% Mizar problem: e6_19_3_2,card_5,875,24 
include('Axioms/SET010^0.ax').
thf(c1_19_type,type,( c1_19__card_5: $i )).
thf(c1_19_3_2_type,type,( c1_19_3_2__card_5: $i )).
thf(c2_19_3_2_type,type,( c2_19_3_2__card_5: $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(v1_card_1_type,type,( v1_card_1: $i > $o )).
thf(v1_card_3_type,type,( v1_card_3: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_19__card_5,axiom,( v1_card_1 @ c1_19__card_5 ),file(card_5,c1_19__card_5)).
thf(dt_c1_19_3_2__card_5,axiom,( ( v1_relat_1 @ c1_19_3_2__card_5 ) & ( v1_funct_1 @ c1_19_3_2__card_5 ) & ( v1_card_3 @ c1_19_3_2__card_5 ) ),file(card_5,c1_19_3_2__card_5)).
thf(dt_c2_19_3_2__card_5,axiom,( ( v1_relat_1 @ c2_19_3_2__card_5 ) & ( v1_funct_1 @ c2_19_3_2__card_5 ) & ( v1_card_3 @ c2_19_3_2__card_5 ) ),file(card_5,c2_19_3_2__card_5)).
thf(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_card_3,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) ) ),file(card_3,rc1_card_3)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e1_19_3_2__card_5,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c1_19_3_2__card_5 ) ) <=> ( ( r2_hidden @ A @ c1_19__card_5 ) & ( v1_card_1 @ A ) ) ) ),file(card_5,e1_19_3_2__card_5)).
thf(e3_19_3_2__card_5,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c2_19_3_2__card_5 ) ) <=> ( ( r2_hidden @ A @ c1_19__card_5 ) & ( v1_card_1 @ A ) ) ) ),file(card_5,e3_19_3_2__card_5)).
thf(s2_xboole_0,axiom,( ! [A: $i] : ! [B: $i > $o] : ! [C: $i] : ( ( ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( B @ D ) ) & ! [D: $i] : ( ( r2_hidden @ D @ A ) <=> ( B @ D ) ) ) => ( = @ C @ A ) ) ),file(xboole_0,s2_xboole_0)).
thf(e6_19_3_2__card_5,conjecture,( = @ ( k9_xtuple_0 @ c1_19_3_2__card_5 ) @ ( k9_xtuple_0 @ c2_19_3_2__card_5 ) ),file(card_5,e6_19_3_2__card_5)).
