% Mizar ND problem: t4_mcart_1,mcart_1,117,65 
fof(dh_c1_4__mcart_1,definition,
    ( ~ ( c1_4__mcart_1 != k1_xboole_0
        & ! [A] : 
            ~ ( r2_hidden(A,c1_4__mcart_1)
              & ! [B,C,D] : 
                  ( ( r2_hidden(B,C)
                    & r2_hidden(C,D)
                    & r2_hidden(D,A) )
                 => r1_xboole_0(B,c1_4__mcart_1) ) ) )
   => ! [E] : 
        ~ ( E != k1_xboole_0
          & ! [F] : 
              ~ ( r2_hidden(F,E)
                & ! [G,H,I] : 
                    ( ( r2_hidden(G,H)
                      & r2_hidden(H,I)
                      & r2_hidden(I,F) )
                   => r1_xboole_0(G,E) ) ) ) ),
    introduced(definition,[new_symbol(c1_4__mcart_1),file(mcart_1,c1_4__mcart_1)]),
    [interesting(0.8),axiom,file(mcart_1,c1_4__mcart_1)]).

fof(e8_4__mcart_1,assumption,(
    c1_4__mcart_1 != k1_xboole_0 ),
    introduced(assumption,[file(mcart_1,e8_4__mcart_1)]),
    [interesting(0.8),axiom,file(mcart_1,e8_4__mcart_1)]).

fof(e13_4__mcart_1,assumption,(
    ! [A] : 
      ~ ( r2_hidden(A,c1_4__mcart_1)
        & ! [B,C,D] : 
            ( ( r2_hidden(B,C)
              & r2_hidden(C,D)
              & r2_hidden(D,A) )
           => r1_xboole_0(B,c1_4__mcart_1) ) ) ),
    introduced(assumption,[file(mcart_1,e13_4__mcart_1)]),
    [interesting(0.8),axiom,file(mcart_1,e13_4__mcart_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(symmetry_r1_xboole_0,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]).

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_4__mcart_1,assumption,(
    $true ),
    introduced(assumption,[file(mcart_1,c1_4__mcart_1)]),
    [interesting(0.8),axiom,file(mcart_1,c1_4__mcart_1)]).

fof(dh_c2_4__mcart_1,definition,
    ( ? [A] : 
      ! [B] : 
        ( r2_hidden(B,A)
      <=> ( r2_hidden(B,k3_tarski(c1_4__mcart_1))
          & ? [C,D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,B)
              & ~ r1_xboole_0(C,c1_4__mcart_1) ) ) )
   => ! [E] : 
        ( r2_hidden(E,c2_4__mcart_1)
      <=> ( r2_hidden(E,k3_tarski(c1_4__mcart_1))
          & ? [F,G] : 
              ( r2_hidden(F,G)
              & r2_hidden(G,E)
              & ~ r1_xboole_0(F,c1_4__mcart_1) ) ) ) ),
    introduced(definition,[new_symbol(c2_4__mcart_1),file(mcart_1,c2_4__mcart_1)]),
    [interesting(0.8),axiom,file(mcart_1,c2_4__mcart_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_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

fof(s1_xboole_0__e1_4__mcart_1,theorem,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(A))
        & ? [D,E] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_1,s1_xboole_0__e1_4__mcart_1),
    [interesting(0.9),axiom,file(mcart_1,s1_xboole_0__e1_4__mcart_1)]).

fof(e1_4__mcart_1,plain,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,k3_tarski(c1_4__mcart_1))
        & ? [C,D] : 
            ( r2_hidden(C,D)
            & r2_hidden(D,B)
            & ~ r1_xboole_0(C,c1_4__mcart_1) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_4__mcart_1])],[symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,s1_xboole_0__e1_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e1_4__mcart_1),[file(mcart_1,e1_4__mcart_1)]]).

fof(dt_c2_4__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_4__mcart_1])],[dh_c2_4__mcart_1,e1_4__mcart_1]),
    [interesting(0.8),file(mcart_1,c2_4__mcart_1),[file(mcart_1,c2_4__mcart_1)]]).

fof(dh_c3_4__mcart_1,definition,
    ( ? [A] : 
      ! [B] : 
        ( r2_hidden(B,A)
      <=> ( r2_hidden(B,k3_tarski(k3_tarski(c1_4__mcart_1)))
          & ? [C] : 
              ( r2_hidden(C,B)
              & ~ r1_xboole_0(C,c1_4__mcart_1) ) ) )
   => ! [D] : 
        ( r2_hidden(D,c3_4__mcart_1)
      <=> ( r2_hidden(D,k3_tarski(k3_tarski(c1_4__mcart_1)))
          & ? [E] : 
              ( r2_hidden(E,D)
              & ~ r1_xboole_0(E,c1_4__mcart_1) ) ) ) ),
    introduced(definition,[new_symbol(c3_4__mcart_1),file(mcart_1,c3_4__mcart_1)]),
    [interesting(0.8),axiom,file(mcart_1,c3_4__mcart_1)]).

fof(s1_xboole_0__e3_4__mcart_1,theorem,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(A)))
        & ? [D] : 
            ( r2_hidden(D,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_1,s1_xboole_0__e3_4__mcart_1),
    [interesting(0.9),axiom,file(mcart_1,s1_xboole_0__e3_4__mcart_1)]).

