%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD008-3 : TPTP v9.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VvdCR8YeKG true
% Computer : n010.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 04:33:07 PM UTC 2025
% Result : Unsatisfiable 34.36s 5.54s
% Output : Refutation 34.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : FLD008-3 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VvdCR8YeKG true
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Oct 1 18:28:53 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % Running portfolio for 300 s
% 0.14/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in FO mode
% 0.53/0.63 % Total configuration time : 435
% 0.53/0.63 % Estimated wc time : 1092
% 0.53/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 34.36/5.54 % Solved by fo/fo13.sh.
% 34.36/5.54 % done 2630 iterations in 4.755s
% 34.36/5.54 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 34.36/5.54 % SZS output start Refutation
% 34.36/5.54 thf(sum_type, type, sum: $i > $i > $i > $o).
% 34.36/5.54 thf(b_type, type, b: $i).
% 34.36/5.54 thf(a_type, type, a: $i).
% 34.36/5.54 thf(add_type, type, add: $i > $i > $i).
% 34.36/5.54 thf(additive_identity_type, type, additive_identity: $i).
% 34.36/5.54 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 34.36/5.54 thf(defined_type, type, defined: $i > $o).
% 34.36/5.54 thf(well_definedness_of_additive_inverse, axiom,
% 34.36/5.54 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(existence_of_inverse_addition, axiom,
% 34.36/5.54 (( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) |
% 34.36/5.54 ( ~( defined @ X ) ))).
% 34.36/5.54 thf(zip_derived_cl3, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 34.36/5.54 | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 34.36/5.54 thf(commutativity_addition, axiom,
% 34.36/5.54 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 34.36/5.54 thf(zip_derived_cl4, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 34.36/5.54 inference('cnf', [status(esa)], [commutativity_addition])).
% 34.36/5.54 thf(zip_derived_cl34, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 34.36/5.54 thf(well_definedness_of_addition, axiom,
% 34.36/5.54 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 34.36/5.54 ( ~( defined @ Y ) ))).
% 34.36/5.54 thf(zip_derived_cl12, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i]:
% 34.36/5.54 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(totality_of_addition, axiom,
% 34.36/5.54 (( sum @ X @ Y @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 34.36/5.54 ( ~( defined @ Y ) ))).
% 34.36/5.54 thf(zip_derived_cl18, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 34.36/5.54 | ~ (defined @ X0)
% 34.36/5.54 | ~ (defined @ X1))),
% 34.36/5.54 inference('cnf', [status(esa)], [totality_of_addition])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(existence_of_identity_addition, axiom,
% 34.36/5.54 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 34.36/5.54 thf(zip_derived_cl2, plain,
% 34.36/5.54 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(zip_derived_cl18, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 34.36/5.54 | ~ (defined @ X0)
% 34.36/5.54 | ~ (defined @ X1))),
% 34.36/5.54 inference('cnf', [status(esa)], [totality_of_addition])).
% 34.36/5.54 thf(zip_derived_cl2, plain,
% 34.36/5.54 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 34.36/5.54 thf(zip_derived_cl4, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 34.36/5.54 inference('cnf', [status(esa)], [commutativity_addition])).
% 34.36/5.54 thf(zip_derived_cl33, plain,
% 34.36/5.54 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 34.36/5.54 thf(zip_derived_cl18, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 34.36/5.54 | ~ (defined @ X0)
% 34.36/5.54 | ~ (defined @ X1))),
% 34.36/5.54 inference('cnf', [status(esa)], [totality_of_addition])).
% 34.36/5.54 thf(zip_derived_cl2, plain,
% 34.36/5.54 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 34.36/5.54 thf(associativity_addition_1, axiom,
% 34.36/5.54 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 34.36/5.54 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 34.36/5.54 thf(zip_derived_cl0, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ X2)
% 34.36/5.54 | ~ (sum @ X0 @ X3 @ X4)
% 34.36/5.54 | ~ (sum @ X3 @ X5 @ X1)
% 34.36/5.54 | ~ (sum @ X4 @ X5 @ X2))),
% 34.36/5.54 inference('cnf', [status(esa)], [associativity_addition_1])).
