SET007 Axioms: SET007+624.ax


%------------------------------------------------------------------------------
% File     : SET007+624 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Technical Preliminaries to Algebraic Specifications
% 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    : algspec1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   87 (   4 unit)
%            Number of atoms       :  646 (  44 equality)
%            Maximal formula depth :   18 (   8 average)
%            Number of connectives :  640 (  81 ~  ;   1  |; 288  &)
%                                         (   9 <=>; 261 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-4 arity)
%            Number of functors    :   31 (   1 constant; 0-5 arity)
%            Number of variables   :  246 (   0 singleton; 238 !;   8 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_algspec1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ( v1_msualg_1(g1_msualg_1(A,B,C,D))
        & ~ v2_msualg_1(g1_msualg_1(A,B,C,D)) ) ) )).

fof(cc1_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m2_algspec1(B,A)
         => ( ~ v3_struct_0(B)
            & v1_instalg1(B) ) ) ) )).

fof(cc2_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m2_algspec1(B,A)
         => ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v1_instalg1(B) ) ) ) )).

fof(rc1_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ? [B] :
          ( m2_algspec1(B,A)
          & ~ v3_struct_0(B)
          & v1_msualg_1(B)
          & ~ v2_msualg_1(B)
          & v1_instalg1(B) ) ) )).

fof(t1_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_tarski(k3_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(C))
               => k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(k1_funct_4(B,A),C) ) ) ) ) )).

fof(t2_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(A,B)
                  & r1_tarski(k3_xboole_0(k2_relat_1(C),k1_relat_1(B)),k1_relat_1(A)) )
               => k5_relat_1(C,B) = k5_relat_1(C,A) ) ) ) ) )).

fof(t3_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(k1_relat_1(A),k2_relat_1(B))
                  & r1_xboole_0(k1_relat_1(A),k2_relat_1(C))
                  & r1_xboole_0(k9_relat_1(B,k1_relat_1(C)),k1_relat_1(A)) )
               => k5_relat_1(k1_funct_4(B,C),A) = k5_relat_1(B,A) ) ) ) ) )).

fof(t4_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_partfun1(A,B)
                      & r1_partfun1(C,D) )
                   => r1_partfun1(k5_relat_1(C,A),k5_relat_1(D,B)) ) ) ) ) ) )).

fof(t5_algspec1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,D)
                            & m2_relset_1(F,B,D) )
                         => ( r1_tarski(E,F)
                           => r1_tarski(k16_lang1(A,C,E),k16_lang1(B,D,F)) ) ) ) ) ) ) ) )).

fof(t6_algspec1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,D)
                            & m2_relset_1(F,B,D) )
                         => ( r1_partfun1(E,F)
                           => r1_partfun1(k16_lang1(A,C,E),k16_lang1(B,D,F)) ) ) ) ) ) ) ) )).

fof(d1_algspec1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_algspec1(A,B) = k1_funct_4(k6_partfun1(A),k7_relat_1(B,A)) ) )).

fof(t7_algspec1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => k2_relat_1(k1_algspec1(A,B)) = k2_xboole_0(k4_xboole_0(A,k1_relat_1(B)),k9_relat_1(B,A)) ) )).

fof(t8_algspec1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => k1_funct_1(k1_algspec1(A,B),C) = k1_funct_1(k1_funct_4(k6_partfun1(A),B),C) ) ) ) )).

fof(t9_algspec1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => ( ( r2_hidden(B,k1_relat_1(C))
           => k1_funct_1(k1_algspec1(A,C),B) = k1_funct_1(C,B) )
          & ( ~ r2_hidden(B,k1_relat_1(C))
           => k1_funct_1(k1_algspec1(A,C),B) = B ) ) ) ) )).

fof(t10_algspec1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = A
       => k1_algspec1(A,B) = B ) ) )).

fof(t11_algspec1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r6_pboole(A,k1_algspec1(A,k1_algspec1(A,B)),k1_algspec1(A,B)) ) )).

fof(t12_algspec1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r6_pboole(A,k1_algspec1(A,k1_funct_4(k6_partfun1(A),B)),k1_algspec1(A,B)) ) )).

