%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD067-2 : TPTP v9.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Qo807Gh4XB true
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:33:23 PM UTC 2025
% Result : Unsatisfiable 22.88s 3.86s
% Output : Refutation 22.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD067-2 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Qo807Gh4XB true
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 18:25:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.57/0.65 % Total configuration time : 435
% 0.57/0.65 % Estimated wc time : 1092
% 0.57/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 22.88/3.86 % Solved by fo/fo3_bce.sh.
% 22.88/3.86 % BCE start: 33
% 22.88/3.86 % BCE eliminated: 0
% 22.88/3.86 % PE start: 33
% 22.88/3.86 logic: neq
% 22.88/3.86 % PE eliminated: 0
% 22.88/3.86 % done 5022 iterations in 3.090s
% 22.88/3.86 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 22.88/3.86 % SZS output start Refutation
% 22.88/3.86 thf(defined_type, type, defined: $i > $o).
% 22.88/3.86 thf(additive_identity_type, type, additive_identity: $i).
% 22.88/3.86 thf(add_type, type, add: $i > $i > $i).
% 22.88/3.86 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 22.88/3.86 thf(b_type, type, b: $i).
% 22.88/3.86 thf(u_type, type, u: $i).
% 22.88/3.86 thf(equalish_type, type, equalish: $i > $i > $o).
% 22.88/3.86 thf(a_type, type, a: $i).
% 22.88/3.86 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 22.88/3.86 thf(well_definedness_of_additive_identity, axiom,
% 22.88/3.86 (defined @ additive_identity)).
% 22.88/3.86 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 22.88/3.86 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.88/3.86 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 22.88/3.86 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.88/3.86 thf(totality_of_order_relation, axiom,
% 22.88/3.86 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 22.88/3.86 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 22.88/3.86 thf(zip_derived_cl17, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]:
% 22.88/3.86 ( (less_or_equal @ X0 @ X1)
% 22.88/3.86 | (less_or_equal @ X1 @ X0)
% 22.88/3.86 | ~ (defined @ X0)
% 22.88/3.86 | ~ (defined @ X1))),
% 22.88/3.86 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 22.88/3.86 thf(zip_derived_cl103, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (defined @ X0)
% 22.88/3.86 | (less_or_equal @ X0 @ additive_identity)
% 22.88/3.86 | (less_or_equal @ additive_identity @ X0))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl17])).
% 22.88/3.86 thf(zip_derived_cl1762, plain,
% 22.88/3.86 (( (less_or_equal @ additive_identity @ additive_identity)
% 22.88/3.86 | (less_or_equal @ additive_identity @ additive_identity))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl103])).
% 22.88/3.86 thf(zip_derived_cl1771, plain,
% 22.88/3.86 ( (less_or_equal @ additive_identity @ additive_identity)),
% 22.88/3.86 inference('simplify', [status(thm)], [zip_derived_cl1762])).
% 22.88/3.86 thf(u_is_defined, axiom, (defined @ u)).
% 22.88/3.86 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 22.88/3.86 inference('cnf', [status(esa)], [u_is_defined])).
% 22.88/3.86 thf(zip_derived_cl103, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (defined @ X0)
% 22.88/3.86 | (less_or_equal @ X0 @ additive_identity)
% 22.88/3.86 | (less_or_equal @ additive_identity @ X0))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl17])).
% 22.88/3.86 thf(zip_derived_cl1770, plain,
% 22.88/3.86 (( (less_or_equal @ additive_identity @ u)
% 22.88/3.86 | (less_or_equal @ u @ additive_identity))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl103])).
% 22.88/3.86 thf(not_less_or_equal_6, conjecture, (less_or_equal @ additive_identity @ u)).
% 22.88/3.86 thf(zf_stmt_0, negated_conjecture,
% 22.88/3.86 (~( less_or_equal @ additive_identity @ u )),
% 22.88/3.86 inference('cnf.neg', [status(esa)], [not_less_or_equal_6])).
% 22.88/3.86 thf(zip_derived_cl32, plain, (~ (less_or_equal @ additive_identity @ u)),
% 22.88/3.86 inference('cnf', [status(esa)], [zf_stmt_0])).
% 22.88/3.86 thf(zip_derived_cl1772, plain, ( (less_or_equal @ u @ additive_identity)),
% 22.88/3.86 inference('demod', [status(thm)], [zip_derived_cl1770, zip_derived_cl32])).
% 22.88/3.86 thf(existence_of_identity_addition, axiom,
% 22.88/3.86 (( equalish @ ( add @ additive_identity @ X ) @ X ) | ( ~( defined @ X ) ))).
