TSTP Solution File: FLD060-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD060-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rBi09DNfve true
% Computer : n026.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 80.65s 12.14s
% Output : Refutation 80.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD060-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rBi09DNfve true
% 0.13/0.34 % Computer : n026.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 : Sun Aug 27 23:48:19 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 80.65/12.14 % Solved by fo/fo5.sh.
% 80.65/12.14 % done 10891 iterations in 11.330s
% 80.65/12.14 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 80.65/12.14 % SZS output start Refutation
% 80.65/12.14 thf(sum_type, type, sum: $i > $i > $i > $o).
% 80.65/12.14 thf(b_type, type, b: $i).
% 80.65/12.14 thf(a_type, type, a: $i).
% 80.65/12.14 thf(add_type, type, add: $i > $i > $i).
% 80.65/12.14 thf(additive_identity_type, type, additive_identity: $i).
% 80.65/12.14 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 80.65/12.14 thf(multiplicative_inverse_type, type, multiplicative_inverse: $i > $i).
% 80.65/12.14 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 80.65/12.14 thf(defined_type, type, defined: $i > $o).
% 80.65/12.14 thf(not_less_or_equal_4, conjecture,
% 80.65/12.14 (less_or_equal @ ( add @ a @ a ) @ ( add @ b @ b ))).
% 80.65/12.14 thf(zf_stmt_0, negated_conjecture,
% 80.65/12.14 (~( less_or_equal @ ( add @ a @ a ) @ ( add @ b @ b ) )),
% 80.65/12.14 inference('cnf.neg', [status(esa)], [not_less_or_equal_4])).
% 80.65/12.14 thf(zip_derived_cl29, plain,
% 80.65/12.14 (~ (less_or_equal @ (add @ a @ a) @ (add @ b @ b))),
% 80.65/12.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 80.65/12.14 thf(less_or_equal_3, conjecture, (~( less_or_equal @ a @ b ))).
% 80.65/12.14 thf(zf_stmt_1, negated_conjecture, (less_or_equal @ a @ b),
% 80.65/12.14 inference('cnf.neg', [status(esa)], [less_or_equal_3])).
% 80.65/12.14 thf(zip_derived_cl28, plain, ( (less_or_equal @ a @ b)),
% 80.65/12.14 inference('cnf', [status(esa)], [zf_stmt_1])).
% 80.65/12.14 thf(totality_of_addition, axiom,
% 80.65/12.14 (( sum @ X @ Y @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 80.65/12.14 ( ~( defined @ Y ) ))).
% 80.65/12.14 thf(zip_derived_cl18, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 80.65/12.14 | ~ (defined @ X0)
% 80.65/12.14 | ~ (defined @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)], [totality_of_addition])).
% 80.65/12.14 thf(zip_derived_cl18, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 80.65/12.14 | ~ (defined @ X0)
% 80.65/12.14 | ~ (defined @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)], [totality_of_addition])).
% 80.65/12.14 thf(existence_of_inverse_addition, axiom,
% 80.65/12.14 (( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) |
% 80.65/12.14 ( ~( defined @ X ) ))).
% 80.65/12.14 thf(zip_derived_cl3, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 80.65/12.14 | ~ (defined @ X0))),
% 80.65/12.14 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 80.65/12.14 thf(commutativity_addition, axiom,
% 80.65/12.14 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 80.65/12.14 thf(zip_derived_cl4, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 80.65/12.14 inference('cnf', [status(esa)], [commutativity_addition])).
% 80.65/12.14 thf(zip_derived_cl61, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 80.65/12.14 thf(totality_of_order_relation, axiom,
% 80.65/12.14 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 80.65/12.14 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 80.65/12.14 thf(zip_derived_cl22, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (less_or_equal @ X0 @ X1)
% 80.65/12.14 | (less_or_equal @ X1 @ X0)
% 80.65/12.14 | ~ (defined @ X0)
% 80.65/12.14 | ~ (defined @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 80.65/12.14 thf(b_is_defined, axiom, (defined @ b)).
% 80.65/12.14 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.14 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.14 thf(zip_derived_cl118, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | (less_or_equal @ X0 @ b)
% 80.65/12.14 | (less_or_equal @ b @ X0))),
% 80.65/12.14 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl27])).
% 80.65/12.14 thf(zip_derived_cl243, plain, (( (less_or_equal @ b @ b) | ~ (defined @ b))),
% 80.65/12.14 inference('eq_fact', [status(thm)], [zip_derived_cl118])).
% 80.65/12.14 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.14 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.14 thf(zip_derived_cl244, plain, ( (less_or_equal @ b @ b)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl243, zip_derived_cl27])).
% 80.65/12.14 thf(antisymmetry_of_order_relation, axiom,
% 80.65/12.14 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 80.65/12.14 ( ~( less_or_equal @ Y @ X ) ))).
% 80.65/12.14 thf(zip_derived_cl20, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (sum @ additive_identity @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ X1 @ X0))),
% 80.65/12.14 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 80.65/12.14 thf(zip_derived_cl250, plain,
% 80.65/12.14 ((~ (less_or_equal @ b @ b) | (sum @ additive_identity @ b @ b))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl244, zip_derived_cl20])).
% 80.65/12.14 thf(zip_derived_cl244, plain, ( (less_or_equal @ b @ b)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl243, zip_derived_cl27])).
% 80.65/12.14 thf(zip_derived_cl254, plain, ( (sum @ additive_identity @ b @ b)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl250, zip_derived_cl244])).
% 80.65/12.14 thf(zip_derived_cl4, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 80.65/12.14 inference('cnf', [status(esa)], [commutativity_addition])).
% 80.65/12.14 thf(zip_derived_cl261, plain, ( (sum @ b @ additive_identity @ b)),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl254, zip_derived_cl4])).
% 80.65/12.14 thf(associativity_addition_2, axiom,
% 80.65/12.14 (( sum @ U @ Z @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 80.65/12.14 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ X @ V @ W ) ))).
% 80.65/12.14 thf(zip_derived_cl1, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ X2)
% 80.65/12.14 | ~ (sum @ X3 @ X4 @ X0)
% 80.65/12.14 | ~ (sum @ X4 @ X1 @ X5)
% 80.65/12.14 | ~ (sum @ X3 @ X5 @ X2))),
% 80.65/12.14 inference('cnf', [status(esa)], [associativity_addition_2])).
% 80.65/12.14 thf(zip_derived_cl77, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.65/12.14 (~ (sum @ X2 @ X1 @ X0)
% 80.65/12.14 | ~ (sum @ X1 @ X3 @ X1)
% 80.65/12.14 | (sum @ X0 @ X3 @ X0))),
% 80.65/12.14 inference('eq_fact', [status(thm)], [zip_derived_cl1])).
