% Mizar ND problem: t5_ami_1,ami_1,42,43 
fof(dh_c1_1__ami_1,definition,
    ( ! [A,B,C] : 
        ( c1_1__ami_1 != A
       => k4_card_3(k4_funct_4(c1_1__ami_1,A,k1_tarski(B),k1_tarski(C))) = k1_tarski(k4_funct_4(c1_1__ami_1,A,B,C)) )
   => ! [D,E,F,G] : 
        ( D != E
       => k4_card_3(k4_funct_4(D,E,k1_tarski(F),k1_tarski(G))) = k1_tarski(k4_funct_4(D,E,F,G)) ) ),
    introduced(definition,[new_symbol(c1_1__ami_1),file(ami_1,c1_1__ami_1)]),
    [interesting(0.8),axiom,file(ami_1,c1_1__ami_1)]).

fof(dh_c2_1__ami_1,definition,
    ( ! [A,B] : 
        ( c1_1__ami_1 != c2_1__ami_1
       => k4_card_3(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(A),k1_tarski(B))) = k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,A,B)) )
   => ! [C,D,E] : 
        ( c1_1__ami_1 != C
       => k4_card_3(k4_funct_4(c1_1__ami_1,C,k1_tarski(D),k1_tarski(E))) = k1_tarski(k4_funct_4(c1_1__ami_1,C,D,E)) ) ),
    introduced(definition,[new_symbol(c2_1__ami_1),file(ami_1,c2_1__ami_1)]),
    [interesting(0.8),axiom,file(ami_1,c2_1__ami_1)]).

fof(dh_c3_1__ami_1,definition,
    ( ! [A] : 
        ( c1_1__ami_1 != c2_1__ami_1
       => k4_card_3(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(A))) = k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,A)) )
   => ! [B,C] : 
        ( c1_1__ami_1 != c2_1__ami_1
       => k4_card_3(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(B),k1_tarski(C))) = k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,B,C)) ) ),
    introduced(definition,[new_symbol(c3_1__ami_1),file(ami_1,c3_1__ami_1)]),
    [interesting(0.8),axiom,file(ami_1,c3_1__ami_1)]).

fof(dh_c4_1__ami_1,definition,
    ( ( c1_1__ami_1 != c2_1__ami_1
     => k4_card_3(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))) = k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)) )
   => ! [A] : 
        ( c1_1__ami_1 != c2_1__ami_1
       => k4_card_3(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(A))) = k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,A)) ) ),
    introduced(definition,[new_symbol(c4_1__ami_1),file(ami_1,c4_1__ami_1)]),
    [interesting(0.8),axiom,file(ami_1,c4_1__ami_1)]).

fof(e1_1__ami_1,assumption,(
    c1_1__ami_1 != c2_1__ami_1 ),
    introduced(assumption,[file(ami_1,e1_1__ami_1)]),
    [interesting(0.8),axiom,file(ami_1,e1_1__ami_1)]).

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

fof(cc1_setfam_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,cc1_setfam_1)]).

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(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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(rc1_setfam_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,rc1_setfam_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(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(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(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_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(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(fc2_setfam_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_setfam_1(k1_tarski(A)) ) ) ),
    file(setfam_1,fc2_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,fc2_setfam_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(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_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(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

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(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

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(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(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(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_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_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

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_k4_funct_4,axiom,(
    $true ),
    file(funct_4,k4_funct_4),
    [interesting(0.9),axiom,file(funct_4,k4_funct_4)]).

fof(dt_c1_1__ami_1,assumption,(
    $true ),
    introduced(assumption,[file(ami_1,c1_1__ami_1)]),
    [interesting(0.8),axiom,file(ami_1,c1_1__ami_1)]).

fof(dt_c2_1__ami_1,assumption,(
    $true ),
    introduced(assumption,[file(ami_1,c2_1__ami_1)]),
    [interesting(0.8),axiom,file(ami_1,c2_1__ami_1)]).

fof(dt_c3_1__ami_1,assumption,(
    $true ),
    introduced(assumption,[file(ami_1,c3_1__ami_1)]),
    [interesting(0.8),axiom,file(ami_1,c3_1__ami_1)]).

fof(dt_c4_1__ami_1,assumption,(
    $true ),
    introduced(assumption,[file(ami_1,c4_1__ami_1)]),
    [interesting(0.8),axiom,file(ami_1,c4_1__ami_1)]).

