% Mizar problem: t33_qmax_1,qmax_1,609,65 
fof(t33_qmax_1,conjecture,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A)))
             => ( ( r2_hidden(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
                  & r2_hidden(C,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
               => ! [D] : 
                    ( m1_subset_1(D,k5_qmax_1(A))
                   => ! [E] : 
                        ( m1_subset_1(E,k5_qmax_1(A))
                       => ( ( r2_hidden(D,B)
                            & r2_hidden(E,B)
                            & r2_hidden(k8_qmax_1(A,D),C) )
                         => r2_hidden(k8_qmax_1(A,E),C) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_eqrel_1,cc1_membered,cc1_partfun1,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_eqrel_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,d12_qmax_1,d2_qmax_1,d3_qmax_1,d4_qmax_1,d5_eqrel_1,d8_qmax_1,d9_qmax_1,dt_k10_prob_1,dt_k14_prob_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_numbers,dt_k1_qmax_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_mcart_1,dt_k2_qmax_1,dt_k2_zfmisc_1,dt_k3_qmax_1,dt_k3_subset_1,dt_k4_qmax_1,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_k5_qmax_1,dt_k6_eqrel_1,dt_k6_qmax_1,dt_k6_xcmplx_0,dt_k7_eqrel_1,dt_k7_qmax_1,dt_k8_eqrel_1,dt_k8_qmax_1,dt_k9_qmax_1,dt_l1_qmax_1,dt_m1_eqrel_1,dt_m1_prob_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_prob_1,dt_m4_prob_1,dt_u1_qmax_1,dt_u2_qmax_1,dt_u3_qmax_1,existence_l1_qmax_1,existence_m1_eqrel_1,existence_m1_prob_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m3_prob_1,existence_m4_prob_1,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_ordinal2,fc1_qmax_1,fc1_subset_1,fc20_xreal_0,fc2_membered,fc2_qmax_1,fc3_eqrel_1,fc3_qmax_1,fc4_eqrel_1,fc4_qmax_1,fc4_subset_1,fc5_membered,fc5_xreal_0,fc6_membered,involutiveness_k3_subset_1,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_partfun1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,redefinition_k10_prob_1,redefinition_k1_domain_1,redefinition_k5_numbers,redefinition_k6_qmax_1,redefinition_k7_qmax_1,redefinition_k8_eqrel_1,redefinition_m2_relset_1,reflexivity_r1_tarski,spc1_boole,spc1_numerals,t12_eqrel_1,t16_qmax_1,t1_subset,t20_qmax_1,t24_qmax_1,t25_qmax_1,t26_qmax_1,t27_eqrel_1,t2_subset,t30_eqrel_1,t3_subset,t4_subset,t50_prob_1,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(qmax_1,t33_qmax_1)]).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_eqrel_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(eqrel_1,cc1_eqrel_1),
    []).

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

fof(cc1_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    []).

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_xreal_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    []).

fof(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => v1_setfam_1(B) ) ),
    file(eqrel_1,cc2_eqrel_1),
    []).

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

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

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

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

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

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

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

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

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

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

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

fof(d12_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,k5_qmax_1(A),k5_qmax_1(A))
            & m2_relset_1(B,k5_qmax_1(A),k5_qmax_1(A)) )
         => ( B = k9_qmax_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,k5_qmax_1(A))
               => ! [D] : 
                    ( m1_subset_1(D,k5_qmax_1(A))
                   => ( r2_hidden(k1_domain_1(k5_qmax_1(A),k5_qmax_1(A),C,D),B)
                    <=> r4_qmax_1(A,C,D) ) ) ) ) ) ) ),
    file(qmax_1,d12_qmax_1),
    []).

fof(d2_qmax_1,axiom,(
    ! [A] : 
      ( l1_qmax_1(A)
     => k2_qmax_1(A) = u1_qmax_1(A) ) ),
    file(qmax_1,d2_qmax_1),
    []).

