SET007 Axioms: SET007+501.ax


%------------------------------------------------------------------------------
% File     : SET007+501 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Institution of Many Sorted Algebras. Part I
% Version  : [Urb08] axioms.
% English  : Institution of Many Sorted Algebras. Part I: Signature Reduct of
%            an Algebra

% 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    : instalg1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   68 (   1 unit)
%            Number of atoms       :  678 (  56 equality)
%            Maximal formula depth :   31 (  11 average)
%            Number of connectives :  739 ( 129 ~  ;   2  |; 290  &)
%                                         (   7 <=>; 311 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   1 propositional; 0-5 arity)
%            Number of functors    :   48 (   4 constant; 0-6 arity)
%            Number of variables   :  283 (   0 singleton; 276 !;   7 ?)
%            Maximal term depth    :    7 (   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(cc1_instalg1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => ! [D] :
          ( m1_subset_1(D,k3_msualg_1(A,C,k11_msafree(A,B)))
         => ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_finseq_1(D)
            & v6_trees_3(D) ) ) ) )).

fof(fc1_instalg1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ( v4_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A)
        & v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) )).

fof(cc2_instalg1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( ~ v3_struct_0(A)
       => v1_instalg1(A) ) ) )).

fof(cc3_instalg1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v2_msualg_1(A)
       => v1_instalg1(A) ) ) )).

fof(cc4_instalg1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( ( v3_struct_0(A)
          & v1_instalg1(A) )
       => v2_msualg_1(A) ) ) )).

fof(cc5_instalg1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( ( ~ v2_msualg_1(A)
          & v1_instalg1(A) )
       => ~ v3_struct_0(A) ) ) )).

fof(rc1_instalg1,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & ~ v2_msualg_1(A)
      & v1_instalg1(A) ) )).

fof(cc6_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_instalg1(B,A)
         => v1_instalg1(B) ) ) )).

fof(rc2_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] :
          ( m1_instalg1(B,A)
          & ~ v3_struct_0(B)
          & v1_instalg1(B) ) ) )).

fof(rc3_instalg1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ? [B] :
          ( m1_instalg1(B,A)
          & ~ v3_struct_0(B)
          & ~ v2_msualg_1(B)
          & v1_instalg1(B) ) ) )).

fof(fc2_instalg1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & m1_instalg1(B,A)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A) )
     => ( v4_msualg_1(k2_instalg1(A,B,C),B)
        & v5_msualg_1(k2_instalg1(A,B,C),B) ) ) )).

fof(fc3_instalg1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v1_relat_1(k13_msafree(A,B))
        & v2_relat_1(k13_msafree(A,B))
        & ~ v3_relat_1(k13_msafree(A,B))
        & v1_funct_1(k13_msafree(A,B))
        & v1_msafree(k13_msafree(A,B),A,k11_msafree(A,B)) ) ) )).

fof(t1_instalg1,axiom,(
    $true )).

fof(t2_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ! [D] :
                  ( m1_msaterm(D,A,C,k2_msaterm(A,C,B))
                <=> m1_subset_1(D,k3_msualg_1(A,B,k11_msafree(A,C))) ) ) ) ) )).

fof(t3_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ( r1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ~ ( k3_msualg_1(A,D,B) != k1_xboole_0
                        & k3_msualg_1(A,D,C) = k1_xboole_0 ) ) ) ) ) ) )).

fof(t4_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,k3_msualg_1(A,B,k11_msafree(A,C)))
                 => k8_funct_2(k3_msualg_1(A,B,k11_msafree(A,C)),k4_msualg_1(A,B,k11_msafree(A,C)),k5_msualg_1(A,B,k11_msafree(A,C)),D) = k4_trees_4(k4_tarski(B,u1_struct_0(A)),D) ) ) ) ) )).

fof(t5_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ( g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) = g3_msualg_1(A,u4_msualg_1(A,C),u5_msualg_1(A,C))
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => k5_msualg_1(A,D,B) = k5_msualg_1(A,D,C) ) ) ) ) ) )).