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(fc1_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( v1_relat_1(k4_funct_4(A,B,C,D))
      & v1_funct_1(k4_funct_4(A,B,C,D)) ) ),
    file(funct_4,fc1_funct_4),
    [interesting(0.9),axiom,file(funct_4,fc1_funct_4)]).

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(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(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(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(dh_c1_1_1__ami_1,definition,
    ( ( ~ ( r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)))
          & ! [A] : 
              ( ( v1_relat_1(A)
                & v1_funct_1(A) )
             => ~ ( c1_1_1__ami_1 = A
                  & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
                  & ! [B] : 
                      ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
                     => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) ) ) )
      & ( ? [A] : 
            ( v1_relat_1(A)
            & v1_funct_1(A)
            & c1_1_1__ami_1 = A
            & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
            & ! [B] : 
                ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
               => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) )
       => r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1))) ) )
   => ! [C] : 
        ( ~ ( r2_hidden(C,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)))
            & ! [D] : 
                ( ( v1_relat_1(D)
                  & v1_funct_1(D) )
               => ~ ( C = D
                    & k1_relat_1(D) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
                    & ! [E] : 
                        ( r2_hidden(E,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
                       => r2_hidden(k1_funct_1(D,E),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),E)) ) ) ) )
        & ( ? [D] : 
              ( v1_relat_1(D)
              & v1_funct_1(D)
              & C = D
              & k1_relat_1(D) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
              & ! [E] : 
                  ( r2_hidden(E,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
                 => r2_hidden(k1_funct_1(D,E),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),E)) ) )
         => r2_hidden(C,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1))) ) ) ),
    introduced(definition,[new_symbol(c1_1_1__ami_1),file(ami_1,c1_1_1__ami_1)]),
    [interesting(0.65),axiom,file(ami_1,c1_1_1__ami_1)]).

fof(e1_1_1_1__ami_1,assumption,(
    r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1))) ),
    introduced(assumption,[file(ami_1,e1_1_1_1__ami_1)]),
    [interesting(0.5),axiom,file(ami_1,e1_1_1_1__ami_1)]).

fof(dt_c1_1_1__ami_1,assumption,(
    $true ),
    introduced(assumption,[file(ami_1,c1_1_1__ami_1)]),
    [interesting(0.65),axiom,file(ami_1,c1_1_1__ami_1)]).

fof(de_c1_1_1_1__ami_1,definition,(
    c1_1_1_1__ami_1 = k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1) ),
    introduced(definition,[new_symbol(c1_1_1_1__ami_1),file(ami_1,c1_1_1_1__ami_1)]),
    [interesting(0.5),axiom,file(ami_1,c1_1_1_1__ami_1)]).

fof(dt_c1_1_1_1__ami_1,plain,(
    $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[rc1_funct_1,dt_k4_funct_4,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_funct_4,de_c1_1_1_1__ami_1]),
    [interesting(0.5),file(ami_1,c1_1_1_1__ami_1),[file(ami_1,c1_1_1_1__ami_1)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e2_1_1_1__ami_1,plain,(
    c1_1_1__ami_1 = c1_1_1_1__ami_1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,e1_1_1_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_setfam_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c1_1_1__ami_1,dt_c1_1_1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,de_c1_1_1_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_subset_1,t1_subset,t7_boole,e1_1_1_1__ami_1,d1_tarski]),
    [interesting(0.5),file(ami_1,e2_1_1_1__ami_1),[file(ami_1,e2_1_1_1__ami_1)]]).

