% Mizar problem: t13_scmring4,scmring4,301,32 
fof(t13_scmring4,conjecture,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & v13_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                 => ! [E] : 
                      ( ( v1_ami_3(E,A,B)
                        & m1_ami_1(E,A,B) )
                     => k4_ami_1(A,B,D,k8_ami_5(A,B,C,E)) = k8_ami_5(A,B,k4_ami_1(A,B,D,C),E) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc14_amistd_2,cc1_amistd_1,cc1_amistd_2,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_relset_1,cc1_scmfsa_4,cc1_scmring1,cc1_setfam_1,cc2_amistd_1,cc2_finset_1,cc2_funct_1,cc3_amistd_1,cc8_amistd_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k4_subset_1,d13_ami_3,d19_amistd_2,d1_tarski,d2_funct_7,d2_xboole_0,d3_tarski,d4_xboole_0,d5_ami_1,d7_ami_1,dt_k13_finseq_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_funct_4,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ami_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k4_ami_1,dt_k4_card_3,dt_k4_subset_1,dt_k4_xboole_0,dt_k7_ami_1,dt_k7_relat_1,dt_k8_ami_5,dt_k8_funct_2,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_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,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_1,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_ami_1,fc12_finset_1,fc14_finset_1,fc16_finseq_1,fc17_finseq_1,fc1_amistd_2,fc1_finset_1,fc1_fraenkel,fc1_struct_0,fc1_xboole_0,fc2_ami_1,fc2_amistd_2,fc2_finseq_1,fc2_finset_1,fc2_fraenkel,fc2_setfam_1,fc2_xboole_0,fc3_ami_1,fc3_amistd_2,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,fc4_amistd_1,fc4_amistd_2,fc4_funct_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,fc9_finset_1,idempotence_k1_funct_4,idempotence_k2_xboole_0,idempotence_k4_subset_1,idempotence_k8_ami_5,irreflexivity_r1_subset_1,l12_scmring4,l13_scmring4,rc1_ami_3,rc1_amistd_1,rc1_amistd_2,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_funct_1,rc1_scmfsa_4,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_funct_1,rc2_xboole_0,rc3_amistd_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_struct_0,rc4_finset_1,rc4_funct_1,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_struct_0,redefinition_k4_subset_1,redefinition_k8_ami_5,redefinition_k8_funct_2,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_subset_1,reflexivity_r1_tarski,symmetry_r1_subset_1,symmetry_r1_xboole_0,t12_xboole_1,t1_boole,t1_subset,t2_subset,t36_ami_3,t39_xboole_1,t3_boole,t3_subset,t3_xboole_0,t41_xboole_1,t48_ami_1,t4_boole,t4_subset,t5_scmfsa_3,t5_subset,t63_xboole_1,t6_boole,t75_funct_4,t76_funct_4,t7_boole,t83_funct_4,t8_boole,t98_relat_1]),
    [file(scmring4,t13_scmring4)]).

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

fof(cc14_amistd_2,axiom,(
    ! [A,B] : 
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & v13_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ! [C] : 
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( ~ v1_xboole_0(C)
            & v12_amistd_2(C,A,B) ) ) ) ),
    file(amistd_2,cc14_amistd_2),
    []).

fof(cc1_amistd_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_1(A)
        & v1_setfam_1(A) ) ) ),
    file(amistd_1,cc1_amistd_1),
    []).

fof(cc1_amistd_2,axiom,(
    ! [A] : 
      ( v1_amistd_2(A)
     => ( v1_fraenkel(A)
        & v1_pralg_2(A) ) ) ),
    file(amistd_2,cc1_amistd_2),
    []).

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_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_scmfsa_4,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finset_1(C) ) ) ) ),
    file(scmfsa_4,cc1_scmfsa_4),
    []).

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

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_amistd_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => ( v1_xboole_0(C)
           => ( v1_relat_1(C)
              & v1_funct_1(C)
              & v1_finset_1(C)
              & v1_setfam_1(C)
              & v1_ami_3(C,A,B) ) ) ) ) ),
    file(amistd_1,cc2_amistd_1),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_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(cc3_amistd_1,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( l1_ami_1(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_ami_1(B,A)
              & v5_ami_1(B,A)
              & v7_ami_1(B,A)
              & v8_ami_1(B,A) )
           => ( ~ v3_struct_0(B)
              & ~ v2_ami_1(B,A)
              & v5_ami_1(B,A)
              & v8_ami_1(B,A)
              & v13_ami_1(B,A) ) ) ) ) ),
    file(amistd_1,cc3_amistd_1),
    []).

