% Mizar problem: t36_qmax_1,qmax_1,700,36 
fof(t36_qmax_1,conjecture,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => r2_qmax_1(k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),g2_qmax_1(k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k10_qmax_1(A),k11_qmax_1(A))) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_qmax_1,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,d11_qmax_1,d12_qmax_1,d14_qmax_1,d1_relat_2,d2_qmax_1,d4_relat_2,d6_qmax_1,d7_orders_1,d7_qmax_1,d8_qmax_1,d8_relat_2,d9_qmax_1,dt_g2_qmax_1,dt_k10_qmax_1,dt_k11_qmax_1,dt_k14_prob_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_mcart_1,dt_k2_qmax_1,dt_k2_zfmisc_1,dt_k3_subset_1,dt_k4_tarski,dt_k5_qmax_1,dt_k6_eqrel_1,dt_k6_qmax_1,dt_k7_eqrel_1,dt_k7_qmax_1,dt_k8_eqrel_1,dt_k8_funct_2,dt_k8_qmax_1,dt_k9_qmax_1,dt_l1_qmax_1,dt_l2_qmax_1,dt_m1_eqrel_1,dt_m1_prob_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_m3_prob_1,dt_u1_qmax_1,dt_u4_qmax_1,dt_u5_qmax_1,existence_l1_qmax_1,existence_l2_qmax_1,existence_m1_eqrel_1,existence_m1_prob_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_prob_1,fc1_subset_1,fc2_membered,fc2_qmax_1,fc3_eqrel_1,fc4_eqrel_1,fc4_qmax_1,fc4_subset_1,fc6_membered,free_g2_qmax_1,involutiveness_k3_subset_1,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_partfun1,rc2_subset_1,rc2_xreal_0,rc3_qmax_1,rc3_xreal_0,rc4_xreal_0,redefinition_k1_domain_1,redefinition_k6_qmax_1,redefinition_k7_qmax_1,redefinition_k8_eqrel_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,t1_subset,t21_qmax_1,t22_qmax_1,t27_qmax_1,t28_qmax_1,t2_subset,t32_qmax_1,t3_subset,t44_eqrel_1,t45_eqrel_1,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(qmax_1,t36_qmax_1)]).

fof(abstractness_v3_qmax_1,axiom,(
    ! [A,B] : 
      ( l2_qmax_1(B,A)
     => ( v3_qmax_1(B,A)
       => B = g2_qmax_1(A,u4_qmax_1(A,B),u5_qmax_1(A,B)) ) ) ),
    file(qmax_1,v3_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(d11_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)
              <=> ( r3_qmax_1(A,B,C)
                  & r3_qmax_1(A,C,B) ) ) ) ) ) ),
    file(qmax_1,d11_qmax_1),
    []).

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(d14_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
            & m2_relset_1(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
         => ( B = k11_qmax_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,k5_qmax_1(A))
               => k1_funct_1(B,k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),C)) = k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),k8_qmax_1(A,C)) ) ) ) ) ),
    file(qmax_1,d14_qmax_1),
    []).

fof(d1_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
        <=> ! [C] : 
              ( r2_hidden(C,B)
             => r2_hidden(k4_tarski(C,C),A) ) ) ) ),
    file(relat_2,d1_relat_2),
    []).

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(d4_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r4_relat_2(A,B)
        <=> ! [C,D] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,C),A) )
             => C = D ) ) ) ),
    file(relat_2,d4_relat_2),
    []).

fof(d6_qmax_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( r1_qmax_1(A,B)
      <=> ! [C] : 
            ( m1_subset_1(C,A)
           => k1_funct_1(B,k1_funct_1(B,C)) = C ) ) ) ),
    file(qmax_1,d6_qmax_1),
    []).

fof(d7_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_orders_1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B) ) ) ) ),
    file(orders_1,d7_orders_1),
    []).

fof(d7_qmax_1,axiom,(
    ! [A,B] : 
      ( l2_qmax_1(B,A)
     => ( r2_qmax_1(A,B)
      <=> ? [C] : 
            ( m2_relset_1(C,A,A)
            & ? [D] : 
                ( v1_funct_1(D)
                & v1_funct_2(D,A,A)
                & m2_relset_1(D,A,A)
                & B = g2_qmax_1(A,C,D)
                & r2_orders_1(C,A)
                & r1_qmax_1(A,D)
                & ! [E] : 
                    ( m1_subset_1(E,A)
                   => ! [F] : 
                        ( m1_subset_1(F,A)
                       => ( r2_hidden(k4_tarski(E,F),C)
                         => r2_hidden(k4_tarski(k1_funct_1(D,F),k1_funct_1(D,E)),C) ) ) ) ) ) ) ) ),
    file(qmax_1,d7_qmax_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(d8_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
        <=> ! [C,D,E] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(E,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,E),A) )
             => r2_hidden(k4_tarski(C,E),A) ) ) ) ),
    file(relat_2,d8_relat_2),
    []).