fof(e3_4__mcart_1,plain,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,k3_tarski(k3_tarski(c1_4__mcart_1)))
        & ? [C] : 
            ( r2_hidden(C,B)
            & ~ r1_xboole_0(C,c1_4__mcart_1) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_4__mcart_1])],[symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,s1_xboole_0__e3_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e3_4__mcart_1),[file(mcart_1,e3_4__mcart_1)]]).

fof(dt_c3_4__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_4__mcart_1])],[dh_c3_4__mcart_1,e3_4__mcart_1]),
    [interesting(0.8),file(mcart_1,c3_4__mcart_1),[file(mcart_1,c3_4__mcart_1)]]).

fof(dh_c4_4__mcart_1,definition,
    ( ? [A] : 
      ! [B] : 
        ( r2_hidden(B,A)
      <=> ( r2_hidden(B,k3_tarski(k3_tarski(k3_tarski(c1_4__mcart_1))))
          & ~ r1_xboole_0(B,c1_4__mcart_1) ) )
   => ! [C] : 
        ( r2_hidden(C,c4_4__mcart_1)
      <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(c1_4__mcart_1))))
          & ~ r1_xboole_0(C,c1_4__mcart_1) ) ) ),
    introduced(definition,[new_symbol(c4_4__mcart_1),file(mcart_1,c4_4__mcart_1)]),
    [interesting(0.8),axiom,file(mcart_1,c4_4__mcart_1)]).

fof(s1_xboole_0__e5_4__mcart_1,theorem,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(A))))
        & ~ r1_xboole_0(C,A) ) ) ),
    file(mcart_1,s1_xboole_0__e5_4__mcart_1),
    [interesting(0.9),axiom,file(mcart_1,s1_xboole_0__e5_4__mcart_1)]).

fof(e5_4__mcart_1,plain,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,k3_tarski(k3_tarski(k3_tarski(c1_4__mcart_1))))
        & ~ r1_xboole_0(B,c1_4__mcart_1) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_4__mcart_1])],[symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,s1_xboole_0__e5_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e5_4__mcart_1),[file(mcart_1,e5_4__mcart_1)]]).

fof(dt_c4_4__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_4__mcart_1])],[dh_c4_4__mcart_1,e5_4__mcart_1]),
    [interesting(0.8),file(mcart_1,c4_4__mcart_1),[file(mcart_1,c4_4__mcart_1)]]).

fof(dh_c6_4__mcart_1,definition,
    ( ? [A] : 
        ( r2_hidden(A,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1))
        & r1_xboole_0(A,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1)) )
   => ( r2_hidden(c6_4__mcart_1,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1))
      & r1_xboole_0(c6_4__mcart_1,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1)) ) ),
    introduced(definition,[new_symbol(c6_4__mcart_1),file(mcart_1,c6_4__mcart_1)]),
    [interesting(0.8),axiom,file(mcart_1,c6_4__mcart_1)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(fc2_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc2_xboole_0)]).

fof(fc3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc3_xboole_0)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

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

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

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(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(t4_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t4_xboole_1)]).

fof(e1_4_1__mcart_1,plain,(
    k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1) = k2_xboole_0(k2_xboole_0(c1_4__mcart_1,k2_xboole_0(c2_4__mcart_1,c3_4__mcart_1)),c4_4__mcart_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__mcart_1])],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,t4_xboole_1]),
    [interesting(0.65),file(mcart_1,e1_4_1__mcart_1),[file(mcart_1,e1_4_1__mcart_1)]]).

fof(e2_4_1__mcart_1,plain,(
    k2_xboole_0(k2_xboole_0(c1_4__mcart_1,k2_xboole_0(c2_4__mcart_1,c3_4__mcart_1)),c4_4__mcart_1) = k2_xboole_0(c1_4__mcart_1,k2_xboole_0(k2_xboole_0(c2_4__mcart_1,c3_4__mcart_1),c4_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__mcart_1])],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,t4_xboole_1]),
    [interesting(0.65),file(mcart_1,e2_4_1__mcart_1),[file(mcart_1,e2_4_1__mcart_1)]]).

fof(e7_4__mcart_1,plain,(
    k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1) = k2_xboole_0(c1_4__mcart_1,k2_xboole_0(k2_xboole_0(c2_4__mcart_1,c3_4__mcart_1),c4_4__mcart_1)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_4__mcart_1])],[e1_4_1__mcart_1,e2_4_1__mcart_1]),
    [interesting(0.8),file(mcart_1,e7_4__mcart_1),[file(mcart_1,e7_4__mcart_1)]]).

fof(t15_xboole_1,theorem,(
    ! [A,B] : 
      ( k2_xboole_0(A,B) = k1_xboole_0
     => A = k1_xboole_0 ) ),
    file(xboole_1,t15_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t15_xboole_1)]).

fof(e9_4__mcart_1,plain,(
    k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,t1_subset,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_xboole_0,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,fc1_xboole_0,t1_boole,t6_boole,e8_4__mcart_1,e7_4__mcart_1,t15_xboole_1]),
    [interesting(0.8),file(mcart_1,e9_4__mcart_1),[file(mcart_1,e9_4__mcart_1)]]).