% 22.88/3.86 thf(zip_derived_cl1, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 22.88/3.86 thf(symmetry_of_equality, axiom,
% 22.88/3.86 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 22.88/3.86 thf(zip_derived_cl21, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 22.88/3.86 thf(zip_derived_cl38, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (defined @ X0) | (equalish @ X0 @ (add @ additive_identity @ X0)))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 22.88/3.86 thf(add_equals_u_5, conjecture,
% 22.88/3.86 (~( equalish @ ( add @ b @ ( additive_inverse @ a ) ) @ u ))).
% 22.88/3.86 thf(zf_stmt_1, negated_conjecture,
% 22.88/3.86 (equalish @ ( add @ b @ ( additive_inverse @ a ) ) @ u),
% 22.88/3.86 inference('cnf.neg', [status(esa)], [add_equals_u_5])).
% 22.88/3.86 thf(zip_derived_cl31, plain,
% 22.88/3.86 ( (equalish @ (add @ b @ (additive_inverse @ a)) @ u)),
% 22.88/3.86 inference('cnf', [status(esa)], [zf_stmt_1])).
% 22.88/3.86 thf(transitivity_of_equality, axiom,
% 22.88/3.86 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 22.88/3.86 ( ~( equalish @ Y @ Z ) ))).
% 22.88/3.86 thf(zip_derived_cl22, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.86 ( (equalish @ X0 @ X1)
% 22.88/3.86 | ~ (equalish @ X0 @ X2)
% 22.88/3.86 | ~ (equalish @ X2 @ X1))),
% 22.88/3.86 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 22.88/3.86 thf(zip_derived_cl56, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (equalish @ u @ X0)
% 22.88/3.86 | (equalish @ (add @ b @ (additive_inverse @ a)) @ X0))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl22])).
% 22.88/3.86 thf(zip_derived_cl21, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 22.88/3.86 thf(zip_derived_cl71, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (equalish @ u @ X0)
% 22.88/3.86 | (equalish @ X0 @ (add @ b @ (additive_inverse @ a))))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl21])).
% 22.88/3.86 thf(zip_derived_cl95, plain,
% 22.88/3.86 ((~ (defined @ u)
% 22.88/3.86 | (equalish @ (add @ additive_identity @ u) @
% 22.88/3.86 (add @ b @ (additive_inverse @ a))))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl71])).
% 22.88/3.86 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 22.88/3.86 inference('cnf', [status(esa)], [u_is_defined])).
% 22.88/3.86 thf(zip_derived_cl100, plain,
% 22.88/3.86 ( (equalish @ (add @ additive_identity @ u) @
% 22.88/3.86 (add @ b @ (additive_inverse @ a)))),
% 22.88/3.86 inference('demod', [status(thm)], [zip_derived_cl95, zip_derived_cl29])).
% 22.88/3.86 thf(zip_derived_cl21, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 22.88/3.86 thf(zip_derived_cl114, plain,
% 22.88/3.86 ( (equalish @ (add @ b @ (additive_inverse @ a)) @
% 22.88/3.86 (add @ additive_identity @ u))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl21])).
% 22.88/3.86 thf(zip_derived_cl31, plain,
% 22.88/3.86 ( (equalish @ (add @ b @ (additive_inverse @ a)) @ u)),
% 22.88/3.86 inference('cnf', [status(esa)], [zf_stmt_1])).
% 22.88/3.86 thf(zip_derived_cl21, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 22.88/3.86 thf(zip_derived_cl34, plain,
% 22.88/3.86 ( (equalish @ u @ (add @ b @ (additive_inverse @ a)))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl21])).
% 22.88/3.86 thf(zip_derived_cl22, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.86 ( (equalish @ X0 @ X1)
% 22.88/3.86 | ~ (equalish @ X0 @ X2)
% 22.88/3.86 | ~ (equalish @ X2 @ X1))),
% 22.88/3.86 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 22.88/3.86 thf(zip_derived_cl58, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (equalish @ (add @ b @ (additive_inverse @ a)) @ X0)
% 22.88/3.86 | (equalish @ u @ X0))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl22])).
% 22.88/3.86 thf(zip_derived_cl120, plain,
% 22.88/3.86 ( (equalish @ u @ (add @ additive_identity @ u))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl58])).
% 22.88/3.86 thf(compatibility_of_equality_and_order_relation, axiom,
% 22.88/3.86 (( less_or_equal @ Y @ Z ) | ( ~( less_or_equal @ X @ Z ) ) |
% 22.88/3.86 ( ~( equalish @ X @ Y ) ))).
