TSTP Solution File: FLD048-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD048-4 : 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.2RRuG8CQWU true
% Computer : n002.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 22:39:26 EDT 2023
% Result : Unsatisfiable 84.24s 12.65s
% Output : Refutation 84.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD048-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2RRuG8CQWU true
% 0.15/0.34 % Computer : n002.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 23:44:19 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.35 % 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
% 0.21/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 1.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.28/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 84.24/12.65 % Solved by fo/fo5.sh.
% 84.24/12.65 % done 16766 iterations in 11.864s
% 84.24/12.65 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 84.24/12.65 % SZS output start Refutation
% 84.24/12.65 thf(sum_type, type, sum: $i > $i > $i > $o).
% 84.24/12.65 thf(t_type, type, t: $i).
% 84.24/12.65 thf(b_type, type, b: $i).
% 84.24/12.65 thf(s_type, type, s: $i).
% 84.24/12.65 thf(a_type, type, a: $i).
% 84.24/12.65 thf(k_type, type, k: $i).
% 84.24/12.65 thf(d_type, type, d: $i).
% 84.24/12.65 thf(product_type, type, product: $i > $i > $i > $o).
% 84.24/12.65 thf(additive_identity_type, type, additive_identity: $i).
% 84.24/12.65 thf(multiply_type, type, multiply: $i > $i > $i).
% 84.24/12.65 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 84.24/12.65 thf(l_type, type, l: $i).
% 84.24/12.65 thf(c_type, type, c: $i).
% 84.24/12.65 thf(u_type, type, u: $i).
% 84.24/12.65 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 84.24/12.65 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 84.24/12.65 thf(defined_type, type, defined: $i > $o).
% 84.24/12.65 thf(different_identities, axiom,
% 84.24/12.65 (~( sum @ additive_identity @ additive_identity @ multiplicative_identity ))).
% 84.24/12.65 thf(zip_derived_cl25, plain,
% 84.24/12.65 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [different_identities])).
% 84.24/12.65 thf(product_12, conjecture, (~( product @ s @ t @ u ))).
% 84.24/12.65 thf(zf_stmt_0, negated_conjecture, (product @ s @ t @ u),
% 84.24/12.65 inference('cnf.neg', [status(esa)], [product_12])).
% 84.24/12.65 thf(zip_derived_cl37, plain, ( (product @ s @ t @ u)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_0])).
% 84.24/12.65 thf(commutativity_multiplication, axiom,
% 84.24/12.65 (( product @ Y @ X @ Z ) | ( ~( product @ X @ Y @ Z ) ))).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl98, plain, ( (product @ t @ s @ u)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl9])).
% 84.24/12.65 thf(totality_of_multiplication, axiom,
% 84.24/12.65 (( product @ X @ Y @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 84.24/12.65 ( ~( defined @ Y ) ))).
% 84.24/12.65 thf(zip_derived_cl19, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 84.24/12.65 | ~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl454, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1)
% 84.24/12.65 | (product @ X0 @ X1 @ (multiply @ X1 @ X0)))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl9])).
% 84.24/12.65 thf(existence_of_inverse_multiplication, axiom,
% 84.24/12.65 (( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity ) |
% 84.24/12.65 ( sum @ additive_identity @ X @ additive_identity ) | ( ~( defined @ X ) ))).
% 84.24/12.65 thf(zip_derived_cl8, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl185, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 84.24/12.65 multiplicative_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 84.24/12.65 thf(existence_of_identity_multiplication, axiom,
% 84.24/12.65 (( product @ multiplicative_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 84.24/12.65 thf(zip_derived_cl7, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl93, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 84.24/12.65 thf(product_16, conjecture, (~( product @ b @ d @ l ))).
% 84.24/12.65 thf(zf_stmt_1, negated_conjecture, (product @ b @ d @ l),
% 84.24/12.65 inference('cnf.neg', [status(esa)], [product_16])).
% 84.24/12.65 thf(zip_derived_cl41, plain, ( (product @ b @ d @ l)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 84.24/12.65 thf(associativity_multiplication_2, axiom,
% 84.24/12.65 (( product @ U @ Z @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 84.24/12.65 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ X @ V @ W ) ))).
% 84.24/12.65 thf(zip_derived_cl6, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X3 @ X4 @ X0)
% 84.24/12.65 | ~ (product @ X4 @ X1 @ X5)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 84.24/12.65 thf(zip_derived_cl142, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (product @ b @ X1 @ X0)
% 84.24/12.65 | ~ (product @ d @ X2 @ X1)
% 84.24/12.65 | (product @ l @ X2 @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl6])).
% 84.24/12.65 thf(zip_derived_cl343, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ b)
% 84.24/12.65 | (product @ l @ X0 @ b)
% 84.24/12.65 | ~ (product @ d @ X0 @ multiplicative_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl142])).
% 84.24/12.65 thf(b_is_defined, axiom, (defined @ b)).
% 84.24/12.65 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 84.24/12.65 inference('cnf', [status(esa)], [b_is_defined])).
% 84.24/12.65 thf(zip_derived_cl345, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ l @ X0 @ b)
% 84.24/12.65 | ~ (product @ d @ X0 @ multiplicative_identity))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl343, zip_derived_cl27])).
% 84.24/12.65 thf(zip_derived_cl2691, plain,
% 84.24/12.65 (( (sum @ additive_identity @ d @ additive_identity)
% 84.24/12.65 | ~ (defined @ d)
% 84.24/12.65 | (product @ l @ (multiplicative_inverse @ d) @ b))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl345])).
% 84.24/12.65 thf(not_sum_11, conjecture,
% 84.24/12.65 (sum @ additive_identity @ d @ additive_identity)).
% 84.24/12.65 thf(zf_stmt_2, negated_conjecture,
% 84.24/12.65 (~( sum @ additive_identity @ d @ additive_identity )),
% 84.24/12.65 inference('cnf.neg', [status(esa)], [not_sum_11])).
% 84.24/12.65 thf(zip_derived_cl36, plain,
% 84.24/12.65 (~ (sum @ additive_identity @ d @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_2])).
% 84.24/12.65 thf(d_is_defined, axiom, (defined @ d)).
% 84.24/12.65 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 84.24/12.65 inference('cnf', [status(esa)], [d_is_defined])).
% 84.24/12.65 thf(zip_derived_cl2742, plain,
% 84.24/12.65 ( (product @ l @ (multiplicative_inverse @ d) @ b)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl2691, zip_derived_cl36, zip_derived_cl29])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl2776, plain,
% 84.24/12.65 ( (product @ (multiplicative_inverse @ d) @ l @ b)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2742, zip_derived_cl9])).
% 84.24/12.65 thf(product_14, conjecture,
% 84.24/12.65 (~( product @ c @ ( multiplicative_inverse @ d ) @ t ))).
