TSTP Solution File: SEU371+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU371+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 07:12:52 EDT 2022
% Result : Theorem 2.12s 2.49s
% Output : Refutation 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU371+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jun 19 05:20:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.76/1.15 *** allocated 10000 integers for termspace/termends
% 0.76/1.15 *** allocated 10000 integers for clauses
% 0.76/1.15 *** allocated 10000 integers for justifications
% 0.76/1.15 Bliksem 1.12
% 0.76/1.15
% 0.76/1.15
% 0.76/1.15 Automatic Strategy Selection
% 0.76/1.15
% 0.76/1.15 *** allocated 15000 integers for termspace/termends
% 0.76/1.15
% 0.76/1.15 Clauses:
% 0.76/1.15
% 0.76/1.15 { ! rel_str( X ), ! strict_rel_str( X ), X = rel_str_of( the_carrier( X ),
% 0.76/1.15 the_InternalRel( X ) ) }.
% 0.76/1.15 { ! latt_str( X ), ! strict_latt_str( X ), X = latt_str_of( the_carrier( X
% 0.76/1.15 ), the_L_join( X ), the_L_meet( X ) ) }.
% 0.76/1.15 { ! in( X, Y ), ! in( Y, X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! lattice( X ), ! complete_latt_str
% 0.76/1.15 ( X ), alpha2( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! lattice( X ), ! complete_latt_str
% 0.76/1.15 ( X ), bounded_lattstr( X ) }.
% 0.76/1.15 { ! alpha2( X ), alpha17( X ) }.
% 0.76/1.15 { ! alpha2( X ), upper_bounded_semilattstr( X ) }.
% 0.76/1.15 { ! alpha17( X ), ! upper_bounded_semilattstr( X ), alpha2( X ) }.
% 0.76/1.15 { ! alpha17( X ), alpha30( X ) }.
% 0.76/1.15 { ! alpha17( X ), lower_bounded_semilattstr( X ) }.
% 0.76/1.15 { ! alpha30( X ), ! lower_bounded_semilattstr( X ), alpha17( X ) }.
% 0.76/1.15 { ! alpha30( X ), alpha38( X ) }.
% 0.76/1.15 { ! alpha30( X ), lattice( X ) }.
% 0.76/1.15 { ! alpha38( X ), ! lattice( X ), alpha30( X ) }.
% 0.76/1.15 { ! alpha38( X ), alpha45( X ) }.
% 0.76/1.15 { ! alpha38( X ), join_absorbing( X ) }.
% 0.76/1.15 { ! alpha45( X ), ! join_absorbing( X ), alpha38( X ) }.
% 0.76/1.15 { ! alpha45( X ), alpha50( X ) }.
% 0.76/1.15 { ! alpha45( X ), meet_absorbing( X ) }.
% 0.76/1.15 { ! alpha50( X ), ! meet_absorbing( X ), alpha45( X ) }.
% 0.76/1.15 { ! alpha50( X ), alpha53( X ) }.
% 0.76/1.15 { ! alpha50( X ), meet_associative( X ) }.
% 0.76/1.15 { ! alpha53( X ), ! meet_associative( X ), alpha50( X ) }.
% 0.76/1.15 { ! alpha53( X ), alpha55( X ) }.
% 0.76/1.15 { ! alpha53( X ), meet_commutative( X ) }.
% 0.76/1.15 { ! alpha55( X ), ! meet_commutative( X ), alpha53( X ) }.
% 0.76/1.15 { ! alpha55( X ), ! empty_carrier( X ) }.
% 0.76/1.15 { ! alpha55( X ), join_commutative( X ) }.
% 0.76/1.15 { ! alpha55( X ), join_associative( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! join_commutative( X ), ! join_associative( X ),
% 0.76/1.15 alpha55( X ) }.
% 0.76/1.15 { ! rel_str( X ), ! with_suprema_relstr( X ), ! empty_carrier( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! lattice( X ), alpha3( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! lattice( X ), join_absorbing( X )
% 0.76/1.15 }.
% 0.76/1.15 { ! alpha3( X ), alpha18( X ) }.
% 0.76/1.15 { ! alpha3( X ), meet_absorbing( X ) }.
% 0.76/1.15 { ! alpha18( X ), ! meet_absorbing( X ), alpha3( X ) }.
% 0.76/1.15 { ! alpha18( X ), alpha31( X ) }.
% 0.76/1.15 { ! alpha18( X ), meet_associative( X ) }.
% 0.76/1.15 { ! alpha31( X ), ! meet_associative( X ), alpha18( X ) }.
% 0.76/1.15 { ! alpha31( X ), alpha39( X ) }.
% 0.76/1.15 { ! alpha31( X ), meet_commutative( X ) }.
% 0.76/1.15 { ! alpha39( X ), ! meet_commutative( X ), alpha31( X ) }.
% 0.76/1.15 { ! alpha39( X ), ! empty_carrier( X ) }.
% 0.76/1.15 { ! alpha39( X ), join_commutative( X ) }.
% 0.76/1.15 { ! alpha39( X ), join_associative( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! join_commutative( X ), ! join_associative( X ),
% 0.76/1.15 alpha39( X ) }.
% 0.76/1.15 { ! element( X, powerset( cartesian_product2( Y, Z ) ) ), relation( X ) }.
% 0.76/1.15 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ), !
% 0.76/1.15 empty_carrier( X ) }.
% 0.76/1.15 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ),
% 0.76/1.15 with_suprema_relstr( X ) }.
% 0.76/1.15 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ),
% 0.76/1.15 with_infima_relstr( X ) }.
% 0.76/1.15 { ! rel_str( X ), ! with_infima_relstr( X ), ! empty_carrier( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! join_commutative( X ), !
% 0.76/1.15 join_associative( X ), ! meet_commutative( X ), ! meet_associative( X ),
% 0.76/1.15 ! meet_absorbing( X ), ! join_absorbing( X ), ! empty_carrier( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! join_commutative( X ), !
% 0.76/1.15 join_associative( X ), ! meet_commutative( X ), ! meet_associative( X ),
% 0.76/1.15 ! meet_absorbing( X ), ! join_absorbing( X ), lattice( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! lower_bounded_semilattstr( X ), !
% 0.76/1.15 upper_bounded_semilattstr( X ), ! empty_carrier( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! lower_bounded_semilattstr( X ), !
% 0.76/1.15 upper_bounded_semilattstr( X ), bounded_lattstr( X ) }.
% 0.76/1.15 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ), !
% 0.76/1.15 empty_carrier( X ) }.
% 0.76/1.15 { ! rel_str( X ), empty_carrier( X ), ! complete_relstr( X ),
% 0.76/1.15 bounded_relstr( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! bounded_lattstr( X ), !
% 0.76/1.15 empty_carrier( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! bounded_lattstr( X ),
% 0.76/1.15 lower_bounded_semilattstr( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! bounded_lattstr( X ),
% 0.76/1.15 upper_bounded_semilattstr( X ) }.
% 0.76/1.15 { ! rel_str( X ), ! bounded_relstr( X ), lower_bounded_relstr( X ) }.
% 0.76/1.15 { ! rel_str( X ), ! bounded_relstr( X ), upper_bounded_relstr( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! boolean_lattstr( X ), alpha4( X )
% 0.76/1.15 }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! boolean_lattstr( X ),
% 0.76/1.15 complemented_lattstr( X ) }.
% 0.76/1.15 { ! alpha4( X ), alpha19( X ) }.
% 0.76/1.15 { ! alpha4( X ), bounded_lattstr( X ) }.
% 0.76/1.15 { ! alpha19( X ), ! bounded_lattstr( X ), alpha4( X ) }.
% 0.76/1.15 { ! alpha19( X ), alpha32( X ) }.
% 0.76/1.15 { ! alpha19( X ), upper_bounded_semilattstr( X ) }.
% 0.76/1.15 { ! alpha32( X ), ! upper_bounded_semilattstr( X ), alpha19( X ) }.
% 0.76/1.15 { ! alpha32( X ), ! empty_carrier( X ) }.
% 0.76/1.15 { ! alpha32( X ), distributive_lattstr( X ) }.
% 0.76/1.15 { ! alpha32( X ), lower_bounded_semilattstr( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! distributive_lattstr( X ), !
% 0.76/1.15 lower_bounded_semilattstr( X ), alpha32( X ) }.
% 0.76/1.15 { ! rel_str( X ), ! lower_bounded_relstr( X ), ! upper_bounded_relstr( X )
% 0.76/1.15 , bounded_relstr( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! distributive_lattstr( X ), !
% 0.76/1.15 bounded_lattstr( X ), ! complemented_lattstr( X ), ! empty_carrier( X ) }
% 0.76/1.15 .
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! distributive_lattstr( X ), !
% 0.76/1.15 bounded_lattstr( X ), ! complemented_lattstr( X ), boolean_lattstr( X ) }
% 0.76/1.15 .
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! lattice( X ), !
% 0.76/1.15 distributive_lattstr( X ), alpha5( X ) }.
% 0.76/1.15 { ! latt_str( X ), empty_carrier( X ), ! lattice( X ), !
% 0.76/1.15 distributive_lattstr( X ), modular_lattstr( X ) }.
% 0.76/1.15 { ! alpha5( X ), alpha20( X ) }.
% 0.76/1.15 { ! alpha5( X ), lattice( X ) }.
% 0.76/1.15 { ! alpha20( X ), ! lattice( X ), alpha5( X ) }.
% 0.76/1.15 { ! alpha20( X ), alpha33( X ) }.
% 0.76/1.15 { ! alpha20( X ), join_absorbing( X ) }.
% 0.76/1.15 { ! alpha33( X ), ! join_absorbing( X ), alpha20( X ) }.
% 0.76/1.15 { ! alpha33( X ), alpha40( X ) }.
% 0.76/1.15 { ! alpha33( X ), meet_absorbing( X ) }.
% 0.76/1.15 { ! alpha40( X ), ! meet_absorbing( X ), alpha33( X ) }.
% 0.76/1.15 { ! alpha40( X ), alpha46( X ) }.
% 0.76/1.15 { ! alpha40( X ), meet_associative( X ) }.
% 0.76/1.15 { ! alpha46( X ), ! meet_associative( X ), alpha40( X ) }.
% 0.76/1.15 { ! alpha46( X ), alpha51( X ) }.
% 0.76/1.15 { ! alpha46( X ), meet_commutative( X ) }.
% 0.76/1.15 { ! alpha51( X ), ! meet_commutative( X ), alpha46( X ) }.
% 0.76/1.15 { ! alpha51( X ), ! empty_carrier( X ) }.
% 0.76/1.15 { ! alpha51( X ), join_commutative( X ) }.
% 0.76/1.15 { ! alpha51( X ), join_associative( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! join_commutative( X ), ! join_associative( X ),
% 0.76/1.15 alpha51( X ) }.
% 0.76/1.15 { ! rel_str( X ), bottom_of_relstr( X ) = join_on_relstr( X, empty_set ) }
% 0.76/1.15 .
% 0.76/1.15 { empty_carrier( X ), ! latt_str( X ), meet_of_latt_set( X, Y ) =
% 0.76/1.15 join_of_latt_set( X, a_2_2_lattice3( X, Y ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), poset_of_lattice( X
% 0.76/1.15 ) = rel_str_of( the_carrier( X ), k2_lattice3( X ) ) }.
% 0.76/1.15 { boole_POSet( X ) = poset_of_lattice( boole_lattice( X ) ) }.
% 0.76/1.15 { ! relation_of2( Y, X, X ), strict_rel_str( rel_str_of( X, Y ) ) }.
% 0.76/1.15 { ! relation_of2( Y, X, X ), rel_str( rel_str_of( X, Y ) ) }.
% 0.76/1.15 { ! function( Y ), ! quasi_total( Y, cartesian_product2( X, X ), X ), !
% 0.76/1.15 relation_of2( Y, cartesian_product2( X, X ), X ), ! function( Z ), !
% 0.76/1.15 quasi_total( Z, cartesian_product2( X, X ), X ), ! relation_of2( Z,
% 0.76/1.15 cartesian_product2( X, X ), X ), strict_latt_str( latt_str_of( X, Y, Z )
% 0.76/1.15 ) }.
% 0.76/1.15 { ! function( Y ), ! quasi_total( Y, cartesian_product2( X, X ), X ), !
% 0.76/1.15 relation_of2( Y, cartesian_product2( X, X ), X ), ! function( Z ), !
% 0.76/1.15 quasi_total( Z, cartesian_product2( X, X ), X ), ! relation_of2( Z,
% 0.76/1.15 cartesian_product2( X, X ), X ), latt_str( latt_str_of( X, Y, Z ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! latt_str( X ), element( join_of_latt_set( X, Y ),
% 0.76/1.15 the_carrier( X ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! latt_str( X ), element( meet_of_latt_set( X, Y ),
% 0.76/1.15 the_carrier( X ) ) }.
% 0.76/1.15 { strict_latt_str( boole_lattice( X ) ) }.
% 0.76/1.15 { latt_str( boole_lattice( X ) ) }.
% 0.76/1.15 { && }.
% 0.76/1.15 { ! rel_str( X ), element( join_on_relstr( X, Y ), the_carrier( X ) ) }.
% 0.76/1.15 { && }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), alpha6( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ),
% 0.76/1.15 relation_of2_as_subset( k2_lattice3( X ), the_carrier( X ), the_carrier(
% 0.76/1.15 X ) ) }.
% 0.76/1.15 { ! alpha6( X ), alpha21( X ) }.
% 0.76/1.15 { ! alpha6( X ), v1_partfun1( k2_lattice3( X ), the_carrier( X ),
% 0.76/1.15 the_carrier( X ) ) }.
% 0.76/1.15 { ! alpha21( X ), ! v1_partfun1( k2_lattice3( X ), the_carrier( X ),
% 0.76/1.15 the_carrier( X ) ), alpha6( X ) }.
% 0.76/1.15 { ! alpha21( X ), reflexive( k2_lattice3( X ) ) }.
% 0.76/1.15 { ! alpha21( X ), antisymmetric( k2_lattice3( X ) ) }.
% 0.76/1.15 { ! alpha21( X ), transitive( k2_lattice3( X ) ) }.
% 0.76/1.15 { ! reflexive( k2_lattice3( X ) ), ! antisymmetric( k2_lattice3( X ) ), !
% 0.76/1.15 transitive( k2_lattice3( X ) ), alpha21( X ) }.
% 0.76/1.15 { ! rel_str( X ), element( meet_on_relstr( X, Y ), the_carrier( X ) ) }.
% 0.76/1.15 { && }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), alpha7( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), rel_str(
% 0.76/1.15 poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha7( X ), alpha22( X ) }.
% 0.76/1.15 { ! alpha7( X ), antisymmetric_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha22( X ), ! antisymmetric_relstr( poset_of_lattice( X ) ), alpha7(
% 0.76/1.15 X ) }.
% 0.76/1.15 { ! alpha22( X ), strict_rel_str( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha22( X ), reflexive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha22( X ), transitive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! strict_rel_str( poset_of_lattice( X ) ), ! reflexive_relstr(
% 0.76/1.15 poset_of_lattice( X ) ), ! transitive_relstr( poset_of_lattice( X ) ),
% 0.76/1.15 alpha22( X ) }.
% 0.76/1.15 { ! rel_str( X ), element( bottom_of_relstr( X ), the_carrier( X ) ) }.
% 0.76/1.15 { strict_rel_str( boole_POSet( X ) ) }.
% 0.76/1.15 { rel_str( boole_POSet( X ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! meet_semilatt_str( X ), element(
% 0.76/1.15 bottom_of_semilattstr( X ), the_carrier( X ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), relation(
% 0.76/1.15 relation_of_lattice( X ) ) }.
% 0.76/1.15 { ! meet_semilatt_str( X ), one_sorted_str( X ) }.
% 0.76/1.15 { ! rel_str( X ), one_sorted_str( X ) }.
% 0.76/1.15 { && }.
% 0.76/1.15 { ! join_semilatt_str( X ), one_sorted_str( X ) }.
% 0.76/1.15 { ! latt_str( X ), meet_semilatt_str( X ) }.
% 0.76/1.15 { ! latt_str( X ), join_semilatt_str( X ) }.
% 0.76/1.15 { && }.
% 0.76/1.15 { && }.
% 0.76/1.15 { ! relation_of2_as_subset( Z, X, Y ), element( Z, powerset(
% 0.76/1.15 cartesian_product2( X, Y ) ) ) }.
% 0.76/1.15 { ! meet_semilatt_str( X ), function( the_L_meet( X ) ) }.
% 0.76/1.15 { ! meet_semilatt_str( X ), quasi_total( the_L_meet( X ),
% 0.76/1.15 cartesian_product2( the_carrier( X ), the_carrier( X ) ), the_carrier( X
% 0.76/1.15 ) ) }.
% 0.76/1.15 { ! meet_semilatt_str( X ), relation_of2_as_subset( the_L_meet( X ),
% 0.76/1.15 cartesian_product2( the_carrier( X ), the_carrier( X ) ), the_carrier( X
% 0.76/1.15 ) ) }.
% 0.76/1.15 { ! rel_str( X ), relation_of2_as_subset( the_InternalRel( X ), the_carrier
% 0.76/1.15 ( X ), the_carrier( X ) ) }.
% 0.76/1.15 { && }.
% 0.76/1.15 { ! join_semilatt_str( X ), function( the_L_join( X ) ) }.
% 0.76/1.15 { ! join_semilatt_str( X ), quasi_total( the_L_join( X ),
% 0.76/1.15 cartesian_product2( the_carrier( X ), the_carrier( X ) ), the_carrier( X
% 0.76/1.15 ) ) }.
% 0.76/1.15 { ! join_semilatt_str( X ), relation_of2_as_subset( the_L_join( X ),
% 0.76/1.15 cartesian_product2( the_carrier( X ), the_carrier( X ) ), the_carrier( X
% 0.76/1.15 ) ) }.
% 0.76/1.15 { meet_semilatt_str( skol1 ) }.
% 0.76/1.15 { rel_str( skol2 ) }.
% 0.76/1.15 { one_sorted_str( skol3 ) }.
% 0.76/1.15 { join_semilatt_str( skol4 ) }.
% 0.76/1.15 { latt_str( skol5 ) }.
% 0.76/1.15 { relation_of2( skol6( X, Y ), X, Y ) }.
% 0.76/1.15 { element( skol7( X ), X ) }.
% 0.76/1.15 { relation_of2_as_subset( skol8( X, Y ), X, Y ) }.
% 0.76/1.15 { ! empty_carrier( boole_lattice( X ) ) }.
% 0.76/1.15 { strict_latt_str( boole_lattice( X ) ) }.
% 0.76/1.15 { join_commutative( boole_lattice( X ) ) }.
% 0.76/1.15 { join_associative( boole_lattice( X ) ) }.
% 0.76/1.15 { meet_commutative( boole_lattice( X ) ) }.
% 0.76/1.15 { meet_associative( boole_lattice( X ) ) }.
% 0.76/1.15 { meet_absorbing( boole_lattice( X ) ) }.
% 0.76/1.15 { join_absorbing( boole_lattice( X ) ) }.
% 0.76/1.15 { lattice( boole_lattice( X ) ) }.
% 0.76/1.15 { distributive_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { modular_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { lower_bounded_semilattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { upper_bounded_semilattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { bounded_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { complemented_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { boolean_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { complete_latt_str( boole_lattice( X ) ) }.
% 0.76/1.15 { ! empty_carrier( boole_lattice( X ) ) }.
% 0.76/1.15 { strict_latt_str( boole_lattice( X ) ) }.
% 0.76/1.15 { empty( X ), ! relation_of2( Y, X, X ), ! empty_carrier( rel_str_of( X, Y
% 0.76/1.15 ) ) }.
% 0.76/1.15 { empty( X ), ! relation_of2( Y, X, X ), strict_rel_str( rel_str_of( X, Y )
% 0.76/1.15 ) }.
% 0.76/1.15 { empty_carrier( X ), ! one_sorted_str( X ), ! empty( the_carrier( X ) ) }
% 0.76/1.15 .
% 0.76/1.15 { ! empty( powerset( X ) ) }.
% 0.76/1.15 { empty( empty_set ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), alpha8( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), with_infima_relstr(
% 0.76/1.15 poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha8( X ), alpha23( X ) }.
% 0.76/1.15 { ! alpha8( X ), with_suprema_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha23( X ), ! with_suprema_relstr( poset_of_lattice( X ) ), alpha8( X
% 0.76/1.15 ) }.
% 0.76/1.15 { ! alpha23( X ), alpha34( X ) }.
% 0.76/1.15 { ! alpha23( X ), antisymmetric_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha34( X ), ! antisymmetric_relstr( poset_of_lattice( X ) ), alpha23
% 0.76/1.15 ( X ) }.
% 0.76/1.15 { ! alpha34( X ), alpha41( X ) }.
% 0.76/1.15 { ! alpha34( X ), transitive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha41( X ), ! transitive_relstr( poset_of_lattice( X ) ), alpha34( X
% 0.76/1.15 ) }.
% 0.76/1.15 { ! alpha41( X ), ! empty_carrier( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha41( X ), strict_rel_str( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha41( X ), reflexive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { empty_carrier( poset_of_lattice( X ) ), ! strict_rel_str(
% 0.76/1.15 poset_of_lattice( X ) ), ! reflexive_relstr( poset_of_lattice( X ) ),
% 0.76/1.15 alpha41( X ) }.
% 0.76/1.15 { ! empty_carrier( boole_lattice( X ) ) }.
% 0.76/1.15 { strict_latt_str( boole_lattice( X ) ) }.
% 0.76/1.15 { join_commutative( boole_lattice( X ) ) }.
% 0.76/1.15 { join_associative( boole_lattice( X ) ) }.
% 0.76/1.15 { meet_commutative( boole_lattice( X ) ) }.
% 0.76/1.15 { meet_associative( boole_lattice( X ) ) }.
% 0.76/1.15 { meet_absorbing( boole_lattice( X ) ) }.
% 0.76/1.15 { join_absorbing( boole_lattice( X ) ) }.
% 0.76/1.15 { lattice( boole_lattice( X ) ) }.
% 0.76/1.15 { ! reflexive_relstr( X ), ! transitive_relstr( X ), ! antisymmetric_relstr
% 0.76/1.15 ( X ), ! rel_str( X ), alpha9( X ) }.
% 0.76/1.15 { ! reflexive_relstr( X ), ! transitive_relstr( X ), ! antisymmetric_relstr
% 0.76/1.15 ( X ), ! rel_str( X ), v1_partfun1( the_InternalRel( X ), the_carrier( X
% 0.76/1.15 ), the_carrier( X ) ) }.
% 0.76/1.15 { ! alpha9( X ), alpha24( X ) }.
% 0.76/1.15 { ! alpha9( X ), transitive( the_InternalRel( X ) ) }.
% 0.76/1.15 { ! alpha24( X ), ! transitive( the_InternalRel( X ) ), alpha9( X ) }.
% 0.76/1.15 { ! alpha24( X ), relation( the_InternalRel( X ) ) }.
% 0.76/1.15 { ! alpha24( X ), reflexive( the_InternalRel( X ) ) }.
% 0.76/1.15 { ! alpha24( X ), antisymmetric( the_InternalRel( X ) ) }.
