SET007 Axioms: SET007+103.ax


%------------------------------------------------------------------------------
% File     : SET007+103 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Partial Functions from a Domain to the Set of Real Numbers
% 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    : rfunct_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  132 (  23 unit)
%            Number of atoms       :  836 ( 100 equality)
%            Maximal formula depth :   14 (   7 average)
%            Number of connectives :  738 (  34 ~  ;   0  |; 410  &)
%                                         (  16 <=>; 278 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   20 (   1 propositional; 0-4 arity)
%            Number of functors    :   42 (   4 constant; 0-4 arity)
%            Number of variables   :  302 (   0 singleton; 299 !;   3 ?)
%            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_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( v1_relat_1(k1_rfunct_1(A,B))
        & v1_funct_1(k1_rfunct_1(A,B))
        & v1_seq_1(k1_rfunct_1(A,B)) ) ) )).

fof(fc2_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k3_rfunct_1(A))
        & v1_funct_1(k3_rfunct_1(A))
        & v1_seq_1(k3_rfunct_1(A)) ) ) )).

fof(d1_rfunct_1,axiom,(
    $true )).

fof(d2_rfunct_1,axiom,(
    $true )).

fof(d3_rfunct_1,axiom,(
    $true )).

fof(d4_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_rfunct_1(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k4_xboole_0(k1_relat_1(B),k10_relat_1(B,k1_tarski(np__0))))
                  & ! [D] :
                      ( r2_hidden(D,k1_relat_1(C))
                     => k1_funct_1(C,D) = k4_real_1(k1_seq_1(A,D),k2_real_1(k1_seq_1(B,D))) ) ) ) ) ) ) )).

fof(d5_rfunct_1,axiom,(
    $true )).

fof(d6_rfunct_1,axiom,(
    $true )).

fof(d7_rfunct_1,axiom,(
    $true )).

fof(d8_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k3_rfunct_1(A)
          <=> ( k1_relat_1(B) = k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(np__0)))
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(B))
                 => k1_funct_1(B,C) = k2_real_1(k1_seq_1(A,C)) ) ) ) ) ) )).

fof(t1_rfunct_1,axiom,(
    $true )).

fof(t2_rfunct_1,axiom,(
    $true )).

fof(t3_rfunct_1,axiom,(
    $true )).

fof(t4_rfunct_1,axiom,(
    $true )).

fof(t5_rfunct_1,axiom,(
    $true )).

fof(t6_rfunct_1,axiom,(
    $true )).

fof(t7_rfunct_1,axiom,(
    $true )).

fof(t8_rfunct_1,axiom,(
    $true )).

fof(t9_rfunct_1,axiom,(
    $true )).

fof(t10_rfunct_1,axiom,(
    $true )).

fof(t11_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( r1_tarski(k1_relat_1(k3_rfunct_1(A)),k1_relat_1(A))
        & k3_xboole_0(k1_relat_1(A),k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(np__0)))) = k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(np__0))) ) ) )).

fof(t12_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k4_xboole_0(k1_relat_1(k5_seq_1(A,B)),k10_relat_1(k5_seq_1(A,B),k1_tarski(np__0))) = k3_xboole_0(k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(np__0))),k4_xboole_0(k1_relat_1(B),k10_relat_1(B,k1_tarski(np__0)))) ) ) )).

fof(t13_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => ~ ( r2_hidden(B,k1_relat_1(k3_rfunct_1(C)))
                  & k1_seq_1(C,B) = np__0 ) ) ) ) )).

fof(t14_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => k10_relat_1(k3_rfunct_1(A),k1_tarski(np__0)) = k1_xboole_0 ) )).

fof(t15_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( k10_relat_1(k20_seq_1(A),k1_tarski(np__0)) = k10_relat_1(A,k1_tarski(np__0))
        & k10_relat_1(k15_seq_1(A),k1_tarski(np__0)) = k10_relat_1(A,k1_tarski(np__0)) ) ) )).