% 22.88/3.86 thf(zip_derived_cl25, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.86 ( (less_or_equal @ X0 @ X1)
% 22.88/3.86 | ~ (less_or_equal @ X2 @ X1)
% 22.88/3.86 | ~ (equalish @ X2 @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)],
% 22.88/3.86 [compatibility_of_equality_and_order_relation])).
% 22.88/3.86 thf(zip_derived_cl124, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (less_or_equal @ u @ X0)
% 22.88/3.86 | (less_or_equal @ (add @ additive_identity @ u) @ X0))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl120, zip_derived_cl25])).
% 22.88/3.86 thf(transitivity_of_order_relation, axiom,
% 22.88/3.86 (( less_or_equal @ X @ Z ) | ( ~( less_or_equal @ X @ Y ) ) |
% 22.88/3.86 ( ~( less_or_equal @ Y @ Z ) ))).
% 22.88/3.86 thf(zip_derived_cl16, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.86 ( (less_or_equal @ X0 @ X1)
% 22.88/3.86 | ~ (less_or_equal @ X0 @ X2)
% 22.88/3.86 | ~ (less_or_equal @ X2 @ X1))),
% 22.88/3.86 inference('cnf', [status(esa)], [transitivity_of_order_relation])).
% 22.88/3.86 thf(zip_derived_cl176, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]:
% 22.88/3.86 (~ (less_or_equal @ u @ X0)
% 22.88/3.86 | ~ (less_or_equal @ X0 @ X1)
% 22.88/3.86 | (less_or_equal @ (add @ additive_identity @ u) @ X1))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl16])).
% 22.88/3.86 thf(zip_derived_cl1796, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 ( (less_or_equal @ (add @ additive_identity @ u) @ X0)
% 22.88/3.86 | ~ (less_or_equal @ additive_identity @ X0))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl1772, zip_derived_cl176])).
% 22.88/3.86 thf(zip_derived_cl120, plain,
% 22.88/3.86 ( (equalish @ u @ (add @ additive_identity @ u))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl58])).
% 22.88/3.86 thf(zip_derived_cl21, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 22.88/3.86 thf(zip_derived_cl122, plain,
% 22.88/3.86 ( (equalish @ (add @ additive_identity @ u) @ u)),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl120, zip_derived_cl21])).
% 22.88/3.86 thf(zip_derived_cl22, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.86 ( (equalish @ X0 @ X1)
% 22.88/3.86 | ~ (equalish @ X0 @ X2)
% 22.88/3.86 | ~ (equalish @ X2 @ X1))),
% 22.88/3.86 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 22.88/3.86 thf(zip_derived_cl146, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (equalish @ u @ X0)
% 22.88/3.86 | (equalish @ (add @ additive_identity @ u) @ X0))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl22])).
% 22.88/3.86 thf(zip_derived_cl25, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.86 ( (less_or_equal @ X0 @ X1)
% 22.88/3.86 | ~ (less_or_equal @ X2 @ X1)
% 22.88/3.86 | ~ (equalish @ X2 @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)],
% 22.88/3.86 [compatibility_of_equality_and_order_relation])).
% 22.88/3.86 thf(zip_derived_cl183, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]:
% 22.88/3.86 (~ (equalish @ u @ X0)
% 22.88/3.86 | ~ (less_or_equal @ (add @ additive_identity @ u) @ X1)
% 22.88/3.86 | (less_or_equal @ X0 @ X1))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl25])).
% 22.88/3.86 thf(zip_derived_cl2587, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]:
% 22.88/3.86 (~ (less_or_equal @ additive_identity @ X0)
% 22.88/3.86 | (less_or_equal @ X1 @ X0)
% 22.88/3.86 | ~ (equalish @ u @ X1))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl1796, zip_derived_cl183])).
% 22.88/3.86 thf(zip_derived_cl2667, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (equalish @ u @ X0) | (less_or_equal @ X0 @ additive_identity))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl1771, zip_derived_cl2587])).
% 22.88/3.86 thf(antisymmetry_of_order_relation, axiom,
% 22.88/3.86 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 22.88/3.86 ( ~( less_or_equal @ Y @ X ) ))).
% 22.88/3.86 thf(zip_derived_cl15, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]:
% 22.88/3.86 ( (equalish @ X0 @ X1)
% 22.88/3.86 | ~ (less_or_equal @ X0 @ X1)
% 22.88/3.86 | ~ (less_or_equal @ X1 @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 22.88/3.86 thf(zip_derived_cl2680, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 (~ (equalish @ u @ X0)
% 22.88/3.86 | ~ (less_or_equal @ additive_identity @ X0)
% 22.88/3.86 | (equalish @ X0 @ additive_identity))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl2667, zip_derived_cl15])).
