SET007 Axioms: SET007+600.ax


%------------------------------------------------------------------------------
% File     : SET007+600 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Basic Properties of Genetic Algorithm
% 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    : genealg1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   85 (   0 unit)
%            Number of atoms       : 1212 ( 198 equality)
%            Maximal formula depth :   37 (  16 average)
%            Number of connectives : 1213 (  86 ~  ;   0  |; 637  &)
%                                         (   1 <=>; 489 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   13 (   0 propositional; 1-3 arity)
%            Number of functors    :   23 (   3 constant; 0-9 arity)
%            Number of variables   :  524 (   0 singleton; 523 !;   1 ?)
%            Maximal term depth    :    4 (   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_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ~ v1_xboole_0(k3_card_3(A)) ) )).

fof(t1_genealg1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(D,k3_finseq_1(B))
                   => k1_rfinseq(A,k8_finseq_1(A,B,C),D) = k8_finseq_1(A,k1_rfinseq(A,B,D),C) ) ) ) ) ) )).

fof(t2_genealg1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k16_finseq_1(A,k8_finseq_1(A,B,C),k1_nat_1(k3_finseq_1(B),D)) = k8_finseq_1(A,B,k16_finseq_1(A,C,D)) ) ) ) ) )).

fof(d1_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,k3_card_3(A))
         => ( m1_genealg1(B,A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => r2_hidden(k1_funct_1(B,C),k1_funct_1(A,C)) ) ) ) ) ) ) )).

fof(d2_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,k3_card_3(A))
         => ! [C] :
              ( m2_finseq_1(C,k3_card_3(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k1_genealg1(A,B,C,D) = k8_finseq_1(k3_card_3(A),k16_finseq_1(k3_card_3(A),B,D),k1_rfinseq(k3_card_3(A),C,D)) ) ) ) ) )).

fof(d3_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,k3_card_3(A))
         => ! [C] :
              ( m2_finseq_1(C,k3_card_3(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => k2_genealg1(A,B,C,D,E) = k1_genealg1(A,k1_genealg1(A,B,C,D),k1_genealg1(A,C,B,D),E) ) ) ) ) ) )).

fof(d4_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,k3_card_3(A))
         => ! [C] :
              ( m2_finseq_1(C,k3_card_3(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => k3_genealg1(A,B,C,D,E,F) = k1_genealg1(A,k2_genealg1(A,B,C,D,E),k2_genealg1(A,C,B,D,E),F) ) ) ) ) ) ) )).

fof(d5_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,k3_card_3(A))
         => ! [C] :
              ( m2_finseq_1(C,k3_card_3(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( m2_subset_1(G,k1_numbers,k5_numbers)
                             => k4_genealg1(A,B,C,D,E,F,G) = k1_genealg1(A,k3_genealg1(A,B,C,D,E,F),k3_genealg1(A,C,B,D,E,F),G) ) ) ) ) ) ) ) )).

fof(d6_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,k3_card_3(A))
         => ! [C] :
              ( m2_finseq_1(C,k3_card_3(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( m2_subset_1(G,k1_numbers,k5_numbers)
                             => ! [H] :
                                  ( m2_subset_1(H,k1_numbers,k5_numbers)
                                 => k5_genealg1(A,B,C,D,E,F,G,H) = k1_genealg1(A,k4_genealg1(A,B,C,D,E,F,G),k4_genealg1(A,C,B,D,E,F,G),H) ) ) ) ) ) ) ) ) )).

fof(d7_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,k3_card_3(A))
         => ! [C] :
              ( m2_finseq_1(C,k3_card_3(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( m2_subset_1(G,k1_numbers,k5_numbers)
                             => ! [H] :
                                  ( m2_subset_1(H,k1_numbers,k5_numbers)
                                 => ! [I] :
                                      ( m2_subset_1(I,k1_numbers,k5_numbers)
                                     => k6_genealg1(A,B,C,D,E,F,G,H,I) = k1_genealg1(A,k5_genealg1(A,B,C,D,E,F,G,H),k5_genealg1(A,C,B,D,E,F,G,H),I) ) ) ) ) ) ) ) ) ) )).

fof(t3_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m1_genealg1(C,B)
             => ! [D] :
                  ( m1_genealg1(D,B)
                 => m1_genealg1(k1_genealg1(B,C,D,A),B) ) ) ) ) )).

fof(t4_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_genealg1(B,A)
         => ! [C] :
              ( m1_genealg1(C,A)
             => k7_genealg1(A,B,C,np__0) = C ) ) ) )).

fof(t5_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m1_genealg1(C,B)
             => ! [D] :
                  ( m1_genealg1(D,B)
                 => ( r1_xreal_0(k3_finseq_1(C),A)
                   => k7_genealg1(B,C,D,A) = C ) ) ) ) ) )).

