% Mizar ND problem: t69_funct_6,funct_6,1669,20 
fof(dh_c1_75__funct_6,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( ( k1_relat_1(A) = c1_75__funct_6
                & k1_relat_1(B) = c1_75__funct_6
                & ! [C] : 
                    ( r2_hidden(C,c1_75__funct_6)
                   => r2_wellord2(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
             => r2_wellord2(k4_card_3(A),k4_card_3(B)) ) ) )
   => ! [D,E] : 
        ( ( v1_relat_1(E)
          & v1_funct_1(E) )
       => ! [F] : 
            ( ( v1_relat_1(F)
              & v1_funct_1(F) )
           => ( ( k1_relat_1(E) = D
                & k1_relat_1(F) = D
                & ! [G] : 
                    ( r2_hidden(G,D)
                   => r2_wellord2(k1_funct_1(E,G),k1_funct_1(F,G)) ) )
             => r2_wellord2(k4_card_3(E),k4_card_3(F)) ) ) ) ),
    introduced(definition,[new_symbol(c1_75__funct_6),file(funct_6,c1_75__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_75__funct_6)]).

fof(dh_c2_75__funct_6,definition,
    ( ( ( v1_relat_1(c2_75__funct_6)
        & v1_funct_1(c2_75__funct_6) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( ( k1_relat_1(c2_75__funct_6) = c1_75__funct_6
              & k1_relat_1(A) = c1_75__funct_6
              & ! [B] : 
                  ( r2_hidden(B,c1_75__funct_6)
                 => r2_wellord2(k1_funct_1(c2_75__funct_6,B),k1_funct_1(A,B)) ) )
           => r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(A)) ) ) )
   => ! [C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ! [D] : 
            ( ( v1_relat_1(D)
              & v1_funct_1(D) )
           => ( ( k1_relat_1(C) = c1_75__funct_6
                & k1_relat_1(D) = c1_75__funct_6
                & ! [E] : 
                    ( r2_hidden(E,c1_75__funct_6)
                   => r2_wellord2(k1_funct_1(C,E),k1_funct_1(D,E)) ) )
             => r2_wellord2(k4_card_3(C),k4_card_3(D)) ) ) ) ),
    introduced(definition,[new_symbol(c2_75__funct_6),file(funct_6,c2_75__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c2_75__funct_6)]).

fof(dh_c3_75__funct_6,definition,
    ( ( ( v1_relat_1(c3_75__funct_6)
        & v1_funct_1(c3_75__funct_6) )
     => ( ( k1_relat_1(c2_75__funct_6) = c1_75__funct_6
          & k1_relat_1(c3_75__funct_6) = c1_75__funct_6
          & ! [A] : 
              ( r2_hidden(A,c1_75__funct_6)
             => r2_wellord2(k1_funct_1(c2_75__funct_6,A),k1_funct_1(c3_75__funct_6,A)) ) )
       => r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ( ( k1_relat_1(c2_75__funct_6) = c1_75__funct_6
            & k1_relat_1(B) = c1_75__funct_6
            & ! [C] : 
                ( r2_hidden(C,c1_75__funct_6)
               => r2_wellord2(k1_funct_1(c2_75__funct_6,C),k1_funct_1(B,C)) ) )
         => r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(B)) ) ) ),
    introduced(definition,[new_symbol(c3_75__funct_6),file(funct_6,c3_75__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c3_75__funct_6)]).

fof(e1_75__funct_6,assumption,
    ( k1_relat_1(c2_75__funct_6) = c1_75__funct_6
    & k1_relat_1(c3_75__funct_6) = c1_75__funct_6
    & ! [A] : 
        ( r2_hidden(A,c1_75__funct_6)
       => r2_wellord2(k1_funct_1(c2_75__funct_6,A),k1_funct_1(c3_75__funct_6,A)) ) ),
    introduced(assumption,[file(funct_6,e1_75__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,e1_75__funct_6)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(symmetry_r2_wellord2,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(reflexivity_r2_wellord2,theorem,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(redefinition_r2_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    [interesting(0.9),axiom,file(card_3,k4_card_3)]).

fof(dt_c2_75__funct_6,assumption,
    ( v1_relat_1(c2_75__funct_6)
    & v1_funct_1(c2_75__funct_6) ),
    introduced(assumption,[file(funct_6,c2_75__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c2_75__funct_6)]).

fof(dt_c3_75__funct_6,assumption,
    ( v1_relat_1(c3_75__funct_6)
    & v1_funct_1(c3_75__funct_6) ),
    introduced(assumption,[file(funct_6,c3_75__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c3_75__funct_6)]).

fof(e1_75_5_1_1__funct_6,assumption,(
    r2_hidden(k1_xboole_0,k2_relat_1(c4_75__funct_6)) ),
    introduced(assumption,[file(funct_6,e1_75_5_1_1__funct_6)]),
    [interesting(0.35),axiom,file(funct_6,e1_75_5_1_1__funct_6)]).

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(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_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(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(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(cc1_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

fof(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

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

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & 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_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

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(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]).

fof(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

fof(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

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_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_c1_75__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_75__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_75__funct_6)]).

fof(dh_c1_75_5_1_1__funct_6,definition,
    ( ? [A] : 
        ( r2_hidden(A,c1_75__funct_6)
        & k1_xboole_0 = k1_funct_1(c4_75__funct_6,A) )
   => ( r2_hidden(c1_75_5_1_1__funct_6,c1_75__funct_6)
      & k1_xboole_0 = k1_funct_1(c4_75__funct_6,c1_75_5_1_1__funct_6) ) ),
    introduced(definition,[new_symbol(c1_75_5_1_1__funct_6),file(funct_6,c1_75_5_1_1__funct_6)]),
    [interesting(0.35),axiom,file(funct_6,c1_75_5_1_1__funct_6)]).

fof(dh_c4_75__funct_6,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = c1_75__funct_6
        & ! [B] : 
            ( r2_hidden(B,c1_75__funct_6)
           => ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & k1_funct_1(A,B) = C
                & v2_funct_1(C)
                & k1_relat_1(C) = k1_funct_1(c2_75__funct_6,B)
                & k2_relat_1(C) = k1_funct_1(c3_75__funct_6,B) ) ) )
   => ( v1_relat_1(c4_75__funct_6)
      & v1_funct_1(c4_75__funct_6)
      & k1_relat_1(c4_75__funct_6) = c1_75__funct_6
      & ! [D] : 
          ( r2_hidden(D,c1_75__funct_6)
         => ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & k1_funct_1(c4_75__funct_6,D) = E
              & v2_funct_1(E)
              & k1_relat_1(E) = k1_funct_1(c2_75__funct_6,D)
              & k2_relat_1(E) = k1_funct_1(c3_75__funct_6,D) ) ) ) ),
    introduced(definition,[new_symbol(c4_75__funct_6),file(funct_6,c4_75__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c4_75__funct_6)]).

fof(s1_zfrefle1__e3_75__funct_6,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ! [D] : 
            ~ ( r2_hidden(D,A)
              & ! [E] : 
                  ~ ? [F] : 
                      ( v1_relat_1(F)
                      & v1_funct_1(F)
                      & E = F
                      & v2_funct_1(F)
                      & k1_relat_1(F) = k1_funct_1(B,D)
                      & k2_relat_1(F) = k1_funct_1(C,D) ) )
       => ? [D] : 
            ( v1_relat_1(D)
            & v1_funct_1(D)
            & k1_relat_1(D) = A
            & ! [E] : 
                ( r2_hidden(E,A)
               => ? [G] : 
                    ( v1_relat_1(G)
                    & v1_funct_1(G)
                    & k1_funct_1(D,E) = G
                    & v2_funct_1(G)
                    & k1_relat_1(G) = k1_funct_1(B,E)
                    & k2_relat_1(G) = k1_funct_1(C,E) ) ) ) ) ) ),
    file(funct_6,s1_zfrefle1__e3_75__funct_6),
    [interesting(0.9),axiom,file(funct_6,s1_zfrefle1__e3_75__funct_6)]).

