SET007 Axioms: SET007+141.ax


%------------------------------------------------------------------------------
% File     : SET007+141 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Correctness of a Cyclic Redundancy Check Code Generator
% 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_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :    4 (   0 unit)
%            Number of atoms       :  466 (   0 equality)
%            Maximal formula depth :  123 ( 108 average)
%            Number of connectives :  870 ( 408 ~  ;  60  |; 400  &)
%                                         (   0 <=>;   2 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    1 (   0 propositional; 1-1 arity)
%            Number of functors    :    2 (   0 constant; 2-2 arity)
%            Number of variables   :  178 (   0 singleton; 178 !;   0 ?)
%            Maximal term depth    :    4 (   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(t1_gate_4,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] :
      ~ ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(M)
        & ~ ( ~ v1_xboole_0(Z)
            & v1_xboole_0(k4_gate_1(L1,k2_gate_1(A,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(L1,k2_gate_1(A,Y)))
            & v1_xboole_0(Z) )
        & ~ ( ~ v1_xboole_0(A1)
            & v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Y)))
            & v1_xboole_0(A1) )
        & ~ ( ~ v1_xboole_0(B1)
            & v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Y)))
            & v1_xboole_0(B1) )
        & ~ ( ~ v1_xboole_0(C1)
            & v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Y)))
            & v1_xboole_0(C1) )
        & ~ ( ~ v1_xboole_0(D1)
            & v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Y)))
            & v1_xboole_0(D1) )
        & ~ ( ~ v1_xboole_0(E1)
            & v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Y)))
            & v1_xboole_0(E1) )
        & ~ ( ~ v1_xboole_0(F1)
            & v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Y)))
            & v1_xboole_0(F1) )
        & ~ ( ~ v1_xboole_0(G1)
            & v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Y)))
            & v1_xboole_0(G1) )
        & ~ ( ~ v1_xboole_0(H1)
            & v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Y)))
            & v1_xboole_0(H1) )
        & ~ ( ~ v1_xboole_0(I1)
            & v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Y)))
            & v1_xboole_0(I1) )
        & ~ ( ~ v1_xboole_0(J1)
            & v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Y)))
            & v1_xboole_0(J1) )
        & ~ ( ~ v1_xboole_0(K1)
            & v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Y))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Y)))
            & v1_xboole_0(K1) )
        & ~ ( ~ ( ~ v1_xboole_0(Y)
                & v1_xboole_0(k2_gate_1(M,Y)) )
            & ~ ( ~ v1_xboole_0(k2_gate_1(M,Y))
                & v1_xboole_0(Y) )
            & ~ ( ~ v1_xboole_0(X)
                & v1_xboole_0(k4_gate_1(K1,k2_gate_1(L,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(K1,k2_gate_1(L,Y)))
                & v1_xboole_0(X) )
            & ~ ( ~ v1_xboole_0(W)
                & v1_xboole_0(k4_gate_1(J1,k2_gate_1(K,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(J1,k2_gate_1(K,Y)))
                & v1_xboole_0(W) )
            & ~ ( ~ v1_xboole_0(V)
                & v1_xboole_0(k4_gate_1(I1,k2_gate_1(J,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(I1,k2_gate_1(J,Y)))
                & v1_xboole_0(V) )
            & ~ ( ~ v1_xboole_0(U)
                & v1_xboole_0(k4_gate_1(H1,k2_gate_1(I,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(H1,k2_gate_1(I,Y)))
                & v1_xboole_0(U) )
            & ~ ( ~ v1_xboole_0(T)