fof(t6_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_relat_1(C)
                & v2_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( m1_genealg1(D,C)
                 => ! [E] :
                      ( m1_genealg1(E,C)
                     => m1_genealg1(k2_genealg1(C,D,E,A,B),C) ) ) ) ) ) )).

fof(t7_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m1_genealg1(C,B)
             => ! [D] :
                  ( m1_genealg1(D,B)
                 => k8_genealg1(B,C,D,np__0,A) = k7_genealg1(B,D,C,A) ) ) ) ) )).

fof(t8_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m1_genealg1(C,B)
             => ! [D] :
                  ( m1_genealg1(D,B)
                 => k8_genealg1(B,C,D,A,np__0) = k7_genealg1(B,D,C,A) ) ) ) ) )).

fof(t9_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_relat_1(C)
                & v2_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( m1_genealg1(D,C)
                 => ! [E] :
                      ( m1_genealg1(E,C)
                     => ( r1_xreal_0(k3_finseq_1(D),A)
                       => k8_genealg1(C,D,E,A,B) = k7_genealg1(C,D,E,B) ) ) ) ) ) ) )).

fof(t10_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_relat_1(C)
                & v2_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( m1_genealg1(D,C)
                 => ! [E] :
                      ( m1_genealg1(E,C)
                     => ( r1_xreal_0(k3_finseq_1(D),A)
                       => k8_genealg1(C,D,E,B,A) = k7_genealg1(C,D,E,B) ) ) ) ) ) ) )).

fof(t11_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_relat_1(C)
                & v2_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( m1_genealg1(D,C)
                 => ! [E] :
                      ( m1_genealg1(E,C)
                     => ( ( r1_xreal_0(k3_finseq_1(D),A)
                          & r1_xreal_0(k3_finseq_1(D),B) )
                       => k8_genealg1(C,D,E,A,B) = D ) ) ) ) ) ) )).

fof(t12_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m1_genealg1(C,B)
             => ! [D] :
                  ( m1_genealg1(D,B)
                 => k8_genealg1(B,C,D,A,A) = C ) ) ) ) )).

fof(t13_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_relat_1(C)
                & v2_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( m1_genealg1(D,C)
                 => ! [E] :
                      ( m1_genealg1(E,C)
                     => k8_genealg1(C,D,E,A,B) = k8_genealg1(C,D,E,B,A) ) ) ) ) ) )).

fof(t14_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => m1_genealg1(k3_genealg1(D,E,F,A,B,C),D) ) ) ) ) ) ) )).

fof(t15_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( k9_genealg1(D,E,F,np__0,A,B) = k8_genealg1(D,F,E,A,B)
                            & k9_genealg1(D,E,F,C,np__0,B) = k8_genealg1(D,F,E,C,B)
                            & k9_genealg1(D,E,F,C,A,np__0) = k8_genealg1(D,F,E,C,A) ) ) ) ) ) ) ) )).

fof(t16_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( k9_genealg1(D,E,F,np__0,np__0,A) = k7_genealg1(D,E,F,A)
                            & k9_genealg1(D,E,F,B,np__0,np__0) = k7_genealg1(D,E,F,B)
                            & k9_genealg1(D,E,F,np__0,C,np__0) = k7_genealg1(D,E,F,C) ) ) ) ) ) ) ) )).

fof(t17_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_genealg1(B,A)
         => ! [C] :
              ( m1_genealg1(C,A)
             => k9_genealg1(A,B,C,np__0,np__0,np__0) = C ) ) ) )).

fof(t18_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( r1_xreal_0(k3_finseq_1(E),A)
                           => k9_genealg1(D,E,F,A,B,C) = k8_genealg1(D,E,F,B,C) ) ) ) ) ) ) ) )).

fof(t19_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( r1_xreal_0(k3_finseq_1(E),A)
                           => k9_genealg1(D,E,F,B,A,C) = k8_genealg1(D,E,F,B,C) ) ) ) ) ) ) ) )).

fof(t20_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( r1_xreal_0(k3_finseq_1(E),A)
                           => k9_genealg1(D,E,F,B,C,A) = k8_genealg1(D,E,F,B,C) ) ) ) ) ) ) ) )).

fof(t21_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( ( r1_xreal_0(k3_finseq_1(E),A)
                              & r1_xreal_0(k3_finseq_1(E),B) )
                           => k9_genealg1(D,E,F,A,B,C) = k7_genealg1(D,E,F,C) ) ) ) ) ) ) ) )).

