% Mizar problem: e4_20_1_1,card_3,435,51 
include('Axioms/SET010^0.ax').
thf(c1_20_type,type,( c1_20__card_3: $i )).
thf(c1_20_1_1_type,type,( c1_20_1_1__card_3: $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_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
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_20__card_3,axiom,( $true ),file(card_3,c1_20__card_3)).
thf(dt_c1_20_1_1__card_3,axiom,( $true ),file(card_3,c1_20_1_1__card_3)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e3_20_1_1__card_3,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ c1_20_1_1__card_3 ) & ! [B: $i] : ~ ( ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ A @ C ) & ( = @ B @ ( k1_funct_1 @ C @ c1_20__card_3 ) ) ) ) ) ),file(card_3,e3_20_1_1__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(e4_20_1_1__card_3,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ c1_20_1_1__card_3 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_20_1_1__card_3 ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ B @ C ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ C @ c1_20__card_3 ) ) ) ) ) ),file(card_3,e4_20_1_1__card_3)).