fof(t1_mcart_1,theorem,(
    ! [A] : 
      ~ ( A != k1_xboole_0
        & ! [B] : 
            ~ ( r2_hidden(B,A)
              & r1_xboole_0(B,A) ) ) ),
    file(mcart_1,t1_mcart_1),
    [interesting(0.9),axiom,file(mcart_1,t1_mcart_1)]).

fof(e10_4__mcart_1,plain,(
    ? [A] : 
      ( r2_hidden(A,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1))
      & r1_xboole_0(A,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1)) ) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1])],[existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,fc1_xboole_0,t1_boole,t1_subset,t6_boole,t7_boole,e9_4__mcart_1,t1_mcart_1]),
    [interesting(0.8),file(mcart_1,e10_4__mcart_1),[file(mcart_1,e10_4__mcart_1)]]).

fof(dt_c6_4__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1])],[dh_c6_4__mcart_1,e10_4__mcart_1]),
    [interesting(0.8),file(mcart_1,c6_4__mcart_1),[file(mcart_1,c6_4__mcart_1)]]).

fof(e1_4_4__mcart_1,assumption,(
    r2_hidden(c6_4__mcart_1,c3_4__mcart_1) ),
    introduced(assumption,[file(mcart_1,e1_4_4__mcart_1)]),
    [interesting(0.65),axiom,file(mcart_1,e1_4_4__mcart_1)]).

fof(dh_c1_4_4__mcart_1,definition,
    ( ? [A] : 
        ( r2_hidden(A,c6_4__mcart_1)
        & ~ r1_xboole_0(A,c1_4__mcart_1) )
   => ( r2_hidden(c1_4_4__mcart_1,c6_4__mcart_1)
      & ~ r1_xboole_0(c1_4_4__mcart_1,c1_4__mcart_1) ) ),
    introduced(definition,[new_symbol(c1_4_4__mcart_1),file(mcart_1,c1_4_4__mcart_1)]),
    [interesting(0.65),axiom,file(mcart_1,c1_4_4__mcart_1)]).

fof(e4_4__mcart_1,plain,(
    ! [A] : 
      ( r2_hidden(A,c3_4__mcart_1)
    <=> ( r2_hidden(A,k3_tarski(k3_tarski(c1_4__mcart_1)))
        & ? [B] : 
            ( r2_hidden(B,A)
            & ~ r1_xboole_0(B,c1_4__mcart_1) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__mcart_1])],[dh_c3_4__mcart_1,e3_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e4_4__mcart_1),[file(mcart_1,e4_4__mcart_1)]]).

fof(e2_4_4__mcart_1,plain,(
    ? [A] : 
      ( r2_hidden(A,c6_4__mcart_1)
      & ~ r1_xboole_0(A,c1_4__mcart_1) ) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c3_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e1_4_4__mcart_1,e4_4__mcart_1]),
    [interesting(0.65),file(mcart_1,e2_4_4__mcart_1),[file(mcart_1,e2_4_4__mcart_1)]]).

fof(dt_c1_4_4__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,e1_4_4__mcart_1,dt_c1_4__mcart_1])],[dh_c1_4_4__mcart_1,e2_4_4__mcart_1]),
    [interesting(0.65),file(mcart_1,c1_4_4__mcart_1),[file(mcart_1,c1_4_4__mcart_1)]]).

fof(e4_4_4__mcart_1,plain,(
    r2_hidden(c6_4__mcart_1,k3_tarski(k3_tarski(c1_4__mcart_1))) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c3_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e4_4__mcart_1,e1_4_4__mcart_1]),
    [interesting(0.65),file(mcart_1,e4_4_4__mcart_1),[file(mcart_1,e4_4_4__mcart_1)]]).

fof(e3_4_4__mcart_1,plain,
    ( r2_hidden(c1_4_4__mcart_1,c6_4__mcart_1)
    & ~ r1_xboole_0(c1_4_4__mcart_1,c1_4__mcart_1) ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,e1_4_4__mcart_1,dt_c1_4__mcart_1])],[dh_c1_4_4__mcart_1,e2_4_4__mcart_1]),
    [interesting(0.65),file(mcart_1,e3_4_4__mcart_1),[file(mcart_1,e3_4_4__mcart_1)]]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.9),axiom,file(tarski,d4_tarski)]).

fof(e5_4_4__mcart_1,plain,(
    r2_hidden(c1_4_4__mcart_1,k3_tarski(k3_tarski(k3_tarski(c1_4__mcart_1)))) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c1_4_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e4_4_4__mcart_1,e3_4_4__mcart_1,d4_tarski]),
    [interesting(0.65),file(mcart_1,e5_4_4__mcart_1),[file(mcart_1,e5_4_4__mcart_1)]]).

fof(e6_4__mcart_1,plain,(
    ! [A] : 
      ( r2_hidden(A,c4_4__mcart_1)
    <=> ( r2_hidden(A,k3_tarski(k3_tarski(k3_tarski(c1_4__mcart_1))))
        & ~ r1_xboole_0(A,c1_4__mcart_1) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__mcart_1])],[dh_c4_4__mcart_1,e5_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e6_4__mcart_1),[file(mcart_1,e6_4__mcart_1)]]).

