%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : FLD016-1 : 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.bdhPepNTQG true
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:33:10 PM UTC 2025
% Result : Unsatisfiable 183.83s 26.90s
% Output : Refutation 183.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD016-1 : TPTP v9.2.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bdhPepNTQG true
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 18:28:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in FO mode
% 0.52/0.64 % Total configuration time : 435
% 0.52/0.64 % Estimated wc time : 1092
% 0.52/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.54/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 183.83/26.90 % Solved by fo/fo5.sh.
% 183.83/26.90 % done 23509 iterations in 26.021s
% 183.83/26.90 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 183.83/26.90 % SZS output start Refutation
% 183.83/26.90 thf(defined_type, type, defined: $i > $o).
% 183.83/26.90 thf(v_type, type, v: $i).
% 183.83/26.90 thf(additive_identity_type, type, additive_identity: $i).
% 183.83/26.90 thf(add_type, type, add: $i > $i > $i).
% 183.83/26.90 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 183.83/26.90 thf(b_type, type, b: $i).
% 183.83/26.90 thf(u_type, type, u: $i).
% 183.83/26.90 thf(equalish_type, type, equalish: $i > $i > $o).
% 183.83/26.90 thf(a_type, type, a: $i).
% 183.83/26.90 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 183.83/26.90 thf(u_not_equal_to_v_7, conjecture, (equalish @ u @ v)).
% 183.83/26.90 thf(zf_stmt_0, negated_conjecture, (~( equalish @ u @ v )),
% 183.83/26.90 inference('cnf.neg', [status(esa)], [u_not_equal_to_v_7])).
% 183.83/26.90 thf(zip_derived_cl33, plain, (~ (equalish @ u @ v)),
% 183.83/26.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 183.83/26.90 thf(well_definedness_of_additive_inverse, axiom,
% 183.83/26.90 (( defined @ ( additive_inverse @ X ) ) | ( ~( defined @ X ) ))).
% 183.83/26.90 thf(zip_derived_cl11, plain,
% 183.83/26.90 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 183.83/26.90 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 183.83/26.90 thf(commutativity_addition, axiom,
% 183.83/26.90 (( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) ) | ( ~( defined @ X ) ) |
% 183.83/26.90 ( ~( defined @ Y ) ))).
% 183.83/26.90 thf(zip_derived_cl3, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]:
% 183.83/26.90 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 183.83/26.90 | ~ (defined @ X0)
% 183.83/26.90 | ~ (defined @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [commutativity_addition])).
% 183.83/26.90 thf(add_equals_b_6, conjecture, (~( equalish @ ( add @ a @ v ) @ b ))).
% 183.83/26.90 thf(zf_stmt_1, negated_conjecture, (equalish @ ( add @ a @ v ) @ b),
% 183.83/26.90 inference('cnf.neg', [status(esa)], [add_equals_b_6])).
% 183.83/26.90 thf(zip_derived_cl32, plain, ( (equalish @ (add @ a @ v) @ b)),
% 183.83/26.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 183.83/26.90 thf(symmetry_of_equality, axiom,
% 183.83/26.90 (( equalish @ X @ Y ) | ( ~( equalish @ Y @ X ) ))).
% 183.83/26.90 thf(zip_derived_cl21, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 183.83/26.90 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 183.83/26.90 thf(zip_derived_cl36, plain, ( (equalish @ b @ (add @ a @ v))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl21])).
% 183.83/26.90 thf(transitivity_of_equality, axiom,
% 183.83/26.90 (( equalish @ X @ Z ) | ( ~( equalish @ X @ Y ) ) |
% 183.83/26.90 ( ~( equalish @ Y @ Z ) ))).
% 183.83/26.90 thf(zip_derived_cl22, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 ( (equalish @ X0 @ X1)
% 183.83/26.90 | ~ (equalish @ X0 @ X2)
% 183.83/26.90 | ~ (equalish @ X2 @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.90 thf(zip_derived_cl48, plain,
% 183.83/26.90 (![X0 : $i]: (~ (equalish @ (add @ a @ v) @ X0) | (equalish @ b @ X0))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl22])).
% 183.83/26.90 thf(zip_derived_cl159, plain,
% 183.83/26.90 ((~ (defined @ v) | ~ (defined @ a) | (equalish @ b @ (add @ v @ a)))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl48])).
% 183.83/26.90 thf(v_is_defined, axiom, (defined @ v)).
% 183.83/26.90 thf(zip_derived_cl30, plain, ( (defined @ v)),
% 183.83/26.90 inference('cnf', [status(esa)], [v_is_defined])).
% 183.83/26.90 thf(a_is_defined, axiom, (defined @ a)).
% 183.83/26.90 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.90 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.90 thf(zip_derived_cl163, plain, ( (equalish @ b @ (add @ v @ a))),
% 183.83/26.90 inference('demod', [status(thm)],
% 183.83/26.90 [zip_derived_cl159, zip_derived_cl30, zip_derived_cl27])).
