SET007 Axioms: SET007+718.ax


%------------------------------------------------------------------------------
% File     : SET007+718 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Combining of Multi Cell Circuits
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : circcmb2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   50 (   0 unit)
%            Number of atoms       : 1387 ( 366 equality)
%            Maximal formula depth :   32 (  19 average)
%            Number of connectives : 1546 ( 209 ~  ;   2  |; 885  &)
%                                         (   1 <=>; 449 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   0 propositional; 1-4 arity)
%            Number of functors    :  171 (  86 constant; 0-4 arity)
%            Number of variables   :  476 (   0 singleton; 398 !;  78 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_circcmb2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k4_finseq_2(A,k10_circcomb),k10_circcomb)
        & m1_relset_1(B,k4_finseq_2(A,k10_circcomb),k10_circcomb)
        & m1_circcomb(C,A) )
     => ( v4_msualg_1(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
        & v5_msualg_1(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
        & v3_msafree2(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
        & v4_msafree2(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
        & v4_circcomb(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
        & v6_circcomb(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C)) ) ) )).

fof(t1_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_circcomb(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k4_finseq_2(B,A),A)
                    & m2_relset_1(D,k4_finseq_2(B,A),A) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_msualg_1(k7_circcomb(D,C)))
                     => ! [F] :
                          ( m1_subset_1(F,k4_card_3(u4_msualg_1(k7_circcomb(D,C),k9_circcomb(B,A,D,C))))
                         => k3_circuit1(k7_circcomb(D,C),k9_circcomb(B,A,D,C),F,E) = k5_relat_1(C,F) ) ) ) ) ) ) )).

fof(t2_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_circcomb(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k4_finseq_2(B,A),A)
                    & m2_relset_1(D,k4_finseq_2(B,A),A) )
                 => ! [E] :
                      ( m1_subset_1(E,k4_card_3(u4_msualg_1(k7_circcomb(D,C),k9_circcomb(B,A,D,C))))
                     => v1_circuit2(k6_circuit2(k7_circcomb(D,C),k9_circcomb(B,A,D,C),E),k7_circcomb(D,C),k9_circcomb(B,A,D,C)) ) ) ) ) ) )).

fof(t3_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
             => ( v1_circuit2(C,A,B)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k9_facirc_1(A,B,C,D) = C ) ) ) ) ) )).

fof(t4_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( v1_circuit2(k9_facirc_1(A,B,C,D),A,B)
                          & r1_xreal_0(D,E) )
                       => k9_facirc_1(A,B,C,E) = k9_facirc_1(A,B,C,D) ) ) ) ) ) ) )).

fof(t5_circcmb2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
           => k2_relat_1(k1_funct_4(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ) )).

fof(t6_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ( r1_circcomb(A,B)
           => k2_msafree2(k3_circcomb(A,B)) = k2_xboole_0(k4_xboole_0(k2_msafree2(A),k3_msafree2(B)),k4_xboole_0(k2_msafree2(B),k3_msafree2(A))) ) ) ) )).

fof(t7_circcmb2,axiom,(
    ! [A] :
      ( ~ v2_facirc_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k4_xboole_0(A,B) = A ) ) )).

fof(t8_circcmb2,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( r1_tarski(C,B)
         => ( v2_facirc_1(k4_xboole_0(B,C))
            | k4_xboole_0(A,B) = k4_xboole_0(A,C) ) ) ) )).

fof(t9_circcmb2,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r1_tarski(B,C)
       => ( v2_facirc_1(k4_xboole_0(A,B))
          | k4_xboole_0(A,C) = k4_xboole_0(A,B) ) ) ) )).

fof(d1_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ( C = k1_circcmb2(A,B)
              <=> C = B ) ) ) ) )).

fof(t10_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k4_msafree2(A),k2_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(B,E)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(C,F)))
                                     => ( G = k7_relat_1(H,u1_struct_0(B))
                                       => k6_circuit2(B,E,G) = k7_relat_1(k6_circuit2(C,F,H),u1_struct_0(B)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t11_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(A,D)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(C,F)))
                                     => ( G = k7_relat_1(H,u1_struct_0(A))
                                       => k6_circuit2(A,D,G) = k7_relat_1(k6_circuit2(C,F,H),u1_struct_0(A)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_circcomb(A,B)
                  & r1_xboole_0(k4_msafree2(A),k2_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(A,D)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(B,E)))
                                     => ! [I] :
                                          ( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
                                         => ( ( G = k7_relat_1(I,u1_struct_0(A))
                                              & H = k7_relat_1(I,u1_struct_0(B))
                                              & v1_circuit2(G,A,D)
                                              & v1_circuit2(H,B,E) )
                                           => v1_circuit2(I,C,F) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_circcomb(A,B)
                  & r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(A,D)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(B,E)))
                                     => ! [I] :
                                          ( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
                                         => ( ( G = k7_relat_1(I,u1_struct_0(A))
                                              & H = k7_relat_1(I,u1_struct_0(B))
                                              & v1_circuit2(G,A,D)
                                              & v1_circuit2(H,B,E) )
                                           => v1_circuit2(I,C,F) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
                                     => ( H = k7_relat_1(G,u1_struct_0(A))
                                       => ! [I] :
                                            ( m2_subset_1(I,k1_numbers,k5_numbers)
                                           => k7_relat_1(k9_facirc_1(C,F,G,I),u1_struct_0(A)) = k9_facirc_1(A,D,H,I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(B),k4_msafree2(A))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(B,E)))
                                     => ( H = k7_relat_1(G,u1_struct_0(B))
                                       => ! [I] :
                                            ( m2_subset_1(I,k1_numbers,k5_numbers)
                                           => k7_relat_1(k9_facirc_1(C,F,G,I),u1_struct_0(B)) = k9_facirc_1(B,E,H,I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
                                     => ( ( H = k7_relat_1(G,u1_struct_0(A))
                                          & v1_circuit2(H,A,D) )
                                       => ! [I] :
                                            ( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
                                           => ( I = k7_relat_1(G,u1_struct_0(B))
                                             => k7_relat_1(k6_circuit2(C,F,G),u1_struct_0(B)) = k6_circuit2(B,E,I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t17_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( C = k3_circcomb(A,B)
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
                                     => ( ( H = k7_relat_1(G,u1_struct_0(A))
                                          & v1_circuit2(H,A,D) )
                                       => ! [I] :
                                            ( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
                                           => ( ( I = k7_relat_1(G,u1_struct_0(B))
                                                & v1_circuit2(I,B,E) )
                                             => v1_circuit2(G,C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( C = k3_circcomb(A,B)
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
                                 => ( v1_circuit2(G,C,F)
                                   => ( ! [H] :
                                          ( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
                                         => ( H = k7_relat_1(G,u1_struct_0(A))
                                           => v1_circuit2(H,A,D) ) )
                                      & ! [H] :
                                          ( m1_subset_1(H,k4_card_3(u4_msualg_1(B,E)))
                                         => ( H = k7_relat_1(G,u1_struct_0(B))
                                           => v1_circuit2(H,B,E) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(A,D)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(B,E)))
                                     => ! [I] :
                                          ( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
                                         => ( ( G = k7_relat_1(I,u1_struct_0(A))
                                              & H = k7_relat_1(I,u1_struct_0(B))
                                              & v1_circuit2(G,A,D) )
                                           => ! [J] :
                                                ( m2_subset_1(J,k1_numbers,k5_numbers)
                                               => k7_relat_1(k9_facirc_1(C,F,I,J),u1_struct_0(B)) = k9_facirc_1(B,E,H,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
                                         => ! [J] :
                                              ( m1_subset_1(J,k4_card_3(u4_msualg_1(A,D)))
                                             => ! [K] :
                                                  ( m1_subset_1(K,k4_card_3(u4_msualg_1(B,E)))
                                                 => ( ( J = k7_relat_1(I,u1_struct_0(A))
                                                      & v1_circuit2(k9_facirc_1(A,D,J,G),A,D)
                                                      & K = k7_relat_1(k9_facirc_1(C,F,I,G),u1_struct_0(B))
                                                      & v1_circuit2(k9_facirc_1(B,E,K,H),B,E) )
                                                   => v1_circuit2(k9_facirc_1(C,F,I,k1_nat_1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t21_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( ( ! [I] :
                                              ( m1_subset_1(I,k4_card_3(u4_msualg_1(A,D)))
                                             => v1_circuit2(k9_facirc_1(A,D,I,G),A,D) )
                                          & ! [I] :
                                              ( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
                                             => v1_circuit2(k9_facirc_1(B,E,I,H),B,E) ) )
                                       => ! [I] :
                                            ( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
                                           => v1_circuit2(k9_facirc_1(C,F,I,k1_nat_1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & r1_xboole_0(k2_msafree2(B),k4_msafree2(A))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
                                     => ( H = k7_relat_1(G,u1_struct_0(A))
                                       => ! [I] :
                                            ( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
                                           => ( I = k7_relat_1(G,u1_struct_0(B))
                                             => ! [J] :
                                                  ( m2_subset_1(J,k1_numbers,k5_numbers)
                                                 => k9_facirc_1(C,F,G,J) = k1_funct_4(k9_facirc_1(A,D,H,J),k9_facirc_1(B,E,I,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & r1_xboole_0(k2_msafree2(B),k4_msafree2(A))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
                                         => ! [J] :
                                              ( m1_subset_1(J,k4_card_3(u4_msualg_1(A,D)))
                                             => ( J = k7_relat_1(I,u1_struct_0(A))
                                               => ! [K] :
                                                    ( m1_subset_1(K,k4_card_3(u4_msualg_1(B,E)))
                                                   => ( ( K = k7_relat_1(I,u1_struct_0(B))
                                                        & v1_circuit2(k9_facirc_1(A,D,J,G),A,D)
                                                        & v1_circuit2(k9_facirc_1(B,E,K,H),B,E) )
                                                     => v1_circuit2(k9_facirc_1(C,F,I,k1_limfunc1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & r1_xboole_0(k2_msafree2(B),k4_msafree2(A))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m1_subset_1(H,k4_card_3(u4_msualg_1(C,F)))
                                     => ! [I] :
                                          ( m1_subset_1(I,k4_card_3(u4_msualg_1(A,D)))
                                         => ( I = k7_relat_1(H,u1_struct_0(A))
                                           => ! [J] :
                                                ( m1_subset_1(J,k4_card_3(u4_msualg_1(B,E)))
                                               => ~ ( J = k7_relat_1(H,u1_struct_0(B))
                                                    & ~ ( v1_circuit2(k9_facirc_1(A,D,I,G),A,D)
                                                        & v1_circuit2(k9_facirc_1(B,E,J,G),B,E) )
                                                    & v1_circuit2(k9_facirc_1(C,F,H,G),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & r1_xboole_0(k2_msafree2(B),k4_msafree2(A))
                  & C = k3_circcomb(A,B) )
               => ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] :
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( ( ! [I] :
                                              ( m1_subset_1(I,k4_card_3(u4_msualg_1(A,D)))
                                             => v1_circuit2(k9_facirc_1(A,D,I,G),A,D) )
                                          & ! [I] :
                                              ( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
                                             => v1_circuit2(k9_facirc_1(B,E,I,H),B,E) ) )
                                       => ! [I] :
                                            ( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
                                           => v1_circuit2(k9_facirc_1(C,F,I,k1_limfunc1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(s1_circcmb2,axiom,(
    ? [A] :
      ( m1_pboole(A,k5_numbers)
      & ? [B] :
          ( m1_pboole(B,k5_numbers)
          & k1_funct_1(A,np__0) = f1_s1_circcmb2
          & k1_funct_1(B,np__0) = f2_s1_circcmb2
          & ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_msualg_1(D) )
                 => ! [E] :
                      ( ( D = k1_funct_1(A,C)
                        & E = k1_funct_1(B,C) )
                     => ( k1_funct_1(A,k1_nat_1(C,np__1)) = f3_s1_circcmb2(D,E,C)
                        & k1_funct_1(B,k1_nat_1(C,np__1)) = f4_s1_circcmb2(E,C) ) ) ) ) ) ) )).