fof(d3_qmax_1,axiom,(
    ! [A] : 
      ( l1_qmax_1(A)
     => k3_qmax_1(A) = u2_qmax_1(A) ) ),
    file(qmax_1,d3_qmax_1),
    []).

fof(d4_qmax_1,axiom,(
    ! [A] : 
      ( l1_qmax_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k2_qmax_1(A))
         => ! [C] : 
              ( m1_subset_1(C,k3_qmax_1(A))
             => k4_qmax_1(A,B,C) = k1_funct_1(u3_qmax_1(A),k1_domain_1(k2_qmax_1(A),k3_qmax_1(A),B,C)) ) ) ) ),
    file(qmax_1,d4_qmax_1),
    []).

fof(d5_eqrel_1,axiom,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k7_eqrel_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> ? [E] : 
                      ( r2_hidden(E,A)
                      & D = k6_eqrel_1(A,B,E) ) ) ) ) ) ) ),
    file(eqrel_1,d5_eqrel_1),
    []).

fof(d8_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => k5_qmax_1(A) = k2_zfmisc_1(k2_qmax_1(A),k14_prob_1) ) ),
    file(qmax_1,d8_qmax_1),
    []).

fof(d9_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k5_qmax_1(A))
         => k8_qmax_1(A,B) = k1_domain_1(k2_qmax_1(A),k1_zfmisc_1(k1_numbers),k6_qmax_1(A,B),k3_subset_1(k1_numbers,k7_qmax_1(A,B))) ) ) ),
    file(qmax_1,d9_qmax_1),
    []).

fof(dt_k10_prob_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,k1_numbers)
        & m1_relset_1(C,B,k1_numbers)
        & m3_prob_1(D,A,B) )
     => m1_subset_1(k10_prob_1(A,B,C,D),k1_numbers) ) ),
    file(prob_1,k10_prob_1),
    []).

fof(dt_k14_prob_1,axiom,(
    m1_prob_1(k14_prob_1,k1_numbers) ),
    file(prob_1,k14_prob_1),
    []).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

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

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

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

fof(dt_k1_qmax_1,axiom,(
    $true ),
    file(qmax_1,k1_qmax_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_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

fof(dt_k2_qmax_1,axiom,(
    $true ),
    file(qmax_1,k2_qmax_1),
    []).

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

fof(dt_k3_qmax_1,axiom,(
    $true ),
    file(qmax_1,k3_qmax_1),
    []).

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_k4_qmax_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_qmax_1(A)
        & m1_subset_1(B,k2_qmax_1(A))
        & m1_subset_1(C,k3_qmax_1(A)) )
     => m4_prob_1(k4_qmax_1(A,B,C),k1_numbers,k14_prob_1) ) ),
    file(qmax_1,k4_qmax_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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_qmax_1,axiom,(
    $true ),
    file(qmax_1,k5_qmax_1),
    []).

fof(dt_k6_eqrel_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_2(B)
        & v3_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(eqrel_1,k6_eqrel_1),
    []).

fof(dt_k6_qmax_1,axiom,(
    ! [A,B] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => m1_subset_1(k6_qmax_1(A,B),k2_qmax_1(A)) ) ),
    file(qmax_1,k6_qmax_1),
    []).

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

fof(dt_k7_eqrel_1,axiom,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,k7_eqrel_1),
    []).

fof(dt_k7_qmax_1,axiom,(
    ! [A,B] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => m3_prob_1(k7_qmax_1(A,B),k1_numbers,k14_prob_1) ) ),
    file(qmax_1,k7_qmax_1),
    []).

fof(dt_k8_eqrel_1,axiom,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => m1_eqrel_1(k8_eqrel_1(A,B),A) ) ),
    file(eqrel_1,k8_eqrel_1),
    []).

fof(dt_k8_qmax_1,axiom,(
    ! [A,B] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => m1_subset_1(k8_qmax_1(A,B),k5_qmax_1(A)) ) ),
    file(qmax_1,k8_qmax_1),
    []).

fof(dt_k9_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ( v3_relat_2(k9_qmax_1(A))
        & v8_relat_2(k9_qmax_1(A))
        & v1_partfun1(k9_qmax_1(A),k5_qmax_1(A),k5_qmax_1(A))
        & m2_relset_1(k9_qmax_1(A),k5_qmax_1(A),k5_qmax_1(A)) ) ) ),
    file(qmax_1,k9_qmax_1),
    []).

fof(dt_l1_qmax_1,axiom,(
    $true ),
    file(qmax_1,l1_qmax_1),
    []).

fof(dt_m1_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,m1_eqrel_1),
    []).

