% Mizar problem: e3_50_2_1,ordinal3,1278,57 
include('Axioms/SET010^0.ax').
thf(c1_50_2_type,type,( c1_50_2__ordinal3: $i )).
thf(c2_50_type,type,( c2_50__ordinal3: $i )).
thf(k11_ordinal2_type,type,( k11_ordinal2: $i > $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_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_ordinal2_type,type,( v1_ordinal2: $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(v5_ordinal1_type,type,( v5_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_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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_50_2__ordinal3,axiom,( v3_ordinal1 @ c1_50_2__ordinal3 ),file(ordinal3,c1_50_2__ordinal3)).
thf(dt_c2_50__ordinal3,axiom,( v3_ordinal1 @ c2_50__ordinal3 ),file(ordinal3,c2_50__ordinal3)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(fc2_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(ordinal2,fc2_ordinal2)).
thf(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc2_ordinal2,axiom,( ? [A: $i] : ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) ),file(ordinal2,rc2_ordinal2)).
thf(s3_ordinal2,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v5_ordinal1 @ C ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v1_ordinal2 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( v3_ordinal1 @ D ) => ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ) ),file(ordinal2,s3_ordinal2)).
thf(e3_50_2_1__ordinal3,conjecture,( ? [A: $i] : ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ c1_50_2__ordinal3 ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ c1_50_2__ordinal3 ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k11_ordinal2 @ B @ c2_50__ordinal3 ) ) ) ) ) ),file(ordinal3,e3_50_2_1__ordinal3)).