% 34.36/5.54 thf(zip_derived_cl30, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | (sum @ additive_identity @ X2 @ X1)
% 34.36/5.54 | ~ (sum @ X0 @ X3 @ X2)
% 34.36/5.54 | ~ (sum @ X0 @ X3 @ X1))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 34.36/5.54 thf(zip_derived_cl239, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | ~ (defined @ X1)
% 34.36/5.54 | ~ (defined @ X1)
% 34.36/5.54 | (sum @ additive_identity @ (add @ X1 @ X0) @ X2)
% 34.36/5.54 | ~ (sum @ X1 @ X0 @ X2))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl30])).
% 34.36/5.54 thf(zip_derived_cl244, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.36/5.54 (~ (sum @ X1 @ X0 @ X2)
% 34.36/5.54 | (sum @ additive_identity @ (add @ X1 @ X0) @ X2)
% 34.36/5.54 | ~ (defined @ X1)
% 34.36/5.54 | ~ (defined @ X0))),
% 34.36/5.54 inference('simplify', [status(thm)], [zip_derived_cl239])).
% 34.36/5.54 thf(zip_derived_cl5506, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | (sum @ additive_identity @ (add @ X0 @ additive_identity) @ X0)
% 34.36/5.54 | ~ (defined @ X0)
% 34.36/5.54 | ~ (defined @ additive_identity))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl244])).
% 34.36/5.54 thf(well_definedness_of_additive_identity, axiom,
% 34.36/5.54 (defined @ additive_identity)).
% 34.36/5.54 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 34.36/5.54 thf(zip_derived_cl5548, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | (sum @ additive_identity @ (add @ X0 @ additive_identity) @ X0)
% 34.36/5.54 | ~ (defined @ X0))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl5506, zip_derived_cl13])).
% 34.36/5.54 thf(zip_derived_cl5549, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 ( (sum @ additive_identity @ (add @ X0 @ additive_identity) @ X0)
% 34.36/5.54 | ~ (defined @ X0))),
% 34.36/5.54 inference('simplify', [status(thm)], [zip_derived_cl5548])).
% 34.36/5.54 thf(not_sum_3, conjecture,
% 34.36/5.54 (sum @
% 34.36/5.54 additive_identity @ ( additive_inverse @ ( add @ a @ b ) ) @
% 34.36/5.54 ( add @ ( additive_inverse @ a ) @ ( additive_inverse @ b ) ))).
% 34.36/5.54 thf(zf_stmt_0, negated_conjecture,
% 34.36/5.54 (~( sum @
% 34.36/5.54 additive_identity @ ( additive_inverse @ ( add @ a @ b ) ) @
% 34.36/5.54 ( add @ ( additive_inverse @ a ) @ ( additive_inverse @ b ) ) )),
% 34.36/5.54 inference('cnf.neg', [status(esa)], [not_sum_3])).
% 34.36/5.54 thf(zip_derived_cl28, plain,
% 34.36/5.54 (~ (sum @ additive_identity @ (additive_inverse @ (add @ a @ b)) @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)))),
% 34.36/5.54 inference('cnf', [status(esa)], [zf_stmt_0])).
% 34.36/5.54 thf(zip_derived_cl0, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ X2)
% 34.36/5.54 | ~ (sum @ X0 @ X3 @ X4)
% 34.36/5.54 | ~ (sum @ X3 @ X5 @ X1)
% 34.36/5.54 | ~ (sum @ X4 @ X5 @ X2))),
% 34.36/5.54 inference('cnf', [status(esa)], [associativity_addition_1])).
% 34.36/5.54 thf(zip_derived_cl29, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.36/5.54 (~ (sum @ additive_identity @ X1 @ X0)
% 34.36/5.54 | ~ (sum @ X1 @ X2 @ (additive_inverse @ (add @ a @ b)))
% 34.36/5.54 | ~ (sum @ X0 @ X2 @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b))))),
% 34.36/5.54 inference('s_sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl0])).
