%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD028-3 : 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.AoBZKjlhQR true
% Computer : n018.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 04:33:13 PM UTC 2025
% Result : Unsatisfiable 6.83s 1.54s
% Output : Refutation 6.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : FLD028-3 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.11/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.AoBZKjlhQR true
% 0.13/0.35 % Computer : n018.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 18:29:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/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
% 0.48/0.61 % Total configuration time : 435
% 0.48/0.61 % Estimated wc time : 1092
% 0.48/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 6.83/1.54 % Solved by fo/fo5.sh.
% 6.83/1.54 % done 1178 iterations in 0.791s
% 6.83/1.54 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 6.83/1.54 % SZS output start Refutation
% 6.83/1.54 thf(sum_type, type, sum: $i > $i > $i > $o).
% 6.83/1.54 thf(b_type, type, b: $i).
% 6.83/1.54 thf(a_type, type, a: $i).
% 6.83/1.54 thf(v_type, type, v: $i).
% 6.83/1.54 thf(product_type, type, product: $i > $i > $i > $o).
% 6.83/1.54 thf(additive_identity_type, type, additive_identity: $i).
% 6.83/1.54 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 6.83/1.54 thf(u_type, type, u: $i).
% 6.83/1.54 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 6.83/1.54 thf(defined_type, type, defined: $i > $o).
% 6.83/1.54 thf(not_product_8, conjecture, (product @ multiplicative_identity @ u @ v)).
% 6.83/1.54 thf(zf_stmt_0, negated_conjecture,
% 6.83/1.54 (~( product @ multiplicative_identity @ u @ v )),
% 6.83/1.54 inference('cnf.neg', [status(esa)], [not_product_8])).
% 6.83/1.54 thf(zip_derived_cl33, plain, (~ (product @ multiplicative_identity @ u @ v)),
% 6.83/1.54 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.83/1.54 thf(existence_of_inverse_multiplication, axiom,
% 6.83/1.54 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 6.83/1.54 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 6.83/1.54 thf(zip_derived_cl8, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 6.83/1.54 multiplicative_identity)
% 6.83/1.54 | (sum @ additive_identity @ X0 @ additive_identity)
% 6.83/1.54 | ~ (defined @ X0))),
% 6.83/1.54 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 6.83/1.54 thf(commutativity_multiplication, axiom,
% 6.83/1.54 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 6.83/1.54 thf(zip_derived_cl9, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 6.83/1.54 thf(zip_derived_cl185, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 (~ (defined @ X0)
% 6.83/1.54 | (sum @ additive_identity @ X0 @ additive_identity)
% 6.83/1.54 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 6.83/1.54 multiplicative_identity))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 6.83/1.54 thf(zip_derived_cl185, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 (~ (defined @ X0)
% 6.83/1.54 | (sum @ additive_identity @ X0 @ additive_identity)
% 6.83/1.54 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 6.83/1.54 multiplicative_identity))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 6.83/1.54 thf(existence_of_identity_multiplication, axiom,
% 6.83/1.54 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 6.83/1.54 thf(zip_derived_cl7, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 6.83/1.54 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 6.83/1.54 thf(zip_derived_cl9, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 6.83/1.54 thf(zip_derived_cl56, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 6.83/1.54 thf(product_6, conjecture, (~( product @ a @ u @ b ))).
% 6.83/1.54 thf(zf_stmt_1, negated_conjecture, (product @ a @ u @ b),
% 6.83/1.54 inference('cnf.neg', [status(esa)], [product_6])).
% 6.83/1.54 thf(zip_derived_cl31, plain, ( (product @ a @ u @ b)),
% 6.83/1.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 6.83/1.54 thf(zip_derived_cl9, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 6.83/1.54 thf(zip_derived_cl57, plain, ( (product @ u @ a @ b)),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl9])).
% 6.83/1.54 thf(associativity_multiplication_2, axiom,
% 6.83/1.54 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 6.83/1.54 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 6.83/1.54 thf(zip_derived_cl6, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2)
% 6.83/1.54 | ~ (product @ X3 @ X4 @ X0)
% 6.83/1.54 | ~ (product @ X4 @ X1 @ X5)
% 6.83/1.54 | ~ (product @ X3 @ X5 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 6.83/1.54 thf(zip_derived_cl152, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 (~ (product @ u @ X1 @ X0)
% 6.83/1.54 | ~ (product @ a @ X2 @ X1)
% 6.83/1.54 | (product @ b @ X2 @ X0))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl6])).