fof(t16_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => k1_relat_1(k3_rfunct_1(k3_rfunct_1(A))) = k1_relat_1(k7_relat_1(A,k1_relat_1(k3_rfunct_1(A)))) ) )).

fof(t17_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( B != np__0
           => k10_relat_1(k12_seq_1(A,B),k1_tarski(np__0)) = k10_relat_1(A,k1_tarski(np__0)) ) ) ) )).

fof(t18_rfunct_1,axiom,(
    $true )).

fof(t19_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k3_seq_1(k3_seq_1(A,B),C) = k3_seq_1(A,k3_seq_1(B,C)) ) ) ) )).

fof(t20_rfunct_1,axiom,(
    $true )).

fof(t21_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k5_seq_1(k5_seq_1(A,B),C) = k5_seq_1(A,k5_seq_1(B,C)) ) ) ) )).

fof(t22_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k5_seq_1(k3_seq_1(A,B),C) = k3_seq_1(k5_seq_1(A,C),k5_seq_1(B,C)) ) ) ) )).

fof(t23_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k5_seq_1(A,k3_seq_1(B,C)) = k3_seq_1(k5_seq_1(A,B),k5_seq_1(A,C)) ) ) ) )).

fof(t24_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( v1_xreal_0(C)
             => k12_seq_1(k5_seq_1(A,B),C) = k5_seq_1(k12_seq_1(A,C),B) ) ) ) )).

fof(t25_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( v1_xreal_0(C)
             => k12_seq_1(k5_seq_1(A,B),C) = k5_seq_1(A,k12_seq_1(B,C)) ) ) ) )).

fof(t26_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k5_seq_1(k4_seq_1(A,B),C) = k4_seq_1(k5_seq_1(A,C),k5_seq_1(B,C)) ) ) ) )).

fof(t27_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k4_seq_1(k5_seq_1(A,B),k5_seq_1(A,C)) = k5_seq_1(A,k4_seq_1(B,C)) ) ) ) )).

fof(t28_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( v1_xreal_0(C)
             => k12_seq_1(k3_seq_1(A,B),C) = k3_seq_1(k12_seq_1(A,C),k12_seq_1(B,C)) ) ) ) )).

fof(t29_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k12_seq_1(A,k3_xcmplx_0(B,C)) = k12_seq_1(k12_seq_1(A,C),B) ) ) ) )).

fof(t30_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( v1_xreal_0(C)
             => k12_seq_1(k4_seq_1(A,B),C) = k4_seq_1(k12_seq_1(A,C),k12_seq_1(B,C)) ) ) ) )).

fof(t31_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k4_seq_1(A,B) = k12_seq_1(k4_seq_1(B,A),k1_real_1(np__1)) ) ) )).

fof(t32_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k4_seq_1(A,k3_seq_1(B,C)) = k4_seq_1(k4_seq_1(A,B),C) ) ) ) )).

fof(t33_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => k12_seq_1(A,np__1) = A ) )).

fof(t34_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k4_seq_1(A,k4_seq_1(B,C)) = k3_seq_1(k4_seq_1(A,B),C) ) ) ) )).

fof(t35_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k3_seq_1(A,k4_seq_1(B,C)) = k4_seq_1(k3_seq_1(A,B),C) ) ) ) )).

fof(t36_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k20_seq_1(k5_seq_1(A,B)) = k5_seq_1(k20_seq_1(A),k20_seq_1(B)) ) ) )).

fof(t37_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( v1_xreal_0(B)
         => k20_seq_1(k12_seq_1(A,B)) = k12_seq_1(k20_seq_1(A),k18_complex1(B)) ) ) )).

fof(t38_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => k15_seq_1(A) = k12_seq_1(A,k1_real_1(np__1)) ) )).

fof(t39_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => k15_seq_1(k15_seq_1(A)) = A ) )).

fof(t40_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k4_seq_1(A,B) = k3_seq_1(A,k15_seq_1(B)) ) ) )).

fof(t41_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k4_seq_1(A,k15_seq_1(B)) = k3_seq_1(A,B) ) ) )).

