% Mizar ND problem: t14_xboole_1,xboole_1,150,79 
fof(dh_c1_14__xboole_1,definition,
    ( ! [A,B] : 
        ( ( r1_tarski(c1_14__xboole_1,A)
          & r1_tarski(B,A)
          & ! [C] : 
              ( ( r1_tarski(c1_14__xboole_1,C)
                & r1_tarski(B,C) )
             => r1_tarski(A,C) ) )
       => A = k2_xboole_0(c1_14__xboole_1,B) )
   => ! [D,E,F] : 
        ( ( r1_tarski(D,E)
          & r1_tarski(F,E)
          & ! [G] : 
              ( ( r1_tarski(D,G)
                & r1_tarski(F,G) )
             => r1_tarski(E,G) ) )
       => E = k2_xboole_0(D,F) ) ),
    introduced(definition,[new_symbol(c1_14__xboole_1),file(xboole_1,c1_14__xboole_1)]),
    [interesting(0.8),axiom,file(xboole_1,c1_14__xboole_1)]).

fof(dh_c2_14__xboole_1,definition,
    ( ! [A] : 
        ( ( r1_tarski(c1_14__xboole_1,c2_14__xboole_1)
          & r1_tarski(A,c2_14__xboole_1)
          & ! [B] : 
              ( ( r1_tarski(c1_14__xboole_1,B)
                & r1_tarski(A,B) )
             => r1_tarski(c2_14__xboole_1,B) ) )
       => c2_14__xboole_1 = k2_xboole_0(c1_14__xboole_1,A) )
   => ! [C,D] : 
        ( ( r1_tarski(c1_14__xboole_1,C)
          & r1_tarski(D,C)
          & ! [E] : 
              ( ( r1_tarski(c1_14__xboole_1,E)
                & r1_tarski(D,E) )
             => r1_tarski(C,E) ) )
       => C = k2_xboole_0(c1_14__xboole_1,D) ) ),
    introduced(definition,[new_symbol(c2_14__xboole_1),file(xboole_1,c2_14__xboole_1)]),
    [interesting(0.8),axiom,file(xboole_1,c2_14__xboole_1)]).

fof(dh_c3_14__xboole_1,definition,
    ( ( ( r1_tarski(c1_14__xboole_1,c2_14__xboole_1)
        & r1_tarski(c3_14__xboole_1,c2_14__xboole_1)
        & ! [A] : 
            ( ( r1_tarski(c1_14__xboole_1,A)
              & r1_tarski(c3_14__xboole_1,A) )
           => r1_tarski(c2_14__xboole_1,A) ) )
     => c2_14__xboole_1 = k2_xboole_0(c1_14__xboole_1,c3_14__xboole_1) )
   => ! [B] : 
        ( ( r1_tarski(c1_14__xboole_1,c2_14__xboole_1)
          & r1_tarski(B,c2_14__xboole_1)
          & ! [C] : 
              ( ( r1_tarski(c1_14__xboole_1,C)
                & r1_tarski(B,C) )
             => r1_tarski(c2_14__xboole_1,C) ) )
       => c2_14__xboole_1 = k2_xboole_0(c1_14__xboole_1,B) ) ),
    introduced(definition,[new_symbol(c3_14__xboole_1),file(xboole_1,c3_14__xboole_1)]),
    [interesting(0.8),axiom,file(xboole_1,c3_14__xboole_1)]).

fof(e1_14__xboole_1,assumption,(
    r1_tarski(c1_14__xboole_1,c2_14__xboole_1) ),
    introduced(assumption,[file(xboole_1,e1_14__xboole_1)]),
    [interesting(0.8),axiom,file(xboole_1,e1_14__xboole_1)]).

fof(e2_14__xboole_1,assumption,(
    r1_tarski(c3_14__xboole_1,c2_14__xboole_1) ),
    introduced(assumption,[file(xboole_1,e2_14__xboole_1)]),
    [interesting(0.8),axiom,file(xboole_1,e2_14__xboole_1)]).

fof(e3_14__xboole_1,assumption,(
    ! [A] : 
      ( ( r1_tarski(c1_14__xboole_1,A)
        & r1_tarski(c3_14__xboole_1,A) )
     => r1_tarski(c2_14__xboole_1,A) ) ),
    introduced(assumption,[file(xboole_1,e3_14__xboole_1)]),
    [interesting(0.8),axiom,file(xboole_1,e3_14__xboole_1)]).

