%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD004-1 : TPTP v9.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.0qmpwPDIms true
% Computer : n028.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 04:33:07 PM UTC 2025
% Result : Unsatisfiable 4.62s 1.25s
% Output : Refutation 4.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : FLD004-1 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.0qmpwPDIms true
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 18:28:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % 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
% 0.58/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.58/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.58/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 4.62/1.25 % Solved by fo/fo13.sh.
% 4.62/1.25 % done 728 iterations in 0.454s
% 4.62/1.25 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.62/1.25 % SZS output start Refutation
% 4.62/1.25 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 4.62/1.25 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 4.62/1.25 thf(defined_type, type, defined: $i > $o).
% 4.62/1.25 thf(additive_identity_type, type, additive_identity: $i).
% 4.62/1.25 thf(multiply_type, type, multiply: $i > $i > $i).
% 4.62/1.25 thf(add_type, type, add: $i > $i > $i).
% 4.62/1.25 thf(b_type, type, b: $i).
% 4.62/1.25 thf(equalish_type, type, equalish: $i > $i > $o).
% 4.62/1.25 thf(a_type, type, a: $i).
% 4.62/1.25 thf(b_not_equal_to_additive_identity_3, conjecture,
% 4.62/1.25 (equalish @ b @ additive_identity)).
% 4.62/1.25 thf(zf_stmt_0, negated_conjecture, (~( equalish @ b @ additive_identity )),
% 4.62/1.25 inference('cnf.neg', [status(esa)], [b_not_equal_to_additive_identity_3])).
% 4.62/1.25 thf(zip_derived_cl29, plain, (~ (equalish @ b @ additive_identity)),
% 4.62/1.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.62/1.25 thf(well_definedness_of_multiplicative_inverse, axiom,
% 4.62/1.25 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 4.62/1.25 ( equalish @ X @ additive_identity ))).
% 4.62/1.25 thf(zip_derived_cl14, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (defined @ (multiplicative_inverse @ X0))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | (equalish @ X0 @ additive_identity))),
% 4.62/1.25 inference('cnf', [status(esa)],
% 4.62/1.25 [well_definedness_of_multiplicative_inverse])).
% 4.62/1.25 thf(well_definedness_of_multiplication, axiom,
% 4.62/1.25 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 4.62/1.25 ( ~( defined @ Y ) ))).
% 4.62/1.25 thf(zip_derived_cl12, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]:
% 4.62/1.25 ( (defined @ (multiply @ X0 @ X1))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | ~ (defined @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 4.62/1.25 thf(existence_of_inverse_multiplication, axiom,
% 4.62/1.25 (( equalish @
% 4.62/1.25 ( multiply @ X @ ( multiplicative_inverse @ X ) ) @
% 4.62/1.25 multiplicative_identity ) |
% 4.62/1.25 ( ~( defined @ X ) ) | ( equalish @ X @ additive_identity ))).
% 4.62/1.25 thf(zip_derived_cl6, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (equalish @ (multiply @ X0 @ (multiplicative_inverse @ X0)) @
% 4.62/1.25 multiplicative_identity)
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | (equalish @ X0 @ additive_identity))),
% 4.62/1.25 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 4.62/1.25 thf(symmetry_of_equality, axiom,
% 4.62/1.25 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 4.62/1.25 thf(zip_derived_cl21, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 4.62/1.25 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 4.62/1.25 thf(zip_derived_cl111, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (equalish @ X0 @ additive_identity)
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | (equalish @ multiplicative_identity @
% 4.62/1.25 (multiply @ X0 @ (multiplicative_inverse @ X0))))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl21])).
% 4.62/1.25 thf(zip_derived_cl14, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (defined @ (multiplicative_inverse @ X0))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | (equalish @ X0 @ additive_identity))),
% 4.62/1.25 inference('cnf', [status(esa)],
% 4.62/1.25 [well_definedness_of_multiplicative_inverse])).