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

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(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(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(fc3_setfam_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( ~ v1_xboole_0(k2_tarski(A,B))
        & v1_setfam_1(k2_tarski(A,B)) ) ) ),
    file(setfam_1,fc3_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,fc3_setfam_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(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_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(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(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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

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

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

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(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(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(t65_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B)
      & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) ) ),
    file(funct_4,t65_funct_4),
    [interesting(0.9),axiom,file(funct_4,t65_funct_4)]).

fof(e2_1__ami_1,plain,(
    k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))) = k2_tarski(c1_1__ami_1,c2_1__ami_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_finset_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc1_subset_1,fc2_setfam_1,fc3_setfam_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_finset_1,fc2_subset_1,fc3_subset_1,t3_subset,t65_funct_4]),
    [interesting(0.8),file(ami_1,e2_1__ami_1),[file(ami_1,e2_1__ami_1)]]).

fof(e3_1_1_1__ami_1,plain,(
    k1_relat_1(c1_1_1_1__ami_1) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_finset_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc1_subset_1,fc2_setfam_1,fc3_setfam_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c1_1_1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,de_c1_1_1_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_finset_1,fc2_subset_1,fc3_subset_1,t3_subset,e2_1__ami_1,t65_funct_4]),
    [interesting(0.5),file(ami_1,e3_1_1_1__ami_1),[file(ami_1,e3_1_1_1__ami_1)]]).

fof(dh_c2_1_1_1__ami_1,definition,
    ( ( r2_hidden(c2_1_1_1__ami_1,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
     => r2_hidden(k1_funct_1(c1_1_1_1__ami_1,c2_1_1_1__ami_1),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c2_1_1_1__ami_1)) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
       => r2_hidden(k1_funct_1(c1_1_1_1__ami_1,A),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),A)) ) ),
    introduced(definition,[new_symbol(c2_1_1_1__ami_1),file(ami_1,c2_1_1_1__ami_1)]),
    [interesting(0.5),axiom,file(ami_1,c2_1_1_1__ami_1)]).

fof(e4_1_1_1__ami_1,assumption,(
    r2_hidden(c2_1_1_1__ami_1,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))) ),
    introduced(assumption,[file(ami_1,e4_1_1_1__ami_1)]),
    [interesting(0.5),axiom,file(ami_1,e4_1_1_1__ami_1)]).

fof(dt_c2_1_1_1__ami_1,assumption,(
    $true ),
    introduced(assumption,[file(ami_1,c2_1_1_1__ami_1)]),
    [interesting(0.5),axiom,file(ami_1,c2_1_1_1__ami_1)]).

fof(t66_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( A != B
     => ( k1_funct_1(k4_funct_4(A,B,C,D),A) = C
        & k1_funct_1(k4_funct_4(A,B,C,D),B) = D ) ) ),
    file(funct_4,t66_funct_4),
    [interesting(0.9),axiom,file(funct_4,t66_funct_4)]).

fof(e6_1_1_1__ami_1,plain,
    ( k1_funct_1(c1_1_1_1__ami_1,c1_1__ami_1) = c3_1__ami_1
    & k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c1_1__ami_1) = k1_tarski(c3_1__ami_1)
    & k1_funct_1(c1_1_1_1__ami_1,c2_1__ami_1) = c4_1__ami_1
    & k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c2_1__ami_1) = k1_tarski(c4_1__ami_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,e1_1__ami_1])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_setfam_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,t1_subset,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_setfam_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t6_boole,t7_boole,t8_boole,dt_k1_funct_1,dt_k1_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c1_1_1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,de_c1_1_1_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_subset_1,e1_1__ami_1,t66_funct_4]),
    [interesting(0.5),file(ami_1,e6_1_1_1__ami_1),[file(ami_1,e6_1_1_1__ami_1)]]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.9),axiom,file(tarski,d2_tarski)]).

