TSTP Solution File: FLD060-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD060-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.pCdqaUCbhw true
% Computer : n024.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 22:39:33 EDT 2023
% Result : Unsatisfiable 22.26s 3.82s
% Output : Refutation 22.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD060-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.pCdqaUCbhw true
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 00:07:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in FO mode
% 0.48/0.63 % Total configuration time : 435
% 0.48/0.63 % Estimated wc time : 1092
% 0.48/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.48/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.48/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.48/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 22.26/3.82 % Solved by fo/fo13.sh.
% 22.26/3.82 % done 3594 iterations in 3.060s
% 22.26/3.82 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 22.26/3.82 % SZS output start Refutation
% 22.26/3.82 thf(sum_type, type, sum: $i > $i > $i > $o).
% 22.26/3.82 thf(b_type, type, b: $i).
% 22.26/3.82 thf(a_type, type, a: $i).
% 22.26/3.82 thf(add_type, type, add: $i > $i > $i).
% 22.26/3.82 thf(v_type, type, v: $i).
% 22.26/3.82 thf(additive_identity_type, type, additive_identity: $i).
% 22.26/3.82 thf(u_type, type, u: $i).
% 22.26/3.82 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 22.26/3.82 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 22.26/3.82 thf(defined_type, type, defined: $i > $o).
% 22.26/3.82 thf(well_definedness_of_additive_inverse, axiom,
% 22.26/3.82 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 22.26/3.82 thf(zip_derived_cl14, plain,
% 22.26/3.82 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 22.26/3.82 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 22.26/3.82 thf(less_or_equal_5, conjecture, (~( less_or_equal @ a @ b ))).
% 22.26/3.82 thf(zf_stmt_0, negated_conjecture, (less_or_equal @ a @ b),
% 22.26/3.82 inference('cnf.neg', [status(esa)], [less_or_equal_5])).
% 22.26/3.82 thf(zip_derived_cl30, plain, ( (less_or_equal @ a @ b)),
% 22.26/3.82 inference('cnf', [status(esa)], [zf_stmt_0])).
% 22.26/3.82 thf(sum_7, conjecture, (~( sum @ b @ b @ v ))).
% 22.26/3.82 thf(zf_stmt_1, negated_conjecture, (sum @ b @ b @ v),
% 22.26/3.82 inference('cnf.neg', [status(esa)], [sum_7])).
% 22.26/3.82 thf(zip_derived_cl32, plain, ( (sum @ b @ b @ v)),
% 22.26/3.82 inference('cnf', [status(esa)], [zf_stmt_1])).
% 22.26/3.82 thf(totality_of_order_relation, axiom,
% 22.26/3.82 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 22.26/3.82 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 22.26/3.82 thf(zip_derived_cl22, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 ( (less_or_equal @ X0 @ X1)
% 22.26/3.82 | (less_or_equal @ X1 @ X0)
% 22.26/3.82 | ~ (defined @ X0)
% 22.26/3.82 | ~ (defined @ X1))),
% 22.26/3.82 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 22.26/3.82 thf(zip_derived_cl117, plain,
% 22.26/3.82 (![X0 : $i]:
% 22.26/3.82 (~ (defined @ X0) | ~ (defined @ X0) | (less_or_equal @ X0 @ X0))),
% 22.26/3.82 inference('eq_fact', [status(thm)], [zip_derived_cl22])).
% 22.26/3.82 thf(zip_derived_cl119, plain,
% 22.26/3.82 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 22.26/3.82 inference('simplify', [status(thm)], [zip_derived_cl117])).
% 22.26/3.82 thf(zip_derived_cl32, plain, ( (sum @ b @ b @ v)),
% 22.26/3.82 inference('cnf', [status(esa)], [zf_stmt_1])).
% 22.26/3.82 thf(compatibility_of_order_relation_and_addition, axiom,
% 22.26/3.82 (( less_or_equal @ U @ V ) | ( ~( less_or_equal @ X @ Y ) ) |
% 22.26/3.82 ( ~( sum @ X @ Z @ U ) ) | ( ~( sum @ Y @ Z @ V ) ))).
% 22.26/3.82 thf(zip_derived_cl23, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.26/3.82 ( (less_or_equal @ X0 @ X1)
% 22.26/3.82 | ~ (less_or_equal @ X2 @ X3)
% 22.26/3.82 | ~ (sum @ X2 @ X4 @ X0)
% 22.26/3.82 | ~ (sum @ X3 @ X4 @ X1))),
% 22.26/3.82 inference('cnf', [status(esa)],
% 22.26/3.82 [compatibility_of_order_relation_and_addition])).
% 22.26/3.82 thf(zip_derived_cl63, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 ( (less_or_equal @ v @ X0)
% 22.26/3.82 | ~ (less_or_equal @ b @ X1)
% 22.26/3.82 | ~ (sum @ X1 @ b @ X0))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl23])).
% 22.26/3.82 thf(zip_derived_cl143, plain,
% 22.26/3.82 (![X0 : $i]:
% 22.26/3.82 (~ (defined @ b) | (less_or_equal @ v @ X0) | ~ (sum @ b @ b @ X0))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl63])).
% 22.26/3.82 thf(b_is_defined, axiom, (defined @ b)).
% 22.26/3.82 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 22.26/3.82 inference('cnf', [status(esa)], [b_is_defined])).
% 22.26/3.82 thf(zip_derived_cl146, plain,
% 22.26/3.82 (![X0 : $i]: ( (less_or_equal @ v @ X0) | ~ (sum @ b @ b @ X0))),
% 22.26/3.82 inference('demod', [status(thm)], [zip_derived_cl143, zip_derived_cl27])).
% 22.26/3.82 thf(zip_derived_cl167, plain, ( (less_or_equal @ v @ v)),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl146])).
% 22.26/3.82 thf(antisymmetry_of_order_relation, axiom,
% 22.26/3.82 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 22.26/3.82 ( ~( less_or_equal @ Y @ X ) ))).
