_derived_cl21])).
% 18.82/3.28 thf(zip_derived_cl22, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.82/3.28 ( (equalish @ X0 @ X1)
% 18.82/3.28 | ~ (equalish @ X0 @ X2)
% 18.82/3.28 | ~ (equalish @ X2 @ X1))),
% 18.82/3.28 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 18.82/3.28 thf(zip_derived_cl10208, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 (~ (equalish @ (multiply @ multiplicative_identity @ a) @ X0)
% 18.82/3.28 | (equalish @ a @ X0))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl10150, zip_derived_cl22])).
% 18.82/3.28 thf(zip_derived_cl22367, plain,
% 18.82/3.28 ((~ (defined @ a)
% 18.82/3.28 | ~ (defined @ multiplicative_identity)
% 18.82/3.28 | (equalish @ a @
% 18.82/3.28 (multiply @ (add @ additive_identity @ multiplicative_identity) @ a)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl825, zip_derived_cl10208])).
% 18.82/3.28 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 18.82/3.28 inference('cnf', [status(esa)], [a_is_defined])).
% 18.82/3.28 thf(zip_derived_cl13, plain, ( (defined @ multiplicative_identity)),
% 18.82/3.28 inference('cnf', [status(esa)],
% 18.82/3.28 [well_definedness_of_multiplicative_identity])).
% 18.82/3.28 thf(zip_derived_cl22434, plain,
% 18.82/3.28 ( (equalish @ a @
% 18.82/3.28 (multiply @ (add @ additive_identity @ multiplicative_identity) @ a))),
% 18.82/3.28 inference('demod', [status(thm)],
% 18.82/3.28 [zip_derived_cl22367, zip_derived_cl27, zip_derived_cl13])).
% 18.82/3.28 thf(zip_derived_cl22, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.82/3.28 ( (equalish @ X0 @ X1)
% 18.82/3.28 | ~ (equalish @ X0 @ X2)
% 18.82/3.28 | ~ (equalish @ X2 @ X1))),
% 18.82/3.28 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 18.82/3.28 thf(zip_derived_cl22806, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 (~ (equalish @
% 18.82/3.28 (multiply @ (add @ additive_identity @ multiplicative_identity) @
% 18.82/3.28 a) @
% 18.82/3.28 X0)
% 18.82/3.28 | (equalish @ a @ X0))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl22434, zip_derived_cl22])).
% 18.82/3.28 thf(zip_derived_cl24985, plain,
% 18.82/3.28 ((~ (defined @ a)
% 18.82/3.28 | (equalish @ a @ (multiply @ (multiplicative_inverse @ a) @ a)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl844, zip_derived_cl22806])).
% 18.82/3.28 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 18.82/3.28 inference('cnf', [status(esa)], [a_is_defined])).
% 18.82/3.28 thf(zip_derived_cl24992, plain,
% 18.82/3.28 ( (equalish @ a @ (multiply @ (multiplicative_inverse @ a) @ a))),
% 18.82/3.28 inference('demod', [status(thm)], [zip_derived_cl24985, zip_derived_cl27])).
% 18.82/3.28 thf(zip_derived_cl21, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 18.82/3.28 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 18.82/3.28 thf(zip_derived_cl25062, plain,
% 18.82/3.28 ( (equalish @ (multiply @ (multiplicative_inverse @ a) @ a) @ a)),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl24992, zip_derived_cl21])).
% 18.82/3.28 thf(commutativity_multiplication, axiom,
% 18.82/3.28 (( equalish @ ( multiply @ X @ Y ) @ ( multiply @ Y @ X ) ) |
% 18.82/3.28 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 18.82/3.28 thf(zip_derived_cl7, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]:
% 18.82/3.28 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0))
% 18.82/3.28 | ~ (defined @ X0)
% 18.82/3.28 | ~ (defined @ X1))),
% 18.82/3.28 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 18.82/3.28 thf(zip_derived_cl22, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.82/3.28 ( (equalish @ X0 @ X1)
% 18.82/3.28 | ~ (equalish @ X0 @ X2)
% 18.82/3.28 | ~ (equalish @ X2 @ X1))),
% 18.82/3.28 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 18.82/3.28 thf(zip_derived_cl210, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.82/3.28 (~ (defined @ X1)
% 18.82/3.28 | ~ (defined @ X0)
% 18.82/3.28 | ~ (equalish @ (multiply @ X1 @ X0) @ X2)
% 18.82/3.28 | (equalish @ (multiply @ X0 @ X1) @ X2))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl22])).
