% Mizar problem: t17_scmpds_8,scmpds_8,1561,27 
fof(t17_scmpds_8,conjecture,(
    ! [A] : 
      ( m1_scmpds_2(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ! [C] : 
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k4_card_1(k3_scmpds_8(A,B,C)) = k1_nat_1(k4_card_1(C),2) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_ami_1,antisymmetry_r2_hidden,cc1_fraenkel,cc1_funct_1,cc1_int_1,cc1_relset_1,cc1_scmfsa_4,cc1_setfam_1,cc1_xreal_0,cc2_funct_1,cc2_int_1,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,d3_scmpds_8,dt_g1_ami_1,dt_k13_finseq_1,dt_k1_card_1,dt_k1_funct_2,dt_k1_nat_1,dt_k1_numbers,dt_k1_scmpds_2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_scmpds_8,dt_k3_tarski,dt_k4_card_1,dt_k4_card_3,dt_k4_numbers,dt_k4_scmpds_2,dt_k4_scmpds_4,dt_k4_xcmplx_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_scmpds_4,dt_k7_ami_1,dt_k9_scmpds_2,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_relset_1,dt_m1_scmpds_2,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_ami_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_1,existence_m1_relset_1,existence_m1_scmpds_2,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_ami_1,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc1_fraenkel,fc1_int_1,fc1_numbers,fc1_ordinal2,fc1_scmpds_2,fc1_scmpds_6,fc1_xreal_0,fc2_ami_1,fc2_fraenkel,fc2_scmpds_2,fc2_scmpds_6,fc2_setfam_1,fc3_ami_1,fc3_int_1,fc3_setfam_1,fc3_xreal_0,fc4_ami_1,fc4_numbers,fc4_scmpds_2,fc4_setfam_1,fc5_int_1,fc5_scmpds_2,fc5_scmpds_5,fc6_int_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,free_g1_ami_1,idempotence_k2_xboole_0,involutiveness_k4_xcmplx_0,rc1_ami_1,rc1_fraenkel,rc1_funct_1,rc1_int_1,rc1_scmfsa_4,rc1_setfam_1,rc1_xreal_0,rc2_ami_1,rc2_funct_1,rc2_int_1,rc2_xreal_0,rc3_ami_1,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,rc5_ami_1,rc6_ami_1,rc7_ami_1,rc8_ami_1,rc9_ami_1,redefinition_k1_nat_1,redefinition_k4_card_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t15_scmpds_6,t1_boole,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t8_scmp_gcd]),
    [file(scmpds_8,t17_scmpds_8)]).

fof(abstractness_v1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v1_ami_1(B,A)
       => B = g1_ami_1(A,u1_struct_0(B),u1_ami_1(A,B),u2_ami_1(A,B),u3_ami_1(A,B),u4_ami_1(A,B),u5_ami_1(A,B),u6_ami_1(A,B)) ) ) ),
    file(ami_1,v1_ami_1),
    []).

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

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k4_numbers)
     => v1_int_1(A) ) ),
    file(int_1,cc1_int_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(cc1_scmfsa_4,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finset_1(C) ) ) ) ),
    file(scmfsa_4,cc1_scmfsa_4),
    []).

fof(cc1_setfam_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    []).

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

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_int_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)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    []).

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

fof(cc3_int_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_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_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    []).

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_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(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

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(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(d3_scmpds_8,axiom,(
    ! [A] : 
      ( m1_scmpds_2(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ! [C] : 
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k3_scmpds_8(A,B,C) = k5_scmpds_4(k4_scmpds_4(k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),2)),C),k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(C),1)))) ) ) ) ),
    file(scmpds_8,d3_scmpds_8),
    []).

fof(dt_g1_ami_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( m1_subset_1(C,B)
        & m1_subset_1(D,k1_zfmisc_1(B))
        & ~ v1_xboole_0(E)
        & ~ v1_xboole_0(F)
        & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B)))))
        & v1_funct_1(G)
        & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D)))
        & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D)))
        & v1_funct_1(H)
        & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G)))
        & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) )
     => ( v1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A)
        & l1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) ) ) ),
    file(ami_1,g1_ami_1),
    []).

fof(dt_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    []).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

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

fof(dt_k1_scmpds_2,axiom,
    ( v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & l1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ),
    file(scmpds_2,k1_scmpds_2),
    []).

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_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_scmpds_8,axiom,(
    ! [A,B,C] : 
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(C)
        & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k3_scmpds_8(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k3_scmpds_8(A,B,C))
        & m1_ami_1(k3_scmpds_8(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ),
    file(scmpds_8,k3_scmpds_8),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k4_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ),
    file(card_1,k4_card_1),
    []).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

fof(dt_k4_numbers,axiom,(
    $true ),
    file(numbers,k4_numbers),
    []).

fof(dt_k4_scmpds_2,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => m2_subset_1(k4_scmpds_2(A),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ),
    file(scmpds_2,k4_scmpds_2),
    []).

fof(dt_k4_scmpds_4,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(B)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k4_scmpds_4(A,B))
        & m1_ami_1(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ),
    file(scmpds_4,k4_scmpds_4),
    []).