% 183.83/26.90 thf(zip_derived_cl3, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]:
% 183.83/26.90 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 183.83/26.90 | ~ (defined @ X0)
% 183.83/26.90 | ~ (defined @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [commutativity_addition])).
% 183.83/26.90 thf(add_equals_b_5, conjecture, (~( equalish @ ( add @ a @ u ) @ b ))).
% 183.83/26.90 thf(zf_stmt_2, negated_conjecture, (equalish @ ( add @ a @ u ) @ b),
% 183.83/26.90 inference('cnf.neg', [status(esa)], [add_equals_b_5])).
% 183.83/26.90 thf(zip_derived_cl31, plain, ( (equalish @ (add @ a @ u) @ b)),
% 183.83/26.90 inference('cnf', [status(esa)], [zf_stmt_2])).
% 183.83/26.90 thf(zip_derived_cl21, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 183.83/26.90 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 183.83/26.90 thf(zip_derived_cl35, plain, ( (equalish @ b @ (add @ a @ u))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl21])).
% 183.83/26.90 thf(zip_derived_cl22, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 ( (equalish @ X0 @ X1)
% 183.83/26.90 | ~ (equalish @ X0 @ X2)
% 183.83/26.90 | ~ (equalish @ X2 @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.90 thf(zip_derived_cl47, plain,
% 183.83/26.90 (![X0 : $i]: (~ (equalish @ (add @ a @ u) @ X0) | (equalish @ b @ X0))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl22])).
% 183.83/26.90 thf(zip_derived_cl158, plain,
% 183.83/26.90 ((~ (defined @ u) | ~ (defined @ a) | (equalish @ b @ (add @ u @ a)))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl47])).
% 183.83/26.90 thf(u_is_defined, axiom, (defined @ u)).
% 183.83/26.90 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 183.83/26.90 inference('cnf', [status(esa)], [u_is_defined])).
% 183.83/26.90 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.90 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.90 thf(zip_derived_cl162, plain, ( (equalish @ b @ (add @ u @ a))),
% 183.83/26.90 inference('demod', [status(thm)],
% 183.83/26.90 [zip_derived_cl158, zip_derived_cl29, zip_derived_cl27])).
% 183.83/26.90 thf(zip_derived_cl21, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 183.83/26.90 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 183.83/26.90 thf(zip_derived_cl165, plain, ( (equalish @ (add @ u @ a) @ b)),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl162, zip_derived_cl21])).
% 183.83/26.90 thf(zip_derived_cl22, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 ( (equalish @ X0 @ X1)
% 183.83/26.90 | ~ (equalish @ X0 @ X2)
% 183.83/26.90 | ~ (equalish @ X2 @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.90 thf(zip_derived_cl217, plain,
% 183.83/26.90 (![X0 : $i]: (~ (equalish @ b @ X0) | (equalish @ (add @ u @ a) @ X0))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl165, zip_derived_cl22])).
% 183.83/26.90 thf(zip_derived_cl263, plain, ( (equalish @ (add @ u @ a) @ (add @ v @ a))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl163, zip_derived_cl217])).
% 183.83/26.90 thf(compatibility_of_equality_and_addition, axiom,
% 183.83/26.90 (( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) ) | ( ~( defined @ Z ) ) |
% 183.83/26.90 ( ~( equalish @ X @ Y ) ))).
% 183.83/26.90 thf(zip_derived_cl23, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 183.83/26.90 | ~ (defined @ X1)
% 183.83/26.90 | ~ (equalish @ X0 @ X2))),
% 183.83/26.90 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 183.83/26.90 thf(zip_derived_cl1216, plain,
% 183.83/26.90 (![X0 : $i]:
% 183.83/26.90 (~ (defined @ X0)
% 183.83/26.90 | (equalish @ (add @ (add @ u @ a) @ X0) @
% 183.83/26.90 (add @ (add @ v @ a) @ X0)))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl263, zip_derived_cl23])).
% 183.83/26.90 thf(zip_derived_cl11, plain,
% 183.83/26.90 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 183.83/26.90 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 183.83/26.90 thf(associativity_addition, axiom,
% 183.83/26.90 (( equalish @ ( add @ X @ ( add @ Y @ Z ) ) @ ( add @ ( add @ X @ Y ) @ Z ) ) |
% 183.83/26.90 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ) | ( ~( defined @ Z ) ))).
% 183.83/26.90 thf(zip_derived_cl0, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 ( (equalish @ (add @ X0 @ (add @ X1 @ X2)) @
% 183.83/26.90 (add @ (add @ X0 @ X1) @ X2))
% 183.83/26.90 | ~ (defined @ X0)
% 183.83/26.90 | ~ (defined @ X1)
% 183.83/26.90 | ~ (defined @ X2))),
% 183.83/26.90 inference('cnf', [status(esa)], [associativity_addition])).
% 183.83/26.90 thf(zip_derived_cl3, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]:
% 183.83/26.90 ( (equalish @ (add @ X0 @ X1) @ (add @ X1 @ X0))
% 183.83/26.90 | ~ (defined @ X0)
% 183.83/26.90 | ~ (defined @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [commutativity_addition])).
