% Mizar problem: t109_euclidlp,euclidlp,2193,69 
fof(t109_euclidlp,conjecture,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_2(B,k1_numbers,k1_euclid(A))
         => ! [C] : 
              ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A))
             => ! [D] : 
                  ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A))
                 => ( ( r2_hidden(B,D)
                      & r1_tarski(C,D)
                      & v1_euclid_4(C,A) )
                   => ( r2_hidden(B,C)
                      | v1_euclidlp(D,A) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_nat_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k2_euclid_4,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_rvsum_1,commutativity_k7_euclid,d10_euclidlp,d11_euclidlp,d4_euclidlp,d9_euclidlp,dt_k1_euclid,dt_k1_euclid_4,dt_k1_euclidlp,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_euclid_4,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_real_1,dt_k3_rvsum_1,dt_k4_euclidlp,dt_k5_euclidlp,dt_k5_numbers,dt_k5_ordinal2,dt_k7_euclid,dt_k7_rvsum_1,dt_k8_euclid,dt_k9_euclid,dt_k9_rvsum_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_euclidlp,fc1_nat_1,fc1_subset_1,fc2_euclidlp,fc2_membered,fc3_euclidlp,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc4_subset_1,fc5_membered,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,fraenkel_a_1_0_euclidlp,fraenkel_a_1_1_euclidlp,fraenkel_a_4_2_euclidlp,rc1_membered,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_subset_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,redefinition_k2_euclid_4,redefinition_k3_real_1,redefinition_k5_numbers,redefinition_k7_euclid,redefinition_k8_euclid,redefinition_k9_euclid,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc1_boole,spc1_numerals,symmetry_r3_euclidlp,t100_euclidlp,t10_euclid_4,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t61_euclidlp,t6_boole,t7_boole,t8_boole]),
    [file(euclidlp,t109_euclidlp)]).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

fof(cc1_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

fof(cc1_xreal_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    []).

fof(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc2_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(cc3_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc4_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    []).

fof(cc5_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(cc6_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    []).

fof(cc7_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    []).

fof(cc8_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    []).

fof(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

fof(commutativity_k2_euclid_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => k2_euclid_4(A,B,C) = k2_euclid_4(A,C,B) ) ),
    file(euclid_4,k2_euclid_4),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(commutativity_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k3_real_1(B,A) ) ),
    file(real_1,k3_real_1),
    []).

fof(commutativity_k3_rvsum_1,axiom,(
    ! [A,B] : 
      ( ( m1_finseq_1(A,k1_numbers)
        & m1_finseq_1(B,k1_numbers) )
     => k3_rvsum_1(A,B) = k3_rvsum_1(B,A) ) ),
    file(rvsum_1,k3_rvsum_1),
    []).

fof(commutativity_k7_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => k7_euclid(A,B,C) = k7_euclid(A,C,B) ) ),
    file(euclid,k7_euclid),
    []).

fof(d10_euclidlp,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A)))
         => ( v1_euclidlp(B,A)
          <=> ? [C] : 
                ( m2_finseq_2(C,k1_numbers,k1_euclid(A))
                & ? [D] : 
                    ( m2_finseq_2(D,k1_numbers,k1_euclid(A))
                    & ? [E] : 
                        ( m2_finseq_2(E,k1_numbers,k1_euclid(A))
                        & r3_euclidlp(A,k8_euclid(A,D,C),k8_euclid(A,E,C))
                        & B = k4_euclidlp(A,C,D,E) ) ) ) ) ) ) ),
    file(euclidlp,d10_euclidlp),
    []).

fof(d11_euclidlp,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k5_euclidlp(A) = a_1_1_euclidlp(A) ) ),
    file(euclidlp,d11_euclidlp),
    []).

fof(d4_euclidlp,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_euclidlp(A) = a_1_0_euclidlp(A) ) ),
    file(euclidlp,d4_euclidlp),
    []).

fof(d9_euclidlp,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_2(B,k1_numbers,k1_euclid(A))
         => ! [C] : 
              ( m2_finseq_2(C,k1_numbers,k1_euclid(A))
             => ! [D] : 
                  ( m2_finseq_2(D,k1_numbers,k1_euclid(A))
                 => k4_euclidlp(A,B,C,D) = a_4_2_euclidlp(A,B,C,D) ) ) ) ) ),
    file(euclidlp,d9_euclidlp),
    []).

fof(dt_k1_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v1_xboole_0(k1_euclid(A))
        & m1_finseq_2(k1_euclid(A),k1_numbers) ) ) ),
    file(euclid,k1_euclid),
    []).

