%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD009-1 : TPTP v9.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.5Ch384E8Bu true
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:33:08 PM UTC 2025
% Result : Unsatisfiable 55.62s 8.60s
% Output : Refutation 55.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD009-1 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.5Ch384E8Bu true
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 18:31:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.56/0.64 % Total configuration time : 435
% 0.56/0.64 % Estimated wc time : 1092
% 0.56/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.79 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 55.62/8.60 % Solved by fo/fo4.sh.
% 55.62/8.60 % done 6481 iterations in 7.783s
% 55.62/8.60 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 55.62/8.60 % SZS output start Refutation
% 55.62/8.60 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 55.62/8.60 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 55.62/8.60 thf(defined_type, type, defined: $i > $o).
% 55.62/8.60 thf(additive_identity_type, type, additive_identity: $i).
% 55.62/8.60 thf(multiply_type, type, multiply: $i > $i > $i).
% 55.62/8.60 thf(b_type, type, b: $i).
% 55.62/8.60 thf(equalish_type, type, equalish: $i > $i > $o).
% 55.62/8.60 thf(a_type, type, a: $i).
% 55.62/8.60 thf(well_definedness_of_multiplication, axiom,
% 55.62/8.60 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 55.62/8.60 ( ~( defined @ Y ) ))).
% 55.62/8.60 thf(zip_derived_cl12, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 ( (defined @ (multiply @ X0 @ X1))
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ X1))),
% 55.62/8.60 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 55.62/8.60 thf(a_is_defined, axiom, (defined @ a)).
% 55.62/8.60 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 55.62/8.60 inference('cnf', [status(esa)], [a_is_defined])).
% 55.62/8.60 thf(existence_of_inverse_multiplication, axiom,
% 55.62/8.60 (( equalish @
% 55.62/8.60 ( multiply @ X @ ( multiplicative_inverse @ X ) ) @
% 55.62/8.60 multiplicative_identity ) |
% 55.62/8.60 ( ~( defined @ X ) ) | ( equalish @ X @ additive_identity ))).
% 55.62/8.60 thf(zip_derived_cl6, plain,
% 55.62/8.60 (![X0 : $i]:
% 55.62/8.60 ( (equalish @ (multiply @ X0 @ (multiplicative_inverse @ X0)) @
% 55.62/8.60 multiplicative_identity)
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | (equalish @ X0 @ additive_identity))),
% 55.62/8.60 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 55.62/8.60 thf(zip_derived_cl187, plain,
% 55.62/8.60 (( (equalish @ a @ additive_identity)
% 55.62/8.60 | (equalish @ (multiply @ a @ (multiplicative_inverse @ a)) @
% 55.62/8.60 multiplicative_identity))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl6])).
% 55.62/8.60 thf(a_not_equal_to_additive_identity_3, conjecture,
% 55.62/8.60 (equalish @ a @ additive_identity)).
% 55.62/8.60 thf(zf_stmt_0, negated_conjecture, (~( equalish @ a @ additive_identity )),
% 55.62/8.60 inference('cnf.neg', [status(esa)], [a_not_equal_to_additive_identity_3])).
% 55.62/8.60 thf(zip_derived_cl29, plain, (~ (equalish @ a @ additive_identity)),
% 55.62/8.60 inference('cnf', [status(esa)], [zf_stmt_0])).
% 55.62/8.60 thf(zip_derived_cl189, plain,
% 55.62/8.60 ( (equalish @ (multiply @ a @ (multiplicative_inverse @ a)) @
% 55.62/8.60 multiplicative_identity)),
% 55.62/8.60 inference('demod', [status(thm)], [zip_derived_cl187, zip_derived_cl29])).
% 55.62/8.60 thf(symmetry_of_equality, axiom,
% 55.62/8.60 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 55.62/8.60 thf(zip_derived_cl21, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 55.62/8.60 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 55.62/8.60 thf(transitivity_of_equality, axiom,
% 55.62/8.60 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 55.62/8.60 ( ~( equalish @ Y @ Z ) ))).
% 55.62/8.60 thf(zip_derived_cl22, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 ( (equalish @ X0 @ X1)
% 55.62/8.60 | ~ (equalish @ X0 @ X2)
% 55.62/8.60 | ~ (equalish @ X2 @ X1))),
% 55.62/8.60 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 55.62/8.60 thf(zip_derived_cl40, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 (~ (equalish @ X0 @ X1)
% 55.62/8.60 | ~ (equalish @ X0 @ X2)
% 55.62/8.60 | (equalish @ X1 @ X2))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl22])).