fof(t22_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( ( r1_xreal_0(k3_finseq_1(E),A)
                              & r1_xreal_0(k3_finseq_1(E),B) )
                           => k9_genealg1(D,E,F,A,C,B) = k7_genealg1(D,E,F,C) ) ) ) ) ) ) ) )).

fof(t23_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( ( r1_xreal_0(k3_finseq_1(E),A)
                              & r1_xreal_0(k3_finseq_1(E),B) )
                           => k9_genealg1(D,E,F,C,A,B) = k7_genealg1(D,E,F,C) ) ) ) ) ) ) ) )).

fof(t24_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( ( r1_xreal_0(k3_finseq_1(E),A)
                              & r1_xreal_0(k3_finseq_1(E),B)
                              & r1_xreal_0(k3_finseq_1(E),C) )
                           => k9_genealg1(D,E,F,A,B,C) = E ) ) ) ) ) ) ) )).

fof(t25_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( k9_genealg1(D,E,F,A,B,C) = k9_genealg1(D,E,F,B,A,C)
                            & k9_genealg1(D,E,F,A,B,C) = k9_genealg1(D,E,F,A,C,B) ) ) ) ) ) ) ) )).

fof(t26_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => k9_genealg1(D,E,F,A,B,C) = k9_genealg1(D,E,F,C,A,B) ) ) ) ) ) ) )).

fof(t27_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( k9_genealg1(D,E,F,A,A,B) = k7_genealg1(D,E,F,B)
                            & k9_genealg1(D,E,F,A,C,A) = k7_genealg1(D,E,F,C)
                            & k9_genealg1(D,E,F,A,C,C) = k7_genealg1(D,E,F,A) ) ) ) ) ) ) ) )).

fof(t28_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => m1_genealg1(k4_genealg1(E,F,G,A,B,C,D),E) ) ) ) ) ) ) ) )).

fof(t29_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => ( k10_genealg1(E,F,G,np__0,A,B,C) = k9_genealg1(E,G,F,A,B,C)
                                & k10_genealg1(E,F,G,D,np__0,B,C) = k9_genealg1(E,G,F,D,B,C)
                                & k10_genealg1(E,F,G,D,A,np__0,C) = k9_genealg1(E,G,F,D,A,C)
                                & k10_genealg1(E,F,G,D,A,B,np__0) = k9_genealg1(E,G,F,D,A,B) ) ) ) ) ) ) ) ) )).

fof(t30_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => ( k10_genealg1(E,F,G,np__0,np__0,A,B) = k8_genealg1(E,F,G,A,B)
                                & k10_genealg1(E,F,G,np__0,C,np__0,B) = k8_genealg1(E,F,G,C,B)
                                & k10_genealg1(E,F,G,np__0,C,A,np__0) = k8_genealg1(E,F,G,C,A)
                                & k10_genealg1(E,F,G,D,np__0,A,np__0) = k8_genealg1(E,F,G,D,A)
                                & k10_genealg1(E,F,G,D,np__0,np__0,B) = k8_genealg1(E,F,G,D,B)
                                & k10_genealg1(E,F,G,D,C,np__0,np__0) = k8_genealg1(E,F,G,D,C) ) ) ) ) ) ) ) ) )).

fof(t31_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => ( k10_genealg1(E,F,G,A,np__0,np__0,np__0) = k7_genealg1(E,G,F,A)
                                & k10_genealg1(E,F,G,np__0,B,np__0,np__0) = k7_genealg1(E,G,F,B)
                                & k10_genealg1(E,F,G,np__0,np__0,C,np__0) = k7_genealg1(E,G,F,C)
                                & k10_genealg1(E,F,G,np__0,np__0,np__0,D) = k7_genealg1(E,G,F,D) ) ) ) ) ) ) ) ) )).

fof(t32_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_genealg1(B,A)
         => ! [C] :
              ( m1_genealg1(C,A)
             => k10_genealg1(A,B,C,np__0,np__0,np__0,np__0) = B ) ) ) )).

fof(t33_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => ( ( r1_xreal_0(k3_finseq_1(F),A)
                                 => k10_genealg1(E,F,G,A,B,C,D) = k9_genealg1(E,F,G,B,C,D) )
                                & ( r1_xreal_0(k3_finseq_1(F),B)
                                 => k10_genealg1(E,F,G,A,B,C,D) = k9_genealg1(E,F,G,A,C,D) )
                                & ( r1_xreal_0(k3_finseq_1(F),C)
                                 => k10_genealg1(E,F,G,A,B,C,D) = k9_genealg1(E,F,G,A,B,D) )
                                & ( r1_xreal_0(k3_finseq_1(F),D)
                                 => k10_genealg1(E,F,G,A,B,C,D) = k9_genealg1(E,F,G,A,B,C) ) ) ) ) ) ) ) ) ) )).

