TSTP Solution File: FLD066-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD066-3 : 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.rdLO3FLpOR true
% Computer : n018.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 22:39:36 EDT 2023
% Result : Unsatisfiable 13.70s 2.49s
% Output : Refutation 13.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD066-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rdLO3FLpOR true
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Aug 28 00:39:01 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Running portfolio for 300 s
% 0.11/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.33 % Number of cores: 8
% 0.17/0.34 % Python version: Python 3.6.8
% 0.17/0.34 % Running in FO mode
% 0.18/0.59 % Total configuration time : 435
% 0.18/0.59 % Estimated wc time : 1092
% 0.18/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.18/0.61 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.18/0.65 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.18/0.65 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.18/0.65 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.18/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.18/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.18/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 13.70/2.49 % Solved by fo/fo13.sh.
% 13.70/2.49 % done 1604 iterations in 1.759s
% 13.70/2.49 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 13.70/2.49 % SZS output start Refutation
% 13.70/2.49 thf(sum_type, type, sum: $i > $i > $i > $o).
% 13.70/2.49 thf(b_type, type, b: $i).
% 13.70/2.49 thf(a_type, type, a: $i).
% 13.70/2.49 thf(u_type, type, u: $i).
% 13.70/2.49 thf(additive_identity_type, type, additive_identity: $i).
% 13.70/2.49 thf(c_type, type, c: $i).
% 13.70/2.49 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 13.70/2.49 thf(v_type, type, v: $i).
% 13.70/2.49 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 13.70/2.49 thf(defined_type, type, defined: $i > $o).
% 13.70/2.49 thf(not_less_or_equal_9, conjecture, (less_or_equal @ a @ b)).
% 13.70/2.49 thf(zf_stmt_0, negated_conjecture, (~( less_or_equal @ a @ b )),
% 13.70/2.49 inference('cnf.neg', [status(esa)], [not_less_or_equal_9])).
% 13.70/2.49 thf(zip_derived_cl34, plain, (~ (less_or_equal @ a @ b)),
% 13.70/2.49 inference('cnf', [status(esa)], [zf_stmt_0])).
% 13.70/2.49 thf(existence_of_identity_addition, axiom,
% 13.70/2.49 (( sum @ additive_identity @ X @ X ) | ( ~( defined @ X ) ))).
% 13.70/2.49 thf(zip_derived_cl2, plain,
% 13.70/2.49 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 13.70/2.49 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 13.70/2.49 thf(existence_of_inverse_addition, axiom,
% 13.70/2.49 (( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) |
% 13.70/2.49 ( ~( defined @ X ) ))).
% 13.70/2.49 thf(zip_derived_cl3, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 13.70/2.49 | ~ (defined @ X0))),
% 13.70/2.49 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 13.70/2.49 thf(commutativity_addition, axiom,
% 13.70/2.49 (( sum @ Y @ X @ Z ) | ( ~( sum @ X @ Y @ Z ) ))).
% 13.70/2.49 thf(zip_derived_cl4, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.70/2.49 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 13.70/2.49 inference('cnf', [status(esa)], [commutativity_addition])).
% 13.70/2.49 thf(zip_derived_cl56, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ X0)
% 13.70/2.49 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 13.70/2.49 thf(zip_derived_cl56, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ X0)
% 13.70/2.49 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 13.70/2.49 thf(sum_6, conjecture, (~( sum @ a @ c @ u ))).
% 13.70/2.49 thf(zf_stmt_1, negated_conjecture, (sum @ a @ c @ u),
% 13.70/2.49 inference('cnf.neg', [status(esa)], [sum_6])).
% 13.70/2.49 thf(zip_derived_cl31, plain, ( (sum @ a @ c @ u)),
% 13.70/2.49 inference('cnf', [status(esa)], [zf_stmt_1])).