fof(t6_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( l3_msualg_1(D,A)
                 => ! [E] :
                      ( l3_msualg_1(E,A)
                     => ( ( g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) = g3_msualg_1(A,u4_msualg_1(A,D),u5_msualg_1(A,D))
                          & g3_msualg_1(A,u4_msualg_1(A,C),u5_msualg_1(A,C)) = g3_msualg_1(A,u4_msualg_1(A,E),u5_msualg_1(A,E)) )
                       => ! [F] :
                            ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                           => ! [G] :
                                ( m3_pboole(G,u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
                               => ( r6_pboole(u1_struct_0(A),F,G)
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_msualg_1(A))
                                     => ~ ( k3_msualg_1(A,H,B) != k1_xboole_0
                                          & k3_msualg_1(A,H,C) != k1_xboole_0
                                          & ? [I] :
                                              ( m1_subset_1(I,k3_msualg_1(A,H,B))
                                              & ? [J] :
                                                  ( m1_subset_1(J,k3_msualg_1(A,H,D))
                                                  & I = J
                                                  & k5_msualg_3(A,B,C,H,F,I) != k5_msualg_3(A,D,E,H,G,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t7_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( l3_msualg_1(D,A)
                 => ! [E] :
                      ( l3_msualg_1(E,A)
                     => ( ( g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) = g3_msualg_1(A,u4_msualg_1(A,D),u5_msualg_1(A,D))
                          & g3_msualg_1(A,u4_msualg_1(A,C),u5_msualg_1(A,C)) = g3_msualg_1(A,u4_msualg_1(A,E),u5_msualg_1(A,E))
                          & r1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) )
                       => ! [F] :
                            ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                           => ~ ( r1_msualg_3(A,B,C,F)
                                & ! [G] :
                                    ( m3_pboole(G,u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
                                   => ~ ( r6_pboole(u1_struct_0(A),G,F)
                                        & r1_msualg_3(A,D,E,G) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_instalg1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v1_instalg1(A)
      <=> ( u1_struct_0(A) = k1_xboole_0
         => u1_msualg_1(A) = k1_xboole_0 ) ) ) )).

fof(t8_instalg1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v1_instalg1(A)
      <=> k1_relat_1(u3_msualg_1(A)) = u1_msualg_1(A) ) ) )).

fof(t9_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => r3_pua2mss1(A,A,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))) ) )).

fof(t10_instalg1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ! [B] :
          ( l1_msualg_1(B)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => ( v1_funct_1(C)
                      & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                      & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
                      & v1_funct_1(D)
                      & v1_funct_2(D,u1_msualg_1(A),u1_msualg_1(B))
                      & m2_relset_1(D,u1_msualg_1(A),u1_msualg_1(B)) ) ) ) ) ) ) )).

fof(d2_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l1_msualg_1(B)
         => ( m1_instalg1(B,A)
          <=> r3_pua2mss1(B,A,k6_partfun1(u1_struct_0(B)),k6_partfun1(u1_msualg_1(B))) ) ) ) )).

fof(t11_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_instalg1(B,A)
         => ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
            & r1_tarski(u1_msualg_1(B),u1_msualg_1(A)) ) ) ) )).

fof(t12_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_instalg1(B,A)
         => ( r1_tarski(u3_msualg_1(B),u3_msualg_1(A))
            & r1_tarski(u2_msualg_1(B),u2_msualg_1(A)) ) ) ) )).

fof(t13_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_instalg1(B,A)
         => ( u2_msualg_1(B) = k2_partfun1(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),u1_msualg_1(B))
            & u3_msualg_1(B) = k2_partfun1(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u1_msualg_1(B)) ) ) ) )).

fof(t14_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & r1_tarski(u2_msualg_1(B),u2_msualg_1(A))
              & r1_tarski(u3_msualg_1(B),u3_msualg_1(A)) )
           => m1_instalg1(B,A) ) ) ) )).

fof(t15_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & u2_msualg_1(B) = k2_partfun1(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),u1_msualg_1(B))
              & u3_msualg_1(B) = k2_partfun1(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u1_msualg_1(B)) )
           => m1_instalg1(B,A) ) ) ) )).

fof(t16_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => m1_instalg1(A,A) ) )).

fof(t17_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_instalg1(B,A)
         => ! [C] :
              ( m1_instalg1(C,B)
             => m1_instalg1(C,A) ) ) ) )).

