% Mizar problem: t40_waybel_2,waybel_2,1760,40 
fof(t40_waybel_2,conjecture,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & v12_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] : 
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & v12_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) )
       => ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] : 
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_finsub_1,cc1_relat_1,cc1_yellow_3,cc2_finset_1,cc2_finsub_1,cc2_lattice3,cc2_yellow_3,cc3_yellow_3,commutativity_k12_lattice3,commutativity_k4_yellow_4,dt_k11_lattice3,dt_k12_lattice3,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_zfmisc_1,dt_k3_yellow_4,dt_k4_waybel_0,dt_k4_yellow_4,dt_l1_orders_2,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_subset_1,fc11_waybel_0,fc12_relat_1,fc16_waybel_0,fc1_finsub_1,fc1_struct_0,fc1_subset_1,fc4_relat_1,fc5_yellow_3,fc5_yellow_4,fc6_yellow_4,fc7_waybel_0,fc8_yellow_4,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc2_relat_1,rc2_subset_1,rc3_finset_1,rc3_relat_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,rc9_waybel_0,redefinition_k12_lattice3,redefinition_k4_yellow_4,reflexivity_r1_tarski,t1_subset,t2_subset,t33_waybel_0,t3_subset,t4_subset,t5_subset,t62_yellow_4,t6_boole,t75_waybel_0,t7_boole,t8_boole]),
    [file(waybel_2,t40_waybel_2)]).

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_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    []).

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

fof(cc1_yellow_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
       => v1_yellow_3(A) ) ) ),
    file(yellow_3,cc1_yellow_3),
    []).

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(cc2_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    []).

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

fof(cc2_yellow_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ~ v1_yellow_3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(yellow_3,cc2_yellow_3),
    []).

fof(cc3_yellow_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & ~ v1_yellow_3(A) ) ) ) ),
    file(yellow_3,cc3_yellow_3),
    []).

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(commutativity_k4_yellow_4,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => k4_yellow_4(A,B,C) = k4_yellow_4(A,C,B) ) ),
    file(yellow_4,k4_yellow_4),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_yellow_0,axiom,(
    ! [A,B] : 
      ( l1_orders_2(A)
     => m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ),
    file(yellow_0,k1_yellow_0),
    []).

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

fof(dt_k3_yellow_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k3_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(yellow_4,k3_yellow_4),
    []).

fof(dt_k4_waybel_0,axiom,(
    ! [A,B] : 
      ( ( l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(waybel_0,k4_waybel_0),
    []).

fof(dt_k4_yellow_4,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(yellow_4,k4_yellow_4),
    []).

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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_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_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(fc11_waybel_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v12_waybel_0(k4_waybel_0(A,B),A) ) ),
    file(waybel_0,fc11_waybel_0),
    []).

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(fc16_waybel_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & v1_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_waybel_0(k4_waybel_0(A,B),A)
        & v12_waybel_0(k4_waybel_0(A,B),A) ) ) ),
    file(waybel_0,fc16_waybel_0),
    []).

fof(fc1_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_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(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(fc5_yellow_3,axiom,(
    ! [A,B] : 
      ( ( l1_orders_2(A)
        & v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_xboole_0(k4_waybel_0(A,B)) ) ),
    file(yellow_3,fc5_yellow_3),
    []).

fof(fc5_yellow_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k3_yellow_4(A,B,C)) ) ),
    file(yellow_4,fc5_yellow_4),
    []).

fof(fc6_yellow_4,axiom,(
    ! [A,B,C] : 
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & v1_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v1_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_waybel_0(k3_yellow_4(A,B,C),A) ) ),
    file(yellow_4,fc6_yellow_4),
    []).

fof(fc7_waybel_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k4_waybel_0(A,B)) ) ),
    file(waybel_0,fc7_waybel_0),
    []).

fof(fc8_yellow_4,axiom,(
    ! [A,B,C] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & v12_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v12_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v12_waybel_0(k3_yellow_4(A,B,C),A) ) ),
    file(yellow_4,fc8_yellow_4),
    []).

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_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(rc9_waybel_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_waybel_0(B,A)
          & v12_waybel_0(B,A) ) ) ),
    file(waybel_0,rc9_waybel_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_k4_yellow_4,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => k4_yellow_4(A,B,C) = k3_yellow_4(A,B,C) ) ),
    file(yellow_4,k4_yellow_4),
    []).

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

fof(t33_waybel_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_yellow_0(A,B)
           => k1_yellow_0(A,B) = k1_yellow_0(A,k4_waybel_0(A,B)) ) ) ) ),
    file(waybel_0,t33_waybel_0),
    []).

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(t62_yellow_4,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_waybel_0(A,k4_yellow_4(A,k4_waybel_0(A,B),k4_waybel_0(A,C))) = k4_waybel_0(A,k4_yellow_4(A,B,C)) ) ) ) ),
    file(yellow_4,t62_yellow_4),
    []).

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

fof(t75_waybel_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v24_waybel_0(A)
      <=> ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => r1_yellow_0(A,B) ) ) ) ),
    file(waybel_0,t75_waybel_0),
    []).

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),
    []).