fof(e5_1_1_1__ami_1,plain,
    ( c2_1_1_1__ami_1 = c1_1__ami_1
    | c2_1_1_1__ami_1 = c2_1__ami_1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1_1_1__ami_1,e4_1_1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc17_finseq_1,fc2_setfam_1,fc3_setfam_1,fc5_relat_1,fc7_relat_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k1_tarski,dt_k2_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c2_1_1_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_finset_1,fc2_subset_1,fc3_subset_1,t1_subset,t7_boole,e4_1_1_1__ami_1,e2_1__ami_1,d2_tarski]),
    [interesting(0.5),file(ami_1,e5_1_1_1__ami_1),[file(ami_1,e5_1_1_1__ami_1)]]).

fof(e7_1_1_1__ami_1,plain,(
    r2_hidden(k1_funct_1(c1_1_1_1__ami_1,c2_1_1_1__ami_1),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c2_1_1_1__ami_1)) ),
    inference(mizar_by,[status(thm),assumptions([e1_1__ami_1,dt_c2_1_1_1__ami_1,e4_1_1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_setfam_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c1_1_1_1__ami_1,dt_c2_1__ami_1,dt_c2_1_1_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,de_c1_1_1_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_subset_1,t1_subset,t7_boole,e6_1_1_1__ami_1,e5_1_1_1__ami_1,d1_tarski]),
    [interesting(0.5),file(ami_1,e7_1_1_1__ami_1),[file(ami_1,e7_1_1_1__ami_1)]]).

fof(i7_1_1_1__ami_1,theorem,(
    $true ),
    introduced(tautology,[file(ami_1,i7_1_1_1__ami_1)]),
    [interesting(0.5),trivial,file(ami_1,i7_1_1_1__ami_1)]).

fof(i6_1_1_1__ami_1,plain,(
    r2_hidden(k1_funct_1(c1_1_1_1__ami_1,c2_1_1_1__ami_1),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c2_1_1_1__ami_1)) ),
    inference(conclusion,[status(thm),assumptions([e1_1__ami_1,dt_c2_1_1_1__ami_1,e4_1_1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[e7_1_1_1__ami_1,i7_1_1_1__ami_1]),
    [interesting(0.5),file(ami_1,i6_1_1_1__ami_1),[file(ami_1,i6_1_1_1__ami_1)]]).

fof(i5_1_1_1__ami_1,plain,
    ( r2_hidden(c2_1_1_1__ami_1,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
   => r2_hidden(k1_funct_1(c1_1_1_1__ami_1,c2_1_1_1__ami_1),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c2_1_1_1__ami_1)) ),
    inference(discharge_asm,[status(thm),assumptions([e1_1__ami_1,dt_c2_1_1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1]),discharge_asm(discharge,[e4_1_1_1__ami_1])],[e4_1_1_1__ami_1,i6_1_1_1__ami_1]),
    [interesting(0.5),file(ami_1,i5_1_1_1__ami_1),[file(ami_1,i5_1_1_1__ami_1)]]).

fof(i5_1_1_1_tmp__ami_1,plain,
    ( r2_hidden(c2_1_1_1__ami_1,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
   => r2_hidden(k1_funct_1(c1_1_1_1__ami_1,c2_1_1_1__ami_1),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c2_1_1_1__ami_1)) ),
    inference(discharge_asm,[status(thm),assumptions([e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1]),discharge_asm(discharge,[dt_c2_1_1_1__ami_1])],[dt_c2_1_1_1__ami_1,i5_1_1_1__ami_1]),
    [interesting(0.5),i4_1_1_1__ami_1]).

fof(i4_1_1_1__ami_1,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
     => r2_hidden(k1_funct_1(c1_1_1_1__ami_1,A),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),A)) ) ),
    inference(let,[status(thm),assumptions([e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[i5_1_1_1_tmp__ami_1,dh_c2_1_1_1__ami_1]),
    [interesting(0.5),file(ami_1,i4_1_1_1__ami_1),[file(ami_1,i4_1_1_1__ami_1)]]).

