
diff -r 624faeda77b5 -r 175ac95720d4 src/HOL/SMT_Examples/SMT_Examples.thy
--- a/src/HOL/SMT_Examples/SMT_Examples.thy	Thu Mar 13 13:18:13 2014 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.thy	Thu Mar 13 13:18:13 2014 +0100
@@ -11,38 +11,40 @@
 declare [[smt_certificates = "SMT_Examples.certs"]]
 declare [[smt_read_only_certificates = true]]
 
+declare [[smt2_certificates = "SMT_Examples.certs2"]]
+declare [[smt2_read_only_certificates = true]]
 
 
 section {* Propositional and first-order logic *}
 
-lemma "True" by smt
+lemma "True" by smt2
 
-lemma "p \<or> \<not>p" by smt
+lemma "p \<or> \<not>p" by smt2
 
-lemma "(p \<and> True) = p" by smt
+lemma "(p \<and> True) = p" by smt2
 
-lemma "(p \<or> q) \<and> \<not>p \<Longrightarrow> q" by smt
+lemma "(p \<or> q) \<and> \<not>p \<Longrightarrow> q" by smt2
 
 lemma "(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)"
-  by smt
+  by smt2
 
-lemma "(p1 \<and> p2) \<or> p3 \<longrightarrow> (p1 \<longrightarrow> (p3 \<and> p2) \<or> (p1 \<and> p3)) \<or> p1" by smt
+lemma "(p1 \<and> p2) \<or> p3 \<longrightarrow> (p1 \<longrightarrow> (p3 \<and> p2) \<or> (p1 \<and> p3)) \<or> p1" by smt2
 
-lemma "P=P=P=P=P=P=P=P=P=P" by smt
+lemma "P = P = P = P = P = P = P = P = P = P" by smt2
 
 lemma
-  assumes "a | b | c | d"
-      and "e | f | (a & d)"
-      and "~(a | (c & ~c)) | b"
-      and "~(b & (x | ~x)) | c"
-      and "~(d | False) | c"
-      and "~(c | (~p & (p | (q & ~q))))"
+  assumes "a \<or> b \<or> c \<or> d"
+      and "e \<or> f \<or> (a \<and> d)"
+      and "\<not> (a \<or> (c \<and> ~c)) \<or> b"
+      and "\<not> (b \<and> (x \<or> \<not> x)) \<or> c"
+      and "\<not> (d \<or> False) \<or> c"
+      and "\<not> (c \<or> (\<not> p \<and> (p \<or> (q \<and> \<not> q))))"
   shows False
-  using assms by smt
+  using assms by smt2
 
 axiomatization symm_f :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" where
   symm_f: "symm_f x y = symm_f y x"
-lemma "a = a \<and> symm_f a b = symm_f b a" by (smt symm_f)
+lemma "a = a \<and> symm_f a b = symm_f b a" by (smt2 symm_f)
 