% 22.88/3.86 thf(less_or_equal_4, conjecture, (~( less_or_equal @ a @ b ))).
% 22.88/3.86 thf(zf_stmt_2, negated_conjecture, (less_or_equal @ a @ b),
% 22.88/3.86 inference('cnf.neg', [status(esa)], [less_or_equal_4])).
% 22.88/3.86 thf(zip_derived_cl30, plain, ( (less_or_equal @ a @ b)),
% 22.88/3.86 inference('cnf', [status(esa)], [zf_stmt_2])).
% 22.88/3.86 thf(existence_of_inverse_addition, axiom,
% 22.88/3.86 (( equalish @ ( add @ X @ ( additive_inverse @ X ) ) @ additive_identity ) |
% 22.88/3.86 ( ~( defined @ X ) ))).
% 22.88/3.86 thf(zip_derived_cl2, plain,
% 22.88/3.86 (![X0 : $i]:
% 22.88/3.86 ( (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ additive_identity)
% 22.88/3.86 | ~ (defined @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 22.88/3.86 thf(zip_derived_cl25, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.86 ( (less_or_equal @ X0 @ X1)
% 22.88/3.86 | ~ (less_or_equal @ X2 @ X1)
% 22.88/3.86 | ~ (equalish @ X2 @ X0))),
% 22.88/3.86 inference('cnf', [status(esa)],
% 22.88/3.86 [compatibility_of_equality_and_order_relation])).
% 22.88/3.86 thf(zip_derived_cl67, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]:
% 22.88/3.86 (~ (defined @ X0)
% 22.88/3.86 | ~ (less_or_equal @ (add @ X0 @ (additive_inverse @ X0)) @ X1)
% 22.88/3.86 | (less_or_equal @ additive_identity @ X1))),
% 22.88/3.86 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl25])).
% 22.88/3.86 thf(compatibility_of_order_relation_and_addition, axiom,
% 22.88/3.86 (( less_or_equal @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) |
% 22.88/3.86 ( ~( defined @ Z ) ) | ( ~( less_or_equal @ X @ Y ) ))).
% 22.88/3.86 thf(zip_derived_cl18, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.86 ( (less_or_equal @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 22.88/3.86 | ~ (defined @ X1)
% 22.88/3.86 | ~ (less_or_equal @ X0 @ X2))),
% 22.88/3.86 inference('cnf', [status(esa)],
% 22.88/3.86 [compatibility_of_order_relation_and_addition])).
% 22.88/3.86 thf(zip_derived_cl1164, plain,
% 22.88/3.86 (![X0 : $i, X1 : $i]:
% 22.88/3.86 ( (less_or_equal @ additive_identity @
% 22.88/3.86 (add @ X1 @ (additive_inverse @ X0)))
% 22.88/3.86 | ~ (defined @ X0)
% 22.88/3.87 | ~ (less_or_equal @ X0 @ X1)
% 22.88/3.87 | ~ (defined @ (additive_inverse @ X0)))),
% 22.88/3.87 inference('sup+', [status(thm)], [zip_derived_cl67, zip_derived_cl18])).
% 22.88/3.87 thf(well_definedness_of_additive_inverse, axiom,
% 22.88/3.87 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 22.88/3.87 thf(zip_derived_cl11, plain,
% 22.88/3.87 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 22.88/3.87 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 22.88/3.87 thf(zip_derived_cl34932, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 (~ (less_or_equal @ X0 @ X1)
% 22.88/3.87 | ~ (defined @ X0)
% 22.88/3.87 | (less_or_equal @ additive_identity @
% 22.88/3.87 (add @ X1 @ (additive_inverse @ X0))))),
% 22.88/3.87 inference('clc', [status(thm)], [zip_derived_cl1164, zip_derived_cl11])).
% 22.88/3.87 thf(zip_derived_cl35112, plain,
% 22.88/3.87 (( (less_or_equal @ additive_identity @
% 22.88/3.87 (add @ b @ (additive_inverse @ a)))
% 22.88/3.87 | ~ (defined @ a))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl34932])).
% 22.88/3.87 thf(a_is_defined, axiom, (defined @ a)).
% 22.88/3.87 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 22.88/3.87 inference('cnf', [status(esa)], [a_is_defined])).
