TSTP Solution File: FLD061-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD061-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.MIS73jTTaE true
% Computer : n003.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 22:39:34 EDT 2023
% Result : Unsatisfiable 106.00s 15.86s
% Output : Refutation 106.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD061-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.MIS73jTTaE true
% 0.13/0.34 % Computer : n003.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 23:19:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.19/0.64 % Total configuration time : 435
% 0.19/0.64 % Estimated wc time : 1092
% 0.19/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.19/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.19/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.19/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.19/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.83/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 106.00/15.86 % Solved by fo/fo13.sh.
% 106.00/15.86 % done 7835 iterations in 15.079s
% 106.00/15.86 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 106.00/15.86 % SZS output start Refutation
% 106.00/15.86 thf(sum_type, type, sum: $i > $i > $i > $o).
% 106.00/15.86 thf(b_type, type, b: $i).
% 106.00/15.86 thf(a_type, type, a: $i).
% 106.00/15.86 thf(add_type, type, add: $i > $i > $i).
% 106.00/15.86 thf(v_type, type, v: $i).
% 106.00/15.86 thf(d_type, type, d: $i).
% 106.00/15.86 thf(additive_identity_type, type, additive_identity: $i).
% 106.00/15.86 thf(c_type, type, c: $i).
% 106.00/15.86 thf(u_type, type, u: $i).
% 106.00/15.86 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 106.00/15.86 thf(defined_type, type, defined: $i > $o).
% 106.00/15.86 thf(not_less_or_equal_11, conjecture, (less_or_equal @ u @ v)).
% 106.00/15.86 thf(zf_stmt_0, negated_conjecture, (~( less_or_equal @ u @ v )),
% 106.00/15.86 inference('cnf.neg', [status(esa)], [not_less_or_equal_11])).
% 106.00/15.86 thf(zip_derived_cl36, plain, (~ (less_or_equal @ u @ v)),
% 106.00/15.86 inference('cnf', [status(esa)], [zf_stmt_0])).
% 106.00/15.86 thf(less_or_equal_7, conjecture, (~( less_or_equal @ a @ b ))).
% 106.00/15.86 thf(zf_stmt_1, negated_conjecture, (less_or_equal @ a @ b),
% 106.00/15.86 inference('cnf.neg', [status(esa)], [less_or_equal_7])).
% 106.00/15.86 thf(zip_derived_cl32, plain, ( (less_or_equal @ a @ b)),
% 106.00/15.86 inference('cnf', [status(esa)], [zf_stmt_1])).
% 106.00/15.86 thf(totality_of_addition, axiom,
% 106.00/15.86 (( sum @ X @ Y @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 106.00/15.86 ( ~( defined @ Y ) ))).
% 106.00/15.86 thf(zip_derived_cl18, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 106.00/15.86 | ~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)], [totality_of_addition])).
% 106.00/15.86 thf(sum_10, conjecture, (~( sum @ d @ b @ v ))).
% 106.00/15.86 thf(zf_stmt_2, negated_conjecture, (sum @ d @ b @ v),
% 106.00/15.86 inference('cnf.neg', [status(esa)], [sum_10])).
% 106.00/15.86 thf(zip_derived_cl35, plain, ( (sum @ d @ b @ v)),
% 106.00/15.86 inference('cnf', [status(esa)], [zf_stmt_2])).
% 106.00/15.86 thf(commutativity_addition, axiom,
% 106.00/15.86 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 106.00/15.86 thf(zip_derived_cl4, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [commutativity_addition])).
% 106.00/15.86 thf(zip_derived_cl50, plain, ( (sum @ b @ d @ v)),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl4])).
% 106.00/15.86 thf(existence_of_identity_addition, axiom,
% 106.00/15.86 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 106.00/15.86 thf(zip_derived_cl2, plain,
% 106.00/15.86 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 106.00/15.86 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 106.00/15.86 thf(associativity_addition_1, axiom,
% 106.00/15.86 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 106.00/15.86 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 106.00/15.86 thf(zip_derived_cl0, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2)
% 106.00/15.86 | ~ (sum @ X0 @ X3 @ X4)
% 106.00/15.86 | ~ (sum @ X3 @ X5 @ X1)
% 106.00/15.86 | ~ (sum @ X4 @ X5 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [associativity_addition_1])).
