%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU387+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 : 0s
% DateTime : Tue Jul 19 07:12:59 EDT 2022
% Result : Theorem 2.39s 2.82s
% Output : Refutation 2.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU387+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jun 19 09:58:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.70/1.12 *** allocated 10000 integers for termspace/termends
% 0.70/1.12 *** allocated 10000 integers for clauses
% 0.70/1.12 *** allocated 10000 integers for justifications
% 0.70/1.12 Bliksem 1.12
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Automatic Strategy Selection
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Clauses:
% 0.70/1.12
% 0.70/1.12 { ! rel_str( X ), ! strict_rel_str( X ), X = rel_str_of( the_carrier( X ),
% 0.70/1.12 the_InternalRel( X ) ) }.
% 0.70/1.12 { ! in( X, Y ), ! in( Y, X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 complete_relstr( X ), alpha1( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 complete_relstr( X ), join_complete_relstr( X ) }.
% 0.70/1.12 { ! alpha1( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! alpha1( X ), reflexive_relstr( X ) }.
% 0.70/1.12 { ! alpha1( X ), up_complete_relstr( X ) }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! up_complete_relstr( X ),
% 0.70/1.12 alpha1( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 join_complete_relstr( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 join_complete_relstr( X ), reflexive_relstr( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 join_complete_relstr( X ), lower_bounded_relstr( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 transitive_relstr( X ), ! antisymmetric_relstr( X ), !
% 0.70/1.12 with_suprema_relstr( X ), ! lower_bounded_relstr( X ), !
% 0.70/1.12 up_complete_relstr( X ), alpha2( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 transitive_relstr( X ), ! antisymmetric_relstr( X ), !
% 0.70/1.12 with_suprema_relstr( X ), ! lower_bounded_relstr( X ), !
% 0.70/1.12 up_complete_relstr( X ), bounded_relstr( X ) }.
% 0.70/1.12 { ! alpha2( X ), alpha10( X ) }.
% 0.70/1.12 { ! alpha2( X ), upper_bounded_relstr( X ) }.
% 0.70/1.12 { ! alpha10( X ), ! upper_bounded_relstr( X ), alpha2( X ) }.
% 0.70/1.12 { ! alpha10( X ), alpha15( X ) }.
% 0.70/1.12 { ! alpha10( X ), lower_bounded_relstr( X ) }.
% 0.70/1.12 { ! alpha15( X ), ! lower_bounded_relstr( X ), alpha10( X ) }.
% 0.70/1.12 { ! alpha15( X ), alpha17( X ) }.
% 0.70/1.12 { ! alpha15( X ), complete_relstr( X ) }.
% 0.70/1.12 { ! alpha17( X ), ! complete_relstr( X ), alpha15( X ) }.
% 0.70/1.12 { ! alpha17( X ), alpha19( X ) }.
% 0.70/1.12 { ! alpha17( X ), with_infima_relstr( X ) }.
% 0.70/1.12 { ! alpha19( X ), ! with_infima_relstr( X ), alpha17( X ) }.
% 0.70/1.12 { ! alpha19( X ), alpha21( X ) }.
% 0.70/1.12 { ! alpha19( X ), with_suprema_relstr( X ) }.
% 0.70/1.12 { ! alpha21( X ), ! with_suprema_relstr( X ), alpha19( X ) }.
% 0.70/1.12 { ! alpha21( X ), alpha23( X ) }.
% 0.70/1.12 { ! alpha21( X ), antisymmetric_relstr( X ) }.
% 0.70/1.12 { ! alpha23( X ), ! antisymmetric_relstr( X ), alpha21( X ) }.
% 0.70/1.12 { ! alpha23( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! alpha23( X ), reflexive_relstr( X ) }.
% 0.70/1.12 { ! alpha23( X ), transitive_relstr( X ) }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! transitive_relstr( X ),
% 0.70/1.12 alpha23( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 antisymmetric_relstr( X ), ! join_complete_relstr( X ), alpha3( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 antisymmetric_relstr( X ), ! join_complete_relstr( X ),
% 0.70/1.12 with_infima_relstr( X ) }.
% 0.70/1.12 { ! alpha3( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! alpha3( X ), reflexive_relstr( X ) }.
% 0.70/1.12 { ! alpha3( X ), antisymmetric_relstr( X ) }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! antisymmetric_relstr( X )
% 0.70/1.12 , alpha3( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 antisymmetric_relstr( X ), ! upper_bounded_relstr( X ), !
% 0.70/1.12 join_complete_relstr( X ), alpha4( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 antisymmetric_relstr( X ), ! upper_bounded_relstr( X ), !
% 0.70/1.12 join_complete_relstr( X ), upper_bounded_relstr( X ) }.
% 0.70/1.12 { ! alpha4( X ), alpha11( X ) }.
% 0.70/1.12 { ! alpha4( X ), with_suprema_relstr( X ) }.
% 0.70/1.12 { ! alpha11( X ), ! with_suprema_relstr( X ), alpha4( X ) }.
% 0.70/1.12 { ! alpha11( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! alpha11( X ), reflexive_relstr( X ) }.
% 0.70/1.12 { ! alpha11( X ), antisymmetric_relstr( X ) }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! antisymmetric_relstr( X )
% 0.70/1.12 , alpha11( X ) }.
% 0.70/1.12 { ! empty( X ), finite( X ) }.
% 0.70/1.12 { ! rel_str( X ), ! with_suprema_relstr( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! empty( X ), relation( X ) }.
% 0.70/1.12 { ! element( X, powerset( cartesian_product2( Y, Z ) ) ), relation( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ), !
% 0.70/1.12 empty_carrier( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ),
% 0.70/1.12 with_suprema_relstr( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ),
% 0.70/1.12 with_infima_relstr( X ) }.
% 0.70/1.12 { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 0.70/1.12 { ! rel_str( X ), ! with_infima_relstr( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 trivial_carrier( X ), alpha5( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 trivial_carrier( X ), complete_relstr( X ) }.
% 0.70/1.12 { ! alpha5( X ), alpha12( X ) }.
% 0.70/1.12 { ! alpha5( X ), antisymmetric_relstr( X ) }.
% 0.70/1.12 { ! alpha12( X ), ! antisymmetric_relstr( X ), alpha5( X ) }.
% 0.70/1.12 { ! alpha12( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! alpha12( X ), reflexive_relstr( X ) }.
% 0.70/1.12 { ! alpha12( X ), transitive_relstr( X ) }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! transitive_relstr( X ),
% 0.70/1.12 alpha12( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ), !
% 0.70/1.12 empty_carrier( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ),
% 0.70/1.12 bounded_relstr( X ) }.
% 0.70/1.12 { ! rel_str( X ), ! bounded_relstr( X ), lower_bounded_relstr( X ) }.
% 0.70/1.12 { ! rel_str( X ), ! bounded_relstr( X ), upper_bounded_relstr( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 trivial_carrier( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 trivial_carrier( X ), reflexive_relstr( X ) }.
% 0.70/1.12 { ! rel_str( X ), empty_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 trivial_carrier( X ), connected_relstr( X ) }.
% 0.70/1.12 { ! rel_str( X ), ! lower_bounded_relstr( X ), ! upper_bounded_relstr( X )
% 0.70/1.12 , bounded_relstr( X ) }.
% 0.70/1.12 { ! rel_str( X ), ! reflexive_relstr( X ), ! with_suprema_relstr( X ), !
% 0.70/1.12 up_complete_relstr( X ), alpha6( X ) }.
% 0.70/1.12 { ! rel_str( X ), ! reflexive_relstr( X ), ! with_suprema_relstr( X ), !
% 0.70/1.12 up_complete_relstr( X ), upper_bounded_relstr( X ) }.
% 0.70/1.12 { ! alpha6( X ), ! empty_carrier( X ) }.
% 0.70/1.12 { ! alpha6( X ), reflexive_relstr( X ) }.
% 0.70/1.12 { ! alpha6( X ), with_suprema_relstr( X ) }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! with_suprema_relstr( X ),
% 0.70/1.12 alpha6( X ) }.
% 0.70/1.12 { ! relation_of2( Y, X, X ), strict_rel_str( rel_str_of( X, Y ) ) }.
% 0.70/1.12 { ! relation_of2( Y, X, X ), rel_str( rel_str_of( X, Y ) ) }.
% 0.70/1.12 { && }.
% 0.70/1.12 { && }.
% 0.70/1.12 { && }.
% 0.70/1.12 { ! rel_str( X ), element( bottom_of_relstr( X ), the_carrier( X ) ) }.
% 0.70/1.12 { strict_rel_str( boole_POSet( X ) ) }.
% 0.70/1.12 { rel_str( boole_POSet( X ) ) }.
% 0.70/1.12 { ! rel_str( X ), one_sorted_str( X ) }.
% 0.70/1.12 { && }.
% 0.70/1.12 { && }.
% 0.70/1.12 { && }.
% 0.70/1.12 { ! relation_of2_as_subset( Z, X, Y ), element( Z, powerset(
% 0.70/1.12 cartesian_product2( X, Y ) ) ) }.
% 0.70/1.12 { ! rel_str( X ), relation_of2_as_subset( the_InternalRel( X ), the_carrier
% 0.70/1.12 ( X ), the_carrier( X ) ) }.
% 0.70/1.12 { && }.
% 0.70/1.12 { rel_str( skol1 ) }.
% 0.70/1.12 { one_sorted_str( skol2 ) }.
% 0.70/1.12 { relation_of2( skol3( X, Y ), X, Y ) }.
% 0.70/1.12 { element( skol4( X ), X ) }.
% 0.70/1.12 { relation_of2_as_subset( skol5( X, Y ), X, Y ) }.
% 0.70/1.12 { empty( empty_set ) }.
% 0.70/1.12 { relation( empty_set ) }.
% 0.70/1.12 { relation_empty_yielding( empty_set ) }.
% 0.70/1.12 { ! finite( X ), ! finite( Y ), finite( cartesian_product2( X, Y ) ) }.
% 0.70/1.12 { empty_carrier( X ), ! one_sorted_str( X ), ! empty( the_carrier( X ) ) }
% 0.70/1.12 .
% 0.70/1.12 { ! empty( powerset( X ) ) }.
% 0.70/1.12 { ! empty_carrier( boole_POSet( X ) ) }.
% 0.70/1.12 { strict_rel_str( boole_POSet( X ) ) }.
% 0.70/1.12 { reflexive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { transitive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { antisymmetric_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { lower_bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { upper_bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { up_complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { join_complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! v1_yellow_3( boole_POSet( X ) ) }.
% 0.70/1.12 { distributive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { heyting_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { complemented_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { boolean_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { with_suprema_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { with_infima_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { empty( X ), alpha7( X ) }.
% 0.70/1.12 { empty( X ), complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha7( X ), alpha13( X ) }.
% 0.70/1.12 { ! alpha7( X ), with_infima_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha13( X ), ! with_infima_relstr( boole_POSet( X ) ), alpha7( X ) }.
% 0.70/1.12 { ! alpha13( X ), alpha16( X ) }.
% 0.70/1.12 { ! alpha13( X ), with_suprema_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha16( X ), ! with_suprema_relstr( boole_POSet( X ) ), alpha13( X ) }
% 0.70/1.12 .
% 0.70/1.12 { ! alpha16( X ), alpha18( X ) }.
% 0.70/1.12 { ! alpha16( X ), boolean_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha18( X ), ! boolean_relstr( boole_POSet( X ) ), alpha16( X ) }.
% 0.70/1.12 { ! alpha18( X ), alpha20( X ) }.
% 0.70/1.12 { ! alpha18( X ), complemented_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha20( X ), ! complemented_relstr( boole_POSet( X ) ), alpha18( X ) }
% 0.70/1.12 .
% 0.70/1.12 { ! alpha20( X ), alpha22( X ) }.
% 0.70/1.12 { ! alpha20( X ), heyting_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha22( X ), ! heyting_relstr( boole_POSet( X ) ), alpha20( X ) }.
% 0.70/1.12 { ! alpha22( X ), alpha24( X ) }.
% 0.70/1.12 { ! alpha22( X ), distributive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha24( X ), ! distributive_relstr( boole_POSet( X ) ), alpha22( X ) }
% 0.70/1.12 .
% 0.70/1.12 { ! alpha24( X ), alpha25( X ) }.
% 0.70/1.12 { ! alpha24( X ), ! v1_yellow_3( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha25( X ), v1_yellow_3( boole_POSet( X ) ), alpha24( X ) }.
% 0.70/1.12 { ! alpha25( X ), alpha26( X ) }.
% 0.70/1.12 { ! alpha25( X ), join_complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha26( X ), ! join_complete_relstr( boole_POSet( X ) ), alpha25( X )
% 0.70/1.12 }.
% 0.70/1.12 { ! alpha26( X ), alpha27( X ) }.
% 0.70/1.12 { ! alpha26( X ), up_complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha27( X ), ! up_complete_relstr( boole_POSet( X ) ), alpha26( X ) }
% 0.70/1.12 .
% 0.70/1.12 { ! alpha27( X ), alpha28( X ) }.
% 0.70/1.12 { ! alpha27( X ), bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha28( X ), ! bounded_relstr( boole_POSet( X ) ), alpha27( X ) }.
% 0.70/1.12 { ! alpha28( X ), alpha29( X ) }.
% 0.70/1.12 { ! alpha28( X ), upper_bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha29( X ), ! upper_bounded_relstr( boole_POSet( X ) ), alpha28( X )
% 0.70/1.12 }.
% 0.70/1.12 { ! alpha29( X ), alpha30( X ) }.
% 0.70/1.12 { ! alpha29( X ), lower_bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha30( X ), ! lower_bounded_relstr( boole_POSet( X ) ), alpha29( X )
% 0.70/1.12 }.
% 0.70/1.12 { ! alpha30( X ), alpha31( X ) }.
% 0.70/1.12 { ! alpha30( X ), antisymmetric_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha31( X ), ! antisymmetric_relstr( boole_POSet( X ) ), alpha30( X )
% 0.70/1.12 }.
% 0.70/1.12 { ! alpha31( X ), alpha32( X ) }.
% 0.70/1.12 { ! alpha31( X ), transitive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha32( X ), ! transitive_relstr( boole_POSet( X ) ), alpha31( X ) }.
% 0.70/1.12 { ! alpha32( X ), alpha33( X ) }.
% 0.70/1.12 { ! alpha32( X ), reflexive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha33( X ), ! reflexive_relstr( boole_POSet( X ) ), alpha32( X ) }.
% 0.70/1.12 { ! alpha33( X ), ! empty_carrier( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha33( X ), ! trivial_carrier( boole_POSet( X ) ) }.
% 0.70/1.12 { ! alpha33( X ), strict_rel_str( boole_POSet( X ) ) }.