% 34.36/5.54 thf(zip_derived_cl6284, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | ~ (sum @ (add @ X0 @ additive_identity) @ X1 @
% 34.36/5.54 (additive_inverse @ (add @ a @ b)))
% 34.36/5.54 | ~ (sum @ X0 @ X1 @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl5549, zip_derived_cl29])).
% 34.36/5.54 thf(zip_derived_cl11974, plain,
% 34.36/5.54 ((~ (defined @ (additive_inverse @ b))
% 34.36/5.54 | ~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (sum @ (add @ (additive_inverse @ a) @ additive_identity) @
% 34.36/5.54 (additive_inverse @ b) @ (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl6284])).
% 34.36/5.54 thf(zip_derived_cl11983, plain,
% 34.36/5.54 ((~ (sum @ (add @ (additive_inverse @ a) @ additive_identity) @
% 34.36/5.54 (additive_inverse @ b) @ (additive_inverse @ (add @ a @ b)))
% 34.36/5.54 | ~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (defined @ (additive_inverse @ b)))),
% 34.36/5.54 inference('simplify', [status(thm)], [zip_derived_cl11974])).
% 34.36/5.54 thf(zip_derived_cl11990, plain,
% 34.36/5.54 ((~ (defined @ a)
% 34.36/5.54 | ~ (sum @ (add @ (additive_inverse @ a) @ additive_identity) @
% 34.36/5.54 (additive_inverse @ b) @ (additive_inverse @ (add @ a @ b)))
% 34.36/5.54 | ~ (defined @ (additive_inverse @ b)))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl14, zip_derived_cl11983])).
% 34.36/5.54 thf(a_is_defined, axiom, (defined @ a)).
% 34.36/5.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 34.36/5.54 inference('cnf', [status(esa)], [a_is_defined])).
% 34.36/5.54 thf(zip_derived_cl11991, plain,
% 34.36/5.54 ((~ (sum @ (add @ (additive_inverse @ a) @ additive_identity) @
% 34.36/5.54 (additive_inverse @ b) @ (additive_inverse @ (add @ a @ b)))
% 34.36/5.54 | ~ (defined @ (additive_inverse @ b)))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl11990, zip_derived_cl26])).
% 34.36/5.54 thf(zip_derived_cl11992, plain,
% 34.36/5.54 ((~ (defined @ b)
% 34.36/5.54 | ~ (sum @ (add @ (additive_inverse @ a) @ additive_identity) @
% 34.36/5.54 (additive_inverse @ b) @ (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl14, zip_derived_cl11991])).
% 34.36/5.54 thf(b_is_defined, axiom, (defined @ b)).
% 34.36/5.54 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 34.36/5.54 inference('cnf', [status(esa)], [b_is_defined])).
% 34.36/5.54 thf(zip_derived_cl11993, plain,
% 34.36/5.54 (~ (sum @ (add @ (additive_inverse @ a) @ additive_identity) @
% 34.36/5.54 (additive_inverse @ b) @ (additive_inverse @ (add @ a @ b)))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl11992, zip_derived_cl27])).
% 34.36/5.54 thf(zip_derived_cl18, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 34.36/5.54 | ~ (defined @ X0)
% 34.36/5.54 | ~ (defined @ X1))),
% 34.36/5.54 inference('cnf', [status(esa)], [totality_of_addition])).
% 34.36/5.54 thf(associativity_addition_2, axiom,
% 34.36/5.54 (( sum @ U @ Z @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 34.36/5.54 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ X @ V @ W ) ))).
% 34.36/5.54 thf(zip_derived_cl1, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ X2)
% 34.36/5.54 | ~ (sum @ X3 @ X4 @ X0)
% 34.36/5.54 | ~ (sum @ X4 @ X1 @ X5)
% 34.36/5.54 | ~ (sum @ X3 @ X5 @ X2))),
% 34.36/5.54 inference('cnf', [status(esa)], [associativity_addition_2])).