% 13.70/2.49 thf(totality_of_order_relation, axiom,
% 13.70/2.49 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 13.70/2.49 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 13.70/2.49 thf(zip_derived_cl22, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 ( (less_or_equal @ X0 @ X1)
% 13.70/2.49 | (less_or_equal @ X1 @ X0)
% 13.70/2.49 | ~ (defined @ X0)
% 13.70/2.49 | ~ (defined @ X1))),
% 13.70/2.49 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 13.70/2.49 thf(zip_derived_cl136, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ X0) | ~ (defined @ X0) | (less_or_equal @ X0 @ X0))),
% 13.70/2.49 inference('eq_fact', [status(thm)], [zip_derived_cl22])).
% 13.70/2.49 thf(zip_derived_cl138, plain,
% 13.70/2.49 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 13.70/2.49 inference('simplify', [status(thm)], [zip_derived_cl136])).
% 13.70/2.49 thf(zip_derived_cl31, plain, ( (sum @ a @ c @ u)),
% 13.70/2.49 inference('cnf', [status(esa)], [zf_stmt_1])).
% 13.70/2.49 thf(compatibility_of_order_relation_and_addition, axiom,
% 13.70/2.49 (( less_or_equal @ U @ V ) | ( ~( less_or_equal @ X @ Y ) ) |
% 13.70/2.49 ( ~( sum @ X @ Z @ U ) ) | ( ~( sum @ Y @ Z @ V ) ))).
% 13.70/2.49 thf(zip_derived_cl23, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.70/2.49 ( (less_or_equal @ X0 @ X1)
% 13.70/2.49 | ~ (less_or_equal @ X2 @ X3)
% 13.70/2.49 | ~ (sum @ X2 @ X4 @ X0)
% 13.70/2.49 | ~ (sum @ X3 @ X4 @ X1))),
% 13.70/2.49 inference('cnf', [status(esa)],
% 13.70/2.49 [compatibility_of_order_relation_and_addition])).
% 13.70/2.49 thf(zip_derived_cl69, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 ( (less_or_equal @ u @ X0)
% 13.70/2.49 | ~ (less_or_equal @ a @ X1)
% 13.70/2.49 | ~ (sum @ X1 @ c @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl23])).
% 13.70/2.49 thf(zip_derived_cl165, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ a) | (less_or_equal @ u @ X0) | ~ (sum @ a @ c @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl138, zip_derived_cl69])).
% 13.70/2.49 thf(a_is_defined, axiom, (defined @ a)).
% 13.70/2.49 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 13.70/2.49 inference('cnf', [status(esa)], [a_is_defined])).
% 13.70/2.49 thf(zip_derived_cl171, plain,
% 13.70/2.49 (![X0 : $i]: ( (less_or_equal @ u @ X0) | ~ (sum @ a @ c @ X0))),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl165, zip_derived_cl26])).
% 13.70/2.49 thf(zip_derived_cl178, plain, ( (less_or_equal @ u @ u)),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl171])).
% 13.70/2.49 thf(antisymmetry_of_order_relation, axiom,
% 13.70/2.49 (( sum @ additive_identity @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 13.70/2.49 ( ~( less_or_equal @ Y @ X ) ))).
% 13.70/2.49 thf(zip_derived_cl20, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 ( (sum @ additive_identity @ X0 @ X1)
% 13.70/2.49 | ~ (less_or_equal @ X0 @ X1)
% 13.70/2.49 | ~ (less_or_equal @ X1 @ X0))),
% 13.70/2.49 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 13.70/2.49 thf(zip_derived_cl180, plain, ( (sum @ additive_identity @ u @ u)),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl178, zip_derived_cl20])).
% 13.70/2.49 thf(associativity_addition_1, axiom,
% 13.70/2.49 (( sum @ X @ V @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 13.70/2.49 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ U @ Z @ W ) ))).
