% Mizar problem: e3_47_2,card_3,1093,59 
include('Axioms/SET010^0.ax').
thf(c1_47_type,type,( c1_47__card_3: $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_card_1_type,type,( k1_card_1: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_funct_2_type,type,( k1_funct_2: $i > $i > $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_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(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(projectivity_k1_card_1,axiom,( ! [A: $i] : ( = @ ( k1_card_1 @ ( k1_card_1 @ A ) ) @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k1_card_1,axiom,( ! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_47__card_3,axiom,( ( v1_relat_1 @ c1_47__card_3 ) & ( v1_funct_1 @ c1_47__card_3 ) ),file(card_3,c1_47__card_3)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e2_47_2__card_3,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c1_47__card_3 ) ) & ! [B: $i] : ~ ( ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ( ( r2_hidden @ C @ ( k1_funct_2 @ ( k1_card_1 @ ( k1_funct_1 @ c1_47__card_3 @ A ) ) @ ( k1_funct_1 @ c1_47__card_3 @ A ) ) ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ C @ D ) & ( = @ ( k10_xtuple_0 @ D ) @ ( k1_funct_1 @ c1_47__card_3 @ A ) ) ) ) ) ) ) ),file(card_3,e2_47_2__card_3)).
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(e3_47_2__card_3,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k9_xtuple_0 @ c1_47__card_3 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c1_47__card_3 ) ) => ! [C: $i] : ( ( r2_hidden @ C @ ( k1_funct_1 @ A @ B ) ) <=> ( ( r2_hidden @ C @ ( k1_funct_2 @ ( k1_card_1 @ ( k1_funct_1 @ c1_47__card_3 @ B ) ) @ ( k1_funct_1 @ c1_47__card_3 @ B ) ) ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ C @ D ) & ( = @ ( k10_xtuple_0 @ D ) @ ( k1_funct_1 @ c1_47__card_3 @ B ) ) ) ) ) ) ) ),file(card_3,e3_47_2__card_3)).
