% Mizar problem: t35_prob_4,prob_4,1274,31 
fof(t35_prob_4,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m4_prob_1(C,A,B)
             => ! [D] : 
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
                 => ( ! [E] : 
                        ( r2_hidden(E,D)
                      <=> ? [F] : 
                            ( r2_hidden(F,B)
                            & ? [G] : 
                                ( m1_prob_4(G,A,B,C)
                                & E = k2_xboole_0(F,G) ) ) )
                   => m1_prob_1(D,A) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_funct_2,cc1_measure1,cc1_prob_1,cc1_relat_1,cc1_relset_1,cc1_seq_1,cc1_xreal_0,cc2_arytm_3,cc2_measure1,cc2_supinf_1,cc2_xreal_0,cc3_arytm_3,cc3_xreal_0,cc4_xreal_0,cc5_funct_2,cc5_xreal_0,cc6_funct_2,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k4_subset_1,d1_funct_2,d3_tarski,d4_card_3,d4_tarski,d4_xboole_0,d5_funct_1,d5_subset_1,d6_prob_4,d7_prob_4,d8_prob_1,d9_prob_4,dt_k1_funct_1,dt_k1_numbers,dt_k1_prob_1,dt_k1_prob_4,dt_k1_pscomp_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_prob_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_card_3,dt_k3_subset_1,dt_k3_tarski,dt_k3_xboole_0,dt_k4_prob_1,dt_k4_relset_1,dt_k4_subset_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_setfam_1,dt_k6_prob_4,dt_k6_subset_1,dt_k8_funct_2,dt_k8_prob_4,dt_m1_prob_1,dt_m1_prob_4,dt_m1_relset_1,dt_m1_subset_1,dt_m2_prob_1,dt_m2_relset_1,dt_m2_subset_1,dt_m4_prob_1,existence_m1_prob_1,existence_m1_prob_4,existence_m1_relset_1,existence_m1_subset_1,existence_m2_prob_1,existence_m2_relset_1,existence_m2_subset_1,existence_m4_prob_1,fc12_relat_1,fc1_pscomp_1,fc1_relat_1,fc1_seq_1,fc1_subset_1,fc2_pscomp_1,fc2_relat_1,fc3_relat_1,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,involutiveness_k3_subset_1,l1_prob_4,rc1_arytm_3,rc1_funct_2,rc1_measure1,rc1_prob_1,rc1_pscomp_1,rc1_relat_1,rc1_seq_1,rc1_subset_1,rc1_xreal_0,rc2_pscomp_1,rc2_relat_1,rc2_subset_1,rc2_xreal_0,rc3_pscomp_1,rc3_relat_1,rc3_supinf_1,rc3_xreal_0,rc4_pscomp_1,rc4_xreal_0,redefinition_k1_prob_1,redefinition_k1_prob_4,redefinition_k1_pscomp_1,redefinition_k2_prob_1,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_setfam_1,redefinition_k6_subset_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc0_boole,t17_xboole_1,t1_boole,t1_numerals,t1_prob_4,t1_subset,t1_xboole_1,t28_xboole_1,t2_boole,t2_subset,t32_prob_4,t33_prob_4,t34_prob_4,t36_xboole_1,t3_boole,t3_subset,t41_xboole_1,t44_prob_1,t46_prob_1,t4_boole,t4_subset,t51_xboole_1,t5_funct_2,t5_prob_4,t5_subset,t6_boole,t7_boole,t8_boole,t9_prob_4]),
    [file(prob_4,t35_prob_4)]).

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

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_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_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_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ( v2_finsub_1(B)
        & v1_prob_1(B,A) ) ) ),
    file(prob_1,cc1_prob_1),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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

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

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

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

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_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    []).

fof(cc4_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc5_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    []).

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

fof(cc6_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    []).

fof(cc7_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    []).

fof(cc8_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    []).

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

fof(d4_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ),
    file(card_3,d4_card_3),
    []).

fof(d4_tarski,axiom,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    []).

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(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

fof(d5_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,B) = k4_xboole_0(A,B) ) ),
    file(subset_1,d5_subset_1),
    []).

fof(d6_prob_4,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m4_prob_1(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( m1_prob_4(D,A,B,C)
                  <=> ? [E] : 
                        ( r2_hidden(E,B)
                        & r1_tarski(D,E)
                        & k1_funct_1(C,E) = 0 ) ) ) ) ) ) ),
    file(prob_4,d6_prob_4),
    []).

fof(d7_prob_4,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m4_prob_1(C,A,B)
             => ! [D] : 
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
                 => ( D = k6_prob_4(A,B,C)
                  <=> ! [E] : 
                        ( r2_hidden(E,D)
                      <=> ? [F] : 
                            ( r2_hidden(F,B)
                            & ? [G] : 
                                ( m1_prob_4(G,A,B,C)
                                & E = k2_xboole_0(F,G) ) ) ) ) ) ) ) ) ),
    file(prob_4,d7_prob_4),
    []).

