% Mizar problem: t15_measure3,measure3,739,24 
fof(t15_measure3,conjecture,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] : 
          ( m1_measure1(C,A,B)
         => ! [D] : 
              ( m1_measure2(D,A,B)
             => ! [E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,k5_numbers,B)
                    & v1_prob_2(E)
                    & m2_relset_1(E,k5_numbers,B) )
                 => ( D = k1_measure3(A,B,E)
                   => r1_supinf_1(k19_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,E,C)),k1_measure1(B,C,k2_measure2(A,B,D))) ) ) ) ) ) ),
    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_arytm_3,cc1_measure1,cc1_membered,cc1_relset_1,cc1_supinf_1,cc20_membered,cc2_arytm_3,cc2_measure1,cc2_membered,cc2_supinf_1,cc3_arytm_3,cc3_measure1,cc3_membered,cc4_measure1,cc4_membered,cc6_membered,cc9_membered,commutativity_k1_nat_1,commutativity_k2_measure1,commutativity_k2_supinf_2,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_measure1,commutativity_k3_xboole_0,commutativity_k4_subset_1,connectedness_r1_supinf_1,connectedness_r1_xreal_0,d1_funct_2,d2_tarski,d3_prob_2,d3_tarski,d5_measure1,d7_xboole_0,dt_k13_supinf_2,dt_k18_supinf_2,dt_k19_supinf_2,dt_k1_funct_1,dt_k1_measure1,dt_k1_measure3,dt_k1_nat_1,dt_k1_numbers,dt_k1_prob_1,dt_k1_relat_1,dt_k1_supinf_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_measure1,dt_k2_measure2,dt_k2_relat_1,dt_k2_supinf_2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_measure1,dt_k3_supinf_1,dt_k3_tarski,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_subset_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k7_funct_2,dt_k8_funct_2,dt_m1_measure1,dt_m1_measure2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_measure1,existence_m1_measure2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_ordinal2,fc1_subset_1,fc1_supinf_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc2_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_subset_1,fc4_subset_1,fc5_membered,fc6_membered,idempotence_k2_measure1,idempotence_k2_xboole_0,idempotence_k3_measure1,idempotence_k3_xboole_0,idempotence_k4_subset_1,rc1_arytm_3,rc1_measure1,rc1_membered,rc1_subset_1,rc2_measure1,rc2_subset_1,rc3_measure1,rc3_supinf_1,rc4_measure1,redefinition_k13_supinf_2,redefinition_k1_measure1,redefinition_k1_measure3,redefinition_k1_nat_1,redefinition_k1_prob_1,redefinition_k2_measure1,redefinition_k2_measure2,redefinition_k3_measure1,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k7_funct_2,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_supinf_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_nat_1__e2_17_3__measure3,s1_nat_1__e2_17_6__measure3,s1_nat_1__e3_17_2_1__measure3,s1_nat_1__e4_17_4__measure3,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_xboole_0,t18_nat_1,t18_supinf_2,t1_arithm,t1_boole,t1_numerals,t1_subset,t22_funct_1,t23_xboole_1,t25_measure1,t2_boole,t2_subset,t2_xboole_1,t38_nat_1,t3_measure3,t3_subset,t40_measure1,t45_measure1,t4_subset,t54_measure1,t5_measure2,t5_subset,t63_supinf_2,t67_supinf_2,t6_boole,t6_funct_2,t7_boole,t8_boole,t8_funct_2,t8_xboole_1,t92_zfmisc_1]),
    [file(measure3,t15_measure3)]).

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_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

fof(cc1_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( v1_finsub_1(B)
          & v1_prob_1(B,A) )
       => v2_finsub_1(B) ) ) ),
    file(measure1,cc1_measure1),
    []).

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

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_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => v3_supinf_1(A) ) ),
    file(supinf_1,cc1_supinf_1),
    []).

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_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

fof(cc2_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( v2_finsub_1(B)
          & v1_prob_1(B,A) )
       => v1_finsub_1(B) ) ) ),
    file(measure1,cc2_measure1),
    []).

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

fof(cc2_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_supinf_1(A) ) ) ),
    file(supinf_1,cc2_supinf_1),
    []).

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

fof(cc3_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) )
       => ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) ) ) ) ),
    file(measure1,cc3_measure1),
    []).

