% Mizar problem: t16_sin_cos,sin_cos,1326,26 
fof(t16_sin_cos,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k2_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k11_complex1(k9_complex1(k1_comseq_1(k7_comseq_3(k6_sin_cos(A)),C),k1_comseq_1(k7_comseq_3(k6_sin_cos(B)),C)),k1_comseq_1(k7_comseq_3(k6_sin_cos(k8_complex1(A,B))),C)) = k1_comseq_1(k7_comseq_3(k15_sin_cos(A,B,C)),C) ) ) ) ),
    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_comseq_2,cc1_membered,cc1_nat_1,cc1_relset_1,cc1_seq_1,cc1_square_1,cc1_xcmplx_0,cc1_xreal_0,cc20_membered,cc2_comseq_2,cc2_membered,cc2_nat_1,cc2_xcmplx_0,cc2_xreal_0,cc3_comseq_3,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_comseq_3,cc4_membered,cc4_xreal_0,cc5_membered,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k2_comseq_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,commutativity_k8_complex1,commutativity_k9_complex1,connectedness_r1_xreal_0,d10_comseq_1,d15_sin_cos,d17_sin_cos,d4_comseq_1,d7_comseq_1,d9_comseq_1,dt_k10_complex1,dt_k11_complex1,dt_k13_sin_cos,dt_k15_sin_cos,dt_k1_comseq_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_comseq_1,dt_k2_numbers,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_xcmplx_0,dt_k4_comseq_1,dt_k4_relset_1,dt_k4_xcmplx_0,dt_k5_binarith,dt_k5_comseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_comseq_1,dt_k6_sin_cos,dt_k6_xcmplx_0,dt_k7_comseq_3,dt_k8_complex1,dt_k8_funct_2,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,fc10_comseq_3,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_comseq_1,fc1_membered,fc1_nat_1,fc1_ordinal2,fc1_seq_1,fc1_xreal_0,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_membered,fc2_nat_1,fc2_sin_cos,fc2_xcmplx_0,fc3_comseq_1,fc3_nat_1,fc3_xcmplx_0,fc3_xreal_0,fc4_comseq_1,fc4_comseq_3,fc4_nat_1,fc4_xcmplx_0,fc4_xreal_0,fc5_comseq_1,fc5_membered,fc5_xreal_0,fc6_membered,fc6_xcmplx_0,fc7_xreal_0,fc8_comseq_3,fc8_xcmplx_0,fc8_xreal_0,fc9_comseq_3,fc9_xreal_0,involutiveness_k10_complex1,involutiveness_k4_xcmplx_0,rc1_comseq_2,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xcmplx_0,rc1_xreal_0,rc2_comseq_2,rc2_comseq_3,rc2_nat_1,rc2_xcmplx_0,rc2_xreal_0,rc3_comseq_3,rc3_nat_1,rc3_xreal_0,rc4_comseq_3,rc4_xreal_0,redefinition_k10_complex1,redefinition_k11_complex1,redefinition_k1_comseq_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k8_complex1,redefinition_k8_funct_2,redefinition_k9_complex1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,t15_sin_cos,t1_arithm,t1_numerals,t1_real,t1_subset,t28_comseq_3,t29_comseq_3,t2_arithm,t2_real,t2_subset,t35_comseq_3,t3_real,t3_subset,t4_arithm,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(sin_cos,t16_sin_cos)]).

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_comseq_2,axiom,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k2_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v2_comseq_2(A) )
       => ( ~ v1_xboole_0(A)
          & v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v1_partfun1(A,k5_numbers,k2_numbers)
          & v1_comseq_2(A) ) ) ) ),
    file(comseq_2,cc1_comseq_2),
    []).