                & v1_xboole_0(k4_gate_1(G1,k2_gate_1(H,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(G1,k2_gate_1(H,Y)))
                & v1_xboole_0(T) )
            & ~ ( ~ v1_xboole_0(S)
                & v1_xboole_0(k4_gate_1(F1,k2_gate_1(G,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(F1,k2_gate_1(G,Y)))
                & v1_xboole_0(S) )
            & ~ ( ~ v1_xboole_0(R)
                & v1_xboole_0(k4_gate_1(E1,k2_gate_1(F,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(E1,k2_gate_1(F,Y)))
                & v1_xboole_0(R) )
            & ~ ( ~ v1_xboole_0(Q)
                & v1_xboole_0(k4_gate_1(D1,k2_gate_1(E,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(D1,k2_gate_1(E,Y)))
                & v1_xboole_0(Q) )
            & ~ ( ~ v1_xboole_0(P)
                & v1_xboole_0(k4_gate_1(C1,k2_gate_1(D,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(C1,k2_gate_1(D,Y)))
                & v1_xboole_0(P) )
            & ~ ( ~ v1_xboole_0(O)
                & v1_xboole_0(k4_gate_1(B1,k2_gate_1(C,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(B1,k2_gate_1(C,Y)))
                & v1_xboole_0(O) )
            & ~ ( ~ v1_xboole_0(N)
                & v1_xboole_0(k4_gate_1(A1,k2_gate_1(B,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(A1,k2_gate_1(B,Y)))
                & v1_xboole_0(N) )
            & ~ ( ~ v1_xboole_0(L1)
                & v1_xboole_0(k4_gate_1(Z,k2_gate_1(A,Y))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(Z,k2_gate_1(A,Y)))
                & v1_xboole_0(L1) ) ) ) )).

fof(t2_gate_4,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,P1,Q1,R1,S1,T1,U1,V1,W1,X1] :
      ~ ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(Q)
        & ~ ( ~ v1_xboole_0(H1)
            & v1_xboole_0(k4_gate_1(X1,k2_gate_1(A,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(X1,k2_gate_1(A,G1)))
            & v1_xboole_0(H1) )
        & ~ ( ~ v1_xboole_0(I1)
            & v1_xboole_0(k4_gate_1(R,k2_gate_1(B,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(B,G1)))
            & v1_xboole_0(I1) )
        & ~ ( ~ v1_xboole_0(J1)
            & v1_xboole_0(k4_gate_1(S,k2_gate_1(C,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(C,G1)))
            & v1_xboole_0(J1) )
        & ~ ( ~ v1_xboole_0(K1)
            & v1_xboole_0(k4_gate_1(T,k2_gate_1(D,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(D,G1)))
            & v1_xboole_0(K1) )
        & ~ ( ~ v1_xboole_0(L1)
            & v1_xboole_0(k4_gate_1(U,k2_gate_1(E,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(E,G1)))
            & v1_xboole_0(L1) )
        & ~ ( ~ v1_xboole_0(M1)
            & v1_xboole_0(k4_gate_1(V,k2_gate_1(F,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(F,G1)))
            & v1_xboole_0(M1) )
        & ~ ( ~ v1_xboole_0(N1)
            & v1_xboole_0(k4_gate_1(W,k2_gate_1(G,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(G,G1)))
            & v1_xboole_0(N1) )
        & ~ ( ~ v1_xboole_0(O1)
            & v1_xboole_0(k4_gate_1(X,k2_gate_1(H,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(H,G1)))
            & v1_xboole_0(O1) )
        & ~ ( ~ v1_xboole_0(P1)
            & v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,G1)))
            & v1_xboole_0(P1) )
        & ~ ( ~ v1_xboole_0(Q1)
            & v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,G1)))
            & v1_xboole_0(Q1) )
        & ~ ( ~ v1_xboole_0(R1)
            & v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,G1)))
            & v1_xboole_0(R1) )
        & ~ ( ~ v1_xboole_0(S1)
            & v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,G1)))
            & v1_xboole_0(S1) )
        & ~ ( ~ v1_xboole_0(T1)
            & v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,G1)))
            & v1_xboole_0(T1) )
        & ~ ( ~ v1_xboole_0(U1)
