% Mizar problem: e2_1_1,xboole_0,34,57 
include('Axioms/SET010^0.ax').
thf(f1_s1_xboole_0_type,type,( f1_s1_xboole_0: $i )).
thf(p1_s1_xboole_0_type,type,( p1_s1_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_f1_s1_xboole_0,axiom,( $true ),file(xboole_0,f1_s1_xboole_0)).
thf(e1_1_1__xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( = @ A @ B ) & ( p1_s1_xboole_0 @ B ) & ( = @ A @ C ) & ( p1_s1_xboole_0 @ C ) ) => ( = @ B @ C ) ) ),file(xboole_0,e1_1_1__xboole_0)).
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_1_1__xboole_0,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ? [C: $i] : ( ( r2_hidden @ C @ f1_s1_xboole_0 ) & ( = @ C @ B ) & ( p1_s1_xboole_0 @ B ) ) ) ),file(xboole_0,e2_1_1__xboole_0)).