fof(dt_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k4_xcmplx_0(A)) ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

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_k5_scmpds_4,axiom,(
    ! [A,B] : 
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
     => ( v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k5_scmpds_4(A,B))
        & m1_ami_1(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ),
    file(scmpds_4,k5_scmpds_4),
    []).

fof(dt_k7_ami_1,axiom,(
    $true ),
    file(ami_1,k7_ami_1),
    []).

fof(dt_k9_scmpds_2,axiom,(
    ! [A,B,C] : 
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => m2_subset_1(k9_scmpds_2(A,B,C),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ),
    file(scmpds_2,k9_scmpds_2),
    []).

fof(dt_l1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => l1_struct_0(B) ) ),
    file(ami_1,l1_ami_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => m1_subset_1(C,k7_ami_1(u5_ami_1(A,B))) ) ) ),
    file(ami_1,m1_ami_1),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_scmpds_2,axiom,(
    ! [A] : 
      ( m1_scmpds_2(A)
     => m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) ),
    file(scmpds_2,m1_scmpds_2),
    []).

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_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(dt_u1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => m1_subset_1(u1_ami_1(A,B),u1_struct_0(B)) ) ),
    file(ami_1,u1_ami_1),
    []).

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

fof(dt_u2_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => m1_subset_1(u2_ami_1(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(ami_1,u2_ami_1),
    []).

fof(dt_u3_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ~ v1_xboole_0(u3_ami_1(A,B)) ) ),
    file(ami_1,u3_ami_1),
    []).

fof(dt_u4_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( ~ v1_xboole_0(u4_ami_1(A,B))
        & m1_subset_1(u4_ami_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))))) ) ) ),
    file(ami_1,u4_ami_1),
    []).

fof(dt_u5_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v1_funct_1(u5_ami_1(A,B))
        & v1_funct_2(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))))
        & m2_relset_1(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ) ),
    file(ami_1,u5_ami_1),
    []).

fof(dt_u6_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v1_funct_1(u6_ami_1(A,B))
        & v1_funct_2(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))))
        & m2_relset_1(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))) ) ) ),
    file(ami_1,u6_ami_1),
    []).

fof(existence_l1_ami_1,axiom,(
    ! [A] : 
    ? [B] : l1_ami_1(B,A) ),
    file(ami_1,l1_ami_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ? [C] : m1_ami_1(C,A,B) ) ),
    file(ami_1,m1_ami_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_scmpds_2,axiom,(
    ? [A] : m1_scmpds_2(A) ),
    file(scmpds_2,m1_scmpds_2),
    []).

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_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_ami_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k7_ami_1(A))
        & v1_fraenkel(k7_ami_1(A)) ) ) ),
    file(ami_1,fc10_ami_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(fc13_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc13_xreal_0),
    []).

fof(fc14_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc14_xreal_0),
    []).

fof(fc1_fraenkel,axiom,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    []).

fof(fc1_int_1,axiom,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v1_int_1(k2_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc1_int_1),
    []).

fof(fc1_numbers,axiom,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc1_scmpds_2,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ),
    file(scmpds_2,fc1_scmpds_2),
    []).

fof(fc1_scmpds_6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => v1_scmpds_5(k4_scmpds_2(k1_nat_1(A,1))) ) ),
    file(scmpds_6,fc1_scmpds_6),
    []).

fof(fc1_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc1_xreal_0),
    []).

fof(fc2_ami_1,axiom,(
    ! [A,B] : 
      ( ( ~ v2_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ~ v1_xboole_0(u2_ami_1(A,B)) ) ),
    file(ami_1,fc2_ami_1),
    []).

fof(fc2_fraenkel,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => ( v1_finset_1(k1_funct_2(A,B))
        & v1_fraenkel(k1_funct_2(A,B)) ) ) ),
    file(fraenkel,fc2_fraenkel),
    []).

fof(fc2_scmpds_2,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ),
    file(scmpds_2,fc2_scmpds_2),
    []).

fof(fc2_scmpds_6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => v1_scmpds_5(k4_scmpds_2(k4_xcmplx_0(k1_nat_1(A,1)))) ) ),
    file(scmpds_6,fc2_scmpds_6),
    []).

fof(fc2_setfam_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_setfam_1(k1_tarski(A)) ) ) ),
    file(setfam_1,fc2_setfam_1),
    []).

fof(fc3_ami_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_fraenkel(k4_card_3(A)) ) ),
    file(ami_1,fc3_ami_1),
    []).

fof(fc3_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc3_int_1),
    []).

fof(fc3_setfam_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( ~ v1_xboole_0(k2_tarski(A,B))
        & v1_setfam_1(k2_tarski(A,B)) ) ) ),
    file(setfam_1,fc3_setfam_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_ami_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_setfam_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( ~ v1_xboole_0(k4_card_3(C))
        & v1_fraenkel(k4_card_3(C)) ) ) ),
    file(ami_1,fc4_ami_1),
    []).

fof(fc4_numbers,axiom,(
    ~ v1_xboole_0(k4_numbers) ),
    file(numbers,fc4_numbers),
    []).

