SET007 Axioms: SET007+124.ax


%------------------------------------------------------------------------------
% File     : SET007+124 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Quadratic Inequalities
% 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    : quin_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   35 (   3 unit)
%            Number of atoms       :  233 (  23 equality)
%            Maximal formula depth :   18 (  11 average)
%            Number of connectives :  271 (  73 ~  ;  11  |;  60  &)
%                                         (   2 <=>; 125 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    6 (   1 propositional; 0-2 arity)
%            Number of functors    :   13 (   4 constant; 0-3 arity)
%            Number of variables   :  121 (   0 singleton; 121 !;   0 ?)
%            Maximal term depth    :    8 (   2 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_quin_1,axiom,(
    ! [A,B,C] :
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => v1_xcmplx_0(k1_quin_1(A,B,C)) ) )).

fof(fc2_quin_1,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( v1_xcmplx_0(k1_quin_1(A,B,C))
        & v1_xreal_0(k1_quin_1(A,B,C)) ) ) )).

fof(d1_quin_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k1_quin_1(A,B,C) = k6_xcmplx_0(k5_square_1(B),k3_xcmplx_0(k3_xcmplx_0(np__4,A),C)) ) ) ) )).

fof(t1_quin_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( A != np__0
                   => k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C) = k6_xcmplx_0(k3_xcmplx_0(A,k5_square_1(k2_xcmplx_0(D,k7_xcmplx_0(B,k3_xcmplx_0(np__2,A))))),k7_xcmplx_0(k1_quin_1(A,B,C),k3_xcmplx_0(np__4,A))) ) ) ) ) ) )).

fof(t2_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(k1_quin_1(A,B,C),np__0)
                   => ( r1_xreal_0(A,np__0)
                      | r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C)) ) ) ) ) ) ) )).

fof(t3_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(A,np__0)
                      & ~ r1_xreal_0(np__0,k1_quin_1(A,B,C))
                      & r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C),np__0) ) ) ) ) ) )).

fof(t4_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(k1_quin_1(A,B,C),np__0)
                   => ( r1_xreal_0(np__0,A)
                      | r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C),np__0) ) ) ) ) ) ) )).

fof(t5_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(np__0,A)
                      & ~ r1_xreal_0(np__0,k1_quin_1(A,B,C))
                      & r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C)) ) ) ) ) ) )).

fof(t6_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(B)),k3_xcmplx_0(C,B)),D))
                   => ( r1_xreal_0(A,np__0)
                      | r1_xreal_0(np__0,k6_xcmplx_0(k5_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__2,A),B),C)),k1_quin_1(A,C,D))) ) ) ) ) ) ) )).

fof(t7_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(A,np__0)
                      & ~ r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(B)),k3_xcmplx_0(C,B)),D),np__0)
                      & r1_xreal_0(k6_xcmplx_0(k5_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__2,A),B),C)),k1_quin_1(A,C,D)),np__0) ) ) ) ) ) )).

fof(t8_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(B)),k3_xcmplx_0(C,B)),D),np__0)
                   => ( r1_xreal_0(np__0,A)
                      | r1_xreal_0(np__0,k6_xcmplx_0(k5_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__2,A),B),C)),k1_quin_1(A,C,D))) ) ) ) ) ) ) )).

fof(t9_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(np__0,A)
                      & ~ r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(B)),k3_xcmplx_0(C,B)),D))
                      & r1_xreal_0(k6_xcmplx_0(k5_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__2,A),B),C)),k1_quin_1(A,C,D)),np__0) ) ) ) ) ) )).

fof(t10_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ! [D] :
                    ( v1_xreal_0(D)
                   => r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C)) )
               => ( r1_xreal_0(A,np__0)
                  | r1_xreal_0(k1_quin_1(A,B,C),np__0) ) ) ) ) ) )).

fof(t11_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ! [D] :
                    ( v1_xreal_0(D)
                   => r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C),np__0) )
               => ( r1_xreal_0(np__0,A)
                  | r1_xreal_0(k1_quin_1(A,B,C),np__0) ) ) ) ) ) )).

fof(t12_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ! [D] :
                      ( v1_xreal_0(D)
                     => ~ r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C),np__0) )
                  & ~ r1_xreal_0(A,np__0)
                  & r1_xreal_0(np__0,k1_quin_1(A,B,C)) ) ) ) ) )).

fof(t13_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ! [D] :
                      ( v1_xreal_0(D)
                     => ~ r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C)) )
                  & ~ r1_xreal_0(np__0,A)
                  & r1_xreal_0(np__0,k1_quin_1(A,B,C)) ) ) ) ) )).

