TSTP Solution File: FLD061-2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD061-2 : 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.AXtSQDvjB2 true
% Computer : n011.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 19.29s 3.39s
% Output : Refutation 19.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD061-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.AXtSQDvjB2 true
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 00:04:25 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.36 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.91/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.91/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.91/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.91/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.91/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.91/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.91/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 19.29/3.39 % Solved by fo/fo3_bce.sh.
% 19.29/3.39 % BCE start: 38
% 19.29/3.39 % BCE eliminated: 0
% 19.29/3.39 % PE start: 38
% 19.29/3.39 logic: neq
% 19.29/3.39 % PE eliminated: 0
% 19.29/3.39 % done 3056 iterations in 2.638s
% 19.29/3.39 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 19.29/3.39 % SZS output start Refutation
% 19.29/3.39 thf(defined_type, type, defined: $i > $o).
% 19.29/3.39 thf(d_type, type, d: $i).
% 19.29/3.39 thf(add_type, type, add: $i > $i > $i).
% 19.29/3.39 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 19.29/3.39 thf(v_type, type, v: $i).
% 19.29/3.39 thf(u_type, type, u: $i).
% 19.29/3.39 thf(b_type, type, b: $i).
% 19.29/3.39 thf(c_type, type, c: $i).
% 19.29/3.39 thf(equalish_type, type, equalish: $i > $i > $o).
% 19.29/3.39 thf(a_type, type, a: $i).
% 19.29/3.39 thf(not_less_or_equal_11, conjecture, (less_or_equal @ u @ v)).
% 19.29/3.39 thf(zf_stmt_0, negated_conjecture, (~( less_or_equal @ u @ v )),
% 19.29/3.39 inference('cnf.neg', [status(esa)], [not_less_or_equal_11])).
% 19.29/3.39 thf(zip_derived_cl37, plain, (~ (less_or_equal @ u @ v)),
% 19.29/3.39 inference('cnf', [status(esa)], [zf_stmt_0])).
% 19.29/3.39 thf(c_is_defined, axiom, (defined @ c)).
% 19.29/3.39 thf(zip_derived_cl29, plain, ( (defined @ c)),
% 19.29/3.39 inference('cnf', [status(esa)], [c_is_defined])).
% 19.29/3.39 thf(zip_derived_cl29, plain, ( (defined @ c)),
% 19.29/3.39 inference('cnf', [status(esa)], [c_is_defined])).
% 19.29/3.39 thf(totality_of_order_relation, axiom,
% 19.29/3.39 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 19.29/3.39 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 19.29/3.39 thf(zip_derived_cl17, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | (less_or_equal @ X1 @ X0)
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (defined @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl157, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (defined @ X0)
% 19.29/3.39 | (less_or_equal @ X0 @ c)
% 19.29/3.39 | (less_or_equal @ c @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl17])).
% 19.29/3.39 thf(zip_derived_cl1693, plain,
% 19.29/3.39 (( (less_or_equal @ c @ c) | (less_or_equal @ c @ c))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl157])).
% 19.29/3.39 thf(zip_derived_cl1697, plain, ( (less_or_equal @ c @ c)),
% 19.29/3.39 inference('simplify', [status(thm)], [zip_derived_cl1693])).
% 19.29/3.39 thf(compatibility_of_order_relation_and_addition, axiom,
% 19.29/3.39 (( less_or_equal @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) |
% 19.29/3.39 ( ~( defined @ Z ) ) | ( ~( less_or_equal @ X @ Y ) ))).
% 19.29/3.39 thf(zip_derived_cl18, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 19.29/3.39 | ~ (defined @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_order_relation_and_addition])).
% 19.29/3.39 thf(add_equals_u_7, conjecture, (~( equalish @ ( add @ a @ c ) @ u ))).
% 19.29/3.39 thf(zf_stmt_1, negated_conjecture, (equalish @ ( add @ a @ c ) @ u),
% 19.29/3.39 inference('cnf.neg', [status(esa)], [add_equals_u_7])).
% 19.29/3.39 thf(zip_derived_cl33, plain, ( (equalish @ (add @ a @ c) @ u)),
% 19.29/3.39 inference('cnf', [status(esa)], [zf_stmt_1])).
% 19.29/3.39 thf(symmetry_of_equality, axiom,
% 19.29/3.39 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 19.29/3.39 thf(zip_derived_cl21, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 19.29/3.39 thf(zip_derived_cl39, plain, ( (equalish @ u @ (add @ a @ c))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl21])).
% 19.29/3.39 thf(transitivity_of_equality, axiom,
% 19.29/3.39 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 19.29/3.39 ( ~( equalish @ Y @ Z ) ))).