% 84.24/12.65 thf(zf_stmt_3, negated_conjecture,
% 84.24/12.65 (product @ c @ ( multiplicative_inverse @ d ) @ t),
% 84.24/12.65 inference('cnf.neg', [status(esa)], [product_14])).
% 84.24/12.65 thf(zip_derived_cl39, plain,
% 84.24/12.65 ( (product @ c @ (multiplicative_inverse @ d) @ t)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_3])).
% 84.24/12.65 thf(associativity_multiplication_1, axiom,
% 84.24/12.65 (( product @ X @ V @ W ) | ( ~( product @ X @ Y @ U ) ) |
% 84.24/12.65 ( ~( product @ Y @ Z @ V ) ) | ( ~( product @ U @ Z @ W ) ))).
% 84.24/12.65 thf(zip_derived_cl5, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (product @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 84.24/12.65 thf(zip_derived_cl107, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (product @ t @ X1 @ X0)
% 84.24/12.65 | ~ (product @ (multiplicative_inverse @ d) @ X1 @ X2)
% 84.24/12.65 | (product @ c @ X2 @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl5])).
% 84.24/12.65 thf(zip_derived_cl2804, plain,
% 84.24/12.65 (![X0 : $i]: ( (product @ c @ b @ X0) | ~ (product @ t @ l @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2776, zip_derived_cl107])).
% 84.24/12.65 thf(zip_derived_cl11896, plain,
% 84.24/12.65 ((~ (defined @ l)
% 84.24/12.65 | ~ (defined @ t)
% 84.24/12.65 | (product @ c @ b @ (multiply @ l @ t)))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl454, zip_derived_cl2804])).
% 84.24/12.65 thf(l_is_defined, axiom, (defined @ l)).
% 84.24/12.65 thf(zip_derived_cl32, plain, ( (defined @ l)),
% 84.24/12.65 inference('cnf', [status(esa)], [l_is_defined])).
% 84.24/12.65 thf(t_is_defined, axiom, (defined @ t)).
% 84.24/12.65 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 84.24/12.65 inference('cnf', [status(esa)], [t_is_defined])).
% 84.24/12.65 thf(zip_derived_cl12071, plain, ( (product @ c @ b @ (multiply @ l @ t))),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl11896, zip_derived_cl32, zip_derived_cl34])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl13119, plain, ( (product @ b @ c @ (multiply @ l @ t))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl12071, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl19, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 84.24/12.65 | ~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 84.24/12.65 thf(totality_of_order_relation, axiom,
% 84.24/12.65 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 84.24/12.65 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 84.24/12.65 thf(zip_derived_cl22, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (less_or_equal @ X0 @ X1)
% 84.24/12.65 | (less_or_equal @ X1 @ X0)
% 84.24/12.65 | ~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 84.24/12.65 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 84.24/12.65 inference('cnf', [status(esa)], [b_is_defined])).
% 84.24/12.65 thf(zip_derived_cl550, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (less_or_equal @ X0 @ b)
% 84.24/12.65 | (less_or_equal @ b @ X0))),
% 84.24/12.65 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl27])).
% 84.24/12.65 thf(zip_derived_cl17673, plain,
% 84.24/12.65 (( (less_or_equal @ b @ b) | ~ (defined @ b))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl550])).
% 84.24/12.65 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 84.24/12.65 inference('cnf', [status(esa)], [b_is_defined])).
% 84.24/12.65 thf(zip_derived_cl17674, plain, ( (less_or_equal @ b @ b)),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl17673, zip_derived_cl27])).
% 84.24/12.65 thf(antisymmetry_of_order_relation, axiom,
% 84.24/12.65 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 84.24/12.65 ( ~( less_or_equal @ Y @ X ) ))).
% 84.24/12.65 thf(zip_derived_cl20, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (sum @ additive_identity @ X0 @ X1)
% 84.24/12.65 | ~ (less_or_equal @ X0 @ X1)
% 84.24/12.65 | ~ (less_or_equal @ X1 @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 84.24/12.65 thf(zip_derived_cl17680, plain,
% 84.24/12.65 ((~ (less_or_equal @ b @ b) | (sum @ additive_identity @ b @ b))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl17674, zip_derived_cl20])).
% 84.24/12.65 thf(zip_derived_cl17674, plain, ( (less_or_equal @ b @ b)),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl17673, zip_derived_cl27])).
% 84.24/12.65 thf(zip_derived_cl17683, plain, ( (sum @ additive_identity @ b @ b)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl17680, zip_derived_cl17674])).
% 84.24/12.65 thf(zip_derived_cl8, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 84.24/12.65 thf(existence_of_identity_addition, axiom,
% 84.24/12.65 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 84.24/12.65 thf(zip_derived_cl2, plain,
% 84.24/12.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 84.24/12.65 thf(zip_derived_cl2, plain,
% 84.24/12.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 84.24/12.65 thf(associativity_addition_1, axiom,
% 84.24/12.65 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 84.24/12.65 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 84.24/12.65 thf(zip_derived_cl0, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (sum @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (sum @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (sum @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (sum @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_addition_1])).
% 84.24/12.65 thf(zip_derived_cl45, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (sum @ X0 @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ X1 @ X1 @ X2)
% 84.24/12.65 | (sum @ X0 @ X2 @ X0))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 84.24/12.65 thf(zip_derived_cl52, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ additive_identity)
% 84.24/12.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl45])).
% 84.24/12.65 thf(well_definedness_of_additive_identity, axiom,
% 84.24/12.65 (defined @ additive_identity)).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl53, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (sum @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl69, plain,
% 84.24/12.65 ((~ (defined @ additive_identity)
% 84.24/12.65 | (sum @ additive_identity @ additive_identity @ additive_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl53])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl72, plain,
% 84.24/12.65 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl0, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (sum @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (sum @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (sum @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (sum @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_addition_1])).
% 84.24/12.65 thf(zip_derived_cl75, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (sum @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ additive_identity @ X1 @ X2)
% 84.24/12.65 | (sum @ additive_identity @ X2 @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl0])).
% 84.24/12.65 thf(zip_derived_cl190, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | (sum @ additive_identity @ X1 @ additive_identity)
% 84.24/12.65 | ~ (sum @ additive_identity @ X0 @ X1))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl75])).
% 84.24/12.65 thf(zip_derived_cl17698, plain,
% 84.24/12.65 (( (sum @ additive_identity @ b @ additive_identity)
% 84.24/12.65 | (product @ (multiplicative_inverse @ b) @ b @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | ~ (defined @ b))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl17683, zip_derived_cl190])).
% 84.24/12.65 thf(not_sum_10, conjecture,
% 84.24/12.65 (sum @ additive_identity @ b @ additive_identity)).
% 84.24/12.65 thf(zf_stmt_4, negated_conjecture,
% 84.24/12.65 (~( sum @ additive_identity @ b @ additive_identity )),
% 84.24/12.65 inference('cnf.neg', [status(esa)], [not_sum_10])).
