% Mizar problem: t41_rcomp_3,rcomp_3,1174,33 
fof(t41_rcomp_3,conjecture,(
    ! [A] : 
      ( ( v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ~ ( ~ v1_xboole_0(A)
          & A != k1_numbers
          & ! [B] : 
              ( v1_xreal_0(B)
             => A != k2_limfunc1(B) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => A != k12_prob_1(B) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => A != k3_limfunc1(B) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => A != k4_limfunc1(B) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => ! [C] : 
                  ( v1_xreal_0(C)
                 => ~ ( r1_xreal_0(B,C)
                      & A = k1_rcomp_1(B,C) ) ) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => ! [C] : 
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,B)
                      & A = k1_rcomp_2(B,C) ) ) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => ! [C] : 
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,B)
                      & A = k2_rcomp_2(B,C) ) ) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => ! [C] : 
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,B)
                      & A = k2_rcomp_1(B,C) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc11_topreal6,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_realset1,cc1_sprect_1,cc1_xreal_0,cc1_yellow13,cc20_membered,cc2_membered,cc2_sprect_1,cc2_xreal_0,cc3_borsuk_5,cc3_int_1,cc3_membered,cc3_nat_1,cc3_sprect_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_sprect_1,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,connectedness_r1_xreal_0,d1_tarski,d3_seq_4,d4_realset1,dt_k12_prob_1,dt_k1_numbers,dt_k1_rcomp_1,dt_k1_rcomp_2,dt_k1_seq_4,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_limfunc1,dt_k2_rcomp_1,dt_k2_rcomp_2,dt_k2_seq_4,dt_k3_limfunc1,dt_k3_pscomp_1,dt_k3_seq_4,dt_k4_limfunc1,dt_k4_pscomp_1,dt_k4_seq_4,dt_k5_seq_4,dt_m1_subset_1,existence_m1_subset_1,fc10_membered,fc10_rcomp_3,fc11_membered,fc11_rcomp_3,fc12_rcomp_3,fc13_rcomp_3,fc14_borsuk_5,fc15_borsuk_5,fc16_borsuk_5,fc17_borsuk_5,fc1_pscomp_1,fc1_rcomp_1,fc1_subset_1,fc2_finseq_1,fc2_membered,fc2_rcomp_1,fc2_subset_1,fc3_fcont_3,fc3_rcomp_3,fc3_realset1,fc4_fcont_3,fc4_rcomp_3,fc5_fcont_3,fc5_rcomp_3,fc6_fcont_3,fc6_membered,fc6_rcomp_3,fc7_membered,fc7_rcomp_3,fc8_membered,fc8_rcomp_3,fc8_topreal6,fc9_membered,fc9_rcomp_3,fc9_sprect_1,rc1_finseq_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_pscomp_1,rc1_rcomp_1,rc1_rcomp_3,rc1_realset1,rc1_sprect_1,rc1_subset_1,rc1_xreal_0,rc2_borsuk_5,rc2_int_1,rc2_pscomp_1,rc2_rcomp_3,rc2_realset1,rc2_subset_1,rc2_waybel_7,rc2_xreal_0,rc3_borsuk_5,rc3_finseq_1,rc3_pscomp_1,rc3_sprect_1,rc3_xreal_0,rc4_pscomp_1,rc4_xreal_0,rc5_pscomp_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_seq_4,redefinition_k3_pscomp_1,redefinition_k4_pscomp_1,redefinition_k4_seq_4,redefinition_k5_seq_4,reflexivity_r1_tarski,reflexivity_r1_xreal_0,t14_rcomp_1,t14_realset1,t1_real,t1_subset,t25_rcomp_3,t25_seq_4,t27_rcomp_3,t29_rcomp_3,t2_real,t2_subset,t31_rcomp_3,t33_rcomp_3,t35_rcomp_3,t37_rcomp_3,t39_rcomp_3,t3_real,t3_subset,t40_rcomp_3,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(rcomp_3,t41_rcomp_3)]).