% 0.76/1.15 { ! relation( the_InternalRel( X ) ), ! reflexive( the_InternalRel( X ) ),
% 0.76/1.15 ! antisymmetric( the_InternalRel( X ) ), alpha24( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! upper_bounded_semilattstr( X ), !
% 0.76/1.15 latt_str( X ), alpha10( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! upper_bounded_semilattstr( X ), !
% 0.76/1.15 latt_str( X ), with_infima_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha10( X ), alpha25( X ) }.
% 0.76/1.15 { ! alpha10( X ), with_suprema_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha25( X ), ! with_suprema_relstr( poset_of_lattice( X ) ), alpha10(
% 0.76/1.15 X ) }.
% 0.76/1.15 { ! alpha25( X ), alpha35( X ) }.
% 0.76/1.15 { ! alpha25( X ), upper_bounded_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha35( X ), ! upper_bounded_relstr( poset_of_lattice( X ) ), alpha25
% 0.76/1.15 ( X ) }.
% 0.76/1.15 { ! alpha35( X ), alpha42( X ) }.
% 0.76/1.15 { ! alpha35( X ), antisymmetric_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha42( X ), ! antisymmetric_relstr( poset_of_lattice( X ) ), alpha35
% 0.76/1.15 ( X ) }.
% 0.76/1.15 { ! alpha42( X ), alpha47( X ) }.
% 0.76/1.15 { ! alpha42( X ), transitive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha47( X ), ! transitive_relstr( poset_of_lattice( X ) ), alpha42( X
% 0.76/1.15 ) }.
% 0.76/1.15 { ! alpha47( X ), ! empty_carrier( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha47( X ), strict_rel_str( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha47( X ), reflexive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { empty_carrier( poset_of_lattice( X ) ), ! strict_rel_str(
% 0.76/1.15 poset_of_lattice( X ) ), ! reflexive_relstr( poset_of_lattice( X ) ),
% 0.76/1.15 alpha47( X ) }.
% 0.76/1.15 { ! empty_carrier( boole_lattice( X ) ) }.
% 0.76/1.15 { strict_latt_str( boole_lattice( X ) ) }.
% 0.76/1.15 { join_commutative( boole_lattice( X ) ) }.
% 0.76/1.15 { join_associative( boole_lattice( X ) ) }.
% 0.76/1.15 { meet_commutative( boole_lattice( X ) ) }.
% 0.76/1.15 { meet_associative( boole_lattice( X ) ) }.
% 0.76/1.15 { meet_absorbing( boole_lattice( X ) ) }.
% 0.76/1.15 { join_absorbing( boole_lattice( X ) ) }.
% 0.76/1.15 { lattice( boole_lattice( X ) ) }.
% 0.76/1.15 { distributive_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { modular_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { lower_bounded_semilattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { upper_bounded_semilattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { bounded_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { complemented_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { boolean_lattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { empty( X ), ! function( Y ), ! quasi_total( Y, cartesian_product2( X, X )
% 0.76/1.15 , X ), ! relation_of2( Y, cartesian_product2( X, X ), X ), ! function( Z
% 0.76/1.15 ), ! quasi_total( Z, cartesian_product2( X, X ), X ), ! relation_of2( Z
% 0.76/1.15 , cartesian_product2( X, X ), X ), ! empty_carrier( latt_str_of( X, Y, Z
% 0.76/1.15 ) ) }.
% 0.76/1.15 { empty( X ), ! function( Y ), ! quasi_total( Y, cartesian_product2( X, X )
% 0.76/1.15 , X ), ! relation_of2( Y, cartesian_product2( X, X ), X ), ! function( Z
% 0.76/1.15 ), ! quasi_total( Z, cartesian_product2( X, X ), X ), ! relation_of2( Z
% 0.76/1.15 , cartesian_product2( X, X ), X ), strict_latt_str( latt_str_of( X, Y, Z
% 0.76/1.15 ) ) }.
% 0.76/1.15 { ! reflexive( Y ), ! antisymmetric( Y ), ! transitive( Y ), ! v1_partfun1
% 0.76/1.15 ( Y, X, X ), ! relation_of2( Y, X, X ), alpha11( X, Y ) }.
% 0.76/1.15 { ! reflexive( Y ), ! antisymmetric( Y ), ! transitive( Y ), ! v1_partfun1
% 0.76/1.15 ( Y, X, X ), ! relation_of2( Y, X, X ), antisymmetric_relstr( rel_str_of
% 0.76/1.15 ( X, Y ) ) }.
% 0.76/1.15 { ! alpha11( X, Y ), strict_rel_str( rel_str_of( X, Y ) ) }.
% 0.76/1.15 { ! alpha11( X, Y ), reflexive_relstr( rel_str_of( X, Y ) ) }.
% 0.76/1.15 { ! alpha11( X, Y ), transitive_relstr( rel_str_of( X, Y ) ) }.
% 0.76/1.15 { ! strict_rel_str( rel_str_of( X, Y ) ), ! reflexive_relstr( rel_str_of( X
% 0.76/1.15 , Y ) ), ! transitive_relstr( rel_str_of( X, Y ) ), alpha11( X, Y ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! lower_bounded_semilattstr( X ), !
% 0.76/1.15 latt_str( X ), alpha12( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! lower_bounded_semilattstr( X ), !
% 0.76/1.15 latt_str( X ), with_infima_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha12( X ), alpha26( X ) }.
% 0.76/1.15 { ! alpha12( X ), with_suprema_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha26( X ), ! with_suprema_relstr( poset_of_lattice( X ) ), alpha12(
% 0.76/1.15 X ) }.
% 0.76/1.15 { ! alpha26( X ), alpha36( X ) }.
% 0.76/1.15 { ! alpha26( X ), lower_bounded_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha36( X ), ! lower_bounded_relstr( poset_of_lattice( X ) ), alpha26
% 0.76/1.15 ( X ) }.
% 0.76/1.15 { ! alpha36( X ), alpha43( X ) }.
% 0.76/1.15 { ! alpha36( X ), antisymmetric_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha43( X ), ! antisymmetric_relstr( poset_of_lattice( X ) ), alpha36
% 0.76/1.15 ( X ) }.
% 0.76/1.15 { ! alpha43( X ), alpha48( X ) }.
% 0.76/1.15 { ! alpha43( X ), transitive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha48( X ), ! transitive_relstr( poset_of_lattice( X ) ), alpha43( X
% 0.76/1.15 ) }.
% 0.76/1.15 { ! alpha48( X ), ! empty_carrier( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha48( X ), strict_rel_str( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha48( X ), reflexive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { empty_carrier( poset_of_lattice( X ) ), ! strict_rel_str(
% 0.76/1.15 poset_of_lattice( X ) ), ! reflexive_relstr( poset_of_lattice( X ) ),
% 0.76/1.15 alpha48( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), alpha13( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), antisymmetric_relstr
% 0.76/1.15 ( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha13( X ), alpha27( X ) }.
% 0.76/1.15 { ! alpha13( X ), transitive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha27( X ), ! transitive_relstr( poset_of_lattice( X ) ), alpha13( X
% 0.76/1.15 ) }.
% 0.76/1.15 { ! alpha27( X ), ! empty_carrier( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha27( X ), strict_rel_str( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha27( X ), reflexive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { empty_carrier( poset_of_lattice( X ) ), ! strict_rel_str(
% 0.76/1.15 poset_of_lattice( X ) ), ! reflexive_relstr( poset_of_lattice( X ) ),
% 0.76/1.15 alpha27( X ) }.
% 0.76/1.15 { empty( X ), empty( Y ), ! empty( cartesian_product2( X, Y ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! complete_latt_str( X ), ! latt_str
% 0.76/1.15 ( X ), alpha14( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! complete_latt_str( X ), ! latt_str
% 0.76/1.15 ( X ), complete_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha14( X ), alpha28( X ) }.
% 0.76/1.15 { ! alpha14( X ), with_infima_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha28( X ), ! with_infima_relstr( poset_of_lattice( X ) ), alpha14( X
% 0.76/1.15 ) }.
% 0.76/1.15 { ! alpha28( X ), alpha37( X ) }.
% 0.76/1.15 { ! alpha28( X ), with_suprema_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha37( X ), ! with_suprema_relstr( poset_of_lattice( X ) ), alpha28(
% 0.76/1.15 X ) }.
% 0.76/1.15 { ! alpha37( X ), alpha44( X ) }.
% 0.76/1.15 { ! alpha37( X ), bounded_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha44( X ), ! bounded_relstr( poset_of_lattice( X ) ), alpha37( X ) }
% 0.76/1.15 .
% 0.76/1.15 { ! alpha44( X ), alpha49( X ) }.
% 0.76/1.15 { ! alpha44( X ), upper_bounded_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha49( X ), ! upper_bounded_relstr( poset_of_lattice( X ) ), alpha44
% 0.76/1.15 ( X ) }.
% 0.76/1.15 { ! alpha49( X ), alpha52( X ) }.
% 0.76/1.15 { ! alpha49( X ), lower_bounded_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha52( X ), ! lower_bounded_relstr( poset_of_lattice( X ) ), alpha49
% 0.76/1.15 ( X ) }.
% 0.76/1.15 { ! alpha52( X ), alpha54( X ) }.
% 0.76/1.15 { ! alpha52( X ), antisymmetric_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha54( X ), ! antisymmetric_relstr( poset_of_lattice( X ) ), alpha52
% 0.76/1.15 ( X ) }.
% 0.76/1.15 { ! alpha54( X ), alpha56( X ) }.
% 0.76/1.15 { ! alpha54( X ), transitive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha56( X ), ! transitive_relstr( poset_of_lattice( X ) ), alpha54( X
% 0.76/1.15 ) }.
% 0.76/1.15 { ! alpha56( X ), ! empty_carrier( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha56( X ), strict_rel_str( poset_of_lattice( X ) ) }.
% 0.76/1.15 { ! alpha56( X ), reflexive_relstr( poset_of_lattice( X ) ) }.
% 0.76/1.15 { empty_carrier( poset_of_lattice( X ) ), ! strict_rel_str(
% 0.76/1.15 poset_of_lattice( X ) ), ! reflexive_relstr( poset_of_lattice( X ) ),
% 0.76/1.15 alpha56( X ) }.
% 0.76/1.15 { ! empty_carrier( boole_POSet( X ) ) }.
% 0.76/1.15 { strict_rel_str( boole_POSet( X ) ) }.
% 0.76/1.15 { reflexive_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { transitive_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { antisymmetric_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { ! empty_carrier( boole_POSet( X ) ) }.
% 0.76/1.15 { strict_rel_str( boole_POSet( X ) ) }.
% 0.76/1.15 { reflexive_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { transitive_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { antisymmetric_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { lower_bounded_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { upper_bounded_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { bounded_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { with_suprema_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { with_infima_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { complete_relstr( boole_POSet( X ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! latt_str( X ), ! in( Y, a_2_2_lattice3( X, Z ) ),
% 0.76/1.15 element( skol9( X, T, U ), the_carrier( X ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! latt_str( X ), ! in( Y, a_2_2_lattice3( X, Z ) ),
% 0.76/1.15 alpha1( X, Y, Z, skol9( X, Y, Z ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! latt_str( X ), ! element( T, the_carrier( X ) ), !
% 0.76/1.15 alpha1( X, Y, Z, T ), in( Y, a_2_2_lattice3( X, Z ) ) }.
% 0.76/1.15 { ! alpha1( X, Y, Z, T ), Y = T }.
% 0.76/1.15 { ! alpha1( X, Y, Z, T ), latt_set_smaller( X, T, Z ) }.
% 0.76/1.15 { ! Y = T, ! latt_set_smaller( X, T, Z ), alpha1( X, Y, Z, T ) }.
% 0.76/1.15 { ! relation_of2( Y, X, X ), ! rel_str_of( X, Y ) = rel_str_of( Z, T ), X =
% 0.76/1.15 Z }.
% 0.76/1.15 { ! relation_of2( Y, X, X ), ! rel_str_of( X, Y ) = rel_str_of( Z, T ), Y =
% 0.76/1.15 T }.
% 0.76/1.15 { ! function( Y ), ! quasi_total( Y, cartesian_product2( X, X ), X ), !
% 0.76/1.15 relation_of2( Y, cartesian_product2( X, X ), X ), ! function( Z ), !
% 0.76/1.15 quasi_total( Z, cartesian_product2( X, X ), X ), ! relation_of2( Z,
% 0.76/1.15 cartesian_product2( X, X ), X ), ! latt_str_of( X, Y, Z ) = latt_str_of(
% 0.76/1.15 T, U, W ), X = T }.
% 0.76/1.15 { ! function( Y ), ! quasi_total( Y, cartesian_product2( X, X ), X ), !
% 0.76/1.15 relation_of2( Y, cartesian_product2( X, X ), X ), ! function( Z ), !
% 0.76/1.15 quasi_total( Z, cartesian_product2( X, X ), X ), ! relation_of2( Z,
% 0.76/1.15 cartesian_product2( X, X ), X ), ! latt_str_of( X, Y, Z ) = latt_str_of(
% 0.76/1.15 T, U, W ), Y = U }.
% 0.76/1.15 { ! function( Y ), ! quasi_total( Y, cartesian_product2( X, X ), X ), !
% 0.76/1.15 relation_of2( Y, cartesian_product2( X, X ), X ), ! function( Z ), !
% 0.76/1.15 quasi_total( Z, cartesian_product2( X, X ), X ), ! relation_of2( Z,
% 0.76/1.15 cartesian_product2( X, X ), X ), ! latt_str_of( X, Y, Z ) = latt_str_of(
% 0.76/1.15 T, U, W ), Z = W }.
% 0.76/1.15 { latt_str( skol10 ) }.
% 0.76/1.15 { ! empty_carrier( skol10 ) }.
% 0.76/1.15 { strict_latt_str( skol10 ) }.
% 0.76/1.15 { join_commutative( skol10 ) }.
% 0.76/1.15 { join_associative( skol10 ) }.
% 0.76/1.15 { meet_commutative( skol10 ) }.
% 0.76/1.15 { meet_associative( skol10 ) }.
% 0.76/1.15 { meet_absorbing( skol10 ) }.
% 0.76/1.15 { join_absorbing( skol10 ) }.
% 0.76/1.15 { lattice( skol10 ) }.
% 0.76/1.15 { distributive_lattstr( skol10 ) }.
% 0.76/1.15 { modular_lattstr( skol10 ) }.
% 0.76/1.15 { lower_bounded_semilattstr( skol10 ) }.
% 0.76/1.15 { upper_bounded_semilattstr( skol10 ) }.
% 0.76/1.15 { latt_str( skol11 ) }.
% 0.76/1.15 { ! empty_carrier( skol11 ) }.
% 0.76/1.15 { strict_latt_str( skol11 ) }.
% 0.76/1.15 { join_commutative( skol11 ) }.
% 0.76/1.15 { join_associative( skol11 ) }.
% 0.76/1.15 { meet_commutative( skol11 ) }.
% 0.76/1.15 { meet_associative( skol11 ) }.
% 0.76/1.15 { meet_absorbing( skol11 ) }.
% 0.76/1.15 { join_absorbing( skol11 ) }.
% 0.76/1.15 { lattice( skol11 ) }.
% 0.76/1.15 { lower_bounded_semilattstr( skol11 ) }.
% 0.76/1.15 { upper_bounded_semilattstr( skol11 ) }.
% 0.76/1.15 { bounded_lattstr( skol11 ) }.
% 0.76/1.15 { latt_str( skol12 ) }.
% 0.76/1.15 { ! empty_carrier( skol12 ) }.
% 0.76/1.15 { strict_latt_str( skol12 ) }.
% 0.76/1.15 { join_commutative( skol12 ) }.
% 0.76/1.15 { join_associative( skol12 ) }.
% 0.76/1.15 { meet_commutative( skol12 ) }.
% 0.76/1.15 { meet_associative( skol12 ) }.
% 0.76/1.15 { meet_absorbing( skol12 ) }.
% 0.76/1.15 { join_absorbing( skol12 ) }.
% 0.76/1.15 { lattice( skol12 ) }.
% 0.76/1.15 { lower_bounded_semilattstr( skol12 ) }.
% 0.76/1.15 { upper_bounded_semilattstr( skol12 ) }.
% 0.76/1.15 { bounded_lattstr( skol12 ) }.
% 0.76/1.15 { complemented_lattstr( skol12 ) }.
% 0.76/1.15 { latt_str( skol13 ) }.
% 0.76/1.15 { ! empty_carrier( skol13 ) }.
% 0.76/1.15 { strict_latt_str( skol13 ) }.
% 0.76/1.15 { join_commutative( skol13 ) }.
% 0.76/1.15 { join_associative( skol13 ) }.
% 0.76/1.15 { meet_commutative( skol13 ) }.
% 0.76/1.15 { meet_associative( skol13 ) }.
% 0.76/1.15 { meet_absorbing( skol13 ) }.
% 0.76/1.15 { join_absorbing( skol13 ) }.
% 0.76/1.15 { lattice( skol13 ) }.
% 0.76/1.15 { distributive_lattstr( skol13 ) }.
% 0.76/1.15 { lower_bounded_semilattstr( skol13 ) }.
% 0.76/1.15 { upper_bounded_semilattstr( skol13 ) }.
% 0.76/1.15 { bounded_lattstr( skol13 ) }.
% 0.76/1.15 { complemented_lattstr( skol13 ) }.
% 0.76/1.15 { boolean_lattstr( skol13 ) }.
% 0.76/1.15 { rel_str( skol14 ) }.
% 0.76/1.15 { ! empty_carrier( skol14 ) }.
% 0.76/1.15 { strict_rel_str( skol14 ) }.
% 0.76/1.15 { reflexive_relstr( skol14 ) }.
% 0.76/1.15 { transitive_relstr( skol14 ) }.
% 0.76/1.15 { antisymmetric_relstr( skol14 ) }.
% 0.76/1.15 { complete_relstr( skol14 ) }.
% 0.76/1.15 { rel_str( skol15 ) }.
% 0.76/1.15 { strict_rel_str( skol15 ) }.
% 0.76/1.15 { empty( X ), ! empty( skol16( Y ) ) }.
% 0.76/1.15 { empty( X ), element( skol16( X ), powerset( X ) ) }.
% 0.76/1.15 { empty( skol17 ) }.
% 0.76/1.15 { rel_str( skol18 ) }.
% 0.76/1.15 { ! empty_carrier( skol18 ) }.
% 0.76/1.15 { strict_rel_str( skol18 ) }.
% 0.76/1.15 { reflexive_relstr( skol18 ) }.
% 0.76/1.15 { transitive_relstr( skol18 ) }.
% 0.76/1.15 { antisymmetric_relstr( skol18 ) }.
% 0.76/1.15 { with_suprema_relstr( skol18 ) }.
% 0.76/1.15 { with_infima_relstr( skol18 ) }.
% 0.76/1.15 { complete_relstr( skol18 ) }.
% 0.76/1.15 { rel_str( skol19 ) }.
% 0.76/1.15 { ! empty_carrier( skol19 ) }.
% 0.76/1.15 { strict_rel_str( skol19 ) }.
% 0.76/1.15 { reflexive_relstr( skol19 ) }.
% 0.76/1.15 { transitive_relstr( skol19 ) }.
% 0.76/1.15 { antisymmetric_relstr( skol19 ) }.
% 0.76/1.15 { relation( skol20( Z, T ) ) }.
% 0.76/1.15 { function( skol20( Z, T ) ) }.
% 0.76/1.15 { relation_of2( skol20( X, Y ), X, Y ) }.
% 0.76/1.15 { empty( skol21( Y ) ) }.
% 0.76/1.15 { element( skol21( X ), powerset( X ) ) }.
% 0.76/1.15 { ! empty( skol22 ) }.
% 0.76/1.15 { rel_str( skol23 ) }.
% 0.76/1.15 { ! empty_carrier( skol23 ) }.
% 0.76/1.15 { reflexive_relstr( skol23 ) }.
% 0.76/1.15 { transitive_relstr( skol23 ) }.
% 0.76/1.15 { antisymmetric_relstr( skol23 ) }.
% 0.76/1.15 { with_suprema_relstr( skol23 ) }.
% 0.76/1.15 { with_infima_relstr( skol23 ) }.
% 0.76/1.15 { complete_relstr( skol23 ) }.
% 0.76/1.15 { lower_bounded_relstr( skol23 ) }.
% 0.76/1.15 { upper_bounded_relstr( skol23 ) }.
% 0.76/1.15 { bounded_relstr( skol23 ) }.
% 0.76/1.15 { latt_str( skol24 ) }.
% 0.76/1.15 { strict_latt_str( skol24 ) }.
% 0.76/1.15 { one_sorted_str( skol25 ) }.
% 0.76/1.15 { ! empty_carrier( skol25 ) }.
% 0.76/1.15 { empty_carrier( X ), ! one_sorted_str( X ), ! empty( skol26( Y ) ) }.
% 0.76/1.15 { empty_carrier( X ), ! one_sorted_str( X ), element( skol26( X ), powerset
% 0.76/1.15 ( the_carrier( X ) ) ) }.
% 0.76/1.15 { latt_str( skol27 ) }.
% 0.76/1.15 { ! empty_carrier( skol27 ) }.
% 0.76/1.15 { strict_latt_str( skol27 ) }.
% 0.76/1.15 { latt_str( skol28 ) }.
% 0.76/1.15 { ! empty_carrier( skol28 ) }.
% 0.76/1.15 { strict_latt_str( skol28 ) }.
% 0.76/1.15 { join_commutative( skol28 ) }.
% 0.76/1.15 { join_associative( skol28 ) }.
% 0.76/1.15 { meet_commutative( skol28 ) }.
% 0.76/1.15 { meet_associative( skol28 ) }.
% 0.76/1.15 { meet_absorbing( skol28 ) }.
% 0.76/1.15 { join_absorbing( skol28 ) }.
% 0.76/1.15 { lattice( skol28 ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! latt_str( X ), k2_lattice3( X ) =
% 0.76/1.15 relation_of_lattice( X ) }.
% 0.76/1.15 { ! relation_of2_as_subset( Z, X, Y ), relation_of2( Z, X, Y ) }.
% 0.76/1.15 { ! relation_of2( Z, X, Y ), relation_of2_as_subset( Z, X, Y ) }.
% 0.76/1.15 { subset( X, X ) }.
% 0.76/1.15 { ! bottom_of_relstr( boole_POSet( skol29 ) ) = empty_set }.
% 0.76/1.15 { ! in( X, Y ), element( X, Y ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! complete_latt_str( X ), ! latt_str
% 0.76/1.15 ( X ), join_of_latt_set( X, Y ) = join_on_relstr( poset_of_lattice( X ),
% 0.76/1.15 Y ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! complete_latt_str( X ), ! latt_str
% 0.76/1.15 ( X ), meet_of_latt_set( X, Y ) = meet_on_relstr( poset_of_lattice( X ),
% 0.76/1.15 Y ) }.
% 0.76/1.15 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.76/1.15 { alpha15( X, Y, skol30( X, Y ) ), in( skol30( X, Y ), Y ), X = Y }.
% 0.76/1.15 { alpha15( X, Y, skol30( X, Y ) ), ! in( skol30( X, Y ), X ), X = Y }.
