SET007 Axioms: SET007+140.ax
%------------------------------------------------------------------------------
% File : SET007+140 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Correctness of Johnson Counter Circuits
% 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_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 6 ( 0 unt; 0 def)
% Number of atoms : 744 ( 0 equ)
% Maximal formula atoms : 208 ( 124 avg)
% Number of connectives : 1494 ( 756 ~; 0 |; 738 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 150 ( 92 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-4 aty)
% Number of variables : 151 ( 151 !; 0 ?)
% 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_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
~ ( ~ ( ~ v1_xboole_0(A)
& v1_xboole_0(k2_gate_1(k1_gate_1(J),k1_gate_1(I))) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J),k1_gate_1(I)))
& v1_xboole_0(A) )
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(k2_gate_1(k1_gate_1(J),I)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J),I))
& v1_xboole_0(B) )
& ~ ( ~ v1_xboole_0(C)
& v1_xboole_0(k2_gate_1(J,k1_gate_1(I))) )
& ~ ( ~ v1_xboole_0(k2_gate_1(J,k1_gate_1(I)))
& v1_xboole_0(C) )
& ~ ( ~ v1_xboole_0(D)
& v1_xboole_0(k2_gate_1(J,I)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(J,I))
& v1_xboole_0(D) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(k2_gate_1(k1_gate_1(L),k1_gate_1(K))) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(L),k1_gate_1(K)))
& v1_xboole_0(E) )
& ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(k2_gate_1(k1_gate_1(L),K)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(L),K))
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(k2_gate_1(L,k1_gate_1(K))) )
& ~ ( ~ v1_xboole_0(k2_gate_1(L,k1_gate_1(K)))
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(k2_gate_1(L,K)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(L,K))
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(K)
& v1_xboole_0(k1_gate_1(J)) )
& ~ ( ~ v1_xboole_0(k1_gate_1(J))
& v1_xboole_0(K) )
& ~ ( ~ v1_xboole_0(L)
& v1_xboole_0(I) )
& ~ ( ~ v1_xboole_0(I)
& v1_xboole_0(L) )
& ~ ( ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(A) )
& ~ ( ~ v1_xboole_0(A)
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(B) )
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(D) )
& ~ ( ~ v1_xboole_0(D)
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(C) )
& ~ ( ~ v1_xboole_0(C)
& v1_xboole_0(E) ) ) ) ).
fof(t2_gate_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M] :
~ ( ~ ( ~ v1_xboole_0(A)
& v1_xboole_0(k2_gate_1(k1_gate_1(J),k1_gate_1(I))) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J),k1_gate_1(I)))
& v1_xboole_0(A) )
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(k2_gate_1(k1_gate_1(J),I)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J),I))
& v1_xboole_0(B) )
& ~ ( ~ v1_xboole_0(C)
& v1_xboole_0(k2_gate_1(J,k1_gate_1(I))) )
& ~ ( ~ v1_xboole_0(k2_gate_1(J,k1_gate_1(I)))
& v1_xboole_0(C) )
& ~ ( ~ v1_xboole_0(D)
& v1_xboole_0(k2_gate_1(J,I)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(J,I))
& v1_xboole_0(D) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(k2_gate_1(k1_gate_1(L),k1_gate_1(K))) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(L),k1_gate_1(K)))
& v1_xboole_0(E) )
& ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(k2_gate_1(k1_gate_1(L),K)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(L),K))
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(k2_gate_1(L,k1_gate_1(K))) )
& ~ ( ~ v1_xboole_0(k2_gate_1(L,k1_gate_1(K)))
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(k2_gate_1(L,K)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(L,K))
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(K)
& v1_xboole_0(k2_gate_1(k1_gate_1(J),M)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J),M))
& v1_xboole_0(K) )
& ~ ( ~ v1_xboole_0(L)
& v1_xboole_0(k2_gate_1(I,M)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(I,M))
& v1_xboole_0(L) )
& ~ ( ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(k2_gate_1(A,M)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(A,M))
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(k2_gate_1(B,M)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(B,M))
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(k2_gate_1(D,M)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(D,M))
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(k3_gate_1(k2_gate_1(C,M),k1_gate_1(M))) )
& ~ ( ~ v1_xboole_0(k3_gate_1(k2_gate_1(C,M),k1_gate_1(M)))
& v1_xboole_0(E) ) ) ) ).