fof(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(dt_c1_14__xboole_1,assumption,(
    $true ),
    introduced(assumption,[file(xboole_1,c1_14__xboole_1)]),
    [interesting(0.8),axiom,file(xboole_1,c1_14__xboole_1)]).

fof(dt_c2_14__xboole_1,assumption,(
    $true ),
    introduced(assumption,[file(xboole_1,c2_14__xboole_1)]),
    [interesting(0.8),axiom,file(xboole_1,c2_14__xboole_1)]).

fof(dt_c3_14__xboole_1,assumption,(
    $true ),
    introduced(assumption,[file(xboole_1,c3_14__xboole_1)]),
    [interesting(0.8),axiom,file(xboole_1,c3_14__xboole_1)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t7_xboole_1)]).

fof(e4_14__xboole_1,plain,
    ( r1_tarski(c1_14__xboole_1,k2_xboole_0(c1_14__xboole_1,c3_14__xboole_1))
    & r1_tarski(c3_14__xboole_1,k2_xboole_0(c1_14__xboole_1,c3_14__xboole_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_14__xboole_1,dt_c3_14__xboole_1])],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_c1_14__xboole_1,dt_c3_14__xboole_1,t7_xboole_1]),
    [interesting(0.8),file(xboole_1,e4_14__xboole_1),[file(xboole_1,e4_14__xboole_1)]]).

fof(e5_14__xboole_1,plain,(
    r1_tarski(c2_14__xboole_1,k2_xboole_0(c1_14__xboole_1,c3_14__xboole_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_14__xboole_1,dt_c1_14__xboole_1,dt_c3_14__xboole_1,e3_14__xboole_1])],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_c1_14__xboole_1,dt_c2_14__xboole_1,dt_c3_14__xboole_1,e4_14__xboole_1,e3_14__xboole_1]),
    [interesting(0.8),file(xboole_1,e5_14__xboole_1),[file(xboole_1,e5_14__xboole_1)]]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t8_xboole_1)]).

fof(e6_14__xboole_1,plain,(
    r1_tarski(k2_xboole_0(c1_14__xboole_1,c3_14__xboole_1),c2_14__xboole_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_14__xboole_1,dt_c2_14__xboole_1,dt_c3_14__xboole_1,e1_14__xboole_1,e2_14__xboole_1])],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_c1_14__xboole_1,dt_c2_14__xboole_1,dt_c3_14__xboole_1,e1_14__xboole_1,e2_14__xboole_1,t8_xboole_1]),
    [interesting(0.8),file(xboole_1,e6_14__xboole_1),[file(xboole_1,e6_14__xboole_1)]]).

fof(i6_14__xboole_1,theorem,(
    $true ),
    introduced(tautology,[file(xboole_1,i6_14__xboole_1)]),
    [interesting(0.8),trivial,file(xboole_1,i6_14__xboole_1)]).

fof(i5_14__xboole_1,plain,(
    r1_tarski(k2_xboole_0(c1_14__xboole_1,c3_14__xboole_1),c2_14__xboole_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_14__xboole_1,dt_c2_14__xboole_1,dt_c3_14__xboole_1,e1_14__xboole_1,e2_14__xboole_1])],[e6_14__xboole_1,i6_14__xboole_1]),
    [interesting(0.8),file(xboole_1,i5_14__xboole_1),[file(xboole_1,i5_14__xboole_1)]]).

fof(i4_14__xboole_1,plain,(
    c2_14__xboole_1 = k2_xboole_0(c1_14__xboole_1,c3_14__xboole_1) ),
    inference(conclusion,[status(thm),assumptions([e3_14__xboole_1,dt_c1_14__xboole_1,dt_c2_14__xboole_1,dt_c3_14__xboole_1,e1_14__xboole_1,e2_14__xboole_1])],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_c1_14__xboole_1,dt_c2_14__xboole_1,dt_c3_14__xboole_1,d10_xboole_0,e5_14__xboole_1,i5_14__xboole_1]),
    [interesting(0.8),file(xboole_1,i4_14__xboole_1),[file(xboole_1,i4_14__xboole_1)]]).

fof(i3_14__xboole_1,plain,
    ( ( r1_tarski(c1_14__xboole_1,c2_14__xboole_1)
      & r1_tarski(c3_14__xboole_1,c2_14__xboole_1)
      & ! [A] : 
          ( ( r1_tarski(c1_14__xboole_1,A)
            & r1_tarski(c3_14__xboole_1,A) )
         => r1_tarski(c2_14__xboole_1,A) ) )
   => c2_14__xboole_1 = k2_xboole_0(c1_14__xboole_1,c3_14__xboole_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_14__xboole_1,dt_c2_14__xboole_1,dt_c3_14__xboole_1]),discharge_asm(discharge,[e1_14__xboole_1,e2_14__xboole_1,e3_14__xboole_1])],[e1_14__xboole_1,e2_14__xboole_1,e3_14__xboole_1,i4_14__xboole_1]),
    [interesting(0.8),file(xboole_1,i3_14__xboole_1),[file(xboole_1,i3_14__xboole_1)]]).

