SET007 Axioms: SET007+139.ax


%------------------------------------------------------------------------------
% File     : SET007+139 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Correctness of Binary 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :    4 (   0 unit)
%            Number of atoms       :  244 (   0 equality)
%            Maximal formula depth :   82 (  48 average)
%            Number of connectives :  486 ( 246 ~  ;   0  |; 237  &)
%                                         (   0 <=>;   3 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    1 (   0 propositional; 1-1 arity)
%            Number of functors    :    5 (   0 constant; 1-3 arity)
%            Number of variables   :   53 (   0 singleton;  53 !;   0 ?)
%            Maximal term depth    :    5 (   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_2,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(Q)) )
        & ~ ( ~ v1_xboole_0(k1_gate_1(Q))
            & v1_xboole_0(T) )
        & ~ ( ~ v1_xboole_0(U)
            & v1_xboole_0(k4_gate_1(Q,R)) )
        & ~ ( ~ v1_xboole_0(k4_gate_1(Q,R))
            & v1_xboole_0(U) )
        & ~ ( ~ v1_xboole_0(V)
            & v1_xboole_0(k3_gate_1(k2_gate_1(S,k1_gate_1(Q)),k2_gate_1(Q,k4_gate_1(R,S)))) )
        & ~ ( ~ v1_xboole_0(k3_gate_1(k2_gate_1(S,k1_gate_1(Q)),k2_gate_1(Q,k4_gate_1(R,S))))
            & v1_xboole_0(V) )
        & ~ ( ~ ( ~ v1_xboole_0(J)
                & v1_xboole_0(A) )
            & ~ ( ~ v1_xboole_0(A)
                & v1_xboole_0(J) )
            & ~ ( ~ v1_xboole_0(K)
                & v1_xboole_0(B) )
            & ~ ( ~ v1_xboole_0(B)
                & v1_xboole_0(K) )
            & ~ ( ~ v1_xboole_0(L)
                & v1_xboole_0(C) )
            & ~ ( ~ v1_xboole_0(C)
                & v1_xboole_0(L) )
            & ~ ( ~ v1_xboole_0(M)
                & v1_xboole_0(D) )
            & ~ ( ~ v1_xboole_0(D)
                & v1_xboole_0(M) )
            & ~ ( ~ v1_xboole_0(N)
                & v1_xboole_0(E) )
            & ~ ( ~ v1_xboole_0(E)
                & v1_xboole_0(N) )
            & ~ ( ~ v1_xboole_0(O)
                & v1_xboole_0(F) )
            & ~ ( ~ v1_xboole_0(F)
                & v1_xboole_0(O) )
            & ~ ( ~ v1_xboole_0(P)
                & v1_xboole_0(G) )
            & ~ ( ~ v1_xboole_0(G)
                & v1_xboole_0(P) )
            & ~ ( ~ v1_xboole_0(I)
                & v1_xboole_0(H) )
            & ~ ( ~ v1_xboole_0(H)
                & v1_xboole_0(I) ) ) ) )).

fof(t2_gate_2,axiom,(
    ! [A,B,C,D] :
      ( ~ ( ~ v1_xboole_0(k8_gate_1(k2_gate_1(A,B),k2_gate_1(C,B),k2_gate_1(D,B)))
          & v1_xboole_0(k2_gate_1(k8_gate_1(A,C,D),B)) )
      & ~ ( ~ v1_xboole_0(k2_gate_1(k8_gate_1(A,C,D),B))
          & v1_xboole_0(k8_gate_1(k2_gate_1(A,B),k2_gate_1(C,B),k2_gate_1(D,B))) ) ) )).

fof(t3_gate_2,axiom,(
    ! [A,B,C,D] :
      ( ~ ( v1_xboole_0(k2_gate_1(A,B))
          & v1_xboole_0(k3_gate_1(k1_gate_1(A),k1_gate_1(B))) )
      & ( ~ v1_xboole_0(k3_gate_1(k1_gate_1(A),k1_gate_1(B)))
       => v1_xboole_0(k2_gate_1(A,B)) )
      & ~ ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ v1_xboole_0(k3_gate_1(C,B))
          & v1_xboole_0(k3_gate_1(k2_gate_1(A,C),B)) )
      & ( ~ v1_xboole_0(k3_gate_1(k2_gate_1(A,C),B))
       => ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ v1_xboole_0(k3_gate_1(C,B)) ) )
      & ~ ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ v1_xboole_0(k3_gate_1(C,B))
          & ~ v1_xboole_0(k3_gate_1(D,B))
          & v1_xboole_0(k3_gate_1(k8_gate_1(A,C,D),B)) )
      & ( ~ v1_xboole_0(k3_gate_1(k8_gate_1(A,C,D),B))
       => ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ v1_xboole_0(k3_gate_1(C,B))
          & ~ v1_xboole_0(k3_gate_1(D,B)) ) )
      & ~ ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(C) )
          & ~ ( ~ v1_xboole_0(C)
              & v1_xboole_0(A) )
          & v1_xboole_0(k3_gate_1(C,B)) ) ) )).

fof(t4_gate_2,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(Q),W)) )
        & ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(Q),W))
            & v1_xboole_0(T) )
        & ~ ( ~ v1_xboole_0(U)
            & v1_xboole_0(k2_gate_1(k4_gate_1(Q,R),W)) )
        & ~ ( ~ v1_xboole_0(k2_gate_1(k4_gate_1(Q,R),W))
            & v1_xboole_0(U) )
        & ~ ( ~ v1_xboole_0(V)
            & v1_xboole_0(k2_gate_1(k3_gate_1(k2_gate_1(S,k1_gate_1(Q)),k2_gate_1(Q,k4_gate_1(R,S))),W)) )
        & ~ ( ~ v1_xboole_0(k2_gate_1(k3_gate_1(k2_gate_1(S,k1_gate_1(Q)),k2_gate_1(Q,k4_gate_1(R,S))),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(K)
                & v1_xboole_0(k2_gate_1(B,W)) )
            & ~ ( ~ v1_xboole_0(k2_gate_1(B,W))
                & v1_xboole_0(K) )
            & ~ ( ~ v1_xboole_0(L)
                & v1_xboole_0(k2_gate_1(C,W)) )
            & ~ ( ~ v1_xboole_0(k2_gate_1(C,W))
                & v1_xboole_0(L) )
            & ~ ( ~ v1_xboole_0(M)
                & v1_xboole_0(k2_gate_1(D,W)) )
            & ~ ( ~ v1_xboole_0(k2_gate_1(D,W))
                & v1_xboole_0(M) )
            & ~ ( ~ v1_xboole_0(N)
                & v1_xboole_0(k2_gate_1(E,W)) )
            & ~ ( ~ v1_xboole_0(k2_gate_1(E,W))
                & v1_xboole_0(N) )
            & ~ ( ~ v1_xboole_0(O)
                & v1_xboole_0(k2_gate_1(F,W)) )
            & ~ ( ~ v1_xboole_0(k2_gate_1(F,W))
                & v1_xboole_0(O) )
            & ~ ( ~ v1_xboole_0(P)
                & v1_xboole_0(k2_gate_1(G,W)) )
            & ~ ( ~ v1_xboole_0(k2_gate_1(G,W))
                & v1_xboole_0(P) )
            & ~ ( ~ v1_xboole_0(I)
                & v1_xboole_0(k3_gate_1(H,k1_gate_1(W))) )
            & ~ ( ~ v1_xboole_0(k3_gate_1(H,k1_gate_1(W)))
                & v1_xboole_0(I) ) ) ) )).
%------------------------------------------------------------------------------