fof(t3_gate_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V] :
~ ( ~ ( ~ v1_xboole_0(A)
& v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),k1_gate_1(Q))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),k1_gate_1(Q)))
& v1_xboole_0(A) )
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),Q)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),Q))
& v1_xboole_0(B) )
& ~ ( ~ v1_xboole_0(C)
& v1_xboole_0(k8_gate_1(k1_gate_1(S),R,k1_gate_1(Q))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),R,k1_gate_1(Q)))
& v1_xboole_0(C) )
& ~ ( ~ v1_xboole_0(D)
& v1_xboole_0(k8_gate_1(k1_gate_1(S),R,Q)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),R,Q))
& v1_xboole_0(D) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(k8_gate_1(S,k1_gate_1(R),k1_gate_1(Q))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(S,k1_gate_1(R),k1_gate_1(Q)))
& v1_xboole_0(E) )
& ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(k8_gate_1(S,k1_gate_1(R),Q)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(S,k1_gate_1(R),Q))
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(k8_gate_1(S,R,k1_gate_1(Q))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(S,R,k1_gate_1(Q)))
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(k8_gate_1(S,R,Q)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(S,R,Q))
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(I)
& v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),k1_gate_1(T))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),k1_gate_1(T)))
& v1_xboole_0(I) )
& ~ ( ~ v1_xboole_0(J)
& v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),T)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),T))
& v1_xboole_0(J) )
& ~ ( ~ v1_xboole_0(K)
& v1_xboole_0(k8_gate_1(k1_gate_1(V),U,k1_gate_1(T))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),U,k1_gate_1(T)))
& v1_xboole_0(K) )
& ~ ( ~ v1_xboole_0(L)
& v1_xboole_0(k8_gate_1(k1_gate_1(V),U,T)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),U,T))
& v1_xboole_0(L) )
& ~ ( ~ v1_xboole_0(M)
& v1_xboole_0(k8_gate_1(V,k1_gate_1(U),k1_gate_1(T))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(V,k1_gate_1(U),k1_gate_1(T)))
& v1_xboole_0(M) )
& ~ ( ~ v1_xboole_0(N)
& v1_xboole_0(k8_gate_1(V,k1_gate_1(U),T)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(V,k1_gate_1(U),T))
& v1_xboole_0(N) )
& ~ ( ~ v1_xboole_0(O)
& v1_xboole_0(k8_gate_1(V,U,k1_gate_1(T))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(V,U,k1_gate_1(T)))
& v1_xboole_0(O) )
& ~ ( ~ v1_xboole_0(P)
& v1_xboole_0(k8_gate_1(V,U,T)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(V,U,T))
& v1_xboole_0(P) )
& ~ ( ~ v1_xboole_0(T)
& v1_xboole_0(k1_gate_1(S)) )
& ~ ( ~ v1_xboole_0(k1_gate_1(S))
& v1_xboole_0(T) )
& ~ ( ~ v1_xboole_0(U)
& v1_xboole_0(Q) )
& ~ ( ~ v1_xboole_0(Q)
& v1_xboole_0(U) )
& ~ ( ~ v1_xboole_0(V)
& v1_xboole_0(R) )
& ~ ( ~ v1_xboole_0(R)
& v1_xboole_0(V) )
& ~ ( ~ ( ~ v1_xboole_0(J)
& v1_xboole_0(A) )
& ~ ( ~ v1_xboole_0(A)
& v1_xboole_0(J) )
& ~ ( ~ v1_xboole_0(L)
& v1_xboole_0(B) )
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(L) )
& ~ ( ~ v1_xboole_0(P)
& v1_xboole_0(D) )
& ~ ( ~ v1_xboole_0(D)
& v1_xboole_0(P) )
& ~ ( ~ v1_xboole_0(O)
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(O) )
& ~ ( ~ v1_xboole_0(M)
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(M) )
& ~ ( ~ v1_xboole_0(I)
& v1_xboole_0(E) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(I) )
& ~ ( ~ v1_xboole_0(K)
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(K) )
& ~ ( ~ v1_xboole_0(N)
& v1_xboole_0(C) )
& ~ ( ~ v1_xboole_0(C)
& v1_xboole_0(N) ) ) ) ).
