TSTP Solution File: FLD029-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD029-3 : 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.HZHMldyagz true
% Computer : n014.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 22:39:17 EDT 2023
% Result : Unsatisfiable 1.34s 1.20s
% Output : Refutation 1.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD029-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HZHMldyagz true
% 0.13/0.35 % Computer : n014.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 : Sun Aug 27 23:51:16 EDT 2023
% 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
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.34/1.20 % Solved by fo/fo3_bce.sh.
% 1.34/1.20 % BCE start: 34
% 1.34/1.20 % BCE eliminated: 0
% 1.34/1.20 % PE start: 34
% 1.34/1.20 logic: neq
% 1.34/1.20 % PE eliminated: 0
% 1.34/1.20 % done 700 iterations in 0.442s
% 1.34/1.20 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.34/1.20 % SZS output start Refutation
% 1.34/1.20 thf(sum_type, type, sum: $i > $i > $i > $o).
% 1.34/1.20 thf(b_type, type, b: $i).
% 1.34/1.20 thf(a_type, type, a: $i).
% 1.34/1.20 thf(v_type, type, v: $i).
% 1.34/1.20 thf(product_type, type, product: $i > $i > $i > $o).
% 1.34/1.20 thf(additive_identity_type, type, additive_identity: $i).
% 1.34/1.20 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.34/1.20 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 1.34/1.20 thf(u_type, type, u: $i).
% 1.34/1.20 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 1.34/1.20 thf(defined_type, type, defined: $i > $o).
% 1.34/1.20 thf(totality_of_multiplication, axiom,
% 1.34/1.20 (( product @ X @ Y @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 1.34/1.20 ( ~( defined @ Y ) ))).
% 1.34/1.20 thf(zip_derived_cl19, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 1.34/1.20 | ~ (defined @ X0)
% 1.34/1.20 | ~ (defined @ X1))),
% 1.34/1.20 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 1.34/1.20 thf(existence_of_inverse_multiplication, axiom,
% 1.34/1.20 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 1.34/1.20 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 1.34/1.20 thf(zip_derived_cl8, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 1.34/1.20 multiplicative_identity)
% 1.34/1.20 | (sum @ additive_identity @ X0 @ additive_identity)
% 1.34/1.20 | ~ (defined @ X0))),
% 1.34/1.20 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 1.34/1.20 thf(commutativity_multiplication, axiom,
% 1.34/1.20 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 1.34/1.20 thf(zip_derived_cl9, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 1.34/1.20 thf(zip_derived_cl147, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 (~ (defined @ X0)
% 1.34/1.20 | (sum @ additive_identity @ X0 @ additive_identity)
% 1.34/1.20 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 1.34/1.20 multiplicative_identity))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 1.34/1.20 thf(product_6, conjecture, (~( product @ a @ u @ b ))).
% 1.34/1.20 thf(zf_stmt_0, negated_conjecture, (product @ a @ u @ b),
% 1.34/1.20 inference('cnf.neg', [status(esa)], [product_6])).
% 1.34/1.20 thf(zip_derived_cl31, plain, ( (product @ a @ u @ b)),
% 1.34/1.20 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.34/1.20 thf(associativity_multiplication_1, axiom,
% 1.34/1.20 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 1.34/1.20 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 1.34/1.20 thf(zip_derived_cl5, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2)
% 1.34/1.20 | ~ (product @ X0 @ X3 @ X4)
% 1.34/1.20 | ~ (product @ X3 @ X5 @ X1)
% 1.34/1.20 | ~ (product @ X4 @ X5 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 1.34/1.20 thf(zip_derived_cl98, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 (~ (product @ b @ X1 @ X0)
% 1.34/1.20 | ~ (product @ u @ X1 @ X2)
% 1.34/1.20 | (product @ a @ X2 @ X0))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl5])).
