% Mizar problem: t26_pencil_3,pencil_3,3049,49 
fof(t26_pencil_3,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] : 
          ( ( v15_pencil_1(B)
            & m1_pboole(B,A) )
         => ( ! [C] : 
                ( m1_subset_1(C,A)
               => v10_pencil_1(k2_pencil_1(A,B,C)) )
           => ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B)))
                  & v1_pencil_2(C,k6_pencil_1(A,B),k6_pencil_1(A,B))
                  & m2_relset_1(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B))) )
               => ! [D] : 
                    ( m1_pencil_2(D,A,B)
                   => ! [E] : 
                        ( m1_pencil_2(E,A,B)
                       => ( ( r1_xboole_0(D,E)
                            & r1_pencil_3(A,B,D,E) )
                         => ! [F] : 
                              ( ( ~ v13_pencil_1(F)
                                & v16_pencil_1(F,A)
                                & m4_pboole(F,A,k12_pralg_1(A,B)) )
                             => ! [G] : 
                                  ( ( ~ v13_pencil_1(G)
                                    & v16_pencil_1(G,A)
                                    & m4_pboole(G,A,k12_pralg_1(A,B)) )
                                 => ( ( k4_card_3(F) = D
                                      & k4_card_3(G) = E )
                                   => k3_pencil_3(A,B,C,F) = k3_pencil_3(A,B,C,G) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_funct_2,cc1_pboole,cc1_pencil_1,cc1_realset1,cc1_relset_1,cc2_finset_1,cc2_funct_2,cc2_pboole,cc2_pencil_1,cc3_funct_2,cc3_pencil_1,cc4_pencil_1,cc5_funct_2,cc5_pencil_1,cc6_funct_2,cc6_pencil_1,commutativity_k3_xboole_0,d12_funct_1,d1_funct_2,d1_tarski,d1_xboole_0,d21_pencil_1,d23_pboole,d2_pencil_2,d3_pboole,d3_pencil_3,d3_pre_topc,d3_xboole_0,d4_funct_2,d4_pencil_2,d4_pencil_3,d4_realset1,d5_pboole,d7_xboole_0,d8_funct_1,dt_k10_pralg_1,dt_k12_pralg_1,dt_k1_funct_1,dt_k1_pencil_1,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funct_7,dt_k2_pencil_1,dt_k2_pencil_3,dt_k2_polynom1,dt_k2_pre_topc,dt_k2_tops_2,dt_k2_zfmisc_1,dt_k3_pencil_1,dt_k3_pencil_3,dt_k3_xboole_0,dt_k4_card_3,dt_k4_pre_topc,dt_k4_relset_1,dt_k5_pencil_1,dt_k6_pencil_1,dt_k8_funct_2,dt_k9_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pboole,dt_m1_pencil_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m4_pboole,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pboole,existence_m1_pencil_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m4_pboole,fc10_finset_1,fc11_finset_1,fc13_finset_1,fc14_finset_1,fc1_finset_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_pboole,fc2_subset_1,fc3_realset1,fc4_pencil_1,fc4_subset_1,idempotence_k3_xboole_0,irreflexivity_r2_subset_1,rc1_finset_1,rc1_funct_2,rc1_pboole,rc1_realset1,rc1_subset_1,rc1_xboole_0,rc2_funct_2,rc2_pboole,rc2_realset1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_pboole,rc3_pencil_1,rc3_struct_0,rc4_finset_1,rc4_pencil_1,rc5_pboole,rc5_pencil_1,rc5_struct_0,rc6_pencil_1,rc7_pencil_1,rc8_pencil_1,redefinition_k10_pralg_1,redefinition_k1_pencil_1,redefinition_k1_struct_0,redefinition_k2_pencil_1,redefinition_k2_polynom1,redefinition_k4_pre_topc,redefinition_k4_relset_1,redefinition_k6_pencil_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_r2_subset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r2_pboole,reflexivity_r6_pboole,symmetry_r1_xboole_0,symmetry_r2_subset_1,symmetry_r6_pboole,t10_pencil_3,t125_funct_1,t14_pencil_1,t17_pencil_3,t18_card_3,t1_pencil_3,t1_subset,t20_pencil_3,t21_pencil_3,t24_pencil_2,t25_pencil_1,t2_boole,t2_subset,t33_funct_7,t34_funct_7,t37_zfmisc_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t7_pencil_3,t8_boole,t9_funct_1]),
    [file(pencil_3,t26_pencil_3)]).