% 22.26/3.82 thf(zip_derived_cl20, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 ( (sum @ additive_identity @ X0 @ X1)
% 22.26/3.82 | ~ (less_or_equal @ X0 @ X1)
% 22.26/3.82 | ~ (less_or_equal @ X1 @ X0))),
% 22.26/3.82 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 22.26/3.82 thf(zip_derived_cl169, plain, ( (sum @ additive_identity @ v @ v)),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl20])).
% 22.26/3.82 thf(commutativity_addition, axiom,
% 22.26/3.82 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 22.26/3.82 thf(zip_derived_cl4, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.26/3.82 thf(zip_derived_cl173, plain, ( (sum @ v @ additive_identity @ v)),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl169, zip_derived_cl4])).
% 22.26/3.82 thf(existence_of_inverse_addition, axiom,
% 22.26/3.82 (( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) |
% 22.26/3.82 ( ~( defined @ X ) ))).
% 22.26/3.82 thf(zip_derived_cl3, plain,
% 22.26/3.82 (![X0 : $i]:
% 22.26/3.82 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 22.26/3.82 | ~ (defined @ X0))),
% 22.26/3.82 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 22.26/3.82 thf(zip_derived_cl4, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.26/3.82 thf(zip_derived_cl47, plain,
% 22.26/3.82 (![X0 : $i]:
% 22.26/3.82 (~ (defined @ X0)
% 22.26/3.82 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 22.26/3.82 thf(zip_derived_cl47, plain,
% 22.26/3.82 (![X0 : $i]:
% 22.26/3.82 (~ (defined @ X0)
% 22.26/3.82 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 22.26/3.82 thf(associativity_addition_2, axiom,
% 22.26/3.82 (( sum @ U @ Z @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 22.26/3.82 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ X @ V @ W ) ))).
% 22.26/3.82 thf(zip_derived_cl1, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2)
% 22.26/3.82 | ~ (sum @ X3 @ X4 @ X0)
% 22.26/3.82 | ~ (sum @ X4 @ X1 @ X5)
% 22.26/3.82 | ~ (sum @ X3 @ X5 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [associativity_addition_2])).
% 22.26/3.82 thf(zip_derived_cl55, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.26/3.82 (~ (defined @ X0)
% 22.26/3.82 | (sum @ additive_identity @ X2 @ X1)
% 22.26/3.82 | ~ (sum @ (additive_inverse @ X0) @ X2 @ X3)
% 22.26/3.82 | ~ (sum @ X0 @ X3 @ X1))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl1])).
% 22.26/3.82 thf(zip_derived_cl743, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 (~ (defined @ (additive_inverse @ X0))
% 22.26/3.82 | ~ (defined @ X0)
% 22.26/3.82 | (sum @ additive_identity @
% 22.26/3.82 (additive_inverse @ (additive_inverse @ X0)) @ X1)
% 22.26/3.82 | ~ (sum @ X0 @ additive_identity @ X1))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl55])).
% 22.26/3.82 thf(zip_derived_cl14, plain,
% 22.26/3.82 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 22.26/3.82 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 22.26/3.82 thf(zip_derived_cl27211, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 (~ (sum @ X0 @ additive_identity @ X1)
% 22.26/3.82 | (sum @ additive_identity @
% 22.26/3.82 (additive_inverse @ (additive_inverse @ X0)) @ X1)
% 22.26/3.82 | ~ (defined @ X0))),
% 22.26/3.82 inference('clc', [status(thm)], [zip_derived_cl743, zip_derived_cl14])).
% 22.26/3.82 thf(zip_derived_cl27256, plain,
% 22.26/3.82 (( (sum @ additive_identity @
% 22.26/3.82 (additive_inverse @ (additive_inverse @ v)) @ v)
% 22.26/3.82 | ~ (defined @ v))),
% 22.26/3.82 inference('s_sup-', [status(thm)],
% 22.26/3.82 [zip_derived_cl173, zip_derived_cl27211])).
% 22.26/3.82 thf(v_is_defined, axiom, (defined @ v)).
% 22.26/3.82 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 22.26/3.82 inference('cnf', [status(esa)], [v_is_defined])).
% 22.26/3.82 thf(zip_derived_cl27284, plain,
% 22.26/3.82 ( (sum @ additive_identity @
% 22.26/3.82 (additive_inverse @ (additive_inverse @ v)) @ v)),
% 22.26/3.82 inference('demod', [status(thm)], [zip_derived_cl27256, zip_derived_cl29])).
% 22.26/3.82 thf(zip_derived_cl4, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.26/3.82 thf(zip_derived_cl27600, plain,
% 22.26/3.82 ( (sum @ (additive_inverse @ (additive_inverse @ v)) @
% 22.26/3.82 additive_identity @ v)),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl27284, zip_derived_cl4])).
% 22.26/3.82 thf(totality_of_addition, axiom,
% 22.26/3.82 (( sum @ X @ Y @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 22.26/3.82 ( ~( defined @ Y ) ))).
% 22.26/3.82 thf(zip_derived_cl18, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 22.26/3.82 | ~ (defined @ X0)
% 22.26/3.82 | ~ (defined @ X1))),
% 22.26/3.82 inference('cnf', [status(esa)], [totality_of_addition])).
% 22.26/3.82 thf(sum_6, conjecture, (~( sum @ a @ a @ u ))).
% 22.26/3.82 thf(zf_stmt_2, negated_conjecture, (sum @ a @ a @ u),
% 22.26/3.82 inference('cnf.neg', [status(esa)], [sum_6])).
% 22.26/3.82 thf(zip_derived_cl31, plain, ( (sum @ a @ a @ u)),
% 22.26/3.82 inference('cnf', [status(esa)], [zf_stmt_2])).
% 22.26/3.82 thf(existence_of_identity_addition, axiom,
% 22.26/3.82 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 22.26/3.82 thf(zip_derived_cl2, plain,
% 22.26/3.82 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 22.26/3.82 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 22.26/3.82 thf(associativity_addition_1, axiom,
% 22.26/3.82 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 22.26/3.82 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 22.26/3.82 thf(zip_derived_cl0, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2)
% 22.26/3.82 | ~ (sum @ X0 @ X3 @ X4)
% 22.26/3.82 | ~ (sum @ X3 @ X5 @ X1)
% 22.26/3.82 | ~ (sum @ X4 @ X5 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [associativity_addition_1])).