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_seq_1,axiom,(
    ! [A,B] : 
      ( v2_membered(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( v1_funct_1(C)
           => ( v1_funct_1(C)
              & v1_seq_1(C) ) ) ) ) ),
    file(seq_1,cc1_seq_1),
    []).

fof(cc1_square_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => v1_xcmplx_0(A) ) ),
    file(square_1,cc1_square_1),
    []).

fof(cc1_xcmplx_0,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc1_xcmplx_0),
    []).

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_comseq_2,axiom,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k2_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & ~ v1_comseq_2(A) )
       => ( ~ v1_xboole_0(A)
          & v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v1_partfun1(A,k5_numbers,k2_numbers)
          & ~ v2_comseq_2(A) ) ) ) ),
    file(comseq_2,cc2_comseq_2),
    []).

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

fof(cc3_comseq_3,axiom,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k2_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v1_comseq_3(A) )
       => ( ~ v1_xboole_0(A)
          & v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v1_comseq_2(A)
          & v2_comseq_2(A)
          & v1_partfun1(A,k5_numbers,k2_numbers) ) ) ) ),
    file(comseq_3,cc3_comseq_3),
    []).

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_comseq_3,axiom,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k2_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v2_comseq_3(A) )
       => ( ~ v1_xboole_0(A)
          & v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v1_comseq_2(A)
          & v2_comseq_2(A)
          & v1_partfun1(A,k5_numbers,k2_numbers)
          & v1_comseq_3(A) ) ) ) ),
    file(comseq_3,cc4_comseq_3),
    []).

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

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_comseq_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k2_numbers)
        & v1_funct_1(C)
        & m1_relset_1(C,A,k2_numbers) )
     => k2_comseq_1(A,B,C) = k2_comseq_1(A,C,B) ) ),
    file(comseq_1,k2_comseq_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(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(d10_comseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k6_comseq_1(A,B,C) = k2_comseq_1(A,B,k5_comseq_1(A,C)) ) ) ) ),
    file(comseq_1,d10_comseq_1),
    []).

fof(d15_sin_cos,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k2_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k2_numbers)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k2_numbers)
                    & m2_relset_1(D,k5_numbers,k2_numbers) )
                 => ( D = k13_sin_cos(A,B,C)
                  <=> ! [E] : 
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( ( r1_xreal_0(E,A)
                           => k1_comseq_1(D,E) = k9_complex1(k1_comseq_1(k6_sin_cos(B),E),k1_comseq_1(k7_comseq_3(k6_sin_cos(C)),k5_binarith(A,E))) )
                          & ( ~ r1_xreal_0(E,A)
                           => k1_comseq_1(D,E) = 0 ) ) ) ) ) ) ) ) ),
    file(sin_cos,d15_sin_cos),
    []).

fof(d17_sin_cos,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k2_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k2_numbers)
                    & m2_relset_1(D,k5_numbers,k2_numbers) )
                 => ( D = k15_sin_cos(A,B,C)
                  <=> ! [E] : 
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( ( r1_xreal_0(E,C)
                           => k1_comseq_1(D,E) = k9_complex1(k1_comseq_1(k6_sin_cos(A),E),k11_complex1(k1_comseq_1(k7_comseq_3(k6_sin_cos(B)),C),k1_comseq_1(k7_comseq_3(k6_sin_cos(B)),k5_binarith(C,E)))) )
                          & ( ~ r1_xreal_0(E,C)
                           => k1_comseq_1(D,E) = 0 ) ) ) ) ) ) ) ) ),
    file(sin_cos,d17_sin_cos),
    []).

fof(d4_comseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k2_numbers)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,k2_numbers)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ( D = k2_comseq_1(A,B,C)
                  <=> ( k4_relset_1(A,k2_numbers,D) = A
                      & ! [E] : 
                          ( m1_subset_1(E,A)
                         => k1_funct_1(D,E) = k8_complex1(k8_funct_2(A,k2_numbers,B,E),k8_funct_2(A,k2_numbers,C,E)) ) ) ) ) ) ) ) ),
    file(comseq_1,d4_comseq_1),
    []).