% 183.83/26.90 thf(zip_derived_cl22, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 ( (equalish @ X0 @ X1)
% 183.83/26.90 | ~ (equalish @ X0 @ X2)
% 183.83/26.90 | ~ (equalish @ X2 @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.90 thf(zip_derived_cl156, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 (~ (defined @ X1)
% 183.83/26.90 | ~ (defined @ X0)
% 183.83/26.90 | ~ (equalish @ (add @ X1 @ X0) @ X2)
% 183.83/26.90 | (equalish @ (add @ X0 @ X1) @ X2))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 183.83/26.90 thf(zip_derived_cl1308, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 (~ (defined @ X0)
% 183.83/26.90 | ~ (defined @ X1)
% 183.83/26.90 | ~ (defined @ X2)
% 183.83/26.90 | (equalish @ (add @ (add @ X1 @ X0) @ X2) @
% 183.83/26.90 (add @ (add @ X2 @ X1) @ X0))
% 183.83/26.90 | ~ (defined @ (add @ X1 @ X0))
% 183.83/26.90 | ~ (defined @ X2))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl156])).
% 183.83/26.90 thf(zip_derived_cl1347, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 (~ (defined @ (add @ X1 @ X0))
% 183.83/26.90 | (equalish @ (add @ (add @ X1 @ X0) @ X2) @
% 183.83/26.90 (add @ (add @ X2 @ X1) @ X0))
% 183.83/26.90 | ~ (defined @ X2)
% 183.83/26.90 | ~ (defined @ X1)
% 183.83/26.90 | ~ (defined @ X0))),
% 183.83/26.90 inference('simplify', [status(thm)], [zip_derived_cl1308])).
% 183.83/26.90 thf(well_definedness_of_addition, axiom,
% 183.83/26.90 (( defined @ ( add @ X @ Y ) ) | ( ~( defined @ X ) ) |
% 183.83/26.90 ( ~( defined @ Y ) ))).
% 183.83/26.90 thf(zip_derived_cl9, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]:
% 183.83/26.90 ( (defined @ (add @ X0 @ X1)) | ~ (defined @ X0) | ~ (defined @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [well_definedness_of_addition])).
% 183.83/26.90 thf(zip_derived_cl46039, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 (~ (defined @ X0)
% 183.83/26.90 | ~ (defined @ X1)
% 183.83/26.90 | ~ (defined @ X2)
% 183.83/26.90 | (equalish @ (add @ (add @ X1 @ X0) @ X2) @
% 183.83/26.90 (add @ (add @ X2 @ X1) @ X0)))),
% 183.83/26.90 inference('clc', [status(thm)], [zip_derived_cl1347, zip_derived_cl9])).
% 183.83/26.90 thf(zip_derived_cl11, plain,
% 183.83/26.90 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 183.83/26.90 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 183.83/26.90 thf(totality_of_order_relation, axiom,
% 183.83/26.90 (( less_or_equal @ X @ Y ) | ( less_or_equal @ Y @ X ) |
% 183.83/26.90 ( ~( defined @ X ) ) | ( ~( defined @ Y ) ))).
% 183.83/26.90 thf(zip_derived_cl17, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]:
% 183.83/26.90 ( (less_or_equal @ X0 @ X1)
% 183.83/26.90 | (less_or_equal @ X1 @ X0)
% 183.83/26.90 | ~ (defined @ X0)
% 183.83/26.90 | ~ (defined @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 183.83/26.90 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.90 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.90 thf(zip_derived_cl933, plain,
% 183.83/26.90 (![X0 : $i]:
% 183.83/26.90 (~ (defined @ X0)
% 183.83/26.90 | (less_or_equal @ X0 @ a)
% 183.83/26.90 | (less_or_equal @ a @ X0))),
% 183.83/26.90 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl27])).
% 183.83/26.90 thf(zip_derived_cl2858, plain,
% 183.83/26.90 (( (less_or_equal @ a @ a) | ~ (defined @ a))),
% 183.83/26.90 inference('eq_fact', [status(thm)], [zip_derived_cl933])).
% 183.83/26.90 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.90 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.90 thf(zip_derived_cl2859, plain, ( (less_or_equal @ a @ a)),
% 183.83/26.90 inference('demod', [status(thm)], [zip_derived_cl2858, zip_derived_cl27])).
% 183.83/26.90 thf(antisymmetry_of_order_relation, axiom,
% 183.83/26.90 (( equalish @ X @ Y ) | ( ~( less_or_equal @ X @ Y ) ) |
% 183.83/26.90 ( ~( less_or_equal @ Y @ X ) ))).