fof(fc4_scmpds_2,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ),
    file(scmpds_2,fc4_scmpds_2),
    []).

fof(fc4_setfam_1,axiom,(
    ! [A,B] : 
      ( ( v1_setfam_1(A)
        & v1_setfam_1(B) )
     => v1_setfam_1(k2_xboole_0(A,B)) ) ),
    file(setfam_1,fc4_setfam_1),
    []).

fof(fc5_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc5_int_1),
    []).

fof(fc5_scmpds_2,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ),
    file(scmpds_2,fc5_scmpds_2),
    []).

fof(fc5_scmpds_5,axiom,(
    ! [A,B,C] : 
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => v1_scmpds_5(k9_scmpds_2(A,B,C)) ) ),
    file(scmpds_5,fc5_scmpds_5),
    []).

fof(fc6_int_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v1_int_1(k2_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc6_int_1),
    []).

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(free_g1_ami_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( m1_subset_1(C,B)
        & m1_subset_1(D,k1_zfmisc_1(B))
        & ~ v1_xboole_0(E)
        & ~ v1_xboole_0(F)
        & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B)))))
        & v1_funct_1(G)
        & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D)))
        & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D)))
        & v1_funct_1(H)
        & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G)))
        & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) )
     => ! [I,J,K,L,M,N,O,P] : 
          ( g1_ami_1(A,B,C,D,E,F,G,H) = g1_ami_1(I,J,K,L,M,N,O,P)
         => ( A = I
            & B = J
            & C = K
            & D = L
            & E = M
            & F = N
            & G = O
            & H = P ) ) ) ),
    file(ami_1,g1_ami_1),
    []).

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

fof(involutiveness_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

fof(rc1_ami_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( l1_ami_1(B,A)
      & v1_ami_1(B,A) ) ),
    file(ami_1,rc1_ami_1),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_int_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_1),
    []).

fof(rc1_scmfsa_4,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ? [C] : 
          ( m1_ami_1(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_ami_3(C,A,B) ) ) ),
    file(scmfsa_4,rc1_scmfsa_4),
    []).

fof(rc1_setfam_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_1),
    []).

fof(rc1_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

fof(rc2_ami_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( l1_ami_1(B,A)
      & ~ v3_struct_0(B)
      & ~ v2_ami_1(B,A) ) ),
    file(ami_1,rc2_ami_1),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_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_ami_1,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ? [B] : 
          ( l1_ami_1(B,A)
          & ~ v2_ami_1(B,A)
          & v4_ami_1(B,A) ) ) ),
    file(ami_1,rc3_ami_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_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(rc5_ami_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( l1_ami_1(B,A)
      & v1_ami_1(B,A)
      & v6_ami_1(B,A) ) ),
    file(ami_1,rc5_ami_1),
    []).

fof(rc6_ami_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( l1_ami_1(B,A)
      & ~ v3_struct_0(B)
      & v1_ami_1(B,A)
      & ~ v2_ami_1(B,A)
      & v5_ami_1(B,A)
      & v6_ami_1(B,A)
      & v8_ami_1(B,A) ) ),
    file(ami_1,rc6_ami_1),
    []).

fof(rc7_ami_1,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ? [B] : 
          ( l1_ami_1(B,A)
          & ~ v3_struct_0(B)
          & v1_ami_1(B,A)
          & ~ v2_ami_1(B,A)
          & v4_ami_1(B,A)
          & v5_ami_1(B,A)
          & v6_ami_1(B,A)
          & v7_ami_1(B,A)
          & v8_ami_1(B,A) ) ) ),
    file(ami_1,rc7_ami_1),
    []).

fof(rc8_ami_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( l1_ami_1(B,A)
      & v1_ami_1(B,A)
      & v6_ami_1(B,A)
      & v10_ami_1(B,A) ) ),
    file(ami_1,rc8_ami_1),
    []).

fof(rc9_ami_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( l1_ami_1(B,A)
      & ~ v3_struct_0(B)
      & v1_ami_1(B,A)
      & ~ v2_ami_1(B,A)
      & v5_ami_1(B,A)
      & v6_ami_1(B,A)
      & v8_ami_1(B,A)
      & v10_ami_1(B,A) ) ),
    file(ami_1,rc9_ami_1),
    []).

fof(redefinition_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(redefinition_k4_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => k4_card_1(A) = k1_card_1(A) ) ),
    file(card_1,k4_card_1),
    []).

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

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(spc2_boole,axiom,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    []).

fof(spc2_numerals,axiom,
    ( v2_xreal_0(2)
    & m1_subset_1(2,k5_numbers) ),
    file(numerals,spc2_numerals),
    []).

fof(t15_scmpds_6,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] : 
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k4_card_1(k4_scmpds_4(A,B)) = k1_nat_1(k4_card_1(B),1) ) ) ),
    file(scmpds_6,t15_scmpds_6),
    []).

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(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),
    []).

fof(t8_scmp_gcd,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] : 
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k4_card_1(k5_scmpds_4(B,A)) = k1_nat_1(k4_card_1(B),1) ) ) ),
    file(scmp_gcd,t8_scmp_gcd),
    []).