% Mizar problem: t16_twoscomp,twoscomp,881,51 
fof(t16_twoscomp,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k10_circcomb)
     => ! [B] : 
          ( m1_subset_1(B,k10_circcomb)
         => ! [C] : 
              ( m1_subset_1(C,k10_circcomb)
             => ( k1_funct_1(k25_twoscomp,k7_facirc_1(A,B,C)) = k3_binarith(k3_binarith(A,B),C)
                & k1_funct_1(k26_twoscomp,k7_facirc_1(A,B,C)) = k3_binarith(k3_binarith(k11_margrel1(A),B),C)
                & k1_funct_1(k27_twoscomp,k7_facirc_1(A,B,C)) = k3_binarith(k3_binarith(k11_margrel1(A),k11_margrel1(B)),C)
                & k1_funct_1(k28_twoscomp,k7_facirc_1(A,B,C)) = k3_binarith(k3_binarith(k11_margrel1(A),k11_margrel1(B)),k11_margrel1(C)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[rc1_circcomb,rc4_facirc_1,rc5_facirc_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_numbers,dt_k5_ordinal2,cc1_facirc_1,rc1_facirc_1,rc2_facirc_1,rc3_facirc_1,cc4_facirc_1,fc14_facirc_1,rc2_margrel1,fc4_margrel1,t1_subset,t4_subset,t5_subset,commutativity_k1_binarith,involutiveness_k9_margrel1,existence_m1_circcomb,existence_m1_finseq_2,existence_m1_relset_1,redefinition_k5_numbers,dt_k11_finseq_1,dt_k1_binarith,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_k6_margrel1,dt_k9_margrel1,dt_m1_circcomb,dt_m1_finseq_2,dt_m1_relset_1,cc2_facirc_1,cc3_facirc_1,cc1_relset_1,fc3_margrel1,cc1_margrel1,t2_subset,t3_subset,involutiveness_k11_margrel1,commutativity_k3_binarith,existence_m1_subset_1,existence_m2_relset_1,redefinition_k10_circcomb,redefinition_k11_margrel1,redefinition_k3_binarith,redefinition_k7_facirc_1,redefinition_m2_relset_1,dt_k10_circcomb,dt_k11_margrel1,dt_k1_funct_1,dt_k25_twoscomp,dt_k26_twoscomp,dt_k27_twoscomp,dt_k28_twoscomp,dt_k3_binarith,dt_k4_finseq_2,dt_k7_facirc_1,dt_m1_subset_1,dt_m2_relset_1,spc3_numerals,d24_twoscomp,d25_twoscomp,d26_twoscomp,d27_twoscomp]),
    [file(twoscomp,t16_twoscomp)]).

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

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

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

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

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

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(fc14_facirc_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_facirc_1(A)
        & ~ v1_facirc_1(B)
        & ~ v1_facirc_1(C) )
     => ( v1_relat_1(k11_finseq_1(A,B,C))
        & v1_funct_1(k11_finseq_1(A,B,C))
        & v1_finset_1(k11_finseq_1(A,B,C))
        & v1_finseq_1(k11_finseq_1(A,B,C))
        & v3_facirc_1(k11_finseq_1(A,B,C)) ) ) ),
    file(facirc_1,fc14_facirc_1),
    []).

fof(rc2_margrel1,axiom,(
    ? [A] : v2_margrel1(A) ),
    file(margrel1,rc2_margrel1),
    []).

fof(fc4_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,fc4_margrel1),
    []).

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_k1_binarith,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k1_binarith(A,B) = k1_binarith(B,A) ) ),
    file(binarith,k1_binarith),
    []).

fof(involutiveness_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,k9_margrel1),
    []).

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

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_k11_finseq_1,axiom,(
    $true ),
    file(finseq_1,k11_finseq_1),
    []).

fof(dt_k1_binarith,axiom,(
    $true ),
    file(binarith,k1_binarith),
    []).

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

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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

fof(dt_k6_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    []).

fof(dt_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,k9_margrel1),
    []).

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_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_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(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(fc3_margrel1,axiom,(
    ~ v1_xboole_0(k6_margrel1) ),
    file(margrel1,fc3_margrel1),
    []).

fof(cc1_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => v2_margrel1(A) ) ),
    file(margrel1,cc1_margrel1),
    []).

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(involutiveness_k11_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => k11_margrel1(k11_margrel1(A)) = A ) ),
    file(margrel1,k11_margrel1),
    []).

fof(commutativity_k3_binarith,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_margrel1)
        & m1_subset_1(B,k6_margrel1) )
     => k3_binarith(A,B) = k3_binarith(B,A) ) ),
    file(binarith,k3_binarith),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_k10_circcomb,axiom,(
    k10_circcomb = k6_margrel1 ),
    file(circcomb,k10_circcomb),
    []).

fof(redefinition_k11_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => k11_margrel1(A) = k9_margrel1(A) ) ),
    file(margrel1,k11_margrel1),
    []).

fof(redefinition_k3_binarith,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_margrel1)
        & m1_subset_1(B,k6_margrel1) )
     => k3_binarith(A,B) = k1_binarith(A,B) ) ),
    file(binarith,k3_binarith),
    []).

fof(redefinition_k7_facirc_1,axiom,(
    ! [A,B,C] : k7_facirc_1(A,B,C) = k11_finseq_1(A,B,C) ),
    file(facirc_1,k7_facirc_1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_k10_circcomb,axiom,
    ( ~ v1_xboole_0(k10_circcomb)
    & v1_finset_1(k10_circcomb)
    & m1_subset_1(k10_circcomb,k1_zfmisc_1(k5_numbers)) ),
    file(circcomb,k10_circcomb),
    []).

fof(dt_k11_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => m1_subset_1(k11_margrel1(A),k6_margrel1) ) ),
    file(margrel1,k11_margrel1),
    []).