fof(t42_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => k3_rfunct_1(k3_rfunct_1(A)) = k7_relat_1(A,k1_relat_1(k3_rfunct_1(A))) ) )).

fof(t43_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k3_rfunct_1(k5_seq_1(A,B)) = k5_seq_1(k3_rfunct_1(A),k3_rfunct_1(B)) ) ) )).

fof(t44_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( B != np__0
           => k3_rfunct_1(k12_seq_1(A,B)) = k12_seq_1(k3_rfunct_1(A),k5_xcmplx_0(B)) ) ) ) )).

fof(t45_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => k3_rfunct_1(k15_seq_1(A)) = k12_seq_1(k3_rfunct_1(A),k1_real_1(np__1)) ) )).

fof(t46_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => k3_rfunct_1(k20_seq_1(A)) = k20_seq_1(k3_rfunct_1(A)) ) )).

fof(t47_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k1_rfunct_1(A,B) = k5_seq_1(A,k3_rfunct_1(B)) ) ) )).

fof(t48_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( v1_xreal_0(C)
             => k12_seq_1(k1_rfunct_1(A,B),C) = k1_rfunct_1(k12_seq_1(A,C),B) ) ) ) )).

fof(t49_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k5_seq_1(k1_rfunct_1(A,B),B) = k7_relat_1(A,k1_relat_1(k3_rfunct_1(B))) ) ) )).

fof(t50_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_seq_1(D) )
                 => k5_seq_1(k1_rfunct_1(A,B),k1_rfunct_1(C,D)) = k1_rfunct_1(k5_seq_1(A,C),k5_seq_1(B,D)) ) ) ) ) )).

fof(t51_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k3_rfunct_1(k1_rfunct_1(A,B)) = k1_rfunct_1(k7_relat_1(B,k1_relat_1(k3_rfunct_1(B))),A) ) ) )).

fof(t52_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k5_seq_1(A,k1_rfunct_1(B,C)) = k1_rfunct_1(k5_seq_1(A,B),C) ) ) ) )).

fof(t53_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => k1_rfunct_1(A,k1_rfunct_1(B,C)) = k1_rfunct_1(k5_seq_1(A,k7_relat_1(C,k1_relat_1(k3_rfunct_1(C)))),B) ) ) ) )).

fof(t54_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ( k15_seq_1(k1_rfunct_1(A,B)) = k1_rfunct_1(k15_seq_1(A),B)
            & k1_rfunct_1(A,k15_seq_1(B)) = k15_seq_1(k1_rfunct_1(A,B)) ) ) ) )).

fof(t55_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => ( k3_seq_1(k1_rfunct_1(A,B),k1_rfunct_1(C,B)) = k1_rfunct_1(k3_seq_1(A,C),B)
                & k4_seq_1(k1_rfunct_1(A,B),k1_rfunct_1(C,B)) = k1_rfunct_1(k4_seq_1(A,C),B) ) ) ) ) )).

fof(t56_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_seq_1(D) )
                 => k3_seq_1(k1_rfunct_1(A,B),k1_rfunct_1(C,D)) = k1_rfunct_1(k3_seq_1(k5_seq_1(A,D),k5_seq_1(C,B)),k5_seq_1(B,D)) ) ) ) ) )).

fof(t57_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_seq_1(D) )
                 => k1_rfunct_1(k1_rfunct_1(A,B),k1_rfunct_1(C,D)) = k1_rfunct_1(k5_seq_1(A,k7_relat_1(D,k1_relat_1(k3_rfunct_1(D)))),k5_seq_1(B,C)) ) ) ) ) )).

fof(t58_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_seq_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_seq_1(D) )
                 => k4_seq_1(k1_rfunct_1(A,B),k1_rfunct_1(C,D)) = k1_rfunct_1(k4_seq_1(k5_seq_1(A,D),k5_seq_1(C,B)),k5_seq_1(B,D)) ) ) ) ) )).