fof(e6_4_4__mcart_1,plain,(
    r2_hidden(c1_4_4__mcart_1,c4_4__mcart_1) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c1_4_4__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e5_4_4__mcart_1,e6_4__mcart_1,e3_4_4__mcart_1]),
    [interesting(0.65),file(mcart_1,e6_4_4__mcart_1),[file(mcart_1,e6_4_4__mcart_1)]]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d2_xboole_0)]).

fof(e7_4_4__mcart_1,plain,(
    r2_hidden(c1_4_4__mcart_1,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c1_4_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,t1_subset,t7_boole,e6_4_4__mcart_1,d2_xboole_0]),
    [interesting(0.65),file(mcart_1,e7_4_4__mcart_1),[file(mcart_1,e7_4_4__mcart_1)]]).

fof(e12_4__mcart_1,plain,(
    r1_xboole_0(c6_4__mcart_1,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1)) ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1])],[dh_c6_4__mcart_1,e10_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e12_4__mcart_1),[file(mcart_1,e12_4__mcart_1)]]).

fof(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : 
              ~ ( r2_hidden(C,A)
                & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,t3_xboole_0)]).

fof(e8_4_4__mcart_1,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c1_4_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e7_4_4__mcart_1,e12_4__mcart_1,e3_4_4__mcart_1,t3_xboole_0]),
    [interesting(0.65),file(mcart_1,e8_4_4__mcart_1),[file(mcart_1,e8_4_4__mcart_1)]]).

fof(i2_4_4__mcart_1,theorem,(
    $true ),
    introduced(tautology,[file(mcart_1,i2_4_4__mcart_1)]),
    [interesting(0.65),trivial,file(mcart_1,i2_4_4__mcart_1)]).

fof(i1_4_4__mcart_1,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e8_4__mcart_1,e1_4_4__mcart_1,dt_c1_4__mcart_1])],[e8_4_4__mcart_1,i2_4_4__mcart_1]),
    [interesting(0.65),file(mcart_1,i1_4_4__mcart_1),[file(mcart_1,i1_4_4__mcart_1)]]).

fof(e19_4__mcart_1,plain,(
    ~ r2_hidden(c6_4__mcart_1,c3_4__mcart_1) ),
    inference(discharge_asm,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1]),discharge_asm(discharge,[e1_4_4__mcart_1])],[e1_4_4__mcart_1,i1_4_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e19_4__mcart_1),[file(mcart_1,e19_4__mcart_1)]]).

fof(e1_4_3__mcart_1,assumption,(
    r2_hidden(c6_4__mcart_1,c2_4__mcart_1) ),
    introduced(assumption,[file(mcart_1,e1_4_3__mcart_1)]),
    [interesting(0.65),axiom,file(mcart_1,e1_4_3__mcart_1)]).

fof(dh_c1_4_3__mcart_1,definition,
    ( ? [A,B] : 
        ( r2_hidden(A,B)
        & r2_hidden(B,c6_4__mcart_1)
        & ~ r1_xboole_0(A,c1_4__mcart_1) )
   => ? [C] : 
        ( r2_hidden(c1_4_3__mcart_1,C)
        & r2_hidden(C,c6_4__mcart_1)
        & ~ r1_xboole_0(c1_4_3__mcart_1,c1_4__mcart_1) ) ),
    introduced(definition,[new_symbol(c1_4_3__mcart_1),file(mcart_1,c1_4_3__mcart_1)]),
    [interesting(0.65),axiom,file(mcart_1,c1_4_3__mcart_1)]).

fof(e2_4__mcart_1,plain,(
    ! [A] : 
      ( r2_hidden(A,c2_4__mcart_1)
    <=> ( r2_hidden(A,k3_tarski(c1_4__mcart_1))
        & ? [B,C] : 
            ( r2_hidden(B,C)
            & r2_hidden(C,A)
            & ~ r1_xboole_0(B,c1_4__mcart_1) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__mcart_1])],[dh_c2_4__mcart_1,e1_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e2_4__mcart_1),[file(mcart_1,e2_4__mcart_1)]]).

fof(e2_4_3__mcart_1,plain,(
    ? [A,B] : 
      ( r2_hidden(A,B)
      & r2_hidden(B,c6_4__mcart_1)
      & ~ r1_xboole_0(A,c1_4__mcart_1) ) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_3__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e1_4_3__mcart_1,e2_4__mcart_1]),
    [interesting(0.65),file(mcart_1,e2_4_3__mcart_1),[file(mcart_1,e2_4_3__mcart_1)]]).

fof(dt_c1_4_3__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,e1_4_3__mcart_1,dt_c1_4__mcart_1])],[dh_c1_4_3__mcart_1,e2_4_3__mcart_1]),
    [interesting(0.65),file(mcart_1,c1_4_3__mcart_1),[file(mcart_1,c1_4_3__mcart_1)]]).

fof(dh_c2_4_3__mcart_1,definition,
    ( ? [A] : 
        ( r2_hidden(c1_4_3__mcart_1,A)
        & r2_hidden(A,c6_4__mcart_1)
        & ~ r1_xboole_0(c1_4_3__mcart_1,c1_4__mcart_1) )
   => ( r2_hidden(c1_4_3__mcart_1,c2_4_3__mcart_1)
      & r2_hidden(c2_4_3__mcart_1,c6_4__mcart_1)
      & ~ r1_xboole_0(c1_4_3__mcart_1,c1_4__mcart_1) ) ),
    introduced(definition,[new_symbol(c2_4_3__mcart_1),file(mcart_1,c2_4_3__mcart_1)]),
    [interesting(0.65),axiom,file(mcart_1,c2_4_3__mcart_1)]).