fof(t4_gate_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W] :
~ ( ~ ( ~ v1_xboole_0(A)
& v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),k1_gate_1(Q))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),k1_gate_1(Q)))
& v1_xboole_0(A) )
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),Q)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),k1_gate_1(R),Q))
& v1_xboole_0(B) )
& ~ ( ~ v1_xboole_0(C)
& v1_xboole_0(k8_gate_1(k1_gate_1(S),R,k1_gate_1(Q))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),R,k1_gate_1(Q)))
& v1_xboole_0(C) )
& ~ ( ~ v1_xboole_0(D)
& v1_xboole_0(k8_gate_1(k1_gate_1(S),R,Q)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(S),R,Q))
& v1_xboole_0(D) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(k8_gate_1(S,k1_gate_1(R),k1_gate_1(Q))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(S,k1_gate_1(R),k1_gate_1(Q)))
& v1_xboole_0(E) )
& ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(k8_gate_1(S,k1_gate_1(R),Q)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(S,k1_gate_1(R),Q))
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(k8_gate_1(S,R,k1_gate_1(Q))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(S,R,k1_gate_1(Q)))
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(k8_gate_1(S,R,Q)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(S,R,Q))
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(I)
& v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),k1_gate_1(T))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),k1_gate_1(T)))
& v1_xboole_0(I) )
& ~ ( ~ v1_xboole_0(J)
& v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),T)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),k1_gate_1(U),T))
& v1_xboole_0(J) )
& ~ ( ~ v1_xboole_0(K)
& v1_xboole_0(k8_gate_1(k1_gate_1(V),U,k1_gate_1(T))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),U,k1_gate_1(T)))
& v1_xboole_0(K) )
& ~ ( ~ v1_xboole_0(L)
& v1_xboole_0(k8_gate_1(k1_gate_1(V),U,T)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(k1_gate_1(V),U,T))
& v1_xboole_0(L) )
& ~ ( ~ v1_xboole_0(M)
& v1_xboole_0(k8_gate_1(V,k1_gate_1(U),k1_gate_1(T))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(V,k1_gate_1(U),k1_gate_1(T)))
& v1_xboole_0(M) )
& ~ ( ~ v1_xboole_0(N)
& v1_xboole_0(k8_gate_1(V,k1_gate_1(U),T)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(V,k1_gate_1(U),T))
& v1_xboole_0(N) )
& ~ ( ~ v1_xboole_0(O)
& v1_xboole_0(k8_gate_1(V,U,k1_gate_1(T))) )
& ~ ( ~ v1_xboole_0(k8_gate_1(V,U,k1_gate_1(T)))
& v1_xboole_0(O) )
& ~ ( ~ v1_xboole_0(P)
& v1_xboole_0(k8_gate_1(V,U,T)) )
& ~ ( ~ v1_xboole_0(k8_gate_1(V,U,T))
& v1_xboole_0(P) )
& ~ ( ~ v1_xboole_0(T)
& v1_xboole_0(k2_gate_1(k1_gate_1(S),W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(S),W))
& v1_xboole_0(T) )
& ~ ( ~ v1_xboole_0(U)
& v1_xboole_0(k2_gate_1(Q,W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(Q,W))
& v1_xboole_0(U) )
& ~ ( ~ v1_xboole_0(V)
& v1_xboole_0(k2_gate_1(R,W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(R,W))
& v1_xboole_0(V) )
& ~ ( ~ ( ~ v1_xboole_0(J)
& v1_xboole_0(k2_gate_1(A,W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(A,W))