% 13.70/2.49 thf(zip_derived_cl0, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.70/2.49 ( (sum @ X0 @ X1 @ X2)
% 13.70/2.49 | ~ (sum @ X0 @ X3 @ X4)
% 13.70/2.49 | ~ (sum @ X3 @ X5 @ X1)
% 13.70/2.49 | ~ (sum @ X4 @ X5 @ X2))),
% 13.70/2.49 inference('cnf', [status(esa)], [associativity_addition_1])).
% 13.70/2.49 thf(zip_derived_cl186, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.70/2.49 ( (sum @ additive_identity @ X1 @ X0)
% 13.70/2.49 | ~ (sum @ u @ X2 @ X1)
% 13.70/2.49 | ~ (sum @ u @ X2 @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl180, zip_derived_cl0])).
% 13.70/2.49 thf(zip_derived_cl1229, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ u)
% 13.70/2.49 | (sum @ additive_identity @ additive_identity @ X0)
% 13.70/2.49 | ~ (sum @ u @ (additive_inverse @ u) @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl186])).
% 13.70/2.49 thf(u_is_defined, axiom, (defined @ u)).
% 13.70/2.49 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 13.70/2.49 inference('cnf', [status(esa)], [u_is_defined])).
% 13.70/2.49 thf(zip_derived_cl1240, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 ( (sum @ additive_identity @ additive_identity @ X0)
% 13.70/2.49 | ~ (sum @ u @ (additive_inverse @ u) @ X0))),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl1229, zip_derived_cl29])).
% 13.70/2.49 thf(zip_derived_cl1242, plain,
% 13.70/2.49 ((~ (defined @ u)
% 13.70/2.49 | (sum @ additive_identity @ additive_identity @ additive_identity))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl1240])).
% 13.70/2.49 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 13.70/2.49 inference('cnf', [status(esa)], [u_is_defined])).
% 13.70/2.49 thf(zip_derived_cl1244, plain,
% 13.70/2.49 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl1242, zip_derived_cl29])).
% 13.70/2.49 thf(zip_derived_cl138, plain,
% 13.70/2.49 (![X0 : $i]: ( (less_or_equal @ X0 @ X0) | ~ (defined @ X0))),
% 13.70/2.49 inference('simplify', [status(thm)], [zip_derived_cl136])).
% 13.70/2.49 thf(zip_derived_cl1244, plain,
% 13.70/2.49 ( (sum @ additive_identity @ additive_identity @ additive_identity)),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl1242, zip_derived_cl29])).
% 13.70/2.49 thf(zip_derived_cl23, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.70/2.49 ( (less_or_equal @ X0 @ X1)
% 13.70/2.49 | ~ (less_or_equal @ X2 @ X3)
% 13.70/2.49 | ~ (sum @ X2 @ X4 @ X0)
% 13.70/2.49 | ~ (sum @ X3 @ X4 @ X1))),
% 13.70/2.49 inference('cnf', [status(esa)],
% 13.70/2.49 [compatibility_of_order_relation_and_addition])).
% 13.70/2.49 thf(zip_derived_cl1250, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 ( (less_or_equal @ additive_identity @ X0)
% 13.70/2.49 | ~ (less_or_equal @ additive_identity @ X1)
% 13.70/2.49 | ~ (sum @ X1 @ additive_identity @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl1244, zip_derived_cl23])).
% 13.70/2.49 thf(zip_derived_cl1514, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ additive_identity)
% 13.70/2.49 | (less_or_equal @ additive_identity @ X0)
% 13.70/2.49 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)],
% 13.70/2.49 [zip_derived_cl138, zip_derived_cl1250])).
% 13.70/2.49 thf(well_definedness_of_additive_identity, axiom,
% 13.70/2.49 (defined @ additive_identity)).
% 13.70/2.49 thf(zip_derived_cl13, plain, ( (defined @ additive_identity)),
% 13.70/2.49 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 13.70/2.49 thf(zip_derived_cl1517, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 ( (less_or_equal @ additive_identity @ X0)
% 13.70/2.49 | ~ (sum @ additive_identity @ additive_identity @ X0))),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl1514, zip_derived_cl13])).