% 84.24/12.65 thf(zip_derived_cl35, plain,
% 84.24/12.65 (~ (sum @ additive_identity @ b @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 84.24/12.65 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 84.24/12.65 inference('cnf', [status(esa)], [b_is_defined])).
% 84.24/12.65 thf(zip_derived_cl17727, plain,
% 84.24/12.65 ( (product @ (multiplicative_inverse @ b) @ b @ multiplicative_identity)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl17698, zip_derived_cl35, zip_derived_cl27])).
% 84.24/12.65 thf(product_13, conjecture,
% 84.24/12.65 (~( product @ a @ ( multiplicative_inverse @ b ) @ s ))).
% 84.24/12.65 thf(zf_stmt_5, negated_conjecture,
% 84.24/12.65 (product @ a @ ( multiplicative_inverse @ b ) @ s),
% 84.24/12.65 inference('cnf.neg', [status(esa)], [product_13])).
% 84.24/12.65 thf(zip_derived_cl38, plain,
% 84.24/12.65 ( (product @ a @ (multiplicative_inverse @ b) @ s)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_5])).
% 84.24/12.65 thf(zip_derived_cl5, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (product @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 84.24/12.65 thf(zip_derived_cl104, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (product @ s @ X1 @ X0)
% 84.24/12.65 | ~ (product @ (multiplicative_inverse @ b) @ X1 @ X2)
% 84.24/12.65 | (product @ a @ X2 @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl5])).
% 84.24/12.65 thf(zip_derived_cl17766, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ a @ multiplicative_identity @ X0)
% 84.24/12.65 | ~ (product @ s @ b @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl17727, zip_derived_cl104])).
% 84.24/12.65 thf(zip_derived_cl18296, plain,
% 84.24/12.65 ((~ (defined @ b)
% 84.24/12.65 | ~ (defined @ s)
% 84.24/12.65 | (product @ a @ multiplicative_identity @ (multiply @ s @ b)))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl17766])).
% 84.24/12.65 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 84.24/12.65 inference('cnf', [status(esa)], [b_is_defined])).
% 84.24/12.65 thf(s_is_defined, axiom, (defined @ s)).
% 84.24/12.65 thf(zip_derived_cl33, plain, ( (defined @ s)),
% 84.24/12.65 inference('cnf', [status(esa)], [s_is_defined])).
% 84.24/12.65 thf(zip_derived_cl18298, plain,
% 84.24/12.65 ( (product @ a @ multiplicative_identity @ (multiply @ s @ b))),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl18296, zip_derived_cl27, zip_derived_cl33])).
% 84.24/12.65 thf(zip_derived_cl93, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 84.24/12.65 thf(product_15, conjecture, (~( product @ a @ c @ k ))).
% 84.24/12.65 thf(zf_stmt_6, negated_conjecture, (product @ a @ c @ k),
% 84.24/12.65 inference('cnf.neg', [status(esa)], [product_15])).
% 84.24/12.65 thf(zip_derived_cl40, plain, ( (product @ a @ c @ k)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_6])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl95, plain, ( (product @ c @ a @ k)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl5, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (product @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 84.24/12.65 thf(zip_derived_cl108, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (product @ k @ X1 @ X0)
% 84.24/12.65 | ~ (product @ a @ X1 @ X2)
% 84.24/12.65 | (product @ c @ X2 @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl95, zip_derived_cl5])).
% 84.24/12.65 thf(zip_derived_cl208, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ k)
% 84.24/12.65 | (product @ c @ X0 @ k)
% 84.24/12.65 | ~ (product @ a @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl108])).
% 84.24/12.65 thf(k_is_defined, axiom, (defined @ k)).
% 84.24/12.65 thf(zip_derived_cl31, plain, ( (defined @ k)),
% 84.24/12.65 inference('cnf', [status(esa)], [k_is_defined])).
% 84.24/12.65 thf(zip_derived_cl209, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ c @ X0 @ k)
% 84.24/12.65 | ~ (product @ a @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl208, zip_derived_cl31])).
% 84.24/12.65 thf(zip_derived_cl24646, plain, ( (product @ c @ (multiply @ s @ b) @ k)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl18298, zip_derived_cl209])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl24738, plain, ( (product @ (multiply @ s @ b) @ c @ k)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl24646, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl19, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 84.24/12.65 | ~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 84.24/12.65 thf(zip_derived_cl5, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (product @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 84.24/12.65 thf(zip_derived_cl452, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1)
% 84.24/12.65 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | (product @ X1 @ X4 @ X2))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 84.24/12.65 thf(zip_derived_cl24783, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ s @ X0 @ k)
% 84.24/12.65 | ~ (product @ b @ c @ X0)
% 84.24/12.65 | ~ (defined @ s)
% 84.24/12.65 | ~ (defined @ b))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl24738, zip_derived_cl452])).
% 84.24/12.65 thf(zip_derived_cl33, plain, ( (defined @ s)),
% 84.24/12.65 inference('cnf', [status(esa)], [s_is_defined])).
% 84.24/12.65 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 84.24/12.65 inference('cnf', [status(esa)], [b_is_defined])).
% 84.24/12.65 thf(zip_derived_cl24785, plain,
% 84.24/12.65 (![X0 : $i]: ( (product @ s @ X0 @ k) | ~ (product @ b @ c @ X0))),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl24783, zip_derived_cl33, zip_derived_cl27])).
% 84.24/12.65 thf(zip_derived_cl24790, plain, ( (product @ s @ (multiply @ l @ t) @ k)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl13119, zip_derived_cl24785])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl24851, plain, ( (product @ (multiply @ l @ t) @ s @ k)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl24790, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl452, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1)
% 84.24/12.65 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | (product @ X1 @ X4 @ X2))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 84.24/12.65 thf(zip_derived_cl25065, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ l @ X0 @ k)
% 84.24/12.65 | ~ (product @ t @ s @ X0)
% 84.24/12.65 | ~ (defined @ l)
% 84.24/12.65 | ~ (defined @ t))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl24851, zip_derived_cl452])).
% 84.24/12.65 thf(zip_derived_cl32, plain, ( (defined @ l)),
% 84.24/12.65 inference('cnf', [status(esa)], [l_is_defined])).
% 84.24/12.65 thf(zip_derived_cl34, plain, ( (defined @ t)),
% 84.24/12.65 inference('cnf', [status(esa)], [t_is_defined])).
% 84.24/12.65 thf(zip_derived_cl25067, plain,
% 84.24/12.65 (![X0 : $i]: ( (product @ l @ X0 @ k) | ~ (product @ t @ s @ X0))),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl25065, zip_derived_cl32, zip_derived_cl34])).
% 84.24/12.65 thf(zip_derived_cl25071, plain, ( (product @ l @ u @ k)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl25067])).
% 84.24/12.65 thf(zip_derived_cl7, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl8, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 84.24/12.65 thf(zip_derived_cl5, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (product @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 84.24/12.65 thf(zip_derived_cl183, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (product @ multiplicative_identity @ X2 @ X1)
% 84.24/12.65 | ~ (product @ X0 @ X2 @ X3)
% 84.24/12.65 | (product @ (multiplicative_inverse @ X0) @ X3 @ X1))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl5])).
