%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD062-3 : TPTP v9.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.uxk6c7DNBa true
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:33:21 PM UTC 2025
% Result : Unsatisfiable 68.18s 10.45s
% Output : Refutation 68.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD062-3 : TPTP v9.2.0. 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.uxk6c7DNBa true
% 0.13/0.34 % Computer : n005.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 : Wed Oct 1 18:24:08 EDT 2025
% 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
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.55/0.66 % Total configuration time : 435
% 0.55/0.67 % Estimated wc time : 1092
% 0.55/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 68.18/10.45 % Solved by fo/fo5.sh.
% 68.18/10.45 % done 11450 iterations in 9.646s
% 68.18/10.45 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 68.18/10.45 % SZS output start Refutation
% 68.18/10.45 thf(sum_type, type, sum: $i > $i > $i > $o).
% 68.18/10.45 thf(b_type, type, b: $i).
% 68.18/10.45 thf(a_type, type, a: $i).
% 68.18/10.45 thf(add_type, type, add: $i > $i > $i).
% 68.18/10.45 thf(additive_identity_type, type, additive_identity: $i).
% 68.18/10.45 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 68.18/10.45 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 68.18/10.45 thf(defined_type, type, defined: $i > $o).
% 68.18/10.45 thf(not_less_or_equal_4, conjecture,
% 68.18/10.45 (less_or_equal @ ( additive_inverse @ b ) @ ( additive_inverse @ a ))).
% 68.18/10.45 thf(zf_stmt_0, negated_conjecture,
% 68.18/10.45 (~( less_or_equal @ ( additive_inverse @ b ) @ ( additive_inverse @ a ) )),
% 68.18/10.45 inference('cnf.neg', [status(esa)], [not_less_or_equal_4])).
% 68.18/10.45 thf(zip_derived_cl29, plain,
% 68.18/10.45 (~ (less_or_equal @ (additive_inverse @ b) @ (additive_inverse @ a))),
% 68.18/10.45 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.18/10.45 thf(well_definedness_of_additive_inverse, axiom,
% 68.18/10.45 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(totality_of_order_relation, axiom,
% 68.18/10.45 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 68.18/10.45 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 68.18/10.45 thf(zip_derived_cl22, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | (less_or_equal @ X1 @ X0)
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl29, plain,
% 68.18/10.45 (~ (less_or_equal @ (additive_inverse @ b) @ (additive_inverse @ a))),
% 68.18/10.45 inference('cnf', [status(esa)], [zf_stmt_0])).
% 68.18/10.45 thf(zip_derived_cl95, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | ~ (defined @ (additive_inverse @ b))
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ a) @ (additive_inverse @ b)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl29])).
% 68.18/10.45 thf(zip_derived_cl146, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ a) @ (additive_inverse @ b))
% 68.18/10.45 | ~ (defined @ (additive_inverse @ b)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl95])).
% 68.18/10.45 thf(a_is_defined, axiom, (defined @ a)).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl147, plain,
% 68.18/10.45 (( (less_or_equal @ (additive_inverse @ a) @ (additive_inverse @ b))
% 68.18/10.45 | ~ (defined @ (additive_inverse @ b)))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl146, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl161, plain,
% 68.18/10.45 ((~ (defined @ b)
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ a) @ (additive_inverse @ b)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl147])).
% 68.18/10.45 thf(b_is_defined, axiom, (defined @ b)).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl162, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ a) @ (additive_inverse @ b))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl161, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(existence_of_identity_addition, axiom,
% 68.18/10.45 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 68.18/10.45 thf(zip_derived_cl2, plain,
% 68.18/10.45 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 68.18/10.45 thf(existence_of_inverse_addition, axiom,
% 68.18/10.45 (( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) |
% 68.18/10.45 ( ~( defined @ X ) ))).
% 68.18/10.45 thf(zip_derived_cl3, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 68.18/10.45 | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 68.18/10.45 thf(commutativity_addition, axiom,
% 68.18/10.45 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl57, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl22, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | (less_or_equal @ X1 @ X0)
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl110, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (less_or_equal @ X0 @ b)
% 68.18/10.45 | (less_or_equal @ b @ X0))),
% 68.18/10.45 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl223, plain, (( (less_or_equal @ b @ b) | ~ (defined @ b))),
% 68.18/10.45 inference('eq_fact', [status(thm)], [zip_derived_cl110])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl224, plain, ( (less_or_equal @ b @ b)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl223, zip_derived_cl27])).
% 68.18/10.45 thf(antisymmetry_of_order_relation, axiom,
% 68.18/10.45 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 68.18/10.45 ( ~( less_or_equal @ Y @ X ) ))).
% 68.18/10.45 thf(zip_derived_cl20, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl229, plain,
% 68.18/10.45 ((~ (less_or_equal @ b @ b) | (sum @ additive_identity @ b @ b))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl224, zip_derived_cl20])).
% 68.18/10.45 thf(zip_derived_cl224, plain, ( (less_or_equal @ b @ b)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl223, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl232, plain, ( (sum @ additive_identity @ b @ b)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl229, zip_derived_cl224])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl235, plain, ( (sum @ b @ additive_identity @ b)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl4])).
% 68.18/10.45 thf(associativity_addition_1, axiom,
% 68.18/10.45 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 68.18/10.45 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 68.18/10.45 thf(zip_derived_cl0, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2)
% 68.18/10.45 | ~ (sum @ X0 @ X3 @ X4)
% 68.18/10.45 | ~ (sum @ X3 @ X5 @ X1)
% 68.18/10.45 | ~ (sum @ X4 @ X5 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [associativity_addition_1])).
% 68.18/10.45 thf(zip_derived_cl236, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (sum @ b @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ additive_identity @ X1 @ X2)
% 68.18/10.45 | (sum @ b @ X2 @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl235, zip_derived_cl0])).
