% Mizar ND problem: t6_funct_7,funct_7,110,25 
fof(dh_c1_6__funct_7,definition,
    ( ( ( v1_relat_1(c1_6__funct_7)
        & v1_funct_1(c1_6__funct_7) )
     => ! [A] : 
          ( r2_hidden(A,k1_relat_1(c1_6__funct_7))
         => k7_relat_1(c1_6__funct_7,k1_tarski(A)) = k3_cqc_lang(A,k1_funct_1(c1_6__funct_7,A)) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( r2_hidden(C,k1_relat_1(B))
           => k7_relat_1(B,k1_tarski(C)) = k3_cqc_lang(C,k1_funct_1(B,C)) ) ) ),
    introduced(definition,[new_symbol(c1_6__funct_7),file(funct_7,c1_6__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c1_6__funct_7)]).

fof(dh_c2_6__funct_7,definition,
    ( ( r2_hidden(c2_6__funct_7,k1_relat_1(c1_6__funct_7))
     => k7_relat_1(c1_6__funct_7,k1_tarski(c2_6__funct_7)) = k3_cqc_lang(c2_6__funct_7,k1_funct_1(c1_6__funct_7,c2_6__funct_7)) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(c1_6__funct_7))
       => k7_relat_1(c1_6__funct_7,k1_tarski(A)) = k3_cqc_lang(A,k1_funct_1(c1_6__funct_7,A)) ) ),
    introduced(definition,[new_symbol(c2_6__funct_7),file(funct_7,c2_6__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c2_6__funct_7)]).

fof(e1_6__funct_7,assumption,(
    r2_hidden(c2_6__funct_7,k1_relat_1(c1_6__funct_7)) ),
    introduced(assumption,[file(funct_7,e1_6__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,e1_6__funct_7)]).

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(fc13_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v3_relat_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v3_relat_1(k7_relat_1(A,B)) ) ) ),
    file(relat_1,fc13_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc13_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(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(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(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(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

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(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(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_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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_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(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(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_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(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_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    [interesting(0.9),axiom,file(relat_1,k7_relat_1)]).

fof(dt_c1_6__funct_7,assumption,
    ( v1_relat_1(c1_6__funct_7)
    & v1_funct_1(c1_6__funct_7) ),
    introduced(assumption,[file(funct_7,c1_6__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c1_6__funct_7)]).

fof(dt_c2_6__funct_7,assumption,(
    $true ),
    introduced(assumption,[file(funct_7,c2_6__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c2_6__funct_7)]).

fof(fc1_zfmisc_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,fc1_zfmisc_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(fc4_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc4_funct_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(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(t89_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k7_relat_1(A,k1_tarski(B)) = k1_tarski(k4_tarski(B,k1_funct_1(A,B))) ) ) ),
    file(grfunc_1,t89_grfunc_1),
    [interesting(0.9),axiom,file(grfunc_1,t89_grfunc_1)]).

fof(e1_6_1__funct_7,plain,(
    k7_relat_1(c1_6__funct_7,k1_tarski(c2_6__funct_7)) = k1_tarski(k4_tarski(c2_6__funct_7,k1_funct_1(c1_6__funct_7,c2_6__funct_7))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__funct_7,dt_c2_6__funct_7,e1_6__funct_7])],[cc1_finseq_1,fc13_relat_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,rc1_partfun1,rc3_funct_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc3_subset_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,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k4_tarski,dt_k7_relat_1,dt_c1_6__funct_7,dt_c2_6__funct_7,fc1_zfmisc_1,fc2_subset_1,fc4_funct_1,rc1_funct_1,t1_subset,t7_boole,d5_tarski,e1_6__funct_7,t89_grfunc_1]),
    [interesting(0.65),file(funct_7,e1_6_1__funct_7),[file(funct_7,e1_6_1__funct_7)]]).