fof(t18_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_instalg1(B,A)
         => ( m1_instalg1(A,B)
           => g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) = g1_msualg_1(u1_struct_0(B),u1_msualg_1(B),u2_msualg_1(B),u3_msualg_1(B)) ) ) ) )).

fof(t19_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_instalg1(B,A)
         => ! [C] :
              ( l1_msualg_1(C)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(A,C,D,E)
                       => r3_pua2mss1(B,C,k7_relat_1(D,u1_struct_0(B)),k7_relat_1(E,u1_msualg_1(B))) ) ) ) ) ) ) )).

fof(t20_instalg1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ! [B] :
          ( ( v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_instalg1(C,B)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(A,C,D,E)
                       => r3_pua2mss1(A,B,D,E) ) ) ) ) ) ) )).

fof(t21_instalg1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ! [B] :
          ( ( v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_instalg1(C,B)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( ( r3_pua2mss1(A,B,D,E)
                          & r1_tarski(k2_relat_1(D),u1_struct_0(C))
                          & r1_tarski(k2_relat_1(E),u1_msualg_1(C)) )
                       => r3_pua2mss1(A,C,D,E) ) ) ) ) ) ) )).

fof(d3_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( l3_msualg_1(C,B)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(A,B,D,E)
                       => ! [F] :
                            ( ( v4_msualg_1(F,A)
                              & l3_msualg_1(F,A) )
                           => ( F = k1_instalg1(A,B,C,D,E)
                            <=> ( u4_msualg_1(A,F) = k5_relat_1(D,u4_msualg_1(B,C))
                                & u5_msualg_1(A,F) = k5_relat_1(E,u5_msualg_1(B,C)) ) ) ) ) ) ) ) ) ) )).

fof(d4_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => k2_instalg1(A,B,C) = k1_instalg1(B,A,C,k6_partfun1(u1_struct_0(B)),k6_partfun1(u1_msualg_1(B))) ) ) ) )).

fof(t22_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( l3_msualg_1(C,B)
             => ! [D] :
                  ( l3_msualg_1(D,B)
                 => ( g3_msualg_1(B,u4_msualg_1(B,C),u5_msualg_1(B,C)) = g3_msualg_1(B,u4_msualg_1(B,D),u5_msualg_1(B,D))
                   => ! [E] :
                        ( ( v1_relat_1(E)
                          & v1_funct_1(E) )
                       => ! [F] :
                            ( ( v1_relat_1(F)
                              & v1_funct_1(F) )
                           => ( r3_pua2mss1(A,B,E,F)
                             => k1_instalg1(A,B,C,E,F) = k1_instalg1(A,B,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t23_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v5_msualg_1(C,B)
                & l3_msualg_1(C,B) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(A,B,D,E)
                       => v5_msualg_1(k1_instalg1(A,B,C,D,E),A) ) ) ) ) ) ) )).

fof(t24_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => ! [E] :
                        ( l3_msualg_1(E,B)
                       => ! [F] :
                            ( m1_subset_1(F,u1_msualg_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_msualg_1(B))
                               => ( G = k1_funct_1(D,F)
                                 => k5_msualg_1(A,F,k1_instalg1(A,B,E,C,D)) = k5_msualg_1(B,G,E) ) ) ) ) ) ) ) ) ) )).

fof(t25_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => ! [E] :
                        ( l3_msualg_1(E,B)
                       => ! [F] :
                            ( m1_subset_1(F,u1_msualg_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_msualg_1(B))
                               => ( G = k1_funct_1(D,F)
                                 => ( k3_msualg_1(B,G,E) = k3_msualg_1(A,F,k1_instalg1(A,B,E,C,D))
                                    & k4_msualg_1(A,F,k1_instalg1(A,B,E,C,D)) = k4_msualg_1(B,G,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t26_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => k1_instalg1(A,A,B,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))) = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) )).

fof(t27_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => k2_instalg1(A,A,B) = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) )).