% 106.00/15.86 thf(zip_derived_cl41, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | (sum @ additive_identity @ X2 @ X1)
% 106.00/15.86 | ~ (sum @ X0 @ X3 @ X2)
% 106.00/15.86 | ~ (sum @ X0 @ X3 @ X1))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 106.00/15.86 thf(zip_derived_cl344, plain,
% 106.00/15.86 (![X0 : $i]:
% 106.00/15.86 (~ (defined @ b)
% 106.00/15.86 | (sum @ additive_identity @ v @ X0)
% 106.00/15.86 | ~ (sum @ b @ d @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl41])).
% 106.00/15.86 thf(b_is_defined, axiom, (defined @ b)).
% 106.00/15.86 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 106.00/15.86 inference('cnf', [status(esa)], [b_is_defined])).
% 106.00/15.86 thf(zip_derived_cl361, plain,
% 106.00/15.86 (![X0 : $i]: ( (sum @ additive_identity @ v @ X0) | ~ (sum @ b @ d @ X0))),
% 106.00/15.86 inference('demod', [status(thm)], [zip_derived_cl344, zip_derived_cl27])).
% 106.00/15.86 thf(zip_derived_cl556, plain,
% 106.00/15.86 ((~ (defined @ d)
% 106.00/15.86 | ~ (defined @ b)
% 106.00/15.86 | (sum @ additive_identity @ v @ (add @ b @ d)))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl361])).
% 106.00/15.86 thf(d_is_defined, axiom, (defined @ d)).
% 106.00/15.86 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 106.00/15.86 inference('cnf', [status(esa)], [d_is_defined])).
% 106.00/15.86 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 106.00/15.86 inference('cnf', [status(esa)], [b_is_defined])).
% 106.00/15.86 thf(zip_derived_cl559, plain,
% 106.00/15.86 ( (sum @ additive_identity @ v @ (add @ b @ d))),
% 106.00/15.86 inference('demod', [status(thm)],
% 106.00/15.86 [zip_derived_cl556, zip_derived_cl29, zip_derived_cl27])).
% 106.00/15.86 thf(zip_derived_cl4, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [commutativity_addition])).
% 106.00/15.86 thf(zip_derived_cl603, plain,
% 106.00/15.86 ( (sum @ v @ additive_identity @ (add @ b @ d))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl559, zip_derived_cl4])).
% 106.00/15.86 thf(zip_derived_cl2, plain,
% 106.00/15.86 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 106.00/15.86 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 106.00/15.86 thf(zip_derived_cl4, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [commutativity_addition])).
% 106.00/15.86 thf(zip_derived_cl47, plain,
% 106.00/15.86 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 106.00/15.86 thf(zip_derived_cl35, plain, ( (sum @ d @ b @ v)),
% 106.00/15.86 inference('cnf', [status(esa)], [zf_stmt_2])).
% 106.00/15.86 thf(zip_derived_cl0, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2)
% 106.00/15.86 | ~ (sum @ X0 @ X3 @ X4)
% 106.00/15.86 | ~ (sum @ X3 @ X5 @ X1)
% 106.00/15.86 | ~ (sum @ X4 @ X5 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [associativity_addition_1])).
% 106.00/15.86 thf(zip_derived_cl38, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ d @ X1 @ X0) | ~ (sum @ b @ X2 @ X1) | ~ (sum @ v @ X2 @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 106.00/15.86 thf(zip_derived_cl88, plain,
% 106.00/15.86 (![X0 : $i]:
% 106.00/15.86 (~ (defined @ b)
% 106.00/15.86 | (sum @ d @ b @ X0)
% 106.00/15.86 | ~ (sum @ v @ additive_identity @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl38])).
% 106.00/15.86 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 106.00/15.86 inference('cnf', [status(esa)], [b_is_defined])).
% 106.00/15.86 thf(zip_derived_cl91, plain,
% 106.00/15.86 (![X0 : $i]: ( (sum @ d @ b @ X0) | ~ (sum @ v @ additive_identity @ X0))),
% 106.00/15.86 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl27])).
% 106.00/15.86 thf(zip_derived_cl654, plain, ( (sum @ d @ b @ (add @ b @ d))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl603, zip_derived_cl91])).
% 106.00/15.86 thf(zip_derived_cl4, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [commutativity_addition])).
% 106.00/15.86 thf(zip_derived_cl669, plain, ( (sum @ b @ d @ (add @ b @ d))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl654, zip_derived_cl4])).