% 19.29/3.39 thf(zip_derived_cl22, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (equalish @ X0 @ X1)
% 19.29/3.39 | ~ (equalish @ X0 @ X2)
% 19.29/3.39 | ~ (equalish @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 19.29/3.39 thf(zip_derived_cl60, plain,
% 19.29/3.39 (![X0 : $i]: (~ (equalish @ (add @ a @ c) @ X0) | (equalish @ u @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl22])).
% 19.29/3.39 thf(commutativity_addition, axiom,
% 19.29/3.39 (( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) ) | ( ~( defined @ X ) ) |
% 19.29/3.39 ( ~( defined @ Y ) ))).
% 19.29/3.39 thf(zip_derived_cl3, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (defined @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [commutativity_addition])).
% 19.29/3.39 thf(zip_derived_cl77, plain,
% 19.29/3.39 (( (equalish @ u @ (add @ c @ a)) | ~ (defined @ c) | ~ (defined @ a))),
% 19.29/3.39 inference('sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl3])).
% 19.29/3.39 thf(zip_derived_cl29, plain, ( (defined @ c)),
% 19.29/3.39 inference('cnf', [status(esa)], [c_is_defined])).
% 19.29/3.39 thf(a_is_defined, axiom, (defined @ a)).
% 19.29/3.39 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 19.29/3.39 inference('cnf', [status(esa)], [a_is_defined])).
% 19.29/3.39 thf(zip_derived_cl78, plain, ( (equalish @ u @ (add @ c @ a))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl77, zip_derived_cl29, zip_derived_cl27])).
% 19.29/3.39 thf(zip_derived_cl21, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 19.29/3.39 thf(zip_derived_cl80, plain, ( (equalish @ (add @ c @ a) @ u)),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl21])).
% 19.29/3.39 thf(compatibility_of_equality_and_order_relation, axiom,
% 19.29/3.39 (( less_or_equal @ Y @ Z ) | ( ~( less_or_equal @ X @ Z ) ) |
% 19.29/3.39 ( ~( equalish @ X @ Y ) ))).
% 19.29/3.39 thf(zip_derived_cl25, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (equalish @ X2 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_equality_and_order_relation])).
% 19.29/3.39 thf(zip_derived_cl107, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (less_or_equal @ (add @ c @ a) @ X0) | (less_or_equal @ u @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl18, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 19.29/3.39 | ~ (defined @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_order_relation_and_addition])).
% 19.29/3.39 thf(zip_derived_cl225, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 ( (less_or_equal @ u @ (add @ X0 @ a))
% 19.29/3.39 | ~ (less_or_equal @ c @ X0)
% 19.29/3.39 | ~ (defined @ a))),
% 19.29/3.39 inference('sup+', [status(thm)], [zip_derived_cl107, zip_derived_cl18])).
% 19.29/3.39 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 19.29/3.39 inference('cnf', [status(esa)], [a_is_defined])).
% 19.29/3.39 thf(zip_derived_cl230, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 ( (less_or_equal @ u @ (add @ X0 @ a)) | ~ (less_or_equal @ c @ X0))),
% 19.29/3.39 inference('demod', [status(thm)], [zip_derived_cl225, zip_derived_cl27])).
% 19.29/3.39 thf(v_is_defined, axiom, (defined @ v)).
% 19.29/3.39 thf(zip_derived_cl32, plain, ( (defined @ v)),
% 19.29/3.39 inference('cnf', [status(esa)], [v_is_defined])).
% 19.29/3.39 thf(u_is_defined, axiom, (defined @ u)).
% 19.29/3.39 thf(zip_derived_cl31, plain, ( (defined @ u)),
% 19.29/3.39 inference('cnf', [status(esa)], [u_is_defined])).
% 19.29/3.39 thf(zip_derived_cl17, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | (less_or_equal @ X1 @ X0)
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (defined @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl159, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (defined @ X0)
% 19.29/3.39 | (less_or_equal @ X0 @ u)
% 19.29/3.39 | (less_or_equal @ u @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl17])).
% 19.29/3.39 thf(zip_derived_cl1786, plain,
% 19.29/3.39 (( (less_or_equal @ u @ v) | (less_or_equal @ v @ u))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl159])).
% 19.29/3.39 thf(zip_derived_cl37, plain, (~ (less_or_equal @ u @ v)),
% 19.29/3.39 inference('cnf', [status(esa)], [zf_stmt_0])).
% 19.29/3.39 thf(zip_derived_cl1788, plain, ( (less_or_equal @ v @ u)),
% 19.29/3.39 inference('demod', [status(thm)], [zip_derived_cl1786, zip_derived_cl37])).
