% Mizar problem: t21_measure4,measure4,708,39 
fof(t21_measure4,conjecture,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ( ~ v1_xboole_0(k3_measure4(A,B))
        & v1_prob_1(k3_measure4(A,B),A)
        & v1_measure1(k3_measure4(A,B),A)
        & m1_subset_1(k3_measure4(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_1,cc1_measure1,cc1_nat_1,cc1_relset_1,cc1_supinf_1,cc2_funct_1,cc2_measure1,cc2_nat_1,cc2_supinf_1,cc3_measure1,cc3_nat_1,cc4_measure1,commutativity_k12_supinf_1,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_real_1,commutativity_k3_xboole_0,commutativity_k4_subset_1,commutativity_k5_subset_1,connectedness_r1_supinf_1,connectedness_r1_xreal_0,d14_supinf_2,d1_supinf_2,d2_measure4,d2_supinf_2,d2_tarski,d2_xboole_0,d3_measure1,d3_measure4,d3_tarski,d3_xboole_0,d4_measure1,d4_xboole_0,d6_supinf_1,d7_xboole_0,d9_measure1,dt_k12_supinf_1,dt_k13_supinf_2,dt_k18_supinf_2,dt_k19_supinf_2,dt_k1_funct_1,dt_k1_measure1,dt_k1_measure3,dt_k1_measure4,dt_k1_nat_1,dt_k1_numbers,dt_k1_supinf_1,dt_k1_supinf_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_measure1,dt_k2_measure4,dt_k2_relat_1,dt_k2_supinf_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_measure4,dt_k3_real_1,dt_k3_supinf_1,dt_k3_tarski,dt_k3_xboole_0,dt_k4_measure1,dt_k4_subset_1,dt_k4_supinf_1,dt_k4_supinf_2,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_relat_1,dt_k5_setfam_1,dt_k5_subset_1,dt_k5_supinf_1,dt_k6_subset_1,dt_k6_supinf_1,dt_k6_xcmplx_0,dt_k7_funct_2,dt_k8_funct_2,dt_m1_measure2,dt_m1_measure4,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_measure2,existence_m1_measure4,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc1_funct_1,fc1_nat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_supinf_1,fc1_xboole_0,fc2_xboole_0,fc3_nat_1,fc3_subset_1,fc3_xboole_0,fc4_nat_1,fc4_subset_1,idempotence_k2_measure1,idempotence_k2_xboole_0,idempotence_k3_measure1,idempotence_k3_xboole_0,idempotence_k4_subset_1,idempotence_k5_subset_1,rc1_funct_1,rc1_measure1,rc1_nat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_measure1,rc2_nat_1,rc2_subset_1,rc2_xboole_0,rc3_funct_1,rc3_measure1,rc3_nat_1,rc3_supinf_1,redefinition_k12_supinf_1,redefinition_k13_supinf_2,redefinition_k1_measure1,redefinition_k1_measure3,redefinition_k1_measure4,redefinition_k1_nat_1,redefinition_k2_measure1,redefinition_k2_measure4,redefinition_k3_measure1,redefinition_k3_real_1,redefinition_k4_measure1,redefinition_k4_subset_1,redefinition_k4_supinf_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_setfam_1,redefinition_k5_subset_1,redefinition_k5_supinf_1,redefinition_k6_subset_1,redefinition_k6_supinf_1,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_funct_2__e4_21_1_1_8__measure4,s1_nat_1__e10_21_1_1__measure4,s1_nat_1__e2_21_1_1_4_2__measure4,s1_nat_1__e31_21_1_1__measure4,s1_nat_1__e35_21_1_1__measure4,s1_nat_1__e4_21_1_1_8_4__measure4,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_xboole_0,t13_xboole_1,t14_measure4,t15_supinf_2,t16_measure4,t17_measure4,t17_xboole_1,t18_supinf_2,t19_measure4,t19_supinf_2,t1_arithm,t1_boole,t1_measure4,t1_numerals,t1_real,t1_subset,t1_xboole_1,t20_measure4,t21_funct_2,t26_xboole_1,t28_xboole_1,t29_supinf_1,t2_boole,t2_measure4,t2_real,t2_subset,t34_xboole_1,t36_xboole_1,t3_boole,t3_measure3,t3_real,t3_subset,t4_arithm,t4_boole,t4_measure4,t4_real,t4_subset,t4_xboole_1,t54_measure1,t58_supinf_2,t59_supinf_2,t5_measure2,t5_measure4,t5_real,t5_subset,t5_supinf_2,t63_supinf_2,t63_xboole_1,t67_supinf_2,t6_boole,t6_funct_2,t6_measure4,t6_real,t79_xboole_1,t7_boole,t7_real,t7_xboole_1,t8_boole,t8_real,t8_xboole_1,t92_zfmisc_1,t9_measure2,t9_xboole_1]),
    [file(measure4,t21_measure4)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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