fof(s2_circcmb2,axiom,
    ( ( ? [A] :
          ( ~ v3_struct_0(A)
          & l1_msualg_1(A)
          & ? [B] :
              ( A = k1_funct_1(f3_s2_circcmb2,np__0)
              & B = k1_funct_1(f4_s2_circcmb2,np__0)
              & p1_s2_circcmb2(A,B,np__0) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( B = k1_funct_1(f3_s2_circcmb2,A)
                    & C = k1_funct_1(f4_s2_circcmb2,A) )
                 => ( k1_funct_1(f3_s2_circcmb2,k1_nat_1(A,np__1)) = f1_s2_circcmb2(B,C,A)
                    & k1_funct_1(f4_s2_circcmb2,k1_nat_1(A,np__1)) = f2_s2_circcmb2(C,A) ) ) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( B = k1_funct_1(f3_s2_circcmb2,A)
                    & C = k1_funct_1(f4_s2_circcmb2,A)
                    & p1_s2_circcmb2(B,C,A) )
                 => p1_s2_circcmb2(f1_s2_circcmb2(B,C,A),f2_s2_circcmb2(C,A),k1_nat_1(A,np__1)) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ? [B] :
            ( ~ v3_struct_0(B)
            & l1_msualg_1(B)
            & B = k1_funct_1(f3_s2_circcmb2,A)
            & p1_s2_circcmb2(B,k1_funct_1(f4_s2_circcmb2,A),A) ) ) )).

fof(s3_circcmb2,axiom,
    ( ( k1_funct_1(f4_s3_circcmb2,np__0) = f1_s3_circcmb2
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( B = k1_funct_1(f4_s3_circcmb2,A)
                    & C = k1_funct_1(f5_s3_circcmb2,A) )
                 => ( k1_funct_1(f4_s3_circcmb2,k1_nat_1(A,np__1)) = f2_s3_circcmb2(B,C,A)
                    & k1_funct_1(f5_s3_circcmb2,k1_nat_1(A,np__1)) = f3_s3_circcmb2(C,A) ) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ! [B] :
            ( B = k1_funct_1(f5_s3_circcmb2,A)
           => k1_funct_1(f5_s3_circcmb2,k1_nat_1(A,np__1)) = f3_s3_circcmb2(B,A) ) ) )).

fof(s4_circcmb2,axiom,(
    ? [A] :
      ( ~ v3_struct_0(A)
      & l1_msualg_1(A)
      & ? [B] :
          ( m1_pboole(B,k5_numbers)
          & ? [C] :
              ( m1_pboole(C,k5_numbers)
              & A = k1_funct_1(B,f5_s4_circcmb2)
              & k1_funct_1(B,np__0) = f1_s4_circcmb2
              & k1_funct_1(C,np__0) = f2_s4_circcmb2
              & ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l1_msualg_1(E) )
                     => ! [F] :
                          ( ( E = k1_funct_1(B,D)
                            & F = k1_funct_1(C,D) )
                         => ( k1_funct_1(B,k1_nat_1(D,np__1)) = f3_s4_circcmb2(E,F,D)
                            & k1_funct_1(C,k1_nat_1(D,np__1)) = f4_s4_circcmb2(F,D) ) ) ) ) ) ) ) )).

fof(s5_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ~ ( ? [C] :
                  ( m1_pboole(C,k5_numbers)
                  & ? [D] :
                      ( m1_pboole(D,k5_numbers)
                      & A = k1_funct_1(C,f5_s5_circcmb2)
                      & k1_funct_1(C,np__0) = f1_s5_circcmb2
                      & k1_funct_1(D,np__0) = f2_s5_circcmb2
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( ( ~ v3_struct_0(F)
                                & l1_msualg_1(F) )
                             => ! [G] :
                                  ( ( F = k1_funct_1(C,E)
                                    & G = k1_funct_1(D,E) )
                                 => ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s5_circcmb2(F,G,E)
                                    & k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s5_circcmb2(G,E) ) ) ) ) ) )
              & ? [C] :
                  ( m1_pboole(C,k5_numbers)
                  & ? [D] :
                      ( m1_pboole(D,k5_numbers)
                      & B = k1_funct_1(C,f5_s5_circcmb2)
                      & k1_funct_1(C,np__0) = f1_s5_circcmb2
                      & k1_funct_1(D,np__0) = f2_s5_circcmb2
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( ( ~ v3_struct_0(F)
                                & l1_msualg_1(F) )
                             => ! [G] :
                                  ( ( F = k1_funct_1(C,E)
                                    & G = k1_funct_1(D,E) )
                                 => ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s5_circcmb2(F,G,E)
                                    & k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s5_circcmb2(G,E) ) ) ) ) ) )
              & A != B ) ) ) )).