% 4.62/1.25 thf(zip_derived_cl14, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (defined @ (multiplicative_inverse @ X0))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | (equalish @ X0 @ additive_identity))),
% 4.62/1.25 inference('cnf', [status(esa)],
% 4.62/1.25 [well_definedness_of_multiplicative_inverse])).
% 4.62/1.25 thf(zip_derived_cl12, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]:
% 4.62/1.25 ( (defined @ (multiply @ X0 @ X1))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | ~ (defined @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 4.62/1.25 thf(zip_derived_cl14, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (defined @ (multiplicative_inverse @ X0))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | (equalish @ X0 @ additive_identity))),
% 4.62/1.25 inference('cnf', [status(esa)],
% 4.62/1.25 [well_definedness_of_multiplicative_inverse])).
% 4.62/1.25 thf(well_definedness_of_addition, axiom,
% 4.62/1.25 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 4.62/1.25 ( ~( defined @ Y ) ))).
% 4.62/1.25 thf(zip_derived_cl9, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]:
% 4.62/1.25 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 4.62/1.25 thf(zip_derived_cl14, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (defined @ (multiplicative_inverse @ X0))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | (equalish @ X0 @ additive_identity))),
% 4.62/1.25 inference('cnf', [status(esa)],
% 4.62/1.25 [well_definedness_of_multiplicative_inverse])).
% 4.62/1.25 thf(associativity_multiplication, axiom,
% 4.62/1.25 (( equalish @
% 4.62/1.25 ( multiply @ X @ ( multiply @ Y @ Z ) ) @
% 4.62/1.25 ( multiply @ ( multiply @ X @ Y ) @ Z ) ) |
% 4.62/1.25 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ) | ( ~( defined @ Z ) ))).
% 4.62/1.25 thf(zip_derived_cl4, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ (multiply @ X0 @ (multiply @ X1 @ X2)) @
% 4.62/1.25 (multiply @ (multiply @ X0 @ X1) @ X2))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | ~ (defined @ X1)
% 4.62/1.25 | ~ (defined @ X2))),
% 4.62/1.25 inference('cnf', [status(esa)], [associativity_multiplication])).
% 4.62/1.25 thf(zip_derived_cl9, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]:
% 4.62/1.25 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 4.62/1.25 thf(existence_of_identity_addition, axiom,
% 4.62/1.25 (( equalish @ ( add @ additive_identity @ X ) @ X ) | ( ~( defined @ X ) ))).
% 4.62/1.25 thf(zip_derived_cl1, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 4.62/1.25 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 4.62/1.25 thf(zip_derived_cl1, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 4.62/1.25 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 4.62/1.25 thf(multiply_not_equal_to_a_4, conjecture,
% 4.62/1.25 (equalish @
% 4.62/1.25 ( multiply @ a @ ( multiply @ b @ ( multiplicative_inverse @ b ) ) ) @ a)).
% 4.62/1.25 thf(zf_stmt_1, negated_conjecture,
% 4.62/1.25 (~( equalish @
% 4.62/1.25 ( multiply @ a @ ( multiply @ b @ ( multiplicative_inverse @ b ) ) ) @
% 4.62/1.25 a )),
% 4.62/1.25 inference('cnf.neg', [status(esa)], [multiply_not_equal_to_a_4])).
% 4.62/1.25 thf(zip_derived_cl30, plain,
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ a @ (multiply @ b @ (multiplicative_inverse @ b))) @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [zf_stmt_1])).
% 4.62/1.25 thf(transitivity_of_equality, axiom,
% 4.62/1.25 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 4.62/1.25 ( ~( equalish @ Y @ Z ) ))).