fof(t59_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_seq_1(B) )
         => k20_seq_1(k1_rfunct_1(A,B)) = k1_rfunct_1(k20_seq_1(A),k20_seq_1(B)) ) ) )).

fof(t60_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( k7_relat_1(k3_seq_1(B,C),A) = k3_seq_1(k7_relat_1(B,A),k7_relat_1(C,A))
            & k7_relat_1(k3_seq_1(B,C),A) = k3_seq_1(k7_relat_1(B,A),C)
            & k7_relat_1(k3_seq_1(B,C),A) = k3_seq_1(B,k7_relat_1(C,A)) ) ) ) )).

fof(t61_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( k7_relat_1(k5_seq_1(B,C),A) = k5_seq_1(k7_relat_1(B,A),k7_relat_1(C,A))
            & k7_relat_1(k5_seq_1(B,C),A) = k5_seq_1(k7_relat_1(B,A),C)
            & k7_relat_1(k5_seq_1(B,C),A) = k5_seq_1(B,k7_relat_1(C,A)) ) ) ) )).

fof(t62_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( k7_relat_1(k15_seq_1(B),A) = k15_seq_1(k7_relat_1(B,A))
        & k7_relat_1(k3_rfunct_1(B),A) = k3_rfunct_1(k7_relat_1(B,A))
        & k7_relat_1(k20_seq_1(B),A) = k20_seq_1(k7_relat_1(B,A)) ) ) )).

fof(t63_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( k7_relat_1(k4_seq_1(B,C),A) = k4_seq_1(k7_relat_1(B,A),k7_relat_1(C,A))
            & k7_relat_1(k4_seq_1(B,C),A) = k4_seq_1(k7_relat_1(B,A),C)
            & k7_relat_1(k4_seq_1(B,C),A) = k4_seq_1(B,k7_relat_1(C,A)) ) ) ) )).

fof(t64_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( k7_relat_1(k1_rfunct_1(B,C),A) = k1_rfunct_1(k7_relat_1(B,A),k7_relat_1(C,A))
            & k7_relat_1(k1_rfunct_1(B,C),A) = k1_rfunct_1(k7_relat_1(B,A),C)
            & k7_relat_1(k1_rfunct_1(B,C),A) = k1_rfunct_1(B,k7_relat_1(C,A)) ) ) ) )).

fof(t65_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ! [C] :
          ( v1_xreal_0(C)
         => k7_relat_1(k12_seq_1(B,C),A) = k12_seq_1(k7_relat_1(B,A),C) ) ) )).

fof(t66_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ( ( ( v1_partfun1(B,A,k1_numbers)
                    & v1_partfun1(C,A,k1_numbers) )
                 => v1_partfun1(k6_seq_1(A,k1_numbers,B,C),A,k1_numbers) )
                & ( v1_partfun1(k6_seq_1(A,k1_numbers,B,C),A,k1_numbers)
                 => ( v1_partfun1(B,A,k1_numbers)
                    & v1_partfun1(C,A,k1_numbers) ) )
                & ( ( v1_partfun1(B,A,k1_numbers)
                    & v1_partfun1(C,A,k1_numbers) )
                 => v1_partfun1(k7_seq_1(A,k1_numbers,B,C),A,k1_numbers) )
                & ( v1_partfun1(k7_seq_1(A,k1_numbers,B,C),A,k1_numbers)
                 => ( v1_partfun1(B,A,k1_numbers)
                    & v1_partfun1(C,A,k1_numbers) ) )
                & ( ( v1_partfun1(B,A,k1_numbers)
                    & v1_partfun1(C,A,k1_numbers) )
                 => v1_partfun1(k8_seq_1(A,k1_numbers,B,C),A,k1_numbers) )
                & ( v1_partfun1(k8_seq_1(A,k1_numbers,B,C),A,k1_numbers)
                 => ( v1_partfun1(B,A,k1_numbers)
                    & v1_partfun1(C,A,k1_numbers) ) ) ) ) ) ) )).