fof(t34_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => ( ( ( r1_xreal_0(k3_finseq_1(F),A)
                                    & r1_xreal_0(k3_finseq_1(F),B) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k8_genealg1(E,F,G,C,D) )
                                & ( ( r1_xreal_0(k3_finseq_1(F),A)
                                    & r1_xreal_0(k3_finseq_1(F),C) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k8_genealg1(E,F,G,B,D) )
                                & ( ( r1_xreal_0(k3_finseq_1(F),A)
                                    & r1_xreal_0(k3_finseq_1(F),D) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k8_genealg1(E,F,G,B,C) )
                                & ( ( r1_xreal_0(k3_finseq_1(F),B)
                                    & r1_xreal_0(k3_finseq_1(F),C) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k8_genealg1(E,F,G,A,D) )
                                & ( ( r1_xreal_0(k3_finseq_1(F),B)
                                    & r1_xreal_0(k3_finseq_1(F),D) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k8_genealg1(E,F,G,A,C) )
                                & ( ( r1_xreal_0(k3_finseq_1(F),C)
                                    & r1_xreal_0(k3_finseq_1(F),D) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k8_genealg1(E,F,G,A,B) ) ) ) ) ) ) ) ) ) )).

fof(t35_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => ( ( ( r1_xreal_0(k3_finseq_1(F),A)
                                    & r1_xreal_0(k3_finseq_1(F),B)
                                    & r1_xreal_0(k3_finseq_1(F),C) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k7_genealg1(E,F,G,D) )
                                & ( ( r1_xreal_0(k3_finseq_1(F),A)
                                    & r1_xreal_0(k3_finseq_1(F),B)
                                    & r1_xreal_0(k3_finseq_1(F),D) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k7_genealg1(E,F,G,C) )
                                & ( ( r1_xreal_0(k3_finseq_1(F),A)
                                    & r1_xreal_0(k3_finseq_1(F),C)
                                    & r1_xreal_0(k3_finseq_1(F),D) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k7_genealg1(E,F,G,B) )
                                & ( ( r1_xreal_0(k3_finseq_1(F),B)
                                    & r1_xreal_0(k3_finseq_1(F),C)
                                    & r1_xreal_0(k3_finseq_1(F),D) )
                                 => k10_genealg1(E,F,G,A,B,C,D) = k7_genealg1(E,F,G,A) ) ) ) ) ) ) ) ) ) )).

fof(t36_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => ( ( r1_xreal_0(k3_finseq_1(F),A)
                                  & r1_xreal_0(k3_finseq_1(F),B)
                                  & r1_xreal_0(k3_finseq_1(F),C)
                                  & r1_xreal_0(k3_finseq_1(F),D) )
                               => k10_genealg1(E,F,G,A,B,C,D) = F ) ) ) ) ) ) ) ) )).

fof(t37_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => ( k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,A,B,D,C)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,A,C,B,D)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,A,C,D,B)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,A,D,B,C)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,A,D,C,B)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,B,A,C,D)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,B,A,D,C)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,B,C,A,D)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,B,C,D,A)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,B,D,A,C)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,B,D,C,A)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,C,A,B,D)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,C,A,D,B)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,C,B,A,D)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,C,B,D,A)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,C,D,A,B)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,C,D,B,A)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,D,A,B,C)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,D,A,C,B)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,D,B,A,C)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,D,B,C,A)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,D,C,A,B)
                                & k10_genealg1(E,F,G,A,B,C,D) = k10_genealg1(E,F,G,D,C,B,A) ) ) ) ) ) ) ) ) )).

fof(t38_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_relat_1(E)
                        & v2_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( m1_genealg1(F,E)
                         => ! [G] :
                              ( m1_genealg1(G,E)
                             => ( k10_genealg1(E,F,G,A,A,B,C) = k8_genealg1(E,F,G,B,C)
                                & k10_genealg1(E,F,G,A,D,A,C) = k8_genealg1(E,F,G,D,C)
                                & k10_genealg1(E,F,G,A,D,B,A) = k8_genealg1(E,F,G,D,B)
                                & k10_genealg1(E,F,G,A,D,D,C) = k8_genealg1(E,F,G,A,C)
                                & k10_genealg1(E,F,G,A,D,B,D) = k8_genealg1(E,F,G,A,B)
                                & k10_genealg1(E,F,G,A,D,B,B) = k8_genealg1(E,F,G,A,D) ) ) ) ) ) ) ) ) )).

fof(t39_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_relat_1(D)
                    & v2_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( m1_genealg1(E,D)
                     => ! [F] :
                          ( m1_genealg1(F,D)
                         => ( k10_genealg1(D,E,F,A,A,B,B) = E
                            & k10_genealg1(D,E,F,A,C,A,C) = E
                            & k10_genealg1(D,E,F,A,C,C,A) = E ) ) ) ) ) ) ) )).