fof(dt_c2_4_3__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,e1_4_3__mcart_1,dt_c1_4__mcart_1])],[dh_c1_4_3__mcart_1,dh_c2_4_3__mcart_1,e2_4_3__mcart_1]),
    [interesting(0.65),file(mcart_1,c2_4_3__mcart_1),[file(mcart_1,c2_4_3__mcart_1)]]).

fof(e4_4_3__mcart_1,plain,(
    r2_hidden(c6_4__mcart_1,k3_tarski(c1_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_3__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e2_4__mcart_1,e1_4_3__mcart_1]),
    [interesting(0.65),file(mcart_1,e4_4_3__mcart_1),[file(mcart_1,e4_4_3__mcart_1)]]).

fof(e3_4_3__mcart_1,plain,
    ( r2_hidden(c1_4_3__mcart_1,c2_4_3__mcart_1)
    & r2_hidden(c2_4_3__mcart_1,c6_4__mcart_1)
    & ~ r1_xboole_0(c1_4_3__mcart_1,c1_4__mcart_1) ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,e1_4_3__mcart_1,dt_c1_4__mcart_1])],[dh_c1_4_3__mcart_1,dh_c2_4_3__mcart_1,e2_4_3__mcart_1]),
    [interesting(0.65),file(mcart_1,e3_4_3__mcart_1),[file(mcart_1,e3_4_3__mcart_1)]]).

fof(e5_4_3__mcart_1,plain,(
    r2_hidden(c2_4_3__mcart_1,k3_tarski(k3_tarski(c1_4__mcart_1))) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_3__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c1_4_3__mcart_1,dt_c2_4_3__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e4_4_3__mcart_1,e3_4_3__mcart_1,d4_tarski]),
    [interesting(0.65),file(mcart_1,e5_4_3__mcart_1),[file(mcart_1,e5_4_3__mcart_1)]]).

fof(e6_4_3__mcart_1,plain,(
    r2_hidden(c2_4_3__mcart_1,c3_4__mcart_1) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_3__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c1_4_3__mcart_1,dt_c2_4_3__mcart_1,dt_c3_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e5_4_3__mcart_1,e4_4__mcart_1,e3_4_3__mcart_1]),
    [interesting(0.65),file(mcart_1,e6_4_3__mcart_1),[file(mcart_1,e6_4_3__mcart_1)]]).

fof(e7_4_3__mcart_1,plain,(
    r2_hidden(c2_4_3__mcart_1,k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_3__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c2_4_3__mcart_1,dt_c3_4__mcart_1,t1_subset,t7_boole,e6_4_3__mcart_1,d2_xboole_0]),
    [interesting(0.65),file(mcart_1,e7_4_3__mcart_1),[file(mcart_1,e7_4_3__mcart_1)]]).

fof(e8_4_3__mcart_1,plain,(
    ~ r1_xboole_0(c6_4__mcart_1,k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,e1_4_3__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c1_4_3__mcart_1,dt_c2_4__mcart_1,dt_c2_4_3__mcart_1,dt_c3_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e7_4_3__mcart_1,e3_4_3__mcart_1,t3_xboole_0]),
    [interesting(0.65),file(mcart_1,e8_4_3__mcart_1),[file(mcart_1,e8_4_3__mcart_1)]]).

fof(t70_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ~ ( ~ r1_xboole_0(A,k2_xboole_0(B,C))
          & r1_xboole_0(A,B)
          & r1_xboole_0(A,C) )
      & ~ ( ~ ( r1_xboole_0(A,B)
              & r1_xboole_0(A,C) )
          & r1_xboole_0(A,k2_xboole_0(B,C)) ) ) ),
    file(xboole_1,t70_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t70_xboole_1)]).

fof(e9_4_3__mcart_1,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_4_3__mcart_1,e8_4__mcart_1,dt_c1_4__mcart_1])],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_xboole_0,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,e8_4_3__mcart_1,e12_4__mcart_1,t70_xboole_1]),
    [interesting(0.65),file(mcart_1,e9_4_3__mcart_1),[file(mcart_1,e9_4_3__mcart_1)]]).

fof(i2_4_3__mcart_1,theorem,(
    $true ),
    introduced(tautology,[file(mcart_1,i2_4_3__mcart_1)]),
    [interesting(0.65),trivial,file(mcart_1,i2_4_3__mcart_1)]).

fof(i1_4_3__mcart_1,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_4_3__mcart_1,e8_4__mcart_1,dt_c1_4__mcart_1])],[e9_4_3__mcart_1,i2_4_3__mcart_1]),
    [interesting(0.65),file(mcart_1,i1_4_3__mcart_1),[file(mcart_1,i1_4_3__mcart_1)]]).

fof(e17_4__mcart_1,plain,(
    ~ r2_hidden(c6_4__mcart_1,c2_4__mcart_1) ),
    inference(discharge_asm,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1]),discharge_asm(discharge,[e1_4_3__mcart_1])],[e1_4_3__mcart_1,i1_4_3__mcart_1]),
    [interesting(0.8),file(mcart_1,e17_4__mcart_1),[file(mcart_1,e17_4__mcart_1)]]).