fof(t13_algspec1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(B,k6_partfun1(A))
       => k1_algspec1(A,B) = k6_partfun1(A) ) ) )).

fof(t14_algspec1,axiom,(
    ! [A] : k1_algspec1(A,k1_xboole_0) = k6_partfun1(A) )).

fof(t15_algspec1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r6_pboole(A,k1_algspec1(A,k7_relat_1(B,A)),k1_algspec1(A,B)) ) )).

fof(t16_algspec1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_algspec1(A,B) = k7_relat_1(B,A) ) ) )).

fof(t17_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k1_algspec1(k1_xboole_0,A) = k1_xboole_0 ) )).

fof(t18_algspec1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(A,B)
       => k7_relat_1(k1_algspec1(B,C),A) = k1_algspec1(A,C) ) ) )).

fof(t19_algspec1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r6_pboole(k2_xboole_0(A,B),k1_algspec1(k2_xboole_0(A,B),C),k1_circcomb(A,B,k1_algspec1(A,C),k1_algspec1(B,C))) ) )).

fof(t20_algspec1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r1_partfun1(k1_algspec1(A,C),k1_algspec1(B,C)) ) )).

fof(t21_algspec1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => k1_algspec1(k2_xboole_0(A,B),C) = k2_xboole_0(k1_algspec1(A,C),k1_algspec1(B,C)) ) )).

fof(t22_algspec1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_tarski(k2_relat_1(C),A)
               => k5_relat_1(C,k1_algspec1(A,B)) = k5_relat_1(C,k1_funct_4(k6_partfun1(A),B)) ) ) ) ) )).

fof(t23_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
              & r1_xboole_0(k2_relat_1(B),k1_relat_1(A)) )
           => ! [C] : k5_relat_1(k1_algspec1(C,B),A) = k7_relat_1(A,C) ) ) ) )).

fof(d2_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( m1_algspec1(B,A)
          <=> ( k1_relat_1(B) = k2_relat_1(A)
              & k5_relat_1(B,A) = k6_partfun1(k2_relat_1(A)) ) ) ) ) )).

fof(t24_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( m1_algspec1(B,A)
         => r1_tarski(k2_relat_1(B),k1_relat_1(A)) ) ) )).

fof(t25_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( m1_algspec1(B,A)
         => ! [C] :
              ( r2_hidden(C,k2_relat_1(A))
             => ( r2_hidden(k1_funct_1(B,C),k1_relat_1(A))
                & k1_funct_1(A,k1_funct_1(B,C)) = C ) ) ) ) )).

fof(t26_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => m1_algspec1(k2_funct_1(A),A) ) ) )).

fof(t27_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ! [B] :
            ( m1_algspec1(B,A)
           => B = k2_funct_1(A) ) ) ) )).

fof(t28_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
           => ! [C] :
                ( m1_algspec1(C,A)
               => ! [D] :
                    ( m1_algspec1(D,B)
                   => m1_algspec1(k1_funct_4(C,D),k1_funct_4(A,B)) ) ) ) ) ) )).

fof(t29_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => ! [C] :
                ( m1_algspec1(C,A)
               => ? [D] :
                    ( m1_algspec1(D,B)
                    & r1_tarski(C,D) ) ) ) ) ) )).

fof(d3_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ( k1_funct_1(k1_funct_4(k6_partfun1(u1_msualg_1(A)),C),D) = k1_funct_1(k1_funct_4(k6_partfun1(u1_msualg_1(A)),C),E)
                         => ( k5_relat_1(k1_msualg_1(A,D),k1_funct_4(k6_partfun1(u1_struct_0(A)),B)) = k5_relat_1(k1_msualg_1(A,E),k1_funct_4(k6_partfun1(u1_struct_0(A)),B))
                            & k1_funct_1(k1_funct_4(k6_partfun1(u1_struct_0(A)),B),k2_msualg_1(A,D)) = k1_funct_1(k1_funct_4(k6_partfun1(u1_struct_0(A)),B),k2_msualg_1(A,E)) ) ) ) ) ) ) ) ) )).