% 22.26/3.82 thf(zip_derived_cl36, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.26/3.82 (~ (defined @ X0)
% 22.26/3.82 | (sum @ additive_identity @ X2 @ X1)
% 22.26/3.82 | ~ (sum @ X0 @ X3 @ X2)
% 22.26/3.82 | ~ (sum @ X0 @ X3 @ X1))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 22.26/3.82 thf(zip_derived_cl283, plain,
% 22.26/3.82 (![X0 : $i]:
% 22.26/3.82 (~ (defined @ a)
% 22.26/3.82 | (sum @ additive_identity @ u @ X0)
% 22.26/3.82 | ~ (sum @ a @ a @ X0))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl36])).
% 22.26/3.82 thf(a_is_defined, axiom, (defined @ a)).
% 22.26/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.26/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.26/3.82 thf(zip_derived_cl295, plain,
% 22.26/3.82 (![X0 : $i]: ( (sum @ additive_identity @ u @ X0) | ~ (sum @ a @ a @ X0))),
% 22.26/3.82 inference('demod', [status(thm)], [zip_derived_cl283, zip_derived_cl26])).
% 22.26/3.82 thf(zip_derived_cl326, plain,
% 22.26/3.82 ((~ (defined @ a)
% 22.26/3.82 | ~ (defined @ a)
% 22.26/3.82 | (sum @ additive_identity @ u @ (add @ a @ a)))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl295])).
% 22.26/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.26/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.26/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.26/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.26/3.82 thf(zip_derived_cl329, plain,
% 22.26/3.82 ( (sum @ additive_identity @ u @ (add @ a @ a))),
% 22.26/3.82 inference('demod', [status(thm)],
% 22.26/3.82 [zip_derived_cl326, zip_derived_cl26, zip_derived_cl26])).
% 22.26/3.82 thf(zip_derived_cl4, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.26/3.82 thf(zip_derived_cl342, plain,
% 22.26/3.82 ( (sum @ u @ additive_identity @ (add @ a @ a))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl329, zip_derived_cl4])).
% 22.26/3.82 thf(zip_derived_cl2, plain,
% 22.26/3.82 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 22.26/3.82 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 22.26/3.82 thf(zip_derived_cl4, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.26/3.82 thf(zip_derived_cl41, plain,
% 22.26/3.82 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 22.26/3.82 thf(zip_derived_cl31, plain, ( (sum @ a @ a @ u)),
% 22.26/3.82 inference('cnf', [status(esa)], [zf_stmt_2])).
% 22.26/3.82 thf(zip_derived_cl0, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2)
% 22.26/3.82 | ~ (sum @ X0 @ X3 @ X4)
% 22.26/3.82 | ~ (sum @ X3 @ X5 @ X1)
% 22.26/3.82 | ~ (sum @ X4 @ X5 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [associativity_addition_1])).
% 22.26/3.82 thf(zip_derived_cl34, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.26/3.82 ( (sum @ a @ X1 @ X0) | ~ (sum @ a @ X2 @ X1) | ~ (sum @ u @ X2 @ X0))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl0])).
% 22.26/3.82 thf(zip_derived_cl65, plain,
% 22.26/3.82 (![X0 : $i]:
% 22.26/3.82 (~ (defined @ a)
% 22.26/3.82 | (sum @ a @ a @ X0)
% 22.26/3.82 | ~ (sum @ u @ additive_identity @ X0))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl34])).
% 22.26/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.26/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.26/3.82 thf(zip_derived_cl68, plain,
% 22.26/3.82 (![X0 : $i]: ( (sum @ a @ a @ X0) | ~ (sum @ u @ additive_identity @ X0))),
% 22.26/3.82 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl26])).
% 22.26/3.82 thf(zip_derived_cl372, plain, ( (sum @ a @ a @ (add @ a @ a))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl342, zip_derived_cl68])).
% 22.26/3.82 thf(zip_derived_cl18, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 22.26/3.82 | ~ (defined @ X0)
% 22.26/3.82 | ~ (defined @ X1))),
% 22.26/3.82 inference('cnf', [status(esa)], [totality_of_addition])).
% 22.26/3.82 thf(zip_derived_cl41, plain,
% 22.26/3.82 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 22.26/3.82 thf(zip_derived_cl18, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 22.26/3.82 | ~ (defined @ X0)
% 22.26/3.82 | ~ (defined @ X1))),
% 22.26/3.82 inference('cnf', [status(esa)], [totality_of_addition])).
% 22.26/3.82 thf(zip_derived_cl34, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.26/3.82 ( (sum @ a @ X1 @ X0) | ~ (sum @ a @ X2 @ X1) | ~ (sum @ u @ X2 @ X0))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl0])).
% 22.26/3.82 thf(zip_derived_cl78, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 (~ (defined @ X0)
% 22.26/3.82 | ~ (defined @ a)
% 22.26/3.82 | (sum @ a @ (add @ a @ X0) @ X1)
% 22.26/3.82 | ~ (sum @ u @ X0 @ X1))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl34])).
% 22.26/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.26/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.26/3.82 thf(zip_derived_cl81, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 (~ (defined @ X0)
% 22.26/3.82 | (sum @ a @ (add @ a @ X0) @ X1)
% 22.26/3.82 | ~ (sum @ u @ X0 @ X1))),
% 22.26/3.82 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl26])).
% 22.26/3.82 thf(zip_derived_cl1520, plain,
% 22.26/3.82 ((~ (defined @ u)
% 22.26/3.82 | ~ (defined @ additive_identity)
% 22.26/3.82 | (sum @ a @ (add @ a @ additive_identity) @ u))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl81])).
% 22.26/3.82 thf(u_is_defined, axiom, (defined @ u)).
% 22.26/3.82 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 22.26/3.82 inference('cnf', [status(esa)], [u_is_defined])).
% 22.26/3.82 thf(well_definedness_of_additive_identity, axiom,
% 22.26/3.82 (defined @ additive_identity)).