fof(i3_1_1_1__ami_1,plain,
    ( k1_relat_1(c1_1_1_1__ami_1) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
    & ! [A] : 
        ( r2_hidden(A,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
       => r2_hidden(k1_funct_1(c1_1_1_1__ami_1,A),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),A)) ) ),
    inference(conclusion,[status(thm),assumptions([e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[e3_1_1_1__ami_1,i4_1_1_1__ami_1]),
    [interesting(0.5),file(ami_1,i3_1_1_1__ami_1),[file(ami_1,i3_1_1_1__ami_1)]]).

fof(i2_1_1_1__ami_1,plain,
    ( c1_1_1__ami_1 = c1_1_1_1__ami_1
    & k1_relat_1(c1_1_1_1__ami_1) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
    & ! [A] : 
        ( r2_hidden(A,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
       => r2_hidden(k1_funct_1(c1_1_1_1__ami_1,A),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),A)) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1_1__ami_1,e1_1_1_1__ami_1,e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[e2_1_1_1__ami_1,i3_1_1_1__ami_1]),
    [interesting(0.5),file(ami_1,i2_1_1_1__ami_1),[file(ami_1,i2_1_1_1__ami_1)]]).

fof(i1_1_1_1__ami_1,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & c1_1_1__ami_1 = A
      & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
      & ! [B] : 
          ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
         => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) ) ),
    inference(take,[status(thm),assumptions([dt_c1_1_1__ami_1,e1_1_1_1__ami_1,e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[rc1_setfam_1,rc3_funct_1,rc6_finseq_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc17_finseq_1,fc2_setfam_1,fc5_relat_1,fc7_relat_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c1_1_1__ami_1,dt_c1_1_1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_subset_1,rc1_funct_1,i2_1_1_1__ami_1]),
    [interesting(0.5),file(ami_1,i1_1_1_1__ami_1),[file(ami_1,i1_1_1_1__ami_1)]]).

fof(e1_1_1__ami_1,plain,(
    ~ ( r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)))
      & ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ~ ( c1_1_1__ami_1 = A
              & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
              & ! [B] : 
                  ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
                 => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1_1__ami_1,e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1]),discharge_asm(discharge,[e1_1_1_1__ami_1])],[e1_1_1_1__ami_1,i1_1_1_1__ami_1]),
    [interesting(0.65),file(ami_1,e1_1_1__ami_1),[file(ami_1,e1_1_1__ami_1)]]).

fof(e2_1_1__ami_1,assumption,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & c1_1_1__ami_1 = A
      & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
      & ! [B] : 
          ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
         => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) ) ),
    introduced(assumption,[file(ami_1,e2_1_1__ami_1)]),
    [interesting(0.65),axiom,file(ami_1,e2_1_1__ami_1)]).

fof(dh_c2_1_1__ami_1,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & c1_1_1__ami_1 = A
        & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
        & ! [B] : 
            ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
           => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) )
   => ( v1_relat_1(c2_1_1__ami_1)
      & v1_funct_1(c2_1_1__ami_1)
      & c1_1_1__ami_1 = c2_1_1__ami_1
      & k1_relat_1(c2_1_1__ami_1) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
      & ! [C] : 
          ( r2_hidden(C,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
         => r2_hidden(k1_funct_1(c2_1_1__ami_1,C),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),C)) ) ) ),
    introduced(definition,[new_symbol(c2_1_1__ami_1),file(ami_1,c2_1_1__ami_1)]),
    [interesting(0.65),axiom,file(ami_1,c2_1_1__ami_1)]).