% 55.62/8.60 thf(zip_derived_cl339, plain,
% 55.62/8.60 (![X0 : $i]:
% 55.62/8.60 ( (equalish @ multiplicative_identity @ X0)
% 55.62/8.60 | ~ (equalish @ (multiply @ a @ (multiplicative_inverse @ a)) @ X0))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl40])).
% 55.62/8.60 thf(zip_derived_cl21, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 55.62/8.60 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 55.62/8.60 thf(zip_derived_cl385, plain,
% 55.62/8.60 (![X0 : $i]:
% 55.62/8.60 ( (equalish @ multiplicative_identity @ X0)
% 55.62/8.60 | ~ (equalish @ X0 @ (multiply @ a @ (multiplicative_inverse @ a))))),
% 55.62/8.60 inference('sup+', [status(thm)], [zip_derived_cl339, zip_derived_cl21])).
% 55.62/8.60 thf(commutativity_multiplication, axiom,
% 55.62/8.60 (( equalish @ ( multiply @ X @ Y ) @ ( multiply @ Y @ X ) ) |
% 55.62/8.60 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 55.62/8.60 thf(zip_derived_cl7, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0))
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ X1))),
% 55.62/8.60 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 55.62/8.60 thf(zip_derived_cl438, plain,
% 55.62/8.60 (( (equalish @ multiplicative_identity @
% 55.62/8.60 (multiply @ (multiplicative_inverse @ a) @ a))
% 55.62/8.60 | ~ (defined @ a)
% 55.62/8.60 | ~ (defined @ (multiplicative_inverse @ a)))),
% 55.62/8.60 inference('sup+', [status(thm)], [zip_derived_cl385, zip_derived_cl7])).
% 55.62/8.60 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 55.62/8.60 inference('cnf', [status(esa)], [a_is_defined])).
% 55.62/8.60 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 55.62/8.60 inference('cnf', [status(esa)], [a_is_defined])).
% 55.62/8.60 thf(well_definedness_of_multiplicative_inverse, axiom,
% 55.62/8.60 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 55.62/8.60 ( equalish @ X @ additive_identity ))).
% 55.62/8.60 thf(zip_derived_cl14, plain,
% 55.62/8.60 (![X0 : $i]:
% 55.62/8.60 ( (defined @ (multiplicative_inverse @ X0))
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | (equalish @ X0 @ additive_identity))),
% 55.62/8.60 inference('cnf', [status(esa)],
% 55.62/8.60 [well_definedness_of_multiplicative_inverse])).
% 55.62/8.60 thf(zip_derived_cl87, plain,
% 55.62/8.60 (( (equalish @ a @ additive_identity)
% 55.62/8.60 | (defined @ (multiplicative_inverse @ a)))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl14])).
% 55.62/8.60 thf(zip_derived_cl29, plain, (~ (equalish @ a @ additive_identity)),
% 55.62/8.60 inference('cnf', [status(esa)], [zf_stmt_0])).
% 55.62/8.60 thf(zip_derived_cl89, plain, ( (defined @ (multiplicative_inverse @ a))),
% 55.62/8.60 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl29])).
% 55.62/8.60 thf(zip_derived_cl442, plain,
% 55.62/8.60 ( (equalish @ multiplicative_identity @
% 55.62/8.60 (multiply @ (multiplicative_inverse @ a) @ a))),
% 55.62/8.60 inference('demod', [status(thm)],
% 55.62/8.60 [zip_derived_cl438, zip_derived_cl27, zip_derived_cl89])).
% 55.62/8.60 thf(zip_derived_cl40, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 (~ (equalish @ X0 @ X1)
% 55.62/8.60 | ~ (equalish @ X0 @ X2)
% 55.62/8.60 | (equalish @ X1 @ X2))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl22])).
% 55.62/8.60 thf(zip_derived_cl449, plain,
% 55.62/8.60 (![X0 : $i]:
% 55.62/8.60 ( (equalish @ (multiply @ (multiplicative_inverse @ a) @ a) @ X0)
% 55.62/8.60 | ~ (equalish @ multiplicative_identity @ X0))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl442, zip_derived_cl40])).
