% Mizar problem: t17_topgen_4,topgen_4,549,51 
fof(t17_topgen_4,conjecture,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ( v4_topgen_4(B,A)
            & v1_prob_1(B,A) )
         => ( v3_topgen_4(B,A)
            & v1_prob_1(B,A) ) )
        & ( ( v3_topgen_4(B,A)
            & v1_prob_1(B,A) )
         => ( v4_topgen_4(B,A)
            & v1_prob_1(B,A) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_ordinal1,cc1_yellow13,cc2_finset_1,cc2_ordinal1,cc2_topgen_4,cc2_waybel12,cc3_ordinal1,cc3_topgen_4,cc6_topgen_4,d1_prob_1,d4_topgen_4,d5_topgen_4,dt_k1_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k3_tarski,dt_k5_setfam_1,dt_k6_setfam_1,dt_k7_setfam_1,dt_m1_subset_1,existence_m1_subset_1,fc1_measure1,fc1_subset_1,fc2_ordinal1,fc4_ordinal1,fc4_topgen_3,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,rc1_finset_1,rc1_ordinal1,rc1_subset_1,rc1_topgen_3,rc1_topgen_4,rc2_measure1,rc2_ordinal1,rc2_subset_1,rc2_waybel12,rc3_finset_1,rc3_ordinal1,rc4_finset_1,rc4_waybel12,rc6_waybel12,redefinition_k5_setfam_1,redefinition_k6_setfam_1,reflexivity_r1_tarski,t11_tops_2,t12_tops_2,t16_topgen_4,t1_subset,t1_topgen_4,t2_setfam_1,t2_subset,t2_zfmisc_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(topgen_4,t17_topgen_4)]).

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

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc1_yellow13,axiom,(
    ! [A] : 
      ( v1_realset1(A)
     => v1_finset_1(A) ) ),
    file(yellow13,cc1_yellow13),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc2_topgen_4,axiom,(
    ! [A] : 
      ( ~ v1_card_4(A)
     => ~ v1_finset_1(A) ) ),
    file(topgen_4,cc2_topgen_4),
    []).

fof(cc2_waybel12,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => v1_card_4(A) ) ),
    file(waybel12,cc2_waybel12),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(cc3_topgen_4,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ~ v1_realset1(A) ) ),
    file(topgen_4,cc3_topgen_4),
    []).

fof(cc6_topgen_4,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v3_topgen_4(B,A)
       => ~ v1_xboole_0(B) ) ) ),
    file(topgen_4,cc6_topgen_4),
    []).

fof(d1_prob_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_prob_1(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(A))
           => ( r2_hidden(C,B)
             => r2_hidden(k3_subset_1(A,C),B) ) ) ) ) ),
    file(prob_1,d1_prob_1),
    []).

fof(d4_topgen_4,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v3_topgen_4(B,A)
      <=> ! [C] : 
            ( ( v1_card_4(C)
              & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
           => ( r1_tarski(C,B)
             => r2_hidden(k5_setfam_1(A,C),B) ) ) ) ) ),
    file(topgen_4,d4_topgen_4),
    []).

fof(d5_topgen_4,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v4_topgen_4(B,A)
      <=> ! [C] : 
            ( ( v1_card_4(C)
              & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
           => ( r1_tarski(C,B)
             => r2_hidden(k6_setfam_1(A,C),B) ) ) ) ) ),
    file(topgen_4,d5_topgen_4),
    []).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_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_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_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_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_1),
    []).

fof(dt_k7_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(setfam_1,k7_setfam_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

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

fof(fc1_measure1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ~ v1_xboole_0(k7_setfam_1(A,B)) ) ),
    file(measure1,fc1_measure1),
    []).

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

fof(fc2_ordinal1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

fof(fc4_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_tarski(A))
        & v2_ordinal1(k3_tarski(A))
        & v3_ordinal1(k3_tarski(A)) ) ) ),
    file(ordinal1,fc4_ordinal1),
    []).

fof(fc4_topgen_3,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ( ~ v1_xboole_0(k1_zfmisc_1(A))
        & ~ v1_finset_1(k1_zfmisc_1(A)) ) ) ),
    file(topgen_3,fc4_topgen_3),
    []).

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(involutiveness_k7_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k7_setfam_1(A,k7_setfam_1(A,B)) = B ) ),
    file(setfam_1,k7_setfam_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

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_topgen_3,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_finset_1(B) ) ) ),
    file(topgen_3,rc1_topgen_3),
    []).

fof(rc1_topgen_4,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_card_4(A) ) ),
    file(topgen_4,rc1_topgen_4),
    []).

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

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

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_waybel12,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc2_waybel12),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

fof(rc4_waybel12,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc4_waybel12),
    []).

fof(rc6_waybel12,axiom,(
    ? [A] : 
      ( ~ v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc6_waybel12),
    []).

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_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_1),
    []).

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

fof(t11_tops_2,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( B != k1_xboole_0
       => k6_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k5_setfam_1(A,B)) ) ) ),
    file(tops_2,t11_tops_2),
    []).

fof(t12_tops_2,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( B != k1_xboole_0
       => k5_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k6_setfam_1(A,B)) ) ) ),
    file(tops_2,t12_tops_2),
    []).

fof(t16_topgen_4,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( ( r1_tarski(B,C)
              & v1_prob_1(C,A) )
           => r1_tarski(k7_setfam_1(A,B),C) ) ) ) ),
    file(topgen_4,t16_topgen_4),
    []).

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

fof(t1_topgen_4,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_card_4(B)
      <=> v1_card_4(k7_setfam_1(A,B)) ) ) ),
    file(topgen_4,t1_topgen_4),
    []).

fof(t2_setfam_1,axiom,(
    k1_setfam_1(k1_xboole_0) = k1_xboole_0 ),
    file(setfam_1,t2_setfam_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(t2_zfmisc_1,axiom,(
    k3_tarski(k1_xboole_0) = k1_xboole_0 ),
    file(zfmisc_1,t2_zfmisc_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(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),
    []).