& v1_xboole_0(J) )
& ~ ( ~ v1_xboole_0(L)
& v1_xboole_0(k2_gate_1(B,W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(B,W))
& v1_xboole_0(L) )
& ~ ( ~ v1_xboole_0(P)
& v1_xboole_0(k2_gate_1(D,W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(D,W))
& v1_xboole_0(P) )
& ~ ( ~ v1_xboole_0(O)
& v1_xboole_0(k2_gate_1(H,W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(H,W))
& v1_xboole_0(O) )
& ~ ( ~ v1_xboole_0(M)
& v1_xboole_0(k2_gate_1(G,W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(G,W))
& v1_xboole_0(M) )
& ~ ( ~ v1_xboole_0(I)
& v1_xboole_0(k3_gate_1(k2_gate_1(E,W),k1_gate_1(W))) )
& ~ ( ~ v1_xboole_0(k3_gate_1(k2_gate_1(E,W),k1_gate_1(W)))
& v1_xboole_0(I) )
& ~ ( ~ v1_xboole_0(K)
& v1_xboole_0(k2_gate_1(F,W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(F,W))
& v1_xboole_0(K) )
& ~ ( ~ v1_xboole_0(N)
& v1_xboole_0(k2_gate_1(C,W)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(C,W))
& v1_xboole_0(N) ) ) ) ).
fof(t5_gate_3,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] :
~ ( ~ ( ~ v1_xboole_0(A)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1)))
& v1_xboole_0(A) )
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),G1))
& v1_xboole_0(B) )
& ~ ( ~ v1_xboole_0(C)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,k1_gate_1(G1)))
& v1_xboole_0(C) )
& ~ ( ~ v1_xboole_0(D)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,G1))
& v1_xboole_0(D) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),k1_gate_1(G1)))
& v1_xboole_0(E) )
& ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),G1))
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,k1_gate_1(G1)))
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,G1))
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(I)
& v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1)))
& v1_xboole_0(I) )
& ~ ( ~ v1_xboole_0(J)
& v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),G1))
& v1_xboole_0(J) )
& ~ ( ~ v1_xboole_0(K)
& v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,k1_gate_1(G1)))
& v1_xboole_0(K) )
& ~ ( ~ v1_xboole_0(L)
& v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,G1))
& v1_xboole_0(L) )
& ~ ( ~ v1_xboole_0(M)
& v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),k1_gate_1(G1)))
& v1_xboole_0(M) )
& ~ ( ~ v1_xboole_0(N)
& v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),G1))
& v1_xboole_0(N) )
& ~ ( ~ v1_xboole_0(O)
& v1_xboole_0(k14_gate_1(J1,I1,H1,k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,H1,k1_gate_1(G1)))
& v1_xboole_0(O) )
& ~ ( ~ v1_xboole_0(P)
& v1_xboole_0(k14_gate_1(J1,I1,H1,G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,H1,G1))
& v1_xboole_0(P) )
& ~ ( ~ v1_xboole_0(Q)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1)))
& v1_xboole_0(Q) )
& ~ ( ~ v1_xboole_0(R)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),K1))
& v1_xboole_0(R) )
& ~ ( ~ v1_xboole_0(S)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,k1_gate_1(K1)))
& v1_xboole_0(S) )
& ~ ( ~ v1_xboole_0(T)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,K1))
& v1_xboole_0(T) )