            & v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,G1)))
            & v1_xboole_0(U1) )
        & ~ ( ~ v1_xboole_0(V1)
            & v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,G1)))
            & v1_xboole_0(V1) )
        & ~ ( ~ v1_xboole_0(W1)
            & v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,G1))) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,G1)))
            & v1_xboole_0(W1) )
        & ~ ( ~ ( ~ v1_xboole_0(G1)
                & v1_xboole_0(k2_gate_1(Q,G1)) )
            & ~ ( ~ v1_xboole_0(k2_gate_1(Q,G1))
                & v1_xboole_0(G1) )
            & ~ ( ~ v1_xboole_0(F1)
                & v1_xboole_0(k4_gate_1(W1,k2_gate_1(P,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(W1,k2_gate_1(P,G1)))
                & v1_xboole_0(F1) )
            & ~ ( ~ v1_xboole_0(E1)
                & v1_xboole_0(k4_gate_1(V1,k2_gate_1(O,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(V1,k2_gate_1(O,G1)))
                & v1_xboole_0(E1) )
            & ~ ( ~ v1_xboole_0(D1)
                & v1_xboole_0(k4_gate_1(U1,k2_gate_1(N,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(U1,k2_gate_1(N,G1)))
                & v1_xboole_0(D1) )
            & ~ ( ~ v1_xboole_0(C1)
                & v1_xboole_0(k4_gate_1(T1,k2_gate_1(M,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(T1,k2_gate_1(M,G1)))
                & v1_xboole_0(C1) )
            & ~ ( ~ v1_xboole_0(B1)
                & v1_xboole_0(k4_gate_1(S1,k2_gate_1(L,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(S1,k2_gate_1(L,G1)))
                & v1_xboole_0(B1) )
            & ~ ( ~ v1_xboole_0(A1)
                & v1_xboole_0(k4_gate_1(R1,k2_gate_1(K,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(R1,k2_gate_1(K,G1)))
                & v1_xboole_0(A1) )
            & ~ ( ~ v1_xboole_0(Z)
                & v1_xboole_0(k4_gate_1(Q1,k2_gate_1(J,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(Q1,k2_gate_1(J,G1)))
                & v1_xboole_0(Z) )
            & ~ ( ~ v1_xboole_0(Y)
                & v1_xboole_0(k4_gate_1(P1,k2_gate_1(I,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(P1,k2_gate_1(I,G1)))
                & v1_xboole_0(Y) )
            & ~ ( ~ v1_xboole_0(X)
                & v1_xboole_0(k4_gate_1(O1,k2_gate_1(H,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(O1,k2_gate_1(H,G1)))
                & v1_xboole_0(X) )
            & ~ ( ~ v1_xboole_0(W)
                & v1_xboole_0(k4_gate_1(N1,k2_gate_1(G,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(N1,k2_gate_1(G,G1)))
                & v1_xboole_0(W) )
            & ~ ( ~ v1_xboole_0(V)
                & v1_xboole_0(k4_gate_1(M1,k2_gate_1(F,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(M1,k2_gate_1(F,G1)))
                & v1_xboole_0(V) )
            & ~ ( ~ v1_xboole_0(U)
                & v1_xboole_0(k4_gate_1(L1,k2_gate_1(E,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(L1,k2_gate_1(E,G1)))
                & v1_xboole_0(U) )
            & ~ ( ~ v1_xboole_0(T)
                & v1_xboole_0(k4_gate_1(K1,k2_gate_1(D,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(K1,k2_gate_1(D,G1)))
                & v1_xboole_0(T) )
            & ~ ( ~ v1_xboole_0(S)
                & v1_xboole_0(k4_gate_1(J1,k2_gate_1(C,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(J1,k2_gate_1(C,G1)))
                & v1_xboole_0(S) )
            & ~ ( ~ v1_xboole_0(R)
                & v1_xboole_0(k4_gate_1(I1,k2_gate_1(B,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(I1,k2_gate_1(B,G1)))
                & v1_xboole_0(R) )
            & ~ ( ~ v1_xboole_0(X1)
                & v1_xboole_0(k4_gate_1(H1,k2_gate_1(A,G1))) )
            & ~ ( ~ v1_xboole_0(k4_gate_1(H1,k2_gate_1(A,G1)))
                & v1_xboole_0(X1) ) ) ) )).