fof(t30_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ( k1_funct_1(k1_algspec1(u1_msualg_1(A),C),D) = k1_funct_1(k1_algspec1(u1_msualg_1(A),C),E)
                         => ( k5_relat_1(k1_msualg_1(A,D),k1_algspec1(u1_struct_0(A),B)) = k5_relat_1(k1_msualg_1(A,E),k1_algspec1(u1_struct_0(A),B))
                            & k1_funct_1(k1_algspec1(u1_struct_0(A),B),k2_msualg_1(A,D)) = k1_funct_1(k1_algspec1(u1_struct_0(A),B),k2_msualg_1(A,E)) ) ) ) ) ) ) ) ) )).

fof(t31_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
              <=> r1_algspec1(A,k1_algspec1(u1_struct_0(A),B),k1_algspec1(u1_msualg_1(A),C)) ) ) ) ) )).

fof(t32_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(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)
                   => r1_algspec1(A,C,D) ) ) ) ) ) )).

fof(t33_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_algspec1(A,B,k1_xboole_0) ) ) )).

fof(t34_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( v2_funct_1(B)
                  & r1_tarski(k3_xboole_0(u1_msualg_1(A),k2_relat_1(B)),k1_relat_1(B)) )
               => r1_algspec1(A,C,B) ) ) ) ) )).

fof(t35_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( v2_funct_1(B)
                  & r1_xboole_0(k2_relat_1(B),u1_msualg_1(A)) )
               => r1_algspec1(A,C,B) ) ) ) ) )).

fof(d4_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => ! [D] :
                    ( ( ~ v3_struct_0(D)
                      & v1_msualg_1(D)
                      & ~ v2_msualg_1(D)
                      & l1_msualg_1(D) )
                   => ( D = k2_algspec1(A,B,C)
                    <=> ( r3_pua2mss1(A,D,k1_algspec1(u1_struct_0(A),B),k1_algspec1(u1_msualg_1(A),C))
                        & u1_struct_0(D) = k2_relat_1(k1_algspec1(u1_struct_0(A),B))
                        & u1_msualg_1(D) = k2_relat_1(k1_algspec1(u1_msualg_1(A),C)) ) ) ) ) ) ) ) )).

fof(t36_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(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)
                   => k7_funct_2(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(A),k16_lang1(u1_struct_0(A),u1_struct_0(B),C)) = k5_relat_1(D,u2_msualg_1(B)) ) ) ) ) ) )).

fof(t37_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => ( v1_funct_1(k1_algspec1(u1_struct_0(A),B))
                  & v1_funct_2(k1_algspec1(u1_struct_0(A),B),u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C)))
                  & m2_relset_1(k1_algspec1(u1_struct_0(A),B),u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C))) ) ) ) ) ) )).

fof(t38_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C)))
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C))) )
                   => ( D = k1_algspec1(u1_struct_0(A),B)
                     => ! [E] :
                          ( m1_algspec1(E,k1_algspec1(u1_msualg_1(A),C))
                         => u2_msualg_1(k2_algspec1(A,B,C)) = k5_relat_1(E,k7_funct_2(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),k3_finseq_2(u1_struct_0(k2_algspec1(A,B,C))),u2_msualg_1(A),k16_lang1(u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C)),D))) ) ) ) ) ) ) ) )).

fof(t39_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => ! [D] :
                    ( m1_algspec1(D,k1_algspec1(u1_msualg_1(A),C))
                   => u3_msualg_1(k2_algspec1(A,B,C)) = k5_relat_1(D,k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k1_algspec1(u1_struct_0(A),B))) ) ) ) ) ) )).

fof(t40_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(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)
                   => m1_instalg1(k2_algspec1(A,C,D),B) ) ) ) ) ) )).

fof(t41_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
              <=> r3_pua2mss1(A,k2_algspec1(A,B,C),k1_algspec1(u1_struct_0(A),B),k1_algspec1(u1_msualg_1(A),C)) ) ) ) ) )).