% 106.00/15.86 thf(zip_derived_cl18, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 106.00/15.86 | ~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)], [totality_of_addition])).
% 106.00/15.86 thf(compatibility_of_order_relation_and_addition, axiom,
% 106.00/15.86 (( less_or_equal @ U @ V ) | ( ~( less_or_equal @ X @ Y ) ) |
% 106.00/15.86 ( ~( sum @ X @ Z @ U ) ) | ( ~( sum @ Y @ Z @ V ) ))).
% 106.00/15.86 thf(zip_derived_cl23, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.00/15.86 ( (less_or_equal @ X0 @ X1)
% 106.00/15.86 | ~ (less_or_equal @ X2 @ X3)
% 106.00/15.86 | ~ (sum @ X2 @ X4 @ X0)
% 106.00/15.86 | ~ (sum @ X3 @ X4 @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)],
% 106.00/15.86 [compatibility_of_order_relation_and_addition])).
% 106.00/15.86 thf(zip_derived_cl101, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1)
% 106.00/15.86 | (less_or_equal @ (add @ X1 @ X0) @ X2)
% 106.00/15.86 | ~ (less_or_equal @ X1 @ X3)
% 106.00/15.86 | ~ (sum @ X3 @ X0 @ X2))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl23])).
% 106.00/15.86 thf(zip_derived_cl1569, plain,
% 106.00/15.86 (![X0 : $i]:
% 106.00/15.86 (~ (defined @ d)
% 106.00/15.86 | ~ (defined @ X0)
% 106.00/15.86 | (less_or_equal @ (add @ X0 @ d) @ (add @ b @ d))
% 106.00/15.86 | ~ (less_or_equal @ X0 @ b))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl669, zip_derived_cl101])).
% 106.00/15.86 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 106.00/15.86 inference('cnf', [status(esa)], [d_is_defined])).
% 106.00/15.86 thf(zip_derived_cl1619, plain,
% 106.00/15.86 (![X0 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | (less_or_equal @ (add @ X0 @ d) @ (add @ b @ d))
% 106.00/15.86 | ~ (less_or_equal @ X0 @ b))),
% 106.00/15.86 inference('demod', [status(thm)], [zip_derived_cl1569, zip_derived_cl29])).
% 106.00/15.86 thf(zip_derived_cl86165, plain,
% 106.00/15.86 ((~ (defined @ a) | (less_or_equal @ (add @ a @ d) @ (add @ b @ d)))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl1619])).
% 106.00/15.86 thf(a_is_defined, axiom, (defined @ a)).
% 106.00/15.86 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 106.00/15.86 inference('cnf', [status(esa)], [a_is_defined])).
% 106.00/15.86 thf(zip_derived_cl86220, plain,
% 106.00/15.86 ( (less_or_equal @ (add @ a @ d) @ (add @ b @ d))),
% 106.00/15.86 inference('demod', [status(thm)], [zip_derived_cl86165, zip_derived_cl26])).
% 106.00/15.86 thf(zip_derived_cl18, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 106.00/15.86 | ~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)], [totality_of_addition])).
% 106.00/15.86 thf(zip_derived_cl4, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [commutativity_addition])).
% 106.00/15.86 thf(zip_derived_cl100, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1)
% 106.00/15.86 | (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 106.00/15.86 thf(less_or_equal_8, conjecture, (~( less_or_equal @ c @ d ))).
% 106.00/15.86 thf(zf_stmt_3, negated_conjecture, (less_or_equal @ c @ d),
% 106.00/15.86 inference('cnf.neg', [status(esa)], [less_or_equal_8])).
% 106.00/15.86 thf(zip_derived_cl33, plain, ( (less_or_equal @ c @ d)),
% 106.00/15.86 inference('cnf', [status(esa)], [zf_stmt_3])).
% 106.00/15.86 thf(sum_9, conjecture, (~( sum @ a @ c @ u ))).
% 106.00/15.86 thf(zf_stmt_4, negated_conjecture, (sum @ a @ c @ u),
% 106.00/15.86 inference('cnf.neg', [status(esa)], [sum_9])).
% 106.00/15.86 thf(zip_derived_cl34, plain, ( (sum @ a @ c @ u)),
% 106.00/15.86 inference('cnf', [status(esa)], [zf_stmt_4])).
% 106.00/15.86 thf(zip_derived_cl4, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [commutativity_addition])).
% 106.00/15.86 thf(zip_derived_cl49, plain, ( (sum @ c @ a @ u)),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl4])).