% 6.83/1.54 thf(zip_derived_cl314, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 (~ (defined @ u)
% 6.83/1.54 | (product @ b @ X0 @ u)
% 6.83/1.54 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl152])).
% 6.83/1.54 thf(u_is_defined, axiom, (defined @ u)).
% 6.83/1.54 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 6.83/1.54 inference('cnf', [status(esa)], [u_is_defined])).
% 6.83/1.54 thf(zip_derived_cl316, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 ( (product @ b @ X0 @ u)
% 6.83/1.54 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 6.83/1.54 inference('demod', [status(thm)], [zip_derived_cl314, zip_derived_cl28])).
% 6.83/1.54 thf(zip_derived_cl2849, plain,
% 6.83/1.54 (( (sum @ additive_identity @ a @ additive_identity)
% 6.83/1.54 | ~ (defined @ a)
% 6.83/1.54 | (product @ b @ (multiplicative_inverse @ a) @ u))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl316])).
% 6.83/1.54 thf(not_sum_5, conjecture, (sum @ additive_identity @ a @ additive_identity)).
% 6.83/1.54 thf(zf_stmt_2, negated_conjecture,
% 6.83/1.54 (~( sum @ additive_identity @ a @ additive_identity )),
% 6.83/1.54 inference('cnf.neg', [status(esa)], [not_sum_5])).
% 6.83/1.54 thf(zip_derived_cl30, plain,
% 6.83/1.54 (~ (sum @ additive_identity @ a @ additive_identity)),
% 6.83/1.54 inference('cnf', [status(esa)], [zf_stmt_2])).
% 6.83/1.54 thf(a_is_defined, axiom, (defined @ a)).
% 6.83/1.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 6.83/1.54 inference('cnf', [status(esa)], [a_is_defined])).
% 6.83/1.54 thf(zip_derived_cl2888, plain,
% 6.83/1.54 ( (product @ b @ (multiplicative_inverse @ a) @ u)),
% 6.83/1.54 inference('demod', [status(thm)],
% 6.83/1.54 [zip_derived_cl2849, zip_derived_cl30, zip_derived_cl26])).
% 6.83/1.54 thf(product_7, conjecture, (~( product @ a @ v @ b ))).
% 6.83/1.54 thf(zf_stmt_3, negated_conjecture, (product @ a @ v @ b),
% 6.83/1.54 inference('cnf.neg', [status(esa)], [product_7])).
% 6.83/1.54 thf(zip_derived_cl32, plain, ( (product @ a @ v @ b)),
% 6.83/1.54 inference('cnf', [status(esa)], [zf_stmt_3])).
% 6.83/1.54 thf(zip_derived_cl9, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 6.83/1.54 thf(zip_derived_cl58, plain, ( (product @ v @ a @ b)),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl9])).
% 6.83/1.54 thf(associativity_multiplication_1, axiom,
% 6.83/1.54 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 6.83/1.54 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 6.83/1.54 thf(zip_derived_cl5, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2)
% 6.83/1.54 | ~ (product @ X0 @ X3 @ X4)
% 6.83/1.54 | ~ (product @ X3 @ X5 @ X1)
% 6.83/1.54 | ~ (product @ X4 @ X5 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 6.83/1.54 thf(zip_derived_cl106, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 (~ (product @ b @ X1 @ X0)
% 6.83/1.54 | ~ (product @ a @ X1 @ X2)
% 6.83/1.54 | (product @ v @ X2 @ X0))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl5])).
% 6.83/1.54 thf(zip_derived_cl2914, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 ( (product @ v @ X0 @ u)
% 6.83/1.54 | ~ (product @ a @ (multiplicative_inverse @ a) @ X0))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl2888, zip_derived_cl106])).
% 6.83/1.54 thf(zip_derived_cl4044, plain,
% 6.83/1.54 (( (sum @ additive_identity @ a @ additive_identity)
% 6.83/1.54 | ~ (defined @ a)
% 6.83/1.54 | (product @ v @ multiplicative_identity @ u))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl2914])).
% 6.83/1.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 6.83/1.54 inference('cnf', [status(esa)], [a_is_defined])).
% 6.83/1.54 thf(zip_derived_cl4046, plain,
% 6.83/1.54 (( (sum @ additive_identity @ a @ additive_identity)
% 6.83/1.54 | (product @ v @ multiplicative_identity @ u))),
% 6.83/1.54 inference('demod', [status(thm)], [zip_derived_cl4044, zip_derived_cl26])).