% 22.88/3.87 thf(zip_derived_cl35226, plain,
% 22.88/3.87 ( (less_or_equal @ additive_identity @ (add @ b @ (additive_inverse @ a)))),
% 22.88/3.87 inference('demod', [status(thm)], [zip_derived_cl35112, zip_derived_cl27])).
% 22.88/3.87 thf(zip_derived_cl35403, plain,
% 22.88/3.87 (( (equalish @ (add @ b @ (additive_inverse @ a)) @ additive_identity)
% 22.88/3.87 | ~ (equalish @ u @ (add @ b @ (additive_inverse @ a))))),
% 22.88/3.87 inference('sup+', [status(thm)],
% 22.88/3.87 [zip_derived_cl2680, zip_derived_cl35226])).
% 22.88/3.87 thf(zip_derived_cl34, plain,
% 22.88/3.87 ( (equalish @ u @ (add @ b @ (additive_inverse @ a)))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl21])).
% 22.88/3.87 thf(zip_derived_cl35414, plain,
% 22.88/3.87 ( (equalish @ (add @ b @ (additive_inverse @ a)) @ additive_identity)),
% 22.88/3.87 inference('demod', [status(thm)], [zip_derived_cl35403, zip_derived_cl34])).
% 22.88/3.87 thf(compatibility_of_equality_and_addition, axiom,
% 22.88/3.87 (( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) | ( ~( defined @ Z ) ) |
% 22.88/3.87 ( ~( equalish @ X @ Y ) ))).
% 22.88/3.87 thf(zip_derived_cl23, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.87 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 22.88/3.87 | ~ (defined @ X1)
% 22.88/3.87 | ~ (equalish @ X0 @ X2))),
% 22.88/3.87 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 22.88/3.87 thf(commutativity_addition, axiom,
% 22.88/3.87 (( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) ) | ( ~( defined @ X ) ) |
% 22.88/3.87 ( ~( defined @ Y ) ))).
% 22.88/3.87 thf(zip_derived_cl3, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 22.88/3.87 | ~ (defined @ X0)
% 22.88/3.87 | ~ (defined @ X1))),
% 22.88/3.87 inference('cnf', [status(esa)], [commutativity_addition])).
% 22.88/3.87 thf(zip_derived_cl120, plain,
% 22.88/3.87 ( (equalish @ u @ (add @ additive_identity @ u))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl58])).
% 22.88/3.87 thf(zip_derived_cl22, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.87 ( (equalish @ X0 @ X1)
% 22.88/3.87 | ~ (equalish @ X0 @ X2)
% 22.88/3.87 | ~ (equalish @ X2 @ X1))),
% 22.88/3.87 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 22.88/3.87 thf(zip_derived_cl123, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ (add @ additive_identity @ u) @ X0)
% 22.88/3.87 | (equalish @ u @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl120, zip_derived_cl22])).
% 22.88/3.87 thf(zip_derived_cl139, plain,
% 22.88/3.87 ((~ (defined @ u)
% 22.88/3.87 | ~ (defined @ additive_identity)
% 22.88/3.87 | (equalish @ u @ (add @ u @ additive_identity)))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl123])).
% 22.88/3.87 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 22.88/3.87 inference('cnf', [status(esa)], [u_is_defined])).
% 22.88/3.87 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 22.88/3.87 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.88/3.87 thf(zip_derived_cl142, plain,
% 22.88/3.87 ( (equalish @ u @ (add @ u @ additive_identity))),
% 22.88/3.87 inference('demod', [status(thm)],
% 22.88/3.87 [zip_derived_cl139, zip_derived_cl29, zip_derived_cl10])).
% 22.88/3.87 thf(zip_derived_cl22, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.87 ( (equalish @ X0 @ X1)
% 22.88/3.87 | ~ (equalish @ X0 @ X2)
% 22.88/3.87 | ~ (equalish @ X2 @ X1))),
% 22.88/3.87 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 22.88/3.87 thf(zip_derived_cl151, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ (add @ u @ additive_identity) @ X0)
% 22.88/3.87 | (equalish @ u @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl22])).
% 22.88/3.87 thf(zip_derived_cl23, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.87 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 22.88/3.87 | ~ (defined @ X1)
% 22.88/3.87 | ~ (equalish @ X0 @ X2))),
% 22.88/3.87 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 22.88/3.87 thf(zip_derived_cl261, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 ( (equalish @ u @ (add @ X0 @ additive_identity))
% 22.88/3.87 | ~ (equalish @ u @ X0)
% 22.88/3.87 | ~ (defined @ additive_identity))),
% 22.88/3.87 inference('sup+', [status(thm)], [zip_derived_cl151, zip_derived_cl23])).