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

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

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    []).

fof(cc1_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v11_pencil_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A) ) ) ),
    file(pencil_1,cc1_pencil_1),
    []).

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

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(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_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc2_funct_2),
    []).

fof(cc2_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(cc2_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v14_pencil_1(A) )
     => ( v1_relat_1(A)
        & v4_waybel_3(A) ) ) ),
    file(pencil_1,cc2_pencil_1),
    []).

fof(cc3_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc3_funct_2),
    []).

fof(cc3_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v15_pencil_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_waybel_3(A)
        & v2_pralg_1(A)
        & v11_pencil_1(A) ) ) ),
    file(pencil_1,cc3_pencil_1),
    []).

fof(cc4_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v11_pencil_1(A)
        & v15_pencil_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A)
        & v11_pencil_1(A)
        & v12_pencil_1(A) ) ) ),
    file(pencil_1,cc4_pencil_1),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc5_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v11_pencil_1(A)
        & v15_pencil_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_waybel_3(A)
        & v2_pralg_1(A)
        & v11_pencil_1(A)
        & v14_pencil_1(A) ) ) ),
    file(pencil_1,cc5_pencil_1),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(cc6_pencil_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( ( ~ v13_pencil_1(B)
              & v16_pencil_1(B,A) )
           => v2_relat_1(B) ) ) ) ),
    file(pencil_1,cc6_pencil_1),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(d12_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

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

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d21_pencil_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v13_pencil_1(B)
            & v16_pencil_1(B,A)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ( C = k3_pencil_1(A,B)
              <=> ~ v1_realset1(k1_funct_1(B,C)) ) ) ) ) ),
    file(pencil_1,d21_pencil_1),
    []).

fof(d23_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( m4_pboole(C,A,B)
          <=> r2_pboole(A,C,B) ) ) ) ),
    file(pboole,d23_pboole),
    []).

fof(d2_pencil_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v11_pencil_1(B)
            & v14_pencil_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pencil_1(A,B))))
             => ( m1_pencil_2(C,A,B)
              <=> ? [D] : 
                    ( ~ v13_pencil_1(D)
                    & v16_pencil_1(D,A)
                    & m4_pboole(D,A,k12_pralg_1(A,B))
                    & C = k4_card_3(D)
                    & k1_funct_1(D,k3_pencil_1(A,D)) = k2_pre_topc(k1_pencil_1(A,B,k3_pencil_1(A,D))) ) ) ) ) ) ),
    file(pencil_2,d2_pencil_2),
    []).

fof(d3_pboole,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    []).

fof(d3_pencil_3,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] : 
          ( ( v15_pencil_1(B)
            & m1_pboole(B,A) )
         => ( ! [C] : 
                ( m1_subset_1(C,A)
               => v10_pencil_1(k2_pencil_1(A,B,C)) )
           => ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B)))
                  & v1_pencil_2(C,k6_pencil_1(A,B),k6_pencil_1(A,B))
                  & m2_relset_1(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B))) )
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,A,A)
                      & v3_funct_2(D,A,A)
                      & m2_relset_1(D,A,A) )
                   => ( D = k2_pencil_3(A,B,C)
                    <=> ! [E] : 
                          ( m1_subset_1(E,A)
                         => ! [F] : 
                              ( m1_subset_1(F,A)
                             => ( k8_funct_2(A,A,D,E) = F
                              <=> ! [G] : 
                                    ( m1_pencil_2(G,A,B)
                                   => ! [H] : 
                                        ( ( ~ v13_pencil_1(H)
                                          & v16_pencil_1(H,A)
                                          & m4_pboole(H,A,k12_pralg_1(A,B)) )
                                       => ! [I] : 
                                            ( ( ~ v13_pencil_1(I)
                                              & v16_pencil_1(I,A)
                                              & m4_pboole(I,A,k12_pralg_1(A,B)) )
                                           => ( ( G = k4_card_3(H)
                                                & k4_pre_topc(k6_pencil_1(A,B),k6_pencil_1(A,B),C,G) = k4_card_3(I)
                                                & k3_pencil_1(A,H) = E )
                                             => k3_pencil_1(A,I) = F ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(pencil_3,d3_pencil_3),
    []).