fof(dt_k1_euclid_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => m1_subset_1(k1_euclid_4(A,B,C),k1_zfmisc_1(k1_euclid(A))) ) ),
    file(euclid_4,k1_euclid_4),
    []).

fof(dt_k1_euclidlp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k1_euclidlp(A),k1_zfmisc_1(k1_zfmisc_1(k1_euclid(A)))) ) ),
    file(euclidlp,k1_euclidlp),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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_euclid_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => m1_subset_1(k2_euclid_4(A,B,C),k1_zfmisc_1(k1_euclid(A))) ) ),
    file(euclid_4,k2_euclid_4),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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

fof(dt_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ),
    file(real_1,k3_real_1),
    []).

fof(dt_k3_rvsum_1,axiom,(
    ! [A,B] : 
      ( ( m1_finseq_1(A,k1_numbers)
        & m1_finseq_1(B,k1_numbers) )
     => m2_finseq_1(k3_rvsum_1(A,B),k1_numbers) ) ),
    file(rvsum_1,k3_rvsum_1),
    []).

fof(dt_k4_euclidlp,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A))
        & m1_subset_1(D,k1_euclid(A)) )
     => m1_subset_1(k4_euclidlp(A,B,C,D),k1_zfmisc_1(k1_euclid(A))) ) ),
    file(euclidlp,k4_euclidlp),
    []).

fof(dt_k5_euclidlp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k5_euclidlp(A),k1_zfmisc_1(k1_zfmisc_1(k1_euclid(A)))) ) ),
    file(euclidlp,k5_euclidlp),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k7_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => m2_finseq_2(k7_euclid(A,B,C),k1_numbers,k1_euclid(A)) ) ),
    file(euclid,k7_euclid),
    []).

fof(dt_k7_rvsum_1,axiom,(
    ! [A,B] : 
      ( ( m1_finseq_1(A,k1_numbers)
        & m1_finseq_1(B,k1_numbers) )
     => m2_finseq_1(k7_rvsum_1(A,B),k1_numbers) ) ),
    file(rvsum_1,k7_rvsum_1),
    []).

fof(dt_k8_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => m2_finseq_2(k8_euclid(A,B,C),k1_numbers,k1_euclid(A)) ) ),
    file(euclid,k8_euclid),
    []).

fof(dt_k9_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_xreal_0(B)
        & m1_subset_1(C,k1_euclid(A)) )
     => m2_finseq_2(k9_euclid(A,B,C),k1_numbers,k1_euclid(A)) ) ),
    file(euclid,k9_euclid),
    []).

fof(dt_k9_rvsum_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & m1_finseq_1(B,k1_numbers) )
     => m2_finseq_1(k9_rvsum_1(A,B),k1_numbers) ) ),
    file(rvsum_1,k9_rvsum_1),
    []).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    []).

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_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(dt_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,m2_finseq_2),
    []).

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_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    []).

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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ? [C] : m2_finseq_2(C,A,B) ) ),
    file(finseq_2,m2_finseq_2),
    []).

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

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc10_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    []).

fof(fc11_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    []).

fof(fc12_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    []).

fof(fc1_euclidlp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ~ v1_xboole_0(k1_euclidlp(A)) ) ),
    file(euclidlp,fc1_euclidlp),
    []).

fof(fc1_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    []).

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

fof(fc2_euclidlp,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A))
        & m1_subset_1(D,k1_euclid(A)) )
     => ~ v1_xboole_0(k4_euclidlp(A,B,C,D)) ) ),
    file(euclidlp,fc2_euclidlp),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc3_euclidlp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ~ v1_xboole_0(k5_euclidlp(A)) ) ),
    file(euclidlp,fc3_euclidlp),
    []).

fof(fc3_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    []).

fof(fc3_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    []).

fof(fc4_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_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(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(fc7_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    []).

fof(fc8_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    []).

fof(fc9_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    []).

fof(fraenkel_a_1_0_euclidlp,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( r2_hidden(A,a_1_0_euclidlp(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(B)))
            & A = C
            & ? [D] : 
                ( m2_finseq_2(D,k1_numbers,k1_euclid(B))
                & ? [E] : 
                    ( m2_finseq_2(E,k1_numbers,k1_euclid(B))
                    & C = k2_euclid_4(B,D,E) ) ) ) ) ) ),
    file(euclidlp,a_1_0_euclidlp),
    []).