% 1.34/1.20 thf(zip_derived_cl3791, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 ( (sum @ additive_identity @ b @ additive_identity)
% 1.34/1.20 | ~ (defined @ b)
% 1.34/1.20 | (product @ a @ X0 @ multiplicative_identity)
% 1.34/1.20 | ~ (product @ u @ (multiplicative_inverse @ b) @ X0))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl147, zip_derived_cl98])).
% 1.34/1.20 thf(not_sum_5, conjecture, (sum @ additive_identity @ b @ additive_identity)).
% 1.34/1.20 thf(zf_stmt_1, negated_conjecture,
% 1.34/1.20 (~( sum @ additive_identity @ b @ additive_identity )),
% 1.34/1.20 inference('cnf.neg', [status(esa)], [not_sum_5])).
% 1.34/1.20 thf(zip_derived_cl30, plain,
% 1.34/1.20 (~ (sum @ additive_identity @ b @ additive_identity)),
% 1.34/1.20 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.34/1.20 thf(b_is_defined, axiom, (defined @ b)).
% 1.34/1.20 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 1.34/1.20 inference('cnf', [status(esa)], [b_is_defined])).
% 1.34/1.20 thf(existence_of_identity_multiplication, axiom,
% 1.34/1.20 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 1.34/1.20 thf(zip_derived_cl7, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 1.34/1.20 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 1.34/1.20 thf(zip_derived_cl9, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 1.34/1.20 thf(zip_derived_cl47, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 1.34/1.20 thf(zip_derived_cl31, plain, ( (product @ a @ u @ b)),
% 1.34/1.20 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.34/1.20 thf(zip_derived_cl9, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 1.34/1.20 thf(zip_derived_cl48, plain, ( (product @ u @ a @ b)),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl9])).
% 1.34/1.20 thf(associativity_multiplication_2, axiom,
% 1.34/1.20 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 1.34/1.20 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 1.34/1.20 thf(zip_derived_cl6, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2)
% 1.34/1.20 | ~ (product @ X3 @ X4 @ X0)
% 1.34/1.20 | ~ (product @ X4 @ X1 @ X5)
% 1.34/1.20 | ~ (product @ X3 @ X5 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 1.34/1.20 thf(zip_derived_cl124, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 (~ (product @ u @ X1 @ X0)
% 1.34/1.20 | ~ (product @ a @ X2 @ X1)
% 1.34/1.20 | (product @ b @ X2 @ X0))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl6])).
% 1.34/1.20 thf(zip_derived_cl401, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 (~ (defined @ u)
% 1.34/1.20 | (product @ b @ X0 @ u)
% 1.34/1.20 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl124])).
% 1.34/1.20 thf(u_is_defined, axiom, (defined @ u)).
% 1.34/1.20 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 1.34/1.20 inference('cnf', [status(esa)], [u_is_defined])).
% 1.34/1.20 thf(zip_derived_cl406, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 ( (product @ b @ X0 @ u)
% 1.34/1.20 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 1.34/1.20 inference('demod', [status(thm)], [zip_derived_cl401, zip_derived_cl28])).
% 1.34/1.20 thf(zip_derived_cl47, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 1.34/1.20 thf(product_7, conjecture, (~( product @ a @ v @ b ))).
% 1.34/1.20 thf(zf_stmt_2, negated_conjecture, (product @ a @ v @ b),
% 1.34/1.20 inference('cnf.neg', [status(esa)], [product_7])).
% 1.34/1.20 thf(zip_derived_cl32, plain, ( (product @ a @ v @ b)),
% 1.34/1.20 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.34/1.20 thf(zip_derived_cl9, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 1.34/1.20 thf(zip_derived_cl49, plain, ( (product @ v @ a @ b)),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl9])).
% 1.34/1.20 thf(zip_derived_cl6, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2)
% 1.34/1.20 | ~ (product @ X3 @ X4 @ X0)
% 1.34/1.20 | ~ (product @ X4 @ X1 @ X5)
% 1.34/1.20 | ~ (product @ X3 @ X5 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 1.34/1.20 thf(zip_derived_cl125, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 (~ (product @ v @ X1 @ X0)
% 1.34/1.20 | ~ (product @ a @ X2 @ X1)
% 1.34/1.20 | (product @ b @ X2 @ X0))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl6])).