% 19.29/3.39 thf(transitivity_of_order_relation, axiom,
% 19.29/3.39 (( less_or_equal @ X @ Z ) | ( ~( less_or_equal @ X @ Y ) ) |
% 19.29/3.39 ( ~( less_or_equal @ Y @ Z ) ))).
% 19.29/3.39 thf(zip_derived_cl16, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl1805, plain,
% 19.29/3.39 (![X0 : $i]: (~ (less_or_equal @ u @ X0) | (less_or_equal @ v @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl1788, zip_derived_cl16])).
% 19.29/3.39 thf(zip_derived_cl16, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl1814, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ u @ X0)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X1)
% 19.29/3.39 | (less_or_equal @ v @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl1805, zip_derived_cl16])).
% 19.29/3.39 thf(zip_derived_cl1822, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ c @ X0)
% 19.29/3.39 | (less_or_equal @ v @ X1)
% 19.29/3.39 | ~ (less_or_equal @ (add @ X0 @ a) @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl230, zip_derived_cl1814])).
% 19.29/3.39 thf(zip_derived_cl1968, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ X1 @ X0)
% 19.29/3.39 | ~ (defined @ a)
% 19.29/3.39 | (less_or_equal @ v @ (add @ X0 @ a))
% 19.29/3.39 | ~ (less_or_equal @ c @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl1822])).
% 19.29/3.39 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 19.29/3.39 inference('cnf', [status(esa)], [a_is_defined])).
% 19.29/3.39 thf(zip_derived_cl1971, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ X1 @ X0)
% 19.29/3.39 | (less_or_equal @ v @ (add @ X0 @ a))
% 19.29/3.39 | ~ (less_or_equal @ c @ X1))),
% 19.29/3.39 inference('demod', [status(thm)], [zip_derived_cl1968, zip_derived_cl27])).
% 19.29/3.39 thf(zip_derived_cl2076, plain,
% 19.29/3.39 ((~ (less_or_equal @ c @ c) | (less_or_equal @ v @ (add @ c @ a)))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl1697, zip_derived_cl1971])).
% 19.29/3.39 thf(zip_derived_cl1697, plain, ( (less_or_equal @ c @ c)),
% 19.29/3.39 inference('simplify', [status(thm)], [zip_derived_cl1693])).
% 19.29/3.39 thf(zip_derived_cl2108, plain, ( (less_or_equal @ v @ (add @ c @ a))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl2076, zip_derived_cl1697])).
% 19.29/3.39 thf(zip_derived_cl3, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (defined @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [commutativity_addition])).
% 19.29/3.39 thf(add_equals_v_8, conjecture, (~( equalish @ ( add @ d @ b ) @ v ))).
% 19.29/3.39 thf(zf_stmt_2, negated_conjecture, (equalish @ ( add @ d @ b ) @ v),
% 19.29/3.39 inference('cnf.neg', [status(esa)], [add_equals_v_8])).
% 19.29/3.39 thf(zip_derived_cl34, plain, ( (equalish @ (add @ d @ b) @ v)),
% 19.29/3.39 inference('cnf', [status(esa)], [zf_stmt_2])).
% 19.29/3.39 thf(zip_derived_cl21, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 19.29/3.39 thf(zip_derived_cl40, plain, ( (equalish @ v @ (add @ d @ b))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl21])).
% 19.29/3.39 thf(zip_derived_cl22, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (equalish @ X0 @ X1)
% 19.29/3.39 | ~ (equalish @ X0 @ X2)
% 19.29/3.39 | ~ (equalish @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 19.29/3.39 thf(zip_derived_cl61, plain,
% 19.29/3.39 (![X0 : $i]: (~ (equalish @ (add @ d @ b) @ X0) | (equalish @ v @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl22])).
% 19.29/3.39 thf(zip_derived_cl98, plain,
% 19.29/3.39 ((~ (defined @ b) | ~ (defined @ d) | (equalish @ v @ (add @ b @ d)))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl61])).
% 19.29/3.39 thf(b_is_defined, axiom, (defined @ b)).
% 19.29/3.39 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 19.29/3.39 inference('cnf', [status(esa)], [b_is_defined])).
% 19.29/3.39 thf(d_is_defined, axiom, (defined @ d)).
% 19.29/3.39 thf(zip_derived_cl30, plain, ( (defined @ d)),
% 19.29/3.39 inference('cnf', [status(esa)], [d_is_defined])).
% 19.29/3.39 thf(zip_derived_cl100, plain, ( (equalish @ v @ (add @ b @ d))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl98, zip_derived_cl28, zip_derived_cl30])).
% 19.29/3.39 thf(zip_derived_cl25, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (equalish @ X2 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_equality_and_order_relation])).
