% Mizar problem: e2_3_2_1,xxreal_2,152,36 
include('Axioms/SET010^0.ax').
thf(c1_3_type,type,( c1_3__xxreal_2: $i )).
thf(m2_xxreal_2_type,type,( m2_xxreal_2: $i > $i > $o )).
thf(r1_xxreal_0_type,type,( r1_xxreal_0: $i > $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v2_membered_type,type,( v2_membered: $i > $o )).
thf(reflexivity_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( r1_xxreal_0 @ A @ A ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(connectedness_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( ( r1_xxreal_0 @ A @ B ) | ( r1_xxreal_0 @ B @ A ) ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_m2_xxreal_2,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m2_xxreal_2 @ B @ A ) => ( v1_xxreal_0 @ B ) ) ) ),file(xxreal_2,m2_xxreal_2)).
thf(dt_c1_3__xxreal_2,axiom,( v2_membered @ c1_3__xxreal_2 ),file(xxreal_2,c1_3__xxreal_2)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(e1_3_2_1__xxreal_2,axiom,( ! [A: $i] : ( ( v1_xxreal_0 @ A ) => ! [B: $i] : ( ( v1_xxreal_0 @ B ) => ( ( ( m2_xxreal_2 @ A @ c1_3__xxreal_2 ) & ( r2_hidden @ B @ c1_3__xxreal_2 ) ) => ( r1_xxreal_0 @ A @ B ) ) ) ) ),file(xxreal_2,e1_3_2_1__xxreal_2)).
thf(s1_xxreal_1,axiom,( ! [A: $i > $o] : ! [B: $i > $o] : ( ! [C: $i] : ( ( v1_xxreal_0 @ C ) => ! [D: $i] : ( ( v1_xxreal_0 @ D ) => ( ( ( B @ C ) & ( A @ D ) ) => ( r1_xxreal_0 @ C @ D ) ) ) ) => ? [C: $i] : ( ( v1_xxreal_0 @ C ) & ! [D: $i] : ( ( v1_xxreal_0 @ D ) => ( ( B @ D ) => ( r1_xxreal_0 @ D @ C ) ) ) & ! [D: $i] : ( ( v1_xxreal_0 @ D ) => ( ( A @ D ) => ( r1_xxreal_0 @ C @ D ) ) ) ) ) ),file(xxreal_1,s1_xxreal_1)).
thf(e2_3_2_1__xxreal_2,conjecture,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ! [B: $i] : ( ( v1_xxreal_0 @ B ) => ( ( m2_xxreal_2 @ B @ c1_3__xxreal_2 ) => ( r1_xxreal_0 @ B @ A ) ) ) & ! [B: $i] : ( ( v1_xxreal_0 @ B ) => ( ( r2_hidden @ B @ c1_3__xxreal_2 ) => ( r1_xxreal_0 @ A @ B ) ) ) ) ),file(xxreal_2,e2_3_2_1__xxreal_2)).