% 34.36/5.54 thf(zip_derived_cl54, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | ~ (defined @ X1)
% 34.36/5.54 | (sum @ (add @ X1 @ X0) @ X3 @ X2)
% 34.36/5.54 | ~ (sum @ X0 @ X3 @ X4)
% 34.36/5.54 | ~ (sum @ X1 @ X4 @ X2))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 34.36/5.54 thf(zip_derived_cl12007, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ additive_identity)
% 34.36/5.54 | ~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (sum @ additive_identity @ (additive_inverse @ b) @ X0)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ a) @ X0 @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup+', [status(thm)],
% 34.36/5.54 [zip_derived_cl11993, zip_derived_cl54])).
% 34.36/5.54 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 34.36/5.54 thf(zip_derived_cl12008, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (sum @ additive_identity @ (additive_inverse @ b) @ X0)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ a) @ X0 @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl12007, zip_derived_cl13])).
% 34.36/5.54 thf(zip_derived_cl12054, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ a)
% 34.36/5.54 | ~ (sum @ additive_identity @ (additive_inverse @ b) @ X0)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ a) @ X0 @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl14, zip_derived_cl12008])).
% 34.36/5.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 34.36/5.54 inference('cnf', [status(esa)], [a_is_defined])).
% 34.36/5.54 thf(zip_derived_cl12055, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (sum @ additive_identity @ (additive_inverse @ b) @ X0)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ a) @ X0 @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl12054, zip_derived_cl26])).
% 34.36/5.54 thf(zip_derived_cl12058, plain,
% 34.36/5.54 ((~ (defined @ (additive_inverse @ b))
% 34.36/5.54 | ~ (sum @ (additive_inverse @ a) @ (additive_inverse @ b) @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl12055])).
% 34.36/5.54 thf(zip_derived_cl12061, plain,
% 34.36/5.54 ((~ (defined @ b)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ a) @ (additive_inverse @ b) @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl14, zip_derived_cl12058])).
% 34.36/5.54 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 34.36/5.54 inference('cnf', [status(esa)], [b_is_defined])).
% 34.36/5.54 thf(zip_derived_cl12062, plain,
% 34.36/5.54 (~ (sum @ (additive_inverse @ a) @ (additive_inverse @ b) @
% 34.36/5.54 (additive_inverse @ (add @ a @ b)))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl12061, zip_derived_cl27])).
% 34.36/5.54 thf(zip_derived_cl2, plain,
% 34.36/5.54 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 34.36/5.54 thf(zip_derived_cl1, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ X2)
% 34.36/5.54 | ~ (sum @ X3 @ X4 @ X0)
% 34.36/5.54 | ~ (sum @ X4 @ X1 @ X5)
% 34.36/5.54 | ~ (sum @ X3 @ X5 @ X2))),
% 34.36/5.54 inference('cnf', [status(esa)], [associativity_addition_2])).
% 34.36/5.54 thf(zip_derived_cl46, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | (sum @ X0 @ X2 @ X1)
% 34.36/5.54 | ~ (sum @ X0 @ X2 @ X3)
% 34.36/5.54 | ~ (sum @ additive_identity @ X3 @ X1))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 34.36/5.54 thf(zip_derived_cl12073, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (sum @ (additive_inverse @ a) @ (additive_inverse @ b) @ X0)
% 34.36/5.54 | ~ (sum @ additive_identity @ X0 @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup+', [status(thm)],
% 34.36/5.54 [zip_derived_cl12062, zip_derived_cl46])).
% 34.36/5.54 thf(zip_derived_cl12407, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ a)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ a) @ (additive_inverse @ b) @ X0)
% 34.36/5.54 | ~ (sum @ additive_identity @ X0 @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl14, zip_derived_cl12073])).
% 34.36/5.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 34.36/5.54 inference('cnf', [status(esa)], [a_is_defined])).
% 34.36/5.54 thf(zip_derived_cl12408, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (sum @ (additive_inverse @ a) @ (additive_inverse @ b) @ X0)
% 34.36/5.54 | ~ (sum @ additive_identity @ X0 @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl12407, zip_derived_cl26])).