% 80.65/12.14 thf(zip_derived_cl1599, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (sum @ b @ X0 @ b)
% 80.65/12.14 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl261, zip_derived_cl77])).
% 80.65/12.14 thf(zip_derived_cl2062, plain,
% 80.65/12.14 ((~ (defined @ additive_identity)
% 80.65/12.14 | (sum @ b @ (additive_inverse @ additive_identity) @ b))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl1599])).
% 80.65/12.14 thf(well_definedness_of_additive_identity, axiom,
% 80.65/12.14 (defined @ additive_identity)).
% 80.65/12.14 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.14 thf(zip_derived_cl2071, plain,
% 80.65/12.14 ( (sum @ b @ (additive_inverse @ additive_identity) @ b)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl2062, zip_derived_cl13])).
% 80.65/12.14 thf(zip_derived_cl22, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (less_or_equal @ X0 @ X1)
% 80.65/12.14 | (less_or_equal @ X1 @ X0)
% 80.65/12.14 | ~ (defined @ X0)
% 80.65/12.14 | ~ (defined @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 80.65/12.14 thf(zip_derived_cl140, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 (~ (defined @ X0) | ~ (defined @ X0) | (less_or_equal @ X0 @ X0))),
% 80.65/12.14 inference('eq_fact', [status(thm)], [zip_derived_cl22])).
% 80.65/12.14 thf(zip_derived_cl144, plain,
% 80.65/12.14 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 80.65/12.14 inference('simplify', [status(thm)], [zip_derived_cl140])).
% 80.65/12.14 thf(zip_derived_cl18, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 80.65/12.14 | ~ (defined @ X0)
% 80.65/12.14 | ~ (defined @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)], [totality_of_addition])).
% 80.65/12.14 thf(zip_derived_cl254, plain, ( (sum @ additive_identity @ b @ b)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl250, zip_derived_cl244])).
% 80.65/12.14 thf(compatibility_of_order_relation_and_addition, axiom,
% 80.65/12.14 (( less_or_equal @ U @ V ) | ( ~( less_or_equal @ X @ Y ) ) |
% 80.65/12.14 ( ~( sum @ X @ Z @ U ) ) | ( ~( sum @ Y @ Z @ V ) ))).
% 80.65/12.14 thf(zip_derived_cl23, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.65/12.14 ( (less_or_equal @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ X2 @ X3)
% 80.65/12.14 | ~ (sum @ X2 @ X4 @ X0)
% 80.65/12.14 | ~ (sum @ X3 @ X4 @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)],
% 80.65/12.14 [compatibility_of_order_relation_and_addition])).
% 80.65/12.14 thf(zip_derived_cl344, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 (~ (sum @ X1 @ b @ X0)
% 80.65/12.14 | ~ (less_or_equal @ additive_identity @ X1)
% 80.65/12.14 | (less_or_equal @ b @ X0))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl254, zip_derived_cl23])).
% 80.65/12.14 thf(zip_derived_cl525, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 (~ (defined @ b)
% 80.65/12.14 | ~ (defined @ X0)
% 80.65/12.14 | (less_or_equal @ b @ (add @ X0 @ b))
% 80.65/12.14 | ~ (less_or_equal @ additive_identity @ X0))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl344])).
% 80.65/12.14 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.14 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.14 thf(zip_derived_cl531, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | (less_or_equal @ b @ (add @ X0 @ b))
% 80.65/12.14 | ~ (less_or_equal @ additive_identity @ X0))),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl525, zip_derived_cl27])).
% 80.65/12.14 thf(zip_derived_cl539, plain,
% 80.65/12.14 ((~ (defined @ additive_identity)
% 80.65/12.14 | (less_or_equal @ b @ (add @ additive_identity @ b))
% 80.65/12.14 | ~ (defined @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl144, zip_derived_cl531])).
% 80.65/12.14 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.14 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.14 thf(zip_derived_cl551, plain,
% 80.65/12.14 ( (less_or_equal @ b @ (add @ additive_identity @ b))),
% 80.65/12.14 inference('demod', [status(thm)],
% 80.65/12.14 [zip_derived_cl539, zip_derived_cl13, zip_derived_cl13])).
% 80.65/12.14 thf(zip_derived_cl20, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (sum @ additive_identity @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ X1 @ X0))),
% 80.65/12.14 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 80.65/12.14 thf(zip_derived_cl556, plain,
% 80.65/12.14 ((~ (less_or_equal @ (add @ additive_identity @ b) @ b)
% 80.65/12.14 | (sum @ additive_identity @ b @ (add @ additive_identity @ b)))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl551, zip_derived_cl20])).
% 80.65/12.14 thf(well_definedness_of_addition, axiom,
% 80.65/12.14 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 80.65/12.14 ( ~( defined @ Y ) ))).
% 80.65/12.14 thf(zip_derived_cl12, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 80.65/12.14 thf(zip_derived_cl18, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 80.65/12.14 | ~ (defined @ X0)
% 80.65/12.14 | ~ (defined @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)], [totality_of_addition])).
% 80.65/12.14 thf(zip_derived_cl254, plain, ( (sum @ additive_identity @ b @ b)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl250, zip_derived_cl244])).
% 80.65/12.14 thf(existence_of_identity_addition, axiom,
% 80.65/12.14 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 80.65/12.14 thf(zip_derived_cl2, plain,
% 80.65/12.14 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 80.65/12.14 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 80.65/12.14 thf(associativity_addition_1, axiom,
% 80.65/12.14 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 80.65/12.14 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 80.65/12.14 thf(zip_derived_cl0, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ X2)
% 80.65/12.14 | ~ (sum @ X0 @ X3 @ X4)
% 80.65/12.14 | ~ (sum @ X3 @ X5 @ X1)
% 80.65/12.14 | ~ (sum @ X4 @ X5 @ X2))),
% 80.65/12.14 inference('cnf', [status(esa)], [associativity_addition_1])).
% 80.65/12.14 thf(zip_derived_cl30, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | ~ (sum @ X0 @ X2 @ X1)
% 80.65/12.14 | ~ (sum @ X0 @ X2 @ X3)
% 80.65/12.14 | (sum @ additive_identity @ X3 @ X1))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 80.65/12.14 thf(zip_derived_cl499, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (sum @ additive_identity @ X0 @ b)
% 80.65/12.14 | ~ (sum @ additive_identity @ b @ X0)
% 80.65/12.14 | ~ (defined @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl254, zip_derived_cl30])).
% 80.65/12.14 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.14 thf(zip_derived_cl519, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (sum @ additive_identity @ X0 @ b)
% 80.65/12.14 | ~ (sum @ additive_identity @ b @ X0))),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl499, zip_derived_cl13])).