% 0.76/1.15 { ! alpha15( X, Y, Z ), in( Z, X ) }.
% 0.76/1.15 { ! alpha15( X, Y, Z ), ! in( Z, Y ) }.
% 0.76/1.15 { ! in( Z, X ), in( Z, Y ), alpha15( X, Y, Z ) }.
% 0.76/1.15 { lower_bounded_semilattstr( boole_lattice( X ) ) }.
% 0.76/1.15 { bottom_of_semilattstr( boole_lattice( X ) ) = empty_set }.
% 0.76/1.15 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.76/1.15 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.76/1.15 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! complete_latt_str( X ), ! latt_str
% 0.76/1.15 ( X ), alpha16( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! complete_latt_str( X ), ! latt_str
% 0.76/1.15 ( X ), bottom_of_semilattstr( X ) = join_of_latt_set( X, empty_set ) }.
% 0.76/1.15 { ! alpha16( X ), alpha29( X ) }.
% 0.76/1.15 { ! alpha16( X ), latt_str( X ) }.
% 0.76/1.15 { ! alpha29( X ), ! latt_str( X ), alpha16( X ) }.
% 0.76/1.15 { ! alpha29( X ), ! empty_carrier( X ) }.
% 0.76/1.15 { ! alpha29( X ), lattice( X ) }.
% 0.76/1.15 { ! alpha29( X ), lower_bounded_semilattstr( X ) }.
% 0.76/1.15 { empty_carrier( X ), ! lattice( X ), ! lower_bounded_semilattstr( X ),
% 0.76/1.15 alpha29( X ) }.
% 0.76/1.15 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.76/1.15 { ! empty( X ), X = empty_set }.
% 0.76/1.15 { ! in( X, Y ), ! empty( Y ) }.
% 0.76/1.15 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.76/1.15
% 0.76/1.15 *** allocated 15000 integers for clauses
% 0.76/1.15 *** allocated 22500 integers for clauses
% 0.76/1.15 percentage equality = 0.028896, percentage horn = 0.867416
% 0.76/1.15 This is a problem with some equality
% 0.76/1.15
% 0.76/1.15
% 0.76/1.15
% 0.76/1.15 Options Used:
% 0.76/1.15
% 0.76/1.15 useres = 1
% 0.76/1.15 useparamod = 1
% 0.76/1.15 useeqrefl = 1
% 0.76/1.15 useeqfact = 1
% 0.76/1.15 usefactor = 1
% 0.76/1.15 usesimpsplitting = 0
% 0.76/1.15 usesimpdemod = 5
% 0.76/1.15 usesimpres = 3
% 0.76/1.15
% 0.76/1.15 resimpinuse = 1000
% 0.76/1.15 resimpclauses = 20000
% 0.76/1.15 substype = eqrewr
% 0.76/1.15 backwardsubs = 1
% 0.76/1.15 selectoldest = 5
% 0.76/1.15
% 0.76/1.15 litorderings [0] = split
% 0.76/1.15 litorderings [1] = extend the termordering, first sorting on arguments
% 0.76/1.15
% 0.76/1.15 termordering = kbo
% 0.76/1.15
% 0.76/1.15 litapriori = 0
% 0.76/1.15 termapriori = 1
% 0.76/1.15 litaposteriori = 0
% 0.76/1.15 termaposteriori = 0
% 0.76/1.15 demodaposteriori = 0
% 0.76/1.15 ordereqreflfact = 0
% 0.76/1.15
% 0.76/1.15 litselect = negord
% 0.76/1.15
% 0.76/1.15 maxweight = 15
% 0.76/1.15 maxdepth = 30000
% 0.76/1.15 maxlength = 115
% 0.76/1.15 maxnrvars = 195
% 0.76/1.15 excuselevel = 1
% 0.76/1.15 increasemaxweight = 1
% 0.76/1.15
% 0.76/1.15 maxselected = 10000000
% 0.76/1.15 maxnrclauses = 10000000
% 0.76/1.15
% 0.76/1.15 showgenerated = 0
% 0.76/1.15 showkept = 0
% 0.76/1.15 showselected = 0
% 0.76/1.15 showdeleted = 0
% 0.76/1.15 showresimp = 1
% 0.76/1.15 showstatus = 2000
% 0.76/1.15
% 0.76/1.15 prologoutput = 0
% 0.76/1.15 nrgoals = 5000000
% 0.76/1.15 totalproof = 1
% 0.76/1.15
% 0.76/1.15 Symbols occurring in the translation:
% 0.76/1.15
% 0.76/1.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.76/1.15 . [1, 2] (w:1, o:146, a:1, s:1, b:0),
% 0.76/1.15 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 0.76/1.15 ! [4, 1] (w:0, o:34, a:1, s:1, b:0),
% 0.76/1.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.15 rel_str [36, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.76/1.15 strict_rel_str [37, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.76/1.15 the_carrier [38, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.76/1.15 the_InternalRel [39, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.76/1.15 rel_str_of [40, 2] (w:1, o:170, a:1, s:1, b:0),
% 0.76/1.15 latt_str [41, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.76/1.15 strict_latt_str [42, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.76/1.15 the_L_join [43, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.76/1.15 the_L_meet [44, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.76/1.15 latt_str_of [45, 3] (w:1, o:185, a:1, s:1, b:0),
% 0.76/1.15 in [47, 2] (w:1, o:171, a:1, s:1, b:0),
% 0.76/1.15 empty_carrier [48, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.76/1.15 lattice [49, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.76/1.15 complete_latt_str [50, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.76/1.15 join_commutative [51, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.76/1.15 join_associative [52, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.76/1.15 meet_commutative [53, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.76/1.15 meet_associative [54, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.76/1.15 meet_absorbing [55, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.76/1.32 join_absorbing [56, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.76/1.32 lower_bounded_semilattstr [57, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.76/1.32 upper_bounded_semilattstr [58, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.76/1.32 bounded_lattstr [59, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.76/1.32 with_suprema_relstr [60, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.76/1.32 cartesian_product2 [62, 2] (w:1, o:172, a:1, s:1, b:0),
% 0.76/1.32 powerset [63, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.76/1.32 element [64, 2] (w:1, o:173, a:1, s:1, b:0),
% 0.76/1.32 relation [65, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.76/1.32 complete_relstr [66, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.76/1.32 with_infima_relstr [67, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.76/1.32 bounded_relstr [68, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.76/1.32 lower_bounded_relstr [69, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.76/1.32 upper_bounded_relstr [70, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.76/1.32 boolean_lattstr [71, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.76/1.32 distributive_lattstr [72, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.76/1.32 complemented_lattstr [73, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.76/1.32 modular_lattstr [74, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.76/1.32 bottom_of_relstr [75, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.76/1.32 empty_set [76, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.76/1.32 join_on_relstr [77, 2] (w:1, o:174, a:1, s:1, b:0),
% 0.76/1.32 meet_of_latt_set [78, 2] (w:1, o:175, a:1, s:1, b:0),
% 0.76/1.32 a_2_2_lattice3 [79, 2] (w:1, o:176, a:1, s:1, b:0),
% 0.76/1.32 join_of_latt_set [80, 2] (w:1, o:177, a:1, s:1, b:0),
% 0.76/1.32 poset_of_lattice [81, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.76/1.32 k2_lattice3 [82, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.76/1.32 boole_POSet [83, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.76/1.32 boole_lattice [84, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.76/1.32 relation_of2 [85, 3] (w:1, o:187, a:1, s:1, b:0),
% 0.76/1.32 function [86, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.76/1.32 quasi_total [87, 3] (w:1, o:186, a:1, s:1, b:0),
% 0.76/1.32 reflexive [88, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.76/1.32 antisymmetric [89, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.76/1.32 transitive [90, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.76/1.32 v1_partfun1 [91, 3] (w:1, o:188, a:1, s:1, b:0),
% 0.76/1.32 relation_of2_as_subset [92, 3] (w:1, o:189, a:1, s:1, b:0),
% 0.76/1.32 meet_on_relstr [93, 2] (w:1, o:178, a:1, s:1, b:0),
% 0.76/1.32 reflexive_relstr [94, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.76/1.32 transitive_relstr [95, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.76/1.32 antisymmetric_relstr [96, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.76/1.32 meet_semilatt_str [97, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.76/1.32 bottom_of_semilattstr [98, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.76/1.32 relation_of_lattice [99, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.76/1.32 one_sorted_str [100, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.76/1.32 join_semilatt_str [101, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.76/1.32 empty [102, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.76/1.32 latt_set_smaller [104, 3] (w:1, o:190, a:1, s:1, b:0),
% 0.76/1.32 subset [107, 2] (w:1, o:179, a:1, s:1, b:0),
% 0.76/1.32 alpha1 [108, 4] (w:1, o:193, a:1, s:1, b:1),
% 0.76/1.32 alpha2 [109, 1] (w:1, o:67, a:1, s:1, b:1),
% 0.76/1.32 alpha3 [110, 1] (w:1, o:78, a:1, s:1, b:1),
% 0.76/1.32 alpha4 [111, 1] (w:1, o:89, a:1, s:1, b:1),
% 0.76/1.32 alpha5 [112, 1] (w:1, o:100, a:1, s:1, b:1),
% 0.76/1.32 alpha6 [113, 1] (w:1, o:108, a:1, s:1, b:1),
% 0.76/1.32 alpha7 [114, 1] (w:1, o:109, a:1, s:1, b:1),
% 0.76/1.32 alpha8 [115, 1] (w:1, o:110, a:1, s:1, b:1),
% 0.76/1.32 alpha9 [116, 1] (w:1, o:111, a:1, s:1, b:1),
% 0.76/1.32 alpha10 [117, 1] (w:1, o:59, a:1, s:1, b:1),
% 0.76/1.32 alpha11 [118, 2] (w:1, o:180, a:1, s:1, b:1),
% 0.76/1.32 alpha12 [119, 1] (w:1, o:60, a:1, s:1, b:1),
% 0.76/1.32 alpha13 [120, 1] (w:1, o:61, a:1, s:1, b:1),
% 0.76/1.32 alpha14 [121, 1] (w:1, o:62, a:1, s:1, b:1),
% 0.76/1.32 alpha15 [122, 3] (w:1, o:191, a:1, s:1, b:1),
% 0.76/1.32 alpha16 [123, 1] (w:1, o:63, a:1, s:1, b:1),
% 0.76/1.32 alpha17 [124, 1] (w:1, o:64, a:1, s:1, b:1),
% 0.76/1.32 alpha18 [125, 1] (w:1, o:65, a:1, s:1, b:1),
% 0.76/1.32 alpha19 [126, 1] (w:1, o:66, a:1, s:1, b:1),
% 0.76/1.32 alpha20 [127, 1] (w:1, o:68, a:1, s:1, b:1),
% 0.76/1.32 alpha21 [128, 1] (w:1, o:69, a:1, s:1, b:1),
% 0.76/1.32 alpha22 [129, 1] (w:1, o:70, a:1, s:1, b:1),
% 0.76/1.32 alpha23 [130, 1] (w:1, o:71, a:1, s:1, b:1),
% 2.07/2.49 alpha24 [131, 1] (w:1, o:72, a:1, s:1, b:1),
% 2.07/2.49 alpha25 [132, 1] (w:1, o:73, a:1, s:1, b:1),
% 2.07/2.49 alpha26 [133, 1] (w:1, o:74, a:1, s:1, b:1),
% 2.07/2.49 alpha27 [134, 1] (w:1, o:75, a:1, s:1, b:1),
% 2.07/2.49 alpha28 [135, 1] (w:1, o:76, a:1, s:1, b:1),
% 2.07/2.49 alpha29 [136, 1] (w:1, o:77, a:1, s:1, b:1),
% 2.07/2.49 alpha30 [137, 1] (w:1, o:79, a:1, s:1, b:1),
% 2.07/2.49 alpha31 [138, 1] (w:1, o:80, a:1, s:1, b:1),
% 2.07/2.49 alpha32 [139, 1] (w:1, o:81, a:1, s:1, b:1),
% 2.07/2.49 alpha33 [140, 1] (w:1, o:82, a:1, s:1, b:1),
% 2.07/2.49 alpha34 [141, 1] (w:1, o:83, a:1, s:1, b:1),
% 2.07/2.49 alpha35 [142, 1] (w:1, o:84, a:1, s:1, b:1),
% 2.07/2.49 alpha36 [143, 1] (w:1, o:85, a:1, s:1, b:1),
% 2.07/2.49 alpha37 [144, 1] (w:1, o:86, a:1, s:1, b:1),
% 2.07/2.49 alpha38 [145, 1] (w:1, o:87, a:1, s:1, b:1),
% 2.07/2.49 alpha39 [146, 1] (w:1, o:88, a:1, s:1, b:1),
% 2.07/2.49 alpha40 [147, 1] (w:1, o:90, a:1, s:1, b:1),
% 2.07/2.49 alpha41 [148, 1] (w:1, o:91, a:1, s:1, b:1),
% 2.07/2.49 alpha42 [149, 1] (w:1, o:92, a:1, s:1, b:1),
% 2.07/2.49 alpha43 [150, 1] (w:1, o:93, a:1, s:1, b:1),
% 2.12/2.49 alpha44 [151, 1] (w:1, o:94, a:1, s:1, b:1),
% 2.12/2.49 alpha45 [152, 1] (w:1, o:95, a:1, s:1, b:1),
% 2.12/2.49 alpha46 [153, 1] (w:1, o:96, a:1, s:1, b:1),
% 2.12/2.49 alpha47 [154, 1] (w:1, o:97, a:1, s:1, b:1),
% 2.12/2.49 alpha48 [155, 1] (w:1, o:98, a:1, s:1, b:1),
% 2.12/2.49 alpha49 [156, 1] (w:1, o:99, a:1, s:1, b:1),
% 2.12/2.49 alpha50 [157, 1] (w:1, o:101, a:1, s:1, b:1),
% 2.12/2.49 alpha51 [158, 1] (w:1, o:102, a:1, s:1, b:1),
% 2.12/2.49 alpha52 [159, 1] (w:1, o:103, a:1, s:1, b:1),
% 2.12/2.49 alpha53 [160, 1] (w:1, o:104, a:1, s:1, b:1),
% 2.12/2.49 alpha54 [161, 1] (w:1, o:105, a:1, s:1, b:1),
% 2.12/2.49 alpha55 [162, 1] (w:1, o:106, a:1, s:1, b:1),
% 2.12/2.49 alpha56 [163, 1] (w:1, o:107, a:1, s:1, b:1),
% 2.12/2.49 skol1 [164, 0] (w:1, o:13, a:1, s:1, b:1),
% 2.12/2.49 skol2 [165, 0] (w:1, o:23, a:1, s:1, b:1),
% 2.12/2.49 skol3 [166, 0] (w:1, o:31, a:1, s:1, b:1),
% 2.12/2.49 skol4 [167, 0] (w:1, o:32, a:1, s:1, b:1),
% 2.12/2.49 skol5 [168, 0] (w:1, o:33, a:1, s:1, b:1),
% 2.12/2.49 skol6 [169, 2] (w:1, o:181, a:1, s:1, b:1),
% 2.12/2.49 skol7 [170, 1] (w:1, o:46, a:1, s:1, b:1),
% 2.12/2.49 skol8 [171, 2] (w:1, o:182, a:1, s:1, b:1),
% 2.12/2.49 skol9 [172, 3] (w:1, o:192, a:1, s:1, b:1),
% 2.12/2.49 skol10 [173, 0] (w:1, o:14, a:1, s:1, b:1),
% 2.12/2.49 skol11 [174, 0] (w:1, o:15, a:1, s:1, b:1),
% 2.12/2.49 skol12 [175, 0] (w:1, o:16, a:1, s:1, b:1),
% 2.12/2.49 skol13 [176, 0] (w:1, o:17, a:1, s:1, b:1),
% 2.12/2.49 skol14 [177, 0] (w:1, o:18, a:1, s:1, b:1),
% 2.12/2.49 skol15 [178, 0] (w:1, o:19, a:1, s:1, b:1),
% 2.12/2.49 skol16 [179, 1] (w:1, o:47, a:1, s:1, b:1),
% 2.12/2.49 skol17 [180, 0] (w:1, o:20, a:1, s:1, b:1),
% 2.12/2.49 skol18 [181, 0] (w:1, o:21, a:1, s:1, b:1),
% 2.12/2.49 skol19 [182, 0] (w:1, o:22, a:1, s:1, b:1),
% 2.12/2.49 skol20 [183, 2] (w:1, o:183, a:1, s:1, b:1),
% 2.12/2.49 skol21 [184, 1] (w:1, o:48, a:1, s:1, b:1),
% 2.12/2.49 skol22 [185, 0] (w:1, o:24, a:1, s:1, b:1),
% 2.12/2.49 skol23 [186, 0] (w:1, o:25, a:1, s:1, b:1),
% 2.12/2.49 skol24 [187, 0] (w:1, o:26, a:1, s:1, b:1),
% 2.12/2.49 skol25 [188, 0] (w:1, o:27, a:1, s:1, b:1),
% 2.12/2.49 skol26 [189, 1] (w:1, o:49, a:1, s:1, b:1),
% 2.12/2.49 skol27 [190, 0] (w:1, o:28, a:1, s:1, b:1),
% 2.12/2.49 skol28 [191, 0] (w:1, o:29, a:1, s:1, b:1),
% 2.12/2.49 skol29 [192, 0] (w:1, o:30, a:1, s:1, b:1),
% 2.12/2.49 skol30 [193, 2] (w:1, o:184, a:1, s:1, b:1).
% 2.12/2.49
% 2.12/2.49
% 2.12/2.49 Starting Search:
% 2.12/2.49
% 2.12/2.49 *** allocated 33750 integers for clauses
% 2.12/2.49 *** allocated 50625 integers for clauses
% 2.12/2.49 *** allocated 22500 integers for termspace/termends
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 *** allocated 75937 integers for clauses
% 2.12/2.49 *** allocated 113905 integers for clauses
% 2.12/2.49 *** allocated 33750 integers for termspace/termends
% 2.12/2.49
% 2.12/2.49 Intermediate Status:
% 2.12/2.49 Generated: 3447
% 2.12/2.49 Kept: 2000
% 2.12/2.49 Inuse: 510
% 2.12/2.49 Deleted: 10
% 2.12/2.49 Deletedinuse: 0
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 *** allocated 170857 integers for clauses
% 2.12/2.49 *** allocated 50625 integers for termspace/termends
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 *** allocated 256285 integers for clauses
% 2.12/2.49
% 2.12/2.49 Intermediate Status:
% 2.12/2.49 Generated: 7333
% 2.12/2.49 Kept: 4003
% 2.12/2.49 Inuse: 907
% 2.12/2.49 Deleted: 88
% 2.12/2.49 Deletedinuse: 4
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 *** allocated 75937 integers for termspace/termends
% 2.12/2.49 *** allocated 384427 integers for clauses
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 *** allocated 113905 integers for termspace/termends
% 2.12/2.49
% 2.12/2.49 Intermediate Status:
% 2.12/2.49 Generated: 12309
% 2.12/2.49 Kept: 6793
% 2.12/2.49 Inuse: 999
% 2.12/2.49 Deleted: 141
% 2.12/2.49 Deletedinuse: 14
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 *** allocated 170857 integers for termspace/termends
% 2.12/2.49 *** allocated 576640 integers for clauses
% 2.12/2.49 *** allocated 256285 integers for termspace/termends
% 2.12/2.49
% 2.12/2.49 Intermediate Status:
% 2.12/2.49 Generated: 23638
% 2.12/2.49 Kept: 9285
% 2.12/2.49 Inuse: 1014
% 2.12/2.49 Deleted: 141
% 2.12/2.49 Deletedinuse: 14
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49
% 2.12/2.49 Intermediate Status:
% 2.12/2.49 Generated: 32441
% 2.12/2.49 Kept: 11877
% 2.12/2.49 Inuse: 1095
% 2.12/2.49 Deleted: 152
% 2.12/2.49 Deletedinuse: 16
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 *** allocated 384427 integers for termspace/termends
% 2.12/2.49 *** allocated 864960 integers for clauses
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49
% 2.12/2.49 Intermediate Status:
% 2.12/2.49 Generated: 36122
% 2.12/2.49 Kept: 14004
% 2.12/2.49 Inuse: 1140
% 2.12/2.49 Deleted: 177
% 2.12/2.49 Deletedinuse: 16
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49
% 2.12/2.49 Intermediate Status:
% 2.12/2.49 Generated: 47874
% 2.12/2.49 Kept: 16007
% 2.12/2.49 Inuse: 1208
% 2.12/2.49 Deleted: 182
% 2.12/2.49 Deletedinuse: 21
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49
% 2.12/2.49 Intermediate Status:
% 2.12/2.49 Generated: 54188
% 2.12/2.49 Kept: 18014
% 2.12/2.49 Inuse: 1285
% 2.12/2.49 Deleted: 186
% 2.12/2.49 Deletedinuse: 21
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 Resimplifying inuse:
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49 Resimplifying clauses:
% 2.12/2.49 *** allocated 1297440 integers for clauses
% 2.12/2.49 Done
% 2.12/2.49
% 2.12/2.49
% 2.12/2.49 Bliksems!, er is een bewijs:
% 2.12/2.49 % SZS status Theorem
% 2.12/2.49 % SZS output start Refutation
% 2.12/2.49
% 2.12/2.49 (92) {G0,W8,D3,L2,V1,M2} I { ! rel_str( X ), join_on_relstr( X, empty_set )
% 2.12/2.49 ==> bottom_of_relstr( X ) }.
% 2.12/2.49 (95) {G0,W6,D4,L1,V1,M1} I { poset_of_lattice( boole_lattice( X ) ) ==>
% 2.12/2.49 boole_POSet( X ) }.
% 2.12/2.49 (103) {G0,W3,D3,L1,V1,M1} I { latt_str( boole_lattice( X ) ) }.
% 2.12/2.49 (127) {G0,W3,D3,L1,V1,M1} I { rel_str( boole_POSet( X ) ) }.
% 2.12/2.49 (151) {G0,W3,D3,L1,V1,M1} I { ! empty_carrier( boole_lattice( X ) ) }.
% 2.12/2.49 (158) {G0,W3,D3,L1,V1,M1} I { lattice( boole_lattice( X ) ) }.
% 2.12/2.49 (166) {G0,W3,D3,L1,V1,M1} I { complete_latt_str( boole_lattice( X ) ) }.
% 2.12/2.49 (170) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 2.12/2.49 (418) {G0,W5,D4,L1,V0,M1} I { ! bottom_of_relstr( boole_POSet( skol29 ) )
% 2.12/2.49 ==> empty_set }.
% 2.12/2.49 (420) {G0,W16,D4,L5,V2,M5} I { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 complete_latt_str( X ), ! latt_str( X ), join_on_relstr( poset_of_lattice
% 2.12/2.49 ( X ), Y ) ==> join_of_latt_set( X, Y ) }.
% 2.12/2.49 (423) {G0,W14,D3,L3,V2,M3} I { alpha15( X, Y, skol30( X, Y ) ), in( skol30
% 2.12/2.49 ( X, Y ), Y ), X = Y }.
% 2.12/2.49 (425) {G0,W7,D2,L2,V3,M2} I { ! alpha15( X, Y, Z ), in( Z, X ) }.