fof(t28_instalg1,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) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(A,B,D,E)
                       => ! [F] :
                            ( ( v1_relat_1(F)
                              & v1_funct_1(F) )
                           => ! [G] :
                                ( ( v1_relat_1(G)
                                  & v1_funct_1(G) )
                               => ( r3_pua2mss1(B,C,F,G)
                                 => ! [H] :
                                      ( l3_msualg_1(H,C)
                                     => k1_instalg1(A,C,H,k5_relat_1(D,F),k5_relat_1(E,G)) = k1_instalg1(A,B,k1_instalg1(B,C,H,F,G),D,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t29_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_instalg1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_instalg1(C,B) )
             => ! [D] :
                  ( l3_msualg_1(D,A)
                 => k2_instalg1(A,C,D) = k2_instalg1(B,C,k2_instalg1(A,B,D)) ) ) ) ) )).

fof(t30_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_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)) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => ! [E] :
                        ( l3_msualg_1(E,B)
                       => ! [F] :
                            ( l3_msualg_1(F,B)
                           => ! [G] :
                                ( m3_pboole(G,u1_struct_0(B),u4_msualg_1(B,E),u4_msualg_1(B,F))
                               => m3_pboole(k7_pboole(u1_struct_0(A),u1_struct_0(B),C,G),u1_struct_0(A),u4_msualg_1(A,k1_instalg1(A,B,E,C,D)),u4_msualg_1(A,k1_instalg1(A,B,F,C,D))) ) ) ) ) ) ) ) ) )).

fof(t31_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_instalg1(B,A) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( l3_msualg_1(D,A)
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                     => m3_pboole(k7_relat_1(E,u1_struct_0(B)),u1_struct_0(B),u4_msualg_1(B,k2_instalg1(A,B,C)),u4_msualg_1(B,k2_instalg1(A,B,D))) ) ) ) ) ) )).

fof(t32_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => ! [E] :
                        ( l3_msualg_1(E,B)
                       => k5_relat_1(C,k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,E))) = k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,k1_instalg1(A,B,E,C,D))) ) ) ) ) ) ) )).

fof(t33_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_instalg1(B,A) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => k7_relat_1(k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,C)),u1_struct_0(B)) = k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,k2_instalg1(A,B,C))) ) ) ) )).

fof(t34_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => ! [E] :
                        ( l3_msualg_1(E,B)
                       => ! [F] :
                            ( l3_msualg_1(F,B)
                           => ! [G] :
                                ( m3_pboole(G,u1_struct_0(B),u4_msualg_1(B,E),u4_msualg_1(B,F))
                               => ! [H] :
                                    ( m3_pboole(H,u1_struct_0(A),u4_msualg_1(A,k1_instalg1(A,B,E,C,D)),u4_msualg_1(A,k1_instalg1(A,B,F,C,D)))
                                   => ( H = k5_relat_1(C,G)
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_msualg_1(A))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_msualg_1(B))
                                             => ( J = k1_funct_1(D,I)
                                               => ( k3_msualg_1(B,J,E) = k1_xboole_0
                                                  | k3_msualg_1(B,J,F) = k1_xboole_0
                                                  | ! [K] :
                                                      ( m1_subset_1(K,k3_msualg_1(B,J,E))
                                                     => ! [L] :
                                                          ( m1_subset_1(L,k3_msualg_1(A,I,k1_instalg1(A,B,E,C,D)))
                                                         => ( K = L
                                                           => k5_msualg_3(A,k1_instalg1(A,B,E,C,D),k1_instalg1(A,B,F,C,D),I,H,L) = k5_msualg_3(B,E,F,J,G,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( l3_msualg_1(D,A)
                 => ( r1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                   => ! [E] :
                        ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                       => ( r1_msualg_3(A,C,D,E)
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,u1_struct_0(B),u1_struct_0(A))
                                & m2_relset_1(F,u1_struct_0(B),u1_struct_0(A)) )
                             => ! [G] :
                                  ( ( v1_relat_1(G)
                                    & v1_funct_1(G) )
                                 => ~ ( r3_pua2mss1(B,A,F,G)
                                      & ! [H] :
                                          ( m3_pboole(H,u1_struct_0(B),u4_msualg_1(B,k1_instalg1(B,A,C,F,G)),u4_msualg_1(B,k1_instalg1(B,A,D,F,G)))
                                         => ~ ( r6_pboole(u1_struct_0(B),H,k7_pboole(u1_struct_0(B),u1_struct_0(A),F,E))
                                              & r1_msualg_3(B,k1_instalg1(B,A,C,F,G),k1_instalg1(B,A,D,F,G),H) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t36_instalg1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v2_msualg_1(B)
            & m1_instalg1(B,A) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( l3_msualg_1(D,A)
                 => ( r1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                   => ! [E] :
                        ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                       => ~ ( r1_msualg_3(A,C,D,E)
                            & ! [F] :
                                ( m3_pboole(F,u1_struct_0(B),u4_msualg_1(B,k2_instalg1(A,B,C)),u4_msualg_1(B,k2_instalg1(A,B,D)))
                               => ~ ( F = k7_relat_1(E,u1_struct_0(B))
                                    & r1_msualg_3(B,k2_instalg1(A,B,C),k2_instalg1(A,B,D),F) ) ) ) ) ) ) ) ) ) )).