% 19.29/3.39 thf(zip_derived_cl110, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (less_or_equal @ v @ X0) | (less_or_equal @ (add @ b @ d) @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl16, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl845, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ v @ X0)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X1)
% 19.29/3.39 | (less_or_equal @ (add @ b @ d) @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl16])).
% 19.29/3.39 thf(zip_derived_cl2121, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 ( (less_or_equal @ (add @ b @ d) @ X0)
% 19.29/3.39 | ~ (less_or_equal @ (add @ c @ a) @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl2108, zip_derived_cl845])).
% 19.29/3.39 thf(less_or_equal_9, conjecture, (~( less_or_equal @ a @ b ))).
% 19.29/3.39 thf(zf_stmt_3, negated_conjecture, (less_or_equal @ a @ b),
% 19.29/3.39 inference('cnf.neg', [status(esa)], [less_or_equal_9])).
% 19.29/3.39 thf(zip_derived_cl35, plain, ( (less_or_equal @ a @ b)),
% 19.29/3.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 19.29/3.39 thf(zip_derived_cl18, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 19.29/3.39 | ~ (defined @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_order_relation_and_addition])).
% 19.29/3.39 thf(zip_derived_cl33, plain, ( (equalish @ (add @ a @ c) @ u)),
% 19.29/3.39 inference('cnf', [status(esa)], [zf_stmt_1])).
% 19.29/3.39 thf(zip_derived_cl22, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (equalish @ X0 @ X1)
% 19.29/3.39 | ~ (equalish @ X0 @ X2)
% 19.29/3.39 | ~ (equalish @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 19.29/3.39 thf(zip_derived_cl58, plain,
% 19.29/3.39 (![X0 : $i]: (~ (equalish @ u @ X0) | (equalish @ (add @ a @ c) @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl22])).
% 19.29/3.39 thf(zip_derived_cl25, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (equalish @ X2 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_equality_and_order_relation])).
% 19.29/3.39 thf(zip_derived_cl84, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (equalish @ u @ X0)
% 19.29/3.39 | ~ (less_or_equal @ (add @ a @ c) @ X1)
% 19.29/3.39 | (less_or_equal @ X0 @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl217, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ a @ X0)
% 19.29/3.39 | ~ (defined @ c)
% 19.29/3.39 | (less_or_equal @ X1 @ (add @ X0 @ c))
% 19.29/3.39 | ~ (equalish @ u @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl84])).
% 19.29/3.39 thf(zip_derived_cl29, plain, ( (defined @ c)),
% 19.29/3.39 inference('cnf', [status(esa)], [c_is_defined])).
% 19.29/3.39 thf(zip_derived_cl234, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ a @ X0)
% 19.29/3.39 | (less_or_equal @ X1 @ (add @ X0 @ c))
% 19.29/3.39 | ~ (equalish @ u @ X1))),
% 19.29/3.39 inference('demod', [status(thm)], [zip_derived_cl217, zip_derived_cl29])).
% 19.29/3.39 thf(zip_derived_cl240, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (equalish @ u @ X0) | (less_or_equal @ X0 @ (add @ b @ c)))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl234])).
% 19.29/3.39 thf(zip_derived_cl4439, plain,
% 19.29/3.39 (( (less_or_equal @ (add @ b @ d) @ (add @ b @ c))
% 19.29/3.39 | ~ (equalish @ u @ (add @ c @ a)))),
% 19.29/3.39 inference('sup+', [status(thm)], [zip_derived_cl2121, zip_derived_cl240])).
% 19.29/3.39 thf(zip_derived_cl78, plain, ( (equalish @ u @ (add @ c @ a))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl77, zip_derived_cl29, zip_derived_cl27])).
% 19.29/3.39 thf(zip_derived_cl4477, plain,
% 19.29/3.39 ( (less_or_equal @ (add @ b @ d) @ (add @ b @ c))),
% 19.29/3.39 inference('demod', [status(thm)], [zip_derived_cl4439, zip_derived_cl78])).
% 19.29/3.39 thf(zip_derived_cl3, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (defined @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [commutativity_addition])).
% 19.29/3.39 thf(zip_derived_cl25, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (equalish @ X2 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_equality_and_order_relation])).
% 19.29/3.39 thf(zip_derived_cl85, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 (~ (defined @ X1)
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (less_or_equal @ (add @ X0 @ X1) @ X2)
% 19.29/3.39 | (less_or_equal @ (add @ X1 @ X0) @ X2))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl4810, plain,
% 19.29/3.39 (( (less_or_equal @ (add @ d @ b) @ (add @ b @ c))
% 19.29/3.39 | ~ (defined @ b)
% 19.29/3.39 | ~ (defined @ d))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl4477, zip_derived_cl85])).