fof(t3_gate_4,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] :
      ( v1_xboole_0(L1)
     => ( v1_xboole_0(A)
        | v1_xboole_0(M)
        | ( ~ v1_xboole_0(Z)
          & v1_xboole_0(k4_gate_1(M1,Y)) )
        | ( ~ v1_xboole_0(k4_gate_1(M1,Y))
          & v1_xboole_0(Z) )
        | ( ~ v1_xboole_0(A1)
          & v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Z)))
          & v1_xboole_0(A1) )
        | ( ~ v1_xboole_0(B1)
          & v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Z)))
          & v1_xboole_0(B1) )
        | ( ~ v1_xboole_0(C1)
          & v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Z)))
          & v1_xboole_0(C1) )
        | ( ~ v1_xboole_0(D1)
          & v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Z)))
          & v1_xboole_0(D1) )
        | ( ~ v1_xboole_0(E1)
          & v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Z)))
          & v1_xboole_0(E1) )
        | ( ~ v1_xboole_0(F1)
          & v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Z)))
          & v1_xboole_0(F1) )
        | ( ~ v1_xboole_0(G1)
          & v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Z)))
          & v1_xboole_0(G1) )
        | ( ~ v1_xboole_0(H1)
          & v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Z)))
          & v1_xboole_0(H1) )
        | ( ~ v1_xboole_0(I1)
          & v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Z)))
          & v1_xboole_0(I1) )
        | ( ~ v1_xboole_0(J1)
          & v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Z)))
          & v1_xboole_0(J1) )
        | ( ~ v1_xboole_0(K1)
          & v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Z)))
          & v1_xboole_0(K1) )
        | ( ~ ( ~ v1_xboole_0(K1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(L,Y)),k4_gate_1(L1,k2_gate_1(L,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(L,Y)),k4_gate_1(L1,k2_gate_1(L,M1))))
              & v1_xboole_0(K1) )
          & ~ ( ~ v1_xboole_0(J1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(K,Y)),k4_gate_1(L1,k2_gate_1(K,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(K,Y)),k4_gate_1(L1,k2_gate_1(K,M1))))
              & v1_xboole_0(J1) )
          & ~ ( ~ v1_xboole_0(I1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(J,Y)),k4_gate_1(L1,k2_gate_1(J,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(J,Y)),k4_gate_1(L1,k2_gate_1(J,M1))))
              & v1_xboole_0(I1) )
          & ~ ( ~ v1_xboole_0(H1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(I,Y)),k4_gate_1(L1,k2_gate_1(I,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(I,Y)),k4_gate_1(L1,k2_gate_1(I,M1))))
              & v1_xboole_0(H1) )
          & ~ ( ~ v1_xboole_0(G1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(H,Y)),k4_gate_1(L1,k2_gate_1(H,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(H,Y)),k4_gate_1(L1,k2_gate_1(H,M1))))
              & v1_xboole_0(G1) )
          & ~ ( ~ v1_xboole_0(F1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(G,Y)),k4_gate_1(L1,k2_gate_1(G,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(G,Y)),k4_gate_1(L1,k2_gate_1(G,M1))))
              & v1_xboole_0(F1) )
          & ~ ( ~ v1_xboole_0(E1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(F,Y)),k4_gate_1(L1,k2_gate_1(F,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(F,Y)),k4_gate_1(L1,k2_gate_1(F,M1))))
              & v1_xboole_0(E1) )
          & ~ ( ~ v1_xboole_0(D1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(Q,k2_gate_1(E,Y)),k4_gate_1(L1,k2_gate_1(E,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(Q,k2_gate_1(E,Y)),k4_gate_1(L1,k2_gate_1(E,M1))))
              & v1_xboole_0(D1) )
          & ~ ( ~ v1_xboole_0(C1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(P,k2_gate_1(D,Y)),k4_gate_1(L1,k2_gate_1(D,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(P,k2_gate_1(D,Y)),k4_gate_1(L1,k2_gate_1(D,M1))))
              & v1_xboole_0(C1) )
          & ~ ( ~ v1_xboole_0(B1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(O,k2_gate_1(C,Y)),k4_gate_1(L1,k2_gate_1(C,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(O,k2_gate_1(C,Y)),k4_gate_1(L1,k2_gate_1(C,M1))))
              & v1_xboole_0(B1) )
          & ~ ( ~ v1_xboole_0(A1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(N,k2_gate_1(B,Y)),k4_gate_1(L1,k2_gate_1(B,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(N,k2_gate_1(B,Y)),k4_gate_1(L1,k2_gate_1(B,M1))))
              & v1_xboole_0(A1) )
          & ~ ( ~ v1_xboole_0(Z)
              & v1_xboole_0(k4_gate_1(k4_gate_1(L1,k2_gate_1(A,Y)),k4_gate_1(L1,k2_gate_1(A,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(L1,k2_gate_1(A,Y)),k4_gate_1(L1,k2_gate_1(A,M1))))
              & v1_xboole_0(Z) ) ) ) ) )).