fof(t40_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => m1_genealg1(k5_genealg1(F,G,H,A,B,C,D,E),F) ) ) ) ) ) ) ) ) )).

fof(t41_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( k11_genealg1(F,G,H,np__0,A,B,C,D) = k10_genealg1(F,H,G,A,B,C,D)
                                    & k11_genealg1(F,G,H,E,np__0,B,C,D) = k10_genealg1(F,H,G,E,B,C,D)
                                    & k11_genealg1(F,G,H,E,A,np__0,C,D) = k10_genealg1(F,H,G,E,A,C,D)
                                    & k11_genealg1(F,G,H,E,A,B,np__0,D) = k10_genealg1(F,H,G,E,A,B,D)
                                    & k11_genealg1(F,G,H,E,A,B,C,np__0) = k10_genealg1(F,H,G,E,A,B,C) ) ) ) ) ) ) ) ) ) )).

fof(t42_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( k11_genealg1(F,G,H,np__0,np__0,A,B,C) = k9_genealg1(F,G,H,A,B,C)
                                    & k11_genealg1(F,G,H,np__0,D,np__0,B,C) = k9_genealg1(F,G,H,D,B,C)
                                    & k11_genealg1(F,G,H,np__0,D,A,np__0,C) = k9_genealg1(F,G,H,D,A,C)
                                    & k11_genealg1(F,G,H,np__0,D,A,B,np__0) = k9_genealg1(F,G,H,D,A,B)
                                    & k11_genealg1(F,G,H,E,np__0,np__0,B,C) = k9_genealg1(F,G,H,E,B,C)
                                    & k11_genealg1(F,G,H,E,np__0,A,np__0,C) = k9_genealg1(F,G,H,E,A,C)
                                    & k11_genealg1(F,G,H,E,np__0,A,B,np__0) = k9_genealg1(F,G,H,E,A,B)
                                    & k11_genealg1(F,G,H,E,D,np__0,np__0,C) = k9_genealg1(F,G,H,E,D,C)
                                    & k11_genealg1(F,G,H,E,D,np__0,B,np__0) = k9_genealg1(F,G,H,E,D,B)
                                    & k11_genealg1(F,G,H,E,D,A,np__0,np__0) = k9_genealg1(F,G,H,E,D,A) ) ) ) ) ) ) ) ) ) )).

fof(t43_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( k11_genealg1(F,G,H,np__0,np__0,np__0,A,B) = k8_genealg1(F,H,G,A,B)
                                    & k11_genealg1(F,G,H,np__0,np__0,C,np__0,B) = k8_genealg1(F,H,G,C,B)
                                    & k11_genealg1(F,G,H,np__0,np__0,C,A,np__0) = k8_genealg1(F,H,G,C,A)
                                    & k11_genealg1(F,G,H,np__0,D,np__0,np__0,B) = k8_genealg1(F,H,G,D,B)
                                    & k11_genealg1(F,G,H,np__0,D,np__0,A,np__0) = k8_genealg1(F,H,G,D,A)
                                    & k11_genealg1(F,G,H,np__0,D,C,np__0,np__0) = k8_genealg1(F,H,G,D,C)
                                    & k11_genealg1(F,G,H,E,np__0,np__0,np__0,B) = k8_genealg1(F,H,G,E,B)
                                    & k11_genealg1(F,G,H,E,np__0,np__0,A,np__0) = k8_genealg1(F,H,G,E,A)
                                    & k11_genealg1(F,G,H,E,np__0,C,np__0,np__0) = k8_genealg1(F,H,G,E,C)
                                    & k11_genealg1(F,G,H,E,D,np__0,np__0,np__0) = k8_genealg1(F,H,G,E,D) ) ) ) ) ) ) ) ) ) )).

fof(t44_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( k11_genealg1(F,G,H,np__0,np__0,np__0,np__0,A) = k7_genealg1(F,G,H,A)
                                    & k11_genealg1(F,G,H,np__0,np__0,np__0,B,np__0) = k7_genealg1(F,G,H,B)
                                    & k11_genealg1(F,G,H,np__0,np__0,C,np__0,np__0) = k7_genealg1(F,G,H,C)
                                    & k11_genealg1(F,G,H,np__0,D,np__0,np__0,np__0) = k7_genealg1(F,G,H,D)
                                    & k11_genealg1(F,G,H,E,np__0,np__0,np__0,np__0) = k7_genealg1(F,G,H,E) ) ) ) ) ) ) ) ) ) )).