fof(d3_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => k2_pre_topc(A) = u1_struct_0(A) ) ),
    file(pre_topc,d3_pre_topc),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_funct_2,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v3_funct_2(C,A,B)
      <=> ( v2_funct_1(C)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,d4_funct_2),
    []).

fof(d4_pencil_2,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_pencil_2(C,A,B)
              <=> ( v3_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & v1_t_0topsp(C,A,B)
                  & v3_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A))
                  & v1_t_0topsp(k2_tops_2(A,B,C),B,A) ) ) ) ) ) ),
    file(pencil_2,d4_pencil_2),
    []).

fof(d4_pencil_3,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] : 
          ( ( v15_pencil_1(B)
            & m1_pboole(B,A) )
         => ( ! [C] : 
                ( m1_subset_1(C,A)
               => v10_pencil_1(k2_pencil_1(A,B,C)) )
           => ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B)))
                  & v1_pencil_2(C,k6_pencil_1(A,B),k6_pencil_1(A,B))
                  & m2_relset_1(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B))) )
               => ! [D] : 
                    ( ( ~ v13_pencil_1(D)
                      & v16_pencil_1(D,A)
                      & m4_pboole(D,A,k12_pralg_1(A,B)) )
                   => ( m1_pencil_2(k4_card_3(D),A,B)
                     => ! [E] : 
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k2_pencil_1(A,B,k3_pencil_1(A,D))),u1_struct_0(k2_pencil_1(A,B,k8_funct_2(A,A,k2_pencil_3(A,B,C),k3_pencil_1(A,D)))))
                            & m2_relset_1(E,u1_struct_0(k2_pencil_1(A,B,k3_pencil_1(A,D))),u1_struct_0(k2_pencil_1(A,B,k8_funct_2(A,A,k2_pencil_3(A,B,C),k3_pencil_1(A,D))))) )
                         => ( E = k3_pencil_3(A,B,C,D)
                          <=> ( v1_pencil_2(E,k2_pencil_1(A,B,k3_pencil_1(A,D)),k2_pencil_1(A,B,k8_funct_2(A,A,k2_pencil_3(A,B,C),k3_pencil_1(A,D))))
                              & ! [F] : 
                                  ( m1_pboole(F,A)
                                 => ( ( m1_subset_1(F,u1_struct_0(k6_pencil_1(A,B)))
                                      & r2_hidden(F,k4_card_3(D)) )
                                   => ! [G] : 
                                        ( m1_pboole(G,A)
                                       => ( G = k1_funct_1(C,F)
                                         => k1_funct_1(G,k8_funct_2(A,A,k2_pencil_3(A,B,C),k3_pencil_1(A,D))) = k1_funct_1(E,k1_funct_1(F,k3_pencil_1(A,D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(pencil_3,d4_pencil_3),
    []).

fof(d4_realset1,axiom,(
    ! [A] : 
      ( v1_realset1(A)
    <=> ~ ( ~ v1_xboole_0(A)
          & ! [B] : A != k1_tarski(B) ) ) ),
    file(realset1,d4_realset1),
    []).

fof(d5_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d5_pboole),
    []).

fof(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

fof(d8_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    []).

fof(dt_k10_pralg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_pralg_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => l1_struct_0(k10_pralg_1(A,B,C)) ) ),
    file(pralg_1,k10_pralg_1),
    []).

fof(dt_k12_pralg_1,axiom,(
    ! [A,B] : 
      ( ( v2_pralg_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k12_pralg_1(A,B),A) ) ),
    file(pralg_1,k12_pralg_1),
    []).