fof(d8_prob_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( m1_prob_1(B,A)
      <=> ( ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
             => ( ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => r2_hidden(k1_prob_1(A,C,D),B) )
               => r2_hidden(k4_prob_1(A,C),B) ) )
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ( r2_hidden(C,B)
               => r2_hidden(k3_subset_1(A,C),B) ) ) ) ) ) ),
    file(prob_1,d8_prob_1),
    []).

fof(d9_prob_4,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m4_prob_1(C,A,B)
             => ! [D] : 
                  ( m2_subset_1(D,k1_zfmisc_1(A),k6_prob_4(A,B,C))
                 => ! [E] : 
                      ( ( ~ v1_xboole_0(E)
                        & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) )
                     => ( E = k8_prob_4(A,B,C,D)
                      <=> ! [F] : 
                            ( r2_hidden(F,E)
                          <=> ( r2_hidden(F,B)
                              & r1_tarski(F,D)
                              & m1_prob_4(k4_xboole_0(D,F),A,B,C) ) ) ) ) ) ) ) ) ),
    file(prob_4,d9_prob_4),
    []).

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

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

fof(dt_k1_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_prob_4,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_prob_1(B,A)
        & m2_prob_1(C,A,B)
        & m1_subset_1(D,k5_numbers) )
     => m2_subset_1(k1_prob_4(A,B,C,D),k1_zfmisc_1(A),B) ) ),
    file(prob_4,k1_prob_4),
    []).

fof(dt_k1_pscomp_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k1_pscomp_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(pscomp_1,k1_pscomp_1),
    []).

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

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_prob_1,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(k2_prob_1(A,B),k1_zfmisc_1(A)) ) ),
    file(prob_1,k2_prob_1),
    []).

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

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

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

fof(dt_k3_card_3,axiom,(
    $true ),
    file(card_3,k3_card_3),
    []).

fof(dt_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ),
    file(subset_1,k3_subset_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_prob_1,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(k4_prob_1(A,B),k1_zfmisc_1(A)) ) ),
    file(prob_1,k4_prob_1),
    []).

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

fof(dt_k4_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_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_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_k6_prob_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m4_prob_1(C,A,B) )
     => ( ~ v1_xboole_0(k6_prob_4(A,B,C))
        & m1_subset_1(k6_prob_4(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ),
    file(prob_4,k6_prob_4),
    []).

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_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_k8_prob_4,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m4_prob_1(C,A,B)
        & m1_subset_1(D,k6_prob_4(A,B,C)) )
     => ( ~ v1_xboole_0(k8_prob_4(A,B,C,D))
        & m1_subset_1(k8_prob_4(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ),
    file(prob_4,k8_prob_4),
    []).

fof(dt_m1_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ),
    file(prob_1,m1_prob_1),
    []).

fof(dt_m1_prob_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m4_prob_1(C,A,B) )
     => ! [D] : 
          ( m1_prob_4(D,A,B,C)
         => m1_subset_1(D,k1_zfmisc_1(A)) ) ) ),
    file(prob_4,m1_prob_4),
    []).

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_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m2_prob_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) ) ) ) ),
    file(prob_1,m2_prob_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(dt_m4_prob_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A) )
     => ! [C] : 
          ( m4_prob_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,B,k1_numbers)
            & m2_relset_1(C,B,k1_numbers) ) ) ) ),
    file(prob_1,m4_prob_1),
    []).

fof(existence_m1_prob_1,axiom,(
    ! [A] : 
    ? [B] : m1_prob_1(B,A) ),
    file(prob_1,m1_prob_1),
    []).

fof(existence_m1_prob_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m4_prob_1(C,A,B) )
     => ? [D] : m1_prob_4(D,A,B,C) ) ),
    file(prob_4,m1_prob_4),
    []).

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_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ? [C] : m2_prob_1(C,A,B) ) ),
    file(prob_1,m2_prob_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(existence_m4_prob_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A) )
     => ? [C] : m4_prob_1(C,A,B) ) ),
    file(prob_1,m4_prob_1),
    []).

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

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

fof(fc1_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_1),
    []).

fof(fc1_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_xcmplx_0(k1_funct_1(A,B))
        & v1_xreal_0(k1_funct_1(A,B)) ) ) ),
    file(seq_1,fc1_seq_1),
    []).

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

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

fof(fc2_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

fof(fc3_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    []).

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

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

fof(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc6_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(fc8_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    []).

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

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(involutiveness_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,k3_subset_1(A,B)) = B ) ),
    file(subset_1,k3_subset_1),
    []).

fof(l1_prob_4,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(C,B)
     => k4_xboole_0(A,C) = k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,k4_xboole_0(B,C))) ) ),
    file(prob_4,l1_prob_4),
    []).

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_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_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_prob_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v2_finsub_1(B)
      & v1_prob_1(B,A) ) ),
    file(prob_1,rc1_prob_1),
    []).