fof(s6_circcmb2,axiom,
    ( ? [A] :
        ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & ? [B] :
            ( m1_pboole(B,k5_numbers)
            & ? [C] :
                ( m1_pboole(C,k5_numbers)
                & A = k1_funct_1(B,f5_s6_circcmb2)
                & k1_funct_1(B,np__0) = f1_s6_circcmb2
                & k1_funct_1(C,np__0) = f2_s6_circcmb2
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( ( ~ v3_struct_0(E)
                          & l1_msualg_1(E) )
                       => ! [F] :
                            ( ( E = k1_funct_1(B,D)
                              & F = k1_funct_1(C,D) )
                           => ( k1_funct_1(B,k1_nat_1(D,np__1)) = f3_s6_circcmb2(E,F,D)
                              & k1_funct_1(C,k1_nat_1(D,np__1)) = f4_s6_circcmb2(F,D) ) ) ) ) ) ) )
    & ! [A] :
        ( ( ~ v3_struct_0(A)
          & l1_msualg_1(A) )
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & l1_msualg_1(B) )
           => ~ ( ? [C] :
                    ( m1_pboole(C,k5_numbers)
                    & ? [D] :
                        ( m1_pboole(D,k5_numbers)
                        & A = k1_funct_1(C,f5_s6_circcmb2)
                        & k1_funct_1(C,np__0) = f1_s6_circcmb2
                        & k1_funct_1(D,np__0) = f2_s6_circcmb2
                        & ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ! [F] :
                                ( ( ~ v3_struct_0(F)
                                  & l1_msualg_1(F) )
                               => ! [G] :
                                    ( ( F = k1_funct_1(C,E)
                                      & G = k1_funct_1(D,E) )
                                   => ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s6_circcmb2(F,G,E)
                                      & k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s6_circcmb2(G,E) ) ) ) ) ) )
                & ? [C] :
                    ( m1_pboole(C,k5_numbers)
                    & ? [D] :
                        ( m1_pboole(D,k5_numbers)
                        & B = k1_funct_1(C,f5_s6_circcmb2)
                        & k1_funct_1(C,np__0) = f1_s6_circcmb2
                        & k1_funct_1(D,np__0) = f2_s6_circcmb2
                        & ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ! [F] :
                                ( ( ~ v3_struct_0(F)
                                  & l1_msualg_1(F) )
                               => ! [G] :
                                    ( ( F = k1_funct_1(C,E)
                                      & G = k1_funct_1(D,E) )
                                   => ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s6_circcmb2(F,G,E)
                                      & k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s6_circcmb2(G,E) ) ) ) ) ) )
                & A != B ) ) ) )).

fof(s7_circcmb2,axiom,
    ( ( v1_circcomb(f1_s7_circcmb2)
      & v2_circcomb(f1_s7_circcmb2)
      & v3_circcomb(f1_s7_circcmb2)
      & ~ v2_msualg_1(f1_s7_circcmb2)
      & ~ v3_struct_0(f1_s7_circcmb2)
      & v1_msualg_1(f1_s7_circcmb2)
      & ! [A] :
          ( ( ~ v3_struct_0(A)
            & v1_msualg_1(A)
            & ~ v2_msualg_1(A)
            & v1_circcomb(A)
            & v2_circcomb(A)
            & v3_circcomb(A)
            & l1_msualg_1(A) )
         => ! [B,C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( v1_circcomb(f2_s7_circcmb2(A,B,C))
                & v2_circcomb(f2_s7_circcmb2(A,B,C))
                & v3_circcomb(f2_s7_circcmb2(A,B,C))
                & ~ v2_msualg_1(f2_s7_circcmb2(A,B,C))
                & ~ v3_struct_0(f2_s7_circcmb2(A,B,C))
                & v1_msualg_1(f2_s7_circcmb2(A,B,C)) ) ) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v1_msualg_1(A)
        & ~ v2_msualg_1(A)
        & v1_circcomb(A)
        & v2_circcomb(A)
        & v3_circcomb(A)
        & l1_msualg_1(A)
        & ? [B] :
            ( m1_pboole(B,k5_numbers)
            & ? [C] :
                ( m1_pboole(C,k5_numbers)
                & A = k1_funct_1(B,f5_s7_circcmb2)
                & k1_funct_1(B,np__0) = f1_s7_circcmb2
                & k1_funct_1(C,np__0) = f3_s7_circcmb2
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( ( ~ v3_struct_0(E)
                          & l1_msualg_1(E) )
                       => ! [F] :
                            ( ( E = k1_funct_1(B,D)
                              & F = k1_funct_1(C,D) )
                           => ( k1_funct_1(B,k1_nat_1(D,np__1)) = f2_s7_circcmb2(E,F,D)
                              & k1_funct_1(C,k1_nat_1(D,np__1)) = f4_s7_circcmb2(F,D) ) ) ) ) ) ) ) )).

fof(s8_circcmb2,axiom,
    ( ( v1_circcomb(f1_s8_circcmb2)
      & v2_circcomb(f1_s8_circcmb2)
      & v3_circcomb(f1_s8_circcmb2)
      & ~ v2_msualg_1(f1_s8_circcmb2)
      & ~ v3_struct_0(f1_s8_circcmb2)
      & v1_msualg_1(f1_s8_circcmb2) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v1_msualg_1(A)
        & ~ v2_msualg_1(A)
        & v1_circcomb(A)
        & v2_circcomb(A)
        & v3_circcomb(A)
        & l1_msualg_1(A)
        & ? [B] :
            ( m1_pboole(B,k5_numbers)
            & ? [C] :
                ( m1_pboole(C,k5_numbers)
                & A = k1_funct_1(B,f5_s8_circcmb2)
                & k1_funct_1(B,np__0) = f1_s8_circcmb2
                & k1_funct_1(C,np__0) = f3_s8_circcmb2
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( ( ~ v3_struct_0(E)
                          & l1_msualg_1(E) )
                       => ! [F] :
                            ( ( E = k1_funct_1(B,D)
                              & F = k1_funct_1(C,D) )
                           => ( k1_funct_1(B,k1_nat_1(D,np__1)) = k3_circcomb(E,f2_s8_circcmb2(F,D))
                              & k1_funct_1(C,k1_nat_1(D,np__1)) = f4_s8_circcmb2(F,D) ) ) ) ) ) ) ) )).

fof(s9_circcmb2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_msualg_1(A)
        & ~ v2_msualg_1(A)
        & v1_circcomb(A)
        & v2_circcomb(A)
        & v3_circcomb(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_msualg_1(B)
            & ~ v2_msualg_1(B)
            & v1_circcomb(B)
            & v2_circcomb(B)
            & v3_circcomb(B)
            & l1_msualg_1(B) )
         => ~ ( ? [C] :
                  ( m1_pboole(C,k5_numbers)
                  & ? [D] :
                      ( m1_pboole(D,k5_numbers)
                      & A = k1_funct_1(C,f5_s9_circcmb2)
                      & k1_funct_1(C,np__0) = f1_s9_circcmb2
                      & k1_funct_1(D,np__0) = f2_s9_circcmb2
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( ( ~ v3_struct_0(F)
                                & l1_msualg_1(F) )
                             => ! [G] :
                                  ( ( F = k1_funct_1(C,E)
                                    & G = k1_funct_1(D,E) )
                                 => ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s9_circcmb2(F,G,E)
                                    & k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s9_circcmb2(G,E) ) ) ) ) ) )
              & ? [C] :
                  ( m1_pboole(C,k5_numbers)
                  & ? [D] :
                      ( m1_pboole(D,k5_numbers)
                      & B = k1_funct_1(C,f5_s9_circcmb2)
                      & k1_funct_1(C,np__0) = f1_s9_circcmb2
                      & k1_funct_1(D,np__0) = f2_s9_circcmb2
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( ( ~ v3_struct_0(F)
                                & l1_msualg_1(F) )
                             => ! [G] :
                                  ( ( F = k1_funct_1(C,E)
                                    & G = k1_funct_1(D,E) )
                                 => ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s9_circcmb2(F,G,E)
                                    & k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s9_circcmb2(G,E) ) ) ) ) ) )
              & A != B ) ) ) )).

