% Mizar problem: e6_161_1_1_2_1,funct_1,3355,16 
include('Axioms/SET010^0.ax').
thf(c1_161_1_1_2_1_type,type,( c1_161_1_1_2_1__funct_1: $i )).
thf(c2_161_1_1_2_1_type,type,( c2_161_1_1_2_1__funct_1: $i )).
thf(c3_161_1_1_2_1_type,type,( c3_161_1_1_2_1__funct_1: $i )).
thf(f2_s5_funct_1_type,type,( f2_s5_funct_1: $i )).
thf(p1_s5_funct_1_type,type,( p1_s5_funct_1: $i > $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_161_1_1_2_1__funct_1,axiom,( $true ),file(funct_1,c1_161_1_1_2_1__funct_1)).
thf(dt_c2_161_1_1_2_1__funct_1,axiom,( $true ),file(funct_1,c2_161_1_1_2_1__funct_1)).
thf(dt_c3_161_1_1_2_1__funct_1,axiom,( $true ),file(funct_1,c3_161_1_1_2_1__funct_1)).
thf(dt_f2_s5_funct_1,axiom,( $true ),file(funct_1,f2_s5_funct_1)).
thf(e3_161_1_1_2_1__funct_1,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ c2_161_1_1_2_1__funct_1 ) <=> ( ( r2_hidden @ A @ f2_s5_funct_1 ) & ( p1_s5_funct_1 @ c1_161_1_1_2_1__funct_1 @ A ) ) ) ),file(funct_1,e3_161_1_1_2_1__funct_1)).
thf(e5_161_1_1_2_1__funct_1,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ c3_161_1_1_2_1__funct_1 ) <=> ( ( r2_hidden @ A @ f2_s5_funct_1 ) & ( p1_s5_funct_1 @ c1_161_1_1_2_1__funct_1 @ A ) ) ) ),file(funct_1,e5_161_1_1_2_1__funct_1)).
thf(s2_xboole_0,axiom,( ! [A: $i] : ! [B: $i > $o] : ! [C: $i] : ( ( ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( B @ D ) ) & ! [D: $i] : ( ( r2_hidden @ D @ A ) <=> ( B @ D ) ) ) => ( = @ C @ A ) ) ),file(xboole_0,s2_xboole_0)).
thf(e6_161_1_1_2_1__funct_1,conjecture,( = @ c2_161_1_1_2_1__funct_1 @ c3_161_1_1_2_1__funct_1 ),file(funct_1,e6_161_1_1_2_1__funct_1)).