fof(cc8_amistd_1,axiom,(
    ! [A,B] : 
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => ( v1_xboole_0(C)
           => ( v1_relat_1(C)
              & v1_funct_1(C)
              & v1_finset_1(C)
              & v1_setfam_1(C)
              & v9_amistd_1(C,A,B) ) ) ) ) ),
    file(amistd_1,cc8_amistd_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(commutativity_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(d13_ami_3,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => ( v1_ami_3(C,A,B)
          <=> r1_tarski(k1_relat_1(C),u2_ami_1(A,B)) ) ) ) ),
    file(ami_3,d13_ami_3),
    []).

fof(d19_amistd_2,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v12_amistd_2(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => ! [E] : 
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
                       => ( r1_funct_7(D,E,u2_ami_1(A,B))
                         => r1_funct_7(k4_ami_1(A,B,C,D),k4_ami_1(A,B,C,E),u2_ami_1(A,B)) ) ) ) ) ) ) ) ),
    file(amistd_2,d19_amistd_2),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d2_funct_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( r1_funct_7(A,B,C)
            <=> k7_relat_1(A,k4_xboole_0(k1_relat_1(A),C)) = k7_relat_1(B,k4_xboole_0(k1_relat_1(B),C)) ) ) ) ),
    file(funct_7,d2_funct_7),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

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

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

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(d7_ami_1,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => k4_ami_1(A,B,C,D) = k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D) ) ) ) ) ),
    file(ami_1,d7_ami_1),
    []).

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

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

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

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_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k1_struct_0),
    []).

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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

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_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_ami_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B))
        & m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) )
     => m1_subset_1(k4_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ),
    file(ami_1,k4_ami_1),
    []).

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

fof(dt_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

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

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(dt_k8_ami_5,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
        & m1_ami_1(D,A,B) )
     => m1_subset_1(k8_ami_5(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ),
    file(ami_5,k8_ami_5),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

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_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => m1_subset_1(C,k7_ami_1(u5_ami_1(A,B))) ) ) ),
    file(ami_1,m1_ami_1),
    []).

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

fof(dt_m1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ! [C] : 
          ( m1_struct_0(C,A,B)
         => m1_subset_1(C,u1_struct_0(A)) ) ) ),
    file(struct_0,m1_struct_0),
    []).

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

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

fof(existence_m1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ? [C] : m1_ami_1(C,A,B) ) ),
    file(ami_1,m1_ami_1),
    []).

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

fof(existence_m1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ? [C] : m1_struct_0(C,A,B) ) ),
    file(struct_0,m1_struct_0),
    []).

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(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(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_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc16_finseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k13_finseq_1(A))
      & v1_fraenkel(k13_finseq_1(A)) ) ),
    file(finseq_1,fc16_finseq_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_amistd_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & ~ v1_xboole_0(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B))
        & ~ v1_xboole_0(k1_funct_4(A,B))
        & v1_setfam_1(k1_funct_4(A,B)) ) ) ),
    file(amistd_2,fc1_amistd_2),
    []).

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

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

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(fc2_amistd_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & ~ v1_xboole_0(B) )
     => ( v1_relat_1(k1_funct_4(B,A))
        & v1_funct_1(k1_funct_4(B,A))
        & ~ v1_xboole_0(k1_funct_4(B,A))
        & v1_setfam_1(k1_funct_4(B,A)) ) ) ),
    file(amistd_2,fc2_amistd_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(fc2_finset_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    []).

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(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_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_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(fc3_amistd_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finset_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B))
        & v1_finset_1(k1_funct_4(A,B))
        & v1_setfam_1(k1_funct_4(A,B)) ) ) ),
    file(amistd_2,fc3_amistd_2),
    []).

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(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(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(fc4_amistd_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B))
        & m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) )
     => ( v1_relat_1(k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D))
        & v1_funct_1(k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D))
        & v1_setfam_1(k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D)) ) ) ),
    file(amistd_1,fc4_amistd_1),
    []).

fof(fc4_amistd_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k4_xboole_0(A,B))
        & v1_funct_1(k4_xboole_0(A,B))
        & v1_setfam_1(k4_xboole_0(A,B)) ) ) ),
    file(amistd_2,fc4_amistd_2),
    []).

fof(fc4_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_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(fc5_amistd_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_fraenkel(k4_card_3(A))
        & v1_amistd_2(k4_card_3(A)) ) ) ),
    file(amistd_2,fc5_amistd_2),
    []).