fof(t67_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ( v1_partfun1(C,A,k1_numbers)
              <=> v1_partfun1(k13_seq_1(A,k1_numbers,C,B),A,k1_numbers) ) ) ) ) )).

fof(t68_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( v1_partfun1(B,A,k1_numbers)
          <=> v1_partfun1(k16_seq_1(A,k1_numbers,B),A,k1_numbers) ) ) ) )).

fof(t69_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( v1_partfun1(B,A,k1_numbers)
          <=> v1_partfun1(k21_seq_1(A,k1_numbers,B),A,k1_numbers) ) ) ) )).

fof(t70_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( v1_partfun1(k4_rfunct_1(A,k1_numbers,B),A,k1_numbers)
          <=> ( k11_relset_1(A,k1_numbers,B,k1_tarski(np__0)) = k1_xboole_0
              & v1_partfun1(B,A,k1_numbers) ) ) ) ) )).

fof(t71_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ( ( v1_partfun1(B,A,k1_numbers)
                  & k11_relset_1(A,k1_numbers,C,k1_tarski(np__0)) = k1_xboole_0
                  & v1_partfun1(C,A,k1_numbers) )
              <=> v1_partfun1(k2_rfunct_1(A,k1_numbers,B,C),A,k1_numbers) ) ) ) ) )).

fof(t72_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => ( ( v1_partfun1(C,A,k1_numbers)
                      & v1_partfun1(D,A,k1_numbers) )
                   => ( k2_seq_1(A,k1_numbers,k6_seq_1(A,k1_numbers,C,D),B) = k3_real_1(k2_seq_1(A,k1_numbers,C,B),k2_seq_1(A,k1_numbers,D,B))
                      & k2_seq_1(A,k1_numbers,k7_seq_1(A,k1_numbers,C,D),B) = k5_real_1(k2_seq_1(A,k1_numbers,C,B),k2_seq_1(A,k1_numbers,D,B))
                      & k2_seq_1(A,k1_numbers,k8_seq_1(A,k1_numbers,C,D),B) = k4_real_1(k2_seq_1(A,k1_numbers,C,B),k2_seq_1(A,k1_numbers,D,B)) ) ) ) ) ) ) )).

fof(t73_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => ( v1_partfun1(D,A,k1_numbers)
                   => k2_seq_1(A,k1_numbers,k13_seq_1(A,k1_numbers,D,C),B) = k3_xcmplx_0(C,k2_seq_1(A,k1_numbers,D,B)) ) ) ) ) ) )).

fof(t74_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ( v1_partfun1(C,A,k1_numbers)
               => ( k2_seq_1(A,k1_numbers,k16_seq_1(A,k1_numbers,C),B) = k1_real_1(k2_seq_1(A,k1_numbers,C,B))
                  & k2_seq_1(A,k1_numbers,k21_seq_1(A,k1_numbers,C),B) = k18_complex1(k2_seq_1(A,k1_numbers,C,B)) ) ) ) ) ) )).

fof(t75_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ( v1_partfun1(k4_rfunct_1(A,k1_numbers,C),A,k1_numbers)
               => k2_seq_1(A,k1_numbers,k4_rfunct_1(A,k1_numbers,C),B) = k2_real_1(k2_seq_1(A,k1_numbers,C,B)) ) ) ) ) )).

fof(t76_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => ( ( v1_partfun1(C,A,k1_numbers)
                      & v1_partfun1(k4_rfunct_1(A,k1_numbers,D),A,k1_numbers) )
                   => k2_seq_1(A,k1_numbers,k2_rfunct_1(A,k1_numbers,C,D),B) = k4_real_1(k2_seq_1(A,k1_numbers,C,B),k2_real_1(k2_seq_1(A,k1_numbers,D,B))) ) ) ) ) ) )).