% 84.24/12.65 thf(zip_derived_cl2559, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (product @ (multiplicative_inverse @ X2) @ X1 @ X0)
% 84.24/12.65 | ~ (product @ X2 @ X0 @ X1)
% 84.24/12.65 | (sum @ additive_identity @ X2 @ additive_identity)
% 84.24/12.65 | ~ (defined @ X2))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl183])).
% 84.24/12.65 thf(zip_derived_cl133123, plain,
% 84.24/12.65 ((~ (defined @ l)
% 84.24/12.65 | (sum @ additive_identity @ l @ additive_identity)
% 84.24/12.65 | (product @ (multiplicative_inverse @ l) @ k @ u)
% 84.24/12.65 | ~ (defined @ u))),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl25071, zip_derived_cl2559])).
% 84.24/12.65 thf(zip_derived_cl32, plain, ( (defined @ l)),
% 84.24/12.65 inference('cnf', [status(esa)], [l_is_defined])).
% 84.24/12.65 thf(u_is_defined, axiom, (defined @ u)).
% 84.24/12.65 thf(zip_derived_cl30, plain, ( (defined @ u)),
% 84.24/12.65 inference('cnf', [status(esa)], [u_is_defined])).
% 84.24/12.65 thf(zip_derived_cl134211, plain,
% 84.24/12.65 (( (sum @ additive_identity @ l @ additive_identity)
% 84.24/12.65 | (product @ (multiplicative_inverse @ l) @ k @ u))),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl133123, zip_derived_cl32, zip_derived_cl30])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl135444, plain,
% 84.24/12.65 (( (sum @ additive_identity @ l @ additive_identity)
% 84.24/12.65 | (product @ k @ (multiplicative_inverse @ l) @ u))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl134211, zip_derived_cl9])).
% 84.24/12.65 thf(not_product_17, conjecture,
% 84.24/12.65 (product @ k @ ( multiplicative_inverse @ l ) @ u)).
% 84.24/12.65 thf(zf_stmt_7, negated_conjecture,
% 84.24/12.65 (~( product @ k @ ( multiplicative_inverse @ l ) @ u )),
% 84.24/12.65 inference('cnf.neg', [status(esa)], [not_product_17])).
% 84.24/12.65 thf(zip_derived_cl42, plain,
% 84.24/12.65 (~ (product @ k @ (multiplicative_inverse @ l) @ u)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_7])).
% 84.24/12.65 thf(zip_derived_cl135810, plain,
% 84.24/12.65 ( (sum @ additive_identity @ l @ additive_identity)),
% 84.24/12.65 inference('clc', [status(thm)], [zip_derived_cl135444, zip_derived_cl42])).
% 84.24/12.65 thf(zip_derived_cl22, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (less_or_equal @ X0 @ X1)
% 84.24/12.65 | (less_or_equal @ X1 @ X0)
% 84.24/12.65 | ~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 84.24/12.65 thf(zip_derived_cl32, plain, ( (defined @ l)),
% 84.24/12.65 inference('cnf', [status(esa)], [l_is_defined])).
% 84.24/12.65 thf(zip_derived_cl555, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (less_or_equal @ X0 @ l)
% 84.24/12.65 | (less_or_equal @ l @ X0))),
% 84.24/12.65 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl32])).
% 84.24/12.65 thf(zip_derived_cl18343, plain,
% 84.24/12.65 (( (less_or_equal @ l @ l) | ~ (defined @ l))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl555])).
% 84.24/12.65 thf(zip_derived_cl32, plain, ( (defined @ l)),
% 84.24/12.65 inference('cnf', [status(esa)], [l_is_defined])).
% 84.24/12.65 thf(zip_derived_cl18344, plain, ( (less_or_equal @ l @ l)),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl18343, zip_derived_cl32])).
% 84.24/12.65 thf(zip_derived_cl20, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (sum @ additive_identity @ X0 @ X1)
% 84.24/12.65 | ~ (less_or_equal @ X0 @ X1)
% 84.24/12.65 | ~ (less_or_equal @ X1 @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 84.24/12.65 thf(zip_derived_cl18350, plain,
% 84.24/12.65 ((~ (less_or_equal @ l @ l) | (sum @ additive_identity @ l @ l))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl18344, zip_derived_cl20])).
% 84.24/12.65 thf(zip_derived_cl18344, plain, ( (less_or_equal @ l @ l)),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl18343, zip_derived_cl32])).
% 84.24/12.65 thf(zip_derived_cl18353, plain, ( (sum @ additive_identity @ l @ l)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl18350, zip_derived_cl18344])).
% 84.24/12.65 thf(zip_derived_cl75, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (sum @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ additive_identity @ X1 @ X2)
% 84.24/12.65 | (sum @ additive_identity @ X2 @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl0])).
% 84.24/12.65 thf(zip_derived_cl18378, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (sum @ additive_identity @ X0 @ l)
% 84.24/12.65 | ~ (sum @ additive_identity @ l @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl18353, zip_derived_cl75])).
% 84.24/12.65 thf(zip_derived_cl135914, plain,
% 84.24/12.65 ( (sum @ additive_identity @ additive_identity @ l)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl135810, zip_derived_cl18378])).
% 84.24/12.65 thf(zip_derived_cl72, plain,
% 84.24/12.65 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl93, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl2, plain,
% 84.24/12.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 84.24/12.65 thf(commutativity_addition, axiom,
% 84.24/12.65 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 84.24/12.65 thf(zip_derived_cl4, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 84.24/12.65 thf(zip_derived_cl88, plain,
% 84.24/12.65 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 84.24/12.65 thf(distributivity_2, axiom,
% 84.24/12.65 (( product @ A @ Z @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 84.24/12.65 ( ~( product @ X @ Z @ C ) ) | ( ~( product @ Y @ Z @ D ) ) |
% 84.24/12.65 ( ~( sum @ C @ D @ B ) ))).
% 84.24/12.65 thf(zip_derived_cl11, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (sum @ X3 @ X4 @ X0)
% 84.24/12.65 | ~ (product @ X3 @ X1 @ X5)
% 84.24/12.65 | ~ (product @ X4 @ X1 @ X6)
% 84.24/12.65 | ~ (sum @ X5 @ X6 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [distributivity_2])).
% 84.24/12.65 thf(zip_derived_cl282, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | ~ (sum @ X3 @ X2 @ X1)
% 84.24/12.65 | ~ (product @ additive_identity @ X4 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X4 @ X3)
% 84.24/12.65 | (product @ X0 @ X4 @ X1))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl11])).
