TSTP Solution File: NUM013-1 by Refute---2015
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%------------------------------------------------------------------------------
% File : Refute---2015
% Problem : NUM013-1 : TPTP v6.4.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : isabelle tptp_refute %d %s
% Computer : n004.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 16091.75MB
% OS : Linux 3.10.0-327.10.1.el7.x86_64
% CPULimit : 300s
% DateTime : Thu Apr 14 01:54:33 EDT 2016
% Result : Timeout 300.07s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM013-1 : TPTP v6.4.0. Bugfixed v1.2.1.
% 0.00/0.04 % Command : isabelle tptp_refute %d %s
% 0.03/0.23 % Computer : n004.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 16091.75MB
% 0.03/0.23 % OS : Linux 3.10.0-327.10.1.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Tue Apr 5 15:11:09 CDT 2016
% 0.03/0.24 % CPUTime :
% 6.26/5.88 > val it = (): unit
% 6.87/6.42 Trying to find a model that refutes: True
% 12.59/12.13 Unfolded term: [| ~ bnd_subset bnd_natural_numbers bnd_f78;
% 12.59/12.13 !!Xk. ~ bnd_member Xk bnd_f78 | bnd_member (bnd_successor Xk) bnd_f78;
% 12.59/12.13 bnd_member bnd_empty_set bnd_f78;
% 12.59/12.13 !!Z X.
% 12.59/12.13 ((bnd_member Z bnd_even_numbers |
% 12.59/12.13 ~ bnd_member Z bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member X bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_apply_to_two_arguments bnd_plus X X = Z;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_even_numbers |
% 12.59/12.13 bnd_apply_to_two_arguments bnd_plus (bnd_f59 Z) (bnd_f59 Z) = Z;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_even_numbers |
% 12.59/12.13 bnd_member (bnd_f59 Z) bnd_natural_numbers;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_even_numbers | bnd_member Z bnd_natural_numbers;
% 12.59/12.13 !!Z. (bnd_member Z bnd_twin_prime_numbers |
% 12.59/12.13 ~ bnd_member Z bnd_prime_numbers) |
% 12.59/12.13 ~ bnd_member (bnd_successor (bnd_successor Z)) bnd_prime_numbers;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_twin_prime_numbers |
% 12.59/12.13 bnd_member (bnd_successor (bnd_successor Z)) bnd_prime_numbers;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_twin_prime_numbers |
% 12.59/12.13 bnd_member Z bnd_prime_numbers;
% 12.59/12.13 !!X Xn Xf.
% 12.59/12.13 (((bnd_finite X | ~ bnd_member Xn bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_maps Xf Xn X) |
% 12.59/12.13 ~ bnd_range_of Xf = X) |
% 12.59/12.13 ~ bnd_one_to_one_function Xf;
% 12.59/12.13 !!X. ~ bnd_finite X | bnd_one_to_one_function (bnd_f58 X);
% 12.59/12.13 !!X. ~ bnd_finite X | bnd_range_of (bnd_f58 X) = X;
% 12.59/12.13 !!X. ~ bnd_finite X | bnd_maps (bnd_f58 X) (bnd_f57 X) X;
% 12.59/12.13 !!X. ~ bnd_finite X | bnd_member (bnd_f57 X) bnd_natural_numbers;
% 12.59/12.13 !!Z. (((bnd_member Z bnd_prime_numbers |
% 12.59/12.13 ~ bnd_member Z bnd_natural_numbers) |
% 12.59/12.13 Z = bnd_empty_set) |
% 12.59/12.13 Z = bnd_successor bnd_empty_set) |
% 12.59/12.13 ~ bnd_member (bnd_f55 Z)
% 12.59/12.13 (bnd_non_ordered_pair (bnd_successor bnd_empty_set) Z);
% 12.59/12.13 !!Z. (((bnd_member Z bnd_prime_numbers |
% 12.59/12.13 ~ bnd_member Z bnd_natural_numbers) |
% 12.59/12.13 Z = bnd_empty_set) |
% 12.59/12.13 Z = bnd_successor bnd_empty_set) |
% 12.59/12.13 bnd_apply_to_two_arguments bnd_times (bnd_f55 Z) (bnd_f56 Z) = Z;
% 12.59/12.13 !!Z. (((bnd_member Z bnd_prime_numbers |
% 12.59/12.13 ~ bnd_member Z bnd_natural_numbers) |
% 12.59/12.13 Z = bnd_empty_set) |
% 12.59/12.13 Z = bnd_successor bnd_empty_set) |
% 12.59/12.13 bnd_member (bnd_f56 Z) bnd_natural_numbers;
% 12.59/12.13 !!Z. (((bnd_member Z bnd_prime_numbers |
% 12.59/12.13 ~ bnd_member Z bnd_natural_numbers) |
% 12.59/12.13 Z = bnd_empty_set) |
% 12.59/12.13 Z = bnd_successor bnd_empty_set) |
% 12.59/12.13 bnd_member (bnd_f55 Z) bnd_natural_numbers;
% 12.59/12.13 !!Z U V.
% 12.59/12.13 (((~ bnd_member Z bnd_prime_numbers |
% 12.59/12.13 ~ bnd_member U bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member V bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_apply_to_two_arguments bnd_times U V = Z) |
% 12.59/12.13 bnd_member U (bnd_non_ordered_pair (bnd_successor bnd_empty_set) Z);
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_prime_numbers |
% 12.59/12.13 ~ Z = bnd_successor bnd_empty_set;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_prime_numbers | ~ Z = bnd_empty_set;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_prime_numbers | bnd_member Z bnd_natural_numbers;
% 12.59/12.13 !!Z. bnd_member Z bnd_times | ~ bnd_member Z (bnd_f54 Z);
% 12.59/12.13 !!Z Uu2 Xj Xk.