% 68.18/10.45 thf(zip_derived_cl7587, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ b)
% 68.18/10.45 | (sum @ b @ X0 @ additive_identity)
% 68.18/10.45 | ~ (sum @ additive_identity @ (additive_inverse @ b) @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl236])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl7599, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ b @ X0 @ additive_identity)
% 68.18/10.45 | ~ (sum @ additive_identity @ (additive_inverse @ b) @ X0))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl7587, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl13531, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ b))
% 68.18/10.45 | (sum @ b @ (additive_inverse @ b) @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl7599])).
% 68.18/10.45 thf(zip_derived_cl13534, plain,
% 68.18/10.45 ((~ (defined @ b)
% 68.18/10.45 | (sum @ b @ (additive_inverse @ b) @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl13531])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl13535, plain,
% 68.18/10.45 ( (sum @ b @ (additive_inverse @ b) @ additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl13534, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl13539, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ b) @ b @ additive_identity)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl13535, zip_derived_cl4])).
% 68.18/10.45 thf(totality_of_addition, axiom,
% 68.18/10.45 (( sum @ X @ Y @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 68.18/10.45 ( ~( defined @ Y ) ))).
% 68.18/10.45 thf(zip_derived_cl18, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_addition])).
% 68.18/10.45 thf(compatibility_of_order_relation_and_addition, axiom,
% 68.18/10.45 (( less_or_equal @ U @ V ) | ( ~( less_or_equal @ X @ Y ) ) |
% 68.18/10.45 ( ~( sum @ X @ Z @ U ) ) | ( ~( sum @ Y @ Z @ V ) ))).
% 68.18/10.45 thf(zip_derived_cl23, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X3)
% 68.18/10.45 | ~ (sum @ X2 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)],
% 68.18/10.45 [compatibility_of_order_relation_and_addition])).
% 68.18/10.45 thf(zip_derived_cl685, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1)
% 68.18/10.45 | ~ (sum @ X3 @ X0 @ X2)
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X3)
% 68.18/10.45 | (less_or_equal @ (add @ X1 @ X0) @ X2))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl29276, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (less_or_equal @ (add @ X0 @ b) @ additive_identity)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ (additive_inverse @ b))
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ b))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl13539, zip_derived_cl685])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl29363, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (less_or_equal @ (add @ X0 @ b) @ additive_identity)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ (additive_inverse @ b))
% 68.18/10.45 | ~ (defined @ X0))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl29276, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl36516, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (less_or_equal @ (add @ (additive_inverse @ a) @ b) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl162, zip_derived_cl29363])).
% 68.18/10.45 thf(zip_derived_cl36598, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (less_or_equal @ (add @ (additive_inverse @ a) @ b) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl36516])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl36599, plain,
% 68.18/10.45 ( (less_or_equal @ (add @ (additive_inverse @ a) @ b) @ additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl36598, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl20, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl36600, plain,
% 68.18/10.45 ((~ (less_or_equal @ additive_identity @
% 68.18/10.45 (add @ (additive_inverse @ a) @ b))
% 68.18/10.45 | (sum @ additive_identity @ (add @ (additive_inverse @ a) @ b) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl36599, zip_derived_cl20])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl18, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_addition])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl515, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1)
% 68.18/10.45 | (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(less_or_equal_3, conjecture, (~( less_or_equal @ a @ b ))).
% 68.18/10.45 thf(zf_stmt_1, negated_conjecture, (less_or_equal @ a @ b),
% 68.18/10.45 inference('cnf.neg', [status(esa)], [less_or_equal_3])).
% 68.18/10.45 thf(zip_derived_cl28, plain, ( (less_or_equal @ a @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [zf_stmt_1])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl3, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 68.18/10.45 | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 68.18/10.45 thf(zip_derived_cl22, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | (less_or_equal @ X1 @ X0)
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl109, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (less_or_equal @ X0 @ a)
% 68.18/10.45 | (less_or_equal @ a @ X0))),
% 68.18/10.45 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl177, plain, (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 68.18/10.45 inference('eq_fact', [status(thm)], [zip_derived_cl109])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl178, plain, ( (less_or_equal @ a @ a)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl177, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl20, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl183, plain,
% 68.18/10.45 ((~ (less_or_equal @ a @ a) | (sum @ additive_identity @ a @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl178, zip_derived_cl20])).
% 68.18/10.45 thf(zip_derived_cl178, plain, ( (less_or_equal @ a @ a)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl177, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl185, plain, ( (sum @ additive_identity @ a @ a)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl178])).
% 68.18/10.45 thf(zip_derived_cl3, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 68.18/10.45 | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 68.18/10.45 thf(zip_derived_cl0, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2)
% 68.18/10.45 | ~ (sum @ X0 @ X3 @ X4)
% 68.18/10.45 | ~ (sum @ X3 @ X5 @ X1)
% 68.18/10.45 | ~ (sum @ X4 @ X5 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [associativity_addition_1])).
% 68.18/10.45 thf(zip_derived_cl31, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (sum @ additive_identity @ X2 @ X1)
% 68.18/10.45 | ~ (sum @ X0 @ X2 @ X3)
% 68.18/10.45 | (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 68.18/10.45 thf(zip_derived_cl923, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ (additive_inverse @ X1) @ X0 @ a)
% 68.18/10.45 | ~ (sum @ X1 @ a @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl31])).
% 68.18/10.45 thf(zip_derived_cl6243, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (sum @ (additive_inverse @ (additive_inverse @ a)) @
% 68.18/10.45 additive_identity @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl923])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl6255, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (sum @ (additive_inverse @ (additive_inverse @ a)) @
% 68.18/10.45 additive_identity @ a))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl6243, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl6310, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (sum @ (additive_inverse @ (additive_inverse @ a)) @
% 68.18/10.45 additive_identity @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl6255])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl6311, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ (additive_inverse @ a)) @
% 68.18/10.45 additive_identity @ a)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl6310, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl6315, plain,
% 68.18/10.45 ( (sum @ additive_identity @
% 68.18/10.45 (additive_inverse @ (additive_inverse @ a)) @ a)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl6311, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl22, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | (less_or_equal @ X1 @ X0)
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 68.18/10.45 thf(well_definedness_of_additive_identity, axiom,
% 68.18/10.45 (defined @ additive_identity)).