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

fof(cc4_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) )
       => ( ~ v1_xboole_0(B)
          & v1_finsub_1(B) ) ) ) ),
    file(measure1,cc4_measure1),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

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

fof(commutativity_k2_measure1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_finsub_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k2_measure1(A,B,C,D) = k2_measure1(A,B,D,C) ) ),
    file(measure1,k2_measure1),
    []).

fof(commutativity_k2_supinf_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k2_supinf_2(A,B) = k2_supinf_2(B,A) ) ),
    file(supinf_2,k2_supinf_2),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(commutativity_k3_measure1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k3_measure1(A,B,C,D) = k3_measure1(A,B,D,C) ) ),
    file(measure1,k3_measure1),
    []).

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_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(connectedness_r1_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => ( r1_supinf_1(A,B)
        | r1_supinf_1(B,A) ) ) ),
    file(supinf_1,r1_supinf_1),
    []).

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_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

fof(d3_prob_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_prob_2(A)
      <=> ! [B,C] : 
            ( B != C
           => r1_xboole_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ),
    file(prob_2,d3_prob_2),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d5_measure1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,k3_supinf_1)
            & m2_relset_1(C,B,k3_supinf_1) )
         => ( m1_measure1(C,A,B)
          <=> ( v6_supinf_2(C,B)
              & k1_funct_1(C,k1_xboole_0) = k1_supinf_2
              & ! [D] : 
                  ( m2_subset_1(D,k1_zfmisc_1(A),B)
                 => ! [E] : 
                      ( m2_subset_1(E,k1_zfmisc_1(A),B)
                     => ( r1_xboole_0(D,E)
                       => k1_funct_1(C,k4_subset_1(A,D,E)) = k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) ) ) ),
    file(measure1,d5_measure1),
    []).

fof(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

fof(dt_k13_supinf_2,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1)
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k13_supinf_2(A,B),k3_supinf_1) ) ),
    file(supinf_2,k13_supinf_2),
    []).

fof(dt_k18_supinf_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v1_funct_1(k18_supinf_2(A))
        & v1_funct_2(k18_supinf_2(A),k5_numbers,k3_supinf_1)
        & m2_relset_1(k18_supinf_2(A),k5_numbers,k3_supinf_1) ) ) ),
    file(supinf_2,k18_supinf_2),
    []).

fof(dt_k19_supinf_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1) )
     => m1_subset_1(k19_supinf_2(A),k3_supinf_1) ) ),
    file(supinf_2,k19_supinf_2),
    []).

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

fof(dt_k1_measure1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k3_supinf_1)
        & m1_relset_1(B,A,k3_supinf_1)
        & m1_subset_1(C,A) )
     => m1_subset_1(k1_measure1(A,B,C),k3_supinf_1) ) ),
    file(measure1,k1_measure1),
    []).

fof(dt_k1_measure3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,B)
        & m1_relset_1(C,k5_numbers,B) )
     => m1_measure2(k1_measure3(A,B,C),A,B) ) ),
    file(measure3,k1_measure3),
    []).

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

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

fof(dt_k1_prob_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k1_prob_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(prob_1,k1_prob_1),
    []).

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

fof(dt_k1_supinf_2,axiom,(
    m1_subset_1(k1_supinf_2,k3_supinf_1) ),
    file(supinf_2,k1_supinf_2),
    []).

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_measure1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_finsub_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => m2_subset_1(k2_measure1(A,B,C,D),k1_zfmisc_1(A),B) ) ),
    file(measure1,k2_measure1),
    []).

fof(dt_k2_measure2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_measure2(C,A,B) )
     => m2_subset_1(k2_measure2(A,B,C),k1_zfmisc_1(A),B) ) ),
    file(measure2,k2_measure2),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_supinf_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k2_supinf_2(A,B),k3_supinf_1) ) ),
    file(supinf_2,k2_supinf_2),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_measure1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => m2_subset_1(k3_measure1(A,B,C,D),k1_zfmisc_1(A),B) ) ),
    file(measure1,k3_measure1),
    []).

fof(dt_k3_supinf_1,axiom,(
    $true ),
    file(supinf_1,k3_supinf_1),
    []).

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

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

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_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(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_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_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    []).

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_m1_measure1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] : 
          ( m1_measure1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,B,k3_supinf_1)
            & m2_relset_1(C,B,k3_supinf_1) ) ) ) ),
    file(measure1,m1_measure1),
    []).

fof(dt_m1_measure2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] : 
          ( m1_measure2(C,A,B)
         => ( ~ v1_xboole_0(C)
            & v1_card_4(C)
            & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ),
    file(measure2,m1_measure2),
    []).