% 22.26/3.82 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 22.26/3.82 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.26/3.82 thf(zip_derived_cl1533, plain,
% 22.26/3.82 ( (sum @ a @ (add @ a @ additive_identity) @ u)),
% 22.26/3.82 inference('demod', [status(thm)],
% 22.26/3.82 [zip_derived_cl1520, zip_derived_cl28, zip_derived_cl13])).
% 22.26/3.82 thf(zip_derived_cl4, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.26/3.82 thf(zip_derived_cl1574, plain,
% 22.26/3.82 ( (sum @ (add @ a @ additive_identity) @ a @ u)),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl1533, zip_derived_cl4])).
% 22.26/3.82 thf(zip_derived_cl18, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 22.26/3.82 | ~ (defined @ X0)
% 22.26/3.82 | ~ (defined @ X1))),
% 22.26/3.82 inference('cnf', [status(esa)], [totality_of_addition])).
% 22.26/3.82 thf(zip_derived_cl0, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2)
% 22.26/3.82 | ~ (sum @ X0 @ X3 @ X4)
% 22.26/3.82 | ~ (sum @ X3 @ X5 @ X1)
% 22.26/3.82 | ~ (sum @ X4 @ X5 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [associativity_addition_1])).
% 22.26/3.82 thf(zip_derived_cl74, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.26/3.82 (~ (defined @ X0)
% 22.26/3.82 | ~ (defined @ X1)
% 22.26/3.82 | (sum @ X1 @ X3 @ X2)
% 22.26/3.82 | ~ (sum @ X0 @ X4 @ X3)
% 22.26/3.82 | ~ (sum @ (add @ X1 @ X0) @ X4 @ X2))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl0])).
% 22.26/3.82 thf(zip_derived_cl1591, plain,
% 22.26/3.82 (![X0 : $i]:
% 22.26/3.82 (~ (defined @ additive_identity)
% 22.26/3.82 | ~ (defined @ a)
% 22.26/3.82 | (sum @ a @ X0 @ u)
% 22.26/3.82 | ~ (sum @ additive_identity @ a @ X0))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl1574, zip_derived_cl74])).
% 22.26/3.82 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 22.26/3.82 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.26/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.26/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.26/3.82 thf(zip_derived_cl1593, plain,
% 22.26/3.82 (![X0 : $i]: ( (sum @ a @ X0 @ u) | ~ (sum @ additive_identity @ a @ X0))),
% 22.26/3.82 inference('demod', [status(thm)],
% 22.26/3.82 [zip_derived_cl1591, zip_derived_cl13, zip_derived_cl26])).
% 22.26/3.82 thf(zip_derived_cl1968, plain,
% 22.26/3.82 ((~ (defined @ a)
% 22.26/3.82 | ~ (defined @ additive_identity)
% 22.26/3.82 | (sum @ a @ (add @ additive_identity @ a) @ u))),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl1593])).
% 22.26/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.26/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.26/3.82 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 22.26/3.82 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.26/3.82 thf(zip_derived_cl1973, plain,
% 22.26/3.82 ( (sum @ a @ (add @ additive_identity @ a) @ u)),
% 22.26/3.82 inference('demod', [status(thm)],
% 22.26/3.82 [zip_derived_cl1968, zip_derived_cl26, zip_derived_cl13])).
% 22.26/3.82 thf(zip_derived_cl4, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.26/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.26/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.26/3.82 thf(zip_derived_cl1983, plain,
% 22.26/3.82 ( (sum @ (add @ additive_identity @ a) @ a @ u)),
% 22.26/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl1973, zip_derived_cl4])).
% 22.26/3.82 thf(zip_derived_cl74, plain,
% 22.26/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.26/3.82 (~ (defined @ X0)
% 22.71/3.82 | ~ (defined @ X1)
% 22.71/3.82 | (sum @ X1 @ X3 @ X2)
% 22.71/3.82 | ~ (sum @ X0 @ X4 @ X3)
% 22.71/3.82 | ~ (sum @ (add @ X1 @ X0) @ X4 @ X2))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl0])).
% 22.71/3.82 thf(zip_derived_cl2002, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 (~ (defined @ a)
% 22.71/3.82 | ~ (defined @ additive_identity)
% 22.71/3.82 | (sum @ additive_identity @ X0 @ u)
% 22.71/3.82 | ~ (sum @ a @ a @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl1983, zip_derived_cl74])).
% 22.71/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.71/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.71/3.82 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 22.71/3.82 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.71/3.82 thf(zip_derived_cl2005, plain,
% 22.71/3.82 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ u) | ~ (sum @ a @ a @ X0))),
% 22.71/3.82 inference('demod', [status(thm)],
% 22.71/3.82 [zip_derived_cl2002, zip_derived_cl26, zip_derived_cl13])).
% 22.71/3.82 thf(zip_derived_cl2212, plain,
% 22.71/3.82 ( (sum @ additive_identity @ (add @ a @ a) @ u)),
% 22.71/3.82 inference('s_sup-', [status(thm)],
% 22.71/3.82 [zip_derived_cl372, zip_derived_cl2005])).
% 22.71/3.82 thf(zip_derived_cl4, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.71/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.71/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.71/3.82 thf(zip_derived_cl2230, plain,
% 22.71/3.82 ( (sum @ (add @ a @ a) @ additive_identity @ u)),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl2212, zip_derived_cl4])).
% 22.71/3.82 thf(zip_derived_cl23, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.71/3.82 ( (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ X2 @ X3)
% 22.71/3.82 | ~ (sum @ X2 @ X4 @ X0)
% 22.71/3.82 | ~ (sum @ X3 @ X4 @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)],
% 22.71/3.82 [compatibility_of_order_relation_and_addition])).
% 22.71/3.82 thf(zip_derived_cl2247, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 ( (less_or_equal @ u @ X0)
% 22.71/3.82 | ~ (less_or_equal @ (add @ a @ a) @ X1)
% 22.71/3.82 | ~ (sum @ X1 @ additive_identity @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl2230, zip_derived_cl23])).
% 22.71/3.82 thf(zip_derived_cl27892, plain,
% 22.71/3.82 (( (less_or_equal @ u @ v)
% 22.71/3.82 | ~ (less_or_equal @ (add @ a @ a) @
% 22.71/3.82 (additive_inverse @ (additive_inverse @ v))))),
% 22.71/3.82 inference('s_sup-', [status(thm)],
% 22.71/3.82 [zip_derived_cl27600, zip_derived_cl2247])).