% 106.00/15.86 thf(zip_derived_cl23, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.00/15.86 ( (less_or_equal @ X0 @ X1)
% 106.00/15.86 | ~ (less_or_equal @ X2 @ X3)
% 106.00/15.86 | ~ (sum @ X2 @ X4 @ X0)
% 106.00/15.86 | ~ (sum @ X3 @ X4 @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)],
% 106.00/15.86 [compatibility_of_order_relation_and_addition])).
% 106.00/15.86 thf(zip_derived_cl84, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 ( (less_or_equal @ u @ X0)
% 106.00/15.86 | ~ (less_or_equal @ c @ X1)
% 106.00/15.86 | ~ (sum @ X1 @ a @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl23])).
% 106.00/15.86 thf(zip_derived_cl87, plain,
% 106.00/15.86 (![X0 : $i]: ( (less_or_equal @ u @ X0) | ~ (sum @ d @ a @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl84])).
% 106.00/15.86 thf(zip_derived_cl1442, plain,
% 106.00/15.86 ((~ (defined @ a)
% 106.00/15.86 | ~ (defined @ d)
% 106.00/15.86 | (less_or_equal @ u @ (add @ a @ d)))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl87])).
% 106.00/15.86 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 106.00/15.86 inference('cnf', [status(esa)], [a_is_defined])).
% 106.00/15.86 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 106.00/15.86 inference('cnf', [status(esa)], [d_is_defined])).
% 106.00/15.86 thf(zip_derived_cl1512, plain, ( (less_or_equal @ u @ (add @ a @ d))),
% 106.00/15.86 inference('demod', [status(thm)],
% 106.00/15.86 [zip_derived_cl1442, zip_derived_cl26, zip_derived_cl29])).
% 106.00/15.86 thf(transitivity_of_order_relation, axiom,
% 106.00/15.86 (( less_or_equal @ X @ Z ) | ( ~( less_or_equal @ X @ Y ) ) |
% 106.00/15.86 ( ~( less_or_equal @ Y @ Z ) ))).
% 106.00/15.86 thf(zip_derived_cl21, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (less_or_equal @ X0 @ X1)
% 106.00/15.86 | ~ (less_or_equal @ X0 @ X2)
% 106.00/15.86 | ~ (less_or_equal @ X2 @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 106.00/15.86 thf(zip_derived_cl1534, plain,
% 106.00/15.86 (![X0 : $i]:
% 106.00/15.86 ( (less_or_equal @ u @ X0) | ~ (less_or_equal @ (add @ a @ d) @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl1512, zip_derived_cl21])).
% 106.00/15.86 thf(zip_derived_cl86344, plain, ( (less_or_equal @ u @ (add @ b @ d))),
% 106.00/15.86 inference('s_sup-', [status(thm)],
% 106.00/15.86 [zip_derived_cl86220, zip_derived_cl1534])).
% 106.00/15.86 thf(zip_derived_cl654, plain, ( (sum @ d @ b @ (add @ b @ d))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl603, zip_derived_cl91])).
% 106.00/15.86 thf(zip_derived_cl18, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 106.00/15.86 | ~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)], [totality_of_addition])).
% 106.00/15.86 thf(zip_derived_cl47, plain,
% 106.00/15.86 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 106.00/15.86 thf(zip_derived_cl18, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 106.00/15.86 | ~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)], [totality_of_addition])).
% 106.00/15.86 thf(zip_derived_cl38, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ d @ X1 @ X0) | ~ (sum @ b @ X2 @ X1) | ~ (sum @ v @ X2 @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 106.00/15.86 thf(zip_derived_cl102, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ b)
% 106.00/15.86 | (sum @ d @ (add @ b @ X0) @ X1)
% 106.00/15.86 | ~ (sum @ v @ X0 @ X1))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl38])).
% 106.00/15.86 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 106.00/15.86 inference('cnf', [status(esa)], [b_is_defined])).
% 106.00/15.86 thf(zip_derived_cl109, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | (sum @ d @ (add @ b @ X0) @ X1)
% 106.00/15.86 | ~ (sum @ v @ X0 @ X1))),
% 106.00/15.86 inference('demod', [status(thm)], [zip_derived_cl102, zip_derived_cl27])).