% 80.65/12.14 thf(zip_derived_cl1992, plain,
% 80.65/12.14 ((~ (defined @ b)
% 80.65/12.14 | ~ (defined @ additive_identity)
% 80.65/12.14 | (sum @ additive_identity @ (add @ additive_identity @ b) @ b))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl519])).
% 80.65/12.14 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.14 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.14 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.14 thf(zip_derived_cl1997, plain,
% 80.65/12.14 ( (sum @ additive_identity @ (add @ additive_identity @ b) @ b)),
% 80.65/12.14 inference('demod', [status(thm)],
% 80.65/12.14 [zip_derived_cl1992, zip_derived_cl27, zip_derived_cl13])).
% 80.65/12.14 thf(well_definedness_of_multiplicative_inverse, axiom,
% 80.65/12.14 (( defined @ ( multiplicative_inverse @ X ) ) | ( ~( defined @ X ) ) |
% 80.65/12.14 ( sum @ additive_identity @ X @ additive_identity ))).
% 80.65/12.14 thf(zip_derived_cl17, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (defined @ (multiplicative_inverse @ X0))
% 80.65/12.14 | ~ (defined @ X0)
% 80.65/12.14 | (sum @ additive_identity @ X0 @ additive_identity))),
% 80.65/12.14 inference('cnf', [status(esa)],
% 80.65/12.14 [well_definedness_of_multiplicative_inverse])).
% 80.65/12.14 thf(zip_derived_cl22, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (less_or_equal @ X0 @ X1)
% 80.65/12.14 | (less_or_equal @ X1 @ X0)
% 80.65/12.14 | ~ (defined @ X0)
% 80.65/12.14 | ~ (defined @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 80.65/12.14 thf(a_is_defined, axiom, (defined @ a)).
% 80.65/12.14 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.14 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.14 thf(zip_derived_cl117, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | (less_or_equal @ X0 @ a)
% 80.65/12.14 | (less_or_equal @ a @ X0))),
% 80.65/12.14 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl26])).
% 80.65/12.14 thf(zip_derived_cl188, plain, (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 80.65/12.14 inference('eq_fact', [status(thm)], [zip_derived_cl117])).
% 80.65/12.14 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.14 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.14 thf(zip_derived_cl189, plain, ( (less_or_equal @ a @ a)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl188, zip_derived_cl26])).
% 80.65/12.14 thf(zip_derived_cl20, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (sum @ additive_identity @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ X1 @ X0))),
% 80.65/12.14 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 80.65/12.14 thf(zip_derived_cl194, plain,
% 80.65/12.14 ((~ (less_or_equal @ a @ a) | (sum @ additive_identity @ a @ a))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl20])).
% 80.65/12.14 thf(zip_derived_cl189, plain, ( (less_or_equal @ a @ a)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl188, zip_derived_cl26])).
% 80.65/12.14 thf(zip_derived_cl196, plain, ( (sum @ additive_identity @ a @ a)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl189])).
% 80.65/12.14 thf(zip_derived_cl30, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | ~ (sum @ X0 @ X2 @ X1)
% 80.65/12.14 | ~ (sum @ X0 @ X2 @ X3)
% 80.65/12.14 | (sum @ additive_identity @ X3 @ X1))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 80.65/12.14 thf(zip_derived_cl498, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (sum @ additive_identity @ X0 @ a)
% 80.65/12.14 | ~ (sum @ additive_identity @ a @ X0)
% 80.65/12.14 | ~ (defined @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl196, zip_derived_cl30])).
% 80.65/12.14 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.14 thf(zip_derived_cl518, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (sum @ additive_identity @ X0 @ a)
% 80.65/12.14 | ~ (sum @ additive_identity @ a @ X0))),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl498, zip_derived_cl13])).
% 80.65/12.14 thf(zip_derived_cl1194, plain,
% 80.65/12.14 ((~ (defined @ a)
% 80.65/12.14 | (defined @ (multiplicative_inverse @ a))
% 80.65/12.14 | (sum @ additive_identity @ additive_identity @ a))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl518])).
% 80.65/12.14 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.14 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.14 thf(zip_derived_cl1199, plain,
% 80.65/12.14 (( (defined @ (multiplicative_inverse @ a))
% 80.65/12.14 | (sum @ additive_identity @ additive_identity @ a))),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl1194, zip_derived_cl26])).
% 80.65/12.14 thf(zip_derived_cl2, plain,
% 80.65/12.14 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 80.65/12.14 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 80.65/12.14 thf(zip_derived_cl2, plain,
% 80.65/12.14 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 80.65/12.14 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 80.65/12.14 thf(zip_derived_cl0, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ X2)
% 80.65/12.14 | ~ (sum @ X0 @ X3 @ X4)
% 80.65/12.14 | ~ (sum @ X3 @ X5 @ X1)
% 80.65/12.14 | ~ (sum @ X4 @ X5 @ X2))),
% 80.65/12.14 inference('cnf', [status(esa)], [associativity_addition_1])).
% 80.65/12.14 thf(zip_derived_cl33, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.14 (~ (sum @ X0 @ X1 @ X2)
% 80.65/12.14 | ~ (sum @ X1 @ X1 @ X0)
% 80.65/12.14 | (sum @ X1 @ X0 @ X2))),
% 80.65/12.14 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 80.65/12.14 thf(zip_derived_cl35, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | (sum @ X0 @ additive_identity @ X0)
% 80.65/12.14 | ~ (sum @ X0 @ X0 @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl33])).
% 80.65/12.14 thf(zip_derived_cl39, plain,
% 80.65/12.14 ((~ (defined @ additive_identity)
% 80.65/12.14 | (sum @ additive_identity @ additive_identity @ additive_identity)
% 80.65/12.14 | ~ (defined @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl35])).
% 80.65/12.14 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.14 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.14 thf(zip_derived_cl41, plain,
% 80.65/12.14 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 80.65/12.14 inference('demod', [status(thm)],
% 80.65/12.14 [zip_derived_cl39, zip_derived_cl13, zip_derived_cl13])).
% 80.65/12.14 thf(zip_derived_cl0, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ X2)
% 80.65/12.14 | ~ (sum @ X0 @ X3 @ X4)
% 80.65/12.14 | ~ (sum @ X3 @ X5 @ X1)
% 80.65/12.14 | ~ (sum @ X4 @ X5 @ X2))),
% 80.65/12.14 inference('cnf', [status(esa)], [associativity_addition_1])).
% 80.65/12.14 thf(zip_derived_cl34, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.14 (~ (sum @ X0 @ X1 @ X0)
% 80.65/12.14 | ~ (sum @ X1 @ X1 @ X2)
% 80.65/12.14 | (sum @ X0 @ X2 @ X0))),
% 80.65/12.14 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 80.65/12.14 thf(zip_derived_cl48, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (sum @ additive_identity @ X0 @ additive_identity)
% 80.65/12.14 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl34])).
