% Mizar problem: t9_scmring2,scmring2,486,7 
fof(t9_scmring2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) = 0 ) ),
    inference(mizar_bg_added,[status(thm)],[existence_l1_group_1,dt_l1_group_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_vectsp_1,existence_l2_struct_0,existence_m1_fraenkel,existence_m1_relset_1,dt_k1_xboole_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_m1_fraenkel,dt_m1_relset_1,fc3_ami_1,fc4_ami_1,rc4_struct_0,fc1_xboole_0,rc1_fraenkel,cc1_fraenkel,rc1_nat_1,rc2_nat_1,rc3_nat_1,rc1_setfam_1,fc4_setfam_1,cc1_setfam_1,t1_boole,t1_subset,t4_subset,t5_subset,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_vectsp_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_relset_1,dt_g1_ami_1,dt_k13_finseq_1,dt_k1_fraenkel,dt_k1_funct_2,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k4_card_3,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_vectsp_1,dt_m1_subset_1,dt_m2_relset_1,rc2_ami_1,fc2_ami_1,cc1_scmring1,fc3_scmring1,rc3_struct_0,fc1_struct_0,rc5_struct_0,cc1_relset_1,cc1_finseq_5,rc1_xboole_0,rc2_xboole_0,fc2_xboole_0,fc3_xboole_0,fc1_fraenkel,fc2_fraenkel,cc1_nat_1,cc2_nat_1,cc3_nat_1,fc1_ordinal2,fc2_setfam_1,fc3_setfam_1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,abstractness_v1_ami_1,existence_l1_ami_1,existence_l3_vectsp_1,redefinition_k5_numbers,dt_k16_scmring1,dt_k1_gr_cy_1,dt_k1_scmring1,dt_k1_scmring2,dt_k1_tarski,dt_k2_ami_1,dt_k2_scmring1,dt_k3_ami_2,dt_k5_numbers,dt_l1_ami_1,dt_l3_vectsp_1,dt_u1_ami_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,fc1_scmring2,fc2_scmring2,rc1_ami_1,fc2_scmring1,d5_ami_1,spc8_numerals,spc0_boole,spc8_boole,d1_scmring2]),
    [file(scmring2,t9_scmring2)]).

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    []).

fof(dt_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_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(existence_l1_vectsp_1,axiom,(
    ? [A] : l1_vectsp_1(A) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

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

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

fof(dt_l1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => l1_group_1(A) ) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(fc3_ami_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_fraenkel(k4_card_3(A)) ) ),
    file(ami_1,fc3_ami_1),
    []).

fof(fc4_ami_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_setfam_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( ~ v1_xboole_0(k4_card_3(C))
        & v1_fraenkel(k4_card_3(C)) ) ) ),
    file(ami_1,fc4_ami_1),
    []).

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

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

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

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(rc1_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

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

fof(fc4_setfam_1,axiom,(
    ! [A,B] : 
      ( ( v1_setfam_1(A)
        & v1_setfam_1(B) )
     => v1_setfam_1(k2_xboole_0(A,B)) ) ),
    file(setfam_1,fc4_setfam_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(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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(free_g1_ami_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( m1_subset_1(C,B)
        & m1_subset_1(D,k1_zfmisc_1(B))
        & ~ v1_xboole_0(E)
        & ~ v1_xboole_0(F)
        & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B)))))
        & v1_funct_1(G)
        & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D)))
        & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D)))
        & v1_funct_1(H)
        & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G)))
        & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) )
     => ! [I,J,K,L,M,N,O,P] : 
          ( g1_ami_1(A,B,C,D,E,F,G,H) = g1_ami_1(I,J,K,L,M,N,O,P)
         => ( A = I
            & B = J
            & C = K
            & D = L
            & E = M
            & F = N
            & G = O
            & H = P ) ) ) ),
    file(ami_1,g1_ami_1),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_vectsp_1,axiom,(
    ? [A] : l2_vectsp_1(A) ),
    file(vectsp_1,l2_vectsp_1),
    []).

