% Mizar problem: t36_waybel21,waybel21,1330,19 
fof(t36_waybel21,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & m2_yellow_6(C,A,B) )
             => ! [D] : 
                  ( m2_waybel21(D,A,B,C)
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(C))
                     => k3_waybel_0(A,C,E) = k3_waybel_0(A,B,k3_yellow_6(u1_struct_0(C),B,D,E)) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_relat_1,cc1_relset_1,cc2_finset_1,d3_waybel21,d8_waybel_0,dt_k1_funct_1,dt_k1_waybel_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_waybel_0,dt_k3_yellow_6,dt_k5_relat_1,dt_k7_funct_2,dt_l1_orders_2,dt_l1_struct_0,dt_l1_waybel_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_waybel21,dt_m2_yellow_6,dt_u1_struct_0,dt_u1_waybel_0,existence_l1_orders_2,existence_l1_struct_0,existence_l1_waybel_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_waybel21,existence_m2_yellow_6,fc10_relat_1,fc12_relat_1,fc14_finset_1,fc15_yellow_6,fc1_struct_0,fc1_subset_1,fc4_relat_1,fc4_subset_1,fc9_relat_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc3_finset_1,rc3_relat_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,redefinition_k1_waybel_0,redefinition_k3_yellow_6,redefinition_k7_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t21_funct_2,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(waybel21,t36_waybel21)]).

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

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

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_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(d3_waybel21,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_waybel_0(C,A) )
             => ( m2_yellow_6(C,A,B)
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
                      & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
                   => ( m2_waybel21(D,A,B,C)
                    <=> ( u1_waybel_0(A,C) = k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,u1_waybel_0(A,B))
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(B))
                           => ? [F] : 
                                ( m1_subset_1(F,u1_struct_0(C))
                                & ! [G] : 
                                    ( m1_subset_1(G,u1_struct_0(C))
                                   => ( r1_orders_2(C,F,G)
                                     => r1_orders_2(B,E,k3_yellow_6(u1_struct_0(C),B,D,G)) ) ) ) ) ) ) ) ) ) ) ) ),
    file(waybel21,d3_waybel21),
    []).

fof(d8_waybel_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_waybel_0(A,B,C) = k1_waybel_0(B,A,u1_waybel_0(A,B),C) ) ) ) ),
    file(waybel_0,d8_waybel_0),
    []).

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

fof(dt_k1_waybel_0,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)) ) ),
    file(waybel_0,k1_waybel_0),
    []).

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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_waybel_0,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => m1_subset_1(k3_waybel_0(A,B,C),u1_struct_0(A)) ) ),
    file(waybel_0,k3_waybel_0),
    []).

fof(dt_k3_yellow_6,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(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(k3_yellow_6(A,B,C,D),u1_struct_0(B)) ) ),
    file(yellow_6,k3_yellow_6),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_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_l1_waybel_0,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_waybel_0(B,A)
         => l1_orders_2(B) ) ) ),
    file(waybel_0,l1_waybel_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_m2_waybel21,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & ~ v3_struct_0(C)
        & l1_waybel_0(C,A) )
     => ! [D] : 
          ( m2_waybel21(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
            & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) ) ) ) ),
    file(waybel21,m2_waybel21),
    []).

fof(dt_m2_yellow_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ! [C] : 
          ( m2_yellow_6(C,A,B)
         => ( ~ v3_struct_0(C)
            & v3_orders_2(C)
            & v7_waybel_0(C)
            & l1_waybel_0(C,A) ) ) ) ),
    file(yellow_6,m2_yellow_6),
    []).

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

fof(dt_u1_waybel_0,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l1_waybel_0(B,A) )
     => ( v1_funct_1(u1_waybel_0(A,B))
        & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A))
        & m2_relset_1(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ),
    file(waybel_0,u1_waybel_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_l1_waybel_0,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l1_waybel_0(B,A) ) ),
    file(waybel_0,l1_waybel_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(existence_m2_waybel21,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & ~ v3_struct_0(C)
        & l1_waybel_0(C,A) )
     => ? [D] : m2_waybel21(D,A,B,C) ) ),
    file(waybel21,m2_waybel21),
    []).

fof(existence_m2_yellow_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ? [C] : m2_yellow_6(C,A,B) ) ),
    file(yellow_6,m2_yellow_6),
    []).

fof(fc10_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_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(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc15_yellow_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A) )
     => ( ~ v1_xboole_0(u1_waybel_0(A,B))
        & v1_relat_1(u1_waybel_0(A,B))
        & v1_funct_1(u1_waybel_0(A,B))
        & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ),
    file(yellow_6,fc15_yellow_6),
    []).

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(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc9_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

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

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_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(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_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(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

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_k1_waybel_0,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(A)) )
     => k1_waybel_0(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(waybel_0,k1_waybel_0),
    []).

fof(redefinition_k3_yellow_6,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(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) )
     => k3_yellow_6(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(yellow_6,k3_yellow_6),
    []).

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_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(t21_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_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(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(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),
    []).