diff -r c44a012cf950 -r d91296e4deb3 src/HOL/ex/mesontest.ML
--- a/src/HOL/ex/mesontest.ML	Fri Mar 15 18:42:36 1996 +0100
+++ b/src/HOL/ex/mesontest.ML	Fri Mar 15 18:43:33 1996 +0100
@@ -1,4 +1,4 @@
-(*  Title:      HOL/ex/meson
+(*  Title:      HOL/ex/mesontest
     ID:         $Id$
     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     Copyright   1992  University of Cambridge
@@ -8,6 +8,7 @@
 
 show_hyps:=false;
 
+full_deriv:=false;
 by (rtac ccontr 1);
 val [prem] = gethyps 1;
 val nnf = make_nnf prem;
@@ -16,10 +17,12 @@
 val [_,sko] = gethyps 1;
 val clauses = make_clauses [sko];       
 val horns = make_horns clauses;
-val go::_ = neg_clauses clauses;
+val goes = neg_clauses clauses;
 
 goal HOL.thy "False";
-by (rtac (make_goal go) 1);
+by (resolve_tac (map make_goal goes) 1);
+full_deriv:=true;
+
 by (prolog_step_tac horns 1);
 by (depth_prolog_tac horns);
 by (best_prolog_tac size_of_subgoals horns);
@@ -27,6 +30,12 @@
 
 writeln"File HOL/ex/meson-test.";
 
+(*Deep unifications can be required, esp. during transformation to clauses*)
+val orig_trace_bound = !Unify.trace_bound
+and orig_search_bound = !Unify.search_bound;
+Unify.trace_bound := 20;
+Unify.search_bound := 40;
+
 (**** Interactive examples ****)
 
 (*Generate nice names for Skolem functions*)
@@ -34,11 +43,11 @@
 
 
 writeln"Problem 25";
-goal HOL.thy "(? x. P(x)) &  \
-\       (! x. L(x) --> ~ (M(x) & R(x))) &  \
-\       (! x. P(x) --> (M(x) & L(x))) &   \
-\       ((! x. P(x)-->Q(x)) | (? x. P(x)&R(x)))  \
-\   --> (? x. Q(x)&P(x))";
+goal HOL.thy "(? x. P x) &  \
+\       (! x. L x --> ~ (M x & R x)) &  \
+\       (! x. P x --> (M x & L x)) &   \
+\       ((! x. P x --> Q x) | (? x. P x & R x))  \
+\   --> (? x. Q x & P x)";
 by (rtac ccontr 1);
 val [prem25] = gethyps 1;
 val nnf25 = make_nnf prem25;
@@ -55,9 +64,9 @@
 
 
 writeln"Problem 26";
-goal HOL.thy "((? x. p(x)) = (? x. q(x))) &     \
-\     (! x. ! y. p(x) & q(y) --> (r(x) = s(y))) \
-\ --> ((! x. p(x)-->r(x)) = (! x. q(x)-->s(x)))";
+goal HOL.thy "((? x. p x) = (? x. q x)) &     \
+\     (! x. ! y. p x & q y --> (r x = s y)) \
+\ --> ((! x. p x --> r x) = (! x. q x --> s x))";
 by (rtac ccontr 1);
 val [prem26] = gethyps 1;
 val nnf26 = make_nnf prem26;
@@ -70,11 +79,11 @@
 
 goal HOL.thy "False";
 by (rtac (make_goal go26) 1);
-by (depth_prolog_tac horns26);  (*6 secs*)
+by (depth_prolog_tac horns26);  (*1.4 secs*)
+(*Proof is of length 107!!*)
 