% 106.00/15.86 thf(zip_derived_cl1666, plain,
% 106.00/15.86 ((~ (defined @ v)
% 106.00/15.86 | ~ (defined @ additive_identity)
% 106.00/15.86 | (sum @ d @ (add @ b @ additive_identity) @ v))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl109])).
% 106.00/15.86 thf(v_is_defined, axiom, (defined @ v)).
% 106.00/15.86 thf(zip_derived_cl31, plain, ( (defined @ v)),
% 106.00/15.86 inference('cnf', [status(esa)], [v_is_defined])).
% 106.00/15.86 thf(well_definedness_of_additive_identity, axiom,
% 106.00/15.86 (defined @ additive_identity)).
% 106.00/15.86 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 106.00/15.86 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 106.00/15.86 thf(zip_derived_cl1676, plain,
% 106.00/15.86 ( (sum @ d @ (add @ b @ additive_identity) @ v)),
% 106.00/15.86 inference('demod', [status(thm)],
% 106.00/15.86 [zip_derived_cl1666, zip_derived_cl31, zip_derived_cl13])).
% 106.00/15.86 thf(zip_derived_cl4, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [commutativity_addition])).
% 106.00/15.86 thf(zip_derived_cl1827, plain,
% 106.00/15.86 ( (sum @ (add @ b @ additive_identity) @ d @ v)),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl1676, zip_derived_cl4])).
% 106.00/15.86 thf(zip_derived_cl18, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ (add @ X0 @ X1))
% 106.00/15.86 | ~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)], [totality_of_addition])).
% 106.00/15.86 thf(zip_derived_cl0, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2)
% 106.00/15.86 | ~ (sum @ X0 @ X3 @ X4)
% 106.00/15.86 | ~ (sum @ X3 @ X5 @ X1)
% 106.00/15.86 | ~ (sum @ X4 @ X5 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [associativity_addition_1])).
% 106.00/15.86 thf(zip_derived_cl98, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1)
% 106.00/15.86 | (sum @ X1 @ X3 @ X2)
% 106.00/15.86 | ~ (sum @ X0 @ X4 @ X3)
% 106.00/15.86 | ~ (sum @ (add @ X1 @ X0) @ X4 @ X2))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl0])).
% 106.00/15.86 thf(zip_derived_cl1936, plain,
% 106.00/15.86 (![X0 : $i]:
% 106.00/15.86 (~ (defined @ additive_identity)
% 106.00/15.86 | ~ (defined @ b)
% 106.00/15.86 | (sum @ b @ X0 @ v)
% 106.00/15.86 | ~ (sum @ additive_identity @ d @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl1827, zip_derived_cl98])).
% 106.00/15.86 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 106.00/15.86 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 106.00/15.86 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 106.00/15.86 inference('cnf', [status(esa)], [b_is_defined])).
% 106.00/15.86 thf(zip_derived_cl1938, plain,
% 106.00/15.86 (![X0 : $i]: ( (sum @ b @ X0 @ v) | ~ (sum @ additive_identity @ d @ X0))),
% 106.00/15.86 inference('demod', [status(thm)],
% 106.00/15.86 [zip_derived_cl1936, zip_derived_cl13, zip_derived_cl27])).
% 106.00/15.86 thf(zip_derived_cl1967, plain,
% 106.00/15.86 ((~ (defined @ d)
% 106.00/15.86 | ~ (defined @ additive_identity)
% 106.00/15.86 | (sum @ b @ (add @ additive_identity @ d) @ v))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl1938])).
% 106.00/15.86 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 106.00/15.86 inference('cnf', [status(esa)], [d_is_defined])).
% 106.00/15.86 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 106.00/15.86 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 106.00/15.86 thf(zip_derived_cl1970, plain,
% 106.00/15.86 ( (sum @ b @ (add @ additive_identity @ d) @ v)),
% 106.00/15.86 inference('demod', [status(thm)],
% 106.00/15.86 [zip_derived_cl1967, zip_derived_cl29, zip_derived_cl13])).
% 106.00/15.86 thf(zip_derived_cl4, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [commutativity_addition])).
% 106.00/15.86 thf(zip_derived_cl2052, plain,
% 106.00/15.86 ( (sum @ (add @ additive_identity @ d) @ b @ v)),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl1970, zip_derived_cl4])).
% 106.00/15.86 thf(zip_derived_cl98, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | ~ (defined @ X1)
% 106.00/15.86 | (sum @ X1 @ X3 @ X2)
% 106.00/15.86 | ~ (sum @ X0 @ X4 @ X3)
% 106.00/15.86 | ~ (sum @ (add @ X1 @ X0) @ X4 @ X2))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl0])).
