%------------------------------------------------------------------------------ % File : Refute---2015 % Problem : NUM262-2 : TPTP v6.4.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp:raw % Command : isabelle tptp_refute %d %s % Computer : n006.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 01:55:07 EDT 2016 % Result : Timeout 300.12s % 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 : NUM262-2 : TPTP v6.4.0. Bugfixed v2.1.0. % 0.00/0.04 % Command : isabelle tptp_refute %d %s % 0.03/0.23 % Computer : n006.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 18:15:24 CDT 2016 % 0.03/0.23 % CPUTime : % 6.33/5.92 > val it = (): unit % 6.73/6.38 Trying to find a model that refutes: True % 11.85/11.42 Unfolded term: [| ~ bnd_apply (bnd_recursion bnd_x bnd_y bnd_z) bnd_null_class = bnd_x; % 11.85/11.42 !!X Z. % 11.85/11.42 (((~ bnd_function X | ~ bnd_compose Z (bnd_rest_of X) = X) | % 11.85/11.42 ~ bnd_domain_of X = bnd_ordinal_numbers) | % 11.85/11.42 ~ bnd_member % 11.85/11.42 (bnd_ordered_pair % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of % 11.85/11.42 (bnd_intersection (bnd_complement X) % 11.85/11.42 (bnd_sum_class (bnd_recursion_equation_functions Z))))) % 11.85/11.42 (bnd_apply (bnd_sum_class (bnd_recursion_equation_functions Z)) % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of % 11.85/11.42 (bnd_intersection (bnd_complement X) % 11.85/11.42 (bnd_sum_class % 11.85/11.42 (bnd_recursion_equation_functions Z))))))) % 11.85/11.42 (bnd_intersection (bnd_complement X) % 11.85/11.42 (bnd_sum_class (bnd_recursion_equation_functions Z)))) | % 11.85/11.42 bnd_subclass (bnd_sum_class (bnd_recursion_equation_functions Z)) X; % 11.85/11.42 !!X Z. % 11.85/11.42 (((~ bnd_function X | ~ bnd_compose Z (bnd_rest_of X) = X) | % 11.85/11.42 ~ bnd_domain_of X = bnd_ordinal_numbers) | % 11.85/11.42 bnd_subclass (bnd_sum_class (bnd_recursion_equation_functions Z)) % 11.85/11.42 X) | % 11.85/11.42 bnd_apply (bnd_sum_class (bnd_recursion_equation_functions Z)) % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of % 11.85/11.42 (bnd_intersection (bnd_complement X) % 11.85/11.42 (bnd_sum_class (bnd_recursion_equation_functions Z))))) = % 11.85/11.42 bnd_apply X % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of % 11.85/11.42 (bnd_intersection (bnd_complement X) % 11.85/11.42 (bnd_sum_class (bnd_recursion_equation_functions Z))))); % 11.85/11.42 !!X Y. % 11.85/11.42 ((((~ bnd_function X | ~ bnd_function Y) | % 11.85/11.42 ~ bnd_domain_of X = bnd_ordinal_numbers) | % 11.85/11.42 ~ bnd_domain_of Y = bnd_ordinal_numbers) | % 11.85/11.42 X = Y) | % 11.85/11.42 bnd_restrict X % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement X) Y))) % 11.85/11.42 bnd_universal_class = % 11.85/11.42 bnd_restrict Y % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement X) Y))) % 11.85/11.42 bnd_universal_class; % 11.85/11.42 !!Z. bnd_image (bnd_comp Z) % 11.85/11.42 (bnd_image bnd_rest_relation % 11.85/11.42 (bnd_recursion_equation_functions Z)) = % 11.85/11.42 bnd_recursion_equation_functions Z; % 11.85/11.42 !!Z. ~ bnd_member Z bnd_universal_class | % 11.85/11.42 bnd_image (bnd_image bnd_composition_function (bnd_singleton Z)) % 11.85/11.42 (bnd_image bnd_rest_relation % 11.85/11.42 (bnd_recursion_equation_functions Z)) = % 11.85/11.42 bnd_recursion_equation_functions Z; % 11.85/11.42 !!X Z Y. % 11.85/11.42 ((~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 ~ bnd_member (bnd_domain_of X) (bnd_domain_of Y)) | % 11.85/11.42 bnd_subclass (bnd_rest_of X) (bnd_rest_of Y); % 11.85/11.42 !!X Z Y U. % 11.85/11.42 (((~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 ~ bnd_member (bnd_domain_of X) (bnd_domain_of Y)) | % 11.85/11.42 ~ bnd_member U (bnd_domain_of X)) | % 11.85/11.42 bnd_restrict X U bnd_universal_class = % 11.85/11.42 bnd_restrict Y U bnd_universal_class; % 