fof(t14_quin_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C) = np__0
                   => ( A = np__0
                      | k6_xcmplx_0(k5_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__2,A),D),B)),k1_quin_1(A,B,C)) = np__0 ) ) ) ) ) ) )).

fof(t15_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( A != np__0
                      & r1_xreal_0(np__0,k1_quin_1(A,B,C))
                      & k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C) = np__0
                      & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))
                      & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)) ) ) ) ) ) )).

fof(t16_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(np__0,k1_quin_1(A,B,C))
                   => ( A = np__0
                      | k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C) = k3_xcmplx_0(k3_xcmplx_0(A,k6_xcmplx_0(D,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)))),k6_xcmplx_0(D,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)))) ) ) ) ) ) ) )).

fof(t17_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(np__0,A)
                  & ~ r1_xreal_0(k1_quin_1(A,B,C),np__0)
                  & r1_xreal_0(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)),k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))) ) ) ) ) )).

fof(t18_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(np__0,A)
                      & ~ r1_xreal_0(k1_quin_1(A,B,C),np__0)
                      & ~ ( ~ r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C),np__0)
                        <=> ( ~ r1_xreal_0(D,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)))
                            & ~ r1_xreal_0(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)),D) ) ) ) ) ) ) ) )).

fof(t19_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(np__0,A)
                      & ~ r1_xreal_0(k1_quin_1(A,B,C),np__0)
                      & ~ ( ~ ( ~ r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C))
                              & r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)),D)
                              & r1_xreal_0(D,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))) )
                          & ~ ( ~ ( r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)),D)
                                  & r1_xreal_0(D,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))) )
                              & r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C)) ) ) ) ) ) ) ) )).

fof(t20_quin_1,axiom,(
    $true )).

fof(t21_quin_1,axiom,(
    $true )).

fof(t22_quin_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( ( k1_quin_1(A,B,C) = np__0
                      & k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C) = np__0 )
                   => ( A = np__0
                      | D = k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(np__2,A))) ) ) ) ) ) ) )).

fof(t23_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(A,np__0)
                      & ~ r1_xreal_0(k6_xcmplx_0(k5_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__2,A),B),C)),k1_quin_1(A,C,D)),np__0)
                      & r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(B)),k3_xcmplx_0(C,B)),D),np__0) ) ) ) ) ) )).

fof(t24_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( k1_quin_1(A,B,C) = np__0
                   => ( r1_xreal_0(A,np__0)
                      | ( ~ ( ~ r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C),np__0)
                            & D = k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(np__2,A))) )
                        & ~ ( D != k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(np__2,A)))
                            & r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C),np__0) ) ) ) ) ) ) ) ) )).

fof(t25_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(np__0,A)
                      & ~ r1_xreal_0(k6_xcmplx_0(k5_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__2,A),B),C)),k1_quin_1(A,C,D)),np__0)
                      & r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(B)),k3_xcmplx_0(C,B)),D)) ) ) ) ) ) )).

fof(t26_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( k1_quin_1(A,B,C) = np__0
                   => ( r1_xreal_0(np__0,A)
                      | ( ~ ( ~ r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C))
                            & D = k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(np__2,A))) )
                        & ~ ( D != k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(np__2,A)))
                            & r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C)) ) ) ) ) ) ) ) ) )).

fof(t27_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(A,np__0)
                  & ~ r1_xreal_0(k1_quin_1(A,B,C),np__0)
                  & r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)),k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))) ) ) ) ) )).

fof(t28_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(A,np__0)
                      & ~ r1_xreal_0(k1_quin_1(A,B,C),np__0)
                      & ~ ( ~ r1_xreal_0(np__0,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C))
                        <=> ( ~ r1_xreal_0(D,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)))
                            & ~ r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)),D) ) ) ) ) ) ) ) )).

fof(t29_quin_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(A,np__0)
                      & ~ r1_xreal_0(k1_quin_1(A,B,C),np__0)
                      & ~ ( ~ ( ~ r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C),np__0)
                              & r1_xreal_0(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)),D)
                              & r1_xreal_0(D,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))) )
                          & ~ ( ~ ( r1_xreal_0(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)),D)
                                  & r1_xreal_0(D,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))) )
                              & r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C),np__0) ) ) ) ) ) ) ) )).

fof(dt_k1_quin_1,axiom,(
    $true )).

fof(dt_k2_quin_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => m1_subset_1(k2_quin_1(A,B,C),k1_numbers) ) )).

fof(redefinition_k2_quin_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => k2_quin_1(A,B,C) = k1_quin_1(A,B,C) ) )).
%------------------------------------------------------------------------------