% 12.59/12.13 (((((bnd_member Z bnd_times | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_member Uu2 bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member Xj bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member Xk bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member (bnd_ordered_pair (bnd_ordered_pair Uu2 Xj) Xk)
% 12.59/12.13 (bnd_f54 Z)) |
% 12.59/12.13 bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair (bnd_successor Uu2) Xj)
% 12.59/12.13 (bnd_apply_to_two_arguments bnd_plus Xk Xj))
% 12.59/12.13 (bnd_f54 Z);
% 12.59/12.13 !!Z Xi.
% 12.59/12.13 ((bnd_member Z bnd_times | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_member Xi bnd_natural_numbers) |
% 12.59/12.13 bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set Xi) bnd_empty_set)
% 12.59/12.13 (bnd_f54 Z);
% 12.59/12.13 !!Z. (bnd_member Z bnd_times | ~ bnd_little_set Z) |
% 12.59/12.13 bnd_little_set (bnd_f54 Z);
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f50 Z Xs))
% 12.59/12.13 bnd_empty_set)
% 12.59/12.13 Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair
% 12.59/12.13 (bnd_ordered_pair (bnd_successor (bnd_f51 Z Xs)) (bnd_f52 Z Xs))
% 12.59/12.13 (bnd_apply_to_two_arguments bnd_plus (bnd_f53 Z Xs)
% 12.59/12.13 (bnd_f52 Z Xs)))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f50 Z Xs))
% 12.59/12.13 bnd_empty_set)
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair (bnd_f51 Z Xs) (bnd_f52 Z Xs))
% 12.59/12.13 (bnd_f53 Z Xs))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f50 Z Xs))
% 12.59/12.13 bnd_empty_set)
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member (bnd_f53 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f50 Z Xs))
% 12.59/12.13 bnd_empty_set)
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member (bnd_f52 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f50 Z Xs))
% 12.59/12.13 bnd_empty_set)
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member (bnd_f51 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f50 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair
% 12.59/12.13 (bnd_ordered_pair (bnd_successor (bnd_f51 Z Xs)) (bnd_f52 Z Xs))
% 12.59/12.13 (bnd_apply_to_two_arguments bnd_plus (bnd_f53 Z Xs)
% 12.59/12.13 (bnd_f52 Z Xs)))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f50 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair (bnd_f51 Z Xs) (bnd_f52 Z Xs))
% 12.59/12.13 (bnd_f53 Z Xs))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f50 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member (bnd_f53 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f50 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member (bnd_f52 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_times | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f50 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member (bnd_f51 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z. bnd_member Z bnd_plus | ~ bnd_member Z (bnd_f49 Z);
% 12.59/12.13 !!Z Uu1 Xj Xk.
% 12.59/12.13 (((((bnd_member Z bnd_plus | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_member Uu1 bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member Xj bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member Xk bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member (bnd_ordered_pair (bnd_ordered_pair Uu1 Xj) Xk)
% 12.59/12.13 (bnd_f49 Z)) |
% 12.59/12.13 bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair (bnd_successor Uu1) Xj)
% 12.59/12.13 (bnd_successor Xk))
% 12.59/12.13 (bnd_f49 Z);
% 12.59/12.13 !!Z Xi.
% 12.59/12.13 ((bnd_member Z bnd_plus | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_member Xi bnd_natural_numbers) |
% 12.59/12.13 bnd_member (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set Xi) Xi)
% 12.59/12.13 (bnd_f49 Z);
% 12.59/12.13 !!Z. (bnd_member Z bnd_plus | ~ bnd_little_set Z) |
% 12.59/12.13 bnd_little_set (bnd_f49 Z);
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f45 Z Xs))
% 12.59/12.13 (bnd_f45 Z Xs))
% 12.59/12.13 Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair
% 12.59/12.13 (bnd_ordered_pair (bnd_successor (bnd_f46 Z Xs)) (bnd_f47 Z Xs))
% 12.59/12.13 (bnd_successor (bnd_f48 Z Xs)))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f45 Z Xs))
% 12.59/12.13 (bnd_f45 Z Xs))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair (bnd_f46 Z Xs) (bnd_f47 Z Xs))
% 12.59/12.13 (bnd_f48 Z Xs))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f45 Z Xs))
% 12.59/12.13 (bnd_f45 Z Xs))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member (bnd_f48 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f45 Z Xs))
% 12.59/12.13 (bnd_f45 Z Xs))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member (bnd_f47 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair bnd_empty_set (bnd_f45 Z Xs))
% 12.59/12.13 (bnd_f45 Z Xs))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member (bnd_f46 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f45 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 ~ bnd_member
% 12.59/12.13 (bnd_ordered_pair
% 12.59/12.13 (bnd_ordered_pair (bnd_successor (bnd_f46 Z Xs)) (bnd_f47 Z Xs))
% 12.59/12.13 (bnd_successor (bnd_f48 Z Xs)))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f45 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_ordered_pair (bnd_f46 Z Xs) (bnd_f47 Z Xs))
% 12.59/12.13 (bnd_f48 Z Xs))
% 12.59/12.13 Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f45 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member (bnd_f48 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f45 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member (bnd_f47 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_plus | ~ bnd_little_set Xs) |
% 12.59/12.13 bnd_member (bnd_f45 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member (bnd_f46 Z Xs) bnd_natural_numbers) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z. bnd_member Z bnd_natural_numbers | ~ bnd_member Z (bnd_f44 Z);
% 12.59/12.13 !!Z Xk.
% 12.59/12.13 ((bnd_member Z bnd_natural_numbers | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_member Xk (bnd_f44 Z)) |
% 12.59/12.13 bnd_member (bnd_successor Xk) (bnd_f44 Z);
% 12.59/12.13 !!Z. (bnd_member Z bnd_natural_numbers | ~ bnd_little_set Z) |
% 12.59/12.13 bnd_member bnd_empty_set (bnd_f44 Z);
% 12.59/12.13 !!Z. (bnd_member Z bnd_natural_numbers | ~ bnd_little_set Z) |
% 12.59/12.13 bnd_little_set (bnd_f44 Z);
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_natural_numbers | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member bnd_empty_set Xs) |
% 12.59/12.13 ~ bnd_member (bnd_successor (bnd_f43 Z Xs)) Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Z Xs.