% 34.36/5.54 thf(zip_derived_cl12409, plain,
% 34.36/5.54 ((~ (defined @ (additive_inverse @ b))
% 34.36/5.54 | ~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (sum @ additive_identity @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl18, zip_derived_cl12408])).
% 34.36/5.54 thf(zip_derived_cl15727, plain,
% 34.36/5.54 ((~ (defined @ b)
% 34.36/5.54 | ~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (sum @ additive_identity @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl14, zip_derived_cl12409])).
% 34.36/5.54 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 34.36/5.54 inference('cnf', [status(esa)], [b_is_defined])).
% 34.36/5.54 thf(zip_derived_cl15728, plain,
% 34.36/5.54 ((~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (sum @ additive_identity @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl15727, zip_derived_cl27])).
% 34.36/5.54 thf(zip_derived_cl15729, plain,
% 34.36/5.54 ((~ (defined @ a)
% 34.36/5.54 | ~ (sum @ additive_identity @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 (additive_inverse @ (add @ a @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl14, zip_derived_cl15728])).
% 34.36/5.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 34.36/5.54 inference('cnf', [status(esa)], [a_is_defined])).
% 34.36/5.54 thf(zip_derived_cl15730, plain,
% 34.36/5.54 (~ (sum @ additive_identity @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 (additive_inverse @ (add @ a @ b)))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl15729, zip_derived_cl26])).
% 34.36/5.54 thf(zip_derived_cl33, plain,
% 34.36/5.54 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 34.36/5.54 thf(zip_derived_cl3, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 34.36/5.54 | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 34.36/5.54 thf(zip_derived_cl1, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ X2)
% 34.36/5.54 | ~ (sum @ X3 @ X4 @ X0)
% 34.36/5.54 | ~ (sum @ X4 @ X1 @ X5)
% 34.36/5.54 | ~ (sum @ X3 @ X5 @ X2))),
% 34.36/5.54 inference('cnf', [status(esa)], [associativity_addition_2])).
% 34.36/5.54 thf(zip_derived_cl47, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | (sum @ additive_identity @ X2 @ X1)
% 34.36/5.54 | ~ (sum @ X0 @ X2 @ X3)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 34.36/5.54 thf(zip_derived_cl670, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i]:
% 34.36/5.54 (~ (defined @ (additive_inverse @ X0))
% 34.36/5.54 | ~ (defined @ X0)
% 34.36/5.54 | (sum @ additive_identity @ X1 @ (additive_inverse @ X0))
% 34.36/5.54 | ~ (sum @ X0 @ X1 @ additive_identity))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl47])).
% 34.36/5.54 thf(zip_derived_cl14, plain,
% 34.36/5.54 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 34.36/5.54 thf(zip_derived_cl13585, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i]:
% 34.36/5.54 (~ (sum @ X0 @ X1 @ additive_identity)
% 34.36/5.54 | (sum @ additive_identity @ X1 @ (additive_inverse @ X0))
% 34.36/5.54 | ~ (defined @ X0))),
% 34.36/5.54 inference('clc', [status(thm)], [zip_derived_cl670, zip_derived_cl14])).
% 34.36/5.54 thf(zip_derived_cl15749, plain,
% 34.36/5.54 ((~ (sum @ (add @ a @ b) @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 additive_identity)
% 34.36/5.54 | ~ (defined @ (add @ a @ b)))),
% 34.36/5.54 inference('s_sup+', [status(thm)],
% 34.36/5.54 [zip_derived_cl15730, zip_derived_cl13585])).
% 34.36/5.54 thf(zip_derived_cl15758, plain,
% 34.36/5.54 ((~ (defined @ b)
% 34.36/5.54 | ~ (defined @ a)
% 34.36/5.54 | ~ (sum @ (add @ a @ b) @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 additive_identity))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl12, zip_derived_cl15749])).
% 34.36/5.54 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 34.36/5.54 inference('cnf', [status(esa)], [b_is_defined])).
% 34.36/5.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 34.36/5.54 inference('cnf', [status(esa)], [a_is_defined])).