fof(t77_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k1_numbers) )
         => ( C = k5_rfunct_1(A,B)
          <=> ( k4_relset_1(B,k1_numbers,C) = B
              & ! [D] :
                  ( m1_subset_1(D,B)
                 => ( ( r2_hidden(D,A)
                     => k2_seq_1(B,k1_numbers,C,D) = np__1 )
                    & ( ~ r2_hidden(D,A)
                     => k2_seq_1(B,k1_numbers,C,D) = np__0 ) ) ) ) ) ) ) )).

fof(t78_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => v1_partfun1(k5_rfunct_1(A,B),B,k1_numbers) ) )).

fof(t79_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,B)
         => ( r2_hidden(C,A)
          <=> k2_seq_1(B,k1_numbers,k5_rfunct_1(A,B),C) = np__1 ) ) ) )).

fof(t80_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,B)
         => ( ~ r2_hidden(C,A)
          <=> k2_seq_1(B,k1_numbers,k5_rfunct_1(A,B),C) = np__0 ) ) ) )).

fof(t81_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,B)
         => ( r2_hidden(C,k4_xboole_0(B,A))
          <=> k2_seq_1(B,k1_numbers,k5_rfunct_1(A,B),C) = np__0 ) ) ) )).

fof(t82_rfunct_1,axiom,(
    $true )).

fof(t83_rfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => k2_seq_1(A,k1_numbers,k5_rfunct_1(A,A),B) = np__1 ) ) )).

fof(t84_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,B)
         => ( k2_seq_1(B,k1_numbers,k5_rfunct_1(A,B),C) != np__1
          <=> k2_seq_1(B,k1_numbers,k5_rfunct_1(A,B),C) = np__0 ) ) ) )).

fof(t85_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ( r1_xboole_0(A,B)
       => k6_seq_1(C,k1_numbers,k5_rfunct_1(A,C),k5_rfunct_1(B,C)) = k5_rfunct_1(k2_xboole_0(A,B),C) ) ) )).

fof(t86_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => k8_seq_1(C,k1_numbers,k5_rfunct_1(A,C),k5_rfunct_1(B,C)) = k5_rfunct_1(k3_xboole_0(A,B),C) ) )).

fof(d9_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( r1_rfunct_1(A,B)
        <=> ? [C] :
              ( v1_xreal_0(C)
              & ! [D] :
                  ( r2_hidden(D,k3_xboole_0(B,k1_relat_1(A)))
                 => r1_xreal_0(k1_seq_1(A,D),C) ) ) ) ) )).

fof(d10_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( r2_rfunct_1(A,B)
        <=> ? [C] :
              ( v1_xreal_0(C)
              & ! [D] :
                  ( r2_hidden(D,k3_xboole_0(B,k1_relat_1(A)))
                 => r1_xreal_0(C,k1_seq_1(A,D)) ) ) ) ) )).

fof(d11_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] :
          ( r3_rfunct_1(A,B)
        <=> ( r1_rfunct_1(A,B)
            & r2_rfunct_1(A,B) ) ) ) )).

fof(t87_rfunct_1,axiom,(
    $true )).

fof(t88_rfunct_1,axiom,(
    $true )).

fof(t89_rfunct_1,axiom,(
    $true )).

fof(t90_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( r3_rfunct_1(B,A)
      <=> ? [C] :
            ( v1_xreal_0(C)
            & ! [D] :
                ( r2_hidden(D,k3_xboole_0(A,k1_relat_1(B)))
               => r1_xreal_0(k18_complex1(k1_seq_1(B,D)),C) ) ) ) ) )).

fof(t91_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ( ( ( r1_tarski(A,B)
            & r1_rfunct_1(C,B) )
         => r1_rfunct_1(C,A) )
        & ( ( r1_tarski(A,B)
            & r2_rfunct_1(C,B) )
         => r2_rfunct_1(C,A) )
        & ( ( r1_tarski(A,B)
            & r3_rfunct_1(C,B) )
         => r3_rfunct_1(C,A) ) ) ) )).

fof(t92_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ( ( r1_rfunct_1(C,A)
          & r2_rfunct_1(C,B) )
       => r3_rfunct_1(C,k3_xboole_0(A,B)) ) ) )).