fof(fraenkel_a_1_1_euclidlp,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( r2_hidden(A,a_1_1_euclidlp(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(B)))
            & A = C
            & ? [D] : 
                ( m2_finseq_2(D,k1_numbers,k1_euclid(B))
                & ? [E] : 
                    ( m2_finseq_2(E,k1_numbers,k1_euclid(B))
                    & ? [F] : 
                        ( m2_finseq_2(F,k1_numbers,k1_euclid(B))
                        & C = k4_euclidlp(B,D,E,F) ) ) ) ) ) ) ),
    file(euclidlp,a_1_1_euclidlp),
    []).

fof(fraenkel_a_4_2_euclidlp,axiom,(
    ! [A,B,C,D,E] : 
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_finseq_2(C,k1_numbers,k1_euclid(B))
        & m2_finseq_2(D,k1_numbers,k1_euclid(B))
        & m2_finseq_2(E,k1_numbers,k1_euclid(B)) )
     => ( r2_hidden(A,a_4_2_euclidlp(B,C,D,E))
      <=> ? [F] : 
            ( m2_finseq_2(F,k1_numbers,k1_euclid(B))
            & A = F
            & ? [G] : 
                ( m1_subset_1(G,k1_numbers)
                & ? [H] : 
                    ( m1_subset_1(H,k1_numbers)
                    & ? [I] : 
                        ( m1_subset_1(I,k1_numbers)
                        & k3_real_1(k3_real_1(G,H),I) = 1
                        & F = k7_euclid(B,k7_euclid(B,k9_euclid(B,G,C),k9_euclid(B,H,D)),k9_euclid(B,I,E)) ) ) ) ) ) ) ),
    file(euclidlp,a_4_2_euclidlp),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(rc1_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_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(rc1_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_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(rc2_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

fof(rc3_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    []).

fof(rc4_xreal_0,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    []).

fof(redefinition_k2_euclid_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => k2_euclid_4(A,B,C) = k1_euclid_4(A,B,C) ) ),
    file(euclid_4,k2_euclid_4),
    []).

fof(redefinition_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(real_1,k3_real_1),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k7_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => k7_euclid(A,B,C) = k3_rvsum_1(B,C) ) ),
    file(euclid,k7_euclid),
    []).

fof(redefinition_k8_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => k8_euclid(A,B,C) = k7_rvsum_1(B,C) ) ),
    file(euclid,k8_euclid),
    []).

fof(redefinition_k9_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_xreal_0(B)
        & m1_subset_1(C,k1_euclid(A)) )
     => k9_euclid(A,B,C) = k9_rvsum_1(B,C) ) ),
    file(euclid,k9_euclid),
    []).

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(redefinition_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(finseq_2,m2_finseq_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(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(symmetry_r3_euclidlp,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_euclid(A))
        & m1_subset_1(C,k1_euclid(A)) )
     => ( r3_euclidlp(A,B,C)
       => r3_euclidlp(A,C,B) ) ) ),
    file(euclidlp,r3_euclidlp),
    []).

fof(t100_euclidlp,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_2(B,k1_numbers,k1_euclid(A))
         => ! [C] : 
              ( m2_finseq_2(C,k1_numbers,k1_euclid(A))
             => ! [D] : 
                  ( m2_finseq_2(D,k1_numbers,k1_euclid(A))
                 => ! [E] : 
                      ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A))
                     => ( ( r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & r2_hidden(D,E)
                          & r3_euclidlp(A,k8_euclid(A,C,B),k8_euclid(A,D,B)) )
                       => E = k4_euclidlp(A,B,C,D) ) ) ) ) ) ) ),
    file(euclidlp,t100_euclidlp),
    []).

fof(t10_euclid_4,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_euclid(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_euclid(A))
             => ( r2_hidden(B,k2_euclid_4(A,B,C))
                & r2_hidden(C,k2_euclid_4(A,B,C)) ) ) ) ) ),
    file(euclid_4,t10_euclid_4),
    []).

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(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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(t61_euclidlp,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_2(B,k1_numbers,k1_euclid(A))
         => ! [C] : 
              ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A))
             => ~ ( ~ r2_hidden(B,C)
                  & v1_euclid_4(C,A)
                  & ! [D] : 
                      ( m2_finseq_2(D,k1_numbers,k1_euclid(A))
                     => ! [E] : 
                          ( m2_finseq_2(E,k1_numbers,k1_euclid(A))
                         => ~ ( C = k2_euclid_4(A,D,E)
                              & r3_euclidlp(A,k8_euclid(A,B,D),k8_euclid(A,E,D)) ) ) ) ) ) ) ) ),
    file(euclidlp,t61_euclidlp),
    []).

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),
    []).