% 4.62/1.25 thf(zip_derived_cl22, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ X0 @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X2)
% 4.62/1.25 | ~ (equalish @ X2 @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 4.62/1.25 thf(zip_derived_cl42, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ a @ (multiply @ b @ (multiplicative_inverse @ b))) @
% 4.62/1.25 X0)
% 4.62/1.25 | ~ (equalish @ X0 @ a))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl52, plain,
% 4.62/1.25 ((~ (defined @ a)
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ a @ (multiply @ b @ (multiplicative_inverse @ b))) @
% 4.62/1.25 (add @ additive_identity @ a)))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl42])).
% 4.62/1.25 thf(a_is_defined, axiom, (defined @ a)).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl55, plain,
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ a @ (multiply @ b @ (multiplicative_inverse @ b))) @
% 4.62/1.25 (add @ additive_identity @ a))),
% 4.62/1.25 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl27])).
% 4.62/1.25 thf(zip_derived_cl22, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ X0 @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X2)
% 4.62/1.25 | ~ (equalish @ X2 @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 4.62/1.25 thf(zip_derived_cl59, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ a @ (multiply @ b @ (multiplicative_inverse @ b))) @
% 4.62/1.25 X0)
% 4.62/1.25 | ~ (equalish @ X0 @ (add @ additive_identity @ a)))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl95, plain,
% 4.62/1.25 ((~ (defined @ (add @ additive_identity @ a))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ a @ (multiply @ b @ (multiplicative_inverse @ b))) @
% 4.62/1.25 (add @ additive_identity @ (add @ additive_identity @ a))))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl59])).
% 4.62/1.25 thf(zip_derived_cl173, plain,
% 4.62/1.25 ((~ (defined @ a)
% 4.62/1.25 | ~ (defined @ additive_identity)
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ a @ (multiply @ b @ (multiplicative_inverse @ b))) @
% 4.62/1.25 (add @ additive_identity @ (add @ additive_identity @ a))))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl95])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(well_definedness_of_additive_identity, axiom,
% 4.62/1.25 (defined @ additive_identity)).
% 4.62/1.25 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 4.62/1.25 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 4.62/1.25 thf(zip_derived_cl174, plain,
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ a @ (multiply @ b @ (multiplicative_inverse @ b))) @
% 4.62/1.25 (add @ additive_identity @ (add @ additive_identity @ a)))),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl173, zip_derived_cl27, zip_derived_cl10])).
% 4.62/1.25 thf(zip_derived_cl22, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ X0 @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X2)
% 4.62/1.25 | ~ (equalish @ X2 @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 4.62/1.25 thf(zip_derived_cl177, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ a @ (multiply @ b @ (multiplicative_inverse @ b))) @
% 4.62/1.25 X0)
% 4.62/1.25 | ~ (equalish @ X0 @
% 4.62/1.25 (add @ additive_identity @ (add @ additive_identity @ a))))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl219, plain,
% 4.62/1.25 ((~ (defined @ (multiplicative_inverse @ b))
% 4.62/1.25 | ~ (defined @ b)
% 4.62/1.25 | ~ (defined @ a)
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b)) @
% 4.62/1.25 (add @ additive_identity @ (add @ additive_identity @ a))))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl177])).
% 4.62/1.25 thf(b_is_defined, axiom, (defined @ b)).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl221, plain,
% 4.62/1.25 ((~ (defined @ (multiplicative_inverse @ b))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b)) @
% 4.62/1.25 (add @ additive_identity @ (add @ additive_identity @ a))))),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl219, zip_derived_cl28, zip_derived_cl27])).
% 4.62/1.25 thf(zip_derived_cl224, plain,
% 4.62/1.25 (( (equalish @ b @ additive_identity)
% 4.62/1.25 | ~ (defined @ b)
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b)) @
% 4.62/1.25 (add @ additive_identity @ (add @ additive_identity @ a))))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl221])).
% 4.62/1.25 thf(zip_derived_cl29, plain, (~ (equalish @ b @ additive_identity)),
% 4.62/1.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl225, plain,
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b)) @
% 4.62/1.25 (add @ additive_identity @ (add @ additive_identity @ a)))),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl224, zip_derived_cl29, zip_derived_cl28])).
