% Mizar problem: t47_ami_1,ami_1,1093,40 
fof(t47_ami_1,conjecture,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D,E] : 
          ( ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(D,k1_funct_1(A,B))
            & r2_hidden(C,k1_relat_1(A))
            & r2_hidden(E,k1_funct_1(A,C)) )
         => r2_hidden(k4_funct_4(B,C,D,E),k7_ami_1(A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_setfam_1,cc2_funct_1,d2_cqc_lang,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_funcop_1,dt_k3_cqc_lang,dt_k4_funct_4,dt_k7_ami_1,dt_m1_subset_1,existence_m1_subset_1,fc10_ami_1,fc12_relat_1,fc17_finseq_1,fc1_cqc_lang,fc1_finset_1,fc1_funcop_1,fc1_funct_4,fc1_xboole_0,fc2_finseq_1,fc2_funcop_1,fc2_setfam_1,fc2_subset_1,fc3_funcop_1,fc4_relat_1,fc5_relat_1,fc7_relat_1,fc9_funcop_1,idempotence_k1_funct_4,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_funct_1,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc5_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t18_ami_1,t1_subset,t2_subset,t36_ami_1,t46_ami_1,t6_boole,t7_boole,t8_boole]),
    [file(ami_1,t47_ami_1)]).

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

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

fof(cc1_setfam_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(d2_cqc_lang,axiom,(
    ! [A,B] : k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B) ),
    file(cqc_lang,d2_cqc_lang),
    []).

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_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    []).

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

fof(dt_k4_funct_4,axiom,(
    $true ),
    file(funct_4,k4_funct_4),
    []).

fof(dt_k7_ami_1,axiom,(
    $true ),
    file(ami_1,k7_ami_1),
    []).

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(fc10_ami_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k7_ami_1(A))
        & v1_fraenkel(k7_ami_1(A)) ) ) ),
    file(ami_1,fc10_ami_1),
    []).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

fof(fc1_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    []).

fof(fc1_funct_4,axiom,(
    ! [A,B,C,D] : 
      ( v1_relat_1(k4_funct_4(A,B,C,D))
      & v1_funct_1(k4_funct_4(A,B,C,D)) ) ),
    file(funct_4,fc1_funct_4),
    []).

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

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_funcop_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    []).

fof(fc2_setfam_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_setfam_1(k1_tarski(A)) ) ) ),
    file(setfam_1,fc2_setfam_1),
    []).

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

fof(fc3_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(fc9_funcop_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_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_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc1_setfam_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_1),
    []).

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

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(rc5_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(t18_ami_1,axiom,(
    ! [A,B,C,D] : k4_funct_4(A,B,C,D) = k1_funct_4(k3_cqc_lang(A,C),k3_cqc_lang(B,D)) ),
    file(ami_1,t18_ami_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(t36_ami_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(B,k1_funct_1(C,A)) )
       => r2_hidden(k3_cqc_lang(A,B),k7_ami_1(C)) ) ) ),
    file(ami_1,t36_ami_1),
    []).

fof(t46_ami_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r2_hidden(A,k7_ami_1(B))
                  & r2_hidden(C,k7_ami_1(B)) )
               => r2_hidden(k1_funct_4(A,C),k7_ami_1(B)) ) ) ) ) ),
    file(ami_1,t46_ami_1),
    []).

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),
    []).