fof(d7_comseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k2_numbers)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ( D = k4_comseq_1(A,B,C)
                  <=> ( k4_relset_1(A,k2_numbers,D) = A
                      & ! [E] : 
                          ( m1_subset_1(E,A)
                         => k1_funct_1(D,E) = k3_xcmplx_0(C,k8_funct_2(A,k2_numbers,B,E)) ) ) ) ) ) ) ) ),
    file(comseq_1,d7_comseq_1),
    []).

fof(d9_comseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k2_numbers)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( C = k5_comseq_1(A,B)
              <=> ( k4_relset_1(A,k2_numbers,C) = A
                  & ! [D] : 
                      ( m1_subset_1(D,A)
                     => k1_funct_1(C,D) = k10_complex1(k8_funct_2(A,k2_numbers,B,D)) ) ) ) ) ) ) ),
    file(comseq_1,d9_comseq_1),
    []).

fof(dt_k10_complex1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => m1_subset_1(k10_complex1(A),k2_numbers) ) ),
    file(complex1,k10_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_k13_sin_cos,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k2_numbers)
        & m1_subset_1(C,k2_numbers) )
     => ( v1_funct_1(k13_sin_cos(A,B,C))
        & v1_funct_2(k13_sin_cos(A,B,C),k5_numbers,k2_numbers)
        & m2_relset_1(k13_sin_cos(A,B,C),k5_numbers,k2_numbers) ) ) ),
    file(sin_cos,k13_sin_cos),
    []).

fof(dt_k15_sin_cos,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers)
        & m1_subset_1(C,k5_numbers) )
     => ( v1_funct_1(k15_sin_cos(A,B,C))
        & v1_funct_2(k15_sin_cos(A,B,C),k5_numbers,k2_numbers)
        & m2_relset_1(k15_sin_cos(A,B,C),k5_numbers,k2_numbers) ) ) ),
    file(sin_cos,k15_sin_cos),
    []).

fof(dt_k1_comseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k1_comseq_1(A,B),k2_numbers) ) ),
    file(comseq_1,k1_comseq_1),
    []).

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

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

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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_comseq_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k2_numbers)
        & v1_funct_1(C)
        & m1_relset_1(C,A,k2_numbers) )
     => ( v1_funct_1(k2_comseq_1(A,B,C))
        & m2_relset_1(k2_comseq_1(A,B,C),A,k2_numbers) ) ) ),
    file(comseq_1,k2_comseq_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_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_xcmplx_0),
    []).

fof(dt_k4_comseq_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k2_numbers)
        & v1_xcmplx_0(C) )
     => ( v1_funct_1(k4_comseq_1(A,B,C))
        & m2_relset_1(k4_comseq_1(A,B,C),A,k2_numbers) ) ) ),
    file(comseq_1,k4_comseq_1),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

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_binarith,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => m2_subset_1(k5_binarith(A,B),k1_numbers,k5_numbers) ) ),
    file(binarith,k5_binarith),
    []).

fof(dt_k5_comseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k2_numbers) )
     => ( v1_funct_1(k5_comseq_1(A,B))
        & m2_relset_1(k5_comseq_1(A,B),A,k2_numbers) ) ) ),
    file(comseq_1,k5_comseq_1),
    []).

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_comseq_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k2_numbers)
        & v1_funct_1(C)
        & m1_relset_1(C,A,k2_numbers) )
     => ( v1_funct_1(k6_comseq_1(A,B,C))
        & m2_relset_1(k6_comseq_1(A,B,C),A,k2_numbers) ) ) ),
    file(comseq_1,k6_comseq_1),
    []).

fof(dt_k6_sin_cos,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => ( v1_funct_1(k6_sin_cos(A))
        & v1_funct_2(k6_sin_cos(A),k5_numbers,k2_numbers)
        & m2_relset_1(k6_sin_cos(A),k5_numbers,k2_numbers) ) ) ),
    file(sin_cos,k6_sin_cos),
    []).

fof(dt_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    []).

fof(dt_k7_comseq_3,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_funct_1(k7_comseq_3(A))
        & v1_funct_2(k7_comseq_3(A),k5_numbers,k2_numbers)
        & m2_relset_1(k7_comseq_3(A),k5_numbers,k2_numbers) ) ) ),
    file(comseq_3,k7_comseq_3),
    []).