fof(e1_4_2__mcart_1,assumption,(
    r2_hidden(c6_4__mcart_1,c1_4__mcart_1) ),
    introduced(assumption,[file(mcart_1,e1_4_2__mcart_1)]),
    [interesting(0.65),axiom,file(mcart_1,e1_4_2__mcart_1)]).

fof(dh_c1_4_2__mcart_1,definition,
    ( ? [A,B,C] : 
        ( r2_hidden(A,B)
        & r2_hidden(B,C)
        & r2_hidden(C,c6_4__mcart_1)
        & ~ r1_xboole_0(A,c1_4__mcart_1) )
   => ? [D,E] : 
        ( r2_hidden(c1_4_2__mcart_1,D)
        & r2_hidden(D,E)
        & r2_hidden(E,c6_4__mcart_1)
        & ~ r1_xboole_0(c1_4_2__mcart_1,c1_4__mcart_1) ) ),
    introduced(definition,[new_symbol(c1_4_2__mcart_1),file(mcart_1,c1_4_2__mcart_1)]),
    [interesting(0.65),axiom,file(mcart_1,c1_4_2__mcart_1)]).

fof(e2_4_2__mcart_1,plain,(
    ? [A,B,C] : 
      ( r2_hidden(A,B)
      & r2_hidden(B,C)
      & r2_hidden(C,c6_4__mcart_1)
      & ~ r1_xboole_0(A,c1_4__mcart_1) ) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_c1_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e1_4_2__mcart_1,e13_4__mcart_1]),
    [interesting(0.65),file(mcart_1,e2_4_2__mcart_1),[file(mcart_1,e2_4_2__mcart_1)]]).

fof(dt_c1_4_2__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dh_c1_4_2__mcart_1,e2_4_2__mcart_1]),
    [interesting(0.65),file(mcart_1,c1_4_2__mcart_1),[file(mcart_1,c1_4_2__mcart_1)]]).

fof(dh_c2_4_2__mcart_1,definition,
    ( ? [A,B] : 
        ( r2_hidden(c1_4_2__mcart_1,A)
        & r2_hidden(A,B)
        & r2_hidden(B,c6_4__mcart_1)
        & ~ r1_xboole_0(c1_4_2__mcart_1,c1_4__mcart_1) )
   => ? [C] : 
        ( r2_hidden(c1_4_2__mcart_1,c2_4_2__mcart_1)
        & r2_hidden(c2_4_2__mcart_1,C)
        & r2_hidden(C,c6_4__mcart_1)
        & ~ r1_xboole_0(c1_4_2__mcart_1,c1_4__mcart_1) ) ),
    introduced(definition,[new_symbol(c2_4_2__mcart_1),file(mcart_1,c2_4_2__mcart_1)]),
    [interesting(0.65),axiom,file(mcart_1,c2_4_2__mcart_1)]).

fof(dt_c2_4_2__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dh_c1_4_2__mcart_1,dh_c2_4_2__mcart_1,e2_4_2__mcart_1]),
    [interesting(0.65),file(mcart_1,c2_4_2__mcart_1),[file(mcart_1,c2_4_2__mcart_1)]]).

fof(dh_c3_4_2__mcart_1,definition,
    ( ? [A] : 
        ( r2_hidden(c1_4_2__mcart_1,c2_4_2__mcart_1)
        & r2_hidden(c2_4_2__mcart_1,A)
        & r2_hidden(A,c6_4__mcart_1)
        & ~ r1_xboole_0(c1_4_2__mcart_1,c1_4__mcart_1) )
   => ( r2_hidden(c1_4_2__mcart_1,c2_4_2__mcart_1)
      & r2_hidden(c2_4_2__mcart_1,c3_4_2__mcart_1)
      & r2_hidden(c3_4_2__mcart_1,c6_4__mcart_1)
      & ~ r1_xboole_0(c1_4_2__mcart_1,c1_4__mcart_1) ) ),
    introduced(definition,[new_symbol(c3_4_2__mcart_1),file(mcart_1,c3_4_2__mcart_1)]),
    [interesting(0.65),axiom,file(mcart_1,c3_4_2__mcart_1)]).

fof(dt_c3_4_2__mcart_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dh_c1_4_2__mcart_1,dh_c2_4_2__mcart_1,dh_c3_4_2__mcart_1,e2_4_2__mcart_1]),
    [interesting(0.65),file(mcart_1,c3_4_2__mcart_1),[file(mcart_1,c3_4_2__mcart_1)]]).

fof(e3_4_2__mcart_1,plain,
    ( r2_hidden(c1_4_2__mcart_1,c2_4_2__mcart_1)
    & r2_hidden(c2_4_2__mcart_1,c3_4_2__mcart_1)
    & r2_hidden(c3_4_2__mcart_1,c6_4__mcart_1)
    & ~ r1_xboole_0(c1_4_2__mcart_1,c1_4__mcart_1) ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dh_c1_4_2__mcart_1,dh_c2_4_2__mcart_1,dh_c3_4_2__mcart_1,e2_4_2__mcart_1]),
    [interesting(0.65),file(mcart_1,e3_4_2__mcart_1),[file(mcart_1,e3_4_2__mcart_1)]]).