fof(dh_c1_75_1__funct_6,definition,
    ( ~ ( r2_hidden(c1_75_1__funct_6,c1_75__funct_6)
        & ! [A] : 
            ~ ? [B] : 
                ( v1_relat_1(B)
                & v1_funct_1(B)
                & A = B
                & v2_funct_1(B)
                & k1_relat_1(B) = k1_funct_1(c2_75__funct_6,c1_75_1__funct_6)
                & k2_relat_1(B) = k1_funct_1(c3_75__funct_6,c1_75_1__funct_6) ) )
   => ! [C] : 
        ~ ( r2_hidden(C,c1_75__funct_6)
          & ! [D] : 
              ~ ? [E] : 
                  ( v1_relat_1(E)
                  & v1_funct_1(E)
                  & D = E
                  & v2_funct_1(E)
                  & k1_relat_1(E) = k1_funct_1(c2_75__funct_6,C)
                  & k2_relat_1(E) = k1_funct_1(c3_75__funct_6,C) ) ) ),
    introduced(definition,[new_symbol(c1_75_1__funct_6),file(funct_6,c1_75_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_75_1__funct_6)]).

fof(e1_75_1__funct_6,assumption,(
    r2_hidden(c1_75_1__funct_6,c1_75__funct_6) ),
    introduced(assumption,[file(funct_6,e1_75_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e1_75_1__funct_6)]).

fof(dt_c1_75_1__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_75_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_75_1__funct_6)]).

fof(e2_75_1__funct_6,plain,(
    r2_wellord2(k1_funct_1(c2_75__funct_6,c1_75_1__funct_6),k1_funct_1(c3_75__funct_6,c1_75_1__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c1_75_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75_1__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_funct_1,dt_k1_relat_1,dt_c1_75__funct_6,dt_c1_75_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,t1_subset,t7_boole,e1_75_1__funct_6,e1_75__funct_6]),
    [interesting(0.65),file(funct_6,e2_75_1__funct_6),[file(funct_6,e2_75_1__funct_6)]]).

fof(d4_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & k1_relat_1(C) = A
          & k2_relat_1(C) = B ) ) ),
    file(wellord2,d4_wellord2),
    [interesting(0.9),axiom,file(wellord2,d4_wellord2)]).

fof(e3_75_1__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & k1_relat_1(A) = k1_funct_1(c2_75__funct_6,c1_75_1__funct_6)
      & k2_relat_1(A) = k1_funct_1(c3_75__funct_6,c1_75_1__funct_6) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c1_75_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75_1__funct_6,e1_75__funct_6])],[symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,rc1_funct_1,rc3_funct_1,e2_75_1__funct_6,d4_wellord2]),
    [interesting(0.65),file(funct_6,e3_75_1__funct_6),[file(funct_6,e3_75_1__funct_6)]]).

fof(e4_75_1__funct_6,plain,(
    ? [A,B] : 
      ( v1_relat_1(B)
      & v1_funct_1(B)
      & A = B
      & v2_funct_1(B)
      & k1_relat_1(B) = k1_funct_1(c2_75__funct_6,c1_75_1__funct_6)
      & k2_relat_1(B) = k1_funct_1(c3_75__funct_6,c1_75_1__funct_6) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c1_75_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75_1__funct_6,e1_75__funct_6])],[dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,rc1_funct_1,rc3_funct_1,e3_75_1__funct_6]),
    [interesting(0.65),file(funct_6,e4_75_1__funct_6),[file(funct_6,e4_75_1__funct_6)]]).

fof(i3_75_1__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_75_1__funct_6)]),
    [interesting(0.65),trivial,file(funct_6,i3_75_1__funct_6)]).

fof(i2_75_1__funct_6,plain,(
    ? [A,B] : 
      ( v1_relat_1(B)
      & v1_funct_1(B)
      & A = B
      & v2_funct_1(B)
      & k1_relat_1(B) = k1_funct_1(c2_75__funct_6,c1_75_1__funct_6)
      & k2_relat_1(B) = k1_funct_1(c3_75__funct_6,c1_75_1__funct_6) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_75__funct_6,dt_c1_75_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75_1__funct_6,e1_75__funct_6])],[e4_75_1__funct_6,i3_75_1__funct_6]),
    [interesting(0.65),file(funct_6,i2_75_1__funct_6),[file(funct_6,i2_75_1__funct_6)]]).

fof(i1_75_1__funct_6,plain,(
    ~ ( r2_hidden(c1_75_1__funct_6,c1_75__funct_6)
      & ! [A] : 
          ~ ? [B] : 
              ( v1_relat_1(B)
              & v1_funct_1(B)
              & A = B
              & v2_funct_1(B)
              & k1_relat_1(B) = k1_funct_1(c2_75__funct_6,c1_75_1__funct_6)
              & k2_relat_1(B) = k1_funct_1(c3_75__funct_6,c1_75_1__funct_6) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c1_75_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[e1_75_1__funct_6])],[e1_75_1__funct_6,i2_75_1__funct_6]),
    [interesting(0.65),file(funct_6,i1_75_1__funct_6),[file(funct_6,i1_75_1__funct_6)]]).

fof(i1_75_1_tmp__funct_6,plain,(
    ~ ( r2_hidden(c1_75_1__funct_6,c1_75__funct_6)
      & ! [A] : 
          ~ ? [B] : 
              ( v1_relat_1(B)
              & v1_funct_1(B)
              & A = B
              & v2_funct_1(B)
              & k1_relat_1(B) = k1_funct_1(c2_75__funct_6,c1_75_1__funct_6)
              & k2_relat_1(B) = k1_funct_1(c3_75__funct_6,c1_75_1__funct_6) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[dt_c1_75_1__funct_6])],[dt_c1_75_1__funct_6,i1_75_1__funct_6]),
    [interesting(0.8),e2_75__funct_6]).

fof(e2_75__funct_6,plain,(
    ! [A] : 
      ~ ( r2_hidden(A,c1_75__funct_6)
        & ! [B] : 
            ~ ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & B = C
                & v2_funct_1(C)
                & k1_relat_1(C) = k1_funct_1(c2_75__funct_6,A)
                & k2_relat_1(C) = k1_funct_1(c3_75__funct_6,A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[i1_75_1_tmp__funct_6,dh_c1_75_1__funct_6]),
    [interesting(0.8),file(funct_6,e2_75__funct_6),[file(funct_6,e2_75__funct_6)]]).

fof(e3_75__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = c1_75__funct_6
      & ! [B] : 
          ( r2_hidden(B,c1_75__funct_6)
         => ? [C] : 
              ( v1_relat_1(C)
              & v1_funct_1(C)
              & k1_funct_1(A,B) = C
              & v2_funct_1(C)
              & k1_relat_1(C) = k1_funct_1(c2_75__funct_6,B)
              & k2_relat_1(C) = k1_funct_1(c3_75__funct_6,B) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,rc1_funct_1,rc3_funct_1,s1_zfrefle1__e3_75__funct_6,e2_75__funct_6]),
    [interesting(0.8),file(funct_6,e3_75__funct_6),[file(funct_6,e3_75__funct_6)]]).