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

fof(dt_k1_pencil_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v11_pencil_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => l1_pre_topc(k1_pencil_1(A,B,C)) ) ),
    file(pencil_1,k1_pencil_1),
    []).

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_funct_7,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_7(A,B,C))
        & v1_funct_1(k2_funct_7(A,B,C)) ) ) ),
    file(funct_7,k2_funct_7),
    []).

fof(dt_k2_pencil_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v15_pencil_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(k2_pencil_1(A,B,C))
        & ~ v3_pencil_1(k2_pencil_1(A,B,C))
        & ~ v4_pencil_1(k2_pencil_1(A,B,C))
        & v5_pencil_1(k2_pencil_1(A,B,C))
        & v6_pencil_1(k2_pencil_1(A,B,C))
        & l1_pre_topc(k2_pencil_1(A,B,C)) ) ) ),
    file(pencil_1,k2_pencil_1),
    []).

fof(dt_k2_pencil_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v15_pencil_1(B)
        & m1_pboole(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B)))
        & v1_pencil_2(C,k6_pencil_1(A,B),k6_pencil_1(A,B))
        & m1_relset_1(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B))) )
     => ( v1_funct_1(k2_pencil_3(A,B,C))
        & v1_funct_2(k2_pencil_3(A,B,C),A,A)
        & v3_funct_2(k2_pencil_3(A,B,C),A,A)
        & m2_relset_1(k2_pencil_3(A,B,C),A,A) ) ) ),
    file(pencil_3,k2_pencil_3),
    []).

fof(dt_k2_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( m1_pboole(B,A)
     => m1_pboole(k2_polynom1(A,B,C,D),A) ) ),
    file(polynom1,k2_polynom1),
    []).

fof(dt_k2_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k2_pre_topc),
    []).

fof(dt_k2_tops_2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_funct_1(k2_tops_2(A,B,C))
        & v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A))
        & m2_relset_1(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) ) ) ),
    file(tops_2,k2_tops_2),
    []).

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

fof(dt_k3_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v13_pencil_1(B)
        & v16_pencil_1(B,A)
        & m1_pboole(B,A) )
     => m1_subset_1(k3_pencil_1(A,B),A) ) ),
    file(pencil_1,k3_pencil_1),
    []).

fof(dt_k3_pencil_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v15_pencil_1(B)
        & m1_pboole(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B)))
        & v1_pencil_2(C,k6_pencil_1(A,B),k6_pencil_1(A,B))
        & m1_relset_1(C,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B)))
        & ~ v13_pencil_1(D)
        & v16_pencil_1(D,A)
        & m4_pboole(D,A,k12_pralg_1(A,B)) )
     => ( v1_funct_1(k3_pencil_3(A,B,C,D))
        & v1_funct_2(k3_pencil_3(A,B,C,D),u1_struct_0(k2_pencil_1(A,B,k3_pencil_1(A,D))),u1_struct_0(k2_pencil_1(A,B,k8_funct_2(A,A,k2_pencil_3(A,B,C),k3_pencil_1(A,D)))))
        & m2_relset_1(k3_pencil_3(A,B,C,D),u1_struct_0(k2_pencil_1(A,B,k3_pencil_1(A,D))),u1_struct_0(k2_pencil_1(A,B,k8_funct_2(A,A,k2_pencil_3(A,B,C),k3_pencil_1(A,D))))) ) ) ),
    file(pencil_3,k3_pencil_3),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

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

fof(dt_k4_pre_topc,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(pre_topc,k4_pre_topc),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k5_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v11_pencil_1(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k5_pencil_1(A,B))
        & l1_pre_topc(k5_pencil_1(A,B)) ) ) ),
    file(pencil_1,k5_pencil_1),
    []).

fof(dt_k6_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v15_pencil_1(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k6_pencil_1(A,B))
        & ~ v3_pencil_1(k6_pencil_1(A,B))
        & ~ v4_pencil_1(k6_pencil_1(A,B))
        & v5_pencil_1(k6_pencil_1(A,B))
        & v6_pencil_1(k6_pencil_1(A,B))
        & l1_pre_topc(k6_pencil_1(A,B)) ) ) ),
    file(pencil_1,k6_pencil_1),
    []).