% 183.83/26.90 thf(zip_derived_cl15, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]:
% 183.83/26.90 ( (equalish @ X0 @ X1)
% 183.83/26.90 | ~ (less_or_equal @ X0 @ X1)
% 183.83/26.90 | ~ (less_or_equal @ X1 @ X0))),
% 183.83/26.90 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 183.83/26.90 thf(zip_derived_cl2874, plain,
% 183.83/26.90 ((~ (less_or_equal @ a @ a) | (equalish @ a @ a))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl2859, zip_derived_cl15])).
% 183.83/26.90 thf(zip_derived_cl2859, plain, ( (less_or_equal @ a @ a)),
% 183.83/26.90 inference('demod', [status(thm)], [zip_derived_cl2858, zip_derived_cl27])).
% 183.83/26.90 thf(zip_derived_cl2879, plain, ( (equalish @ a @ a)),
% 183.83/26.90 inference('demod', [status(thm)],
% 183.83/26.90 [zip_derived_cl2874, zip_derived_cl2859])).
% 183.83/26.90 thf(zip_derived_cl23, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 183.83/26.90 | ~ (defined @ X1)
% 183.83/26.90 | ~ (equalish @ X0 @ X2))),
% 183.83/26.90 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 183.83/26.90 thf(zip_derived_cl2888, plain,
% 183.83/26.90 (![X0 : $i]:
% 183.83/26.90 (~ (defined @ X0) | (equalish @ (add @ a @ X0) @ (add @ a @ X0)))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl2879, zip_derived_cl23])).
% 183.83/26.90 thf(existence_of_inverse_addition, axiom,
% 183.83/26.90 (( equalish @ ( add @ X @ ( additive_inverse @ X ) ) @ additive_identity ) |
% 183.83/26.90 ( ~( defined @ X ) ))).
% 183.83/26.90 thf(zip_derived_cl2, plain,
% 183.83/26.90 (![X0 : $i]:
% 183.83/26.90 ( (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ additive_identity)
% 183.83/26.90 | ~ (defined @ X0))),
% 183.83/26.90 inference('cnf', [status(esa)], [existence_of_inverse_addition])).
% 183.83/26.90 thf(zip_derived_cl21, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 183.83/26.90 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 183.83/26.90 thf(zip_derived_cl118, plain,
% 183.83/26.90 (![X0 : $i]:
% 183.83/26.90 (~ (defined @ X0)
% 183.83/26.90 | (equalish @ additive_identity @
% 183.83/26.90 (add @ X0 @ (additive_inverse @ X0))))),
% 183.83/26.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl21])).
% 183.83/26.90 thf(zip_derived_cl22, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.90 ( (equalish @ X0 @ X1)
% 183.83/26.90 | ~ (equalish @ X0 @ X2)
% 183.83/26.90 | ~ (equalish @ X2 @ X1))),
% 183.83/26.90 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.90 thf(zip_derived_cl2631, plain,
% 183.83/26.90 (![X0 : $i, X1 : $i]:
% 183.83/26.91 (~ (defined @ X0)
% 183.83/26.91 | ~ (equalish @ (add @ X0 @ (additive_inverse @ X0)) @ X1)
% 183.83/26.91 | (equalish @ additive_identity @ X1))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl22])).
% 183.83/26.91 thf(zip_derived_cl3452, plain,
% 183.83/26.91 ((~ (defined @ (additive_inverse @ a))
% 183.83/26.91 | (equalish @ additive_identity @ (add @ a @ (additive_inverse @ a)))
% 183.83/26.91 | ~ (defined @ a))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl2888, zip_derived_cl2631])).
% 183.83/26.91 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.91 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.91 thf(zip_derived_cl3466, plain,
% 183.83/26.91 ((~ (defined @ (additive_inverse @ a))
% 183.83/26.91 | (equalish @ additive_identity @ (add @ a @ (additive_inverse @ a))))),
% 183.83/26.91 inference('demod', [status(thm)], [zip_derived_cl3452, zip_derived_cl27])).
% 183.83/26.91 thf(zip_derived_cl3479, plain,
% 183.83/26.91 ((~ (defined @ a)
% 183.83/26.91 | (equalish @ additive_identity @ (add @ a @ (additive_inverse @ a))))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl3466])).
% 183.83/26.91 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.91 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.91 thf(zip_derived_cl3480, plain,
% 183.83/26.91 ( (equalish @ additive_identity @ (add @ a @ (additive_inverse @ a)))),
% 183.83/26.91 inference('demod', [status(thm)], [zip_derived_cl3479, zip_derived_cl27])).
% 183.83/26.91 thf(zip_derived_cl23, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.91 ( (equalish @ (add @ X0 @ X1) @ (add @ X2 @ X1))
% 183.83/26.91 | ~ (defined @ X1)
% 183.83/26.91 | ~ (equalish @ X0 @ X2))),
% 183.83/26.91 inference('cnf', [status(esa)], [compatibility_of_equality_and_addition])).
% 183.83/26.91 thf(zip_derived_cl3487, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (defined @ X0)
% 183.83/26.91 | (equalish @ (add @ additive_identity @ X0) @
% 183.83/26.91 (add @ (add @ a @ (additive_inverse @ a)) @ X0)))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl3480, zip_derived_cl23])).