% 19.29/3.39 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 19.29/3.39 inference('cnf', [status(esa)], [b_is_defined])).
% 19.29/3.39 thf(zip_derived_cl30, plain, ( (defined @ d)),
% 19.29/3.39 inference('cnf', [status(esa)], [d_is_defined])).
% 19.29/3.39 thf(zip_derived_cl4820, plain,
% 19.29/3.39 ( (less_or_equal @ (add @ d @ b) @ (add @ b @ c))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl4810, zip_derived_cl28, zip_derived_cl30])).
% 19.29/3.39 thf(antisymmetry_of_order_relation, axiom,
% 19.29/3.39 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 19.29/3.39 ( ~( less_or_equal @ Y @ X ) ))).
% 19.29/3.39 thf(zip_derived_cl15, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 ( (equalish @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X1 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl5039, plain,
% 19.29/3.39 ((~ (less_or_equal @ (add @ b @ c) @ (add @ d @ b))
% 19.29/3.39 | (equalish @ (add @ d @ b) @ (add @ b @ c)))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl4820, zip_derived_cl15])).
% 19.29/3.39 thf(zip_derived_cl18, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 19.29/3.39 | ~ (defined @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_order_relation_and_addition])).
% 19.29/3.39 thf(zip_derived_cl85, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 (~ (defined @ X1)
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (less_or_equal @ (add @ X0 @ X1) @ X2)
% 19.29/3.39 | (less_or_equal @ (add @ X1 @ X0) @ X2))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl727, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 (~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | (less_or_equal @ (add @ X0 @ X2) @ (add @ X1 @ X0))
% 19.29/3.39 | ~ (defined @ X2)
% 19.29/3.39 | ~ (defined @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl85])).
% 19.29/3.39 thf(zip_derived_cl733, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 (~ (defined @ X2)
% 19.29/3.39 | (less_or_equal @ (add @ X0 @ X2) @ (add @ X1 @ X0))
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1))),
% 19.29/3.39 inference('simplify', [status(thm)], [zip_derived_cl727])).
% 19.29/3.39 thf(zip_derived_cl27253, plain,
% 19.29/3.39 (( (equalish @ (add @ d @ b) @ (add @ b @ c))
% 19.29/3.39 | ~ (less_or_equal @ c @ d)
% 19.29/3.39 | ~ (defined @ b)
% 19.29/3.39 | ~ (defined @ c))),
% 19.29/3.39 inference('sup+', [status(thm)], [zip_derived_cl5039, zip_derived_cl733])).
% 19.29/3.39 thf(less_or_equal_10, conjecture, (~( less_or_equal @ c @ d ))).
% 19.29/3.39 thf(zf_stmt_4, negated_conjecture, (less_or_equal @ c @ d),
% 19.29/3.39 inference('cnf.neg', [status(esa)], [less_or_equal_10])).
% 19.29/3.39 thf(zip_derived_cl36, plain, ( (less_or_equal @ c @ d)),
% 19.29/3.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 19.29/3.39 thf(zip_derived_cl28, plain, ( (defined @ b)),
% 19.29/3.39 inference('cnf', [status(esa)], [b_is_defined])).
% 19.29/3.39 thf(zip_derived_cl29, plain, ( (defined @ c)),
% 19.29/3.39 inference('cnf', [status(esa)], [c_is_defined])).
% 19.29/3.39 thf(zip_derived_cl27312, plain,
% 19.29/3.39 ( (equalish @ (add @ d @ b) @ (add @ b @ c))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl27253, zip_derived_cl36, zip_derived_cl28,
% 19.29/3.39 zip_derived_cl29])).
% 19.29/3.39 thf(zip_derived_cl61, plain,
% 19.29/3.39 (![X0 : $i]: (~ (equalish @ (add @ d @ b) @ X0) | (equalish @ v @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl22])).
% 19.29/3.39 thf(zip_derived_cl27403, plain, ( (equalish @ v @ (add @ b @ c))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl27312, zip_derived_cl61])).
% 19.29/3.39 thf(zip_derived_cl22, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (equalish @ X0 @ X1)
% 19.29/3.39 | ~ (equalish @ X0 @ X2)
% 19.29/3.39 | ~ (equalish @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 19.29/3.39 thf(zip_derived_cl27422, plain,
% 19.29/3.39 (![X0 : $i]: (~ (equalish @ (add @ b @ c) @ X0) | (equalish @ v @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl27403, zip_derived_cl22])).
% 19.29/3.39 thf(zip_derived_cl2121, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 ( (less_or_equal @ (add @ b @ d) @ X0)
% 19.29/3.39 | ~ (less_or_equal @ (add @ c @ a) @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl2108, zip_derived_cl845])).
