% Mizar ND problem: t1_funct_7,funct_7,36,60 
fof(dh_c1_1__funct_7,definition,
    ( ( ( v1_relat_1(c1_1__funct_7)
        & v1_funct_1(c1_1__funct_7) )
     => ! [A] : 
          ( r1_tarski(k2_relat_1(c1_1__funct_7),A)
         => k5_relat_1(c1_1__funct_7,k6_partfun1(A)) = c1_1__funct_7 ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( r1_tarski(k2_relat_1(B),C)
           => k5_relat_1(B,k6_partfun1(C)) = B ) ) ),
    introduced(definition,[new_symbol(c1_1__funct_7),file(funct_7,c1_1__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c1_1__funct_7)]).

fof(dh_c2_1__funct_7,definition,
    ( ( r1_tarski(k2_relat_1(c1_1__funct_7),c2_1__funct_7)
     => k5_relat_1(c1_1__funct_7,k6_partfun1(c2_1__funct_7)) = c1_1__funct_7 )
   => ! [A] : 
        ( r1_tarski(k2_relat_1(c1_1__funct_7),A)
       => k5_relat_1(c1_1__funct_7,k6_partfun1(A)) = c1_1__funct_7 ) ),
    introduced(definition,[new_symbol(c2_1__funct_7),file(funct_7,c2_1__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c2_1__funct_7)]).

fof(e1_1__funct_7,assumption,(
    r1_tarski(k2_relat_1(c1_1__funct_7),c2_1__funct_7) ),
    introduced(assumption,[file(funct_7,e1_1__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,e1_1__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(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(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

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

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

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

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

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

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(fc10_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc10_relat_1)]).

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(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(fc9_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc9_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(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_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_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

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

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

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

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

fof(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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc1_partfun1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,cc1_partfun1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(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(rc3_partfun1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_relat_2(B)
      & v3_relat_2(B)
      & v4_relat_2(B)
      & v8_relat_2(B)
      & v1_partfun1(B,A,A) ) ),
    file(partfun1,rc3_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc3_partfun1)]).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

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

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    [interesting(0.9),axiom,file(relat_1,k6_relat_1)]).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(fc1_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]).

fof(fc2_funct_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A)) ) ),
    file(funct_1,fc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc2_funct_1)]).

fof(fc2_partfun1,theorem,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A))
      & v1_relat_2(k6_relat_1(A))
      & v3_relat_2(k6_relat_1(A))
      & v4_relat_2(k6_relat_1(A))
      & v8_relat_2(k6_relat_1(A)) ) ),
    file(partfun1,fc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,fc2_partfun1)]).

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

fof(redefinition_k1_partfun1,definition,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(partfun1,k1_partfun1),
    [interesting(0.9),axiom,file(partfun1,k1_partfun1)]).

fof(redefinition_k6_partfun1,definition,(
    ! [A] : k6_partfun1(A) = k6_relat_1(A) ),
    file(partfun1,k6_partfun1),
    [interesting(0.9),axiom,file(partfun1,k6_partfun1)]).

fof(dt_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F))
        & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) ),
    file(partfun1,k1_partfun1),
    [interesting(0.9),axiom,file(partfun1,k1_partfun1)]).

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_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    [interesting(0.9),axiom,file(relat_1,k5_relat_1)]).

fof(dt_k6_partfun1,axiom,(
    ! [A] : 
      ( v1_partfun1(k6_partfun1(A),A,A)
      & m2_relset_1(k6_partfun1(A),A,A) ) ),
    file(partfun1,k6_partfun1),
    [interesting(0.9),axiom,file(partfun1,k6_partfun1)]).

fof(dt_c1_1__funct_7,assumption,
    ( v1_relat_1(c1_1__funct_7)
    & v1_funct_1(c1_1__funct_7) ),
    introduced(assumption,[file(funct_7,c1_1__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c1_1__funct_7)]).

fof(dt_c2_1__funct_7,assumption,(
    $true ),
    introduced(assumption,[file(funct_7,c2_1__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c2_1__funct_7)]).

fof(de_c3_1__funct_7,definition,(
    c3_1__funct_7 = c1_1__funct_7 ),
    introduced(definition,[new_symbol(c3_1__funct_7),file(funct_7,c3_1__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c3_1__funct_7)]).