11.85/11.42 !!X Z Y. % 11.85/11.42 (~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 bnd_function (bnd_union X Y); % 11.85/11.42 !!X Z Y. % 11.85/11.42 (~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 bnd_member (bnd_union X Y) (bnd_recursion_equation_functions Z); % 11.85/11.42 !!X Z Y. % 11.85/11.42 ((~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 ~ bnd_member (bnd_domain_of X) (bnd_domain_of Y)) | % 11.85/11.42 bnd_subclass X Y; % 11.85/11.42 !!X Z Y. % 11.85/11.42 (((~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 ~ bnd_member (bnd_domain_of X) (bnd_domain_of Y)) | % 11.85/11.42 bnd_subclass X Y) | % 11.85/11.42 bnd_member % 11.85/11.42 (bnd_ordered_pair % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement Y) X))) % 11.85/11.42 (bnd_apply Y % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement Y) X))))) % 11.85/11.42 Y; % 11.85/11.42 !!X Z Y. % 11.85/11.42 (((~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 ~ bnd_member (bnd_domain_of X) (bnd_domain_of Y)) | % 11.85/11.42 bnd_subclass X Y) | % 11.85/11.42 bnd_apply Y % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement Y) X))) = % 11.85/11.42 bnd_apply X % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement Y) X))); % 11.85/11.42 !!X Z Y. % 11.85/11.42 ((~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 bnd_subclass X Y) | % 11.85/11.42 bnd_restrict X % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement Y) X))) % 11.85/11.42 bnd_universal_class = % 11.85/11.42 bnd_restrict Y % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement Y) X))) % 11.85/11.42 bnd_universal_class; % 11.85/11.42 !!X Z Y U V. % 11.85/11.42 ((((~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 ~ bnd_member (bnd_ordered_pair U V) Y) | % 11.85/11.42 ~ bnd_member U % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement Y) X)))) | % 11.85/11.42 bnd_subclass X Y) | % 11.85/11.42 bnd_member (bnd_ordered_pair U V) X; % 11.85/11.42 !!X Z Y U V. % 11.85/11.42 (((~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 ~ bnd_member (bnd_ordered_pair U V) X) | % 11.85/11.42 ~ bnd_member U % 11.85/11.42 (bnd_least bnd_element_relation % 11.85/11.42 (bnd_domain_of (bnd_intersection (bnd_complement Y) X)))) | % 11.85/11.42 bnd_member (bnd_ordered_pair U V) Y; % 11.85/11.42 !!X Z Y. % 11.85/11.42 (~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 ~ bnd_member Y (bnd_recursion_equation_functions Z)) | % 11.85/11.42 bnd_subclass (bnd_domain_of (bnd_intersection (bnd_complement Y) X)) % 11.85/11.42 bnd_ordinal_numbers; % 11.85/11.42 !!X. bnd_member X bnd_omega | bnd_integer_of X = bnd_null_class; % 11.85/11.42 !!X. ~ bnd_member X bnd_omega | bnd_integer_of X = X; % 11.85/11.42 !!X Y. % 11.85/11.42 bnd_recursion bnd_null_class (bnd_apply bnd_add_relation X) % 11.85/11.42 bnd_union_of_range_map = % 11.85/11.42 bnd_ordinal_multiply X Y; % 11.85/11.42 !!X Y. % 11.85/11.42 bnd_apply % 11.85/11.42 (bnd_recursion X bnd_successor_relation bnd_union_of_range_map) Y = % 11.85/11.42 bnd_ordinal_add X Y; % 11.85/11.42 !!X Y. % 11.85/11.42 (~ bnd_member (bnd_ordered_pair X Y) % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) | % 11.85/11.42 ~ bnd_sum_class (bnd_range_of X) = Y) | % 11.85/11.42 bnd_member (bnd_ordered_pair X Y) bnd_union_of_range_map; % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X Y) bnd_union_of_range_map | % 11.85/11.42 bnd_sum_class (bnd_range_of X) = Y; % 11.85/11.42 bnd_subclass bnd_union_of_range_map % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class); % 11.85/11.42 !!Z X. % 11.85/11.42 (((~ bnd_function Z | ~ bnd_function X) | % 11.85/11.42 ~ bnd_member (bnd_domain_of X) bnd_ordinal_numbers) | % 11.85/11.42 ~ bnd_compose Z (bnd_rest_of X) = X) | % 11.85/11.42 bnd_member X (bnd_recursion_equation_functions Z); % 11.85/11.42 !!X Z. % 11.85/11.42 ~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 bnd_compose Z (bnd_rest_of X) = X; % 11.85/11.42 !!X Z. % 11.85/11.42 ~ bnd_member X (bnd_recursion_equation_functions Z) | % 11.85/11.42 bnd_member (bnd_domain_of X) bnd_ordinal_numbers; % 11.85/11.42 !!X Z. % 11.85/11.42 ~ bnd_member X (bnd_recursion_equation_functions Z) | bnd_function X; % 11.85/11.42 !!X Z. % 11.85/11.42 ~ bnd_member X (bnd_recursion_equation_functions Z) | bnd_function Z; % 11.85/11.42 !!X. ~ bnd_member X bnd_universal_class | % 11.85/11.42 bnd_member (bnd_ordered_pair X (bnd_rest_of X)) bnd_rest_relation; % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X Y) bnd_rest_relation | % 11.85/11.42 bnd_rest_of X = Y; % 11.85/11.42 bnd_subclass bnd_rest_relation % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class); % 11.85/11.42 !!U X V. % 11.85/11.42 (~ bnd_member U (bnd_domain_of X) | % 11.85/11.42 ~ bnd_restrict X U bnd_universal_class = V) | % 11.85/11.42 bnd_member (bnd_ordered_pair U V) (bnd_rest_of X); % 11.85/11.42 !!U V X. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair U V) (bnd_rest_of X) | % 11.85/11.42 bnd_restrict X U bnd_universal_class = V; % 11.85/11.42 !!U V X. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair U V) (bnd_rest_of X) | % 11.85/11.42 bnd_member U (bnd_domain_of X); % 11.85/11.42 !!X. bnd_subclass (bnd_rest_of X) % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class); % 11.85/11.42 bnd_intersection (bnd_complement bnd_kind_1_ordinals) % 11.85/11.42 bnd_ordinal_numbers = % 11.85/11.42 bnd_limit_ordinals; % 11.85/11.42 bnd_union (bnd_singleton bnd_null_class) % 11.85/11.42 (bnd_image bnd_successor_relation bnd_ordinal_numbers) = % 11.85/11.42 bnd_kind_1_ordinals; % 11.85/11.42 !!X. ((~ bnd_well_ordering bnd_element_relation X | % 11.85/11.42 ~ bnd_subclass (bnd_sum_class X) X) | % 11.85/11.42 bnd_member X bnd_ordinal_numbers) | % 11.85/11.42 X = bnd_ordinal_numbers; % 11.85/11.42 !!X. ((~ bnd_well_ordering bnd_element_relation X | % 11.85/11.42 ~ bnd_subclass (bnd_sum_class X) X) | % 11.85/11.42 ~ bnd_member X bnd_universal_class) | % 11.85/11.42 bnd_member X bnd_ordinal_numbers; % 11.85/11.42 !!X. ~ bnd_member X bnd_ordinal_numbers | % 11.85/11.42 bnd_subclass (bnd_sum_class X) X; % 11.85/11.42 !!X. ~ bnd_member X bnd_ordinal_numbers | % 11.85/11.42 bnd_well_ordering bnd_element_relation X; % 11.85/11.42 !!Y Z Xr. % 11.85/11.42 (~ bnd_subclass Y Z | % 11.85/11.42 ~ bnd_subclass (bnd_domain_of (bnd_restrict Xr Z Y)) Y) | % 11.85/11.42 bnd_section Xr Y Z; % 11.85/11.42 !!Xr Y Z. % 11.85/11.42 ~ bnd_section Xr Y Z | % 11.85/11.42 bnd_subclass (bnd_domain_of (bnd_restrict Xr Z Y)) Y; % 11.85/11.42 !!Xr Y Z. ~ bnd_section Xr Y Z | bnd_subclass Y Z; % 11.85/11.42 !!V Xr Y. % 11.85/11.42 ((~ bnd_member V (bnd_not_well_ordering Xr Y) | % 11.85/11.42 ~ bnd_segment Xr (bnd_not_well_ordering Xr Y) V = bnd_null_class) | % 11.85/11.42 ~ bnd_connected Xr Y) | % 11.85/11.42 bnd_well_ordering Xr Y; % 11.85/11.42 !!Xr Y. % 11.85/11.42 (~ bnd_connected Xr Y | bnd_subclass (bnd_not_well_ordering Xr Y) Y) | % 11.85/11.42 bnd_well_ordering Xr Y; % 11.85/11.42 !!Xr Y. % 11.85/11.42 (~ bnd_connected Xr Y | % 11.85/11.42 ~ bnd_not_well_ordering Xr Y = bnd_null_class) | % 11.85/11.42 bnd_well_ordering Xr Y; % 11.85/11.42 !!Xr Y U V. % 11.85/11.42 ((~ bnd_well_ordering Xr Y | ~ bnd_subclass U Y) | ~ bnd_member V U) | % 11.85/11.42 ~ bnd_member (bnd_ordered_pair V (bnd_least Xr U)) Xr; % 11.85/11.42 !!Xr Y U. % 11.85/11.42 (~ bnd_well_ordering Xr Y | ~ bnd_subclass U Y) | % 11.85/11.42 bnd_segment Xr U (bnd_least Xr U) = bnd_null_class; % 11.85/11.42 !!Xr Y U V. % 11.85/11.42 ((~ bnd_well_ordering Xr Y | ~ bnd_subclass U Y) | ~ bnd_member V U) | % 11.85/11.42 bnd_member (bnd_least Xr U) U; % 11.85/11.42 !!Xr Y U. % 11.85/11.42 ((~ bnd_well_ordering Xr Y | ~ bnd_subclass U Y) | % 11.85/11.42 U = bnd_null_class) | % 