 
-
-writeln"Problem 43  NOW PROVED AUTOMATICALLY!!";
+writeln"Problem 43  NOW PROVED AUTOMATICALLY!!";  (*16 Horn clauses*)
 goal HOL.thy "(! x. ! y. q x y = (! z. p z x = (p z y::bool)))  \
 \         --> (! x. (! y. q x y = (q y x::bool)))";
 by (rtac ccontr 1);
@@ -89,8 +98,42 @@
 
 goal HOL.thy "False";
 by (rtac (make_goal go43) 1);
-by (best_prolog_tac size_of_subgoals horns43);
-(*8.7 secs*)
+by (best_prolog_tac size_of_subgoals horns43);   (*1.6 secs*)
+
+(* 
+#1  (q x xa ==> ~ q x xa) ==> q xa x
+#2  (q xa x ==> ~ q xa x) ==> q x xa
+#3  (~ q x xa ==> q x xa) ==> ~ q xa x
+#4  (~ q xa x ==> q xa x) ==> ~ q x xa
+#5  [| ~ q ?U ?V ==> q ?U ?V; ~ p ?W ?U ==> p ?W ?U |] ==> p ?W ?V
+#6  [| ~ p ?W ?U ==> p ?W ?U; p ?W ?V ==> ~ p ?W ?V |] ==> ~ q ?U ?V
+#7  [| p ?W ?V ==> ~ p ?W ?V; ~ q ?U ?V ==> q ?U ?V |] ==> ~ p ?W ?U
+#8  [| ~ q ?U ?V ==> q ?U ?V; ~ p ?W ?V ==> p ?W ?V |] ==> p ?W ?U
+#9  [| ~ p ?W ?V ==> p ?W ?V; p ?W ?U ==> ~ p ?W ?U |] ==> ~ q ?U ?V
+#10 [| p ?W ?U ==> ~ p ?W ?U; ~ q ?U ?V ==> q ?U ?V |] ==> ~ p ?W ?V
+#11 [| p (xb ?U ?V) ?U ==> ~ p (xb ?U ?V) ?U;
+       p (xb ?U ?V) ?V ==> ~ p (xb ?U ?V) ?V |] ==> q ?U ?V
+#12 [| p (xb ?U ?V) ?V ==> ~ p (xb ?U ?V) ?V; q ?U ?V ==> ~ q ?U ?V |] ==>
+    p (xb ?U ?V) ?U
+#13 [| q ?U ?V ==> ~ q ?U ?V; p (xb ?U ?V) ?U ==> ~ p (xb ?U ?V) ?U |] ==>
+    p (xb ?U ?V) ?V
+#14 [| ~ p (xb ?U ?V) ?U ==> p (xb ?U ?V) ?U;
+       ~ p (xb ?U ?V) ?V ==> p (xb ?U ?V) ?V |] ==> q ?U ?V
+#15 [| ~ p (xb ?U ?V) ?V ==> p (xb ?U ?V) ?V; q ?U ?V ==> ~ q ?U ?V |] ==>
+    ~ p (xb ?U ?V) ?U
+#16 [| q ?U ?V ==> ~ q ?U ?V; ~ p (xb ?U ?V) ?U ==> p (xb ?U ?V) ?U |] ==>
+    ~ p (xb ?U ?V) ?V
+
+And here is the proof!  (Unkn is the start state after use of goal clause)
+[Unkn, Res ([Thm "#14"], false, 1), Res ([Thm "#5"], false, 1),
+   Res ([Thm "#1"], false, 1), Asm 1, Res ([Thm "#13"], false, 1), Asm 2,
+   Asm 1, Res ([Thm "#13"], false, 1), Asm 1, Res ([Thm "#10"], false, 1),
+   Res ([Thm "#16"], false, 1), Asm 2, Asm 1, Res ([Thm "#1"], false, 1),
+   Asm 1, Res ([Thm "#14"], false, 1), Res ([Thm "#5"], false, 1),
+   Res ([Thm "#2"], false, 1), Asm 1, Res ([Thm "#13"], false, 1), Asm 2,
+   Asm 1, Res ([Thm "#8"], false, 1), Res ([Thm "#2"], false, 1), Asm 1,
+   Res ([Thm "#12"], false, 1), Asm 2, Asm 1] : lderiv list
+*)
 
