% Mizar ND problem: t6_funct_4,funct_4,134,34 
fof(dh_c1_7__funct_4,definition,
    ( ! [A,B,C] : 
        ( r1_tarski(k2_funcop_1(c1_7__funct_4,A),k2_funcop_1(B,C))
       => r1_tarski(c1_7__funct_4,B) )
   => ! [D,E,F,G] : 
        ( r1_tarski(k2_funcop_1(D,E),k2_funcop_1(F,G))
       => r1_tarski(D,F) ) ),
    introduced(definition,[new_symbol(c1_7__funct_4),file(funct_4,c1_7__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_7__funct_4)]).

fof(dh_c2_7__funct_4,definition,
    ( ! [A,B] : 
        ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(A,B))
       => r1_tarski(c1_7__funct_4,A) )
   => ! [C,D,E] : 
        ( r1_tarski(k2_funcop_1(c1_7__funct_4,C),k2_funcop_1(D,E))
       => r1_tarski(c1_7__funct_4,D) ) ),
    introduced(definition,[new_symbol(c2_7__funct_4),file(funct_4,c2_7__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c2_7__funct_4)]).

fof(dh_c3_7__funct_4,definition,
    ( ! [A] : 
        ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(c3_7__funct_4,A))
       => r1_tarski(c1_7__funct_4,c3_7__funct_4) )
   => ! [B,C] : 
        ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(B,C))
       => r1_tarski(c1_7__funct_4,B) ) ),
    introduced(definition,[new_symbol(c3_7__funct_4),file(funct_4,c3_7__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c3_7__funct_4)]).

fof(dh_c4_7__funct_4,definition,
    ( ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(c3_7__funct_4,c4_7__funct_4))
     => r1_tarski(c1_7__funct_4,c3_7__funct_4) )
   => ! [A] : 
        ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(c3_7__funct_4,A))
       => r1_tarski(c1_7__funct_4,c3_7__funct_4) ) ),
    introduced(definition,[new_symbol(c4_7__funct_4),file(funct_4,c4_7__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c4_7__funct_4)]).

fof(e1_7__funct_4,assumption,(
    r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(c3_7__funct_4,c4_7__funct_4)) ),
    introduced(assumption,[file(funct_4,e1_7__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,e1_7__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(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_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_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(dt_c1_7__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c1_7__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_7__funct_4)]).

fof(dt_c2_7__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c2_7__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c2_7__funct_4)]).

fof(dt_c3_7__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c3_7__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c3_7__funct_4)]).

fof(dt_c4_7__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c4_7__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c4_7__funct_4)]).

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(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(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_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(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t19_funcop_1)]).

fof(t25_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) ) ),
    file(relat_1,t25_relat_1),
    [interesting(0.9),axiom,file(relat_1,t25_relat_1)]).

fof(e2_7__funct_4,plain,
    ( r1_tarski(k1_relat_1(k2_funcop_1(c1_7__funct_4,c2_7__funct_4)),k1_relat_1(k2_funcop_1(c3_7__funct_4,c4_7__funct_4)))
    & k1_relat_1(k2_funcop_1(c1_7__funct_4,c2_7__funct_4)) = c1_7__funct_4
    & k1_relat_1(k2_funcop_1(c3_7__funct_4,c4_7__funct_4)) = c3_7__funct_4 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__funct_4,dt_c2_7__funct_4,dt_c3_7__funct_4,dt_c4_7__funct_4,e1_7__funct_4])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,rc1_funct_1,reflexivity_r1_tarski,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_c1_7__funct_4,dt_c2_7__funct_4,dt_c3_7__funct_4,dt_c4_7__funct_4,fc1_funcop_1,t3_subset,e1_7__funct_4,t19_funcop_1,t25_relat_1]),
    [interesting(0.8),file(funct_4,e2_7__funct_4),[file(funct_4,e2_7__funct_4)]]).

fof(e3_7__funct_4,plain,(
    r1_tarski(c1_7__funct_4,c3_7__funct_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__funct_4,dt_c2_7__funct_4,dt_c3_7__funct_4,dt_c4_7__funct_4,e1_7__funct_4])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,rc1_funct_1,reflexivity_r1_tarski,dt_k1_relat_1,dt_k2_funcop_1,dt_c1_7__funct_4,dt_c2_7__funct_4,dt_c3_7__funct_4,dt_c4_7__funct_4,fc1_funcop_1,t3_subset,e2_7__funct_4]),
    [interesting(0.8),file(funct_4,e3_7__funct_4),[file(funct_4,e3_7__funct_4)]]).