% 6.83/1.54 thf(zip_derived_cl30, plain,
% 6.83/1.54 (~ (sum @ additive_identity @ a @ additive_identity)),
% 6.83/1.54 inference('cnf', [status(esa)], [zf_stmt_2])).
% 6.83/1.54 thf(zip_derived_cl4047, plain,
% 6.83/1.54 ( (product @ v @ multiplicative_identity @ u)),
% 6.83/1.54 inference('clc', [status(thm)], [zip_derived_cl4046, zip_derived_cl30])).
% 6.83/1.54 thf(zip_derived_cl185, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 (~ (defined @ X0)
% 6.83/1.54 | (sum @ additive_identity @ X0 @ additive_identity)
% 6.83/1.54 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 6.83/1.54 multiplicative_identity))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 6.83/1.54 thf(zip_derived_cl56, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 6.83/1.54 thf(zip_derived_cl58, plain, ( (product @ v @ a @ b)),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl9])).
% 6.83/1.54 thf(zip_derived_cl6, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2)
% 6.83/1.54 | ~ (product @ X3 @ X4 @ X0)
% 6.83/1.54 | ~ (product @ X4 @ X1 @ X5)
% 6.83/1.54 | ~ (product @ X3 @ X5 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 6.83/1.54 thf(zip_derived_cl153, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 (~ (product @ v @ X1 @ X0)
% 6.83/1.54 | ~ (product @ a @ X2 @ X1)
% 6.83/1.54 | (product @ b @ X2 @ X0))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl6])).
% 6.83/1.54 thf(zip_derived_cl332, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 (~ (defined @ v)
% 6.83/1.54 | (product @ b @ X0 @ v)
% 6.83/1.54 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl153])).
% 6.83/1.54 thf(v_is_defined, axiom, (defined @ v)).
% 6.83/1.54 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 6.83/1.54 inference('cnf', [status(esa)], [v_is_defined])).
% 6.83/1.54 thf(zip_derived_cl334, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 ( (product @ b @ X0 @ v)
% 6.83/1.54 | ~ (product @ a @ X0 @ multiplicative_identity))),
% 6.83/1.54 inference('demod', [status(thm)], [zip_derived_cl332, zip_derived_cl29])).
% 6.83/1.54 thf(zip_derived_cl2850, plain,
% 6.83/1.54 (( (sum @ additive_identity @ a @ additive_identity)
% 6.83/1.54 | ~ (defined @ a)
% 6.83/1.54 | (product @ b @ (multiplicative_inverse @ a) @ v))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl334])).
% 6.83/1.54 thf(zip_derived_cl30, plain,
% 6.83/1.54 (~ (sum @ additive_identity @ a @ additive_identity)),
% 6.83/1.54 inference('cnf', [status(esa)], [zf_stmt_2])).
% 6.83/1.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 6.83/1.54 inference('cnf', [status(esa)], [a_is_defined])).
% 6.83/1.54 thf(zip_derived_cl2889, plain,
% 6.83/1.54 ( (product @ b @ (multiplicative_inverse @ a) @ v)),
% 6.83/1.54 inference('demod', [status(thm)],
% 6.83/1.54 [zip_derived_cl2850, zip_derived_cl30, zip_derived_cl26])).
% 6.83/1.54 thf(zip_derived_cl56, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 6.83/1.54 thf(zip_derived_cl31, plain, ( (product @ a @ u @ b)),
% 6.83/1.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 6.83/1.54 thf(zip_derived_cl31, plain, ( (product @ a @ u @ b)),
% 6.83/1.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 6.83/1.54 thf(zip_derived_cl6, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2)
% 6.83/1.54 | ~ (product @ X3 @ X4 @ X0)
% 6.83/1.54 | ~ (product @ X4 @ X1 @ X5)
% 6.83/1.54 | ~ (product @ X3 @ X5 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 6.83/1.54 thf(zip_derived_cl150, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 (~ (product @ a @ X1 @ X0)
% 6.83/1.54 | ~ (product @ u @ X2 @ X1)
% 6.83/1.54 | (product @ b @ X2 @ X0))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl6])).
% 6.83/1.54 thf(zip_derived_cl220, plain,
% 6.83/1.54 (![X0 : $i]: ( (product @ b @ X0 @ b) | ~ (product @ u @ X0 @ u))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl150])).