 
 (*Restore variable name preservation*)
@@ -111,7 +154,7 @@
 
 writeln"Pelletier's examples";
 (*1*)
-goal HOL.thy "(P-->Q)  =  (~Q --> ~P)";
+goal HOL.thy "(P --> Q)  =  (~Q --> ~P)";
 by (safe_meson_tac 1);
 result();
 
@@ -167,7 +210,7 @@
 
 (*12.  "Dijkstra's law"*)
 goal HOL.thy "((P = Q) = R) = (P = (Q = R))";
-by (best_meson_tac size_of_subgoals 1);
+by (safe_meson_tac 1);
 result();
 
 (*13.  Distributive law*)
@@ -197,151 +240,152 @@
 
 writeln"Classical Logic: examples with quantifiers";
 
-goal HOL.thy "(! x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
+goal HOL.thy "(! x. P x & Q x) = ((! x. P x) & (! x. Q x))";
 by (safe_meson_tac 1);
 result(); 
 
-goal HOL.thy "(? x. P-->Q(x))  =  (P --> (? x.Q(x)))";
+goal HOL.thy "(? x. P --> Q x)  =  (P --> (? x.Q x))";
 by (safe_meson_tac 1);
 result(); 
 
-goal HOL.thy "(? x.P(x)-->Q) = ((! x.P(x)) --> Q)";
+goal HOL.thy "(? x.P x --> Q) = ((! x.P x) --> Q)";
 by (safe_meson_tac 1);
 result(); 
 
-goal HOL.thy "((! x.P(x)) | Q)  =  (! x. P(x) | Q)";
+goal HOL.thy "((! x.P x) | Q)  =  (! x. P x | Q)";
 by (safe_meson_tac 1);
 result(); 
 
-goal HOL.thy "(! x. P(x)-->P(f(x)))  &  P(d)-->P(f(f(f(d))))";
+goal HOL.thy "(! x. P x --> P(f x))  &  P d --> P(f(f(f d)))";
 by (safe_meson_tac 1);
 result();
 
 (*Needs double instantiation of EXISTS*)
-goal HOL.thy "? x. P(x) --> P(a) & P(b)";
+goal HOL.thy "? x. P x --> P a & P b";
 by (safe_meson_tac 1);
 result();
 
-goal HOL.thy "? z. P(z) --> (! x. P(x))";
+goal HOL.thy "? z. P z --> (! x. P x)";
 by (safe_meson_tac 1);
 result();
 
 writeln"Hard examples with quantifiers";
 
 writeln"Problem 18";
-goal HOL.thy "? y. ! x. P(y)-->P(x)";
+goal HOL.thy "? y. ! x. P y --> P x";
 by (safe_meson_tac 1);
 result(); 
 
 writeln"Problem 19";
-goal HOL.thy "? x. ! y z. (P(y)-->Q(z)) --> (P(x)-->Q(x))";
+goal HOL.thy "? x. ! y z. (P y --> Q z) --> (P x --> Q x)";
 by (safe_meson_tac 1);
 result();
 
 writeln"Problem 20";
-goal HOL.thy "(! x y. ? z. ! w. (P(x)&Q(y)-->R(z)&S(w)))     \
-\   --> (? x y. P(x) & Q(y)) --> (? z. R(z))";
+goal HOL.thy "(! x y. ? z. ! w. (P x & Q y --> R z & S w))     \
+\   --> (? x y. P x & Q y) --> (? z. R z)";
 by (safe_meson_tac 1); 
 result();
 
 writeln"Problem 21";
-goal HOL.thy "(? x. P-->Q(x)) & (? x. Q(x)-->P) --> (? x. P=Q(x))";
+goal HOL.thy "(? x. P --> Q x) & (? x. Q x --> P) --> (? x. P=Q x)";
 by (safe_meson_tac 1); 
 result();
 
 writeln"Problem 22";
-goal HOL.thy "(! x. P = Q(x))  -->  (P = (! x. Q(x)))";
+goal HOL.thy "(! x. P = Q x)  -->  (P = (! x. Q x))";
 by (safe_meson_tac 1); 
 result();
 
 writeln"Problem 23";
-goal HOL.thy "(! x. P | Q(x))  =  (P | (! x. Q(x)))";
+goal HOL.thy "(! x. P | Q x)  =  (P | (! x. Q x))";
 by (safe_meson_tac 1);  
 result();
 