fof(fc9_finseq_1,axiom,(
    ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ),
    file(finseq_1,fc9_finseq_1),
    []).

fof(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_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(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

fof(idempotence_k8_ami_5,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
        & m1_ami_1(D,A,B) )
     => k8_ami_5(A,B,C,C) = C ) ),
    file(ami_5,k8_ami_5),
    []).

fof(irreflexivity_r1_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ r1_subset_1(A,A) ) ),
    file(subset_1,r1_subset_1),
    []).

fof(l12_scmring4,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,C)
        & r1_tarski(B,k4_xboole_0(C,A)) )
     => C = k2_xboole_0(k2_xboole_0(A,k4_xboole_0(C,k2_xboole_0(A,B))),B) ) ),
    file(scmring4,l12_scmring4),
    []).

fof(l13_scmring4,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => r1_tarski(u2_ami_1(A,B),k4_xboole_0(u1_struct_0(B),k1_struct_0(B,k2_ami_1(A,B)))) ) ) ),
    file(scmring4,l13_scmring4),
    []).

fof(rc1_ami_3,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ? [C] : 
          ( m1_ami_1(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_ami_3(C,A,B) ) ) ),
    file(ami_3,rc1_ami_3),
    []).

fof(rc1_amistd_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & ~ v1_realset1(A) ) ),
    file(amistd_1,rc1_amistd_1),
    []).

fof(rc1_amistd_2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A)
      & v1_pralg_2(A)
      & v1_amistd_2(A) ) ),
    file(amistd_2,rc1_amistd_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(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_scmfsa_4,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ? [C] : 
          ( m1_ami_1(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_ami_3(C,A,B) ) ) ),
    file(scmfsa_4,rc1_scmfsa_4),
    []).

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_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(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_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_amistd_1,axiom,(
    ! [A,B] : 
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ? [C] : 
          ( m1_ami_1(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_realset1(C)
          & v1_setfam_1(C)
          & v1_ami_3(C,A,B) ) ) ),
    file(amistd_1,rc3_amistd_1),
    []).

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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_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_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(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(redefinition_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k1_struct_0(A,B) = k1_tarski(B) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(redefinition_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(redefinition_k8_ami_5,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
        & m1_ami_1(D,A,B) )
     => k8_ami_5(A,B,C,D) = k1_funct_4(C,D) ) ),
    file(ami_5,k8_ami_5),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ! [C] : 
          ( m1_struct_0(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(struct_0,m1_struct_0),
    []).

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(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(redefinition_r1_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r1_subset_1(A,B)
      <=> r1_xboole_0(A,B) ) ) ),
    file(subset_1,r1_subset_1),
    []).

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

fof(symmetry_r1_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r1_subset_1(A,B)
       => r1_subset_1(B,A) ) ) ),
    file(subset_1,r1_subset_1),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t12_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_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(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_3,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => k1_relat_1(C) = u1_struct_0(B) ) ) ) ),
    file(ami_3,t36_ami_3),
    []).

fof(t39_xboole_1,axiom,(
    ! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) ),
    file(xboole_1,t39_xboole_1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    []).

fof(t41_xboole_1,axiom,(
    ! [A,B,C] : k4_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t41_xboole_1),
    []).

fof(t48_ami_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ( v10_ami_1(B,A)
       => ! [C] : 
            ( m1_struct_0(C,B,u2_ami_1(A,B))
           => k2_ami_1(A,B) != C ) ) ) ),
    file(ami_1,t48_ami_1),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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_scmfsa_3,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v7_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => k7_relat_1(k4_ami_1(A,B,C,D),u2_ami_1(A,B)) = k7_relat_1(D,u2_ami_1(A,B)) ) ) ) ) ),
    file(scmfsa_3,t5_scmfsa_3),
    []).

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(t63_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_xboole_0(B,C) )
     => r1_xboole_0(A,C) ) ),
    file(xboole_1,t63_xboole_1),
    []).

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

fof(t75_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k7_relat_1(k1_funct_4(A,B),C) = k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C)) ) ) ),
    file(funct_4,t75_funct_4),
    []).

fof(t76_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( r1_xboole_0(C,k1_relat_1(B))
             => k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C) ) ) ) ),
    file(funct_4,t76_funct_4),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t83_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k7_relat_1(A,k2_xboole_0(B,C)) = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) ) ),
    file(funct_4,t83_funct_4),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t98_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k7_relat_1(A,k1_relat_1(A)) = A ) ),
    file(relat_1,t98_relat_1),
    []).