fof(i3_14_tmp__xboole_1,plain,
    ( ( r1_tarski(c1_14__xboole_1,c2_14__xboole_1)
      & r1_tarski(c3_14__xboole_1,c2_14__xboole_1)
      & ! [A] : 
          ( ( r1_tarski(c1_14__xboole_1,A)
            & r1_tarski(c3_14__xboole_1,A) )
         => r1_tarski(c2_14__xboole_1,A) ) )
   => c2_14__xboole_1 = k2_xboole_0(c1_14__xboole_1,c3_14__xboole_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_14__xboole_1,dt_c2_14__xboole_1]),discharge_asm(discharge,[dt_c3_14__xboole_1])],[dt_c3_14__xboole_1,i3_14__xboole_1]),
    [interesting(0.8),i2_14__xboole_1]).

fof(i2_14__xboole_1,plain,(
    ! [A] : 
      ( ( r1_tarski(c1_14__xboole_1,c2_14__xboole_1)
        & r1_tarski(A,c2_14__xboole_1)
        & ! [B] : 
            ( ( r1_tarski(c1_14__xboole_1,B)
              & r1_tarski(A,B) )
           => r1_tarski(c2_14__xboole_1,B) ) )
     => c2_14__xboole_1 = k2_xboole_0(c1_14__xboole_1,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_14__xboole_1,dt_c2_14__xboole_1])],[i3_14_tmp__xboole_1,dh_c3_14__xboole_1]),
    [interesting(0.8),file(xboole_1,i2_14__xboole_1),[file(xboole_1,i2_14__xboole_1)]]).

fof(i2_14_tmp__xboole_1,plain,(
    ! [A] : 
      ( ( r1_tarski(c1_14__xboole_1,c2_14__xboole_1)
        & r1_tarski(A,c2_14__xboole_1)
        & ! [B] : 
            ( ( r1_tarski(c1_14__xboole_1,B)
              & r1_tarski(A,B) )
           => r1_tarski(c2_14__xboole_1,B) ) )
     => c2_14__xboole_1 = k2_xboole_0(c1_14__xboole_1,A) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_14__xboole_1]),discharge_asm(discharge,[dt_c2_14__xboole_1])],[dt_c2_14__xboole_1,i2_14__xboole_1]),
    [interesting(0.8),i1_14__xboole_1]).

fof(i1_14__xboole_1,plain,(
    ! [A,B] : 
      ( ( r1_tarski(c1_14__xboole_1,A)
        & r1_tarski(B,A)
        & ! [C] : 
            ( ( r1_tarski(c1_14__xboole_1,C)
              & r1_tarski(B,C) )
           => r1_tarski(A,C) ) )
     => A = k2_xboole_0(c1_14__xboole_1,B) ) ),
    inference(let,[status(thm),assumptions([dt_c1_14__xboole_1])],[i2_14_tmp__xboole_1,dh_c2_14__xboole_1]),
    [interesting(0.8),file(xboole_1,i1_14__xboole_1),[file(xboole_1,i1_14__xboole_1)]]).

fof(i1_14_tmp__xboole_1,plain,(
    ! [A,B] : 
      ( ( r1_tarski(c1_14__xboole_1,A)
        & r1_tarski(B,A)
        & ! [C] : 
            ( ( r1_tarski(c1_14__xboole_1,C)
              & r1_tarski(B,C) )
           => r1_tarski(A,C) ) )
     => A = k2_xboole_0(c1_14__xboole_1,B) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_14__xboole_1])],[dt_c1_14__xboole_1,i1_14__xboole_1]),
    [interesting(1),t14_xboole_1]).

fof(t14_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B)
        & ! [D] : 
            ( ( r1_tarski(A,D)
              & r1_tarski(C,D) )
           => r1_tarski(B,D) ) )
     => B = k2_xboole_0(A,C) ) ),
    inference(let,[status(thm),assumptions([])],[i1_14_tmp__xboole_1,dh_c1_14__xboole_1]),
    [interesting(1),file(xboole_1,t14_xboole_1),[file(xboole_1,t14_xboole_1)]]).