% Mizar problem: t44_bvfunc24,bvfunc24,2487,30 
fof(t44_bvfunc24,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( ( v1_relat_1(J)
        & v1_funct_1(J) )
     => ! [K,L,M,N,O,P,Q,R,S] : 
          ( J = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,L),k3_cqc_lang(C,M)),k3_cqc_lang(D,N)),k3_cqc_lang(E,O)),k3_cqc_lang(F,P)),k3_cqc_lang(G,Q)),k3_cqc_lang(H,R)),k3_cqc_lang(I,S)),k3_cqc_lang(A,K))
         => ( A = B
            | A = C
            | A = D
            | A = E
            | A = F
            | A = G
            | A = H
            | A = I
            | B = C
            | B = D
            | B = E
            | B = F
            | B = G
            | B = H
            | B = I
            | C = D
            | C = E
            | C = F
            | C = G
            | C = H
            | C = I
            | D = E
            | D = F
            | D = G
            | D = H
            | D = I
            | E = F
            | E = G
            | E = H
            | E = I
            | F = G
            | F = H
            | F = I
            | G = H
            | G = I
            | H = I
            | ( k1_funct_1(J,A) = K
              & k1_funct_1(J,B) = L
              & k1_funct_1(J,C) = M
              & k1_funct_1(J,D) = N
              & k1_funct_1(J,E) = O
              & k1_funct_1(J,F) = P
              & k1_funct_1(J,G) = Q
              & k1_funct_1(J,H) = R
              & k1_funct_1(J,I) = S ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_tarski,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_k3_cqc_lang,dt_m1_subset_1,existence_m1_subset_1,fc1_cqc_lang,fc1_xboole_0,fc2_subset_1,idempotence_k1_funct_4,rc1_xboole_0,rc2_xboole_0,t12_funct_4,t14_funct_4,t15_bvfunc14,t1_subset,t21_bvfunc24,t2_subset,t3_yellow14,t5_cqc_lang,t6_boole,t6_cqc_lang,t7_boole,t8_boole]),
    [file(bvfunc24,t44_bvfunc24)]).

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

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k3_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k3_cqc_lang),
    []).

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_cqc_lang,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B)) ) ),
    file(cqc_lang,fc1_cqc_lang),
    []).

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

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(idempotence_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    []).

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(t12_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    []).

fof(t14_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    []).

fof(t15_bvfunc14,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D,E] : 
          ( B != C
         => k1_funct_1(k1_funct_4(k1_funct_4(A,k3_cqc_lang(B,D)),k3_cqc_lang(C,E)),B) = D ) ) ),
    file(bvfunc14,t15_bvfunc14),
    []).

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

fof(t21_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( ( v1_relat_1(I)
        & v1_funct_1(I) )
     => ! [J,K,L,M,N,O,P,Q] : 
          ( I = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,K),k3_cqc_lang(C,L)),k3_cqc_lang(D,M)),k3_cqc_lang(E,N)),k3_cqc_lang(F,O)),k3_cqc_lang(G,P)),k3_cqc_lang(H,Q)),k3_cqc_lang(A,J))
         => ( A = B
            | A = C
            | A = D
            | A = E
            | A = F
            | A = G
            | A = H
            | B = C
            | B = D
            | B = E
            | B = F
            | B = G
            | B = H
            | C = D
            | C = E
            | C = F
            | C = G
            | C = H
            | D = E
            | D = F
            | D = G
            | D = H
            | E = F
            | E = G
            | E = H
            | F = G
            | F = H
            | G = H
            | ( k1_funct_1(I,B) = K
              & k1_funct_1(I,C) = L
              & k1_funct_1(I,D) = M
              & k1_funct_1(I,E) = N
              & k1_funct_1(I,F) = O
              & k1_funct_1(I,G) = P ) ) ) ) ),
    file(bvfunc24,t21_bvfunc24),
    []).

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_yellow14,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_funct_1(k1_funct_4(A,k3_cqc_lang(B,C)),B) = C ) ),
    file(yellow14,t3_yellow14),
    []).

fof(t5_cqc_lang,axiom,(
    ! [A,B] : 
      ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A)
      & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ),
    file(cqc_lang,t5_cqc_lang),
    []).

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

fof(t6_cqc_lang,axiom,(
    ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ),
    file(cqc_lang,t6_cqc_lang),
    []).

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),
    []).