& ~ ( ~ v1_xboole_0(U)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),k1_gate_1(K1)))
& v1_xboole_0(U) )
& ~ ( ~ v1_xboole_0(V)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),K1))
& v1_xboole_0(V) )
& ~ ( ~ v1_xboole_0(W)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,k1_gate_1(K1)))
& v1_xboole_0(W) )
& ~ ( ~ v1_xboole_0(X)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,K1))
& v1_xboole_0(X) )
& ~ ( ~ v1_xboole_0(Y)
& v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1)))
& v1_xboole_0(Y) )
& ~ ( ~ v1_xboole_0(Z)
& v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),K1))
& v1_xboole_0(Z) )
& ~ ( ~ v1_xboole_0(A1)
& v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,k1_gate_1(K1)))
& v1_xboole_0(A1) )
& ~ ( ~ v1_xboole_0(B1)
& v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,K1))
& v1_xboole_0(B1) )
& ~ ( ~ v1_xboole_0(C1)
& v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),k1_gate_1(K1)))
& v1_xboole_0(C1) )
& ~ ( ~ v1_xboole_0(D1)
& v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),K1))
& v1_xboole_0(D1) )
& ~ ( ~ v1_xboole_0(E1)
& v1_xboole_0(k14_gate_1(N1,M1,L1,k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,L1,k1_gate_1(K1)))
& v1_xboole_0(E1) )
& ~ ( ~ v1_xboole_0(F1)
& v1_xboole_0(k14_gate_1(N1,M1,L1,K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,L1,K1))
& v1_xboole_0(F1) )
& ~ ( ~ v1_xboole_0(K1)
& v1_xboole_0(k1_gate_1(J1)) )
& ~ ( ~ v1_xboole_0(k1_gate_1(J1))
& v1_xboole_0(K1) )
& ~ ( ~ v1_xboole_0(L1)
& v1_xboole_0(G1) )
& ~ ( ~ v1_xboole_0(G1)
& v1_xboole_0(L1) )
& ~ ( ~ v1_xboole_0(M1)
& v1_xboole_0(H1) )
& ~ ( ~ v1_xboole_0(H1)
& v1_xboole_0(M1) )
& ~ ( ~ v1_xboole_0(N1)
& v1_xboole_0(I1) )
& ~ ( ~ v1_xboole_0(I1)
& v1_xboole_0(N1) )
& ~ ( ~ ( ~ v1_xboole_0(R)
& v1_xboole_0(A) )
& ~ ( ~ v1_xboole_0(A)
& v1_xboole_0(R) )
& ~ ( ~ v1_xboole_0(T)
& v1_xboole_0(B) )
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(T) )
& ~ ( ~ v1_xboole_0(X)
& v1_xboole_0(D) )
& ~ ( ~ v1_xboole_0(D)
& v1_xboole_0(X) )
& ~ ( ~ v1_xboole_0(F1)
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(F1) )
& ~ ( ~ v1_xboole_0(E1)
& v1_xboole_0(P) )
& ~ ( ~ v1_xboole_0(P)
& v1_xboole_0(E1) )
& ~ ( ~ v1_xboole_0(C1)
& v1_xboole_0(O) )
& ~ ( ~ v1_xboole_0(O)
& v1_xboole_0(C1) )
& ~ ( ~ v1_xboole_0(Y)
& v1_xboole_0(M) )
& ~ ( ~ v1_xboole_0(M)
& v1_xboole_0(Y) )
& ~ ( ~ v1_xboole_0(Q)
& v1_xboole_0(I) )
& ~ ( ~ v1_xboole_0(I)
& v1_xboole_0(Q) )
& ~ ( ~ v1_xboole_0(V)
& v1_xboole_0(C) )
& ~ ( ~ v1_xboole_0(C)
& v1_xboole_0(V) )
& ~ ( ~ v1_xboole_0(B1)
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(B1) )
& ~ ( ~ v1_xboole_0(W)
& v1_xboole_0(L) )
& ~ ( ~ v1_xboole_0(L)
& v1_xboole_0(W) )
& ~ ( ~ v1_xboole_0(D1)
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(D1) )
& ~ ( ~ v1_xboole_0(A1)
& v1_xboole_0(N) )
& ~ ( ~ v1_xboole_0(N)
& v1_xboole_0(A1) )
& ~ ( ~ v1_xboole_0(U)
& v1_xboole_0(K) )
& ~ ( ~ v1_xboole_0(K)
& v1_xboole_0(U) )
& ~ ( ~ v1_xboole_0(Z)
& v1_xboole_0(E) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(Z) )
& ~ ( ~ v1_xboole_0(S)
& v1_xboole_0(J) )
& ~ ( ~ v1_xboole_0(J)
& v1_xboole_0(S) ) ) ) ).