% 1.34/1.20 thf(zip_derived_cl464, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 (~ (defined @ v)
% 1.34/1.20 | (product @ b @ X0 @ v)
% 1.34/1.20 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl125])).
% 1.34/1.20 thf(v_is_defined, axiom, (defined @ v)).
% 1.34/1.20 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 1.34/1.20 inference('cnf', [status(esa)], [v_is_defined])).
% 1.34/1.20 thf(zip_derived_cl469, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 ( (product @ b @ X0 @ v)
% 1.34/1.20 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 1.34/1.20 inference('demod', [status(thm)], [zip_derived_cl464, zip_derived_cl29])).
% 1.34/1.20 thf(zip_derived_cl47, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 1.34/1.20 thf(zip_derived_cl31, plain, ( (product @ a @ u @ b)),
% 1.34/1.20 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.34/1.20 thf(zip_derived_cl31, plain, ( (product @ a @ u @ b)),
% 1.34/1.20 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.34/1.20 thf(zip_derived_cl6, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2)
% 1.34/1.20 | ~ (product @ X3 @ X4 @ X0)
% 1.34/1.20 | ~ (product @ X4 @ X1 @ X5)
% 1.34/1.20 | ~ (product @ X3 @ X5 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 1.34/1.20 thf(zip_derived_cl122, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 (~ (product @ a @ X1 @ X0)
% 1.34/1.20 | ~ (product @ u @ X2 @ X1)
% 1.34/1.20 | (product @ b @ X2 @ X0))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl6])).
% 1.34/1.20 thf(zip_derived_cl215, plain,
% 1.34/1.20 (![X0 : $i]: ( (product @ b @ X0 @ b) | ~ (product @ u @ X0 @ u))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl122])).
% 1.34/1.20 thf(zip_derived_cl219, plain,
% 1.34/1.20 ((~ (defined @ u) | (product @ b @ multiplicative_identity @ b))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl215])).
% 1.34/1.20 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 1.34/1.20 inference('cnf', [status(esa)], [u_is_defined])).
% 1.34/1.20 thf(zip_derived_cl220, plain, ( (product @ b @ multiplicative_identity @ b)),
% 1.34/1.20 inference('demod', [status(thm)], [zip_derived_cl219, zip_derived_cl28])).
% 1.34/1.20 thf(zip_derived_cl9, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 1.34/1.20 thf(zip_derived_cl224, plain, ( (product @ multiplicative_identity @ b @ b)),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl220, zip_derived_cl9])).
% 1.34/1.20 thf(zip_derived_cl5, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.34/1.20 ( (product @ X0 @ X1 @ X2)
% 1.34/1.20 | ~ (product @ X0 @ X3 @ X4)
% 1.34/1.20 | ~ (product @ X3 @ X5 @ X1)
% 1.34/1.20 | ~ (product @ X4 @ X5 @ X2))),
% 1.34/1.20 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 1.34/1.20 thf(zip_derived_cl230, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/1.20 (~ (product @ b @ X1 @ X0)
% 1.34/1.20 | ~ (product @ b @ X1 @ X2)
% 1.34/1.20 | (product @ multiplicative_identity @ X2 @ X0))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl224, zip_derived_cl5])).
% 1.34/1.20 thf(zip_derived_cl600, plain,
% 1.34/1.20 (![X0 : $i, X1 : $i]:
% 1.34/1.20 (~ (product @ a @ X0 @ multiplicative_identity)
% 1.34/1.20 | (product @ multiplicative_identity @ X1 @ v)
% 1.34/1.20 | ~ (product @ b @ X0 @ X1))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl469, zip_derived_cl230])).