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_measure1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] : m1_measure1(C,A,B) ) ),
    file(measure1,m1_measure1),
    []).

fof(existence_m1_measure2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] : m1_measure2(C,A,B) ) ),
    file(measure2,m1_measure2),
    []).

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(fc12_membered,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    []).

fof(fc13_membered,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    []).

fof(fc14_membered,axiom,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    []).

fof(fc15_membered,axiom,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    []).

fof(fc16_membered,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    []).

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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_supinf_1,axiom,(
    ~ v1_xboole_0(k3_supinf_1) ),
    file(supinf_1,fc1_supinf_1),
    []).

fof(fc22_membered,axiom,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    []).

fof(fc23_membered,axiom,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    []).

fof(fc24_membered,axiom,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    []).

fof(fc25_membered,axiom,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    []).

fof(fc26_membered,axiom,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    []).

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

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_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_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(idempotence_k2_measure1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_finsub_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k2_measure1(A,B,C,C) = C ) ),
    file(measure1,k2_measure1),
    []).

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

fof(idempotence_k3_measure1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k3_measure1(A,B,C,C) = C ) ),
    file(measure1,k3_measure1),
    []).

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

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_measure1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_finsub_1(B)
      & v2_finsub_1(B)
      & v1_prob_1(B,A) ) ),
    file(measure1,rc1_measure1),
    []).

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_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(rc2_measure1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_card_4(B) ) ),
    file(measure1,rc2_measure1),
    []).

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(rc3_measure1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_prob_1(B,A)
      & v1_measure1(B,A) ) ),
    file(measure1,rc3_measure1),
    []).

fof(rc3_supinf_1,axiom,(
    ? [A] : v3_supinf_1(A) ),
    file(supinf_1,rc3_supinf_1),
    []).

fof(rc4_measure1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] : 
          ( m1_relset_1(C,k5_numbers,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k5_numbers,B)
          & v1_prob_2(C) ) ) ),
    file(measure1,rc4_measure1),
    []).

fof(redefinition_k13_supinf_2,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1)
        & m1_subset_1(B,k5_numbers) )
     => k13_supinf_2(A,B) = k1_funct_1(A,B) ) ),
    file(supinf_2,k13_supinf_2),
    []).

fof(redefinition_k1_measure1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k3_supinf_1)
        & m1_relset_1(B,A,k3_supinf_1)
        & m1_subset_1(C,A) )
     => k1_measure1(A,B,C) = k1_funct_1(B,C) ) ),
    file(measure1,k1_measure1),
    []).

fof(redefinition_k1_measure3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,B)
        & m1_relset_1(C,k5_numbers,B) )
     => k1_measure3(A,B,C) = k2_relat_1(C) ) ),
    file(measure3,k1_measure3),
    []).

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

fof(redefinition_k1_prob_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => k1_prob_1(A,B,C) = k1_funct_1(B,C) ) ),
    file(prob_1,k1_prob_1),
    []).

fof(redefinition_k2_measure1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_finsub_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k2_measure1(A,B,C,D) = k2_xboole_0(C,D) ) ),
    file(measure1,k2_measure1),
    []).

fof(redefinition_k2_measure2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_measure2(C,A,B) )
     => k2_measure2(A,B,C) = k3_tarski(C) ) ),
    file(measure2,k2_measure2),
    []).

fof(redefinition_k3_measure1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k3_measure1(A,B,C,D) = k3_xboole_0(C,D) ) ),
    file(measure1,k3_measure1),
    []).

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_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

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

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    []).

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_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_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => r1_supinf_1(A,A) ) ),
    file(supinf_1,r1_supinf_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(s1_nat_1__e2_17_3__measure3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_measure1(C,A,B)
        & v1_funct_1(D)
        & v1_funct_2(D,k5_numbers,B)
        & v1_prob_2(D)
        & m2_relset_1(D,k5_numbers,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k5_numbers,B)
        & m2_relset_1(E,k5_numbers,B) )
     => ( ( k1_measure1(k5_numbers,k18_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,D,C)),0) = k1_measure1(B,C,k8_funct_2(k5_numbers,B,E,0))
          & ! [F] : 
              ( m2_subset_1(F,k1_numbers,k5_numbers)
             => ( k1_measure1(k5_numbers,k18_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,D,C)),F) = k1_measure1(B,C,k8_funct_2(k5_numbers,B,E,F))
               => k1_measure1(k5_numbers,k18_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,D,C)),k1_nat_1(F,1)) = k1_measure1(B,C,k8_funct_2(k5_numbers,B,E,k1_nat_1(F,1))) ) ) )
       => ! [F] : 
            ( m2_subset_1(F,k1_numbers,k5_numbers)
           => k1_measure1(k5_numbers,k18_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,D,C)),F) = k1_measure1(B,C,k8_funct_2(k5_numbers,B,E,F)) ) ) ) ),
    file(measure3,s1_nat_1__e2_17_3__measure3),
    []).

