SET007 Axioms: SET007+129.ax


%------------------------------------------------------------------------------
% File     : SET007+129 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Logic Gates and Logical Equivalence of Adders
% 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    : gate_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  126 (  51 unit)
%            Number of atoms       :  956 (  75 equality)
%            Maximal formula depth :  120 (   9 average)
%            Number of connectives : 1552 ( 722 ~  ;   8  |; 769  &)
%                                         (  18 <=>;  35 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    3 (   1 propositional; 0-2 arity)
%            Number of functors    :   42 (   1 constant; 0-9 arity)
%            Number of variables   :  416 (   0 singleton; 416 !;   0 ?)
%            Maximal term depth    :    3 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_gate_1,axiom,(
    ! [A] :
      ~ ( A = k1_tarski(k1_xboole_0)
        & v1_xboole_0(A) ) )).

fof(t2_gate_1,axiom,(
    ~ ! [A] : v1_xboole_0(A) )).

fof(d1_gate_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
       => k1_gate_1(A) = k1_xboole_0 )
      & ( v1_xboole_0(A)
       => k1_gate_1(A) = k1_tarski(k1_xboole_0) ) ) )).

fof(t3_gate_1,axiom,(
    $true )).

fof(t4_gate_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k1_gate_1(A))
    <=> v1_xboole_0(A) ) )).

fof(t5_gate_1,axiom,(
    ~ v1_xboole_0(k1_gate_1(k1_xboole_0)) )).

fof(d2_gate_1,axiom,(
    ! [A,B] :
      ( ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & k2_gate_1(A,B) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B) )
       => k2_gate_1(A,B) = k1_xboole_0 ) ) )).

fof(t6_gate_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(k2_gate_1(A,B))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) ) ) )).

fof(d3_gate_1,axiom,(
    ! [A,B] :
      ( ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B) )
       => k3_gate_1(A,B) = k1_gate_1(k1_xboole_0) )
      & ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & k3_gate_1(A,B) != k1_xboole_0 ) ) )).

fof(t7_gate_1,axiom,(
    ! [A,B] :
      ( ~ ( ~ v1_xboole_0(k3_gate_1(A,B))
          & v1_xboole_0(A)
          & v1_xboole_0(B) )
      & ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B) )
          & v1_xboole_0(k3_gate_1(A,B)) ) ) )).

fof(d4_gate_1,axiom,(
    ! [A,B] :
      ( ( ( ( ~ v1_xboole_0(A)
            & v1_xboole_0(B) )
          | ( v1_xboole_0(A)
            & ~ v1_xboole_0(B) ) )
       => k4_gate_1(A,B) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
          & ~ ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) )
          & k4_gate_1(A,B) != k1_xboole_0 ) ) )).

fof(t8_gate_1,axiom,(
    ! [A,B] :
      ( ~ ( ~ v1_xboole_0(k4_gate_1(A,B))
          & ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
          & ~ ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) ) )
      & ~ ( ( ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
            | ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) ) )
          & v1_xboole_0(k4_gate_1(A,B)) ) ) )).

fof(t9_gate_1,axiom,(
    ! [A] :
      ( v1_xboole_0(k4_gate_1(A,A))
      & ~ ( ~ $true
          & v1_xboole_0(k4_gate_1(A,A)) ) ) )).

fof(t10_gate_1,axiom,(
    ! [A] :
      ( ~ ( ~ v1_xboole_0(k4_gate_1(A,k1_xboole_0))
          & v1_xboole_0(A) )
      & ~ ( ~ v1_xboole_0(A)
          & v1_xboole_0(k4_gate_1(A,k1_xboole_0)) ) ) )).

fof(t11_gate_1,axiom,(
    ! [A,B] :
      ( ~ ( ~ v1_xboole_0(k4_gate_1(A,B))
          & v1_xboole_0(k4_gate_1(B,A)) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(B,A))
          & v1_xboole_0(k4_gate_1(A,B)) ) ) )).

fof(d5_gate_1,axiom,(
    ! [A,B] :
      ( ~ ( ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
          & ~ ( ~ v1_xboole_0(B)
              & v1_xboole_0(A) )
          & k5_gate_1(A,B) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ ( ~ v1_xboole_0(A)
                & v1_xboole_0(B) )
            & ~ ( ~ v1_xboole_0(B)
                & v1_xboole_0(A) ) )
       => k5_gate_1(A,B) = k1_xboole_0 ) ) )).

fof(t12_gate_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(k5_gate_1(A,B))
    <=> ( ~ ( ~ v1_xboole_0(A)
            & v1_xboole_0(B) )
        & ~ ( ~ v1_xboole_0(B)
            & v1_xboole_0(A) ) ) ) )).

fof(t13_gate_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(k5_gate_1(A,B))
    <=> v1_xboole_0(k4_gate_1(A,B)) ) )).

fof(d6_gate_1,axiom,(
    ! [A,B] :
      ( ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B) )
       => k6_gate_1(A,B) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & k6_gate_1(A,B) != k1_xboole_0 ) ) )).

