% Mizar problem: e1_4_4_1,xboole_0,124,68 
include('Axioms/SET010^0.ax').
thf(c1_4_type,type,( c1_4__xboole_0: $i )).
thf(c2_4_type,type,( c2_4__xboole_0: $i )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_c1_4__xboole_0,axiom,( $true ),file(xboole_0,c1_4__xboole_0)).
thf(dt_c2_4__xboole_0,axiom,( $true ),file(xboole_0,c2_4__xboole_0)).
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_4_4_1__xboole_0,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ c1_4__xboole_0 ) & ~ ( r2_hidden @ B @ c2_4__xboole_0 ) ) ) ),file(xboole_0,e1_4_4_1__xboole_0)).
