% Mizar problem: e1_9_1_1,card_3,144,61 
include('Axioms/SET010^0.ax').
thf(c1_9_type,type,( c1_9__card_3: $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(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(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_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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_9__card_3,axiom,( ( v1_relat_1 @ c1_9__card_3 ) & ( v1_funct_1 @ c1_9__card_3 ) ),file(card_3,c1_9__card_3)).
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(s1_card_3,axiom,( ! [A: $i] : ! [B: $i > $i] : ( ! [C: $i] : ( v1_card_1 @ ( B @ C ) ) => ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v1_card_3 @ D ) & ( = @ ( k9_xtuple_0 @ D ) @ A ) & ! [E: $i] : ( ( r2_hidden @ E @ A ) => ( = @ ( k1_funct_1 @ D @ E ) @ ( B @ E ) ) ) ) ) ),file(card_3,s1_card_3)).
thf(e1_9_1_1__card_3,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k9_xtuple_0 @ c1_9__card_3 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c1_9__card_3 ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_card_1 @ ( k1_funct_1 @ c1_9__card_3 @ B ) ) ) ) ) ),file(card_3,e1_9_1_1__card_3)).