 (*
 Taken from ~~/src/HOL/ex/SAT_Examples.thy.
@@ -53,253 +55,253 @@
   and "~x30"
   and "~x29"
   and "~x59"
-  and "x1 | x31 | x0"
-  and "x2 | x32 | x1"
-  and "x3 | x33 | x2"
-  and "x4 | x34 | x3"
-  and "x35 | x4"
-  and "x5 | x36 | x30"
-  and "x6 | x37 | x5 | x31"
-  and "x7 | x38 | x6 | x32"
-  and "x8 | x39 | x7 | x33"
-  and "x9 | x40 | x8 | x34"
-  and "x41 | x9 | x35"
-  and "x10 | x42 | x36"
-  and "x11 | x43 | x10 | x37"
-  and "x12 | x44 | x11 | x38"
-  and "x13 | x45 | x12 | x39"
-  and "x14 | x46 | x13 | x40"
-  and "x47 | x14 | x41"
-  and "x15 | x48 | x42"
-  and "x16 | x49 | x15 | x43"
-  and "x17 | x50 | x16 | x44"
-  and "x18 | x51 | x17 | x45"
-  and "x19 | x52 | x18 | x46"
-  and "x53 | x19 | x47"
-  and "x20 | x54 | x48"
-  and "x21 | x55 | x20 | x49"
-  and "x22 | x56 | x21 | x50"
-  and "x23 | x57 | x22 | x51"
-  and "x24 | x58 | x23 | x52"
-  and "x59 | x24 | x53"
-  and "x25 | x54"
-  and "x26 | x25 | x55"
-  and "x27 | x26 | x56"
-  and "x28 | x27 | x57"
-  and "x29 | x28 | x58"
-  and "~x1 | ~x31"
-  and "~x1 | ~x0"
-  and "~x31 | ~x0"
-  and "~x2 | ~x32"
-  and "~x2 | ~x1"
-  and "~x32 | ~x1"
-  and "~x3 | ~x33"
-  and "~x3 | ~x2"
-  and "~x33 | ~x2"
-  and "~x4 | ~x34"
-  and "~x4 | ~x3"
-  and "~x34 | ~x3"
-  and "~x35 | ~x4"
-  and "~x5 | ~x36"
-  and "~x5 | ~x30"
-  and "~x36 | ~x30"
-  and "~x6 | ~x37"
-  and "~x6 | ~x5"
-  and "~x6 | ~x31"
-  and "~x37 | ~x5"
-  and "~x37 | ~x31"
-  and "~x5 | ~x31"
-  and "~x7 | ~x38"
-  and "~x7 | ~x6"
-  and "~x7 | ~x32"
-  and "~x38 | ~x6"
-  and "~x38 | ~x32"
-  and "~x6 | ~x32"
-  and "~x8 | ~x39"
-  and "~x8 | ~x7"
-  and "~x8 | ~x33"
-  and "~x39 | ~x7"
-  and "~x39 | ~x33"
-  and "~x7 | ~x33"
-  and "~x9 | ~x40"
-  and "~x9 | ~x8"
-  and "~x9 | ~x34"
-  and "~x40 | ~x8"
-  and "~x40 | ~x34"
-  and "~x8 | ~x34"
-  and "~x41 | ~x9"
-  and "~x41 | ~x35"
-  and "~x9 | ~x35"
-  and "~x10 | ~x42"
-  and "~x10 | ~x36"
-  and "~x42 | ~x36"
-  and "~x11 | ~x43"
-  and "~x11 | ~x10"
-  and "~x11 | ~x37"
-  and "~x43 | ~x10"
-  and "~x43 | ~x37"
-  and "~x10 | ~x37"
-  and "~x12 | ~x44"
-  and "~x12 | ~x11"
-  and "~x12 | ~x38"
-  and "~x44 | ~x11"
-  and "~x44 | ~x38"
-  and "~x11 | ~x38"
-  and "~x13 | ~x45"
-  and "~x13 | ~x12"
-  and "~x13 | ~x39"
-  and "~x45 | ~x12"
-  and "~x45 | ~x39"
-  and "~x12 | ~x39"
-  and "~x14 | ~x46"
-  and "~x14 | ~x13"
-  and "~x14 | ~x40"
-  and "~x46 | ~x13"
-  and "~x46 | ~x40"
-  and "~x13 | ~x40"
-  and "~x47 | ~x14"
-  and "~x47 | ~x41"
-  and "~x14 | ~x41"
-  and "~x15 | ~x48"
-  and "~x15 | ~x42"
-  and "~x48 | ~x42"
-  and "~x16 | ~x49"
-  and "~x16 | ~x15"
-  and "~x16 | ~x43"
-  and "~x49 | ~x15"
-  and "~x49 | ~x43"
-  and "~x15 | ~x43"
-  and "~x17 | ~x50"
-  and "~x17 | ~x16"
-  and "~x17 | ~x44"
-  and "~x50 | ~x16"
-  and "~x50 | ~x44"
-  and "~x16 | ~x44"
-  and "~x18 | ~x51"
-  and "~x18 | ~x17"
-  and "~x18 | ~x45"
-  and "~x51 | ~x17"
-  and "~x51 | ~x45"
-  and "~x17 | ~x45"
-  and "~x19 | ~x52"
-  and "~x19 | ~x18"
-  and "~x19 | ~x46"
-  and "~x52 | ~x18"
-  and "~x52 | ~x46"
-  and "~x18 | ~x46"
-  and "~x53 | ~x19"
-  and "~x53 | ~x47"
-  and "~x19 | ~x47"
-  and "~x20 | ~x54"
-  and "~x20 | ~x48"
-  and "~x54 | ~x48"
-  and "~x21 | ~x55"
-  and "~x21 | ~x20"
-  and "~x21 | ~x49"
-  and "~x55 | ~x20"