% 4.62/1.25 thf(zip_derived_cl21, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 4.62/1.25 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 4.62/1.25 thf(zip_derived_cl227, plain,
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (add @ additive_identity @ (add @ additive_identity @ a)) @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b)))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl225, zip_derived_cl21])).
% 4.62/1.25 thf(zip_derived_cl1, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 4.62/1.25 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 4.62/1.25 thf(zip_derived_cl22, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ X0 @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X2)
% 4.62/1.25 | ~ (equalish @ X2 @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 4.62/1.25 thf(zip_derived_cl47, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]:
% 4.62/1.25 (~ (defined @ X0)
% 4.62/1.25 | (equalish @ (add @ additive_identity @ X0) @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X1))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl570, plain,
% 4.62/1.25 ((~ (defined @ (add @ additive_identity @ a))
% 4.62/1.25 | ~ (equalish @ (add @ additive_identity @ a) @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b))))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl227, zip_derived_cl47])).
% 4.62/1.25 thf(zip_derived_cl600, plain,
% 4.62/1.25 ((~ (defined @ a)
% 4.62/1.25 | ~ (defined @ additive_identity)
% 4.62/1.25 | ~ (equalish @ (add @ additive_identity @ a) @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b))))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl570])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 4.62/1.25 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 4.62/1.25 thf(zip_derived_cl601, plain,
% 4.62/1.25 (~ (equalish @ (add @ additive_identity @ a) @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b)))),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl600, zip_derived_cl27, zip_derived_cl10])).
% 4.62/1.25 thf(zip_derived_cl47, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]:
% 4.62/1.25 (~ (defined @ X0)
% 4.62/1.25 | (equalish @ (add @ additive_identity @ X0) @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X1))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl607, plain,
% 4.62/1.25 ((~ (defined @ a)
% 4.62/1.25 | ~ (equalish @ a @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b))))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl601, zip_derived_cl47])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl608, plain,
% 4.62/1.25 (~ (equalish @ a @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b)))),
% 4.62/1.25 inference('demod', [status(thm)], [zip_derived_cl607, zip_derived_cl27])).
% 4.62/1.25 thf(zip_derived_cl21, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 4.62/1.25 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 4.62/1.25 thf(zip_derived_cl610, plain,
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ a @ b) @ (multiplicative_inverse @ b)) @ a)),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl608, zip_derived_cl21])).
% 4.62/1.25 thf(commutativity_multiplication, axiom,
% 4.62/1.25 (( equalish @ ( multiply @ X @ Y ) @ ( multiply @ Y @ X ) ) |
% 4.62/1.25 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 4.62/1.25 thf(zip_derived_cl7, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]:
% 4.62/1.25 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | ~ (defined @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 4.62/1.25 thf(zip_derived_cl22, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ X0 @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X2)
% 4.62/1.25 | ~ (equalish @ X2 @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 4.62/1.25 thf(zip_derived_cl137, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 (~ (defined @ X1)
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | (equalish @ (multiply @ X0 @ X1) @ X2)
% 4.62/1.25 | ~ (equalish @ (multiply @ X1 @ X0) @ X2))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl1801, plain,
% 4.62/1.25 ((~ (defined @ (multiplicative_inverse @ b))
% 4.62/1.25 | ~ (defined @ (multiply @ a @ b))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiplicative_inverse @ b) @ (multiply @ a @ b)) @ a))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl610, zip_derived_cl137])).
% 4.62/1.25 thf(zip_derived_cl1878, plain,
% 4.62/1.25 (( (equalish @ b @ additive_identity)
% 4.62/1.25 | ~ (defined @ b)
% 4.62/1.25 | ~ (defined @ (multiply @ a @ b))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiplicative_inverse @ b) @ (multiply @ a @ b)) @ a))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl1801])).