11.85/11.42 bnd_member (bnd_least Xr U) U; % 11.85/11.42 !!X Y. ~ bnd_well_ordering X Y | bnd_connected X Y; % 11.85/11.42 !!Xr Y Z. % 11.85/11.42 bnd_segment Xr Y Z = % 11.85/11.42 bnd_domain_of (bnd_restrict Xr Y (bnd_singleton Z)); % 11.85/11.42 !!Xr Y. % 11.85/11.42 ~ bnd_restrict (bnd_intersection Xr (bnd_inverse Xr)) Y Y = % 11.85/11.42 bnd_null_class | % 11.85/11.42 bnd_asymmetric Xr Y; % 11.85/11.42 !!Xr Y. % 11.85/11.42 ~ bnd_asymmetric Xr Y | % 11.85/11.42 bnd_restrict (bnd_intersection Xr (bnd_inverse Xr)) Y Y = % 11.85/11.42 bnd_null_class; % 11.85/11.42 !!Xr Y. % 11.85/11.42 ~ bnd_subclass % 11.85/11.42 (bnd_compose (bnd_restrict Xr Y Y) (bnd_restrict Xr Y Y)) % 11.85/11.42 (bnd_restrict Xr Y Y) | % 11.85/11.42 bnd_transitive Xr Y; % 11.85/11.42 !!Xr Y. % 11.85/11.42 ~ bnd_transitive Xr Y | % 11.85/11.42 bnd_subclass (bnd_compose (bnd_restrict Xr Y Y) (bnd_restrict Xr Y Y)) % 11.85/11.42 (bnd_restrict Xr Y Y); % 11.85/11.42 !!Y X. % 11.85/11.42 ~ bnd_subclass (bnd_cross_product Y Y) % 11.85/11.42 (bnd_union bnd_identity_relation (bnd_symmetrization_of X)) | % 11.85/11.42 bnd_connected X Y; % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_connected X Y | % 11.85/11.42 bnd_subclass (bnd_cross_product Y Y) % 11.85/11.42 (bnd_union bnd_identity_relation (bnd_symmetrization_of X)); % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_subclass (bnd_restrict X Y Y) % 11.85/11.42 (bnd_complement bnd_identity_relation) | % 11.85/11.42 bnd_irreflexive X Y; % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_irreflexive X Y | % 11.85/11.42 bnd_subclass (bnd_restrict X Y Y) % 11.85/11.42 (bnd_complement bnd_identity_relation); % 11.85/11.42 !!X. bnd_union X (bnd_inverse X) = bnd_symmetrization_of X; % 11.85/11.42 !!Xf Y. % 11.85/11.42 (~ bnd_function Xf | ~ bnd_subclass (bnd_range_of Xf) Y) | % 11.85/11.42 bnd_maps Xf (bnd_domain_of Xf) Y; % 11.85/11.42 !!Xf X Y. ~ bnd_maps Xf X Y | bnd_subclass (bnd_range_of Xf) Y; % 11.85/11.42 !!Xf X Y. ~ bnd_maps Xf X Y | bnd_domain_of Xf = X; % 11.85/11.42 !!Xf X Y. ~ bnd_maps Xf X Y | bnd_function Xf; % 11.85/11.42 !!X Y Z. % 11.85/11.42 (~ bnd_member (bnd_ordered_pair X (bnd_ordered_pair Y Z)) % 11.85/11.42 (bnd_cross_product bnd_universal_class % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class)) | % 11.85/11.42 ~ bnd_member Y (bnd_domain_of X)) | % 11.85/11.42 bnd_member (bnd_ordered_pair X (bnd_ordered_pair Y (bnd_apply X Y))) % 11.85/11.42 bnd_application_function; % 11.85/11.42 !!X Y Z. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X (bnd_ordered_pair Y Z)) % 11.85/11.42 bnd_application_function | % 11.85/11.42 bnd_apply X Y = Z; % 11.85/11.42 !!X Y Z. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X (bnd_ordered_pair Y Z)) % 11.85/11.42 bnd_application_function | % 11.85/11.42 bnd_member Y (bnd_domain_of X); % 11.85/11.42 bnd_subclass bnd_application_function % 11.85/11.42 (bnd_cross_product bnd_universal_class % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class)); % 11.85/11.42 bnd_intersection % 11.85/11.42 (bnd_complement % 11.85/11.42 (bnd_compose bnd_element_relation % 11.85/11.42 (bnd_complement bnd_identity_relation))) % 11.85/11.42 bnd_element_relation = % 11.85/11.42 bnd_singleton_relation; % 11.85/11.42 !!X. bnd_domain X % 11.85/11.42 (bnd_image (bnd_inverse X) (bnd_singleton (bnd_single_valued1 X))) % 11.85/11.42 (bnd_single_valued2 X) = % 11.85/11.42 bnd_single_valued3 X; % 11.85/11.42 !!X. bnd_second % 11.85/11.42 (bnd_not_subclass_element (bnd_compose X (bnd_inverse X)) % 11.85/11.42 bnd_identity_relation) = % 11.85/11.42 bnd_single_valued2 X; % 11.85/11.42 !!X. bnd_first % 11.85/11.42 (bnd_not_subclass_element (bnd_compose X (bnd_inverse X)) % 11.85/11.42 bnd_identity_relation) = % 11.85/11.42 bnd_single_valued1 X; % 11.85/11.42 !!X. ~ bnd_member X bnd_universal_class | % 11.85/11.42 bnd_member (bnd_ordered_pair X (bnd_domain_of X)) % 11.85/11.42 bnd_domain_relation; % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X Y) bnd_domain_relation | % 11.85/11.42 bnd_domain_of X = Y; % 11.85/11.42 bnd_subclass bnd_domain_relation % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class); % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X Y) % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) | % 11.85/11.42 bnd_member (bnd_ordered_pair X (bnd_ordered_pair Y (bnd_compose X Y))) % 11.85/11.42 bnd_composition_function; % 11.85/11.42 !!X Y Z. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X (bnd_ordered_pair Y Z)) % 11.85/11.42 bnd_composition_function | % 11.85/11.42 bnd_compose X Y = Z; % 11.85/11.42 bnd_subclass bnd_composition_function % 11.85/11.42 (bnd_cross_product bnd_universal_class % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class)); % 11.85/11.42 !!Y Z X. % 11.85/11.42 (~ bnd_member (bnd_ordered_pair Y Z) % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) | % 11.85/11.42 ~ bnd_compose X Y = Z) | % 11.85/11.42 bnd_member (bnd_ordered_pair Y Z) (bnd_compose_class X); % 11.85/11.42 !!Y Z X. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair Y Z) (bnd_compose_class X) | % 11.85/11.42 bnd_compose X Y = Z; % 11.85/11.42 !!X. bnd_subclass (bnd_compose_class X) % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class); % 11.85/11.42 !!Xf1 Xf2 Xh. % 11.85/11.42 (((~ bnd_operation Xf1 | ~ bnd_operation Xf2) | % 11.85/11.42 ~ bnd_compatible Xh Xf1 Xf2) | % 11.85/11.42 ~ bnd_apply Xf2 % 11.85/11.42 (bnd_ordered_pair % 11.85/11.42 (bnd_apply Xh (bnd_not_homomorphism1 Xh Xf1 Xf2)) % 11.85/11.42 (bnd_apply Xh (bnd_not_homomorphism2 Xh Xf1 Xf2))) = % 11.85/11.42 bnd_apply Xh % 11.85/11.42 (bnd_apply Xf1 % 11.85/11.42 (bnd_ordered_pair (bnd_not_homomorphism1 Xh Xf1 Xf2) % 11.85/11.42 (bnd_not_homomorphism2 Xh Xf1 Xf2)))) | % 11.85/11.42 bnd_homomorphism Xh Xf1 Xf2; % 11.85/11.42 !!Xf1 Xf2 Xh. % 11.85/11.42 (((~ bnd_operation Xf1 | ~ bnd_operation Xf2) | % 11.85/11.42 ~ bnd_compatible Xh Xf1 Xf2) | % 11.85/11.42 bnd_member % 11.85/11.42 (bnd_ordered_pair (bnd_not_homomorphism1 Xh Xf1 Xf2) % 11.85/11.42 (bnd_not_homomorphism2 Xh Xf1 Xf2)) % 11.85/11.42 (bnd_domain_of Xf1)) | % 11.85/11.42 bnd_homomorphism Xh Xf1 Xf2; % 11.85/11.42 !!Xh Xf1 Xf2 X Y. % 11.85/11.42 (~ bnd_homomorphism Xh Xf1 Xf2 | % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X Y) (bnd_domain_of Xf1)) | % 11.85/11.42 bnd_apply Xf2 (bnd_ordered_pair (bnd_apply Xh X) (bnd_apply Xh Y)) = % 11.85/11.42 bnd_apply Xh (bnd_apply Xf1 (bnd_ordered_pair X Y)); % 11.85/11.42 !!Xh Xf1 Xf2. ~ bnd_homomorphism Xh Xf1 Xf2 | bnd_compatible Xh Xf1 Xf2; % 11.85/11.42 !!Xh Xf1 Xf2. ~ bnd_homomorphism Xh Xf1 Xf2 | bnd_operation Xf2; % 11.85/11.42 !!Xh Xf1 Xf2. ~ bnd_homomorphism Xh Xf1 Xf2 | bnd_operation Xf1; % 11.85/11.42 !!Xh Xf1 Xf2. % 11.85/11.42 ((~ bnd_function Xh | % 11.85/11.42 ~ bnd_domain_of (bnd_domain_of Xf1) = bnd_domain_of Xh) | % 11.85/11.42 ~ bnd_subclass (bnd_range_of Xh) % 11.85/11.42 (bnd_domain_of (bnd_domain_of Xf2))) | % 11.85/11.42 bnd_compatible Xh Xf1 Xf2; % 11.85/11.42 !!Xh Xf1 Xf2. % 11.85/11.42 ~ bnd_compatible Xh Xf1 Xf2 | % 11.85/11.42 bnd_subclass (bnd_range_of Xh) (bnd_domain_of (bnd_domain_of Xf2)); % 11.85/11.42 !!Xh Xf1 Xf2. % 11.85/11.42 ~ bnd_compatible Xh Xf1 Xf2 | % 11.85/11.42 bnd_domain_of (bnd_domain_of Xf1) = bnd_domain_of Xh; % 11.85/11.42 !!Xh Xf1 Xf2. ~ bnd_compatible Xh Xf1 Xf2 | bnd_function Xh; % 11.85/11.42 !!Xf. ((~ bnd_function Xf | % 11.85/11.42 ~ bnd_cross_product (bnd_domain_of (bnd_domain_of Xf)) % 11.85/11.42 (bnd_domain_of (bnd_domain_of Xf)) = % 11.85/11.42 bnd_domain_of Xf) | % 11.85/11.42 ~ bnd_subclass (bnd_range_of Xf) % 11.85/11.42 (bnd_domain_of (bnd_domain_of Xf))) | % 11.85/11.42 bnd_operation Xf; % 11.85/11.42 !!Xf. ~ bnd_operation