% 2.12/2.49 (428) {G0,W5,D4,L1,V1,M1} I { bottom_of_semilattstr( boole_lattice( X ) )
% 2.12/2.49 ==> empty_set }.
% 2.12/2.49 (433) {G0,W14,D3,L5,V1,M5} I { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 complete_latt_str( X ), ! latt_str( X ), join_of_latt_set( X, empty_set )
% 2.12/2.49 ==> bottom_of_semilattstr( X ) }.
% 2.12/2.49 (443) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 2.12/2.49 (1807) {G1,W8,D4,L1,V1,M1} R(92,127) { join_on_relstr( boole_POSet( X ),
% 2.12/2.49 empty_set ) ==> bottom_of_relstr( boole_POSet( X ) ) }.
% 2.12/2.49 (10651) {G1,W15,D4,L3,V2,M3} R(420,103);d(95);r(151) { ! lattice(
% 2.12/2.49 boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) ),
% 2.12/2.49 join_of_latt_set( boole_lattice( X ), Y ) ==> join_on_relstr( boole_POSet
% 2.12/2.49 ( X ), Y ) }.
% 2.12/2.49 (10803) {G1,W20,D5,L3,V1,M3} P(423,418) { ! X = empty_set, alpha15(
% 2.12/2.49 bottom_of_relstr( boole_POSet( skol29 ) ), X, skol30( bottom_of_relstr(
% 2.12/2.49 boole_POSet( skol29 ) ), X ) ), in( skol30( bottom_of_relstr( boole_POSet
% 2.12/2.49 ( skol29 ) ), X ), X ) }.
% 2.12/2.49 (13237) {G2,W11,D4,L3,V1,M3} R(433,103);d(10651);d(1807);d(428);r(151) { !
% 2.12/2.49 lattice( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) )
% 2.12/2.49 , bottom_of_relstr( boole_POSet( X ) ) ==> empty_set }.
% 2.12/2.49 (14089) {G1,W3,D2,L1,V1,M1} R(443,170) { ! in( X, empty_set ) }.
% 2.12/2.49 (14091) {G2,W4,D2,L1,V2,M1} R(14089,425) { ! alpha15( empty_set, X, Y ) }.
% 2.12/2.49 (20209) {G3,W5,D4,L1,V1,M1} S(13237);r(158);r(166) { bottom_of_relstr(
% 2.12/2.49 boole_POSet( X ) ) ==> empty_set }.
% 2.12/2.49 (20217) {G4,W8,D3,L2,V1,M2} S(10803);d(20209);d(20209);r(14091) { ! X =
% 2.12/2.49 empty_set, in( skol30( empty_set, X ), X ) }.
% 2.12/2.49 (20768) {G5,W0,D0,L0,V0,M0} Q(20217);r(14089) { }.
% 2.12/2.49
% 2.12/2.49
% 2.12/2.49 % SZS output end Refutation
% 2.12/2.49 found a proof!
% 2.12/2.49
% 2.12/2.49
% 2.12/2.49 Unprocessed initial clauses:
% 2.12/2.49
% 2.12/2.49 (20770) {G0,W11,D4,L3,V1,M3} { ! rel_str( X ), ! strict_rel_str( X ), X =
% 2.12/2.49 rel_str_of( the_carrier( X ), the_InternalRel( X ) ) }.
% 2.12/2.49 (20771) {G0,W13,D4,L3,V1,M3} { ! latt_str( X ), ! strict_latt_str( X ), X
% 2.12/2.49 = latt_str_of( the_carrier( X ), the_L_join( X ), the_L_meet( X ) ) }.
% 2.12/2.49 (20772) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 2.12/2.49 (20773) {G0,W10,D2,L5,V1,M5} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 lattice( X ), ! complete_latt_str( X ), alpha2( X ) }.
% 2.12/2.49 (20774) {G0,W10,D2,L5,V1,M5} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 lattice( X ), ! complete_latt_str( X ), bounded_lattstr( X ) }.
% 2.12/2.49 (20775) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), alpha17( X ) }.
% 2.12/2.49 (20776) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), upper_bounded_semilattstr( X
% 2.12/2.49 ) }.
% 2.12/2.49 (20777) {G0,W6,D2,L3,V1,M3} { ! alpha17( X ), ! upper_bounded_semilattstr
% 2.12/2.49 ( X ), alpha2( X ) }.
% 2.12/2.49 (20778) {G0,W4,D2,L2,V1,M2} { ! alpha17( X ), alpha30( X ) }.
% 2.12/2.49 (20779) {G0,W4,D2,L2,V1,M2} { ! alpha17( X ), lower_bounded_semilattstr( X
% 2.12/2.49 ) }.
% 2.12/2.49 (20780) {G0,W6,D2,L3,V1,M3} { ! alpha30( X ), ! lower_bounded_semilattstr
% 2.12/2.49 ( X ), alpha17( X ) }.
% 2.12/2.49 (20781) {G0,W4,D2,L2,V1,M2} { ! alpha30( X ), alpha38( X ) }.
% 2.12/2.49 (20782) {G0,W4,D2,L2,V1,M2} { ! alpha30( X ), lattice( X ) }.
% 2.12/2.49 (20783) {G0,W6,D2,L3,V1,M3} { ! alpha38( X ), ! lattice( X ), alpha30( X )
% 2.12/2.49 }.
% 2.12/2.49 (20784) {G0,W4,D2,L2,V1,M2} { ! alpha38( X ), alpha45( X ) }.
% 2.12/2.49 (20785) {G0,W4,D2,L2,V1,M2} { ! alpha38( X ), join_absorbing( X ) }.
% 2.12/2.49 (20786) {G0,W6,D2,L3,V1,M3} { ! alpha45( X ), ! join_absorbing( X ),
% 2.12/2.49 alpha38( X ) }.
% 2.12/2.49 (20787) {G0,W4,D2,L2,V1,M2} { ! alpha45( X ), alpha50( X ) }.
% 2.12/2.49 (20788) {G0,W4,D2,L2,V1,M2} { ! alpha45( X ), meet_absorbing( X ) }.
% 2.12/2.49 (20789) {G0,W6,D2,L3,V1,M3} { ! alpha50( X ), ! meet_absorbing( X ),
% 2.12/2.49 alpha45( X ) }.
% 2.12/2.49 (20790) {G0,W4,D2,L2,V1,M2} { ! alpha50( X ), alpha53( X ) }.
% 2.12/2.49 (20791) {G0,W4,D2,L2,V1,M2} { ! alpha50( X ), meet_associative( X ) }.
% 2.12/2.49 (20792) {G0,W6,D2,L3,V1,M3} { ! alpha53( X ), ! meet_associative( X ),
% 2.12/2.49 alpha50( X ) }.
% 2.12/2.49 (20793) {G0,W4,D2,L2,V1,M2} { ! alpha53( X ), alpha55( X ) }.
% 2.12/2.49 (20794) {G0,W4,D2,L2,V1,M2} { ! alpha53( X ), meet_commutative( X ) }.
% 2.12/2.49 (20795) {G0,W6,D2,L3,V1,M3} { ! alpha55( X ), ! meet_commutative( X ),
% 2.12/2.49 alpha53( X ) }.
% 2.12/2.49 (20796) {G0,W4,D2,L2,V1,M2} { ! alpha55( X ), ! empty_carrier( X ) }.
% 2.12/2.49 (20797) {G0,W4,D2,L2,V1,M2} { ! alpha55( X ), join_commutative( X ) }.
% 2.12/2.49 (20798) {G0,W4,D2,L2,V1,M2} { ! alpha55( X ), join_associative( X ) }.
% 2.12/2.49 (20799) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! join_commutative( X )
% 2.12/2.49 , ! join_associative( X ), alpha55( X ) }.
% 2.12/2.49 (20800) {G0,W6,D2,L3,V1,M3} { ! rel_str( X ), ! with_suprema_relstr( X ),
% 2.12/2.49 ! empty_carrier( X ) }.
% 2.12/2.49 (20801) {G0,W8,D2,L4,V1,M4} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 lattice( X ), alpha3( X ) }.
% 2.12/2.49 (20802) {G0,W8,D2,L4,V1,M4} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 lattice( X ), join_absorbing( X ) }.
% 2.12/2.49 (20803) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), alpha18( X ) }.
% 2.12/2.49 (20804) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), meet_absorbing( X ) }.
% 2.12/2.49 (20805) {G0,W6,D2,L3,V1,M3} { ! alpha18( X ), ! meet_absorbing( X ),
% 2.12/2.49 alpha3( X ) }.
% 2.12/2.49 (20806) {G0,W4,D2,L2,V1,M2} { ! alpha18( X ), alpha31( X ) }.
% 2.12/2.49 (20807) {G0,W4,D2,L2,V1,M2} { ! alpha18( X ), meet_associative( X ) }.
% 2.12/2.49 (20808) {G0,W6,D2,L3,V1,M3} { ! alpha31( X ), ! meet_associative( X ),
% 2.12/2.49 alpha18( X ) }.
% 2.12/2.49 (20809) {G0,W4,D2,L2,V1,M2} { ! alpha31( X ), alpha39( X ) }.
% 2.12/2.49 (20810) {G0,W4,D2,L2,V1,M2} { ! alpha31( X ), meet_commutative( X ) }.
% 2.12/2.49 (20811) {G0,W6,D2,L3,V1,M3} { ! alpha39( X ), ! meet_commutative( X ),
% 2.12/2.49 alpha31( X ) }.
% 2.12/2.49 (20812) {G0,W4,D2,L2,V1,M2} { ! alpha39( X ), ! empty_carrier( X ) }.
% 2.12/2.49 (20813) {G0,W4,D2,L2,V1,M2} { ! alpha39( X ), join_commutative( X ) }.
% 2.12/2.49 (20814) {G0,W4,D2,L2,V1,M2} { ! alpha39( X ), join_associative( X ) }.
% 2.12/2.49 (20815) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! join_commutative( X )
% 2.12/2.49 , ! join_associative( X ), alpha39( X ) }.
% 2.12/2.49 (20816) {G0,W8,D4,L2,V3,M2} { ! element( X, powerset( cartesian_product2(
% 2.12/2.49 Y, Z ) ) ), relation( X ) }.
% 2.12/2.49 (20817) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.12/2.49 complete_relstr( X ), ! empty_carrier( X ) }.
% 2.12/2.49 (20818) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.12/2.49 complete_relstr( X ), with_suprema_relstr( X ) }.
% 2.12/2.49 (20819) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.12/2.49 complete_relstr( X ), with_infima_relstr( X ) }.
% 2.12/2.49 (20820) {G0,W6,D2,L3,V1,M3} { ! rel_str( X ), ! with_infima_relstr( X ), !
% 2.12/2.49 empty_carrier( X ) }.
% 2.12/2.49 (20821) {G0,W18,D2,L9,V1,M9} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 join_commutative( X ), ! join_associative( X ), ! meet_commutative( X ),
% 2.12/2.49 ! meet_associative( X ), ! meet_absorbing( X ), ! join_absorbing( X ), !
% 2.12/2.49 empty_carrier( X ) }.
% 2.12/2.49 (20822) {G0,W18,D2,L9,V1,M9} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 join_commutative( X ), ! join_associative( X ), ! meet_commutative( X ),
% 2.12/2.49 ! meet_associative( X ), ! meet_absorbing( X ), ! join_absorbing( X ),
% 2.12/2.49 lattice( X ) }.
% 2.12/2.49 (20823) {G0,W10,D2,L5,V1,M5} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 lower_bounded_semilattstr( X ), ! upper_bounded_semilattstr( X ), !
% 2.12/2.49 empty_carrier( X ) }.
% 2.12/2.49 (20824) {G0,W10,D2,L5,V1,M5} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 lower_bounded_semilattstr( X ), ! upper_bounded_semilattstr( X ),
% 2.12/2.49 bounded_lattstr( X ) }.
% 2.12/2.49 (20825) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.12/2.49 complete_relstr( X ), ! empty_carrier( X ) }.
% 2.12/2.49 (20826) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), empty_carrier( X ), !
% 2.12/2.49 complete_relstr( X ), bounded_relstr( X ) }.
% 2.12/2.49 (20827) {G0,W8,D2,L4,V1,M4} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 bounded_lattstr( X ), ! empty_carrier( X ) }.
% 2.12/2.49 (20828) {G0,W8,D2,L4,V1,M4} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 bounded_lattstr( X ), lower_bounded_semilattstr( X ) }.
% 2.12/2.49 (20829) {G0,W8,D2,L4,V1,M4} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 bounded_lattstr( X ), upper_bounded_semilattstr( X ) }.
% 2.12/2.49 (20830) {G0,W6,D2,L3,V1,M3} { ! rel_str( X ), ! bounded_relstr( X ),
% 2.12/2.49 lower_bounded_relstr( X ) }.
% 2.12/2.49 (20831) {G0,W6,D2,L3,V1,M3} { ! rel_str( X ), ! bounded_relstr( X ),
% 2.12/2.49 upper_bounded_relstr( X ) }.
% 2.12/2.49 (20832) {G0,W8,D2,L4,V1,M4} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 boolean_lattstr( X ), alpha4( X ) }.
% 2.12/2.49 (20833) {G0,W8,D2,L4,V1,M4} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 boolean_lattstr( X ), complemented_lattstr( X ) }.
% 2.12/2.49 (20834) {G0,W4,D2,L2,V1,M2} { ! alpha4( X ), alpha19( X ) }.
% 2.12/2.49 (20835) {G0,W4,D2,L2,V1,M2} { ! alpha4( X ), bounded_lattstr( X ) }.
% 2.12/2.49 (20836) {G0,W6,D2,L3,V1,M3} { ! alpha19( X ), ! bounded_lattstr( X ),
% 2.12/2.49 alpha4( X ) }.
% 2.12/2.49 (20837) {G0,W4,D2,L2,V1,M2} { ! alpha19( X ), alpha32( X ) }.
% 2.12/2.49 (20838) {G0,W4,D2,L2,V1,M2} { ! alpha19( X ), upper_bounded_semilattstr( X
% 2.12/2.49 ) }.
% 2.12/2.49 (20839) {G0,W6,D2,L3,V1,M3} { ! alpha32( X ), ! upper_bounded_semilattstr
% 2.12/2.49 ( X ), alpha19( X ) }.
% 2.12/2.49 (20840) {G0,W4,D2,L2,V1,M2} { ! alpha32( X ), ! empty_carrier( X ) }.
% 2.12/2.49 (20841) {G0,W4,D2,L2,V1,M2} { ! alpha32( X ), distributive_lattstr( X )
% 2.12/2.49 }.
% 2.12/2.49 (20842) {G0,W4,D2,L2,V1,M2} { ! alpha32( X ), lower_bounded_semilattstr( X
% 2.12/2.49 ) }.
% 2.12/2.49 (20843) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! distributive_lattstr(
% 2.12/2.49 X ), ! lower_bounded_semilattstr( X ), alpha32( X ) }.
% 2.12/2.49 (20844) {G0,W8,D2,L4,V1,M4} { ! rel_str( X ), ! lower_bounded_relstr( X )
% 2.12/2.49 , ! upper_bounded_relstr( X ), bounded_relstr( X ) }.
% 2.12/2.49 (20845) {G0,W12,D2,L6,V1,M6} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 distributive_lattstr( X ), ! bounded_lattstr( X ), ! complemented_lattstr
% 2.12/2.49 ( X ), ! empty_carrier( X ) }.
% 2.12/2.49 (20846) {G0,W12,D2,L6,V1,M6} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 distributive_lattstr( X ), ! bounded_lattstr( X ), ! complemented_lattstr
% 2.12/2.49 ( X ), boolean_lattstr( X ) }.
% 2.12/2.49 (20847) {G0,W10,D2,L5,V1,M5} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 lattice( X ), ! distributive_lattstr( X ), alpha5( X ) }.
% 2.12/2.49 (20848) {G0,W10,D2,L5,V1,M5} { ! latt_str( X ), empty_carrier( X ), !
% 2.12/2.49 lattice( X ), ! distributive_lattstr( X ), modular_lattstr( X ) }.
% 2.12/2.49 (20849) {G0,W4,D2,L2,V1,M2} { ! alpha5( X ), alpha20( X ) }.
% 2.12/2.49 (20850) {G0,W4,D2,L2,V1,M2} { ! alpha5( X ), lattice( X ) }.
% 2.12/2.49 (20851) {G0,W6,D2,L3,V1,M3} { ! alpha20( X ), ! lattice( X ), alpha5( X )
% 2.12/2.49 }.
% 2.12/2.49 (20852) {G0,W4,D2,L2,V1,M2} { ! alpha20( X ), alpha33( X ) }.
% 2.12/2.49 (20853) {G0,W4,D2,L2,V1,M2} { ! alpha20( X ), join_absorbing( X ) }.
% 2.12/2.49 (20854) {G0,W6,D2,L3,V1,M3} { ! alpha33( X ), ! join_absorbing( X ),
% 2.12/2.49 alpha20( X ) }.
% 2.12/2.49 (20855) {G0,W4,D2,L2,V1,M2} { ! alpha33( X ), alpha40( X ) }.
% 2.12/2.49 (20856) {G0,W4,D2,L2,V1,M2} { ! alpha33( X ), meet_absorbing( X ) }.
% 2.12/2.49 (20857) {G0,W6,D2,L3,V1,M3} { ! alpha40( X ), ! meet_absorbing( X ),
% 2.12/2.49 alpha33( X ) }.
% 2.12/2.49 (20858) {G0,W4,D2,L2,V1,M2} { ! alpha40( X ), alpha46( X ) }.
% 2.12/2.49 (20859) {G0,W4,D2,L2,V1,M2} { ! alpha40( X ), meet_associative( X ) }.
% 2.12/2.49 (20860) {G0,W6,D2,L3,V1,M3} { ! alpha46( X ), ! meet_associative( X ),
% 2.12/2.49 alpha40( X ) }.
% 2.12/2.49 (20861) {G0,W4,D2,L2,V1,M2} { ! alpha46( X ), alpha51( X ) }.
% 2.12/2.49 (20862) {G0,W4,D2,L2,V1,M2} { ! alpha46( X ), meet_commutative( X ) }.
% 2.12/2.49 (20863) {G0,W6,D2,L3,V1,M3} { ! alpha51( X ), ! meet_commutative( X ),
% 2.12/2.49 alpha46( X ) }.
% 2.12/2.49 (20864) {G0,W4,D2,L2,V1,M2} { ! alpha51( X ), ! empty_carrier( X ) }.
% 2.12/2.49 (20865) {G0,W4,D2,L2,V1,M2} { ! alpha51( X ), join_commutative( X ) }.
% 2.12/2.49 (20866) {G0,W4,D2,L2,V1,M2} { ! alpha51( X ), join_associative( X ) }.
% 2.12/2.49 (20867) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! join_commutative( X )
% 2.12/2.49 , ! join_associative( X ), alpha51( X ) }.
% 2.12/2.49 (20868) {G0,W8,D3,L2,V1,M2} { ! rel_str( X ), bottom_of_relstr( X ) =
% 2.12/2.49 join_on_relstr( X, empty_set ) }.
% 2.12/2.49 (20869) {G0,W13,D4,L3,V2,M3} { empty_carrier( X ), ! latt_str( X ),
% 2.12/2.49 meet_of_latt_set( X, Y ) = join_of_latt_set( X, a_2_2_lattice3( X, Y ) )
% 2.12/2.49 }.
% 2.12/2.49 (20870) {G0,W14,D4,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), poset_of_lattice( X ) = rel_str_of( the_carrier( X ),
% 2.12/2.49 k2_lattice3( X ) ) }.
% 2.12/2.49 (20871) {G0,W6,D4,L1,V1,M1} { boole_POSet( X ) = poset_of_lattice(
% 2.12/2.49 boole_lattice( X ) ) }.
% 2.12/2.49 (20872) {G0,W8,D3,L2,V2,M2} { ! relation_of2( Y, X, X ), strict_rel_str(
% 2.12/2.49 rel_str_of( X, Y ) ) }.
% 2.12/2.49 (20873) {G0,W8,D3,L2,V2,M2} { ! relation_of2( Y, X, X ), rel_str(
% 2.12/2.49 rel_str_of( X, Y ) ) }.
% 2.12/2.49 (20874) {G0,W33,D3,L7,V3,M7} { ! function( Y ), ! quasi_total( Y,
% 2.12/2.49 cartesian_product2( X, X ), X ), ! relation_of2( Y, cartesian_product2( X
% 2.12/2.49 , X ), X ), ! function( Z ), ! quasi_total( Z, cartesian_product2( X, X )
% 2.12/2.49 , X ), ! relation_of2( Z, cartesian_product2( X, X ), X ),
% 2.12/2.49 strict_latt_str( latt_str_of( X, Y, Z ) ) }.
% 2.12/2.49 (20875) {G0,W33,D3,L7,V3,M7} { ! function( Y ), ! quasi_total( Y,
% 2.12/2.49 cartesian_product2( X, X ), X ), ! relation_of2( Y, cartesian_product2( X
% 2.12/2.49 , X ), X ), ! function( Z ), ! quasi_total( Z, cartesian_product2( X, X )
% 2.12/2.49 , X ), ! relation_of2( Z, cartesian_product2( X, X ), X ), latt_str(
% 2.12/2.49 latt_str_of( X, Y, Z ) ) }.
% 2.12/2.49 (20876) {G0,W10,D3,L3,V2,M3} { empty_carrier( X ), ! latt_str( X ),
% 2.12/2.49 element( join_of_latt_set( X, Y ), the_carrier( X ) ) }.
% 2.12/2.49 (20877) {G0,W10,D3,L3,V2,M3} { empty_carrier( X ), ! latt_str( X ),
% 2.12/2.49 element( meet_of_latt_set( X, Y ), the_carrier( X ) ) }.
% 2.12/2.49 (20878) {G0,W3,D3,L1,V1,M1} { strict_latt_str( boole_lattice( X ) ) }.
% 2.12/2.49 (20879) {G0,W3,D3,L1,V1,M1} { latt_str( boole_lattice( X ) ) }.
% 2.12/2.49 (20880) {G0,W1,D1,L1,V0,M1} { && }.
% 2.12/2.49 (20881) {G0,W8,D3,L2,V2,M2} { ! rel_str( X ), element( join_on_relstr( X,
% 2.12/2.49 Y ), the_carrier( X ) ) }.
% 2.12/2.49 (20882) {G0,W1,D1,L1,V0,M1} { && }.
% 2.12/2.49 (20883) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), alpha6( X ) }.
% 2.12/2.49 (20884) {G0,W13,D3,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), relation_of2_as_subset( k2_lattice3( X ), the_carrier( X )
% 2.12/2.49 , the_carrier( X ) ) }.
% 2.12/2.49 (20885) {G0,W4,D2,L2,V1,M2} { ! alpha6( X ), alpha21( X ) }.
% 2.12/2.49 (20886) {G0,W9,D3,L2,V1,M2} { ! alpha6( X ), v1_partfun1( k2_lattice3( X )
% 2.12/2.49 , the_carrier( X ), the_carrier( X ) ) }.
% 2.12/2.49 (20887) {G0,W11,D3,L3,V1,M3} { ! alpha21( X ), ! v1_partfun1( k2_lattice3
% 2.12/2.49 ( X ), the_carrier( X ), the_carrier( X ) ), alpha6( X ) }.