% 12.59/12.13 (((~ bnd_member Z bnd_natural_numbers | ~ bnd_little_set Xs) |
% 12.59/12.13 ~ bnd_member bnd_empty_set Xs) |
% 12.59/12.13 bnd_member (bnd_f43 Z Xs) Xs) |
% 12.59/12.13 bnd_member Z Xs;
% 12.59/12.13 !!Xs Xf.
% 12.59/12.13 bnd_commutes Xs Xf |
% 12.59/12.13 ~ bnd_apply_to_two_arguments Xf (bnd_f41 Xs Xf) (bnd_f42 Xs Xf) =
% 12.59/12.13 bnd_apply_to_two_arguments Xf (bnd_f42 Xs Xf) (bnd_f41 Xs Xf);
% 12.59/12.13 !!Xs Xf. bnd_commutes Xs Xf | bnd_member (bnd_f42 Xs Xf) Xs;
% 12.59/12.13 !!Xs Xf. bnd_commutes Xs Xf | bnd_member (bnd_f41 Xs Xf) Xs;
% 12.59/12.13 !!Xs Xf X Y.
% 12.59/12.13 ((~ bnd_commutes Xs Xf | ~ bnd_member X Xs) | ~ bnd_member Y Xs) |
% 12.59/12.13 bnd_apply_to_two_arguments Xf X Y = bnd_apply_to_two_arguments Xf Y X;
% 12.59/12.13 !!Xs Xf Xe Xg.
% 12.59/12.13 (((bnd_group Xs Xf | ~ bnd_closed Xs Xf) | ~ bnd_associative Xs Xf) |
% 12.59/12.13 ~ bnd_identity Xs Xf Xe) |
% 12.59/12.13 ~ bnd_inverse Xs Xf Xe Xg;
% 12.59/12.13 !!Xs Xf.
% 12.59/12.13 ~ bnd_group Xs Xf | bnd_inverse Xs Xf (bnd_f39 Xs Xf) (bnd_f40 Xs Xf);
% 12.59/12.13 !!Xs Xf. ~ bnd_group Xs Xf | bnd_identity Xs Xf (bnd_f39 Xs Xf);
% 12.59/12.13 !!Xs Xf. ~ bnd_group Xs Xf | bnd_associative Xs Xf;
% 12.59/12.13 !!Xs Xf. ~ bnd_group Xs Xf | bnd_closed Xs Xf;
% 12.59/12.13 !!Xs Xf Xe Xg.
% 12.59/12.13 ((bnd_inverse Xs Xf Xe Xg | ~ bnd_maps Xg Xs Xs) |
% 12.59/12.13 ~ bnd_apply_to_two_arguments Xf (bnd_apply Xg (bnd_f38 Xs Xf Xe Xg))
% 12.59/12.13 (bnd_f38 Xs Xf Xe Xg) =
% 12.59/12.13 Xe) |
% 12.59/12.13 ~ bnd_apply_to_two_arguments Xf (bnd_f38 Xs Xf Xe Xg)
% 12.59/12.13 (bnd_apply Xg (bnd_f38 Xs Xf Xe Xg)) =
% 12.59/12.13 Xe;
% 12.59/12.13 !!Xs Xf Xe Xg.
% 12.59/12.13 (bnd_inverse Xs Xf Xe Xg | ~ bnd_maps Xg Xs Xs) |
% 12.59/12.13 bnd_member (bnd_f38 Xs Xf Xe Xg) Xs;
% 12.59/12.13 !!Xs Xf Xe Xg X.
% 12.59/12.13 (~ bnd_inverse Xs Xf Xe Xg | ~ bnd_member X Xs) |
% 12.59/12.13 bnd_apply_to_two_arguments Xf X (bnd_apply Xg X) = Xe;
% 12.59/12.13 !!Xs Xf Xe Xg X.
% 12.59/12.13 (~ bnd_inverse Xs Xf Xe Xg | ~ bnd_member X Xs) |
% 12.59/12.13 bnd_apply_to_two_arguments Xf (bnd_apply Xg X) X = Xe;
% 12.59/12.13 !!Xs Xf Xe Xg. ~ bnd_inverse Xs Xf Xe Xg | bnd_maps Xg Xs Xs;
% 12.59/12.13 !!Xs Xf Xe.
% 12.59/12.13 ((bnd_identity Xs Xf Xe | ~ bnd_member Xe Xs) |
% 12.59/12.13 ~ bnd_apply_to_two_arguments Xf Xe (bnd_f37 Xs Xf Xe) =
% 12.59/12.13 bnd_f37 Xs Xf Xe) |
% 12.59/12.13 ~ bnd_apply_to_two_arguments Xf (bnd_f37 Xs Xf Xe) Xe =
% 12.59/12.13 bnd_f37 Xs Xf Xe;
% 12.59/12.13 !!Xs Xf Xe.
% 12.59/12.13 (bnd_identity Xs Xf Xe | ~ bnd_member Xe Xs) |
% 12.59/12.13 bnd_member (bnd_f37 Xs Xf Xe) Xs;
% 12.59/12.13 !!Xs Xf Xe X.
% 12.59/12.13 (~ bnd_identity Xs Xf Xe | ~ bnd_member X Xs) |
% 12.59/12.13 bnd_apply_to_two_arguments Xf X Xe = X;
% 12.59/12.13 !!Xs Xf Xe X.
% 12.59/12.13 (~ bnd_identity Xs Xf Xe | ~ bnd_member X Xs) |
% 12.59/12.13 bnd_apply_to_two_arguments Xf Xe X = X;
% 12.59/12.13 !!Xs Xf Xe. ~ bnd_identity Xs Xf Xe | bnd_member Xe Xs;
% 12.59/12.13 !!Xs Xf.