% 0.70/1.12 { empty_carrier( boole_POSet( X ) ), trivial_carrier( boole_POSet( X ) ), !
% 0.70/1.12 strict_rel_str( boole_POSet( X ) ), alpha33( X ) }.
% 0.70/1.12 { empty( empty_set ) }.
% 0.70/1.12 { relation( empty_set ) }.
% 0.70/1.12 { empty( X ), empty( Y ), ! empty( cartesian_product2( X, Y ) ) }.
% 0.70/1.12 { ! empty_carrier( boole_POSet( X ) ) }.
% 0.70/1.12 { strict_rel_str( boole_POSet( X ) ) }.
% 0.70/1.12 { reflexive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { transitive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { antisymmetric_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! empty_carrier( boole_POSet( X ) ) }.
% 0.70/1.12 { strict_rel_str( boole_POSet( X ) ) }.
% 0.70/1.12 { reflexive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { transitive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { antisymmetric_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { lower_bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { upper_bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { with_suprema_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { with_infima_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! empty_carrier( boole_POSet( X ) ) }.
% 0.70/1.12 { strict_rel_str( boole_POSet( X ) ) }.
% 0.70/1.12 { reflexive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { transitive_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { antisymmetric_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { lower_bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { upper_bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { bounded_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { directed_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { up_complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { join_complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! v1_yellow_3( boole_POSet( X ) ) }.
% 0.70/1.12 { with_suprema_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { with_infima_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { complete_relstr( boole_POSet( X ) ) }.
% 0.70/1.12 { ! relation_of2( Y, X, X ), ! rel_str_of( X, Y ) = rel_str_of( Z, T ), X =
% 0.70/1.12 Z }.
% 0.70/1.12 { ! relation_of2( Y, X, X ), ! rel_str_of( X, Y ) = rel_str_of( Z, T ), Y =
% 0.70/1.12 T }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! transitive_relstr( X ), !
% 0.70/1.12 rel_str( X ), alpha8( X, skol6( X ) ) }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! transitive_relstr( X ), !
% 0.70/1.12 rel_str( X ), upper_relstr_subset( skol6( X ), X ) }.
% 0.70/1.12 { ! alpha8( X, Y ), element( Y, powerset( the_carrier( X ) ) ) }.
% 0.70/1.12 { ! alpha8( X, Y ), ! empty( Y ) }.
% 0.70/1.12 { ! alpha8( X, Y ), filtered_subset( Y, X ) }.
% 0.70/1.12 { ! element( Y, powerset( the_carrier( X ) ) ), empty( Y ), !
% 0.70/1.12 filtered_subset( Y, X ), alpha8( X, Y ) }.
% 0.70/1.12 { rel_str( skol7 ) }.
% 0.70/1.12 { ! empty_carrier( skol7 ) }.
% 0.70/1.12 { reflexive_relstr( skol7 ) }.
% 0.70/1.12 { transitive_relstr( skol7 ) }.
% 0.70/1.12 { antisymmetric_relstr( skol7 ) }.
% 0.70/1.12 { connected_relstr( skol7 ) }.
% 0.70/1.12 { rel_str( skol8 ) }.
% 0.70/1.12 { ! empty_carrier( skol8 ) }.
% 0.70/1.12 { strict_rel_str( skol8 ) }.
% 0.70/1.12 { reflexive_relstr( skol8 ) }.
% 0.70/1.12 { transitive_relstr( skol8 ) }.
% 0.70/1.12 { antisymmetric_relstr( skol8 ) }.
% 0.70/1.12 { with_suprema_relstr( skol8 ) }.
% 0.70/1.12 { with_infima_relstr( skol8 ) }.
% 0.70/1.12 { complete_relstr( skol8 ) }.
% 0.70/1.12 { lower_bounded_relstr( skol8 ) }.
% 0.70/1.12 { upper_bounded_relstr( skol8 ) }.
% 0.70/1.12 { bounded_relstr( skol8 ) }.
% 0.70/1.12 { up_complete_relstr( skol8 ) }.
% 0.70/1.12 { join_complete_relstr( skol8 ) }.
% 0.70/1.12 { ! empty( skol9 ) }.
% 0.70/1.12 { finite( skol9 ) }.
% 0.70/1.12 { rel_str( skol10 ) }.
% 0.70/1.12 { ! empty_carrier( skol10 ) }.
% 0.70/1.12 { strict_rel_str( skol10 ) }.
% 0.70/1.12 { reflexive_relstr( skol10 ) }.
% 0.70/1.12 { transitive_relstr( skol10 ) }.
% 0.70/1.12 { antisymmetric_relstr( skol10 ) }.
% 0.70/1.12 { complete_relstr( skol10 ) }.
% 0.70/1.12 { empty( skol11 ) }.
% 0.70/1.12 { relation( skol11 ) }.
% 0.70/1.12 { empty( X ), ! empty( skol12( Y ) ) }.
% 0.70/1.12 { empty( X ), element( skol12( X ), powerset( X ) ) }.
% 0.70/1.12 { rel_str( skol13 ) }.
% 0.70/1.12 { ! empty_carrier( skol13 ) }.
% 0.70/1.12 { ! trivial_carrier( skol13 ) }.
% 0.70/1.12 { strict_rel_str( skol13 ) }.
% 0.70/1.12 { reflexive_relstr( skol13 ) }.
% 0.70/1.12 { transitive_relstr( skol13 ) }.
% 0.70/1.12 { antisymmetric_relstr( skol13 ) }.
% 0.70/1.12 { lower_bounded_relstr( skol13 ) }.
% 0.70/1.12 { upper_bounded_relstr( skol13 ) }.
% 0.70/1.12 { bounded_relstr( skol13 ) }.
% 0.70/1.12 { ! v1_yellow_3( skol13 ) }.
% 0.70/1.12 { distributive_relstr( skol13 ) }.
% 0.70/1.12 { heyting_relstr( skol13 ) }.
% 0.70/1.12 { complemented_relstr( skol13 ) }.
% 0.70/1.12 { boolean_relstr( skol13 ) }.
% 0.70/1.12 { with_suprema_relstr( skol13 ) }.
% 0.70/1.12 { with_infima_relstr( skol13 ) }.
% 0.70/1.12 { rel_str( skol14 ) }.
% 0.70/1.12 { ! empty_carrier( skol14 ) }.
% 0.70/1.12 { strict_rel_str( skol14 ) }.
% 0.70/1.12 { reflexive_relstr( skol14 ) }.
% 0.70/1.12 { transitive_relstr( skol14 ) }.
% 0.70/1.12 { antisymmetric_relstr( skol14 ) }.
% 0.70/1.12 { with_suprema_relstr( skol14 ) }.
% 0.70/1.12 { with_infima_relstr( skol14 ) }.
% 0.70/1.12 { complete_relstr( skol14 ) }.
% 0.70/1.12 { trivial_carrier( skol14 ) }.
% 0.70/1.12 { rel_str( skol15 ) }.
% 0.70/1.12 { ! empty_carrier( skol15 ) }.
% 0.70/1.12 { strict_rel_str( skol15 ) }.
% 0.70/1.12 { reflexive_relstr( skol15 ) }.
% 0.70/1.12 { transitive_relstr( skol15 ) }.
% 0.70/1.12 { antisymmetric_relstr( skol15 ) }.
% 0.70/1.12 { with_suprema_relstr( skol15 ) }.
% 0.70/1.12 { with_infima_relstr( skol15 ) }.
% 0.70/1.12 { complete_relstr( skol15 ) }.
% 0.70/1.12 { ! empty( skol16 ) }.
% 0.70/1.12 { relation( skol16 ) }.
% 0.70/1.12 { empty( skol17( Y ) ) }.
% 0.70/1.12 { element( skol17( X ), powerset( X ) ) }.
% 0.70/1.12 { ! empty( skol18( Y ) ) }.
% 0.70/1.12 { finite( skol18( Y ) ) }.
% 0.70/1.12 { element( skol18( X ), powerset( powerset( X ) ) ) }.
% 0.70/1.12 { rel_str( skol19 ) }.
% 0.70/1.12 { ! empty_carrier( skol19 ) }.
% 0.70/1.12 { reflexive_relstr( skol19 ) }.
% 0.70/1.12 { transitive_relstr( skol19 ) }.
% 0.70/1.12 { antisymmetric_relstr( skol19 ) }.
% 0.70/1.12 { with_suprema_relstr( skol19 ) }.
% 0.70/1.12 { with_infima_relstr( skol19 ) }.
% 0.70/1.12 { complete_relstr( skol19 ) }.
% 0.70/1.12 { lower_bounded_relstr( skol19 ) }.
% 0.70/1.12 { upper_bounded_relstr( skol19 ) }.
% 0.70/1.12 { bounded_relstr( skol19 ) }.
% 0.70/1.12 { empty( X ), ! empty( skol20( Y ) ) }.
% 0.70/1.12 { empty( X ), finite( skol20( Y ) ) }.
% 0.70/1.12 { empty( X ), element( skol20( X ), powerset( X ) ) }.
% 0.70/1.12 { relation( skol21 ) }.
% 0.70/1.12 { relation_empty_yielding( skol21 ) }.
% 0.70/1.12 { one_sorted_str( skol22 ) }.
% 0.70/1.12 { ! empty_carrier( skol22 ) }.
% 0.70/1.12 { ! one_sorted_str( X ), ! empty( skol23( Y ) ) }.
% 0.70/1.12 { ! one_sorted_str( X ), finite( skol23( Y ) ) }.
% 0.70/1.12 { ! one_sorted_str( X ), element( skol23( X ), powerset( powerset(
% 0.70/1.12 the_carrier( X ) ) ) ) }.
% 0.70/1.12 { empty( X ), ! empty( skol24( Y ) ) }.
% 0.70/1.12 { empty( X ), finite( skol24( Y ) ) }.
% 0.70/1.12 { empty( X ), element( skol24( X ), powerset( X ) ) }.
% 0.70/1.12 { empty_carrier( X ), trivial_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 transitive_relstr( X ), ! antisymmetric_relstr( X ), !
% 0.70/1.12 upper_bounded_relstr( X ), ! rel_str( X ), alpha9( X, skol25( X ) ) }.
% 0.70/1.12 { empty_carrier( X ), trivial_carrier( X ), ! reflexive_relstr( X ), !
% 0.70/1.12 transitive_relstr( X ), ! antisymmetric_relstr( X ), !
% 0.70/1.12 upper_bounded_relstr( X ), ! rel_str( X ), upper_relstr_subset( skol25( X
% 0.70/1.12 ), X ) }.
% 0.70/1.12 { ! alpha9( X, Y ), alpha14( X, Y ) }.
% 0.70/1.12 { ! alpha9( X, Y ), filtered_subset( Y, X ) }.
% 0.70/1.12 { ! alpha14( X, Y ), ! filtered_subset( Y, X ), alpha9( X, Y ) }.
% 0.70/1.12 { ! alpha14( X, Y ), element( Y, powerset( the_carrier( X ) ) ) }.
% 0.70/1.12 { ! alpha14( X, Y ), ! empty( Y ) }.
% 0.70/1.12 { ! alpha14( X, Y ), proper_element( Y, powerset( the_carrier( X ) ) ) }.
% 0.70/1.12 { ! element( Y, powerset( the_carrier( X ) ) ), empty( Y ), !
% 0.70/1.12 proper_element( Y, powerset( the_carrier( X ) ) ), alpha14( X, Y ) }.
% 0.70/1.12 { rel_str( skol26 ) }.
% 0.70/1.12 { ! empty_carrier( skol26 ) }.
% 0.70/1.12 { strict_rel_str( skol26 ) }.
% 0.70/1.12 { transitive_relstr( skol26 ) }.
% 0.70/1.12 { directed_relstr( skol26 ) }.
% 0.70/1.12 { empty_carrier( X ), ! one_sorted_str( X ), ! empty( skol27( Y ) ) }.
% 0.70/1.12 { empty_carrier( X ), ! one_sorted_str( X ), element( skol27( X ), powerset
% 0.70/1.12 ( the_carrier( X ) ) ) }.
% 0.70/1.12 { ! relation_of2_as_subset( Z, X, Y ), relation_of2( Z, X, Y ) }.
% 0.70/1.12 { ! relation_of2( Z, X, Y ), relation_of2_as_subset( Z, X, Y ) }.
% 0.70/1.12 { subset( X, X ) }.
% 0.70/1.12 { bottom_of_relstr( boole_POSet( X ) ) = empty_set }.
% 0.70/1.12 { ! in( X, Y ), element( X, Y ) }.
% 0.70/1.12 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.70/1.12 { ! empty( skol28 ) }.
% 0.70/1.12 { ! empty( skol29 ) }.
% 0.70/1.12 { filtered_subset( skol29, boole_POSet( skol28 ) ) }.
% 0.70/1.12 { upper_relstr_subset( skol29, boole_POSet( skol28 ) ) }.
% 0.70/1.12 { proper_element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) )
% 0.70/1.12 ) }.
% 0.70/1.12 { element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 0.70/1.12 { in( skol30, skol29 ) }.
% 0.70/1.12 { empty( skol30 ) }.
% 0.70/1.12 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.70/1.12 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.70/1.12 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.70/1.12 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.70/1.12 { ! empty( X ), X = empty_set }.
% 0.70/1.12 { ! in( X, Y ), ! empty( Y ) }.
% 0.70/1.12 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! transitive_relstr( X ), !
% 0.70/1.12 antisymmetric_relstr( X ), ! lower_bounded_relstr( X ), ! rel_str( X ),
% 0.70/1.12 empty( Y ), ! filtered_subset( Y, X ), ! upper_relstr_subset( Y, X ), !
% 0.70/1.12 element( Y, powerset( the_carrier( X ) ) ), ! proper_element( Y, powerset
% 0.70/1.12 ( the_carrier( X ) ) ), ! in( bottom_of_relstr( X ), Y ) }.
% 0.70/1.12 { empty_carrier( X ), ! reflexive_relstr( X ), ! transitive_relstr( X ), !
% 0.70/1.12 antisymmetric_relstr( X ), ! lower_bounded_relstr( X ), ! rel_str( X ),
% 0.70/1.12 empty( Y ), ! filtered_subset( Y, X ), ! upper_relstr_subset( Y, X ), !
% 0.70/1.12 element( Y, powerset( the_carrier( X ) ) ), in( bottom_of_relstr( X ), Y
% 0.70/1.12 ), proper_element( Y, powerset( the_carrier( X ) ) ) }.