% 55.62/8.60 thf(existence_of_identity_multiplication, axiom,
% 55.62/8.60 (( equalish @ ( multiply @ multiplicative_identity @ X ) @ X ) |
% 55.62/8.60 ( ~( defined @ X ) ))).
% 55.62/8.60 thf(zip_derived_cl5, plain,
% 55.62/8.60 (![X0 : $i]:
% 55.62/8.60 ( (equalish @ (multiply @ multiplicative_identity @ X0) @ X0)
% 55.62/8.60 | ~ (defined @ X0))),
% 55.62/8.60 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 55.62/8.60 thf(zip_derived_cl40, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 (~ (equalish @ X0 @ X1)
% 55.62/8.60 | ~ (equalish @ X0 @ X2)
% 55.62/8.60 | (equalish @ X1 @ X2))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl22])).
% 55.62/8.60 thf(zip_derived_cl163, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 (~ (defined @ X0)
% 55.62/8.60 | (equalish @ X0 @ X1)
% 55.62/8.60 | ~ (equalish @ (multiply @ multiplicative_identity @ X0) @ X1))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl40])).
% 55.62/8.60 thf(zip_derived_cl21, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 55.62/8.60 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 55.62/8.60 thf(zip_derived_cl465, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 ( (equalish @ X1 @ X0)
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (equalish @ X0 @ (multiply @ multiplicative_identity @ X1)))),
% 55.62/8.60 inference('sup+', [status(thm)], [zip_derived_cl163, zip_derived_cl21])).
% 55.62/8.60 thf(compatibility_of_equality_and_multiplication, axiom,
% 55.62/8.60 (( equalish @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) |
% 55.62/8.60 ( ~( defined @ Z ) ) | ( ~( equalish @ X @ Y ) ))).
% 55.62/8.60 thf(zip_derived_cl24, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1))
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (equalish @ X0 @ X2))),
% 55.62/8.60 inference('cnf', [status(esa)],
% 55.62/8.60 [compatibility_of_equality_and_multiplication])).
% 55.62/8.60 thf(zip_derived_cl823, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 (~ (defined @ X0)
% 55.62/8.60 | (equalish @ X0 @ (multiply @ X1 @ X0))
% 55.62/8.60 | ~ (equalish @ X1 @ multiplicative_identity)
% 55.62/8.60 | ~ (defined @ X0))),
% 55.62/8.60 inference('sup+', [status(thm)], [zip_derived_cl465, zip_derived_cl24])).
% 55.62/8.60 thf(zip_derived_cl832, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 (~ (equalish @ X1 @ multiplicative_identity)
% 55.62/8.60 | (equalish @ X0 @ (multiply @ X1 @ X0))
% 55.62/8.60 | ~ (defined @ X0))),
% 55.62/8.60 inference('simplify', [status(thm)], [zip_derived_cl823])).
% 55.62/8.60 thf(zip_derived_cl21, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 55.62/8.60 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 55.62/8.60 thf(zip_derived_cl7, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0))
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ X1))),
% 55.62/8.60 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 55.62/8.60 thf(zip_derived_cl40, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 (~ (equalish @ X0 @ X1)
% 55.62/8.60 | ~ (equalish @ X0 @ X2)
% 55.62/8.60 | (equalish @ X1 @ X2))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl22])).
% 55.62/8.60 thf(zip_derived_cl427, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 (~ (defined @ X1)
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | (equalish @ (multiply @ X1 @ X0) @ X2)
% 55.62/8.60 | ~ (equalish @ (multiply @ X0 @ X1) @ X2))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl40])).
% 55.62/8.60 thf(associativity_multiplication, axiom,
% 55.62/8.60 (( equalish @
% 55.62/8.60 ( multiply @ X @ ( multiply @ Y @ Z ) ) @
% 55.62/8.60 ( multiply @ ( multiply @ X @ Y ) @ Z ) ) |
% 55.62/8.60 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ) | ( ~( defined @ Z ) ))).
% 55.62/8.60 thf(zip_derived_cl4, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 ( (equalish @ (multiply @ X0 @ (multiply @ X1 @ X2)) @
% 55.62/8.60 (multiply @ (multiply @ X0 @ X1) @ X2))
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (defined @ X2))),
% 55.62/8.60 inference('cnf', [status(esa)], [associativity_multiplication])).
