SET007 Axioms: SET007+139.ax
%------------------------------------------------------------------------------
% File : SET007+139 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 244 ( 0 equ)
% Maximal formula atoms : 108 ( 61 avg)
% Number of connectives : 486 ( 246 ~; 0 |; 237 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 82 ( 48 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-3 aty)
% Number of variables : 53 ( 53 !; 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_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) ) ) ) ).
%------------------------------------------------------------------------------