fof(t4_gate_4,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,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1] :
      ( v1_xboole_0(X1)
     => ( v1_xboole_0(A)
        | v1_xboole_0(Q)
        | ( ~ v1_xboole_0(H1)
          & v1_xboole_0(k4_gate_1(Y1,G1)) )
        | ( ~ v1_xboole_0(k4_gate_1(Y1,G1))
          & v1_xboole_0(H1) )
        | ( ~ v1_xboole_0(I1)
          & v1_xboole_0(k4_gate_1(R,k2_gate_1(B,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(B,H1)))
          & v1_xboole_0(I1) )
        | ( ~ v1_xboole_0(J1)
          & v1_xboole_0(k4_gate_1(S,k2_gate_1(C,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(C,H1)))
          & v1_xboole_0(J1) )
        | ( ~ v1_xboole_0(K1)
          & v1_xboole_0(k4_gate_1(T,k2_gate_1(D,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(D,H1)))
          & v1_xboole_0(K1) )
        | ( ~ v1_xboole_0(L1)
          & v1_xboole_0(k4_gate_1(U,k2_gate_1(E,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(E,H1)))
          & v1_xboole_0(L1) )
        | ( ~ v1_xboole_0(M1)
          & v1_xboole_0(k4_gate_1(V,k2_gate_1(F,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(F,H1)))
          & v1_xboole_0(M1) )
        | ( ~ v1_xboole_0(N1)
          & v1_xboole_0(k4_gate_1(W,k2_gate_1(G,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(G,H1)))
          & v1_xboole_0(N1) )
        | ( ~ v1_xboole_0(O1)
          & v1_xboole_0(k4_gate_1(X,k2_gate_1(H,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(H,H1)))
          & v1_xboole_0(O1) )
        | ( ~ v1_xboole_0(P1)
          & v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,H1)))
          & v1_xboole_0(P1) )
        | ( ~ v1_xboole_0(Q1)
          & v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,H1)))
          & v1_xboole_0(Q1) )
        | ( ~ v1_xboole_0(R1)
          & v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,H1)))
          & v1_xboole_0(R1) )
        | ( ~ v1_xboole_0(S1)
          & v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,H1)))
          & v1_xboole_0(S1) )
        | ( ~ v1_xboole_0(T1)
          & v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,H1)))
          & v1_xboole_0(T1) )
        | ( ~ v1_xboole_0(U1)
          & v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,H1)))
          & v1_xboole_0(U1) )
        | ( ~ v1_xboole_0(V1)
          & v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,H1)))
          & v1_xboole_0(V1) )
        | ( ~ v1_xboole_0(W1)
          & v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,H1)))
          & v1_xboole_0(W1) )
        | ( ~ ( ~ v1_xboole_0(W1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(F1,k2_gate_1(P,G1)),k4_gate_1(X1,k2_gate_1(P,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(F1,k2_gate_1(P,G1)),k4_gate_1(X1,k2_gate_1(P,Y1))))
              & v1_xboole_0(W1) )
          & ~ ( ~ v1_xboole_0(V1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(E1,k2_gate_1(O,G1)),k4_gate_1(X1,k2_gate_1(O,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(E1,k2_gate_1(O,G1)),k4_gate_1(X1,k2_gate_1(O,Y1))))
              & v1_xboole_0(V1) )
          & ~ ( ~ v1_xboole_0(U1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(D1,k2_gate_1(N,G1)),k4_gate_1(X1,k2_gate_1(N,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(D1,k2_gate_1(N,G1)),k4_gate_1(X1,k2_gate_1(N,Y1))))
              & v1_xboole_0(U1) )
