% Mizar problem: e2_56_1_1,ringcat1,890,56 
include('Axioms/SET010^0.ax').
thf(c1_56_type,type,( c1_56__ringcat1: $i )).
thf(r2_ringcat1_type,type,( r2_ringcat1: $i > $i > $o )).
thf(v1_classes2_type,type,( v1_classes2: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $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_c1_56__ringcat1,axiom,( ~ ( v1_xboole_0 @ c1_56__ringcat1 ) & ( v1_classes2 @ c1_56__ringcat1 ) ),file(ringcat1,c1_56__ringcat1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(e1_56_1_1__ringcat1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_ringcat1 @ A @ B ) & ( r2_ringcat1 @ A @ C ) ) => ( = @ B @ C ) ) ),file(ringcat1,e1_56_1_1__ringcat1)).
thf(s1_tarski,axiom,( ! [A: $i] : ! [B: $i > $i > $o] : ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( B @ C @ D ) & ( B @ C @ E ) ) => ( = @ D @ E ) ) => ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ? [E: $i] : ( ( r2_hidden @ E @ A ) & ( B @ E @ D ) ) ) ) ),file(tarski,s1_tarski)).
thf(e2_56_1_1__ringcat1,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ? [C: $i] : ( ( r2_hidden @ C @ c1_56__ringcat1 ) & ( r2_ringcat1 @ C @ B ) ) ) ),file(ringcat1,e2_56_1_1__ringcat1)).