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_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

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

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_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_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc2_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_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_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(cc4_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(commutativity_k12_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k12_supinf_1(A,B) = k12_supinf_1(B,A) ) ),
    file(supinf_1,k12_supinf_1),
    []).

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_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k3_real_1(B,A) ) ),
    file(real_1,k3_real_1),
    []).

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(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(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(d14_supinf_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_card_4(B)
          <=> ~ ( ~ v1_xboole_0(B)
                & ! [C] : 
                    ( ( v1_funct_1(C)
                      & v1_funct_2(C,k5_numbers,A)
                      & m2_relset_1(C,k5_numbers,A) )
                   => B != k2_relat_1(C) ) ) ) ) ) ),
    file(supinf_2,d14_supinf_2),
    []).

fof(d1_supinf_2,axiom,(
    k1_supinf_2 = 0 ),
    file(supinf_2,d1_supinf_2),
    []).

fof(d2_measure4,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k3_supinf_1)
        & m2_relset_1(B,k1_zfmisc_1(A),k3_supinf_1) )
     => ( m1_measure4(B,A)
      <=> ( v6_supinf_2(B,k1_zfmisc_1(A))
          & k1_funct_1(B,k1_xboole_0) = k1_supinf_2
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( r1_tarski(C,D)
                   => ( r1_supinf_1(k1_measure1(k1_zfmisc_1(A),B,C),k1_measure1(k1_zfmisc_1(A),B,D))
                      & ! [E] : 
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k5_numbers,k1_zfmisc_1(A))
                            & m2_relset_1(E,k5_numbers,k1_zfmisc_1(A)) )
                         => r1_supinf_1(k1_measure1(k1_zfmisc_1(A),B,k5_setfam_1(A,k1_measure4(A,E))),k19_supinf_2(k2_measure4(k5_numbers,k1_zfmisc_1(A),k3_supinf_1,E,B))) ) ) ) ) ) ) ) ) ),
    file(measure4,d2_measure4),
    []).

fof(d2_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( ( r2_hidden(A,k6_supinf_1)
                    & r2_hidden(B,k6_supinf_1) )
                 => ( C = k2_supinf_2(A,B)
                  <=> ? [D] : 
                        ( m1_subset_1(D,k1_numbers)
                        & ? [E] : 
                            ( m1_subset_1(E,k1_numbers)
                            & A = D
                            & B = E
                            & C = k3_real_1(D,E) ) ) ) )
                & ( ( ( A = k4_supinf_1
                      & B != k5_supinf_1 )
                    | ( B = k4_supinf_1
                      & A != k5_supinf_1 ) )
                 => ( C = k2_supinf_2(A,B)
                  <=> C = k4_supinf_1 ) )
                & ( ( ( A = k5_supinf_1
                      & B != k4_supinf_1 )
                    | ( B = k5_supinf_1
                      & A != k4_supinf_1 ) )
                 => ( C = k2_supinf_2(A,B)
                  <=> C = k5_supinf_1 ) )
                & ~ ( ~ ( r2_hidden(A,k6_supinf_1)
                        & r2_hidden(B,k6_supinf_1) )
                    & ~ ( A = k4_supinf_1
                        & B != k5_supinf_1 )
                    & ~ ( B = k4_supinf_1
                        & A != k5_supinf_1 )
                    & ~ ( A = k5_supinf_1
                        & B != k4_supinf_1 )
                    & ~ ( B = k5_supinf_1
                        & A != k4_supinf_1 )
                    & ~ ( C = k2_supinf_2(A,B)
                      <=> C = k1_supinf_2 ) ) ) ) ) ) ),
    file(supinf_2,d2_supinf_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(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d3_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_prob_1(B,A)
      <=> ! [C] : 
            ( r2_hidden(C,B)
           => r2_hidden(k4_xboole_0(A,C),B) ) ) ) ),
    file(measure1,d3_measure1),
    []).