Xf | % 11.85/11.42 bnd_subclass (bnd_range_of Xf) (bnd_domain_of (bnd_domain_of Xf)); % 11.85/11.42 !!Xf. ~ bnd_operation Xf | % 11.85/11.42 bnd_cross_product (bnd_domain_of (bnd_domain_of Xf)) % 11.85/11.42 (bnd_domain_of (bnd_domain_of Xf)) = % 11.85/11.42 bnd_domain_of Xf; % 11.85/11.42 !!Xf. ~ bnd_operation Xf | bnd_function Xf; % 11.85/11.42 !!X. bnd_intersection (bnd_domain_of X) % 11.85/11.42 (bnd_diagonalise % 11.85/11.42 (bnd_compose (bnd_inverse bnd_element_relation) X)) = % 11.85/11.42 bnd_cantor X; % 11.85/11.42 !!Xr. bnd_complement % 11.85/11.42 (bnd_domain_of (bnd_intersection Xr bnd_identity_relation)) = % 11.85/11.42 bnd_diagonalise Xr; % 11.85/11.42 bnd_intersection (bnd_inverse bnd_subset_relation) bnd_subset_relation = % 11.85/11.42 bnd_identity_relation; % 11.85/11.42 bnd_intersection % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) % 11.85/11.42 (bnd_intersection % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) % 11.85/11.42 (bnd_complement % 11.85/11.42 (bnd_compose (bnd_complement bnd_element_relation) % 11.85/11.42 (bnd_inverse bnd_element_relation)))) = % 11.85/11.42 bnd_subset_relation; % 11.85/11.42 !!Xf. (~ bnd_function (bnd_inverse Xf) | ~ bnd_function Xf) | % 11.85/11.42 bnd_one_to_one Xf; % 11.85/11.42 !!Xf. ~ bnd_one_to_one Xf | bnd_function (bnd_inverse Xf); % 11.85/11.42 !!Xf. ~ bnd_one_to_one Xf | bnd_function Xf; % 11.85/11.42 !!Y. (~ bnd_member Y bnd_universal_class | Y = bnd_null_class) | % 11.85/11.42 bnd_member (bnd_apply bnd_choice Y) Y; % 11.85/11.42 bnd_function bnd_choice; % 11.85/11.42 !!Xf Y. bnd_sum_class (bnd_image Xf (bnd_singleton Y)) = bnd_apply Xf Y; % 11.85/11.42 !!X. X = bnd_null_class | % 11.85/11.42 bnd_intersection X (bnd_regular X) = bnd_null_class; % 11.85/11.42 !!X. X = bnd_null_class | bnd_member (bnd_regular X) X; % 11.85/11.42 !!Xf X. % 11.85/11.42 (~ bnd_function Xf | ~ bnd_member X bnd_universal_class) | % 11.85/11.42 bnd_member (bnd_image Xf X) bnd_universal_class; % 11.85/11.42 !!Xf. (~ bnd_subclass Xf % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) | % 11.85/11.42 ~ bnd_subclass (bnd_compose Xf (bnd_inverse Xf)) % 11.85/11.42 bnd_identity_relation) | % 11.85/11.42 bnd_function Xf; % 11.85/11.42 !!Xf. ~ bnd_function Xf | % 11.85/11.42 bnd_subclass (bnd_compose Xf (bnd_inverse Xf)) % 11.85/11.42 bnd_identity_relation; % 11.85/11.42 !!Xf. ~ bnd_function Xf | % 11.85/11.42 bnd_subclass Xf % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class); % 11.85/11.42 !!X. ~ bnd_subclass (bnd_compose X (bnd_inverse X)) % 11.85/11.42 bnd_identity_relation | % 11.85/11.42 bnd_single_valued_class X; % 11.85/11.42 !!X. ~ bnd_single_valued_class X | % 11.85/11.42 bnd_subclass (bnd_compose X (bnd_inverse X)) bnd_identity_relation; % 11.85/11.42 !!Z Yr Xr Y. % 11.85/11.42 (~ bnd_member Z (bnd_image Yr (bnd_image Xr (bnd_singleton Y))) | % 11.85/11.42 ~ bnd_member (bnd_ordered_pair Y Z) % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class)) | % 11.85/11.42 bnd_member (bnd_ordered_pair Y Z) (bnd_compose Yr Xr); % 11.85/11.42 !!Y Z Yr Xr. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair Y Z) (bnd_compose Yr Xr) | % 11.85/11.42 bnd_member Z (bnd_image Yr (bnd_image Xr (bnd_singleton Y))); % 11.85/11.42 !!Yr Xr. % 11.85/11.42 bnd_subclass (bnd_compose Yr Xr) % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class); % 11.85/11.42 !!U. ~ bnd_member U bnd_universal_class | % 11.85/11.42 bnd_member (bnd_power_class U) bnd_universal_class; % 11.85/11.42 !!X. bnd_complement (bnd_image bnd_element_relation (bnd_complement X)) = % 11.85/11.42 bnd_power_class X; % 11.85/11.42 !!X. ~ bnd_member X bnd_universal_class | % 11.85/11.42 bnd_member (bnd_sum_class X) bnd_universal_class; % 11.85/11.42 !!X. bnd_domain_of % 11.85/11.42 (bnd_restrict bnd_element_relation bnd_universal_class X) = % 11.85/11.42 bnd_sum_class