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(cc11_topreal6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_finset_1(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v1_rcomp_1(A) ) ) ) ),
    file(topreal6,cc11_topreal6),
    []).

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_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

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

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

fof(cc1_sprect_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v5_seqm_3(A) )
     => ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_realset1(A) ) ) ),
    file(sprect_1,cc1_sprect_1),
    []).

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

fof(cc1_yellow13,axiom,(
    ! [A] : 
      ( v1_realset1(A)
     => v1_finset_1(A) ) ),
    file(yellow13,cc1_yellow13),
    []).

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_sprect_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_realset1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_seqm_3(A) ) ) ),
    file(sprect_1,cc2_sprect_1),
    []).

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

fof(cc3_borsuk_5,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v1_rat_1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) ),
    file(borsuk_5,cc3_borsuk_5),
    []).

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

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_sprect_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v3_seq_4(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v1_seq_4(A)
          & v2_seq_4(A) ) ) ) ),
    file(sprect_1,cc3_sprect_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_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc4_sprect_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( ( v1_seq_4(A)
          & v2_seq_4(A) )
       => ( v1_membered(A)
          & v2_membered(A)
          & v3_seq_4(A) ) ) ) ),
    file(sprect_1,cc4_sprect_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_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(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(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d3_seq_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v3_seq_4(A)
      <=> ( v2_seq_4(A)
          & v1_seq_4(A) ) ) ) ),
    file(seq_4,d3_seq_4),
    []).

fof(d4_realset1,axiom,(
    ! [A] : 
      ( v1_realset1(A)
    <=> ~ ( ~ v1_xboole_0(A)
          & ! [B] : A != k1_tarski(B) ) ) ),
    file(realset1,d4_realset1),
    []).

fof(dt_k12_prob_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_subset_1(k12_prob_1(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(prob_1,k12_prob_1),
    []).

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

fof(dt_k1_rcomp_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k1_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) ),
    file(rcomp_1,k1_rcomp_1),
    []).

fof(dt_k1_rcomp_2,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k1_rcomp_2(A,B),k1_zfmisc_1(k1_numbers)) ) ),
    file(rcomp_2,k1_rcomp_2),
    []).

fof(dt_k1_seq_4,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_subset_1(k1_seq_4(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(seq_4,k1_seq_4),
    []).

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_limfunc1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_subset_1(k2_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(limfunc1,k2_limfunc1),
    []).

fof(dt_k2_rcomp_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k2_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) ),
    file(rcomp_1,k2_rcomp_1),
    []).

fof(dt_k2_rcomp_2,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k2_rcomp_2(A,B),k1_zfmisc_1(k1_numbers)) ) ),
    file(rcomp_2,k2_rcomp_2),
    []).

fof(dt_k2_seq_4,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_xreal_0(k2_seq_4(A)) ) ),
    file(seq_4,k2_seq_4),
    []).

fof(dt_k3_limfunc1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_subset_1(k3_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(limfunc1,k3_limfunc1),
    []).

fof(dt_k3_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k3_pscomp_1(A),k1_numbers) ) ),
    file(pscomp_1,k3_pscomp_1),
    []).

fof(dt_k3_seq_4,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_xreal_0(k3_seq_4(A)) ) ),
    file(seq_4,k3_seq_4),
    []).

fof(dt_k4_limfunc1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_subset_1(k4_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(limfunc1,k4_limfunc1),
    []).

fof(dt_k4_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k4_pscomp_1(A),k1_numbers) ) ),
    file(pscomp_1,k4_pscomp_1),
    []).

fof(dt_k4_seq_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k4_seq_4(A),k1_numbers) ) ),
    file(seq_4,k4_seq_4),
    []).

fof(dt_k5_seq_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k5_seq_4(A),k1_numbers) ) ),
    file(seq_4,k5_seq_4),
    []).