% 80.65/12.14 thf(zip_derived_cl1332, plain,
% 80.65/12.14 (( (defined @ (multiplicative_inverse @ a))
% 80.65/12.14 | (sum @ additive_identity @ a @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl1199, zip_derived_cl48])).
% 80.65/12.14 thf(zip_derived_cl4, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 80.65/12.14 inference('cnf', [status(esa)], [commutativity_addition])).
% 80.65/12.14 thf(zip_derived_cl1341, plain,
% 80.65/12.14 (( (defined @ (multiplicative_inverse @ a))
% 80.65/12.14 | (sum @ a @ additive_identity @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl1332, zip_derived_cl4])).
% 80.65/12.14 thf(zip_derived_cl23, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.65/12.14 ( (less_or_equal @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ X2 @ X3)
% 80.65/12.14 | ~ (sum @ X2 @ X4 @ X0)
% 80.65/12.14 | ~ (sum @ X3 @ X4 @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)],
% 80.65/12.14 [compatibility_of_order_relation_and_addition])).
% 80.65/12.14 thf(zip_derived_cl351, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.14 (~ (sum @ X2 @ X1 @ X0)
% 80.65/12.14 | ~ (less_or_equal @ X2 @ X2)
% 80.65/12.14 | (less_or_equal @ X0 @ X0))),
% 80.65/12.14 inference('eq_fact', [status(thm)], [zip_derived_cl23])).
% 80.65/12.14 thf(zip_derived_cl1493, plain,
% 80.65/12.14 (( (defined @ (multiplicative_inverse @ a))
% 80.65/12.14 | (less_or_equal @ additive_identity @ additive_identity)
% 80.65/12.14 | ~ (less_or_equal @ a @ a))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl1341, zip_derived_cl351])).
% 80.65/12.14 thf(zip_derived_cl189, plain, ( (less_or_equal @ a @ a)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl188, zip_derived_cl26])).
% 80.65/12.14 thf(zip_derived_cl1497, plain,
% 80.65/12.14 (( (defined @ (multiplicative_inverse @ a))
% 80.65/12.14 | (less_or_equal @ additive_identity @ additive_identity))),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl1493, zip_derived_cl189])).
% 80.65/12.14 thf(zip_derived_cl61, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 80.65/12.14 thf(zip_derived_cl351, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.14 (~ (sum @ X2 @ X1 @ X0)
% 80.65/12.14 | ~ (less_or_equal @ X2 @ X2)
% 80.65/12.14 | (less_or_equal @ X0 @ X0))),
% 80.65/12.14 inference('eq_fact', [status(thm)], [zip_derived_cl23])).
% 80.65/12.14 thf(zip_derived_cl1396, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | (less_or_equal @ additive_identity @ additive_identity)
% 80.65/12.14 | ~ (less_or_equal @ X0 @ X0))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl351])).
% 80.65/12.14 thf(zip_derived_cl144, plain,
% 80.65/12.14 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 80.65/12.14 inference('simplify', [status(thm)], [zip_derived_cl140])).
% 80.65/12.14 thf(zip_derived_cl1426, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (less_or_equal @ additive_identity @ additive_identity)
% 80.65/12.14 | ~ (defined @ X0))),
% 80.65/12.14 inference('clc', [status(thm)], [zip_derived_cl1396, zip_derived_cl144])).
% 80.65/12.14 thf(zip_derived_cl1499, plain,
% 80.65/12.14 ( (less_or_equal @ additive_identity @ additive_identity)),
% 80.65/12.14 inference('clc', [status(thm)], [zip_derived_cl1497, zip_derived_cl1426])).
% 80.65/12.14 thf(zip_derived_cl2, plain,
% 80.65/12.14 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 80.65/12.14 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 80.65/12.14 thf(zip_derived_cl23, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.65/12.14 ( (less_or_equal @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ X2 @ X3)
% 80.65/12.14 | ~ (sum @ X2 @ X4 @ X0)
% 80.65/12.14 | ~ (sum @ X3 @ X4 @ X1))),
% 80.65/12.14 inference('cnf', [status(esa)],
% 80.65/12.14 [compatibility_of_order_relation_and_addition])).
% 80.65/12.14 thf(zip_derived_cl338, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.14 (~ (defined @ X0)
% 80.65/12.14 | ~ (sum @ X2 @ X0 @ X1)
% 80.65/12.14 | ~ (less_or_equal @ additive_identity @ X2)
% 80.65/12.14 | (less_or_equal @ X0 @ X1))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl23])).
% 80.65/12.14 thf(zip_derived_cl9926, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i]:
% 80.65/12.14 ( (less_or_equal @ X1 @ X0)
% 80.65/12.14 | ~ (sum @ additive_identity @ X1 @ X0)
% 80.65/12.14 | ~ (defined @ X1))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl1499, zip_derived_cl338])).
% 80.65/12.14 thf(zip_derived_cl10047, plain,
% 80.65/12.14 ((~ (defined @ (add @ additive_identity @ b))
% 80.65/12.14 | (less_or_equal @ (add @ additive_identity @ b) @ b))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl1997, zip_derived_cl9926])).
% 80.65/12.14 thf(zip_derived_cl10560, plain,
% 80.65/12.14 ((~ (defined @ b)
% 80.65/12.14 | ~ (defined @ additive_identity)
% 80.65/12.14 | (less_or_equal @ (add @ additive_identity @ b) @ b))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl10047])).
% 80.65/12.14 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.14 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.14 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.14 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.14 thf(zip_derived_cl10561, plain,
% 80.65/12.14 ( (less_or_equal @ (add @ additive_identity @ b) @ b)),
% 80.65/12.14 inference('demod', [status(thm)],
% 80.65/12.14 [zip_derived_cl10560, zip_derived_cl27, zip_derived_cl13])).
% 80.65/12.14 thf(zip_derived_cl10582, plain,
% 80.65/12.14 ( (sum @ additive_identity @ b @ (add @ additive_identity @ b))),
% 80.65/12.14 inference('demod', [status(thm)],
% 80.65/12.14 [zip_derived_cl556, zip_derived_cl10561])).
% 80.65/12.14 thf(zip_derived_cl254, plain, ( (sum @ additive_identity @ b @ b)),
% 80.65/12.14 inference('demod', [status(thm)], [zip_derived_cl250, zip_derived_cl244])).