% 4.62/1.25 thf(zip_derived_cl29, plain, (~ (equalish @ b @ additive_identity)),
% 4.62/1.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl1879, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ a @ b))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiplicative_inverse @ b) @ (multiply @ a @ b)) @ a))),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl1878, zip_derived_cl29, zip_derived_cl28])).
% 4.62/1.25 thf(zip_derived_cl1880, plain,
% 4.62/1.25 ((~ (defined @ b)
% 4.62/1.25 | ~ (defined @ a)
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiplicative_inverse @ b) @ (multiply @ a @ b)) @ a))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl1879])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl1881, plain,
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ (multiplicative_inverse @ b) @ (multiply @ a @ b)) @ a)),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl1880, zip_derived_cl28, zip_derived_cl27])).
% 4.62/1.25 thf(zip_derived_cl4, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ (multiply @ X0 @ (multiply @ X1 @ X2)) @
% 4.62/1.25 (multiply @ (multiply @ X0 @ X1) @ X2))
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | ~ (defined @ X1)
% 4.62/1.25 | ~ (defined @ X2))),
% 4.62/1.25 inference('cnf', [status(esa)], [associativity_multiplication])).
% 4.62/1.25 thf(zip_derived_cl22, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ X0 @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X2)
% 4.62/1.25 | ~ (equalish @ X2 @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 4.62/1.25 thf(zip_derived_cl88, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.62/1.25 (~ (defined @ X0)
% 4.62/1.25 | ~ (defined @ X1)
% 4.62/1.25 | ~ (defined @ X2)
% 4.62/1.25 | (equalish @ (multiply @ X2 @ (multiply @ X1 @ X0)) @ X3)
% 4.62/1.25 | ~ (equalish @ (multiply @ (multiply @ X2 @ X1) @ X0) @ X3))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl1888, plain,
% 4.62/1.25 ((~ (defined @ b)
% 4.62/1.25 | ~ (defined @ a)
% 4.62/1.25 | ~ (defined @ (multiplicative_inverse @ b))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ (multiplicative_inverse @ b) @ a) @ b) @ a))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl1881, zip_derived_cl88])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl1889, plain,
% 4.62/1.25 ((~ (defined @ (multiplicative_inverse @ b))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ (multiplicative_inverse @ b) @ a) @ b) @ a))),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl1888, zip_derived_cl28, zip_derived_cl27])).
% 4.62/1.25 thf(zip_derived_cl1940, plain,
% 4.62/1.25 (( (equalish @ b @ additive_identity)
% 4.62/1.25 | ~ (defined @ b)
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ (multiplicative_inverse @ b) @ a) @ b) @ a))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl1889])).
% 4.62/1.25 thf(zip_derived_cl29, plain, (~ (equalish @ b @ additive_identity)),
% 4.62/1.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl1941, plain,
% 4.62/1.25 (~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ (multiplicative_inverse @ b) @ a) @ b) @ a)),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl1940, zip_derived_cl29, zip_derived_cl28])).
% 4.62/1.25 thf(zip_derived_cl137, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 (~ (defined @ X1)
% 4.62/1.25 | ~ (defined @ X0)
% 4.62/1.25 | (equalish @ (multiply @ X0 @ X1) @ X2)
% 4.62/1.25 | ~ (equalish @ (multiply @ X1 @ X0) @ X2))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl1947, plain,
% 4.62/1.25 ((~ (defined @ b)
% 4.62/1.25 | ~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ b @ (multiply @ (multiplicative_inverse @ b) @ a)) @ a))),
% 4.62/1.25 inference('s_sup+', [status(thm)],
% 4.62/1.25 [zip_derived_cl1941, zip_derived_cl137])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl1948, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ b @ (multiply @ (multiplicative_inverse @ b) @ a)) @ a))),
% 4.62/1.25 inference('demod', [status(thm)], [zip_derived_cl1947, zip_derived_cl28])).