% 2.12/2.49 (20888) {G0,W5,D3,L2,V1,M2} { ! alpha21( X ), reflexive( k2_lattice3( X )
% 2.12/2.49 ) }.
% 2.12/2.49 (20889) {G0,W5,D3,L2,V1,M2} { ! alpha21( X ), antisymmetric( k2_lattice3(
% 2.12/2.49 X ) ) }.
% 2.12/2.49 (20890) {G0,W5,D3,L2,V1,M2} { ! alpha21( X ), transitive( k2_lattice3( X )
% 2.12/2.49 ) }.
% 2.12/2.49 (20891) {G0,W11,D3,L4,V1,M4} { ! reflexive( k2_lattice3( X ) ), !
% 2.12/2.49 antisymmetric( k2_lattice3( X ) ), ! transitive( k2_lattice3( X ) ),
% 2.12/2.49 alpha21( X ) }.
% 2.12/2.49 (20892) {G0,W8,D3,L2,V2,M2} { ! rel_str( X ), element( meet_on_relstr( X,
% 2.12/2.49 Y ), the_carrier( X ) ) }.
% 2.12/2.49 (20893) {G0,W1,D1,L1,V0,M1} { && }.
% 2.12/2.49 (20894) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), alpha7( X ) }.
% 2.12/2.49 (20895) {G0,W9,D3,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), rel_str( poset_of_lattice( X ) ) }.
% 2.12/2.49 (20896) {G0,W4,D2,L2,V1,M2} { ! alpha7( X ), alpha22( X ) }.
% 2.12/2.49 (20897) {G0,W5,D3,L2,V1,M2} { ! alpha7( X ), antisymmetric_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20898) {G0,W7,D3,L3,V1,M3} { ! alpha22( X ), ! antisymmetric_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha7( X ) }.
% 2.12/2.49 (20899) {G0,W5,D3,L2,V1,M2} { ! alpha22( X ), strict_rel_str(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20900) {G0,W5,D3,L2,V1,M2} { ! alpha22( X ), reflexive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20901) {G0,W5,D3,L2,V1,M2} { ! alpha22( X ), transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20902) {G0,W11,D3,L4,V1,M4} { ! strict_rel_str( poset_of_lattice( X ) ),
% 2.12/2.49 ! reflexive_relstr( poset_of_lattice( X ) ), ! transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha22( X ) }.
% 2.12/2.49 (20903) {G0,W7,D3,L2,V1,M2} { ! rel_str( X ), element( bottom_of_relstr( X
% 2.12/2.49 ), the_carrier( X ) ) }.
% 2.12/2.49 (20904) {G0,W3,D3,L1,V1,M1} { strict_rel_str( boole_POSet( X ) ) }.
% 2.12/2.49 (20905) {G0,W3,D3,L1,V1,M1} { rel_str( boole_POSet( X ) ) }.
% 2.12/2.49 (20906) {G0,W9,D3,L3,V1,M3} { empty_carrier( X ), ! meet_semilatt_str( X )
% 2.12/2.49 , element( bottom_of_semilattstr( X ), the_carrier( X ) ) }.
% 2.12/2.49 (20907) {G0,W9,D3,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), relation( relation_of_lattice( X ) ) }.
% 2.12/2.49 (20908) {G0,W4,D2,L2,V1,M2} { ! meet_semilatt_str( X ), one_sorted_str( X
% 2.12/2.49 ) }.
% 2.12/2.49 (20909) {G0,W4,D2,L2,V1,M2} { ! rel_str( X ), one_sorted_str( X ) }.
% 2.12/2.49 (20910) {G0,W1,D1,L1,V0,M1} { && }.
% 2.12/2.49 (20911) {G0,W4,D2,L2,V1,M2} { ! join_semilatt_str( X ), one_sorted_str( X
% 2.12/2.49 ) }.
% 2.12/2.49 (20912) {G0,W4,D2,L2,V1,M2} { ! latt_str( X ), meet_semilatt_str( X ) }.
% 2.12/2.49 (20913) {G0,W4,D2,L2,V1,M2} { ! latt_str( X ), join_semilatt_str( X ) }.
% 2.12/2.49 (20914) {G0,W1,D1,L1,V0,M1} { && }.
% 2.12/2.49 (20915) {G0,W1,D1,L1,V0,M1} { && }.
% 2.12/2.49 (20916) {G0,W10,D4,L2,V3,M2} { ! relation_of2_as_subset( Z, X, Y ),
% 2.12/2.49 element( Z, powerset( cartesian_product2( X, Y ) ) ) }.
% 2.12/2.49 (20917) {G0,W5,D3,L2,V1,M2} { ! meet_semilatt_str( X ), function(
% 2.12/2.49 the_L_meet( X ) ) }.
% 2.12/2.49 (20918) {G0,W12,D4,L2,V1,M2} { ! meet_semilatt_str( X ), quasi_total(
% 2.12/2.49 the_L_meet( X ), cartesian_product2( the_carrier( X ), the_carrier( X ) )
% 2.12/2.49 , the_carrier( X ) ) }.
% 2.12/2.49 (20919) {G0,W12,D4,L2,V1,M2} { ! meet_semilatt_str( X ),
% 2.12/2.49 relation_of2_as_subset( the_L_meet( X ), cartesian_product2( the_carrier
% 2.12/2.49 ( X ), the_carrier( X ) ), the_carrier( X ) ) }.
% 2.12/2.49 (20920) {G0,W9,D3,L2,V1,M2} { ! rel_str( X ), relation_of2_as_subset(
% 2.12/2.49 the_InternalRel( X ), the_carrier( X ), the_carrier( X ) ) }.
% 2.12/2.49 (20921) {G0,W1,D1,L1,V0,M1} { && }.
% 2.12/2.49 (20922) {G0,W5,D3,L2,V1,M2} { ! join_semilatt_str( X ), function(
% 2.12/2.49 the_L_join( X ) ) }.
% 2.12/2.49 (20923) {G0,W12,D4,L2,V1,M2} { ! join_semilatt_str( X ), quasi_total(
% 2.12/2.49 the_L_join( X ), cartesian_product2( the_carrier( X ), the_carrier( X ) )
% 2.12/2.49 , the_carrier( X ) ) }.
% 2.12/2.49 (20924) {G0,W12,D4,L2,V1,M2} { ! join_semilatt_str( X ),
% 2.12/2.49 relation_of2_as_subset( the_L_join( X ), cartesian_product2( the_carrier
% 2.12/2.49 ( X ), the_carrier( X ) ), the_carrier( X ) ) }.
% 2.12/2.49 (20925) {G0,W2,D2,L1,V0,M1} { meet_semilatt_str( skol1 ) }.
% 2.12/2.49 (20926) {G0,W2,D2,L1,V0,M1} { rel_str( skol2 ) }.
% 2.12/2.49 (20927) {G0,W2,D2,L1,V0,M1} { one_sorted_str( skol3 ) }.
% 2.12/2.49 (20928) {G0,W2,D2,L1,V0,M1} { join_semilatt_str( skol4 ) }.
% 2.12/2.49 (20929) {G0,W2,D2,L1,V0,M1} { latt_str( skol5 ) }.
% 2.12/2.49 (20930) {G0,W6,D3,L1,V2,M1} { relation_of2( skol6( X, Y ), X, Y ) }.
% 2.12/2.49 (20931) {G0,W4,D3,L1,V1,M1} { element( skol7( X ), X ) }.
% 2.12/2.49 (20932) {G0,W6,D3,L1,V2,M1} { relation_of2_as_subset( skol8( X, Y ), X, Y
% 2.12/2.49 ) }.
% 2.12/2.49 (20933) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_lattice( X ) ) }.
% 2.12/2.49 (20934) {G0,W3,D3,L1,V1,M1} { strict_latt_str( boole_lattice( X ) ) }.
% 2.12/2.49 (20935) {G0,W3,D3,L1,V1,M1} { join_commutative( boole_lattice( X ) ) }.
% 2.12/2.49 (20936) {G0,W3,D3,L1,V1,M1} { join_associative( boole_lattice( X ) ) }.
% 2.12/2.49 (20937) {G0,W3,D3,L1,V1,M1} { meet_commutative( boole_lattice( X ) ) }.
% 2.12/2.49 (20938) {G0,W3,D3,L1,V1,M1} { meet_associative( boole_lattice( X ) ) }.
% 2.12/2.49 (20939) {G0,W3,D3,L1,V1,M1} { meet_absorbing( boole_lattice( X ) ) }.
% 2.12/2.49 (20940) {G0,W3,D3,L1,V1,M1} { join_absorbing( boole_lattice( X ) ) }.
% 2.12/2.49 (20941) {G0,W3,D3,L1,V1,M1} { lattice( boole_lattice( X ) ) }.
% 2.12/2.49 (20942) {G0,W3,D3,L1,V1,M1} { distributive_lattstr( boole_lattice( X ) )
% 2.12/2.49 }.
% 2.12/2.49 (20943) {G0,W3,D3,L1,V1,M1} { modular_lattstr( boole_lattice( X ) ) }.
% 2.12/2.49 (20944) {G0,W3,D3,L1,V1,M1} { lower_bounded_semilattstr( boole_lattice( X
% 2.12/2.49 ) ) }.
% 2.12/2.49 (20945) {G0,W3,D3,L1,V1,M1} { upper_bounded_semilattstr( boole_lattice( X
% 2.12/2.49 ) ) }.
% 2.12/2.49 (20946) {G0,W3,D3,L1,V1,M1} { bounded_lattstr( boole_lattice( X ) ) }.
% 2.12/2.49 (20947) {G0,W3,D3,L1,V1,M1} { complemented_lattstr( boole_lattice( X ) )
% 2.12/2.49 }.
% 2.12/2.49 (20948) {G0,W3,D3,L1,V1,M1} { boolean_lattstr( boole_lattice( X ) ) }.
% 2.12/2.49 (20949) {G0,W3,D3,L1,V1,M1} { complete_latt_str( boole_lattice( X ) ) }.
% 2.12/2.49 (20950) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_lattice( X ) ) }.
% 2.12/2.49 (20951) {G0,W3,D3,L1,V1,M1} { strict_latt_str( boole_lattice( X ) ) }.
% 2.12/2.49 (20952) {G0,W10,D3,L3,V2,M3} { empty( X ), ! relation_of2( Y, X, X ), !
% 2.12/2.49 empty_carrier( rel_str_of( X, Y ) ) }.
% 2.12/2.49 (20953) {G0,W10,D3,L3,V2,M3} { empty( X ), ! relation_of2( Y, X, X ),
% 2.12/2.49 strict_rel_str( rel_str_of( X, Y ) ) }.
% 2.12/2.49 (20954) {G0,W7,D3,L3,V1,M3} { empty_carrier( X ), ! one_sorted_str( X ), !
% 2.12/2.49 empty( the_carrier( X ) ) }.
% 2.12/2.49 (20955) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 2.12/2.49 (20956) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 2.12/2.49 (20957) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), alpha8( X ) }.
% 2.12/2.49 (20958) {G0,W9,D3,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), with_infima_relstr( poset_of_lattice( X ) ) }.
% 2.12/2.49 (20959) {G0,W4,D2,L2,V1,M2} { ! alpha8( X ), alpha23( X ) }.
% 2.12/2.49 (20960) {G0,W5,D3,L2,V1,M2} { ! alpha8( X ), with_suprema_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20961) {G0,W7,D3,L3,V1,M3} { ! alpha23( X ), ! with_suprema_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha8( X ) }.
% 2.12/2.49 (20962) {G0,W4,D2,L2,V1,M2} { ! alpha23( X ), alpha34( X ) }.
% 2.12/2.49 (20963) {G0,W5,D3,L2,V1,M2} { ! alpha23( X ), antisymmetric_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20964) {G0,W7,D3,L3,V1,M3} { ! alpha34( X ), ! antisymmetric_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha23( X ) }.
% 2.12/2.49 (20965) {G0,W4,D2,L2,V1,M2} { ! alpha34( X ), alpha41( X ) }.
% 2.12/2.49 (20966) {G0,W5,D3,L2,V1,M2} { ! alpha34( X ), transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20967) {G0,W7,D3,L3,V1,M3} { ! alpha41( X ), ! transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha34( X ) }.
% 2.12/2.49 (20968) {G0,W5,D3,L2,V1,M2} { ! alpha41( X ), ! empty_carrier(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20969) {G0,W5,D3,L2,V1,M2} { ! alpha41( X ), strict_rel_str(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20970) {G0,W5,D3,L2,V1,M2} { ! alpha41( X ), reflexive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20971) {G0,W11,D3,L4,V1,M4} { empty_carrier( poset_of_lattice( X ) ), !
% 2.12/2.49 strict_rel_str( poset_of_lattice( X ) ), ! reflexive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha41( X ) }.
% 2.12/2.49 (20972) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_lattice( X ) ) }.
% 2.12/2.49 (20973) {G0,W3,D3,L1,V1,M1} { strict_latt_str( boole_lattice( X ) ) }.
% 2.12/2.49 (20974) {G0,W3,D3,L1,V1,M1} { join_commutative( boole_lattice( X ) ) }.
% 2.12/2.49 (20975) {G0,W3,D3,L1,V1,M1} { join_associative( boole_lattice( X ) ) }.
% 2.12/2.49 (20976) {G0,W3,D3,L1,V1,M1} { meet_commutative( boole_lattice( X ) ) }.
% 2.12/2.49 (20977) {G0,W3,D3,L1,V1,M1} { meet_associative( boole_lattice( X ) ) }.
% 2.12/2.49 (20978) {G0,W3,D3,L1,V1,M1} { meet_absorbing( boole_lattice( X ) ) }.
% 2.12/2.49 (20979) {G0,W3,D3,L1,V1,M1} { join_absorbing( boole_lattice( X ) ) }.
% 2.12/2.49 (20980) {G0,W3,D3,L1,V1,M1} { lattice( boole_lattice( X ) ) }.
% 2.12/2.49 (20981) {G0,W10,D2,L5,V1,M5} { ! reflexive_relstr( X ), !
% 2.12/2.49 transitive_relstr( X ), ! antisymmetric_relstr( X ), ! rel_str( X ),
% 2.12/2.49 alpha9( X ) }.
% 2.12/2.49 (20982) {G0,W15,D3,L5,V1,M5} { ! reflexive_relstr( X ), !
% 2.12/2.49 transitive_relstr( X ), ! antisymmetric_relstr( X ), ! rel_str( X ),
% 2.12/2.49 v1_partfun1( the_InternalRel( X ), the_carrier( X ), the_carrier( X ) )
% 2.12/2.49 }.
% 2.12/2.49 (20983) {G0,W4,D2,L2,V1,M2} { ! alpha9( X ), alpha24( X ) }.
% 2.12/2.49 (20984) {G0,W5,D3,L2,V1,M2} { ! alpha9( X ), transitive( the_InternalRel(
% 2.12/2.49 X ) ) }.
% 2.12/2.49 (20985) {G0,W7,D3,L3,V1,M3} { ! alpha24( X ), ! transitive(
% 2.12/2.49 the_InternalRel( X ) ), alpha9( X ) }.
% 2.12/2.49 (20986) {G0,W5,D3,L2,V1,M2} { ! alpha24( X ), relation( the_InternalRel( X
% 2.12/2.49 ) ) }.
% 2.12/2.49 (20987) {G0,W5,D3,L2,V1,M2} { ! alpha24( X ), reflexive( the_InternalRel(
% 2.12/2.49 X ) ) }.
% 2.12/2.49 (20988) {G0,W5,D3,L2,V1,M2} { ! alpha24( X ), antisymmetric(
% 2.12/2.49 the_InternalRel( X ) ) }.
% 2.12/2.49 (20989) {G0,W11,D3,L4,V1,M4} { ! relation( the_InternalRel( X ) ), !
% 2.12/2.49 reflexive( the_InternalRel( X ) ), ! antisymmetric( the_InternalRel( X )
% 2.12/2.49 ), alpha24( X ) }.
% 2.12/2.49 (20990) {G0,W10,D2,L5,V1,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 upper_bounded_semilattstr( X ), ! latt_str( X ), alpha10( X ) }.
% 2.12/2.49 (20991) {G0,W11,D3,L5,V1,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 upper_bounded_semilattstr( X ), ! latt_str( X ), with_infima_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20992) {G0,W4,D2,L2,V1,M2} { ! alpha10( X ), alpha25( X ) }.
% 2.12/2.49 (20993) {G0,W5,D3,L2,V1,M2} { ! alpha10( X ), with_suprema_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20994) {G0,W7,D3,L3,V1,M3} { ! alpha25( X ), ! with_suprema_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha10( X ) }.
% 2.12/2.49 (20995) {G0,W4,D2,L2,V1,M2} { ! alpha25( X ), alpha35( X ) }.
% 2.12/2.49 (20996) {G0,W5,D3,L2,V1,M2} { ! alpha25( X ), upper_bounded_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (20997) {G0,W7,D3,L3,V1,M3} { ! alpha35( X ), ! upper_bounded_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha25( X ) }.
% 2.12/2.49 (20998) {G0,W4,D2,L2,V1,M2} { ! alpha35( X ), alpha42( X ) }.
% 2.12/2.49 (20999) {G0,W5,D3,L2,V1,M2} { ! alpha35( X ), antisymmetric_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21000) {G0,W7,D3,L3,V1,M3} { ! alpha42( X ), ! antisymmetric_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha35( X ) }.
% 2.12/2.49 (21001) {G0,W4,D2,L2,V1,M2} { ! alpha42( X ), alpha47( X ) }.
% 2.12/2.49 (21002) {G0,W5,D3,L2,V1,M2} { ! alpha42( X ), transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21003) {G0,W7,D3,L3,V1,M3} { ! alpha47( X ), ! transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha42( X ) }.
% 2.12/2.49 (21004) {G0,W5,D3,L2,V1,M2} { ! alpha47( X ), ! empty_carrier(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21005) {G0,W5,D3,L2,V1,M2} { ! alpha47( X ), strict_rel_str(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21006) {G0,W5,D3,L2,V1,M2} { ! alpha47( X ), reflexive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21007) {G0,W11,D3,L4,V1,M4} { empty_carrier( poset_of_lattice( X ) ), !
% 2.12/2.49 strict_rel_str( poset_of_lattice( X ) ), ! reflexive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha47( X ) }.
% 2.12/2.49 (21008) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_lattice( X ) ) }.
% 2.12/2.49 (21009) {G0,W3,D3,L1,V1,M1} { strict_latt_str( boole_lattice( X ) ) }.
% 2.12/2.49 (21010) {G0,W3,D3,L1,V1,M1} { join_commutative( boole_lattice( X ) ) }.
% 2.12/2.49 (21011) {G0,W3,D3,L1,V1,M1} { join_associative( boole_lattice( X ) ) }.
% 2.12/2.49 (21012) {G0,W3,D3,L1,V1,M1} { meet_commutative( boole_lattice( X ) ) }.
% 2.12/2.49 (21013) {G0,W3,D3,L1,V1,M1} { meet_associative( boole_lattice( X ) ) }.
% 2.12/2.49 (21014) {G0,W3,D3,L1,V1,M1} { meet_absorbing( boole_lattice( X ) ) }.
% 2.12/2.49 (21015) {G0,W3,D3,L1,V1,M1} { join_absorbing( boole_lattice( X ) ) }.
% 2.12/2.49 (21016) {G0,W3,D3,L1,V1,M1} { lattice( boole_lattice( X ) ) }.
% 2.12/2.49 (21017) {G0,W3,D3,L1,V1,M1} { distributive_lattstr( boole_lattice( X ) )
% 2.12/2.49 }.
% 2.12/2.49 (21018) {G0,W3,D3,L1,V1,M1} { modular_lattstr( boole_lattice( X ) ) }.
% 2.12/2.49 (21019) {G0,W3,D3,L1,V1,M1} { lower_bounded_semilattstr( boole_lattice( X
% 2.12/2.49 ) ) }.
% 2.12/2.49 (21020) {G0,W3,D3,L1,V1,M1} { upper_bounded_semilattstr( boole_lattice( X
% 2.12/2.49 ) ) }.
% 2.12/2.49 (21021) {G0,W3,D3,L1,V1,M1} { bounded_lattstr( boole_lattice( X ) ) }.
% 2.12/2.49 (21022) {G0,W3,D3,L1,V1,M1} { complemented_lattstr( boole_lattice( X ) )
% 2.12/2.49 }.
% 2.12/2.49 (21023) {G0,W3,D3,L1,V1,M1} { boolean_lattstr( boole_lattice( X ) ) }.
% 2.12/2.49 (21024) {G0,W35,D3,L8,V3,M8} { empty( X ), ! function( Y ), ! quasi_total
% 2.12/2.49 ( Y, cartesian_product2( X, X ), X ), ! relation_of2( Y,
% 2.12/2.49 cartesian_product2( X, X ), X ), ! function( Z ), ! quasi_total( Z,
% 2.12/2.49 cartesian_product2( X, X ), X ), ! relation_of2( Z, cartesian_product2( X
% 2.12/2.49 , X ), X ), ! empty_carrier( latt_str_of( X, Y, Z ) ) }.
% 2.12/2.49 (21025) {G0,W35,D3,L8,V3,M8} { empty( X ), ! function( Y ), ! quasi_total
% 2.12/2.49 ( Y, cartesian_product2( X, X ), X ), ! relation_of2( Y,
% 2.12/2.49 cartesian_product2( X, X ), X ), ! function( Z ), ! quasi_total( Z,
% 2.12/2.49 cartesian_product2( X, X ), X ), ! relation_of2( Z, cartesian_product2( X
% 2.12/2.49 , X ), X ), strict_latt_str( latt_str_of( X, Y, Z ) ) }.
% 2.12/2.49 (21026) {G0,W17,D2,L6,V2,M6} { ! reflexive( Y ), ! antisymmetric( Y ), !
% 2.12/2.49 transitive( Y ), ! v1_partfun1( Y, X, X ), ! relation_of2( Y, X, X ),
% 2.12/2.49 alpha11( X, Y ) }.
% 2.12/2.49 (21027) {G0,W18,D3,L6,V2,M6} { ! reflexive( Y ), ! antisymmetric( Y ), !
% 2.12/2.49 transitive( Y ), ! v1_partfun1( Y, X, X ), ! relation_of2( Y, X, X ),
% 2.12/2.49 antisymmetric_relstr( rel_str_of( X, Y ) ) }.
% 2.12/2.49 (21028) {G0,W7,D3,L2,V2,M2} { ! alpha11( X, Y ), strict_rel_str(
% 2.12/2.49 rel_str_of( X, Y ) ) }.
% 2.12/2.49 (21029) {G0,W7,D3,L2,V2,M2} { ! alpha11( X, Y ), reflexive_relstr(
% 2.12/2.49 rel_str_of( X, Y ) ) }.
% 2.12/2.49 (21030) {G0,W7,D3,L2,V2,M2} { ! alpha11( X, Y ), transitive_relstr(
% 2.12/2.49 rel_str_of( X, Y ) ) }.
% 2.12/2.49 (21031) {G0,W15,D3,L4,V2,M4} { ! strict_rel_str( rel_str_of( X, Y ) ), !
% 2.12/2.49 reflexive_relstr( rel_str_of( X, Y ) ), ! transitive_relstr( rel_str_of(
% 2.12/2.49 X, Y ) ), alpha11( X, Y ) }.