% 22.71/3.82 thf(not_less_or_equal_8, conjecture, (less_or_equal @ u @ v)).
% 22.71/3.82 thf(zf_stmt_3, negated_conjecture, (~( less_or_equal @ u @ v )),
% 22.71/3.82 inference('cnf.neg', [status(esa)], [not_less_or_equal_8])).
% 22.71/3.82 thf(zip_derived_cl33, plain, (~ (less_or_equal @ u @ v)),
% 22.71/3.82 inference('cnf', [status(esa)], [zf_stmt_3])).
% 22.71/3.82 thf(zip_derived_cl27917, plain,
% 22.71/3.82 (~ (less_or_equal @ (add @ a @ a) @
% 22.71/3.82 (additive_inverse @ (additive_inverse @ v)))),
% 22.71/3.82 inference('demod', [status(thm)], [zip_derived_cl27892, zip_derived_cl33])).
% 22.71/3.82 thf(well_definedness_of_addition, axiom,
% 22.71/3.82 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 22.71/3.82 ( ~( defined @ Y ) ))).
% 22.71/3.82 thf(zip_derived_cl12, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 22.71/3.82 thf(zip_derived_cl2212, plain,
% 22.71/3.82 ( (sum @ additive_identity @ (add @ a @ a) @ u)),
% 22.71/3.82 inference('s_sup-', [status(thm)],
% 22.71/3.82 [zip_derived_cl372, zip_derived_cl2005])).
% 22.71/3.82 thf(zip_derived_cl47, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 (~ (defined @ X0)
% 22.71/3.82 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 22.71/3.82 thf(zip_derived_cl47, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 (~ (defined @ X0)
% 22.71/3.82 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 22.71/3.82 thf(zip_derived_cl31, plain, ( (sum @ a @ a @ u)),
% 22.71/3.82 inference('cnf', [status(esa)], [zf_stmt_2])).
% 22.71/3.82 thf(zip_derived_cl119, plain,
% 22.71/3.82 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 22.71/3.82 inference('simplify', [status(thm)], [zip_derived_cl117])).
% 22.71/3.82 thf(zip_derived_cl31, plain, ( (sum @ a @ a @ u)),
% 22.71/3.82 inference('cnf', [status(esa)], [zf_stmt_2])).
% 22.71/3.82 thf(zip_derived_cl23, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.71/3.82 ( (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ X2 @ X3)
% 22.71/3.82 | ~ (sum @ X2 @ X4 @ X0)
% 22.71/3.82 | ~ (sum @ X3 @ X4 @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)],
% 22.71/3.82 [compatibility_of_order_relation_and_addition])).
% 22.71/3.82 thf(zip_derived_cl62, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 ( (less_or_equal @ u @ X0)
% 22.71/3.82 | ~ (less_or_equal @ a @ X1)
% 22.71/3.82 | ~ (sum @ X1 @ a @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl23])).
% 22.71/3.82 thf(zip_derived_cl141, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 (~ (defined @ a) | (less_or_equal @ u @ X0) | ~ (sum @ a @ a @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl62])).
% 22.71/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.71/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.71/3.82 thf(zip_derived_cl144, plain,
% 22.71/3.82 (![X0 : $i]: ( (less_or_equal @ u @ X0) | ~ (sum @ a @ a @ X0))),
% 22.71/3.82 inference('demod', [status(thm)], [zip_derived_cl141, zip_derived_cl26])).
% 22.71/3.82 thf(zip_derived_cl149, plain, ( (less_or_equal @ u @ u)),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl144])).
% 22.71/3.82 thf(zip_derived_cl20, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 ( (sum @ additive_identity @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ X1 @ X0))),
% 22.71/3.82 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 22.71/3.82 thf(zip_derived_cl151, plain, ( (sum @ additive_identity @ u @ u)),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl149, zip_derived_cl20])).
% 22.71/3.82 thf(zip_derived_cl0, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.71/3.82 ( (sum @ X0 @ X1 @ X2)
% 22.71/3.82 | ~ (sum @ X0 @ X3 @ X4)
% 22.71/3.82 | ~ (sum @ X3 @ X5 @ X1)
% 22.71/3.82 | ~ (sum @ X4 @ X5 @ X2))),
% 22.71/3.82 inference('cnf', [status(esa)], [associativity_addition_1])).
% 22.71/3.82 thf(zip_derived_cl157, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.71/3.82 ( (sum @ additive_identity @ X1 @ X0)
% 22.71/3.82 | ~ (sum @ u @ X2 @ X1)
% 22.71/3.82 | ~ (sum @ u @ X2 @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl0])).
% 22.71/3.82 thf(zip_derived_cl576, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 (~ (defined @ u)
% 22.71/3.82 | (sum @ additive_identity @ additive_identity @ X0)
% 22.71/3.82 | ~ (sum @ u @ (additive_inverse @ u) @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl157])).
% 22.71/3.82 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 22.71/3.82 inference('cnf', [status(esa)], [u_is_defined])).
% 22.71/3.82 thf(zip_derived_cl582, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 ( (sum @ additive_identity @ additive_identity @ X0)
% 22.71/3.82 | ~ (sum @ u @ (additive_inverse @ u) @ X0))),
% 22.71/3.82 inference('demod', [status(thm)], [zip_derived_cl576, zip_derived_cl28])).
% 22.71/3.82 thf(zip_derived_cl641, plain,
% 22.71/3.82 ((~ (defined @ u)
% 22.71/3.82 | (sum @ additive_identity @ additive_identity @ additive_identity))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl582])).
% 22.71/3.82 thf(zip_derived_cl28, plain, ( (defined @ u)),
% 22.71/3.82 inference('cnf', [status(esa)], [u_is_defined])).
% 22.71/3.82 thf(zip_derived_cl643, plain,
% 22.71/3.82 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 22.71/3.82 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl28])).