fof(s10_circcmb2,axiom,
    ( ( v1_relat_1(k4_msafree2(f1_s10_circcmb2))
      & ~ v2_facirc_1(k2_msafree2(f1_s10_circcmb2))
      & f2_s10_circcmb2(np__0) = f1_s10_circcmb2
      & r2_hidden(k1_funct_1(f3_s10_circcmb2,np__0),k4_msafree2(f1_s10_circcmb2))
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] : v1_relat_1(k4_msafree2(f4_s10_circcmb2(B,A))) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ~ ( B = k1_funct_1(f3_s10_circcmb2,A)
                & v2_facirc_1(k4_xboole_0(k2_msafree2(f4_s10_circcmb2(B,A)),k1_tarski(B))) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( B = f2_s10_circcmb2(A)
                    & C = k1_funct_1(f3_s10_circcmb2,A) )
                 => ( f2_s10_circcmb2(k1_nat_1(A,np__1)) = k3_circcomb(B,f4_s10_circcmb2(C,A))
                    & k1_funct_1(f3_s10_circcmb2,k1_nat_1(A,np__1)) = f5_s10_circcmb2(C,A)
                    & r2_hidden(C,k2_msafree2(f4_s10_circcmb2(C,A)))
                    & r2_hidden(f5_s10_circcmb2(C,A),k4_msafree2(f4_s10_circcmb2(C,A))) ) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ? [B] :
            ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v1_circcomb(B)
            & v2_circcomb(B)
            & v3_circcomb(B)
            & l1_msualg_1(B)
            & ? [C] :
                ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v1_circcomb(C)
                & v2_circcomb(C)
                & v3_circcomb(C)
                & l1_msualg_1(C)
                & B = f2_s10_circcmb2(A)
                & C = f2_s10_circcmb2(k1_nat_1(A,np__1))
                & k2_msafree2(C) = k2_xboole_0(k2_msafree2(B),k4_xboole_0(k2_msafree2(f4_s10_circcmb2(k1_funct_1(f3_s10_circcmb2,A),A)),k1_tarski(k1_funct_1(f3_s10_circcmb2,A))))
                & v1_relat_1(k4_msafree2(B))
                & ~ v2_facirc_1(k2_msafree2(B)) ) ) ) )).

fof(s11_circcmb2,axiom,
    ( ( v1_relat_1(k4_msafree2(f1_s11_circcmb2(np__0)))
      & ~ v2_facirc_1(k2_msafree2(f1_s11_circcmb2(np__0)))
      & r2_hidden(k1_funct_1(f2_s11_circcmb2,np__0),k4_msafree2(f1_s11_circcmb2(np__0)))
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] : v1_relat_1(k4_msafree2(f3_s11_circcmb2(B,A))) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ~ ( B = k1_funct_1(f2_s11_circcmb2,A)
                & v2_facirc_1(k4_xboole_0(k2_msafree2(f3_s11_circcmb2(B,A)),k1_tarski(B))) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( B = f1_s11_circcmb2(A)
                    & C = k1_funct_1(f2_s11_circcmb2,A) )
                 => ( f1_s11_circcmb2(k1_nat_1(A,np__1)) = k3_circcomb(B,f3_s11_circcmb2(C,A))
                    & k1_funct_1(f2_s11_circcmb2,k1_nat_1(A,np__1)) = f4_s11_circcmb2(C,A)
                    & r2_hidden(C,k2_msafree2(f3_s11_circcmb2(C,A)))
                    & r2_hidden(f4_s11_circcmb2(C,A),k4_msafree2(f3_s11_circcmb2(C,A))) ) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( k2_msafree2(f1_s11_circcmb2(k1_nat_1(A,np__1))) = k2_xboole_0(k2_msafree2(f1_s11_circcmb2(A)),k4_xboole_0(k2_msafree2(f3_s11_circcmb2(k1_funct_1(f2_s11_circcmb2,A),A)),k1_tarski(k1_funct_1(f2_s11_circcmb2,A))))
          & v1_relat_1(k4_msafree2(f1_s11_circcmb2(A)))
          & ~ v2_facirc_1(k2_msafree2(f1_s11_circcmb2(A))) ) ) )).

fof(s12_circcmb2,axiom,(
    ? [A] :
      ( m1_pboole(A,k5_numbers)
      & ? [B] :
          ( m1_pboole(B,k5_numbers)
          & ? [C] :
              ( m1_pboole(C,k5_numbers)
              & k1_funct_1(A,np__0) = f1_s12_circcmb2
              & k1_funct_1(B,np__0) = f2_s12_circcmb2
              & k1_funct_1(C,np__0) = f3_s12_circcmb2
              & ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l1_msualg_1(E) )
                     => ! [F] :
                          ( ( v5_msualg_1(F,E)
                            & l3_msualg_1(F,E) )
                         => ! [G] :
                              ( ( E = k1_funct_1(A,D)
                                & F = k1_funct_1(B,D)
                                & G = k1_funct_1(C,D) )
                             => ( k1_funct_1(A,k1_nat_1(D,np__1)) = f4_s12_circcmb2(E,G,D)
                                & k1_funct_1(B,k1_nat_1(D,np__1)) = f5_s12_circcmb2(E,F,G,D)
                                & k1_funct_1(C,k1_nat_1(D,np__1)) = f6_s12_circcmb2(G,D) ) ) ) ) ) ) ) ) )).

fof(s13_circcmb2,axiom,
    ( ( ? [A] :
          ( ~ v3_struct_0(A)
          & l1_msualg_1(A)
          & ? [B] :
              ( v5_msualg_1(B,A)
              & l3_msualg_1(B,A)
              & ? [C] :
                  ( A = k1_funct_1(f4_s13_circcmb2,np__0)
                  & B = k1_funct_1(f5_s13_circcmb2,np__0)
                  & C = k1_funct_1(f6_s13_circcmb2,np__0)
                  & p1_s13_circcmb2(A,B,C,np__0) ) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( v5_msualg_1(C,B)
                    & l3_msualg_1(C,B) )
                 => ! [D] :
                      ( ( B = k1_funct_1(f4_s13_circcmb2,A)
                        & C = k1_funct_1(f5_s13_circcmb2,A)
                        & D = k1_funct_1(f6_s13_circcmb2,A) )
                     => ( k1_funct_1(f4_s13_circcmb2,k1_nat_1(A,np__1)) = f1_s13_circcmb2(B,D,A)
                        & k1_funct_1(f5_s13_circcmb2,k1_nat_1(A,np__1)) = f2_s13_circcmb2(B,C,D,A)
                        & k1_funct_1(f6_s13_circcmb2,k1_nat_1(A,np__1)) = f3_s13_circcmb2(D,A) ) ) ) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( v5_msualg_1(C,B)
                    & l3_msualg_1(C,B) )
                 => ! [D] :
                      ( ( B = k1_funct_1(f4_s13_circcmb2,A)
                        & C = k1_funct_1(f5_s13_circcmb2,A)
                        & D = k1_funct_1(f6_s13_circcmb2,A)
                        & p1_s13_circcmb2(B,C,D,A) )
                     => p1_s13_circcmb2(f1_s13_circcmb2(B,D,A),f2_s13_circcmb2(B,C,D,A),f3_s13_circcmb2(D,A),k1_nat_1(A,np__1)) ) ) ) )
      & ! [A] :
          ( ( ~ v3_struct_0(A)
            & l1_msualg_1(A) )
         => ! [B] :
              ( ( v5_msualg_1(B,A)
                & l3_msualg_1(B,A) )
             => ! [C,D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v5_msualg_1(f2_s13_circcmb2(A,B,C,D),f1_s13_circcmb2(A,C,D))
                    & l3_msualg_1(f2_s13_circcmb2(A,B,C,D),f1_s13_circcmb2(A,C,D)) ) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ? [B] :
            ( ~ v3_struct_0(B)
            & l1_msualg_1(B)
            & ? [C] :
                ( v5_msualg_1(C,B)
                & l3_msualg_1(C,B)
                & B = k1_funct_1(f4_s13_circcmb2,A)
                & C = k1_funct_1(f5_s13_circcmb2,A)
                & p1_s13_circcmb2(B,C,k1_funct_1(f6_s13_circcmb2,A),A) ) ) ) )).