% 13.70/2.49 thf(zip_derived_cl1522, plain,
% 13.70/2.49 ( (less_or_equal @ additive_identity @ additive_identity)),
% 13.70/2.49 inference('s_sup-', [status(thm)],
% 13.70/2.49 [zip_derived_cl1244, zip_derived_cl1517])).
% 13.70/2.49 thf(zip_derived_cl31, plain, ( (sum @ a @ c @ u)),
% 13.70/2.49 inference('cnf', [status(esa)], [zf_stmt_1])).
% 13.70/2.49 thf(zip_derived_cl22, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 ( (less_or_equal @ X0 @ X1)
% 13.70/2.49 | (less_or_equal @ X1 @ X0)
% 13.70/2.49 | ~ (defined @ X0)
% 13.70/2.49 | ~ (defined @ X1))),
% 13.70/2.49 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 13.70/2.49 thf(sum_7, conjecture, (~( sum @ b @ c @ v ))).
% 13.70/2.49 thf(zf_stmt_2, negated_conjecture, (sum @ b @ c @ v),
% 13.70/2.49 inference('cnf.neg', [status(esa)], [sum_7])).
% 13.70/2.49 thf(zip_derived_cl32, plain, ( (sum @ b @ c @ v)),
% 13.70/2.49 inference('cnf', [status(esa)], [zf_stmt_2])).
% 13.70/2.49 thf(zip_derived_cl23, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.70/2.49 ( (less_or_equal @ X0 @ X1)
% 13.70/2.49 | ~ (less_or_equal @ X2 @ X3)
% 13.70/2.49 | ~ (sum @ X2 @ X4 @ X0)
% 13.70/2.49 | ~ (sum @ X3 @ X4 @ X1))),
% 13.70/2.49 inference('cnf', [status(esa)],
% 13.70/2.49 [compatibility_of_order_relation_and_addition])).
% 13.70/2.49 thf(zip_derived_cl70, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 ( (less_or_equal @ v @ X0)
% 13.70/2.49 | ~ (less_or_equal @ b @ X1)
% 13.70/2.49 | ~ (sum @ X1 @ c @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl23])).
% 13.70/2.49 thf(zip_derived_cl123, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 (~ (defined @ X0)
% 13.70/2.49 | ~ (defined @ b)
% 13.70/2.49 | (less_or_equal @ X0 @ b)
% 13.70/2.49 | (less_or_equal @ v @ X1)
% 13.70/2.49 | ~ (sum @ X0 @ c @ X1))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl70])).
% 13.70/2.49 thf(b_is_defined, axiom, (defined @ b)).
% 13.70/2.49 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 13.70/2.49 inference('cnf', [status(esa)], [b_is_defined])).
% 13.70/2.49 thf(zip_derived_cl141, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 (~ (defined @ X0)
% 13.70/2.49 | (less_or_equal @ X0 @ b)
% 13.70/2.49 | (less_or_equal @ v @ X1)
% 13.70/2.49 | ~ (sum @ X0 @ c @ X1))),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl123, zip_derived_cl27])).
% 13.70/2.49 thf(zip_derived_cl2826, plain,
% 13.70/2.49 ((~ (defined @ a) | (less_or_equal @ a @ b) | (less_or_equal @ v @ u))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl141])).
% 13.70/2.49 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 13.70/2.49 inference('cnf', [status(esa)], [a_is_defined])).
% 13.70/2.49 thf(zip_derived_cl34, plain, (~ (less_or_equal @ a @ b)),
% 13.70/2.49 inference('cnf', [status(esa)], [zf_stmt_0])).
% 13.70/2.49 thf(zip_derived_cl2842, plain, ( (less_or_equal @ v @ u)),
% 13.70/2.49 inference('demod', [status(thm)],
% 13.70/2.49 [zip_derived_cl2826, zip_derived_cl26, zip_derived_cl34])).