fof(t45_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_genealg1(B,A)
         => ! [C] :
              ( m1_genealg1(C,A)
             => k11_genealg1(A,B,C,np__0,np__0,np__0,np__0,np__0) = C ) ) ) )).

fof(t46_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( ( r1_xreal_0(k3_finseq_1(G),A)
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k10_genealg1(F,G,H,B,C,D,E) )
                                    & ( r1_xreal_0(k3_finseq_1(G),B)
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k10_genealg1(F,G,H,A,C,D,E) )
                                    & ( r1_xreal_0(k3_finseq_1(G),C)
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k10_genealg1(F,G,H,A,B,D,E) )
                                    & ( r1_xreal_0(k3_finseq_1(G),D)
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k10_genealg1(F,G,H,A,B,C,E) )
                                    & ( r1_xreal_0(k3_finseq_1(G),E)
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k10_genealg1(F,G,H,A,B,C,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t47_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),B) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,C,D,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),C) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,B,D,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),D) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,B,C,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,B,C,D) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),C) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,A,D,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),D) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,A,C,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,A,C,D) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),D) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,A,B,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,A,B,D) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),D)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k9_genealg1(F,G,H,A,B,C) ) ) ) ) ) ) ) ) ) ) )).

fof(t48_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),C) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,D,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),D) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,C,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,C,D) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),D) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,B,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,B,D) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),D)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,B,C) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),D) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,A,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,A,D) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),D)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,A,C) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),D)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k8_genealg1(F,G,H,A,B) ) ) ) ) ) ) ) ) ) ) )).

fof(t49_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),D) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k7_genealg1(F,G,H,E) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k7_genealg1(F,G,H,D) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),D)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k7_genealg1(F,G,H,C) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),A)
                                        & r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),D)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k7_genealg1(F,G,H,B) )
                                    & ( ( r1_xreal_0(k3_finseq_1(G),B)
                                        & r1_xreal_0(k3_finseq_1(G),C)
                                        & r1_xreal_0(k3_finseq_1(G),D)
                                        & r1_xreal_0(k3_finseq_1(G),E) )
                                     => k11_genealg1(F,G,H,A,B,C,D,E) = k7_genealg1(F,G,H,A) ) ) ) ) ) ) ) ) ) ) )).

fof(t50_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( ( r1_xreal_0(k3_finseq_1(G),A)
                                      & r1_xreal_0(k3_finseq_1(G),B)
                                      & r1_xreal_0(k3_finseq_1(G),C)
                                      & r1_xreal_0(k3_finseq_1(G),D)
                                      & r1_xreal_0(k3_finseq_1(G),E) )
                                   => k11_genealg1(F,G,H,A,B,C,D,E) = G ) ) ) ) ) ) ) ) ) )).

fof(t51_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( k11_genealg1(F,G,H,A,B,C,D,E) = k11_genealg1(F,G,H,B,A,C,D,E)
                                    & k11_genealg1(F,G,H,A,B,C,D,E) = k11_genealg1(F,G,H,C,B,A,D,E)
                                    & k11_genealg1(F,G,H,A,B,C,D,E) = k11_genealg1(F,G,H,D,B,C,A,E)
                                    & k11_genealg1(F,G,H,A,B,C,D,E) = k11_genealg1(F,G,H,E,B,C,D,A) ) ) ) ) ) ) ) ) ) )).

fof(t52_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v1_relat_1(F)
                            & v2_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( m1_genealg1(G,F)
                             => ! [H] :
                                  ( m1_genealg1(H,F)
                                 => ( k11_genealg1(F,G,H,A,A,B,C,D) = k9_genealg1(F,G,H,B,C,D)
                                    & k11_genealg1(F,G,H,A,E,A,C,D) = k9_genealg1(F,G,H,E,C,D)
                                    & k11_genealg1(F,G,H,A,E,B,A,D) = k9_genealg1(F,G,H,E,B,D)
                                    & k11_genealg1(F,G,H,A,E,B,C,A) = k9_genealg1(F,G,H,E,B,C) ) ) ) ) ) ) ) ) ) )).

fof(t53_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( ( ~ v1_xboole_0(G)
                                & v1_relat_1(G)
                                & v2_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finseq_1(G) )
                             => ! [H] :
                                  ( m1_genealg1(H,G)
                                 => ! [I] :
                                      ( m1_genealg1(I,G)
                                     => m1_genealg1(k6_genealg1(G,H,I,A,B,C,D,E,F),G) ) ) ) ) ) ) ) ) ) )).