fof(t6_gate_3,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(A)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1)))
& v1_xboole_0(A) )
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),G1))
& v1_xboole_0(B) )
& ~ ( ~ v1_xboole_0(C)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,k1_gate_1(G1)))
& v1_xboole_0(C) )
& ~ ( ~ v1_xboole_0(D)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,G1))
& v1_xboole_0(D) )
& ~ ( ~ v1_xboole_0(E)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),k1_gate_1(G1)))
& v1_xboole_0(E) )
& ~ ( ~ v1_xboole_0(F)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),G1))
& v1_xboole_0(F) )
& ~ ( ~ v1_xboole_0(G)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,k1_gate_1(G1)))
& v1_xboole_0(G) )
& ~ ( ~ v1_xboole_0(H)
& v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,G1))
& v1_xboole_0(H) )
& ~ ( ~ v1_xboole_0(I)
& v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1)))
& v1_xboole_0(I) )
& ~ ( ~ v1_xboole_0(J)
& v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),G1))
& v1_xboole_0(J) )
& ~ ( ~ v1_xboole_0(K)
& v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,k1_gate_1(G1)))
& v1_xboole_0(K) )
& ~ ( ~ v1_xboole_0(L)
& v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,G1))
& v1_xboole_0(L) )
& ~ ( ~ v1_xboole_0(M)
& v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),k1_gate_1(G1)))
& v1_xboole_0(M) )
& ~ ( ~ v1_xboole_0(N)
& v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),G1))
& v1_xboole_0(N) )
& ~ ( ~ v1_xboole_0(O)
& v1_xboole_0(k14_gate_1(J1,I1,H1,k1_gate_1(G1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,H1,k1_gate_1(G1)))
& v1_xboole_0(O) )
& ~ ( ~ v1_xboole_0(P)
& v1_xboole_0(k14_gate_1(J1,I1,H1,G1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,H1,G1))
& v1_xboole_0(P) )
& ~ ( ~ v1_xboole_0(Q)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1)))
& v1_xboole_0(Q) )
& ~ ( ~ v1_xboole_0(R)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),K1))
& v1_xboole_0(R) )
& ~ ( ~ v1_xboole_0(S)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,k1_gate_1(K1)))
& v1_xboole_0(S) )
& ~ ( ~ v1_xboole_0(T)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,K1))
& v1_xboole_0(T) )
& ~ ( ~ v1_xboole_0(U)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),k1_gate_1(K1)))
& v1_xboole_0(U) )
& ~ ( ~ v1_xboole_0(V)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),K1))
& v1_xboole_0(V) )
& ~ ( ~ v1_xboole_0(W)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,k1_gate_1(K1)))
& v1_xboole_0(W) )
& ~ ( ~ v1_xboole_0(X)
& v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,K1))
& v1_xboole_0(X) )
& ~ ( ~ v1_xboole_0(Y)
& v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1)))
& v1_xboole_0(Y) )
& ~ ( ~ v1_xboole_0(Z)
& v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),K1))
& v1_xboole_0(Z) )
& ~ ( ~ v1_xboole_0(A1)
& v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,k1_gate_1(K1)))
& v1_xboole_0(A1) )
& ~ ( ~ v1_xboole_0(B1)
& v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,K1))
& v1_xboole_0(B1) )
& ~ ( ~ v1_xboole_0(C1)
& v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),k1_gate_1(K1)))