% 22.88/3.87 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 22.88/3.87 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.88/3.87 thf(zip_derived_cl263, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 ( (equalish @ u @ (add @ X0 @ additive_identity))
% 22.88/3.87 | ~ (equalish @ u @ X0))),
% 22.88/3.87 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl10])).
% 22.88/3.87 thf(zip_derived_cl22, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.87 ( (equalish @ X0 @ X1)
% 22.88/3.87 | ~ (equalish @ X0 @ X2)
% 22.88/3.87 | ~ (equalish @ X2 @ X1))),
% 22.88/3.87 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 22.88/3.87 thf(zip_derived_cl673, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 (~ (equalish @ u @ X0)
% 22.88/3.87 | ~ (equalish @ (add @ X0 @ additive_identity) @ X1)
% 22.88/3.87 | (equalish @ u @ X1))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl263, zip_derived_cl22])).
% 22.88/3.87 thf(zip_derived_cl716, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 (~ (equalish @ X1 @ X0)
% 22.88/3.87 | ~ (defined @ additive_identity)
% 22.88/3.87 | (equalish @ u @ (add @ X0 @ additive_identity))
% 22.88/3.87 | ~ (equalish @ u @ X1))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl673])).
% 22.88/3.87 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 22.88/3.87 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.88/3.87 thf(zip_derived_cl726, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 (~ (equalish @ X1 @ X0)
% 22.88/3.87 | (equalish @ u @ (add @ X0 @ additive_identity))
% 22.88/3.87 | ~ (equalish @ u @ X1))),
% 22.88/3.87 inference('demod', [status(thm)], [zip_derived_cl716, zip_derived_cl10])).
% 22.88/3.87 thf(zip_derived_cl35766, plain,
% 22.88/3.87 ((~ (equalish @ u @ (add @ b @ (additive_inverse @ a)))
% 22.88/3.87 | (equalish @ u @ (add @ additive_identity @ additive_identity)))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl35414, zip_derived_cl726])).
% 22.88/3.87 thf(zip_derived_cl34, plain,
% 22.88/3.87 ( (equalish @ u @ (add @ b @ (additive_inverse @ a)))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl21])).
% 22.88/3.87 thf(zip_derived_cl2680, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ u @ X0)
% 22.88/3.87 | ~ (less_or_equal @ additive_identity @ X0)
% 22.88/3.87 | (equalish @ X0 @ additive_identity))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl2667, zip_derived_cl15])).
% 22.88/3.87 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 22.88/3.87 inference('cnf', [status(esa)], [u_is_defined])).
% 22.88/3.87 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 22.88/3.87 inference('cnf', [status(esa)], [u_is_defined])).
% 22.88/3.87 thf(zip_derived_cl17, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 ( (less_or_equal @ X0 @ X1)
% 22.88/3.87 | (less_or_equal @ X1 @ X0)
% 22.88/3.87 | ~ (defined @ X0)
% 22.88/3.87 | ~ (defined @ X1))),
% 22.88/3.87 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 22.88/3.87 thf(zip_derived_cl109, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (defined @ X0)
% 22.88/3.87 | (less_or_equal @ X0 @ u)
% 22.88/3.87 | (less_or_equal @ u @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl17])).
% 22.88/3.87 thf(zip_derived_cl2079, plain,
% 22.88/3.87 (( (less_or_equal @ u @ u) | (less_or_equal @ u @ u))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl109])).
% 22.88/3.87 thf(zip_derived_cl2081, plain, ( (less_or_equal @ u @ u)),
% 22.88/3.87 inference('simplify', [status(thm)], [zip_derived_cl2079])).
% 22.88/3.87 thf(zip_derived_cl142, plain,
% 22.88/3.87 ( (equalish @ u @ (add @ u @ additive_identity))),
% 22.88/3.87 inference('demod', [status(thm)],
% 22.88/3.87 [zip_derived_cl139, zip_derived_cl29, zip_derived_cl10])).
% 22.88/3.87 thf(zip_derived_cl25, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.87 ( (less_or_equal @ X0 @ X1)
% 22.88/3.87 | ~ (less_or_equal @ X2 @ X1)
% 22.88/3.87 | ~ (equalish @ X2 @ X0))),
% 22.88/3.87 inference('cnf', [status(esa)],
% 22.88/3.87 [compatibility_of_equality_and_order_relation])).