% 55.62/8.60 thf(zip_derived_cl40, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 (~ (equalish @ X0 @ X1)
% 55.62/8.60 | ~ (equalish @ X0 @ X2)
% 55.62/8.60 | (equalish @ X1 @ X2))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl22])).
% 55.62/8.60 thf(zip_derived_cl401, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.62/8.60 (~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (defined @ X2)
% 55.62/8.60 | (equalish @ (multiply @ (multiply @ X2 @ X1) @ X0) @ X3)
% 55.62/8.60 | ~ (equalish @ (multiply @ X2 @ (multiply @ X1 @ X0)) @ X3))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl40])).
% 55.62/8.60 thf(zip_derived_cl427, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 (~ (defined @ X1)
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | (equalish @ (multiply @ X1 @ X0) @ X2)
% 55.62/8.60 | ~ (equalish @ (multiply @ X0 @ X1) @ X2))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl40])).
% 55.62/8.60 thf(multiply_not_equal_to_b_4, conjecture,
% 55.62/8.60 (equalish @ ( multiply @ a @ X ) @ b)).
% 55.62/8.60 thf(zf_stmt_1, negated_conjecture,
% 55.62/8.60 (~( equalish @ ( multiply @ a @ X ) @ b )),
% 55.62/8.60 inference('cnf.neg', [status(esa)], [multiply_not_equal_to_b_4])).
% 55.62/8.60 thf(zip_derived_cl30, plain,
% 55.62/8.60 (![X0 : $i]: ~ (equalish @ (multiply @ a @ X0) @ b)),
% 55.62/8.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 55.62/8.60 thf(zip_derived_cl20997, plain,
% 55.62/8.60 (![X0 : $i]:
% 55.62/8.60 (~ (equalish @ (multiply @ X0 @ a) @ b)
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ a))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl427, zip_derived_cl30])).
% 55.62/8.60 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 55.62/8.60 inference('cnf', [status(esa)], [a_is_defined])).
% 55.62/8.60 thf(zip_derived_cl21317, plain,
% 55.62/8.60 (![X0 : $i]: (~ (equalish @ (multiply @ X0 @ a) @ b) | ~ (defined @ X0))),
% 55.62/8.60 inference('demod', [status(thm)], [zip_derived_cl20997, zip_derived_cl27])).
% 55.62/8.60 thf(zip_derived_cl21337, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 (~ (equalish @ (multiply @ X1 @ (multiply @ X0 @ a)) @ b)
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ a)
% 55.62/8.60 | ~ (defined @ (multiply @ X1 @ X0)))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl401, zip_derived_cl21317])).
% 55.62/8.60 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 55.62/8.60 inference('cnf', [status(esa)], [a_is_defined])).
% 55.62/8.60 thf(zip_derived_cl21341, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 (~ (equalish @ (multiply @ X1 @ (multiply @ X0 @ a)) @ b)
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ (multiply @ X1 @ X0)))),
% 55.62/8.60 inference('demod', [status(thm)], [zip_derived_cl21337, zip_derived_cl27])).
% 55.62/8.60 thf(zip_derived_cl12, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 ( (defined @ (multiply @ X0 @ X1))
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ X1))),
% 55.62/8.60 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 55.62/8.60 thf(zip_derived_cl22081, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 (~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (equalish @ (multiply @ X1 @ (multiply @ X0 @ a)) @ b))),
% 55.62/8.60 inference('clc', [status(thm)], [zip_derived_cl21341, zip_derived_cl12])).
% 55.62/8.60 thf(zip_derived_cl22083, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 (~ (equalish @ (multiply @ (multiply @ X0 @ a) @ X1) @ b)
% 55.62/8.60 | ~ (defined @ (multiply @ X0 @ a))
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (defined @ X0))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl427, zip_derived_cl22081])).
% 55.62/8.60 thf(zip_derived_cl22086, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 (~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ X1)
% 55.62/8.60 | ~ (defined @ (multiply @ X0 @ a))
% 55.62/8.60 | ~ (equalish @ (multiply @ (multiply @ X0 @ a) @ X1) @ b))),
% 55.62/8.60 inference('simplify', [status(thm)], [zip_derived_cl22083])).
% 55.62/8.60 thf(zip_derived_cl22131, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]:
% 55.62/8.60 (~ (equalish @ b @ (multiply @ (multiply @ X1 @ a) @ X0))
% 55.62/8.60 | ~ (defined @ (multiply @ X1 @ a))
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ X1))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl22086])).