% 0.70/1.12
% 0.70/1.12 *** allocated 15000 integers for clauses
% 0.70/1.12 percentage equality = 0.013115, percentage horn = 0.867347
% 0.70/1.12 This is a problem with some equality
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Options Used:
% 0.70/1.12
% 0.70/1.12 useres = 1
% 0.70/1.12 useparamod = 1
% 0.70/1.12 useeqrefl = 1
% 0.70/1.12 useeqfact = 1
% 0.70/1.12 usefactor = 1
% 0.70/1.12 usesimpsplitting = 0
% 0.70/1.12 usesimpdemod = 5
% 0.70/1.12 usesimpres = 3
% 0.70/1.12
% 0.70/1.12 resimpinuse = 1000
% 0.70/1.12 resimpclauses = 20000
% 0.70/1.12 substype = eqrewr
% 0.70/1.12 backwardsubs = 1
% 0.70/1.12 selectoldest = 5
% 0.70/1.12
% 0.70/1.12 litorderings [0] = split
% 0.70/1.12 litorderings [1] = extend the termordering, first sorting on arguments
% 0.70/1.12
% 0.70/1.12 termordering = kbo
% 0.70/1.12
% 0.70/1.12 litapriori = 0
% 0.70/1.12 termapriori = 1
% 0.70/1.12 litaposteriori = 0
% 0.70/1.12 termaposteriori = 0
% 0.70/1.12 demodaposteriori = 0
% 0.70/1.12 ordereqreflfact = 0
% 0.70/1.12
% 0.70/1.12 litselect = negord
% 0.70/1.12
% 0.70/1.12 maxweight = 15
% 0.70/1.12 maxdepth = 30000
% 0.70/1.12 maxlength = 115
% 0.70/1.12 maxnrvars = 195
% 0.70/1.12 excuselevel = 1
% 0.70/1.12 increasemaxweight = 1
% 0.70/1.12
% 0.70/1.12 maxselected = 10000000
% 0.70/1.12 maxnrclauses = 10000000
% 0.70/1.12
% 0.70/1.12 showgenerated = 0
% 0.70/1.12 showkept = 0
% 0.70/1.12 showselected = 0
% 0.70/1.12 showdeleted = 0
% 0.70/1.12 showresimp = 1
% 1.55/1.92 showstatus = 2000
% 1.55/1.92
% 1.55/1.92 prologoutput = 0
% 1.55/1.92 nrgoals = 5000000
% 1.55/1.92 totalproof = 1
% 1.55/1.92
% 1.55/1.92 Symbols occurring in the translation:
% 1.55/1.92
% 1.55/1.92 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.55/1.92 . [1, 2] (w:1, o:106, a:1, s:1, b:0),
% 1.55/1.92 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 1.55/1.92 ! [4, 1] (w:0, o:29, a:1, s:1, b:0),
% 1.55/1.92 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.55/1.92 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.55/1.92 rel_str [36, 1] (w:1, o:34, a:1, s:1, b:0),
% 1.55/1.92 strict_rel_str [37, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.55/1.92 the_carrier [38, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.55/1.92 the_InternalRel [39, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.55/1.92 rel_str_of [40, 2] (w:1, o:130, a:1, s:1, b:0),
% 1.55/1.92 in [42, 2] (w:1, o:131, a:1, s:1, b:0),
% 1.55/1.92 empty_carrier [43, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.55/1.92 reflexive_relstr [44, 1] (w:1, o:35, a:1, s:1, b:0),
% 1.55/1.92 complete_relstr [45, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.55/1.92 up_complete_relstr [46, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.55/1.92 join_complete_relstr [47, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.55/1.92 lower_bounded_relstr [48, 1] (w:1, o:94, a:1, s:1, b:0),
% 1.55/1.92 transitive_relstr [49, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.55/1.92 antisymmetric_relstr [50, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.55/1.92 with_suprema_relstr [51, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.55/1.92 with_infima_relstr [52, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.55/1.92 upper_bounded_relstr [53, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.55/1.92 bounded_relstr [54, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.55/1.92 empty [55, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.55/1.92 finite [56, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.55/1.92 relation [57, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.55/1.92 cartesian_product2 [59, 2] (w:1, o:132, a:1, s:1, b:0),
% 1.55/1.92 powerset [60, 1] (w:1, o:103, a:1, s:1, b:0),
% 1.55/1.92 element [61, 2] (w:1, o:133, a:1, s:1, b:0),
% 1.55/1.92 trivial_carrier [62, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.55/1.92 connected_relstr [63, 1] (w:1, o:104, a:1, s:1, b:0),
% 1.55/1.92 relation_of2 [64, 3] (w:1, o:143, a:1, s:1, b:0),
% 1.55/1.92 bottom_of_relstr [65, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.55/1.92 boole_POSet [66, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.55/1.92 one_sorted_str [67, 1] (w:1, o:102, a:1, s:1, b:0),
% 1.55/1.92 relation_of2_as_subset [68, 3] (w:1, o:144, a:1, s:1, b:0),
% 1.55/1.92 empty_set [69, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.55/1.92 relation_empty_yielding [70, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.55/1.92 v1_yellow_3 [71, 1] (w:1, o:96, a:1, s:1, b:0),
% 1.55/1.92 distributive_relstr [72, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.55/1.92 heyting_relstr [73, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.55/1.92 complemented_relstr [74, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.55/1.92 boolean_relstr [75, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.55/1.92 directed_relstr [76, 1] (w:1, o:83, a:1, s:1, b:0),
% 1.55/1.92 filtered_subset [78, 2] (w:1, o:134, a:1, s:1, b:0),
% 1.55/1.92 upper_relstr_subset [79, 2] (w:1, o:135, a:1, s:1, b:0),
% 1.55/1.92 proper_element [80, 2] (w:1, o:136, a:1, s:1, b:0),
% 1.55/1.92 subset [81, 2] (w:1, o:137, a:1, s:1, b:0),
% 1.55/1.92 alpha1 [82, 1] (w:1, o:51, a:1, s:1, b:1),
% 1.55/1.92 alpha2 [83, 1] (w:1, o:61, a:1, s:1, b:1),
% 1.55/1.92 alpha3 [84, 1] (w:1, o:72, a:1, s:1, b:1),
% 1.55/1.92 alpha4 [85, 1] (w:1, o:77, a:1, s:1, b:1),
% 1.55/1.92 alpha5 [86, 1] (w:1, o:78, a:1, s:1, b:1),
% 1.55/1.92 alpha6 [87, 1] (w:1, o:79, a:1, s:1, b:1),
% 1.55/1.92 alpha7 [88, 1] (w:1, o:80, a:1, s:1, b:1),
% 1.55/1.92 alpha8 [89, 2] (w:1, o:138, a:1, s:1, b:1),
% 1.55/1.92 alpha9 [90, 2] (w:1, o:139, a:1, s:1, b:1),
% 1.55/1.92 alpha10 [91, 1] (w:1, o:52, a:1, s:1, b:1),
% 1.55/1.92 alpha11 [92, 1] (w:1, o:53, a:1, s:1, b:1),
% 1.55/1.92 alpha12 [93, 1] (w:1, o:54, a:1, s:1, b:1),
% 1.55/1.92 alpha13 [94, 1] (w:1, o:55, a:1, s:1, b:1),
% 1.55/1.92 alpha14 [95, 2] (w:1, o:140, a:1, s:1, b:1),
% 1.55/1.92 alpha15 [96, 1] (w:1, o:56, a:1, s:1, b:1),
% 1.55/1.92 alpha16 [97, 1] (w:1, o:57, a:1, s:1, b:1),
% 1.55/1.92 alpha17 [98, 1] (w:1, o:58, a:1, s:1, b:1),
% 1.55/1.92 alpha18 [99, 1] (w:1, o:59, a:1, s:1, b:1),
% 1.55/1.92 alpha19 [100, 1] (w:1, o:60, a:1, s:1, b:1),
% 1.55/1.92 alpha20 [101, 1] (w:1, o:62, a:1, s:1, b:1),
% 1.55/1.92 alpha21 [102, 1] (w:1, o:63, a:1, s:1, b:1),
% 1.55/1.92 alpha22 [103, 1] (w:1, o:64, a:1, s:1, b:1),
% 1.55/1.92 alpha23 [104, 1] (w:1, o:65, a:1, s:1, b:1),
% 2.39/2.81 alpha24 [105, 1] (w:1, o:66, a:1, s:1, b:1),
% 2.39/2.81 alpha25 [106, 1] (w:1, o:67, a:1, s:1, b:1),
% 2.39/2.81 alpha26 [107, 1] (w:1, o:68, a:1, s:1, b:1),
% 2.39/2.81 alpha27 [108, 1] (w:1, o:69, a:1, s:1, b:1),
% 2.39/2.81 alpha28 [109, 1] (w:1, o:70, a:1, s:1, b:1),
% 2.39/2.81 alpha29 [110, 1] (w:1, o:71, a:1, s:1, b:1),
% 2.39/2.81 alpha30 [111, 1] (w:1, o:73, a:1, s:1, b:1),
% 2.39/2.81 alpha31 [112, 1] (w:1, o:74, a:1, s:1, b:1),
% 2.39/2.81 alpha32 [113, 1] (w:1, o:75, a:1, s:1, b:1),
% 2.39/2.81 alpha33 [114, 1] (w:1, o:76, a:1, s:1, b:1),
% 2.39/2.81 skol1 [115, 0] (w:1, o:11, a:1, s:1, b:1),
% 2.39/2.81 skol2 [116, 0] (w:1, o:19, a:1, s:1, b:1),
% 2.39/2.81 skol3 [117, 2] (w:1, o:141, a:1, s:1, b:1),
% 2.39/2.81 skol4 [118, 1] (w:1, o:39, a:1, s:1, b:1),
% 2.39/2.81 skol5 [119, 2] (w:1, o:142, a:1, s:1, b:1),
% 2.39/2.81 skol6 [120, 1] (w:1, o:40, a:1, s:1, b:1),
% 2.39/2.81 skol7 [121, 0] (w:1, o:20, a:1, s:1, b:1),
% 2.39/2.81 skol8 [122, 0] (w:1, o:21, a:1, s:1, b:1),
% 2.39/2.81 skol9 [123, 0] (w:1, o:22, a:1, s:1, b:1),
% 2.39/2.81 skol10 [124, 0] (w:1, o:12, a:1, s:1, b:1),
% 2.39/2.82 skol11 [125, 0] (w:1, o:13, a:1, s:1, b:1),
% 2.39/2.82 skol12 [126, 1] (w:1, o:41, a:1, s:1, b:1),
% 2.39/2.82 skol13 [127, 0] (w:1, o:14, a:1, s:1, b:1),
% 2.39/2.82 skol14 [128, 0] (w:1, o:15, a:1, s:1, b:1),
% 2.39/2.82 skol15 [129, 0] (w:1, o:16, a:1, s:1, b:1),
% 2.39/2.82 skol16 [130, 0] (w:1, o:17, a:1, s:1, b:1),
% 2.39/2.82 skol17 [131, 1] (w:1, o:42, a:1, s:1, b:1),
% 2.39/2.82 skol18 [132, 1] (w:1, o:43, a:1, s:1, b:1),
% 2.39/2.82 skol19 [133, 0] (w:1, o:18, a:1, s:1, b:1),
% 2.39/2.82 skol20 [134, 1] (w:1, o:44, a:1, s:1, b:1),
% 2.39/2.82 skol21 [135, 0] (w:1, o:23, a:1, s:1, b:1),
% 2.39/2.82 skol22 [136, 0] (w:1, o:24, a:1, s:1, b:1),
% 2.39/2.82 skol23 [137, 1] (w:1, o:45, a:1, s:1, b:1),
% 2.39/2.82 skol24 [138, 1] (w:1, o:46, a:1, s:1, b:1),
% 2.39/2.82 skol25 [139, 1] (w:1, o:47, a:1, s:1, b:1),
% 2.39/2.82 skol26 [140, 0] (w:1, o:25, a:1, s:1, b:1),
% 2.39/2.82 skol27 [141, 1] (w:1, o:48, a:1, s:1, b:1),
% 2.39/2.82 skol28 [142, 0] (w:1, o:26, a:1, s:1, b:1),
% 2.39/2.82 skol29 [143, 0] (w:1, o:27, a:1, s:1, b:1),
% 2.39/2.82 skol30 [144, 0] (w:1, o:28, a:1, s:1, b:1).
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Starting Search:
% 2.39/2.82
% 2.39/2.82 *** allocated 22500 integers for clauses
% 2.39/2.82 *** allocated 33750 integers for clauses
% 2.39/2.82 *** allocated 15000 integers for termspace/termends
% 2.39/2.82 *** allocated 50625 integers for clauses
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 *** allocated 75937 integers for clauses
% 2.39/2.82 *** allocated 22500 integers for termspace/termends
% 2.39/2.82 *** allocated 113905 integers for clauses
% 2.39/2.82 *** allocated 33750 integers for termspace/termends
% 2.39/2.82
% 2.39/2.82 Intermediate Status:
% 2.39/2.82 Generated: 5748
% 2.39/2.82 Kept: 2236
% 2.39/2.82 Inuse: 487
% 2.39/2.82 Deleted: 4
% 2.39/2.82 Deletedinuse: 0
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 *** allocated 170857 integers for clauses
% 2.39/2.82 *** allocated 50625 integers for termspace/termends
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 *** allocated 256285 integers for clauses
% 2.39/2.82 *** allocated 75937 integers for termspace/termends
% 2.39/2.82
% 2.39/2.82 Intermediate Status:
% 2.39/2.82 Generated: 12372
% 2.39/2.82 Kept: 4240
% 2.39/2.82 Inuse: 847
% 2.39/2.82 Deleted: 26
% 2.39/2.82 Deletedinuse: 9
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 *** allocated 384427 integers for clauses
% 2.39/2.82 *** allocated 113905 integers for termspace/termends
% 2.39/2.82
% 2.39/2.82 Intermediate Status:
% 2.39/2.82 Generated: 24455
% 2.39/2.82 Kept: 6241
% 2.39/2.82 Inuse: 1263
% 2.39/2.82 Deleted: 91
% 2.39/2.82 Deletedinuse: 29
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Intermediate Status:
% 2.39/2.82 Generated: 31798
% 2.39/2.82 Kept: 8241
% 2.39/2.82 Inuse: 1512
% 2.39/2.82 Deleted: 147
% 2.39/2.82 Deletedinuse: 29
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 *** allocated 170857 integers for termspace/termends
% 2.39/2.82 *** allocated 576640 integers for clauses
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Intermediate Status:
% 2.39/2.82 Generated: 37007
% 2.39/2.82 Kept: 10265
% 2.39/2.82 Inuse: 1634
% 2.39/2.82 Deleted: 250
% 2.39/2.82 Deletedinuse: 115
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Intermediate Status:
% 2.39/2.82 Generated: 40932
% 2.39/2.82 Kept: 12283
% 2.39/2.82 Inuse: 1703
% 2.39/2.82 Deleted: 260
% 2.39/2.82 Deletedinuse: 115
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Intermediate Status:
% 2.39/2.82 Generated: 45548
% 2.39/2.82 Kept: 14285
% 2.39/2.82 Inuse: 1815
% 2.39/2.82 Deleted: 303
% 2.39/2.82 Deletedinuse: 123
% 2.39/2.82
% 2.39/2.82 *** allocated 256285 integers for termspace/termends
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 *** allocated 864960 integers for clauses
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Intermediate Status:
% 2.39/2.82 Generated: 50531
% 2.39/2.82 Kept: 16297
% 2.39/2.82 Inuse: 1932
% 2.39/2.82 Deleted: 328
% 2.39/2.82 Deletedinuse: 123
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Intermediate Status:
% 2.39/2.82 Generated: 56408
% 2.39/2.82 Kept: 18310
% 2.39/2.82 Inuse: 2083
% 2.39/2.82 Deleted: 359
% 2.39/2.82 Deletedinuse: 123
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 Resimplifying inuse:
% 2.39/2.82 Done
% 2.39/2.82
% 2.39/2.82 Resimplifying clauses:
% 2.39/2.82
% 2.39/2.82 Bliksems!, er is een bewijs:
% 2.39/2.82 % SZS status Theorem
% 2.39/2.82 % SZS output start Refutation
% 2.39/2.82
% 2.39/2.82 (80) {G0,W3,D3,L1,V1,M1} I { rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 (89) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 2.39/2.82 (95) {G0,W3,D3,L1,V1,M1} I { ! empty_carrier( boole_POSet( X ) ) }.