% 22.88/3.87 thf(zip_derived_cl152, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (less_or_equal @ u @ X0)
% 22.88/3.87 | (less_or_equal @ (add @ u @ additive_identity) @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl25])).
% 22.88/3.87 thf(zip_derived_cl142, plain,
% 22.88/3.87 ( (equalish @ u @ (add @ u @ additive_identity))),
% 22.88/3.87 inference('demod', [status(thm)],
% 22.88/3.87 [zip_derived_cl139, zip_derived_cl29, zip_derived_cl10])).
% 22.88/3.87 thf(zip_derived_cl146, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ u @ X0)
% 22.88/3.87 | (equalish @ (add @ additive_identity @ u) @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl22])).
% 22.88/3.87 thf(zip_derived_cl21, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 22.88/3.87 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 22.88/3.87 thf(zip_derived_cl181, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ u @ X0)
% 22.88/3.87 | (equalish @ X0 @ (add @ additive_identity @ u)))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl21])).
% 22.88/3.87 thf(zip_derived_cl216, plain,
% 22.88/3.87 ( (equalish @ (add @ u @ additive_identity) @
% 22.88/3.87 (add @ additive_identity @ u))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl181])).
% 22.88/3.87 thf(zip_derived_cl22, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.87 ( (equalish @ X0 @ X1)
% 22.88/3.87 | ~ (equalish @ X0 @ X2)
% 22.88/3.87 | ~ (equalish @ X2 @ X1))),
% 22.88/3.87 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 22.88/3.87 thf(zip_derived_cl233, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ (add @ additive_identity @ u) @ X0)
% 22.88/3.87 | (equalish @ (add @ u @ additive_identity) @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl216, zip_derived_cl22])).
% 22.88/3.87 thf(zip_derived_cl25, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.87 ( (less_or_equal @ X0 @ X1)
% 22.88/3.87 | ~ (less_or_equal @ X2 @ X1)
% 22.88/3.87 | ~ (equalish @ X2 @ X0))),
% 22.88/3.87 inference('cnf', [status(esa)],
% 22.88/3.87 [compatibility_of_equality_and_order_relation])).
% 22.88/3.87 thf(zip_derived_cl4192, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 (~ (equalish @ (add @ additive_identity @ u) @ X0)
% 22.88/3.87 | ~ (less_or_equal @ (add @ u @ additive_identity) @ X1)
% 22.88/3.87 | (less_or_equal @ X0 @ X1))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl233, zip_derived_cl25])).
% 22.88/3.87 thf(zip_derived_cl4248, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 (~ (less_or_equal @ u @ X0)
% 22.88/3.87 | (less_or_equal @ X1 @ X0)
% 22.88/3.87 | ~ (equalish @ (add @ additive_identity @ u) @ X1))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl4192])).
% 22.88/3.87 thf(zip_derived_cl4671, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ (add @ additive_identity @ u) @ X0)
% 22.88/3.87 | (less_or_equal @ X0 @ u))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl2081, zip_derived_cl4248])).
% 22.88/3.87 thf(zip_derived_cl183, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 (~ (equalish @ u @ X0)
% 22.88/3.87 | ~ (less_or_equal @ (add @ additive_identity @ u) @ X1)
% 22.88/3.87 | (less_or_equal @ X0 @ X1))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl25])).
% 22.88/3.87 thf(zip_derived_cl4783, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ (add @ additive_identity @ u) @
% 22.88/3.87 (add @ additive_identity @ u))
% 22.88/3.87 | (less_or_equal @ X0 @ u)
% 22.88/3.87 | ~ (equalish @ u @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl4671, zip_derived_cl183])).
% 22.88/3.87 thf(zip_derived_cl120, plain,
% 22.88/3.87 ( (equalish @ u @ (add @ additive_identity @ u))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl58])).
% 22.88/3.87 thf(zip_derived_cl181, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ u @ X0)
% 22.88/3.87 | (equalish @ X0 @ (add @ additive_identity @ u)))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl21])).
% 22.88/3.87 thf(zip_derived_cl215, plain,
% 22.88/3.87 ( (equalish @ (add @ additive_identity @ u) @
% 22.88/3.87 (add @ additive_identity @ u))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl120, zip_derived_cl181])).
% 22.88/3.87 thf(zip_derived_cl4891, plain,
% 22.88/3.87 (![X0 : $i]: ( (less_or_equal @ X0 @ u) | ~ (equalish @ u @ X0))),
% 22.88/3.87 inference('demod', [status(thm)], [zip_derived_cl4783, zip_derived_cl215])).