fof(t14_gate_1,axiom,(
    ! [A,B] :
      ( ~ ( ~ v1_xboole_0(k6_gate_1(A,B))
          & ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B) )
          & v1_xboole_0(k6_gate_1(A,B)) ) ) )).

fof(d7_gate_1,axiom,(
    ! [A,B] :
      ( ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & k7_gate_1(A,B) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B) )
       => k7_gate_1(A,B) = k1_xboole_0 ) ) )).

fof(t15_gate_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(k7_gate_1(A,B))
    <=> ( v1_xboole_0(A)
        & v1_xboole_0(B) ) ) )).

fof(d8_gate_1,axiom,(
    ! [A,B,C] :
      ( ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & k8_gate_1(A,B,C) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C) )
       => k8_gate_1(A,B,C) = k1_xboole_0 ) ) )).

fof(t16_gate_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(k8_gate_1(A,B,C))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C) ) ) )).

fof(d9_gate_1,axiom,(
    ! [A,B,C] :
      ( ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C) )
       => k9_gate_1(A,B,C) = k1_gate_1(k1_xboole_0) )
      & ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & k9_gate_1(A,B,C) != k1_xboole_0 ) ) )).

fof(t17_gate_1,axiom,(
    ! [A,B,C] :
      ( ~ ( ~ v1_xboole_0(k9_gate_1(A,B,C))
          & v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C) )
      & ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B)
              & v1_xboole_0(C) )
          & v1_xboole_0(k9_gate_1(A,B,C)) ) ) )).

fof(d10_gate_1,axiom,(
    ! [A,B,C] :
      ( ( ( ( ( ( ~ v1_xboole_0(A)
                & v1_xboole_0(B) )
              | ( v1_xboole_0(A)
                & ~ v1_xboole_0(B) ) )
            & v1_xboole_0(C) )
          | ( ~ ( ~ v1_xboole_0(A)
                & v1_xboole_0(B) )
            & ~ ( v1_xboole_0(A)
                & ~ v1_xboole_0(B) )
            & ~ v1_xboole_0(C) ) )
       => k10_gate_1(A,B,C) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ ( ( ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
                | ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) ) )
              & v1_xboole_0(C) )
          & ~ ( ~ ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
              & ~ ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) )
              & ~ v1_xboole_0(C) )
          & k10_gate_1(A,B,C) != k1_xboole_0 ) ) )).

fof(t18_gate_1,axiom,(
    ! [A,B,C] :
      ( ~ ( ~ v1_xboole_0(k10_gate_1(A,B,C))
          & ~ ( ( ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
                | ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) ) )
              & v1_xboole_0(C) )
          & ~ ( ~ ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
              & ~ ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) )
              & ~ v1_xboole_0(C) ) )
      & ~ ( ( ( ( ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
                | ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) ) )
              & v1_xboole_0(C) )
            | ( ~ ( ~ v1_xboole_0(A)
                  & v1_xboole_0(B) )
              & ~ ( v1_xboole_0(A)
                  & ~ v1_xboole_0(B) )
              & ~ v1_xboole_0(C) ) )
          & v1_xboole_0(k10_gate_1(A,B,C)) ) ) )).

fof(d11_gate_1,axiom,(
    ! [A,B,C] :
      ( ( ~ ( ~ ( ~ v1_xboole_0(A)
                & ~ v1_xboole_0(B) )
            & ~ ( ~ v1_xboole_0(B)
                & ~ v1_xboole_0(C) )
            & ~ ( ~ v1_xboole_0(C)
                & ~ v1_xboole_0(A) ) )
       => k11_gate_1(A,B,C) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B) )
          & ~ ( ~ v1_xboole_0(B)
              & ~ v1_xboole_0(C) )
          & ~ ( ~ v1_xboole_0(C)
              & ~ v1_xboole_0(A) )
          & k11_gate_1(A,B,C) != k1_xboole_0 ) ) )).

fof(t19_gate_1,axiom,(
    ! [A,B,C] :
      ( ~ ( ~ v1_xboole_0(k11_gate_1(A,B,C))
          & ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B) )
          & ~ ( ~ v1_xboole_0(B)
              & ~ v1_xboole_0(C) )
          & ~ ( ~ v1_xboole_0(C)
              & ~ v1_xboole_0(A) ) )
      & ~ ( ~ ( ~ ( ~ v1_xboole_0(A)
                  & ~ v1_xboole_0(B) )
              & ~ ( ~ v1_xboole_0(B)
                  & ~ v1_xboole_0(C) )
              & ~ ( ~ v1_xboole_0(C)
                  & ~ v1_xboole_0(A) ) )
          & v1_xboole_0(k11_gate_1(A,B,C)) ) ) )).

fof(d12_gate_1,axiom,(
    ! [A,B,C] :
      ( ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C) )
       => k12_gate_1(A,B,C) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & k12_gate_1(A,B,C) != k1_xboole_0 ) ) )).

fof(t20_gate_1,axiom,(
    ! [A,B,C] :
      ( ~ ( ~ v1_xboole_0(k12_gate_1(A,B,C))
          & ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B)
              & ~ v1_xboole_0(C) )
          & v1_xboole_0(k12_gate_1(A,B,C)) ) ) )).