fof(dt_c4_75__funct_6,plain,
    ( v1_relat_1(c4_75__funct_6)
    & v1_funct_1(c4_75__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[dh_c4_75__funct_6,e3_75__funct_6]),
    [interesting(0.8),file(funct_6,c4_75__funct_6),[file(funct_6,c4_75__funct_6)]]).

fof(e4_75__funct_6,plain,
    ( k1_relat_1(c4_75__funct_6) = c1_75__funct_6
    & ! [A] : 
        ( r2_hidden(A,c1_75__funct_6)
       => ? [B] : 
            ( v1_relat_1(B)
            & v1_funct_1(B)
            & k1_funct_1(c4_75__funct_6,A) = B
            & v2_funct_1(B)
            & k1_relat_1(B) = k1_funct_1(c2_75__funct_6,A)
            & k2_relat_1(B) = k1_funct_1(c3_75__funct_6,A) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[dh_c4_75__funct_6,e3_75__funct_6]),
    [interesting(0.8),file(funct_6,e4_75__funct_6),[file(funct_6,e4_75__funct_6)]]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e2_75_5_1_1__funct_6,plain,(
    ? [A] : 
      ( r2_hidden(A,c1_75__funct_6)
      & k1_xboole_0 = k1_funct_1(c4_75__funct_6,A) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_75_5_1_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,rc3_funct_1,t1_subset,t6_boole,t7_boole,e1_75_5_1_1__funct_6,e4_75__funct_6,d5_funct_1]),
    [interesting(0.35),file(funct_6,e2_75_5_1_1__funct_6),[file(funct_6,e2_75_5_1_1__funct_6)]]).

fof(dt_c1_75_5_1_1__funct_6,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e1_75_5_1_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[dh_c1_75_5_1_1__funct_6,e2_75_5_1_1__funct_6]),
    [interesting(0.35),file(funct_6,c1_75_5_1_1__funct_6),[file(funct_6,c1_75_5_1_1__funct_6)]]).

fof(e3_75_5_1_1__funct_6,plain,
    ( r2_hidden(c1_75_5_1_1__funct_6,c1_75__funct_6)
    & k1_xboole_0 = k1_funct_1(c4_75__funct_6,c1_75_5_1_1__funct_6) ),
    inference(consider,[status(thm),assumptions([e1_75_5_1_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[dh_c1_75_5_1_1__funct_6,e2_75_5_1_1__funct_6]),
    [interesting(0.35),file(funct_6,e3_75_5_1_1__funct_6),[file(funct_6,e3_75_5_1_1__funct_6)]]).

fof(e4_75_5_1_1__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_xboole_0 = A
      & v2_funct_1(A)
      & k1_relat_1(A) = k1_funct_1(c2_75__funct_6,c1_75_5_1_1__funct_6)
      & k2_relat_1(A) = k1_funct_1(c3_75__funct_6,c1_75_5_1_1__funct_6) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_75_5_1_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_75__funct_6,dt_c1_75_5_1_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,rc3_funct_1,t1_subset,t6_boole,t7_boole,e4_75__funct_6,e3_75_5_1_1__funct_6]),
    [interesting(0.35),file(funct_6,e4_75_5_1_1__funct_6),[file(funct_6,e4_75_5_1_1__funct_6)]]).

fof(t60_relat_1,theorem,
    ( k1_relat_1(k1_xboole_0) = k1_xboole_0
    & k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(relat_1,t60_relat_1),
    [interesting(0.9),axiom,file(relat_1,t60_relat_1)]).

fof(e5_75_5_1_1__funct_6,plain,
    ( r2_hidden(k1_xboole_0,k2_relat_1(c2_75__funct_6))
    & r2_hidden(k1_xboole_0,k2_relat_1(c3_75__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([e1_75_5_1_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_75__funct_6,dt_c1_75_5_1_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,rc3_funct_1,t1_subset,t6_boole,t7_boole,e4_75_5_1_1__funct_6,e1_75__funct_6,e3_75_5_1_1__funct_6,d5_funct_1,t60_relat_1]),
    [interesting(0.35),file(funct_6,e5_75_5_1_1__funct_6),[file(funct_6,e5_75_5_1_1__funct_6)]]).

fof(t37_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k4_card_3(A) = k1_xboole_0
      <=> r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) ),
    file(card_3,t37_card_3),
    [interesting(0.9),axiom,file(card_3,t37_card_3)]).

fof(e6_75_5_1_1__funct_6,plain,
    ( k4_card_3(c2_75__funct_6) = k1_xboole_0
    & k4_card_3(c3_75__funct_6) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e1_75_5_1_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc6_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_relat_1,dt_k4_card_3,dt_c2_75__funct_6,dt_c3_75__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,t1_subset,t6_boole,t7_boole,e5_75_5_1_1__funct_6,t37_card_3]),
    [interesting(0.35),file(funct_6,e6_75_5_1_1__funct_6),[file(funct_6,e6_75_5_1_1__funct_6)]]).

fof(e7_75_5_1_1__funct_6,plain,(
    r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([e1_75_5_1_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,t1_subset,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_xboole_0,dt_k4_card_3,dt_c2_75__funct_6,dt_c3_75__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,t6_boole,e6_75_5_1_1__funct_6]),
    [interesting(0.35),file(funct_6,e7_75_5_1_1__funct_6),[file(funct_6,e7_75_5_1_1__funct_6)]]).

fof(i2_75_5_1_1__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i2_75_5_1_1__funct_6)]),
    [interesting(0.35),trivial,file(funct_6,i2_75_5_1_1__funct_6)]).

fof(i1_75_5_1_1__funct_6,plain,(
    r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(conclusion,[status(thm),assumptions([e1_75_5_1_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[e7_75_5_1_1__funct_6,i2_75_5_1_1__funct_6]),
    [interesting(0.35),file(funct_6,i1_75_5_1_1__funct_6),[file(funct_6,i1_75_5_1_1__funct_6)]]).

fof(i1_75_5_1__funct_6,plain,
    ( r2_hidden(k1_xboole_0,k2_relat_1(c4_75__funct_6))
   => r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[e1_75_5_1_1__funct_6])],[e1_75_5_1_1__funct_6,i1_75_5_1_1__funct_6]),
    [interesting(0.5),file(funct_6,i1_75_5_1__funct_6),[file(funct_6,i1_75_5_1__funct_6)]]).

fof(e1_75_5_1_2__funct_6,assumption,(
    ~ r2_hidden(k1_xboole_0,k2_relat_1(c4_75__funct_6)) ),
    introduced(assumption,[file(funct_6,e1_75_5_1_2__funct_6)]),
    [interesting(0.35),axiom,file(funct_6,e1_75_5_1_2__funct_6)]).

fof(dt_k7_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_funct_6(A))
        & v1_funct_1(k7_funct_6(A)) ) ) ),
    file(funct_6,k7_funct_6),
    [interesting(0.9),axiom,file(funct_6,k7_funct_6)]).

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(fc18_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k10_relat_1(A,B)) ) ),
    file(finseq_1,fc18_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc18_finseq_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_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    [interesting(0.9),axiom,file(relat_1,k10_relat_1)]).

fof(dt_k1_funct_6,axiom,(
    $true ),
    file(funct_6,k1_funct_6),
    [interesting(0.9),axiom,file(funct_6,k1_funct_6)]).

fof(dt_k2_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_6(A))
        & v1_funct_1(k2_funct_6(A)) ) ) ),
    file(funct_6,k2_funct_6),
    [interesting(0.9),axiom,file(funct_6,k2_funct_6)]).

fof(dt_k3_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_funct_6(A))
        & v1_funct_1(k3_funct_6(A)) ) ) ),
    file(funct_6,k3_funct_6),
    [interesting(0.9),axiom,file(funct_6,k3_funct_6)]).

fof(dt_k4_funct_5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k4_funct_5(A))
        & v1_funct_1(k4_funct_5(A)) ) ) ),
    file(funct_5,k4_funct_5),
    [interesting(0.9),axiom,file(funct_5,k4_funct_5)]).