fof(s14_circcmb2,axiom,
    ( ( ? [A] :
          ( ~ v3_struct_0(A)
          & l1_msualg_1(A)
          & ? [B] :
              ( v5_msualg_1(B,A)
              & l3_msualg_1(B,A)
              & A = k1_funct_1(f4_s14_circcmb2,np__0)
              & B = k1_funct_1(f6_s14_circcmb2,np__0) ) )
      & k1_funct_1(f4_s14_circcmb2,np__0) = k1_funct_1(f5_s14_circcmb2,np__0)
      & k1_funct_1(f6_s14_circcmb2,np__0) = k1_funct_1(f7_s14_circcmb2,np__0)
      & k1_funct_1(f8_s14_circcmb2,np__0) = k1_funct_1(f9_s14_circcmb2,np__0)
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( v5_msualg_1(C,B)
                    & l3_msualg_1(C,B) )
                 => ! [D] :
                      ( ( B = k1_funct_1(f4_s14_circcmb2,A)
                        & C = k1_funct_1(f6_s14_circcmb2,A)
                        & D = k1_funct_1(f8_s14_circcmb2,A) )
                     => ( k1_funct_1(f4_s14_circcmb2,k1_nat_1(A,np__1)) = f1_s14_circcmb2(B,D,A)
                        & k1_funct_1(f6_s14_circcmb2,k1_nat_1(A,np__1)) = f2_s14_circcmb2(B,C,D,A)
                        & k1_funct_1(f8_s14_circcmb2,k1_nat_1(A,np__1)) = f3_s14_circcmb2(D,A) ) ) ) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( v5_msualg_1(C,B)
                    & l3_msualg_1(C,B) )
                 => ! [D] :
                      ( ( B = k1_funct_1(f5_s14_circcmb2,A)
                        & C = k1_funct_1(f7_s14_circcmb2,A)
                        & D = k1_funct_1(f9_s14_circcmb2,A) )
                     => ( k1_funct_1(f5_s14_circcmb2,k1_nat_1(A,np__1)) = f1_s14_circcmb2(B,D,A)
                        & k1_funct_1(f7_s14_circcmb2,k1_nat_1(A,np__1)) = f2_s14_circcmb2(B,C,D,A)
                        & k1_funct_1(f9_s14_circcmb2,k1_nat_1(A,np__1)) = f3_s14_circcmb2(D,A) ) ) ) ) )
      & ! [A] :
          ( ( ~ v3_struct_0(A)
            & l1_msualg_1(A) )
         => ! [B] :
              ( ( v5_msualg_1(B,A)
                & l3_msualg_1(B,A) )
             => ! [C,D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v5_msualg_1(f2_s14_circcmb2(A,B,C,D),f1_s14_circcmb2(A,C,D))
                    & l3_msualg_1(f2_s14_circcmb2(A,B,C,D),f1_s14_circcmb2(A,C,D)) ) ) ) ) )
   => ( r6_pboole(k5_numbers,f4_s14_circcmb2,f5_s14_circcmb2)
      & r6_pboole(k5_numbers,f6_s14_circcmb2,f7_s14_circcmb2)
      & r6_pboole(k5_numbers,f8_s14_circcmb2,f9_s14_circcmb2) ) )).

fof(s15_circcmb2,axiom,
    ( ( k1_funct_1(f6_s15_circcmb2,np__0) = f1_s15_circcmb2
      & k1_funct_1(f7_s15_circcmb2,np__0) = f2_s15_circcmb2
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( v5_msualg_1(C,B)
                    & l3_msualg_1(C,B) )
                 => ! [D] :
                      ( ( B = k1_funct_1(f6_s15_circcmb2,A)
                        & C = k1_funct_1(f7_s15_circcmb2,A)
                        & D = k1_funct_1(f8_s15_circcmb2,A) )
                     => ( k1_funct_1(f6_s15_circcmb2,k1_nat_1(A,np__1)) = f3_s15_circcmb2(B,D,A)
                        & k1_funct_1(f7_s15_circcmb2,k1_nat_1(A,np__1)) = f4_s15_circcmb2(B,C,D,A)
                        & k1_funct_1(f8_s15_circcmb2,k1_nat_1(A,np__1)) = f5_s15_circcmb2(D,A) ) ) ) ) )
      & ! [A] :
          ( ( ~ v3_struct_0(A)
            & l1_msualg_1(A) )
         => ! [B] :
              ( ( v5_msualg_1(B,A)
                & l3_msualg_1(B,A) )
             => ! [C,D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v5_msualg_1(f4_s15_circcmb2(A,B,C,D),f3_s15_circcmb2(A,C,D))
                    & l3_msualg_1(f4_s15_circcmb2(A,B,C,D),f3_s15_circcmb2(A,C,D)) ) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & l1_msualg_1(B) )
           => ! [C] :
                ( ( B = k1_funct_1(f6_s15_circcmb2,A)
                  & C = k1_funct_1(f8_s15_circcmb2,A) )
               => ( k1_funct_1(f6_s15_circcmb2,k1_nat_1(A,np__1)) = f3_s15_circcmb2(B,C,A)
                  & k1_funct_1(f8_s15_circcmb2,k1_nat_1(A,np__1)) = f5_s15_circcmb2(C,A) ) ) ) ) )).

fof(s16_circcmb2,axiom,
    ( ! [A] :
        ( ( ~ v3_struct_0(A)
          & l1_msualg_1(A) )
       => ! [B] :
            ( ( v5_msualg_1(B,A)
              & l3_msualg_1(B,A) )
           => ! [C,D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ( v5_msualg_1(f5_s16_circcmb2(A,B,C,D),f4_s16_circcmb2(A,C,D))
                  & l3_msualg_1(f5_s16_circcmb2(A,B,C,D),f4_s16_circcmb2(A,C,D)) ) ) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & ? [B] :
            ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A)
            & ? [C] :
                ( m1_pboole(C,k5_numbers)
                & ? [D] :
                    ( m1_pboole(D,k5_numbers)
                    & ? [E] :
                        ( m1_pboole(E,k5_numbers)
                        & A = k1_funct_1(C,f7_s16_circcmb2)
                        & B = k1_funct_1(D,f7_s16_circcmb2)
                        & k1_funct_1(C,np__0) = f1_s16_circcmb2
                        & k1_funct_1(D,np__0) = f2_s16_circcmb2
                        & k1_funct_1(E,np__0) = f3_s16_circcmb2
                        & ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ! [G] :
                                ( ( ~ v3_struct_0(G)
                                  & l1_msualg_1(G) )
                               => ! [H] :
                                    ( ( v5_msualg_1(H,G)
                                      & l3_msualg_1(H,G) )
                                   => ! [I] :
                                        ( ( G = k1_funct_1(C,F)
                                          & H = k1_funct_1(D,F)
                                          & I = k1_funct_1(E,F) )
                                       => ( k1_funct_1(C,k1_nat_1(F,np__1)) = f4_s16_circcmb2(G,I,F)
                                          & k1_funct_1(D,k1_nat_1(F,np__1)) = f5_s16_circcmb2(G,H,I,F)
                                          & k1_funct_1(E,k1_nat_1(F,np__1)) = f6_s16_circcmb2(I,F) ) ) ) ) ) ) ) ) ) ) )).