% 68.18/10.45 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 68.18/10.45 thf(zip_derived_cl104, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (less_or_equal @ X0 @ additive_identity)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0))),
% 68.18/10.45 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl312, plain,
% 68.18/10.45 (( (less_or_equal @ additive_identity @ additive_identity)
% 68.18/10.45 | ~ (defined @ additive_identity))),
% 68.18/10.45 inference('eq_fact', [status(thm)], [zip_derived_cl104])).
% 68.18/10.45 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 68.18/10.45 thf(zip_derived_cl313, plain,
% 68.18/10.45 ( (less_or_equal @ additive_identity @ additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl312, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl2, plain,
% 68.18/10.45 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 68.18/10.45 thf(zip_derived_cl23, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X3)
% 68.18/10.45 | ~ (sum @ X2 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)],
% 68.18/10.45 [compatibility_of_order_relation_and_addition])).
% 68.18/10.45 thf(zip_derived_cl689, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (sum @ X2 @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ additive_identity @ X2)
% 68.18/10.45 | (less_or_equal @ X0 @ X1))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl4463, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (less_or_equal @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ additive_identity @ X1 @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl313, zip_derived_cl689])).
% 68.18/10.45 thf(zip_derived_cl6379, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ (additive_inverse @ a)))
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ (additive_inverse @ a)) @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl6315, zip_derived_cl4463])).
% 68.18/10.45 thf(zip_derived_cl6407, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ (additive_inverse @ a)) @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl6379])).
% 68.18/10.45 thf(zip_derived_cl6408, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ (additive_inverse @ a)) @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl6407])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl6409, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ (additive_inverse @ a)) @ a)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl6408, zip_derived_cl26])).
% 68.18/10.45 thf(transitivity_of_order_relation, axiom,
% 68.18/10.45 (( less_or_equal @ X @ Z ) | ( ~( less_or_equal @ X @ Y ) ) |
% 68.18/10.45 ( ~( less_or_equal @ Y @ Z ) ))).
% 68.18/10.45 thf(zip_derived_cl21, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ X2)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl6413, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (less_or_equal @ a @ X0)
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ (additive_inverse @ a)) @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl6409, zip_derived_cl21])).
% 68.18/10.45 thf(zip_derived_cl6462, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ (additive_inverse @ a)) @ b)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl6413])).
% 68.18/10.45 thf(zip_derived_cl3, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 68.18/10.45 | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 68.18/10.45 thf(zip_derived_cl23, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X3)
% 68.18/10.45 | ~ (sum @ X2 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)],
% 68.18/10.45 [compatibility_of_order_relation_and_addition])).
% 68.18/10.45 thf(zip_derived_cl697, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (sum @ X2 @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ (additive_inverse @ X0) @ X2)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X1))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl30942, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (less_or_equal @ additive_identity @ X0)
% 68.18/10.45 | ~ (sum @ b @ (additive_inverse @ a) @ X0)
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl6462, zip_derived_cl697])).
% 68.18/10.45 thf(zip_derived_cl32595, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ a)
% 68.18/10.45 | ~ (sum @ b @ (additive_inverse @ a) @ X0)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl30942])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl32596, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (sum @ b @ (additive_inverse @ a) @ X0)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl32595, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl32699, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | ~ (defined @ b)
% 68.18/10.45 | (less_or_equal @ additive_identity @
% 68.18/10.45 (add @ (additive_inverse @ a) @ b)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl515, zip_derived_cl32596])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl32702, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (less_or_equal @ additive_identity @
% 68.18/10.45 (add @ (additive_inverse @ a) @ b)))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl32699, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl32705, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (less_or_equal @ additive_identity @
% 68.18/10.45 (add @ (additive_inverse @ a) @ b)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl32702])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl32706, plain,
% 68.18/10.45 ( (less_or_equal @ additive_identity @ (add @ (additive_inverse @ a) @ b))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl32705, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl36612, plain,
% 68.18/10.45 ( (sum @ additive_identity @ (add @ (additive_inverse @ a) @ b) @
% 68.18/10.45 additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl36600, zip_derived_cl32706])).
% 68.18/10.45 thf(zip_derived_cl185, plain, ( (sum @ additive_identity @ a @ a)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl178])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl201, plain, ( (sum @ a @ additive_identity @ a)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl4])).
% 68.18/10.45 thf(associativity_addition_2, axiom,
% 68.18/10.45 (( sum @ U @ Z @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 68.18/10.45 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ X @ V @ W ) ))).
% 68.18/10.45 thf(zip_derived_cl1, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X4 @ X1 @ X5)
% 68.18/10.45 | ~ (sum @ X3 @ X5 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [associativity_addition_2])).
% 68.18/10.45 thf(zip_derived_cl72, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.18/10.45 (~ (sum @ X2 @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ X1 @ X3 @ X1)
% 68.18/10.45 | (sum @ X0 @ X3 @ X0))),
% 68.18/10.45 inference('eq_fact', [status(thm)], [zip_derived_cl1])).
% 68.18/10.45 thf(zip_derived_cl2102, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ a @ X0 @ a)
% 68.18/10.45 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl72])).
% 68.18/10.45 thf(zip_derived_cl89711, plain,
% 68.18/10.45 ( (sum @ a @ (add @ (additive_inverse @ a) @ b) @ a)),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl36612, zip_derived_cl2102])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl89857, plain,
% 68.18/10.45 ( (sum @ (add @ (additive_inverse @ a) @ b) @ a @ a)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl89711, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl18, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_addition])).
% 68.18/10.45 thf(zip_derived_cl23, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X3)
% 68.18/10.45 | ~ (sum @ X2 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)],
% 68.18/10.45 [compatibility_of_order_relation_and_addition])).
% 68.18/10.45 thf(zip_derived_cl702, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (sum @ X2 @ X1 @ X0)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X2)
% 68.18/10.45 | (less_or_equal @ X0 @ X0))),
% 68.18/10.45 inference('eq_fact', [status(thm)], [zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl1509, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1)
% 68.18/10.45 | (less_or_equal @ (add @ X1 @ X0) @ (add @ X1 @ X0))
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X1))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl702])).