% 19.29/3.39 thf(zip_derived_cl31, plain, ( (defined @ u)),
% 19.29/3.39 inference('cnf', [status(esa)], [u_is_defined])).
% 19.29/3.39 thf(zip_derived_cl159, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (defined @ X0)
% 19.29/3.39 | (less_or_equal @ X0 @ u)
% 19.29/3.39 | (less_or_equal @ u @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl17])).
% 19.29/3.39 thf(zip_derived_cl1785, plain,
% 19.29/3.39 (( (less_or_equal @ u @ u) | (less_or_equal @ u @ u))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl159])).
% 19.29/3.39 thf(zip_derived_cl1787, plain, ( (less_or_equal @ u @ u)),
% 19.29/3.39 inference('simplify', [status(thm)], [zip_derived_cl1785])).
% 19.29/3.39 thf(zip_derived_cl78, plain, ( (equalish @ u @ (add @ c @ a))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl77, zip_derived_cl29, zip_derived_cl27])).
% 19.29/3.39 thf(zip_derived_cl25, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (equalish @ X2 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_equality_and_order_relation])).
% 19.29/3.39 thf(zip_derived_cl91, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (less_or_equal @ u @ X0) | (less_or_equal @ (add @ c @ a) @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl78, plain, ( (equalish @ u @ (add @ c @ a))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl77, zip_derived_cl29, zip_derived_cl27])).
% 19.29/3.39 thf(zip_derived_cl58, plain,
% 19.29/3.39 (![X0 : $i]: (~ (equalish @ u @ X0) | (equalish @ (add @ a @ c) @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl22])).
% 19.29/3.39 thf(zip_derived_cl21, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 19.29/3.39 thf(zip_derived_cl64, plain,
% 19.29/3.39 (![X0 : $i]: (~ (equalish @ u @ X0) | (equalish @ X0 @ (add @ a @ c)))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl21])).
% 19.29/3.39 thf(zip_derived_cl131, plain, ( (equalish @ (add @ c @ a) @ (add @ a @ c))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl64])).
% 19.29/3.39 thf(zip_derived_cl22, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (equalish @ X0 @ X1)
% 19.29/3.39 | ~ (equalish @ X0 @ X2)
% 19.29/3.39 | ~ (equalish @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 19.29/3.39 thf(zip_derived_cl162, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (equalish @ (add @ a @ c) @ X0) | (equalish @ (add @ c @ a) @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl22])).
% 19.29/3.39 thf(zip_derived_cl25, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (equalish @ X2 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_equality_and_order_relation])).
% 19.29/3.39 thf(zip_derived_cl1884, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (equalish @ (add @ a @ c) @ X0)
% 19.29/3.39 | ~ (less_or_equal @ (add @ c @ a) @ X1)
% 19.29/3.39 | (less_or_equal @ X0 @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl162, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl3542, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ u @ X0)
% 19.29/3.39 | (less_or_equal @ X1 @ X0)
% 19.29/3.39 | ~ (equalish @ (add @ a @ c) @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl1884])).
% 19.29/3.39 thf(zip_derived_cl3580, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (equalish @ (add @ a @ c) @ X0) | (less_or_equal @ X0 @ u))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl1787, zip_derived_cl3542])).
% 19.29/3.39 thf(zip_derived_cl3697, plain,
% 19.29/3.39 (( (less_or_equal @ (add @ b @ d) @ u)
% 19.29/3.39 | ~ (equalish @ (add @ a @ c) @ (add @ c @ a)))),
% 19.29/3.39 inference('sup+', [status(thm)], [zip_derived_cl2121, zip_derived_cl3580])).
% 19.29/3.39 thf(zip_derived_cl131, plain, ( (equalish @ (add @ c @ a) @ (add @ a @ c))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl64])).
% 19.29/3.39 thf(zip_derived_cl21, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 19.29/3.39 thf(zip_derived_cl161, plain, ( (equalish @ (add @ a @ c) @ (add @ c @ a))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl21])).
% 19.29/3.39 thf(zip_derived_cl3740, plain, ( (less_or_equal @ (add @ b @ d) @ u)),
% 19.29/3.39 inference('demod', [status(thm)], [zip_derived_cl3697, zip_derived_cl161])).
% 19.29/3.39 thf(zip_derived_cl100, plain, ( (equalish @ v @ (add @ b @ d))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl98, zip_derived_cl28, zip_derived_cl30])).
% 19.29/3.39 thf(zip_derived_cl21, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 19.29/3.39 thf(zip_derived_cl108, plain, ( (equalish @ (add @ b @ d) @ v)),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl21])).