          & ~ ( ~ v1_xboole_0(T1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(C1,k2_gate_1(M,G1)),k4_gate_1(X1,k2_gate_1(M,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(C1,k2_gate_1(M,G1)),k4_gate_1(X1,k2_gate_1(M,Y1))))
              & v1_xboole_0(T1) )
          & ~ ( ~ v1_xboole_0(S1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(B1,k2_gate_1(L,G1)),k4_gate_1(X1,k2_gate_1(L,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(B1,k2_gate_1(L,G1)),k4_gate_1(X1,k2_gate_1(L,Y1))))
              & v1_xboole_0(S1) )
          & ~ ( ~ v1_xboole_0(R1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(A1,k2_gate_1(K,G1)),k4_gate_1(X1,k2_gate_1(K,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(A1,k2_gate_1(K,G1)),k4_gate_1(X1,k2_gate_1(K,Y1))))
              & v1_xboole_0(R1) )
          & ~ ( ~ v1_xboole_0(Q1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(Z,k2_gate_1(J,G1)),k4_gate_1(X1,k2_gate_1(J,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(Z,k2_gate_1(J,G1)),k4_gate_1(X1,k2_gate_1(J,Y1))))
              & v1_xboole_0(Q1) )
          & ~ ( ~ v1_xboole_0(P1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(Y,k2_gate_1(I,G1)),k4_gate_1(X1,k2_gate_1(I,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(Y,k2_gate_1(I,G1)),k4_gate_1(X1,k2_gate_1(I,Y1))))
              & v1_xboole_0(P1) )
          & ~ ( ~ v1_xboole_0(O1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(H,G1)),k4_gate_1(X1,k2_gate_1(H,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(H,G1)),k4_gate_1(X1,k2_gate_1(H,Y1))))
              & v1_xboole_0(O1) )
          & ~ ( ~ v1_xboole_0(N1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(G,G1)),k4_gate_1(X1,k2_gate_1(G,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(G,G1)),k4_gate_1(X1,k2_gate_1(G,Y1))))
              & v1_xboole_0(N1) )
          & ~ ( ~ v1_xboole_0(M1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(F,G1)),k4_gate_1(X1,k2_gate_1(F,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(F,G1)),k4_gate_1(X1,k2_gate_1(F,Y1))))
              & v1_xboole_0(M1) )
          & ~ ( ~ v1_xboole_0(L1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(E,G1)),k4_gate_1(X1,k2_gate_1(E,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(E,G1)),k4_gate_1(X1,k2_gate_1(E,Y1))))
              & v1_xboole_0(L1) )
          & ~ ( ~ v1_xboole_0(K1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(D,G1)),k4_gate_1(X1,k2_gate_1(D,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(D,G1)),k4_gate_1(X1,k2_gate_1(D,Y1))))
              & v1_xboole_0(K1) )
          & ~ ( ~ v1_xboole_0(J1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(C,G1)),k4_gate_1(X1,k2_gate_1(C,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(C,G1)),k4_gate_1(X1,k2_gate_1(C,Y1))))
              & v1_xboole_0(J1) )
          & ~ ( ~ v1_xboole_0(I1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(B,G1)),k4_gate_1(X1,k2_gate_1(B,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(B,G1)),k4_gate_1(X1,k2_gate_1(B,Y1))))
              & v1_xboole_0(I1) )
          & ~ ( ~ v1_xboole_0(H1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(X1,k2_gate_1(A,G1)),k4_gate_1(X1,k2_gate_1(A,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(X1,k2_gate_1(A,G1)),k4_gate_1(X1,k2_gate_1(A,Y1))))
              & v1_xboole_0(H1) ) ) ) ) )).
%------------------------------------------------------------------------------