% 13.70/2.49 thf(zip_derived_cl20, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 ( (sum @ additive_identity @ X0 @ X1)
% 13.70/2.49 | ~ (less_or_equal @ X0 @ X1)
% 13.70/2.49 | ~ (less_or_equal @ X1 @ X0))),
% 13.70/2.49 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 13.70/2.49 thf(zip_derived_cl2849, plain,
% 13.70/2.49 (( (sum @ additive_identity @ v @ u) | ~ (less_or_equal @ u @ v))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl2842, zip_derived_cl20])).
% 13.70/2.49 thf(less_or_equal_8, conjecture, (~( less_or_equal @ u @ v ))).
% 13.70/2.49 thf(zf_stmt_3, negated_conjecture, (less_or_equal @ u @ v),
% 13.70/2.49 inference('cnf.neg', [status(esa)], [less_or_equal_8])).
% 13.70/2.49 thf(zip_derived_cl33, plain, ( (less_or_equal @ u @ v)),
% 13.70/2.49 inference('cnf', [status(esa)], [zf_stmt_3])).
% 13.70/2.49 thf(zip_derived_cl2855, plain, ( (sum @ additive_identity @ v @ u)),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl2849, zip_derived_cl33])).
% 13.70/2.49 thf(zip_derived_cl4, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.70/2.49 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 13.70/2.49 inference('cnf', [status(esa)], [commutativity_addition])).
% 13.70/2.49 thf(zip_derived_cl2881, plain, ( (sum @ v @ additive_identity @ u)),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl2855, zip_derived_cl4])).
% 13.70/2.49 thf(zip_derived_cl2, plain,
% 13.70/2.49 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ X0) | ~ (defined @ X0))),
% 13.70/2.49 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 13.70/2.49 thf(zip_derived_cl4, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.70/2.49 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 13.70/2.49 inference('cnf', [status(esa)], [commutativity_addition])).
% 13.70/2.49 thf(zip_derived_cl42, plain,
% 13.70/2.49 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 13.70/2.49 thf(zip_derived_cl32, plain, ( (sum @ b @ c @ v)),
% 13.70/2.49 inference('cnf', [status(esa)], [zf_stmt_2])).
% 13.70/2.49 thf(zip_derived_cl4, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.70/2.49 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 13.70/2.49 inference('cnf', [status(esa)], [commutativity_addition])).
% 13.70/2.49 thf(zip_derived_cl44, plain, ( (sum @ c @ b @ v)),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl4])).
% 13.70/2.49 thf(zip_derived_cl0, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.70/2.49 ( (sum @ X0 @ X1 @ X2)
% 13.70/2.49 | ~ (sum @ X0 @ X3 @ X4)
% 13.70/2.49 | ~ (sum @ X3 @ X5 @ X1)
% 13.70/2.49 | ~ (sum @ X4 @ X5 @ X2))),
% 13.70/2.49 inference('cnf', [status(esa)], [associativity_addition_1])).
% 13.70/2.49 thf(zip_derived_cl48, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.70/2.49 ( (sum @ c @ X1 @ X0) | ~ (sum @ b @ X2 @ X1) | ~ (sum @ v @ X2 @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl0])).
% 13.70/2.49 thf(zip_derived_cl563, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ b)
% 13.70/2.49 | (sum @ c @ b @ X0)
% 13.70/2.49 | ~ (sum @ v @ additive_identity @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl48])).
% 13.70/2.49 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 13.70/2.49 inference('cnf', [status(esa)], [b_is_defined])).
% 13.70/2.49 thf(zip_derived_cl570, plain,
% 13.70/2.49 (![X0 : $i]: ( (sum @ c @ b @ X0) | ~ (sum @ v @ additive_identity @ X0))),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl563, zip_derived_cl27])).
