% Mizar problem: t125_pscomp_1,pscomp_1,3521,48 
fof(t125_pscomp_1,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( k33_pscomp_1(A) = k34_pscomp_1(A)
       => k33_pscomp_1(A) = k24_pscomp_1(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_funct_2,cc1_membered,cc1_pre_topc,cc1_relat_1,cc1_relset_1,cc1_seq_1,cc1_seq_2,cc1_setfam_1,cc1_xreal_0,cc20_membered,cc2_funct_1,cc2_int_1,cc2_membered,cc2_pscomp_1,cc2_seq_2,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_pscomp_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_funct_2,cc5_xreal_0,cc6_funct_2,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k3_topreal1,commutativity_k3_xboole_0,commutativity_k5_subset_1,d20_pscomp_1,d21_pscomp_1,d26_pscomp_1,d30_pscomp_1,d31_pscomp_1,d32_pscomp_1,d33_pscomp_1,d35_pscomp_1,d36_pscomp_1,d37_pscomp_1,d39_pscomp_1,d40_pscomp_1,d44_pscomp_1,d45_pscomp_1,d46_pscomp_1,d47_pscomp_1,dt_g1_pre_topc,dt_k12_pscomp_1,dt_k13_pscomp_1,dt_k15_euclid,dt_k15_pscomp_1,dt_k16_pscomp_1,dt_k17_pscomp_1,dt_k18_pscomp_1,dt_k19_pscomp_1,dt_k1_numbers,dt_k1_topreal1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_pscomp_1,dt_k21_euclid,dt_k21_pscomp_1,dt_k22_euclid,dt_k23_euclid,dt_k23_pscomp_1,dt_k24_pscomp_1,dt_k25_pscomp_1,dt_k27_pscomp_1,dt_k28_pscomp_1,dt_k2_funct_2,dt_k2_seq_4,dt_k2_zfmisc_1,dt_k32_pscomp_1,dt_k33_pscomp_1,dt_k34_pscomp_1,dt_k35_pscomp_1,dt_k3_pre_topc,dt_k3_pscomp_1,dt_k3_seq_4,dt_k3_topreal1,dt_k3_xboole_0,dt_k4_pscomp_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_subset_1,dt_k7_relat_1,dt_k9_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_pscomp_1,fc11_pscomp_1,fc11_sppol_2,fc12_pscomp_1,fc12_relat_1,fc13_relat_1,fc14_pscomp_1,fc15_pscomp_1,fc1_ordinal2,fc1_pscomp_1,fc1_relat_1,fc1_struct_0,fc1_subset_1,fc27_membered,fc28_membered,fc29_membered,fc2_euclid,fc2_membered,fc2_pscomp_1,fc2_seq_1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_pre_topc,fc3_pscomp_1,fc4_funct_1,fc4_pre_topc,fc4_relat_1,fc4_subset_1,fc5_membered,fc6_membered,fc9_pscomp_1,free_g1_pre_topc,idempotence_k3_xboole_0,idempotence_k5_subset_1,rc10_pscomp_1,rc1_funct_1,rc1_funct_2,rc1_int_1,rc1_membered,rc1_pre_topc,rc1_pscomp_1,rc1_relat_1,rc1_seq_1,rc1_setfam_1,rc1_subset_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_pre_topc,rc2_pscomp_1,rc2_relat_1,rc2_subset_1,rc2_xreal_0,rc3_funct_1,rc3_pre_topc,rc3_pscomp_1,rc3_relat_1,rc3_struct_0,rc3_xreal_0,rc4_funct_1,rc4_pre_topc,rc4_pscomp_1,rc4_xreal_0,rc5_pre_topc,rc5_struct_0,rc6_pscomp_1,rc7_pscomp_1,rc8_pscomp_1,rc9_pscomp_1,redefinition_k2_funct_2,redefinition_k3_pscomp_1,redefinition_k3_topreal1,redefinition_k4_pscomp_1,redefinition_k5_numbers,redefinition_k5_subset_1,redefinition_m2_relset_1,reflexivity_r1_tarski,spc2_boole,spc2_numerals,t104_pscomp_1,t1_subset,t2_boole,t2_subset,t3_subset,t4_subset,t57_euclid,t5_subset,t6_boole,t76_pscomp_1,t77_pscomp_1,t7_boole,t8_boole,t94_pscomp_1]),
    [file(pscomp_1,t125_pscomp_1)]).

fof(abstractness_v1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_pre_topc(A)
       => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ),
    file(pre_topc,v1_pre_topc),
    []).