fof(t93_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( r1_xboole_0(A,k1_relat_1(B))
       => r3_rfunct_1(B,A) ) ) )).

fof(t94_rfunct_1,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( np__0 = B
           => r3_rfunct_1(k12_seq_1(C,B),A) ) ) ) )).

fof(t95_rfunct_1,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( ( ( r1_rfunct_1(C,A)
                & r1_xreal_0(np__0,B) )
             => r1_rfunct_1(k12_seq_1(C,B),A) )
            & ( ( r1_rfunct_1(C,A)
                & r1_xreal_0(B,np__0) )
             => r2_rfunct_1(k12_seq_1(C,B),A) ) ) ) ) )).

fof(t96_rfunct_1,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( ( ( r2_rfunct_1(C,A)
                & r1_xreal_0(np__0,B) )
             => r2_rfunct_1(k12_seq_1(C,B),A) )
            & ( ( r2_rfunct_1(C,A)
                & r1_xreal_0(B,np__0) )
             => r1_rfunct_1(k12_seq_1(C,B),A) ) ) ) ) )).

fof(t97_rfunct_1,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_seq_1(C) )
         => ( r3_rfunct_1(C,A)
           => r3_rfunct_1(k12_seq_1(C,B),A) ) ) ) )).

fof(t98_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => r2_rfunct_1(k20_seq_1(B),A) ) )).

fof(t99_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( r3_rfunct_1(B,A)
       => ( r3_rfunct_1(k20_seq_1(B),A)
          & r3_rfunct_1(k15_seq_1(B),A) ) ) ) )).

fof(t100_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_seq_1(D) )
         => ( ( ( r1_rfunct_1(C,A)
                & r1_rfunct_1(D,B) )
             => r1_rfunct_1(k3_seq_1(C,D),k3_xboole_0(A,B)) )
            & ( ( r2_rfunct_1(C,A)
                & r2_rfunct_1(D,B) )
             => r2_rfunct_1(k3_seq_1(C,D),k3_xboole_0(A,B)) )
            & ( ( r3_rfunct_1(C,A)
                & r3_rfunct_1(D,B) )
             => r3_rfunct_1(k3_seq_1(C,D),k3_xboole_0(A,B)) ) ) ) ) )).

fof(t101_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_seq_1(D) )
         => ( ( r3_rfunct_1(C,A)
              & r3_rfunct_1(D,B) )
           => ( r3_rfunct_1(k5_seq_1(C,D),k3_xboole_0(A,B))
              & r3_rfunct_1(k4_seq_1(C,D),k3_xboole_0(A,B)) ) ) ) ) )).

fof(t102_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ( ( r1_rfunct_1(C,A)
          & r1_rfunct_1(C,B) )
       => r1_rfunct_1(C,k2_xboole_0(A,B)) ) ) )).

fof(t103_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ( ( r2_rfunct_1(C,A)
          & r2_rfunct_1(C,B) )
       => r2_rfunct_1(C,k2_xboole_0(A,B)) ) ) )).

fof(t104_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_seq_1(C) )
     => ( ( r3_rfunct_1(C,A)
          & r3_rfunct_1(C,B) )
       => r3_rfunct_1(C,k2_xboole_0(A,B)) ) ) )).

fof(t105_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k1_numbers) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,k1_numbers) )
             => ( ( r1_partfun2(C,k1_numbers,D,A)
                  & r1_partfun2(C,k1_numbers,E,B) )
               => ( r1_partfun2(C,k1_numbers,k6_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B))
                  & r1_partfun2(C,k1_numbers,k7_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B))
                  & r1_partfun2(C,k1_numbers,k8_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(t106_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( v1_xreal_0(C)
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,B,k1_numbers) )
             => ( r1_partfun2(B,k1_numbers,D,A)
               => r1_partfun2(B,k1_numbers,k13_seq_1(B,k1_numbers,D,C),A) ) ) ) ) )).