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(dh_c1_75_3__funct_6,definition,
    ( ( r2_hidden(c1_75_3__funct_6,c1_75__funct_6)
     => k1_funct_1(k2_funct_6(c4_75__funct_6),c1_75_3__funct_6) = k1_funct_1(c2_75__funct_6,c1_75_3__funct_6) )
   => ! [A] : 
        ( r2_hidden(A,c1_75__funct_6)
       => k1_funct_1(k2_funct_6(c4_75__funct_6),A) = k1_funct_1(c2_75__funct_6,A) ) ),
    introduced(definition,[new_symbol(c1_75_3__funct_6),file(funct_6,c1_75_3__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_75_3__funct_6)]).

fof(e1_75_3__funct_6,assumption,(
    r2_hidden(c1_75_3__funct_6,c1_75__funct_6) ),
    introduced(assumption,[file(funct_6,e1_75_3__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e1_75_3__funct_6)]).

fof(dt_c1_75_3__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_75_3__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_75_3__funct_6)]).

fof(e2_75_3__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_funct_1(c4_75__funct_6,c1_75_3__funct_6) = A
      & v2_funct_1(A)
      & k1_relat_1(A) = k1_funct_1(c2_75__funct_6,c1_75_3__funct_6)
      & k2_relat_1(A) = k1_funct_1(c3_75__funct_6,c1_75_3__funct_6) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_3__funct_6,e1_75_3__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75__funct_6,dt_c1_75_3__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e1_75_3__funct_6,e4_75__funct_6]),
    [interesting(0.65),file(funct_6,e2_75_3__funct_6),[file(funct_6,e2_75_3__funct_6)]]).

fof(t31_funct_6,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r2_hidden(A,k1_relat_1(B))
              & C = k1_funct_1(B,A) )
           => ( r2_hidden(A,k1_relat_1(k2_funct_6(B)))
              & k1_funct_1(k2_funct_6(B),A) = k1_relat_1(C)
              & r2_hidden(A,k1_relat_1(k3_funct_6(B)))
              & k1_funct_1(k3_funct_6(B),A) = k2_relat_1(C) ) ) ) ) ),
    file(funct_6,t31_funct_6),
    [interesting(0.9),axiom,file(funct_6,t31_funct_6)]).

fof(e3_75_3__funct_6,plain,(
    k1_funct_1(k2_funct_6(c4_75__funct_6),c1_75_3__funct_6) = k1_funct_1(c2_75__funct_6,c1_75_3__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_3__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6,e1_75_3__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k3_funct_6,dt_c1_75__funct_6,dt_c1_75_3__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e2_75_3__funct_6,e4_75__funct_6,e1_75_3__funct_6,t31_funct_6]),
    [interesting(0.65),file(funct_6,e3_75_3__funct_6),[file(funct_6,e3_75_3__funct_6)]]).

fof(i3_75_3__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_75_3__funct_6)]),
    [interesting(0.65),trivial,file(funct_6,i3_75_3__funct_6)]).

fof(i2_75_3__funct_6,plain,(
    k1_funct_1(k2_funct_6(c4_75__funct_6),c1_75_3__funct_6) = k1_funct_1(c2_75__funct_6,c1_75_3__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_75_3__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6,e1_75_3__funct_6])],[e3_75_3__funct_6,i3_75_3__funct_6]),
    [interesting(0.65),file(funct_6,i2_75_3__funct_6),[file(funct_6,i2_75_3__funct_6)]]).

fof(i1_75_3__funct_6,plain,
    ( r2_hidden(c1_75_3__funct_6,c1_75__funct_6)
   => k1_funct_1(k2_funct_6(c4_75__funct_6),c1_75_3__funct_6) = k1_funct_1(c2_75__funct_6,c1_75_3__funct_6) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75_3__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[e1_75_3__funct_6])],[e1_75_3__funct_6,i2_75_3__funct_6]),
    [interesting(0.65),file(funct_6,i1_75_3__funct_6),[file(funct_6,i1_75_3__funct_6)]]).

fof(i1_75_3_tmp__funct_6,plain,
    ( r2_hidden(c1_75_3__funct_6,c1_75__funct_6)
   => k1_funct_1(k2_funct_6(c4_75__funct_6),c1_75_3__funct_6) = k1_funct_1(c2_75__funct_6,c1_75_3__funct_6) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[dt_c1_75_3__funct_6])],[dt_c1_75_3__funct_6,i1_75_3__funct_6]),
    [interesting(0.8),e9_75__funct_6]).

fof(e9_75__funct_6,plain,(
    ! [A] : 
      ( r2_hidden(A,c1_75__funct_6)
     => k1_funct_1(k2_funct_6(c4_75__funct_6),A) = k1_funct_1(c2_75__funct_6,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[i1_75_3_tmp__funct_6,dh_c1_75_3__funct_6]),
    [interesting(0.8),file(funct_6,e9_75__funct_6),[file(funct_6,e9_75__funct_6)]]).

fof(dt_k1_funct_5,axiom,(
    $true ),
    file(funct_5,k1_funct_5),
    [interesting(0.9),axiom,file(funct_5,k1_funct_5)]).

fof(dt_k2_funct_5,axiom,(
    $true ),
    file(funct_5,k2_funct_5),
    [interesting(0.9),axiom,file(funct_5,k2_funct_5)]).

fof(dh_c1_75_2__funct_6,definition,
    ( ( r2_hidden(c1_75_2__funct_6,k2_relat_1(c4_75__funct_6))
     => ( v1_relat_1(c1_75_2__funct_6)
        & v1_funct_1(c1_75_2__funct_6) ) )
   => ! [A] : 
        ( r2_hidden(A,k2_relat_1(c4_75__funct_6))
       => ( v1_relat_1(A)
          & v1_funct_1(A) ) ) ),
    introduced(definition,[new_symbol(c1_75_2__funct_6),file(funct_6,c1_75_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_75_2__funct_6)]).

fof(e1_75_2__funct_6,assumption,(
    r2_hidden(c1_75_2__funct_6,k2_relat_1(c4_75__funct_6)) ),
    introduced(assumption,[file(funct_6,e1_75_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e1_75_2__funct_6)]).

fof(dt_c1_75_2__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_75_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_75_2__funct_6)]).

fof(dh_c2_75_2__funct_6,definition,
    ( ? [A] : 
        ( r2_hidden(A,c1_75__funct_6)
        & c1_75_2__funct_6 = k1_funct_1(c4_75__funct_6,A) )
   => ( r2_hidden(c2_75_2__funct_6,c1_75__funct_6)
      & c1_75_2__funct_6 = k1_funct_1(c4_75__funct_6,c2_75_2__funct_6) ) ),
    introduced(definition,[new_symbol(c2_75_2__funct_6),file(funct_6,c2_75_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c2_75_2__funct_6)]).

fof(e2_75_2__funct_6,plain,(
    ? [A] : 
      ( r2_hidden(A,c1_75__funct_6)
      & c1_75_2__funct_6 = k1_funct_1(c4_75__funct_6,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_2__funct_6,e1_75_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75__funct_6,dt_c1_75_2__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e1_75_2__funct_6,e4_75__funct_6,d5_funct_1]),
    [interesting(0.65),file(funct_6,e2_75_2__funct_6),[file(funct_6,e2_75_2__funct_6)]]).