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

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

fof(t35_zfmisc_1,theorem,(
    ! [A,B] : k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B)) ),
    file(zfmisc_1,t35_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t35_zfmisc_1)]).

fof(e2_6_1__funct_7,plain,(
    k1_tarski(k4_tarski(c2_6__funct_7,k1_funct_1(c1_6__funct_7,c2_6__funct_7))) = k2_zfmisc_1(k1_tarski(c2_6__funct_7),k1_tarski(k1_funct_1(c1_6__funct_7,c2_6__funct_7))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__funct_7,dt_c2_6__funct_7])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_partfun1,rc3_funct_1,t1_subset,commutativity_k2_tarski,dt_k2_tarski,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc3_subset_1,fc4_subset_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t6_boole,t7_boole,t8_boole,dt_k1_funct_1,dt_k1_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_6__funct_7,dt_c2_6__funct_7,fc1_zfmisc_1,fc2_subset_1,d5_tarski,t35_zfmisc_1]),
    [interesting(0.65),file(funct_7,e2_6_1__funct_7),[file(funct_7,e2_6_1__funct_7)]]).

fof(fc2_funcop_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc2_funcop_1)]).

fof(rc5_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc5_funct_1)]).

fof(fc3_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc3_funcop_1)]).

fof(fc9_funcop_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc9_funcop_1)]).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_1)]).

fof(fc1_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc1_funcop_1)]).

fof(d2_funcop_1,definition,(
    ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ),
    file(funcop_1,d2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,d2_funcop_1)]).

fof(e3_6_1__funct_7,plain,(
    k2_zfmisc_1(k1_tarski(c2_6__funct_7),k1_tarski(k1_funct_1(c1_6__funct_7,c2_6__funct_7))) = k2_funcop_1(k1_tarski(c2_6__funct_7),k1_funct_1(c1_6__funct_7,c2_6__funct_7)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__funct_7,dt_c2_6__funct_7])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc2_funcop_1,fc4_relat_1,rc1_partfun1,rc3_funct_1,rc5_funct_1,t1_subset,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc3_funcop_1,fc4_subset_1,fc9_funcop_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t6_boole,t7_boole,t8_boole,dt_k1_funct_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_c1_6__funct_7,dt_c2_6__funct_7,fc1_funcop_1,fc2_subset_1,d2_funcop_1]),
    [interesting(0.65),file(funct_7,e3_6_1__funct_7),[file(funct_7,e3_6_1__funct_7)]]).

fof(dt_k3_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k3_cqc_lang),
    [interesting(0.9),axiom,file(cqc_lang,k3_cqc_lang)]).

fof(fc1_cqc_lang,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B)) ) ),
    file(cqc_lang,fc1_cqc_lang),
    [interesting(0.9),axiom,file(cqc_lang,fc1_cqc_lang)]).

fof(d2_cqc_lang,definition,(
    ! [A,B] : k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B) ),
    file(cqc_lang,d2_cqc_lang),
    [interesting(0.9),axiom,file(cqc_lang,d2_cqc_lang)]).

fof(e4_6_1__funct_7,plain,(
    k2_funcop_1(k1_tarski(c2_6__funct_7),k1_funct_1(c1_6__funct_7,c2_6__funct_7)) = k3_cqc_lang(c2_6__funct_7,k1_funct_1(c1_6__funct_7,c2_6__funct_7)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__funct_7,dt_c2_6__funct_7])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc2_funcop_1,fc4_relat_1,rc1_partfun1,rc3_funct_1,rc5_funct_1,t1_subset,dt_k2_zfmisc_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc3_funcop_1,fc4_subset_1,fc9_funcop_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t6_boole,t7_boole,t8_boole,dt_k1_funct_1,dt_k1_tarski,dt_k2_funcop_1,dt_k3_cqc_lang,dt_c1_6__funct_7,dt_c2_6__funct_7,fc1_cqc_lang,fc1_funcop_1,fc2_subset_1,d2_funcop_1,d2_cqc_lang]),
    [interesting(0.65),file(funct_7,e4_6_1__funct_7),[file(funct_7,e4_6_1__funct_7)]]).