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_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

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

fof(cc1_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => v2_pre_topc(B) ) ) ),
    file(pre_topc,cc1_pre_topc),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_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_seq_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v3_seq_2(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_seq_2(A)
        & v2_seq_2(A) ) ) ),
    file(seq_2,cc1_seq_2),
    []).

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

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

fof(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_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    []).

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

fof(cc2_pscomp_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_compts_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v10_pscomp_1(A) ) ) ) ),
    file(pscomp_1,cc2_pscomp_1),
    []).

fof(cc2_seq_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_seq_2(A)
        & v2_seq_2(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v3_seq_2(A) ) ) ),
    file(seq_2,cc2_seq_2),
    []).

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

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

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

fof(cc3_pscomp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v10_pscomp_1(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_relset_1(B,u1_struct_0(A),k1_numbers)
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k1_numbers)
              & v9_pscomp_1(B,A) )
           => ( ~ v1_xboole_0(B)
              & v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k1_numbers)
              & v1_seq_1(B)
              & v3_seq_2(B)
              & v1_partfun1(B,u1_struct_0(A),k1_numbers)
              & v7_pscomp_1(B,u1_struct_0(A))
              & v8_pscomp_1(B,u1_struct_0(A)) ) ) ) ) ),
    file(pscomp_1,cc3_pscomp_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_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_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

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_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

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_k3_topreal1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => k3_topreal1(A,B,C) = k3_topreal1(A,C,B) ) ),
    file(topreal1,k3_topreal1),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(d20_pscomp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => k12_pscomp_1(A,B) = k4_pscomp_1(k2_funct_2(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) ),
    file(pscomp_1,d20_pscomp_1),
    []).

fof(d21_pscomp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => k13_pscomp_1(A,B) = k3_pscomp_1(k2_funct_2(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) ),
    file(pscomp_1,d21_pscomp_1),
    []).

fof(d26_pscomp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),k1_numbers)
                & m2_relset_1(C,u1_struct_0(A),k1_numbers) )
             => k15_pscomp_1(A,B,C) = k7_relat_1(C,B) ) ) ) ),
    file(pscomp_1,d26_pscomp_1),
    []).

fof(d30_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k18_pscomp_1(A) = k12_pscomp_1(k3_pre_topc(k15_euclid(2),A),k15_pscomp_1(k15_euclid(2),A,k16_pscomp_1)) ) ),
    file(pscomp_1,d30_pscomp_1),
    []).

fof(d31_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k19_pscomp_1(A) = k13_pscomp_1(k3_pre_topc(k15_euclid(2),A),k15_pscomp_1(k15_euclid(2),A,k17_pscomp_1)) ) ),
    file(pscomp_1,d31_pscomp_1),
    []).

fof(d32_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k20_pscomp_1(A) = k13_pscomp_1(k3_pre_topc(k15_euclid(2),A),k15_pscomp_1(k15_euclid(2),A,k16_pscomp_1)) ) ),
    file(pscomp_1,d32_pscomp_1),
    []).

fof(d33_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k21_pscomp_1(A) = k12_pscomp_1(k3_pre_topc(k15_euclid(2),A),k15_pscomp_1(k15_euclid(2),A,k17_pscomp_1)) ) ),
    file(pscomp_1,d33_pscomp_1),
    []).

fof(d35_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k23_pscomp_1(A) = k23_euclid(k18_pscomp_1(A),k19_pscomp_1(A)) ) ),
    file(pscomp_1,d35_pscomp_1),
    []).

fof(d36_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k24_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k19_pscomp_1(A)) ) ),
    file(pscomp_1,d36_pscomp_1),
    []).

fof(d37_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k25_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k21_pscomp_1(A)) ) ),
    file(pscomp_1,d37_pscomp_1),
    []).

fof(d39_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k27_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k23_pscomp_1(A),k24_pscomp_1(A)),A) ) ),
    file(pscomp_1,d39_pscomp_1),
    []).

fof(d40_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k28_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k25_pscomp_1(A),k24_pscomp_1(A)),A) ) ),
    file(pscomp_1,d40_pscomp_1),
    []).

fof(d44_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k32_pscomp_1(A) = k23_euclid(k12_pscomp_1(k3_pre_topc(k15_euclid(2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(2),k27_pscomp_1(A),k16_pscomp_1)),k19_pscomp_1(A)) ) ),
    file(pscomp_1,d44_pscomp_1),
    []).

