clear(print_given).
set(binary_res).
set(para_into).
clear(detailed_history).
clear(print_kept).
clear(print_back_sub).
assign(max_seconds,10).
assign(stats_level,0).

% This corresponds to the knowledge in Section 8.4.
% I use u, u1, u2, ... for gates, 
% x, x1, x2, ... for terminals, 
% and y, y1, y2, ... for signals

list(usable).
% if x1 is connected to x2, then they have the same signal
-connected(x1,x2) | signal(x1) = signal(x2).

% all signals are either 1 or 0
signal(x) = 1 | signal(x) = 0.
0 != 1.
y = y.

% if x1 is connected to x2, then x2 is connected to x1
-connected(x1,x2) | connected(x2,x1).


% the output of an OR is 0 iff 
% both of its two inputs are 0.
type(u) != OR | signal(in1(u)) != 1
 | signal(out(u)) = 1.

type(u) != OR | signal(in2(u)) != 1
 | signal(out(u)) = 1.

type(u) != OR
 | signal(in1(u)) != 0 | signal(in2(u)) != 0 
 | signal(out(u)) = 0.


% the output of an AND is 1 iff 
% both of its two inputs is 1
type(u) != AND | signal(in1(u)) != 0
 | signal(out(u)) = 0.

type(u) != AND | signal(in2(u)) != 0
 | signal(out(u)) = 0.

type(u) != AND
 | signal(in1(u)) != 1 | signal(in2(u)) != 1
 | signal(out(u)) = 1.


% the output of an XOR is 1 iff 
% its inputs are different
type(u) != XOR
 | signal(in1(u)) != signal(in2(u))
 | signal(out(u)) = 0.

type(u) != XOR
 | signal(in1(u)) = signal(in2(u))
 | signal(out(u)) = 1.

% gates in the circuit
type(exor1) = XOR.
type(exor2) = XOR.
type(and1) = AND.
type(and2) = AND.
type(or1) = OR.

% the connections using b1, b2, b3 as inputs, and add and carry as outputs
connected(b1,in1(exor1)).
connected(b2,in2(exor1)).
connected(b1,in1(and1)).
connected(b2,in2(and1)).
connected(out(exor1),in1(exor2)).
connected(b3,in2(exor2)).
connected(b3,in1(and2)).
connected(out(exor1),in2(and2)).
connected(out(and1),in1(or1)).
connected(out(and2),in2(or1)).
connected(out(exor2),add).
connected(out(or1),carry).

% a test case
signal(b1) = 1.
signal(b2) = 0.
signal(b3) = 1.
end_of_list.

list(sos).
% prove that add = 0 and carry = 1
% signal(add) = 1.
signal(carry) = 0.
end_of_list.