% 68.18/10.45 thf(zip_derived_cl22, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | (less_or_equal @ X1 @ X0)
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl132, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ X0) | ~ (defined @ X0) | (less_or_equal @ X0 @ X0))),
% 68.18/10.45 inference('eq_fact', [status(thm)], [zip_derived_cl22])).
% 68.18/10.45 thf(zip_derived_cl136, plain,
% 68.18/10.45 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 68.18/10.45 inference('simplify', [status(thm)], [zip_derived_cl132])).
% 68.18/10.45 thf(zip_derived_cl73358, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (less_or_equal @ (add @ X1 @ X0) @ (add @ X1 @ X0))
% 68.18/10.45 | ~ (defined @ X1)
% 68.18/10.45 | ~ (defined @ X0))),
% 68.18/10.45 inference('clc', [status(thm)], [zip_derived_cl1509, zip_derived_cl136])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl515, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1)
% 68.18/10.45 | (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl18, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_addition])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl136, plain,
% 68.18/10.45 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 68.18/10.45 inference('simplify', [status(thm)], [zip_derived_cl132])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl2, plain,
% 68.18/10.45 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 68.18/10.45 thf(zip_derived_cl57, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl201, plain, ( (sum @ a @ additive_identity @ a)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl0, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2)
% 68.18/10.45 | ~ (sum @ X0 @ X3 @ X4)
% 68.18/10.45 | ~ (sum @ X3 @ X5 @ X1)
% 68.18/10.45 | ~ (sum @ X4 @ X5 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [associativity_addition_1])).
% 68.18/10.45 thf(zip_derived_cl202, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (sum @ a @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ additive_identity @ X1 @ X2)
% 68.18/10.45 | (sum @ a @ X2 @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl0])).
% 68.18/10.45 thf(zip_derived_cl6774, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ a)
% 68.18/10.45 | (sum @ a @ X0 @ additive_identity)
% 68.18/10.45 | ~ (sum @ additive_identity @ (additive_inverse @ a) @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl202])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl6787, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ a @ X0 @ additive_identity)
% 68.18/10.45 | ~ (sum @ additive_identity @ (additive_inverse @ a) @ X0))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl6774, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl10315, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (sum @ a @ (additive_inverse @ a) @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl6787])).
% 68.18/10.45 thf(zip_derived_cl10318, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (sum @ a @ (additive_inverse @ a) @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl10315])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl10319, plain,
% 68.18/10.45 ( (sum @ a @ (additive_inverse @ a) @ additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl10318, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl10323, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ a) @ a @ additive_identity)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl10319, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl685, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1)
% 68.18/10.45 | ~ (sum @ X3 @ X0 @ X2)
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X3)
% 68.18/10.45 | (less_or_equal @ (add @ X1 @ X0) @ X2))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl29268, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (less_or_equal @ (add @ X0 @ a) @ additive_identity)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ (additive_inverse @ a))
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl10323, zip_derived_cl685])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl29355, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (less_or_equal @ (add @ X0 @ a) @ additive_identity)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ (additive_inverse @ a))
% 68.18/10.45 | ~ (defined @ X0))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl29268, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl35245, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (less_or_equal @ (add @ (additive_inverse @ a) @ a) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl29355])).
% 68.18/10.45 thf(zip_derived_cl35279, plain,
% 68.18/10.45 (( (less_or_equal @ (add @ (additive_inverse @ a) @ a) @
% 68.18/10.45 additive_identity)
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a)))),
% 68.18/10.45 inference('simplify', [status(thm)], [zip_derived_cl35245])).
% 68.18/10.45 thf(zip_derived_cl35299, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (less_or_equal @ (add @ (additive_inverse @ a) @ a) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl35279])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl35300, plain,
% 68.18/10.45 ( (less_or_equal @ (add @ (additive_inverse @ a) @ a) @ additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl35299, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl20, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl35301, plain,
% 68.18/10.45 ((~ (less_or_equal @ additive_identity @
% 68.18/10.45 (add @ (additive_inverse @ a) @ a))
% 68.18/10.45 | (sum @ additive_identity @ (add @ (additive_inverse @ a) @ a) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl35300, zip_derived_cl20])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl18, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_addition])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl136, plain,
% 68.18/10.45 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 68.18/10.45 inference('simplify', [status(thm)], [zip_derived_cl132])).
% 68.18/10.45 thf(zip_derived_cl10323, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ a) @ a @ additive_identity)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl10319, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl23, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X3)
% 68.18/10.45 | ~ (sum @ X2 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)],
% 68.18/10.45 [compatibility_of_order_relation_and_addition])).
% 68.18/10.45 thf(zip_derived_cl10338, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 (~ (sum @ X1 @ a @ X0)
% 68.18/10.45 | ~ (less_or_equal @ (additive_inverse @ a) @ X1)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl10323, zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl11242, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0)
% 68.18/10.45 | ~ (sum @ (additive_inverse @ a) @ a @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl10338])).
% 68.18/10.45 thf(zip_derived_cl11299, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ a)
% 68.18/10.45 | ~ (sum @ (additive_inverse @ a) @ a @ X0)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl11242])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl11300, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (sum @ (additive_inverse @ a) @ a @ X0)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl11299, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl11301, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (less_or_equal @ additive_identity @
% 68.18/10.45 (add @ (additive_inverse @ a) @ a)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl11300])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl11305, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (less_or_equal @ additive_identity @
% 68.18/10.45 (add @ (additive_inverse @ a) @ a)))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl11301, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl11407, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (less_or_equal @ additive_identity @
% 68.18/10.45 (add @ (additive_inverse @ a) @ a)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl11305])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl11408, plain,
% 68.18/10.45 ( (less_or_equal @ additive_identity @ (add @ (additive_inverse @ a) @ a))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl11407, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl35316, plain,
% 68.18/10.45 ( (sum @ additive_identity @ (add @ (additive_inverse @ a) @ a) @
% 68.18/10.45 additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl35301, zip_derived_cl11408])).