fof(d3_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ! [C] : 
          ( ( ~ v1_xboole_0(C)
            & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
         => ( C = k3_measure4(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(A))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(A))
                         => ( ( r1_tarski(E,D)
                              & r1_tarski(F,k4_xboole_0(A,D)) )
                           => r1_supinf_1(k2_supinf_2(k1_measure1(k1_zfmisc_1(A),B,E),k1_measure1(k1_zfmisc_1(A),B,F)),k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,E,F))) ) ) ) ) ) ) ) ) ),
    file(measure4,d3_measure4),
    []).

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

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_measure1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k3_supinf_1)
            & m2_relset_1(B,A,k3_supinf_1) )
         => ( v6_supinf_2(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => r1_supinf_1(k1_supinf_2,k1_measure1(A,B,C)) ) ) ) ) ),
    file(measure1,d4_measure1),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d6_supinf_1,axiom,(
    k3_supinf_1 = k2_xboole_0(k1_numbers,k2_tarski(k2_supinf_1,k1_supinf_1)) ),
    file(supinf_1,d6_supinf_1),
    []).

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(d9_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_measure1(B,A)
      <=> ! [C] : 
            ( ( ~ v1_xboole_0(C)
              & v1_card_4(C)
              & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
           => ( r1_tarski(C,B)
             => r2_hidden(k5_setfam_1(A,C),B) ) ) ) ) ),
    file(measure1,d9_measure1),
    []).

fof(dt_k12_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k12_supinf_1(A,B),k1_zfmisc_1(k3_supinf_1)) ) ),
    file(supinf_1,k12_supinf_1),
    []).

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_measure4,axiom,(
    ! [A,B] : 
      ( ( 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(k1_measure4(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(measure4,k1_measure4),
    []).

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_supinf_1,axiom,(
    $true ),
    file(supinf_1,k1_supinf_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_measure4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & 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(k2_measure4(A,B,C,D,E))
        & v1_funct_2(k2_measure4(A,B,C,D,E),A,C)
        & m2_relset_1(k2_measure4(A,B,C,D,E),A,C) ) ) ),
    file(measure4,k2_measure4),
    []).

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

fof(dt_k2_supinf_1,axiom,(
    $true ),
    file(supinf_1,k2_supinf_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_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ( ~ v1_xboole_0(k3_measure4(A,B))
        & m1_subset_1(k3_measure4(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ),
    file(measure4,k3_measure4),
    []).

fof(dt_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ),
    file(real_1,k3_real_1),
    []).

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_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(k4_measure1(A,B,C,D),k1_zfmisc_1(A),B) ) ),
    file(measure1,k4_measure1),
    []).

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_k4_supinf_1,axiom,(
    m1_subset_1(k4_supinf_1,k3_supinf_1) ),
    file(supinf_1,k4_supinf_1),
    []).

fof(dt_k4_supinf_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k4_supinf_2(A,B),k3_supinf_1) ) ),
    file(supinf_2,k4_supinf_2),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

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_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ),
    file(real_1,k5_real_1),
    []).

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_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    []).

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_k5_supinf_1,axiom,(
    m1_subset_1(k5_supinf_1,k3_supinf_1) ),
    file(supinf_1,k5_supinf_1),
    []).

fof(dt_k6_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(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(dt_k6_supinf_1,axiom,
    ( ~ v1_xboole_0(k6_supinf_1)
    & m1_subset_1(k6_supinf_1,k1_zfmisc_1(k3_supinf_1)) ),
    file(supinf_1,k6_supinf_1),
    []).

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

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_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_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k3_supinf_1)
        & m2_relset_1(B,k1_zfmisc_1(A),k3_supinf_1) ) ) ),
    file(measure4,m1_measure4),
    []).

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_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_measure4,axiom,(
    ! [A] : 
    ? [B] : m1_measure4(B,A) ),
    file(measure4,m1_measure4),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

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

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    []).

fof(fc1_numbers,axiom,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    []).