fof(t37_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(B,A,D,E)
                       => ! [F] :
                            ( ( v5_msualg_1(F,B)
                              & l3_msualg_1(F,B) )
                           => ( F = k1_instalg1(B,A,C,D,E)
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(B))
                                     => ! [I] :
                                          ( ( v1_relat_1(I)
                                            & v1_funct_1(I) )
                                         => ( r1_msualg_6(B,G,H,F,I)
                                           => r1_msualg_6(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,G),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,H),C,I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t38_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(B,A,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ( r1_rewrite1(k3_msualg_6(B),E,F)
                             => r1_rewrite1(k3_msualg_6(A),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,F)) ) ) ) ) ) ) ) ) )).

fof(t39_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(B,A,D,E)
                       => ! [F] :
                            ( ( v5_msualg_1(F,B)
                              & l3_msualg_1(F,B) )
                           => ( F = k1_instalg1(B,A,C,D,E)
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(B))
                                     => ( r1_rewrite1(k3_msualg_6(B),G,H)
                                       => ! [I] :
                                            ( m2_msualg_6(I,B,F,G,H)
                                           => m2_msualg_6(I,A,C,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,G),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,H)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t40_instalg1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m4_pboole(D,A,B)
             => ! [E] :
                  ( m3_pboole(E,A,B,C)
                 => ! [F] :
                      ( r2_hidden(F,A)
                     => ! [G] :
                          ( ( v1_relat_1(G)
                            & v1_funct_1(G) )
                         => ! [H] :
                              ( ( v1_relat_1(H)
                                & v1_funct_1(H) )
                             => ( ( G = k1_funct_1(E,F)
                                  & H = k1_funct_1(k1_msafree(A,B,C,D,E),F) )
                               => ! [I] :
                                    ( r2_hidden(I,k1_funct_1(D,F))
                                   => k1_funct_1(H,I) = k1_funct_1(G,I) ) ) ) ) ) ) ) ) ) )).

fof(d5_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(B)) )
             => ! [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_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(A,B,D,E)
                       => ! [F] :
                            ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E)))
                           => ( F = k3_instalg1(A,B,C,D,E)
                            <=> ( r1_msualg_3(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)),k1_instalg1(A,B,k11_msafree(B,C),D,E),F)
                                & ! [G] :
                                    ( m1_subset_1(G,u1_struct_0(A))
                                   => ! [H] :
                                        ( m1_subset_1(H,k1_funct_1(k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C),G))
                                       => k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E)),F,G),k1_trees_4(k4_tarski(H,G))) = k1_trees_4(k4_tarski(H,k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,G))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t41_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(B)) )
             => ! [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_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(A,B,D,E)
                       => ! [F] :
                            ( m1_subset_1(F,u1_msualg_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,k3_msualg_1(A,F,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))))
                               => ! [H] :
                                    ( ( v1_relat_1(H)
                                      & v1_funct_1(H)
                                      & v1_finseq_1(H) )
                                   => ( H = k5_msualg_3(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)),k1_instalg1(A,B,k11_msafree(B,C),D,E),F,k3_instalg1(A,B,C,D,E),G)
                                     => k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E)),k3_instalg1(A,B,C,D,E),k2_msualg_1(A,F)),k4_trees_4(k4_tarski(F,u1_struct_0(A)),G)) = k4_trees_4(k4_tarski(k1_funct_1(E,F),u1_struct_0(B)),H) ) ) ) ) ) ) ) ) ) ) )).