fof(i6_7__funct_4,theorem,(
    $true ),
    introduced(tautology,[file(funct_4,i6_7__funct_4)]),
    [interesting(0.8),trivial,file(funct_4,i6_7__funct_4)]).

fof(i5_7__funct_4,plain,(
    r1_tarski(c1_7__funct_4,c3_7__funct_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__funct_4,dt_c2_7__funct_4,dt_c3_7__funct_4,dt_c4_7__funct_4,e1_7__funct_4])],[e3_7__funct_4,i6_7__funct_4]),
    [interesting(0.8),file(funct_4,i5_7__funct_4),[file(funct_4,i5_7__funct_4)]]).

fof(i4_7__funct_4,plain,
    ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(c3_7__funct_4,c4_7__funct_4))
   => r1_tarski(c1_7__funct_4,c3_7__funct_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__funct_4,dt_c2_7__funct_4,dt_c3_7__funct_4,dt_c4_7__funct_4]),discharge_asm(discharge,[e1_7__funct_4])],[e1_7__funct_4,i5_7__funct_4]),
    [interesting(0.8),file(funct_4,i4_7__funct_4),[file(funct_4,i4_7__funct_4)]]).

fof(i4_7_tmp__funct_4,plain,
    ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(c3_7__funct_4,c4_7__funct_4))
   => r1_tarski(c1_7__funct_4,c3_7__funct_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__funct_4,dt_c2_7__funct_4,dt_c3_7__funct_4]),discharge_asm(discharge,[dt_c4_7__funct_4])],[dt_c4_7__funct_4,i4_7__funct_4]),
    [interesting(0.8),i3_7__funct_4]).

fof(i3_7__funct_4,plain,(
    ! [A] : 
      ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(c3_7__funct_4,A))
     => r1_tarski(c1_7__funct_4,c3_7__funct_4) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__funct_4,dt_c2_7__funct_4,dt_c3_7__funct_4])],[i4_7_tmp__funct_4,dh_c4_7__funct_4]),
    [interesting(0.8),file(funct_4,i3_7__funct_4),[file(funct_4,i3_7__funct_4)]]).

fof(i3_7_tmp__funct_4,plain,(
    ! [A] : 
      ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(c3_7__funct_4,A))
     => r1_tarski(c1_7__funct_4,c3_7__funct_4) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__funct_4,dt_c2_7__funct_4]),discharge_asm(discharge,[dt_c3_7__funct_4])],[dt_c3_7__funct_4,i3_7__funct_4]),
    [interesting(0.8),i2_7__funct_4]).

fof(i2_7__funct_4,plain,(
    ! [A,B] : 
      ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(A,B))
     => r1_tarski(c1_7__funct_4,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__funct_4,dt_c2_7__funct_4])],[i3_7_tmp__funct_4,dh_c3_7__funct_4]),
    [interesting(0.8),file(funct_4,i2_7__funct_4),[file(funct_4,i2_7__funct_4)]]).

fof(i2_7_tmp__funct_4,plain,(
    ! [A,B] : 
      ( r1_tarski(k2_funcop_1(c1_7__funct_4,c2_7__funct_4),k2_funcop_1(A,B))
     => r1_tarski(c1_7__funct_4,A) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__funct_4]),discharge_asm(discharge,[dt_c2_7__funct_4])],[dt_c2_7__funct_4,i2_7__funct_4]),
    [interesting(0.8),i1_7__funct_4]).

fof(i1_7__funct_4,plain,(
    ! [A,B,C] : 
      ( r1_tarski(k2_funcop_1(c1_7__funct_4,A),k2_funcop_1(B,C))
     => r1_tarski(c1_7__funct_4,B) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__funct_4])],[i2_7_tmp__funct_4,dh_c2_7__funct_4]),
    [interesting(0.8),file(funct_4,i1_7__funct_4),[file(funct_4,i1_7__funct_4)]]).

fof(i1_7_tmp__funct_4,plain,(
    ! [A,B,C] : 
      ( r1_tarski(k2_funcop_1(c1_7__funct_4,A),k2_funcop_1(B,C))
     => r1_tarski(c1_7__funct_4,B) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__funct_4])],[dt_c1_7__funct_4,i1_7__funct_4]),
    [interesting(1),t6_funct_4]).

fof(t6_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D))
     => r1_tarski(A,C) ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__funct_4,dh_c1_7__funct_4]),
    [interesting(1),file(funct_4,t6_funct_4),[file(funct_4,t6_funct_4)]]).