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(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(fc4_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_1),
    []).

fof(fc4_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(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(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(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

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_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

fof(rc1_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_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_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_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_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

fof(rc2_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_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_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_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_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

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

fof(redefinition_k12_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k12_supinf_1(A,B) = k2_tarski(A,B) ) ),
    file(supinf_1,k12_supinf_1),
    []).

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_measure4,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => k1_measure4(A,B) = k2_relat_1(B) ) ),
    file(measure4,k1_measure4),
    []).

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

fof(redefinition_k2_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_measure4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & 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) )
     => k2_measure4(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(measure4,k2_measure4),
    []).

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_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(real_1,k3_real_1),
    []).

fof(redefinition_k4_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) )
     => k4_measure1(A,B,C,D) = k4_xboole_0(C,D) ) ),
    file(measure1,k4_measure1),
    []).

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_k4_supinf_1,axiom,(
    k4_supinf_1 = k1_supinf_1 ),
    file(supinf_1,k4_supinf_1),
    []).

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

fof(redefinition_k5_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ),
    file(real_1,k5_real_1),
    []).

fof(redefinition_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    []).

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_k5_supinf_1,axiom,(
    k5_supinf_1 = k2_supinf_1 ),
    file(supinf_1,k5_supinf_1),
    []).

fof(redefinition_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(redefinition_k6_supinf_1,axiom,(
    k6_supinf_1 = k1_numbers ),
    file(supinf_1,k6_supinf_1),
    []).

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_funct_2__e4_21_1_1_8__measure4,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_measure4(B,A)
        & m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,k1_zfmisc_1(A)) )
     => ( ! [E] : ~ ( r2_hidden(E,k5_numbers)
            & ! [F] : ~ ( r2_hidden(F,k3_supinf_1)
                & ( E = 0
                 => F = k4_supinf_2(k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,D,C)),k1_measure1(k1_zfmisc_1(A),B,D)) )
                & ( E != 0
                 => F = k1_supinf_2 ) ) )
       => ? [E] : 
            ( v1_funct_1(E)
            & v1_funct_2(E,k5_numbers,k3_supinf_1)
            & m2_relset_1(E,k5_numbers,k3_supinf_1)
            & ! [F] : 
                ( r2_hidden(F,k5_numbers)
               => ( ( F = 0
                   => k1_funct_1(E,F) = k4_supinf_2(k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,D,C)),k1_measure1(k1_zfmisc_1(A),B,D)) )
                  & ( F != 0
                   => k1_funct_1(E,F) = k1_supinf_2 ) ) ) ) ) ) ),
    file(measure4,s1_funct_2__e4_21_1_1_8__measure4),
    []).

fof(s1_nat_1__e10_21_1_1__measure4,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_measure4(B,A)
        & ~ v1_xboole_0(C)
        & v1_prob_1(C,A)
        & v1_measure1(C,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
        & v1_funct_1(D)
        & v1_funct_2(D,k5_numbers,C)
        & m2_relset_1(D,k5_numbers,C) )
     => ( ( r2_hidden(k8_funct_2(k5_numbers,C,D,0),k3_measure4(A,B))
          & ! [E] : 
              ( m2_subset_1(E,k1_numbers,k5_numbers)
             => ( r2_hidden(k8_funct_2(k5_numbers,C,D,E),k3_measure4(A,B))
               => r2_hidden(k8_funct_2(k5_numbers,C,D,k1_nat_1(E,1)),k3_measure4(A,B)) ) ) )
       => ! [E] : 
            ( m2_subset_1(E,k1_numbers,k5_numbers)
           => r2_hidden(k8_funct_2(k5_numbers,C,D,E),k3_measure4(A,B)) ) ) ) ),
    file(measure4,s1_nat_1__e10_21_1_1__measure4),
    []).

fof(s1_nat_1__e2_21_1_1_4_2__measure4,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
     => ( ( r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(A),B,0),k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,0))
          & ! [D] : 
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(A),B,D),k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D))
               => r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(A),B,k1_nat_1(D,1)),k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,k1_nat_1(D,1))) ) ) )
       => ! [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
           => r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(A),B,D),k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D)) ) ) ) ),
    file(measure4,s1_nat_1__e2_21_1_1_4_2__measure4),
    []).