% 2.12/2.49 (21032) {G0,W10,D2,L5,V1,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 lower_bounded_semilattstr( X ), ! latt_str( X ), alpha12( X ) }.
% 2.12/2.49 (21033) {G0,W11,D3,L5,V1,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 lower_bounded_semilattstr( X ), ! latt_str( X ), with_infima_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21034) {G0,W4,D2,L2,V1,M2} { ! alpha12( X ), alpha26( X ) }.
% 2.12/2.49 (21035) {G0,W5,D3,L2,V1,M2} { ! alpha12( X ), with_suprema_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21036) {G0,W7,D3,L3,V1,M3} { ! alpha26( X ), ! with_suprema_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha12( X ) }.
% 2.12/2.49 (21037) {G0,W4,D2,L2,V1,M2} { ! alpha26( X ), alpha36( X ) }.
% 2.12/2.49 (21038) {G0,W5,D3,L2,V1,M2} { ! alpha26( X ), lower_bounded_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21039) {G0,W7,D3,L3,V1,M3} { ! alpha36( X ), ! lower_bounded_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha26( X ) }.
% 2.12/2.49 (21040) {G0,W4,D2,L2,V1,M2} { ! alpha36( X ), alpha43( X ) }.
% 2.12/2.49 (21041) {G0,W5,D3,L2,V1,M2} { ! alpha36( X ), antisymmetric_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21042) {G0,W7,D3,L3,V1,M3} { ! alpha43( X ), ! antisymmetric_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha36( X ) }.
% 2.12/2.49 (21043) {G0,W4,D2,L2,V1,M2} { ! alpha43( X ), alpha48( X ) }.
% 2.12/2.49 (21044) {G0,W5,D3,L2,V1,M2} { ! alpha43( X ), transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21045) {G0,W7,D3,L3,V1,M3} { ! alpha48( X ), ! transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha43( X ) }.
% 2.12/2.49 (21046) {G0,W5,D3,L2,V1,M2} { ! alpha48( X ), ! empty_carrier(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21047) {G0,W5,D3,L2,V1,M2} { ! alpha48( X ), strict_rel_str(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21048) {G0,W5,D3,L2,V1,M2} { ! alpha48( X ), reflexive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21049) {G0,W11,D3,L4,V1,M4} { empty_carrier( poset_of_lattice( X ) ), !
% 2.12/2.49 strict_rel_str( poset_of_lattice( X ) ), ! reflexive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha48( X ) }.
% 2.12/2.49 (21050) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), alpha13( X ) }.
% 2.12/2.49 (21051) {G0,W9,D3,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.49 latt_str( X ), antisymmetric_relstr( poset_of_lattice( X ) ) }.
% 2.12/2.49 (21052) {G0,W4,D2,L2,V1,M2} { ! alpha13( X ), alpha27( X ) }.
% 2.12/2.49 (21053) {G0,W5,D3,L2,V1,M2} { ! alpha13( X ), transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21054) {G0,W7,D3,L3,V1,M3} { ! alpha27( X ), ! transitive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha13( X ) }.
% 2.12/2.49 (21055) {G0,W5,D3,L2,V1,M2} { ! alpha27( X ), ! empty_carrier(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21056) {G0,W5,D3,L2,V1,M2} { ! alpha27( X ), strict_rel_str(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21057) {G0,W5,D3,L2,V1,M2} { ! alpha27( X ), reflexive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ) }.
% 2.12/2.49 (21058) {G0,W11,D3,L4,V1,M4} { empty_carrier( poset_of_lattice( X ) ), !
% 2.12/2.49 strict_rel_str( poset_of_lattice( X ) ), ! reflexive_relstr(
% 2.12/2.49 poset_of_lattice( X ) ), alpha27( X ) }.
% 2.12/2.50 (21059) {G0,W8,D3,L3,V2,M3} { empty( X ), empty( Y ), ! empty(
% 2.12/2.50 cartesian_product2( X, Y ) ) }.
% 2.12/2.50 (21060) {G0,W10,D2,L5,V1,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 complete_latt_str( X ), ! latt_str( X ), alpha14( X ) }.
% 2.12/2.50 (21061) {G0,W11,D3,L5,V1,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 complete_latt_str( X ), ! latt_str( X ), complete_relstr(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21062) {G0,W4,D2,L2,V1,M2} { ! alpha14( X ), alpha28( X ) }.
% 2.12/2.50 (21063) {G0,W5,D3,L2,V1,M2} { ! alpha14( X ), with_infima_relstr(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21064) {G0,W7,D3,L3,V1,M3} { ! alpha28( X ), ! with_infima_relstr(
% 2.12/2.50 poset_of_lattice( X ) ), alpha14( X ) }.
% 2.12/2.50 (21065) {G0,W4,D2,L2,V1,M2} { ! alpha28( X ), alpha37( X ) }.
% 2.12/2.50 (21066) {G0,W5,D3,L2,V1,M2} { ! alpha28( X ), with_suprema_relstr(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21067) {G0,W7,D3,L3,V1,M3} { ! alpha37( X ), ! with_suprema_relstr(
% 2.12/2.50 poset_of_lattice( X ) ), alpha28( X ) }.
% 2.12/2.50 (21068) {G0,W4,D2,L2,V1,M2} { ! alpha37( X ), alpha44( X ) }.
% 2.12/2.50 (21069) {G0,W5,D3,L2,V1,M2} { ! alpha37( X ), bounded_relstr(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21070) {G0,W7,D3,L3,V1,M3} { ! alpha44( X ), ! bounded_relstr(
% 2.12/2.50 poset_of_lattice( X ) ), alpha37( X ) }.
% 2.12/2.50 (21071) {G0,W4,D2,L2,V1,M2} { ! alpha44( X ), alpha49( X ) }.
% 2.12/2.50 (21072) {G0,W5,D3,L2,V1,M2} { ! alpha44( X ), upper_bounded_relstr(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21073) {G0,W7,D3,L3,V1,M3} { ! alpha49( X ), ! upper_bounded_relstr(
% 2.12/2.50 poset_of_lattice( X ) ), alpha44( X ) }.
% 2.12/2.50 (21074) {G0,W4,D2,L2,V1,M2} { ! alpha49( X ), alpha52( X ) }.
% 2.12/2.50 (21075) {G0,W5,D3,L2,V1,M2} { ! alpha49( X ), lower_bounded_relstr(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21076) {G0,W7,D3,L3,V1,M3} { ! alpha52( X ), ! lower_bounded_relstr(
% 2.12/2.50 poset_of_lattice( X ) ), alpha49( X ) }.
% 2.12/2.50 (21077) {G0,W4,D2,L2,V1,M2} { ! alpha52( X ), alpha54( X ) }.
% 2.12/2.50 (21078) {G0,W5,D3,L2,V1,M2} { ! alpha52( X ), antisymmetric_relstr(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21079) {G0,W7,D3,L3,V1,M3} { ! alpha54( X ), ! antisymmetric_relstr(
% 2.12/2.50 poset_of_lattice( X ) ), alpha52( X ) }.
% 2.12/2.50 (21080) {G0,W4,D2,L2,V1,M2} { ! alpha54( X ), alpha56( X ) }.
% 2.12/2.50 (21081) {G0,W5,D3,L2,V1,M2} { ! alpha54( X ), transitive_relstr(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21082) {G0,W7,D3,L3,V1,M3} { ! alpha56( X ), ! transitive_relstr(
% 2.12/2.50 poset_of_lattice( X ) ), alpha54( X ) }.
% 2.12/2.50 (21083) {G0,W5,D3,L2,V1,M2} { ! alpha56( X ), ! empty_carrier(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21084) {G0,W5,D3,L2,V1,M2} { ! alpha56( X ), strict_rel_str(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21085) {G0,W5,D3,L2,V1,M2} { ! alpha56( X ), reflexive_relstr(
% 2.12/2.50 poset_of_lattice( X ) ) }.
% 2.12/2.50 (21086) {G0,W11,D3,L4,V1,M4} { empty_carrier( poset_of_lattice( X ) ), !
% 2.12/2.50 strict_rel_str( poset_of_lattice( X ) ), ! reflexive_relstr(
% 2.12/2.50 poset_of_lattice( X ) ), alpha56( X ) }.
% 2.12/2.50 (21087) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_POSet( X ) ) }.
% 2.12/2.50 (21088) {G0,W3,D3,L1,V1,M1} { strict_rel_str( boole_POSet( X ) ) }.
% 2.12/2.50 (21089) {G0,W3,D3,L1,V1,M1} { reflexive_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21090) {G0,W3,D3,L1,V1,M1} { transitive_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21091) {G0,W3,D3,L1,V1,M1} { antisymmetric_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21092) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_POSet( X ) ) }.
% 2.12/2.50 (21093) {G0,W3,D3,L1,V1,M1} { strict_rel_str( boole_POSet( X ) ) }.
% 2.12/2.50 (21094) {G0,W3,D3,L1,V1,M1} { reflexive_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21095) {G0,W3,D3,L1,V1,M1} { transitive_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21096) {G0,W3,D3,L1,V1,M1} { antisymmetric_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21097) {G0,W3,D3,L1,V1,M1} { lower_bounded_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21098) {G0,W3,D3,L1,V1,M1} { upper_bounded_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21099) {G0,W3,D3,L1,V1,M1} { bounded_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21100) {G0,W3,D3,L1,V1,M1} { with_suprema_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21101) {G0,W3,D3,L1,V1,M1} { with_infima_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21102) {G0,W3,D3,L1,V1,M1} { complete_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 (21103) {G0,W16,D3,L4,V5,M4} { empty_carrier( X ), ! latt_str( X ), ! in(
% 2.12/2.50 Y, a_2_2_lattice3( X, Z ) ), element( skol9( X, T, U ), the_carrier( X )
% 2.12/2.50 ) }.
% 2.12/2.50 (21104) {G0,W17,D3,L4,V3,M4} { empty_carrier( X ), ! latt_str( X ), ! in(
% 2.12/2.50 Y, a_2_2_lattice3( X, Z ) ), alpha1( X, Y, Z, skol9( X, Y, Z ) ) }.
% 2.12/2.50 (21105) {G0,W18,D3,L5,V4,M5} { empty_carrier( X ), ! latt_str( X ), !
% 2.12/2.50 element( T, the_carrier( X ) ), ! alpha1( X, Y, Z, T ), in( Y,
% 2.12/2.50 a_2_2_lattice3( X, Z ) ) }.
% 2.12/2.50 (21106) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Y = T }.
% 2.12/2.50 (21107) {G0,W9,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), latt_set_smaller( X
% 2.12/2.50 , T, Z ) }.
% 2.12/2.50 (21108) {G0,W12,D2,L3,V4,M3} { ! Y = T, ! latt_set_smaller( X, T, Z ),
% 2.12/2.50 alpha1( X, Y, Z, T ) }.
% 2.12/2.50 (21109) {G0,W14,D3,L3,V4,M3} { ! relation_of2( Y, X, X ), ! rel_str_of( X
% 2.12/2.50 , Y ) = rel_str_of( Z, T ), X = Z }.
% 2.12/2.50 (21110) {G0,W14,D3,L3,V4,M3} { ! relation_of2( Y, X, X ), ! rel_str_of( X
% 2.12/2.50 , Y ) = rel_str_of( Z, T ), Y = T }.
% 2.12/2.50 (21111) {G0,W40,D3,L8,V6,M8} { ! function( Y ), ! quasi_total( Y,
% 2.12/2.50 cartesian_product2( X, X ), X ), ! relation_of2( Y, cartesian_product2( X
% 2.12/2.50 , X ), X ), ! function( Z ), ! quasi_total( Z, cartesian_product2( X, X )
% 2.12/2.50 , X ), ! relation_of2( Z, cartesian_product2( X, X ), X ), ! latt_str_of
% 2.12/2.50 ( X, Y, Z ) = latt_str_of( T, U, W ), X = T }.
% 2.12/2.50 (21112) {G0,W40,D3,L8,V6,M8} { ! function( Y ), ! quasi_total( Y,
% 2.12/2.50 cartesian_product2( X, X ), X ), ! relation_of2( Y, cartesian_product2( X
% 2.12/2.50 , X ), X ), ! function( Z ), ! quasi_total( Z, cartesian_product2( X, X )
% 2.12/2.50 , X ), ! relation_of2( Z, cartesian_product2( X, X ), X ), ! latt_str_of
% 2.12/2.50 ( X, Y, Z ) = latt_str_of( T, U, W ), Y = U }.
% 2.12/2.50 (21113) {G0,W40,D3,L8,V6,M8} { ! function( Y ), ! quasi_total( Y,
% 2.12/2.50 cartesian_product2( X, X ), X ), ! relation_of2( Y, cartesian_product2( X
% 2.12/2.50 , X ), X ), ! function( Z ), ! quasi_total( Z, cartesian_product2( X, X )
% 2.12/2.50 , X ), ! relation_of2( Z, cartesian_product2( X, X ), X ), ! latt_str_of
% 2.12/2.50 ( X, Y, Z ) = latt_str_of( T, U, W ), Z = W }.
% 2.12/2.50 (21114) {G0,W2,D2,L1,V0,M1} { latt_str( skol10 ) }.
% 2.12/2.50 (21115) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol10 ) }.
% 2.12/2.50 (21116) {G0,W2,D2,L1,V0,M1} { strict_latt_str( skol10 ) }.
% 2.12/2.50 (21117) {G0,W2,D2,L1,V0,M1} { join_commutative( skol10 ) }.
% 2.12/2.50 (21118) {G0,W2,D2,L1,V0,M1} { join_associative( skol10 ) }.
% 2.12/2.50 (21119) {G0,W2,D2,L1,V0,M1} { meet_commutative( skol10 ) }.
% 2.12/2.50 (21120) {G0,W2,D2,L1,V0,M1} { meet_associative( skol10 ) }.
% 2.12/2.50 (21121) {G0,W2,D2,L1,V0,M1} { meet_absorbing( skol10 ) }.
% 2.12/2.50 (21122) {G0,W2,D2,L1,V0,M1} { join_absorbing( skol10 ) }.
% 2.12/2.50 (21123) {G0,W2,D2,L1,V0,M1} { lattice( skol10 ) }.
% 2.12/2.50 (21124) {G0,W2,D2,L1,V0,M1} { distributive_lattstr( skol10 ) }.
% 2.12/2.50 (21125) {G0,W2,D2,L1,V0,M1} { modular_lattstr( skol10 ) }.
% 2.12/2.50 (21126) {G0,W2,D2,L1,V0,M1} { lower_bounded_semilattstr( skol10 ) }.
% 2.12/2.50 (21127) {G0,W2,D2,L1,V0,M1} { upper_bounded_semilattstr( skol10 ) }.
% 2.12/2.50 (21128) {G0,W2,D2,L1,V0,M1} { latt_str( skol11 ) }.
% 2.12/2.50 (21129) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol11 ) }.
% 2.12/2.50 (21130) {G0,W2,D2,L1,V0,M1} { strict_latt_str( skol11 ) }.
% 2.12/2.50 (21131) {G0,W2,D2,L1,V0,M1} { join_commutative( skol11 ) }.
% 2.12/2.50 (21132) {G0,W2,D2,L1,V0,M1} { join_associative( skol11 ) }.
% 2.12/2.50 (21133) {G0,W2,D2,L1,V0,M1} { meet_commutative( skol11 ) }.
% 2.12/2.50 (21134) {G0,W2,D2,L1,V0,M1} { meet_associative( skol11 ) }.
% 2.12/2.50 (21135) {G0,W2,D2,L1,V0,M1} { meet_absorbing( skol11 ) }.
% 2.12/2.50 (21136) {G0,W2,D2,L1,V0,M1} { join_absorbing( skol11 ) }.
% 2.12/2.50 (21137) {G0,W2,D2,L1,V0,M1} { lattice( skol11 ) }.
% 2.12/2.50 (21138) {G0,W2,D2,L1,V0,M1} { lower_bounded_semilattstr( skol11 ) }.
% 2.12/2.50 (21139) {G0,W2,D2,L1,V0,M1} { upper_bounded_semilattstr( skol11 ) }.
% 2.12/2.50 (21140) {G0,W2,D2,L1,V0,M1} { bounded_lattstr( skol11 ) }.
% 2.12/2.50 (21141) {G0,W2,D2,L1,V0,M1} { latt_str( skol12 ) }.
% 2.12/2.50 (21142) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol12 ) }.
% 2.12/2.50 (21143) {G0,W2,D2,L1,V0,M1} { strict_latt_str( skol12 ) }.
% 2.12/2.50 (21144) {G0,W2,D2,L1,V0,M1} { join_commutative( skol12 ) }.
% 2.12/2.50 (21145) {G0,W2,D2,L1,V0,M1} { join_associative( skol12 ) }.
% 2.12/2.50 (21146) {G0,W2,D2,L1,V0,M1} { meet_commutative( skol12 ) }.
% 2.12/2.50 (21147) {G0,W2,D2,L1,V0,M1} { meet_associative( skol12 ) }.
% 2.12/2.50 (21148) {G0,W2,D2,L1,V0,M1} { meet_absorbing( skol12 ) }.
% 2.12/2.50 (21149) {G0,W2,D2,L1,V0,M1} { join_absorbing( skol12 ) }.
% 2.12/2.50 (21150) {G0,W2,D2,L1,V0,M1} { lattice( skol12 ) }.
% 2.12/2.50 (21151) {G0,W2,D2,L1,V0,M1} { lower_bounded_semilattstr( skol12 ) }.
% 2.12/2.50 (21152) {G0,W2,D2,L1,V0,M1} { upper_bounded_semilattstr( skol12 ) }.
% 2.12/2.50 (21153) {G0,W2,D2,L1,V0,M1} { bounded_lattstr( skol12 ) }.
% 2.12/2.50 (21154) {G0,W2,D2,L1,V0,M1} { complemented_lattstr( skol12 ) }.
% 2.12/2.50 (21155) {G0,W2,D2,L1,V0,M1} { latt_str( skol13 ) }.
% 2.12/2.50 (21156) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol13 ) }.
% 2.12/2.50 (21157) {G0,W2,D2,L1,V0,M1} { strict_latt_str( skol13 ) }.
% 2.12/2.50 (21158) {G0,W2,D2,L1,V0,M1} { join_commutative( skol13 ) }.
% 2.12/2.50 (21159) {G0,W2,D2,L1,V0,M1} { join_associative( skol13 ) }.
% 2.12/2.50 (21160) {G0,W2,D2,L1,V0,M1} { meet_commutative( skol13 ) }.
% 2.12/2.50 (21161) {G0,W2,D2,L1,V0,M1} { meet_associative( skol13 ) }.
% 2.12/2.50 (21162) {G0,W2,D2,L1,V0,M1} { meet_absorbing( skol13 ) }.
% 2.12/2.50 (21163) {G0,W2,D2,L1,V0,M1} { join_absorbing( skol13 ) }.
% 2.12/2.50 (21164) {G0,W2,D2,L1,V0,M1} { lattice( skol13 ) }.
% 2.12/2.50 (21165) {G0,W2,D2,L1,V0,M1} { distributive_lattstr( skol13 ) }.
% 2.12/2.50 (21166) {G0,W2,D2,L1,V0,M1} { lower_bounded_semilattstr( skol13 ) }.
% 2.12/2.50 (21167) {G0,W2,D2,L1,V0,M1} { upper_bounded_semilattstr( skol13 ) }.
% 2.12/2.50 (21168) {G0,W2,D2,L1,V0,M1} { bounded_lattstr( skol13 ) }.
% 2.12/2.50 (21169) {G0,W2,D2,L1,V0,M1} { complemented_lattstr( skol13 ) }.
% 2.12/2.50 (21170) {G0,W2,D2,L1,V0,M1} { boolean_lattstr( skol13 ) }.
% 2.12/2.50 (21171) {G0,W2,D2,L1,V0,M1} { rel_str( skol14 ) }.
% 2.12/2.50 (21172) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol14 ) }.
% 2.12/2.50 (21173) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol14 ) }.
% 2.12/2.50 (21174) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol14 ) }.
% 2.12/2.50 (21175) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol14 ) }.
% 2.12/2.50 (21176) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol14 ) }.
% 2.12/2.50 (21177) {G0,W2,D2,L1,V0,M1} { complete_relstr( skol14 ) }.
% 2.12/2.50 (21178) {G0,W2,D2,L1,V0,M1} { rel_str( skol15 ) }.
% 2.12/2.50 (21179) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol15 ) }.
% 2.12/2.50 (21180) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol16( Y ) ) }.
% 2.12/2.50 (21181) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol16( X ), powerset(
% 2.12/2.50 X ) ) }.
% 2.12/2.50 (21182) {G0,W2,D2,L1,V0,M1} { empty( skol17 ) }.
% 2.12/2.50 (21183) {G0,W2,D2,L1,V0,M1} { rel_str( skol18 ) }.
% 2.12/2.50 (21184) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol18 ) }.
% 2.12/2.50 (21185) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol18 ) }.
% 2.12/2.50 (21186) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol18 ) }.
% 2.12/2.50 (21187) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol18 ) }.
% 2.12/2.50 (21188) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol18 ) }.
% 2.12/2.50 (21189) {G0,W2,D2,L1,V0,M1} { with_suprema_relstr( skol18 ) }.
% 2.12/2.50 (21190) {G0,W2,D2,L1,V0,M1} { with_infima_relstr( skol18 ) }.
% 2.12/2.50 (21191) {G0,W2,D2,L1,V0,M1} { complete_relstr( skol18 ) }.
% 2.12/2.50 (21192) {G0,W2,D2,L1,V0,M1} { rel_str( skol19 ) }.
% 2.12/2.50 (21193) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol19 ) }.
% 2.12/2.50 (21194) {G0,W2,D2,L1,V0,M1} { strict_rel_str( skol19 ) }.
% 2.12/2.50 (21195) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol19 ) }.
% 2.12/2.50 (21196) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol19 ) }.
% 2.12/2.50 (21197) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol19 ) }.
% 2.12/2.50 (21198) {G0,W4,D3,L1,V2,M1} { relation( skol20( Z, T ) ) }.
% 2.12/2.50 (21199) {G0,W4,D3,L1,V2,M1} { function( skol20( Z, T ) ) }.
% 2.12/2.50 (21200) {G0,W6,D3,L1,V2,M1} { relation_of2( skol20( X, Y ), X, Y ) }.
% 2.12/2.50 (21201) {G0,W3,D3,L1,V1,M1} { empty( skol21( Y ) ) }.
% 2.12/2.50 (21202) {G0,W5,D3,L1,V1,M1} { element( skol21( X ), powerset( X ) ) }.
% 2.12/2.50 (21203) {G0,W2,D2,L1,V0,M1} { ! empty( skol22 ) }.
% 2.12/2.50 (21204) {G0,W2,D2,L1,V0,M1} { rel_str( skol23 ) }.
% 2.12/2.50 (21205) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol23 ) }.
% 2.12/2.50 (21206) {G0,W2,D2,L1,V0,M1} { reflexive_relstr( skol23 ) }.
% 2.12/2.50 (21207) {G0,W2,D2,L1,V0,M1} { transitive_relstr( skol23 ) }.