% 80.65/12.14 thf(zip_derived_cl1, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 80.65/12.14 ( (sum @ X0 @ X1 @ X2)
% 80.65/12.14 | ~ (sum @ X3 @ X4 @ X0)
% 80.65/12.14 | ~ (sum @ X4 @ X1 @ X5)
% 80.65/12.14 | ~ (sum @ X3 @ X5 @ X2))),
% 80.65/12.14 inference('cnf', [status(esa)], [associativity_addition_2])).
% 80.65/12.14 thf(zip_derived_cl260, plain,
% 80.65/12.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.14 (~ (sum @ additive_identity @ X1 @ X0)
% 80.65/12.14 | ~ (sum @ b @ X2 @ X1)
% 80.65/12.14 | (sum @ b @ X2 @ X0))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl254, zip_derived_cl1])).
% 80.65/12.14 thf(zip_derived_cl11511, plain,
% 80.65/12.14 (![X0 : $i]:
% 80.65/12.14 ( (sum @ b @ X0 @ (add @ additive_identity @ b))
% 80.65/12.14 | ~ (sum @ b @ X0 @ b))),
% 80.65/12.14 inference('sup-', [status(thm)], [zip_derived_cl10582, zip_derived_cl260])).
% 80.65/12.14 thf(zip_derived_cl17445, plain,
% 80.65/12.15 ( (sum @ b @ (additive_inverse @ additive_identity) @
% 80.65/12.15 (add @ additive_identity @ b))),
% 80.65/12.15 inference('sup-', [status(thm)],
% 80.65/12.15 [zip_derived_cl2071, zip_derived_cl11511])).
% 80.65/12.15 thf(zip_derived_cl4, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 80.65/12.15 inference('cnf', [status(esa)], [commutativity_addition])).
% 80.65/12.15 thf(zip_derived_cl23792, plain,
% 80.65/12.15 ( (sum @ (additive_inverse @ additive_identity) @ b @
% 80.65/12.15 (add @ additive_identity @ b))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl17445, zip_derived_cl4])).
% 80.65/12.15 thf(zip_derived_cl61, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 (~ (defined @ X0)
% 80.65/12.15 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 80.65/12.15 thf(zip_derived_cl196, plain, ( (sum @ additive_identity @ a @ a)),
% 80.65/12.15 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl189])).
% 80.65/12.15 thf(zip_derived_cl4, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 80.65/12.15 inference('cnf', [status(esa)], [commutativity_addition])).
% 80.65/12.15 thf(zip_derived_cl213, plain, ( (sum @ a @ additive_identity @ a)),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl196, zip_derived_cl4])).
% 80.65/12.15 thf(zip_derived_cl77, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.65/12.15 (~ (sum @ X2 @ X1 @ X0)
% 80.65/12.15 | ~ (sum @ X1 @ X3 @ X1)
% 80.65/12.15 | (sum @ X0 @ X3 @ X0))),
% 80.65/12.15 inference('eq_fact', [status(thm)], [zip_derived_cl1])).
% 80.65/12.15 thf(zip_derived_cl1596, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 ( (sum @ a @ X0 @ a)
% 80.65/12.15 | ~ (sum @ additive_identity @ X0 @ additive_identity))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl213, zip_derived_cl77])).
% 80.65/12.15 thf(zip_derived_cl2002, plain,
% 80.65/12.15 ((~ (defined @ additive_identity)
% 80.65/12.15 | (sum @ a @ (additive_inverse @ additive_identity) @ a))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl1596])).
% 80.65/12.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.15 thf(zip_derived_cl2011, plain,
% 80.65/12.15 ( (sum @ a @ (additive_inverse @ additive_identity) @ a)),
% 80.65/12.15 inference('demod', [status(thm)], [zip_derived_cl2002, zip_derived_cl13])).
% 80.65/12.15 thf(zip_derived_cl0, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ X2)
% 80.65/12.15 | ~ (sum @ X0 @ X3 @ X4)
% 80.65/12.15 | ~ (sum @ X3 @ X5 @ X1)
% 80.65/12.15 | ~ (sum @ X4 @ X5 @ X2))),
% 80.65/12.15 inference('cnf', [status(esa)], [associativity_addition_1])).
% 80.65/12.15 thf(zip_derived_cl2034, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 (~ (sum @ a @ X1 @ X0)
% 80.65/12.15 | ~ (sum @ (additive_inverse @ additive_identity) @ X1 @ X2)
% 80.65/12.15 | (sum @ a @ X2 @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl2011, zip_derived_cl0])).
% 80.65/12.15 thf(zip_derived_cl116503, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 ( (sum @ a @ (add @ additive_identity @ b) @ X0)
% 80.65/12.15 | ~ (sum @ a @ b @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)],
% 80.65/12.15 [zip_derived_cl23792, zip_derived_cl2034])).
% 80.65/12.15 thf(zip_derived_cl117189, plain,
% 80.65/12.15 ((~ (defined @ b)
% 80.65/12.15 | ~ (defined @ a)
% 80.65/12.15 | (sum @ a @ (add @ additive_identity @ b) @ (add @ a @ b)))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl116503])).
% 80.65/12.15 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.15 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.15 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.15 thf(zip_derived_cl117194, plain,
% 80.65/12.15 ( (sum @ a @ (add @ additive_identity @ b) @ (add @ a @ b))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl117189, zip_derived_cl27, zip_derived_cl26])).
% 80.65/12.15 thf(zip_derived_cl10582, plain,
% 80.65/12.15 ( (sum @ additive_identity @ b @ (add @ additive_identity @ b))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl556, zip_derived_cl10561])).
% 80.65/12.15 thf(zip_derived_cl2, plain,
% 80.65/12.15 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 80.65/12.15 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 80.65/12.15 thf(zip_derived_cl3, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 80.65/12.15 | ~ (defined @ X0))),
% 80.65/12.15 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 80.65/12.15 thf(zip_derived_cl0, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ X2)
% 80.65/12.15 | ~ (sum @ X0 @ X3 @ X4)
% 80.65/12.15 | ~ (sum @ X3 @ X5 @ X1)
% 80.65/12.15 | ~ (sum @ X4 @ X5 @ X2))),
% 80.65/12.15 inference('cnf', [status(esa)], [associativity_addition_1])).
% 80.65/12.15 thf(zip_derived_cl31, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.65/12.15 (~ (defined @ X0)
% 80.65/12.15 | ~ (sum @ additive_identity @ X2 @ X1)
% 80.65/12.15 | ~ (sum @ X0 @ X2 @ X3)
% 80.65/12.15 | (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 80.65/12.15 thf(zip_derived_cl613, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 (~ (defined @ X0)
% 80.65/12.15 | (sum @ (additive_inverse @ X2) @ X1 @ X0)
% 80.65/12.15 | ~ (sum @ X2 @ X0 @ X1)
% 80.65/12.15 | ~ (defined @ X2))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl31])).