% 183.83/26.91 thf(zip_derived_cl17, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]:
% 183.83/26.91 ( (less_or_equal @ X0 @ X1)
% 183.83/26.91 | (less_or_equal @ X1 @ X0)
% 183.83/26.91 | ~ (defined @ X0)
% 183.83/26.91 | ~ (defined @ X1))),
% 183.83/26.91 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 183.83/26.91 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 183.83/26.91 inference('cnf', [status(esa)], [u_is_defined])).
% 183.83/26.91 thf(zip_derived_cl935, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (defined @ X0)
% 183.83/26.91 | (less_or_equal @ X0 @ u)
% 183.83/26.91 | (less_or_equal @ u @ X0))),
% 183.83/26.91 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl29])).
% 183.83/26.91 thf(zip_derived_cl16884, plain,
% 183.83/26.91 (( (less_or_equal @ u @ u) | ~ (defined @ u))),
% 183.83/26.91 inference('eq_fact', [status(thm)], [zip_derived_cl935])).
% 183.83/26.91 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 183.83/26.91 inference('cnf', [status(esa)], [u_is_defined])).
% 183.83/26.91 thf(zip_derived_cl16885, plain, ( (less_or_equal @ u @ u)),
% 183.83/26.91 inference('demod', [status(thm)], [zip_derived_cl16884, zip_derived_cl29])).
% 183.83/26.91 thf(zip_derived_cl15, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]:
% 183.83/26.91 ( (equalish @ X0 @ X1)
% 183.83/26.91 | ~ (less_or_equal @ X0 @ X1)
% 183.83/26.91 | ~ (less_or_equal @ X1 @ X0))),
% 183.83/26.91 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 183.83/26.91 thf(zip_derived_cl16903, plain,
% 183.83/26.91 ((~ (less_or_equal @ u @ u) | (equalish @ u @ u))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl16885, zip_derived_cl15])).
% 183.83/26.91 thf(zip_derived_cl16885, plain, ( (less_or_equal @ u @ u)),
% 183.83/26.91 inference('demod', [status(thm)], [zip_derived_cl16884, zip_derived_cl29])).
% 183.83/26.91 thf(zip_derived_cl16908, plain, ( (equalish @ u @ u)),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl16903, zip_derived_cl16885])).
% 183.83/26.91 thf(existence_of_identity_addition, axiom,
% 183.83/26.91 (( equalish @ ( add @ additive_identity @ X ) @ X ) | ( ~( defined @ X ) ))).
% 183.83/26.91 thf(zip_derived_cl1, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 ( (equalish @ (add @ additive_identity @ X0) @ X0) | ~ (defined @ X0))),
% 183.83/26.91 inference('cnf', [status(esa)], [existence_of_identity_addition])).
% 183.83/26.91 thf(zip_derived_cl22, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.91 ( (equalish @ X0 @ X1)
% 183.83/26.91 | ~ (equalish @ X0 @ X2)
% 183.83/26.91 | ~ (equalish @ X2 @ X1))),
% 183.83/26.91 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.91 thf(zip_derived_cl66, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]:
% 183.83/26.91 (~ (defined @ X0)
% 183.83/26.91 | ~ (equalish @ X0 @ X1)
% 183.83/26.91 | (equalish @ (add @ additive_identity @ X0) @ X1))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 183.83/26.91 thf(zip_derived_cl16911, plain,
% 183.83/26.91 (( (equalish @ (add @ additive_identity @ u) @ u) | ~ (defined @ u))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl16908, zip_derived_cl66])).
% 183.83/26.91 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 183.83/26.91 inference('cnf', [status(esa)], [u_is_defined])).
% 183.83/26.91 thf(zip_derived_cl16920, plain,
% 183.83/26.91 ( (equalish @ (add @ additive_identity @ u) @ u)),
% 183.83/26.91 inference('demod', [status(thm)], [zip_derived_cl16911, zip_derived_cl29])).
% 183.83/26.91 thf(zip_derived_cl21, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 183.83/26.91 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 183.83/26.91 thf(zip_derived_cl16940, plain,
% 183.83/26.91 ( (equalish @ u @ (add @ additive_identity @ u))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl16920, zip_derived_cl21])).
% 183.83/26.91 thf(zip_derived_cl22, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.91 ( (equalish @ X0 @ X1)
% 183.83/26.91 | ~ (equalish @ X0 @ X2)
% 183.83/26.91 | ~ (equalish @ X2 @ X1))),
% 183.83/26.91 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.91 thf(zip_derived_cl16971, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (equalish @ (add @ additive_identity @ u) @ X0)
% 183.83/26.91 | (equalish @ u @ X0))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl16940, zip_derived_cl22])).
% 183.83/26.91 thf(zip_derived_cl142302, plain,
% 183.83/26.91 ((~ (defined @ u)
% 183.83/26.91 | (equalish @ u @ (add @ (add @ a @ (additive_inverse @ a)) @ u)))),
% 183.83/26.91 inference('sup-', [status(thm)],
% 183.83/26.91 [zip_derived_cl3487, zip_derived_cl16971])).