% 2.12/2.50 (21208) {G0,W2,D2,L1,V0,M1} { antisymmetric_relstr( skol23 ) }.
% 2.12/2.50 (21209) {G0,W2,D2,L1,V0,M1} { with_suprema_relstr( skol23 ) }.
% 2.12/2.50 (21210) {G0,W2,D2,L1,V0,M1} { with_infima_relstr( skol23 ) }.
% 2.12/2.50 (21211) {G0,W2,D2,L1,V0,M1} { complete_relstr( skol23 ) }.
% 2.12/2.50 (21212) {G0,W2,D2,L1,V0,M1} { lower_bounded_relstr( skol23 ) }.
% 2.12/2.50 (21213) {G0,W2,D2,L1,V0,M1} { upper_bounded_relstr( skol23 ) }.
% 2.12/2.50 (21214) {G0,W2,D2,L1,V0,M1} { bounded_relstr( skol23 ) }.
% 2.12/2.50 (21215) {G0,W2,D2,L1,V0,M1} { latt_str( skol24 ) }.
% 2.12/2.50 (21216) {G0,W2,D2,L1,V0,M1} { strict_latt_str( skol24 ) }.
% 2.12/2.50 (21217) {G0,W2,D2,L1,V0,M1} { one_sorted_str( skol25 ) }.
% 2.12/2.50 (21218) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol25 ) }.
% 2.12/2.50 (21219) {G0,W7,D3,L3,V2,M3} { empty_carrier( X ), ! one_sorted_str( X ), !
% 2.12/2.50 empty( skol26( Y ) ) }.
% 2.12/2.50 (21220) {G0,W10,D4,L3,V1,M3} { empty_carrier( X ), ! one_sorted_str( X ),
% 2.12/2.50 element( skol26( X ), powerset( the_carrier( X ) ) ) }.
% 2.12/2.50 (21221) {G0,W2,D2,L1,V0,M1} { latt_str( skol27 ) }.
% 2.12/2.50 (21222) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol27 ) }.
% 2.12/2.50 (21223) {G0,W2,D2,L1,V0,M1} { strict_latt_str( skol27 ) }.
% 2.12/2.50 (21224) {G0,W2,D2,L1,V0,M1} { latt_str( skol28 ) }.
% 2.12/2.50 (21225) {G0,W2,D2,L1,V0,M1} { ! empty_carrier( skol28 ) }.
% 2.12/2.50 (21226) {G0,W2,D2,L1,V0,M1} { strict_latt_str( skol28 ) }.
% 2.12/2.50 (21227) {G0,W2,D2,L1,V0,M1} { join_commutative( skol28 ) }.
% 2.12/2.50 (21228) {G0,W2,D2,L1,V0,M1} { join_associative( skol28 ) }.
% 2.12/2.50 (21229) {G0,W2,D2,L1,V0,M1} { meet_commutative( skol28 ) }.
% 2.12/2.50 (21230) {G0,W2,D2,L1,V0,M1} { meet_associative( skol28 ) }.
% 2.12/2.50 (21231) {G0,W2,D2,L1,V0,M1} { meet_absorbing( skol28 ) }.
% 2.12/2.50 (21232) {G0,W2,D2,L1,V0,M1} { join_absorbing( skol28 ) }.
% 2.12/2.50 (21233) {G0,W2,D2,L1,V0,M1} { lattice( skol28 ) }.
% 2.12/2.50 (21234) {G0,W11,D3,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 latt_str( X ), k2_lattice3( X ) = relation_of_lattice( X ) }.
% 2.12/2.50 (21235) {G0,W8,D2,L2,V3,M2} { ! relation_of2_as_subset( Z, X, Y ),
% 2.12/2.50 relation_of2( Z, X, Y ) }.
% 2.12/2.50 (21236) {G0,W8,D2,L2,V3,M2} { ! relation_of2( Z, X, Y ),
% 2.12/2.50 relation_of2_as_subset( Z, X, Y ) }.
% 2.12/2.50 (21237) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 2.12/2.50 (21238) {G0,W5,D4,L1,V0,M1} { ! bottom_of_relstr( boole_POSet( skol29 ) )
% 2.12/2.50 = empty_set }.
% 2.12/2.50 (21239) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 2.12/2.50 (21240) {G0,W16,D4,L5,V2,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 complete_latt_str( X ), ! latt_str( X ), join_of_latt_set( X, Y ) =
% 2.12/2.50 join_on_relstr( poset_of_lattice( X ), Y ) }.
% 2.12/2.50 (21241) {G0,W16,D4,L5,V2,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 complete_latt_str( X ), ! latt_str( X ), meet_of_latt_set( X, Y ) =
% 2.12/2.50 meet_on_relstr( poset_of_lattice( X ), Y ) }.
% 2.12/2.50 (21242) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 2.12/2.50 }.
% 2.12/2.50 (21243) {G0,W14,D3,L3,V2,M3} { alpha15( X, Y, skol30( X, Y ) ), in( skol30
% 2.12/2.50 ( X, Y ), Y ), X = Y }.
% 2.12/2.50 (21244) {G0,W14,D3,L3,V2,M3} { alpha15( X, Y, skol30( X, Y ) ), ! in(
% 2.12/2.50 skol30( X, Y ), X ), X = Y }.
% 2.12/2.50 (21245) {G0,W7,D2,L2,V3,M2} { ! alpha15( X, Y, Z ), in( Z, X ) }.
% 2.12/2.50 (21246) {G0,W7,D2,L2,V3,M2} { ! alpha15( X, Y, Z ), ! in( Z, Y ) }.
% 2.12/2.50 (21247) {G0,W10,D2,L3,V3,M3} { ! in( Z, X ), in( Z, Y ), alpha15( X, Y, Z
% 2.12/2.50 ) }.
% 2.12/2.50 (21248) {G0,W3,D3,L1,V1,M1} { lower_bounded_semilattstr( boole_lattice( X
% 2.12/2.50 ) ) }.
% 2.12/2.50 (21249) {G0,W5,D4,L1,V1,M1} { bottom_of_semilattstr( boole_lattice( X ) )
% 2.12/2.50 = empty_set }.
% 2.12/2.50 (21250) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 2.12/2.50 ) }.
% 2.12/2.50 (21251) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 2.12/2.50 ) }.
% 2.12/2.50 (21252) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 2.12/2.50 , element( X, Y ) }.
% 2.12/2.50 (21253) {G0,W10,D2,L5,V1,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 complete_latt_str( X ), ! latt_str( X ), alpha16( X ) }.
% 2.12/2.50 (21254) {G0,W14,D3,L5,V1,M5} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 complete_latt_str( X ), ! latt_str( X ), bottom_of_semilattstr( X ) =
% 2.12/2.50 join_of_latt_set( X, empty_set ) }.
% 2.12/2.50 (21255) {G0,W4,D2,L2,V1,M2} { ! alpha16( X ), alpha29( X ) }.
% 2.12/2.50 (21256) {G0,W4,D2,L2,V1,M2} { ! alpha16( X ), latt_str( X ) }.
% 2.12/2.50 (21257) {G0,W6,D2,L3,V1,M3} { ! alpha29( X ), ! latt_str( X ), alpha16( X
% 2.12/2.50 ) }.
% 2.12/2.50 (21258) {G0,W4,D2,L2,V1,M2} { ! alpha29( X ), ! empty_carrier( X ) }.
% 2.12/2.50 (21259) {G0,W4,D2,L2,V1,M2} { ! alpha29( X ), lattice( X ) }.
% 2.12/2.50 (21260) {G0,W4,D2,L2,V1,M2} { ! alpha29( X ), lower_bounded_semilattstr( X
% 2.12/2.50 ) }.
% 2.12/2.50 (21261) {G0,W8,D2,L4,V1,M4} { empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 lower_bounded_semilattstr( X ), alpha29( X ) }.
% 2.12/2.50 (21262) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 2.12/2.50 , ! empty( Z ) }.
% 2.12/2.50 (21263) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 2.12/2.50 (21264) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 2.12/2.50 (21265) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 2.12/2.50
% 2.12/2.50
% 2.12/2.50 Total Proof:
% 2.12/2.50
% 2.12/2.50 eqswap: (21269) {G0,W8,D3,L2,V1,M2} { join_on_relstr( X, empty_set ) =
% 2.12/2.50 bottom_of_relstr( X ), ! rel_str( X ) }.
% 2.12/2.50 parent0[1]: (20868) {G0,W8,D3,L2,V1,M2} { ! rel_str( X ), bottom_of_relstr
% 2.12/2.50 ( X ) = join_on_relstr( X, empty_set ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (92) {G0,W8,D3,L2,V1,M2} I { ! rel_str( X ), join_on_relstr( X
% 2.12/2.50 , empty_set ) ==> bottom_of_relstr( X ) }.
% 2.12/2.50 parent0: (21269) {G0,W8,D3,L2,V1,M2} { join_on_relstr( X, empty_set ) =
% 2.12/2.50 bottom_of_relstr( X ), ! rel_str( X ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 1
% 2.12/2.50 1 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 eqswap: (21276) {G0,W6,D4,L1,V1,M1} { poset_of_lattice( boole_lattice( X )
% 2.12/2.50 ) = boole_POSet( X ) }.
% 2.12/2.50 parent0[0]: (20871) {G0,W6,D4,L1,V1,M1} { boole_POSet( X ) =
% 2.12/2.50 poset_of_lattice( boole_lattice( X ) ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (95) {G0,W6,D4,L1,V1,M1} I { poset_of_lattice( boole_lattice(
% 2.12/2.50 X ) ) ==> boole_POSet( X ) }.
% 2.12/2.50 parent0: (21276) {G0,W6,D4,L1,V1,M1} { poset_of_lattice( boole_lattice( X
% 2.12/2.50 ) ) = boole_POSet( X ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (103) {G0,W3,D3,L1,V1,M1} I { latt_str( boole_lattice( X ) )
% 2.12/2.50 }.
% 2.12/2.50 parent0: (20879) {G0,W3,D3,L1,V1,M1} { latt_str( boole_lattice( X ) ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (127) {G0,W3,D3,L1,V1,M1} I { rel_str( boole_POSet( X ) ) }.
% 2.12/2.50 parent0: (20905) {G0,W3,D3,L1,V1,M1} { rel_str( boole_POSet( X ) ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (151) {G0,W3,D3,L1,V1,M1} I { ! empty_carrier( boole_lattice(
% 2.12/2.50 X ) ) }.
% 2.12/2.50 parent0: (20933) {G0,W3,D3,L1,V1,M1} { ! empty_carrier( boole_lattice( X )
% 2.12/2.50 ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (158) {G0,W3,D3,L1,V1,M1} I { lattice( boole_lattice( X ) )
% 2.12/2.50 }.
% 2.12/2.50 parent0: (20941) {G0,W3,D3,L1,V1,M1} { lattice( boole_lattice( X ) ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (166) {G0,W3,D3,L1,V1,M1} I { complete_latt_str( boole_lattice
% 2.12/2.50 ( X ) ) }.
% 2.12/2.50 parent0: (20949) {G0,W3,D3,L1,V1,M1} { complete_latt_str( boole_lattice( X
% 2.12/2.50 ) ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (170) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 2.12/2.50 parent0: (20956) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (418) {G0,W5,D4,L1,V0,M1} I { ! bottom_of_relstr( boole_POSet
% 2.12/2.50 ( skol29 ) ) ==> empty_set }.
% 2.12/2.50 parent0: (21238) {G0,W5,D4,L1,V0,M1} { ! bottom_of_relstr( boole_POSet(
% 2.12/2.50 skol29 ) ) = empty_set }.
% 2.12/2.50 substitution0:
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 eqswap: (21593) {G0,W16,D4,L5,V2,M5} { join_on_relstr( poset_of_lattice( X
% 2.12/2.50 ), Y ) = join_of_latt_set( X, Y ), empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 complete_latt_str( X ), ! latt_str( X ) }.
% 2.12/2.50 parent0[4]: (21240) {G0,W16,D4,L5,V2,M5} { empty_carrier( X ), ! lattice(
% 2.12/2.50 X ), ! complete_latt_str( X ), ! latt_str( X ), join_of_latt_set( X, Y )
% 2.12/2.50 = join_on_relstr( poset_of_lattice( X ), Y ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 Y := Y
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (420) {G0,W16,D4,L5,V2,M5} I { empty_carrier( X ), ! lattice(
% 2.12/2.50 X ), ! complete_latt_str( X ), ! latt_str( X ), join_on_relstr(
% 2.12/2.50 poset_of_lattice( X ), Y ) ==> join_of_latt_set( X, Y ) }.
% 2.12/2.50 parent0: (21593) {G0,W16,D4,L5,V2,M5} { join_on_relstr( poset_of_lattice(
% 2.12/2.50 X ), Y ) = join_of_latt_set( X, Y ), empty_carrier( X ), ! lattice( X ),
% 2.12/2.50 ! complete_latt_str( X ), ! latt_str( X ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 Y := Y
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 4
% 2.12/2.50 1 ==> 0
% 2.12/2.50 2 ==> 1
% 2.12/2.50 3 ==> 2
% 2.12/2.50 4 ==> 3
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 *** allocated 576640 integers for termspace/termends
% 2.12/2.50 subsumption: (423) {G0,W14,D3,L3,V2,M3} I { alpha15( X, Y, skol30( X, Y ) )
% 2.12/2.50 , in( skol30( X, Y ), Y ), X = Y }.
% 2.12/2.50 parent0: (21243) {G0,W14,D3,L3,V2,M3} { alpha15( X, Y, skol30( X, Y ) ),
% 2.12/2.50 in( skol30( X, Y ), Y ), X = Y }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 Y := Y
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 1 ==> 1
% 2.12/2.50 2 ==> 2
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (425) {G0,W7,D2,L2,V3,M2} I { ! alpha15( X, Y, Z ), in( Z, X )
% 2.12/2.50 }.
% 2.12/2.50 parent0: (21245) {G0,W7,D2,L2,V3,M2} { ! alpha15( X, Y, Z ), in( Z, X )
% 2.12/2.50 }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 Y := Y
% 2.12/2.50 Z := Z
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 1 ==> 1
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (428) {G0,W5,D4,L1,V1,M1} I { bottom_of_semilattstr(
% 2.12/2.50 boole_lattice( X ) ) ==> empty_set }.
% 2.12/2.50 parent0: (21249) {G0,W5,D4,L1,V1,M1} { bottom_of_semilattstr(
% 2.12/2.50 boole_lattice( X ) ) = empty_set }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 eqswap: (22039) {G0,W14,D3,L5,V1,M5} { join_of_latt_set( X, empty_set ) =
% 2.12/2.50 bottom_of_semilattstr( X ), empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 complete_latt_str( X ), ! latt_str( X ) }.
% 2.12/2.50 parent0[4]: (21254) {G0,W14,D3,L5,V1,M5} { empty_carrier( X ), ! lattice(
% 2.12/2.50 X ), ! complete_latt_str( X ), ! latt_str( X ), bottom_of_semilattstr( X
% 2.12/2.50 ) = join_of_latt_set( X, empty_set ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (433) {G0,W14,D3,L5,V1,M5} I { empty_carrier( X ), ! lattice(
% 2.12/2.50 X ), ! complete_latt_str( X ), ! latt_str( X ), join_of_latt_set( X,
% 2.12/2.50 empty_set ) ==> bottom_of_semilattstr( X ) }.
% 2.12/2.50 parent0: (22039) {G0,W14,D3,L5,V1,M5} { join_of_latt_set( X, empty_set ) =
% 2.12/2.50 bottom_of_semilattstr( X ), empty_carrier( X ), ! lattice( X ), !
% 2.12/2.50 complete_latt_str( X ), ! latt_str( X ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 4
% 2.12/2.50 1 ==> 0
% 2.12/2.50 2 ==> 1
% 2.12/2.50 3 ==> 2
% 2.12/2.50 4 ==> 3
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (443) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 2.12/2.50 parent0: (21264) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 Y := Y
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 1 ==> 1
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 eqswap: (22154) {G0,W8,D3,L2,V1,M2} { bottom_of_relstr( X ) ==>
% 2.12/2.50 join_on_relstr( X, empty_set ), ! rel_str( X ) }.
% 2.12/2.50 parent0[1]: (92) {G0,W8,D3,L2,V1,M2} I { ! rel_str( X ), join_on_relstr( X
% 2.12/2.50 , empty_set ) ==> bottom_of_relstr( X ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 resolution: (22155) {G1,W8,D4,L1,V1,M1} { bottom_of_relstr( boole_POSet( X
% 2.12/2.50 ) ) ==> join_on_relstr( boole_POSet( X ), empty_set ) }.
% 2.12/2.50 parent0[1]: (22154) {G0,W8,D3,L2,V1,M2} { bottom_of_relstr( X ) ==>
% 2.12/2.50 join_on_relstr( X, empty_set ), ! rel_str( X ) }.
% 2.12/2.50 parent1[0]: (127) {G0,W3,D3,L1,V1,M1} I { rel_str( boole_POSet( X ) ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := boole_POSet( X )
% 2.12/2.50 end
% 2.12/2.50 substitution1:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 eqswap: (22156) {G1,W8,D4,L1,V1,M1} { join_on_relstr( boole_POSet( X ),
% 2.12/2.50 empty_set ) ==> bottom_of_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 parent0[0]: (22155) {G1,W8,D4,L1,V1,M1} { bottom_of_relstr( boole_POSet( X
% 2.12/2.50 ) ) ==> join_on_relstr( boole_POSet( X ), empty_set ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 subsumption: (1807) {G1,W8,D4,L1,V1,M1} R(92,127) { join_on_relstr(
% 2.12/2.50 boole_POSet( X ), empty_set ) ==> bottom_of_relstr( boole_POSet( X ) )
% 2.12/2.50 }.
% 2.12/2.50 parent0: (22156) {G1,W8,D4,L1,V1,M1} { join_on_relstr( boole_POSet( X ),
% 2.12/2.50 empty_set ) ==> bottom_of_relstr( boole_POSet( X ) ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50 permutation0:
% 2.12/2.50 0 ==> 0
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 eqswap: (22157) {G0,W16,D4,L5,V2,M5} { join_of_latt_set( X, Y ) ==>
% 2.12/2.50 join_on_relstr( poset_of_lattice( X ), Y ), empty_carrier( X ), ! lattice
% 2.12/2.50 ( X ), ! complete_latt_str( X ), ! latt_str( X ) }.
% 2.12/2.50 parent0[4]: (420) {G0,W16,D4,L5,V2,M5} I { empty_carrier( X ), ! lattice( X
% 2.12/2.50 ), ! complete_latt_str( X ), ! latt_str( X ), join_on_relstr(
% 2.12/2.50 poset_of_lattice( X ), Y ) ==> join_of_latt_set( X, Y ) }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := X
% 2.12/2.50 Y := Y
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 resolution: (22159) {G1,W19,D5,L4,V2,M4} { join_of_latt_set( boole_lattice
% 2.12/2.50 ( X ), Y ) ==> join_on_relstr( poset_of_lattice( boole_lattice( X ) ), Y
% 2.12/2.50 ), empty_carrier( boole_lattice( X ) ), ! lattice( boole_lattice( X ) )
% 2.12/2.50 , ! complete_latt_str( boole_lattice( X ) ) }.
% 2.12/2.50 parent0[4]: (22157) {G0,W16,D4,L5,V2,M5} { join_of_latt_set( X, Y ) ==>
% 2.12/2.50 join_on_relstr( poset_of_lattice( X ), Y ), empty_carrier( X ), ! lattice
% 2.12/2.50 ( X ), ! complete_latt_str( X ), ! latt_str( X ) }.
% 2.12/2.50 parent1[0]: (103) {G0,W3,D3,L1,V1,M1} I { latt_str( boole_lattice( X ) )
% 2.12/2.50 }.
% 2.12/2.50 substitution0:
% 2.12/2.50 X := boole_lattice( X )
% 2.12/2.50 Y := Y
% 2.12/2.50 end
% 2.12/2.50 substitution1:
% 2.12/2.50 X := X
% 2.12/2.50 end
% 2.12/2.50
% 2.12/2.50 paramod: (22160) {G1,W18,D4,L4,V2,M4} { join_of_latt_set( boole_lattice( X
% 2.12/2.50 ), Y ) ==> join_on_relstr( boole_POSet( X ), Y ), empty_carrier(
% 2.12/2.50 boole_lattice( X ) ), ! lattice( boole_lattice( X ) ), !
% 2.12/2.50 complete_latt_str( boole_lattice( X ) ) }.
% 2.12/2.50 parent0[0]: (95) {G0,W6,D4,L1,V1,M1} I { poset_of_lattice( boole_lattice( X
% 4.41/4.80 ) ) ==> boole_POSet( X ) }.
% 4.41/4.80 parent1[0; 6]: (22159) {G1,W19,D5,L4,V2,M4} { join_of_latt_set(
% 4.41/4.80 boole_lattice( X ), Y ) ==> join_on_relstr( poset_of_lattice(
% 4.41/4.80 boole_lattice( X ) ), Y ), empty_carrier( boole_lattice( X ) ), ! lattice
% 4.41/4.80 ( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := X
% 4.41/4.80 Y := Y
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 resolution: (22161) {G1,W15,D4,L3,V2,M3} { join_of_latt_set( boole_lattice
% 4.41/4.80 ( X ), Y ) ==> join_on_relstr( boole_POSet( X ), Y ), ! lattice(
% 4.41/4.80 boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 parent0[0]: (151) {G0,W3,D3,L1,V1,M1} I { ! empty_carrier( boole_lattice( X
% 4.41/4.80 ) ) }.
% 4.41/4.80 parent1[1]: (22160) {G1,W18,D4,L4,V2,M4} { join_of_latt_set( boole_lattice
% 4.41/4.80 ( X ), Y ) ==> join_on_relstr( boole_POSet( X ), Y ), empty_carrier(
% 4.41/4.80 boole_lattice( X ) ), ! lattice( boole_lattice( X ) ), !
% 4.41/4.80 complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := X
% 4.41/4.80 Y := Y
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 subsumption: (10651) {G1,W15,D4,L3,V2,M3} R(420,103);d(95);r(151) { !
% 4.41/4.80 lattice( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) )
% 4.41/4.80 , join_of_latt_set( boole_lattice( X ), Y ) ==> join_on_relstr(
% 4.41/4.80 boole_POSet( X ), Y ) }.
% 4.41/4.80 parent0: (22161) {G1,W15,D4,L3,V2,M3} { join_of_latt_set( boole_lattice( X
% 4.41/4.80 ), Y ) ==> join_on_relstr( boole_POSet( X ), Y ), ! lattice(
% 4.41/4.80 boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 Y := Y
% 4.41/4.80 end
% 4.41/4.80 permutation0:
% 4.41/4.80 0 ==> 2
% 4.41/4.80 1 ==> 0
% 4.41/4.80 2 ==> 1
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 *** allocated 15000 integers for justifications
% 4.41/4.80 *** allocated 22500 integers for justifications
% 4.41/4.80 *** allocated 33750 integers for justifications
% 4.41/4.80 *** allocated 50625 integers for justifications
% 4.41/4.80 *** allocated 75937 integers for justifications
% 4.41/4.80 *** allocated 864960 integers for termspace/termends
% 4.41/4.80 *** allocated 113905 integers for justifications
% 4.41/4.80 *** allocated 170857 integers for justifications
% 4.41/4.80 eqswap: (22164) {G0,W5,D4,L1,V0,M1} { ! empty_set ==> bottom_of_relstr(
% 4.41/4.80 boole_POSet( skol29 ) ) }.