% 12.59/12.13 bnd_associative Xs Xf |
% 12.59/12.13 ~ bnd_apply_to_two_arguments Xf
% 12.59/12.13 (bnd_apply_to_two_arguments Xf (bnd_f34 Xs Xf) (bnd_f35 Xs Xf))
% 12.59/12.13 (bnd_f36 Xs Xf) =
% 12.59/12.13 bnd_apply_to_two_arguments Xf (bnd_f34 Xs Xf)
% 12.59/12.13 (bnd_apply_to_two_arguments Xf (bnd_f35 Xs Xf) (bnd_f36 Xs Xf));
% 12.59/12.13 !!Xs Xf. bnd_associative Xs Xf | bnd_member (bnd_f36 Xs Xf) Xs;
% 12.59/12.13 !!Xs Xf. bnd_associative Xs Xf | bnd_member (bnd_f35 Xs Xf) Xs;
% 12.59/12.13 !!Xs Xf. bnd_associative Xs Xf | bnd_member (bnd_f34 Xs Xf) Xs;
% 12.59/12.13 !!Xs Xf X Y Z.
% 12.59/12.13 (((~ bnd_associative Xs Xf | ~ bnd_member X Xs) | ~ bnd_member Y Xs) |
% 12.59/12.13 ~ bnd_member Z Xs) |
% 12.59/12.13 bnd_apply_to_two_arguments Xf (bnd_apply_to_two_arguments Xf X Y) Z =
% 12.59/12.13 bnd_apply_to_two_arguments Xf X (bnd_apply_to_two_arguments Xf Y Z);
% 12.59/12.13 !!Xh Xs1 Xf1 Xs2 Xf2.
% 12.59/12.13 (((bnd_homomorphism Xh Xs1 Xf1 Xs2 Xf2 | ~ bnd_closed Xs1 Xf1) |
% 12.59/12.13 ~ bnd_closed Xs2 Xf2) |
% 12.59/12.13 ~ bnd_maps Xh Xs1 Xs2) |
% 12.59/12.13 ~ bnd_apply Xh
% 12.59/12.13 (bnd_apply_to_two_arguments Xf1 (bnd_f32 Xh Xs1 Xf1 Xs2 Xf2)
% 12.59/12.13 (bnd_f33 Xh Xs1 Xf1 Xs2 Xf2)) =
% 12.59/12.13 bnd_apply_to_two_arguments Xf2
% 12.59/12.13 (bnd_apply Xh (bnd_f32 Xh Xs1 Xf1 Xs2 Xf2))
% 12.59/12.13 (bnd_apply Xh (bnd_f33 Xh Xs1 Xf1 Xs2 Xf2));
% 12.59/12.13 !!Xh Xs1 Xf1 Xs2 Xf2.
% 12.59/12.13 (((bnd_homomorphism Xh Xs1 Xf1 Xs2 Xf2 | ~ bnd_closed Xs1 Xf1) |
% 12.59/12.13 ~ bnd_closed Xs2 Xf2) |
% 12.59/12.13 ~ bnd_maps Xh Xs1 Xs2) |
% 12.59/12.13 bnd_member (bnd_f33 Xh Xs1 Xf1 Xs2 Xf2) Xs1;
% 12.59/12.13 !!Xh Xs1 Xf1 Xs2 Xf2.
% 12.59/12.13 (((bnd_homomorphism Xh Xs1 Xf1 Xs2 Xf2 | ~ bnd_closed Xs1 Xf1) |
% 12.59/12.13 ~ bnd_closed Xs2 Xf2) |
% 12.59/12.13 ~ bnd_maps Xh Xs1 Xs2) |
% 12.59/12.13 bnd_member (bnd_f32 Xh Xs1 Xf1 Xs2 Xf2) Xs1;
% 12.59/12.13 !!Xh Xs1 Xf1 Xs2 Xf2 X Y.
% 12.59/12.13 ((~ bnd_homomorphism Xh Xs1 Xf1 Xs2 Xf2 | ~ bnd_member X Xs1) |
% 12.59/12.13 ~ bnd_member Y Xs1) |
% 12.59/12.13 bnd_apply Xh (bnd_apply_to_two_arguments Xf1 X Y) =
% 12.59/12.13 bnd_apply_to_two_arguments Xf2 (bnd_apply Xh X) (bnd_apply Xh Y);
% 12.59/12.13 !!Xh Xs1 Xf1 Xs2 Xf2.
% 12.59/12.13 ~ bnd_homomorphism Xh Xs1 Xf1 Xs2 Xf2 | bnd_maps Xh Xs1 Xs2;
% 12.59/12.13 !!Xh Xs1 Xf1 Xs2 Xf2.
% 12.59/12.13 ~ bnd_homomorphism Xh Xs1 Xf1 Xs2 Xf2 | bnd_closed Xs2 Xf2;
% 12.59/12.13 !!Xh Xs1 Xf1 Xs2 Xf2.
% 12.59/12.13 ~ bnd_homomorphism Xh Xs1 Xf1 Xs2 Xf2 | bnd_closed Xs1 Xf1;
% 12.59/12.13 !!Z Xf Xg X Y W.
% 12.59/12.13 ((((((bnd_member Z (bnd_compose Xf Xg) | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_little_set X) |
% 12.59/12.13 ~ bnd_little_set Y) |
% 12.59/12.13 ~ bnd_little_set W) |
% 12.59/12.13 ~ Z = bnd_ordered_pair X Y) |
% 12.59/12.13 ~ bnd_member (bnd_ordered_pair X W) Xf) |
% 12.59/12.13 ~ bnd_member (bnd_ordered_pair W Y) Xg;
% 12.59/12.13 !!Z Xf Xg.
% 12.59/12.13 ~ bnd_member Z (bnd_compose Xf Xg) |
% 12.59/12.13 bnd_member (bnd_ordered_pair (bnd_f31 Z Xf Xg) (bnd_f30 Z Xf Xg)) Xg;
% 12.59/12.13 !!Z Xf Xg.