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

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

fof(fc10_membered,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    []).

fof(fc10_rcomp_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k2_limfunc1(A))
        & v1_membered(k2_limfunc1(A))
        & v2_membered(k2_limfunc1(A))
        & v1_seq_4(k2_limfunc1(A))
        & ~ v2_seq_4(k2_limfunc1(A))
        & v2_rcomp_1(k2_limfunc1(A))
        & v1_jct_misc(k2_limfunc1(A)) ) ) ),
    file(rcomp_3,fc10_rcomp_3),
    []).

fof(fc11_membered,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    []).

fof(fc11_rcomp_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k12_prob_1(A))
        & v1_membered(k12_prob_1(A))
        & v2_membered(k12_prob_1(A))
        & v1_seq_4(k12_prob_1(A))
        & ~ v2_seq_4(k12_prob_1(A))
        & v3_rcomp_1(k12_prob_1(A))
        & v1_jct_misc(k12_prob_1(A)) ) ) ),
    file(rcomp_3,fc11_rcomp_3),
    []).

fof(fc12_rcomp_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k3_limfunc1(A))
        & v1_membered(k3_limfunc1(A))
        & v2_membered(k3_limfunc1(A))
        & ~ v1_seq_4(k3_limfunc1(A))
        & v2_seq_4(k3_limfunc1(A))
        & v2_rcomp_1(k3_limfunc1(A))
        & v1_jct_misc(k3_limfunc1(A)) ) ) ),
    file(rcomp_3,fc12_rcomp_3),
    []).

fof(fc13_rcomp_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k4_limfunc1(A))
        & v1_membered(k4_limfunc1(A))
        & v2_membered(k4_limfunc1(A))
        & ~ v1_seq_4(k4_limfunc1(A))
        & v2_seq_4(k4_limfunc1(A))
        & v3_rcomp_1(k4_limfunc1(A))
        & v1_jct_misc(k4_limfunc1(A)) ) ) ),
    file(rcomp_3,fc13_rcomp_3),
    []).

fof(fc14_borsuk_5,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k4_limfunc1(A))
        & v1_membered(k4_limfunc1(A))
        & v2_membered(k4_limfunc1(A)) ) ) ),
    file(borsuk_5,fc14_borsuk_5),
    []).

fof(fc15_borsuk_5,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k2_limfunc1(A))
        & v1_membered(k2_limfunc1(A))
        & v2_membered(k2_limfunc1(A)) ) ) ),
    file(borsuk_5,fc15_borsuk_5),
    []).

fof(fc16_borsuk_5,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k12_prob_1(A))
        & v1_membered(k12_prob_1(A))
        & v2_membered(k12_prob_1(A)) ) ) ),
    file(borsuk_5,fc16_borsuk_5),
    []).

fof(fc17_borsuk_5,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k3_limfunc1(A))
        & v1_membered(k3_limfunc1(A))
        & v2_membered(k3_limfunc1(A)) ) ) ),
    file(borsuk_5,fc17_borsuk_5),
    []).

fof(fc1_pscomp_1,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers)
    & ~ v1_setfam_1(k1_numbers) ),
    file(pscomp_1,fc1_pscomp_1),
    []).

fof(fc1_rcomp_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_1(A,B))
        & v2_membered(k2_rcomp_1(A,B))
        & v3_rcomp_1(k2_rcomp_1(A,B)) ) ) ),
    file(rcomp_1,fc1_rcomp_1),
    []).

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

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

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

fof(fc2_rcomp_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,B)) ) ) ),
    file(rcomp_1,fc2_rcomp_1),
    []).

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

fof(fc3_fcont_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k4_limfunc1(A))
        & v2_membered(k4_limfunc1(A))
        & v3_rcomp_1(k4_limfunc1(A)) ) ) ),
    file(fcont_3,fc3_fcont_3),
    []).

fof(fc3_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_2(A,B))
        & v2_membered(k1_rcomp_2(A,B))
        & v1_seq_4(k1_rcomp_2(A,B))
        & v2_seq_4(k1_rcomp_2(A,B))
        & v3_seq_4(k1_rcomp_2(A,B)) ) ) ),
    file(rcomp_3,fc3_rcomp_3),
    []).

