update agentz3 sample based on hugging face training/test data

https://huggingface.co/datasets/CardinalOperations/IndustryOR/blob/main/IndustryOR.json

Author: NikolajBjorner

genaisrc/agentz3.genai.mts

@@ -0,0 +1,44 @@
+script({
+    tools: ["agent_z3"],
+})
+
+$`Solve the following problems using Z3:
+
+The Zhang family has 6 children: Harry, Hermione, Ron, Fred, George, and Ginny. 
+The cost of taking Harry is $1200, Hermione is $1650, Ron is $750, Fred is $800, 
+George is $800, and Ginny is $1500. Which children should the couple take to minimize 
+the total cost of taking the children? They can take up to four children on the upcoming trip.
+
+Ginny is the youngest, so the Zhang family will definitely take her.
+
+If the couple takes Harry, they will not take Fred because Harry does not get along with him.
+
+If the couple takes Harry, they will not take George because Harry does not get along with him.
+
+If they take George, they must also take Fred.
+
+If they take George, they must also take Hermione.
+
+Even though it will cost them a lot of money, the Zhang family has decided to take at least three children.
+
+The SMTLIB2 formula must not contain forall or exists. 
+Use the Z3 command "minimize" to instruct the solver to minimize the cost of taking the children.
+use the Z3 command "(check-sat)" to check if the formula is satisfiable.
+`
+
+
+/*
+
+
+Twenty golfers wish to play in foursomes for 5 days. Is it possible for each golfer to play no more
+ than once with any other golfer?
+
+Use SMTLIB2 to formulate the problem as a quantifier free formula over linear integer arithmetic, 
+also known as QF_LIA. 
+
+For every golfer and for every day assign a slot.
+The golfers are numbered from 1 to 20 and the days are numbered from 1 to 5.
+Express the problem as a set of integer variables, where each variable represents a golfer's slot on a given day.
+The variables should be named as follows: golfer_1_day_1, golfer_1_day_2, ..., golfer_20_day_5.
+
+*/