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(t4_funct_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_relat_1(B),A)
          & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ),
    file(funct_2,t4_funct_2),
    [interesting(0.9),axiom,file(funct_2,t4_funct_2)]).

fof(e2_1__funct_7,plain,
    ( v1_funct_1(c1_1__funct_7)
    & v1_funct_2(c1_1__funct_7,k1_relat_1(c1_1__funct_7),c2_1__funct_7)
    & m2_relset_1(c1_1__funct_7,k1_relat_1(c1_1__funct_7),c2_1__funct_7) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__funct_7,dt_c2_1__funct_7,e1_1__funct_7])],[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,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_partfun1,rc3_funct_1,t1_subset,t4_subset,t5_subset,t8_boole,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_subset_1,rc2_partfun1,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k2_relat_1,dt_m2_relset_1,dt_c1_1__funct_7,dt_c2_1__funct_7,rc1_funct_1,t3_subset,e1_1__funct_7,t4_funct_2]),
    [interesting(0.8),file(funct_7,e2_1__funct_7),[file(funct_7,e2_1__funct_7)]]).

fof(dt_c3_1__funct_7,plain,
    ( v1_funct_1(c3_1__funct_7)
    & v1_funct_2(c3_1__funct_7,k1_relat_1(c1_1__funct_7),c2_1__funct_7)
    & m2_relset_1(c3_1__funct_7,k1_relat_1(c1_1__funct_7),c2_1__funct_7) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__funct_7,dt_c2_1__funct_7,e1_1__funct_7])],[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,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_partfun1,rc3_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_subset_1,rc1_funct_1,rc2_partfun1,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_m2_relset_1,dt_c1_1__funct_7,dt_c2_1__funct_7,de_c3_1__funct_7,e2_1__funct_7]),
    [interesting(0.8),file(funct_7,c3_1__funct_7),[file(funct_7,c3_1__funct_7)]]).

fof(redefinition_k7_relset_1,definition,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(relset_1,k7_relset_1),
    [interesting(0.9),axiom,file(relset_1,k7_relset_1)]).

fof(dt_k7_relset_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D) ) ),
    file(relset_1,k7_relset_1),
    [interesting(0.9),axiom,file(relset_1,k7_relset_1)]).

fof(t23_funct_2,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
        & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ),
    file(funct_2,t23_funct_2),
    [interesting(0.9),axiom,file(funct_2,t23_funct_2)]).

fof(e3_1__funct_7,plain,(
    k1_partfun1(k1_relat_1(c1_1__funct_7),c2_1__funct_7,c2_1__funct_7,c2_1__funct_7,c3_1__funct_7,k6_partfun1(c2_1__funct_7)) = c3_1__funct_7 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__funct_7,dt_c2_1__funct_7,e1_1__funct_7])],[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,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_partfun1,rc3_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_funct_1,cc1_partfun1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_partfun1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_relat_1,dt_k6_relat_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_funct_1,fc1_subset_1,fc2_funct_1,fc2_partfun1,rc1_funct_1,rc2_partfun1,t3_subset,existence_m2_relset_1,redefinition_k1_partfun1,redefinition_k6_partfun1,redefinition_k7_relset_1,redefinition_m2_relset_1,dt_k1_partfun1,dt_k1_relat_1,dt_k6_partfun1,dt_k7_relset_1,dt_m2_relset_1,dt_c1_1__funct_7,dt_c2_1__funct_7,dt_c3_1__funct_7,de_c3_1__funct_7,t23_funct_2]),
    [interesting(0.8),file(funct_7,e3_1__funct_7),[file(funct_7,e3_1__funct_7)]]).