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_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

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_g1_ami_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( m1_subset_1(C,B)
        & m1_subset_1(D,k1_zfmisc_1(B))
        & ~ v1_xboole_0(E)
        & ~ v1_xboole_0(F)
        & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B)))))
        & v1_funct_1(G)
        & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D)))
        & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D)))
        & v1_funct_1(H)
        & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G)))
        & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) )
     => ( v1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A)
        & l1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) ) ) ),
    file(ami_1,g1_ami_1),
    []).

fof(dt_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    []).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

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

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

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

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

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_vectsp_1,axiom,(
    ! [A] : 
      ( l2_vectsp_1(A)
     => ( l1_vectsp_1(A)
        & l2_struct_0(A) ) ) ),
    file(vectsp_1,l2_vectsp_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(rc2_ami_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( l1_ami_1(B,A)
      & ~ v3_struct_0(B)
      & ~ v2_ami_1(B,A) ) ),
    file(ami_1,rc2_ami_1),
    []).

fof(fc2_ami_1,axiom,(
    ! [A,B] : 
      ( ( ~ v2_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ~ v1_xboole_0(u2_ami_1(A,B)) ) ),
    file(ami_1,fc2_ami_1),
    []).

fof(cc1_scmring1,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) ) ) ),
    file(scmring1,cc1_scmring1),
    []).

fof(fc3_scmring1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ( v1_relat_1(k1_scmring1(A))
        & ~ v1_xboole_0(k1_scmring1(A))
        & ~ v1_realset1(k1_scmring1(A)) ) ) ),
    file(scmring1,fc3_scmring1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

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(cc1_finseq_5,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_realset1(A) ) ),
    file(finseq_5,cc1_finseq_5),
    []).

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(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(fc1_fraenkel,axiom,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    []).

fof(fc2_fraenkel,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => ( v1_finset_1(k1_funct_2(A,B))
        & v1_fraenkel(k1_funct_2(A,B)) ) ) ),
    file(fraenkel,fc2_fraenkel),
    []).

fof(cc1_nat_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) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

fof(cc2_nat_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)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_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(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(fc3_setfam_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( ~ v1_xboole_0(k2_tarski(A,B))
        & v1_setfam_1(k2_tarski(A,B)) ) ) ),
    file(setfam_1,fc3_setfam_1),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

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(abstractness_v1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v1_ami_1(B,A)
       => B = g1_ami_1(A,u1_struct_0(B),u1_ami_1(A,B),u2_ami_1(A,B),u3_ami_1(A,B),u4_ami_1(A,B),u5_ami_1(A,B),u6_ami_1(A,B)) ) ) ),
    file(ami_1,v1_ami_1),
    []).

fof(existence_l1_ami_1,axiom,(
    ! [A] : 
    ? [B] : l1_ami_1(B,A) ),
    file(ami_1,l1_ami_1),
    []).

fof(existence_l3_vectsp_1,axiom,(
    ? [A] : l3_vectsp_1(A) ),
    file(vectsp_1,l3_vectsp_1),
    []).

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

fof(dt_k16_scmring1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k16_scmring1(A))
        & v1_funct_2(k16_scmring1(A),k1_scmring1(A),k1_fraenkel(k4_card_3(k2_scmring1(A)),k4_card_3(k2_scmring1(A))))
        & m2_relset_1(k16_scmring1(A),k1_scmring1(A),k1_fraenkel(k4_card_3(k2_scmring1(A)),k4_card_3(k2_scmring1(A)))) ) ) ),
    file(scmring1,k16_scmring1),
    []).

fof(dt_k1_gr_cy_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( ~ v1_xboole_0(k1_gr_cy_1(A))
        & m1_subset_1(k1_gr_cy_1(A),k1_zfmisc_1(k5_numbers)) ) ) ),
    file(gr_cy_1,k1_gr_cy_1),
    []).

fof(dt_k1_scmring1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => m1_subset_1(k1_scmring1(A),k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(8),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),k5_numbers))))) ) ),
    file(scmring1,k1_scmring1),
    []).

fof(dt_k1_scmring2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & l1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ),
    file(scmring2,k1_scmring2),
    []).