% 2.39/2.82 (96) {G0,W3,D3,L1,V1,M1} I { reflexive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (97) {G0,W3,D3,L1,V1,M1} I { transitive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (98) {G0,W3,D3,L1,V1,M1} I { antisymmetric_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (99) {G0,W3,D3,L1,V1,M1} I { lower_bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (274) {G0,W5,D4,L1,V1,M1} I { bottom_of_relstr( boole_POSet( X ) ) ==>
% 2.39/2.82 empty_set }.
% 2.39/2.82 (278) {G0,W2,D2,L1,V0,M1} I { ! empty( skol29 ) }.
% 2.39/2.82 (279) {G0,W4,D3,L1,V0,M1} I { filtered_subset( skol29, boole_POSet( skol28
% 2.39/2.82 ) ) }.
% 2.39/2.82 (280) {G0,W4,D3,L1,V0,M1} I { upper_relstr_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ) }.
% 2.39/2.82 (281) {G0,W6,D5,L1,V0,M1} I { proper_element( skol29, powerset( the_carrier
% 2.39/2.82 ( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 (282) {G0,W6,D5,L1,V0,M1} I { element( skol29, powerset( the_carrier(
% 2.39/2.82 boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 (283) {G0,W3,D2,L1,V0,M1} I { in( skol30, skol29 ) }.
% 2.39/2.82 (284) {G0,W2,D2,L1,V0,M1} I { empty( skol30 ) }.
% 2.39/2.82 (289) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 2.39/2.82 (292) {G0,W34,D4,L12,V2,M12} I { empty_carrier( X ), ! reflexive_relstr( X
% 2.39/2.82 ), ! transitive_relstr( X ), ! antisymmetric_relstr( X ), !
% 2.39/2.82 lower_bounded_relstr( X ), ! rel_str( X ), empty( Y ), ! filtered_subset
% 2.39/2.82 ( Y, X ), ! upper_relstr_subset( Y, X ), ! element( Y, powerset(
% 2.39/2.82 the_carrier( X ) ) ), ! proper_element( Y, powerset( the_carrier( X ) ) )
% 2.39/2.82 , ! in( bottom_of_relstr( X ), Y ) }.
% 2.39/2.82 (3310) {G1,W3,D2,L1,V0,M1} R(289,284) { skol30 ==> empty_set }.
% 2.39/2.82 (3384) {G2,W3,D2,L1,V0,M1} P(289,283);d(3310);r(89) { in( empty_set, skol29
% 2.39/2.82 ) }.
% 2.39/2.82 (3682) {G1,W34,D5,L10,V0,M10} R(292,282);d(274);r(95) { ! reflexive_relstr
% 2.39/2.82 ( boole_POSet( skol28 ) ), ! transitive_relstr( boole_POSet( skol28 ) ),
% 2.39/2.82 ! antisymmetric_relstr( boole_POSet( skol28 ) ), ! lower_bounded_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! rel_str( boole_POSet( skol28 ) ), empty(
% 2.39/2.82 skol29 ), ! filtered_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 upper_relstr_subset( skol29, boole_POSet( skol28 ) ), ! proper_element(
% 2.39/2.82 skol29, powerset( the_carrier( boole_POSet( skol28 ) ) ) ), ! in(
% 2.39/2.82 empty_set, skol29 ) }.
% 2.39/2.82 (20950) {G3,W0,D0,L0,V0,M0} S(3682);r(96);r(97);r(98);r(99);r(80);r(278);r(
% 2.39/2.82 279);r(280);r(281);r(3384) { }.
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 % SZS output end Refutation
% 2.39/2.82 found a proof!
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Unprocessed initial clauses:
% 2.39/2.82
% 2.39/2.82 (20952) {G0,W11,D4,L3,V1,M3} { ! rel_str( X ), ! strict_rel_str( X ), X =
% 2.39/2.82 rel_str_of( the_carrier( X ), the_InternalRel( X ) ) }.
% 2.39/2.82 (20953) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 2.39/2.82 (20954) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! complete_relstr( X ), alpha1( X ) }.
% 2.39/2.82 (20955) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! complete_relstr( X ), join_complete_relstr( X )
% 2.39/2.82 }.
% 2.39/2.82 (20956) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), ! empty_carrier( X ) }.
% 2.39/2.82 (20957) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), reflexive_relstr( X ) }.
% 2.39/2.82 (20958) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), up_complete_relstr( X ) }.
% 2.39/2.82 (20959) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! reflexive_relstr( X )
% 2.39/2.82 , ! up_complete_relstr( X ), alpha1( X ) }.
% 2.39/2.82 (20960) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! join_complete_relstr( X ), ! empty_carrier( X )
% 2.39/2.82 }.
% 2.39/2.82 (20961) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! join_complete_relstr( X ), reflexive_relstr( X )
% 2.39/2.82 }.
% 2.39/2.82 (20962) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! join_complete_relstr( X ), lower_bounded_relstr
% 2.39/2.82 ( X ) }.
% 2.39/2.82 (20963) {G0,W18,D2,L9,V1,M9} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! transitive_relstr( X ), ! antisymmetric_relstr(
% 2.39/2.82 X ), ! with_suprema_relstr( X ), ! lower_bounded_relstr( X ), !
% 2.39/2.82 up_complete_relstr( X ), alpha2( X ) }.
% 2.39/2.82 (20964) {G0,W18,D2,L9,V1,M9} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! transitive_relstr( X ), ! antisymmetric_relstr(
% 2.39/2.82 X ), ! with_suprema_relstr( X ), ! lower_bounded_relstr( X ), !
% 2.39/2.82 up_complete_relstr( X ), bounded_relstr( X ) }.
% 2.39/2.82 (20965) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), alpha10( X ) }.
% 2.39/2.82 (20966) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), upper_bounded_relstr( X ) }.
% 2.39/2.82 (20967) {G0,W6,D2,L3,V1,M3} { ! alpha10( X ), ! upper_bounded_relstr( X )
% 2.39/2.82 , alpha2( X ) }.
% 2.39/2.82 (20968) {G0,W4,D2,L2,V1,M2} { ! alpha10( X ), alpha15( X ) }.
% 2.39/2.82 (20969) {G0,W4,D2,L2,V1,M2} { ! alpha10( X ), lower_bounded_relstr( X )
% 2.39/2.82 }.
% 2.39/2.82 (20970) {G0,W6,D2,L3,V1,M3} { ! alpha15( X ), ! lower_bounded_relstr( X )
% 2.39/2.82 , alpha10( X ) }.
% 2.39/2.82 (20971) {G0,W4,D2,L2,V1,M2} { ! alpha15( X ), alpha17( X ) }.
% 2.39/2.82 (20972) {G0,W4,D2,L2,V1,M2} { ! alpha15( X ), complete_relstr( X ) }.
% 2.39/2.82 (20973) {G0,W6,D2,L3,V1,M3} { ! alpha17( X ), ! complete_relstr( X ),
% 2.39/2.82 alpha15( X ) }.
% 2.39/2.82 (20974) {G0,W4,D2,L2,V1,M2} { ! alpha17( X ), alpha19( X ) }.
% 2.39/2.82 (20975) {G0,W4,D2,L2,V1,M2} { ! alpha17( X ), with_infima_relstr( X ) }.
% 2.39/2.82 (20976) {G0,W6,D2,L3,V1,M3} { ! alpha19( X ), ! with_infima_relstr( X ),
% 2.39/2.82 alpha17( X ) }.
% 2.39/2.82 (20977) {G0,W4,D2,L2,V1,M2} { ! alpha19( X ), alpha21( X ) }.
% 2.39/2.82 (20978) {G0,W4,D2,L2,V1,M2} { ! alpha19( X ), with_suprema_relstr( X ) }.
% 2.39/2.82 (20979) {G0,W6,D2,L3,V1,M3} { ! alpha21( X ), ! with_suprema_relstr( X ),
% 2.39/2.82 alpha19( X ) }.
% 2.39/2.82 (20980) {G0,W4,D2,L2,V1,M2} { ! alpha21( X ), alpha23( X ) }.
% 2.39/2.82 (20981) {G0,W4,D2,L2,V1,M2} { ! alpha21( X ), antisymmetric_relstr( X )
% 2.39/2.82 }.
% 2.39/2.82 (20982) {G0,W6,D2,L3,V1,M3} { ! alpha23( X ), ! antisymmetric_relstr( X )
% 2.39/2.82 , alpha21( X ) }.
% 2.39/2.82 (20983) {G0,W4,D2,L2,V1,M2} { ! alpha23( X ), ! empty_carrier( X ) }.
% 2.39/2.82 (20984) {G0,W4,D2,L2,V1,M2} { ! alpha23( X ), reflexive_relstr( X ) }.
% 2.39/2.82 (20985) {G0,W4,D2,L2,V1,M2} { ! alpha23( X ), transitive_relstr( X ) }.
% 2.39/2.82 (20986) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! reflexive_relstr( X )
% 2.39/2.82 , ! transitive_relstr( X ), alpha23( X ) }.
% 2.39/2.82 (20987) {G0,W12,D2,L6,V1,M6} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! antisymmetric_relstr( X ), !
% 2.39/2.82 join_complete_relstr( X ), alpha3( X ) }.
% 2.39/2.82 (20988) {G0,W12,D2,L6,V1,M6} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! antisymmetric_relstr( X ), !
% 2.39/2.82 join_complete_relstr( X ), with_infima_relstr( X ) }.
% 2.39/2.82 (20989) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), ! empty_carrier( X ) }.
% 2.39/2.82 (20990) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), reflexive_relstr( X ) }.
% 2.39/2.82 (20991) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), antisymmetric_relstr( X ) }.
% 2.39/2.82 (20992) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! reflexive_relstr( X )
% 2.39/2.82 , ! antisymmetric_relstr( X ), alpha3( X ) }.
% 2.39/2.82 (20993) {G0,W14,D2,L7,V1,M7} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! antisymmetric_relstr( X ), !
% 2.39/2.82 upper_bounded_relstr( X ), ! join_complete_relstr( X ), alpha4( X ) }.
% 2.39/2.82 (20994) {G0,W14,D2,L7,V1,M7} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! antisymmetric_relstr( X ), !
% 2.39/2.82 upper_bounded_relstr( X ), ! join_complete_relstr( X ),
% 2.39/2.82 upper_bounded_relstr( X ) }.
% 2.39/2.82 (20995) {G0,W4,D2,L2,V1,M2} { ! alpha4( X ), alpha11( X ) }.
% 2.39/2.82 (20996) {G0,W4,D2,L2,V1,M2} { ! alpha4( X ), with_suprema_relstr( X ) }.
% 2.39/2.82 (20997) {G0,W6,D2,L3,V1,M3} { ! alpha11( X ), ! with_suprema_relstr( X ),
% 2.39/2.82 alpha4( X ) }.
% 2.39/2.82 (20998) {G0,W4,D2,L2,V1,M2} { ! alpha11( X ), ! empty_carrier( X ) }.
% 2.39/2.82 (20999) {G0,W4,D2,L2,V1,M2} { ! alpha11( X ), reflexive_relstr( X ) }.
% 2.39/2.82 (21000) {G0,W4,D2,L2,V1,M2} { ! alpha11( X ), antisymmetric_relstr( X )
% 2.39/2.82 }.
% 2.39/2.82 (21001) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! reflexive_relstr( X )
% 2.39/2.82 , ! antisymmetric_relstr( X ), alpha11( X ) }.
% 2.39/2.82 (21002) {G0,W4,D2,L2,V1,M2} { ! empty( X ), finite( X ) }.
% 2.39/2.82 (21003) {G0,W6,D2,L3,V1,M3} { ! rel_str( X ), ! with_suprema_relstr( X ),
% 2.39/2.82 ! empty_carrier( X ) }.
% 2.39/2.82 (21004) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 2.39/2.82 (21005) {G0,W8,D4,L2,V3,M2} { ! element( X, powerset( cartesian_product2(
% 2.39/2.82 Y, Z ) ) ), relation( X ) }.
% 2.39/2.82 (21006) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 complete_relstr( X ), ! empty_carrier( X ) }.
% 2.39/2.82 (21007) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 complete_relstr( X ), with_suprema_relstr( X ) }.
% 2.39/2.82 (21008) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 complete_relstr( X ), with_infima_relstr( X ) }.
% 2.39/2.82 (21009) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! element( Y, powerset( X ) )
% 2.39/2.82 , finite( Y ) }.
% 2.39/2.82 (21010) {G0,W6,D2,L3,V1,M3} { ! rel_str( X ), ! with_infima_relstr( X ), !
% 2.39/2.82 empty_carrier( X ) }.
% 2.39/2.82 (21011) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! trivial_carrier( X ), alpha5( X ) }.
% 2.39/2.82 (21012) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! trivial_carrier( X ), complete_relstr( X ) }.
% 2.39/2.82 (21013) {G0,W4,D2,L2,V1,M2} { ! alpha5( X ), alpha12( X ) }.
% 2.39/2.82 (21014) {G0,W4,D2,L2,V1,M2} { ! alpha5( X ), antisymmetric_relstr( X ) }.
% 2.39/2.82 (21015) {G0,W6,D2,L3,V1,M3} { ! alpha12( X ), ! antisymmetric_relstr( X )
% 2.39/2.82 , alpha5( X ) }.
% 2.39/2.82 (21016) {G0,W4,D2,L2,V1,M2} { ! alpha12( X ), ! empty_carrier( X ) }.