X; % 11.85/11.42 bnd_member bnd_omega bnd_universal_class; % 11.85/11.42 !!Y. ~ bnd_inductive Y | bnd_subclass bnd_omega Y; % 11.85/11.42 bnd_inductive bnd_omega; % 11.85/11.42 !!X. (~ bnd_member bnd_null_class X | % 11.85/11.42 ~ bnd_subclass (bnd_image bnd_successor_relation X) X) | % 11.85/11.42 bnd_inductive X; % 11.85/11.42 !!X. ~ bnd_inductive X | % 11.85/11.42 bnd_subclass (bnd_image bnd_successor_relation X) X; % 11.85/11.42 !!X. ~ bnd_inductive X | bnd_member bnd_null_class X; % 11.85/11.42 !!X Y. % 11.85/11.42 (~ bnd_successor X = Y | % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X Y) % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class)) | % 11.85/11.42 bnd_member (bnd_ordered_pair X Y) bnd_successor_relation; % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X Y) bnd_successor_relation | % 11.85/11.42 bnd_successor X = Y; % 11.85/11.42 bnd_subclass bnd_successor_relation % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class); % 11.85/11.42 !!X. bnd_union X (bnd_singleton X) = bnd_successor X; % 11.85/11.42 !!Xr X. % 11.85/11.42 bnd_range_of (bnd_restrict Xr X bnd_universal_class) = bnd_image Xr X; % 11.85/11.42 !!Z X Y. % 11.85/11.42 bnd_second % 11.85/11.42 (bnd_not_subclass_element (bnd_restrict Z (bnd_singleton X) Y) % 11.85/11.42 bnd_null_class) = % 11.85/11.42 bnd_range Z X Y; % 11.85/11.42 !!Z X Y. % 11.85/11.42 bnd_first % 11.85/11.42 (bnd_not_subclass_element (bnd_restrict Z X (bnd_singleton Y)) % 11.85/11.42 bnd_null_class) = % 11.85/11.42 bnd_domain Z X Y; % 11.85/11.42 !!Z. bnd_domain_of (bnd_inverse Z) = bnd_range_of Z; % 11.85/11.42 !!Y. bnd_domain_of (bnd_flip (bnd_cross_product Y bnd_universal_class)) = % 11.85/11.42 bnd_inverse Y; % 11.85/11.42 !!V U W X. % 11.85/11.42 (~ bnd_member (bnd_ordered_pair (bnd_ordered_pair V U) W) X | % 11.85/11.42 ~ bnd_member (bnd_ordered_pair (bnd_ordered_pair U V) W) % 11.85/11.42 (bnd_cross_product % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) % 11.85/11.42 bnd_universal_class)) | % 11.85/11.42 bnd_member (bnd_ordered_pair (bnd_ordered_pair U V) W) (bnd_flip X); % 11.85/11.42 !!U V W X. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair (bnd_ordered_pair U V) W) % 11.85/11.42 (bnd_flip X) | % 11.85/11.42 bnd_member (bnd_ordered_pair (bnd_ordered_pair V U) W) X; % 11.85/11.42 !!X. bnd_subclass (bnd_flip X) % 11.85/11.42 (bnd_cross_product % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) % 11.85/11.42 bnd_universal_class); % 11.85/11.42 !!V W U X. % 11.85/11.42 (~ bnd_member (bnd_ordered_pair (bnd_ordered_pair V W) U) X | % 11.85/11.42 ~ bnd_member (bnd_ordered_pair (bnd_ordered_pair U V) W) % 11.85/11.42 (bnd_cross_product % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) % 11.85/11.42 bnd_universal_class)) | % 11.85/11.42 bnd_member (bnd_ordered_pair (bnd_ordered_pair U V) W) (bnd_rotate X); % 11.85/11.42 !!U V W X. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair (bnd_ordered_pair U V) W) % 11.85/11.42 (bnd_rotate X) | % 11.85/11.42 bnd_member (bnd_ordered_pair (bnd_ordered_pair V W) U) X; % 11.85/11.42 !!X. bnd_subclass (bnd_rotate X) % 11.85/11.42 (bnd_cross_product % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) % 11.85/11.42 bnd_universal_class); % 11.85/11.42 !!Z X. % 11.85/11.42 (~ bnd_member Z bnd_universal_class | % 11.85/11.42 bnd_restrict X (bnd_singleton Z) bnd_universal_class = % 11.85/11.42 bnd_null_class) | % 11.85/11.42 bnd_member Z (bnd_domain_of X); % 11.85/11.42 !!X Z. % 11.85/11.42 ~ bnd_restrict X (bnd_singleton Z) bnd_universal_class = % 11.85/11.42 bnd_null_class | % 11.85/11.42 ~ bnd_member Z (bnd_domain_of X); % 11.85/11.42 !!X Y Xr. % 11.85/11.42 bnd_intersection (bnd_cross_product X Y) Xr = bnd_restrict Xr X Y; % 11.85/11.42 !!Xr X Y. % 11.85/11.42 bnd_intersection Xr (bnd_cross_product X Y) = bnd_restrict Xr X Y; % 11.85/11.42 !!X Y. % 