% Mizar problem: t20_lattice5,lattice5,1922,33 
fof(t20_lattice5,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( ( v1_lattice5(C,A,B)
                  & v3_lattice5(C,A,B) )
               => ! [D] : 
                    ( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
                   => ( r3_orders_2(B,k4_lattice5(A,B,C,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k13_lattice3(B,k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)))
                     => v3_lattice5(k7_lattice5(A,B,C,D),k6_lattice5(A),B) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_abian,cc1_arytm_3,cc1_finseq_1,cc1_lattice3,cc1_ordinal1,cc1_relset_1,cc2_arytm_3,cc2_lattice3,cc2_ordinal1,cc3_int_1,cc3_ordinal1,cc4_int_1,commutativity_k13_lattice3,commutativity_k2_tarski,commutativity_k2_xboole_0,d10_lattice5,d11_lattice5,d1_binop_1,d1_enumset1,d2_xboole_0,d5_tarski,d6_lattice5,d8_lattice5,dt_k10_lattice3,dt_k10_mcart_1,dt_k11_lattice3,dt_k11_mcart_1,dt_k13_lattice3,dt_k1_binop_1,dt_k1_enumset1,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_yellow_0,dt_k4_lattice5,dt_k4_tarski,dt_k4_zfmisc_1,dt_k6_lattice5,dt_k7_lattice5,dt_k8_mcart_1,dt_k9_mcart_1,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,fc17_abian,fc1_struct_0,fc1_subset_1,fc2_finseq_1,fc2_ordinal1,fc2_subset_1,fc3_lattice5,fc3_subset_1,fc4_subset_1,fc6_subset_1,idempotence_k2_xboole_0,rc1_arytm_3,rc1_finseq_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_int_1,rc2_ordinal1,rc2_partfun1,rc2_subset_1,rc3_finseq_1,rc3_ordinal1,rc3_struct_0,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k13_lattice3,redefinition_k4_lattice5,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,t14_lattice3,t1_boole,t1_subset,t1_yellow_5,t22_yellow_0,t26_orders_2,t2_subset,t3_subset,t3_waybel_1,t3_yellow_3,t44_yellow_0,t4_subset,t4_waybel_1,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(lattice5,t20_lattice5)]).

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

fof(cc1_abian,axiom,(
    ! [A] : 
      ( v2_setfam_1(A)
     => v1_realset1(A) ) ),
    file(abian,cc1_abian),
    []).

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

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

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

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_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

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

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc3_int_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(cc4_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    []).

fof(commutativity_k13_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k13_lattice3(A,B,C) = k13_lattice3(A,C,B) ) ),
    file(lattice3,k13_lattice3),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(d10_lattice5,axiom,(
    ! [A] : k6_lattice5(A) = k2_xboole_0(A,k1_enumset1(k1_tarski(A),k1_tarski(k1_tarski(A)),k1_tarski(k1_tarski(k1_tarski(A))))) ),
    file(lattice5,d10_lattice5),
    []).

