% Mizar problem: t36_facirc_2,facirc_2,1942,40 
fof(t36_facirc_2,conjecture,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v3_facirc_1(B)
            & m1_circcomb(B,k1_nat_1(A,1)) )
         => ? [C] : 
              ( v3_facirc_1(C)
              & m1_circcomb(C,A)
              & ? [D] : 
                  ( ~ v1_facirc_1(D)
                  & B = k8_facirc_1(A,1,C,k5_facirc_1(D)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[rc3_finseq_1,rc6_finseq_1,rc1_margrel1,rc1_circcomb,rc4_facirc_1,rc5_facirc_1,rc3_relat_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_facirc_2,fc2_finseq_1,rc7_finseq_1,rc8_finseq_1,fc1_margrel1,rc3_facirc_1,cc4_facirc_1,fc4_relat_1,fc12_relat_1,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_subset_1,cc2_facirc_2,rc1_finseq_1,cc1_finseq_1,fc3_finseq_1,fc4_finseq_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,rc1_facirc_1,cc2_facirc_1,cc3_facirc_1,fc12_facirc_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,rc1_relat_1,cc1_relat_1,rc2_relat_1,fc1_ordinal2,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,existence_m1_circcomb,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k5_facirc_1,redefinition_k5_numbers,redefinition_k8_facirc_1,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k5_facirc_1,dt_k5_numbers,dt_k8_facirc_1,dt_m1_circcomb,dt_m2_subset_1,cc1_facirc_1,rc2_facirc_1,spc1_numerals,spc1_boole,l24_facirc_2]),
    [file(facirc_2,t36_facirc_2)]).

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(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(rc1_margrel1,axiom,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    []).

fof(rc1_circcomb,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(circcomb,rc1_circcomb),
    []).

fof(rc4_facirc_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : 
          ( m1_circcomb(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v3_facirc_1(B) ) ) ),
    file(facirc_1,rc4_facirc_1),
    []).

fof(rc5_facirc_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v3_facirc_1(A) ) ),
    file(facirc_1,rc5_facirc_1),
    []).

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

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

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

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

fof(fc2_facirc_2,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_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0)
    & v4_ordinal2(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_xreal_0(k1_xboole_0)
    & ~ v2_xreal_0(k1_xboole_0)
    & ~ v3_xreal_0(k1_xboole_0)
    & v1_xcmplx_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0)
    & ~ v1_facirc_1(k1_xboole_0)
    & ~ v2_facirc_1(k1_xboole_0)
    & v3_facirc_1(k1_xboole_0) ),
    file(facirc_2,fc2_facirc_2),
    []).

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(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(fc1_margrel1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    []).

fof(rc3_facirc_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v2_facirc_1(A) ) ),
    file(facirc_1,rc3_facirc_1),
    []).

fof(cc4_facirc_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & ~ v2_facirc_1(A) )
     => ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A)
        & ~ v2_facirc_1(A) ) ) ),
    file(facirc_1,cc4_facirc_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(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(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

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(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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

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

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(dt_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_1),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k7_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,k7_finseq_1),
    []).

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

fof(cc2_facirc_2,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ~ v1_facirc_1(A) ) ),
    file(facirc_2,cc2_facirc_2),
    []).

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(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(fc3_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc3_finseq_1),
    []).

fof(fc4_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc4_finseq_1),
    []).

fof(fc12_finseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finseq_1(A))
      & v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc12_finseq_1),
    []).

fof(fc13_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(A,B))
        & v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,fc13_finseq_1),
    []).

fof(fc14_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(B,A))
        & v1_relat_1(k7_finseq_1(B,A))
        & v1_funct_1(k7_finseq_1(B,A))
        & v1_finset_1(k7_finseq_1(B,A))
        & v1_finseq_1(k7_finseq_1(B,A)) ) ) ),
    file(finseq_1,fc14_finseq_1),
    []).

fof(rc1_facirc_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_facirc_1(A) ) ),
    file(facirc_1,rc1_facirc_1),
    []).

fof(cc2_facirc_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v1_facirc_1(A) ) ) ),
    file(facirc_1,cc2_facirc_1),
    []).

fof(cc3_facirc_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ~ v2_facirc_1(A) ) ),
    file(facirc_1,cc3_facirc_1),
    []).

fof(fc12_facirc_1,axiom,(
    ! [A] : 
      ( ~ v1_facirc_1(A)
     => ( ~ v1_xboole_0(k5_finseq_1(A))
        & v1_relat_1(k5_finseq_1(A))
        & v1_funct_1(k5_finseq_1(A))
        & v1_finset_1(k5_finseq_1(A))
        & v1_finseq_1(k5_finseq_1(A))
        & v3_facirc_1(k5_finseq_1(A)) ) ) ),
    file(facirc_1,fc12_facirc_1),
    []).

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

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

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

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

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

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(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),
    []).

fof(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(existence_m1_circcomb,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : m1_circcomb(B,A) ) ),
    file(circcomb,m1_circcomb),
    []).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(redefinition_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(redefinition_k5_facirc_1,axiom,(
    ! [A] : k5_facirc_1(A) = k5_finseq_1(A) ),
    file(facirc_1,k5_facirc_1),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k8_facirc_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_circcomb(C,A)
        & m1_circcomb(D,B) )
     => k8_facirc_1(A,B,C,D) = k7_finseq_1(C,D) ) ),
    file(facirc_1,k8_facirc_1),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k5_facirc_1,axiom,(
    ! [A] : m1_circcomb(k5_facirc_1(A),1) ),
    file(facirc_1,k5_facirc_1),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k8_facirc_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_circcomb(C,A)
        & m1_circcomb(D,B) )
     => m1_circcomb(k8_facirc_1(A,B,C,D),k1_nat_1(A,B)) ) ),
    file(facirc_1,k8_facirc_1),
    []).

fof(dt_m1_circcomb,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ! [B] : 
          ( m1_circcomb(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) ) ) ) ),
    file(circcomb,m1_circcomb),
    []).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(cc1_facirc_1,axiom,(
    ! [A] : 
      ( v1_facirc_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(facirc_1,cc1_facirc_1),
    []).

fof(rc2_facirc_1,axiom,(
    ? [A] : ~ v1_facirc_1(A) ),
    file(facirc_1,rc2_facirc_1),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(l24_facirc_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v3_facirc_1(B)
            & m1_circcomb(B,k1_nat_1(A,1)) )
         => ? [C] : 
              ( v3_facirc_1(C)
              & m1_circcomb(C,A)
              & ? [D] : 
                  ( ~ v1_facirc_1(D)
                  & B = k8_facirc_1(A,1,C,k5_facirc_1(D)) ) ) ) ) ),
    file(facirc_2,l24_facirc_2),
    []).