% Mizar ND problem: t9_funct_4,funct_4,177,8 
fof(dh_c1_11__funct_4,definition,
    ( ! [A,B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,B),A),B) )
   => ! [C,D,E] : 
        ( ( v1_relat_1(E)
          & v1_funct_1(E) )
       => r1_tarski(k7_relat_1(k8_relat_1(C,E),D),E) ) ),
    introduced(definition,[new_symbol(c1_11__funct_4),file(funct_4,c1_11__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_11__funct_4)]).

fof(dh_c2_11__funct_4,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,A),c2_11__funct_4),A) )
   => ! [B,C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,C),B),C) ) ),
    introduced(definition,[new_symbol(c2_11__funct_4),file(funct_4,c2_11__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c2_11__funct_4)]).

fof(dh_c3_11__funct_4,definition,
    ( ( ( v1_relat_1(c3_11__funct_4)
        & v1_funct_1(c3_11__funct_4) )
     => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,c3_11__funct_4),c2_11__funct_4),c3_11__funct_4) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,A),c2_11__funct_4),A) ) ),
    introduced(definition,[new_symbol(c3_11__funct_4),file(funct_4,c3_11__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c3_11__funct_4)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_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(fc5_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k8_relat_1(A,B))
        & v1_funct_1(k8_relat_1(A,B)) ) ) ),
    file(funct_1,fc5_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc5_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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_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_k8_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => v1_relat_1(k8_relat_1(A,B)) ) ),
    file(relat_1,k8_relat_1),
    [interesting(0.9),axiom,file(relat_1,k8_relat_1)]).

fof(dt_c1_11__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c1_11__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_11__funct_4)]).

fof(dt_c2_11__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c2_11__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c2_11__funct_4)]).

fof(dt_c3_11__funct_4,assumption,
    ( v1_relat_1(c3_11__funct_4)
    & v1_funct_1(c3_11__funct_4) ),
    introduced(assumption,[file(funct_4,c3_11__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c3_11__funct_4)]).

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(t88_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k7_relat_1(B,A),B) ) ),
    file(relat_1,t88_relat_1),
    [interesting(0.9),axiom,file(relat_1,t88_relat_1)]).

fof(t117_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k8_relat_1(A,B),B) ) ),
    file(relat_1,t117_relat_1),
    [interesting(0.9),axiom,file(relat_1,t117_relat_1)]).

fof(e1_11__funct_4,plain,
    ( r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,c3_11__funct_4),c2_11__funct_4),k8_relat_1(c1_11__funct_4,c3_11__funct_4))
    & r1_tarski(k8_relat_1(c1_11__funct_4,c3_11__funct_4),c3_11__funct_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_11__funct_4,dt_c2_11__funct_4,dt_c3_11__funct_4])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc4_funct_1,fc5_funct_1,rc1_funct_1,reflexivity_r1_tarski,dt_k7_relat_1,dt_k8_relat_1,dt_c1_11__funct_4,dt_c2_11__funct_4,dt_c3_11__funct_4,t3_subset,t88_relat_1,t117_relat_1]),
    [interesting(0.8),file(funct_4,e1_11__funct_4),[file(funct_4,e1_11__funct_4)]]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t1_xboole_1)]).

fof(e2_11__funct_4,plain,(
    r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,c3_11__funct_4),c2_11__funct_4),c3_11__funct_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_11__funct_4,dt_c2_11__funct_4,dt_c3_11__funct_4])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc4_funct_1,fc5_funct_1,rc1_funct_1,reflexivity_r1_tarski,dt_k7_relat_1,dt_k8_relat_1,dt_c1_11__funct_4,dt_c2_11__funct_4,dt_c3_11__funct_4,t3_subset,e1_11__funct_4,t1_xboole_1]),
    [interesting(0.8),file(funct_4,e2_11__funct_4),[file(funct_4,e2_11__funct_4)]]).

fof(i4_11__funct_4,theorem,(
    $true ),
    introduced(tautology,[file(funct_4,i4_11__funct_4)]),
    [interesting(0.8),trivial,file(funct_4,i4_11__funct_4)]).

fof(i3_11__funct_4,plain,(
    r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,c3_11__funct_4),c2_11__funct_4),c3_11__funct_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_11__funct_4,dt_c2_11__funct_4,dt_c3_11__funct_4])],[e2_11__funct_4,i4_11__funct_4]),
    [interesting(0.8),file(funct_4,i3_11__funct_4),[file(funct_4,i3_11__funct_4)]]).

fof(i3_11_tmp__funct_4,plain,
    ( ( v1_relat_1(c3_11__funct_4)
      & v1_funct_1(c3_11__funct_4) )
   => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,c3_11__funct_4),c2_11__funct_4),c3_11__funct_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_11__funct_4,dt_c2_11__funct_4]),discharge_asm(discharge,[dt_c3_11__funct_4])],[dt_c3_11__funct_4,i3_11__funct_4]),
    [interesting(0.8),i2_11__funct_4]).

fof(i2_11__funct_4,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,A),c2_11__funct_4),A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_11__funct_4,dt_c2_11__funct_4])],[i3_11_tmp__funct_4,dh_c3_11__funct_4]),
    [interesting(0.8),file(funct_4,i2_11__funct_4),[file(funct_4,i2_11__funct_4)]]).

fof(i2_11_tmp__funct_4,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,A),c2_11__funct_4),A) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_11__funct_4]),discharge_asm(discharge,[dt_c2_11__funct_4])],[dt_c2_11__funct_4,i2_11__funct_4]),
    [interesting(0.8),i1_11__funct_4]).

fof(i1_11__funct_4,plain,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,B),A),B) ) ),
    inference(let,[status(thm),assumptions([dt_c1_11__funct_4])],[i2_11_tmp__funct_4,dh_c2_11__funct_4]),
    [interesting(0.8),file(funct_4,i1_11__funct_4),[file(funct_4,i1_11__funct_4)]]).

fof(i1_11_tmp__funct_4,plain,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_tarski(k7_relat_1(k8_relat_1(c1_11__funct_4,B),A),B) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_11__funct_4])],[dt_c1_11__funct_4,i1_11__funct_4]),
    [interesting(1),t9_funct_4]).

fof(t9_funct_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C) ) ),
    inference(let,[status(thm),assumptions([])],[i1_11_tmp__funct_4,dh_c1_11__funct_4]),
    [interesting(1),file(funct_4,t9_funct_4),[file(funct_4,t9_funct_4)]]).