fof(dt_c2_1_1__ami_1,plain,
    ( v1_relat_1(c2_1_1__ami_1)
    & v1_funct_1(c2_1_1__ami_1) ),
    inference(consider,[status(thm),assumptions([e2_1_1__ami_1])],[dh_c2_1_1__ami_1,e2_1_1__ami_1]),
    [interesting(0.65),file(ami_1,c2_1_1__ami_1),[file(ami_1,c2_1_1__ami_1)]]).

fof(e6_1_1__ami_1,plain,
    ( r2_hidden(c1_1__ami_1,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
    & r2_hidden(c2_1__ami_1,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc17_finseq_1,fc2_setfam_1,fc3_setfam_1,fc5_relat_1,fc7_relat_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k1_tarski,dt_k2_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_finset_1,fc2_subset_1,fc3_subset_1,t1_subset,t7_boole,e2_1__ami_1,d2_tarski]),
    [interesting(0.65),file(ami_1,e6_1_1__ami_1),[file(ami_1,e6_1_1__ami_1)]]).

fof(e5_1_1__ami_1,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
     => r2_hidden(k1_funct_1(c2_1_1__ami_1,A),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),A)) ) ),
    inference(consider,[status(thm),assumptions([e2_1_1__ami_1])],[dh_c2_1_1__ami_1,e2_1_1__ami_1]),
    [interesting(0.65),file(ami_1,e5_1_1__ami_1),[file(ami_1,e5_1_1__ami_1)]]).

fof(e7_1_1__ami_1,plain,
    ( r2_hidden(k1_funct_1(c2_1_1__ami_1,c1_1__ami_1),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c1_1__ami_1))
    & r2_hidden(k1_funct_1(c2_1_1__ami_1,c2_1__ami_1),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c2_1__ami_1))
    & k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c1_1__ami_1) = k1_tarski(c3_1__ami_1)
    & k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),c2_1__ami_1) = k1_tarski(c4_1__ami_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,e1_1__ami_1,e2_1_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc17_finseq_1,fc2_setfam_1,fc5_relat_1,fc7_relat_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c2_1_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_subset_1,t1_subset,t7_boole,e6_1_1__ami_1,e1_1__ami_1,e5_1_1__ami_1,t66_funct_4]),
    [interesting(0.65),file(ami_1,e7_1_1__ami_1),[file(ami_1,e7_1_1__ami_1)]]).

fof(e8_1_1__ami_1,plain,
    ( k1_funct_1(c2_1_1__ami_1,c1_1__ami_1) = c3_1__ami_1
    & k1_funct_1(c2_1_1__ami_1,c2_1__ami_1) = c4_1__ami_1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,e1_1__ami_1,e2_1_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_setfam_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c2_1_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_subset_1,t1_subset,t7_boole,e7_1_1__ami_1,d1_tarski]),
    [interesting(0.65),file(ami_1,e8_1_1__ami_1),[file(ami_1,e8_1_1__ami_1)]]).

fof(e4_1_1__ami_1,plain,(
    k1_relat_1(c2_1_1__ami_1) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))) ),
    inference(consider,[status(thm),assumptions([e2_1_1__ami_1])],[dh_c2_1_1__ami_1,e2_1_1__ami_1]),
    [interesting(0.65),file(ami_1,e4_1_1__ami_1),[file(ami_1,e4_1_1__ami_1)]]).

fof(t69_funct_4,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v1_relat_1(E)
        & v1_funct_1(E) )
     => ( ( k1_relat_1(E) = k2_tarski(A,B)
          & k1_funct_1(E,A) = C
          & k1_funct_1(E,B) = D )
       => E = k4_funct_4(A,B,C,D) ) ) ),
    file(funct_4,t69_funct_4),
    [interesting(0.9),axiom,file(funct_4,t69_funct_4)]).