fof(e4_4_2__mcart_1,plain,
    ( r2_hidden(c3_4_2__mcart_1,k3_tarski(c1_4__mcart_1))
    & ~ r1_xboole_0(c1_4_2__mcart_1,c1_4__mcart_1) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c1_4_2__mcart_1,dt_c2_4_2__mcart_1,dt_c3_4_2__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e1_4_2__mcart_1,e3_4_2__mcart_1,d4_tarski]),
    [interesting(0.65),file(mcart_1,e4_4_2__mcart_1),[file(mcart_1,e4_4_2__mcart_1)]]).

fof(e5_4_2__mcart_1,plain,(
    r2_hidden(c3_4_2__mcart_1,c2_4__mcart_1) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c1_4_2__mcart_1,dt_c2_4__mcart_1,dt_c2_4_2__mcart_1,dt_c3_4_2__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e4_4_2__mcart_1,e2_4__mcart_1,e3_4_2__mcart_1]),
    [interesting(0.65),file(mcart_1,e5_4_2__mcart_1),[file(mcart_1,e5_4_2__mcart_1)]]).

fof(e6_4_2__mcart_1,plain,(
    r2_hidden(c3_4_2__mcart_1,k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4_2__mcart_1,t1_subset,t7_boole,e5_4_2__mcart_1,d2_xboole_0]),
    [interesting(0.65),file(mcart_1,e6_4_2__mcart_1),[file(mcart_1,e6_4_2__mcart_1)]]).

fof(e7_4_2__mcart_1,plain,(
    r2_hidden(c3_4_2__mcart_1,k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c3_4_2__mcart_1,t1_subset,t7_boole,e6_4_2__mcart_1,d2_xboole_0]),
    [interesting(0.65),file(mcart_1,e7_4_2__mcart_1),[file(mcart_1,e7_4_2__mcart_1)]]).

fof(e8_4_2__mcart_1,plain,(
    r2_hidden(c3_4_2__mcart_1,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c3_4_2__mcart_1,dt_c4_4__mcart_1,t1_subset,t7_boole,e7_4_2__mcart_1,d2_xboole_0]),
    [interesting(0.65),file(mcart_1,e8_4_2__mcart_1),[file(mcart_1,e8_4_2__mcart_1)]]).

fof(e9_4_2__mcart_1,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c1_4_2__mcart_1,dt_c2_4__mcart_1,dt_c2_4_2__mcart_1,dt_c3_4__mcart_1,dt_c3_4_2__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e8_4_2__mcart_1,e12_4__mcart_1,e3_4_2__mcart_1,t3_xboole_0]),
    [interesting(0.65),file(mcart_1,e9_4_2__mcart_1),[file(mcart_1,e9_4_2__mcart_1)]]).

fof(i2_4_2__mcart_1,theorem,(
    $true ),
    introduced(tautology,[file(mcart_1,i2_4_2__mcart_1)]),
    [interesting(0.65),trivial,file(mcart_1,i2_4_2__mcart_1)]).

fof(i1_4_2__mcart_1,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e1_4_2__mcart_1,e13_4__mcart_1])],[e9_4_2__mcart_1,i2_4_2__mcart_1]),
    [interesting(0.65),file(mcart_1,i1_4_2__mcart_1),[file(mcart_1,i1_4_2__mcart_1)]]).

fof(e14_4__mcart_1,plain,(
    ~ r2_hidden(c6_4__mcart_1,c1_4__mcart_1) ),
    inference(discharge_asm,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1,e13_4__mcart_1]),discharge_asm(discharge,[e1_4_2__mcart_1])],[e1_4_2__mcart_1,i1_4_2__mcart_1]),
    [interesting(0.8),file(mcart_1,e14_4__mcart_1),[file(mcart_1,e14_4__mcart_1)]]).

fof(e11_4__mcart_1,plain,(
    r2_hidden(c6_4__mcart_1,k2_xboole_0(k2_xboole_0(k2_xboole_0(c1_4__mcart_1,c2_4__mcart_1),c3_4__mcart_1),c4_4__mcart_1)) ),
    inference(consider,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1])],[dh_c6_4__mcart_1,e10_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e11_4__mcart_1),[file(mcart_1,e11_4__mcart_1)]]).

fof(e15_4__mcart_1,plain,(
    r2_hidden(c6_4__mcart_1,k2_xboole_0(k2_xboole_0(c2_4__mcart_1,c3_4__mcart_1),c4_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([e13_4__mcart_1,e8_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e14_4__mcart_1,e7_4__mcart_1,e11_4__mcart_1,d2_xboole_0]),
    [interesting(0.8),file(mcart_1,e15_4__mcart_1),[file(mcart_1,e15_4__mcart_1)]]).

fof(e16_4__mcart_1,plain,(
    r2_hidden(c6_4__mcart_1,k2_xboole_0(c2_4__mcart_1,k2_xboole_0(c3_4__mcart_1,c4_4__mcart_1))) ),
    inference(mizar_by,[status(thm),assumptions([e13_4__mcart_1,e8_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e15_4__mcart_1,t4_xboole_1]),
    [interesting(0.8),file(mcart_1,e16_4__mcart_1),[file(mcart_1,e16_4__mcart_1)]]).

