% Mizar problem: e4_6_2,wellset1,197,41 
include('Axioms/SET010^0.ax').
thf(c1_6_2_type,type,( c1_6_2__wellset1: $i )).
thf(c2_6_2_type,type,( c2_6_2__wellset1: $i )).
thf(k1_relat_1_type,type,( k1_relat_1: $i > $i )).
thf(k1_wellord1_type,type,( k1_wellord1: $i > $i > $i )).
thf(k2_wellord1_type,type,( k2_wellord1: $i > $i > $i )).
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_relat_1,axiom,( $true ),file(relat_1,k1_relat_1)).
thf(dt_k1_wellord1,axiom,( $true ),file(wellord1,k1_wellord1)).
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_6_2__wellset1,axiom,( v1_relat_1 @ c1_6_2__wellset1 ),file(wellset1,c1_6_2__wellset1)).
thf(dt_c2_6_2__wellset1,axiom,( v1_relat_1 @ c2_6_2__wellset1 ),file(wellset1,c2_6_2__wellset1)).
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(e4_6_2__wellset1,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( k1_relat_1 @ c1_6_2__wellset1 ) ) & ( r2_hidden @ B @ ( k1_relat_1 @ c2_6_2__wellset1 ) ) & ( = @ ( k2_wellord1 @ c1_6_2__wellset1 @ ( k1_wellord1 @ c1_6_2__wellset1 @ B ) ) @ ( k2_wellord1 @ c2_6_2__wellset1 @ ( k1_wellord1 @ c2_6_2__wellset1 @ B ) ) ) ) ) ),file(wellset1,e4_6_2__wellset1)).
