% Mizar problem: e1_37_1,ordinal2,568,35 
include('Axioms/SET010^0.ax').
thf(f1_s4_ordinal2_type,type,( f1_s4_ordinal2: $i )).
thf(f5_s4_ordinal2_type,type,( f5_s4_ordinal2: $i )).
thf(f6_s4_ordinal2_type,type,( f6_s4_ordinal2: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $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(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(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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(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_f1_s4_ordinal2,axiom,( v3_ordinal1 @ f1_s4_ordinal2 ),file(ordinal2,f1_s4_ordinal2)).
thf(dt_f5_s4_ordinal2,axiom,( ( v5_ordinal1 @ f5_s4_ordinal2 ) & ( v1_relat_1 @ f5_s4_ordinal2 ) & ( v1_funct_1 @ f5_s4_ordinal2 ) ),file(ordinal2,f5_s4_ordinal2)).
thf(dt_f6_s4_ordinal2,axiom,( ( v5_ordinal1 @ f6_s4_ordinal2 ) & ( v1_relat_1 @ f6_s4_ordinal2 ) & ( v1_funct_1 @ f6_s4_ordinal2 ) ),file(ordinal2,f6_s4_ordinal2)).
thf(s1_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ B ) & ( A @ D ) ) ) ),file(xboole_0,s1_xboole_0)).
thf(e1_37_1__ordinal2,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ f1_s4_ordinal2 ) & ~ ( = @ ( k1_funct_1 @ f5_s4_ordinal2 @ B ) @ ( k1_funct_1 @ f6_s4_ordinal2 @ B ) ) ) ) ),file(ordinal2,e1_37_1__ordinal2)).