% 1.34/1.20 thf(zip_derived_cl1383, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 (~ (product @ a @ X0 @ multiplicative_identity)
% 1.34/1.20 | (product @ multiplicative_identity @ u @ v)
% 1.34/1.20 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl406, zip_derived_cl600])).
% 1.34/1.20 thf(not_product_8, conjecture, (product @ multiplicative_identity @ u @ v)).
% 1.34/1.20 thf(zf_stmt_3, negated_conjecture,
% 1.34/1.20 (~( product @ multiplicative_identity @ u @ v )),
% 1.34/1.20 inference('cnf.neg', [status(esa)], [not_product_8])).
% 1.34/1.20 thf(zip_derived_cl33, plain, (~ (product @ multiplicative_identity @ u @ v)),
% 1.34/1.20 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.34/1.20 thf(zip_derived_cl1392, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 (~ (product @ a @ X0 @ multiplicative_identity)
% 1.34/1.20 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 1.34/1.20 inference('demod', [status(thm)], [zip_derived_cl1383, zip_derived_cl33])).
% 1.34/1.20 thf(zip_derived_cl1393, plain,
% 1.34/1.20 (![X0 : $i]: ~ (product @ a @ X0 @ multiplicative_identity)),
% 1.34/1.20 inference('simplify', [status(thm)], [zip_derived_cl1392])).
% 1.34/1.20 thf(zip_derived_cl3856, plain,
% 1.34/1.20 (![X0 : $i]: ~ (product @ u @ (multiplicative_inverse @ b) @ X0)),
% 1.34/1.20 inference('demod', [status(thm)],
% 1.34/1.20 [zip_derived_cl3791, zip_derived_cl30, zip_derived_cl27,
% 1.34/1.20 zip_derived_cl1393])).
% 1.34/1.20 thf(zip_derived_cl3918, plain,
% 1.34/1.20 ((~ (defined @ (multiplicative_inverse @ b)) | ~ (defined @ u))),
% 1.34/1.20 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl3856])).
% 1.34/1.20 thf(zip_derived_cl30, plain,
% 1.34/1.20 (~ (sum @ additive_identity @ b @ additive_identity)),
% 1.34/1.20 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.34/1.20 thf(well_definedness_of_multiplicative_inverse, axiom,
% 1.34/1.20 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 1.34/1.20 ( sum @ additive_identity @ X @ additive_identity ))).
% 1.34/1.20 thf(zip_derived_cl17, plain,
% 1.34/1.20 (![X0 : $i]:
% 1.34/1.20 ( (defined @ (multiplicative_inverse @ X0))
% 1.34/1.20 | ~ (defined @ X0)
% 1.34/1.20 | (sum @ additive_identity @ X0 @ additive_identity))),
% 1.34/1.20 inference('cnf', [status(esa)],
% 1.34/1.20 [well_definedness_of_multiplicative_inverse])).
% 1.34/1.20 thf(zip_derived_cl81, plain,
% 1.34/1.20 ((~ (defined @ b) | (defined @ (multiplicative_inverse @ b)))),
% 1.34/1.20 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl17])).
% 1.34/1.20 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 1.34/1.20 inference('cnf', [status(esa)], [b_is_defined])).
% 1.34/1.20 thf(zip_derived_cl82, plain, ( (defined @ (multiplicative_inverse @ b))),
% 1.34/1.20 inference('demod', [status(thm)], [zip_derived_cl81, zip_derived_cl27])).
% 1.34/1.20 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 1.34/1.20 inference('cnf', [status(esa)], [u_is_defined])).
% 1.34/1.20 thf(zip_derived_cl3922, plain, ($false),
% 1.34/1.20 inference('demod', [status(thm)],
% 1.34/1.20 [zip_derived_cl3918, zip_derived_cl82, zip_derived_cl28])).
% 1.34/1.20
% 1.34/1.20 % SZS output end Refutation
% 1.34/1.20
% 1.34/1.20
% 1.34/1.20 % Terminating...
% 1.80/1.27 % Runner terminated.
% 1.80/1.27 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------