% 22.71/3.82 thf(zip_derived_cl119, plain,
% 22.71/3.82 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 22.71/3.82 inference('simplify', [status(thm)], [zip_derived_cl117])).
% 22.71/3.82 thf(zip_derived_cl643, plain,
% 22.71/3.82 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 22.71/3.82 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl28])).
% 22.71/3.82 thf(zip_derived_cl23, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.71/3.82 ( (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ X2 @ X3)
% 22.71/3.82 | ~ (sum @ X2 @ X4 @ X0)
% 22.71/3.82 | ~ (sum @ X3 @ X4 @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)],
% 22.71/3.82 [compatibility_of_order_relation_and_addition])).
% 22.71/3.82 thf(zip_derived_cl648, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 ( (less_or_equal @ additive_identity @ X0)
% 22.71/3.82 | ~ (less_or_equal @ additive_identity @ X1)
% 22.71/3.82 | ~ (sum @ X1 @ additive_identity @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl643, zip_derived_cl23])).
% 22.71/3.82 thf(zip_derived_cl657, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 (~ (defined @ additive_identity)
% 22.71/3.82 | (less_or_equal @ additive_identity @ X0)
% 22.71/3.82 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl648])).
% 22.71/3.82 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 22.71/3.82 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.71/3.82 thf(zip_derived_cl660, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 ( (less_or_equal @ additive_identity @ X0)
% 22.71/3.82 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 22.71/3.82 inference('demod', [status(thm)], [zip_derived_cl657, zip_derived_cl13])).
% 22.71/3.82 thf(zip_derived_cl664, plain,
% 22.71/3.82 ( (less_or_equal @ additive_identity @ additive_identity)),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl643, zip_derived_cl660])).
% 22.71/3.82 thf(zip_derived_cl2, plain,
% 22.71/3.82 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 22.71/3.82 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 22.71/3.82 thf(zip_derived_cl23, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.71/3.82 ( (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ X2 @ X3)
% 22.71/3.82 | ~ (sum @ X2 @ X4 @ X0)
% 22.71/3.82 | ~ (sum @ X3 @ X4 @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)],
% 22.71/3.82 [compatibility_of_order_relation_and_addition])).
% 22.71/3.82 thf(zip_derived_cl60, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.71/3.82 (~ (defined @ X0)
% 22.71/3.82 | (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ additive_identity @ X2)
% 22.71/3.82 | ~ (sum @ X2 @ X0 @ X1))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl23])).
% 22.71/3.82 thf(zip_derived_cl873, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 (~ (defined @ X0)
% 22.71/3.82 | (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (sum @ additive_identity @ X0 @ X1))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl664, zip_derived_cl60])).
% 22.71/3.82 thf(zip_derived_cl2234, plain,
% 22.71/3.82 ((~ (defined @ (add @ a @ a)) | (less_or_equal @ (add @ a @ a) @ u))),
% 22.71/3.82 inference('s_sup-', [status(thm)],
% 22.71/3.82 [zip_derived_cl2212, zip_derived_cl873])).
% 22.71/3.82 thf(zip_derived_cl3347, plain,
% 22.71/3.82 ((~ (defined @ a)
% 22.71/3.82 | ~ (defined @ a)
% 22.71/3.82 | (less_or_equal @ (add @ a @ a) @ u))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl2234])).
% 22.71/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.71/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.71/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.71/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.71/3.82 thf(zip_derived_cl3348, plain, ( (less_or_equal @ (add @ a @ a) @ u)),
% 22.71/3.82 inference('demod', [status(thm)],
% 22.71/3.82 [zip_derived_cl3347, zip_derived_cl26, zip_derived_cl26])).
% 22.71/3.82 thf(transitivity_of_order_relation, axiom,
% 22.71/3.82 (( less_or_equal @ X @ Z ) | ( ~( less_or_equal @ X @ Y ) ) |
% 22.71/3.82 ( ~( less_or_equal @ Y @ Z ) ))).
% 22.71/3.82 thf(zip_derived_cl21, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.71/3.82 ( (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ X0 @ X2)
% 22.71/3.82 | ~ (less_or_equal @ X2 @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 22.71/3.82 thf(zip_derived_cl3372, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 ( (less_or_equal @ (add @ a @ a) @ X0) | ~ (less_or_equal @ u @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl3348, zip_derived_cl21])).
% 22.71/3.82 thf(zip_derived_cl27944, plain,
% 22.71/3.82 (~ (less_or_equal @ u @ (additive_inverse @ (additive_inverse @ v)))),
% 22.71/3.82 inference('s_sup+', [status(thm)],
% 22.71/3.82 [zip_derived_cl27917, zip_derived_cl3372])).
% 22.71/3.82 thf(zip_derived_cl18, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 22.71/3.82 | ~ (defined @ X0)
% 22.71/3.82 | ~ (defined @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)], [totality_of_addition])).
% 22.71/3.82 thf(zip_derived_cl4, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.71/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.71/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.71/3.82 thf(zip_derived_cl76, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 (~ (defined @ X0)
% 22.71/3.82 | ~ (defined @ X1)
% 22.71/3.82 | (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 22.71/3.82 thf(zip_derived_cl30, plain, ( (less_or_equal @ a @ b)),
% 22.71/3.82 inference('cnf', [status(esa)], [zf_stmt_0])).
% 22.71/3.82 thf(zip_derived_cl62, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 ( (less_or_equal @ u @ X0)
% 22.71/3.82 | ~ (less_or_equal @ a @ X1)
% 22.71/3.82 | ~ (sum @ X1 @ a @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl23])).
% 22.71/3.82 thf(zip_derived_cl64, plain,
% 22.71/3.82 (![X0 : $i]: ( (less_or_equal @ u @ X0) | ~ (sum @ b @ a @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl62])).
% 22.71/3.82 thf(zip_derived_cl1281, plain,
% 22.71/3.82 ((~ (defined @ a)
% 22.71/3.82 | ~ (defined @ b)
% 22.71/3.82 | (less_or_equal @ u @ (add @ a @ b)))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl64])).
% 22.71/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.71/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.71/3.82 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 22.71/3.82 inference('cnf', [status(esa)], [b_is_defined])).