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_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

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(fc10_comseq_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & v1_comseq_3(B)
        & m1_relset_1(B,k5_numbers,k2_numbers) )
     => ( ~ v1_xboole_0(k4_comseq_1(k5_numbers,B,A))
        & v1_relat_1(k4_comseq_1(k5_numbers,B,A))
        & v1_funct_1(k4_comseq_1(k5_numbers,B,A))
        & v1_funct_2(k4_comseq_1(k5_numbers,B,A),k5_numbers,k2_numbers)
        & v1_comseq_2(k4_comseq_1(k5_numbers,B,A))
        & v2_comseq_2(k4_comseq_1(k5_numbers,B,A))
        & v1_partfun1(k4_comseq_1(k5_numbers,B,A),k5_numbers,k2_numbers)
        & v1_comseq_3(k4_comseq_1(k5_numbers,B,A)) ) ) ),
    file(comseq_3,fc10_comseq_3),
    []).

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(fc15_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc15_xreal_0),
    []).

fof(fc16_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc16_xreal_0),
    []).

fof(fc17_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v2_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc17_xreal_0),
    []).

fof(fc18_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A))
        & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc18_xreal_0),
    []).

fof(fc19_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v2_xreal_0(k6_xcmplx_0(A,B))
        & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc19_xreal_0),
    []).

fof(fc1_comseq_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k2_numbers)
        & m1_relset_1(B,A,k2_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,A,k2_numbers)
        & m1_relset_1(C,A,k2_numbers) )
     => ( ~ v1_xboole_0(k2_comseq_1(A,B,C))
        & v1_relat_1(k2_comseq_1(A,B,C))
        & v1_funct_1(k2_comseq_1(A,B,C))
        & v1_funct_2(k2_comseq_1(A,B,C),A,k2_numbers)
        & v1_partfun1(k2_comseq_1(A,B,C),A,k2_numbers) ) ) ),
    file(comseq_1,fc1_comseq_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(fc1_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_xcmplx_0(k1_funct_1(A,B))
        & v1_xreal_0(k1_funct_1(A,B)) ) ) ),
    file(seq_1,fc1_seq_1),
    []).

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(fc20_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v2_xreal_0(k6_xcmplx_0(B,A))
        & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc20_xreal_0),
    []).

fof(fc21_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc21_xreal_0),
    []).

fof(fc22_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(B,A))
        & v1_xreal_0(k3_xcmplx_0(B,A))
        & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc22_xreal_0),
    []).

fof(fc23_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc23_xreal_0),
    []).

fof(fc24_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc24_xreal_0),
    []).

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_sin_cos,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => ( ~ v1_xboole_0(k6_sin_cos(A))
        & v1_relat_1(k6_sin_cos(A))
        & v1_funct_1(k6_sin_cos(A))
        & v1_funct_2(k6_sin_cos(A),k5_numbers,k2_numbers)
        & v1_comseq_3(k6_sin_cos(A))
        & v2_comseq_3(k6_sin_cos(A))
        & v1_comseq_2(k6_sin_cos(A))
        & v2_comseq_2(k6_sin_cos(A))
        & v1_partfun1(k6_sin_cos(A),k5_numbers,k2_numbers) ) ) ),
    file(sin_cos,fc2_sin_cos),
    []).