% 183.83/26.91 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 183.83/26.91 inference('cnf', [status(esa)], [u_is_defined])).
% 183.83/26.91 thf(zip_derived_cl142344, plain,
% 183.83/26.91 ( (equalish @ u @ (add @ (add @ a @ (additive_inverse @ a)) @ u))),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl142302, zip_derived_cl29])).
% 183.83/26.91 thf(zip_derived_cl22, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.91 ( (equalish @ X0 @ X1)
% 183.83/26.91 | ~ (equalish @ X0 @ X2)
% 183.83/26.91 | ~ (equalish @ X2 @ X1))),
% 183.83/26.91 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.91 thf(zip_derived_cl142464, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (equalish @ (add @ (add @ a @ (additive_inverse @ a)) @ u) @ X0)
% 183.83/26.91 | (equalish @ u @ X0))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl142344, zip_derived_cl22])).
% 183.83/26.91 thf(zip_derived_cl142532, plain,
% 183.83/26.91 ((~ (defined @ u)
% 183.83/26.91 | ~ (defined @ a)
% 183.83/26.91 | ~ (defined @ (additive_inverse @ a))
% 183.83/26.91 | (equalish @ u @ (add @ (add @ u @ a) @ (additive_inverse @ a))))),
% 183.83/26.91 inference('sup-', [status(thm)],
% 183.83/26.91 [zip_derived_cl46039, zip_derived_cl142464])).
% 183.83/26.91 thf(zip_derived_cl29, plain, ( (defined @ u)),
% 183.83/26.91 inference('cnf', [status(esa)], [u_is_defined])).
% 183.83/26.91 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.91 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.91 thf(zip_derived_cl142556, plain,
% 183.83/26.91 ((~ (defined @ (additive_inverse @ a))
% 183.83/26.91 | (equalish @ u @ (add @ (add @ u @ a) @ (additive_inverse @ a))))),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl142532, zip_derived_cl29, zip_derived_cl27])).
% 183.83/26.91 thf(zip_derived_cl146481, plain,
% 183.83/26.91 ((~ (defined @ a)
% 183.83/26.91 | (equalish @ u @ (add @ (add @ u @ a) @ (additive_inverse @ a))))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl142556])).
% 183.83/26.91 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.91 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.91 thf(zip_derived_cl146482, plain,
% 183.83/26.91 ( (equalish @ u @ (add @ (add @ u @ a) @ (additive_inverse @ a)))),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl146481, zip_derived_cl27])).
% 183.83/26.91 thf(zip_derived_cl22, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.91 ( (equalish @ X0 @ X1)
% 183.83/26.91 | ~ (equalish @ X0 @ X2)
% 183.83/26.91 | ~ (equalish @ X2 @ X1))),
% 183.83/26.91 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.91 thf(zip_derived_cl146489, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (equalish @ (add @ (add @ u @ a) @ (additive_inverse @ a)) @ X0)
% 183.83/26.91 | (equalish @ u @ X0))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl146482, zip_derived_cl22])).
% 183.83/26.91 thf(zip_derived_cl146561, plain,
% 183.83/26.91 ((~ (defined @ (additive_inverse @ a))
% 183.83/26.91 | (equalish @ u @ (add @ (add @ v @ a) @ (additive_inverse @ a))))),
% 183.83/26.91 inference('sup-', [status(thm)],
% 183.83/26.91 [zip_derived_cl1216, zip_derived_cl146489])).
% 183.83/26.91 thf(zip_derived_cl147914, plain,
% 183.83/26.91 ((~ (defined @ a)
% 183.83/26.91 | (equalish @ u @ (add @ (add @ v @ a) @ (additive_inverse @ a))))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl146561])).
% 183.83/26.91 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.91 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.91 thf(zip_derived_cl147915, plain,
% 183.83/26.91 ( (equalish @ u @ (add @ (add @ v @ a) @ (additive_inverse @ a)))),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl147914, zip_derived_cl27])).
% 183.83/26.91 thf(zip_derived_cl21, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 183.83/26.91 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 183.83/26.91 thf(zip_derived_cl147921, plain,
% 183.83/26.91 ( (equalish @ (add @ (add @ v @ a) @ (additive_inverse @ a)) @ u)),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl147915, zip_derived_cl21])).
% 183.83/26.91 thf(zip_derived_cl11, plain,
% 183.83/26.91 (![X0 : $i]: ( (defined @ (additive_inverse @ X0)) | ~ (defined @ X0))),
% 183.83/26.91 inference('cnf', [status(esa)], [well_definedness_of_additive_inverse])).
