% Mizar problem: t2_mcart_6,mcart_6,588,23 
fof(t2_mcart_6,conjecture,(
    ! [A] : ~ ( A != k1_xboole_0
      & ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q] : 
              ( ( r2_hidden(C,D)
                & r2_hidden(D,E)
                & r2_hidden(E,F)
                & r2_hidden(F,G)
                & r2_hidden(G,H)
                & r2_hidden(H,I)
                & r2_hidden(I,J)
                & r2_hidden(J,K)
                & r2_hidden(K,L)
                & r2_hidden(L,M)
                & r2_hidden(M,N)
                & r2_hidden(N,O)
                & r2_hidden(O,P)
                & r2_hidden(P,Q)
                & r2_hidden(Q,B) )
             => r1_xboole_0(C,A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,commutativity_k2_xboole_0,d2_xboole_0,d4_tarski,dt_k1_xboole_0,dt_k2_xboole_0,dt_k3_tarski,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,fc2_xboole_0,fc3_xboole_0,idempotence_k2_xboole_0,rc1_xboole_0,rc2_xboole_0,s1_xboole_0__e11_2__mcart_6,s1_xboole_0__e13_2__mcart_6,s1_xboole_0__e15_2__mcart_6,s1_xboole_0__e17_2__mcart_6,s1_xboole_0__e19_2__mcart_6,s1_xboole_0__e1_2__mcart_6,s1_xboole_0__e21_2__mcart_6,s1_xboole_0__e23_2__mcart_6,s1_xboole_0__e25_2__mcart_6,s1_xboole_0__e27_2__mcart_6,s1_xboole_0__e29_2__mcart_6,s1_xboole_0__e3_2__mcart_6,s1_xboole_0__e5_2__mcart_6,s1_xboole_0__e7_2__mcart_6,s1_xboole_0__e9_2__mcart_6,symmetry_r1_xboole_0,t15_xboole_1,t1_boole,t1_mcart_1,t1_subset,t2_subset,t3_xboole_0,t4_xboole_1,t6_boole,t70_xboole_1,t7_boole,t8_boole]),
    [file(mcart_6,t2_mcart_6)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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

fof(d2_xboole_0,axiom,(
    ! [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),
    []).

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

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

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

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

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

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

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

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

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

fof(s1_xboole_0__e11_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A)))))))
        & ? [D,E,F,G,H,I,J,K,L] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,I)
            & r2_hidden(I,J)
            & r2_hidden(J,K)
            & r2_hidden(K,L)
            & r2_hidden(L,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e11_2__mcart_6),
    []).

fof(s1_xboole_0__e13_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A))))))))
        & ? [D,E,F,G,H,I,J,K] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,I)
            & r2_hidden(I,J)
            & r2_hidden(J,K)
            & r2_hidden(K,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e13_2__mcart_6),
    []).

fof(s1_xboole_0__e15_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A)))))))))
        & ? [D,E,F,G,H,I,J] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,I)
            & r2_hidden(I,J)
            & r2_hidden(J,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e15_2__mcart_6),
    []).

fof(s1_xboole_0__e17_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A))))))))))
        & ? [D,E,F,G,H,I] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,I)
            & r2_hidden(I,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e17_2__mcart_6),
    []).

fof(s1_xboole_0__e19_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A)))))))))))
        & ? [D,E,F,G,H] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e19_2__mcart_6),
    []).

fof(s1_xboole_0__e1_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(A))
        & ? [D,E,F,G,H,I,J,K,L,M,N,O,P,Q] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,I)
            & r2_hidden(I,J)
            & r2_hidden(J,K)
            & r2_hidden(K,L)
            & r2_hidden(L,M)
            & r2_hidden(M,N)
            & r2_hidden(N,O)
            & r2_hidden(O,P)
            & r2_hidden(P,Q)
            & r2_hidden(Q,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e1_2__mcart_6),
    []).

fof(s1_xboole_0__e21_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A))))))))))))
        & ? [D,E,F,G] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e21_2__mcart_6),
    []).

fof(s1_xboole_0__e23_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A)))))))))))))
        & ? [D,E,F] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e23_2__mcart_6),
    []).

fof(s1_xboole_0__e25_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A))))))))))))))
        & ? [D,E] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e25_2__mcart_6),
    []).

fof(s1_xboole_0__e27_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A)))))))))))))))
        & ? [D] : 
            ( r2_hidden(D,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e27_2__mcart_6),
    []).

fof(s1_xboole_0__e29_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A))))))))))))))))
        & ~ r1_xboole_0(C,A) ) ) ),
    file(mcart_6,s1_xboole_0__e29_2__mcart_6),
    []).

fof(s1_xboole_0__e3_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(A)))
        & ? [D,E,F,G,H,I,J,K,L,M,N,O,P] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,I)
            & r2_hidden(I,J)
            & r2_hidden(J,K)
            & r2_hidden(K,L)
            & r2_hidden(L,M)
            & r2_hidden(M,N)
            & r2_hidden(N,O)
            & r2_hidden(O,P)
            & r2_hidden(P,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e3_2__mcart_6),
    []).

fof(s1_xboole_0__e5_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(A))))
        & ? [D,E,F,G,H,I,J,K,L,M,N,O] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,I)
            & r2_hidden(I,J)
            & r2_hidden(J,K)
            & r2_hidden(K,L)
            & r2_hidden(L,M)
            & r2_hidden(M,N)
            & r2_hidden(N,O)
            & r2_hidden(O,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e5_2__mcart_6),
    []).

fof(s1_xboole_0__e7_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(A)))))
        & ? [D,E,F,G,H,I,J,K,L,M,N] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,I)
            & r2_hidden(I,J)
            & r2_hidden(J,K)
            & r2_hidden(K,L)
            & r2_hidden(L,M)
            & r2_hidden(M,N)
            & r2_hidden(N,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e7_2__mcart_6),
    []).

fof(s1_xboole_0__e9_2__mcart_6,axiom,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(k3_tarski(k3_tarski(k3_tarski(A))))))
        & ? [D,E,F,G,H,I,J,K,L,M] : 
            ( r2_hidden(D,E)
            & r2_hidden(E,F)
            & r2_hidden(F,G)
            & r2_hidden(G,H)
            & r2_hidden(H,I)
            & r2_hidden(I,J)
            & r2_hidden(J,K)
            & r2_hidden(K,L)
            & r2_hidden(L,M)
            & r2_hidden(M,C)
            & ~ r1_xboole_0(D,A) ) ) ) ),
    file(mcart_6,s1_xboole_0__e9_2__mcart_6),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

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

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

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

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

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

fof(t3_xboole_0,axiom,(
    ! [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),
    []).

fof(t4_xboole_1,axiom,(
    ! [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),
    []).

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

fof(t70_xboole_1,axiom,(
    ! [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),
    []).

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

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