fof(d45_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k33_pscomp_1(A) = k23_euclid(k13_pscomp_1(k3_pre_topc(k15_euclid(2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(2),k27_pscomp_1(A),k16_pscomp_1)),k19_pscomp_1(A)) ) ),
    file(pscomp_1,d45_pscomp_1),
    []).

fof(d46_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k34_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k13_pscomp_1(k3_pre_topc(k15_euclid(2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(2),k28_pscomp_1(A),k17_pscomp_1))) ) ),
    file(pscomp_1,d46_pscomp_1),
    []).

fof(d47_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k35_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k12_pscomp_1(k3_pre_topc(k15_euclid(2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(2),k28_pscomp_1(A),k17_pscomp_1))) ) ),
    file(pscomp_1,d47_pscomp_1),
    []).

fof(dt_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_pre_topc(g1_pre_topc(A,B))
        & l1_pre_topc(g1_pre_topc(A,B)) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(dt_k12_pscomp_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),k1_numbers)
        & m1_relset_1(B,u1_struct_0(A),k1_numbers) )
     => m1_subset_1(k12_pscomp_1(A,B),k1_numbers) ) ),
    file(pscomp_1,k12_pscomp_1),
    []).

fof(dt_k13_pscomp_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),k1_numbers)
        & m1_relset_1(B,u1_struct_0(A),k1_numbers) )
     => m1_subset_1(k13_pscomp_1(A,B),k1_numbers) ) ),
    file(pscomp_1,k13_pscomp_1),
    []).

fof(dt_k15_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & l1_pre_topc(k15_euclid(A)) ) ) ),
    file(euclid,k15_euclid),
    []).

fof(dt_k15_pscomp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),k1_numbers)
        & m1_relset_1(C,u1_struct_0(A),k1_numbers) )
     => ( v1_funct_1(k15_pscomp_1(A,B,C))
        & v1_funct_2(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers)
        & m2_relset_1(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers) ) ) ),
    file(pscomp_1,k15_pscomp_1),
    []).

fof(dt_k16_pscomp_1,axiom,
    ( v1_funct_1(k16_pscomp_1)
    & v1_funct_2(k16_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers)
    & m2_relset_1(k16_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) ),
    file(pscomp_1,k16_pscomp_1),
    []).

fof(dt_k17_pscomp_1,axiom,
    ( v1_funct_1(k17_pscomp_1)
    & v1_funct_2(k17_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers)
    & m2_relset_1(k17_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) ),
    file(pscomp_1,k17_pscomp_1),
    []).

fof(dt_k18_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k18_pscomp_1(A),k1_numbers) ) ),
    file(pscomp_1,k18_pscomp_1),
    []).

fof(dt_k19_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k19_pscomp_1(A),k1_numbers) ) ),
    file(pscomp_1,k19_pscomp_1),
    []).

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

fof(dt_k1_topreal1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => m1_subset_1(k1_topreal1(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ),
    file(topreal1,k1_topreal1),
    []).

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_k20_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k20_pscomp_1(A),k1_numbers) ) ),
    file(pscomp_1,k20_pscomp_1),
    []).

fof(dt_k21_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => m1_subset_1(k21_euclid(A),k1_numbers) ) ),
    file(euclid,k21_euclid),
    []).

fof(dt_k21_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k21_pscomp_1(A),k1_numbers) ) ),
    file(pscomp_1,k21_pscomp_1),
    []).

fof(dt_k22_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => m1_subset_1(k22_euclid(A),k1_numbers) ) ),
    file(euclid,k22_euclid),
    []).

fof(dt_k23_euclid,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k23_euclid(A,B),u1_struct_0(k15_euclid(2))) ) ),
    file(euclid,k23_euclid),
    []).

fof(dt_k23_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k23_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ),
    file(pscomp_1,k23_pscomp_1),
    []).

fof(dt_k24_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k24_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ),
    file(pscomp_1,k24_pscomp_1),
    []).

fof(dt_k25_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k25_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ),
    file(pscomp_1,k25_pscomp_1),
    []).

fof(dt_k27_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k27_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ),
    file(pscomp_1,k27_pscomp_1),
    []).

fof(dt_k28_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k28_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ),
    file(pscomp_1,k28_pscomp_1),
    []).

fof(dt_k2_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ),
    file(funct_2,k2_funct_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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k32_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k32_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ),
    file(pscomp_1,k32_pscomp_1),
    []).

fof(dt_k33_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k33_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ),
    file(pscomp_1,k33_pscomp_1),
    []).

fof(dt_k34_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k34_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ),
    file(pscomp_1,k34_pscomp_1),
    []).

fof(dt_k35_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => m1_subset_1(k35_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ),
    file(pscomp_1,k35_pscomp_1),
    []).

fof(dt_k3_pre_topc,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_pre_topc(k3_pre_topc(A,B))
        & m1_pre_topc(k3_pre_topc(A,B),A) ) ) ),
    file(pre_topc,k3_pre_topc),
    []).