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_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_m3_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m3_prob_1(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(A)) ) ) ),
    file(prob_1,m3_prob_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(dt_u1_qmax_1,axiom,(
    ! [A] : 
      ( l1_qmax_1(A)
     => ~ v1_xboole_0(u1_qmax_1(A)) ) ),
    file(qmax_1,u1_qmax_1),
    []).

fof(dt_u2_qmax_1,axiom,(
    ! [A] : 
      ( l1_qmax_1(A)
     => ~ v1_xboole_0(u2_qmax_1(A)) ) ),
    file(qmax_1,u2_qmax_1),
    []).

fof(dt_u3_qmax_1,axiom,(
    ! [A] : 
      ( l1_qmax_1(A)
     => ( v1_funct_1(u3_qmax_1(A))
        & v1_funct_2(u3_qmax_1(A),k2_zfmisc_1(u1_qmax_1(A),u2_qmax_1(A)),k1_qmax_1(k1_numbers,k14_prob_1))
        & m2_relset_1(u3_qmax_1(A),k2_zfmisc_1(u1_qmax_1(A),u2_qmax_1(A)),k1_qmax_1(k1_numbers,k14_prob_1)) ) ) ),
    file(qmax_1,u3_qmax_1),
    []).

fof(existence_l1_qmax_1,axiom,(
    ? [A] : l1_qmax_1(A) ),
    file(qmax_1,l1_qmax_1),
    []).

fof(existence_m1_eqrel_1,axiom,(
    ! [A] : 
    ? [B] : m1_eqrel_1(B,A) ),
    file(eqrel_1,m1_eqrel_1),
    []).

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

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_m3_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ? [C] : m3_prob_1(C,A,B) ) ),
    file(prob_1,m3_prob_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(fc15_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc15_xreal_0),
    []).

fof(fc16_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc16_xreal_0),
    []).

fof(fc17_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v2_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc17_xreal_0),
    []).

fof(fc18_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A))
        & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc18_xreal_0),
    []).

fof(fc19_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v2_xreal_0(k6_xcmplx_0(A,B))
        & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc19_xreal_0),
    []).

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_qmax_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A) )
     => ~ v1_xboole_0(k1_qmax_1(A,B)) ) ),
    file(qmax_1,fc1_qmax_1),
    []).

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

fof(fc20_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v2_xreal_0(k6_xcmplx_0(B,A))
        & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc20_xreal_0),
    []).

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

fof(fc2_qmax_1,axiom,(
    ! [A] : 
      ( l1_qmax_1(A)
     => ~ v1_xboole_0(k2_qmax_1(A)) ) ),
    file(qmax_1,fc2_qmax_1),
    []).

fof(fc3_eqrel_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => ~ v1_xboole_0(k7_eqrel_1(A,B)) ) ),
    file(eqrel_1,fc3_eqrel_1),
    []).

fof(fc3_qmax_1,axiom,(
    ! [A] : 
      ( l1_qmax_1(A)
     => ~ v1_xboole_0(k3_qmax_1(A)) ) ),
    file(qmax_1,fc3_qmax_1),
    []).

fof(fc4_eqrel_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => ( ~ v1_xboole_0(k7_eqrel_1(A,B))
        & v1_setfam_1(k7_eqrel_1(A,B)) ) ) ),
    file(eqrel_1,fc4_eqrel_1),
    []).

fof(fc4_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ~ v1_xboole_0(k5_qmax_1(A)) ) ),
    file(qmax_1,fc4_qmax_1),
    []).

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

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

fof(fc5_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    []).