% 68.18/10.45 thf(zip_derived_cl235, plain, ( (sum @ b @ additive_identity @ b)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl72, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.18/10.45 (~ (sum @ X2 @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ X1 @ X3 @ X1)
% 68.18/10.45 | (sum @ X0 @ X3 @ X0))),
% 68.18/10.45 inference('eq_fact', [status(thm)], [zip_derived_cl1])).
% 68.18/10.45 thf(zip_derived_cl2106, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ b @ X0 @ b)
% 68.18/10.45 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl235, zip_derived_cl72])).
% 68.18/10.45 thf(zip_derived_cl86342, plain,
% 68.18/10.45 ( (sum @ b @ (add @ (additive_inverse @ a) @ a) @ b)),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl35316, zip_derived_cl2106])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl86435, plain,
% 68.18/10.45 ( (sum @ (add @ (additive_inverse @ a) @ a) @ b @ b)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl86342, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl18, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 68.18/10.45 | ~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [totality_of_addition])).
% 68.18/10.45 thf(zip_derived_cl0, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2)
% 68.18/10.45 | ~ (sum @ X0 @ X3 @ X4)
% 68.18/10.45 | ~ (sum @ X3 @ X5 @ X1)
% 68.18/10.45 | ~ (sum @ X4 @ X5 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [associativity_addition_1])).
% 68.18/10.45 thf(zip_derived_cl512, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1)
% 68.18/10.45 | ~ (sum @ (add @ X1 @ X0) @ X3 @ X2)
% 68.18/10.45 | ~ (sum @ X0 @ X3 @ X4)
% 68.18/10.45 | (sum @ X1 @ X4 @ X2))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl0])).
% 68.18/10.45 thf(zip_derived_cl87119, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ (additive_inverse @ a) @ X0 @ b)
% 68.18/10.45 | ~ (sum @ a @ b @ X0)
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | ~ (defined @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl86435, zip_derived_cl512])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl87138, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ (additive_inverse @ a) @ X0 @ b)
% 68.18/10.45 | ~ (sum @ a @ b @ X0)
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a)))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl87119, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl87802, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ a)
% 68.18/10.45 | ~ (sum @ a @ b @ X0)
% 68.18/10.45 | (sum @ (additive_inverse @ a) @ X0 @ b))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl87138])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl87803, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (sum @ a @ b @ X0) | (sum @ (additive_inverse @ a) @ X0 @ b))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl87802, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl87804, plain,
% 68.18/10.45 ((~ (defined @ b)
% 68.18/10.45 | ~ (defined @ a)
% 68.18/10.45 | (sum @ (additive_inverse @ a) @ (add @ a @ b) @ b))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl87803])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl87806, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ a) @ (add @ a @ b) @ b)),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl87804, zip_derived_cl27, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl89156, plain,
% 68.18/10.45 ( (sum @ (add @ a @ b) @ (additive_inverse @ a) @ b)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl87806, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl512, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (defined @ X1)
% 68.18/10.45 | ~ (sum @ (add @ X1 @ X0) @ X3 @ X2)
% 68.18/10.45 | ~ (sum @ X0 @ X3 @ X4)
% 68.18/10.45 | (sum @ X1 @ X4 @ X2))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl0])).
% 68.18/10.45 thf(zip_derived_cl89640, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ a @ X0 @ b)
% 68.18/10.45 | ~ (sum @ b @ (additive_inverse @ a) @ X0)
% 68.18/10.45 | ~ (defined @ a)
% 68.18/10.45 | ~ (defined @ b))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl89156, zip_derived_cl512])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl89646, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ a @ X0 @ b) | ~ (sum @ b @ (additive_inverse @ a) @ X0))),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl89640, zip_derived_cl26, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl89767, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | ~ (defined @ b)
% 68.18/10.45 | (sum @ a @ (add @ (additive_inverse @ a) @ b) @ b))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl515, zip_derived_cl89646])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl89769, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (sum @ a @ (add @ (additive_inverse @ a) @ b) @ b))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl89767, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl89954, plain,
% 68.18/10.45 ((~ (defined @ a) | (sum @ a @ (add @ (additive_inverse @ a) @ b) @ b))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl89769])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl89955, plain,
% 68.18/10.45 ( (sum @ a @ (add @ (additive_inverse @ a) @ b) @ b)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl89954, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl93249, plain,
% 68.18/10.45 ( (sum @ (add @ (additive_inverse @ a) @ b) @ a @ b)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl89955, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl23, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X3)
% 68.18/10.45 | ~ (sum @ X2 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)],
% 68.18/10.45 [compatibility_of_order_relation_and_addition])).
% 68.18/10.45 thf(zip_derived_cl94976, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 (~ (sum @ X1 @ a @ X0)
% 68.18/10.45 | ~ (less_or_equal @ (add @ (additive_inverse @ a) @ b) @ X1)
% 68.18/10.45 | (less_or_equal @ b @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl93249, zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl95061, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ b)
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (less_or_equal @ b @ X0)
% 68.18/10.45 | ~ (sum @ (add @ (additive_inverse @ a) @ b) @ a @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl73358, zip_derived_cl94976])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl95067, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ (additive_inverse @ a))
% 68.18/10.45 | (less_or_equal @ b @ X0)
% 68.18/10.45 | ~ (sum @ (add @ (additive_inverse @ a) @ b) @ a @ X0))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl95061, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl95068, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ a)
% 68.18/10.45 | ~ (sum @ (add @ (additive_inverse @ a) @ b) @ a @ X0)
% 68.18/10.45 | (less_or_equal @ b @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl95067])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl95069, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (sum @ (add @ (additive_inverse @ a) @ b) @ a @ X0)
% 68.18/10.45 | (less_or_equal @ b @ X0))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl95068, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl95072, plain, ( (less_or_equal @ b @ a)),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl89857, zip_derived_cl95069])).
