% Mizar problem: t57_yellow_0,yellow_0,1524,60 
fof(t57_yellow_0,conjecture,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A)
            & m1_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,cc1_relset_1,d13_yellow_0,d14_yellow_0,dt_g1_orders_2,dt_k1_toler_1,dt_k1_zfmisc_1,dt_k2_wellord1,dt_k2_zfmisc_1,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m1_yellow_0,dt_m2_relset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m1_yellow_0,existence_m2_relset_1,free_g1_orders_2,rc1_orders_2,rc3_yellow_0,redefinition_k1_toler_1,redefinition_m2_relset_1,reflexivity_r1_tarski,t15_wellord1,t3_subset]),
    [file(yellow_0,t57_yellow_0)]).

fof(abstractness_v1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_orders_2(A)
       => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ),
    file(orders_2,v1_orders_2),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(d13_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( l1_orders_2(B)
         => ( m1_yellow_0(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & r1_tarski(u1_orders_2(B),u1_orders_2(A)) ) ) ) ) ),
    file(yellow_0,d13_yellow_0),
    []).

fof(d14_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
          <=> u1_orders_2(B) = k1_toler_1(u1_orders_2(A),u1_struct_0(B)) ) ) ) ),
    file(yellow_0,d14_yellow_0),
    []).

fof(dt_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( v1_orders_2(g1_orders_2(A,B))
        & l1_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(dt_k1_toler_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => m2_relset_1(k1_toler_1(A,B),B,B) ) ),
    file(toler_1,k1_toler_1),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k2_wellord1(A,B)) ) ),
    file(wellord1,k2_wellord1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m1_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => l1_orders_2(B) ) ) ),
    file(yellow_0,m1_yellow_0),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(orders_2,u1_orders_2),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ? [B] : m1_yellow_0(B,A) ) ),
    file(yellow_0,m1_yellow_0),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(free_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ! [C,D] : 
          ( g1_orders_2(A,B) = g1_orders_2(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(rc1_orders_2,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & v1_orders_2(A) ) ),
    file(orders_2,rc1_orders_2),
    []).

fof(rc3_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ? [B] : 
          ( m1_yellow_0(B,A)
          & v1_orders_2(B)
          & v4_yellow_0(B,A) ) ) ),
    file(yellow_0,rc3_yellow_0),
    []).

fof(redefinition_k1_toler_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => k1_toler_1(A,B) = k2_wellord1(A,B) ) ),
    file(toler_1,k1_toler_1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t15_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_wellord1(B,A),B)
        & r1_tarski(k2_wellord1(B,A),k2_zfmisc_1(A,A)) ) ) ),
    file(wellord1,t15_wellord1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).