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_comseq_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k2_numbers)
        & m1_relset_1(B,A,k2_numbers)
        & v1_xcmplx_0(C) )
     => ( ~ v1_xboole_0(k4_comseq_1(A,B,C))
        & v1_relat_1(k4_comseq_1(A,B,C))
        & v1_funct_1(k4_comseq_1(A,B,C))
        & v1_funct_2(k4_comseq_1(A,B,C),A,k2_numbers)
        & v1_partfun1(k4_comseq_1(A,B,C),A,k2_numbers) ) ) ),
    file(comseq_1,fc3_comseq_1),
    []).

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(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_comseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k2_numbers)
        & m1_relset_1(B,A,k2_numbers) )
     => ( ~ v1_xboole_0(k5_comseq_1(A,B))
        & v1_relat_1(k5_comseq_1(A,B))
        & v1_funct_1(k5_comseq_1(A,B))
        & v1_funct_2(k5_comseq_1(A,B),A,k2_numbers)
        & v1_partfun1(k5_comseq_1(A,B),A,k2_numbers) ) ) ),
    file(comseq_1,fc4_comseq_1),
    []).

fof(fc4_comseq_3,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v1_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( ~ v1_xboole_0(k7_comseq_3(A))
        & v1_relat_1(k7_comseq_3(A))
        & v1_funct_1(k7_comseq_3(A))
        & v1_funct_2(k7_comseq_3(A),k5_numbers,k2_numbers)
        & v1_comseq_2(k7_comseq_3(A))
        & v2_comseq_2(k7_comseq_3(A))
        & v1_partfun1(k7_comseq_3(A),k5_numbers,k2_numbers) ) ) ),
    file(comseq_3,fc4_comseq_3),
    []).

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(fc4_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc4_xreal_0),
    []).

fof(fc5_comseq_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k2_numbers)
        & m1_relset_1(B,A,k2_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,A,k2_numbers)
        & m1_relset_1(C,A,k2_numbers) )
     => ( ~ v1_xboole_0(k6_comseq_1(A,B,C))
        & v1_relat_1(k6_comseq_1(A,B,C))
        & v1_funct_1(k6_comseq_1(A,B,C))
        & v1_funct_2(k6_comseq_1(A,B,C),A,k2_numbers)
        & v1_partfun1(k6_comseq_1(A,B,C),A,k2_numbers) ) ) ),
    file(comseq_1,fc5_comseq_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(fc5_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    []).

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(fc6_xcmplx_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A) )
     => ( ~ v1_xboole_0(k4_xcmplx_0(A))
        & v1_xcmplx_0(k4_xcmplx_0(A)) ) ) ),
    file(xcmplx_0,fc6_xcmplx_0),
    []).

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_comseq_3,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v1_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & v1_comseq_3(B)
        & m1_relset_1(B,k5_numbers,k2_numbers) )
     => ( ~ v1_xboole_0(k2_comseq_1(k5_numbers,A,B))
        & v1_relat_1(k2_comseq_1(k5_numbers,A,B))
        & v1_funct_1(k2_comseq_1(k5_numbers,A,B))
        & v1_funct_2(k2_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
        & v1_comseq_2(k2_comseq_1(k5_numbers,A,B))
        & v2_comseq_2(k2_comseq_1(k5_numbers,A,B))
        & v1_partfun1(k2_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
        & v1_comseq_3(k2_comseq_1(k5_numbers,A,B)) ) ) ),
    file(comseq_3,fc8_comseq_3),
    []).

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(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_comseq_3,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v1_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & v1_comseq_3(B)
        & m1_relset_1(B,k5_numbers,k2_numbers) )
     => ( ~ v1_xboole_0(k6_comseq_1(k5_numbers,A,B))
        & v1_relat_1(k6_comseq_1(k5_numbers,A,B))
        & v1_funct_1(k6_comseq_1(k5_numbers,A,B))
        & v1_funct_2(k6_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
        & v1_comseq_2(k6_comseq_1(k5_numbers,A,B))
        & v2_comseq_2(k6_comseq_1(k5_numbers,A,B))
        & v1_partfun1(k6_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
        & v1_comseq_3(k6_comseq_1(k5_numbers,A,B)) ) ) ),
    file(comseq_3,fc9_comseq_3),
    []).