fof(d13_gate_1,axiom,(
    ! [A,B,C] :
      ( ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & k13_gate_1(A,B,C) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C) )
       => k13_gate_1(A,B,C) = k1_xboole_0 ) ) )).

fof(t21_gate_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(k13_gate_1(A,B,C))
    <=> ( v1_xboole_0(A)
        & v1_xboole_0(B)
        & v1_xboole_0(C) ) ) )).

fof(d14_gate_1,axiom,(
    ! [A,B,C,D] :
      ( ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & k14_gate_1(A,B,C,D) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D) )
       => k14_gate_1(A,B,C,D) = k1_xboole_0 ) ) )).

fof(t22_gate_1,axiom,(
    ! [A,B,C,D] :
      ( ~ v1_xboole_0(k14_gate_1(A,B,C,D))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D) ) ) )).

fof(d15_gate_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D) )
       => k15_gate_1(A,B,C,D) = k1_gate_1(k1_xboole_0) )
      & ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & k15_gate_1(A,B,C,D) != k1_xboole_0 ) ) )).

fof(t23_gate_1,axiom,(
    ! [A,B,C,D] :
      ( ~ ( ~ v1_xboole_0(k15_gate_1(A,B,C,D))
          & v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D) )
      & ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B)
              & v1_xboole_0(C)
              & v1_xboole_0(D) )
          & v1_xboole_0(k15_gate_1(A,B,C,D)) ) ) )).

fof(d16_gate_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D) )
       => k16_gate_1(A,B,C,D) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & k16_gate_1(A,B,C,D) != k1_xboole_0 ) ) )).

fof(t24_gate_1,axiom,(
    ! [A,B,C,D] :
      ( ~ ( ~ v1_xboole_0(k16_gate_1(A,B,C,D))
          & ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B)
              & ~ v1_xboole_0(C)
              & ~ v1_xboole_0(D) )
          & v1_xboole_0(k16_gate_1(A,B,C,D)) ) ) )).

fof(d17_gate_1,axiom,(
    ! [A,B,C,D] :
      ( ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & k17_gate_1(A,B,C,D) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D) )
       => k17_gate_1(A,B,C,D) = k1_xboole_0 ) ) )).

fof(t25_gate_1,axiom,(
    ! [A,B,C,D] :
      ( ~ v1_xboole_0(k17_gate_1(A,B,C,D))
    <=> ( v1_xboole_0(A)
        & v1_xboole_0(B)
        & v1_xboole_0(C)
        & v1_xboole_0(D) ) ) )).

fof(d18_gate_1,axiom,(
    ! [A,B,C,D,E] :
      ( ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & k18_gate_1(A,B,C,D,E) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D)
            & ~ v1_xboole_0(E) )
       => k18_gate_1(A,B,C,D,E) = k1_xboole_0 ) ) )).

fof(t26_gate_1,axiom,(
    ! [A,B,C,D,E] :
      ( ~ v1_xboole_0(k18_gate_1(A,B,C,D,E))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & ~ v1_xboole_0(E) ) ) )).

fof(d19_gate_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D)
            & v1_xboole_0(E) )
       => k19_gate_1(A,B,C,D,E) = k1_gate_1(k1_xboole_0) )
      & ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & k19_gate_1(A,B,C,D,E) != k1_xboole_0 ) ) )).

fof(t27_gate_1,axiom,(
    ! [A,B,C,D,E] :
      ( ~ ( ~ v1_xboole_0(k19_gate_1(A,B,C,D,E))
          & v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E) )
      & ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B)
              & v1_xboole_0(C)
              & v1_xboole_0(D)
              & v1_xboole_0(E) )
          & v1_xboole_0(k19_gate_1(A,B,C,D,E)) ) ) )).

fof(d20_gate_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D)
            & ~ v1_xboole_0(E) )
       => k20_gate_1(A,B,C,D,E) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & k20_gate_1(A,B,C,D,E) != k1_xboole_0 ) ) )).

fof(t28_gate_1,axiom,(
    ! [A,B,C,D,E] :
      ( ~ ( ~ v1_xboole_0(k20_gate_1(A,B,C,D,E))
          & ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B)
              & ~ v1_xboole_0(C)
              & ~ v1_xboole_0(D)
              & ~ v1_xboole_0(E) )
          & v1_xboole_0(k20_gate_1(A,B,C,D,E)) ) ) )).

fof(d21_gate_1,axiom,(
    ! [A,B,C,D,E] :
      ( ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & k21_gate_1(A,B,C,D,E) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D)
            & v1_xboole_0(E) )
       => k21_gate_1(A,B,C,D,E) = k1_xboole_0 ) ) )).

fof(t29_gate_1,axiom,(
    ! [A,B,C,D,E] :
      ( ~ v1_xboole_0(k21_gate_1(A,B,C,D,E))
    <=> ( v1_xboole_0(A)
        & v1_xboole_0(B)
        & v1_xboole_0(C)
        & v1_xboole_0(D)
        & v1_xboole_0(E) ) ) )).