% 183.83/26.91 thf(zip_derived_cl46039, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.91 (~ (defined @ X0)
% 183.83/26.91 | ~ (defined @ X1)
% 183.83/26.91 | ~ (defined @ X2)
% 183.83/26.91 | (equalish @ (add @ (add @ X1 @ X0) @ X2) @
% 183.83/26.91 (add @ (add @ X2 @ X1) @ X0)))),
% 183.83/26.91 inference('clc', [status(thm)], [zip_derived_cl1347, zip_derived_cl9])).
% 183.83/26.91 thf(zip_derived_cl3487, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (defined @ X0)
% 183.83/26.91 | (equalish @ (add @ additive_identity @ X0) @
% 183.83/26.91 (add @ (add @ a @ (additive_inverse @ a)) @ X0)))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl3480, zip_derived_cl23])).
% 183.83/26.91 thf(zip_derived_cl17, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]:
% 183.83/26.91 ( (less_or_equal @ X0 @ X1)
% 183.83/26.91 | (less_or_equal @ X1 @ X0)
% 183.83/26.91 | ~ (defined @ X0)
% 183.83/26.91 | ~ (defined @ X1))),
% 183.83/26.91 inference('cnf', [status(esa)], [totality_of_order_relation])).
% 183.83/26.91 thf(zip_derived_cl30, plain, ( (defined @ v)),
% 183.83/26.91 inference('cnf', [status(esa)], [v_is_defined])).
% 183.83/26.91 thf(zip_derived_cl936, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (defined @ X0)
% 183.83/26.91 | (less_or_equal @ X0 @ v)
% 183.83/26.91 | (less_or_equal @ v @ X0))),
% 183.83/26.91 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl30])).
% 183.83/26.91 thf(zip_derived_cl21582, plain,
% 183.83/26.91 (( (less_or_equal @ v @ v) | ~ (defined @ v))),
% 183.83/26.91 inference('eq_fact', [status(thm)], [zip_derived_cl936])).
% 183.83/26.91 thf(zip_derived_cl30, plain, ( (defined @ v)),
% 183.83/26.91 inference('cnf', [status(esa)], [v_is_defined])).
% 183.83/26.91 thf(zip_derived_cl21583, plain, ( (less_or_equal @ v @ v)),
% 183.83/26.91 inference('demod', [status(thm)], [zip_derived_cl21582, zip_derived_cl30])).
% 183.83/26.91 thf(zip_derived_cl15, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]:
% 183.83/26.91 ( (equalish @ X0 @ X1)
% 183.83/26.91 | ~ (less_or_equal @ X0 @ X1)
% 183.83/26.91 | ~ (less_or_equal @ X1 @ X0))),
% 183.83/26.91 inference('cnf', [status(esa)], [antisymmetry_of_order_relation])).
% 183.83/26.91 thf(zip_derived_cl21603, plain,
% 183.83/26.91 ((~ (less_or_equal @ v @ v) | (equalish @ v @ v))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl21583, zip_derived_cl15])).
% 183.83/26.91 thf(zip_derived_cl21583, plain, ( (less_or_equal @ v @ v)),
% 183.83/26.91 inference('demod', [status(thm)], [zip_derived_cl21582, zip_derived_cl30])).
% 183.83/26.91 thf(zip_derived_cl21609, plain, ( (equalish @ v @ v)),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl21603, zip_derived_cl21583])).
% 183.83/26.91 thf(zip_derived_cl66, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]:
% 183.83/26.91 (~ (defined @ X0)
% 183.83/26.91 | ~ (equalish @ X0 @ X1)
% 183.83/26.91 | (equalish @ (add @ additive_identity @ X0) @ X1))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 183.83/26.91 thf(zip_derived_cl21613, plain,
% 183.83/26.91 (( (equalish @ (add @ additive_identity @ v) @ v) | ~ (defined @ v))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl21609, zip_derived_cl66])).
% 183.83/26.91 thf(zip_derived_cl30, plain, ( (defined @ v)),
% 183.83/26.91 inference('cnf', [status(esa)], [v_is_defined])).
% 183.83/26.91 thf(zip_derived_cl21622, plain,
% 183.83/26.91 ( (equalish @ (add @ additive_identity @ v) @ v)),
% 183.83/26.91 inference('demod', [status(thm)], [zip_derived_cl21613, zip_derived_cl30])).
% 183.83/26.91 thf(zip_derived_cl21, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 183.83/26.91 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 183.83/26.91 thf(zip_derived_cl21630, plain,
% 183.83/26.91 ( (equalish @ v @ (add @ additive_identity @ v))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl21622, zip_derived_cl21])).
% 183.83/26.91 thf(zip_derived_cl22, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.91 ( (equalish @ X0 @ X1)
% 183.83/26.91 | ~ (equalish @ X0 @ X2)
% 183.83/26.91 | ~ (equalish @ X2 @ X1))),
% 183.83/26.91 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.91 thf(zip_derived_cl21699, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (equalish @ (add @ additive_identity @ v) @ X0)
% 183.83/26.91 | (equalish @ v @ X0))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl21630, zip_derived_cl22])).