fof(s17_circcmb2,axiom,
    ( ( ? [A] :
          ( m1_pboole(A,k5_numbers)
          & ? [B] :
              ( m1_pboole(B,k5_numbers)
              & f2_s17_circcmb2 = k1_funct_1(A,f8_s17_circcmb2)
              & k1_funct_1(A,np__0) = f1_s17_circcmb2
              & k1_funct_1(B,np__0) = f4_s17_circcmb2
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & l1_msualg_1(D) )
                     => ! [E] :
                          ( ( D = k1_funct_1(A,C)
                            & E = k1_funct_1(B,C) )
                         => ( k1_funct_1(A,k1_nat_1(C,np__1)) = f5_s17_circcmb2(D,E,C)
                            & k1_funct_1(B,k1_nat_1(C,np__1)) = f7_s17_circcmb2(E,C) ) ) ) ) ) )
      & ! [A] :
          ( ( ~ v3_struct_0(A)
            & l1_msualg_1(A) )
         => ! [B] :
              ( ( v5_msualg_1(B,A)
                & l3_msualg_1(B,A) )
             => ! [C,D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v5_msualg_1(f6_s17_circcmb2(A,B,C,D),f5_s17_circcmb2(A,C,D))
                    & l3_msualg_1(f6_s17_circcmb2(A,B,C,D),f5_s17_circcmb2(A,C,D)) ) ) ) ) )
   => ? [A] :
        ( v5_msualg_1(A,f2_s17_circcmb2)
        & l3_msualg_1(A,f2_s17_circcmb2)
        & ? [B] :
            ( m1_pboole(B,k5_numbers)
            & ? [C] :
                ( m1_pboole(C,k5_numbers)
                & ? [D] :
                    ( m1_pboole(D,k5_numbers)
                    & f2_s17_circcmb2 = k1_funct_1(B,f8_s17_circcmb2)
                    & A = k1_funct_1(C,f8_s17_circcmb2)
                    & k1_funct_1(B,np__0) = f1_s17_circcmb2
                    & k1_funct_1(C,np__0) = f3_s17_circcmb2
                    & k1_funct_1(D,np__0) = f4_s17_circcmb2
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ! [F] :
                            ( ( ~ v3_struct_0(F)
                              & l1_msualg_1(F) )
                           => ! [G] :
                                ( ( v5_msualg_1(G,F)
                                  & l3_msualg_1(G,F) )
                               => ! [H] :
                                    ( ( F = k1_funct_1(B,E)
                                      & G = k1_funct_1(C,E)
                                      & H = k1_funct_1(D,E) )
                                   => ( k1_funct_1(B,k1_nat_1(E,np__1)) = f5_s17_circcmb2(F,H,E)
                                      & k1_funct_1(C,k1_nat_1(E,np__1)) = f6_s17_circcmb2(F,G,H,E)
                                      & k1_funct_1(D,k1_nat_1(E,np__1)) = f7_s17_circcmb2(H,E) ) ) ) ) ) ) ) ) ) )).

fof(s18_circcmb2,axiom,
    ( ! [A] :
        ( ( ~ v3_struct_0(A)
          & l1_msualg_1(A) )
       => ! [B] :
            ( ( v5_msualg_1(B,A)
              & l3_msualg_1(B,A) )
           => ! [C,D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ( v5_msualg_1(f6_s18_circcmb2(A,B,C,D),f5_s18_circcmb2(A,C,D))
                  & l3_msualg_1(f6_s18_circcmb2(A,B,C,D),f5_s18_circcmb2(A,C,D)) ) ) ) )
   => ! [A] :
        ( ( v5_msualg_1(A,f2_s18_circcmb2)
          & l3_msualg_1(A,f2_s18_circcmb2) )
       => ! [B] :
            ( ( v5_msualg_1(B,f2_s18_circcmb2)
              & l3_msualg_1(B,f2_s18_circcmb2) )
           => ~ ( ? [C] :
                    ( m1_pboole(C,k5_numbers)
                    & ? [D] :
                        ( m1_pboole(D,k5_numbers)
                        & ? [E] :
                            ( m1_pboole(E,k5_numbers)
                            & f2_s18_circcmb2 = k1_funct_1(C,f8_s18_circcmb2)
                            & A = k1_funct_1(D,f8_s18_circcmb2)
                            & k1_funct_1(C,np__0) = f1_s18_circcmb2
                            & k1_funct_1(D,np__0) = f3_s18_circcmb2
                            & k1_funct_1(E,np__0) = f4_s18_circcmb2
                            & ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ! [G] :
                                    ( ( ~ v3_struct_0(G)
                                      & l1_msualg_1(G) )
                                   => ! [H] :
                                        ( ( v5_msualg_1(H,G)
                                          & l3_msualg_1(H,G) )
                                       => ! [I] :
                                            ( ( G = k1_funct_1(C,F)
                                              & H = k1_funct_1(D,F)
                                              & I = k1_funct_1(E,F) )
                                           => ( k1_funct_1(C,k1_nat_1(F,np__1)) = f5_s18_circcmb2(G,I,F)
                                              & k1_funct_1(D,k1_nat_1(F,np__1)) = f6_s18_circcmb2(G,H,I,F)
                                              & k1_funct_1(E,k1_nat_1(F,np__1)) = f7_s18_circcmb2(I,F) ) ) ) ) ) ) ) )
                & ? [C] :
                    ( m1_pboole(C,k5_numbers)
                    & ? [D] :
                        ( m1_pboole(D,k5_numbers)
                        & ? [E] :
                            ( m1_pboole(E,k5_numbers)
                            & f2_s18_circcmb2 = k1_funct_1(C,f8_s18_circcmb2)
                            & B = k1_funct_1(D,f8_s18_circcmb2)
                            & k1_funct_1(C,np__0) = f1_s18_circcmb2
                            & k1_funct_1(D,np__0) = f3_s18_circcmb2
                            & k1_funct_1(E,np__0) = f4_s18_circcmb2
                            & ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ! [G] :
                                    ( ( ~ v3_struct_0(G)
                                      & l1_msualg_1(G) )
                                   => ! [H] :
                                        ( ( v5_msualg_1(H,G)
                                          & l3_msualg_1(H,G) )
                                       => ! [I] :
                                            ( ( G = k1_funct_1(C,F)
                                              & H = k1_funct_1(D,F)
                                              & I = k1_funct_1(E,F) )
                                           => ( k1_funct_1(C,k1_nat_1(F,np__1)) = f5_s18_circcmb2(G,I,F)
                                              & k1_funct_1(D,k1_nat_1(F,np__1)) = f6_s18_circcmb2(G,H,I,F)
                                              & k1_funct_1(E,k1_nat_1(F,np__1)) = f7_s18_circcmb2(I,F) ) ) ) ) ) ) ) )
                & A != B ) ) ) )).