fof(s1_nat_1__e2_17_6__measure3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_measure1(C,A,B)
        & m1_measure2(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k5_numbers,B)
        & m2_relset_1(E,k5_numbers,B) )
     => ( ( k1_measure1(k5_numbers,k18_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,E,C)),0) = k1_measure1(B,C,k2_measure2(A,B,D))
          & ! [F] : 
              ( m2_subset_1(F,k1_numbers,k5_numbers)
             => ( k1_measure1(k5_numbers,k18_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,E,C)),F) = k1_measure1(B,C,k2_measure2(A,B,D))
               => k1_measure1(k5_numbers,k18_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,E,C)),k1_nat_1(F,1)) = k1_measure1(B,C,k2_measure2(A,B,D)) ) ) )
       => ! [F] : 
            ( m2_subset_1(F,k1_numbers,k5_numbers)
           => k1_measure1(k5_numbers,k18_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,E,C)),F) = k1_measure1(B,C,k2_measure2(A,B,D)) ) ) ) ),
    file(measure3,s1_nat_1__e2_17_6__measure3),
    []).

fof(s1_nat_1__e3_17_2_1__measure3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,B)
        & v1_prob_2(C)
        & m2_relset_1(C,k5_numbers,B)
        & v1_funct_1(D)
        & v1_funct_2(D,k5_numbers,B)
        & m2_relset_1(D,k5_numbers,B) )
     => ( ( ! [E] : 
              ( m2_subset_1(E,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(E,0)
               => k3_measure1(A,B,k8_funct_2(k5_numbers,B,D,0),k8_funct_2(k5_numbers,B,C,E)) = k1_xboole_0 ) )
          & ! [F] : 
              ( m2_subset_1(F,k1_numbers,k5_numbers)
             => ( ! [G] : 
                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(G,F)
                     => k3_measure1(A,B,k8_funct_2(k5_numbers,B,D,F),k8_funct_2(k5_numbers,B,C,G)) = k1_xboole_0 ) )
               => ! [H] : 
                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(H,k1_nat_1(F,1))
                     => k3_measure1(A,B,k8_funct_2(k5_numbers,B,D,k1_nat_1(F,1)),k8_funct_2(k5_numbers,B,C,H)) = k1_xboole_0 ) ) ) ) )
       => ! [F] : 
            ( m2_subset_1(F,k1_numbers,k5_numbers)
           => ! [I] : 
                ( m2_subset_1(I,k1_numbers,k5_numbers)
               => ( ~ r1_xreal_0(I,F)
                 => k3_measure1(A,B,k8_funct_2(k5_numbers,B,D,F),k8_funct_2(k5_numbers,B,C,I)) = k1_xboole_0 ) ) ) ) ) ),
    file(measure3,s1_nat_1__e3_17_2_1__measure3),
    []).

fof(s1_nat_1__e4_17_4__measure3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_measure2(C,A,B)
        & v1_funct_1(D)
        & v1_funct_2(D,k5_numbers,B)
        & m2_relset_1(D,k5_numbers,B) )
     => ( ( r1_tarski(k8_funct_2(k5_numbers,B,D,0),k2_measure2(A,B,C))
          & ! [E] : 
              ( m2_subset_1(E,k1_numbers,k5_numbers)
             => ( r1_tarski(k8_funct_2(k5_numbers,B,D,E),k2_measure2(A,B,C))
               => r1_tarski(k8_funct_2(k5_numbers,B,D,k1_nat_1(E,1)),k2_measure2(A,B,C)) ) ) )
       => ! [E] : 
            ( m2_subset_1(E,k1_numbers,k5_numbers)
           => r1_tarski(k8_funct_2(k5_numbers,B,D,E),k2_measure2(A,B,C)) ) ) ) ),
    file(measure3,s1_nat_1__e4_17_4__measure3),
    []).