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

fof(dt_k25_twoscomp,axiom,
    ( v1_funct_1(k25_twoscomp)
    & v1_funct_2(k25_twoscomp,k4_finseq_2(3,k10_circcomb),k10_circcomb)
    & m2_relset_1(k25_twoscomp,k4_finseq_2(3,k10_circcomb),k10_circcomb) ),
    file(twoscomp,k25_twoscomp),
    []).

fof(dt_k26_twoscomp,axiom,
    ( v1_funct_1(k26_twoscomp)
    & v1_funct_2(k26_twoscomp,k4_finseq_2(3,k10_circcomb),k10_circcomb)
    & m2_relset_1(k26_twoscomp,k4_finseq_2(3,k10_circcomb),k10_circcomb) ),
    file(twoscomp,k26_twoscomp),
    []).

fof(dt_k27_twoscomp,axiom,
    ( v1_funct_1(k27_twoscomp)
    & v1_funct_2(k27_twoscomp,k4_finseq_2(3,k10_circcomb),k10_circcomb)
    & m2_relset_1(k27_twoscomp,k4_finseq_2(3,k10_circcomb),k10_circcomb) ),
    file(twoscomp,k27_twoscomp),
    []).

fof(dt_k28_twoscomp,axiom,
    ( v1_funct_1(k28_twoscomp)
    & v1_funct_2(k28_twoscomp,k4_finseq_2(3,k10_circcomb),k10_circcomb)
    & m2_relset_1(k28_twoscomp,k4_finseq_2(3,k10_circcomb),k10_circcomb) ),
    file(twoscomp,k28_twoscomp),
    []).

fof(dt_k3_binarith,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_margrel1)
        & m1_subset_1(B,k6_margrel1) )
     => m1_subset_1(k3_binarith(A,B),k6_margrel1) ) ),
    file(binarith,k3_binarith),
    []).

fof(dt_k4_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => m1_finseq_2(k4_finseq_2(A,B),B) ) ),
    file(finseq_2,k4_finseq_2),
    []).

fof(dt_k7_facirc_1,axiom,(
    ! [A,B,C] : m1_circcomb(k7_facirc_1(A,B,C),3) ),
    file(facirc_1,k7_facirc_1),
    []).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(spc3_numerals,axiom,
    ( v2_xreal_0(3)
    & m1_subset_1(3,k5_numbers) ),
    file(numerals,spc3_numerals),
    []).

fof(d24_twoscomp,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k4_finseq_2(3,k10_circcomb),k10_circcomb)
        & m2_relset_1(A,k4_finseq_2(3,k10_circcomb),k10_circcomb) )
     => ( A = k25_twoscomp
      <=> ! [B] : 
            ( m1_subset_1(B,k10_circcomb)
           => ! [C] : 
                ( m1_subset_1(C,k10_circcomb)
               => ! [D] : 
                    ( m1_subset_1(D,k10_circcomb)
                   => k1_funct_1(A,k7_facirc_1(B,C,D)) = k3_binarith(k3_binarith(B,C),D) ) ) ) ) ) ),
    file(twoscomp,d24_twoscomp),
    []).

fof(d25_twoscomp,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k4_finseq_2(3,k10_circcomb),k10_circcomb)
        & m2_relset_1(A,k4_finseq_2(3,k10_circcomb),k10_circcomb) )
     => ( A = k26_twoscomp
      <=> ! [B] : 
            ( m1_subset_1(B,k10_circcomb)
           => ! [C] : 
                ( m1_subset_1(C,k10_circcomb)
               => ! [D] : 
                    ( m1_subset_1(D,k10_circcomb)
                   => k1_funct_1(A,k7_facirc_1(B,C,D)) = k3_binarith(k3_binarith(k11_margrel1(B),C),D) ) ) ) ) ) ),
    file(twoscomp,d25_twoscomp),
    []).

fof(d26_twoscomp,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k4_finseq_2(3,k10_circcomb),k10_circcomb)
        & m2_relset_1(A,k4_finseq_2(3,k10_circcomb),k10_circcomb) )
     => ( A = k27_twoscomp
      <=> ! [B] : 
            ( m1_subset_1(B,k10_circcomb)
           => ! [C] : 
                ( m1_subset_1(C,k10_circcomb)
               => ! [D] : 
                    ( m1_subset_1(D,k10_circcomb)
                   => k1_funct_1(A,k7_facirc_1(B,C,D)) = k3_binarith(k3_binarith(k11_margrel1(B),k11_margrel1(C)),D) ) ) ) ) ) ),
    file(twoscomp,d26_twoscomp),
    []).

fof(d27_twoscomp,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k4_finseq_2(3,k10_circcomb),k10_circcomb)
        & m2_relset_1(A,k4_finseq_2(3,k10_circcomb),k10_circcomb) )
     => ( A = k28_twoscomp
      <=> ! [B] : 
            ( m1_subset_1(B,k10_circcomb)
           => ! [C] : 
                ( m1_subset_1(C,k10_circcomb)
               => ! [D] : 
                    ( m1_subset_1(D,k10_circcomb)
                   => k1_funct_1(A,k7_facirc_1(B,C,D)) = k3_binarith(k3_binarith(k11_margrel1(B),k11_margrel1(C)),k11_margrel1(D)) ) ) ) ) ) ),
    file(twoscomp,d27_twoscomp),
    []).