% Mizar problem: e2_13,card_2,606,63 
include('Axioms/SET010^0.ax').
thf(c1_13_type,type,( c1_13__card_2: $i )).
thf(c2_13_type,type,( c2_13__card_2: $i )).
thf(k10_ordinal2_type,type,( k10_ordinal2: $i > $i > $i )).
thf(k11_ordinal2_type,type,( k11_ordinal2: $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_xtuple_0_type,type,( k1_xtuple_0: $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k10_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k10_ordinal2 @ A @ B ) ) ) ),file(ordinal2,k10_ordinal2)).
thf(dt_k11_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k11_ordinal2 @ A @ B ) ) ) ),file(ordinal2,k11_ordinal2)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_xtuple_0,axiom,( $true ),file(xtuple_0,k1_xtuple_0)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_13__card_2,axiom,( v3_ordinal1 @ c1_13__card_2 ),file(card_2,c1_13__card_2)).
thf(dt_c2_13__card_2,axiom,( v3_ordinal1 @ c2_13__card_2 ),file(card_2,c2_13__card_2)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(e1_13__card_2,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ c1_13__card_2 @ c2_13__card_2 ) ) & ! [B: $i] : ~ ( ? [C: $i] : ( ( v3_ordinal1 @ C ) & ? [D: $i] : ( ( v3_ordinal1 @ D ) & ( = @ C @ ( k1_xtuple_0 @ A ) ) & ( = @ D @ ( k2_xtuple_0 @ A ) ) & ( = @ B @ ( k10_ordinal2 @ ( k11_ordinal2 @ C @ c2_13__card_2 ) @ D ) ) ) ) ) ) ),file(card_2,e1_13__card_2)).
thf(s1_classes1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(classes1,s1_classes1)).
thf(e2_13__card_2,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k2_zfmisc_1 @ c1_13__card_2 @ c2_13__card_2 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ c1_13__card_2 @ c2_13__card_2 ) ) => ? [C: $i] : ( ( v3_ordinal1 @ C ) & ? [D: $i] : ( ( v3_ordinal1 @ D ) & ( = @ C @ ( k1_xtuple_0 @ B ) ) & ( = @ D @ ( k2_xtuple_0 @ B ) ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( k10_ordinal2 @ ( k11_ordinal2 @ C @ c2_13__card_2 ) @ D ) ) ) ) ) ) ),file(card_2,e2_13__card_2)).