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_k3_topreal1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => m1_subset_1(k3_topreal1(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ),
    file(topreal1,k3_topreal1),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

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_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

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

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

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

fof(dt_m1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => l1_pre_topc(B) ) ) ),
    file(pre_topc,m1_pre_topc),
    []).

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_u1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(pre_topc,u1_pre_topc),
    []).

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

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

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

fof(existence_m1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : m1_pre_topc(B,A) ) ),
    file(pre_topc,m1_pre_topc),
    []).

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(fc10_pscomp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & v6_compts_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k3_pre_topc(A,B))
        & v1_pre_topc(k3_pre_topc(A,B))
        & v2_pre_topc(k3_pre_topc(A,B))
        & v2_compts_1(k3_pre_topc(A,B)) ) ) ),
    file(pscomp_1,fc10_pscomp_1),
    []).

fof(fc11_pscomp_1,axiom,
    ( ~ v1_xboole_0(k16_pscomp_1)
    & v1_relat_1(k16_pscomp_1)
    & v1_funct_1(k16_pscomp_1)
    & v1_funct_2(k16_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers)
    & v1_seq_1(k16_pscomp_1)
    & v1_partfun1(k16_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers)
    & v9_pscomp_1(k16_pscomp_1,k15_euclid(2)) ),
    file(pscomp_1,fc11_pscomp_1),
    []).

fof(fc11_sppol_2,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => ( ~ v1_xboole_0(k1_topreal1(A,B,C))
        & v6_compts_1(k1_topreal1(A,B,C),k15_euclid(A)) ) ) ),
    file(sppol_2,fc11_sppol_2),
    []).

fof(fc12_pscomp_1,axiom,
    ( ~ v1_xboole_0(k17_pscomp_1)
    & v1_relat_1(k17_pscomp_1)
    & v1_funct_1(k17_pscomp_1)
    & v1_funct_2(k17_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers)
    & v1_seq_1(k17_pscomp_1)
    & v1_partfun1(k17_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers)
    & v9_pscomp_1(k17_pscomp_1,k15_euclid(2)) ),
    file(pscomp_1,fc12_pscomp_1),
    []).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc13_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v3_relat_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v3_relat_1(k7_relat_1(A,B)) ) ) ),
    file(relat_1,fc13_relat_1),
    []).

fof(fc14_pscomp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) )
     => ( ~ v1_xboole_0(k27_pscomp_1(A))
        & v6_compts_1(k27_pscomp_1(A),k15_euclid(2)) ) ) ),
    file(pscomp_1,fc14_pscomp_1),
    []).

fof(fc15_pscomp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) )
     => ( ~ v1_xboole_0(k28_pscomp_1(A))
        & v6_compts_1(k28_pscomp_1(A),k15_euclid(2)) ) ) ),
    file(pscomp_1,fc15_pscomp_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_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_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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

fof(fc27_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(A,B)) ) ),
    file(membered,fc27_membered),
    []).

fof(fc28_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(B,A)) ) ),
    file(membered,fc28_membered),
    []).

fof(fc29_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc29_membered),
    []).

fof(fc2_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A)) ) ) ),
    file(euclid,fc2_euclid),
    []).

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

fof(fc2_pscomp_1,axiom,
    ( ~ v1_xboole_0(k5_ordinal2)
    & v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2)
    & ~ v1_setfam_1(k5_ordinal2) ),
    file(pscomp_1,fc2_pscomp_1),
    []).

fof(fc2_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_seq_1(k7_relat_1(A,B)) ) ) ),
    file(seq_1,fc2_seq_1),
    []).

fof(fc30_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc30_membered),
    []).

fof(fc31_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc31_membered),
    []).

fof(fc32_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc32_membered),
    []).

fof(fc33_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc33_membered),
    []).

fof(fc34_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc34_membered),
    []).

fof(fc35_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B))
        & v5_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc35_membered),
    []).

fof(fc36_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A))
        & v5_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc36_membered),
    []).

fof(fc3_pre_topc,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k3_pre_topc(A,B))
        & v1_pre_topc(k3_pre_topc(A,B)) ) ) ),
    file(pre_topc,fc3_pre_topc),
    []).