% 68.18/10.45 thf(zip_derived_cl20, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl95083, plain,
% 68.18/10.45 ((~ (less_or_equal @ a @ b) | (sum @ additive_identity @ b @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl95072, zip_derived_cl20])).
% 68.18/10.45 thf(zip_derived_cl28, plain, ( (less_or_equal @ a @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [zf_stmt_1])).
% 68.18/10.45 thf(zip_derived_cl95141, plain, ( (sum @ additive_identity @ b @ a)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl95083, zip_derived_cl28])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl95407, plain, ( (sum @ b @ additive_identity @ a)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl95141, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl2, plain,
% 68.18/10.45 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 68.18/10.45 thf(zip_derived_cl31, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (sum @ additive_identity @ X2 @ X1)
% 68.18/10.45 | ~ (sum @ X0 @ X2 @ X3)
% 68.18/10.45 | (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 68.18/10.45 thf(zip_derived_cl917, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (sum @ (additive_inverse @ X2) @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ X2 @ X0 @ X1)
% 68.18/10.45 | ~ (defined @ X2))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl31])).
% 68.18/10.45 thf(zip_derived_cl96343, plain,
% 68.18/10.45 ((~ (defined @ b)
% 68.18/10.45 | (sum @ (additive_inverse @ b) @ a @ additive_identity)
% 68.18/10.45 | ~ (defined @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl95407, zip_derived_cl917])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 68.18/10.45 thf(zip_derived_cl96386, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ b) @ a @ additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl96343, zip_derived_cl27, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl98090, plain,
% 68.18/10.45 ( (sum @ a @ (additive_inverse @ b) @ additive_identity)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl96386, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl10319, plain,
% 68.18/10.45 ( (sum @ a @ (additive_inverse @ a) @ additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl10318, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl2, plain,
% 68.18/10.45 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl55, plain,
% 68.18/10.45 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl136, plain,
% 68.18/10.45 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 68.18/10.45 inference('simplify', [status(thm)], [zip_derived_cl132])).
% 68.18/10.45 thf(zip_derived_cl57, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl2102, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ a @ X0 @ a)
% 68.18/10.45 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl72])).
% 68.18/10.45 thf(zip_derived_cl2138, plain,
% 68.18/10.45 ((~ (defined @ additive_identity)
% 68.18/10.45 | (sum @ a @ (additive_inverse @ additive_identity) @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl2102])).
% 68.18/10.45 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 68.18/10.45 thf(zip_derived_cl2147, plain,
% 68.18/10.45 ( (sum @ a @ (additive_inverse @ additive_identity) @ a)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl2138, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl10323, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ a) @ a @ additive_identity)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl10319, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl72, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.18/10.45 (~ (sum @ X2 @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ X1 @ X3 @ X1)
% 68.18/10.45 | (sum @ X0 @ X3 @ X0))),
% 68.18/10.45 inference('eq_fact', [status(thm)], [zip_derived_cl1])).
% 68.18/10.45 thf(zip_derived_cl10340, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ additive_identity)
% 68.18/10.45 | ~ (sum @ a @ X0 @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl10323, zip_derived_cl72])).
% 68.18/10.45 thf(zip_derived_cl12092, plain,
% 68.18/10.45 ( (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity)),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl2147, zip_derived_cl10340])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl12129, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ additive_identity) @ additive_identity @
% 68.18/10.45 additive_identity)),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl12092, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl23, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X3)
% 68.18/10.45 | ~ (sum @ X2 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)],
% 68.18/10.45 [compatibility_of_order_relation_and_addition])).
% 68.18/10.45 thf(zip_derived_cl12206, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 (~ (sum @ X1 @ additive_identity @ X0)
% 68.18/10.45 | ~ (less_or_equal @ (additive_inverse @ additive_identity) @ X1)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl12129, zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl15963, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ (additive_inverse @ additive_identity))
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0)
% 68.18/10.45 | ~ (sum @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl12206])).
% 68.18/10.45 thf(zip_derived_cl19310, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ additive_identity)
% 68.18/10.45 | ~ (sum @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity @ X0)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl15963])).
% 68.18/10.45 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 68.18/10.45 thf(zip_derived_cl19311, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (sum @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity @ X0)
% 68.18/10.45 | (less_or_equal @ additive_identity @ X0))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl19310, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl19336, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ additive_identity))
% 68.18/10.45 | (less_or_equal @ additive_identity @
% 68.18/10.45 (additive_inverse @ additive_identity)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl19311])).
% 68.18/10.45 thf(zip_derived_cl19345, plain,
% 68.18/10.45 ((~ (defined @ additive_identity)
% 68.18/10.45 | (less_or_equal @ additive_identity @
% 68.18/10.45 (additive_inverse @ additive_identity)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl19336])).
% 68.18/10.45 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 68.18/10.45 thf(zip_derived_cl19346, plain,
% 68.18/10.45 ( (less_or_equal @ additive_identity @
% 68.18/10.45 (additive_inverse @ additive_identity))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl19345, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl20, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl19347, plain,
% 68.18/10.45 ((~ (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity)
% 68.18/10.45 | (sum @ additive_identity @ additive_identity @
% 68.18/10.45 (additive_inverse @ additive_identity)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl19346, zip_derived_cl20])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl57, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl4463, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (less_or_equal @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ additive_identity @ X1 @ X0)
% 68.18/10.45 | ~ (defined @ X1))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl313, zip_derived_cl689])).
% 68.18/10.45 thf(zip_derived_cl4502, plain,
% 68.18/10.45 ((~ (defined @ additive_identity)
% 68.18/10.45 | ~ (defined @ (additive_inverse @ additive_identity))
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl4463])).
% 68.18/10.45 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 68.18/10.45 thf(zip_derived_cl4523, plain,
% 68.18/10.45 ((~ (defined @ (additive_inverse @ additive_identity))
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl4502, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl4610, plain,
% 68.18/10.45 ((~ (defined @ additive_identity)
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl4523])).
% 68.18/10.45 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 68.18/10.45 thf(zip_derived_cl4611, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl4610, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl19375, plain,
% 68.18/10.45 ( (sum @ additive_identity @ additive_identity @
% 68.18/10.45 (additive_inverse @ additive_identity))),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl19347, zip_derived_cl4611])).