fof(e4_1__funct_7,plain,(
    k5_relat_1(c1_1__funct_7,k6_partfun1(c2_1__funct_7)) = c1_1__funct_7 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__funct_7,dt_c2_1__funct_7,e1_1__funct_7])],[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,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_partfun1,rc3_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_subset_1,cc1_partfun1,cc1_relset_1,fc1_subset_1,rc3_partfun1,t3_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k6_relat_1,dt_m1_relset_1,dt_m2_relset_1,fc1_funct_1,fc2_funct_1,fc2_partfun1,rc1_funct_1,rc2_partfun1,redefinition_k1_partfun1,redefinition_k6_partfun1,dt_k1_partfun1,dt_k1_relat_1,dt_k5_relat_1,dt_k6_partfun1,dt_c1_1__funct_7,dt_c2_1__funct_7,dt_c3_1__funct_7,de_c3_1__funct_7,e3_1__funct_7]),
    [interesting(0.8),file(funct_7,e4_1__funct_7),[file(funct_7,e4_1__funct_7)]]).

fof(i4_1__funct_7,theorem,(
    $true ),
    introduced(tautology,[file(funct_7,i4_1__funct_7)]),
    [interesting(0.8),trivial,file(funct_7,i4_1__funct_7)]).

fof(i3_1__funct_7,plain,(
    k5_relat_1(c1_1__funct_7,k6_partfun1(c2_1__funct_7)) = c1_1__funct_7 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1__funct_7,dt_c2_1__funct_7,e1_1__funct_7])],[e4_1__funct_7,i4_1__funct_7]),
    [interesting(0.8),file(funct_7,i3_1__funct_7),[file(funct_7,i3_1__funct_7)]]).

fof(i2_1__funct_7,plain,
    ( r1_tarski(k2_relat_1(c1_1__funct_7),c2_1__funct_7)
   => k5_relat_1(c1_1__funct_7,k6_partfun1(c2_1__funct_7)) = c1_1__funct_7 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__funct_7,dt_c2_1__funct_7]),discharge_asm(discharge,[e1_1__funct_7])],[e1_1__funct_7,i3_1__funct_7]),
    [interesting(0.8),file(funct_7,i2_1__funct_7),[file(funct_7,i2_1__funct_7)]]).

fof(i2_1_tmp__funct_7,plain,
    ( r1_tarski(k2_relat_1(c1_1__funct_7),c2_1__funct_7)
   => k5_relat_1(c1_1__funct_7,k6_partfun1(c2_1__funct_7)) = c1_1__funct_7 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__funct_7]),discharge_asm(discharge,[dt_c2_1__funct_7])],[dt_c2_1__funct_7,i2_1__funct_7]),
    [interesting(0.8),i1_1__funct_7]).

fof(i1_1__funct_7,plain,(
    ! [A] : 
      ( r1_tarski(k2_relat_1(c1_1__funct_7),A)
     => k5_relat_1(c1_1__funct_7,k6_partfun1(A)) = c1_1__funct_7 ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__funct_7])],[i2_1_tmp__funct_7,dh_c2_1__funct_7]),
    [interesting(0.8),file(funct_7,i1_1__funct_7),[file(funct_7,i1_1__funct_7)]]).

fof(i1_1_tmp__funct_7,plain,
    ( ( v1_relat_1(c1_1__funct_7)
      & v1_funct_1(c1_1__funct_7) )
   => ! [A] : 
        ( r1_tarski(k2_relat_1(c1_1__funct_7),A)
       => k5_relat_1(c1_1__funct_7,k6_partfun1(A)) = c1_1__funct_7 ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__funct_7])],[dt_c1_1__funct_7,i1_1__funct_7]),
    [interesting(1),t1_funct_7]).

fof(t1_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r1_tarski(k2_relat_1(A),B)
         => k5_relat_1(A,k6_partfun1(B)) = A ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__funct_7,dh_c1_1__funct_7]),
    [interesting(1),file(funct_7,t1_funct_7),[file(funct_7,t1_funct_7)]]).