% Mizar problem: t63_sin_cos3,sin_cos3,1601,65 
fof(t63_sin_cos3,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k2_numbers)
         => ( k8_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,A)),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,B))) = k3_xcmplx_0(k3_xcmplx_0(2,k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k8_complex1(A,B))),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k11_complex1(A,B)))
            & k11_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,A)),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,B))) = k3_xcmplx_0(k3_xcmplx_0(2,k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,k8_complex1(A,B))),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,k11_complex1(A,B))) ) ) ) ),
    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_complex1,cc1_membered,cc1_nat_1,cc1_relset_1,cc1_xcmplx_0,cc20_membered,cc2_membered,cc2_nat_1,cc2_xcmplx_0,cc3_membered,cc3_nat_1,cc4_membered,cc5_membered,cc6_membered,cc9_membered,commutativity_k1_nat_1,commutativity_k2_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,commutativity_k8_complex1,commutativity_k9_complex1,dt_k11_complex1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_nat_1,dt_k2_numbers,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_sin_cos3,dt_k3_xcmplx_0,dt_k4_finseq_4,dt_k4_sin_cos3,dt_k5_numbers,dt_k5_ordinal2,dt_k6_xcmplx_0,dt_k8_complex1,dt_k9_complex1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc1_membered,fc1_nat_1,fc1_ordinal2,fc2_membered,fc2_nat_1,fc2_xcmplx_0,fc3_nat_1,fc3_xcmplx_0,fc4_nat_1,fc4_xcmplx_0,fc5_membered,fc6_membered,fc8_xcmplx_0,l80_sin_cos3,rc1_membered,rc1_nat_1,rc1_xcmplx_0,rc2_nat_1,rc2_xcmplx_0,rc3_nat_1,redefinition_k11_complex1,redefinition_k1_nat_1,redefinition_k2_nat_1,redefinition_k5_numbers,redefinition_k8_complex1,redefinition_k9_complex1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t1_subset,t2_subset,t3_arithm,t3_subset,t4_subset,t59_sin_cos3,t5_subset,t60_sin_cos3,t61_sin_cos3,t6_boole,t7_boole,t8_boole]),
    [file(sin_cos3,t63_sin_cos3)]).

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_complex1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => v1_xcmplx_0(A) ) ),
    file(complex1,cc1_complex1),
    []).

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_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_xcmplx_0,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc1_xcmplx_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_xcmplx_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc2_xcmplx_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(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc5_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k2_numbers))
     => v1_membered(A) ) ),
    file(membered,cc5_membered),
    []).

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(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_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_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k2_nat_1(A,B) = k2_nat_1(B,A) ) ),
    file(nat_1,k2_nat_1),
    []).

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_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k3_xcmplx_0),
    []).

fof(commutativity_k8_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k8_complex1(A,B) = k8_complex1(B,A) ) ),
    file(complex1,k8_complex1),
    []).

fof(commutativity_k9_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k9_complex1(A,B) = k9_complex1(B,A) ) ),
    file(complex1,k9_complex1),
    []).

fof(dt_k11_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => m1_subset_1(k11_complex1(A,B),k2_numbers) ) ),
    file(complex1,k11_complex1),
    []).

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_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_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k2_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k2_nat_1),
    []).

fof(dt_k2_numbers,axiom,(
    $true ),
    file(numbers,k2_numbers),
    []).

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_sin_cos3,axiom,
    ( v1_funct_1(k3_sin_cos3)
    & v1_funct_2(k3_sin_cos3,k2_numbers,k2_numbers)
    & m2_relset_1(k3_sin_cos3,k2_numbers,k2_numbers) ),
    file(sin_cos3,k3_sin_cos3),
    []).

fof(dt_k3_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_xcmplx_0),
    []).

fof(dt_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    []).

fof(dt_k4_sin_cos3,axiom,
    ( v1_funct_1(k4_sin_cos3)
    & v1_funct_2(k4_sin_cos3,k2_numbers,k2_numbers)
    & m2_relset_1(k4_sin_cos3,k2_numbers,k2_numbers) ),
    file(sin_cos3,k4_sin_cos3),
    []).

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_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    []).

fof(dt_k8_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => m1_subset_1(k8_complex1(A,B),k2_numbers) ) ),
    file(complex1,k8_complex1),
    []).

fof(dt_k9_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => m1_subset_1(k9_complex1(A,B),k2_numbers) ) ),
    file(complex1,k9_complex1),
    []).

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_m2_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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

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

fof(existence_m2_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(fc1_membered,axiom,
    ( ~ v1_xboole_0(k2_numbers)
    & v1_membered(k2_numbers) ),
    file(membered,fc1_membered),
    []).

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_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

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

fof(fc2_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k3_xcmplx_0(A,B))
        & v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc2_nat_1),
    []).

fof(fc2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k2_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc2_xcmplx_0),
    []).

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_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc3_xcmplx_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_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k6_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc4_xcmplx_0),
    []).

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(fc8_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & ~ v1_xboole_0(B)
        & v1_xcmplx_0(B) )
     => ( ~ v1_xboole_0(k3_xcmplx_0(A,B))
        & v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xcmplx_0,fc8_xcmplx_0),
    []).

fof(l80_sin_cos3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A)) = k6_xcmplx_0(k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A)),1) ) ),
    file(sin_cos3,l80_sin_cos3),
    []).

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_xcmplx_0,axiom,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_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_xcmplx_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A) ) ),
    file(xcmplx_0,rc2_xcmplx_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(redefinition_k11_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k11_complex1(A,B) = k6_xcmplx_0(A,B) ) ),
    file(complex1,k11_complex1),
    []).

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_k2_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k2_nat_1(A,B) = k3_xcmplx_0(A,B) ) ),
    file(nat_1,k2_nat_1),
    []).

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

fof(redefinition_k8_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k8_complex1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(complex1,k8_complex1),
    []).

fof(redefinition_k9_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k9_complex1(A,B) = k3_xcmplx_0(A,B) ) ),
    file(complex1,k9_complex1),
    []).

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(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_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(1,A) = A ) ),
    file(arithm,t3_arithm),
    []).

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(t59_sin_cos3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => ( k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,k3_xcmplx_0(2,A)) = k3_xcmplx_0(k3_xcmplx_0(2,k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A)),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A))
        & k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,A)) = k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A)),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A)),1) ) ) ),
    file(sin_cos3,t59_sin_cos3),
    []).

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(t60_sin_cos3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k2_numbers)
         => ( k11_complex1(k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A)),k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,B),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,B))) = k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,k8_complex1(A,B)),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,k11_complex1(A,B)))
            & k11_complex1(k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A)),k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,B),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,B))) = k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,k8_complex1(A,B)),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,k11_complex1(A,B)))
            & k11_complex1(k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A)),k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,B),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,B))) = k11_complex1(k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A)),k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,B),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,B))) ) ) ) ),
    file(sin_cos3,t60_sin_cos3),
    []).

fof(t61_sin_cos3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k2_numbers)
         => ( k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k8_complex1(A,B)),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k11_complex1(A,B))) = k8_complex1(k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A)),k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,B),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,B)))
            & k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k8_complex1(A,B)),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,k11_complex1(A,B))) = k8_complex1(k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A)),k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,B),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,B)))
            & k8_complex1(k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,A)),k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,B),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,B))) = k8_complex1(k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A),k4_finseq_4(k2_numbers,k2_numbers,k4_sin_cos3,A)),k9_complex1(k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,B),k4_finseq_4(k2_numbers,k2_numbers,k3_sin_cos3,B))) ) ) ) ),
    file(sin_cos3,t61_sin_cos3),
    []).

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),
    []).