% 2.39/2.82 (21017) {G0,W4,D2,L2,V1,M2} { ! alpha12( X ), reflexive_relstr( X ) }.
% 2.39/2.82 (21018) {G0,W4,D2,L2,V1,M2} { ! alpha12( X ), transitive_relstr( X ) }.
% 2.39/2.82 (21019) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! reflexive_relstr( X )
% 2.39/2.82 , ! transitive_relstr( X ), alpha12( X ) }.
% 2.39/2.82 (21020) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 complete_relstr( X ), ! empty_carrier( X ) }.
% 2.39/2.82 (21021) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 complete_relstr( X ), bounded_relstr( X ) }.
% 2.39/2.82 (21022) {G0,W6,D2,L3,V1,M3} { ! rel_str( X ), ! bounded_relstr( X ),
% 2.39/2.82 lower_bounded_relstr( X ) }.
% 2.39/2.82 (21023) {G0,W6,D2,L3,V1,M3} { ! rel_str( X ), ! bounded_relstr( X ),
% 2.39/2.82 upper_bounded_relstr( X ) }.
% 2.39/2.82 (21024) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! trivial_carrier( X ), ! empty_carrier( X ) }.
% 2.39/2.82 (21025) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! trivial_carrier( X ), reflexive_relstr( X ) }.
% 2.39/2.82 (21026) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! trivial_carrier( X ), connected_relstr( X ) }.
% 2.39/2.82 (21027) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), ! lower_bounded_relstr( X )
% 2.39/2.82 , ! upper_bounded_relstr( X ), bounded_relstr( X ) }.
% 2.39/2.82 (21028) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), ! reflexive_relstr( X ), !
% 2.39/2.82 with_suprema_relstr( X ), ! up_complete_relstr( X ), alpha6( X ) }.
% 2.39/2.82 (21029) {G0,W10,D2,L5,V1,M5} { ! rel_str( X ), ! reflexive_relstr( X ), !
% 2.39/2.82 with_suprema_relstr( X ), ! up_complete_relstr( X ), upper_bounded_relstr
% 2.39/2.82 ( X ) }.
% 2.39/2.82 (21030) {G0,W4,D2,L2,V1,M2} { ! alpha6( X ), ! empty_carrier( X ) }.
% 2.39/2.82 (21031) {G0,W4,D2,L2,V1,M2} { ! alpha6( X ), reflexive_relstr( X ) }.
% 2.39/2.82 (21032) {G0,W4,D2,L2,V1,M2} { ! alpha6( X ), with_suprema_relstr( X ) }.
% 2.39/2.82 (21033) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! reflexive_relstr( X )
% 2.39/2.82 , ! with_suprema_relstr( X ), alpha6( X ) }.
% 2.39/2.82 (21034) {G0,W8,D3,L2,V2,M2} { ! relation_of2( Y, X, X ), strict_rel_str(
% 2.39/2.82 rel_str_of( X, Y ) ) }.
% 2.39/2.82 (21035) {G0,W8,D3,L2,V2,M2} { ! relation_of2( Y, X, X ), rel_str(
% 2.39/2.82 rel_str_of( X, Y ) ) }.
% 2.39/2.82 (21036) {G0,W1,D1,L1,V0,M1} { && }.
% 2.39/2.82 (21037) {G0,W1,D1,L1,V0,M1} { && }.
% 2.39/2.82 (21038) {G0,W1,D1,L1,V0,M1} { && }.
% 2.39/2.82 (21039) {G0,W7,D3,L2,V1,M2} { ! rel_str( X ), element( bottom_of_relstr( X
% 2.39/2.82 ), the_carrier( X ) ) }.
% 2.39/2.82 (21040) {G0,W3,D3,L1,V1,M1} { strict_rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 (21041) {G0,W3,D3,L1,V1,M1} { rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 (21042) {G0,W4,D2,L2,V1,M2} { ! rel_str( X ), one_sorted_str( X ) }.
% 2.39/2.82 (21043) {G0,W1,D1,L1,V0,M1} { && }.
% 2.39/2.82 (21044) {G0,W1,D1,L1,V0,M1} { && }.
% 2.39/2.82 (21045) {G0,W1,D1,L1,V0,M1} { && }.
% 2.39/2.82 (21046) {G0,W10,D4,L2,V3,M2} { ! relation_of2_as_subset( Z, X, Y ),
% 2.39/2.82 element( Z, powerset( cartesian_product2( X, Y ) ) ) }.
% 2.39/2.82 (21047) {G0,W9,D3,L2,V1,M2} { ! rel_str( X ), relation_of2_as_subset(
% 2.39/2.82 the_InternalRel( X ), the_carrier( X ), the_carrier( X ) ) }.
% 2.39/2.82 (21048) {G0,W1,D1,L1,V0,M1} { && }.
% 2.39/2.82 (21049) {G0,W2,D2,L1,V0,M1} { rel_str( skol1 ) }.
% 2.39/2.82 (21050) {G0,W2,D2,L1,V0,M1} { one_sorted_str( skol2 ) }.
% 2.39/2.82 (21051) {G0,W6,D3,L1,V2,M1} { relation_of2( skol3( X, Y ), X, Y ) }.
% 2.39/2.82 (21052) {G0,W4,D3,L1,V1,M1} { element( skol4( X ), X ) }.
% 2.39/2.82 (21053) {G0,W6,D3,L1,V2,M1} { relation_of2_as_subset( skol5( X, Y ), X, Y
% 2.39/2.82 ) }.
% 2.39/2.82 (21054) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 2.39/2.82 (21055) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 2.39/2.82 (21056) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 2.39/2.82 (21057) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! finite( Y ), finite(
% 2.39/2.82 cartesian_product2( X, Y ) ) }.
% 2.39/2.82 (21058) {G0,W7,D3,L3,V1,M3} { empty_carrier( X ), ! one_sorted_str( X ), !
% 2.39/2.82 empty( the_carrier( X ) ) }.
% 2.39/2.82 (21059) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 2.39/2.82 (21060) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_POSet( X ) ) }.
% 2.39/2.82 (21061) {G0,W3,D3,L1,V1,M1} { strict_rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 (21062) {G0,W3,D3,L1,V1,M1} { reflexive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21063) {G0,W3,D3,L1,V1,M1} { transitive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21064) {G0,W3,D3,L1,V1,M1} { antisymmetric_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21065) {G0,W3,D3,L1,V1,M1} { lower_bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21066) {G0,W3,D3,L1,V1,M1} { upper_bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21067) {G0,W3,D3,L1,V1,M1} { bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21068) {G0,W3,D3,L1,V1,M1} { up_complete_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21069) {G0,W3,D3,L1,V1,M1} { join_complete_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21070) {G0,W3,D3,L1,V1,M1} { ! v1_yellow_3( boole_POSet( X ) ) }.
% 2.39/2.82 (21071) {G0,W3,D3,L1,V1,M1} { distributive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21072) {G0,W3,D3,L1,V1,M1} { heyting_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21073) {G0,W3,D3,L1,V1,M1} { complemented_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21074) {G0,W3,D3,L1,V1,M1} { boolean_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21075) {G0,W3,D3,L1,V1,M1} { with_suprema_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21076) {G0,W3,D3,L1,V1,M1} { with_infima_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21077) {G0,W3,D3,L1,V1,M1} { complete_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21078) {G0,W4,D2,L2,V1,M2} { empty( X ), alpha7( X ) }.
% 2.39/2.82 (21079) {G0,W5,D3,L2,V1,M2} { empty( X ), complete_relstr( boole_POSet( X
% 2.39/2.82 ) ) }.
% 2.39/2.82 (21080) {G0,W4,D2,L2,V1,M2} { ! alpha7( X ), alpha13( X ) }.
% 2.39/2.82 (21081) {G0,W5,D3,L2,V1,M2} { ! alpha7( X ), with_infima_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21082) {G0,W7,D3,L3,V1,M3} { ! alpha13( X ), ! with_infima_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha7( X ) }.
% 2.39/2.82 (21083) {G0,W4,D2,L2,V1,M2} { ! alpha13( X ), alpha16( X ) }.
% 2.39/2.82 (21084) {G0,W5,D3,L2,V1,M2} { ! alpha13( X ), with_suprema_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21085) {G0,W7,D3,L3,V1,M3} { ! alpha16( X ), ! with_suprema_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha13( X ) }.
% 2.39/2.82 (21086) {G0,W4,D2,L2,V1,M2} { ! alpha16( X ), alpha18( X ) }.
% 2.39/2.82 (21087) {G0,W5,D3,L2,V1,M2} { ! alpha16( X ), boolean_relstr( boole_POSet
% 2.39/2.82 ( X ) ) }.
% 2.39/2.82 (21088) {G0,W7,D3,L3,V1,M3} { ! alpha18( X ), ! boolean_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha16( X ) }.
% 2.39/2.82 (21089) {G0,W4,D2,L2,V1,M2} { ! alpha18( X ), alpha20( X ) }.
% 2.39/2.82 (21090) {G0,W5,D3,L2,V1,M2} { ! alpha18( X ), complemented_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21091) {G0,W7,D3,L3,V1,M3} { ! alpha20( X ), ! complemented_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha18( X ) }.
% 2.39/2.82 (21092) {G0,W4,D2,L2,V1,M2} { ! alpha20( X ), alpha22( X ) }.
% 2.39/2.82 (21093) {G0,W5,D3,L2,V1,M2} { ! alpha20( X ), heyting_relstr( boole_POSet
% 2.39/2.82 ( X ) ) }.
% 2.39/2.82 (21094) {G0,W7,D3,L3,V1,M3} { ! alpha22( X ), ! heyting_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha20( X ) }.
% 2.39/2.82 (21095) {G0,W4,D2,L2,V1,M2} { ! alpha22( X ), alpha24( X ) }.
% 2.39/2.82 (21096) {G0,W5,D3,L2,V1,M2} { ! alpha22( X ), distributive_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21097) {G0,W7,D3,L3,V1,M3} { ! alpha24( X ), ! distributive_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha22( X ) }.
% 2.39/2.82 (21098) {G0,W4,D2,L2,V1,M2} { ! alpha24( X ), alpha25( X ) }.
% 2.39/2.82 (21099) {G0,W5,D3,L2,V1,M2} { ! alpha24( X ), ! v1_yellow_3( boole_POSet(
% 2.39/2.82 X ) ) }.
% 2.39/2.82 (21100) {G0,W7,D3,L3,V1,M3} { ! alpha25( X ), v1_yellow_3( boole_POSet( X
% 2.39/2.82 ) ), alpha24( X ) }.
% 2.39/2.82 (21101) {G0,W4,D2,L2,V1,M2} { ! alpha25( X ), alpha26( X ) }.
% 2.39/2.82 (21102) {G0,W5,D3,L2,V1,M2} { ! alpha25( X ), join_complete_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21103) {G0,W7,D3,L3,V1,M3} { ! alpha26( X ), ! join_complete_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha25( X ) }.
% 2.39/2.82 (21104) {G0,W4,D2,L2,V1,M2} { ! alpha26( X ), alpha27( X ) }.
% 2.39/2.82 (21105) {G0,W5,D3,L2,V1,M2} { ! alpha26( X ), up_complete_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21106) {G0,W7,D3,L3,V1,M3} { ! alpha27( X ), ! up_complete_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha26( X ) }.
% 2.39/2.82 (21107) {G0,W4,D2,L2,V1,M2} { ! alpha27( X ), alpha28( X ) }.
% 2.39/2.82 (21108) {G0,W5,D3,L2,V1,M2} { ! alpha27( X ), bounded_relstr( boole_POSet
% 2.39/2.82 ( X ) ) }.
% 2.39/2.82 (21109) {G0,W7,D3,L3,V1,M3} { ! alpha28( X ), ! bounded_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha27( X ) }.
% 2.39/2.82 (21110) {G0,W4,D2,L2,V1,M2} { ! alpha28( X ), alpha29( X ) }.
% 2.39/2.82 (21111) {G0,W5,D3,L2,V1,M2} { ! alpha28( X ), upper_bounded_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21112) {G0,W7,D3,L3,V1,M3} { ! alpha29( X ), ! upper_bounded_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha28( X ) }.
% 2.39/2.82 (21113) {G0,W4,D2,L2,V1,M2} { ! alpha29( X ), alpha30( X ) }.
% 2.39/2.82 (21114) {G0,W5,D3,L2,V1,M2} { ! alpha29( X ), lower_bounded_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21115) {G0,W7,D3,L3,V1,M3} { ! alpha30( X ), ! lower_bounded_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha29( X ) }.
% 2.39/2.82 (21116) {G0,W4,D2,L2,V1,M2} { ! alpha30( X ), alpha31( X ) }.
% 2.39/2.82 (21117) {G0,W5,D3,L2,V1,M2} { ! alpha30( X ), antisymmetric_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21118) {G0,W7,D3,L3,V1,M3} { ! alpha31( X ), ! antisymmetric_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha30( X ) }.
% 2.39/2.82 (21119) {G0,W4,D2,L2,V1,M2} { ! alpha31( X ), alpha32( X ) }.
% 2.39/2.82 (21120) {G0,W5,D3,L2,V1,M2} { ! alpha31( X ), transitive_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21121) {G0,W7,D3,L3,V1,M3} { ! alpha32( X ), ! transitive_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha31( X ) }.
% 2.39/2.82 (21122) {G0,W4,D2,L2,V1,M2} { ! alpha32( X ), alpha33( X ) }.
% 2.39/2.82 (21123) {G0,W5,D3,L2,V1,M2} { ! alpha32( X ), reflexive_relstr(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21124) {G0,W7,D3,L3,V1,M3} { ! alpha33( X ), ! reflexive_relstr(
% 2.39/2.82 boole_POSet( X ) ), alpha32( X ) }.
% 2.39/2.82 (21125) {G0,W5,D3,L2,V1,M2} { ! alpha33( X ), ! empty_carrier( boole_POSet
% 2.39/2.82 ( X ) ) }.
% 2.39/2.82 (21126) {G0,W5,D3,L2,V1,M2} { ! alpha33( X ), ! trivial_carrier(
% 2.39/2.82 boole_POSet( X ) ) }.
% 2.39/2.82 (21127) {G0,W5,D3,L2,V1,M2} { ! alpha33( X ), strict_rel_str( boole_POSet
% 2.39/2.82 ( X ) ) }.
% 2.39/2.82 (21128) {G0,W11,D3,L4,V1,M4} { empty_carrier( boole_POSet( X ) ),
% 2.39/2.82 trivial_carrier( boole_POSet( X ) ), ! strict_rel_str( boole_POSet( X ) )
% 2.39/2.82 , alpha33( X ) }.
% 2.39/2.82 (21129) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 2.39/2.82 (21130) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 2.39/2.82 (21131) {G0,W8,D3,L3,V2,M3} { empty( X ), empty( Y ), ! empty(
% 2.39/2.82 cartesian_product2( X, Y ) ) }.