-writeln"Problem 24";
-goal HOL.thy "~(? x. S(x)&Q(x)) & (! x. P(x) --> Q(x)|R(x)) &  \
-\    ~(? x.P(x)) --> (? x.Q(x)) & (! x. Q(x)|R(x) --> S(x))  \
-\   --> (? x. P(x)&R(x))";
+writeln"Problem 24";  (*The first goal clause is useless*)
+goal HOL.thy "~(? x. S x & Q x) & (! x. P x --> Q x | R x) &  \
+\    ~(? x.P x) --> (? x.Q x) & (! x. Q x | R x --> S x)  \
+\   --> (? x. P x & R x)";
 by (safe_meson_tac 1); 
 result();
 
 writeln"Problem 25";
-goal HOL.thy "(? x. P(x)) &  \
-\       (! x. L(x) --> ~ (M(x) & R(x))) &  \
-\       (! x. P(x) --> (M(x) & L(x))) &   \
-\       ((! x. P(x)-->Q(x)) | (? x. P(x)&R(x)))  \
-\   --> (? x. Q(x)&P(x))";
+goal HOL.thy "(? x. P x) &  \
+\       (! x. L x --> ~ (M x & R x)) &  \
+\       (! x. P x --> (M x & L x)) &   \
+\       ((! x. P x --> Q x) | (? x. P x & R x))  \
+\   --> (? x. Q x & P x)";
 by (safe_meson_tac 1); 
 result();
 
-writeln"Problem 26";
-goal HOL.thy "((? x. p(x)) = (? x. q(x))) &     \
-\     (! x. ! y. p(x) & q(y) --> (r(x) = s(y))) \
-\ --> ((! x. p(x)-->r(x)) = (! x. q(x)-->s(x)))";
+writeln"Problem 26";  (*24 Horn clauses*)
+goal HOL.thy "((? x. p x) = (? x. q x)) &     \
+\     (! x. ! y. p x & q y --> (r x = s y)) \
+\ --> ((! x. p x --> r x) = (! x. q x --> s x))";
 by (safe_meson_tac 1); 
 result();
 
-writeln"Problem 27";
-goal HOL.thy "(? x. P(x) & ~Q(x)) &   \
-\             (! x. P(x) --> R(x)) &   \
-\             (! x. M(x) & L(x) --> P(x)) &   \
-\             ((? x. R(x) & ~ Q(x)) --> (! x. L(x) --> ~ R(x)))  \
-\         --> (! x. M(x) --> ~L(x))";
+writeln"Problem 27";	(*13 Horn clauses*)
+goal HOL.thy "(? x. P x & ~Q x) &   \
+\             (! x. P x --> R x) &   \
+\             (! x. M x & L x --> P x) &   \
+\             ((? x. R x & ~ Q x) --> (! x. L x --> ~ R x))  \
+\         --> (! x. M x --> ~L x)";
 by (safe_meson_tac 1); 
 result();
 