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_g2_qmax_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v3_qmax_1(g2_qmax_1(A,B,C),A)
        & l2_qmax_1(g2_qmax_1(A,B,C),A) ) ) ),
    file(qmax_1,g2_qmax_1),
    []).

fof(dt_k10_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => m2_relset_1(k10_qmax_1(A),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) ) ),
    file(qmax_1,k10_qmax_1),
    []).

fof(dt_k11_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ( v1_funct_1(k11_qmax_1(A))
        & v1_funct_2(k11_qmax_1(A),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
        & m2_relset_1(k11_qmax_1(A),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) ) ) ),
    file(qmax_1,k11_qmax_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_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_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_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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_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_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_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_l2_qmax_1,axiom,(
    $true ),
    file(qmax_1,l2_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_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_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_u1_qmax_1,axiom,(
    ! [A] : 
      ( l1_qmax_1(A)
     => ~ v1_xboole_0(u1_qmax_1(A)) ) ),
    file(qmax_1,u1_qmax_1),
    []).

fof(dt_u4_qmax_1,axiom,(
    ! [A,B] : 
      ( l2_qmax_1(B,A)
     => m2_relset_1(u4_qmax_1(A,B),A,A) ) ),
    file(qmax_1,u4_qmax_1),
    []).

fof(dt_u5_qmax_1,axiom,(
    ! [A,B] : 
      ( l2_qmax_1(B,A)
     => ( v1_funct_1(u5_qmax_1(A,B))
        & v1_funct_2(u5_qmax_1(A,B),A,A)
        & m2_relset_1(u5_qmax_1(A,B),A,A) ) ) ),
    file(qmax_1,u5_qmax_1),
    []).

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

fof(existence_l2_qmax_1,axiom,(
    ! [A] : 
    ? [B] : l2_qmax_1(B,A) ),
    file(qmax_1,l2_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_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_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(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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(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(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(free_g2_qmax_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ! [D,E,F] : 
          ( g2_qmax_1(A,B,C) = g2_qmax_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(qmax_1,g2_qmax_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(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_qmax_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( l2_qmax_1(B,A)
      & v3_qmax_1(B,A) ) ),
    file(qmax_1,rc3_qmax_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_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_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_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_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(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t21_qmax_1,axiom,(
    ! [A] : 
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k5_qmax_1(A))
         => r3_qmax_1(A,B,B) ) ) ),
    file(qmax_1,t21_qmax_1),
    []).

fof(t22_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))
                 => ( ( r3_qmax_1(A,B,C)
                      & r3_qmax_1(A,C,D) )
                   => r3_qmax_1(A,B,D) ) ) ) ) ) ),
    file(qmax_1,t22_qmax_1),
    []).

fof(t27_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,k8_qmax_1(A,B)) = B ) ) ),
    file(qmax_1,t27_qmax_1),
    []).

fof(t28_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))
             => ( r3_qmax_1(A,B,C)
               => r3_qmax_1(A,k8_qmax_1(A,C),k8_qmax_1(A,B)) ) ) ) ) ),
    file(qmax_1,t28_qmax_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(t32_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))
             => ( r3_qmax_1(A,B,C)
              <=> r2_hidden(k1_domain_1(k1_zfmisc_1(k5_qmax_1(A)),k1_zfmisc_1(k5_qmax_1(A)),k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),B),k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),C)),k10_qmax_1(A)) ) ) ) ) ),
    file(qmax_1,t32_qmax_1),
    []).

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

fof(t44_eqrel_1,axiom,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ! [D] : 
          ( r2_hidden(D,A)
         => ( r2_hidden(k4_tarski(D,B),C)
          <=> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) ) ) ) ),
    file(eqrel_1,t44_eqrel_1),
    []).

fof(t45_eqrel_1,axiom,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,B,B)
        & m2_relset_1(C,B,B) )
     => ~ ( r2_hidden(A,k7_eqrel_1(B,C))
          & ! [D] : 
              ( m1_subset_1(D,B)
             => A != k6_eqrel_1(B,C,D) ) ) ) ),
    file(eqrel_1,t45_eqrel_1),
    []).

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(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),
    []).