% 22.71/3.82 thf(zip_derived_cl1338, plain, ( (less_or_equal @ u @ (add @ a @ b))),
% 22.71/3.82 inference('demod', [status(thm)],
% 22.71/3.82 [zip_derived_cl1281, zip_derived_cl26, zip_derived_cl27])).
% 22.71/3.82 thf(zip_derived_cl21, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.71/3.82 ( (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ X0 @ X2)
% 22.71/3.82 | ~ (less_or_equal @ X2 @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 22.71/3.82 thf(zip_derived_cl1402, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 ( (less_or_equal @ u @ X0) | ~ (less_or_equal @ (add @ a @ b) @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl1338, zip_derived_cl21])).
% 22.71/3.82 thf(zip_derived_cl27980, plain,
% 22.71/3.82 (~ (less_or_equal @ (add @ a @ b) @
% 22.71/3.82 (additive_inverse @ (additive_inverse @ v)))),
% 22.71/3.82 inference('s_sup+', [status(thm)],
% 22.71/3.82 [zip_derived_cl27944, zip_derived_cl1402])).
% 22.71/3.82 thf(zip_derived_cl18, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 22.71/3.82 | ~ (defined @ X0)
% 22.71/3.82 | ~ (defined @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)], [totality_of_addition])).
% 22.71/3.82 thf(zip_derived_cl23, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.71/3.82 ( (less_or_equal @ X0 @ X1)
% 22.71/3.82 | ~ (less_or_equal @ X2 @ X3)
% 22.71/3.82 | ~ (sum @ X2 @ X4 @ X0)
% 22.71/3.82 | ~ (sum @ X3 @ X4 @ X1))),
% 22.71/3.82 inference('cnf', [status(esa)],
% 22.71/3.82 [compatibility_of_order_relation_and_addition])).
% 22.71/3.82 thf(zip_derived_cl77, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.71/3.82 (~ (defined @ X0)
% 22.71/3.82 | ~ (defined @ X1)
% 22.71/3.82 | (less_or_equal @ (add @ X1 @ X0) @ X2)
% 22.71/3.82 | ~ (less_or_equal @ X1 @ X3)
% 22.71/3.82 | ~ (sum @ X3 @ X0 @ X2))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl23])).
% 22.71/3.82 thf(zip_derived_cl28559, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 (~ (defined @ b)
% 22.71/3.82 | ~ (defined @ a)
% 22.71/3.82 | ~ (less_or_equal @ a @ X0)
% 22.71/3.82 | ~ (sum @ X0 @ b @ (additive_inverse @ (additive_inverse @ v))))),
% 22.71/3.82 inference('s_sup+', [status(thm)],
% 22.71/3.82 [zip_derived_cl27980, zip_derived_cl77])).
% 22.71/3.82 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 22.71/3.82 inference('cnf', [status(esa)], [b_is_defined])).
% 22.71/3.82 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 22.71/3.82 inference('cnf', [status(esa)], [a_is_defined])).
% 22.71/3.82 thf(zip_derived_cl28560, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 (~ (less_or_equal @ a @ X0)
% 22.71/3.82 | ~ (sum @ X0 @ b @ (additive_inverse @ (additive_inverse @ v))))),
% 22.71/3.82 inference('demod', [status(thm)],
% 22.71/3.82 [zip_derived_cl28559, zip_derived_cl27, zip_derived_cl26])).
% 22.71/3.82 thf(zip_derived_cl28772, plain,
% 22.71/3.82 (~ (sum @ b @ b @ (additive_inverse @ (additive_inverse @ v)))),
% 22.71/3.82 inference('s_sup-', [status(thm)],
% 22.71/3.82 [zip_derived_cl30, zip_derived_cl28560])).
% 22.71/3.82 thf(zip_derived_cl41, plain,
% 22.71/3.82 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 22.71/3.82 thf(zip_derived_cl32, plain, ( (sum @ b @ b @ v)),
% 22.71/3.82 inference('cnf', [status(esa)], [zf_stmt_1])).
% 22.71/3.82 thf(zip_derived_cl0, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.71/3.82 ( (sum @ X0 @ X1 @ X2)
% 22.71/3.82 | ~ (sum @ X0 @ X3 @ X4)
% 22.71/3.82 | ~ (sum @ X3 @ X5 @ X1)
% 22.71/3.82 | ~ (sum @ X4 @ X5 @ X2))),
% 22.71/3.82 inference('cnf', [status(esa)], [associativity_addition_1])).
% 22.71/3.82 thf(zip_derived_cl35, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.71/3.82 ( (sum @ b @ X1 @ X0) | ~ (sum @ b @ X2 @ X1) | ~ (sum @ v @ X2 @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl0])).
% 22.71/3.82 thf(zip_derived_cl246, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 (~ (defined @ b)
% 22.71/3.82 | (sum @ b @ b @ X0)
% 22.71/3.82 | ~ (sum @ v @ additive_identity @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl35])).
% 22.71/3.82 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 22.71/3.82 inference('cnf', [status(esa)], [b_is_defined])).
% 22.71/3.82 thf(zip_derived_cl250, plain,
% 22.71/3.82 (![X0 : $i]: ( (sum @ b @ b @ X0) | ~ (sum @ v @ additive_identity @ X0))),
% 22.71/3.82 inference('demod', [status(thm)], [zip_derived_cl246, zip_derived_cl27])).
% 22.71/3.82 thf(zip_derived_cl28797, plain,
% 22.71/3.82 (~ (sum @ v @ additive_identity @
% 22.71/3.82 (additive_inverse @ (additive_inverse @ v)))),
% 22.71/3.82 inference('s_sup+', [status(thm)],
% 22.71/3.82 [zip_derived_cl28772, zip_derived_cl250])).
% 22.71/3.82 thf(zip_derived_cl4, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.71/3.82 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 22.71/3.82 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.71/3.82 thf(zip_derived_cl28816, plain,
% 22.71/3.82 (~ (sum @ additive_identity @ v @
% 22.71/3.82 (additive_inverse @ (additive_inverse @ v)))),
% 22.71/3.82 inference('s_sup+', [status(thm)], [zip_derived_cl28797, zip_derived_cl4])).