% 13.70/2.49 thf(zip_derived_cl2967, plain, ( (sum @ c @ b @ u)),
% 13.70/2.49 inference('s_sup-', [status(thm)],
% 13.70/2.49 [zip_derived_cl2881, zip_derived_cl570])).
% 13.70/2.49 thf(zip_derived_cl42, plain,
% 13.70/2.49 (![X0 : $i]: (~ (defined @ X0) | (sum @ X0 @ additive_identity @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 13.70/2.49 thf(zip_derived_cl56, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ X0)
% 13.70/2.49 | (sum @ X0 @ (additive_inverse @ X0) @ additive_identity))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 13.70/2.49 thf(zip_derived_cl31, plain, ( (sum @ a @ c @ u)),
% 13.70/2.49 inference('cnf', [status(esa)], [zf_stmt_1])).
% 13.70/2.49 thf(associativity_addition_2, axiom,
% 13.70/2.49 (( sum @ U @ Z @ W ) | ( ~( sum @ X @ Y @ U ) ) |
% 13.70/2.49 ( ~( sum @ Y @ Z @ V ) ) | ( ~( sum @ X @ V @ W ) ))).
% 13.70/2.49 thf(zip_derived_cl1, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.70/2.49 ( (sum @ X0 @ X1 @ X2)
% 13.70/2.49 | ~ (sum @ X3 @ X4 @ X0)
% 13.70/2.49 | ~ (sum @ X4 @ X1 @ X5)
% 13.70/2.49 | ~ (sum @ X3 @ X5 @ X2))),
% 13.70/2.49 inference('cnf', [status(esa)], [associativity_addition_2])).
% 13.70/2.49 thf(zip_derived_cl37, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.70/2.49 ( (sum @ u @ X1 @ X0) | ~ (sum @ c @ X1 @ X2) | ~ (sum @ a @ X2 @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl1])).
% 13.70/2.49 thf(zip_derived_cl294, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ c)
% 13.70/2.49 | (sum @ u @ (additive_inverse @ c) @ X0)
% 13.70/2.49 | ~ (sum @ a @ additive_identity @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl37])).
% 13.70/2.49 thf(c_is_defined, axiom, (defined @ c)).
% 13.70/2.49 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 13.70/2.49 inference('cnf', [status(esa)], [c_is_defined])).
% 13.70/2.49 thf(zip_derived_cl300, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 ( (sum @ u @ (additive_inverse @ c) @ X0)
% 13.70/2.49 | ~ (sum @ a @ additive_identity @ X0))),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl294, zip_derived_cl28])).
% 13.70/2.49 thf(zip_derived_cl8338, plain,
% 13.70/2.49 ((~ (defined @ a) | (sum @ u @ (additive_inverse @ c) @ a))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl300])).
% 13.70/2.49 thf(zip_derived_cl26, plain, ( (defined @ a)),
% 13.70/2.49 inference('cnf', [status(esa)], [a_is_defined])).
% 13.70/2.49 thf(zip_derived_cl8341, plain, ( (sum @ u @ (additive_inverse @ c) @ a)),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl8338, zip_derived_cl26])).
% 13.70/2.49 thf(zip_derived_cl4, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.70/2.49 ( (sum @ X0 @ X1 @ X2) | ~ (sum @ X1 @ X0 @ X2))),
% 13.70/2.49 inference('cnf', [status(esa)], [commutativity_addition])).
% 13.70/2.49 thf(zip_derived_cl8347, plain, ( (sum @ (additive_inverse @ c) @ u @ a)),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl8341, zip_derived_cl4])).