fof(e2_6__funct_7,plain,(
    k7_relat_1(c1_6__funct_7,k1_tarski(c2_6__funct_7)) = k3_cqc_lang(c2_6__funct_7,k1_funct_1(c1_6__funct_7,c2_6__funct_7)) ),
    inference(iterative_eq,[status(thm),assumptions([e1_6__funct_7,dt_c1_6__funct_7,dt_c2_6__funct_7])],[e1_6_1__funct_7,e2_6_1__funct_7,e3_6_1__funct_7,e4_6_1__funct_7]),
    [interesting(0.8),file(funct_7,e2_6__funct_7),[file(funct_7,e2_6__funct_7)]]).

fof(i4_6__funct_7,theorem,(
    $true ),
    introduced(tautology,[file(funct_7,i4_6__funct_7)]),
    [interesting(0.8),trivial,file(funct_7,i4_6__funct_7)]).

fof(i3_6__funct_7,plain,(
    k7_relat_1(c1_6__funct_7,k1_tarski(c2_6__funct_7)) = k3_cqc_lang(c2_6__funct_7,k1_funct_1(c1_6__funct_7,c2_6__funct_7)) ),
    inference(conclusion,[status(thm),assumptions([e1_6__funct_7,dt_c1_6__funct_7,dt_c2_6__funct_7])],[e2_6__funct_7,i4_6__funct_7]),
    [interesting(0.8),file(funct_7,i3_6__funct_7),[file(funct_7,i3_6__funct_7)]]).

fof(i2_6__funct_7,plain,
    ( r2_hidden(c2_6__funct_7,k1_relat_1(c1_6__funct_7))
   => k7_relat_1(c1_6__funct_7,k1_tarski(c2_6__funct_7)) = k3_cqc_lang(c2_6__funct_7,k1_funct_1(c1_6__funct_7,c2_6__funct_7)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__funct_7,dt_c2_6__funct_7]),discharge_asm(discharge,[e1_6__funct_7])],[e1_6__funct_7,i3_6__funct_7]),
    [interesting(0.8),file(funct_7,i2_6__funct_7),[file(funct_7,i2_6__funct_7)]]).

fof(i2_6_tmp__funct_7,plain,
    ( r2_hidden(c2_6__funct_7,k1_relat_1(c1_6__funct_7))
   => k7_relat_1(c1_6__funct_7,k1_tarski(c2_6__funct_7)) = k3_cqc_lang(c2_6__funct_7,k1_funct_1(c1_6__funct_7,c2_6__funct_7)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__funct_7]),discharge_asm(discharge,[dt_c2_6__funct_7])],[dt_c2_6__funct_7,i2_6__funct_7]),
    [interesting(0.8),i1_6__funct_7]).

fof(i1_6__funct_7,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(c1_6__funct_7))
     => k7_relat_1(c1_6__funct_7,k1_tarski(A)) = k3_cqc_lang(A,k1_funct_1(c1_6__funct_7,A)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__funct_7])],[i2_6_tmp__funct_7,dh_c2_6__funct_7]),
    [interesting(0.8),file(funct_7,i1_6__funct_7),[file(funct_7,i1_6__funct_7)]]).

fof(i1_6_tmp__funct_7,plain,
    ( ( v1_relat_1(c1_6__funct_7)
      & v1_funct_1(c1_6__funct_7) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(c1_6__funct_7))
       => k7_relat_1(c1_6__funct_7,k1_tarski(A)) = k3_cqc_lang(A,k1_funct_1(c1_6__funct_7,A)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__funct_7])],[dt_c1_6__funct_7,i1_6__funct_7]),
    [interesting(1),t6_funct_7]).

fof(t6_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k7_relat_1(A,k1_tarski(B)) = k3_cqc_lang(B,k1_funct_1(A,B)) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__funct_7,dh_c1_6__funct_7]),
    [interesting(1),file(funct_7,t6_funct_7),[file(funct_7,t6_funct_7)]]).