% 68.18/10.45 thf(zip_derived_cl185, plain, ( (sum @ additive_identity @ a @ a)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl178])).
% 68.18/10.45 thf(zip_derived_cl1, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X4 @ X1 @ X5)
% 68.18/10.45 | ~ (sum @ X3 @ X5 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [associativity_addition_2])).
% 68.18/10.45 thf(zip_derived_cl200, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (sum @ additive_identity @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ a @ X2 @ X1)
% 68.18/10.45 | (sum @ a @ X2 @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl1])).
% 68.18/10.45 thf(zip_derived_cl19533, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ a @ X0 @ (additive_inverse @ additive_identity))
% 68.18/10.45 | ~ (sum @ a @ X0 @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl19375, zip_derived_cl200])).
% 68.18/10.45 thf(zip_derived_cl23798, plain,
% 68.18/10.45 ( (sum @ a @ (additive_inverse @ a) @
% 68.18/10.45 (additive_inverse @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl10319, zip_derived_cl19533])).
% 68.18/10.45 thf(zip_derived_cl917, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (sum @ (additive_inverse @ X2) @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ X2 @ X0 @ X1)
% 68.18/10.45 | ~ (defined @ X2))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl31])).
% 68.18/10.45 thf(zip_derived_cl40008, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (sum @ (additive_inverse @ a) @
% 68.18/10.45 (additive_inverse @ additive_identity) @ (additive_inverse @ a))
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl23798, zip_derived_cl917])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl40120, plain,
% 68.18/10.45 (( (sum @ (additive_inverse @ a) @
% 68.18/10.45 (additive_inverse @ additive_identity) @ (additive_inverse @ a))
% 68.18/10.45 | ~ (defined @ (additive_inverse @ a)))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl40008, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl40436, plain,
% 68.18/10.45 ((~ (defined @ a)
% 68.18/10.45 | (sum @ (additive_inverse @ a) @
% 68.18/10.45 (additive_inverse @ additive_identity) @ (additive_inverse @ a)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl40120])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl40437, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ a) @
% 68.18/10.45 (additive_inverse @ additive_identity) @ (additive_inverse @ a))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl40436, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl48618, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ additive_identity) @
% 68.18/10.45 (additive_inverse @ a) @ (additive_inverse @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl40437, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl702, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (sum @ X2 @ X1 @ X0)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X2)
% 68.18/10.45 | (less_or_equal @ X0 @ X0))),
% 68.18/10.45 inference('eq_fact', [status(thm)], [zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl53691, plain,
% 68.18/10.45 (( (less_or_equal @ (additive_inverse @ a) @ (additive_inverse @ a))
% 68.18/10.45 | ~ (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 (additive_inverse @ additive_identity)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl48618, zip_derived_cl702])).
% 68.18/10.45 thf(zip_derived_cl19346, plain,
% 68.18/10.45 ( (less_or_equal @ additive_identity @
% 68.18/10.45 (additive_inverse @ additive_identity))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl19345, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl4611, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl4610, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl21, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ X2)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl4615, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 (~ (less_or_equal @ additive_identity @ X0)
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ additive_identity) @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl4611, zip_derived_cl21])).
% 68.18/10.45 thf(zip_derived_cl19363, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 (additive_inverse @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl19346, zip_derived_cl4615])).
% 68.18/10.45 thf(zip_derived_cl53706, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ a) @ (additive_inverse @ a))),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl53691, zip_derived_cl19363])).
% 68.18/10.45 thf(zip_derived_cl20, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X1 @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 68.18/10.45 thf(zip_derived_cl53710, plain,
% 68.18/10.45 ((~ (less_or_equal @ (additive_inverse @ a) @ (additive_inverse @ a))
% 68.18/10.45 | (sum @ additive_identity @ (additive_inverse @ a) @
% 68.18/10.45 (additive_inverse @ a)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl53706, zip_derived_cl20])).
% 68.18/10.45 thf(zip_derived_cl53706, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ a) @ (additive_inverse @ a))),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl53691, zip_derived_cl19363])).
% 68.18/10.45 thf(zip_derived_cl53737, plain,
% 68.18/10.45 ( (sum @ additive_identity @ (additive_inverse @ a) @
% 68.18/10.45 (additive_inverse @ a))),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl53710, zip_derived_cl53706])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl53882, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ a) @ additive_identity @
% 68.18/10.45 (additive_inverse @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl53737, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl3, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 68.18/10.45 | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 68.18/10.45 thf(zip_derived_cl1, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X4 @ X1 @ X5)
% 68.18/10.45 | ~ (sum @ X3 @ X5 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [associativity_addition_2])).
% 68.18/10.45 thf(zip_derived_cl69, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | ~ (sum @ (additive_inverse @ X0) @ X2 @ X1)
% 68.18/10.45 | ~ (sum @ X0 @ X3 @ X2)
% 68.18/10.45 | (sum @ additive_identity @ X3 @ X1))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 68.18/10.45 thf(zip_derived_cl54546, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ (additive_inverse @ a))
% 68.18/10.45 | ~ (sum @ a @ X0 @ additive_identity)
% 68.18/10.45 | ~ (defined @ a))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl53882, zip_derived_cl69])).
% 68.18/10.45 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 68.18/10.45 inference('cnf', [status(esa)], [a_is_defined])).
% 68.18/10.45 thf(zip_derived_cl54556, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ additive_identity @ X0 @ (additive_inverse @ a))
% 68.18/10.45 | ~ (sum @ a @ X0 @ additive_identity))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl54546, zip_derived_cl26])).
% 68.18/10.45 thf(zip_derived_cl99077, plain,
% 68.18/10.45 ( (sum @ additive_identity @ (additive_inverse @ b) @
% 68.18/10.45 (additive_inverse @ a))),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl98090, zip_derived_cl54556])).