% 12.59/12.13 ~ bnd_member Z (bnd_compose Xf Xg) |
% 12.59/12.13 bnd_member (bnd_ordered_pair (bnd_f29 Z Xf Xg) (bnd_f31 Z Xf Xg)) Xf;
% 12.59/12.13 !!Z Xf Xg.
% 12.59/12.13 ~ bnd_member Z (bnd_compose Xf Xg) |
% 12.59/12.13 Z = bnd_ordered_pair (bnd_f29 Z Xf Xg) (bnd_f30 Z Xf Xg);
% 12.59/12.13 !!Z Xf Xg.
% 12.59/12.13 ~ bnd_member Z (bnd_compose Xf Xg) | bnd_little_set (bnd_f31 Z Xf Xg);
% 12.59/12.13 !!Z Xf Xg.
% 12.59/12.13 ~ bnd_member Z (bnd_compose Xf Xg) | bnd_little_set (bnd_f30 Z Xf Xg);
% 12.59/12.13 !!Z Xf Xg.
% 12.59/12.13 ~ bnd_member Z (bnd_compose Xf Xg) | bnd_little_set (bnd_f29 Z Xf Xg);
% 12.59/12.13 !!Xs Xf.
% 12.59/12.13 ((bnd_closed Xs Xf | ~ bnd_little_set Xs) | ~ bnd_little_set Xf) |
% 12.59/12.13 ~ bnd_maps Xf (bnd_cross_product Xs Xs) Xs;
% 12.59/12.13 !!Xs Xf. ~ bnd_closed Xs Xf | bnd_maps Xf (bnd_cross_product Xs Xs) Xs;
% 12.59/12.13 !!Xs Xf. ~ bnd_closed Xs Xf | bnd_little_set Xf;
% 12.59/12.13 !!Xs Xf. ~ bnd_closed Xs Xf | bnd_little_set Xs;
% 12.59/12.13 !!Xf X Y.
% 12.59/12.13 ((bnd_maps Xf X Y | ~ bnd_function Xf) | ~ bnd_domain_of Xf = X) |
% 12.59/12.13 ~ bnd_subset (bnd_range_of Xf) Y;
% 12.59/12.13 !!Xf X Y. ~ bnd_maps Xf X Y | bnd_subset (bnd_range_of Xf) Y;
% 12.59/12.13 !!Xf X Y. ~ bnd_maps Xf X Y | bnd_domain_of Xf = X;
% 12.59/12.13 !!Xf X Y. ~ bnd_maps Xf X Y | bnd_function Xf;
% 12.59/12.13 !!Xf X Y.
% 12.59/12.13 bnd_apply_to_two_arguments Xf X Y =
% 12.59/12.13 bnd_apply Xf (bnd_ordered_pair X Y);
% 12.59/12.13 !!Z Xf Y W.
% 12.59/12.13 (((bnd_member Z (bnd_apply Xf Y) | ~ bnd_ordered_pair_predicate W) |
% 12.59/12.13 ~ bnd_member W Xf) |
% 12.59/12.13 ~ bnd_first W = Y) |
% 12.59/12.13 ~ bnd_member Z (bnd_second W);
% 12.59/12.13 !!Z Xf Y.
% 12.59/12.13 ~ bnd_member Z (bnd_apply Xf Y) |
% 12.59/12.13 bnd_member Z (bnd_second (bnd_f28 Z Xf Y));
% 12.59/12.13 !!Z Xf Y.
% 12.59/12.13 ~ bnd_member Z (bnd_apply Xf Y) | bnd_first (bnd_f28 Z Xf Y) = Y;
% 12.59/12.13 !!Z Xf Y.
% 12.59/12.13 ~ bnd_member Z (bnd_apply Xf Y) | bnd_member (bnd_f28 Z Xf Y) Xf;
% 12.59/12.13 !!Z Xf Y.
% 12.59/12.13 ~ bnd_member Z (bnd_apply Xf Y) |
% 12.59/12.13 bnd_ordered_pair_predicate (bnd_f28 Z Xf Y);
% 12.59/12.13 !!Xf. (bnd_one_to_one_function Xf | ~ bnd_function Xf) |
% 12.59/12.13 ~ bnd_function (bnd_converse Xf);
% 12.59/12.13 !!Xf. ~ bnd_one_to_one_function Xf | bnd_function (bnd_converse Xf);
% 12.59/12.13 !!Xf. ~ bnd_one_to_one_function Xf | bnd_function Xf;
% 12.59/12.13 !!X Y.
% 12.59/12.13 bnd_restrict X Y =
% 12.59/12.13 bnd_intersection X (bnd_cross_product Y bnd_universal_set);
% 12.59/12.13 !!Z. ((bnd_member Z bnd_identity_relation | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_ordered_pair_predicate Z) |
% 12.59/12.13 ~ bnd_first Z = bnd_second Z;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_identity_relation | bnd_first Z = bnd_second Z;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_identity_relation | bnd_ordered_pair_predicate Z;
% 12.59/12.13 !!Z X Xp.
% 12.59/12.13 (((bnd_member Z (bnd_range_of X) | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_ordered_pair_predicate Xp) |
% 12.59/12.13 ~ bnd_member Xp X) |
% 12.59/12.13 ~ Z = bnd_second Xp;
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_range_of X) | Z = bnd_second (bnd_f27 Z X);
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_range_of X) | bnd_member (bnd_f27 Z X) X;
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_range_of X) |
% 12.59/12.13 bnd_ordered_pair_predicate (bnd_f27 Z X);
% 12.59/12.13 !!X. (~ bnd_little_set X | X = bnd_empty_set) |
% 12.59/12.13 bnd_member (bnd_ordered_pair X (bnd_f26 X)) bnd_f25;
% 12.59/12.13 !!X. (~ bnd_little_set X | X = bnd_empty_set) | bnd_member (bnd_f26 X) X;
% 12.59/12.13 bnd_function bnd_f25;
% 12.59/12.13 !!X. X = bnd_empty_set | bnd_disjoint (bnd_f24 X) X;
% 12.59/12.13 !!X. X = bnd_empty_set | bnd_member (bnd_f24 X) X;
% 12.59/12.13 !!X Y. bnd_disjoint X Y | bnd_member (bnd_f23 X Y) Y;
% 12.59/12.13 !!X Y. bnd_disjoint X Y | bnd_member (bnd_f23 X Y) X;
% 12.59/12.13 !!X Y U. (~ bnd_disjoint X Y | ~ bnd_member U X) | ~ bnd_member U Y;
% 12.59/12.13 !!X Xf.