-writeln"Problem 28.  AMENDED";
-goal HOL.thy "(! x. P(x) --> (! x. Q(x))) &   \
-\       ((! x. Q(x)|R(x)) --> (? x. Q(x)&S(x))) &  \
-\       ((? x.S(x)) --> (! x. L(x) --> M(x)))  \
-\   --> (! x. P(x) & L(x) --> M(x))";
+writeln"Problem 28.  AMENDED";	(*14 Horn clauses*)
+goal HOL.thy "(! x. P x --> (! x. Q x)) &   \
+\       ((! x. Q x | R x) --> (? x. Q x & S x)) &  \
+\       ((? x.S x) --> (! x. L x --> M x))  \
+\   --> (! x. P x & L x --> M x)";
 by (safe_meson_tac 1);  
 result();
 
 writeln"Problem 29.  Essentially the same as Principia Mathematica *11.71";
-goal HOL.thy "(? x. F(x)) & (? y. G(y))  \
-\   --> ( ((! x. F(x)-->H(x)) & (! y. G(y)-->J(y)))  =   \
-\         (! x y. F(x) & G(y) --> H(x) & J(y)))";
-by (safe_meson_tac 1);          (*5 secs*)
+	(*62 Horn clauses*)
+goal HOL.thy "(? x. F x) & (? y. G y)  \
+\   --> ( ((! x. F x --> H x) & (! y. G y --> J y))  =   \
+\         (! x y. F x & G y --> H x & J y))";
+by (safe_meson_tac 1);          (*0.7 secs*)
 result();
 
 writeln"Problem 30";
-goal HOL.thy "(! x. P(x) | Q(x) --> ~ R(x)) & \
-\       (! x. (Q(x) --> ~ S(x)) --> P(x) & R(x))  \
-\   --> (! x. S(x))";
+goal HOL.thy "(! x. P x | Q x --> ~ R x) & \
+\       (! x. (Q x --> ~ S x) --> P x & R x)  \
+\   --> (! x. S x)";
 by (safe_meson_tac 1);  
 result();
 
-writeln"Problem 31";
-goal HOL.thy "~(? x.P(x) & (Q(x) | R(x))) & \
-\       (? x. L(x) & P(x)) & \
-\       (! x. ~ R(x) --> M(x))  \
-\   --> (? x. L(x) & M(x))";
+writeln"Problem 31";  (*10 Horn clauses; first negative clauses is useless*)
+goal HOL.thy "~(? x.P x & (Q x | R x)) & \
+\       (? x. L x & P x) & \
+\       (! x. ~ R x --> M x)  \
+\   --> (? x. L x & M x)";
 by (safe_meson_tac 1);
 result();
 
 writeln"Problem 32";
-goal HOL.thy "(! x. P(x) & (Q(x)|R(x))-->S(x)) & \
-\       (! x. S(x) & R(x) --> L(x)) & \
-\       (! x. M(x) --> R(x))  \
-\   --> (! x. P(x) & M(x) --> L(x))";
+goal HOL.thy "(! x. P x & (Q x | R x)-->S x) & \
+\       (! x. S x & R x --> L x) & \
+\       (! x. M x --> R x)  \
+\   --> (! x. P x & M x --> L x)";
 by (safe_meson_tac 1);
 result();
 
-writeln"Problem 33";
-goal HOL.thy "(! x. P(a) & (P(x)-->P(b))-->P(c))  =    \
-\    (! x. (~P(a) | P(x) | P(c)) & (~P(a) | ~P(b) | P(c)))";
+writeln"Problem 33";  (*55 Horn clauses*)
+goal HOL.thy "(! x. P a & (P x --> P b)-->P c)  =    \
+\    (! x. (~P a | P x | P c) & (~P a | ~P b | P c))";
 by (safe_meson_tac 1);          (*5.6 secs*)
 result();
 
-writeln"Problem 34  AMENDED (TWICE!!)";
+writeln"Problem 34  AMENDED (TWICE!!)"; (*924 Horn clauses*)
 (*Andrews's challenge*)
-goal HOL.thy "((? x. ! y. p(x) = p(y))  =               \
-\              ((? x. q(x)) = (! y. p(y))))     =       \
-\             ((? x. ! y. q(x) = q(y))  =               \
-\              ((? x. p(x)) = (! y. q(y))))";
-by (safe_meson_tac 1);          (*90 secs*)
+goal HOL.thy "((? x. ! y. p x = p y)  =               \
+\              ((? x. q x) = (! y. p y)))     =       \
+\             ((? x. ! y. q x = q y)  =               \
+\              ((? x. p x) = (! y. q y)))";
+by (safe_meson_tac 1);          (*13 secs*)
 result();
 
 writeln"Problem 35";
@@ -349,7 +393,7 @@
 by (safe_meson_tac 1);
 result();
 