fof(t42_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(k1_relat_1(B),u1_struct_0(A))
                  & r1_tarski(k1_relat_1(C),u1_msualg_1(A))
                  & r1_algspec1(A,B,C) )
               => r3_pua2mss1(A,k2_algspec1(A,B,C),k1_funct_4(k6_partfun1(u1_struct_0(A)),B),k1_funct_4(k6_partfun1(u1_msualg_1(A)),C)) ) ) ) ) )).

fof(t43_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( k1_relat_1(B) = u1_struct_0(A)
                  & k1_relat_1(C) = u1_msualg_1(A)
                  & r1_algspec1(A,B,C) )
               => r3_pua2mss1(A,k2_algspec1(A,B,C),B,C) ) ) ) ) )).

fof(t44_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => k2_algspec1(A,k1_algspec1(u1_struct_0(A),B),C) = k2_algspec1(A,B,C) ) ) ) ) )).

fof(t45_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => k2_algspec1(A,B,k1_algspec1(u1_msualg_1(A),C)) = k2_algspec1(A,B,C) ) ) ) ) )).

fof(d5_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( m2_algspec1(B,A)
          <=> m1_instalg1(A,B) ) ) ) )).

fof(t46_algspec1,axiom,(
    $true )).

fof(t47_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => m2_algspec1(A,A) ) )).

fof(t48_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m2_algspec1(B,A)
         => ! [C] :
              ( m2_algspec1(C,B)
             => m2_algspec1(C,A) ) ) ) )).

fof(t49_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( r1_circcomb(A,B)
           => m2_algspec1(k3_circcomb(A,B),A) ) ) ) )).

fof(t50_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => m2_algspec1(k3_circcomb(A,B),B) ) ) )).

fof(t51_algspec1,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) )
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G) )
                             => ( ( r1_partfun1(D,F)
                                  & r3_pua2mss1(A,C,D,E)
                                  & r3_pua2mss1(B,C,F,G) )
                               => r3_pua2mss1(k3_circcomb(A,B),C,k1_funct_4(D,F),k1_funct_4(E,G)) ) ) ) ) ) ) ) ) )).

fof(t52_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v1_instalg1(C)
                & l1_msualg_1(C) )
             => ( ( ( m2_algspec1(C,A)
                    & m2_algspec1(C,B) )
                 => ( r1_circcomb(A,B)
                    & m2_algspec1(C,k3_circcomb(A,B)) ) )
                & ( ( r1_circcomb(A,B)
                    & m2_algspec1(C,k3_circcomb(A,B)) )
                 => ( m2_algspec1(C,A)
                    & m2_algspec1(C,B) ) ) ) ) ) ) )).

fof(t53_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( v3_struct_0(A)
           => m2_algspec1(B,A) ) ) ) )).

fof(t54_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( ~ v2_msualg_1(C)
                & v1_instalg1(C)
                & l1_msualg_1(C) )
             => ! [D] :
                  ( m2_algspec1(D,C)
                 => ( r1_algspec1(D,A,B)
                   => r1_algspec1(C,A,B) ) ) ) ) ) )).

fof(t55_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( ~ v2_msualg_1(C)
                & v1_instalg1(C)
                & l1_msualg_1(C) )
             => ! [D] :
                  ( m2_algspec1(D,C)
                 => ( r1_algspec1(D,A,B)
                   => m2_algspec1(k2_algspec1(D,A,B),k2_algspec1(C,A,B)) ) ) ) ) ) )).

fof(t56_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( r1_circcomb(A,B)
           => ! [C] :
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ! [D] :
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D) )
                   => ( r1_algspec1(k3_circcomb(A,B),C,D)
                     => k2_algspec1(k3_circcomb(A,B),C,D) = k3_circcomb(k2_algspec1(A,C,D),k2_algspec1(B,C,D)) ) ) ) ) ) ) )).

fof(d6_algspec1,axiom,(
    ! [A] :
      ( m3_algspec1(A)
    <=> ? [B] :
          ( ~ v2_msualg_1(B)
          & v1_instalg1(B)
          & l1_msualg_1(B)
          & v1_msualg_6(A,B)
          & l3_msualg_1(A,B) ) ) )).

