% Mizar problem: e2_27_1_1,orders_3,464,70 
include('Axioms/SET010^0.ax').
thf(c1_27_type,type,( c1_27__orders_3: $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_struct_0_type,type,( l1_struct_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_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_27__orders_3,axiom,( $true ),file(orders_3,c1_27__orders_3)).
thf(e1_27_1_1__orders_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ? [D: $i] : ( ( l1_struct_0 @ D ) & ( = @ D @ A ) & ( = @ B @ ( u1_struct_0 @ D ) ) ) & ? [D: $i] : ( ( l1_struct_0 @ D ) & ( = @ D @ A ) & ( = @ C @ ( u1_struct_0 @ D ) ) ) ) => ( = @ B @ C ) ) ),file(orders_3,e1_27_1_1__orders_3)).
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_27_1_1__orders_3,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ? [C: $i] : ( ( r2_hidden @ C @ c1_27__orders_3 ) & ? [D: $i] : ( ( l1_struct_0 @ D ) & ( = @ D @ C ) & ( = @ B @ ( u1_struct_0 @ D ) ) ) ) ) ),file(orders_3,e2_27_1_1__orders_3)).