fof(dt_c2_75_2__funct_6,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_75_2__funct_6,e1_75_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[dh_c2_75_2__funct_6,e2_75_2__funct_6]),
    [interesting(0.65),file(funct_6,c2_75_2__funct_6),[file(funct_6,c2_75_2__funct_6)]]).

fof(e3_75_2__funct_6,plain,
    ( r2_hidden(c2_75_2__funct_6,c1_75__funct_6)
    & c1_75_2__funct_6 = k1_funct_1(c4_75__funct_6,c2_75_2__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c1_75_2__funct_6,e1_75_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[dh_c2_75_2__funct_6,e2_75_2__funct_6]),
    [interesting(0.65),file(funct_6,e3_75_2__funct_6),[file(funct_6,e3_75_2__funct_6)]]).

fof(e4_75_2__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & c1_75_2__funct_6 = A
      & v2_funct_1(A)
      & k1_relat_1(A) = k1_funct_1(c2_75__funct_6,c2_75_2__funct_6)
      & k2_relat_1(A) = k1_funct_1(c3_75__funct_6,c2_75_2__funct_6) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_2__funct_6,e1_75_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75__funct_6,dt_c1_75_2__funct_6,dt_c2_75__funct_6,dt_c2_75_2__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e4_75__funct_6,e3_75_2__funct_6]),
    [interesting(0.65),file(funct_6,e4_75_2__funct_6),[file(funct_6,e4_75_2__funct_6)]]).

fof(e5_75_2__funct_6,plain,
    ( v1_relat_1(c1_75_2__funct_6)
    & v1_funct_1(c1_75_2__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_2__funct_6,e1_75_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75_2__funct_6,dt_c2_75__funct_6,dt_c2_75_2__funct_6,dt_c3_75__funct_6,rc1_funct_1,rc3_funct_1,e4_75_2__funct_6]),
    [interesting(0.65),file(funct_6,e5_75_2__funct_6),[file(funct_6,e5_75_2__funct_6)]]).

fof(i3_75_2__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_75_2__funct_6)]),
    [interesting(0.65),trivial,file(funct_6,i3_75_2__funct_6)]).

fof(i2_75_2__funct_6,plain,
    ( v1_relat_1(c1_75_2__funct_6)
    & v1_funct_1(c1_75_2__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_75_2__funct_6,e1_75_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[e5_75_2__funct_6,i3_75_2__funct_6]),
    [interesting(0.65),file(funct_6,i2_75_2__funct_6),[file(funct_6,i2_75_2__funct_6)]]).

fof(i1_75_2__funct_6,plain,
    ( r2_hidden(c1_75_2__funct_6,k2_relat_1(c4_75__funct_6))
   => ( v1_relat_1(c1_75_2__funct_6)
      & v1_funct_1(c1_75_2__funct_6) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[e1_75_2__funct_6])],[e1_75_2__funct_6,i2_75_2__funct_6]),
    [interesting(0.65),file(funct_6,i1_75_2__funct_6),[file(funct_6,i1_75_2__funct_6)]]).

fof(i1_75_2_tmp__funct_6,plain,
    ( r2_hidden(c1_75_2__funct_6,k2_relat_1(c4_75__funct_6))
   => ( v1_relat_1(c1_75_2__funct_6)
      & v1_funct_1(c1_75_2__funct_6) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[dt_c1_75_2__funct_6])],[dt_c1_75_2__funct_6,i1_75_2__funct_6]),
    [interesting(0.8),e5_75__funct_6]).

fof(e5_75__funct_6,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_relat_1(c4_75__funct_6))
     => ( v1_relat_1(A)
        & v1_funct_1(A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[i1_75_2_tmp__funct_6,dh_c1_75_2__funct_6]),
    [interesting(0.8),file(funct_6,e5_75__funct_6),[file(funct_6,e5_75__funct_6)]]).

fof(l30_funct_6,plain,(
    ! [A] : 
      ( ! [B] : 
          ( r2_hidden(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) )
     => k1_funct_6(A) = A ) ),
    file(funct_6,l30_funct_6),
    [interesting(0.9),axiom,file(funct_6,l30_funct_6)]).

fof(e6_75__funct_6,plain,(
    k1_funct_6(k2_relat_1(c4_75__funct_6)) = k2_relat_1(c4_75__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc6_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_6,dt_k2_relat_1,dt_c4_75__funct_6,rc1_funct_1,t1_subset,t7_boole,e5_75__funct_6,l30_funct_6]),
    [interesting(0.8),file(funct_6,e6_75__funct_6),[file(funct_6,e6_75__funct_6)]]).

fof(t169_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A) ) ),
    file(relat_1,t169_relat_1),
    [interesting(0.9),axiom,file(relat_1,t169_relat_1)]).

fof(e7_75__funct_6,plain,(
    k10_relat_1(c4_75__funct_6,k1_funct_6(k2_relat_1(c4_75__funct_6))) = c1_75__funct_6 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e6_75__funct_6,e4_75__funct_6,t169_relat_1]),
    [interesting(0.8),file(funct_6,e7_75__funct_6),[file(funct_6,e7_75__funct_6)]]).

fof(d2_funct_6,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k2_funct_6(A)
          <=> ( k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))
              & ! [C] : 
                  ( r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A))))
                 => k1_funct_1(B,C) = k1_funct_5(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(funct_6,d2_funct_6),
    [interesting(0.9),axiom,file(funct_6,d2_funct_6)]).

fof(d3_funct_6,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k3_funct_6(A)
          <=> ( k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))
              & ! [C] : 
                  ( r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A))))
                 => k1_funct_1(B,C) = k2_funct_5(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(funct_6,d3_funct_6),
    [interesting(0.9),axiom,file(funct_6,d3_funct_6)]).

fof(e8_75__funct_6,plain,
    ( k1_relat_1(k2_funct_6(c4_75__funct_6)) = c1_75__funct_6
    & k1_relat_1(k3_funct_6(c4_75__funct_6)) = c1_75__funct_6 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_5,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_5,dt_k2_funct_6,dt_k2_relat_1,dt_k3_funct_6,dt_c1_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,t1_subset,t7_boole,e7_75__funct_6,d2_funct_6,d3_funct_6]),
    [interesting(0.8),file(funct_6,e8_75__funct_6),[file(funct_6,e8_75__funct_6)]]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.9),axiom,file(funct_1,t9_funct_1)]).

fof(e10_75__funct_6,plain,(
    k2_funct_6(c4_75__funct_6) = c2_75__funct_6 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_6,dt_k3_funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,t1_subset,t7_boole,e9_75__funct_6,e1_75__funct_6,e8_75__funct_6,t9_funct_1]),
    [interesting(0.8),file(funct_6,e10_75__funct_6),[file(funct_6,e10_75__funct_6)]]).

fof(dh_c1_75_4__funct_6,definition,
    ( ( r2_hidden(c1_75_4__funct_6,c1_75__funct_6)
     => k1_funct_1(k3_funct_6(c4_75__funct_6),c1_75_4__funct_6) = k1_funct_1(c3_75__funct_6,c1_75_4__funct_6) )
   => ! [A] : 
        ( r2_hidden(A,c1_75__funct_6)
       => k1_funct_1(k3_funct_6(c4_75__funct_6),A) = k1_funct_1(c3_75__funct_6,A) ) ),
    introduced(definition,[new_symbol(c1_75_4__funct_6),file(funct_6,c1_75_4__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_75_4__funct_6)]).