% 2.39/2.82 (21132) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_POSet( X ) ) }.
% 2.39/2.82 (21133) {G0,W3,D3,L1,V1,M1} { strict_rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 (21134) {G0,W3,D3,L1,V1,M1} { reflexive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21135) {G0,W3,D3,L1,V1,M1} { transitive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21136) {G0,W3,D3,L1,V1,M1} { antisymmetric_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21137) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_POSet( X ) ) }.
% 2.39/2.82 (21138) {G0,W3,D3,L1,V1,M1} { strict_rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 (21139) {G0,W3,D3,L1,V1,M1} { reflexive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21140) {G0,W3,D3,L1,V1,M1} { transitive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21141) {G0,W3,D3,L1,V1,M1} { antisymmetric_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21142) {G0,W3,D3,L1,V1,M1} { lower_bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21143) {G0,W3,D3,L1,V1,M1} { upper_bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21144) {G0,W3,D3,L1,V1,M1} { bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21145) {G0,W3,D3,L1,V1,M1} { with_suprema_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21146) {G0,W3,D3,L1,V1,M1} { with_infima_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21147) {G0,W3,D3,L1,V1,M1} { complete_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21148) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_POSet( X ) ) }.
% 2.39/2.82 (21149) {G0,W3,D3,L1,V1,M1} { strict_rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 (21150) {G0,W3,D3,L1,V1,M1} { reflexive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21151) {G0,W3,D3,L1,V1,M1} { transitive_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21152) {G0,W3,D3,L1,V1,M1} { antisymmetric_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21153) {G0,W3,D3,L1,V1,M1} { lower_bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21154) {G0,W3,D3,L1,V1,M1} { upper_bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21155) {G0,W3,D3,L1,V1,M1} { bounded_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21156) {G0,W3,D3,L1,V1,M1} { directed_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21157) {G0,W3,D3,L1,V1,M1} { up_complete_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21158) {G0,W3,D3,L1,V1,M1} { join_complete_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21159) {G0,W3,D3,L1,V1,M1} { ! v1_yellow_3( boole_POSet( X ) ) }.
% 2.39/2.82 (21160) {G0,W3,D3,L1,V1,M1} { with_suprema_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21161) {G0,W3,D3,L1,V1,M1} { with_infima_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21162) {G0,W3,D3,L1,V1,M1} { complete_relstr( boole_POSet( X ) ) }.
% 2.39/2.82 (21163) {G0,W14,D3,L3,V4,M3} { ! relation_of2( Y, X, X ), ! rel_str_of( X
% 2.39/2.82 , Y ) = rel_str_of( Z, T ), X = Z }.
% 2.39/2.82 (21164) {G0,W14,D3,L3,V4,M3} { ! relation_of2( Y, X, X ), ! rel_str_of( X
% 2.39/2.82 , Y ) = rel_str_of( Z, T ), Y = T }.
% 2.39/2.82 (21165) {G0,W12,D3,L5,V1,M5} { empty_carrier( X ), ! reflexive_relstr( X )
% 2.39/2.82 , ! transitive_relstr( X ), ! rel_str( X ), alpha8( X, skol6( X ) ) }.
% 2.39/2.82 (21166) {G0,W12,D3,L5,V1,M5} { empty_carrier( X ), ! reflexive_relstr( X )
% 2.39/2.82 , ! transitive_relstr( X ), ! rel_str( X ), upper_relstr_subset( skol6( X
% 2.39/2.82 ), X ) }.
% 2.39/2.82 (21167) {G0,W8,D4,L2,V2,M2} { ! alpha8( X, Y ), element( Y, powerset(
% 2.39/2.82 the_carrier( X ) ) ) }.
% 2.39/2.82 (21168) {G0,W5,D2,L2,V2,M2} { ! alpha8( X, Y ), ! empty( Y ) }.
% 2.39/2.82 (21169) {G0,W6,D2,L2,V2,M2} { ! alpha8( X, Y ), filtered_subset( Y, X )
% 2.39/2.82 }.
% 2.39/2.82 (21170) {G0,W13,D4,L4,V2,M4} { ! element( Y, powerset( the_carrier( X ) )
% 2.39/2.82 ), empty( Y ), ! filtered_subset( Y, X ), alpha8( X, Y ) }.
% 2.39/2.82 (21171) {G0,W2,D2,L1,V0,M1} { rel_str( skol7 ) }.
% 2.39/2.82 (21172) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol7 ) }.
% 2.39/2.82 (21173) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol7 ) }.
% 2.39/2.82 (21174) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol7 ) }.
% 2.39/2.82 (21175) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol7 ) }.
% 2.39/2.82 (21176) {G0,W2,D2,L1,V0,M1} { connected_relstr( skol7 ) }.
% 2.39/2.82 (21177) {G0,W2,D2,L1,V0,M1} { rel_str( skol8 ) }.
% 2.39/2.82 (21178) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol8 ) }.
% 2.39/2.82 (21179) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol8 ) }.
% 2.39/2.82 (21180) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol8 ) }.
% 2.39/2.82 (21181) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol8 ) }.
% 2.39/2.82 (21182) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol8 ) }.
% 2.39/2.82 (21183) {G0,W2,D2,L1,V0,M1} { with_suprema_relstr( skol8 ) }.
% 2.39/2.82 (21184) {G0,W2,D2,L1,V0,M1} { with_infima_relstr( skol8 ) }.
% 2.39/2.82 (21185) {G0,W2,D2,L1,V0,M1} { complete_relstr( skol8 ) }.
% 2.39/2.82 (21186) {G0,W2,D2,L1,V0,M1} { lower_bounded_relstr( skol8 ) }.
% 2.39/2.82 (21187) {G0,W2,D2,L1,V0,M1} { upper_bounded_relstr( skol8 ) }.
% 2.39/2.82 (21188) {G0,W2,D2,L1,V0,M1} { bounded_relstr( skol8 ) }.
% 2.39/2.82 (21189) {G0,W2,D2,L1,V0,M1} { up_complete_relstr( skol8 ) }.
% 2.39/2.82 (21190) {G0,W2,D2,L1,V0,M1} { join_complete_relstr( skol8 ) }.
% 2.39/2.82 (21191) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 2.39/2.82 (21192) {G0,W2,D2,L1,V0,M1} { finite( skol9 ) }.
% 2.39/2.82 (21193) {G0,W2,D2,L1,V0,M1} { rel_str( skol10 ) }.
% 2.39/2.82 (21194) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol10 ) }.
% 2.39/2.82 (21195) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol10 ) }.
% 2.39/2.82 (21196) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol10 ) }.
% 2.39/2.82 (21197) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol10 ) }.
% 2.39/2.82 (21198) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol10 ) }.
% 2.39/2.82 (21199) {G0,W2,D2,L1,V0,M1} { complete_relstr( skol10 ) }.
% 2.39/2.82 (21200) {G0,W2,D2,L1,V0,M1} { empty( skol11 ) }.
% 2.39/2.82 (21201) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 2.39/2.82 (21202) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol12( Y ) ) }.
% 2.39/2.82 (21203) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol12( X ), powerset(
% 2.39/2.82 X ) ) }.
% 2.39/2.82 (21204) {G0,W2,D2,L1,V0,M1} { rel_str( skol13 ) }.
% 2.39/2.82 (21205) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol13 ) }.
% 2.39/2.82 (21206) {G0,W2,D2,L1,V0,M1} { ! trivial_carrier( skol13 ) }.
% 2.39/2.82 (21207) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol13 ) }.
% 2.39/2.82 (21208) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol13 ) }.
% 2.39/2.82 (21209) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol13 ) }.
% 2.39/2.82 (21210) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol13 ) }.
% 2.39/2.82 (21211) {G0,W2,D2,L1,V0,M1} { lower_bounded_relstr( skol13 ) }.
% 2.39/2.82 (21212) {G0,W2,D2,L1,V0,M1} { upper_bounded_relstr( skol13 ) }.
% 2.39/2.82 (21213) {G0,W2,D2,L1,V0,M1} { bounded_relstr( skol13 ) }.
% 2.39/2.82 (21214) {G0,W2,D2,L1,V0,M1} { ! v1_yellow_3( skol13 ) }.
% 2.39/2.82 (21215) {G0,W2,D2,L1,V0,M1} { distributive_relstr( skol13 ) }.
% 2.39/2.82 (21216) {G0,W2,D2,L1,V0,M1} { heyting_relstr( skol13 ) }.
% 2.39/2.82 (21217) {G0,W2,D2,L1,V0,M1} { complemented_relstr( skol13 ) }.
% 2.39/2.82 (21218) {G0,W2,D2,L1,V0,M1} { boolean_relstr( skol13 ) }.
% 2.39/2.82 (21219) {G0,W2,D2,L1,V0,M1} { with_suprema_relstr( skol13 ) }.
% 2.39/2.82 (21220) {G0,W2,D2,L1,V0,M1} { with_infima_relstr( skol13 ) }.
% 2.39/2.82 (21221) {G0,W2,D2,L1,V0,M1} { rel_str( skol14 ) }.
% 2.39/2.82 (21222) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol14 ) }.
% 2.39/2.82 (21223) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol14 ) }.
% 2.39/2.82 (21224) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol14 ) }.
% 2.39/2.82 (21225) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol14 ) }.
% 2.39/2.82 (21226) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol14 ) }.
% 2.39/2.82 (21227) {G0,W2,D2,L1,V0,M1} { with_suprema_relstr( skol14 ) }.
% 2.39/2.82 (21228) {G0,W2,D2,L1,V0,M1} { with_infima_relstr( skol14 ) }.
% 2.39/2.82 (21229) {G0,W2,D2,L1,V0,M1} { complete_relstr( skol14 ) }.
% 2.39/2.82 (21230) {G0,W2,D2,L1,V0,M1} { trivial_carrier( skol14 ) }.
% 2.39/2.82 (21231) {G0,W2,D2,L1,V0,M1} { rel_str( skol15 ) }.
% 2.39/2.82 (21232) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol15 ) }.
% 2.39/2.82 (21233) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol15 ) }.
% 2.39/2.82 (21234) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol15 ) }.
% 2.39/2.82 (21235) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol15 ) }.
% 2.39/2.82 (21236) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol15 ) }.
% 2.39/2.82 (21237) {G0,W2,D2,L1,V0,M1} { with_suprema_relstr( skol15 ) }.
% 2.39/2.82 (21238) {G0,W2,D2,L1,V0,M1} { with_infima_relstr( skol15 ) }.
% 2.39/2.82 (21239) {G0,W2,D2,L1,V0,M1} { complete_relstr( skol15 ) }.
% 2.39/2.82 (21240) {G0,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 2.39/2.82 (21241) {G0,W2,D2,L1,V0,M1} { relation( skol16 ) }.
% 2.39/2.82 (21242) {G0,W3,D3,L1,V1,M1} { empty( skol17( Y ) ) }.
% 2.39/2.82 (21243) {G0,W5,D3,L1,V1,M1} { element( skol17( X ), powerset( X ) ) }.
% 2.39/2.82 (21244) {G0,W3,D3,L1,V1,M1} { ! empty( skol18( Y ) ) }.
% 2.39/2.82 (21245) {G0,W3,D3,L1,V1,M1} { finite( skol18( Y ) ) }.
% 2.39/2.82 (21246) {G0,W6,D4,L1,V1,M1} { element( skol18( X ), powerset( powerset( X
% 2.39/2.82 ) ) ) }.
% 2.39/2.82 (21247) {G0,W2,D2,L1,V0,M1} { rel_str( skol19 ) }.
% 2.39/2.82 (21248) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol19 ) }.
% 2.39/2.82 (21249) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol19 ) }.
% 2.39/2.82 (21250) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol19 ) }.
% 2.39/2.82 (21251) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol19 ) }.
% 2.39/2.82 (21252) {G0,W2,D2,L1,V0,M1} { with_suprema_relstr( skol19 ) }.
% 2.39/2.82 (21253) {G0,W2,D2,L1,V0,M1} { with_infima_relstr( skol19 ) }.
% 2.39/2.82 (21254) {G0,W2,D2,L1,V0,M1} { complete_relstr( skol19 ) }.
% 2.39/2.82 (21255) {G0,W2,D2,L1,V0,M1} { lower_bounded_relstr( skol19 ) }.
% 2.39/2.82 (21256) {G0,W2,D2,L1,V0,M1} { upper_bounded_relstr( skol19 ) }.
% 2.39/2.82 (21257) {G0,W2,D2,L1,V0,M1} { bounded_relstr( skol19 ) }.
% 2.39/2.82 (21258) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol20( Y ) ) }.
% 2.39/2.82 (21259) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol20( Y ) ) }.
% 2.39/2.82 (21260) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol20( X ), powerset(
% 2.39/2.82 X ) ) }.
% 2.39/2.82 (21261) {G0,W2,D2,L1,V0,M1} { relation( skol21 ) }.
% 2.39/2.82 (21262) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol21 ) }.
% 2.39/2.82 (21263) {G0,W2,D2,L1,V0,M1} { one_sorted_str( skol22 ) }.
% 2.39/2.82 (21264) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol22 ) }.
% 2.39/2.82 (21265) {G0,W5,D3,L2,V2,M2} { ! one_sorted_str( X ), ! empty( skol23( Y )
% 2.39/2.82 ) }.
% 2.39/2.82 (21266) {G0,W5,D3,L2,V2,M2} { ! one_sorted_str( X ), finite( skol23( Y ) )
% 2.39/2.82 }.
% 2.39/2.82 (21267) {G0,W9,D5,L2,V1,M2} { ! one_sorted_str( X ), element( skol23( X )
% 2.39/2.82 , powerset( powerset( the_carrier( X ) ) ) ) }.
% 2.39/2.82 (21268) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol24( Y ) ) }.
% 2.39/2.82 (21269) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol24( Y ) ) }.
% 2.39/2.82 (21270) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol24( X ), powerset(
% 2.39/2.82 X ) ) }.
% 2.39/2.82 (21271) {G0,W18,D3,L8,V1,M8} { empty_carrier( X ), trivial_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! transitive_relstr( X ), ! antisymmetric_relstr
% 2.39/2.82 ( X ), ! upper_bounded_relstr( X ), ! rel_str( X ), alpha9( X, skol25( X
% 2.39/2.82 ) ) }.
% 2.39/2.82 (21272) {G0,W18,D3,L8,V1,M8} { empty_carrier( X ), trivial_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! transitive_relstr( X ), ! antisymmetric_relstr
% 2.39/2.82 ( X ), ! upper_bounded_relstr( X ), ! rel_str( X ), upper_relstr_subset(
% 2.39/2.82 skol25( X ), X ) }.
% 2.39/2.82 (21273) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), alpha14( X, Y ) }.