fof(d7_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m3_algspec1(B)
         => ( m4_algspec1(B,A)
          <=> ? [C] :
                ( ~ v2_msualg_1(C)
                & m2_algspec1(C,A)
                & v1_msualg_6(B,C)
                & l3_msualg_1(B,C) ) ) ) ) )).

fof(t57_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_msualg_6(B,A)
            & l3_msualg_1(B,A) )
         => m4_algspec1(B,A) ) ) )).

fof(t58_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m2_algspec1(B,A)
         => ! [C] :
              ( m4_algspec1(C,B)
             => m4_algspec1(C,A) ) ) ) )).

fof(t59_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( l3_msualg_1(C,B)
             => ( m4_algspec1(C,A)
               => ( r1_tarski(u1_struct_0(A),u1_struct_0(B))
                  & r1_tarski(u1_msualg_1(A),u1_msualg_1(B)) ) ) ) ) ) )).

fof(t60_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( l3_msualg_1(C,B)
             => ( m4_algspec1(C,A)
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ( v1_funct_1(k1_funct_1(u5_msualg_1(B,C),D))
                      & v1_funct_2(k1_funct_1(u5_msualg_1(B,C),D),k1_funct_1(k6_pboole(u1_struct_0(B),u4_msualg_1(B,C)),k1_msualg_1(A,D)),k1_funct_1(u4_msualg_1(B,C),k2_msualg_1(A,D)))
                      & m2_relset_1(k1_funct_1(u5_msualg_1(B,C),D),k1_funct_1(k6_pboole(u1_struct_0(B),u4_msualg_1(B,C)),k1_msualg_1(A,D)),k1_funct_1(u4_msualg_1(B,C),k2_msualg_1(A,D))) ) ) ) ) ) ) )).

fof(t61_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m4_algspec1(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_msualg_1(C) )
             => ( l3_msualg_1(B,C)
               => l3_msualg_1(B,k3_circcomb(C,A)) ) ) ) ) )).

fof(t62_algspec1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ( l3_msualg_1(C,B)
               => ( u1_struct_0(A) = u1_struct_0(B)
                  & u1_msualg_1(A) = u1_msualg_1(B) ) ) ) ) ) )).

fof(t63_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v1_msafree1(B,A)
            & l3_msualg_1(B,A) )
         => v2_funct_1(u4_msualg_1(A,B)) ) ) )).

fof(t64_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_msafree1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,k2_relat_1(u4_msualg_1(A,B)))
                 => ( C = D
                    | r1_xboole_0(C,D) ) ) ) ) ) )).

fof(t65_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v1_msafree1(C,A)
                & l3_msualg_1(C,A) )
             => ( l3_msualg_1(C,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(t66_algspec1,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v1_msafree1(C,A)
                & l3_msualg_1(C,A) )
             => ( m4_algspec1(C,B)
               => m2_algspec1(A,B) ) ) ) ) )).

fof(dt_m1_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( m1_algspec1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) )).

fof(existence_m1_algspec1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ? [B] : m1_algspec1(B,A) ) )).

fof(dt_m2_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m2_algspec1(B,A)
         => ( v1_instalg1(B)
            & l1_msualg_1(B) ) ) ) )).

fof(existence_m2_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ? [B] : m2_algspec1(B,A) ) )).

fof(dt_m3_algspec1,axiom,(
    $true )).

fof(existence_m3_algspec1,axiom,(
    ? [A] : m3_algspec1(A) )).

fof(dt_m4_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m4_algspec1(B,A)
         => m3_algspec1(B) ) ) )).

fof(existence_m4_algspec1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ? [B] : m4_algspec1(B,A) ) )).

fof(dt_k1_algspec1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => m1_pboole(k1_algspec1(A,B),A) ) )).

fof(dt_k2_algspec1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ~ v3_struct_0(k2_algspec1(A,B,C))
        & v1_msualg_1(k2_algspec1(A,B,C))
        & ~ v2_msualg_1(k2_algspec1(A,B,C))
        & l1_msualg_1(k2_algspec1(A,B,C)) ) ) )).
%------------------------------------------------------------------------------