% 34.36/5.54 thf(zip_derived_cl15759, plain,
% 34.36/5.54 (~ (sum @ (add @ a @ b) @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 additive_identity)),
% 34.36/5.54 inference('demod', [status(thm)],
% 34.36/5.54 [zip_derived_cl15758, zip_derived_cl27, zip_derived_cl26])).
% 34.36/5.54 thf(zip_derived_cl54, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | ~ (defined @ X1)
% 34.36/5.54 | (sum @ (add @ X1 @ X0) @ X3 @ X2)
% 34.36/5.54 | ~ (sum @ X0 @ X3 @ X4)
% 34.36/5.54 | ~ (sum @ X1 @ X4 @ X2))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 34.36/5.54 thf(zip_derived_cl15776, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ b)
% 34.36/5.54 | ~ (defined @ a)
% 34.36/5.54 | ~ (sum @ b @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @ X0)
% 34.36/5.54 | ~ (sum @ a @ X0 @ additive_identity))),
% 34.36/5.54 inference('s_sup+', [status(thm)],
% 34.36/5.54 [zip_derived_cl15759, zip_derived_cl54])).
% 34.36/5.54 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 34.36/5.54 inference('cnf', [status(esa)], [b_is_defined])).
% 34.36/5.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 34.36/5.54 inference('cnf', [status(esa)], [a_is_defined])).
% 34.36/5.54 thf(zip_derived_cl15780, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (sum @ b @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @ X0)
% 34.36/5.54 | ~ (sum @ a @ X0 @ additive_identity))),
% 34.36/5.54 inference('demod', [status(thm)],
% 34.36/5.54 [zip_derived_cl15776, zip_derived_cl27, zip_derived_cl26])).
% 34.36/5.54 thf(zip_derived_cl15828, plain,
% 34.36/5.54 ((~ (defined @ a)
% 34.36/5.54 | ~ (sum @ b @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 (additive_inverse @ a)))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl34, zip_derived_cl15780])).
% 34.36/5.54 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 34.36/5.54 inference('cnf', [status(esa)], [a_is_defined])).
% 34.36/5.54 thf(zip_derived_cl15829, plain,
% 34.36/5.54 (~ (sum @ b @ (add @ (additive_inverse @ a) @ (additive_inverse @ b)) @
% 34.36/5.54 (additive_inverse @ a))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl15828, zip_derived_cl26])).
% 34.36/5.54 thf(zip_derived_cl2, plain,
% 34.36/5.54 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 34.36/5.54 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 34.36/5.54 thf(zip_derived_cl34, plain,
% 34.36/5.54 (![X0 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 34.36/5.54 thf(zip_derived_cl0, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 34.36/5.54 ( (sum @ X0 @ X1 @ X2)
% 34.36/5.54 | ~ (sum @ X0 @ X3 @ X4)
% 34.36/5.54 | ~ (sum @ X3 @ X5 @ X1)
% 34.36/5.54 | ~ (sum @ X4 @ X5 @ X2))),
% 34.36/5.54 inference('cnf', [status(esa)], [associativity_addition_1])).
% 34.36/5.54 thf(zip_derived_cl40, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | (sum @ X0 @ X2 @ X1)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X2)
% 34.36/5.54 | ~ (sum @ additive_identity @ X3 @ X1))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl0])).
% 34.36/5.54 thf(zip_derived_cl411, plain,
% 34.36/5.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.36/5.54 (~ (defined @ X0)
% 34.36/5.54 | ~ (defined @ X1)
% 34.36/5.54 | (sum @ X1 @ X2 @ X0)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ X1) @ X0 @ X2))),
% 34.36/5.54 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl40])).
% 34.36/5.54 thf(zip_derived_cl15842, plain,
% 34.36/5.54 ((~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (defined @ b)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ b) @ (additive_inverse @ a) @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b))))),
% 34.36/5.54 inference('s_sup+', [status(thm)],
% 34.36/5.54 [zip_derived_cl15829, zip_derived_cl411])).
% 34.36/5.54 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 34.36/5.54 inference('cnf', [status(esa)], [b_is_defined])).