% 4.41/4.80 parent0[0]: (418) {G0,W5,D4,L1,V0,M1} I { ! bottom_of_relstr( boole_POSet(
% 4.41/4.80 skol29 ) ) ==> empty_set }.
% 4.41/4.80 substitution0:
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 paramod: (28190) {G1,W20,D5,L3,V1,M3} { ! empty_set ==> X, alpha15(
% 4.41/4.80 bottom_of_relstr( boole_POSet( skol29 ) ), X, skol30( bottom_of_relstr(
% 4.41/4.80 boole_POSet( skol29 ) ), X ) ), in( skol30( bottom_of_relstr( boole_POSet
% 4.41/4.80 ( skol29 ) ), X ), X ) }.
% 4.41/4.80 parent0[2]: (423) {G0,W14,D3,L3,V2,M3} I { alpha15( X, Y, skol30( X, Y ) )
% 4.41/4.80 , in( skol30( X, Y ), Y ), X = Y }.
% 4.41/4.80 parent1[0; 3]: (22164) {G0,W5,D4,L1,V0,M1} { ! empty_set ==>
% 4.41/4.80 bottom_of_relstr( boole_POSet( skol29 ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := bottom_of_relstr( boole_POSet( skol29 ) )
% 4.41/4.80 Y := X
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 eqswap: (28312) {G1,W20,D5,L3,V1,M3} { ! X ==> empty_set, alpha15(
% 4.41/4.80 bottom_of_relstr( boole_POSet( skol29 ) ), X, skol30( bottom_of_relstr(
% 4.41/4.80 boole_POSet( skol29 ) ), X ) ), in( skol30( bottom_of_relstr( boole_POSet
% 4.41/4.80 ( skol29 ) ), X ), X ) }.
% 4.41/4.80 parent0[0]: (28190) {G1,W20,D5,L3,V1,M3} { ! empty_set ==> X, alpha15(
% 4.41/4.80 bottom_of_relstr( boole_POSet( skol29 ) ), X, skol30( bottom_of_relstr(
% 4.41/4.80 boole_POSet( skol29 ) ), X ) ), in( skol30( bottom_of_relstr( boole_POSet
% 4.41/4.80 ( skol29 ) ), X ), X ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 subsumption: (10803) {G1,W20,D5,L3,V1,M3} P(423,418) { ! X = empty_set,
% 4.41/4.80 alpha15( bottom_of_relstr( boole_POSet( skol29 ) ), X, skol30(
% 4.41/4.80 bottom_of_relstr( boole_POSet( skol29 ) ), X ) ), in( skol30(
% 4.41/4.80 bottom_of_relstr( boole_POSet( skol29 ) ), X ), X ) }.
% 4.41/4.80 parent0: (28312) {G1,W20,D5,L3,V1,M3} { ! X ==> empty_set, alpha15(
% 4.41/4.80 bottom_of_relstr( boole_POSet( skol29 ) ), X, skol30( bottom_of_relstr(
% 4.41/4.80 boole_POSet( skol29 ) ), X ) ), in( skol30( bottom_of_relstr( boole_POSet
% 4.41/4.80 ( skol29 ) ), X ), X ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 permutation0:
% 4.41/4.80 0 ==> 0
% 4.41/4.80 1 ==> 1
% 4.41/4.80 2 ==> 2
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 eqswap: (33419) {G0,W14,D3,L5,V1,M5} { bottom_of_semilattstr( X ) ==>
% 4.41/4.80 join_of_latt_set( X, empty_set ), empty_carrier( X ), ! lattice( X ), !
% 4.41/4.80 complete_latt_str( X ), ! latt_str( X ) }.
% 4.41/4.80 parent0[4]: (433) {G0,W14,D3,L5,V1,M5} I { empty_carrier( X ), ! lattice( X
% 4.41/4.80 ), ! complete_latt_str( X ), ! latt_str( X ), join_of_latt_set( X,
% 4.41/4.80 empty_set ) ==> bottom_of_semilattstr( X ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 resolution: (33423) {G1,W17,D4,L4,V1,M4} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> join_of_latt_set( boole_lattice( X ), empty_set
% 4.41/4.80 ), empty_carrier( boole_lattice( X ) ), ! lattice( boole_lattice( X ) )
% 4.41/4.80 , ! complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 parent0[4]: (33419) {G0,W14,D3,L5,V1,M5} { bottom_of_semilattstr( X ) ==>
% 4.41/4.80 join_of_latt_set( X, empty_set ), empty_carrier( X ), ! lattice( X ), !
% 4.41/4.80 complete_latt_str( X ), ! latt_str( X ) }.
% 4.41/4.80 parent1[0]: (103) {G0,W3,D3,L1,V1,M1} I { latt_str( boole_lattice( X ) )
% 4.41/4.80 }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := boole_lattice( X )
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 paramod: (33424) {G2,W23,D4,L6,V1,M6} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> join_on_relstr( boole_POSet( X ), empty_set ), !
% 4.41/4.80 lattice( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) )
% 4.41/4.80 , empty_carrier( boole_lattice( X ) ), ! lattice( boole_lattice( X ) ), !
% 4.41/4.80 complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 parent0[2]: (10651) {G1,W15,D4,L3,V2,M3} R(420,103);d(95);r(151) { !
% 4.41/4.80 lattice( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) )
% 4.41/4.80 , join_of_latt_set( boole_lattice( X ), Y ) ==> join_on_relstr(
% 4.41/4.80 boole_POSet( X ), Y ) }.
% 4.41/4.80 parent1[0; 4]: (33423) {G1,W17,D4,L4,V1,M4} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> join_of_latt_set( boole_lattice( X ), empty_set
% 4.41/4.80 ), empty_carrier( boole_lattice( X ) ), ! lattice( boole_lattice( X ) )
% 4.41/4.80 , ! complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 Y := empty_set
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 factor: (33425) {G2,W20,D4,L5,V1,M5} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> join_on_relstr( boole_POSet( X ), empty_set ), !
% 4.41/4.80 lattice( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) )
% 4.41/4.80 , empty_carrier( boole_lattice( X ) ), ! complete_latt_str( boole_lattice
% 4.41/4.80 ( X ) ) }.
% 4.41/4.80 parent0[1, 4]: (33424) {G2,W23,D4,L6,V1,M6} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> join_on_relstr( boole_POSet( X ), empty_set ), !
% 4.41/4.80 lattice( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) )
% 4.41/4.80 , empty_carrier( boole_lattice( X ) ), ! lattice( boole_lattice( X ) ), !
% 4.41/4.80 complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 factor: (33426) {G2,W17,D4,L4,V1,M4} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> join_on_relstr( boole_POSet( X ), empty_set ), !
% 4.41/4.80 lattice( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) )
% 4.41/4.80 , empty_carrier( boole_lattice( X ) ) }.
% 4.41/4.80 parent0[2, 4]: (33425) {G2,W20,D4,L5,V1,M5} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> join_on_relstr( boole_POSet( X ), empty_set ), !
% 4.41/4.80 lattice( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) )
% 4.41/4.80 , empty_carrier( boole_lattice( X ) ), ! complete_latt_str( boole_lattice
% 4.41/4.80 ( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 paramod: (33427) {G2,W16,D4,L4,V1,M4} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> bottom_of_relstr( boole_POSet( X ) ), ! lattice
% 4.41/4.80 ( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) ),
% 4.41/4.80 empty_carrier( boole_lattice( X ) ) }.
% 4.41/4.80 parent0[0]: (1807) {G1,W8,D4,L1,V1,M1} R(92,127) { join_on_relstr(
% 4.41/4.80 boole_POSet( X ), empty_set ) ==> bottom_of_relstr( boole_POSet( X ) )
% 4.41/4.80 }.
% 4.41/4.80 parent1[0; 4]: (33426) {G2,W17,D4,L4,V1,M4} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> join_on_relstr( boole_POSet( X ), empty_set ), !
% 4.41/4.80 lattice( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) )
% 4.41/4.80 , empty_carrier( boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 paramod: (33428) {G1,W14,D4,L4,V1,M4} { empty_set ==> bottom_of_relstr(
% 4.41/4.80 boole_POSet( X ) ), ! lattice( boole_lattice( X ) ), ! complete_latt_str
% 4.41/4.80 ( boole_lattice( X ) ), empty_carrier( boole_lattice( X ) ) }.
% 4.41/4.80 parent0[0]: (428) {G0,W5,D4,L1,V1,M1} I { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> empty_set }.
% 4.41/4.80 parent1[0; 1]: (33427) {G2,W16,D4,L4,V1,M4} { bottom_of_semilattstr(
% 4.41/4.80 boole_lattice( X ) ) ==> bottom_of_relstr( boole_POSet( X ) ), ! lattice
% 4.41/4.80 ( boole_lattice( X ) ), ! complete_latt_str( boole_lattice( X ) ),
% 4.41/4.80 empty_carrier( boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 resolution: (33429) {G1,W11,D4,L3,V1,M3} { empty_set ==> bottom_of_relstr
% 4.41/4.80 ( boole_POSet( X ) ), ! lattice( boole_lattice( X ) ), !
% 4.41/4.80 complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 parent0[0]: (151) {G0,W3,D3,L1,V1,M1} I { ! empty_carrier( boole_lattice( X
% 4.41/4.80 ) ) }.
% 4.41/4.80 parent1[3]: (33428) {G1,W14,D4,L4,V1,M4} { empty_set ==> bottom_of_relstr
% 4.41/4.80 ( boole_POSet( X ) ), ! lattice( boole_lattice( X ) ), !
% 4.41/4.80 complete_latt_str( boole_lattice( X ) ), empty_carrier( boole_lattice( X
% 4.41/4.80 ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 eqswap: (33430) {G1,W11,D4,L3,V1,M3} { bottom_of_relstr( boole_POSet( X )
% 4.41/4.80 ) ==> empty_set, ! lattice( boole_lattice( X ) ), ! complete_latt_str(
% 4.41/4.80 boole_lattice( X ) ) }.
% 4.41/4.80 parent0[0]: (33429) {G1,W11,D4,L3,V1,M3} { empty_set ==> bottom_of_relstr
% 4.41/4.80 ( boole_POSet( X ) ), ! lattice( boole_lattice( X ) ), !
% 4.41/4.80 complete_latt_str( boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 subsumption: (13237) {G2,W11,D4,L3,V1,M3} R(433,103);d(10651);d(1807);d(428
% 4.41/4.80 );r(151) { ! lattice( boole_lattice( X ) ), ! complete_latt_str(
% 4.41/4.80 boole_lattice( X ) ), bottom_of_relstr( boole_POSet( X ) ) ==> empty_set
% 4.41/4.80 }.
% 4.41/4.80 parent0: (33430) {G1,W11,D4,L3,V1,M3} { bottom_of_relstr( boole_POSet( X )
% 4.41/4.80 ) ==> empty_set, ! lattice( boole_lattice( X ) ), ! complete_latt_str(
% 4.41/4.80 boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 permutation0:
% 4.41/4.80 0 ==> 2
% 4.41/4.80 1 ==> 0
% 4.41/4.80 2 ==> 1
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 resolution: (33431) {G1,W3,D2,L1,V1,M1} { ! in( X, empty_set ) }.
% 4.41/4.80 parent0[1]: (443) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 4.41/4.80 parent1[0]: (170) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 Y := empty_set
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 subsumption: (14089) {G1,W3,D2,L1,V1,M1} R(443,170) { ! in( X, empty_set )
% 4.41/4.80 }.
% 4.41/4.80 parent0: (33431) {G1,W3,D2,L1,V1,M1} { ! in( X, empty_set ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 permutation0:
% 4.41/4.80 0 ==> 0
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 resolution: (33432) {G1,W4,D2,L1,V2,M1} { ! alpha15( empty_set, Y, X ) }.
% 4.41/4.80 parent0[0]: (14089) {G1,W3,D2,L1,V1,M1} R(443,170) { ! in( X, empty_set )
% 4.41/4.80 }.
% 4.41/4.80 parent1[1]: (425) {G0,W7,D2,L2,V3,M2} I { ! alpha15( X, Y, Z ), in( Z, X )
% 4.41/4.80 }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := empty_set
% 4.41/4.80 Y := Y
% 4.41/4.80 Z := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 subsumption: (14091) {G2,W4,D2,L1,V2,M1} R(14089,425) { ! alpha15(
% 4.41/4.80 empty_set, X, Y ) }.
% 4.41/4.80 parent0: (33432) {G1,W4,D2,L1,V2,M1} { ! alpha15( empty_set, Y, X ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := Y
% 4.41/4.80 Y := X
% 4.41/4.80 end
% 4.41/4.80 permutation0:
% 4.41/4.80 0 ==> 0
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 resolution: (33434) {G1,W8,D4,L2,V1,M2} { ! complete_latt_str(
% 4.41/4.80 boole_lattice( X ) ), bottom_of_relstr( boole_POSet( X ) ) ==> empty_set
% 4.41/4.80 }.
% 4.41/4.80 parent0[0]: (13237) {G2,W11,D4,L3,V1,M3} R(433,103);d(10651);d(1807);d(428)
% 4.41/4.80 ;r(151) { ! lattice( boole_lattice( X ) ), ! complete_latt_str(
% 4.41/4.80 boole_lattice( X ) ), bottom_of_relstr( boole_POSet( X ) ) ==> empty_set
% 4.41/4.80 }.
% 4.41/4.80 parent1[0]: (158) {G0,W3,D3,L1,V1,M1} I { lattice( boole_lattice( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 resolution: (33435) {G1,W5,D4,L1,V1,M1} { bottom_of_relstr( boole_POSet( X
% 4.41/4.80 ) ) ==> empty_set }.
% 4.41/4.80 parent0[0]: (33434) {G1,W8,D4,L2,V1,M2} { ! complete_latt_str(
% 4.41/4.80 boole_lattice( X ) ), bottom_of_relstr( boole_POSet( X ) ) ==> empty_set
% 4.41/4.80 }.
% 4.41/4.80 parent1[0]: (166) {G0,W3,D3,L1,V1,M1} I { complete_latt_str( boole_lattice
% 4.41/4.80 ( X ) ) }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 substitution1:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 subsumption: (20209) {G3,W5,D4,L1,V1,M1} S(13237);r(158);r(166) {
% 4.41/4.80 bottom_of_relstr( boole_POSet( X ) ) ==> empty_set }.
% 4.41/4.80 parent0: (33435) {G1,W5,D4,L1,V1,M1} { bottom_of_relstr( boole_POSet( X )
% 4.41/4.80 ) ==> empty_set }.
% 4.41/4.80 substitution0:
% 4.41/4.80 X := X
% 4.41/4.80 end
% 4.41/4.80 permutation0:
% 4.41/4.80 0 ==> 0
% 4.41/4.80 end
% 4.41/4.80
% 4.41/4.80 paramod: (33442) {G2,W18,D5,L3,V1,M3} { in( skol30( empty_set, X ), X ), !
% 4.41/4.80 X = empty_set, alpha15( bottom_of_relstr( boole_POSet( skol29 ) ), X,
% 4.41/4.80 skol30( bottom_of_relstr( boole_POSet( skol29 ) ), X ) ) }.
% 4.41/4.81 parent0[0]: (20209) {G3,W5,D4,L1,V1,M1} S(13237);r(158);r(166) {
% 4.41/4.81 bottom_of_relstr( boole_POSet( X ) ) ==> empty_set }.
% 4.41/4.81 parent1[2; 2]: (10803) {G1,W20,D5,L3,V1,M3} P(423,418) { ! X = empty_set,
% 4.41/4.81 alpha15( bottom_of_relstr( boole_POSet( skol29 ) ), X, skol30(
% 4.41/4.81 bottom_of_relstr( boole_POSet( skol29 ) ), X ) ), in( skol30(
% 4.41/4.81 bottom_of_relstr( boole_POSet( skol29 ) ), X ), X ) }.
% 4.41/4.81 substitution0:
% 4.41/4.81 X := skol29
% 4.41/4.81 end
% 4.41/4.81 substitution1:
% 4.41/4.81 X := X
% 4.41/4.81 end
% 4.41/4.81
% 4.41/4.81 paramod: (33448) {G3,W16,D4,L3,V1,M3} { alpha15( bottom_of_relstr(
% 4.41/4.81 boole_POSet( skol29 ) ), X, skol30( empty_set, X ) ), in( skol30(
% 4.41/4.81 empty_set, X ), X ), ! X = empty_set }.
% 4.41/4.81 parent0[0]: (20209) {G3,W5,D4,L1,V1,M1} S(13237);r(158);r(166) {
% 4.41/4.81 bottom_of_relstr( boole_POSet( X ) ) ==> empty_set }.
% 4.41/4.81 parent1[2; 6]: (33442) {G2,W18,D5,L3,V1,M3} { in( skol30( empty_set, X ),
% 4.41/4.81 X ), ! X = empty_set, alpha15( bottom_of_relstr( boole_POSet( skol29 ) )
% 4.41/4.81 , X, skol30( bottom_of_relstr( boole_POSet( skol29 ) ), X ) ) }.
% 4.41/4.81 substitution0:
% 4.41/4.81 X := skol29
% 4.41/4.81 end
% 4.41/4.81 substitution1:
% 4.41/4.81 X := X
% 4.41/4.81 end
% 4.41/4.81
% 4.41/4.81 paramod: (33449) {G4,W14,D3,L3,V1,M3} { alpha15( empty_set, X, skol30(
% 4.41/4.81 empty_set, X ) ), in( skol30( empty_set, X ), X ), ! X = empty_set }.
% 4.41/4.81 parent0[0]: (20209) {G3,W5,D4,L1,V1,M1} S(13237);r(158);r(166) {
% 4.41/4.81 bottom_of_relstr( boole_POSet( X ) ) ==> empty_set }.
% 4.41/4.81 parent1[0; 1]: (33448) {G3,W16,D4,L3,V1,M3} { alpha15( bottom_of_relstr(
% 4.41/4.81 boole_POSet( skol29 ) ), X, skol30( empty_set, X ) ), in( skol30(
% 4.41/4.81 empty_set, X ), X ), ! X = empty_set }.
% 4.41/4.81 substitution0:
% 4.41/4.81 X := skol29
% 4.41/4.81 end
% 4.41/4.81 substitution1:
% 4.41/4.81 X := X
% 4.41/4.81 end
% 4.41/4.81
% 4.41/4.81 resolution: (33450) {G3,W8,D3,L2,V1,M2} { in( skol30( empty_set, X ), X )
% 4.41/4.81 , ! X = empty_set }.
% 4.41/4.81 parent0[0]: (14091) {G2,W4,D2,L1,V2,M1} R(14089,425) { ! alpha15( empty_set
% 4.41/4.81 , X, Y ) }.
% 4.41/4.81 parent1[0]: (33449) {G4,W14,D3,L3,V1,M3} { alpha15( empty_set, X, skol30(
% 4.41/4.81 empty_set, X ) ), in( skol30( empty_set, X ), X ), ! X = empty_set }.
% 4.41/4.81 substitution0:
% 4.41/4.81 X := X
% 4.41/4.81 Y := skol30( empty_set, X )
% 4.41/4.81 end
% 4.41/4.81 substitution1:
% 4.41/4.81 X := X
% 4.41/4.81 end
% 4.41/4.81
% 4.41/4.81 subsumption: (20217) {G4,W8,D3,L2,V1,M2} S(10803);d(20209);d(20209);r(14091
% 4.41/4.81 ) { ! X = empty_set, in( skol30( empty_set, X ), X ) }.
% 4.41/4.81 parent0: (33450) {G3,W8,D3,L2,V1,M2} { in( skol30( empty_set, X ), X ), !
% 4.41/4.81 X = empty_set }.
% 4.41/4.81 substitution0:
% 4.41/4.81 X := X
% 4.41/4.81 end
% 4.41/4.81 permutation0:
% 4.41/4.81 0 ==> 1
% 4.41/4.81 1 ==> 0
% 4.41/4.81 end
% 4.41/4.81
% 4.41/4.81 eqswap: (33452) {G4,W8,D3,L2,V1,M2} { ! empty_set = X, in( skol30(
% 4.41/4.81 empty_set, X ), X ) }.
% 4.41/4.81 parent0[0]: (20217) {G4,W8,D3,L2,V1,M2} S(10803);d(20209);d(20209);r(14091)
% 4.41/4.81 { ! X = empty_set, in( skol30( empty_set, X ), X ) }.
% 4.41/4.81 substitution0:
% 4.41/4.81 X := X
% 4.41/4.81 end
% 4.41/4.81
% 4.41/4.81 eqrefl: (33453) {G0,W5,D3,L1,V0,M1} { in( skol30( empty_set, empty_set ),
% 4.41/4.81 empty_set ) }.
% 4.41/4.81 parent0[0]: (33452) {G4,W8,D3,L2,V1,M2} { ! empty_set = X, in( skol30(
% 4.41/4.81 empty_set, X ), X ) }.
% 4.41/4.81 substitution0:
% 4.41/4.81 X := empty_set
% 4.41/4.81 end
% 4.41/4.81
% 4.41/4.81 resolution: (33454) {G1,W0,D0,L0,V0,M0} { }.
% 4.41/4.81 parent0[0]: (14089) {G1,W3,D2,L1,V1,M1} R(443,170) { ! in( X, empty_set )
% 4.41/4.81 }.
% 4.41/4.81 parent1[0]: (33453) {G0,W5,D3,L1,V0,M1} { in( skol30( empty_set, empty_set
% 4.41/4.81 ), empty_set ) }.
% 4.41/4.81 substitution0:
% 4.41/4.81 X := skol30( empty_set, empty_set )
% 4.41/4.81 end
% 4.41/4.81 substitution1:
% 4.41/4.81 end
% 4.41/4.81
% 4.41/4.81 subsumption: (20768) {G5,W0,D0,L0,V0,M0} Q(20217);r(14089) { }.
% 4.41/4.81 parent0: (33454) {G1,W0,D0,L0,V0,M0} { }.
% 4.41/4.81 substitution0:
% 4.41/4.81 end
% 4.41/4.81 permutation0:
% 4.41/4.81 end
% 4.41/4.81
% 4.41/4.81 Proof check complete!
% 4.41/4.81
% 4.41/4.81 Memory use:
% 4.41/4.81
% 4.41/4.81 space for terms: 371796
% 4.41/4.81 space for clauses: 897140
% 4.41/4.81
% 4.41/4.81
% 4.41/4.81 clauses generated: 62020
% 4.41/4.81 clauses kept: 20769
% 4.41/4.81 clauses selected: 1389
% 4.41/4.81 clauses deleted: 1774
% 4.41/4.81 clauses inuse deleted: 21
% 4.41/4.81
% 4.41/4.81 subsentry: 5869915
% 4.41/4.81 literals s-matched: 678958
% 4.41/4.81 literals matched: 506414
% 4.41/4.81 full subsumption: 461471
% 4.41/4.81
% 4.41/4.81 checksum: 637152271
% 4.41/4.81
% 4.41/4.81
% 4.41/4.81 Bliksem ended
%------------------------------------------------------------------------------