% 19.29/3.39 thf(zip_derived_cl22, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (equalish @ X0 @ X1)
% 19.29/3.39 | ~ (equalish @ X0 @ X2)
% 19.29/3.39 | ~ (equalish @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 19.29/3.39 thf(zip_derived_cl123, plain,
% 19.29/3.39 (![X0 : $i]: (~ (equalish @ v @ X0) | (equalish @ (add @ b @ d) @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl108, zip_derived_cl22])).
% 19.29/3.39 thf(zip_derived_cl25, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (equalish @ X2 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_equality_and_order_relation])).
% 19.29/3.39 thf(zip_derived_cl898, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (equalish @ v @ X0)
% 19.29/3.39 | ~ (less_or_equal @ (add @ b @ d) @ X1)
% 19.29/3.39 | (less_or_equal @ X0 @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl3842, plain,
% 19.29/3.39 (![X0 : $i]: ( (less_or_equal @ X0 @ u) | ~ (equalish @ v @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl3740, zip_derived_cl898])).
% 19.29/3.39 thf(zip_derived_cl15, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 ( (equalish @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X1 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl4152, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (equalish @ v @ X0)
% 19.29/3.39 | ~ (less_or_equal @ u @ X0)
% 19.29/3.39 | (equalish @ X0 @ u))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl3842, zip_derived_cl15])).
% 19.29/3.39 thf(zip_derived_cl35, plain, ( (less_or_equal @ a @ b)),
% 19.29/3.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 19.29/3.39 thf(zip_derived_cl18, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 19.29/3.39 | ~ (defined @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_order_relation_and_addition])).
% 19.29/3.39 thf(zip_derived_cl33, plain, ( (equalish @ (add @ a @ c) @ u)),
% 19.29/3.39 inference('cnf', [status(esa)], [zf_stmt_1])).
% 19.29/3.39 thf(zip_derived_cl25, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (equalish @ X2 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_equality_and_order_relation])).
% 19.29/3.39 thf(zip_derived_cl88, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (less_or_equal @ (add @ a @ c) @ X0) | (less_or_equal @ u @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl18, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 19.29/3.39 | ~ (defined @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_order_relation_and_addition])).
% 19.29/3.39 thf(zip_derived_cl223, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 ( (less_or_equal @ u @ (add @ X0 @ c))
% 19.29/3.39 | ~ (less_or_equal @ a @ X0)
% 19.29/3.39 | ~ (defined @ c))),
% 19.29/3.39 inference('sup+', [status(thm)], [zip_derived_cl88, zip_derived_cl18])).
% 19.29/3.39 thf(zip_derived_cl29, plain, ( (defined @ c)),
% 19.29/3.39 inference('cnf', [status(esa)], [c_is_defined])).
% 19.29/3.39 thf(zip_derived_cl228, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 ( (less_or_equal @ u @ (add @ X0 @ c)) | ~ (less_or_equal @ a @ X0))),
% 19.29/3.39 inference('demod', [status(thm)], [zip_derived_cl223, zip_derived_cl29])).
% 19.29/3.39 thf(zip_derived_cl16, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X0 @ X2)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl1198, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ a @ X0)
% 19.29/3.39 | ~ (less_or_equal @ (add @ X0 @ c) @ X1)
% 19.29/3.39 | (less_or_equal @ u @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl228, zip_derived_cl16])).
% 19.29/3.39 thf(zip_derived_cl1206, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ X1 @ X0)
% 19.29/3.39 | ~ (defined @ c)
% 19.29/3.39 | (less_or_equal @ u @ (add @ X0 @ c))
% 19.29/3.39 | ~ (less_or_equal @ a @ X1))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl1198])).
% 19.29/3.39 thf(zip_derived_cl29, plain, ( (defined @ c)),
% 19.29/3.39 inference('cnf', [status(esa)], [c_is_defined])).
% 19.29/3.39 thf(zip_derived_cl1208, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 (~ (less_or_equal @ X1 @ X0)
% 19.29/3.39 | (less_or_equal @ u @ (add @ X0 @ c))
% 19.29/3.39 | ~ (less_or_equal @ a @ X1))),
% 19.29/3.39 inference('demod', [status(thm)], [zip_derived_cl1206, zip_derived_cl29])).
% 19.29/3.39 thf(zip_derived_cl1230, plain,
% 19.29/3.39 ((~ (less_or_equal @ a @ a) | (less_or_equal @ u @ (add @ b @ c)))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl1208])).
% 19.29/3.39 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 19.29/3.39 inference('cnf', [status(esa)], [a_is_defined])).
% 19.29/3.39 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 19.29/3.39 inference('cnf', [status(esa)], [a_is_defined])).