% 80.65/12.15 thf(zip_derived_cl29134, plain,
% 80.65/12.15 ((~ (defined @ additive_identity)
% 80.65/12.15 | (sum @ (additive_inverse @ additive_identity) @
% 80.65/12.15 (add @ additive_identity @ b) @ b)
% 80.65/12.15 | ~ (defined @ b))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl10582, zip_derived_cl613])).
% 80.65/12.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.15 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.15 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.15 thf(zip_derived_cl29201, plain,
% 80.65/12.15 ( (sum @ (additive_inverse @ additive_identity) @
% 80.65/12.15 (add @ additive_identity @ b) @ b)),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl29134, zip_derived_cl13, zip_derived_cl27])).
% 80.65/12.15 thf(zip_derived_cl2034, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 (~ (sum @ a @ X1 @ X0)
% 80.65/12.15 | ~ (sum @ (additive_inverse @ additive_identity) @ X1 @ X2)
% 80.65/12.15 | (sum @ a @ X2 @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl2011, zip_derived_cl0])).
% 80.65/12.15 thf(zip_derived_cl116497, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 ( (sum @ a @ b @ X0)
% 80.65/12.15 | ~ (sum @ a @ (add @ additive_identity @ b) @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)],
% 80.65/12.15 [zip_derived_cl29201, zip_derived_cl2034])).
% 80.65/12.15 thf(zip_derived_cl128010, plain, ( (sum @ a @ b @ (add @ a @ b))),
% 80.65/12.15 inference('sup-', [status(thm)],
% 80.65/12.15 [zip_derived_cl117194, zip_derived_cl116497])).
% 80.65/12.15 thf(zip_derived_cl23, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.65/12.15 ( (less_or_equal @ X0 @ X1)
% 80.65/12.15 | ~ (less_or_equal @ X2 @ X3)
% 80.65/12.15 | ~ (sum @ X2 @ X4 @ X0)
% 80.65/12.15 | ~ (sum @ X3 @ X4 @ X1))),
% 80.65/12.15 inference('cnf', [status(esa)],
% 80.65/12.15 [compatibility_of_order_relation_and_addition])).
% 80.65/12.15 thf(zip_derived_cl128188, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 (~ (sum @ X1 @ b @ X0)
% 80.65/12.15 | ~ (less_or_equal @ a @ X1)
% 80.65/12.15 | (less_or_equal @ (add @ a @ b) @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl128010, zip_derived_cl23])).
% 80.65/12.15 thf(zip_derived_cl129847, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 (~ (defined @ b)
% 80.65/12.15 | ~ (defined @ X0)
% 80.65/12.15 | (less_or_equal @ (add @ a @ b) @ (add @ X0 @ b))
% 80.65/12.15 | ~ (less_or_equal @ a @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl128188])).
% 80.65/12.15 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.15 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.15 thf(zip_derived_cl129878, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 (~ (defined @ X0)
% 80.65/12.15 | (less_or_equal @ (add @ a @ b) @ (add @ X0 @ b))
% 80.65/12.15 | ~ (less_or_equal @ a @ X0))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl129847, zip_derived_cl27])).
% 80.65/12.15 thf(zip_derived_cl130439, plain,
% 80.65/12.15 (( (less_or_equal @ (add @ a @ b) @ (add @ b @ b)) | ~ (defined @ b))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl129878])).
% 80.65/12.15 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.15 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.15 thf(zip_derived_cl130491, plain,
% 80.65/12.15 ( (less_or_equal @ (add @ a @ b) @ (add @ b @ b))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl130439, zip_derived_cl27])).
% 80.65/12.15 thf(zip_derived_cl28, plain, ( (less_or_equal @ a @ b)),
% 80.65/12.15 inference('cnf', [status(esa)], [zf_stmt_1])).
% 80.65/12.15 thf(zip_derived_cl18, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 80.65/12.15 | ~ (defined @ X0)
% 80.65/12.15 | ~ (defined @ X1))),
% 80.65/12.15 inference('cnf', [status(esa)], [totality_of_addition])).
% 80.65/12.15 thf(zip_derived_cl4, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 80.65/12.15 inference('cnf', [status(esa)], [commutativity_addition])).
% 80.65/12.15 thf(zip_derived_cl97, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 (~ (defined @ X0)
% 80.65/12.15 | ~ (defined @ X1)
% 80.65/12.15 | (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 80.65/12.15 thf(zip_derived_cl18, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 80.65/12.15 | ~ (defined @ X0)
% 80.65/12.15 | ~ (defined @ X1))),
% 80.65/12.15 inference('cnf', [status(esa)], [totality_of_addition])).
% 80.65/12.15 thf(zip_derived_cl2011, plain,
% 80.65/12.15 ( (sum @ a @ (additive_inverse @ additive_identity) @ a)),
% 80.65/12.15 inference('demod', [status(thm)], [zip_derived_cl2002, zip_derived_cl13])).
% 80.65/12.15 thf(zip_derived_cl144, plain,
% 80.65/12.15 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 80.65/12.15 inference('simplify', [status(thm)], [zip_derived_cl140])).
% 80.65/12.15 thf(zip_derived_cl18, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 80.65/12.15 | ~ (defined @ X0)
% 80.65/12.15 | ~ (defined @ X1))),
% 80.65/12.15 inference('cnf', [status(esa)], [totality_of_addition])).
% 80.65/12.15 thf(zip_derived_cl196, plain, ( (sum @ additive_identity @ a @ a)),
% 80.65/12.15 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl189])).
% 80.65/12.15 thf(zip_derived_cl23, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.65/12.15 ( (less_or_equal @ X0 @ X1)
% 80.65/12.15 | ~ (less_or_equal @ X2 @ X3)
% 80.65/12.15 | ~ (sum @ X2 @ X4 @ X0)
% 80.65/12.15 | ~ (sum @ X3 @ X4 @ X1))),
% 80.65/12.15 inference('cnf', [status(esa)],
% 80.65/12.15 [compatibility_of_order_relation_and_addition])).
% 80.65/12.15 thf(zip_derived_cl343, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 (~ (sum @ X1 @ a @ X0)
% 80.65/12.15 | ~ (less_or_equal @ additive_identity @ X1)
% 80.65/12.15 | (less_or_equal @ a @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl196, zip_derived_cl23])).
% 80.65/12.15 thf(zip_derived_cl405, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 (~ (defined @ a)
% 80.65/12.15 | ~ (defined @ X0)
% 80.65/12.15 | (less_or_equal @ a @ (add @ X0 @ a))
% 80.65/12.15 | ~ (less_or_equal @ additive_identity @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl343])).