% 68.18/10.45 thf(zip_derived_cl14, plain,
% 68.18/10.45 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 68.18/10.45 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 68.18/10.45 thf(zip_derived_cl13535, plain,
% 68.18/10.45 ( (sum @ b @ (additive_inverse @ b) @ additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl13534, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl19375, plain,
% 68.18/10.45 ( (sum @ additive_identity @ additive_identity @
% 68.18/10.45 (additive_inverse @ additive_identity))),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl19347, zip_derived_cl4611])).
% 68.18/10.45 thf(zip_derived_cl232, plain, ( (sum @ additive_identity @ b @ b)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl229, zip_derived_cl224])).
% 68.18/10.45 thf(zip_derived_cl1, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X4 @ X1 @ X5)
% 68.18/10.45 | ~ (sum @ X3 @ X5 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [associativity_addition_2])).
% 68.18/10.45 thf(zip_derived_cl234, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (sum @ additive_identity @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ b @ X2 @ X1)
% 68.18/10.45 | (sum @ b @ X2 @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl1])).
% 68.18/10.45 thf(zip_derived_cl19534, plain,
% 68.18/10.45 (![X0 : $i]:
% 68.18/10.45 ( (sum @ b @ X0 @ (additive_inverse @ additive_identity))
% 68.18/10.45 | ~ (sum @ b @ X0 @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl19375, zip_derived_cl234])).
% 68.18/10.45 thf(zip_derived_cl24789, plain,
% 68.18/10.45 ( (sum @ b @ (additive_inverse @ b) @
% 68.18/10.45 (additive_inverse @ additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl13535, zip_derived_cl19534])).
% 68.18/10.45 thf(zip_derived_cl917, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 (~ (defined @ X0)
% 68.18/10.45 | (sum @ (additive_inverse @ X2) @ X1 @ X0)
% 68.18/10.45 | ~ (sum @ X2 @ X0 @ X1)
% 68.18/10.45 | ~ (defined @ X2))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl31])).
% 68.18/10.45 thf(zip_derived_cl40023, plain,
% 68.18/10.45 ((~ (defined @ b)
% 68.18/10.45 | (sum @ (additive_inverse @ b) @
% 68.18/10.45 (additive_inverse @ additive_identity) @ (additive_inverse @ b))
% 68.18/10.45 | ~ (defined @ (additive_inverse @ b)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl24789, zip_derived_cl917])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl40135, plain,
% 68.18/10.45 (( (sum @ (additive_inverse @ b) @
% 68.18/10.45 (additive_inverse @ additive_identity) @ (additive_inverse @ b))
% 68.18/10.45 | ~ (defined @ (additive_inverse @ b)))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl40023, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl42765, plain,
% 68.18/10.45 ((~ (defined @ b)
% 68.18/10.45 | (sum @ (additive_inverse @ b) @
% 68.18/10.45 (additive_inverse @ additive_identity) @ (additive_inverse @ b)))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl40135])).
% 68.18/10.45 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 68.18/10.45 inference('cnf', [status(esa)], [b_is_defined])).
% 68.18/10.45 thf(zip_derived_cl42766, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ b) @
% 68.18/10.45 (additive_inverse @ additive_identity) @ (additive_inverse @ b))),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl42765, zip_derived_cl27])).
% 68.18/10.45 thf(zip_derived_cl4, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i]:
% 68.18/10.45 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 68.18/10.45 inference('cnf', [status(esa)], [commutativity_addition])).
% 68.18/10.45 thf(zip_derived_cl50139, plain,
% 68.18/10.45 ( (sum @ (additive_inverse @ additive_identity) @
% 68.18/10.45 (additive_inverse @ b) @ (additive_inverse @ b))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl42766, zip_derived_cl4])).
% 68.18/10.45 thf(zip_derived_cl23, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 68.18/10.45 ( (less_or_equal @ X0 @ X1)
% 68.18/10.45 | ~ (less_or_equal @ X2 @ X3)
% 68.18/10.45 | ~ (sum @ X2 @ X4 @ X0)
% 68.18/10.45 | ~ (sum @ X3 @ X4 @ X1))),
% 68.18/10.45 inference('cnf', [status(esa)],
% 68.18/10.45 [compatibility_of_order_relation_and_addition])).
% 68.18/10.45 thf(zip_derived_cl59834, plain,
% 68.18/10.45 (![X0 : $i, X1 : $i]:
% 68.18/10.45 (~ (sum @ X1 @ (additive_inverse @ b) @ X0)
% 68.18/10.45 | ~ (less_or_equal @ (additive_inverse @ additive_identity) @ X1)
% 68.18/10.45 | (less_or_equal @ (additive_inverse @ b) @ X0))),
% 68.18/10.45 inference('sup-', [status(thm)], [zip_derived_cl50139, zip_derived_cl23])).
% 68.18/10.45 thf(zip_derived_cl104017, plain,
% 68.18/10.45 (( (less_or_equal @ (additive_inverse @ b) @ (additive_inverse @ a))
% 68.18/10.45 | ~ (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity))),
% 68.18/10.45 inference('sup-', [status(thm)],
% 68.18/10.45 [zip_derived_cl99077, zip_derived_cl59834])).
% 68.18/10.45 thf(zip_derived_cl4611, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ additive_identity) @
% 68.18/10.45 additive_identity)),
% 68.18/10.45 inference('demod', [status(thm)], [zip_derived_cl4610, zip_derived_cl13])).
% 68.18/10.45 thf(zip_derived_cl104065, plain,
% 68.18/10.45 ( (less_or_equal @ (additive_inverse @ b) @ (additive_inverse @ a))),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl104017, zip_derived_cl4611])).
% 68.18/10.45 thf(zip_derived_cl104067, plain, ($false),
% 68.18/10.45 inference('demod', [status(thm)],
% 68.18/10.45 [zip_derived_cl29, zip_derived_cl104065])).
% 68.18/10.45
% 68.18/10.45 % SZS output end Refutation
% 68.18/10.45
% 68.18/10.45
% 68.18/10.45 % Terminating...
% 68.19/10.50 % Runner terminated.
% 68.19/10.51 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------