fof(e9_1_1__ami_1,plain,(
    c2_1_1__ami_1 = k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,e2_1_1__ami_1])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_setfam_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,t1_subset,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc17_finseq_1,fc2_setfam_1,fc3_setfam_1,fc5_relat_1,fc7_relat_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c2_1_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_funct_1,e8_1_1__ami_1,e2_1__ami_1,e4_1_1__ami_1,t69_funct_4]),
    [interesting(0.65),file(ami_1,e9_1_1__ami_1),[file(ami_1,e9_1_1__ami_1)]]).

fof(e3_1_1__ami_1,plain,(
    c1_1_1__ami_1 = c2_1_1__ami_1 ),
    inference(consider,[status(thm),assumptions([e2_1_1__ami_1])],[dh_c2_1_1__ami_1,e2_1_1__ami_1]),
    [interesting(0.65),file(ami_1,e3_1_1__ami_1),[file(ami_1,e3_1_1__ami_1)]]).

fof(e10_1_1__ami_1,plain,(
    r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_1__ami_1,e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,e2_1_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_setfam_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k4_funct_4,dt_c1_1__ami_1,dt_c1_1_1__ami_1,dt_c2_1__ami_1,dt_c2_1_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_subset_1,t1_subset,t7_boole,e9_1_1__ami_1,e3_1_1__ami_1,d1_tarski]),
    [interesting(0.65),file(ami_1,e10_1_1__ami_1),[file(ami_1,e10_1_1__ami_1)]]).

fof(i4_1_1__ami_1,theorem,(
    $true ),
    introduced(tautology,[file(ami_1,i4_1_1__ami_1)]),
    [interesting(0.65),trivial,file(ami_1,i4_1_1__ami_1)]).

fof(i3_1_1__ami_1,plain,(
    r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1_1__ami_1,e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,e2_1_1__ami_1])],[e10_1_1__ami_1,i4_1_1__ami_1]),
    [interesting(0.65),file(ami_1,i3_1_1__ami_1),[file(ami_1,i3_1_1__ami_1)]]).

fof(i2_1_1__ami_1,plain,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & c1_1_1__ami_1 = A
        & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
        & ! [B] : 
            ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
           => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) )
   => r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1_1__ami_1,e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1]),discharge_asm(discharge,[e2_1_1__ami_1])],[e2_1_1__ami_1,i3_1_1__ami_1]),
    [interesting(0.65),file(ami_1,i2_1_1__ami_1),[file(ami_1,i2_1_1__ami_1)]]).

fof(i1_1_1__ami_1,plain,
    ( ~ ( r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)))
        & ! [A] : 
            ( ( v1_relat_1(A)
              & v1_funct_1(A) )
           => ~ ( c1_1_1__ami_1 = A
                & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
                & ! [B] : 
                    ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
                   => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) ) ) )
    & ( ? [A] : 
          ( v1_relat_1(A)
          & v1_funct_1(A)
          & c1_1_1__ami_1 = A
          & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
          & ! [B] : 
              ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
             => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) )
     => r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1))) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1_1__ami_1,e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[e1_1_1__ami_1,i2_1_1__ami_1]),
    [interesting(0.65),file(ami_1,i1_1_1__ami_1),[file(ami_1,i1_1_1__ami_1)]]).

fof(i1_1_1_tmp__ami_1,plain,
    ( ~ ( r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)))
        & ! [A] : 
            ( ( v1_relat_1(A)
              & v1_funct_1(A) )
           => ~ ( c1_1_1__ami_1 = A
                & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
                & ! [B] : 
                    ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
                   => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) ) ) )
    & ( ? [A] : 
          ( v1_relat_1(A)
          & v1_funct_1(A)
          & c1_1_1__ami_1 = A
          & k1_relat_1(A) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
          & ! [B] : 
              ( r2_hidden(B,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
             => r2_hidden(k1_funct_1(A,B),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),B)) ) )
     => r2_hidden(c1_1_1__ami_1,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1))) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1]),discharge_asm(discharge,[dt_c1_1_1__ami_1])],[dt_c1_1_1__ami_1,i1_1_1__ami_1]),
    [interesting(0.8),e3_1__ami_1]).