% 4.62/1.25 thf(zip_derived_cl88, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.62/1.25 (~ (defined @ X0)
% 4.62/1.25 | ~ (defined @ X1)
% 4.62/1.25 | ~ (defined @ X2)
% 4.62/1.25 | (equalish @ (multiply @ X2 @ (multiply @ X1 @ X0)) @ X3)
% 4.62/1.25 | ~ (equalish @ (multiply @ (multiply @ X2 @ X1) @ X0) @ X3))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl2359, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (defined @ a)
% 4.62/1.25 | ~ (defined @ (multiplicative_inverse @ b))
% 4.62/1.25 | ~ (defined @ b)
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ b @ (multiplicative_inverse @ b)) @ a) @ a))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl1948, zip_derived_cl88])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl2362, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (defined @ (multiplicative_inverse @ b))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ b @ (multiplicative_inverse @ b)) @ a) @ a))),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl2359, zip_derived_cl27, zip_derived_cl28])).
% 4.62/1.25 thf(zip_derived_cl2524, plain,
% 4.62/1.25 (( (equalish @ b @ additive_identity)
% 4.62/1.25 | ~ (defined @ b)
% 4.62/1.25 | ~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ b @ (multiplicative_inverse @ b)) @ a) @ a))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl2362])).
% 4.62/1.25 thf(zip_derived_cl29, plain, (~ (equalish @ b @ additive_identity)),
% 4.62/1.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl2525, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (equalish @
% 4.62/1.25 (multiply @ (multiply @ b @ (multiplicative_inverse @ b)) @ a) @ a))),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl2524, zip_derived_cl29, zip_derived_cl28])).
% 4.62/1.25 thf(zip_derived_cl21, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 4.62/1.25 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 4.62/1.25 thf(zip_derived_cl2527, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (equalish @ a @
% 4.62/1.25 (multiply @ (multiply @ b @ (multiplicative_inverse @ b)) @ a)))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl2525, zip_derived_cl21])).
% 4.62/1.25 thf(existence_of_identity_multiplication, axiom,
% 4.62/1.25 (( equalish @ ( multiply @ multiplicative_identity @ X ) @ X ) |
% 4.62/1.25 ( ~( defined @ X ) ))).
% 4.62/1.25 thf(zip_derived_cl5, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 ( (equalish @ (multiply @ multiplicative_identity @ X0) @ X0)
% 4.62/1.25 | ~ (defined @ X0))),
% 4.62/1.25 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 4.62/1.25 thf(zip_derived_cl21, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 4.62/1.25 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 4.62/1.25 thf(zip_derived_cl36, plain,
% 4.62/1.25 (![X0 : $i]:
% 4.62/1.25 (~ (defined @ X0)
% 4.62/1.25 | (equalish @ X0 @ (multiply @ multiplicative_identity @ X0)))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl21])).
% 4.62/1.25 thf(zip_derived_cl22, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ X0 @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X2)
% 4.62/1.25 | ~ (equalish @ X2 @ X1))),
% 4.62/1.25 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 4.62/1.25 thf(zip_derived_cl46, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i]:
% 4.62/1.25 (~ (defined @ X0)
% 4.62/1.25 | (equalish @ X0 @ X1)
% 4.62/1.25 | ~ (equalish @ (multiply @ multiplicative_identity @ X0) @ X1))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl22])).
% 4.62/1.25 thf(zip_derived_cl2537, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (defined @ a)
% 4.62/1.25 | ~ (equalish @ (multiply @ multiplicative_identity @ a) @
% 4.62/1.25 (multiply @ (multiply @ b @ (multiplicative_inverse @ b)) @ a)))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl2527, zip_derived_cl46])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl2539, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (equalish @ (multiply @ multiplicative_identity @ a) @
% 4.62/1.25 (multiply @ (multiply @ b @ (multiplicative_inverse @ b)) @ a)))),
% 4.62/1.25 inference('demod', [status(thm)], [zip_derived_cl2537, zip_derived_cl27])).