fof(d22_gate_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & ~ v1_xboole_0(F)
          & k22_gate_1(A,B,C,D,E,F) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D)
            & ~ v1_xboole_0(E)
            & ~ v1_xboole_0(F) )
       => k22_gate_1(A,B,C,D,E,F) = k1_xboole_0 ) ) )).

fof(t30_gate_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ~ v1_xboole_0(k22_gate_1(A,B,C,D,E,F))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & ~ v1_xboole_0(E)
        & ~ v1_xboole_0(F) ) ) )).

fof(d23_gate_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D)
            & v1_xboole_0(E)
            & v1_xboole_0(F) )
       => k23_gate_1(A,B,C,D,E,F) = k1_gate_1(k1_xboole_0) )
      & ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & v1_xboole_0(F)
          & k23_gate_1(A,B,C,D,E,F) != k1_xboole_0 ) ) )).

fof(t31_gate_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ~ ( ~ v1_xboole_0(k23_gate_1(A,B,C,D,E,F))
          & v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & v1_xboole_0(F) )
      & ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B)
              & v1_xboole_0(C)
              & v1_xboole_0(D)
              & v1_xboole_0(E)
              & v1_xboole_0(F) )
          & v1_xboole_0(k23_gate_1(A,B,C,D,E,F)) ) ) )).

fof(d24_gate_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D)
            & ~ v1_xboole_0(E)
            & ~ v1_xboole_0(F) )
       => k24_gate_1(A,B,C,D,E,F) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & ~ v1_xboole_0(F)
          & k24_gate_1(A,B,C,D,E,F) != k1_xboole_0 ) ) )).

fof(t32_gate_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ~ ( ~ v1_xboole_0(k24_gate_1(A,B,C,D,E,F))
          & ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & ~ v1_xboole_0(F) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B)
              & ~ v1_xboole_0(C)
              & ~ v1_xboole_0(D)
              & ~ v1_xboole_0(E)
              & ~ v1_xboole_0(F) )
          & v1_xboole_0(k24_gate_1(A,B,C,D,E,F)) ) ) )).

fof(d25_gate_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & v1_xboole_0(F)
          & k25_gate_1(A,B,C,D,E,F) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D)
            & v1_xboole_0(E)
            & v1_xboole_0(F) )
       => k25_gate_1(A,B,C,D,E,F) = k1_xboole_0 ) ) )).

fof(t33_gate_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ~ v1_xboole_0(k25_gate_1(A,B,C,D,E,F))
    <=> ( v1_xboole_0(A)
        & v1_xboole_0(B)
        & v1_xboole_0(C)
        & v1_xboole_0(D)
        & v1_xboole_0(E)
        & v1_xboole_0(F) ) ) )).

fof(d26_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & ~ v1_xboole_0(F)
          & ~ v1_xboole_0(G)
          & k26_gate_1(A,B,C,D,E,F,G) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D)
            & ~ v1_xboole_0(E)
            & ~ v1_xboole_0(F)
            & ~ v1_xboole_0(G) )
       => k26_gate_1(A,B,C,D,E,F,G) = k1_xboole_0 ) ) )).

fof(t34_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ~ v1_xboole_0(k26_gate_1(A,B,C,D,E,F,G))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & ~ v1_xboole_0(E)
        & ~ v1_xboole_0(F)
        & ~ v1_xboole_0(G) ) ) )).

fof(d27_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D)
            & v1_xboole_0(E)
            & v1_xboole_0(F)
            & v1_xboole_0(G) )
       => k27_gate_1(A,B,C,D,E,F,G) = k1_gate_1(k1_xboole_0) )
      & ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & v1_xboole_0(F)
          & v1_xboole_0(G)
          & k27_gate_1(A,B,C,D,E,F,G) != k1_xboole_0 ) ) )).

fof(t35_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ~ ( ~ v1_xboole_0(k27_gate_1(A,B,C,D,E,F,G))
          & v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & v1_xboole_0(F)
          & v1_xboole_0(G) )
      & ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B)
              & v1_xboole_0(C)
              & v1_xboole_0(D)
              & v1_xboole_0(E)
              & v1_xboole_0(F)
              & v1_xboole_0(G) )
          & v1_xboole_0(k27_gate_1(A,B,C,D,E,F,G)) ) ) )).

fof(d28_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D)
            & ~ v1_xboole_0(E)
            & ~ v1_xboole_0(F)
            & ~ v1_xboole_0(G) )
       => k28_gate_1(A,B,C,D,E,F,G) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & ~ v1_xboole_0(F)
          & ~ v1_xboole_0(G)
          & k28_gate_1(A,B,C,D,E,F,G) != k1_xboole_0 ) ) )).

fof(t36_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ~ ( ~ v1_xboole_0(k28_gate_1(A,B,C,D,E,F,G))
          & ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & ~ v1_xboole_0(F)
          & ~ v1_xboole_0(G) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B)
              & ~ v1_xboole_0(C)
              & ~ v1_xboole_0(D)
              & ~ v1_xboole_0(E)
              & ~ v1_xboole_0(F)
              & ~ v1_xboole_0(G) )
          & v1_xboole_0(k28_gate_1(A,B,C,D,E,F,G)) ) ) )).