fof(fc3_pscomp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ~ v1_xboole_0(k9_relat_1(C,A)) ) ),
    file(pscomp_1,fc3_pscomp_1),
    []).

fof(fc4_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    []).

fof(fc4_pre_topc,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_pre_topc(k3_pre_topc(A,B))
        & v2_pre_topc(k3_pre_topc(A,B)) ) ) ),
    file(pre_topc,fc4_pre_topc),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

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

fof(fc9_pscomp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),k1_numbers)
        & v9_pscomp_1(B,A)
        & m1_relset_1(B,u1_struct_0(A),k1_numbers)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_relat_1(k15_pscomp_1(A,C,B))
        & v1_funct_1(k15_pscomp_1(A,C,B))
        & v1_funct_2(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers)
        & v1_seq_1(k15_pscomp_1(A,C,B))
        & v1_partfun1(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers)
        & v9_pscomp_1(k15_pscomp_1(A,C,B),k3_pre_topc(A,C)) ) ) ),
    file(pscomp_1,fc9_pscomp_1),
    []).

fof(free_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C,D] : 
          ( g1_pre_topc(A,B) = g1_pre_topc(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

fof(rc10_pscomp_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v2_compts_1(A)
      & v10_pscomp_1(A) ) ),
    file(pscomp_1,rc10_pscomp_1),
    []).

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

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

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_pre_topc,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v1_pre_topc(A) ) ),
    file(pre_topc,rc1_pre_topc),
    []).

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

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_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_setfam_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

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

fof(rc2_pre_topc,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(pre_topc,rc2_pre_topc),
    []).

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

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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

fof(rc2_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B) ) ) ),
    file(pre_topc,rc3_pre_topc),
    []).

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_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(rc4_pre_topc,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B) ) ) ),
    file(pre_topc,rc4_pre_topc),
    []).

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_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B) ) ) ),
    file(pre_topc,rc5_pre_topc),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc6_pscomp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_relset_1(B,u1_struct_0(A),k1_numbers)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),k1_numbers)
          & v1_seq_1(B)
          & v1_seq_2(B)
          & v2_seq_2(B)
          & v3_seq_2(B)
          & v1_partfun1(B,u1_struct_0(A),k1_numbers) ) ) ),
    file(pscomp_1,rc6_pscomp_1),
    []).

fof(rc7_pscomp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_relset_1(B,u1_struct_0(A),k1_numbers)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),k1_numbers)
          & v1_seq_1(B)
          & v1_partfun1(B,u1_struct_0(A),k1_numbers)
          & v9_pscomp_1(B,A) ) ) ),
    file(pscomp_1,rc7_pscomp_1),
    []).

fof(rc8_pscomp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A) )
     => ? [C] : 
          ( m1_relset_1(C,u1_struct_0(B),k1_numbers)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(B),k1_numbers)
          & v1_seq_1(C)
          & v1_partfun1(C,u1_struct_0(B),k1_numbers)
          & v9_pscomp_1(C,B) ) ) ),
    file(pscomp_1,rc8_pscomp_1),
    []).

fof(rc9_pscomp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v6_compts_1(B,A) ) ) ),
    file(pscomp_1,rc9_pscomp_1),
    []).

fof(redefinition_k2_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(funct_2,k2_funct_2),
    []).

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_k3_topreal1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => k3_topreal1(A,B,C) = k1_topreal1(A,B,C) ) ),
    file(topreal1,k3_topreal1),
    []).

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_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

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

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(t104_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( k21_euclid(k35_pscomp_1(A)) = k20_pscomp_1(A)
        & k21_euclid(k34_pscomp_1(A)) = k20_pscomp_1(A) ) ) ),
    file(pscomp_1,t104_pscomp_1),
    []).

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

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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

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

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t57_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => A = k23_euclid(k21_euclid(A),k22_euclid(A)) ) ),
    file(euclid,t57_euclid),
    []).

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(t76_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k21_euclid(k24_pscomp_1(A)) = k20_pscomp_1(A) ) ),
    file(pscomp_1,t76_pscomp_1),
    []).

fof(t77_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => k22_euclid(k24_pscomp_1(A)) = k19_pscomp_1(A) ) ),
    file(pscomp_1,t77_pscomp_1),
    []).

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

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

fof(t94_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( k22_euclid(k32_pscomp_1(A)) = k19_pscomp_1(A)
        & k22_euclid(k33_pscomp_1(A)) = k19_pscomp_1(A) ) ) ),
    file(pscomp_1,t94_pscomp_1),
    []).