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc4_fcont_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k12_prob_1(A))
        & v2_membered(k12_prob_1(A))
        & v3_rcomp_1(k12_prob_1(A)) ) ) ),
    file(fcont_3,fc4_fcont_3),
    []).

fof(fc4_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_2(A,B))
        & v2_membered(k2_rcomp_2(A,B))
        & v1_seq_4(k2_rcomp_2(A,B))
        & v2_seq_4(k2_rcomp_2(A,B))
        & v3_seq_4(k2_rcomp_2(A,B)) ) ) ),
    file(rcomp_3,fc4_rcomp_3),
    []).

fof(fc5_fcont_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k3_limfunc1(A))
        & v2_membered(k3_limfunc1(A))
        & v2_rcomp_1(k3_limfunc1(A)) ) ) ),
    file(fcont_3,fc5_fcont_3),
    []).

fof(fc5_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_1(A,B))
        & v2_membered(k2_rcomp_1(A,B))
        & v1_seq_4(k2_rcomp_1(A,B))
        & v2_seq_4(k2_rcomp_1(A,B))
        & v3_seq_4(k2_rcomp_1(A,B))
        & v3_rcomp_1(k2_rcomp_1(A,B)) ) ) ),
    file(rcomp_3,fc5_rcomp_3),
    []).

fof(fc6_fcont_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k2_limfunc1(A))
        & v2_membered(k2_limfunc1(A))
        & v2_rcomp_1(k2_limfunc1(A)) ) ) ),
    file(fcont_3,fc6_fcont_3),
    []).

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_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v1_seq_4(k1_rcomp_1(A,B))
        & v2_seq_4(k1_rcomp_1(A,B))
        & v3_seq_4(k1_rcomp_1(A,B))
        & v1_rcomp_1(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,B))
        & v1_jct_misc(k1_rcomp_1(A,B)) ) ) ),
    file(rcomp_3,fc6_rcomp_3),
    []).

fof(fc7_membered,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    []).

fof(fc7_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_2(A,B))
        & v2_membered(k1_rcomp_2(A,B))
        & v1_seq_4(k1_rcomp_2(A,B))
        & v2_seq_4(k1_rcomp_2(A,B))
        & v3_seq_4(k1_rcomp_2(A,B))
        & v1_jct_misc(k1_rcomp_2(A,B)) ) ) ),
    file(rcomp_3,fc7_rcomp_3),
    []).

fof(fc8_membered,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    []).

fof(fc8_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_2(A,B))
        & v2_membered(k2_rcomp_2(A,B))
        & v1_seq_4(k2_rcomp_2(A,B))
        & v2_seq_4(k2_rcomp_2(A,B))
        & v3_seq_4(k2_rcomp_2(A,B))
        & v1_jct_misc(k2_rcomp_2(A,B)) ) ) ),
    file(rcomp_3,fc8_rcomp_3),
    []).

fof(fc8_topreal6,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v1_seq_4(k1_rcomp_1(A,B))
        & v2_seq_4(k1_rcomp_1(A,B))
        & v3_seq_4(k1_rcomp_1(A,B))
        & v1_rcomp_1(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,B)) ) ) ),
    file(topreal6,fc8_topreal6),
    []).

fof(fc9_membered,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    []).

fof(fc9_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_1(A,B))
        & v2_membered(k2_rcomp_1(A,B))
        & v1_seq_4(k2_rcomp_1(A,B))
        & v2_seq_4(k2_rcomp_1(A,B))
        & v3_seq_4(k2_rcomp_1(A,B))
        & v3_rcomp_1(k2_rcomp_1(A,B))
        & v1_jct_misc(k2_rcomp_1(A,B)) ) ) ),
    file(rcomp_3,fc9_rcomp_3),
    []).

fof(fc9_sprect_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v3_seq_4(k1_rcomp_1(A,B)) ) ) ),
    file(sprect_1,fc9_sprect_1),
    []).