% 12.59/12.13 (~ bnd_little_set X | ~ bnd_function Xf) |
% 12.59/12.13 bnd_little_set (bnd_image X Xf);
% 12.59/12.13 !!Z X Xf Y.
% 12.59/12.13 ((((bnd_member Z (bnd_image X Xf) | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_ordered_pair_predicate Y) |
% 12.59/12.13 ~ bnd_member Y Xf) |
% 12.59/12.13 ~ bnd_member (bnd_first Y) X) |
% 12.59/12.13 ~ bnd_second Y = Z;
% 12.59/12.13 !!Z X Xf.
% 12.59/12.13 ~ bnd_member Z (bnd_image X Xf) | bnd_second (bnd_f22 Z X Xf) = Z;
% 12.59/12.13 !!Z X Xf.
% 12.59/12.13 ~ bnd_member Z (bnd_image X Xf) |
% 12.59/12.13 bnd_member (bnd_first (bnd_f22 Z X Xf)) X;
% 12.59/12.13 !!Z X Xf.
% 12.59/12.13 ~ bnd_member Z (bnd_image X Xf) | bnd_member (bnd_f22 Z X Xf) Xf;
% 12.59/12.13 !!Z X Xf.
% 12.59/12.13 ~ bnd_member Z (bnd_image X Xf) |
% 12.59/12.13 bnd_ordered_pair_predicate (bnd_f22 Z X Xf);
% 12.59/12.13 !!Xf. (bnd_function Xf | ~ bnd_relation Xf) | ~ bnd_single_valued_set Xf;
% 12.59/12.13 !!Xf. ~ bnd_function Xf | bnd_single_valued_set Xf;
% 12.59/12.13 !!Xf. ~ bnd_function Xf | bnd_relation Xf;
% 12.59/12.13 !!X. bnd_single_valued_set X | ~ bnd_f20 X = bnd_f21 X;
% 12.59/12.13 !!X. bnd_single_valued_set X |
% 12.59/12.13 bnd_member (bnd_ordered_pair (bnd_f19 X) (bnd_f21 X)) X;
% 12.59/12.13 !!X. bnd_single_valued_set X |
% 12.59/12.13 bnd_member (bnd_ordered_pair (bnd_f19 X) (bnd_f20 X)) X;
% 12.59/12.13 !!X. bnd_single_valued_set X | bnd_little_set (bnd_f21 X);
% 12.59/12.13 !!X. bnd_single_valued_set X | bnd_little_set (bnd_f20 X);
% 12.59/12.13 !!X. bnd_single_valued_set X | bnd_little_set (bnd_f19 X);
% 12.59/12.13 !!X U V W.
% 12.59/12.13 (((((~ bnd_single_valued_set X | ~ bnd_little_set U) |
% 12.59/12.13 ~ bnd_little_set V) |
% 12.59/12.13 ~ bnd_little_set W) |
% 12.59/12.13 ~ bnd_member (bnd_ordered_pair U V) X) |
% 12.59/12.13 ~ bnd_member (bnd_ordered_pair U W) X) |
% 12.59/12.13 V = W;
% 12.59/12.13 !!Z. bnd_relation Z | ~ bnd_ordered_pair_predicate (bnd_f18 Z);
% 12.59/12.13 !!Z. bnd_relation Z | bnd_member (bnd_f18 Z) Z;
% 12.59/12.13 !!Z X.
% 12.59/12.13 (~ bnd_relation Z | ~ bnd_member X Z) | bnd_ordered_pair_predicate X;
% 12.59/12.13 !!U. ~ bnd_little_set U | bnd_little_set (bnd_powerset U);
% 12.59/12.13 !!Z X.
% 12.59/12.13 (bnd_member Z (bnd_powerset X) | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_subset Z X;
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_powerset X) | bnd_subset Z X;
% 12.59/12.13 !!X Y. (bnd_proper_subset X Y | ~ bnd_subset X Y) | X = Y;
% 12.59/12.13 !!X Y. ~ bnd_proper_subset X Y | ~ X = Y;
% 12.59/12.13 !!X Y. ~ bnd_proper_subset X Y | bnd_subset X Y;
% 12.59/12.13 !!X Y. bnd_subset X Y | ~ bnd_member (bnd_f17 X Y) Y;
% 12.59/12.13 !!X Y. bnd_subset X Y | bnd_member (bnd_f17 X Y) X;
% 12.59/12.13 !!X Y U. (~ bnd_subset X Y | ~ bnd_member U X) | bnd_member U Y;
% 12.59/12.13 !!U. ~ bnd_little_set U | bnd_little_set (bnd_sigma U);
% 12.59/12.13 !!Z X Y.
% 12.59/12.13 (bnd_member Z (bnd_sigma X) | ~ bnd_member Y X) | ~ bnd_member Z Y;
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_sigma X) | bnd_member Z (bnd_f16 Z X);
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_sigma X) | bnd_member (bnd_f16 Z X) X;
% 12.59/12.13 !!X. ~ bnd_member X bnd_infinity |
% 12.59/12.13 bnd_member (bnd_successor X) bnd_infinity;
% 12.59/12.13 bnd_member bnd_empty_set bnd_infinity; bnd_little_set bnd_infinity;
% 12.59/12.13 !!Z. bnd_member Z bnd_universal_set | ~ bnd_little_set Z;
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_empty_set;
% 12.59/12.13 !!X. bnd_successor X = bnd_union X (bnd_singleton_set X);
% 12.59/12.13 !!Z X U V W.