fof(s19_circcmb2,axiom,
    ( ( ! [A] :
          ( ( ~ v3_struct_0(A)
            & v1_msualg_1(A)
            & ~ v2_msualg_1(A)
            & v1_circcomb(A)
            & v2_circcomb(A)
            & v3_circcomb(A)
            & l1_msualg_1(A) )
         => ! [B,C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( v1_circcomb(f4_s19_circcmb2(A,B,C))
                & v2_circcomb(f4_s19_circcmb2(A,B,C))
                & v3_circcomb(f4_s19_circcmb2(A,B,C))
                & ~ v2_msualg_1(f4_s19_circcmb2(A,B,C))
                & v1_msualg_1(f4_s19_circcmb2(A,B,C)) ) ) )
      & ? [A] :
          ( m1_pboole(A,k5_numbers)
          & ? [B] :
              ( m1_pboole(B,k5_numbers)
              & f2_s19_circcmb2 = k1_funct_1(A,f8_s19_circcmb2)
              & k1_funct_1(A,np__0) = f1_s19_circcmb2
              & k1_funct_1(B,np__0) = f6_s19_circcmb2
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & l1_msualg_1(D) )
                     => ! [E] :
                          ( ( D = k1_funct_1(A,C)
                            & E = k1_funct_1(B,C) )
                         => ( k1_funct_1(A,k1_nat_1(C,np__1)) = f4_s19_circcmb2(D,E,C)
                            & k1_funct_1(B,k1_nat_1(C,np__1)) = f7_s19_circcmb2(E,C) ) ) ) ) ) )
      & ! [A] :
          ( ( ~ v3_struct_0(A)
            & l1_msualg_1(A) )
         => ! [B] :
              ( ( v5_msualg_1(B,A)
                & l3_msualg_1(B,A) )
             => ! [C,D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v5_msualg_1(f5_s19_circcmb2(A,B,C,D),f4_s19_circcmb2(A,C,D))
                    & l3_msualg_1(f5_s19_circcmb2(A,B,C,D),f4_s19_circcmb2(A,C,D)) ) ) ) )
      & ! [A] :
          ( ( ~ v3_struct_0(A)
            & v1_msualg_1(A)
            & ~ v2_msualg_1(A)
            & v1_circcomb(A)
            & v2_circcomb(A)
            & v3_circcomb(A)
            & l1_msualg_1(A) )
         => ! [B] :
              ( ( ~ v3_struct_0(B)
                & v1_msualg_1(B)
                & ~ v2_msualg_1(B)
                & v1_circcomb(B)
                & v2_circcomb(B)
                & v3_circcomb(B)
                & l1_msualg_1(B) )
             => ! [C] :
                  ( ( v4_msualg_1(C,A)
                    & v4_msafree2(C,A)
                    & v4_circcomb(C,A)
                    & v6_circcomb(C,A)
                    & l3_msualg_1(C,A) )
                 => ! [D,E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( B = f4_s19_circcmb2(A,D,E)
                       => ( v4_msualg_1(f5_s19_circcmb2(A,C,D,E),B)
                          & v4_msafree2(f5_s19_circcmb2(A,C,D,E),B)
                          & v4_circcomb(f5_s19_circcmb2(A,C,D,E),B)
                          & v6_circcomb(f5_s19_circcmb2(A,C,D,E),B)
                          & l3_msualg_1(f5_s19_circcmb2(A,C,D,E),B) ) ) ) ) ) ) )
   => ? [A] :
        ( v4_msualg_1(A,f2_s19_circcmb2)
        & v4_msafree2(A,f2_s19_circcmb2)
        & v4_circcomb(A,f2_s19_circcmb2)
        & v6_circcomb(A,f2_s19_circcmb2)
        & l3_msualg_1(A,f2_s19_circcmb2)
        & ? [B] :
            ( m1_pboole(B,k5_numbers)
            & ? [C] :
                ( m1_pboole(C,k5_numbers)
                & ? [D] :
                    ( m1_pboole(D,k5_numbers)
                    & f2_s19_circcmb2 = k1_funct_1(B,f8_s19_circcmb2)
                    & A = k1_funct_1(C,f8_s19_circcmb2)
                    & k1_funct_1(B,np__0) = f1_s19_circcmb2
                    & k1_funct_1(C,np__0) = f3_s19_circcmb2
                    & k1_funct_1(D,np__0) = f6_s19_circcmb2
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ! [F] :
                            ( ( ~ v3_struct_0(F)
                              & l1_msualg_1(F) )
                           => ! [G] :
                                ( ( v5_msualg_1(G,F)
                                  & l3_msualg_1(G,F) )
                               => ! [H] :
                                    ( ( F = k1_funct_1(B,E)
                                      & G = k1_funct_1(C,E)
                                      & H = k1_funct_1(D,E) )
                                   => ( k1_funct_1(B,k1_nat_1(E,np__1)) = f4_s19_circcmb2(F,H,E)
                                      & k1_funct_1(C,k1_nat_1(E,np__1)) = f5_s19_circcmb2(F,G,H,E)
                                      & k1_funct_1(D,k1_nat_1(E,np__1)) = f7_s19_circcmb2(H,E) ) ) ) ) ) ) ) ) ) )).

fof(s20_circcmb2,axiom,
    ( ( ? [A] :
          ( m1_pboole(A,k5_numbers)
          & ? [B] :
              ( m1_pboole(B,k5_numbers)
              & f2_s20_circcmb2 = k1_funct_1(A,f8_s20_circcmb2)
              & k1_funct_1(A,np__0) = f1_s20_circcmb2
              & k1_funct_1(B,np__0) = f6_s20_circcmb2
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & l1_msualg_1(D) )
                     => ! [E] :
                          ( ( D = k1_funct_1(A,C)
                            & E = k1_funct_1(B,C) )
                         => ( k1_funct_1(A,k1_nat_1(C,np__1)) = k3_circcomb(D,f4_s20_circcmb2(E,C))
                            & k1_funct_1(B,k1_nat_1(C,np__1)) = f7_s20_circcmb2(E,C) ) ) ) ) ) )
      & ! [A,B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( v4_msualg_1(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B))
            & v4_msafree2(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B))
            & v4_circcomb(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B))
            & v6_circcomb(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B))
            & l3_msualg_1(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B)) ) ) )
   => ? [A] :
        ( v4_msualg_1(A,f2_s20_circcmb2)
        & v4_msafree2(A,f2_s20_circcmb2)
        & v4_circcomb(A,f2_s20_circcmb2)
        & v6_circcomb(A,f2_s20_circcmb2)
        & l3_msualg_1(A,f2_s20_circcmb2)
        & ? [B] :
            ( m1_pboole(B,k5_numbers)
            & ? [C] :
                ( m1_pboole(C,k5_numbers)
                & ? [D] :
                    ( m1_pboole(D,k5_numbers)
                    & f2_s20_circcmb2 = k1_funct_1(B,f8_s20_circcmb2)
                    & A = k1_funct_1(C,f8_s20_circcmb2)
                    & k1_funct_1(B,np__0) = f1_s20_circcmb2
                    & k1_funct_1(C,np__0) = f3_s20_circcmb2
                    & k1_funct_1(D,np__0) = f6_s20_circcmb2
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ! [F] :
                            ( ( ~ v3_struct_0(F)
                              & l1_msualg_1(F) )
                           => ! [G] :
                                ( ( v5_msualg_1(G,F)
                                  & l3_msualg_1(G,F) )
                               => ! [H,I] :
                                    ( ( v5_msualg_1(I,f4_s20_circcmb2(H,E))
                                      & l3_msualg_1(I,f4_s20_circcmb2(H,E)) )
                                   => ( ( F = k1_funct_1(B,E)
                                        & G = k1_funct_1(C,E)
                                        & H = k1_funct_1(D,E)
                                        & I = f5_s20_circcmb2(H,E) )
                                     => ( k1_funct_1(B,k1_nat_1(E,np__1)) = k3_circcomb(F,f4_s20_circcmb2(H,E))
                                        & k1_funct_1(C,k1_nat_1(E,np__1)) = k4_circcomb(F,f4_s20_circcmb2(H,E),G,I)
                                        & k1_funct_1(D,k1_nat_1(E,np__1)) = f7_s20_circcmb2(H,E) ) ) ) ) ) ) ) ) ) ) )).