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_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

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

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

fof(dt_m1_pencil_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v11_pencil_1(B)
        & v14_pencil_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( m1_pencil_2(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pencil_1(A,B)))) ) ) ),
    file(pencil_2,m1_pencil_2),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_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(dt_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,B)
         => m1_pboole(C,A) ) ) ),
    file(pboole,m4_pboole),
    []).

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

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

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

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

fof(existence_m1_pencil_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v11_pencil_1(B)
        & v14_pencil_1(B)
        & m1_pboole(B,A) )
     => ? [C] : m1_pencil_2(C,A,B) ) ),
    file(pencil_2,m1_pencil_2),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_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(existence_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : m4_pboole(C,A,B) ) ),
    file(pboole,m4_pboole),
    []).

fof(fc10_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    []).

fof(fc11_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    []).

fof(fc13_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k9_relat_1(A,B)) ) ),
    file(finset_1,fc13_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(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_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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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

fof(fc2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    []).

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

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc4_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v13_pencil_1(B)
        & v16_pencil_1(B,A)
        & m1_pboole(B,A) )
     => ( ~ v1_xboole_0(k4_card_3(B))
        & v1_fraenkel(k4_card_3(B))
        & ~ v1_realset1(k4_card_3(B)) ) ) ),
    file(pencil_1,fc4_pencil_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(irreflexivity_r2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ r2_subset_1(A,A) ) ),
    file(subset_1,r2_subset_1),
    []).

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

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

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

fof(rc2_funct_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_funct_2(B,A,A)
      & v2_funct_2(B,A,A)
      & v3_funct_2(B,A,A) ) ),
    file(funct_2,rc2_funct_2),
    []).

fof(rc2_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

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

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_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

fof(rc3_pencil_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v11_pencil_1(B) ) ),
    file(pencil_1,rc3_pencil_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_pencil_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_pralg_1(A)
      & v11_pencil_1(A) ) ),
    file(pencil_1,rc4_pencil_1),
    []).

fof(rc5_pboole,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) ),
    file(pboole,rc5_pboole),
    []).

fof(rc5_pencil_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v4_waybel_3(B)
      & v2_pralg_1(B)
      & v11_pencil_1(B)
      & v12_pencil_1(B)
      & v14_pencil_1(B)
      & v15_pencil_1(B) ) ),
    file(pencil_1,rc5_pencil_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_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v2_pralg_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,k12_pralg_1(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C)
          & v13_pencil_1(C)
          & v16_pencil_1(C,A) ) ) ),
    file(pencil_1,rc6_pencil_1),
    []).

fof(rc7_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v2_pralg_1(B)
        & v14_pencil_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,k12_pralg_1(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C)
          & ~ v13_pencil_1(C)
          & v16_pencil_1(C,A) ) ) ),
    file(pencil_1,rc7_pencil_1),
    []).

fof(rc8_pencil_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_pboole(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & ~ v13_pencil_1(B)
          & v16_pencil_1(B,A) ) ) ),
    file(pencil_1,rc8_pencil_1),
    []).

fof(redefinition_k10_pralg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_pralg_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k10_pralg_1(A,B,C) = k1_funct_1(B,C) ) ),
    file(pralg_1,k10_pralg_1),
    []).

fof(redefinition_k1_pencil_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v11_pencil_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k1_pencil_1(A,B,C) = k1_funct_1(B,C) ) ),
    file(pencil_1,k1_pencil_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_k2_pencil_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v15_pencil_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k2_pencil_1(A,B,C) = k1_funct_1(B,C) ) ),
    file(pencil_1,k2_pencil_1),
    []).

fof(redefinition_k2_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( m1_pboole(B,A)
     => k2_polynom1(A,B,C,D) = k2_funct_7(B,C,D) ) ),
    file(polynom1,k2_polynom1),
    []).

fof(redefinition_k4_pre_topc,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => k4_pre_topc(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(pre_topc,k4_pre_topc),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_k6_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v15_pencil_1(B)
        & m1_pboole(B,A) )
     => k6_pencil_1(A,B) = k5_pencil_1(A,B) ) ),
    file(pencil_1,k6_pencil_1),
    []).