% 12.59/12.13 (((((bnd_member Z (bnd_flip_range_of X) | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_little_set U) |
% 12.59/12.13 ~ bnd_little_set V) |
% 12.59/12.13 ~ bnd_little_set W) |
% 12.59/12.13 ~ Z = bnd_ordered_pair U (bnd_ordered_pair V W)) |
% 12.59/12.13 ~ bnd_member (bnd_ordered_pair U (bnd_ordered_pair W V)) X;
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_flip_range_of X) |
% 12.59/12.13 bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_f12 Z X)
% 12.59/12.13 (bnd_ordered_pair (bnd_f14 Z X) (bnd_f13 Z X)))
% 12.59/12.13 X;
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_flip_range_of X) |
% 12.59/12.13 Z =
% 12.59/12.13 bnd_ordered_pair (bnd_f12 Z X)
% 12.59/12.13 (bnd_ordered_pair (bnd_f13 Z X) (bnd_f14 Z X));
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_flip_range_of X) | bnd_little_set (bnd_f14 Z X);
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_flip_range_of X) | bnd_little_set (bnd_f13 Z X);
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_flip_range_of X) | bnd_little_set (bnd_f12 Z X);
% 12.59/12.13 !!Z X U V W.
% 12.59/12.13 (((((bnd_member Z (bnd_rotate_right X) | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_little_set U) |
% 12.59/12.13 ~ bnd_little_set V) |
% 12.59/12.13 ~ bnd_little_set W) |
% 12.59/12.13 ~ Z = bnd_ordered_pair U (bnd_ordered_pair V W)) |
% 12.59/12.13 ~ bnd_member (bnd_ordered_pair V (bnd_ordered_pair W U)) X;
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_rotate_right X) |
% 12.59/12.13 bnd_member
% 12.59/12.13 (bnd_ordered_pair (bnd_f10 Z X)
% 12.59/12.13 (bnd_ordered_pair (bnd_f11 Z X) (bnd_f9 Z X)))
% 12.59/12.13 X;
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_rotate_right X) |
% 12.59/12.13 Z =
% 12.59/12.13 bnd_ordered_pair (bnd_f9 Z X)
% 12.59/12.13 (bnd_ordered_pair (bnd_f10 Z X) (bnd_f11 Z X));
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_rotate_right X) | bnd_little_set (bnd_f11 Z X);
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_rotate_right X) | bnd_little_set (bnd_f10 Z X);
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_rotate_right X) | bnd_little_set (bnd_f9 Z X);
% 12.59/12.13 !!Z X.
% 12.59/12.13 ((bnd_member Z (bnd_converse X) | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_ordered_pair_predicate Z) |
% 12.59/12.13 ~ bnd_member (bnd_ordered_pair (bnd_second Z) (bnd_first Z)) X;
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_converse X) |
% 12.59/12.13 bnd_member (bnd_ordered_pair (bnd_second Z) (bnd_first Z)) X;
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_converse X) | bnd_ordered_pair_predicate Z;
% 12.59/12.13 !!Z X Y.
% 12.59/12.13 (((bnd_member Z (bnd_cross_product X Y) | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_ordered_pair_predicate Z) |
% 12.59/12.13 ~ bnd_member (bnd_first Z) X) |
% 12.59/12.13 ~ bnd_member (bnd_second Z) Y;
% 12.59/12.13 !!Z X Y.
% 12.59/12.13 ~ bnd_member Z (bnd_cross_product X Y) | bnd_member (bnd_second Z) Y;
% 12.59/12.13 !!Z X Y.
% 12.59/12.13 ~ bnd_member Z (bnd_cross_product X Y) | bnd_member (bnd_first Z) X;
% 12.59/12.13 !!Z X Y.
% 12.59/12.13 ~ bnd_member Z (bnd_cross_product X Y) | bnd_ordered_pair_predicate Z;
% 12.59/12.13 !!Z X Xp.
% 12.59/12.13 (((bnd_member Z (bnd_domain_of X) | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_ordered_pair_predicate Xp) |
% 12.59/12.13 ~ bnd_member Xp X) |
% 12.59/12.13 ~ Z = bnd_first Xp;
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_domain_of X) | Z = bnd_first (bnd_f8 Z X);
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_domain_of X) | bnd_member (bnd_f8 Z X) X;
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_domain_of X) |
% 12.59/12.13 bnd_ordered_pair_predicate (bnd_f8 Z X);
% 12.59/12.13 !!X Y.
% 12.59/12.13 bnd_union X Y =
% 12.59/12.13 bnd_complement
% 12.59/12.13 (bnd_intersection (bnd_complement X) (bnd_complement Y));
% 12.59/12.13 !!Z X.
% 12.59/12.13 (bnd_member Z (bnd_complement X) | ~ bnd_little_set Z) |
% 12.59/12.13 bnd_member Z X;
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_complement X) | ~ bnd_member Z X;
% 12.59/12.13 !!Z X Y.
% 12.59/12.13 (bnd_member Z (bnd_intersection X Y) | ~ bnd_member Z X) |
% 12.59/12.13 ~ bnd_member Z Y;
% 12.59/12.13 !!Z X Y. ~ bnd_member Z (bnd_intersection X Y) | bnd_member Z Y;
% 12.59/12.13 !!Z X Y. ~ bnd_member Z (bnd_intersection X Y) | bnd_member Z X;
% 12.59/12.13 !!Z. ((bnd_member Z bnd_estin | ~ bnd_little_set Z) |
% 12.59/12.13 ~ bnd_ordered_pair_predicate Z) |
% 12.59/12.13 ~ bnd_member (bnd_first Z) (bnd_second Z);
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_estin | bnd_member (bnd_first Z) (bnd_second Z);
% 12.59/12.13 !!Z. ~ bnd_member Z bnd_estin | bnd_ordered_pair_predicate Z;
% 12.59/12.13 !!Z X U V.