% 2.39/2.82 (21274) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), filtered_subset( Y, X )
% 2.39/2.82 }.
% 2.39/2.82 (21275) {G0,W9,D2,L3,V2,M3} { ! alpha14( X, Y ), ! filtered_subset( Y, X )
% 2.39/2.82 , alpha9( X, Y ) }.
% 2.39/2.82 (21276) {G0,W8,D4,L2,V2,M2} { ! alpha14( X, Y ), element( Y, powerset(
% 2.39/2.82 the_carrier( X ) ) ) }.
% 2.39/2.82 (21277) {G0,W5,D2,L2,V2,M2} { ! alpha14( X, Y ), ! empty( Y ) }.
% 2.39/2.82 (21278) {G0,W8,D4,L2,V2,M2} { ! alpha14( X, Y ), proper_element( Y,
% 2.39/2.82 powerset( the_carrier( X ) ) ) }.
% 2.39/2.82 (21279) {G0,W15,D4,L4,V2,M4} { ! element( Y, powerset( the_carrier( X ) )
% 2.39/2.82 ), empty( Y ), ! proper_element( Y, powerset( the_carrier( X ) ) ),
% 2.39/2.82 alpha14( X, Y ) }.
% 2.39/2.82 (21280) {G0,W2,D2,L1,V0,M1} { rel_str( skol26 ) }.
% 2.39/2.82 (21281) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol26 ) }.
% 2.39/2.82 (21282) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol26 ) }.
% 2.39/2.82 (21283) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol26 ) }.
% 2.39/2.82 (21284) {G0,W2,D2,L1,V0,M1} { directed_relstr( skol26 ) }.
% 2.39/2.82 (21285) {G0,W7,D3,L3,V2,M3} { empty_carrier( X ), ! one_sorted_str( X ), !
% 2.39/2.82 empty( skol27( Y ) ) }.
% 2.39/2.82 (21286) {G0,W10,D4,L3,V1,M3} { empty_carrier( X ), ! one_sorted_str( X ),
% 2.39/2.82 element( skol27( X ), powerset( the_carrier( X ) ) ) }.
% 2.39/2.82 (21287) {G0,W8,D2,L2,V3,M2} { ! relation_of2_as_subset( Z, X, Y ),
% 2.39/2.82 relation_of2( Z, X, Y ) }.
% 2.39/2.82 (21288) {G0,W8,D2,L2,V3,M2} { ! relation_of2( Z, X, Y ),
% 2.39/2.82 relation_of2_as_subset( Z, X, Y ) }.
% 2.39/2.82 (21289) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 2.39/2.82 (21290) {G0,W5,D4,L1,V1,M1} { bottom_of_relstr( boole_POSet( X ) ) =
% 2.39/2.82 empty_set }.
% 2.39/2.82 (21291) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 2.39/2.82 (21292) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 2.39/2.82 }.
% 2.39/2.82 (21293) {G0,W2,D2,L1,V0,M1} { ! empty( skol28 ) }.
% 2.39/2.82 (21294) {G0,W2,D2,L1,V0,M1} { ! empty( skol29 ) }.
% 2.39/2.82 (21295) {G0,W4,D3,L1,V0,M1} { filtered_subset( skol29, boole_POSet( skol28
% 2.39/2.82 ) ) }.
% 2.39/2.82 (21296) {G0,W4,D3,L1,V0,M1} { upper_relstr_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ) }.
% 2.39/2.82 (21297) {G0,W6,D5,L1,V0,M1} { proper_element( skol29, powerset(
% 2.39/2.82 the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 (21298) {G0,W6,D5,L1,V0,M1} { element( skol29, powerset( the_carrier(
% 2.39/2.82 boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 (21299) {G0,W3,D2,L1,V0,M1} { in( skol30, skol29 ) }.
% 2.39/2.82 (21300) {G0,W2,D2,L1,V0,M1} { empty( skol30 ) }.
% 2.39/2.82 (21301) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 2.39/2.82 ) }.
% 2.39/2.82 (21302) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 2.39/2.82 ) }.
% 2.39/2.82 (21303) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 2.39/2.82 , element( X, Y ) }.
% 2.39/2.82 (21304) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 2.39/2.82 , ! empty( Z ) }.
% 2.39/2.82 (21305) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 2.39/2.82 (21306) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 2.39/2.82 (21307) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 2.39/2.82 (21308) {G0,W34,D4,L12,V2,M12} { empty_carrier( X ), ! reflexive_relstr( X
% 2.39/2.82 ), ! transitive_relstr( X ), ! antisymmetric_relstr( X ), !
% 2.39/2.82 lower_bounded_relstr( X ), ! rel_str( X ), empty( Y ), ! filtered_subset
% 2.39/2.82 ( Y, X ), ! upper_relstr_subset( Y, X ), ! element( Y, powerset(
% 2.39/2.82 the_carrier( X ) ) ), ! proper_element( Y, powerset( the_carrier( X ) ) )
% 2.39/2.82 , ! in( bottom_of_relstr( X ), Y ) }.
% 2.39/2.82 (21309) {G0,W34,D4,L12,V2,M12} { empty_carrier( X ), ! reflexive_relstr( X
% 2.39/2.82 ), ! transitive_relstr( X ), ! antisymmetric_relstr( X ), !
% 2.39/2.82 lower_bounded_relstr( X ), ! rel_str( X ), empty( Y ), ! filtered_subset
% 2.39/2.82 ( Y, X ), ! upper_relstr_subset( Y, X ), ! element( Y, powerset(
% 2.39/2.82 the_carrier( X ) ) ), in( bottom_of_relstr( X ), Y ), proper_element( Y,
% 2.39/2.82 powerset( the_carrier( X ) ) ) }.
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Total Proof:
% 2.39/2.82
% 2.39/2.82 subsumption: (80) {G0,W3,D3,L1,V1,M1} I { rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 parent0: (21041) {G0,W3,D3,L1,V1,M1} { rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (89) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 2.39/2.82 parent0: (21054) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (95) {G0,W3,D3,L1,V1,M1} I { ! empty_carrier( boole_POSet( X )
% 2.39/2.82 ) }.
% 2.39/2.82 parent0: (21060) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_POSet( X ) )
% 2.39/2.82 }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (96) {G0,W3,D3,L1,V1,M1} I { reflexive_relstr( boole_POSet( X
% 2.39/2.82 ) ) }.
% 2.39/2.82 parent0: (21062) {G0,W3,D3,L1,V1,M1} { reflexive_relstr( boole_POSet( X )
% 2.39/2.82 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (97) {G0,W3,D3,L1,V1,M1} I { transitive_relstr( boole_POSet( X
% 2.39/2.82 ) ) }.
% 2.39/2.82 parent0: (21063) {G0,W3,D3,L1,V1,M1} { transitive_relstr( boole_POSet( X )
% 2.39/2.82 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (98) {G0,W3,D3,L1,V1,M1} I { antisymmetric_relstr( boole_POSet
% 2.39/2.82 ( X ) ) }.
% 2.39/2.82 parent0: (21064) {G0,W3,D3,L1,V1,M1} { antisymmetric_relstr( boole_POSet(
% 2.39/2.82 X ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (99) {G0,W3,D3,L1,V1,M1} I { lower_bounded_relstr( boole_POSet
% 2.39/2.82 ( X ) ) }.
% 2.39/2.82 parent0: (21065) {G0,W3,D3,L1,V1,M1} { lower_bounded_relstr( boole_POSet(
% 2.39/2.82 X ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (274) {G0,W5,D4,L1,V1,M1} I { bottom_of_relstr( boole_POSet( X
% 2.39/2.82 ) ) ==> empty_set }.
% 2.39/2.82 parent0: (21290) {G0,W5,D4,L1,V1,M1} { bottom_of_relstr( boole_POSet( X )
% 2.39/2.82 ) = empty_set }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (278) {G0,W2,D2,L1,V0,M1} I { ! empty( skol29 ) }.
% 2.39/2.82 parent0: (21294) {G0,W2,D2,L1,V0,M1} { ! empty( skol29 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (279) {G0,W4,D3,L1,V0,M1} I { filtered_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ) }.
% 2.39/2.82 parent0: (21295) {G0,W4,D3,L1,V0,M1} { filtered_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (280) {G0,W4,D3,L1,V0,M1} I { upper_relstr_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ) }.
% 2.39/2.82 parent0: (21296) {G0,W4,D3,L1,V0,M1} { upper_relstr_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (281) {G0,W6,D5,L1,V0,M1} I { proper_element( skol29, powerset
% 2.39/2.82 ( the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 parent0: (21297) {G0,W6,D5,L1,V0,M1} { proper_element( skol29, powerset(
% 2.39/2.82 the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (282) {G0,W6,D5,L1,V0,M1} I { element( skol29, powerset(
% 2.39/2.82 the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 parent0: (21298) {G0,W6,D5,L1,V0,M1} { element( skol29, powerset(
% 2.39/2.82 the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (283) {G0,W3,D2,L1,V0,M1} I { in( skol30, skol29 ) }.
% 2.39/2.82 parent0: (21299) {G0,W3,D2,L1,V0,M1} { in( skol30, skol29 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (284) {G0,W2,D2,L1,V0,M1} I { empty( skol30 ) }.
% 2.39/2.82 parent0: (21300) {G0,W2,D2,L1,V0,M1} { empty( skol30 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (289) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 2.39/2.82 parent0: (21305) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 1 ==> 1
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (292) {G0,W34,D4,L12,V2,M12} I { empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! transitive_relstr( X ), ! antisymmetric_relstr(
% 2.39/2.82 X ), ! lower_bounded_relstr( X ), ! rel_str( X ), empty( Y ), !
% 2.39/2.82 filtered_subset( Y, X ), ! upper_relstr_subset( Y, X ), ! element( Y,
% 2.39/2.82 powerset( the_carrier( X ) ) ), ! proper_element( Y, powerset(
% 2.39/2.82 the_carrier( X ) ) ), ! in( bottom_of_relstr( X ), Y ) }.
% 2.39/2.82 parent0: (21308) {G0,W34,D4,L12,V2,M12} { empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! transitive_relstr( X ), ! antisymmetric_relstr(
% 2.39/2.82 X ), ! lower_bounded_relstr( X ), ! rel_str( X ), empty( Y ), !
% 2.39/2.82 filtered_subset( Y, X ), ! upper_relstr_subset( Y, X ), ! element( Y,
% 2.39/2.82 powerset( the_carrier( X ) ) ), ! proper_element( Y, powerset(
% 2.39/2.82 the_carrier( X ) ) ), ! in( bottom_of_relstr( X ), Y ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 Y := Y
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 1 ==> 1
% 2.39/2.82 2 ==> 2
% 2.39/2.82 3 ==> 3
% 2.39/2.82 4 ==> 4
% 2.39/2.82 5 ==> 5
% 2.39/2.82 6 ==> 6
% 2.39/2.82 7 ==> 7
% 2.39/2.82 8 ==> 8
% 2.39/2.82 9 ==> 9
% 2.39/2.82 10 ==> 10
% 2.39/2.82 11 ==> 11
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 eqswap: (21442) {G0,W5,D2,L2,V1,M2} { empty_set = X, ! empty( X ) }.
% 2.39/2.82 parent0[1]: (289) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := X
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21443) {G1,W3,D2,L1,V0,M1} { empty_set = skol30 }.
% 2.39/2.82 parent0[1]: (21442) {G0,W5,D2,L2,V1,M2} { empty_set = X, ! empty( X ) }.
% 2.39/2.82 parent1[0]: (284) {G0,W2,D2,L1,V0,M1} I { empty( skol30 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := skol30
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 eqswap: (21444) {G1,W3,D2,L1,V0,M1} { skol30 = empty_set }.
% 2.39/2.82 parent0[0]: (21443) {G1,W3,D2,L1,V0,M1} { empty_set = skol30 }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (3310) {G1,W3,D2,L1,V0,M1} R(289,284) { skol30 ==> empty_set
% 2.39/2.82 }.
% 2.39/2.82 parent0: (21444) {G1,W3,D2,L1,V0,M1} { skol30 = empty_set }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 paramod: (21447) {G1,W5,D2,L2,V0,M2} { in( empty_set, skol29 ), ! empty(
% 2.39/2.82 skol30 ) }.
% 2.39/2.82 parent0[1]: (289) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 2.39/2.82 parent1[0; 1]: (283) {G0,W3,D2,L1,V0,M1} I { in( skol30, skol29 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := skol30
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 paramod: (21930) {G2,W5,D2,L2,V0,M2} { ! empty( empty_set ), in( empty_set
% 2.39/2.82 , skol29 ) }.
% 2.39/2.82 parent0[0]: (3310) {G1,W3,D2,L1,V0,M1} R(289,284) { skol30 ==> empty_set
% 2.39/2.82 }.
% 2.39/2.82 parent1[1; 2]: (21447) {G1,W5,D2,L2,V0,M2} { in( empty_set, skol29 ), !
% 2.39/2.82 empty( skol30 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21931) {G1,W3,D2,L1,V0,M1} { in( empty_set, skol29 ) }.
% 2.39/2.82 parent0[0]: (21930) {G2,W5,D2,L2,V0,M2} { ! empty( empty_set ), in(
% 2.39/2.82 empty_set, skol29 ) }.
% 2.39/2.82 parent1[0]: (89) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (3384) {G2,W3,D2,L1,V0,M1} P(289,283);d(3310);r(89) { in(
% 2.39/2.82 empty_set, skol29 ) }.
% 2.39/2.82 parent0: (21931) {G1,W3,D2,L1,V0,M1} { in( empty_set, skol29 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 0
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21933) {G1,W39,D5,L11,V0,M11} { empty_carrier( boole_POSet(
% 2.39/2.82 skol28 ) ), ! reflexive_relstr( boole_POSet( skol28 ) ), !
% 2.39/2.82 transitive_relstr( boole_POSet( skol28 ) ), ! antisymmetric_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! lower_bounded_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! rel_str( boole_POSet( skol28 ) ), empty( skol29 ), ! filtered_subset
% 2.39/2.82 ( skol29, boole_POSet( skol28 ) ), ! upper_relstr_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ), ! proper_element( skol29, powerset( the_carrier
% 2.39/2.82 ( boole_POSet( skol28 ) ) ) ), ! in( bottom_of_relstr( boole_POSet(
% 2.39/2.82 skol28 ) ), skol29 ) }.
% 2.39/2.82 parent0[9]: (292) {G0,W34,D4,L12,V2,M12} I { empty_carrier( X ), !
% 2.39/2.82 reflexive_relstr( X ), ! transitive_relstr( X ), ! antisymmetric_relstr(
% 2.39/2.82 X ), ! lower_bounded_relstr( X ), ! rel_str( X ), empty( Y ), !