fof(d29_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & v1_xboole_0(F)
          & v1_xboole_0(G)
          & k29_gate_1(A,B,C,D,E,F,G) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D)
            & v1_xboole_0(E)
            & v1_xboole_0(F)
            & v1_xboole_0(G) )
       => k29_gate_1(A,B,C,D,E,F,G) = k1_xboole_0 ) ) )).

fof(t37_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ~ v1_xboole_0(k29_gate_1(A,B,C,D,E,F,G))
    <=> ( v1_xboole_0(A)
        & v1_xboole_0(B)
        & v1_xboole_0(C)
        & v1_xboole_0(D)
        & v1_xboole_0(E)
        & v1_xboole_0(F)
        & v1_xboole_0(G) ) ) )).

fof(d30_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & ~ v1_xboole_0(F)
          & ~ v1_xboole_0(G)
          & ~ v1_xboole_0(H)
          & k30_gate_1(A,B,C,D,E,F,G,H) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D)
            & ~ v1_xboole_0(E)
            & ~ v1_xboole_0(F)
            & ~ v1_xboole_0(G)
            & ~ v1_xboole_0(H) )
       => k30_gate_1(A,B,C,D,E,F,G,H) = k1_xboole_0 ) ) )).

fof(t38_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ~ v1_xboole_0(k30_gate_1(A,B,C,D,E,F,G,H))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & ~ v1_xboole_0(E)
        & ~ v1_xboole_0(F)
        & ~ v1_xboole_0(G)
        & ~ v1_xboole_0(H) ) ) )).

fof(d31_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D)
            & v1_xboole_0(E)
            & v1_xboole_0(F)
            & v1_xboole_0(G)
            & v1_xboole_0(H) )
       => k31_gate_1(A,B,C,D,E,F,G,H) = k1_gate_1(k1_xboole_0) )
      & ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & v1_xboole_0(F)
          & v1_xboole_0(G)
          & v1_xboole_0(H)
          & k31_gate_1(A,B,C,D,E,F,G,H) != k1_xboole_0 ) ) )).

fof(t39_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ~ ( ~ v1_xboole_0(k31_gate_1(A,B,C,D,E,F,G,H))
          & v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & v1_xboole_0(F)
          & v1_xboole_0(G)
          & v1_xboole_0(H) )
      & ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B)
              & v1_xboole_0(C)
              & v1_xboole_0(D)
              & v1_xboole_0(E)
              & v1_xboole_0(F)
              & v1_xboole_0(G)
              & v1_xboole_0(H) )
          & v1_xboole_0(k31_gate_1(A,B,C,D,E,F,G,H)) ) ) )).

fof(d32_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C)
            & ~ v1_xboole_0(D)
            & ~ v1_xboole_0(E)
            & ~ v1_xboole_0(F)
            & ~ v1_xboole_0(G)
            & ~ v1_xboole_0(H) )
       => k32_gate_1(A,B,C,D,E,F,G,H) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & ~ v1_xboole_0(F)
          & ~ v1_xboole_0(G)
          & ~ v1_xboole_0(H)
          & k32_gate_1(A,B,C,D,E,F,G,H) != k1_xboole_0 ) ) )).

fof(t40_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ~ ( ~ v1_xboole_0(k32_gate_1(A,B,C,D,E,F,G,H))
          & ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & ~ v1_xboole_0(D)
          & ~ v1_xboole_0(E)
          & ~ v1_xboole_0(F)
          & ~ v1_xboole_0(G)
          & ~ v1_xboole_0(H) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B)
              & ~ v1_xboole_0(C)
              & ~ v1_xboole_0(D)
              & ~ v1_xboole_0(E)
              & ~ v1_xboole_0(F)
              & ~ v1_xboole_0(G)
              & ~ v1_xboole_0(H) )
          & v1_xboole_0(k32_gate_1(A,B,C,D,E,F,G,H)) ) ) )).

fof(d33_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ~ ( v1_xboole_0(A)
          & v1_xboole_0(B)
          & v1_xboole_0(C)
          & v1_xboole_0(D)
          & v1_xboole_0(E)
          & v1_xboole_0(F)
          & v1_xboole_0(G)
          & v1_xboole_0(H)
          & k33_gate_1(A,B,C,D,E,F,G,H) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B)
            & v1_xboole_0(C)
            & v1_xboole_0(D)
            & v1_xboole_0(E)
            & v1_xboole_0(F)
            & v1_xboole_0(G)
            & v1_xboole_0(H) )
       => k33_gate_1(A,B,C,D,E,F,G,H) = k1_xboole_0 ) ) )).

fof(t41_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ~ v1_xboole_0(k33_gate_1(A,B,C,D,E,F,G,H))
    <=> ( v1_xboole_0(A)
        & v1_xboole_0(B)
        & v1_xboole_0(C)
        & v1_xboole_0(D)
        & v1_xboole_0(E)
        & v1_xboole_0(F)
        & v1_xboole_0(G)
        & v1_xboole_0(H) ) ) )).

