% Mizar ND problem: t9_borsuk_1,borsuk_1,65,43 
fof(dh_c1_4__borsuk_1,definition,
    ( ! [A,B] : 
        ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(A,B))
       => k1_funct_1(k1_funct_3(k9_funct_3(A,B)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(A,B),A,k9_funct_3(A,B),c1_4__borsuk_1) )
   => ! [C,D,E] : 
        ( r1_tarski(C,k2_zfmisc_1(D,E))
       => k1_funct_1(k1_funct_3(k9_funct_3(D,E)),C) = k2_funct_2(k2_zfmisc_1(D,E),D,k9_funct_3(D,E),C) ) ),
    introduced(definition,[new_symbol(c1_4__borsuk_1),file(borsuk_1,c1_4__borsuk_1)]),
    [interesting(0.8),axiom,file(borsuk_1,c1_4__borsuk_1)]).

fof(dh_c2_4__borsuk_1,definition,
    ( ! [A] : 
        ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(c2_4__borsuk_1,A))
       => k1_funct_1(k1_funct_3(k9_funct_3(c2_4__borsuk_1,A)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(c2_4__borsuk_1,A),c2_4__borsuk_1,k9_funct_3(c2_4__borsuk_1,A),c1_4__borsuk_1) )
   => ! [B,C] : 
        ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(B,C))
       => k1_funct_1(k1_funct_3(k9_funct_3(B,C)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(B,C),B,k9_funct_3(B,C),c1_4__borsuk_1) ) ),
    introduced(definition,[new_symbol(c2_4__borsuk_1),file(borsuk_1,c2_4__borsuk_1)]),
    [interesting(0.8),axiom,file(borsuk_1,c2_4__borsuk_1)]).

fof(dh_c3_4__borsuk_1,definition,
    ( ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(c2_4__borsuk_1,c3_4__borsuk_1))
     => k1_funct_1(k1_funct_3(k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(c2_4__borsuk_1,c3_4__borsuk_1),c2_4__borsuk_1,k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1),c1_4__borsuk_1) )
   => ! [A] : 
        ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(c2_4__borsuk_1,A))
       => k1_funct_1(k1_funct_3(k9_funct_3(c2_4__borsuk_1,A)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(c2_4__borsuk_1,A),c2_4__borsuk_1,k9_funct_3(c2_4__borsuk_1,A),c1_4__borsuk_1) ) ),
    introduced(definition,[new_symbol(c3_4__borsuk_1),file(borsuk_1,c3_4__borsuk_1)]),
    [interesting(0.8),axiom,file(borsuk_1,c3_4__borsuk_1)]).

fof(e1_4__borsuk_1,assumption,(
    r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(c2_4__borsuk_1,c3_4__borsuk_1)) ),
    introduced(assumption,[file(borsuk_1,e1_4__borsuk_1)]),
    [interesting(0.8),axiom,file(borsuk_1,e1_4__borsuk_1)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_funct_2,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(fc13_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k9_relat_1(A,B)) ) ),
    file(finset_1,fc13_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc13_finset_1)]).

fof(fc14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]).

fof(fc6_membered,theorem,
    ( 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),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(rc3_finset_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc4_finset_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k7_funct_3,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k7_funct_3(A,B))
      & v1_funct_1(k7_funct_3(A,B)) ) ),
    file(funct_3,k7_funct_3),
    [interesting(0.9),axiom,file(funct_3,k7_funct_3)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

fof(cc1_relset_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(cc5_funct_2,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]).

fof(cc6_funct_2,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(rc1_funct_2,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_partfun1,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(redefinition_k2_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(funct_2,k2_funct_2),
    [interesting(0.9),axiom,file(funct_2,k2_funct_2)]).

fof(redefinition_k9_funct_3,definition,(
    ! [A,B] : k9_funct_3(A,B) = k7_funct_3(A,B) ),
    file(funct_3,k9_funct_3),
    [interesting(0.9),axiom,file(funct_3,k9_funct_3)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_funct_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k1_funct_3(A))
        & v1_funct_1(k1_funct_3(A)) ) ) ),
    file(funct_3,k1_funct_3),
    [interesting(0.9),axiom,file(funct_3,k1_funct_3)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ),
    file(funct_2,k2_funct_2),
    [interesting(0.9),axiom,file(funct_2,k2_funct_2)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_k9_funct_3,axiom,(
    ! [A,B] : 
      ( v1_funct_1(k9_funct_3(A,B))
      & v1_funct_2(k9_funct_3(A,B),k2_zfmisc_1(A,B),A)
      & m2_relset_1(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) ) ),
    file(funct_3,k9_funct_3),
    [interesting(0.9),axiom,file(funct_3,k9_funct_3)]).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    [interesting(0.9),axiom,file(relat_1,k9_relat_1)]).