% 2.39/2.82 filtered_subset( Y, X ), ! upper_relstr_subset( Y, X ), ! element( Y,
% 2.39/2.82 powerset( the_carrier( X ) ) ), ! proper_element( Y, powerset(
% 2.39/2.82 the_carrier( X ) ) ), ! in( bottom_of_relstr( X ), Y ) }.
% 2.39/2.82 parent1[0]: (282) {G0,W6,D5,L1,V0,M1} I { element( skol29, powerset(
% 2.39/2.82 the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := boole_POSet( skol28 )
% 2.39/2.82 Y := skol29
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 paramod: (21934) {G1,W37,D5,L11,V0,M11} { ! in( empty_set, skol29 ),
% 2.39/2.82 empty_carrier( boole_POSet( skol28 ) ), ! reflexive_relstr( boole_POSet(
% 2.39/2.82 skol28 ) ), ! transitive_relstr( boole_POSet( skol28 ) ), !
% 2.39/2.82 antisymmetric_relstr( boole_POSet( skol28 ) ), ! lower_bounded_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! rel_str( boole_POSet( skol28 ) ), empty(
% 2.39/2.82 skol29 ), ! filtered_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 upper_relstr_subset( skol29, boole_POSet( skol28 ) ), ! proper_element(
% 2.39/2.82 skol29, powerset( the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 parent0[0]: (274) {G0,W5,D4,L1,V1,M1} I { bottom_of_relstr( boole_POSet( X
% 2.39/2.82 ) ) ==> empty_set }.
% 2.39/2.82 parent1[10; 2]: (21933) {G1,W39,D5,L11,V0,M11} { empty_carrier(
% 2.39/2.82 boole_POSet( skol28 ) ), ! reflexive_relstr( boole_POSet( skol28 ) ), !
% 2.39/2.82 transitive_relstr( boole_POSet( skol28 ) ), ! antisymmetric_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! lower_bounded_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! rel_str( boole_POSet( skol28 ) ), empty( skol29 ), ! filtered_subset
% 2.39/2.82 ( skol29, boole_POSet( skol28 ) ), ! upper_relstr_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ), ! proper_element( skol29, powerset( the_carrier
% 2.39/2.82 ( boole_POSet( skol28 ) ) ) ), ! in( bottom_of_relstr( boole_POSet(
% 2.39/2.82 skol28 ) ), skol29 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := skol28
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21935) {G1,W34,D5,L10,V0,M10} { ! in( empty_set, skol29 ), !
% 2.39/2.82 reflexive_relstr( boole_POSet( skol28 ) ), ! transitive_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! antisymmetric_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! lower_bounded_relstr( boole_POSet( skol28 ) ), ! rel_str( boole_POSet
% 2.39/2.82 ( skol28 ) ), empty( skol29 ), ! filtered_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ), ! upper_relstr_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 proper_element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) )
% 2.39/2.82 ) }.
% 2.39/2.82 parent0[0]: (95) {G0,W3,D3,L1,V1,M1} I { ! empty_carrier( boole_POSet( X )
% 2.39/2.82 ) }.
% 2.39/2.82 parent1[1]: (21934) {G1,W37,D5,L11,V0,M11} { ! in( empty_set, skol29 ),
% 2.39/2.82 empty_carrier( boole_POSet( skol28 ) ), ! reflexive_relstr( boole_POSet(
% 2.39/2.82 skol28 ) ), ! transitive_relstr( boole_POSet( skol28 ) ), !
% 2.39/2.82 antisymmetric_relstr( boole_POSet( skol28 ) ), ! lower_bounded_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! rel_str( boole_POSet( skol28 ) ), empty(
% 2.39/2.82 skol29 ), ! filtered_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 upper_relstr_subset( skol29, boole_POSet( skol28 ) ), ! proper_element(
% 2.39/2.82 skol29, powerset( the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 X := skol28
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (3682) {G1,W34,D5,L10,V0,M10} R(292,282);d(274);r(95) { !
% 2.39/2.82 reflexive_relstr( boole_POSet( skol28 ) ), ! transitive_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! antisymmetric_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! lower_bounded_relstr( boole_POSet( skol28 ) ), ! rel_str( boole_POSet
% 2.39/2.82 ( skol28 ) ), empty( skol29 ), ! filtered_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ), ! upper_relstr_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 proper_element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) )
% 2.39/2.82 ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent0: (21935) {G1,W34,D5,L10,V0,M10} { ! in( empty_set, skol29 ), !
% 2.39/2.82 reflexive_relstr( boole_POSet( skol28 ) ), ! transitive_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! antisymmetric_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! lower_bounded_relstr( boole_POSet( skol28 ) ), ! rel_str( boole_POSet
% 2.39/2.82 ( skol28 ) ), empty( skol29 ), ! filtered_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ), ! upper_relstr_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 proper_element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) )
% 2.39/2.82 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 0 ==> 9
% 2.39/2.82 1 ==> 0
% 2.39/2.82 2 ==> 1
% 2.39/2.82 3 ==> 2
% 2.39/2.82 4 ==> 3
% 2.39/2.82 5 ==> 4
% 2.39/2.82 6 ==> 5
% 2.39/2.82 7 ==> 6
% 2.39/2.82 8 ==> 7
% 2.39/2.82 9 ==> 8
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21936) {G1,W31,D5,L9,V0,M9} { ! transitive_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! antisymmetric_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! lower_bounded_relstr( boole_POSet( skol28 ) ), ! rel_str( boole_POSet
% 2.39/2.82 ( skol28 ) ), empty( skol29 ), ! filtered_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ), ! upper_relstr_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 proper_element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) )
% 2.39/2.82 ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent0[0]: (3682) {G1,W34,D5,L10,V0,M10} R(292,282);d(274);r(95) { !
% 2.39/2.82 reflexive_relstr( boole_POSet( skol28 ) ), ! transitive_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! antisymmetric_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! lower_bounded_relstr( boole_POSet( skol28 ) ), ! rel_str( boole_POSet
% 2.39/2.82 ( skol28 ) ), empty( skol29 ), ! filtered_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ), ! upper_relstr_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 proper_element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) )
% 2.39/2.82 ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent1[0]: (96) {G0,W3,D3,L1,V1,M1} I { reflexive_relstr( boole_POSet( X )
% 2.39/2.82 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 X := skol28
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21937) {G1,W28,D5,L8,V0,M8} { ! antisymmetric_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! lower_bounded_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! rel_str( boole_POSet( skol28 ) ), empty( skol29 ), ! filtered_subset
% 2.39/2.82 ( skol29, boole_POSet( skol28 ) ), ! upper_relstr_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ), ! proper_element( skol29, powerset( the_carrier
% 2.39/2.82 ( boole_POSet( skol28 ) ) ) ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent0[0]: (21936) {G1,W31,D5,L9,V0,M9} { ! transitive_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! antisymmetric_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! lower_bounded_relstr( boole_POSet( skol28 ) ), ! rel_str( boole_POSet
% 2.39/2.82 ( skol28 ) ), empty( skol29 ), ! filtered_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ), ! upper_relstr_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 proper_element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) )
% 2.39/2.82 ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent1[0]: (97) {G0,W3,D3,L1,V1,M1} I { transitive_relstr( boole_POSet( X
% 2.39/2.82 ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 X := skol28
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21938) {G1,W25,D5,L7,V0,M7} { ! lower_bounded_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! rel_str( boole_POSet( skol28 ) ), empty(
% 2.39/2.82 skol29 ), ! filtered_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 upper_relstr_subset( skol29, boole_POSet( skol28 ) ), ! proper_element(
% 2.39/2.82 skol29, powerset( the_carrier( boole_POSet( skol28 ) ) ) ), ! in(
% 2.39/2.82 empty_set, skol29 ) }.
% 2.39/2.82 parent0[0]: (21937) {G1,W28,D5,L8,V0,M8} { ! antisymmetric_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! lower_bounded_relstr( boole_POSet( skol28 ) )
% 2.39/2.82 , ! rel_str( boole_POSet( skol28 ) ), empty( skol29 ), ! filtered_subset
% 2.39/2.82 ( skol29, boole_POSet( skol28 ) ), ! upper_relstr_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ), ! proper_element( skol29, powerset( the_carrier
% 2.39/2.82 ( boole_POSet( skol28 ) ) ) ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent1[0]: (98) {G0,W3,D3,L1,V1,M1} I { antisymmetric_relstr( boole_POSet
% 2.39/2.82 ( X ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 X := skol28
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21939) {G1,W22,D5,L6,V0,M6} { ! rel_str( boole_POSet( skol28
% 2.39/2.82 ) ), empty( skol29 ), ! filtered_subset( skol29, boole_POSet( skol28 ) )
% 2.39/2.82 , ! upper_relstr_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 proper_element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) )
% 2.39/2.82 ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent0[0]: (21938) {G1,W25,D5,L7,V0,M7} { ! lower_bounded_relstr(
% 2.39/2.82 boole_POSet( skol28 ) ), ! rel_str( boole_POSet( skol28 ) ), empty(
% 2.39/2.82 skol29 ), ! filtered_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 upper_relstr_subset( skol29, boole_POSet( skol28 ) ), ! proper_element(
% 2.39/2.82 skol29, powerset( the_carrier( boole_POSet( skol28 ) ) ) ), ! in(
% 2.39/2.82 empty_set, skol29 ) }.
% 2.39/2.82 parent1[0]: (99) {G0,W3,D3,L1,V1,M1} I { lower_bounded_relstr( boole_POSet
% 2.39/2.82 ( X ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 X := skol28
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21940) {G1,W19,D5,L5,V0,M5} { empty( skol29 ), !
% 2.39/2.82 filtered_subset( skol29, boole_POSet( skol28 ) ), ! upper_relstr_subset(
% 2.39/2.82 skol29, boole_POSet( skol28 ) ), ! proper_element( skol29, powerset(
% 2.39/2.82 the_carrier( boole_POSet( skol28 ) ) ) ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent0[0]: (21939) {G1,W22,D5,L6,V0,M6} { ! rel_str( boole_POSet( skol28
% 2.39/2.82 ) ), empty( skol29 ), ! filtered_subset( skol29, boole_POSet( skol28 ) )
% 2.39/2.82 , ! upper_relstr_subset( skol29, boole_POSet( skol28 ) ), !
% 2.39/2.82 proper_element( skol29, powerset( the_carrier( boole_POSet( skol28 ) ) )
% 2.39/2.82 ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent1[0]: (80) {G0,W3,D3,L1,V1,M1} I { rel_str( boole_POSet( X ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 X := skol28
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21941) {G1,W17,D5,L4,V0,M4} { ! filtered_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ), ! upper_relstr_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ), ! proper_element( skol29, powerset( the_carrier( boole_POSet
% 2.39/2.82 ( skol28 ) ) ) ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent0[0]: (278) {G0,W2,D2,L1,V0,M1} I { ! empty( skol29 ) }.
% 2.39/2.82 parent1[0]: (21940) {G1,W19,D5,L5,V0,M5} { empty( skol29 ), !
% 2.39/2.82 filtered_subset( skol29, boole_POSet( skol28 ) ), ! upper_relstr_subset(
% 2.39/2.82 skol29, boole_POSet( skol28 ) ), ! proper_element( skol29, powerset(
% 2.39/2.82 the_carrier( boole_POSet( skol28 ) ) ) ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21942) {G1,W13,D5,L3,V0,M3} { ! upper_relstr_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ), ! proper_element( skol29, powerset( the_carrier
% 2.39/2.82 ( boole_POSet( skol28 ) ) ) ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent0[0]: (21941) {G1,W17,D5,L4,V0,M4} { ! filtered_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ), ! upper_relstr_subset( skol29, boole_POSet(
% 2.39/2.82 skol28 ) ), ! proper_element( skol29, powerset( the_carrier( boole_POSet
% 2.39/2.82 ( skol28 ) ) ) ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent1[0]: (279) {G0,W4,D3,L1,V0,M1} I { filtered_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21943) {G1,W9,D5,L2,V0,M2} { ! proper_element( skol29,
% 2.39/2.82 powerset( the_carrier( boole_POSet( skol28 ) ) ) ), ! in( empty_set,
% 2.39/2.82 skol29 ) }.
% 2.39/2.82 parent0[0]: (21942) {G1,W13,D5,L3,V0,M3} { ! upper_relstr_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ), ! proper_element( skol29, powerset( the_carrier
% 2.39/2.82 ( boole_POSet( skol28 ) ) ) ), ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent1[0]: (280) {G0,W4,D3,L1,V0,M1} I { upper_relstr_subset( skol29,
% 2.39/2.82 boole_POSet( skol28 ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21944) {G1,W3,D2,L1,V0,M1} { ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent0[0]: (21943) {G1,W9,D5,L2,V0,M2} { ! proper_element( skol29,
% 2.39/2.82 powerset( the_carrier( boole_POSet( skol28 ) ) ) ), ! in( empty_set,
% 2.39/2.82 skol29 ) }.
% 2.39/2.82 parent1[0]: (281) {G0,W6,D5,L1,V0,M1} I { proper_element( skol29, powerset
% 2.39/2.82 ( the_carrier( boole_POSet( skol28 ) ) ) ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 resolution: (21945) {G2,W0,D0,L0,V0,M0} { }.
% 2.39/2.82 parent0[0]: (21944) {G1,W3,D2,L1,V0,M1} { ! in( empty_set, skol29 ) }.
% 2.39/2.82 parent1[0]: (3384) {G2,W3,D2,L1,V0,M1} P(289,283);d(3310);r(89) { in(
% 2.39/2.82 empty_set, skol29 ) }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 substitution1:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 subsumption: (20950) {G3,W0,D0,L0,V0,M0} S(3682);r(96);r(97);r(98);r(99);r(
% 2.39/2.82 80);r(278);r(279);r(280);r(281);r(3384) { }.
% 2.39/2.82 parent0: (21945) {G2,W0,D0,L0,V0,M0} { }.
% 2.39/2.82 substitution0:
% 2.39/2.82 end
% 2.39/2.82 permutation0:
% 2.39/2.82 end
% 2.39/2.82
% 2.39/2.82 Proof check complete!
% 2.39/2.82
% 2.39/2.82 Memory use:
% 2.39/2.82
% 2.39/2.82 space for terms: 250818
% 2.39/2.82 space for clauses: 823184
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 clauses generated: 61990
% 2.39/2.82 clauses kept: 20951
% 2.39/2.82 clauses selected: 2172
% 2.39/2.82 clauses deleted: 6238
% 2.39/2.82 clauses inuse deleted: 123
% 2.39/2.82
% 2.39/2.82 subsentry: 73041
% 2.39/2.82 literals s-matched: 52076
% 2.39/2.82 literals matched: 52076
% 2.39/2.82 full subsumption: 1143
% 2.39/2.82
% 2.39/2.82 checksum: 2095809802
% 2.39/2.82
% 2.39/2.82
% 2.39/2.82 Bliksem ended
%------------------------------------------------------------------------------