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_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_r2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r2_subset_1(A,B)
      <=> r1_xboole_0(A,B) ) ) ),
    file(subset_1,r2_subset_1),
    []).

fof(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

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

fof(reflexivity_r2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r2_pboole(A,B,B) ) ),
    file(pboole,r2_pboole),
    []).

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

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(symmetry_r2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r2_subset_1(A,B)
       => r2_subset_1(B,A) ) ) ),
    file(subset_1,r2_subset_1),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

fof(t10_pencil_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v11_pencil_1(B)
            & v14_pencil_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( ( ~ v13_pencil_1(C)
                & v16_pencil_1(C,A)
                & m4_pboole(C,A,k12_pralg_1(A,B)) )
             => ( m1_pencil_2(k4_card_3(C),A,B)
               => k1_funct_1(C,k3_pencil_1(A,C)) = k2_pre_topc(k1_pencil_1(A,B,k3_pencil_1(A,C))) ) ) ) ) ),
    file(pencil_3,t10_pencil_3),
    []).

fof(t125_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r1_xboole_0(A,B)
          & v2_funct_1(C) )
       => r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) ) ) ),
    file(funct_1,t125_funct_1),
    []).

fof(t14_pencil_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v4_waybel_3(B)
            & v11_pencil_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_pencil_1(A,B)))
             => m1_pboole(C,A) ) ) ) ),
    file(pencil_1,t14_pencil_1),
    []).

fof(t17_pencil_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v15_pencil_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k6_pencil_1(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k6_pencil_1(A,B)))
                 => ( C != D
                   => ( r1_pencil_1(k6_pencil_1(A,B),C,D)
                    <=> ! [E] : 
                          ( m1_pboole(E,A)
                         => ! [F] : 
                              ( m1_pboole(F,A)
                             => ~ ( E = C
                                  & F = D
                                  & ! [G] : 
                                      ( m1_subset_1(G,A)
                                     => ~ ( ! [H] : 
                                              ( m1_subset_1(H,u1_struct_0(k2_pencil_1(A,B,G)))
                                             => ! [I] : 
                                                  ( m1_subset_1(I,u1_struct_0(k2_pencil_1(A,B,G)))
                                                 => ( ( H = k1_funct_1(E,G)
                                                      & I = k1_funct_1(F,G) )
                                                   => ( H != I
                                                      & r1_pencil_1(k2_pencil_1(A,B,G),H,I) ) ) ) )
                                          & ! [H] : 
                                              ( m1_subset_1(H,A)
                                             => ( H != G
                                               => k1_funct_1(E,H) = k1_funct_1(F,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(pencil_3,t17_pencil_3),
    []).

fof(t18_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(card_3,t18_card_3),
    []).

fof(t1_pencil_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_pencil_1(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v1_pencil_2(B,A,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_pencil_1(A,C,D)
                   => r1_pencil_1(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ),
    file(pencil_3,t1_pencil_3),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t20_pencil_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v15_pencil_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_pencil_2(C,A,B)
             => ! [D] : 
                  ( m1_pencil_2(D,A,B)
                 => ( r1_pencil_3(A,B,C,D)
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B)))
                          & v1_pencil_2(E,k6_pencil_1(A,B),k6_pencil_1(A,B))
                          & m2_relset_1(E,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B))) )
                       => ! [F] : 
                            ( m1_pencil_2(F,A,B)
                           => ! [G] : 
                                ( m1_pencil_2(G,A,B)
                               => ( ( F = k4_pre_topc(k6_pencil_1(A,B),k6_pencil_1(A,B),E,C)
                                    & G = k4_pre_topc(k6_pencil_1(A,B),k6_pencil_1(A,B),E,D) )
                                 => r1_pencil_3(A,B,F,G) ) ) ) ) ) ) ) ) ) ),
    file(pencil_3,t20_pencil_3),
    []).