% 22.71/3.82 thf(zip_derived_cl41, plain,
% 22.71/3.82 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 22.71/3.82 thf(zip_derived_cl3, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 22.71/3.82 | ~ (defined @ X0))),
% 22.71/3.82 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 22.71/3.82 thf(zip_derived_cl1, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.71/3.82 ( (sum @ X0 @ X1 @ X2)
% 22.71/3.82 | ~ (sum @ X3 @ X4 @ X0)
% 22.71/3.82 | ~ (sum @ X4 @ X1 @ X5)
% 22.71/3.82 | ~ (sum @ X3 @ X5 @ X2))),
% 22.71/3.82 inference('cnf', [status(esa)], [associativity_addition_2])).
% 22.71/3.82 thf(zip_derived_cl46, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.71/3.82 (~ (defined @ X0)
% 22.71/3.82 | (sum @ additive_identity @ X2 @ X1)
% 22.71/3.82 | ~ (sum @ X0 @ X2 @ X3)
% 22.71/3.82 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 22.71/3.82 thf(zip_derived_cl485, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 (~ (defined @ (additive_inverse @ X0))
% 22.71/3.82 | ~ (defined @ X0)
% 22.71/3.82 | (sum @ additive_identity @ X1 @ (additive_inverse @ X0))
% 22.71/3.82 | ~ (sum @ X0 @ X1 @ additive_identity))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl46])).
% 22.71/3.82 thf(zip_derived_cl14, plain,
% 22.71/3.82 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 22.71/3.82 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 22.71/3.82 thf(zip_derived_cl16247, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i]:
% 22.71/3.82 (~ (sum @ X0 @ X1 @ additive_identity)
% 22.71/3.82 | (sum @ additive_identity @ X1 @ (additive_inverse @ X0))
% 22.71/3.82 | ~ (defined @ X0))),
% 22.71/3.82 inference('clc', [status(thm)], [zip_derived_cl485, zip_derived_cl14])).
% 22.71/3.82 thf(zip_derived_cl28875, plain,
% 22.71/3.82 ((~ (sum @ (additive_inverse @ v) @ v @ additive_identity)
% 22.71/3.82 | ~ (defined @ (additive_inverse @ v)))),
% 22.71/3.82 inference('s_sup+', [status(thm)],
% 22.71/3.82 [zip_derived_cl28816, zip_derived_cl16247])).
% 22.71/3.82 thf(zip_derived_cl173, plain, ( (sum @ v @ additive_identity @ v)),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl169, zip_derived_cl4])).
% 22.71/3.82 thf(zip_derived_cl2, plain,
% 22.71/3.82 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 22.71/3.82 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 22.71/3.82 thf(zip_derived_cl3, plain,
% 22.71/3.82 (![X0 : $i]:
% 22.71/3.82 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 22.71/3.82 | ~ (defined @ X0))),
% 22.71/3.82 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 22.71/3.82 thf(zip_derived_cl0, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.71/3.82 ( (sum @ X0 @ X1 @ X2)
% 22.71/3.82 | ~ (sum @ X0 @ X3 @ X4)
% 22.71/3.82 | ~ (sum @ X3 @ X5 @ X1)
% 22.71/3.82 | ~ (sum @ X4 @ X5 @ X2))),
% 22.71/3.82 inference('cnf', [status(esa)], [associativity_addition_1])).
% 22.71/3.82 thf(zip_derived_cl45, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.71/3.82 (~ (defined @ X0)
% 22.71/3.82 | (sum @ (additive_inverse @ X0) @ X2 @ X1)
% 22.71/3.82 | ~ (sum @ X0 @ X3 @ X2)
% 22.71/3.82 | ~ (sum @ additive_identity @ X3 @ X1))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 22.71/3.82 thf(zip_derived_cl458, plain,
% 22.71/3.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.71/3.82 (~ (defined @ X0)
% 22.71/3.82 | ~ (defined @ X1)
% 22.71/3.82 | (sum @ (additive_inverse @ X1) @ X2 @ X0)
% 22.71/3.82 | ~ (sum @ X1 @ X0 @ X2))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl45])).
% 22.71/3.82 thf(zip_derived_cl13709, plain,
% 22.71/3.82 ((~ (defined @ additive_identity)
% 22.71/3.82 | ~ (defined @ v)
% 22.71/3.82 | (sum @ (additive_inverse @ v) @ v @ additive_identity))),
% 22.71/3.82 inference('s_sup-', [status(thm)], [zip_derived_cl173, zip_derived_cl458])).
% 22.71/3.82 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 22.71/3.82 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.71/3.82 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 22.71/3.82 inference('cnf', [status(esa)], [v_is_defined])).
% 22.71/3.82 thf(zip_derived_cl13883, plain,
% 22.71/3.82 ( (sum @ (additive_inverse @ v) @ v @ additive_identity)),
% 22.71/3.82 inference('demod', [status(thm)],
% 22.71/3.82 [zip_derived_cl13709, zip_derived_cl13, zip_derived_cl29])).
% 22.71/3.82 thf(zip_derived_cl28887, plain, (~ (defined @ (additive_inverse @ v))),
% 22.71/3.82 inference('demod', [status(thm)],
% 22.71/3.82 [zip_derived_cl28875, zip_derived_cl13883])).
% 22.71/3.82 thf(zip_derived_cl28888, plain, (~ (defined @ v)),
% 22.71/3.82 inference('s_sup-', [status(thm)],
% 22.71/3.82 [zip_derived_cl14, zip_derived_cl28887])).
% 22.71/3.82 thf(zip_derived_cl29, plain, ( (defined @ v)),
% 22.71/3.82 inference('cnf', [status(esa)], [v_is_defined])).
% 22.71/3.82 thf(zip_derived_cl28889, plain, ($false),
% 22.71/3.82 inference('demod', [status(thm)], [zip_derived_cl28888, zip_derived_cl29])).
% 22.71/3.82
% 22.71/3.82 % SZS output end Refutation
% 22.71/3.82
% 22.71/3.82
% 22.71/3.83 % Terminating...
% 22.95/3.88 % Runner terminated.
% 22.95/3.89 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------