SET007 Axioms: SET007+422.ax


%------------------------------------------------------------------------------
% File     : SET007+422 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Correspondence Between Homomorphisms of Universal Algebra
% 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    : msuhom_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   34 (   0 unit)
%            Number of atoms       :  378 (  18 equality)
%            Maximal formula depth :   17 (   9 average)
%            Number of connectives :  401 (  57 ~  ;   0  |; 232  &)
%                                         (   2 <=>; 110 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   0 propositional; 1-4 arity)
%            Number of functors    :   40 (   4 constant; 0-6 arity)
%            Number of variables   :  103 (   0 singleton; 103 !;   0 ?)
%            Maximal term depth    :    5 (   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(t1_msuhom_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( r1_tarski(k2_relat_1(A),C)
             => k5_relat_1(A,k7_relat_1(B,C)) = k5_relat_1(A,B) ) ) ) )).

fof(t2_msuhom_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => r1_tarski(k3_finseq_2(B),k3_finseq_2(A)) ) )).

fof(t3_msuhom_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( v1_funcop_1(A)
         => v1_funcop_1(k7_relat_1(A,B)) ) ) )).

fof(t4_msuhom_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] :
          ( m1_pboole(C,A)
         => k6_pboole(B,k3_pre_circ(A,C,B)) = k7_relat_1(k6_pboole(A,C),k3_finseq_2(B)) ) ) )).

fof(d1_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ( r1_msuhom_1(A,B)
          <=> ( r1_tarski(u1_struct_0(A),u1_struct_0(B))
              & r1_tarski(u1_msualg_1(A),u1_msualg_1(B))
              & k2_partfun1(u1_msualg_1(B),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(B),u1_msualg_1(A)) = u2_msualg_1(A)
              & k2_partfun1(u1_msualg_1(B),u1_struct_0(B),u3_msualg_1(B),u1_msualg_1(A)) = u3_msualg_1(A) ) ) ) ) )).

fof(t5_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_msualg_1(C) )
             => ( ( r1_msuhom_1(A,B)
                  & r1_msuhom_1(B,C) )
               => r1_msuhom_1(A,C) ) ) ) ) )).

fof(t6_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_msualg_1(B)
            & l1_msualg_1(B) )
         => ( ( r1_msuhom_1(A,B)
              & r1_msuhom_1(B,A) )
           => A = B ) ) ) )).

fof(t7_msuhom_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,E)
                          & r1_xreal_0(E,A) )
                       => k1_funct_1(k3_cqc_lang(D,C),k4_finseq_4(k5_numbers,B,k1_msuhom_1(B,A,D),E)) = C ) ) ) ) ) ) )).

fof(t8_msuhom_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m3_pboole(E,A,C,D)
                 => ! [F] :
                      ( m1_pboole(F,B)
                     => ! [G] :
                          ( m1_pboole(G,B)
                         => ( ( r6_pboole(B,F,k3_pre_circ(A,C,B))
                              & r6_pboole(B,G,k3_pre_circ(A,D,B)) )
                           => m3_pboole(k3_pre_circ(A,E,B),B,F,G) ) ) ) ) ) ) ) )).

fof(d2_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_msualg_1(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_msualg_1(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v4_msualg_1(C,B)
                & v5_msualg_1(C,B)
                & l3_msualg_1(C,B) )
             => ( r1_msuhom_1(A,B)
               => ! [D] :
                    ( ( v4_msualg_1(D,A)
                      & v5_msualg_1(D,A)
                      & l3_msualg_1(D,A) )
                   => ( D = k2_msuhom_1(A,B,C)
                    <=> ( u4_msualg_1(A,D) = k7_relat_1(u4_msualg_1(B,C),u1_struct_0(A))
                        & u5_msualg_1(A,D) = k7_relat_1(u5_msualg_1(B,C),u1_msualg_1(A)) ) ) ) ) ) ) ) )).

fof(t9_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_msualg_1(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,A)
            & v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => B = k2_msuhom_1(A,A,B) ) ) )).

fof(t10_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => k7_msualg_1(A) = k7_msualg_1(B) ) ) ) )).