% 22.88/3.87 thf(zip_derived_cl1, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 22.88/3.87 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 22.88/3.87 thf(zip_derived_cl25, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.88/3.87 ( (less_or_equal @ X0 @ X1)
% 22.88/3.87 | ~ (less_or_equal @ X2 @ X1)
% 22.88/3.87 | ~ (equalish @ X2 @ X0))),
% 22.88/3.87 inference('cnf', [status(esa)],
% 22.88/3.87 [compatibility_of_equality_and_order_relation])).
% 22.88/3.87 thf(zip_derived_cl64, plain,
% 22.88/3.87 (![X0 : $i, X1 : $i]:
% 22.88/3.87 (~ (defined @ X0)
% 22.88/3.87 | ~ (less_or_equal @ (add @ additive_identity @ X0) @ X1)
% 22.88/3.87 | (less_or_equal @ X0 @ X1))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl25])).
% 22.88/3.87 thf(zip_derived_cl5029, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ u @ (add @ additive_identity @ X0))
% 22.88/3.87 | (less_or_equal @ X0 @ u)
% 22.88/3.87 | ~ (defined @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl4891, zip_derived_cl64])).
% 22.88/3.87 thf(zip_derived_cl6083, plain,
% 22.88/3.87 (( (equalish @ u @ additive_identity)
% 22.88/3.87 | ~ (equalish @ u @ u)
% 22.88/3.87 | ~ (defined @ additive_identity)
% 22.88/3.87 | ~ (equalish @ u @ (add @ additive_identity @ additive_identity)))),
% 22.88/3.87 inference('sup+', [status(thm)], [zip_derived_cl2680, zip_derived_cl5029])).
% 22.88/3.87 thf(zip_derived_cl4671, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ (add @ additive_identity @ u) @ X0)
% 22.88/3.87 | (less_or_equal @ X0 @ u))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl2081, zip_derived_cl4248])).
% 22.88/3.87 thf(zip_derived_cl32, plain, (~ (less_or_equal @ additive_identity @ u)),
% 22.88/3.87 inference('cnf', [status(esa)], [zf_stmt_0])).
% 22.88/3.87 thf(zip_derived_cl4816, plain,
% 22.88/3.87 (~ (equalish @ (add @ additive_identity @ u) @ additive_identity)),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl4671, zip_derived_cl32])).
% 22.88/3.87 thf(zip_derived_cl146, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ u @ X0)
% 22.88/3.87 | (equalish @ (add @ additive_identity @ u) @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl22])).
% 22.88/3.87 thf(zip_derived_cl4913, plain, (~ (equalish @ u @ additive_identity)),
% 22.88/3.87 inference('sup+', [status(thm)], [zip_derived_cl4816, zip_derived_cl146])).
% 22.88/3.87 thf(zip_derived_cl58, plain,
% 22.88/3.87 (![X0 : $i]:
% 22.88/3.87 (~ (equalish @ (add @ b @ (additive_inverse @ a)) @ X0)
% 22.88/3.87 | (equalish @ u @ X0))),
% 22.88/3.87 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl22])).
% 22.88/3.87 thf(zip_derived_cl31, plain,
% 22.88/3.87 ( (equalish @ (add @ b @ (additive_inverse @ a)) @ u)),
% 22.88/3.87 inference('cnf', [status(esa)], [zf_stmt_1])).
% 22.88/3.87 thf(zip_derived_cl79, plain, ( (equalish @ u @ u)),
% 22.88/3.87 inference('sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl31])).
% 22.88/3.87 thf(zip_derived_cl10, plain, ( (defined @ additive_identity)),
% 22.88/3.87 inference('cnf', [status(esa)], [well_definedness_of_additive_identity])).
% 22.88/3.87 thf(zip_derived_cl6102, plain,
% 22.88/3.87 (~ (equalish @ u @ (add @ additive_identity @ additive_identity))),
% 22.88/3.87 inference('demod', [status(thm)],
% 22.88/3.87 [zip_derived_cl6083, zip_derived_cl4913, zip_derived_cl79,
% 22.88/3.87 zip_derived_cl10])).
% 22.88/3.87 thf(zip_derived_cl35781, plain, ($false),
% 22.88/3.87 inference('demod', [status(thm)],
% 22.88/3.87 [zip_derived_cl35766, zip_derived_cl34, zip_derived_cl6102])).
% 22.88/3.87
% 22.88/3.87 % SZS output end Refutation
% 22.88/3.87
% 22.88/3.87
% 22.88/3.87 % Terminating...
% 22.88/3.97 % Runner terminated.
% 22.88/3.98 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------