fof(d11_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] : 
                  ( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(k6_lattice5(A),k6_lattice5(A)),u1_struct_0(B))
                        & m2_relset_1(E,k2_zfmisc_1(k6_lattice5(A),k6_lattice5(A)),u1_struct_0(B)) )
                     => ( E = k7_lattice5(A,B,C,D)
                      <=> ( ! [F] : 
                              ( m1_subset_1(F,A)
                             => ! [G] : 
                                  ( m1_subset_1(G,A)
                                 => k1_binop_1(E,F,G) = k4_lattice5(A,B,C,F,G) ) )
                          & k1_binop_1(E,k1_tarski(A),k1_tarski(A)) = k3_yellow_0(B)
                          & k1_binop_1(E,k1_tarski(k1_tarski(A)),k1_tarski(k1_tarski(A))) = k3_yellow_0(B)
                          & k1_binop_1(E,k1_tarski(k1_tarski(k1_tarski(A))),k1_tarski(k1_tarski(k1_tarski(A)))) = k3_yellow_0(B)
                          & k1_binop_1(E,k1_tarski(k1_tarski(A)),k1_tarski(k1_tarski(k1_tarski(A)))) = k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)
                          & k1_binop_1(E,k1_tarski(k1_tarski(k1_tarski(A))),k1_tarski(k1_tarski(A))) = k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)
                          & k1_binop_1(E,k1_tarski(A),k1_tarski(k1_tarski(A))) = k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)
                          & k1_binop_1(E,k1_tarski(k1_tarski(A)),k1_tarski(A)) = k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)
                          & k1_binop_1(E,k1_tarski(A),k1_tarski(k1_tarski(k1_tarski(A)))) = k13_lattice3(B,k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                          & k1_binop_1(E,k1_tarski(k1_tarski(k1_tarski(A))),k1_tarski(A)) = k13_lattice3(B,k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                          & ! [F] : 
                              ( m1_subset_1(F,A)
                             => ( k1_binop_1(E,F,k1_tarski(A)) = k13_lattice3(B,k4_lattice5(A,B,C,F,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                                & k1_binop_1(E,k1_tarski(A),F) = k13_lattice3(B,k4_lattice5(A,B,C,F,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                                & k1_binop_1(E,F,k1_tarski(k1_tarski(A))) = k13_lattice3(B,k13_lattice3(B,k4_lattice5(A,B,C,F,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                                & k1_binop_1(E,k1_tarski(k1_tarski(A)),F) = k13_lattice3(B,k13_lattice3(B,k4_lattice5(A,B,C,F,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                                & k1_binop_1(E,F,k1_tarski(k1_tarski(k1_tarski(A)))) = k13_lattice3(B,k4_lattice5(A,B,C,F,k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                                & k1_binop_1(E,k1_tarski(k1_tarski(k1_tarski(A))),F) = k13_lattice3(B,k4_lattice5(A,B,C,F,k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)) ) ) ) ) ) ) ) ) ) ),
    file(lattice5,d11_lattice5),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d1_enumset1,axiom,(
    ! [A,B,C,D] : 
      ( D = k1_enumset1(A,B,C)
    <=> ! [E] : 
          ( r2_hidden(E,D)
        <=> ~ ( E != A
              & E != B
              & E != C ) ) ) ),
    file(enumset1,d1_enumset1),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d6_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( v1_lattice5(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => k4_lattice5(A,B,C,D,E) = k4_lattice5(A,B,C,E,D) ) ) ) ) ) ) ),
    file(lattice5,d6_lattice5),
    []).

fof(d8_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( v3_lattice5(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => ! [F] : 
                            ( m1_subset_1(F,A)
                           => r1_orders_2(B,k4_lattice5(A,B,C,D,F),k13_lattice3(B,k4_lattice5(A,B,C,D,E),k4_lattice5(A,B,C,E,F))) ) ) ) ) ) ) ) ),
    file(lattice5,d8_lattice5),
    []).

fof(dt_k10_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(k10_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k10_lattice3),
    []).

fof(dt_k10_mcart_1,axiom,(
    ! [A,B,C,D,E] : 
      ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
     => m1_subset_1(k10_mcart_1(A,B,C,D,E),C) ) ),
    file(mcart_1,k10_mcart_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_k11_mcart_1,axiom,(
    ! [A,B,C,D,E] : 
      ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
     => m1_subset_1(k11_mcart_1(A,B,C,D,E),D) ) ),
    file(mcart_1,k11_mcart_1),
    []).

fof(dt_k13_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v1_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(k13_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k13_lattice3),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

fof(dt_k1_enumset1,axiom,(
    $true ),
    file(enumset1,k1_enumset1),
    []).

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

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ) ),
    file(yellow_0,k3_yellow_0),
    []).

fof(dt_k4_lattice5,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => m1_subset_1(k4_lattice5(A,B,C,D,E),u1_struct_0(B)) ) ),
    file(lattice5,k4_lattice5),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k4_zfmisc_1),
    []).

fof(dt_k6_lattice5,axiom,(
    $true ),
    file(lattice5,k6_lattice5),
    []).

fof(dt_k7_lattice5,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B))) )
     => ( v1_funct_1(k7_lattice5(A,B,C,D))
        & v1_funct_2(k7_lattice5(A,B,C,D),k2_zfmisc_1(k6_lattice5(A),k6_lattice5(A)),u1_struct_0(B))
        & m2_relset_1(k7_lattice5(A,B,C,D),k2_zfmisc_1(k6_lattice5(A),k6_lattice5(A)),u1_struct_0(B)) ) ) ),
    file(lattice5,k7_lattice5),
    []).