% 34.36/5.54 thf(zip_derived_cl15849, plain,
% 34.36/5.54 ((~ (defined @ (additive_inverse @ a))
% 34.36/5.54 | ~ (sum @ (additive_inverse @ b) @ (additive_inverse @ a) @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b))))),
% 34.36/5.54 inference('demod', [status(thm)], [zip_derived_cl15842, zip_derived_cl27])).
% 34.36/5.54 thf(zip_derived_cl15865, plain,
% 34.36/5.54 ((~ (defined @ a)
% 34.36/5.54 | ~ (sum @ (additive_inverse @ b) @ (additive_inverse @ a) @
% 34.36/5.54 (add @ (additive_inverse @ a) @ (additive_inverse @ b))))),
% 34.36/5.54 inference('s_sup-', [status(thm)],
% 34.36/5.54 [zip_derived_cl14, zip_derived_cl15849])).
% 34.36/5.55 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 34.36/5.55 inference('cnf', [status(esa)], [a_is_defined])).
% 34.36/5.55 thf(zip_derived_cl15866, plain,
% 34.36/5.55 (~ (sum @ (additive_inverse @ b) @ (additive_inverse @ a) @
% 34.36/5.55 (add @ (additive_inverse @ a) @ (additive_inverse @ b)))),
% 34.36/5.55 inference('demod', [status(thm)], [zip_derived_cl15865, zip_derived_cl26])).
% 34.36/5.55 thf(zip_derived_cl18, plain,
% 34.36/5.55 (![X0 : $i, X1 : $i]:
% 34.36/5.55 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 34.36/5.55 | ~ (defined @ X0)
% 34.36/5.55 | ~ (defined @ X1))),
% 34.36/5.55 inference('cnf', [status(esa)], [totality_of_addition])).
% 34.36/5.55 thf(zip_derived_cl4, plain,
% 34.36/5.55 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.36/5.55 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 34.36/5.55 inference('cnf', [status(esa)], [commutativity_addition])).
% 34.36/5.55 thf(zip_derived_cl55, plain,
% 34.36/5.55 (![X0 : $i, X1 : $i]:
% 34.36/5.55 (~ (defined @ X0)
% 34.36/5.55 | ~ (defined @ X1)
% 34.36/5.55 | (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 34.36/5.55 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 34.36/5.55 thf(zip_derived_cl15880, plain,
% 34.36/5.55 ((~ (defined @ (additive_inverse @ b))
% 34.36/5.55 | ~ (defined @ (additive_inverse @ a)))),
% 34.36/5.55 inference('s_sup+', [status(thm)],
% 34.36/5.55 [zip_derived_cl15866, zip_derived_cl55])).
% 34.36/5.55 thf(zip_derived_cl15932, plain,
% 34.36/5.55 ((~ (defined @ b) | ~ (defined @ (additive_inverse @ a)))),
% 34.36/5.55 inference('s_sup-', [status(thm)],
% 34.36/5.55 [zip_derived_cl14, zip_derived_cl15880])).
% 34.36/5.55 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 34.36/5.55 inference('cnf', [status(esa)], [b_is_defined])).
% 34.36/5.55 thf(zip_derived_cl15933, plain, (~ (defined @ (additive_inverse @ a))),
% 34.36/5.55 inference('demod', [status(thm)], [zip_derived_cl15932, zip_derived_cl27])).
% 34.36/5.55 thf(zip_derived_cl15934, plain, (~ (defined @ a)),
% 34.36/5.55 inference('s_sup-', [status(thm)],
% 34.36/5.55 [zip_derived_cl14, zip_derived_cl15933])).
% 34.36/5.55 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 34.36/5.55 inference('cnf', [status(esa)], [a_is_defined])).
% 34.36/5.55 thf(zip_derived_cl15935, plain, ($false),
% 34.36/5.55 inference('demod', [status(thm)], [zip_derived_cl15934, zip_derived_cl26])).
% 34.36/5.55
% 34.36/5.55 % SZS output end Refutation
% 34.36/5.55
% 34.36/5.55
% 34.36/5.55 % Terminating...
% 34.86/5.70 % Runner terminated.
% 34.89/5.70 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------