-writeln"Problem 36";
+writeln"Problem 36";  (*15 Horn clauses*)
 goal HOL.thy "(! x. ? y. J x y) & \
 \       (! x. ? y. G x y) & \
 \       (! x y. J x y | G x y -->       \
@@ -358,23 +402,23 @@
 by (safe_meson_tac 1);
 result();
 
-writeln"Problem 37";
+writeln"Problem 37";  (*10 Horn clauses*)
 goal HOL.thy "(! z. ? w. ! x. ? y. \
-\          (P x z-->P y w) & P y z & (P y w --> (? u.Q u w))) & \
+\          (P x z --> P y w) & P y z & (P y w --> (? u.Q u w))) & \
 \       (! x z. ~P x z --> (? y. Q y z)) & \
 \       ((? x y. Q x y) --> (! x. R x x))  \
 \   --> (! x. ? y. R x y)";
 by (safe_meson_tac 1);   (*causes unification tracing messages*)
 result();
 
-writeln"Problem 38";
+writeln"Problem 38";  (*Quite hard: 422 Horn clauses!!*)
 goal HOL.thy
-    "(! x. p(a) & (p(x) --> (? y. p(y) & r x y)) -->            \
-\          (? z. ? w. p(z) & r x w & r w z))  =                 \
-\    (! x. (~p(a) | p(x) | (? z. ? w. p(z) & r x w & r w z)) &  \
-\          (~p(a) | ~(? y. p(y) & r x y) |                      \
-\           (? z. ? w. p(z) & r x w & r w z)))";
-by (safe_meson_tac 1);          (*62 secs*)
+    "(! x. p a & (p x --> (? y. p y & r x y)) -->            \
+\          (? z. ? w. p z & r x w & r w z))  =                 \
+\    (! x. (~p a | p x | (? z. ? w. p z & r x w & r w z)) &  \
+\          (~p a | ~(? y. p y & r x y) |                      \
+\           (? z. ? w. p z & r x w & r w z)))";
+by (safe_best_meson_tac 1);  (*10 secs; iter. deepening is slightly slower*)
 result();
 
 writeln"Problem 39";
@@ -402,35 +446,61 @@
 writeln"Problem 43  NOW PROVED AUTOMATICALLY!!";
 goal HOL.thy "(! x. ! y. q x y = (! z. p z x = (p z y::bool)))  \
 \         --> (! x. (! y. q x y = (q y x::bool)))";
-by (safe_meson_tac 1);
+by (safe_best_meson_tac 1);	
+(*1.6 secs; iter. deepening is slightly slower*)
 result();
 
-writeln"Problem 44";
-goal HOL.thy "(! x. f(x) -->                                    \
-\             (? y. g(y) & h x y & (? y. g(y) & ~ h x y)))  &   \
-\             (? x. j(x) & (! y. g(y) --> h x y))               \
-\             --> (? x. j(x) & ~f(x))";
+writeln"Problem 44";  (*13 Horn clauses; 7-step proof*)
+goal HOL.thy "(! x. f x -->                                    \
+\             (? y. g y & h x y & (? y. g y & ~ h x y)))  &   \
+\             (? x. j x & (! y. g y --> h x y))               \
+\             --> (? x. j x & ~f x)";
 by (safe_meson_tac 1);
 result();
 