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

fof(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(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

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

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

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

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_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_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_k10_prob_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,k1_numbers)
        & m1_relset_1(C,B,k1_numbers)
        & m3_prob_1(D,A,B) )
     => k10_prob_1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(prob_1,k10_prob_1),
    []).

fof(redefinition_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

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

fof(redefinition_k6_qmax_1,axiom,(
    ! [A,B] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => k6_qmax_1(A,B) = k1_mcart_1(B) ) ),
    file(qmax_1,k6_qmax_1),
    []).

fof(redefinition_k7_qmax_1,axiom,(
    ! [A,B] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => k7_qmax_1(A,B) = k2_mcart_1(B) ) ),
    file(qmax_1,k7_qmax_1),
    []).

fof(redefinition_k8_eqrel_1,axiom,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => k8_eqrel_1(A,B) = k7_eqrel_1(A,B) ) ),
    file(eqrel_1,k8_eqrel_1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

fof(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(t12_eqrel_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(k4_tarski(B,C),D)
       => r2_hidden(k4_tarski(C,B),D) ) ) ),
    file(eqrel_1,t12_eqrel_1),
    []).

fof(t16_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k3_qmax_1(A))
         => ! [C] : 
              ( m1_subset_1(C,k5_qmax_1(A))
             => ! [D] : 
                  ( m3_prob_1(D,k1_numbers,k14_prob_1)
                 => ( D = k3_subset_1(k1_numbers,k7_qmax_1(A,C))
                   => k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),B),k7_qmax_1(A,C)) = k6_xcmplx_0(1,k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),B),D)) ) ) ) ) ) ),
    file(qmax_1,t16_qmax_1),
    []).

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

fof(t20_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] : 
              ( m1_subset_1(C,k5_qmax_1(A))
             => ( r4_qmax_1(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,k3_qmax_1(A))
                   => k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,B),D),k7_qmax_1(A,B)) = k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),D),k7_qmax_1(A,C)) ) ) ) ) ) ),
    file(qmax_1,t20_qmax_1),
    []).

fof(t24_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] : 
              ( m1_subset_1(C,k5_qmax_1(A))
             => ( r4_qmax_1(A,B,C)
               => r4_qmax_1(A,C,B) ) ) ) ) ),
    file(qmax_1,t24_qmax_1),
    []).

fof(t25_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] : 
              ( m1_subset_1(C,k5_qmax_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,k5_qmax_1(A))
                 => ( ( r4_qmax_1(A,B,C)
                      & r4_qmax_1(A,C,D) )
                   => r4_qmax_1(A,B,D) ) ) ) ) ) ),
    file(qmax_1,t25_qmax_1),
    []).

fof(t26_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k5_qmax_1(A))
         => ( k6_qmax_1(A,k8_qmax_1(A,B)) = k6_qmax_1(A,B)
            & k7_qmax_1(A,k8_qmax_1(A,B)) = k3_subset_1(k1_numbers,k7_qmax_1(A,B)) ) ) ) ),
    file(qmax_1,t26_qmax_1),
    []).

fof(t27_eqrel_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_relat_2(D)
        & v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(B,k6_eqrel_1(A,D,C))
      <=> r2_hidden(k4_tarski(B,C),D) ) ) ),
    file(eqrel_1,t27_eqrel_1),
    []).

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

fof(t30_eqrel_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_relat_2(E)
        & v3_relat_2(E)
        & v8_relat_2(E)
        & v1_partfun1(E,A,A)
        & m2_relset_1(E,A,A) )
     => ( ( r2_hidden(B,k6_eqrel_1(A,E,C))
          & r2_hidden(D,k6_eqrel_1(A,E,C)) )
       => r2_hidden(k4_tarski(B,D),E) ) ) ),
    file(eqrel_1,t30_eqrel_1),
    []).

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

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

fof(t50_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m3_prob_1(C,A,B)
         => m3_prob_1(k3_subset_1(A,C),A,B) ) ) ),
    file(prob_1,t50_prob_1),
    []).

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),
    []).