% Mizar problem: t46_bvfunc24,bvfunc24,2615,49 
fof(t46_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))
         => k2_relat_1(J) = k1_bvfunc24(k1_funct_1(J,A),k1_funct_1(J,B),k1_funct_1(J,C),k1_funct_1(J,D),k1_funct_1(J,E),k1_funct_1(J,F),k1_funct_1(J,G),k1_funct_1(J,H),k1_funct_1(J,I)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d10_xboole_0,d1_bvfunc24,d3_tarski,d5_funct_1,dt_k1_bvfunc24,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k3_cqc_lang,dt_m1_subset_1,existence_m1_subset_1,fc1_cqc_lang,fc1_subset_1,fc1_xboole_0,idempotence_k1_funct_4,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,reflexivity_r1_tarski,t1_subset,t2_subset,t3_subset,t45_bvfunc24,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(bvfunc24,t46_bvfunc24)]).

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

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

fof(d1_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( J = k1_bvfunc24(A,B,C,D,E,F,G,H,I)
    <=> ! [K] : 
          ( r2_hidden(K,J)
        <=> ~ ( K != A
              & K != B
              & K != C
              & K != D
              & K != E
              & K != F
              & K != G
              & K != H
              & K != I ) ) ) ),
    file(bvfunc24,d1_bvfunc24),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

fof(dt_k1_bvfunc24,axiom,(
    $true ),
    file(bvfunc24,k1_bvfunc24),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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

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_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

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

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

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

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

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_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t45_bvfunc24,axiom,(
    ! [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))
         => k1_relat_1(J) = k1_bvfunc24(A,B,C,D,E,F,G,H,I) ) ) ),
    file(bvfunc24,t45_bvfunc24),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

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

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),
    []).