% 12.59/12.13 (((bnd_member Z (bnd_second X) | ~ bnd_little_set U) |
% 12.59/12.13 ~ bnd_little_set V) |
% 12.59/12.13 ~ X = bnd_ordered_pair U V) |
% 12.59/12.13 ~ bnd_member Z V;
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_second X) | bnd_member Z (bnd_f7 Z X);
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_second X) |
% 12.59/12.13 X = bnd_ordered_pair (bnd_f6 Z X) (bnd_f7 Z X);
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_second X) | bnd_little_set (bnd_f7 Z X);
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_second X) | bnd_little_set (bnd_f6 Z X);
% 12.59/12.13 !!Z X U V.
% 12.59/12.13 (((bnd_member Z (bnd_first X) | ~ bnd_little_set U) |
% 12.59/12.13 ~ bnd_little_set V) |
% 12.59/12.13 ~ X = bnd_ordered_pair U V) |
% 12.59/12.13 ~ bnd_member Z U;
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_first X) | bnd_member Z (bnd_f4 Z X);
% 12.59/12.13 !!Z X.
% 12.59/12.13 ~ bnd_member Z (bnd_first X) |
% 12.59/12.13 X = bnd_ordered_pair (bnd_f4 Z X) (bnd_f5 Z X);
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_first X) | bnd_little_set (bnd_f5 Z X);
% 12.59/12.13 !!Z X. ~ bnd_member Z (bnd_first X) | bnd_little_set (bnd_f4 Z X);
% 12.59/12.13 !!X Y Z.
% 12.59/12.13 ((bnd_ordered_pair_predicate X | ~ bnd_little_set Y) |
% 12.59/12.13 ~ bnd_little_set Z) |
% 12.59/12.13 ~ X = bnd_ordered_pair Y Z;
% 12.59/12.13 !!X. ~ bnd_ordered_pair_predicate X |
% 12.59/12.13 X = bnd_ordered_pair (bnd_f2 X) (bnd_f3 X);
% 12.59/12.13 !!X. ~ bnd_ordered_pair_predicate X | bnd_little_set (bnd_f3 X);
% 12.59/12.13 !!X. ~ bnd_ordered_pair_predicate X | bnd_little_set (bnd_f2 X);
% 12.59/12.13 !!X Y.
% 12.59/12.13 bnd_ordered_pair X Y =
% 12.59/12.13 bnd_non_ordered_pair (bnd_singleton_set X) (bnd_non_ordered_pair X Y);
% 12.59/12.13 !!X. bnd_singleton_set X = bnd_non_ordered_pair X X;
% 12.59/12.13 !!X Y. bnd_little_set (bnd_non_ordered_pair X Y);
% 12.59/12.13 !!U X Y.
% 12.59/12.13 (bnd_member U (bnd_non_ordered_pair X Y) | ~ bnd_little_set U) |
% 12.59/12.13 ~ U = Y;
% 12.59/12.13 !!U X Y.
% 12.59/12.13 (bnd_member U (bnd_non_ordered_pair X Y) | ~ bnd_little_set U) |
% 12.59/12.13 ~ U = X;
% 12.59/12.13 !!U X Y. (~ bnd_member U (bnd_non_ordered_pair X Y) | U = X) | U = Y;
% 12.59/12.13 !!X Y.
% 12.59/12.13 (~ bnd_member (bnd_f1 X Y) X | ~ bnd_member (bnd_f1 X Y) Y) | X = Y;
% 12.59/12.13 !!X Y. (bnd_member (bnd_f1 X Y) X | bnd_member (bnd_f1 X Y) Y) | X = Y;
% 12.59/12.13 !!X Y. bnd_little_set (bnd_f1 X Y) | X = Y;
% 12.59/12.13 !!X Y. ~ bnd_member X Y | bnd_little_set X |]
% 12.59/12.13 ==> True
% 12.59/12.13 Adding axioms...
% 12.59/12.14 Typedef.type_definition_def
% 42.82/42.33 ...done.
% 42.82/42.38 Ground types: ?'b, TPTP_Interpret.ind
% 42.82/42.38 Translating term (sizes: 1, 1) ...
% 65.48/64.99 Invoking SAT solver...
% 65.48/64.99 No model exists.
% 65.48/64.99 Translating term (sizes: 2, 1) ...
% 88.84/88.28 Invoking SAT solver...
% 88.84/88.28 No model exists.
% 88.84/88.28 Translating term (sizes: 1, 2) ...
% 282.30/280.52 Invoking SAT solver...
% 282.30/280.52 No model exists.
% 282.30/280.52 Translating term (sizes: 3, 1) ...
% 300.07/298.13 /export/starexec/sandbox2/solver/lib/scripts/run-polyml-5.5.2: line 82: 2889 CPU time limit exceeded (core dumped) "$ISABELLE_HOME/lib/scripts/feeder" -p -h "$MLTEXT" -t "$MLEXIT" $FEEDER_OPTS
% 300.07/298.13 2890 (core dumped) | { read FPID; "$POLY" -q -i $ML_OPTIONS; RC="$?"; kill -TERM "$FPID"; exit "$RC"; }
% 300.07/298.14 /export/starexec/sandbox2/solver/src/HOL/TPTP/lib/Tools/tptp_refute: line 26: 2816 Exit 152 "$ISABELLE_PROCESS" -q -e "use_thy \"/tmp/$SCRATCH\"; exit 1;" HOL-TPTP
% 300.07/298.14 2818 CPU time limit exceeded (core dumped) | grep --line-buffered -v "^###\|^PROOF FAILED for depth\|^Failure node\|inferences so far. Searching to depth\|^val \|^Loading theory\|^Warning-The type of\|^ monotype.$"
%------------------------------------------------------------------------------