fof(dt_c1_4__borsuk_1,assumption,(
    $true ),
    introduced(assumption,[file(borsuk_1,c1_4__borsuk_1)]),
    [interesting(0.8),axiom,file(borsuk_1,c1_4__borsuk_1)]).

fof(dt_c2_4__borsuk_1,assumption,(
    $true ),
    introduced(assumption,[file(borsuk_1,c2_4__borsuk_1)]),
    [interesting(0.8),axiom,file(borsuk_1,c2_4__borsuk_1)]).

fof(dt_c3_4__borsuk_1,assumption,(
    $true ),
    introduced(assumption,[file(borsuk_1,c3_4__borsuk_1)]),
    [interesting(0.8),axiom,file(borsuk_1,c3_4__borsuk_1)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(fc10_membered,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    [interesting(0.9),axiom,file(membered,fc10_membered)]).

fof(fc11_membered,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    [interesting(0.9),axiom,file(membered,fc11_membered)]).

fof(fc12_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    [interesting(0.9),axiom,file(membered,fc12_membered)]).

fof(fc13_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    [interesting(0.9),axiom,file(membered,fc13_membered)]).

fof(fc14_membered,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    [interesting(0.9),axiom,file(membered,fc14_membered)]).

fof(fc15_membered,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    [interesting(0.9),axiom,file(membered,fc15_membered)]).

fof(fc16_membered,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    [interesting(0.9),axiom,file(membered,fc16_membered)]).

fof(fc7_membered,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    [interesting(0.9),axiom,file(membered,fc7_membered)]).

fof(fc8_membered,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    [interesting(0.9),axiom,file(membered,fc8_membered)]).

fof(fc9_membered,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    [interesting(0.9),axiom,file(membered,fc9_membered)]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(fc1_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

fof(fc2_finset_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(d5_funct_3,definition,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( C = k7_funct_3(A,B)
      <=> ( k1_relat_1(C) = k2_zfmisc_1(A,B)
          & ! [D,E] : 
              ( ( r2_hidden(D,A)
                & r2_hidden(E,B) )
             => k1_funct_1(C,k4_tarski(D,E)) = D ) ) ) ) ),
    file(funct_3,d5_funct_3),
    [interesting(0.9),axiom,file(funct_3,d5_funct_3)]).

fof(e2_4__borsuk_1,plain,(
    r1_tarski(c1_4__borsuk_1,k1_relat_1(k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__borsuk_1,dt_c2_4__borsuk_1,dt_c3_4__borsuk_1,e1_4__borsuk_1])],[cc1_funct_2,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k9_funct_3,dt_k1_funct_1,dt_k1_relat_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k7_funct_3,dt_k9_funct_3,dt_c1_4__borsuk_1,dt_c2_4__borsuk_1,dt_c3_4__borsuk_1,t1_subset,t3_subset,t7_boole,d5_tarski,e1_4__borsuk_1,d5_funct_3]),
    [interesting(0.8),file(borsuk_1,e2_4__borsuk_1),[file(borsuk_1,e2_4__borsuk_1)]]).

fof(d1_funct_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k1_funct_3(A)
          <=> ( k1_relat_1(B) = k1_zfmisc_1(k1_relat_1(A))
              & ! [C] : 
                  ( r1_tarski(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k9_relat_1(A,C) ) ) ) ) ) ),
    file(funct_3,d1_funct_3),
    [interesting(0.9),axiom,file(funct_3,d1_funct_3)]).

fof(e3_4__borsuk_1,plain,(
    k1_funct_1(k1_funct_3(k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(c2_4__borsuk_1,c3_4__borsuk_1),c2_4__borsuk_1,k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1),c1_4__borsuk_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__borsuk_1,dt_c2_4__borsuk_1,dt_c3_4__borsuk_1,e1_4__borsuk_1])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k7_funct_3,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k2_funct_2,redefinition_k9_funct_3,dt_k1_funct_1,dt_k1_funct_3,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k9_funct_3,dt_k9_relat_1,dt_c1_4__borsuk_1,dt_c2_4__borsuk_1,dt_c3_4__borsuk_1,fc1_subset_1,t3_subset,e2_4__borsuk_1,d1_funct_3]),
    [interesting(0.8),file(borsuk_1,e3_4__borsuk_1),[file(borsuk_1,e3_4__borsuk_1)]]).

fof(i5_4__borsuk_1,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_1,i5_4__borsuk_1)]),
    [interesting(0.8),trivial,file(borsuk_1,i5_4__borsuk_1)]).