& v1_xboole_0(C1) )
& ~ ( ~ v1_xboole_0(D1)
& v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),K1))
& v1_xboole_0(D1) )
& ~ ( ~ v1_xboole_0(E1)
& v1_xboole_0(k14_gate_1(N1,M1,L1,k1_gate_1(K1))) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,L1,k1_gate_1(K1)))
& v1_xboole_0(E1) )
& ~ ( ~ v1_xboole_0(F1)
& v1_xboole_0(k14_gate_1(N1,M1,L1,K1)) )
& ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,L1,K1))
& v1_xboole_0(F1) )
& ~ ( ~ v1_xboole_0(K1)
& v1_xboole_0(k2_gate_1(k1_gate_1(J1),O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J1),O1))
& v1_xboole_0(K1) )
& ~ ( ~ v1_xboole_0(L1)
& v1_xboole_0(k2_gate_1(G1,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(G1,O1))
& v1_xboole_0(L1) )
& ~ ( ~ v1_xboole_0(M1)
& v1_xboole_0(k2_gate_1(H1,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(H1,O1))
& v1_xboole_0(M1) )
& ~ ( ~ v1_xboole_0(N1)
& v1_xboole_0(k2_gate_1(I1,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(I1,O1))
& v1_xboole_0(N1) )
& ~ ( ~ ( ~ v1_xboole_0(R)
& v1_xboole_0(k2_gate_1(A,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(A,O1))
& v1_xboole_0(R) )
& ~ ( ~ v1_xboole_0(T)
& v1_xboole_0(k2_gate_1(B,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(B,O1))
& v1_xboole_0(T) )
& ~ ( ~ v1_xboole_0(X)
& v1_xboole_0(k2_gate_1(D,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(D,O1))
& v1_xboole_0(X) )
& ~ ( ~ v1_xboole_0(F1)
& v1_xboole_0(k2_gate_1(H,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(H,O1))
& v1_xboole_0(F1) )
& ~ ( ~ v1_xboole_0(E1)
& v1_xboole_0(k2_gate_1(P,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(P,O1))
& v1_xboole_0(E1) )
& ~ ( ~ v1_xboole_0(C1)
& v1_xboole_0(k2_gate_1(O,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(O,O1))
& v1_xboole_0(C1) )
& ~ ( ~ v1_xboole_0(Y)
& v1_xboole_0(k2_gate_1(M,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(M,O1))
& v1_xboole_0(Y) )
& ~ ( ~ v1_xboole_0(Q)
& v1_xboole_0(k3_gate_1(k2_gate_1(I,O1),k1_gate_1(O1))) )
& ~ ( ~ v1_xboole_0(k3_gate_1(k2_gate_1(I,O1),k1_gate_1(O1)))
& v1_xboole_0(Q) )
& ~ ( ~ v1_xboole_0(V)
& v1_xboole_0(k2_gate_1(C,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(C,O1))
& v1_xboole_0(V) )
& ~ ( ~ v1_xboole_0(B1)
& v1_xboole_0(k2_gate_1(F,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(F,O1))
& v1_xboole_0(B1) )
& ~ ( ~ v1_xboole_0(W)
& v1_xboole_0(k2_gate_1(L,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(L,O1))
& v1_xboole_0(W) )
& ~ ( ~ v1_xboole_0(D1)
& v1_xboole_0(k2_gate_1(G,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(G,O1))
& v1_xboole_0(D1) )
& ~ ( ~ v1_xboole_0(A1)
& v1_xboole_0(k2_gate_1(N,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(N,O1))
& v1_xboole_0(A1) )
& ~ ( ~ v1_xboole_0(U)
& v1_xboole_0(k2_gate_1(K,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(K,O1))
& v1_xboole_0(U) )
& ~ ( ~ v1_xboole_0(Z)
& v1_xboole_0(k2_gate_1(E,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(E,O1))
& v1_xboole_0(Z) )
& ~ ( ~ v1_xboole_0(S)
& v1_xboole_0(k2_gate_1(J,O1)) )
& ~ ( ~ v1_xboole_0(k2_gate_1(J,O1))
& v1_xboole_0(S) ) ) ) ).
%------------------------------------------------------------------------------