fof(e1_75_4__funct_6,assumption,(
    r2_hidden(c1_75_4__funct_6,c1_75__funct_6) ),
    introduced(assumption,[file(funct_6,e1_75_4__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e1_75_4__funct_6)]).

fof(dt_c1_75_4__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_75_4__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_75_4__funct_6)]).

fof(e2_75_4__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_funct_1(c4_75__funct_6,c1_75_4__funct_6) = A
      & v2_funct_1(A)
      & k1_relat_1(A) = k1_funct_1(c2_75__funct_6,c1_75_4__funct_6)
      & k2_relat_1(A) = k1_funct_1(c3_75__funct_6,c1_75_4__funct_6) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_4__funct_6,e1_75_4__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75__funct_6,dt_c1_75_4__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e1_75_4__funct_6,e4_75__funct_6]),
    [interesting(0.65),file(funct_6,e2_75_4__funct_6),[file(funct_6,e2_75_4__funct_6)]]).

fof(e3_75_4__funct_6,plain,(
    k1_funct_1(k3_funct_6(c4_75__funct_6),c1_75_4__funct_6) = k1_funct_1(c3_75__funct_6,c1_75_4__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_4__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6,e1_75_4__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k3_funct_6,dt_c1_75__funct_6,dt_c1_75_4__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e2_75_4__funct_6,e4_75__funct_6,e1_75_4__funct_6,t31_funct_6]),
    [interesting(0.65),file(funct_6,e3_75_4__funct_6),[file(funct_6,e3_75_4__funct_6)]]).

fof(i3_75_4__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_75_4__funct_6)]),
    [interesting(0.65),trivial,file(funct_6,i3_75_4__funct_6)]).

fof(i2_75_4__funct_6,plain,(
    k1_funct_1(k3_funct_6(c4_75__funct_6),c1_75_4__funct_6) = k1_funct_1(c3_75__funct_6,c1_75_4__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_75_4__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6,e1_75_4__funct_6])],[e3_75_4__funct_6,i3_75_4__funct_6]),
    [interesting(0.65),file(funct_6,i2_75_4__funct_6),[file(funct_6,i2_75_4__funct_6)]]).

fof(i1_75_4__funct_6,plain,
    ( r2_hidden(c1_75_4__funct_6,c1_75__funct_6)
   => k1_funct_1(k3_funct_6(c4_75__funct_6),c1_75_4__funct_6) = k1_funct_1(c3_75__funct_6,c1_75_4__funct_6) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75_4__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[e1_75_4__funct_6])],[e1_75_4__funct_6,i2_75_4__funct_6]),
    [interesting(0.65),file(funct_6,i1_75_4__funct_6),[file(funct_6,i1_75_4__funct_6)]]).

fof(i1_75_4_tmp__funct_6,plain,
    ( r2_hidden(c1_75_4__funct_6,c1_75__funct_6)
   => k1_funct_1(k3_funct_6(c4_75__funct_6),c1_75_4__funct_6) = k1_funct_1(c3_75__funct_6,c1_75_4__funct_6) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[dt_c1_75_4__funct_6])],[dt_c1_75_4__funct_6,i1_75_4__funct_6]),
    [interesting(0.8),e11_75__funct_6]).

fof(e11_75__funct_6,plain,(
    ! [A] : 
      ( r2_hidden(A,c1_75__funct_6)
     => k1_funct_1(k3_funct_6(c4_75__funct_6),A) = k1_funct_1(c3_75__funct_6,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[i1_75_4_tmp__funct_6,dh_c1_75_4__funct_6]),
    [interesting(0.8),file(funct_6,e11_75__funct_6),[file(funct_6,e11_75__funct_6)]]).

fof(e12_75__funct_6,plain,(
    k3_funct_6(c4_75__funct_6) = c3_75__funct_6 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_6,dt_k3_funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,t1_subset,t7_boole,e11_75__funct_6,e1_75__funct_6,e8_75__funct_6,t9_funct_1]),
    [interesting(0.8),file(funct_6,e12_75__funct_6),[file(funct_6,e12_75__funct_6)]]).

fof(dh_c1_75_5_1_2_1__funct_6,definition,
    ( ( ( v1_relat_1(c1_75_5_1_2_1__funct_6)
        & v1_funct_1(c1_75_5_1_2_1__funct_6) )
     => ( r2_hidden(c1_75_5_1_2_1__funct_6,k2_relat_1(c4_75__funct_6))
       => v2_funct_1(c1_75_5_1_2_1__funct_6) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r2_hidden(A,k2_relat_1(c4_75__funct_6))
         => v2_funct_1(A) ) ) ),
    introduced(definition,[new_symbol(c1_75_5_1_2_1__funct_6),file(funct_6,c1_75_5_1_2_1__funct_6)]),
    [interesting(0.2),axiom,file(funct_6,c1_75_5_1_2_1__funct_6)]).

fof(e1_75_5_1_2_1__funct_6,assumption,(
    r2_hidden(c1_75_5_1_2_1__funct_6,k2_relat_1(c4_75__funct_6)) ),
    introduced(assumption,[file(funct_6,e1_75_5_1_2_1__funct_6)]),
    [interesting(0.2),axiom,file(funct_6,e1_75_5_1_2_1__funct_6)]).

fof(dt_c1_75_5_1_2_1__funct_6,assumption,
    ( v1_relat_1(c1_75_5_1_2_1__funct_6)
    & v1_funct_1(c1_75_5_1_2_1__funct_6) ),
    introduced(assumption,[file(funct_6,c1_75_5_1_2_1__funct_6)]),
    [interesting(0.2),axiom,file(funct_6,c1_75_5_1_2_1__funct_6)]).

fof(dh_c2_75_5_1_2_1__funct_6,definition,
    ( ? [A] : 
        ( r2_hidden(A,c1_75__funct_6)
        & c1_75_5_1_2_1__funct_6 = k1_funct_1(c4_75__funct_6,A) )
   => ( r2_hidden(c2_75_5_1_2_1__funct_6,c1_75__funct_6)
      & c1_75_5_1_2_1__funct_6 = k1_funct_1(c4_75__funct_6,c2_75_5_1_2_1__funct_6) ) ),
    introduced(definition,[new_symbol(c2_75_5_1_2_1__funct_6),file(funct_6,c2_75_5_1_2_1__funct_6)]),
    [interesting(0.2),axiom,file(funct_6,c2_75_5_1_2_1__funct_6)]).

fof(e2_75_5_1_2_1__funct_6,plain,(
    ? [A] : 
      ( r2_hidden(A,c1_75__funct_6)
      & c1_75_5_1_2_1__funct_6 = k1_funct_1(c4_75__funct_6,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_5_1_2_1__funct_6,e1_75_5_1_2_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75__funct_6,dt_c1_75_5_1_2_1__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e1_75_5_1_2_1__funct_6,e4_75__funct_6,d5_funct_1]),
    [interesting(0.2),file(funct_6,e2_75_5_1_2_1__funct_6),[file(funct_6,e2_75_5_1_2_1__funct_6)]]).

fof(dt_c2_75_5_1_2_1__funct_6,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_75_5_1_2_1__funct_6,e1_75_5_1_2_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[dh_c2_75_5_1_2_1__funct_6,e2_75_5_1_2_1__funct_6]),
    [interesting(0.2),file(funct_6,c2_75_5_1_2_1__funct_6),[file(funct_6,c2_75_5_1_2_1__funct_6)]]).