fof(d3_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( k7_msualg_1(A) = k7_msualg_1(B)
               => k3_msuhom_1(A,B,C) = k2_pre_circ(k1_tarski(np__0),C) ) ) ) ) )).

fof(t11_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( r1_unialg_2(A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(k7_msualg_1(A)))
                   => k1_msualg_3(u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))),k3_msuhom_1(A,B,C),k2_msualg_1(k7_msualg_1(A),D)) = C ) ) ) ) ) )).

fof(t12_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(k7_msualg_1(A)))
         => k5_msualg_1(k7_msualg_1(A),B,k10_msualg_1(A)) = k1_funct_1(u1_unialg_1(A),B) ) ) )).

fof(t13_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(k7_msualg_1(A)))
         => m2_unialg_2(k5_msualg_1(k7_msualg_1(A),B,k10_msualg_1(A)),u1_struct_0(A),k1_unialg_2(A)) ) ) )).

fof(t14_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(k7_msualg_1(A)))
         => ! [C] :
              ( m1_subset_1(C,k3_msualg_1(k7_msualg_1(A),B,k10_msualg_1(A)))
             => m2_finseq_1(C,u1_struct_0(A)) ) ) ) )).

fof(t15_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( r1_unialg_2(A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(k7_msualg_1(A)))
                   => ! [E] :
                        ( m1_subset_1(E,k3_msualg_1(k7_msualg_1(A),D,k10_msualg_1(A)))
                       => k6_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),D,k3_msuhom_1(A,B,C),E) = k5_relat_1(E,C) ) ) ) ) ) ) )).

fof(t16_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( r1_alg_1(A,B,C)
               => r1_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) ) ) ) ) )).

fof(t17_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( r1_unialg_2(A,B)
               => m1_pboole(k3_msuhom_1(A,B,C),k1_tarski(np__0)) ) ) ) ) )).

fof(t18_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( r3_alg_1(A,B,C)
               => r2_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) ) ) ) ) )).

fof(t19_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( r2_alg_1(A,B,C)
               => r3_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) ) ) ) ) )).

fof(t20_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( r4_alg_1(A,B,C)
               => r4_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) ) ) ) ) )).

fof(t21_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( r1_unialg_2(A,B)
                  & r1_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) )
               => r1_alg_1(A,B,C) ) ) ) ) )).

fof(t22_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( r1_unialg_2(A,B)
                  & r2_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) )
               => r3_alg_1(A,B,C) ) ) ) ) )).

fof(t23_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( r1_unialg_2(A,B)
                  & r3_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) )
               => r2_alg_1(A,B,C) ) ) ) ) )).

fof(t24_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( r1_unialg_2(A,B)
                  & r4_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) )
               => r4_alg_1(A,B,C) ) ) ) ) )).

fof(t25_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => r6_pboole(u1_struct_0(k7_msualg_1(A)),k3_msuhom_1(A,A,k6_partfun1(u1_struct_0(A))),k2_msualg_3(u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)))) ) )).

fof(t26_msuhom_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ( ( r1_unialg_2(A,B)
                  & r1_unialg_2(B,C) )
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                          & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                       => k13_pboole(k3_msuhom_1(A,B,D),k3_msuhom_1(B,C,E)) = k3_msuhom_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) )).

fof(reflexivity_r1_msuhom_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => r1_msuhom_1(A,A) ) )).

fof(dt_k1_msuhom_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => m2_finseq_1(k1_msuhom_1(A,B,C),A) ) )).

fof(redefinition_k1_msuhom_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => k1_msuhom_1(A,B,C) = k2_finseq_2(B,C) ) )).

fof(dt_k2_msuhom_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v1_msualg_1(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & v1_msualg_1(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & v4_msualg_1(C,B)
        & v5_msualg_1(C,B)
        & l3_msualg_1(C,B) )
     => ( v4_msualg_1(k2_msuhom_1(A,B,C),A)
        & v5_msualg_1(k2_msuhom_1(A,B,C),A)
        & l3_msualg_1(k2_msuhom_1(A,B,C),A) ) ) )).

fof(dt_k3_msuhom_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => m3_pboole(k3_msuhom_1(A,B,C),u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)))) ) )).
%------------------------------------------------------------------------------