% Mizar problem: t73_waybel_1,waybel_1,2722,47 
fof(t73_waybel_1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v9_waybel_1(A)
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => k4_yellow_0(A) = k6_waybel_1(A,B,B) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_2,cc1_lattice3,cc1_relat_1,cc1_relset_1,cc2_lattice3,cc2_waybel_1,cc5_funct_2,cc5_waybel_1,cc6_funct_2,cc6_waybel_1,cc7_waybel_0,cc7_waybel_1,commutativity_k12_lattice3,d12_yellow_0,d19_waybel_1,d21_waybel_1,dt_k11_lattice3,dt_k12_lattice3,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_yellow_0,dt_k2_zfmisc_1,dt_k4_waybel_1,dt_k4_yellow_0,dt_k5_waybel_1,dt_k6_waybel_1,dt_k7_yellow_2,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc12_relat_1,fc1_struct_0,fc4_relat_1,fc8_waybel_1,rc1_funct_2,rc1_relat_1,rc2_partfun1,rc2_relat_1,rc3_relat_1,rc3_struct_0,rc5_struct_0,redefinition_k12_lattice3,redefinition_k7_yellow_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t23_yellow_0,t25_orders_2,t2_subset,t3_subset,t45_yellow_0,t4_subset,t5_subset,t6_boole,t70_waybel_1,t71_waybel_1,t7_boole,t8_boole]),
    [file(waybel_1,t73_waybel_1)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc1_lattice3),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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(cc2_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v2_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc2_lattice3),
    []).

fof(cc2_waybel_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ! [C] : 
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v5_waybel_1(C,B,A) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
              & v18_waybel_0(C,A,B)
              & v20_waybel_0(C,A,B)
              & v22_waybel_0(C,A,B) ) ) ) ) ),
    file(waybel_1,cc2_waybel_1),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc5_waybel_1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v9_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A) ) ) ) ),
    file(waybel_1,cc5_waybel_1),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(cc6_waybel_1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v9_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_waybel_1(A) ) ) ) ),
    file(waybel_1,cc6_waybel_1),
    []).

fof(cc7_waybel_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ! [C] : 
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v18_waybel_0(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v20_waybel_0(C,A,B)
              & v22_waybel_0(C,A,B) ) ) ) ) ),
    file(waybel_0,cc7_waybel_0),
    []).

fof(cc7_waybel_1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v9_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_yellow_0(A) ) ) ) ),
    file(waybel_1,cc7_waybel_1),
    []).

fof(commutativity_k12_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k12_lattice3(A,B,C) = k12_lattice3(A,C,B) ) ),
    file(lattice3,k12_lattice3),
    []).

fof(d12_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => k4_yellow_0(A) = k2_yellow_0(A,k1_xboole_0) ) ),
    file(yellow_0,d12_yellow_0),
    []).

fof(d19_waybel_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v9_waybel_1(A)
      <=> ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & l1_orders_2(A)
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => v5_waybel_1(k4_waybel_1(A,B),A,A) ) ) ) ) ),
    file(waybel_1,d19_waybel_1),
    []).

fof(d21_waybel_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k6_waybel_1(A,B,C) = k7_yellow_2(u1_struct_0(A),A,k5_waybel_1(A,B),C) ) ) ) ),
    file(waybel_1,d21_waybel_1),
    []).

fof(dt_k11_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k11_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k11_lattice3),
    []).

fof(dt_k12_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k12_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k12_lattice3),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

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

fof(dt_k2_yellow_0,axiom,(
    ! [A,B] : 
      ( l1_orders_2(A)
     => m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) ),
    file(yellow_0,k2_yellow_0),
    []).

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

fof(dt_k4_waybel_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k4_waybel_1(A,B))
        & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(waybel_1,k4_waybel_1),
    []).

fof(dt_k4_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m1_subset_1(k4_yellow_0(A),u1_struct_0(A)) ) ),
    file(yellow_0,k4_yellow_0),
    []).

fof(dt_k5_waybel_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k5_waybel_1(A,B))
        & v1_funct_2(k5_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k5_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(waybel_1,k5_waybel_1),
    []).

fof(dt_k6_waybel_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_waybel_1(A,B,C),u1_struct_0(A)) ) ),
    file(waybel_1,k6_waybel_1),
    []).

fof(dt_k7_yellow_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B))
        & m1_subset_1(D,A) )
     => m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)) ) ),
    file(yellow_2,k7_yellow_2),
    []).

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_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_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_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc8_waybel_1,axiom,(
    ! [A,B] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_relat_1(k4_waybel_1(A,B))
        & v1_funct_1(k4_waybel_1(A,B))
        & ~ v1_xboole_0(k4_waybel_1(A,B))
        & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v1_partfun1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v5_orders_3(k4_waybel_1(A,B),A,A) ) ) ),
    file(waybel_1,fc8_waybel_1),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(redefinition_k12_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k12_lattice3(A,B,C) = k11_lattice3(A,B,C) ) ),
    file(lattice3,k12_lattice3),
    []).

fof(redefinition_k7_yellow_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B))
        & m1_subset_1(D,A) )
     => k7_yellow_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(yellow_2,k7_yellow_2),
    []).

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(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t23_yellow_0,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( D = k12_lattice3(A,B,C)
                  <=> ( r1_orders_2(A,D,B)
                      & r1_orders_2(A,D,C)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,E,B)
                              & r1_orders_2(A,E,C) )
                           => r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ),
    file(yellow_0,t23_yellow_0),
    []).

fof(t25_orders_2,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r1_orders_2(A,B,C)
                  & r1_orders_2(A,C,B) )
               => B = C ) ) ) ) ),
    file(orders_2,t25_orders_2),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

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

fof(t45_yellow_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_orders_2(A,B,k4_yellow_0(A)) ) ) ),
    file(yellow_0,t45_yellow_0),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t70_waybel_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v9_waybel_1(A)
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_orders_2(A,k11_lattice3(A,C,D),B)
                    <=> r1_orders_2(A,D,k6_waybel_1(A,C,B)) ) ) ) ) ) ) ),
    file(waybel_1,t70_waybel_1),
    []).

fof(t71_waybel_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v9_waybel_1(A)
       => v2_yellow_0(A) ) ) ),
    file(waybel_1,t71_waybel_1),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).