-writeln"Problem 45";
-goal HOL.thy "(! x. f(x) & (! y. g(y) & h x y --> j x y)        \
-\                     --> (! y. g(y) & h x y --> k(y))) &       \
-\     ~ (? y. l(y) & k(y)) &                                    \
-\     (? x. f(x) & (! y. h x y --> l(y))                        \
-\                  & (! y. g(y) & h x y --> j x y))             \
-\     --> (? x. f(x) & ~ (? y. g(y) & h x y))";
-by (safe_meson_tac 1);          (*11 secs*)
+writeln"Problem 45";  (*27 Horn clauses; 54-step proof*)
+goal HOL.thy "(! x. f x & (! y. g y & h x y --> j x y)        \
+\                     --> (! y. g y & h x y --> k y)) &       \
+\     ~ (? y. l y & k y) &                                    \
+\     (? x. f x & (! y. h x y --> l y)                        \
+\                  & (! y. g y & h x y --> j x y))             \
+\     --> (? x. f x & ~ (? y. g y & h x y))";
+by (safe_best_meson_tac 1);	
+(*1.6 secs; iter. deepening is slightly slower*)
+result();
+
+writeln"Problem 46";  (*26 Horn clauses; 21-step proof*)
+goal HOL.thy
+    "(! x. f x & (! y. f y & h y x --> g y) --> g x) &      \
+\    ((? x.f x & ~g x) -->                                    \
+\     (? x. f x & ~g x & (! y. f y & ~g y --> j x y))) &    \
+\    (! x y. f x & f y & h x y --> ~j y x)                    \
+\     --> (! x. f x --> g x)";
+by (safe_best_meson_tac 1);	
+(*1.7 secs; iter. deepening is slightly slower*)
 result();
 
-writeln"Problem 46";
+writeln"Problem 47.  Schubert's Steamroller";
+	(*26 clauses; 63 Horn clauses*)
 goal HOL.thy
-    "(! x. f(x) & (! y. f(y) & h y x --> g(y)) --> g(x)) &      \
-\    ((? x.f(x) & ~g(x)) -->                                    \
-\     (? x. f(x) & ~g(x) & (! y. f(y) & ~g(y) --> j x y))) &    \
-\    (! x y. f(x) & f(y) & h x y --> ~j y x)                    \
-\     --> (! x. f(x) --> g(x))";
-by (safe_meson_tac 1);          (*11 secs*)
+    "(! x. P1 x --> P0 x) & (? x.P1 x) &     \
+\    (! x. P2 x --> P0 x) & (? x.P2 x) &     \
+\    (! x. P3 x --> P0 x) & (? x.P3 x) &     \
+\    (! x. P4 x --> P0 x) & (? x.P4 x) &     \
+\    (! x. P5 x --> P0 x) & (? x.P5 x) &     \
+\    (! x. Q1 x --> Q0 x) & (? x.Q1 x) &     \
+\    (! x. P0 x --> ((! y.Q0 y-->R x y) |    \
+\                     (! y.P0 y & S y x &     \
+\                          (? z.Q0 z&R y z) --> R x y))) &   \
+\    (! x y. P3 y & (P5 x|P4 x) --> S x y) &        \
+\    (! x y. P3 x & P2 y --> S x y) &        \
+\    (! x y. P2 x & P1 y --> S x y) &        \
+\    (! x y. P1 x & (P2 y|Q1 y) --> ~R x y) &       \
+\    (! x y. P3 x & P4 y --> R x y) &        \
+\    (! x y. P3 x & P5 y --> ~R x y) &       \
+\    (! x. (P4 x|P5 x) --> (? y.Q0 y & R x y))      \
+\    --> (? x y. P0 x & P0 y & (? z. Q1 z & R y z & R x y))";
+by (safe_meson_tac 1);	 (*119 secs*)
 result();
 
 (*The Los problem?  Circulated by John Harrison*)
@@ -439,7 +509,7 @@
 \      (! x y. P x y --> P y x) &       \
 \      (! (x::'a) y. P x y | Q x y)     \
 \      --> (! x y. P x y) | (! x y. Q x y)";
-by (safe_meson_tac 1);
+by (safe_best_meson_tac 1);	(*3 secs; iter. deepening is VERY slow*)
 result();
 