% 6.83/1.54 thf(zip_derived_cl223, plain,
% 6.83/1.54 ((~ (defined @ u) | (product @ b @ multiplicative_identity @ b))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl220])).
% 6.83/1.54 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 6.83/1.54 inference('cnf', [status(esa)], [u_is_defined])).
% 6.83/1.54 thf(zip_derived_cl224, plain, ( (product @ b @ multiplicative_identity @ b)),
% 6.83/1.54 inference('demod', [status(thm)], [zip_derived_cl223, zip_derived_cl28])).
% 6.83/1.54 thf(zip_derived_cl9, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 6.83/1.54 thf(zip_derived_cl227, plain, ( (product @ multiplicative_identity @ b @ b)),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl224, zip_derived_cl9])).
% 6.83/1.54 thf(zip_derived_cl5, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2)
% 6.83/1.54 | ~ (product @ X0 @ X3 @ X4)
% 6.83/1.54 | ~ (product @ X3 @ X5 @ X1)
% 6.83/1.54 | ~ (product @ X4 @ X5 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 6.83/1.54 thf(zip_derived_cl232, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 (~ (product @ b @ X1 @ X0)
% 6.83/1.54 | ~ (product @ b @ X1 @ X2)
% 6.83/1.54 | (product @ multiplicative_identity @ X2 @ X0))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl227, zip_derived_cl5])).
% 6.83/1.54 thf(zip_derived_cl403, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i]:
% 6.83/1.54 ( (product @ multiplicative_identity @ X0 @ X0)
% 6.83/1.54 | ~ (product @ b @ X1 @ X0))),
% 6.83/1.54 inference('eq_fact', [status(thm)], [zip_derived_cl232])).
% 6.83/1.54 thf(zip_derived_cl3009, plain,
% 6.83/1.54 ( (product @ multiplicative_identity @ v @ v)),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl2889, zip_derived_cl403])).
% 6.83/1.54 thf(zip_derived_cl9, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 6.83/1.54 thf(zip_derived_cl3014, plain,
% 6.83/1.54 ( (product @ v @ multiplicative_identity @ v)),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl3009, zip_derived_cl9])).
% 6.83/1.54 thf(zip_derived_cl7, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 6.83/1.54 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 6.83/1.54 thf(zip_derived_cl5, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.83/1.54 ( (product @ X0 @ X1 @ X2)
% 6.83/1.54 | ~ (product @ X0 @ X3 @ X4)
% 6.83/1.54 | ~ (product @ X3 @ X5 @ X1)
% 6.83/1.54 | ~ (product @ X4 @ X5 @ X2))),
% 6.83/1.54 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 6.83/1.54 thf(zip_derived_cl102, plain,
% 6.83/1.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.83/1.54 (~ (defined @ X0)
% 6.83/1.54 | ~ (product @ X0 @ X2 @ X1)
% 6.83/1.54 | ~ (product @ X0 @ X2 @ X3)
% 6.83/1.54 | (product @ multiplicative_identity @ X3 @ X1))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 6.83/1.54 thf(zip_derived_cl3037, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 ( (product @ multiplicative_identity @ X0 @ v)
% 6.83/1.54 | ~ (product @ v @ multiplicative_identity @ X0)
% 6.83/1.54 | ~ (defined @ v))),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl3014, zip_derived_cl102])).
% 6.83/1.54 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 6.83/1.54 inference('cnf', [status(esa)], [v_is_defined])).
% 6.83/1.54 thf(zip_derived_cl3046, plain,
% 6.83/1.54 (![X0 : $i]:
% 6.83/1.54 ( (product @ multiplicative_identity @ X0 @ v)
% 6.83/1.54 | ~ (product @ v @ multiplicative_identity @ X0))),
% 6.83/1.54 inference('demod', [status(thm)], [zip_derived_cl3037, zip_derived_cl29])).
% 6.83/1.54 thf(zip_derived_cl4062, plain,
% 6.83/1.54 ( (product @ multiplicative_identity @ u @ v)),
% 6.83/1.54 inference('sup-', [status(thm)], [zip_derived_cl4047, zip_derived_cl3046])).
% 6.83/1.54 thf(zip_derived_cl4086, plain, ($false),
% 6.83/1.54 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl4062])).
% 6.83/1.54
% 6.83/1.54 % SZS output end Refutation
% 6.83/1.54
% 6.83/1.54
% 6.83/1.54 % Terminating...
% 7.27/1.64 % Runner terminated.
% 7.27/1.66 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------