% 13.70/2.49 thf(zip_derived_cl3, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 ( (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)
% 13.70/2.49 | ~ (defined @ X0))),
% 13.70/2.49 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 13.70/2.49 thf(zip_derived_cl1, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.70/2.49 ( (sum @ X0 @ X1 @ X2)
% 13.70/2.49 | ~ (sum @ X3 @ X4 @ X0)
% 13.70/2.49 | ~ (sum @ X4 @ X1 @ X5)
% 13.70/2.49 | ~ (sum @ X3 @ X5 @ X2))),
% 13.70/2.49 inference('cnf', [status(esa)], [associativity_addition_2])).
% 13.70/2.49 thf(zip_derived_cl55, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.70/2.49 (~ (defined @ X0)
% 13.70/2.49 | (sum @ additive_identity @ X2 @ X1)
% 13.70/2.49 | ~ (sum @ X0 @ X2 @ X3)
% 13.70/2.49 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X1))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 13.70/2.49 thf(zip_derived_cl8437, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 (~ (defined @ c)
% 13.70/2.49 | (sum @ additive_identity @ X0 @ a)
% 13.70/2.49 | ~ (sum @ c @ X0 @ u))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl8347, zip_derived_cl55])).
% 13.70/2.49 thf(zip_derived_cl28, plain, ( (defined @ c)),
% 13.70/2.49 inference('cnf', [status(esa)], [c_is_defined])).
% 13.70/2.49 thf(zip_derived_cl8441, plain,
% 13.70/2.49 (![X0 : $i]: ( (sum @ additive_identity @ X0 @ a) | ~ (sum @ c @ X0 @ u))),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl8437, zip_derived_cl28])).
% 13.70/2.49 thf(zip_derived_cl8741, plain, ( (sum @ additive_identity @ b @ a)),
% 13.70/2.49 inference('s_sup-', [status(thm)],
% 13.70/2.49 [zip_derived_cl2967, zip_derived_cl8441])).
% 13.70/2.49 thf(zip_derived_cl23, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.70/2.49 ( (less_or_equal @ X0 @ X1)
% 13.70/2.49 | ~ (less_or_equal @ X2 @ X3)
% 13.70/2.49 | ~ (sum @ X2 @ X4 @ X0)
% 13.70/2.49 | ~ (sum @ X3 @ X4 @ X1))),
% 13.70/2.49 inference('cnf', [status(esa)],
% 13.70/2.49 [compatibility_of_order_relation_and_addition])).
% 13.70/2.49 thf(zip_derived_cl8748, plain,
% 13.70/2.49 (![X0 : $i, X1 : $i]:
% 13.70/2.49 ( (less_or_equal @ a @ X0)
% 13.70/2.49 | ~ (less_or_equal @ additive_identity @ X1)
% 13.70/2.49 | ~ (sum @ X1 @ b @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl8741, zip_derived_cl23])).
% 13.70/2.49 thf(zip_derived_cl8878, plain,
% 13.70/2.49 (![X0 : $i]:
% 13.70/2.49 ( (less_or_equal @ a @ X0) | ~ (sum @ additive_identity @ b @ X0))),
% 13.70/2.49 inference('s_sup-', [status(thm)],
% 13.70/2.49 [zip_derived_cl1522, zip_derived_cl8748])).
% 13.70/2.49 thf(zip_derived_cl8888, plain,
% 13.70/2.49 ((~ (defined @ b) | (less_or_equal @ a @ b))),
% 13.70/2.49 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl8878])).
% 13.70/2.49 thf(zip_derived_cl27, plain, ( (defined @ b)),
% 13.70/2.49 inference('cnf', [status(esa)], [b_is_defined])).
% 13.70/2.49 thf(zip_derived_cl8892, plain, ( (less_or_equal @ a @ b)),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl8888, zip_derived_cl27])).
% 13.70/2.49 thf(zip_derived_cl8893, plain, ($false),
% 13.70/2.49 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl8892])).
% 13.70/2.49
% 13.70/2.49 % SZS output end Refutation
% 13.70/2.49
% 13.70/2.49
% 13.70/2.49 % Terminating...
% 13.94/2.60 % Runner terminated.
% 13.94/2.63 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------