% 4.62/1.25 thf(compatibility_of_equality_and_multiplication, axiom,
% 4.62/1.25 (( equalish @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) |
% 4.62/1.25 ( ~( defined @ Z ) ) | ( ~( equalish @ X @ Y ) ))).
% 4.62/1.25 thf(zip_derived_cl24, plain,
% 4.62/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.62/1.25 ( (equalish @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1))
% 4.62/1.25 | ~ (defined @ X1)
% 4.62/1.25 | ~ (equalish @ X0 @ X2))),
% 4.62/1.25 inference('cnf', [status(esa)],
% 4.62/1.25 [compatibility_of_equality_and_multiplication])).
% 4.62/1.25 thf(zip_derived_cl2734, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (defined @ a)
% 4.62/1.25 | ~ (equalish @ multiplicative_identity @
% 4.62/1.25 (multiply @ b @ (multiplicative_inverse @ b))))),
% 4.62/1.25 inference('s_sup+', [status(thm)], [zip_derived_cl2539, zip_derived_cl24])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl2737, plain,
% 4.62/1.25 ((~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))
% 4.62/1.25 | ~ (equalish @ multiplicative_identity @
% 4.62/1.25 (multiply @ b @ (multiplicative_inverse @ b))))),
% 4.62/1.25 inference('demod', [status(thm)], [zip_derived_cl2734, zip_derived_cl27])).
% 4.62/1.25 thf(zip_derived_cl2745, plain,
% 4.62/1.25 ((~ (defined @ b)
% 4.62/1.25 | (equalish @ b @ additive_identity)
% 4.62/1.25 | ~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a)))),
% 4.62/1.25 inference('s_sup-', [status(thm)],
% 4.62/1.25 [zip_derived_cl111, zip_derived_cl2737])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl29, plain, (~ (equalish @ b @ additive_identity)),
% 4.62/1.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.62/1.25 thf(zip_derived_cl2746, plain,
% 4.62/1.25 (~ (defined @ (multiply @ (multiplicative_inverse @ b) @ a))),
% 4.62/1.25 inference('demod', [status(thm)],
% 4.62/1.25 [zip_derived_cl2745, zip_derived_cl28, zip_derived_cl29])).
% 4.62/1.25 thf(zip_derived_cl2751, plain,
% 4.62/1.25 ((~ (defined @ a) | ~ (defined @ (multiplicative_inverse @ b)))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl2746])).
% 4.62/1.25 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 4.62/1.25 inference('cnf', [status(esa)], [a_is_defined])).
% 4.62/1.25 thf(zip_derived_cl2752, plain, (~ (defined @ (multiplicative_inverse @ b))),
% 4.62/1.25 inference('demod', [status(thm)], [zip_derived_cl2751, zip_derived_cl27])).
% 4.62/1.25 thf(zip_derived_cl2754, plain,
% 4.62/1.25 (( (equalish @ b @ additive_identity) | ~ (defined @ b))),
% 4.62/1.25 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl2752])).
% 4.62/1.25 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 4.62/1.25 inference('cnf', [status(esa)], [b_is_defined])).
% 4.62/1.25 thf(zip_derived_cl2755, plain, ( (equalish @ b @ additive_identity)),
% 4.62/1.25 inference('demod', [status(thm)], [zip_derived_cl2754, zip_derived_cl28])).
% 4.62/1.25 thf(zip_derived_cl2756, plain, ($false),
% 4.62/1.25 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl2755])).
% 4.62/1.25
% 4.62/1.25 % SZS output end Refutation
% 4.62/1.25
% 4.62/1.25
% 4.62/1.25 % Terminating...
% 5.05/1.36 % Runner terminated.
% 5.05/1.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------