 (*A similar example, suggested by Johannes Schumann and credited to Pelletier*)
@@ -447,7 +517,7 @@
 \       (!x y z. Q x y --> Q y z --> Q x z) --> \
 \       (!x y.Q x y --> Q y x) -->  (!x y. P x y | Q x y) --> \
 \       (!x y.P x y) | (!x y.Q x y)";
-by (safe_meson_tac 1);          (*32 secs*)
+by (safe_best_meson_tac 1);          (*2.7 secs*)
 result();
 
 writeln"Problem 50";  
@@ -460,12 +530,12 @@
 
 (*Non-equational version, from Manthey and Bry, CADE-9 (Springer, 1988).
   meson_tac cannot report who killed Agatha. *)
-goal HOL.thy "lives(agatha) & lives(butler) & lives(charles) & \
+goal HOL.thy "lives agatha & lives butler & lives charles & \
 \  (killed agatha agatha | killed butler agatha | killed charles agatha) & \
 \  (!x y. killed x y --> hates x y & ~richer x y) & \
 \  (!x. hates agatha x --> ~hates charles x) & \
 \  (hates agatha agatha & hates agatha charles) & \
-\  (!x. lives(x) & ~richer x agatha --> hates butler x) & \
+\  (!x. lives x & ~richer x agatha --> hates butler x) & \
 \  (!x. hates agatha x --> hates butler x) & \
 \  (!x. ~hates x agatha | ~hates x butler | ~hates x charles) --> \
 \  (? x. killed x agatha)";
@@ -482,12 +552,12 @@
 writeln"Problem 58";
 (* Challenge found on info-hol *)
 goal HOL.thy
-    "! P Q R x. ? v w. ! y z. P(x) & Q(y) --> (P(v) | R(w)) & (R(z) --> Q(v))";
+    "! P Q R x. ? v w. ! y z. P x & Q y --> (P v | R w) & (R z --> Q v)";
 by (safe_meson_tac 1);
 result();
 
 writeln"Problem 59";
-goal HOL.thy "(! x. P(x) = (~P(f(x)))) --> (? x. P(x) & ~P(f(x)))";
+goal HOL.thy "(! x. P x = (~P(f x))) --> (? x. P x & ~P(f x))";
 by (safe_meson_tac 1);
 result();
 
@@ -504,6 +574,40 @@
 by (safe_meson_tac 1);
 result();
 
+
+(** Charles Morgan's problems **)
+
+val axa = "! x y.   T(i x(i y x))";
+val axb = "! x y z. T(i(i x(i y z))(i(i x y)(i x z)))";
+val axc = "! x y.   T(i(i(n x)(n y))(i y x))";
+val axd = "! x y.   T(i x y) & T x --> T y";
+
+fun axjoin ([],   q) = q
+  | axjoin (p::ps, q) = "(" ^ p ^ ") --> (" ^ axjoin(ps,q) ^ ")";
+
+goal HOL.thy (axjoin([axa,axb,axd], "! x. T(i x x)"));
+by (safe_meson_tac 1);  
+result();
+
+writeln"Problem 66";  
+goal HOL.thy (axjoin([axa,axb,axc,axd], "! x. T(i x(n(n x)))"));
+(*TOO SLOW: more than 24 minutes!
+by (safe_meson_tac 1);
+result();
+*)
+
+writeln"Problem 67";  
+goal HOL.thy (axjoin([axa,axb,axc,axd], "! x. T(i(n(n x)) x)"));
+(*TOO SLOW: more than 3 minutes!
+by (safe_meson_tac 1);
+result();
+*)
+
+
+(*Restore original values*)
+Unify.trace_bound := orig_trace_bound;
+Unify.search_bound := orig_search_bound;
+
 writeln"Reached end of file.";
 
 (*26 August 1992: loaded in 277 secs.  New Jersey v 75*)