% 84.24/12.65 thf(zip_derived_cl5657, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ additive_identity @ X1 @ X2)
% 84.24/12.65 | ~ (product @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ X0 @ X0 @ X2)
% 84.24/12.65 | ~ (defined @ additive_identity))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl282])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl5659, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ additive_identity @ X1 @ X2)
% 84.24/12.65 | ~ (product @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ X0 @ X0 @ X2))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl5657, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl5714, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ additive_identity)
% 84.24/12.65 | ~ (sum @ additive_identity @ additive_identity @ X0)
% 84.24/12.65 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl5659])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl5718, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (sum @ additive_identity @ additive_identity @ X0)
% 84.24/12.65 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl5714, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl5727, plain,
% 84.24/12.65 ( (product @ additive_identity @ multiplicative_identity @
% 84.24/12.65 additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl5718])).
% 84.24/12.65 thf(well_definedness_of_multiplication, axiom,
% 84.24/12.65 (( defined @ ( multiply @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 84.24/12.65 ( ~( defined @ Y ) ))).
% 84.24/12.65 thf(zip_derived_cl15, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (defined @ (multiply @ X0 @ X1))
% 84.24/12.65 | ~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_multiplication])).
% 84.24/12.65 thf(zip_derived_cl19, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ (multiply @ X0 @ X1))
% 84.24/12.65 | ~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [totality_of_multiplication])).
% 84.24/12.65 thf(zip_derived_cl88, plain,
% 84.24/12.65 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 84.24/12.65 thf(zip_derived_cl8, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ (multiplicative_inverse @ X0) @ X0 @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_inverse_multiplication])).
% 84.24/12.65 thf(zip_derived_cl2, plain,
% 84.24/12.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 84.24/12.65 thf(zip_derived_cl75, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (sum @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ additive_identity @ X1 @ X2)
% 84.24/12.65 | (sum @ additive_identity @ X2 @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl0])).
% 84.24/12.65 thf(zip_derived_cl158, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (sum @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ additive_identity @ X0 @ X1))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl75])).
% 84.24/12.65 thf(zip_derived_cl250, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | (sum @ additive_identity @ additive_identity @ X0)
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl158])).
% 84.24/12.65 thf(zip_derived_cl259, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 84.24/12.65 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('simplify', [status(thm)], [zip_derived_cl250])).
% 84.24/12.65 thf(zip_derived_cl5727, plain,
% 84.24/12.65 ( (product @ additive_identity @ multiplicative_identity @
% 84.24/12.65 additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl5718])).
% 84.24/12.65 thf(distributivity_1, axiom,
% 84.24/12.65 (( sum @ C @ D @ B ) | ( ~( sum @ X @ Y @ A ) ) |
% 84.24/12.65 ( ~( product @ A @ Z @ B ) ) | ( ~( product @ X @ Z @ C ) ) |
% 84.24/12.65 ( ~( product @ Y @ Z @ D ) ))).
% 84.24/12.65 thf(zip_derived_cl10, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 84.24/12.65 ( (sum @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (sum @ X3 @ X4 @ X5)
% 84.24/12.65 | ~ (product @ X5 @ X6 @ X2)
% 84.24/12.65 | ~ (product @ X3 @ X6 @ X0)
% 84.24/12.65 | ~ (product @ X4 @ X6 @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [distributivity_1])).
% 84.24/12.65 thf(zip_derived_cl243, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 84.24/12.65 (~ (product @ X4 @ X1 @ X3)
% 84.24/12.65 | ~ (product @ X2 @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ X2 @ X4 @ X2)
% 84.24/12.65 | (sum @ X0 @ X3 @ X0))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 84.24/12.65 thf(zip_derived_cl5745, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (sum @ X0 @ additive_identity @ X0)
% 84.24/12.65 | ~ (sum @ X1 @ additive_identity @ X1)
% 84.24/12.65 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl5727, zip_derived_cl243])).
% 84.24/12.65 thf(zip_derived_cl8207, plain,
% 84.24/12.65 ((~ (defined @ multiplicative_identity)
% 84.24/12.65 | (sum @ additive_identity @ additive_identity @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | ~ (sum @ (multiplicative_inverse @ multiplicative_identity) @
% 84.24/12.65 additive_identity @
% 84.24/12.65 (multiplicative_inverse @ multiplicative_identity))
% 84.24/12.65 | (sum @ multiplicative_identity @ additive_identity @
% 84.24/12.65 multiplicative_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl259, zip_derived_cl5745])).
% 84.24/12.65 thf(well_definedness_of_multiplicative_identity, axiom,
% 84.24/12.65 (defined @ multiplicative_identity)).
% 84.24/12.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 84.24/12.65 inference('cnf', [status(esa)],
% 84.24/12.65 [well_definedness_of_multiplicative_identity])).
% 84.24/12.65 thf(zip_derived_cl25, plain,
% 84.24/12.65 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [different_identities])).
% 84.24/12.65 thf(zip_derived_cl8269, plain,
% 84.24/12.65 ((~ (sum @ (multiplicative_inverse @ multiplicative_identity) @
% 84.24/12.65 additive_identity @
% 84.24/12.65 (multiplicative_inverse @ multiplicative_identity))
% 84.24/12.65 | (sum @ multiplicative_identity @ additive_identity @
% 84.24/12.65 multiplicative_identity))),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl8207, zip_derived_cl16, zip_derived_cl25])).
% 84.24/12.65 thf(zip_derived_cl8273, plain,
% 84.24/12.65 ((~ (defined @ (multiplicative_inverse @ multiplicative_identity))
% 84.24/12.65 | (sum @ multiplicative_identity @ additive_identity @
% 84.24/12.65 multiplicative_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl8269])).
% 84.24/12.65 thf(well_definedness_of_multiplicative_inverse, axiom,
% 84.24/12.65 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 84.24/12.65 ( sum @ additive_identity @ X @ additive_identity ))).
% 84.24/12.65 thf(zip_derived_cl17, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (defined @ (multiplicative_inverse @ X0))
% 84.24/12.65 | ~ (defined @ X0)
% 84.24/12.65 | (sum @ additive_identity @ X0 @ additive_identity))),
% 84.24/12.65 inference('cnf', [status(esa)],
% 84.24/12.65 [well_definedness_of_multiplicative_inverse])).
% 84.24/12.65 thf(zip_derived_cl158, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (sum @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ additive_identity @ X0 @ X1))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl75])).
% 84.24/12.65 thf(zip_derived_cl251, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (defined @ (multiplicative_inverse @ X0))
% 84.24/12.65 | (sum @ additive_identity @ additive_identity @ X0)
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl158])).
% 84.24/12.65 thf(zip_derived_cl260, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (sum @ additive_identity @ additive_identity @ X0)
% 84.24/12.65 | (defined @ (multiplicative_inverse @ X0))
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('simplify', [status(thm)], [zip_derived_cl251])).
% 84.24/12.65 thf(zip_derived_cl25, plain,
% 84.24/12.65 (~ (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [different_identities])).