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

fof(rc1_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_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_pscomp_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(pscomp_1,rc1_pscomp_1),
    []).

fof(rc1_rcomp_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & v1_membered(A)
      & v2_membered(A)
      & v3_rcomp_1(A) ) ),
    file(rcomp_1,rc1_rcomp_1),
    []).

fof(rc1_rcomp_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_seq_4(A)
      & v2_seq_4(A) ) ),
    file(rcomp_3,rc1_rcomp_3),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

fof(rc1_sprect_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v5_seqm_3(A) ) ),
    file(sprect_1,rc1_sprect_1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

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

fof(rc2_borsuk_5,axiom,(
    ? [A] : 
      ( v1_xreal_0(A)
      & v1_xcmplx_0(A)
      & ~ v1_rat_1(A) ) ),
    file(borsuk_5,rc2_borsuk_5),
    []).

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

fof(rc2_pscomp_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_setfam_1(A) ) ),
    file(pscomp_1,rc2_pscomp_1),
    []).

fof(rc2_rcomp_3,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_seq_4(A)
      & v2_seq_4(A)
      & v3_seq_4(A)
      & v3_rcomp_1(A)
      & v1_jct_misc(A) ) ),
    file(rcomp_3,rc2_rcomp_3),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_waybel_7,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_finset_1(B) ) ),
    file(waybel_7,rc2_waybel_7),
    []).

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_borsuk_5,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xreal_0(A)
      & v1_xcmplx_0(A)
      & v1_rat_1(A) ) ),
    file(borsuk_5,rc3_borsuk_5),
    []).

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

fof(rc3_pscomp_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_setfam_1(A) ) ),
    file(pscomp_1,rc3_pscomp_1),
    []).

fof(rc3_sprect_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_seq_4(A)
      & v2_seq_4(A) ) ),
    file(sprect_1,rc3_sprect_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_pscomp_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & ~ v1_setfam_1(A) ) ),
    file(pscomp_1,rc4_pscomp_1),
    []).

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_pscomp_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_seq_4(A)
      & v2_rcomp_1(A) ) ),
    file(pscomp_1,rc5_pscomp_1),
    []).

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

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

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

fof(redefinition_k1_seq_4,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => k1_seq_4(A) = k1_tarski(A) ) ),
    file(seq_4,k1_seq_4),
    []).

fof(redefinition_k3_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k3_pscomp_1(A) = k2_seq_4(A) ) ),
    file(pscomp_1,k3_pscomp_1),
    []).

fof(redefinition_k4_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k4_pscomp_1(A) = k3_seq_4(A) ) ),
    file(pscomp_1,k4_pscomp_1),
    []).

fof(redefinition_k4_seq_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k4_seq_4(A) = k2_seq_4(A) ) ),
    file(seq_4,k4_seq_4),
    []).

fof(redefinition_k5_seq_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k5_seq_4(A) = k3_seq_4(A) ) ),
    file(seq_4,k5_seq_4),
    []).

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(t14_rcomp_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => k1_rcomp_1(A,A) = k1_seq_4(A) ) ),
    file(rcomp_1,t14_rcomp_1),
    []).

fof(t14_realset1,axiom,(
    ! [A] : 
      ( ~ ( ~ v1_realset1(A)
          & ! [B,C] : ~ ( r2_hidden(B,A)
              & r2_hidden(C,A)
              & B != C ) )
      & ~ ( ? [B,C] : 
              ( r2_hidden(B,A)
              & r2_hidden(C,A)
              & B != C )
          & v1_realset1(A) ) ) ),
    file(realset1,t14_realset1),
    []).