fof(t54_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( ( ~ v1_xboole_0(G)
                                & v1_relat_1(G)
                                & v2_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finseq_1(G) )
                             => ! [H] :
                                  ( m1_genealg1(H,G)
                                 => ! [I] :
                                      ( m1_genealg1(I,G)
                                     => ( k12_genealg1(G,H,I,np__0,A,B,C,D,E) = k11_genealg1(G,I,H,A,B,C,D,E)
                                        & k12_genealg1(G,H,I,F,np__0,B,C,D,E) = k11_genealg1(G,I,H,F,B,C,D,E)
                                        & k12_genealg1(G,H,I,F,A,np__0,C,D,E) = k11_genealg1(G,I,H,F,A,C,D,E)
                                        & k12_genealg1(G,H,I,F,A,B,np__0,D,E) = k11_genealg1(G,I,H,F,A,B,D,E)
                                        & k12_genealg1(G,H,I,F,A,B,C,np__0,E) = k11_genealg1(G,I,H,F,A,B,C,E)
                                        & k12_genealg1(G,H,I,F,A,B,C,D,np__0) = k11_genealg1(G,I,H,F,A,B,C,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t55_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( ( ~ v1_xboole_0(G)
                                & v1_relat_1(G)
                                & v2_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finseq_1(G) )
                             => ! [H] :
                                  ( m1_genealg1(H,G)
                                 => ! [I] :
                                      ( m1_genealg1(I,G)
                                     => ( ( r1_xreal_0(k3_finseq_1(H),A)
                                         => k12_genealg1(G,H,I,A,B,C,D,E,F) = k11_genealg1(G,H,I,B,C,D,E,F) )
                                        & ( r1_xreal_0(k3_finseq_1(H),B)
                                         => k12_genealg1(G,H,I,A,B,C,D,E,F) = k11_genealg1(G,H,I,A,C,D,E,F) )
                                        & ( r1_xreal_0(k3_finseq_1(H),C)
                                         => k12_genealg1(G,H,I,A,B,C,D,E,F) = k11_genealg1(G,H,I,A,B,D,E,F) )
                                        & ( r1_xreal_0(k3_finseq_1(H),D)
                                         => k12_genealg1(G,H,I,A,B,C,D,E,F) = k11_genealg1(G,H,I,A,B,C,E,F) )
                                        & ( r1_xreal_0(k3_finseq_1(H),E)
                                         => k12_genealg1(G,H,I,A,B,C,D,E,F) = k11_genealg1(G,H,I,A,B,C,D,F) )
                                        & ( r1_xreal_0(k3_finseq_1(H),F)
                                         => k12_genealg1(G,H,I,A,B,C,D,E,F) = k11_genealg1(G,H,I,A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t56_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( ( ~ v1_xboole_0(G)
                                & v1_relat_1(G)
                                & v2_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finseq_1(G) )
                             => ! [H] :
                                  ( m1_genealg1(H,G)
                                 => ! [I] :
                                      ( m1_genealg1(I,G)
                                     => ( k12_genealg1(G,H,I,A,B,C,D,E,F) = k12_genealg1(G,H,I,B,A,C,D,E,F)
                                        & k12_genealg1(G,H,I,A,B,C,D,E,F) = k12_genealg1(G,H,I,C,B,A,D,E,F)
                                        & k12_genealg1(G,H,I,A,B,C,D,E,F) = k12_genealg1(G,H,I,D,B,C,A,E,F)
                                        & k12_genealg1(G,H,I,A,B,C,D,E,F) = k12_genealg1(G,H,I,E,B,C,D,A,F)
                                        & k12_genealg1(G,H,I,A,B,C,D,E,F) = k12_genealg1(G,H,I,F,B,C,D,E,A) ) ) ) ) ) ) ) ) ) ) )).

fof(t57_genealg1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( ( ~ v1_xboole_0(G)
                                & v1_relat_1(G)
                                & v2_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finseq_1(G) )
                             => ! [H] :
                                  ( m1_genealg1(H,G)
                                 => ! [I] :
                                      ( m1_genealg1(I,G)
                                     => ( k12_genealg1(G,H,I,A,A,B,C,D,E) = k10_genealg1(G,H,I,B,C,D,E)
                                        & k12_genealg1(G,H,I,A,F,A,C,D,E) = k10_genealg1(G,H,I,F,C,D,E)
                                        & k12_genealg1(G,H,I,A,F,B,A,D,E) = k10_genealg1(G,H,I,F,B,D,E)
                                        & k12_genealg1(G,H,I,A,F,B,C,A,E) = k10_genealg1(G,H,I,F,B,C,E)
                                        & k12_genealg1(G,H,I,A,F,B,C,D,A) = k10_genealg1(G,H,I,F,B,C,D) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_m1_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_genealg1(B,A)
         => m2_finseq_1(B,k3_card_3(A)) ) ) )).

