Read("ex-gp2.g");
Print("g = ",g,"\n");
Print("G = ", G,"\n");
Print("Query: prove that g is in G.\n");
Print("Answer:\n");
VerbalIsIn_Proof(g,G,"g","G");


Print("H = ",H,"\n");
Print("Query: prove that H is a subgroup of G.\n");
Print("Answer:\n");
VerbalIsSubgroup_Proof( H, G, "H","G" ) ;

Print("x = ", x," and G = ", G,".\n");
Print("Query: the G-orbit of x.\n");
Print("Answer:\n");
VerbalOrbit_Proof(G,x,"G");


Print("Query: the Schreier data of G at x.\n"); x := 1;
VerbalSchreierData(G,x,"G");

Print("Query: determine the stabilizer of G at x.\n");
G1 := Stabilizer(G,x);
VerbalIsStabiliser_Proof(G, x ,G1,"G","H");

Print("Query: a base for G and the corresponding stabilizer chain of G.\n");
B := BaseOfGroup(G);
VerbalIsBase_Proof(G,B,"G",0);

Print("\n\nQuery: ");
Print("Is h = ",h," in G =\n ",G,"?\n");
Print("Answer:\n");
VerbalIsNotIn_Proof(h,G,"h","G");

#Size of G
Print("Query: The size of G =\n ",G,"?\n");
Print("Answer:\n");
VerbalOrder_Proof(G);