fof(t21_pencil_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v15_pencil_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_pencil_2(C,A,B)
             => ! [D] : 
                  ( m1_pencil_2(D,A,B)
                 => ( r1_xboole_0(C,D)
                   => ( r1_pencil_3(A,B,C,D)
                    <=> ! [E] : 
                          ( ( ~ v13_pencil_1(E)
                            & v16_pencil_1(E,A)
                            & m4_pboole(E,A,k12_pralg_1(A,B)) )
                         => ! [F] : 
                              ( ( ~ v13_pencil_1(F)
                                & v16_pencil_1(F,A)
                                & m4_pboole(F,A,k12_pralg_1(A,B)) )
                             => ( ( C = k4_card_3(E)
                                  & D = k4_card_3(F) )
                               => ( k3_pencil_1(A,E) = k3_pencil_1(A,F)
                                  & ? [G] : 
                                      ( m1_subset_1(G,A)
                                      & G != k3_pencil_1(A,E)
                                      & ! [H] : 
                                          ( m1_subset_1(H,A)
                                         => ( H != G
                                           => k1_funct_1(E,H) = k1_funct_1(F,H) ) )
                                      & ! [H] : 
                                          ( m1_subset_1(H,u1_struct_0(k2_pencil_1(A,B,G)))
                                         => ! [I] : 
                                              ( m1_subset_1(I,u1_struct_0(k2_pencil_1(A,B,G)))
                                             => ( ( k1_funct_1(E,G) = k1_struct_0(k2_pencil_1(A,B,G),H)
                                                  & k1_funct_1(F,G) = k1_struct_0(k2_pencil_1(A,B,G),I) )
                                               => r1_pencil_1(k2_pencil_1(A,B,G),H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(pencil_3,t21_pencil_3),
    []).

fof(t24_pencil_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v15_pencil_1(B)
            & m1_pboole(B,A) )
         => ( ! [C] : 
                ( m1_subset_1(C,A)
               => v10_pencil_1(k2_pencil_1(A,B,C)) )
           => ! [C] : 
                ( m1_pencil_2(C,A,B)
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B)))
                      & v1_pencil_2(D,k6_pencil_1(A,B),k6_pencil_1(A,B))
                      & m2_relset_1(D,u1_struct_0(k6_pencil_1(A,B)),u1_struct_0(k6_pencil_1(A,B))) )
                   => m1_pencil_2(k4_pre_topc(k6_pencil_1(A,B),k6_pencil_1(A,B),D,C),A,B) ) ) ) ) ) ),
    file(pencil_2,t24_pencil_2),
    []).

fof(t25_pencil_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v15_pencil_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_pboole(C,A)
             => ( m1_subset_1(C,u1_struct_0(k6_pencil_1(A,B)))
               => ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(k2_pencil_1(A,B,D)))
                       => m1_subset_1(k2_polynom1(A,C,D,E),u1_struct_0(k6_pencil_1(A,B))) ) ) ) ) ) ) ),
    file(pencil_1,t25_pencil_1),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t33_funct_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( r2_hidden(C,k1_relat_1(A))
         => k1_funct_1(k2_funct_7(A,C,B),C) = B ) ) ),
    file(funct_7,t33_funct_7),
    []).

fof(t34_funct_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D] : 
          ( C != D
         => k1_funct_1(k2_funct_7(A,C,B),D) = k1_funct_1(A,D) ) ) ),
    file(funct_7,t34_funct_7),
    []).

fof(t37_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_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(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(t7_pencil_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_pralg_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => k1_funct_1(k12_pralg_1(A,B),C) = k2_pre_topc(k10_pralg_1(A,B,C)) ) ) ) ),
    file(pencil_3,t7_pencil_3),
    []).

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

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).