% 19.29/3.39 thf(zip_derived_cl17, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | (less_or_equal @ X1 @ X0)
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (defined @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl155, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (defined @ X0)
% 19.29/3.39 | (less_or_equal @ X0 @ a)
% 19.29/3.39 | (less_or_equal @ a @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl17])).
% 19.29/3.39 thf(zip_derived_cl1598, plain,
% 19.29/3.39 (( (less_or_equal @ a @ a) | (less_or_equal @ a @ a))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl155])).
% 19.29/3.39 thf(zip_derived_cl1604, plain, ( (less_or_equal @ a @ a)),
% 19.29/3.39 inference('simplify', [status(thm)], [zip_derived_cl1598])).
% 19.29/3.39 thf(zip_derived_cl1606, plain, ( (less_or_equal @ u @ (add @ b @ c))),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl1230, zip_derived_cl1604])).
% 19.29/3.39 thf(zip_derived_cl4602, plain,
% 19.29/3.39 (( (equalish @ (add @ b @ c) @ u) | ~ (equalish @ v @ (add @ b @ c)))),
% 19.29/3.39 inference('sup+', [status(thm)], [zip_derived_cl4152, zip_derived_cl1606])).
% 19.29/3.39 thf(zip_derived_cl27403, plain, ( (equalish @ v @ (add @ b @ c))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl27312, zip_derived_cl61])).
% 19.29/3.39 thf(zip_derived_cl27415, plain, ( (equalish @ (add @ b @ c) @ u)),
% 19.29/3.39 inference('demod', [status(thm)],
% 19.29/3.39 [zip_derived_cl4602, zip_derived_cl27403])).
% 19.29/3.39 thf(zip_derived_cl27690, plain, ( (equalish @ v @ u)),
% 19.29/3.39 inference('sup+', [status(thm)],
% 19.29/3.39 [zip_derived_cl27422, zip_derived_cl27415])).
% 19.29/3.39 thf(zip_derived_cl25, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | ~ (less_or_equal @ X2 @ X1)
% 19.29/3.39 | ~ (equalish @ X2 @ X0))),
% 19.29/3.39 inference('cnf', [status(esa)],
% 19.29/3.39 [compatibility_of_equality_and_order_relation])).
% 19.29/3.39 thf(zip_derived_cl27732, plain,
% 19.29/3.39 (![X0 : $i]: (~ (less_or_equal @ v @ X0) | (less_or_equal @ u @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl27690, zip_derived_cl25])).
% 19.29/3.39 thf(zip_derived_cl32, plain, ( (defined @ v)),
% 19.29/3.39 inference('cnf', [status(esa)], [v_is_defined])).
% 19.29/3.39 thf(zip_derived_cl32, plain, ( (defined @ v)),
% 19.29/3.39 inference('cnf', [status(esa)], [v_is_defined])).
% 19.29/3.39 thf(zip_derived_cl17, plain,
% 19.29/3.39 (![X0 : $i, X1 : $i]:
% 19.29/3.39 ( (less_or_equal @ X0 @ X1)
% 19.29/3.39 | (less_or_equal @ X1 @ X0)
% 19.29/3.39 | ~ (defined @ X0)
% 19.29/3.39 | ~ (defined @ X1))),
% 19.29/3.39 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 19.29/3.39 thf(zip_derived_cl160, plain,
% 19.29/3.39 (![X0 : $i]:
% 19.29/3.39 (~ (defined @ X0)
% 19.29/3.39 | (less_or_equal @ X0 @ v)
% 19.29/3.39 | (less_or_equal @ v @ X0))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl17])).
% 19.29/3.39 thf(zip_derived_cl1846, plain,
% 19.29/3.39 (( (less_or_equal @ v @ v) | (less_or_equal @ v @ v))),
% 19.29/3.39 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl160])).
% 19.29/3.39 thf(zip_derived_cl1848, plain, ( (less_or_equal @ v @ v)),
% 19.29/3.39 inference('simplify', [status(thm)], [zip_derived_cl1846])).
% 19.29/3.39 thf(zip_derived_cl27941, plain, ( (less_or_equal @ u @ v)),
% 19.29/3.39 inference('sup+', [status(thm)],
% 19.29/3.39 [zip_derived_cl27732, zip_derived_cl1848])).
% 19.29/3.39 thf(zip_derived_cl28130, plain, ($false),
% 19.29/3.39 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl27941])).
% 19.29/3.39
% 19.29/3.39 % SZS output end Refutation
% 19.29/3.39
% 19.29/3.39
% 19.29/3.39 % Terminating...
% 19.83/3.46 % Runner terminated.
% 19.83/3.47 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------