% Mizar problem: e2_16,wellord2,511,39 
include('Axioms/SET010^0.ax').
thf(c1_16_type,type,( c1_16__wellord2: $i )).
thf(k1_relat_1_type,type,( k1_relat_1: $i > $i )).
thf(k1_wellord1_type,type,( k1_wellord1: $i > $i > $i )).
thf(k1_wellord2_type,type,( k1_wellord2: $i > $i )).
thf(k2_wellord1_type,type,( k2_wellord1: $i > $i > $i )).
thf(r4_wellord1_type,type,( r4_wellord1: $i > $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_relat_2_type,type,( v1_relat_2: $i > $o )).
thf(v1_wellord1_type,type,( v1_wellord1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_wellord1_type,type,( v2_wellord1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v4_relat_2_type,type,( v4_relat_2: $i > $o )).
thf(v6_relat_2_type,type,( v6_relat_2: $i > $o )).
thf(v8_relat_2_type,type,( v8_relat_2: $i > $o )).
thf(cc1_wellord1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_wellord1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v4_relat_2 @ A ) & ( v6_relat_2 @ A ) & ( v8_relat_2 @ A ) & ( v1_wellord1 @ A ) ) ) ),file(wellord1,cc1_wellord1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_wellord1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v4_relat_2 @ A ) & ( v6_relat_2 @ A ) & ( v8_relat_2 @ A ) & ( v1_wellord1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_wellord1 @ A ) ) ) ),file(wellord1,cc2_wellord1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k1_relat_1,axiom,( $true ),file(relat_1,k1_relat_1)).
thf(dt_k1_wellord1,axiom,( $true ),file(wellord1,k1_wellord1)).
thf(dt_k1_wellord2,axiom,( ! [A: $i] : ( v1_relat_1 @ ( k1_wellord2 @ A ) ) ),file(wellord2,k1_wellord2)).
thf(dt_k2_wellord1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k2_wellord1 @ A @ B ) ) ) ),file(wellord1,k2_wellord1)).
thf(dt_c1_16__wellord2,axiom,( v1_relat_1 @ c1_16__wellord2 ),file(wellord2,c1_16__wellord2)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(fc1_wellord2,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v1_relat_2 @ ( k1_wellord2 @ A ) ) ) ),file(wellord2,fc1_wellord2)).
thf(fc2_wellord2,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v8_relat_2 @ ( k1_wellord2 @ A ) ) ) ),file(wellord2,fc2_wellord2)).
thf(fc3_wellord2,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v4_relat_2 @ ( k1_wellord2 @ A ) ) ) ),file(wellord2,fc3_wellord2)).
thf(fc4_wellord2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v6_relat_2 @ ( k1_wellord2 @ A ) ) ) ) ),file(wellord2,fc4_wellord2)).
thf(fc5_wellord2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v1_wellord1 @ ( k1_wellord2 @ A ) ) ) ) ),file(wellord2,fc5_wellord2)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
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(e2_16__wellord2,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( k1_relat_1 @ c1_16__wellord2 ) ) & ? [C: $i] : ( ( v3_ordinal1 @ C ) & ( r4_wellord1 @ ( k2_wellord1 @ c1_16__wellord2 @ ( k1_wellord1 @ c1_16__wellord2 @ B ) ) @ ( k1_wellord2 @ C ) ) ) ) ) ),file(wellord2,e2_16__wellord2)).