fof(s1_nat_1__e31_21_1_1__measure4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( m1_measure4(B,A)
        & m1_subset_1(C,k1_zfmisc_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(D,k5_numbers,k1_zfmisc_1(A))
        & v1_funct_1(E)
        & v1_funct_2(E,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(E,k5_numbers,k1_zfmisc_1(A)) )
     => ( ( k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,C,k8_funct_2(k5_numbers,k1_zfmisc_1(A),E,0))) = k2_supinf_2(k1_measure1(k1_zfmisc_1(A),B,C),k1_measure1(k5_numbers,k18_supinf_2(k2_measure4(k5_numbers,k1_zfmisc_1(A),k3_supinf_1,D,B)),0))
          & ! [F] : 
              ( m2_subset_1(F,k1_numbers,k5_numbers)
             => ( k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,C,k8_funct_2(k5_numbers,k1_zfmisc_1(A),E,F))) = k2_supinf_2(k1_measure1(k1_zfmisc_1(A),B,C),k1_measure1(k5_numbers,k18_supinf_2(k2_measure4(k5_numbers,k1_zfmisc_1(A),k3_supinf_1,D,B)),F))
               => k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,C,k8_funct_2(k5_numbers,k1_zfmisc_1(A),E,k1_nat_1(F,1)))) = k2_supinf_2(k1_measure1(k1_zfmisc_1(A),B,C),k1_measure1(k5_numbers,k18_supinf_2(k2_measure4(k5_numbers,k1_zfmisc_1(A),k3_supinf_1,D,B)),k1_nat_1(F,1))) ) ) )
       => ! [F] : 
            ( m2_subset_1(F,k1_numbers,k5_numbers)
           => k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,C,k8_funct_2(k5_numbers,k1_zfmisc_1(A),E,F))) = k2_supinf_2(k1_measure1(k1_zfmisc_1(A),B,C),k1_measure1(k5_numbers,k18_supinf_2(k2_measure4(k5_numbers,k1_zfmisc_1(A),k3_supinf_1,D,B)),F)) ) ) ) ),
    file(measure4,s1_nat_1__e31_21_1_1__measure4),
    []).

fof(s1_nat_1__e35_21_1_1__measure4,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
     => ( ( r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,0),B)
          & ! [D] : 
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D),B)
               => r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,k1_nat_1(D,1)),B) ) ) )
       => ! [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
           => r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D),B) ) ) ) ),
    file(measure4,s1_nat_1__e35_21_1_1__measure4),
    []).

fof(s1_nat_1__e4_21_1_1_8_4__measure4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( m1_measure4(B,A)
        & m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,k1_zfmisc_1(A))
        & v1_funct_1(E)
        & v1_funct_2(E,k5_numbers,k3_supinf_1)
        & m2_relset_1(E,k5_numbers,k3_supinf_1) )
     => ( ( k1_measure1(k5_numbers,k18_supinf_2(E),0) = k4_supinf_2(k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,D,C)),k1_measure1(k1_zfmisc_1(A),B,D))
          & ! [F] : 
              ( m2_subset_1(F,k1_numbers,k5_numbers)
             => ( k1_measure1(k5_numbers,k18_supinf_2(E),F) = k4_supinf_2(k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,D,C)),k1_measure1(k1_zfmisc_1(A),B,D))
               => k1_measure1(k5_numbers,k18_supinf_2(E),k1_nat_1(F,1)) = k4_supinf_2(k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,D,C)),k1_measure1(k1_zfmisc_1(A),B,D)) ) ) )
       => ! [F] : 
            ( m2_subset_1(F,k1_numbers,k5_numbers)
           => k1_measure1(k5_numbers,k18_supinf_2(E),F) = k4_supinf_2(k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,D,C)),k1_measure1(k1_zfmisc_1(A),B,D)) ) ) ) ),
    file(measure4,s1_nat_1__e4_21_1_1_8_4__measure4),
    []).