fof(t42_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S] :
      ~ ( ~ ( ~ v1_xboole_0(k11_gate_1(B,F,A))
            & v1_xboole_0(J) )
        & ~ ( ~ v1_xboole_0(k11_gate_1(C,G,J))
            & v1_xboole_0(K) )
        & ~ ( ~ v1_xboole_0(k11_gate_1(D,H,K))
            & v1_xboole_0(L) )
        & ~ ( ~ v1_xboole_0(k11_gate_1(E,I,L))
            & v1_xboole_0(M) )
        & ~ ( ~ v1_xboole_0(N)
            & v1_xboole_0(k3_gate_1(B,F)) )
        & ~ ( ~ v1_xboole_0(O)
            & v1_xboole_0(k3_gate_1(C,G)) )
        & ~ ( ~ v1_xboole_0(P)
            & v1_xboole_0(k3_gate_1(D,H)) )
        & ~ ( ~ v1_xboole_0(Q)
            & v1_xboole_0(k3_gate_1(E,I)) )
        & ~ ( ~ v1_xboole_0(R)
            & v1_xboole_0(k18_gate_1(A,N,O,P,Q)) )
        & ~ ( ~ v1_xboole_0(S)
            & v1_xboole_0(k3_gate_1(M,R)) )
        & ~ ( ~ v1_xboole_0(k3_gate_1(M,R))
            & v1_xboole_0(S) )
        & ~ ( ~ ( ~ v1_xboole_0(M)
                & v1_xboole_0(S) )
            & ~ ( ~ v1_xboole_0(S)
                & v1_xboole_0(M) ) ) ) )).

fof(d34_gate_1,axiom,(
    ! [A,B] :
      ( ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B) )
          & ~ ( ~ v1_xboole_0(A)
              & ~ v1_xboole_0(B) )
          & k34_gate_1(A,B) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ ( v1_xboole_0(A)
                & v1_xboole_0(B) )
            & ~ ( ~ v1_xboole_0(A)
                & ~ v1_xboole_0(B) ) )
       => k34_gate_1(A,B) = k1_xboole_0 ) ) )).

fof(t43_gate_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(k34_gate_1(A,B))
    <=> ( ~ ( v1_xboole_0(A)
            & v1_xboole_0(B) )
        & ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B) ) ) ) )).

fof(d35_gate_1,axiom,(
    $true )).

fof(d36_gate_1,axiom,(
    $true )).

fof(d37_gate_1,axiom,(
    ! [A,B,C,D,E] : k35_gate_1(A,B,C,D,E) = k10_gate_1(C,D,k11_gate_1(A,B,E)) )).

fof(d38_gate_1,axiom,(
    ! [A,B,C,D,E] : k36_gate_1(A,B,C,D,E) = k11_gate_1(C,D,k11_gate_1(A,B,E)) )).

fof(d39_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] : k37_gate_1(A,B,C,D,E,F,G) = k10_gate_1(E,F,k36_gate_1(A,B,C,D,G)) )).

fof(d40_gate_1,axiom,(
    ! [A,B,C,D,E,F,G] : k38_gate_1(A,B,C,D,E,F,G) = k11_gate_1(E,F,k36_gate_1(A,B,C,D,G)) )).

fof(d41_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k39_gate_1(A,B,C,D,E,F,G,H,I) = k10_gate_1(G,H,k38_gate_1(A,B,C,D,E,F,I)) )).

fof(d42_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k40_gate_1(A,B,C,D,E,F,G,H,I) = k11_gate_1(G,H,k38_gate_1(A,B,C,D,E,F,I)) )).