% 80.65/12.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.15 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.15 thf(zip_derived_cl411, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 (~ (defined @ X0)
% 80.65/12.15 | (less_or_equal @ a @ (add @ X0 @ a))
% 80.65/12.15 | ~ (less_or_equal @ additive_identity @ X0))),
% 80.65/12.15 inference('demod', [status(thm)], [zip_derived_cl405, zip_derived_cl26])).
% 80.65/12.15 thf(zip_derived_cl419, plain,
% 80.65/12.15 ((~ (defined @ additive_identity)
% 80.65/12.15 | (less_or_equal @ a @ (add @ additive_identity @ a))
% 80.65/12.15 | ~ (defined @ additive_identity))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl144, zip_derived_cl411])).
% 80.65/12.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.15 thf(zip_derived_cl428, plain,
% 80.65/12.15 ( (less_or_equal @ a @ (add @ additive_identity @ a))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl419, zip_derived_cl13, zip_derived_cl13])).
% 80.65/12.15 thf(zip_derived_cl20, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 ( (sum @ additive_identity @ X0 @ X1)
% 80.65/12.15 | ~ (less_or_equal @ X0 @ X1)
% 80.65/12.15 | ~ (less_or_equal @ X1 @ X0))),
% 80.65/12.15 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 80.65/12.15 thf(zip_derived_cl433, plain,
% 80.65/12.15 ((~ (less_or_equal @ (add @ additive_identity @ a) @ a)
% 80.65/12.15 | (sum @ additive_identity @ a @ (add @ additive_identity @ a)))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl428, zip_derived_cl20])).
% 80.65/12.15 thf(zip_derived_cl12, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 80.65/12.15 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 80.65/12.15 thf(zip_derived_cl18, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 80.65/12.15 | ~ (defined @ X0)
% 80.65/12.15 | ~ (defined @ X1))),
% 80.65/12.15 inference('cnf', [status(esa)], [totality_of_addition])).
% 80.65/12.15 thf(zip_derived_cl518, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 ( (sum @ additive_identity @ X0 @ a)
% 80.65/12.15 | ~ (sum @ additive_identity @ a @ X0))),
% 80.65/12.15 inference('demod', [status(thm)], [zip_derived_cl498, zip_derived_cl13])).
% 80.65/12.15 thf(zip_derived_cl1192, plain,
% 80.65/12.15 ((~ (defined @ a)
% 80.65/12.15 | ~ (defined @ additive_identity)
% 80.65/12.15 | (sum @ additive_identity @ (add @ additive_identity @ a) @ a))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl518])).
% 80.65/12.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.15 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.15 thf(zip_derived_cl1197, plain,
% 80.65/12.15 ( (sum @ additive_identity @ (add @ additive_identity @ a) @ a)),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl1192, zip_derived_cl26, zip_derived_cl13])).
% 80.65/12.15 thf(zip_derived_cl9926, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 ( (less_or_equal @ X1 @ X0)
% 80.65/12.15 | ~ (sum @ additive_identity @ X1 @ X0)
% 80.65/12.15 | ~ (defined @ X1))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl1499, zip_derived_cl338])).
% 80.65/12.15 thf(zip_derived_cl10045, plain,
% 80.65/12.15 ((~ (defined @ (add @ additive_identity @ a))
% 80.65/12.15 | (less_or_equal @ (add @ additive_identity @ a) @ a))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl1197, zip_derived_cl9926])).
% 80.65/12.15 thf(zip_derived_cl10133, plain,
% 80.65/12.15 ((~ (defined @ a)
% 80.65/12.15 | ~ (defined @ additive_identity)
% 80.65/12.15 | (less_or_equal @ (add @ additive_identity @ a) @ a))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl10045])).
% 80.65/12.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.15 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.15 thf(zip_derived_cl10134, plain,
% 80.65/12.15 ( (less_or_equal @ (add @ additive_identity @ a) @ a)),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl10133, zip_derived_cl26, zip_derived_cl13])).
% 80.65/12.15 thf(zip_derived_cl10135, plain,
% 80.65/12.15 ( (sum @ additive_identity @ a @ (add @ additive_identity @ a))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl433, zip_derived_cl10134])).
% 80.65/12.15 thf(zip_derived_cl196, plain, ( (sum @ additive_identity @ a @ a)),
% 80.65/12.15 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl189])).
% 80.65/12.15 thf(zip_derived_cl1, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ X2)
% 80.65/12.15 | ~ (sum @ X3 @ X4 @ X0)
% 80.65/12.15 | ~ (sum @ X4 @ X1 @ X5)
% 80.65/12.15 | ~ (sum @ X3 @ X5 @ X2))),
% 80.65/12.15 inference('cnf', [status(esa)], [associativity_addition_2])).
% 80.65/12.15 thf(zip_derived_cl212, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 (~ (sum @ additive_identity @ X1 @ X0)
% 80.65/12.15 | ~ (sum @ a @ X2 @ X1)
% 80.65/12.15 | (sum @ a @ X2 @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl196, zip_derived_cl1])).
% 80.65/12.15 thf(zip_derived_cl10423, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 ( (sum @ a @ X0 @ (add @ additive_identity @ a))
% 80.65/12.15 | ~ (sum @ a @ X0 @ a))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl10135, zip_derived_cl212])).
% 80.65/12.15 thf(zip_derived_cl17154, plain,
% 80.65/12.15 ( (sum @ a @ (additive_inverse @ additive_identity) @
% 80.65/12.15 (add @ additive_identity @ a))),
% 80.65/12.15 inference('sup-', [status(thm)],
% 80.65/12.15 [zip_derived_cl2011, zip_derived_cl10423])).
% 80.65/12.15 thf(zip_derived_cl4, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 80.65/12.15 inference('cnf', [status(esa)], [commutativity_addition])).
% 80.65/12.15 thf(zip_derived_cl23342, plain,
% 80.65/12.15 ( (sum @ (additive_inverse @ additive_identity) @ a @
% 80.65/12.15 (add @ additive_identity @ a))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl17154, zip_derived_cl4])).
% 80.65/12.15 thf(zip_derived_cl2034, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 (~ (sum @ a @ X1 @ X0)
% 80.65/12.15 | ~ (sum @ (additive_inverse @ additive_identity) @ X1 @ X2)
% 80.65/12.15 | (sum @ a @ X2 @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl2011, zip_derived_cl0])).
% 80.65/12.15 thf(zip_derived_cl116500, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 ( (sum @ a @ (add @ additive_identity @ a) @ X0)
% 80.65/12.15 | ~ (sum @ a @ a @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)],
% 80.65/12.15 [zip_derived_cl23342, zip_derived_cl2034])).
