% Mizar problem: e1_3_1_1,supinf_1,56,58 
include('Axioms/SET010^0.ax').
thf(c1_3_type,type,( c1_3__supinf_1: $i )).
thf(m1_xxreal_2_type,type,( m1_xxreal_2: $i > $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v2_membered_type,type,( v2_membered: $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_m1_xxreal_2,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_xxreal_2 @ B @ A ) => ( v1_xxreal_0 @ B ) ) ) ),file(xxreal_2,m1_xxreal_2)).
thf(dt_c1_3__supinf_1,axiom,( v2_membered @ c1_3__supinf_1 ),file(supinf_1,c1_3__supinf_1)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(s2_membered,axiom,( ! [A: $i > $o] : ? [B: $i] : ( ( v2_membered @ B ) & ! [C: $i] : ( ( v1_xxreal_0 @ C ) => ( ( r2_hidden @ C @ B ) <=> ( A @ C ) ) ) ) ),file(membered,s2_membered)).
thf(e1_3_1_1__supinf_1,conjecture,( ? [A: $i] : ( ( v2_membered @ A ) & ! [B: $i] : ( ( v1_xxreal_0 @ B ) => ( ( r2_hidden @ B @ A ) <=> ( m1_xxreal_2 @ B @ c1_3__supinf_1 ) ) ) ) ),file(supinf_1,e1_3_1_1__supinf_1)).