fof(e3_1__ami_1,plain,(
    ! [A] : 
      ( ~ ( r2_hidden(A,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)))
          & ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ~ ( A = B
                  & k1_relat_1(B) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
                  & ! [C] : 
                      ( r2_hidden(C,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
                     => r2_hidden(k1_funct_1(B,C),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),C)) ) ) ) )
      & ( ? [B] : 
            ( v1_relat_1(B)
            & v1_funct_1(B)
            & A = B
            & k1_relat_1(B) = k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)))
            & ! [C] : 
                ( r2_hidden(C,k1_relat_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))))
               => r2_hidden(k1_funct_1(B,C),k1_funct_1(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1)),C)) ) )
       => r2_hidden(A,k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1))) ) ) ),
    inference(let,[status(thm),assumptions([e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[i1_1_1_tmp__ami_1,dh_c1_1_1__ami_1]),
    [interesting(0.8),file(ami_1,e3_1__ami_1),[file(ami_1,e3_1__ami_1)]]).

fof(d5_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    [interesting(0.9),axiom,file(card_3,d5_card_3)]).

fof(e4_1__ami_1,plain,(
    k4_card_3(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))) = k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)) ),
    inference(mizar_by,[status(thm),assumptions([e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc1_setfam_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_setfam_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc17_finseq_1,fc2_setfam_1,fc5_relat_1,fc7_relat_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k4_card_3,dt_k4_funct_4,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,fc1_finset_1,fc1_funct_4,fc2_subset_1,rc1_funct_1,t1_subset,t7_boole,e3_1__ami_1,d5_card_3]),
    [interesting(0.8),file(ami_1,e4_1__ami_1),[file(ami_1,e4_1__ami_1)]]).

fof(i3_1__ami_1,theorem,(
    $true ),
    introduced(tautology,[file(ami_1,i3_1__ami_1)]),
    [interesting(0.8),trivial,file(ami_1,i3_1__ami_1)]).

fof(i2_1__ami_1,plain,(
    k4_card_3(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))) = k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)) ),
    inference(conclusion,[status(thm),assumptions([e1_1__ami_1,dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[e4_1__ami_1,i3_1__ami_1]),
    [interesting(0.8),file(ami_1,i2_1__ami_1),[file(ami_1,i2_1__ami_1)]]).

fof(i1_1__ami_1,plain,
    ( c1_1__ami_1 != c2_1__ami_1
   => k4_card_3(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))) = k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1]),discharge_asm(discharge,[e1_1__ami_1])],[e1_1__ami_1,i2_1__ami_1]),
    [interesting(0.8),file(ami_1,i1_1__ami_1),[file(ami_1,i1_1__ami_1)]]).

fof(i1_1_tmp__ami_1,plain,
    ( c1_1__ami_1 != c2_1__ami_1
   => k4_card_3(k4_funct_4(c1_1__ami_1,c2_1__ami_1,k1_tarski(c3_1__ami_1),k1_tarski(c4_1__ami_1))) = k1_tarski(k4_funct_4(c1_1__ami_1,c2_1__ami_1,c3_1__ami_1,c4_1__ami_1)) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1])],[dt_c1_1__ami_1,dt_c2_1__ami_1,dt_c3_1__ami_1,dt_c4_1__ami_1,i1_1__ami_1]),
    [interesting(1),t5_ami_1]).

fof(t5_ami_1,theorem,(
    ! [A,B,C,D] : 
      ( A != B
     => k4_card_3(k4_funct_4(A,B,k1_tarski(C),k1_tarski(D))) = k1_tarski(k4_funct_4(A,B,C,D)) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__ami_1,dh_c1_1__ami_1,dh_c2_1__ami_1,dh_c3_1__ami_1,dh_c4_1__ami_1]),
    [interesting(1),file(ami_1,t5_ami_1),[file(ami_1,t5_ami_1)]]).