% 84.24/12.65 thf(zip_derived_cl1791, plain,
% 84.24/12.65 ((~ (defined @ multiplicative_identity)
% 84.24/12.65 | (defined @ (multiplicative_inverse @ multiplicative_identity)))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl260, zip_derived_cl25])).
% 84.24/12.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 84.24/12.65 inference('cnf', [status(esa)],
% 84.24/12.65 [well_definedness_of_multiplicative_identity])).
% 84.24/12.65 thf(zip_derived_cl1806, plain,
% 84.24/12.65 ( (defined @ (multiplicative_inverse @ multiplicative_identity))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl1791, zip_derived_cl16])).
% 84.24/12.65 thf(zip_derived_cl8274, plain,
% 84.24/12.65 ( (sum @ multiplicative_identity @ additive_identity @
% 84.24/12.65 multiplicative_identity)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl8273, zip_derived_cl1806])).
% 84.24/12.65 thf(zip_derived_cl4, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_addition])).
% 84.24/12.65 thf(zip_derived_cl8278, plain,
% 84.24/12.65 ( (sum @ additive_identity @ multiplicative_identity @
% 84.24/12.65 multiplicative_identity)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl8274, zip_derived_cl4])).
% 84.24/12.65 thf(zip_derived_cl5727, plain,
% 84.24/12.65 ( (product @ additive_identity @ multiplicative_identity @
% 84.24/12.65 additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl5718])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl5739, plain,
% 84.24/12.65 ( (product @ multiplicative_identity @ additive_identity @
% 84.24/12.65 additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl5727, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl10, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 84.24/12.65 ( (sum @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (sum @ X3 @ X4 @ X5)
% 84.24/12.65 | ~ (product @ X5 @ X6 @ X2)
% 84.24/12.65 | ~ (product @ X3 @ X6 @ X0)
% 84.24/12.65 | ~ (product @ X4 @ X6 @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [distributivity_1])).
% 84.24/12.65 thf(zip_derived_cl244, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 84.24/12.65 (~ (product @ X2 @ X1 @ X0)
% 84.24/12.65 | ~ (product @ X4 @ X1 @ X3)
% 84.24/12.65 | ~ (sum @ X4 @ X2 @ X2)
% 84.24/12.65 | (sum @ X3 @ X0 @ X0))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 84.24/12.65 thf(zip_derived_cl5775, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (sum @ X0 @ additive_identity @ additive_identity)
% 84.24/12.65 | ~ (sum @ X1 @ multiplicative_identity @ multiplicative_identity)
% 84.24/12.65 | ~ (product @ X1 @ additive_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl5739, zip_derived_cl244])).
% 84.24/12.65 thf(zip_derived_cl10459, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (product @ additive_identity @ additive_identity @ X0)
% 84.24/12.65 | (sum @ X0 @ additive_identity @ additive_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl8278, zip_derived_cl5775])).
% 84.24/12.65 thf(zip_derived_cl10632, plain,
% 84.24/12.65 ((~ (defined @ additive_identity)
% 84.24/12.65 | ~ (defined @ additive_identity)
% 84.24/12.65 | (sum @ (multiply @ additive_identity @ additive_identity) @
% 84.24/12.65 additive_identity @ additive_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl10459])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl10633, plain,
% 84.24/12.65 ( (sum @ (multiply @ additive_identity @ additive_identity) @
% 84.24/12.65 additive_identity @ additive_identity)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl10632, zip_derived_cl13, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl88, plain,
% 84.24/12.65 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 84.24/12.65 thf(zip_derived_cl2, plain,
% 84.24/12.65 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 84.24/12.65 thf(zip_derived_cl0, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (sum @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (sum @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (sum @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (sum @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_addition_1])).
% 84.24/12.65 thf(zip_derived_cl51, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | ~ (sum @ X0 @ X2 @ X1)
% 84.24/12.65 | ~ (sum @ X0 @ X2 @ X3)
% 84.24/12.65 | (sum @ additive_identity @ X3 @ X1))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 84.24/12.65 thf(zip_derived_cl766, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (sum @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ X0 @ additive_identity @ X1)
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl51])).
% 84.24/12.65 thf(zip_derived_cl786, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 (~ (sum @ X0 @ additive_identity @ X1)
% 84.24/12.65 | (sum @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (defined @ X0))),
% 84.24/12.65 inference('simplify', [status(thm)], [zip_derived_cl766])).
% 84.24/12.65 thf(zip_derived_cl10650, plain,
% 84.24/12.65 ((~ (defined @ (multiply @ additive_identity @ additive_identity))
% 84.24/12.65 | (sum @ additive_identity @ additive_identity @
% 84.24/12.65 (multiply @ additive_identity @ additive_identity)))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl10633, zip_derived_cl786])).
% 84.24/12.65 thf(zip_derived_cl10960, plain,
% 84.24/12.65 ((~ (defined @ additive_identity)
% 84.24/12.65 | ~ (defined @ additive_identity)
% 84.24/12.65 | (sum @ additive_identity @ additive_identity @
% 84.24/12.65 (multiply @ additive_identity @ additive_identity)))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl10650])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl10961, plain,
% 84.24/12.65 ( (sum @ additive_identity @ additive_identity @
% 84.24/12.65 (multiply @ additive_identity @ additive_identity))),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl10960, zip_derived_cl13, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl5718, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (sum @ additive_identity @ additive_identity @ X0)
% 84.24/12.65 | (product @ additive_identity @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl5714, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl11169, plain,
% 84.24/12.65 ( (product @ additive_identity @ multiplicative_identity @
% 84.24/12.65 (multiply @ additive_identity @ additive_identity))),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl10961, zip_derived_cl5718])).
% 84.24/12.65 thf(zip_derived_cl5727, plain,
% 84.24/12.65 ( (product @ additive_identity @ multiplicative_identity @
% 84.24/12.65 additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl5718])).
% 84.24/12.65 thf(zip_derived_cl7, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ multiplicative_identity @ X0 @ X0) | ~ (defined @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [existence_of_identity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl5, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (product @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 84.24/12.65 thf(zip_derived_cl103, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | ~ (product @ X0 @ X2 @ X1)
% 84.24/12.65 | ~ (product @ X0 @ X2 @ X3)
% 84.24/12.65 | (product @ multiplicative_identity @ X3 @ X1))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 84.24/12.65 thf(zip_derived_cl5741, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 84.24/12.65 | ~ (defined @ additive_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl5727, zip_derived_cl103])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl5751, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ multiplicative_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl5741, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl12698, plain,
% 84.24/12.65 ( (product @ multiplicative_identity @
% 84.24/12.65 (multiply @ additive_identity @ additive_identity) @ additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl11169, zip_derived_cl5751])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl12875, plain,
% 84.24/12.65 ( (product @ (multiply @ additive_identity @ additive_identity) @
% 84.24/12.65 multiplicative_identity @ additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl12698, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl452, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1)
% 84.24/12.65 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | (product @ X1 @ X4 @ X2))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl5])).