fof(e3_75_5_1_2_1__funct_6,plain,
    ( r2_hidden(c2_75_5_1_2_1__funct_6,c1_75__funct_6)
    & c1_75_5_1_2_1__funct_6 = k1_funct_1(c4_75__funct_6,c2_75_5_1_2_1__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c1_75_5_1_2_1__funct_6,e1_75_5_1_2_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[dh_c2_75_5_1_2_1__funct_6,e2_75_5_1_2_1__funct_6]),
    [interesting(0.2),file(funct_6,e3_75_5_1_2_1__funct_6),[file(funct_6,e3_75_5_1_2_1__funct_6)]]).

fof(e4_75_5_1_2_1__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_funct_1(c4_75__funct_6,c2_75_5_1_2_1__funct_6) = A
      & v2_funct_1(A)
      & k1_relat_1(A) = k1_funct_1(c2_75__funct_6,c2_75_5_1_2_1__funct_6)
      & k2_relat_1(A) = k1_funct_1(c3_75__funct_6,c2_75_5_1_2_1__funct_6) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_5_1_2_1__funct_6,e1_75_5_1_2_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75__funct_6,dt_c1_75_5_1_2_1__funct_6,dt_c2_75__funct_6,dt_c2_75_5_1_2_1__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e4_75__funct_6,e3_75_5_1_2_1__funct_6]),
    [interesting(0.2),file(funct_6,e4_75_5_1_2_1__funct_6),[file(funct_6,e4_75_5_1_2_1__funct_6)]]).

fof(e5_75_5_1_2_1__funct_6,plain,(
    v2_funct_1(c1_75_5_1_2_1__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75_5_1_2_1__funct_6,e1_75_5_1_2_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_75__funct_6,dt_c1_75_5_1_2_1__funct_6,dt_c2_75__funct_6,dt_c2_75_5_1_2_1__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e4_75_5_1_2_1__funct_6,e3_75_5_1_2_1__funct_6]),
    [interesting(0.2),file(funct_6,e5_75_5_1_2_1__funct_6),[file(funct_6,e5_75_5_1_2_1__funct_6)]]).

fof(i3_75_5_1_2_1__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_75_5_1_2_1__funct_6)]),
    [interesting(0.2),trivial,file(funct_6,i3_75_5_1_2_1__funct_6)]).

fof(i2_75_5_1_2_1__funct_6,plain,(
    v2_funct_1(c1_75_5_1_2_1__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_75_5_1_2_1__funct_6,e1_75_5_1_2_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[e5_75_5_1_2_1__funct_6,i3_75_5_1_2_1__funct_6]),
    [interesting(0.2),file(funct_6,i2_75_5_1_2_1__funct_6),[file(funct_6,i2_75_5_1_2_1__funct_6)]]).

fof(i1_75_5_1_2_1__funct_6,plain,
    ( r2_hidden(c1_75_5_1_2_1__funct_6,k2_relat_1(c4_75__funct_6))
   => v2_funct_1(c1_75_5_1_2_1__funct_6) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75_5_1_2_1__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[e1_75_5_1_2_1__funct_6])],[e1_75_5_1_2_1__funct_6,i2_75_5_1_2_1__funct_6]),
    [interesting(0.2),file(funct_6,i1_75_5_1_2_1__funct_6),[file(funct_6,i1_75_5_1_2_1__funct_6)]]).

fof(i1_75_5_1_2_1_tmp__funct_6,plain,
    ( ( v1_relat_1(c1_75_5_1_2_1__funct_6)
      & v1_funct_1(c1_75_5_1_2_1__funct_6) )
   => ( r2_hidden(c1_75_5_1_2_1__funct_6,k2_relat_1(c4_75__funct_6))
     => v2_funct_1(c1_75_5_1_2_1__funct_6) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[dt_c1_75_5_1_2_1__funct_6])],[dt_c1_75_5_1_2_1__funct_6,i1_75_5_1_2_1__funct_6]),
    [interesting(0.35),e2_75_5_1_2__funct_6]).

fof(e2_75_5_1_2__funct_6,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( r2_hidden(A,k2_relat_1(c4_75__funct_6))
       => v2_funct_1(A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[i1_75_5_1_2_1_tmp__funct_6,dh_c1_75_5_1_2_1__funct_6]),
    [interesting(0.35),file(funct_6,e2_75_5_1_2__funct_6),[file(funct_6,e2_75_5_1_2__funct_6)]]).

fof(d7_funct_6,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k7_funct_6(A)
          <=> ( k1_relat_1(B) = k4_card_3(k2_funct_6(A))
              & ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C) )
                 => ~ ( r2_hidden(C,k4_card_3(k2_funct_6(A)))
                      & ! [D] : 
                          ( ( v1_relat_1(D)
                            & v1_funct_1(D) )
                         => ~ ( k1_funct_1(B,C) = D
                              & k1_relat_1(D) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))
                              & ! [E] : 
                                  ( r2_hidden(E,k1_relat_1(D))
                                 => k1_funct_1(D,E) = k1_funct_1(k4_funct_5(A),k4_tarski(E,k1_funct_1(C,E))) ) ) ) ) ) ) ) ) ) ),
    file(funct_6,d7_funct_6),
    [interesting(0.9),axiom,file(funct_6,d7_funct_6)]).

fof(t58_funct_6,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k2_relat_1(k7_funct_6(A)) = k4_card_3(k3_funct_6(A)) ) ),
    file(funct_6,t58_funct_6),
    [interesting(0.9),axiom,file(funct_6,t58_funct_6)]).

fof(t59_funct_6,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ r2_hidden(k1_xboole_0,k2_relat_1(A))
       => ( v2_funct_1(k7_funct_6(A))
        <=> ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ( r2_hidden(B,k2_relat_1(A))
               => v2_funct_1(B) ) ) ) ) ) ),
    file(funct_6,t59_funct_6),
    [interesting(0.9),axiom,file(funct_6,t59_funct_6)]).

fof(e1_75_5_1_2_2__funct_6,plain,
    ( v2_funct_1(k7_funct_6(c4_75__funct_6))
    & k1_relat_1(k7_funct_6(c4_75__funct_6)) = k4_card_3(c2_75__funct_6)
    & k2_relat_1(k7_funct_6(c4_75__funct_6)) = k4_card_3(c3_75__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([e1_75_5_1_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,fc2_subset_1,fc3_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_funct_6,dt_k2_relat_1,dt_k3_funct_6,dt_k4_card_3,dt_k4_funct_5,dt_k4_tarski,dt_k7_funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,rc3_funct_1,t1_subset,t6_boole,t7_boole,d5_tarski,e10_75__funct_6,e12_75__funct_6,e1_75_5_1_2__funct_6,e2_75_5_1_2__funct_6,d7_funct_6,t58_funct_6,t59_funct_6]),
    [interesting(0.2),file(funct_6,e1_75_5_1_2_2__funct_6),[file(funct_6,e1_75_5_1_2_2__funct_6)]]).

fof(i2_75_5_1_2_2__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i2_75_5_1_2_2__funct_6)]),
    [interesting(0.2),trivial,file(funct_6,i2_75_5_1_2_2__funct_6)]).

fof(i1_75_5_1_2_2__funct_6,plain,
    ( v2_funct_1(k7_funct_6(c4_75__funct_6))
    & k1_relat_1(k7_funct_6(c4_75__funct_6)) = k4_card_3(c2_75__funct_6)
    & k2_relat_1(k7_funct_6(c4_75__funct_6)) = k4_card_3(c3_75__funct_6) ),
    inference(conclusion,[status(thm),assumptions([e1_75_5_1_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[e1_75_5_1_2_2__funct_6,i2_75_5_1_2_2__funct_6]),
    [interesting(0.2),file(funct_6,i1_75_5_1_2_2__funct_6),[file(funct_6,i1_75_5_1_2_2__funct_6)]]).

