% Mizar problem: e14_25,classes2,618,38 
include('Axioms/SET010^0.ax').
thf(c1_25_type,type,( c1_25__classes2: $i )).
thf(c4_25_type,type,( c4_25__classes2: $i )).
thf(k2_ordinal1_type,type,( k2_ordinal1: $i > $i )).
thf(k6_classes1_type,type,( k6_classes1: $i > $i )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k2_ordinal1,axiom,( $true ),file(ordinal1,k2_ordinal1)).
thf(dt_k6_classes1,axiom,( ! [A: $i] : ( v3_ordinal1 @ ( k6_classes1 @ A ) ) ),file(classes1,k6_classes1)).
thf(dt_c1_25__classes2,axiom,( $true ),file(classes2,c1_25__classes2)).
thf(dt_c4_25__classes2,axiom,( $true ),file(classes2,c4_25__classes2)).
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(e14_25__classes2,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( k2_ordinal1 @ c1_25__classes2 ) ) & ? [C: $i] : ( ( r2_hidden @ C @ c4_25__classes2 ) & ( = @ B @ ( k6_classes1 @ C ) ) ) ) ) ),file(classes2,e14_25__classes2)).