fof(t107_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k1_numbers) )
         => ( r1_partfun2(B,k1_numbers,C,A)
           => ( r1_partfun2(B,k1_numbers,k21_seq_1(B,k1_numbers,C),A)
              & r1_partfun2(B,k1_numbers,k16_seq_1(B,k1_numbers,C),A) ) ) ) ) )).

fof(t108_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k1_numbers) )
         => ( r1_partfun2(B,k1_numbers,C,A)
           => r3_rfunct_1(C,A) ) ) ) )).

fof(t109_rfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k1_numbers) )
         => ( r1_partfun2(B,k1_numbers,C,A)
           => ( ! [D] :
                  ( v1_xreal_0(D)
                 => r3_rfunct_1(k13_seq_1(B,k1_numbers,C,D),A) )
              & r3_rfunct_1(k16_seq_1(B,k1_numbers,C),A)
              & r3_rfunct_1(k21_seq_1(B,k1_numbers,C),A) ) ) ) ) )).

fof(t110_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k1_numbers) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,k1_numbers) )
             => ( ( ( r1_rfunct_1(D,A)
                    & r1_partfun2(C,k1_numbers,E,B) )
                 => r1_rfunct_1(k6_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B)) )
                & ( ( r2_rfunct_1(D,A)
                    & r1_partfun2(C,k1_numbers,E,B) )
                 => r2_rfunct_1(k6_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B)) )
                & ( ( r3_rfunct_1(D,A)
                    & r1_partfun2(C,k1_numbers,E,B) )
                 => r3_rfunct_1(k6_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(t111_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k1_numbers) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,k1_numbers) )
             => ( ( ( r1_rfunct_1(D,A)
                    & r1_partfun2(C,k1_numbers,E,B) )
                 => r1_rfunct_1(k7_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B)) )
                & ( ( r2_rfunct_1(D,A)
                    & r1_partfun2(C,k1_numbers,E,B) )
                 => r2_rfunct_1(k7_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B)) )
                & ( ( r3_rfunct_1(D,A)
                    & r1_partfun2(C,k1_numbers,E,B) )
                 => ( r3_rfunct_1(k7_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B))
                    & r3_rfunct_1(k7_seq_1(C,k1_numbers,E,D),k3_xboole_0(A,B))
                    & r3_rfunct_1(k8_seq_1(C,k1_numbers,D,E),k3_xboole_0(A,B)) ) ) ) ) ) ) )).

fof(dt_k1_rfunct_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( v1_relat_1(k1_rfunct_1(A,B))
        & v1_funct_1(k1_rfunct_1(A,B)) ) ) )).

fof(dt_k2_rfunct_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B)
        & v1_funct_1(D)
        & m1_relset_1(D,A,B) )
     => ( v1_funct_1(k2_rfunct_1(A,B,C,D))
        & m2_relset_1(k2_rfunct_1(A,B,C,D),A,k1_numbers) ) ) )).

fof(redefinition_k2_rfunct_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B)
        & v1_funct_1(D)
        & m1_relset_1(D,A,B) )
     => k2_rfunct_1(A,B,C,D) = k1_rfunct_1(C,D) ) )).

fof(dt_k3_rfunct_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k3_rfunct_1(A))
        & v1_funct_1(k3_rfunct_1(A)) ) ) )).

fof(dt_k4_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k4_rfunct_1(A,B,C))
        & m2_relset_1(k4_rfunct_1(A,B,C),A,k1_numbers) ) ) )).

fof(redefinition_k4_rfunct_1,axiom,(
    ! [A,B,C] :
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k4_rfunct_1(A,B,C) = k3_rfunct_1(C) ) )).

fof(dt_k5_rfunct_1,axiom,(
    ! [A,B] :
      ( v1_funct_1(k5_rfunct_1(A,B))
      & m2_relset_1(k5_rfunct_1(A,B),B,k1_numbers) ) )).

fof(redefinition_k5_rfunct_1,axiom,(
    ! [A,B] : k5_rfunct_1(A,B) = k4_funct_3(A,B) )).
%------------------------------------------------------------------------------