fof(s21_circcmb2,axiom,
    ( ! [A] :
        ( ( ~ v3_struct_0(A)
          & l1_msualg_1(A) )
       => ! [B] :
            ( ( v5_msualg_1(B,A)
              & l3_msualg_1(B,A) )
           => ! [C,D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ( v5_msualg_1(f6_s21_circcmb2(A,B,C,D),f5_s21_circcmb2(A,C,D))
                  & l3_msualg_1(f6_s21_circcmb2(A,B,C,D),f5_s21_circcmb2(A,C,D)) ) ) ) )
   => ! [A] :
        ( ( v4_msualg_1(A,f2_s21_circcmb2)
          & v4_msafree2(A,f2_s21_circcmb2)
          & v4_circcomb(A,f2_s21_circcmb2)
          & v6_circcomb(A,f2_s21_circcmb2)
          & l3_msualg_1(A,f2_s21_circcmb2) )
       => ! [B] :
            ( ( v4_msualg_1(B,f2_s21_circcmb2)
              & v4_msafree2(B,f2_s21_circcmb2)
              & v4_circcomb(B,f2_s21_circcmb2)
              & v6_circcomb(B,f2_s21_circcmb2)
              & l3_msualg_1(B,f2_s21_circcmb2) )
           => ~ ( ? [C] :
                    ( m1_pboole(C,k5_numbers)
                    & ? [D] :
                        ( m1_pboole(D,k5_numbers)
                        & ? [E] :
                            ( m1_pboole(E,k5_numbers)
                            & f2_s21_circcmb2 = k1_funct_1(C,f8_s21_circcmb2)
                            & A = k1_funct_1(D,f8_s21_circcmb2)
                            & k1_funct_1(C,np__0) = f1_s21_circcmb2
                            & k1_funct_1(D,np__0) = f3_s21_circcmb2
                            & k1_funct_1(E,np__0) = f4_s21_circcmb2
                            & ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ! [G] :
                                    ( ( ~ v3_struct_0(G)
                                      & l1_msualg_1(G) )
                                   => ! [H] :
                                        ( ( v5_msualg_1(H,G)
                                          & l3_msualg_1(H,G) )
                                       => ! [I] :
                                            ( ( G = k1_funct_1(C,F)
                                              & H = k1_funct_1(D,F)
                                              & I = k1_funct_1(E,F) )
                                           => ( k1_funct_1(C,k1_nat_1(F,np__1)) = f5_s21_circcmb2(G,I,F)
                                              & k1_funct_1(D,k1_nat_1(F,np__1)) = f6_s21_circcmb2(G,H,I,F)
                                              & k1_funct_1(E,k1_nat_1(F,np__1)) = f7_s21_circcmb2(I,F) ) ) ) ) ) ) ) )
                & ? [C] :
                    ( m1_pboole(C,k5_numbers)
                    & ? [D] :
                        ( m1_pboole(D,k5_numbers)
                        & ? [E] :
                            ( m1_pboole(E,k5_numbers)
                            & f2_s21_circcmb2 = k1_funct_1(C,f8_s21_circcmb2)
                            & B = k1_funct_1(D,f8_s21_circcmb2)
                            & k1_funct_1(C,np__0) = f1_s21_circcmb2
                            & k1_funct_1(D,np__0) = f3_s21_circcmb2
                            & k1_funct_1(E,np__0) = f4_s21_circcmb2
                            & ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ! [G] :
                                    ( ( ~ v3_struct_0(G)
                                      & l1_msualg_1(G) )
                                   => ! [H] :
                                        ( ( v5_msualg_1(H,G)
                                          & l3_msualg_1(H,G) )
                                       => ! [I] :
                                            ( ( G = k1_funct_1(C,F)
                                              & H = k1_funct_1(D,F)
                                              & I = k1_funct_1(E,F) )
                                           => ( k1_funct_1(C,k1_nat_1(F,np__1)) = f5_s21_circcmb2(G,I,F)
                                              & k1_funct_1(D,k1_nat_1(F,np__1)) = f6_s21_circcmb2(G,H,I,F)
                                              & k1_funct_1(E,k1_nat_1(F,np__1)) = f7_s21_circcmb2(I,F) ) ) ) ) ) ) ) )
                & A != B ) ) ) )).

fof(s22_circcmb2,axiom,
    ( ( ! [A,B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( v4_msualg_1(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B))
            & v4_msafree2(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B))
            & v4_circcomb(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B))
            & v6_circcomb(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B))
            & l3_msualg_1(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B)) ) )
      & ! [A] :
          ( m1_subset_1(A,k4_card_3(u4_msualg_1(f1_s22_circcmb2,f3_s22_circcmb2)))
         => v1_circuit2(k9_facirc_1(f1_s22_circcmb2,f3_s22_circcmb2,A,f10_s22_circcmb2(np__0)),f1_s22_circcmb2,f3_s22_circcmb2) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B,C] :
              ( ( v5_msualg_1(C,f5_s22_circcmb2(B,A))
                & v4_msafree2(C,f5_s22_circcmb2(B,A))
                & l3_msualg_1(C,f5_s22_circcmb2(B,A)) )
             => ( ( B = k1_funct_1(f7_s22_circcmb2,A)
                  & C = f6_s22_circcmb2(B,A) )
               => ! [D] :
                    ( m1_subset_1(D,k4_card_3(u4_msualg_1(f5_s22_circcmb2(B,A),C)))
                   => v1_circuit2(k9_facirc_1(f5_s22_circcmb2(B,A),C,D,f10_s22_circcmb2(np__1)),f5_s22_circcmb2(B,A),C) ) ) ) )
      & ? [A] :
          ( m1_pboole(A,k5_numbers)
          & ? [B] :
              ( m1_pboole(B,k5_numbers)
              & f2_s22_circcmb2 = k1_funct_1(A,f10_s22_circcmb2(np__2))
              & f4_s22_circcmb2 = k1_funct_1(B,f10_s22_circcmb2(np__2))
              & k1_funct_1(A,np__0) = f1_s22_circcmb2
              & k1_funct_1(B,np__0) = f3_s22_circcmb2
              & k1_funct_1(f7_s22_circcmb2,np__0) = f8_s22_circcmb2
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & l1_msualg_1(D) )
                     => ! [E] :
                          ( ( v5_msualg_1(E,D)
                            & l3_msualg_1(E,D) )
                         => ! [F,G] :
                              ( ( v5_msualg_1(G,f5_s22_circcmb2(F,C))
                                & l3_msualg_1(G,f5_s22_circcmb2(F,C)) )
                             => ( ( D = k1_funct_1(A,C)
                                  & E = k1_funct_1(B,C)
                                  & F = k1_funct_1(f7_s22_circcmb2,C)
                                  & G = f6_s22_circcmb2(F,C) )
                               => ( k1_funct_1(A,k1_nat_1(C,np__1)) = k3_circcomb(D,f5_s22_circcmb2(F,C))
                                  & k1_funct_1(B,k1_nat_1(C,np__1)) = k4_circcomb(D,f5_s22_circcmb2(F,C),E,G)
                                  & k1_funct_1(f7_s22_circcmb2,k1_nat_1(C,np__1)) = f9_s22_circcmb2(F,C) ) ) ) ) ) ) ) )
      & v1_relat_1(k4_msafree2(f1_s22_circcmb2))
      & ~ v2_facirc_1(k2_msafree2(f1_s22_circcmb2))
      & k1_funct_1(f7_s22_circcmb2,np__0) = f8_s22_circcmb2
      & r2_hidden(f8_s22_circcmb2,k4_msafree2(f1_s22_circcmb2))
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] : v1_relat_1(k4_msafree2(f5_s22_circcmb2(B,A))) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ~ ( B = k1_funct_1(f7_s22_circcmb2,A)
                & v2_facirc_1(k4_xboole_0(k2_msafree2(f5_s22_circcmb2(B,A)),k1_tarski(B))) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( B = k1_funct_1(f7_s22_circcmb2,A)
             => ( k1_funct_1(f7_s22_circcmb2,k1_nat_1(A,np__1)) = f9_s22_circcmb2(B,A)
                & r2_hidden(B,k2_msafree2(f5_s22_circcmb2(B,A)))
                & r2_hidden(f9_s22_circcmb2(B,A),k4_msafree2(f5_s22_circcmb2(B,A))) ) ) ) )
   => ! [A] :
        ( m1_subset_1(A,k4_card_3(u4_msualg_1(f2_s22_circcmb2,f4_s22_circcmb2)))
       => v1_circuit2(k9_facirc_1(f2_s22_circcmb2,f4_s22_circcmb2,A,k1_nat_1(f10_s22_circcmb2(np__0),k2_nat_1(f10_s22_circcmb2(np__2),f10_s22_circcmb2(np__1)))),f2_s22_circcmb2,f4_s22_circcmb2) ) )).

fof(dt_k1_circcmb2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ( v5_msualg_1(k1_circcmb2(A,B),A)
        & l3_msualg_1(k1_circcmb2(A,B),A) ) ) )).
%------------------------------------------------------------------------------