fof(t42_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(B)) )
             => ! [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_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(A,B,D,E)
                       => ! [F] :
                            ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),k5_trees_3(u1_struct_0(k5_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)))),k1_msaterm(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)))
                           => ( m2_msaterm(k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E)),k3_instalg1(A,B,C,D,E),k7_msaterm(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C),F)),F),B,C)
                            <=> m2_msaterm(F,A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)) ) ) ) ) ) ) ) ) )).

fof(t43_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(B)) )
             => ! [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_relat_1(E)
                        & v1_funct_1(E)
                        & v2_funct_1(E) )
                     => ( r3_pua2mss1(A,B,D,E)
                       => r3_msualg_3(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)),k1_instalg1(A,B,k11_msafree(B,C),D,E),k3_instalg1(A,B,C,D,E)) ) ) ) ) ) ) )).

fof(t44_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => r6_pboole(u1_struct_0(A),k3_instalg1(A,A,B,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))),k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,B)))) ) ) )).

fof(t45_instalg1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & l1_msualg_1(C) )
             => ! [D] :
                  ( ( v2_relat_1(D)
                    & m1_pboole(D,u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ( r3_pua2mss1(A,B,E,F)
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,u1_struct_0(B),u1_struct_0(C))
                                  & m2_relset_1(G,u1_struct_0(B),u1_struct_0(C)) )
                               => ! [H] :
                                    ( ( v1_relat_1(H)
                                      & v1_funct_1(H) )
                                   => ( r3_pua2mss1(B,C,G,H)
                                     => k3_instalg1(A,C,D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),E,G),k5_relat_1(F,H)) = k13_pboole(k3_instalg1(A,B,k8_pboole(u1_struct_0(B),u1_struct_0(C),G,D),E,F),k7_pboole(u1_struct_0(A),u1_struct_0(B),E,k3_instalg1(B,C,D,G,H))) ) ) ) ) ) ) ) ) ) ) )).

fof(s1_instalg1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,u1_struct_0(f1_s1_instalg1))
       => ! [B] :
            ( m1_subset_1(B,k1_funct_1(f3_s1_instalg1,A))
           => r2_hidden(f4_s1_instalg1(B,A),k1_funct_1(u4_msualg_1(f1_s1_instalg1,f2_s1_instalg1),A)) ) )
   => ? [A] :
        ( m3_pboole(A,u1_struct_0(f1_s1_instalg1),u4_msualg_1(f1_s1_instalg1,k11_msafree(f1_s1_instalg1,f3_s1_instalg1)),u4_msualg_1(f1_s1_instalg1,f2_s1_instalg1))
        & r1_msualg_3(f1_s1_instalg1,k11_msafree(f1_s1_instalg1,f3_s1_instalg1),f2_s1_instalg1,A)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s1_instalg1))
           => ! [C] :
                ( m1_subset_1(C,k1_funct_1(f3_s1_instalg1,B))
               => k1_funct_1(k1_msualg_3(u1_struct_0(f1_s1_instalg1),u4_msualg_1(f1_s1_instalg1,k11_msafree(f1_s1_instalg1,f3_s1_instalg1)),u4_msualg_1(f1_s1_instalg1,f2_s1_instalg1),A,B),k1_trees_4(k4_tarski(C,B))) = f4_s1_instalg1(C,B) ) ) ) )).

fof(dt_m1_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_instalg1(B,A)
         => l1_msualg_1(B) ) ) )).

fof(existence_m1_instalg1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ? [B] : m1_instalg1(B,A) ) )).

fof(dt_k1_instalg1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & l3_msualg_1(C,B)
        & v1_relat_1(D)
        & v1_funct_1(D)
        & v1_relat_1(E)
        & v1_funct_1(E) )
     => ( v4_msualg_1(k1_instalg1(A,B,C,D,E),A)
        & l3_msualg_1(k1_instalg1(A,B,C,D,E),A) ) ) )).

fof(dt_k2_instalg1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & l3_msualg_1(C,A) )
     => ( v4_msualg_1(k2_instalg1(A,B,C),B)
        & l3_msualg_1(k2_instalg1(A,B,C),B) ) ) )).

fof(dt_k3_instalg1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
        & v1_relat_1(E)
        & v1_funct_1(E) )
     => m3_pboole(k3_instalg1(A,B,C,D,E),u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E))) ) )).
%------------------------------------------------------------------------------