% 183.83/26.91 thf(zip_derived_cl142307, plain,
% 183.83/26.91 ((~ (defined @ v)
% 183.83/26.91 | (equalish @ v @ (add @ (add @ a @ (additive_inverse @ a)) @ v)))),
% 183.83/26.91 inference('sup-', [status(thm)],
% 183.83/26.91 [zip_derived_cl3487, zip_derived_cl21699])).
% 183.83/26.91 thf(zip_derived_cl30, plain, ( (defined @ v)),
% 183.83/26.91 inference('cnf', [status(esa)], [v_is_defined])).
% 183.83/26.91 thf(zip_derived_cl142349, plain,
% 183.83/26.91 ( (equalish @ v @ (add @ (add @ a @ (additive_inverse @ a)) @ v))),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl142307, zip_derived_cl30])).
% 183.83/26.91 thf(zip_derived_cl22, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.91 ( (equalish @ X0 @ X1)
% 183.83/26.91 | ~ (equalish @ X0 @ X2)
% 183.83/26.91 | ~ (equalish @ X2 @ X1))),
% 183.83/26.91 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.91 thf(zip_derived_cl142593, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (equalish @ (add @ (add @ a @ (additive_inverse @ a)) @ v) @ X0)
% 183.83/26.91 | (equalish @ v @ X0))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl142349, zip_derived_cl22])).
% 183.83/26.91 thf(zip_derived_cl142661, plain,
% 183.83/26.91 ((~ (defined @ v)
% 183.83/26.91 | ~ (defined @ a)
% 183.83/26.91 | ~ (defined @ (additive_inverse @ a))
% 183.83/26.91 | (equalish @ v @ (add @ (add @ v @ a) @ (additive_inverse @ a))))),
% 183.83/26.91 inference('sup-', [status(thm)],
% 183.83/26.91 [zip_derived_cl46039, zip_derived_cl142593])).
% 183.83/26.91 thf(zip_derived_cl30, plain, ( (defined @ v)),
% 183.83/26.91 inference('cnf', [status(esa)], [v_is_defined])).
% 183.83/26.91 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.91 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.91 thf(zip_derived_cl142685, plain,
% 183.83/26.91 ((~ (defined @ (additive_inverse @ a))
% 183.83/26.91 | (equalish @ v @ (add @ (add @ v @ a) @ (additive_inverse @ a))))),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl142661, zip_derived_cl30, zip_derived_cl27])).
% 183.83/26.91 thf(zip_derived_cl148045, plain,
% 183.83/26.91 ((~ (defined @ a)
% 183.83/26.91 | (equalish @ v @ (add @ (add @ v @ a) @ (additive_inverse @ a))))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl142685])).
% 183.83/26.91 thf(zip_derived_cl27, plain, ( (defined @ a)),
% 183.83/26.91 inference('cnf', [status(esa)], [a_is_defined])).
% 183.83/26.91 thf(zip_derived_cl148046, plain,
% 183.83/26.91 ( (equalish @ v @ (add @ (add @ v @ a) @ (additive_inverse @ a)))),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl148045, zip_derived_cl27])).
% 183.83/26.91 thf(zip_derived_cl22, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 183.83/26.91 ( (equalish @ X0 @ X1)
% 183.83/26.91 | ~ (equalish @ X0 @ X2)
% 183.83/26.91 | ~ (equalish @ X2 @ X1))),
% 183.83/26.91 inference('cnf', [status(esa)], [transitivity_of_equality])).
% 183.83/26.91 thf(zip_derived_cl148053, plain,
% 183.83/26.91 (![X0 : $i]:
% 183.83/26.91 (~ (equalish @ (add @ (add @ v @ a) @ (additive_inverse @ a)) @ X0)
% 183.83/26.91 | (equalish @ v @ X0))),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl148046, zip_derived_cl22])).
% 183.83/26.91 thf(zip_derived_cl148137, plain, ( (equalish @ v @ u)),
% 183.83/26.91 inference('sup-', [status(thm)],
% 183.83/26.91 [zip_derived_cl147921, zip_derived_cl148053])).
% 183.83/26.91 thf(zip_derived_cl21, plain,
% 183.83/26.91 (![X0 : $i, X1 : $i]: ( (equalish @ X0 @ X1) | ~ (equalish @ X1 @ X0))),
% 183.83/26.91 inference('cnf', [status(esa)], [symmetry_of_equality])).
% 183.83/26.91 thf(zip_derived_cl148150, plain, ( (equalish @ u @ v)),
% 183.83/26.91 inference('sup-', [status(thm)], [zip_derived_cl148137, zip_derived_cl21])).
% 183.83/26.91 thf(zip_derived_cl148187, plain, ($false),
% 183.83/26.91 inference('demod', [status(thm)],
% 183.83/26.91 [zip_derived_cl33, zip_derived_cl148150])).
% 183.83/26.91
% 183.83/26.91 % SZS output end Refutation
% 183.83/26.91
% 183.83/26.91
% 183.83/26.91 % Terminating...
% 184.27/26.99 % Runner terminated.
% 184.27/27.02 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------