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(involutiveness_k10_complex1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => k10_complex1(k10_complex1(A)) = A ) ),
    file(complex1,k10_complex1),
    []).

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_comseq_2,axiom,(
    ? [A] : 
      ( m1_relset_1(A,k5_numbers,k2_numbers)
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k2_numbers)
      & v1_partfun1(A,k5_numbers,k2_numbers)
      & v1_comseq_2(A) ) ),
    file(comseq_2,rc1_comseq_2),
    []).

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_seq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A) ) ),
    file(seq_1,rc1_seq_1),
    []).

fof(rc1_xcmplx_0,axiom,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    []).

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

fof(rc2_comseq_2,axiom,(
    ? [A] : 
      ( m1_relset_1(A,k5_numbers,k2_numbers)
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k2_numbers)
      & v1_partfun1(A,k5_numbers,k2_numbers)
      & v2_comseq_2(A) ) ),
    file(comseq_2,rc2_comseq_2),
    []).

fof(rc2_comseq_3,axiom,(
    ? [A] : 
      ( m1_relset_1(A,k5_numbers,k2_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k2_numbers)
      & v1_comseq_3(A) ) ),
    file(comseq_3,rc2_comseq_3),
    []).

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(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_comseq_3,axiom,(
    ? [A] : 
      ( m1_relset_1(A,k5_numbers,k2_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k2_numbers)
      & v2_comseq_3(A) ) ),
    file(comseq_3,rc3_comseq_3),
    []).

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_comseq_3,axiom,(
    ? [A] : 
      ( m1_relset_1(A,k5_numbers,k2_numbers)
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k2_numbers)
      & v1_comseq_2(A)
      & v2_comseq_2(A)
      & v1_partfun1(A,k5_numbers,k2_numbers)
      & v1_comseq_3(A)
      & v2_comseq_3(A) ) ),
    file(comseq_3,rc4_comseq_3),
    []).

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_k10_complex1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => k10_complex1(A) = k4_xcmplx_0(A) ) ),
    file(complex1,k10_complex1),
    []).

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_comseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_comseq_1(A,B) = k1_funct_1(A,B) ) ),
    file(comseq_1,k1_comseq_1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_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_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

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(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(t15_sin_cos,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k2_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k1_comseq_1(k7_comseq_3(k6_sin_cos(k8_complex1(A,B))),C) = k1_comseq_1(k7_comseq_3(k13_sin_cos(C,A,B)),C) ) ) ) ),
    file(sin_cos,t15_sin_cos),
    []).

fof(t1_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

fof(t1_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    []).

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

fof(t28_comseq_3,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => k6_comseq_1(k5_numbers,k7_comseq_3(A),k7_comseq_3(B)) = k7_comseq_3(k6_comseq_1(k5_numbers,A,B)) ) ) ),
    file(comseq_3,t28_comseq_3),
    []).

fof(t29_comseq_3,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] : 
          ( m1_subset_1(B,k2_numbers)
         => k7_comseq_3(k4_comseq_1(k5_numbers,A,B)) = k4_comseq_1(k5_numbers,k7_comseq_3(A),B) ) ) ),
    file(comseq_3,t29_comseq_3),
    []).

fof(t2_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,0) = 0 ) ),
    file(arithm,t2_arithm),
    []).

fof(t2_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    []).

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

fof(t35_comseq_3,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(D,C)
                     => k1_comseq_1(A,D) = k1_comseq_1(B,D) ) )
               => k1_comseq_1(k7_comseq_3(A),C) = k1_comseq_1(k7_comseq_3(B),C) ) ) ) ) ),
    file(comseq_3,t35_comseq_3),
    []).

fof(t3_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,0) = A ) ),
    file(arithm,t4_arithm),
    []).

fof(t4_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    []).

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_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    []).

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(t6_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t7_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t8_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    []).