% 55.62/8.60 thf(zip_derived_cl49164, plain,
% 55.62/8.60 (![X0 : $i]:
% 55.62/8.60 (~ (defined @ b)
% 55.62/8.60 | ~ (equalish @ (multiply @ X0 @ a) @ multiplicative_identity)
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ b)
% 55.62/8.60 | ~ (defined @ (multiply @ X0 @ a)))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl832, zip_derived_cl22131])).
% 55.62/8.60 thf(b_is_defined, axiom, (defined @ b)).
% 55.62/8.60 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 55.62/8.60 inference('cnf', [status(esa)], [b_is_defined])).
% 55.62/8.60 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 55.62/8.60 inference('cnf', [status(esa)], [b_is_defined])).
% 55.62/8.60 thf(zip_derived_cl49853, plain,
% 55.62/8.60 (![X0 : $i]:
% 55.62/8.60 (~ (equalish @ (multiply @ X0 @ a) @ multiplicative_identity)
% 55.62/8.60 | ~ (defined @ X0)
% 55.62/8.60 | ~ (defined @ (multiply @ X0 @ a)))),
% 55.62/8.60 inference('demod', [status(thm)],
% 55.62/8.60 [zip_derived_cl49164, zip_derived_cl28, zip_derived_cl28])).
% 55.62/8.60 thf(zip_derived_cl49872, plain,
% 55.62/8.60 ((~ (equalish @ multiplicative_identity @ multiplicative_identity)
% 55.62/8.60 | ~ (defined @ (multiply @ (multiplicative_inverse @ a) @ a))
% 55.62/8.60 | ~ (defined @ (multiplicative_inverse @ a)))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl449, zip_derived_cl49853])).
% 55.62/8.60 thf(zip_derived_cl189, plain,
% 55.62/8.60 ( (equalish @ (multiply @ a @ (multiplicative_inverse @ a)) @
% 55.62/8.60 multiplicative_identity)),
% 55.62/8.60 inference('demod', [status(thm)], [zip_derived_cl187, zip_derived_cl29])).
% 55.62/8.60 thf(zip_derived_cl40, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.62/8.60 (~ (equalish @ X0 @ X1)
% 55.62/8.60 | ~ (equalish @ X0 @ X2)
% 55.62/8.60 | (equalish @ X1 @ X2))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl22])).
% 55.62/8.60 thf(zip_derived_cl48, plain,
% 55.62/8.60 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X0) | ~ (equalish @ X1 @ X0))),
% 55.62/8.60 inference('eq_fact', [status(thm)], [zip_derived_cl40])).
% 55.62/8.60 thf(zip_derived_cl342, plain,
% 55.62/8.60 ( (equalish @ multiplicative_identity @ multiplicative_identity)),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl48])).
% 55.62/8.60 thf(zip_derived_cl89, plain, ( (defined @ (multiplicative_inverse @ a))),
% 55.62/8.60 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl29])).
% 55.62/8.60 thf(zip_derived_cl49878, plain,
% 55.62/8.60 (~ (defined @ (multiply @ (multiplicative_inverse @ a) @ a))),
% 55.62/8.60 inference('demod', [status(thm)],
% 55.62/8.60 [zip_derived_cl49872, zip_derived_cl342, zip_derived_cl89])).
% 55.62/8.60 thf(zip_derived_cl49880, plain,
% 55.62/8.60 ((~ (defined @ a) | ~ (defined @ (multiplicative_inverse @ a)))),
% 55.62/8.60 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl49878])).
% 55.62/8.60 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 55.62/8.60 inference('cnf', [status(esa)], [a_is_defined])).
% 55.62/8.60 thf(zip_derived_cl89, plain, ( (defined @ (multiplicative_inverse @ a))),
% 55.62/8.60 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl29])).
% 55.62/8.60 thf(zip_derived_cl49881, plain, ($false),
% 55.62/8.60 inference('demod', [status(thm)],
% 55.62/8.60 [zip_derived_cl49880, zip_derived_cl27, zip_derived_cl89])).
% 55.62/8.60
% 55.62/8.60 % SZS output end Refutation
% 55.62/8.60
% 55.62/8.60
% 55.62/8.60 % Terminating...
% 56.14/8.67 % Runner terminated.
% 56.14/8.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------