11.85/11.42 bnd_intersection (bnd_complement (bnd_intersection X Y)) % 11.85/11.42 (bnd_complement % 11.85/11.42 (bnd_intersection (bnd_complement X) (bnd_complement Y))) = % 11.85/11.42 bnd_symmetric_difference X Y; % 11.85/11.42 !!X Y. % 11.85/11.42 bnd_complement % 11.85/11.42 (bnd_intersection (bnd_complement X) (bnd_complement Y)) = % 11.85/11.42 bnd_union X Y; % 11.85/11.42 !!Z X. % 11.85/11.42 (~ bnd_member Z bnd_universal_class | % 11.85/11.42 bnd_member Z (bnd_complement X)) | % 11.85/11.42 bnd_member Z X; % 11.85/11.42 !!Z X. ~ bnd_member Z (bnd_complement X) | ~ bnd_member Z X; % 11.85/11.42 !!Z X Y. % 11.85/11.42 (~ bnd_member Z X | ~ bnd_member Z Y) | % 11.85/11.42 bnd_member Z (bnd_intersection X Y); % 11.85/11.42 !!Z X Y. ~ bnd_member Z (bnd_intersection X Y) | bnd_member Z Y; % 11.85/11.42 !!Z X Y. ~ bnd_member Z (bnd_intersection X Y) | bnd_member Z X; % 11.85/11.42 !!X Y. % 11.85/11.42 (~ bnd_member (bnd_ordered_pair X Y) % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class) | % 11.85/11.42 ~ bnd_member X Y) | % 11.85/11.42 bnd_member (bnd_ordered_pair X Y) bnd_element_relation; % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair X Y) bnd_element_relation | % 11.85/11.42 bnd_member X Y; % 11.85/11.42 bnd_subclass bnd_element_relation % 11.85/11.42 (bnd_cross_product bnd_universal_class bnd_universal_class); % 11.85/11.42 !!Z X Y. % 11.85/11.42 ~ bnd_member Z (bnd_cross_product X Y) | % 11.85/11.42 bnd_ordered_pair (bnd_first Z) (bnd_second Z) = Z; % 11.85/11.42 !!U X V Y. % 11.85/11.42 (~ bnd_member U X | ~ bnd_member V Y) | % 11.85/11.42 bnd_member (bnd_ordered_pair U V) (bnd_cross_product X Y); % 11.85/11.42 !!U V X Y. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair U V) (bnd_cross_product X Y) | % 11.85/11.42 bnd_member V Y; % 11.85/11.42 !!U V X Y. % 11.85/11.42 ~ bnd_member (bnd_ordered_pair U V) (bnd_cross_product X Y) | % 11.85/11.42 bnd_member U X; % 11.85/11.42 !!X Y. % 11.85/11.42 bnd_unordered_pair (bnd_singleton X) % 11.85/11.42 (bnd_unordered_pair X (bnd_singleton Y)) = % 11.85/11.42 bnd_ordered_pair X Y; % 11.85/11.42 !!X. bnd_unordered_pair X X = bnd_singleton X; % 11.85/11.42 !!X Y. bnd_member (bnd_unordered_pair X Y) bnd_universal_class; % 11.85/11.42 !!Y X. % 11.85/11.42 ~ bnd_member Y bnd_universal_class | % 11.85/11.42 bnd_member Y (bnd_unordered_pair X Y); % 11.85/11.42 !!X Y. % 11.85/11.42 ~ bnd_member X bnd_universal_class | % 11.85/11.42 bnd_member X (bnd_unordered_pair X Y); % 11.85/11.42 !!U X Y. (~ bnd_member U (bnd_unordered_pair X Y) | U = X) | U = Y; % 11.85/11.42 !!X Y. (~ bnd_subclass X Y | ~ bnd_subclass Y X) | X = Y; % 11.85/11.42 !!X Y. ~ X = Y | bnd_subclass Y X; !!X Y. ~ X = Y | bnd_subclass X Y; % 11.85/11.42 !!X. bnd_subclass X bnd_universal_class; % 11.85/11.42 !!X Y. ~ bnd_member (bnd_not_subclass_element X Y) Y | bnd_subclass X Y; % 11.85/11.42 !!X Y. bnd_member (bnd_not_subclass_element X Y) X | bnd_subclass X Y; % 11.85/11.42 !!X Y U. (~ bnd_subclass X Y | ~ bnd_member U X) | bnd_member U Y |] % 11.85/11.42 ==> True % 11.85/11.42 Adding axioms... % 11.85/11.43 Typedef.type_definition_def % 38.37/37.96 ...done. % 38.47/38.00 Ground types: ?'b, TPTP_Interpret.ind % 38.47/38.00 Translating term (sizes: 1, 1) ... % 55.71/55.27 Invoking SAT solver... % 55.71/55.27 No model exists. % 55.71/55.27 Translating term (sizes: 2, 1) ... % 73.67/73.12 Invoking SAT solver... % 73.67/73.12 No model exists. % 73.67/73.12 Translating term (sizes: 1, 2) ... % 181.42/180.47 Invoking SAT solver... % 181.42/180.47 No model exists. % 181.42/180.47 Translating term (sizes: 3, 1) ... % 201.84/200.72 Invoking SAT solver... % 201.84/200.72 No model exists. % 201.84/200.72 Translating term (sizes: 2, 2) ... % 300.12/298.15 Cputime limit exceeded (core dumped) %------------------------------------------------------------------------------