% 18.82/3.28 thf(zip_derived_cl25129, plain,
% 18.82/3.28 (( (equalish @ (multiply @ a @ (multiplicative_inverse @ a)) @ a)
% 18.82/3.28 | ~ (defined @ a)
% 18.82/3.28 | ~ (defined @ (multiplicative_inverse @ a)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl25062, zip_derived_cl210])).
% 18.82/3.28 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 18.82/3.28 inference('cnf', [status(esa)], [a_is_defined])).
% 18.82/3.28 thf(well_definedness_of_multiplicative_inverse, axiom,
% 18.82/3.28 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 18.82/3.28 ( equalish @ X @ additive_identity ))).
% 18.82/3.28 thf(zip_derived_cl14, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 ( (defined @ (multiplicative_inverse @ X0))
% 18.82/3.28 | ~ (defined @ X0)
% 18.82/3.28 | (equalish @ X0 @ additive_identity))),
% 18.82/3.28 inference('cnf', [status(esa)],
% 18.82/3.28 [well_definedness_of_multiplicative_inverse])).
% 18.82/3.28 thf(zip_derived_cl28, plain, (~ (equalish @ a @ additive_identity)),
% 18.82/3.28 inference('cnf', [status(esa)], [zf_stmt_0])).
% 18.82/3.28 thf(zip_derived_cl31, plain,
% 18.82/3.28 ((~ (defined @ a) | (defined @ (multiplicative_inverse @ a)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl28])).
% 18.82/3.28 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 18.82/3.28 inference('cnf', [status(esa)], [a_is_defined])).
% 18.82/3.28 thf(zip_derived_cl32, plain, ( (defined @ (multiplicative_inverse @ a))),
% 18.82/3.28 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl27])).
% 18.82/3.28 thf(zip_derived_cl25130, plain,
% 18.82/3.28 ( (equalish @ (multiply @ a @ (multiplicative_inverse @ a)) @ a)),
% 18.82/3.28 inference('demod', [status(thm)],
% 18.82/3.28 [zip_derived_cl25129, zip_derived_cl27, zip_derived_cl32])).
% 18.82/3.28 thf(zip_derived_cl21, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 18.82/3.28 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 18.82/3.28 thf(zip_derived_cl25149, plain,
% 18.82/3.28 ( (equalish @ a @ (multiply @ a @ (multiplicative_inverse @ a)))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl25130, zip_derived_cl21])).
% 18.82/3.28 thf(zip_derived_cl22, plain,
% 18.82/3.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.82/3.28 ( (equalish @ X0 @ X1)
% 18.82/3.28 | ~ (equalish @ X0 @ X2)
% 18.82/3.28 | ~ (equalish @ X2 @ X1))),
% 18.82/3.28 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 18.82/3.28 thf(zip_derived_cl25247, plain,
% 18.82/3.28 (![X0 : $i]:
% 18.82/3.28 (~ (equalish @ (multiply @ a @ (multiplicative_inverse @ a)) @ X0)
% 18.82/3.28 | (equalish @ a @ X0))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl25149, zip_derived_cl22])).
% 18.82/3.28 thf(zip_derived_cl25890, plain,
% 18.82/3.28 (( (equalish @ a @ additive_identity)
% 18.82/3.28 | ~ (defined @ a)
% 18.82/3.28 | (equalish @ a @ multiplicative_identity))),
% 18.82/3.28 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl25247])).
% 18.82/3.28 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 18.82/3.28 inference('cnf', [status(esa)], [a_is_defined])).
% 18.82/3.28 thf(a_not_equal_to_multiplicative_identity_4, conjecture,
% 18.82/3.28 (equalish @ a @ multiplicative_identity)).
% 18.82/3.28 thf(zf_stmt_2, negated_conjecture,
% 18.82/3.28 (~( equalish @ a @ multiplicative_identity )),
% 18.82/3.28 inference('cnf.neg', [status(esa)],
% 18.82/3.28 [a_not_equal_to_multiplicative_identity_4])).
% 18.82/3.28 thf(zip_derived_cl30, plain, (~ (equalish @ a @ multiplicative_identity)),
% 18.82/3.28 inference('cnf', [status(esa)], [zf_stmt_2])).
% 18.82/3.28 thf(zip_derived_cl25898, plain, ( (equalish @ a @ additive_identity)),
% 18.82/3.28 inference('demod', [status(thm)],
% 18.82/3.28 [zip_derived_cl25890, zip_derived_cl27, zip_derived_cl30])).
% 18.82/3.28 thf(zip_derived_cl25955, plain, ($false),
% 18.82/3.28 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl25898])).
% 18.82/3.28
% 18.82/3.28 % SZS output end Refutation
% 18.82/3.28
% 18.82/3.28
% 18.82/3.28 % Terminating...
% 19.14/3.35 % Runner terminated.
% 19.14/3.36 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------