% 106.00/15.86 thf(zip_derived_cl2152, plain,
% 106.00/15.86 (![X0 : $i]:
% 106.00/15.86 (~ (defined @ d)
% 106.00/15.86 | ~ (defined @ additive_identity)
% 106.00/15.86 | (sum @ additive_identity @ X0 @ v)
% 106.00/15.86 | ~ (sum @ d @ b @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl2052, zip_derived_cl98])).
% 106.00/15.86 thf(zip_derived_cl29, plain, ( (defined @ d)),
% 106.00/15.86 inference('cnf', [status(esa)], [d_is_defined])).
% 106.00/15.86 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 106.00/15.86 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 106.00/15.86 thf(zip_derived_cl2154, plain,
% 106.00/15.86 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ v) | ~ (sum @ d @ b @ X0))),
% 106.00/15.86 inference('demod', [status(thm)],
% 106.00/15.86 [zip_derived_cl2152, zip_derived_cl29, zip_derived_cl13])).
% 106.00/15.86 thf(zip_derived_cl2188, plain,
% 106.00/15.86 ( (sum @ additive_identity @ (add @ b @ d) @ v)),
% 106.00/15.86 inference('s_sup-', [status(thm)],
% 106.00/15.86 [zip_derived_cl654, zip_derived_cl2154])).
% 106.00/15.86 thf(zip_derived_cl4, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 106.00/15.86 inference('cnf', [status(esa)], [commutativity_addition])).
% 106.00/15.86 thf(zip_derived_cl2258, plain,
% 106.00/15.86 ( (sum @ (add @ b @ d) @ additive_identity @ v)),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl2188, zip_derived_cl4])).
% 106.00/15.86 thf(zip_derived_cl47, plain,
% 106.00/15.86 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 106.00/15.86 thf(zip_derived_cl23, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.00/15.86 ( (less_or_equal @ X0 @ X1)
% 106.00/15.86 | ~ (less_or_equal @ X2 @ X3)
% 106.00/15.86 | ~ (sum @ X2 @ X4 @ X0)
% 106.00/15.86 | ~ (sum @ X3 @ X4 @ X1))),
% 106.00/15.86 inference('cnf', [status(esa)],
% 106.00/15.86 [compatibility_of_order_relation_and_addition])).
% 106.00/15.86 thf(zip_derived_cl78, plain,
% 106.00/15.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | (less_or_equal @ X0 @ X1)
% 106.00/15.86 | ~ (less_or_equal @ X0 @ X2)
% 106.00/15.86 | ~ (sum @ X2 @ additive_identity @ X1))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl23])).
% 106.00/15.86 thf(zip_derived_cl2329, plain,
% 106.00/15.86 (![X0 : $i]:
% 106.00/15.86 (~ (defined @ X0)
% 106.00/15.86 | (less_or_equal @ X0 @ v)
% 106.00/15.86 | ~ (less_or_equal @ X0 @ (add @ b @ d)))),
% 106.00/15.86 inference('s_sup-', [status(thm)], [zip_derived_cl2258, zip_derived_cl78])).
% 106.00/15.86 thf(zip_derived_cl86481, plain,
% 106.00/15.86 ((~ (defined @ u) | (less_or_equal @ u @ v))),
% 106.00/15.86 inference('s_sup-', [status(thm)],
% 106.00/15.86 [zip_derived_cl86344, zip_derived_cl2329])).
% 106.00/15.86 thf(u_is_defined, axiom, (defined @ u)).
% 106.00/15.86 thf(zip_derived_cl30, plain, ( (defined @ u)),
% 106.00/15.86 inference('cnf', [status(esa)], [u_is_defined])).
% 106.00/15.86 thf(zip_derived_cl86503, plain, ( (less_or_equal @ u @ v)),
% 106.00/15.86 inference('demod', [status(thm)], [zip_derived_cl86481, zip_derived_cl30])).
% 106.00/15.86 thf(zip_derived_cl86504, plain, ($false),
% 106.00/15.86 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl86503])).
% 106.00/15.86
% 106.00/15.86 % SZS output end Refutation
% 106.00/15.86
% 106.00/15.86
% 106.00/15.86 % Terminating...
% 106.00/15.92 % Runner terminated.
% 106.00/15.93 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------