fof(e3_75_5_1_2__funct_6,plain,(
    r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(take,[status(thm),assumptions([e1_75_5_1_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_relat_1,dt_k2_relat_1,dt_k4_card_3,dt_k7_funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,dt_c4_75__funct_6,rc1_funct_1,rc3_funct_1,d4_wellord2,i1_75_5_1_2_2__funct_6]),
    [interesting(0.35),file(funct_6,e3_75_5_1_2__funct_6),[file(funct_6,e3_75_5_1_2__funct_6)]]).

fof(i2_75_5_1_2__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i2_75_5_1_2__funct_6)]),
    [interesting(0.35),trivial,file(funct_6,i2_75_5_1_2__funct_6)]).

fof(i1_75_5_1_2__funct_6,plain,(
    r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(conclusion,[status(thm),assumptions([e1_75_5_1_2__funct_6,dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[e3_75_5_1_2__funct_6,i2_75_5_1_2__funct_6]),
    [interesting(0.35),file(funct_6,i1_75_5_1_2__funct_6),[file(funct_6,i1_75_5_1_2__funct_6)]]).

fof(i2_75_5_1__funct_6,plain,
    ( ~ r2_hidden(k1_xboole_0,k2_relat_1(c4_75__funct_6))
   => r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6]),discharge_asm(discharge,[e1_75_5_1_2__funct_6])],[e1_75_5_1_2__funct_6,i1_75_5_1_2__funct_6]),
    [interesting(0.5),file(funct_6,i2_75_5_1__funct_6),[file(funct_6,i2_75_5_1__funct_6)]]).

fof(e1_75_5_1__funct_6,plain,(
    ~ ( ~ r2_hidden(k1_xboole_0,k2_relat_1(c4_75__funct_6))
      & r2_hidden(k1_xboole_0,k2_relat_1(c4_75__funct_6)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc6_relat_1,fc8_relat_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_relat_1,dt_c4_75__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,t1_subset,t6_boole,t7_boole]),
    [interesting(0.5),file(funct_6,e1_75_5_1__funct_6),[file(funct_6,e1_75_5_1__funct_6)]]).

fof(e13_75__funct_6,plain,(
    r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(percases,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[i1_75_5_1__funct_6,i2_75_5_1__funct_6,e1_75_5_1__funct_6]),
    [interesting(0.8),file(funct_6,e13_75__funct_6),[file(funct_6,e13_75__funct_6)]]).

fof(e14_75__funct_6,plain,(
    r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[rc1_funct_1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k4_card_3,dt_c2_75__funct_6,dt_c3_75__funct_6,e13_75__funct_6]),
    [interesting(0.8),file(funct_6,e14_75__funct_6),[file(funct_6,e14_75__funct_6)]]).

fof(i5_75__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i5_75__funct_6)]),
    [interesting(0.8),trivial,file(funct_6,i5_75__funct_6)]).

fof(i4_75__funct_6,plain,(
    r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6,e1_75__funct_6])],[e14_75__funct_6,i5_75__funct_6]),
    [interesting(0.8),file(funct_6,i4_75__funct_6),[file(funct_6,i4_75__funct_6)]]).

fof(i3_75__funct_6,plain,
    ( ( k1_relat_1(c2_75__funct_6) = c1_75__funct_6
      & k1_relat_1(c3_75__funct_6) = c1_75__funct_6
      & ! [A] : 
          ( r2_hidden(A,c1_75__funct_6)
         => r2_wellord2(k1_funct_1(c2_75__funct_6,A),k1_funct_1(c3_75__funct_6,A)) ) )
   => r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6,dt_c3_75__funct_6]),discharge_asm(discharge,[e1_75__funct_6])],[e1_75__funct_6,i4_75__funct_6]),
    [interesting(0.8),file(funct_6,i3_75__funct_6),[file(funct_6,i3_75__funct_6)]]).

fof(i3_75_tmp__funct_6,plain,
    ( ( v1_relat_1(c3_75__funct_6)
      & v1_funct_1(c3_75__funct_6) )
   => ( ( k1_relat_1(c2_75__funct_6) = c1_75__funct_6
        & k1_relat_1(c3_75__funct_6) = c1_75__funct_6
        & ! [A] : 
            ( r2_hidden(A,c1_75__funct_6)
           => r2_wellord2(k1_funct_1(c2_75__funct_6,A),k1_funct_1(c3_75__funct_6,A)) ) )
     => r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(c3_75__funct_6)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6]),discharge_asm(discharge,[dt_c3_75__funct_6])],[dt_c3_75__funct_6,i3_75__funct_6]),
    [interesting(0.8),i2_75__funct_6]).

fof(i2_75__funct_6,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ( k1_relat_1(c2_75__funct_6) = c1_75__funct_6
          & k1_relat_1(A) = c1_75__funct_6
          & ! [B] : 
              ( r2_hidden(B,c1_75__funct_6)
             => r2_wellord2(k1_funct_1(c2_75__funct_6,B),k1_funct_1(A,B)) ) )
       => r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_75__funct_6,dt_c2_75__funct_6])],[i3_75_tmp__funct_6,dh_c3_75__funct_6]),
    [interesting(0.8),file(funct_6,i2_75__funct_6),[file(funct_6,i2_75__funct_6)]]).

fof(i2_75_tmp__funct_6,plain,
    ( ( v1_relat_1(c2_75__funct_6)
      & v1_funct_1(c2_75__funct_6) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( ( k1_relat_1(c2_75__funct_6) = c1_75__funct_6
            & k1_relat_1(A) = c1_75__funct_6
            & ! [B] : 
                ( r2_hidden(B,c1_75__funct_6)
               => r2_wellord2(k1_funct_1(c2_75__funct_6,B),k1_funct_1(A,B)) ) )
         => r2_wellord2(k4_card_3(c2_75__funct_6),k4_card_3(A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_75__funct_6]),discharge_asm(discharge,[dt_c2_75__funct_6])],[dt_c2_75__funct_6,i2_75__funct_6]),
    [interesting(0.8),i1_75__funct_6]).

fof(i1_75__funct_6,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = c1_75__funct_6
              & k1_relat_1(B) = c1_75__funct_6
              & ! [C] : 
                  ( r2_hidden(C,c1_75__funct_6)
                 => r2_wellord2(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r2_wellord2(k4_card_3(A),k4_card_3(B)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_75__funct_6])],[i2_75_tmp__funct_6,dh_c2_75__funct_6]),
    [interesting(0.8),file(funct_6,i1_75__funct_6),[file(funct_6,i1_75__funct_6)]]).

fof(i1_75_tmp__funct_6,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = c1_75__funct_6
              & k1_relat_1(B) = c1_75__funct_6
              & ! [C] : 
                  ( r2_hidden(C,c1_75__funct_6)
                 => r2_wellord2(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r2_wellord2(k4_card_3(A),k4_card_3(B)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_75__funct_6])],[dt_c1_75__funct_6,i1_75__funct_6]),
    [interesting(1),t69_funct_6]).

fof(t69_funct_6,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( k1_relat_1(B) = A
              & k1_relat_1(C) = A
              & ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_wellord2(k1_funct_1(B,D),k1_funct_1(C,D)) ) )
           => r2_wellord2(k4_card_3(B),k4_card_3(C)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_75_tmp__funct_6,dh_c1_75__funct_6]),
    [interesting(1),file(funct_6,t69_funct_6),[file(funct_6,t69_funct_6)]]).