% 80.65/12.15 thf(zip_derived_cl116771, plain,
% 80.65/12.15 ((~ (defined @ a)
% 80.65/12.15 | ~ (defined @ a)
% 80.65/12.15 | (sum @ a @ (add @ additive_identity @ a) @ (add @ a @ a)))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl116500])).
% 80.65/12.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.15 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.15 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.15 thf(zip_derived_cl116775, plain,
% 80.65/12.15 ( (sum @ a @ (add @ additive_identity @ a) @ (add @ a @ a))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl116771, zip_derived_cl26, zip_derived_cl26])).
% 80.65/12.15 thf(zip_derived_cl10135, plain,
% 80.65/12.15 ( (sum @ additive_identity @ a @ (add @ additive_identity @ a))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl433, zip_derived_cl10134])).
% 80.65/12.15 thf(zip_derived_cl613, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 (~ (defined @ X0)
% 80.65/12.15 | (sum @ (additive_inverse @ X2) @ X1 @ X0)
% 80.65/12.15 | ~ (sum @ X2 @ X0 @ X1)
% 80.65/12.15 | ~ (defined @ X2))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl31])).
% 80.65/12.15 thf(zip_derived_cl29131, plain,
% 80.65/12.15 ((~ (defined @ additive_identity)
% 80.65/12.15 | (sum @ (additive_inverse @ additive_identity) @
% 80.65/12.15 (add @ additive_identity @ a) @ a)
% 80.65/12.15 | ~ (defined @ a))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl10135, zip_derived_cl613])).
% 80.65/12.15 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 80.65/12.15 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 80.65/12.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.15 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.15 thf(zip_derived_cl29198, plain,
% 80.65/12.15 ( (sum @ (additive_inverse @ additive_identity) @
% 80.65/12.15 (add @ additive_identity @ a) @ a)),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl29131, zip_derived_cl13, zip_derived_cl26])).
% 80.65/12.15 thf(zip_derived_cl2034, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 (~ (sum @ a @ X1 @ X0)
% 80.65/12.15 | ~ (sum @ (additive_inverse @ additive_identity) @ X1 @ X2)
% 80.65/12.15 | (sum @ a @ X2 @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl2011, zip_derived_cl0])).
% 80.65/12.15 thf(zip_derived_cl116495, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 ( (sum @ a @ a @ X0)
% 80.65/12.15 | ~ (sum @ a @ (add @ additive_identity @ a) @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)],
% 80.65/12.15 [zip_derived_cl29198, zip_derived_cl2034])).
% 80.65/12.15 thf(zip_derived_cl118352, plain, ( (sum @ a @ a @ (add @ a @ a))),
% 80.65/12.15 inference('sup-', [status(thm)],
% 80.65/12.15 [zip_derived_cl116775, zip_derived_cl116495])).
% 80.65/12.15 thf(zip_derived_cl23, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.65/12.15 ( (less_or_equal @ X0 @ X1)
% 80.65/12.15 | ~ (less_or_equal @ X2 @ X3)
% 80.65/12.15 | ~ (sum @ X2 @ X4 @ X0)
% 80.65/12.15 | ~ (sum @ X3 @ X4 @ X1))),
% 80.65/12.15 inference('cnf', [status(esa)],
% 80.65/12.15 [compatibility_of_order_relation_and_addition])).
% 80.65/12.15 thf(zip_derived_cl118434, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i]:
% 80.65/12.15 (~ (sum @ X1 @ a @ X0)
% 80.65/12.15 | ~ (less_or_equal @ a @ X1)
% 80.65/12.15 | (less_or_equal @ (add @ a @ a) @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl118352, zip_derived_cl23])).
% 80.65/12.15 thf(zip_derived_cl119265, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 (~ (defined @ a)
% 80.65/12.15 | ~ (defined @ X0)
% 80.65/12.15 | (less_or_equal @ (add @ a @ a) @ (add @ a @ X0))
% 80.65/12.15 | ~ (less_or_equal @ a @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl97, zip_derived_cl118434])).
% 80.65/12.15 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 80.65/12.15 inference('cnf', [status(esa)], [a_is_defined])).
% 80.65/12.15 thf(zip_derived_cl119294, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 (~ (defined @ X0)
% 80.65/12.15 | (less_or_equal @ (add @ a @ a) @ (add @ a @ X0))
% 80.65/12.15 | ~ (less_or_equal @ a @ X0))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl119265, zip_derived_cl26])).
% 80.65/12.15 thf(zip_derived_cl119994, plain,
% 80.65/12.15 (( (less_or_equal @ (add @ a @ a) @ (add @ a @ b)) | ~ (defined @ b))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl119294])).
% 80.65/12.15 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 80.65/12.15 inference('cnf', [status(esa)], [b_is_defined])).
% 80.65/12.15 thf(zip_derived_cl120046, plain,
% 80.65/12.15 ( (less_or_equal @ (add @ a @ a) @ (add @ a @ b))),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl119994, zip_derived_cl27])).
% 80.65/12.15 thf(transitivity_of_order_relation, axiom,
% 80.65/12.15 (( less_or_equal @ X @ Z ) | ( ~( less_or_equal @ X @ Y ) ) |
% 80.65/12.15 ( ~( less_or_equal @ Y @ Z ) ))).
% 80.65/12.15 thf(zip_derived_cl21, plain,
% 80.65/12.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.65/12.15 ( (less_or_equal @ X0 @ X1)
% 80.65/12.15 | ~ (less_or_equal @ X0 @ X2)
% 80.65/12.15 | ~ (less_or_equal @ X2 @ X1))),
% 80.65/12.15 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 80.65/12.15 thf(zip_derived_cl120077, plain,
% 80.65/12.15 (![X0 : $i]:
% 80.65/12.15 (~ (less_or_equal @ (add @ a @ b) @ X0)
% 80.65/12.15 | (less_or_equal @ (add @ a @ a) @ X0))),
% 80.65/12.15 inference('sup-', [status(thm)], [zip_derived_cl120046, zip_derived_cl21])).
% 80.65/12.15 thf(zip_derived_cl130516, plain,
% 80.65/12.15 ( (less_or_equal @ (add @ a @ a) @ (add @ b @ b))),
% 80.65/12.15 inference('sup-', [status(thm)],
% 80.65/12.15 [zip_derived_cl130491, zip_derived_cl120077])).
% 80.65/12.15 thf(zip_derived_cl130528, plain, ($false),
% 80.65/12.15 inference('demod', [status(thm)],
% 80.65/12.15 [zip_derived_cl29, zip_derived_cl130516])).
% 80.65/12.15
% 80.65/12.15 % SZS output end Refutation
% 80.65/12.15
% 80.65/12.15
% 80.65/12.15 % Terminating...
% 81.05/12.21 % Runner terminated.
% 81.05/12.22 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------