% 84.24/12.65 thf(zip_derived_cl13354, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (product @ additive_identity @ multiplicative_identity @ X0)
% 84.24/12.65 | ~ (defined @ additive_identity)
% 84.24/12.65 | ~ (defined @ additive_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl12875, zip_derived_cl452])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 84.24/12.65 thf(zip_derived_cl13358, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | ~ (product @ additive_identity @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl13354, zip_derived_cl13, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl13362, plain,
% 84.24/12.65 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl5727, zip_derived_cl13358])).
% 84.24/12.65 thf(zip_derived_cl5659, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ additive_identity @ X1 @ X2)
% 84.24/12.65 | ~ (product @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (sum @ X0 @ X0 @ X2))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl5657, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl13455, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (sum @ additive_identity @ additive_identity @ X0)
% 84.24/12.65 | (product @ additive_identity @ additive_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl13362, zip_derived_cl5659])).
% 84.24/12.65 thf(zip_derived_cl136993, plain,
% 84.24/12.65 ( (product @ additive_identity @ additive_identity @ l)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl135914, zip_derived_cl13455])).
% 84.24/12.65 thf(zip_derived_cl13362, plain,
% 84.24/12.65 ( (product @ additive_identity @ additive_identity @ additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl5727, zip_derived_cl13358])).
% 84.24/12.65 thf(zip_derived_cl5, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X0 @ X3 @ X4)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X1)
% 84.24/12.65 | ~ (product @ X4 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_1])).
% 84.24/12.65 thf(zip_derived_cl13435, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (product @ additive_identity @ X1 @ X0)
% 84.24/12.65 | ~ (product @ additive_identity @ X1 @ X2)
% 84.24/12.65 | (product @ additive_identity @ X2 @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl13362, zip_derived_cl5])).
% 84.24/12.65 thf(zip_derived_cl16289, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (product @ additive_identity @ X0 @ X0)
% 84.24/12.65 | ~ (product @ additive_identity @ X1 @ X0))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl13435])).
% 84.24/12.65 thf(zip_derived_cl138256, plain, ( (product @ additive_identity @ l @ l)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl136993, zip_derived_cl16289])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl138815, plain, ( (product @ l @ additive_identity @ l)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl138256, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl185, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (sum @ additive_identity @ X0 @ additive_identity)
% 84.24/12.65 | (product @ X0 @ (multiplicative_inverse @ X0) @
% 84.24/12.65 multiplicative_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl93, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0) | (product @ X0 @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl41, plain, ( (product @ b @ d @ l)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl96, plain, ( (product @ d @ b @ l)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl6, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X3 @ X4 @ X0)
% 84.24/12.65 | ~ (product @ X4 @ X1 @ X5)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 84.24/12.65 thf(zip_derived_cl145, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 (~ (product @ d @ X1 @ X0)
% 84.24/12.65 | ~ (product @ b @ X2 @ X1)
% 84.24/12.65 | (product @ l @ X2 @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl96, zip_derived_cl6])).
% 84.24/12.65 thf(zip_derived_cl442, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ d)
% 84.24/12.65 | (product @ l @ X0 @ d)
% 84.24/12.65 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl145])).
% 84.24/12.65 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 84.24/12.65 inference('cnf', [status(esa)], [d_is_defined])).
% 84.24/12.65 thf(zip_derived_cl444, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ l @ X0 @ d)
% 84.24/12.65 | ~ (product @ b @ X0 @ multiplicative_identity))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl442, zip_derived_cl29])).
% 84.24/12.65 thf(zip_derived_cl2686, plain,
% 84.24/12.65 (( (sum @ additive_identity @ b @ additive_identity)
% 84.24/12.65 | ~ (defined @ b)
% 84.24/12.65 | (product @ l @ (multiplicative_inverse @ b) @ d))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl444])).
% 84.24/12.65 thf(zip_derived_cl35, plain,
% 84.24/12.65 (~ (sum @ additive_identity @ b @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 84.24/12.65 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 84.24/12.65 inference('cnf', [status(esa)], [b_is_defined])).
% 84.24/12.65 thf(zip_derived_cl2737, plain,
% 84.24/12.65 ( (product @ l @ (multiplicative_inverse @ b) @ d)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl2686, zip_derived_cl35, zip_derived_cl27])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl2763, plain,
% 84.24/12.65 ( (product @ (multiplicative_inverse @ b) @ l @ d)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2737, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl6, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2)
% 84.24/12.65 | ~ (product @ X3 @ X4 @ X0)
% 84.24/12.65 | ~ (product @ X4 @ X1 @ X5)
% 84.24/12.65 | ~ (product @ X3 @ X5 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [associativity_multiplication_2])).
% 84.24/12.65 thf(zip_derived_cl150, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 84.24/12.65 (~ (product @ X2 @ X1 @ X0)
% 84.24/12.65 | ~ (product @ X1 @ X3 @ X1)
% 84.24/12.65 | (product @ X0 @ X3 @ X0))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 84.24/12.65 thf(zip_derived_cl2790, plain,
% 84.24/12.65 (![X0 : $i]: ( (product @ d @ X0 @ d) | ~ (product @ l @ X0 @ l))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2763, zip_derived_cl150])).
% 84.24/12.65 thf(zip_derived_cl139100, plain, ( (product @ d @ additive_identity @ d)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl138815, zip_derived_cl2790])).
% 84.24/12.65 thf(zip_derived_cl22, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (less_or_equal @ X0 @ X1)
% 84.24/12.65 | (less_or_equal @ X1 @ X0)
% 84.24/12.65 | ~ (defined @ X0)
% 84.24/12.65 | ~ (defined @ X1))),
% 84.24/12.65 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 84.24/12.65 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 84.24/12.65 inference('cnf', [status(esa)], [d_is_defined])).
% 84.24/12.65 thf(zip_derived_cl552, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (less_or_equal @ X0 @ d)
% 84.24/12.65 | (less_or_equal @ d @ X0))),
% 84.24/12.65 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl29])).
% 84.24/12.65 thf(zip_derived_cl17939, plain,
% 84.24/12.65 (( (less_or_equal @ d @ d) | ~ (defined @ d))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl552])).
% 84.24/12.65 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 84.24/12.65 inference('cnf', [status(esa)], [d_is_defined])).
% 84.24/12.65 thf(zip_derived_cl17940, plain, ( (less_or_equal @ d @ d)),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl17939, zip_derived_cl29])).
% 84.24/12.65 thf(zip_derived_cl20, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (sum @ additive_identity @ X0 @ X1)
% 84.24/12.65 | ~ (less_or_equal @ X0 @ X1)
% 84.24/12.65 | ~ (less_or_equal @ X1 @ X0))),
% 84.24/12.65 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 84.24/12.65 thf(zip_derived_cl17946, plain,
% 84.24/12.65 ((~ (less_or_equal @ d @ d) | (sum @ additive_identity @ d @ d))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl17940, zip_derived_cl20])).