fof(t44_gate_1,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1] :
      ~ ( ~ ( ~ v1_xboole_0(K)
            & v1_xboole_0(k7_gate_1(B,C)) )
        & ~ ( ~ v1_xboole_0(k7_gate_1(B,C))
            & v1_xboole_0(K) )
        & ~ ( ~ v1_xboole_0(L)
            & v1_xboole_0(k6_gate_1(B,C)) )
        & ~ ( ~ v1_xboole_0(k6_gate_1(B,C))
            & v1_xboole_0(L) )
        & ~ ( ~ v1_xboole_0(M)
            & v1_xboole_0(k34_gate_1(B,C)) )
        & ~ ( ~ v1_xboole_0(k34_gate_1(B,C))
            & v1_xboole_0(M) )
        & ~ ( ~ v1_xboole_0(N)
            & v1_xboole_0(k7_gate_1(D,E)) )
        & ~ ( ~ v1_xboole_0(k7_gate_1(D,E))
            & v1_xboole_0(N) )
        & ~ ( ~ v1_xboole_0(O)
            & v1_xboole_0(k6_gate_1(D,E)) )
        & ~ ( ~ v1_xboole_0(k6_gate_1(D,E))
            & v1_xboole_0(O) )
        & ~ ( ~ v1_xboole_0(P)
            & v1_xboole_0(k34_gate_1(D,E)) )
        & ~ ( ~ v1_xboole_0(k34_gate_1(D,E))
            & v1_xboole_0(P) )
        & ~ ( ~ v1_xboole_0(Q)
            & v1_xboole_0(k7_gate_1(F,G)) )
        & ~ ( ~ v1_xboole_0(k7_gate_1(F,G))
            & v1_xboole_0(Q) )
        & ~ ( ~ v1_xboole_0(R)
            & v1_xboole_0(k6_gate_1(F,G)) )
        & ~ ( ~ v1_xboole_0(k6_gate_1(F,G))
            & v1_xboole_0(R) )
        & ~ ( ~ v1_xboole_0(S)
            & v1_xboole_0(k34_gate_1(F,G)) )
        & ~ ( ~ v1_xboole_0(k34_gate_1(F,G))
            & v1_xboole_0(S) )
        & ~ ( ~ v1_xboole_0(T)
            & v1_xboole_0(k7_gate_1(H,I)) )
        & ~ ( ~ v1_xboole_0(k7_gate_1(H,I))
            & v1_xboole_0(T) )
        & ~ ( ~ v1_xboole_0(U)
            & v1_xboole_0(k6_gate_1(H,I)) )
        & ~ ( ~ v1_xboole_0(k6_gate_1(H,I))
            & v1_xboole_0(U) )
        & ~ ( ~ v1_xboole_0(V)
            & v1_xboole_0(k34_gate_1(H,I)) )
        & ~ ( ~ v1_xboole_0(k34_gate_1(H,I))
            & v1_xboole_0(V) )
        & ~ ( ~ v1_xboole_0(W)
            & v1_xboole_0(k1_gate_1(A)) )
        & ~ ( ~ v1_xboole_0(k1_gate_1(A))
            & v1_xboole_0(W) )
        & ~ ( ~ v1_xboole_0(X)
            & v1_xboole_0(k1_gate_1(W)) )
        & ~ ( ~ v1_xboole_0(k1_gate_1(W))
            & v1_xboole_0(X) )
        & ~ ( ~ v1_xboole_0(L1)
            & v1_xboole_0(k4_gate_1(X,M)) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(X,M))
            & v1_xboole_0(L1) )
        & ~ ( ~ v1_xboole_0(Y)
            & v1_xboole_0(k2_gate_1(W,L)) )
        & ~ ( ~ v1_xboole_0(k2_gate_1(W,L))
            & v1_xboole_0(Y) )
        & ~ ( ~ v1_xboole_0(Z)
            & v1_xboole_0(k7_gate_1(Y,K)) )
        & ~ ( ~ v1_xboole_0(k7_gate_1(Y,K))
            & v1_xboole_0(Z) )
        & ~ ( ~ v1_xboole_0(M1)
            & v1_xboole_0(k4_gate_1(Z,P)) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(Z,P))
            & v1_xboole_0(M1) )
        & ~ ( ~ v1_xboole_0(A1)
            & v1_xboole_0(k2_gate_1(K,O)) )
        & ~ ( ~ v1_xboole_0(k2_gate_1(K,O))
            & v1_xboole_0(A1) )
        & ~ ( ~ v1_xboole_0(B1)
            & v1_xboole_0(k8_gate_1(O,L,W)) )
        & ~ ( ~ v1_xboole_0(k8_gate_1(O,L,W))
            & v1_xboole_0(B1) )
        & ~ ( ~ v1_xboole_0(C1)
            & v1_xboole_0(k13_gate_1(A1,B1,N)) )
        & ~ ( ~ v1_xboole_0(k13_gate_1(A1,B1,N))
            & v1_xboole_0(C1) )
        & ~ ( ~ v1_xboole_0(N1)
            & v1_xboole_0(k4_gate_1(C1,S)) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(C1,S))
            & v1_xboole_0(N1) )
        & ~ ( ~ v1_xboole_0(D1)
            & v1_xboole_0(k2_gate_1(N,R)) )
        & ~ ( ~ v1_xboole_0(k2_gate_1(N,R))
            & v1_xboole_0(D1) )
        & ~ ( ~ v1_xboole_0(E1)
            & v1_xboole_0(k8_gate_1(K,R,O)) )
        & ~ ( ~ v1_xboole_0(k8_gate_1(K,R,O))
            & v1_xboole_0(E1) )
        & ~ ( ~ v1_xboole_0(F1)
            & v1_xboole_0(k14_gate_1(R,O,L,W)) )
        & ~ ( ~ v1_xboole_0(k14_gate_1(R,O,L,W))
            & v1_xboole_0(F1) )
        & ~ ( ~ v1_xboole_0(G1)
            & v1_xboole_0(k17_gate_1(D1,E1,F1,Q)) )
        & ~ ( ~ v1_xboole_0(k17_gate_1(D1,E1,F1,Q))
            & v1_xboole_0(G1) )
        & ~ ( ~ v1_xboole_0(O1)
            & v1_xboole_0(k4_gate_1(G1,V)) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(G1,V))
            & v1_xboole_0(O1) )
        & ~ ( ~ v1_xboole_0(H1)
            & v1_xboole_0(k2_gate_1(Q,U)) )
        & ~ ( ~ v1_xboole_0(k2_gate_1(Q,U))
            & v1_xboole_0(H1) )
        & ~ ( ~ v1_xboole_0(I1)
            & v1_xboole_0(k8_gate_1(N,U,R)) )
        & ~ ( ~ v1_xboole_0(k8_gate_1(N,U,R))
            & v1_xboole_0(I1) )
        & ~ ( ~ v1_xboole_0(J1)
            & v1_xboole_0(k14_gate_1(K,U,R,O)) )
        & ~ ( ~ v1_xboole_0(k14_gate_1(K,U,R,O))
            & v1_xboole_0(J1) )
        & ~ ( ~ v1_xboole_0(K1)
            & v1_xboole_0(k18_gate_1(U,R,O,L,W)) )
        & ~ ( ~ v1_xboole_0(k18_gate_1(U,R,O,L,W))
            & v1_xboole_0(K1) )
        & ~ ( ~ v1_xboole_0(J)
            & v1_xboole_0(k21_gate_1(T,H1,I1,J1,K1)) )
        & ~ ( ~ v1_xboole_0(k21_gate_1(T,H1,I1,J1,K1))
            & v1_xboole_0(J) )
        & ~ ( ~ ( ~ v1_xboole_0(L1)
                & v1_xboole_0(k10_gate_1(B,C,A)) )
            & ~ ( ~ v1_xboole_0(k10_gate_1(B,C,A))
                & v1_xboole_0(L1) )
            & ~ ( ~ v1_xboole_0(M1)
                & v1_xboole_0(k35_gate_1(B,C,D,E,A)) )
            & ~ ( ~ v1_xboole_0(k35_gate_1(B,C,D,E,A))
                & v1_xboole_0(M1) )
            & ~ ( ~ v1_xboole_0(N1)
                & v1_xboole_0(k37_gate_1(B,C,D,E,F,G,A)) )
            & ~ ( ~ v1_xboole_0(k37_gate_1(B,C,D,E,F,G,A))
                & v1_xboole_0(N1) )
            & ~ ( ~ v1_xboole_0(O1)
                & v1_xboole_0(k39_gate_1(B,C,D,E,F,G,H,I,A)) )
            & ~ ( ~ v1_xboole_0(k39_gate_1(B,C,D,E,F,G,H,I,A))
                & v1_xboole_0(O1) )
            & ~ ( ~ v1_xboole_0(J)
                & v1_xboole_0(k40_gate_1(B,C,D,E,F,G,H,I,A)) )
            & ~ ( ~ v1_xboole_0(k40_gate_1(B,C,D,E,F,G,H,I,A))
                & v1_xboole_0(J) ) ) ) )).