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(t13_xboole_1,axiom,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    []).

fof(t14_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r2_hidden(C,k3_measure4(A,B))
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ! [E] : 
                    ( m1_subset_1(E,k1_zfmisc_1(A))
                   => ( ( r1_tarski(D,C)
                        & r1_tarski(E,k4_xboole_0(A,C)) )
                     => k2_supinf_2(k1_measure1(k1_zfmisc_1(A),B,D),k1_measure1(k1_zfmisc_1(A),B,E)) = k1_measure1(k1_zfmisc_1(A),B,k4_subset_1(A,D,E)) ) ) ) ) ) ) ),
    file(measure4,t14_measure4),
    []).

fof(t15_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ! [D] : 
                  ( m1_subset_1(D,k3_supinf_1)
                 => ~ ( ~ ( A = k4_supinf_1
                          & D = k4_supinf_1 )
                      & ~ ( A = k5_supinf_1
                          & D = k5_supinf_1 )
                      & ~ ( B = k4_supinf_1
                          & C = k4_supinf_1 )
                      & ~ ( B = k5_supinf_1
                          & C = k5_supinf_1 )
                      & r1_supinf_1(A,B)
                      & r1_supinf_1(C,D)
                      & ~ r1_supinf_1(k4_supinf_2(A,D),k4_supinf_2(B,C)) ) ) ) ) ) ),
    file(supinf_2,t15_supinf_2),
    []).

fof(t16_measure4,axiom,(
    ! [A,B,C] : 
      ( m1_measure4(C,B)
     => ( r2_hidden(A,k3_measure4(B,C))
       => r2_hidden(k4_xboole_0(B,A),k3_measure4(B,C)) ) ) ),
    file(measure4,t16_measure4),
    []).

fof(t17_measure4,axiom,(
    ! [A,B,C,D] : 
      ( m1_measure4(D,A)
     => ( ( r2_hidden(B,k3_measure4(A,D))
          & r2_hidden(C,k3_measure4(A,D)) )
       => r2_hidden(k2_xboole_0(B,C),k3_measure4(A,D)) ) ) ),
    file(measure4,t17_measure4),
    []).

fof(t17_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_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(t19_measure4,axiom,(
    ! [A,B,C,D] : 
      ( m1_measure4(D,A)
     => ( ( r2_hidden(B,k3_measure4(A,D))
          & r2_hidden(C,k3_measure4(A,D)) )
       => r2_hidden(k4_xboole_0(B,C),k3_measure4(A,D)) ) ) ),
    file(measure4,t19_measure4),
    []).

fof(t19_supinf_2,axiom,
    ( ~ r1_supinf_1(k1_supinf_2,k5_supinf_1)
    & ~ r1_supinf_1(k4_supinf_1,k1_supinf_2) ),
    file(supinf_2,t19_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_measure4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( r1_supinf_1(k1_supinf_2,A)
                  & r1_supinf_1(k1_supinf_2,B)
                  & r1_supinf_1(k1_supinf_2,C) )
               => k2_supinf_2(k2_supinf_2(A,B),C) = k2_supinf_2(A,k2_supinf_2(B,C)) ) ) ) ) ),
    file(measure4,t1_measure4),
    []).

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

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

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

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t20_measure4,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] : 
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ? [E] : 
                  ( v1_funct_1(E)
                  & v1_funct_2(E,k5_numbers,B)
                  & m2_relset_1(E,k5_numbers,B)
                  & ! [F] : 
                      ( m2_subset_1(F,k1_numbers,k5_numbers)
                     => k8_funct_2(k5_numbers,B,E,F) = k3_measure1(A,B,D,k8_funct_2(k5_numbers,B,C,F)) ) ) ) ) ) ),
    file(measure4,t20_measure4),
    []).

fof(t21_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    []).

fof(t26_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) ),
    file(xboole_1,t26_xboole_1),
    []).

fof(t28_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    []).

fof(t29_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( r1_supinf_1(A,B)
                  & r1_supinf_1(B,C) )
               => r1_supinf_1(A,C) ) ) ) ) ),
    file(supinf_1,t29_supinf_1),
    []).

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

fof(t2_measure4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ~ ( A != k5_supinf_1
                  & A != k4_supinf_1
                  & ~ ( r1_supinf_1(k2_supinf_2(B,A),C)
                    <=> r1_supinf_1(B,k4_supinf_2(C,A)) ) ) ) ) ) ),
    file(measure4,t2_measure4),
    []).