% 84.24/12.65 thf(zip_derived_cl17940, plain, ( (less_or_equal @ d @ d)),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl17939, zip_derived_cl29])).
% 84.24/12.65 thf(zip_derived_cl17949, plain, ( (sum @ additive_identity @ d @ d)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl17946, zip_derived_cl17940])).
% 84.24/12.65 thf(zip_derived_cl190, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | (product @ (multiplicative_inverse @ X0) @ X0 @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | (sum @ additive_identity @ X1 @ additive_identity)
% 84.24/12.65 | ~ (sum @ additive_identity @ X0 @ X1))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl75])).
% 84.24/12.65 thf(zip_derived_cl17964, plain,
% 84.24/12.65 (( (sum @ additive_identity @ d @ additive_identity)
% 84.24/12.65 | (product @ (multiplicative_inverse @ d) @ d @
% 84.24/12.65 multiplicative_identity)
% 84.24/12.65 | ~ (defined @ d))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl17949, zip_derived_cl190])).
% 84.24/12.65 thf(zip_derived_cl36, plain,
% 84.24/12.65 (~ (sum @ additive_identity @ d @ additive_identity)),
% 84.24/12.65 inference('cnf', [status(esa)], [zf_stmt_2])).
% 84.24/12.65 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 84.24/12.65 inference('cnf', [status(esa)], [d_is_defined])).
% 84.24/12.65 thf(zip_derived_cl17993, plain,
% 84.24/12.65 ( (product @ (multiplicative_inverse @ d) @ d @ multiplicative_identity)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl17964, zip_derived_cl36, zip_derived_cl29])).
% 84.24/12.65 thf(zip_derived_cl150, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 84.24/12.65 (~ (product @ X2 @ X1 @ X0)
% 84.24/12.65 | ~ (product @ X1 @ X3 @ X1)
% 84.24/12.65 | (product @ X0 @ X3 @ X0))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 84.24/12.65 thf(zip_derived_cl18025, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (product @ multiplicative_identity @ X0 @ multiplicative_identity)
% 84.24/12.65 | ~ (product @ d @ X0 @ d))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl17993, zip_derived_cl150])).
% 84.24/12.65 thf(zip_derived_cl141532, plain,
% 84.24/12.65 ( (product @ multiplicative_identity @ additive_identity @
% 84.24/12.65 multiplicative_identity)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl139100, zip_derived_cl18025])).
% 84.24/12.65 thf(zip_derived_cl9, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 84.24/12.65 ( (product @ X0 @ X1 @ X2) | ~ (product @ X1 @ X0 @ X2))),
% 84.24/12.65 inference('cnf', [status(esa)], [commutativity_multiplication])).
% 84.24/12.65 thf(zip_derived_cl142322, plain,
% 84.24/12.65 ( (product @ additive_identity @ multiplicative_identity @
% 84.24/12.65 multiplicative_identity)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl141532, zip_derived_cl9])).
% 84.24/12.65 thf(zip_derived_cl72, plain,
% 84.24/12.65 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl13])).
% 84.24/12.65 thf(zip_derived_cl5727, plain,
% 84.24/12.65 ( (product @ additive_identity @ multiplicative_identity @
% 84.24/12.65 additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl5718])).
% 84.24/12.65 thf(zip_derived_cl244, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 84.24/12.65 (~ (product @ X2 @ X1 @ X0)
% 84.24/12.65 | ~ (product @ X4 @ X1 @ X3)
% 84.24/12.65 | ~ (sum @ X4 @ X2 @ X2)
% 84.24/12.65 | (sum @ X3 @ X0 @ X0))),
% 84.24/12.65 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 84.24/12.65 thf(zip_derived_cl5743, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i]:
% 84.24/12.65 ( (sum @ X0 @ additive_identity @ additive_identity)
% 84.24/12.65 | ~ (sum @ X1 @ additive_identity @ additive_identity)
% 84.24/12.65 | ~ (product @ X1 @ multiplicative_identity @ X0))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl5727, zip_derived_cl244])).
% 84.24/12.65 thf(zip_derived_cl5933, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 (~ (product @ additive_identity @ multiplicative_identity @ X0)
% 84.24/12.65 | (sum @ X0 @ additive_identity @ additive_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl5743])).
% 84.24/12.65 thf(zip_derived_cl145186, plain,
% 84.24/12.65 ( (sum @ multiplicative_identity @ additive_identity @ additive_identity)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl142322, zip_derived_cl5933])).
% 84.24/12.65 thf(zip_derived_cl8274, plain,
% 84.24/12.65 ( (sum @ multiplicative_identity @ additive_identity @
% 84.24/12.65 multiplicative_identity)),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl8273, zip_derived_cl1806])).
% 84.24/12.65 thf(zip_derived_cl51, plain,
% 84.24/12.65 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 84.24/12.65 (~ (defined @ X0)
% 84.24/12.65 | ~ (sum @ X0 @ X2 @ X1)
% 84.24/12.65 | ~ (sum @ X0 @ X2 @ X3)
% 84.24/12.65 | (sum @ additive_identity @ X3 @ X1))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 84.24/12.65 thf(zip_derived_cl8285, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 84.24/12.65 | ~ (sum @ multiplicative_identity @ additive_identity @ X0)
% 84.24/12.65 | ~ (defined @ multiplicative_identity))),
% 84.24/12.65 inference('sup-', [status(thm)], [zip_derived_cl8274, zip_derived_cl51])).
% 84.24/12.65 thf(zip_derived_cl16, plain, ( (defined @ multiplicative_identity)),
% 84.24/12.65 inference('cnf', [status(esa)],
% 84.24/12.65 [well_definedness_of_multiplicative_identity])).
% 84.24/12.65 thf(zip_derived_cl8292, plain,
% 84.24/12.65 (![X0 : $i]:
% 84.24/12.65 ( (sum @ additive_identity @ X0 @ multiplicative_identity)
% 84.24/12.65 | ~ (sum @ multiplicative_identity @ additive_identity @ X0))),
% 84.24/12.65 inference('demod', [status(thm)], [zip_derived_cl8285, zip_derived_cl16])).
% 84.24/12.65 thf(zip_derived_cl145628, plain,
% 84.24/12.65 ( (sum @ additive_identity @ additive_identity @ multiplicative_identity)),
% 84.24/12.65 inference('sup-', [status(thm)],
% 84.24/12.65 [zip_derived_cl145186, zip_derived_cl8292])).
% 84.24/12.65 thf(zip_derived_cl146535, plain, ($false),
% 84.24/12.65 inference('demod', [status(thm)],
% 84.24/12.65 [zip_derived_cl25, zip_derived_cl145628])).
% 84.24/12.65
% 84.24/12.65 % SZS output end Refutation
% 84.24/12.65
% 84.24/12.65
% 84.24/12.65 % Terminating...
% 84.66/12.68 % Runner terminated.
% 84.66/12.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------