fof(dt_k1_gate_1,axiom,(
    $true )).

fof(dt_k2_gate_1,axiom,(
    $true )).

fof(dt_k3_gate_1,axiom,(
    $true )).

fof(dt_k4_gate_1,axiom,(
    $true )).

fof(dt_k5_gate_1,axiom,(
    $true )).

fof(dt_k6_gate_1,axiom,(
    $true )).

fof(dt_k7_gate_1,axiom,(
    $true )).

fof(dt_k8_gate_1,axiom,(
    $true )).

fof(dt_k9_gate_1,axiom,(
    $true )).

fof(dt_k10_gate_1,axiom,(
    $true )).

fof(dt_k11_gate_1,axiom,(
    $true )).

fof(dt_k12_gate_1,axiom,(
    $true )).

fof(dt_k13_gate_1,axiom,(
    $true )).

fof(dt_k14_gate_1,axiom,(
    $true )).

fof(dt_k15_gate_1,axiom,(
    $true )).

fof(dt_k16_gate_1,axiom,(
    $true )).

fof(dt_k17_gate_1,axiom,(
    $true )).

fof(dt_k18_gate_1,axiom,(
    $true )).

fof(dt_k19_gate_1,axiom,(
    $true )).

fof(dt_k20_gate_1,axiom,(
    $true )).

fof(dt_k21_gate_1,axiom,(
    $true )).

fof(dt_k22_gate_1,axiom,(
    $true )).

fof(dt_k23_gate_1,axiom,(
    $true )).

fof(dt_k24_gate_1,axiom,(
    $true )).

fof(dt_k25_gate_1,axiom,(
    $true )).

fof(dt_k26_gate_1,axiom,(
    $true )).

fof(dt_k27_gate_1,axiom,(
    $true )).

fof(dt_k28_gate_1,axiom,(
    $true )).

fof(dt_k29_gate_1,axiom,(
    $true )).

fof(dt_k30_gate_1,axiom,(
    $true )).

fof(dt_k31_gate_1,axiom,(
    $true )).

fof(dt_k32_gate_1,axiom,(
    $true )).

fof(dt_k33_gate_1,axiom,(
    $true )).

fof(dt_k34_gate_1,axiom,(
    $true )).

fof(dt_k35_gate_1,axiom,(
    $true )).

fof(dt_k36_gate_1,axiom,(
    $true )).

fof(dt_k37_gate_1,axiom,(
    $true )).

fof(dt_k38_gate_1,axiom,(
    $true )).

fof(dt_k39_gate_1,axiom,(
    $true )).

fof(dt_k40_gate_1,axiom,(
    $true )).
%------------------------------------------------------------------------------