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

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t18_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r1_xreal_0(0,A) ) ),
    file(nat_1,t18_nat_1),
    []).

fof(t18_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ( k2_supinf_2(A,k1_supinf_2) = A
        & k2_supinf_2(k1_supinf_2,A) = A ) ) ),
    file(supinf_2,t18_supinf_2),
    []).

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

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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

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

fof(t22_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    []).

fof(t23_xboole_1,axiom,(
    ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ),
    file(xboole_1,t23_xboole_1),
    []).

fof(t25_measure1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] : 
          ( m1_measure1(C,A,B)
         => ! [D] : 
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] : 
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => ( r1_tarski(D,E)
                   => r1_supinf_1(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) ),
    file(measure1,t25_measure1),
    []).

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(t2_xboole_1,axiom,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    []).

fof(t38_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A)
          <=> r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,t38_nat_1),
    []).

fof(t3_measure3,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k3_supinf_1)
            & m2_relset_1(B,k5_numbers,k3_supinf_1) )
         => ( ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_supinf_1(k1_measure1(k5_numbers,k18_supinf_2(A),C),k1_measure1(k5_numbers,k18_supinf_2(B),C)) )
           => r1_supinf_1(k19_supinf_2(A),k19_supinf_2(B)) ) ) ) ),
    file(measure3,t3_measure3),
    []).

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

fof(t40_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ? [D] : 
              ( v1_funct_1(D)
              & v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
              & m2_relset_1(D,k5_numbers,k1_zfmisc_1(A))
              & k2_relat_1(D) = k2_tarski(B,C)
              & k1_prob_1(A,D,0) = B
              & ! [E] : 
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(E,0)
                   => k1_prob_1(A,D,E) = C ) ) ) ) ) ),
    file(measure1,t40_measure1),
    []).

fof(t45_measure1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( r2_hidden(k1_xboole_0,B)
        & r2_hidden(A,B) ) ) ),
    file(measure1,t45_measure1),
    []).

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(t54_measure1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,k3_supinf_1)
                    & m2_relset_1(D,B,k3_supinf_1) )
                 => ( v6_supinf_2(D,B)
                   => v6_supinf_2(k7_funct_2(A,B,k3_supinf_1,C,D),A) ) ) ) ) ) ),
    file(measure1,t54_measure1),
    []).

fof(t5_measure2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,B)
            & m2_relset_1(C,k5_numbers,B) )
         => ? [D] : 
              ( v1_funct_1(D)
              & v1_funct_2(D,k5_numbers,B)
              & m2_relset_1(D,k5_numbers,B)
              & k8_funct_2(k5_numbers,B,D,0) = k8_funct_2(k5_numbers,B,C,0)
              & ! [E] : 
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                 => k8_funct_2(k5_numbers,B,D,k1_nat_1(E,1)) = k2_measure1(A,B,k8_funct_2(k5_numbers,B,C,k1_nat_1(E,1)),k8_funct_2(k5_numbers,B,D,E)) ) ) ) ) ),
    file(measure2,t5_measure2),
    []).

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(t63_supinf_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( k13_supinf_2(k18_supinf_2(A),0) = k13_supinf_2(A,0)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] : 
                ( m1_subset_1(C,k3_supinf_1)
               => ( C = k13_supinf_2(k18_supinf_2(A),B)
                 => k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,1)) = k2_supinf_2(C,k13_supinf_2(A,k1_nat_1(B,1))) ) ) ) ) ) ),
    file(supinf_2,t63_supinf_2),
    []).

fof(t67_supinf_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v6_supinf_2(A,k5_numbers)
       => ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(B,C)
                   => k13_supinf_2(A,C) = k1_supinf_2 ) )
             => k19_supinf_2(A) = k13_supinf_2(k18_supinf_2(A),B) ) ) ) ) ),
    file(supinf_2,t67_supinf_2),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t6_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) ) ) ) ),
    file(funct_2,t6_funct_2),
    []).

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

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

fof(t8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(k2_relat_1(D),C)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | ( v1_funct_1(D)
            & v1_funct_2(D,A,C)
            & m2_relset_1(D,A,C) ) ) ) ) ),
    file(funct_2,t8_funct_2),
    []).

fof(t8_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    []).

fof(t92_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    []).