fof(dt_k8_mcart_1,axiom,(
    ! [A,B,C,D,E] : 
      ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
     => m1_subset_1(k8_mcart_1(A,B,C,D,E),A) ) ),
    file(mcart_1,k8_mcart_1),
    []).

fof(dt_k9_mcart_1,axiom,(
    ! [A,B,C,D,E] : 
      ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
     => m1_subset_1(k9_mcart_1(A,B,C,D,E),B) ) ),
    file(mcart_1,k9_mcart_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_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(fc17_abian,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_zfmisc_1(A))
        & ~ v2_setfam_1(k1_zfmisc_1(A)) ) ) ),
    file(abian,fc17_abian),
    []).

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(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_ordinal1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_lattice5,axiom,(
    ! [A] : ~ v1_xboole_0(k6_lattice5(A)) ),
    file(lattice5,fc3_lattice5),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_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(fc6_subset_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D) )
     => ~ v1_xboole_0(k4_zfmisc_1(A,B,C,D)) ) ),
    file(subset_1,fc6_subset_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

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_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    []).

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

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_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_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

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(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(redefinition_k13_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k13_lattice3(A,B,C) = k10_lattice3(A,B,C) ) ),
    file(lattice3,k13_lattice3),
    []).

fof(redefinition_k4_lattice5,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => k4_lattice5(A,B,C,D,E) = k1_binop_1(C,D,E) ) ),
    file(lattice5,k4_lattice5),
    []).

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(redefinition_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_orders_2(A,B,C)
      <=> r1_orders_2(A,B,C) ) ) ),
    file(orders_2,r3_orders_2),
    []).

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

fof(reflexivity_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r3_orders_2(A,B,B) ) ),
    file(orders_2,r3_orders_2),
    []).

fof(t14_lattice3,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & v1_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))
                 => ( v3_orders_2(A)
                   => k10_lattice3(A,k10_lattice3(A,B,C),D) = k10_lattice3(A,B,k10_lattice3(A,C,D)) ) ) ) ) ) ),
    file(lattice3,t14_lattice3),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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

fof(t1_yellow_5,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k13_lattice3(A,B,B) = B ) ) ),
    file(yellow_5,t1_yellow_5),
    []).

fof(t22_yellow_0,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & v1_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 = k13_lattice3(A,B,C)
                  <=> ( r1_orders_2(A,B,D)
                      & r1_orders_2(A,C,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,B,E)
                              & r1_orders_2(A,C,E) )
                           => r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ),
    file(yellow_0,t22_yellow_0),
    []).

fof(t26_orders_2,axiom,(
    ! [A] : 
      ( ( v3_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))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_orders_2(A,B,C)
                      & r1_orders_2(A,C,D) )
                   => r1_orders_2(A,B,D) ) ) ) ) ) ),
    file(orders_2,t26_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(t3_waybel_1,axiom,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_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))
                 => ( r1_orders_2(A,B,C)
                   => r1_orders_2(A,k13_lattice3(A,B,D),k13_lattice3(A,C,D)) ) ) ) ) ) ),
    file(waybel_1,t3_waybel_1),
    []).

fof(t3_yellow_3,axiom,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_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))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_orders_2(A,B,D)
                          & r1_orders_2(A,C,E) )
                       => r1_orders_2(A,k13_lattice3(A,B,C),k13_lattice3(A,D,E)) ) ) ) ) ) ) ),
    file(yellow_3,t3_yellow_3),
    []).

fof(t44_yellow_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_orders_2(A,k3_yellow_0(A),B) ) ) ),
    file(yellow_0,t44_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(t4_waybel_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( v2_lattice3(A)
             => k11_lattice3(A,k3_yellow_0(A),B) = k3_yellow_0(A) )
            & ( ( v1_lattice3(A)
                & v2_orders_2(A)
                & v3_orders_2(A) )
             => k10_lattice3(A,k3_yellow_0(A),B) = B ) ) ) ) ),
    file(waybel_1,t4_waybel_1),
    []).

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),
    []).