fof(i4_4__borsuk_1,plain,(
    k1_funct_1(k1_funct_3(k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(c2_4__borsuk_1,c3_4__borsuk_1),c2_4__borsuk_1,k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1),c1_4__borsuk_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__borsuk_1,dt_c2_4__borsuk_1,dt_c3_4__borsuk_1,e1_4__borsuk_1])],[e3_4__borsuk_1,i5_4__borsuk_1]),
    [interesting(0.8),file(borsuk_1,i4_4__borsuk_1),[file(borsuk_1,i4_4__borsuk_1)]]).

fof(i3_4__borsuk_1,plain,
    ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(c2_4__borsuk_1,c3_4__borsuk_1))
   => k1_funct_1(k1_funct_3(k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(c2_4__borsuk_1,c3_4__borsuk_1),c2_4__borsuk_1,k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1),c1_4__borsuk_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__borsuk_1,dt_c2_4__borsuk_1,dt_c3_4__borsuk_1]),discharge_asm(discharge,[e1_4__borsuk_1])],[e1_4__borsuk_1,i4_4__borsuk_1]),
    [interesting(0.8),file(borsuk_1,i3_4__borsuk_1),[file(borsuk_1,i3_4__borsuk_1)]]).

fof(i3_4_tmp__borsuk_1,plain,
    ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(c2_4__borsuk_1,c3_4__borsuk_1))
   => k1_funct_1(k1_funct_3(k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(c2_4__borsuk_1,c3_4__borsuk_1),c2_4__borsuk_1,k9_funct_3(c2_4__borsuk_1,c3_4__borsuk_1),c1_4__borsuk_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__borsuk_1,dt_c2_4__borsuk_1]),discharge_asm(discharge,[dt_c3_4__borsuk_1])],[dt_c3_4__borsuk_1,i3_4__borsuk_1]),
    [interesting(0.8),i2_4__borsuk_1]).

fof(i2_4__borsuk_1,plain,(
    ! [A] : 
      ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(c2_4__borsuk_1,A))
     => k1_funct_1(k1_funct_3(k9_funct_3(c2_4__borsuk_1,A)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(c2_4__borsuk_1,A),c2_4__borsuk_1,k9_funct_3(c2_4__borsuk_1,A),c1_4__borsuk_1) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__borsuk_1,dt_c2_4__borsuk_1])],[i3_4_tmp__borsuk_1,dh_c3_4__borsuk_1]),
    [interesting(0.8),file(borsuk_1,i2_4__borsuk_1),[file(borsuk_1,i2_4__borsuk_1)]]).

fof(i2_4_tmp__borsuk_1,plain,(
    ! [A] : 
      ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(c2_4__borsuk_1,A))
     => k1_funct_1(k1_funct_3(k9_funct_3(c2_4__borsuk_1,A)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(c2_4__borsuk_1,A),c2_4__borsuk_1,k9_funct_3(c2_4__borsuk_1,A),c1_4__borsuk_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__borsuk_1]),discharge_asm(discharge,[dt_c2_4__borsuk_1])],[dt_c2_4__borsuk_1,i2_4__borsuk_1]),
    [interesting(0.8),i1_4__borsuk_1]).

fof(i1_4__borsuk_1,plain,(
    ! [A,B] : 
      ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(A,B))
     => k1_funct_1(k1_funct_3(k9_funct_3(A,B)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(A,B),A,k9_funct_3(A,B),c1_4__borsuk_1) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__borsuk_1])],[i2_4_tmp__borsuk_1,dh_c2_4__borsuk_1]),
    [interesting(0.8),file(borsuk_1,i1_4__borsuk_1),[file(borsuk_1,i1_4__borsuk_1)]]).

fof(i1_4_tmp__borsuk_1,plain,(
    ! [A,B] : 
      ( r1_tarski(c1_4__borsuk_1,k2_zfmisc_1(A,B))
     => k1_funct_1(k1_funct_3(k9_funct_3(A,B)),c1_4__borsuk_1) = k2_funct_2(k2_zfmisc_1(A,B),A,k9_funct_3(A,B),c1_4__borsuk_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__borsuk_1])],[dt_c1_4__borsuk_1,i1_4__borsuk_1]),
    [interesting(1),t9_borsuk_1]).

fof(t9_borsuk_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,k2_zfmisc_1(B,C))
     => k1_funct_1(k1_funct_3(k9_funct_3(B,C)),A) = k2_funct_2(k2_zfmisc_1(B,C),B,k9_funct_3(B,C),A) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__borsuk_1,dh_c1_4__borsuk_1]),
    [interesting(1),file(borsuk_1,t9_borsuk_1),[file(borsuk_1,t9_borsuk_1)]]).