fof(e18_4__mcart_1,plain,(
    r2_hidden(c6_4__mcart_1,k2_xboole_0(c3_4__mcart_1,c4_4__mcart_1)) ),
    inference(mizar_by,[status(thm),assumptions([e13_4__mcart_1,e8_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e17_4__mcart_1,e16_4__mcart_1,d2_xboole_0]),
    [interesting(0.8),file(mcart_1,e18_4__mcart_1),[file(mcart_1,e18_4__mcart_1)]]).

fof(e20_4__mcart_1,plain,(
    r2_hidden(c6_4__mcart_1,c4_4__mcart_1) ),
    inference(mizar_by,[status(thm),assumptions([e13_4__mcart_1,e8_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k2_xboole_0,dt_c3_4__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e19_4__mcart_1,e18_4__mcart_1,d2_xboole_0]),
    [interesting(0.8),file(mcart_1,e20_4__mcart_1),[file(mcart_1,e20_4__mcart_1)]]).

fof(e21_4__mcart_1,plain,(
    ~ r1_xboole_0(c6_4__mcart_1,c1_4__mcart_1) ),
    inference(mizar_by,[status(thm),assumptions([e13_4__mcart_1,e8_4__mcart_1,dt_c1_4__mcart_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_4__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,t1_subset,t7_boole,e20_4__mcart_1,e6_4__mcart_1]),
    [interesting(0.8),file(mcart_1,e21_4__mcart_1),[file(mcart_1,e21_4__mcart_1)]]).

fof(e22_4__mcart_1,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e13_4__mcart_1,e8_4__mcart_1,dt_c1_4__mcart_1])],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_xboole_0,dt_k2_xboole_0,dt_c1_4__mcart_1,dt_c2_4__mcart_1,dt_c3_4__mcart_1,dt_c4_4__mcart_1,dt_c6_4__mcart_1,e21_4__mcart_1,e7_4__mcart_1,e12_4__mcart_1,t70_xboole_1]),
    [interesting(0.8),file(mcart_1,e22_4__mcart_1),[file(mcart_1,e22_4__mcart_1)]]).

fof(i4_4__mcart_1,theorem,(
    $true ),
    introduced(tautology,[file(mcart_1,i4_4__mcart_1)]),
    [interesting(0.8),trivial,file(mcart_1,i4_4__mcart_1)]).

fof(i3_4__mcart_1,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e13_4__mcart_1,e8_4__mcart_1,dt_c1_4__mcart_1])],[e22_4__mcart_1,i4_4__mcart_1]),
    [interesting(0.8),file(mcart_1,i3_4__mcart_1),[file(mcart_1,i3_4__mcart_1)]]).

fof(i2_4__mcart_1,plain,(
    ? [A] : 
      ( r2_hidden(A,c1_4__mcart_1)
      & ! [B,C,D] : 
          ( ( r2_hidden(B,C)
            & r2_hidden(C,D)
            & r2_hidden(D,A) )
         => r1_xboole_0(B,c1_4__mcart_1) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e8_4__mcart_1,dt_c1_4__mcart_1]),discharge_asm(discharge,[e13_4__mcart_1])],[e13_4__mcart_1,i3_4__mcart_1]),
    [interesting(0.8),file(mcart_1,i2_4__mcart_1),[file(mcart_1,i2_4__mcart_1)]]).

fof(i1_4__mcart_1,plain,(
    ~ ( c1_4__mcart_1 != k1_xboole_0
      & ! [A] : 
          ~ ( r2_hidden(A,c1_4__mcart_1)
            & ! [B,C,D] : 
                ( ( r2_hidden(B,C)
                  & r2_hidden(C,D)
                  & r2_hidden(D,A) )
               => r1_xboole_0(B,c1_4__mcart_1) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__mcart_1]),discharge_asm(discharge,[e8_4__mcart_1])],[e8_4__mcart_1,i2_4__mcart_1]),
    [interesting(0.8),file(mcart_1,i1_4__mcart_1),[file(mcart_1,i1_4__mcart_1)]]).

fof(i1_4_tmp__mcart_1,plain,(
    ~ ( c1_4__mcart_1 != k1_xboole_0
      & ! [A] : 
          ~ ( r2_hidden(A,c1_4__mcart_1)
            & ! [B,C,D] : 
                ( ( r2_hidden(B,C)
                  & r2_hidden(C,D)
                  & r2_hidden(D,A) )
               => r1_xboole_0(B,c1_4__mcart_1) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__mcart_1])],[dt_c1_4__mcart_1,i1_4__mcart_1]),
    [interesting(1),t4_mcart_1]).

fof(t4_mcart_1,theorem,(
    ! [A] : 
      ~ ( A != k1_xboole_0
        & ! [B] : 
            ~ ( r2_hidden(B,A)
              & ! [C,D,E] : 
                  ( ( r2_hidden(C,D)
                    & r2_hidden(D,E)
                    & r2_hidden(E,B) )
                 => r1_xboole_0(C,A) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__mcart_1,dh_c1_4__mcart_1]),
    [interesting(1),file(mcart_1,t4_mcart_1),[file(mcart_1,t4_mcart_1)]]).