fof(existence_m1_genealg1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ? [B] : m1_genealg1(B,A) ) )).

fof(dt_k1_genealg1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_finseq_1(B,k3_card_3(A))
        & m1_finseq_1(C,k3_card_3(A))
        & m1_subset_1(D,k5_numbers) )
     => m2_finseq_1(k1_genealg1(A,B,C,D),k3_card_3(A)) ) )).

fof(dt_k2_genealg1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_finseq_1(B,k3_card_3(A))
        & m1_finseq_1(C,k3_card_3(A))
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers) )
     => m2_finseq_1(k2_genealg1(A,B,C,D,E),k3_card_3(A)) ) )).

fof(dt_k3_genealg1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_finseq_1(B,k3_card_3(A))
        & m1_finseq_1(C,k3_card_3(A))
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers) )
     => m2_finseq_1(k3_genealg1(A,B,C,D,E,F),k3_card_3(A)) ) )).

fof(dt_k4_genealg1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_finseq_1(B,k3_card_3(A))
        & m1_finseq_1(C,k3_card_3(A))
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers)
        & m1_subset_1(G,k5_numbers) )
     => m2_finseq_1(k4_genealg1(A,B,C,D,E,F,G),k3_card_3(A)) ) )).

fof(dt_k5_genealg1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_finseq_1(B,k3_card_3(A))
        & m1_finseq_1(C,k3_card_3(A))
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers)
        & m1_subset_1(G,k5_numbers)
        & m1_subset_1(H,k5_numbers) )
     => m2_finseq_1(k5_genealg1(A,B,C,D,E,F,G,H),k3_card_3(A)) ) )).

fof(dt_k6_genealg1,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_finseq_1(B,k3_card_3(A))
        & m1_finseq_1(C,k3_card_3(A))
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers)
        & m1_subset_1(G,k5_numbers)
        & m1_subset_1(H,k5_numbers)
        & m1_subset_1(I,k5_numbers) )
     => m2_finseq_1(k6_genealg1(A,B,C,D,E,F,G,H,I),k3_card_3(A)) ) )).

fof(dt_k7_genealg1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers) )
     => m1_genealg1(k7_genealg1(A,B,C,D),A) ) )).

fof(redefinition_k7_genealg1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers) )
     => k7_genealg1(A,B,C,D) = k1_genealg1(A,B,C,D) ) )).

fof(dt_k8_genealg1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers) )
     => m1_genealg1(k8_genealg1(A,B,C,D,E),A) ) )).

fof(redefinition_k8_genealg1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers) )
     => k8_genealg1(A,B,C,D,E) = k2_genealg1(A,B,C,D,E) ) )).

fof(dt_k9_genealg1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers) )
     => m1_genealg1(k9_genealg1(A,B,C,D,E,F),A) ) )).

fof(redefinition_k9_genealg1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers) )
     => k9_genealg1(A,B,C,D,E,F) = k3_genealg1(A,B,C,D,E,F) ) )).

fof(dt_k10_genealg1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers)
        & m1_subset_1(G,k5_numbers) )
     => m1_genealg1(k10_genealg1(A,B,C,D,E,F,G),A) ) )).

fof(redefinition_k10_genealg1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers)
        & m1_subset_1(G,k5_numbers) )
     => k10_genealg1(A,B,C,D,E,F,G) = k4_genealg1(A,B,C,D,E,F,G) ) )).

fof(dt_k11_genealg1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers)
        & m1_subset_1(G,k5_numbers)
        & m1_subset_1(H,k5_numbers) )
     => m1_genealg1(k11_genealg1(A,B,C,D,E,F,G,H),A) ) )).

fof(redefinition_k11_genealg1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers)
        & m1_subset_1(G,k5_numbers)
        & m1_subset_1(H,k5_numbers) )
     => k11_genealg1(A,B,C,D,E,F,G,H) = k5_genealg1(A,B,C,D,E,F,G,H) ) )).

fof(dt_k12_genealg1,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers)
        & m1_subset_1(G,k5_numbers)
        & m1_subset_1(H,k5_numbers)
        & m1_subset_1(I,k5_numbers) )
     => m1_genealg1(k12_genealg1(A,B,C,D,E,F,G,H,I),A) ) )).

fof(redefinition_k12_genealg1,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & m1_genealg1(B,A)
        & m1_genealg1(C,A)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,k5_numbers)
        & m1_subset_1(G,k5_numbers)
        & m1_subset_1(H,k5_numbers)
        & m1_subset_1(I,k5_numbers) )
     => k12_genealg1(A,B,C,D,E,F,G,H,I) = k6_genealg1(A,B,C,D,E,F,G,H,I) ) )).
%------------------------------------------------------------------------------