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

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

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

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

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

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

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

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

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

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

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

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

fof(rc3_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    []).

fof(rc4_pscomp_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & ~ v1_setfam_1(A) ) ),
    file(pscomp_1,rc4_pscomp_1),
    []).

fof(rc4_xreal_0,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    []).

fof(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_k1_prob_4,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_prob_1(B,A)
        & m2_prob_1(C,A,B)
        & m1_subset_1(D,k5_numbers) )
     => k1_prob_4(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(prob_4,k1_prob_4),
    []).

fof(redefinition_k1_pscomp_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k1_pscomp_1(A,B,C) = k2_relat_1(C) ) ),
    file(pscomp_1,k1_pscomp_1),
    []).

fof(redefinition_k2_prob_1,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)) )
     => k2_prob_1(A,B) = k3_card_3(B) ) ),
    file(prob_1,k2_prob_1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_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_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_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_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_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

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

fof(t17_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    []).

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_prob_4,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m2_prob_1(C,A,B)
         => r1_tarski(k1_pscomp_1(k5_numbers,k1_zfmisc_1(A),C),B) ) ) ),
    file(prob_4,t1_prob_4),
    []).

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

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(t32_prob_4,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m4_prob_1(C,A,B)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k6_prob_4(A,B,C))
                    & m2_relset_1(D,k5_numbers,k6_prob_4(A,B,C)) )
                 => ? [E] : 
                      ( m2_prob_1(E,A,B)
                      & ! [F] : 
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => r2_hidden(k1_prob_4(A,B,E,F),k8_prob_4(A,B,C,k8_funct_2(k5_numbers,k6_prob_4(A,B,C),D,F))) ) ) ) ) ) ) ),
    file(prob_4,t32_prob_4),
    []).

fof(t33_prob_4,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m4_prob_1(C,A,B)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k6_prob_4(A,B,C))
                    & m2_relset_1(D,k5_numbers,k6_prob_4(A,B,C)) )
                 => ! [E] : 
                      ( m2_prob_1(E,A,B)
                     => ? [F] : 
                          ( v1_funct_1(F)
                          & v1_funct_2(F,k5_numbers,k1_zfmisc_1(A))
                          & m2_relset_1(F,k5_numbers,k1_zfmisc_1(A))
                          & ! [G] : 
                              ( m2_subset_1(G,k1_numbers,k5_numbers)
                             => k1_prob_1(A,F,G) = k4_xboole_0(k8_funct_2(k5_numbers,k6_prob_4(A,B,C),D,G),k1_prob_4(A,B,E,G)) ) ) ) ) ) ) ) ),
    file(prob_4,t33_prob_4),
    []).

fof(t34_prob_4,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m4_prob_1(C,A,B)
             => ! [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)) )
                 => ~ ( ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => m1_prob_4(k1_prob_1(A,D,E),A,B,C) )
                      & ! [E] : 
                          ( m2_prob_1(E,A,B)
                         => ~ ! [F] : 
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ( r1_tarski(k1_prob_1(A,D,F),k1_prob_4(A,B,E,F))
                                  & k8_funct_2(B,k1_numbers,C,k1_prob_4(A,B,E,F)) = 0 ) ) ) ) ) ) ) ) ),
    file(prob_4,t34_prob_4),
    []).

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

fof(t41_xboole_1,axiom,(
    ! [A,B,C] : k4_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t41_xboole_1),
    []).

fof(t44_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( ( r2_hidden(C,B)
                  & r2_hidden(D,B) )
               => r2_hidden(k6_subset_1(A,C,D),B) ) ) ) ) ),
    file(prob_1,t44_prob_1),
    []).

fof(t46_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m2_prob_1(C,A,B)
         => r2_hidden(k2_prob_1(A,C),B) ) ) ),
    file(prob_1,t46_prob_1),
    []).

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

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(t51_xboole_1,axiom,(
    ! [A,B] : k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A ),
    file(xboole_1,t51_xboole_1),
    []).

fof(t5_funct_2,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( k1_relat_1(C) = A
          & ! [D] : 
              ( r2_hidden(D,A)
             => r2_hidden(k1_funct_1(C,D),B) ) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & m2_relset_1(C,A,B) ) ) ) ),
    file(funct_2,t5_funct_2),
    []).

fof(t5_prob_4,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( m1_prob_1(B,A)
      <=> ( r1_tarski(B,k1_zfmisc_1(A))
          & ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
             => ( ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => r2_hidden(k1_prob_1(A,C,D),B) )
               => r2_hidden(k2_prob_1(A,C),B) ) )
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ( r2_hidden(C,B)
               => r2_hidden(k3_subset_1(A,C),B) ) ) ) ) ) ),
    file(prob_4,t5_prob_4),
    []).

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

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

fof(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(t9_prob_4,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m2_prob_1(C,A,B)
             => ! [D] : 
                  ( m4_prob_1(D,A,B)
                 => ( ! [E] : 
                        ( r2_hidden(E,k1_pscomp_1(k5_numbers,k1_zfmisc_1(A),C))
                       => k1_funct_1(D,E) = 0 )
                  <=> k1_funct_1(D,k5_setfam_1(A,k1_pscomp_1(k5_numbers,k1_zfmisc_1(A),C))) = 0 ) ) ) ) ) ),
    file(prob_4,t9_prob_4),
    []).