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(t25_rcomp_3,axiom,(
    ! [A] : 
      ( ( v3_seq_4(A)
        & v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( r2_hidden(k4_pscomp_1(A),A)
          & r2_hidden(k3_pscomp_1(A),A) )
       => A = k1_rcomp_1(k4_pscomp_1(A),k3_pscomp_1(A)) ) ) ),
    file(rcomp_3,t25_rcomp_3),
    []).

fof(t25_seq_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v3_seq_4(A)
       => ( v1_xboole_0(A)
          | ( ~ ( ? [B] : 
                    ( v1_xreal_0(B)
                    & ? [C] : 
                        ( v1_xreal_0(C)
                        & r2_hidden(B,A)
                        & r2_hidden(C,A)
                        & C != B ) )
                & r1_xreal_0(k4_seq_4(A),k5_seq_4(A)) )
            & ~ ( ~ r1_xreal_0(k4_seq_4(A),k5_seq_4(A))
                & ! [B] : 
                    ( v1_xreal_0(B)
                   => ! [C] : 
                        ( v1_xreal_0(C)
                       => ~ ( r2_hidden(B,A)
                            & r2_hidden(C,A)
                            & C != B ) ) ) ) ) ) ) ) ),
    file(seq_4,t25_seq_4),
    []).

fof(t27_rcomp_3,axiom,(
    ! [A] : 
      ( ( v3_seq_4(A)
        & v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( r2_hidden(k3_pscomp_1(A),A)
       => ( r2_hidden(k4_pscomp_1(A),A)
          | A = k2_rcomp_2(k4_pscomp_1(A),k3_pscomp_1(A)) ) ) ) ),
    file(rcomp_3,t27_rcomp_3),
    []).

fof(t29_rcomp_3,axiom,(
    ! [A] : 
      ( ( v3_seq_4(A)
        & v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( r2_hidden(k4_pscomp_1(A),A)
       => ( r2_hidden(k3_pscomp_1(A),A)
          | A = k1_rcomp_2(k4_pscomp_1(A),k3_pscomp_1(A)) ) ) ) ),
    file(rcomp_3,t29_rcomp_3),
    []).

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(t31_rcomp_3,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v3_seq_4(A)
        & v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ~ ( ~ r2_hidden(k4_pscomp_1(A),A)
          & ~ r2_hidden(k3_pscomp_1(A),A)
          & A != k2_rcomp_1(k4_pscomp_1(A),k3_pscomp_1(A)) ) ) ),
    file(rcomp_3,t31_rcomp_3),
    []).

fof(t33_rcomp_3,axiom,(
    ! [A] : 
      ( ( v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( v1_seq_4(A)
          & r2_hidden(k3_pscomp_1(A),A) )
       => ( v2_seq_4(A)
          | A = k2_limfunc1(k3_pscomp_1(A)) ) ) ) ),
    file(rcomp_3,t33_rcomp_3),
    []).

fof(t35_rcomp_3,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_seq_4(A)
       => ( v2_seq_4(A)
          | r2_hidden(k3_pscomp_1(A),A)
          | A = k12_prob_1(k3_pscomp_1(A)) ) ) ) ),
    file(rcomp_3,t35_rcomp_3),
    []).

fof(t37_rcomp_3,axiom,(
    ! [A] : 
      ( ( v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( v2_seq_4(A)
          & r2_hidden(k4_pscomp_1(A),A) )
       => ( v1_seq_4(A)
          | A = k3_limfunc1(k4_pscomp_1(A)) ) ) ) ),
    file(rcomp_3,t37_rcomp_3),
    []).

fof(t39_rcomp_3,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v2_seq_4(A)
       => ( v1_seq_4(A)
          | r2_hidden(k4_pscomp_1(A),A)
          | A = k4_limfunc1(k4_pscomp_1(A)) ) ) ) ),
    file(rcomp_3,t39_rcomp_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(t40_rcomp_3,axiom,(
    ! [A] : 
      ( ( v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ~ ( ~ v1_seq_4(A)
          & ~ v2_seq_4(A)
          & A != k1_numbers ) ) ),
    file(rcomp_3,t40_rcomp_3),
    []).

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),
    []).