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

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

fof(t34_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)) ) ),
    file(xboole_1,t34_xboole_1),
    []).

fof(t36_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

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

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

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

fof(t4_measure4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & 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) )
             => ! [E] : 
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => ( ! [F] : 
                        ( m2_subset_1(F,k1_numbers,k5_numbers)
                       => k8_funct_2(k5_numbers,B,D,F) = k3_xboole_0(E,k8_funct_2(k5_numbers,B,C,F)) )
                   => k3_tarski(k2_relat_1(D)) = k3_xboole_0(E,k3_tarski(k2_relat_1(C))) ) ) ) ) ) ),
    file(measure4,t4_measure4),
    []).

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

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

fof(t4_xboole_1,axiom,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    []).

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(t58_supinf_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k3_supinf_1)
            & m2_relset_1(B,A,k3_supinf_1) )
         => ( v6_supinf_2(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => r1_supinf_1(k1_supinf_2,k8_funct_2(A,k3_supinf_1,B,C)) ) ) ) ) ),
    file(supinf_2,t58_supinf_2),
    []).

fof(t59_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) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( v6_supinf_2(A,k5_numbers)
           => ( r1_supinf_1(k13_supinf_2(k18_supinf_2(A),B),k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,1)))
              & r1_supinf_1(k1_supinf_2,k13_supinf_2(k18_supinf_2(A),B)) ) ) ) ) ),
    file(supinf_2,t59_supinf_2),
    []).

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_measure4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & 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_xboole_0(k8_funct_2(k5_numbers,B,C,k1_nat_1(E,1)),k8_funct_2(k5_numbers,B,D,E)) ) )
               => ! [E] : 
                    ( ( v1_funct_1(E)
                      & v1_funct_2(E,k5_numbers,B)
                      & m2_relset_1(E,k5_numbers,B) )
                   => ( ( k8_funct_2(k5_numbers,B,E,0) = k8_funct_2(k5_numbers,B,C,0)
                        & ! [F] : 
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => k8_funct_2(k5_numbers,B,E,k1_nat_1(F,1)) = k4_xboole_0(k8_funct_2(k5_numbers,B,C,k1_nat_1(F,1)),k8_funct_2(k5_numbers,B,D,F)) ) )
                     => k3_tarski(k2_relat_1(C)) = k3_tarski(k2_relat_1(E)) ) ) ) ) ) ) ),
    file(measure4,t5_measure4),
    []).

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

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t5_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( A = C
                      & B = D )
                   => k4_supinf_2(A,B) = k5_real_1(C,D) ) ) ) ) ) ),
    file(supinf_2,t5_supinf_2),
    []).

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(t63_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_xboole_0(B,C) )
     => r1_xboole_0(A,C) ) ),
    file(xboole_1,t63_xboole_1),
    []).

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(t6_measure4,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_prob_1(k1_zfmisc_1(A),A)
      & v1_measure1(k1_zfmisc_1(A),A)
      & m1_subset_1(k1_zfmisc_1(A),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(measure4,t6_measure4),
    []).

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

fof(t79_xboole_1,axiom,(
    ! [A,B] : r1_xboole_0(k4_xboole_0(A,B),B) ),
    file(xboole_1,t79_xboole_1),
    []).

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

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

fof(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

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

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

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),
    []).

fof(t9_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) )
             => ? [E] : 
                  ( v1_funct_1(E)
                  & v1_funct_2(E,k5_numbers,B)
                  & m2_relset_1(E,k5_numbers,B)
                  & k8_funct_2(k5_numbers,B,E,0) = k8_funct_2(k5_numbers,B,C,0)
                  & ! [F] : 
                      ( m2_subset_1(F,k1_numbers,k5_numbers)
                     => k8_funct_2(k5_numbers,B,E,k1_nat_1(F,1)) = k4_measure1(A,B,k8_funct_2(k5_numbers,B,C,k1_nat_1(F,1)),k8_funct_2(k5_numbers,B,D,F)) ) ) ) ) ) ),
    file(measure2,t9_measure2),
    []).

fof(t9_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)) ) ),
    file(xboole_1,t9_xboole_1),
    []).