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

fof(dt_k2_ami_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => m1_subset_1(k2_ami_1(A,B),u1_struct_0(B)) ) ),
    file(ami_1,k2_ami_1),
    []).

fof(dt_k2_scmring1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ( v1_funct_1(k2_scmring1(A))
        & v1_funct_2(k2_scmring1(A),k5_numbers,k2_xboole_0(k1_tarski(u1_struct_0(A)),k2_tarski(k1_scmring1(A),k3_ami_2)))
        & m2_relset_1(k2_scmring1(A),k5_numbers,k2_xboole_0(k1_tarski(u1_struct_0(A)),k2_tarski(k1_scmring1(A),k3_ami_2))) ) ) ),
    file(scmring1,k2_scmring1),
    []).

fof(dt_k3_ami_2,axiom,(
    m1_subset_1(k3_ami_2,k1_zfmisc_1(k5_numbers)) ),
    file(ami_2,k3_ami_2),
    []).

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

fof(dt_l1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => l1_struct_0(B) ) ),
    file(ami_1,l1_ami_1),
    []).

fof(dt_l3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( l1_rlvect_1(A)
        & l2_vectsp_1(A) ) ) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(dt_u1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => m1_subset_1(u1_ami_1(A,B),u1_struct_0(B)) ) ),
    file(ami_1,u1_ami_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => m1_subset_1(u2_ami_1(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(ami_1,u2_ami_1),
    []).

fof(dt_u3_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ~ v1_xboole_0(u3_ami_1(A,B)) ) ),
    file(ami_1,u3_ami_1),
    []).

fof(dt_u4_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( ~ v1_xboole_0(u4_ami_1(A,B))
        & m1_subset_1(u4_ami_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))))) ) ) ),
    file(ami_1,u4_ami_1),
    []).

fof(dt_u5_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v1_funct_1(u5_ami_1(A,B))
        & v1_funct_2(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))))
        & m2_relset_1(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ) ),
    file(ami_1,u5_ami_1),
    []).

fof(dt_u6_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v1_funct_1(u6_ami_1(A,B))
        & v1_funct_2(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))))
        & m2_relset_1(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))) ) ) ),
    file(ami_1,u6_ami_1),
    []).

fof(fc1_scmring2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_scmring2(A))
        & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ),
    file(scmring2,fc1_scmring2),
    []).

fof(fc2_scmring2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_scmring2(A))
        & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ),
    file(scmring2,fc2_scmring2),
    []).

fof(rc1_ami_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( l1_ami_1(B,A)
      & v1_ami_1(B,A) ) ),
    file(ami_1,rc1_ami_1),
    []).

fof(fc2_scmring1,axiom,
    ( ~ v1_xboole_0(k3_ami_2)
    & ~ v1_finset_1(k3_ami_2)
    & ~ v1_realset1(k3_ami_2)
    & v1_membered(k3_ami_2)
    & v2_membered(k3_ami_2)
    & v3_membered(k3_ami_2)
    & v4_membered(k3_ami_2)
    & v5_membered(k3_ami_2) ),
    file(scmring1,fc2_scmring1),
    []).

fof(d5_ami_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => k2_ami_1(A,B) = u1_ami_1(A,B) ) ),
    file(ami_1,d5_ami_1),
    []).

fof(spc8_numerals,axiom,
    ( v2_xreal_0(8)
    & m1_subset_1(8,k5_numbers) ),
    file(numerals,spc8_numerals),
    []).

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(spc8_boole,axiom,(
    ~ v1_xboole_0(8) ),
    file(boole,spc8_boole),
    []).

fof(d1_scmring2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( v1_ami_1(B,k1_tarski(u1_struct_0(A)))
            & l1_ami_1(B,k1_tarski(u1_struct_0(A))) )
         => ( B = k1_scmring2(A)
          <=> ( u1_struct_0(B) = k5_numbers
              & u1_ami_1(k1_tarski(u1_struct_0(A)),B) = 0
              & u2_ami_1(k1_tarski(u1_struct_0(A)),B) = k3_ami_2
              & u3_ami_1(k1_tarski(u1_struct_0(A)),B) = k1_gr_cy_1(8)
              & u4_ami_1(k1_tarski(u1_struct_0(A)),B) = k1_scmring1(A)
              & u5_ami_1(k1_tarski(u1_struct_0(A)),B) = k2_scmring1(A)
              & u6_ami_1(k1_tarski(u1_struct_0(A)),B) = k16_scmring1(A) ) ) ) ) ),
    file(scmring2,d1_scmring2),
    []).