-  and "~x55 | ~x49"
-  and "~x20 | ~x49"
-  and "~x22 | ~x56"
-  and "~x22 | ~x21"
-  and "~x22 | ~x50"
-  and "~x56 | ~x21"
-  and "~x56 | ~x50"
-  and "~x21 | ~x50"
-  and "~x23 | ~x57"
-  and "~x23 | ~x22"
-  and "~x23 | ~x51"
-  and "~x57 | ~x22"
-  and "~x57 | ~x51"
-  and "~x22 | ~x51"
-  and "~x24 | ~x58"
-  and "~x24 | ~x23"
-  and "~x24 | ~x52"
-  and "~x58 | ~x23"
-  and "~x58 | ~x52"
-  and "~x23 | ~x52"
-  and "~x59 | ~x24"
-  and "~x59 | ~x53"
-  and "~x24 | ~x53"
-  and "~x25 | ~x54"
-  and "~x26 | ~x25"
-  and "~x26 | ~x55"
-  and "~x25 | ~x55"
-  and "~x27 | ~x26"
-  and "~x27 | ~x56"
-  and "~x26 | ~x56"
-  and "~x28 | ~x27"
-  and "~x28 | ~x57"
-  and "~x27 | ~x57"
-  and "~x29 | ~x28"
-  and "~x29 | ~x58"
-  and "~x28 | ~x58"
+  and "x1 \<or> x31 \<or> x0"
+  and "x2 \<or> x32 \<or> x1"
+  and "x3 \<or> x33 \<or> x2"
+  and "x4 \<or> x34 \<or> x3"
+  and "x35 \<or> x4"
+  and "x5 \<or> x36 \<or> x30"
+  and "x6 \<or> x37 \<or> x5 \<or> x31"
+  and "x7 \<or> x38 \<or> x6 \<or> x32"
+  and "x8 \<or> x39 \<or> x7 \<or> x33"
+  and "x9 \<or> x40 \<or> x8 \<or> x34"
+  and "x41 \<or> x9 \<or> x35"
+  and "x10 \<or> x42 \<or> x36"
+  and "x11 \<or> x43 \<or> x10 \<or> x37"
+  and "x12 \<or> x44 \<or> x11 \<or> x38"
+  and "x13 \<or> x45 \<or> x12 \<or> x39"
+  and "x14 \<or> x46 \<or> x13 \<or> x40"
+  and "x47 \<or> x14 \<or> x41"
+  and "x15 \<or> x48 \<or> x42"
+  and "x16 \<or> x49 \<or> x15 \<or> x43"
+  and "x17 \<or> x50 \<or> x16 \<or> x44"
+  and "x18 \<or> x51 \<or> x17 \<or> x45"
+  and "x19 \<or> x52 \<or> x18 \<or> x46"
+  and "x53 \<or> x19 \<or> x47"
+  and "x20 \<or> x54 \<or> x48"
+  and "x21 \<or> x55 \<or> x20 \<or> x49"
+  and "x22 \<or> x56 \<or> x21 \<or> x50"
+  and "x23 \<or> x57 \<or> x22 \<or> x51"
+  and "x24 \<or> x58 \<or> x23 \<or> x52"
+  and "x59 \<or> x24 \<or> x53"
+  and "x25 \<or> x54"
+  and "x26 \<or> x25 \<or> x55"
+  and "x27 \<or> x26 \<or> x56"
+  and "x28 \<or> x27 \<or> x57"
+  and "x29 \<or> x28 \<or> x58"
+  and "~x1 \<or> ~x31"
+  and "~x1 \<or> ~x0"
+  and "~x31 \<or> ~x0"
+  and "~x2 \<or> ~x32"
+  and "~x2 \<or> ~x1"
+  and "~x32 \<or> ~x1"
+  and "~x3 \<or> ~x33"
+  and "~x3 \<or> ~x2"
+  and "~x33 \<or> ~x2"
+  and "~x4 \<or> ~x34"
+  and "~x4 \<or> ~x3"
+  and "~x34 \<or> ~x3"
+  and "~x35 \<or> ~x4"
+  and "~x5 \<or> ~x36"
+  and "~x5 \<or> ~x30"
+  and "~x36 \<or> ~x30"
+  and "~x6 \<or> ~x37"
+  and "~x6 \<or> ~x5"
+  and "~x6 \<or> ~x31"
+  and "~x37 \<or> ~x5"
+  and "~x37 \<or> ~x31"
+  and "~x5 \<or> ~x31"
+  and "~x7 \<or> ~x38"
+  and "~x7 \<or> ~x6"
+  and "~x7 \<or> ~x32"
+  and "~x38 \<or> ~x6"
+  and "~x38 \<or> ~x32"
+  and "~x6 \<or> ~x32"
+  and "~x8 \<or> ~x39"
+  and "~x8 \<or> ~x7"
+  and "~x8 \<or> ~x33"
+  and "~x39 \<or> ~x7"
+  and "~x39 \<or> ~x33"
+  and "~x7 \<or> ~x33"
+  and "~x9 \<or> ~x40"
+  and "~x9 \<or> ~x8"
+  and "~x9 \<or> ~x34"
+  and "~x40 \<or> ~x8"
+  and "~x40 \<or> ~x34"
+  and "~x8 \<or> ~x34"
+  and "~x41 \<or> ~x9"
+  and "~x41 \<or> ~x35"
+  and "~x9 \<or> ~x35"
+  and "~x10 \<or> ~x42"
+  and "~x10 \<or> ~x36"
+  and "~x42 \<or> ~x36"
+  and "~x11 \<or> ~x43"
+  and "~x11 \<or> ~x10"
+  and "~x11 \<or> ~x37"
+  and "~x43 \<or> ~x10"
+  and "~x43 \<or> ~x37"
+  and "~x10 \<or> ~x37"
+  and "~x12 \<or> ~x44"
+  and "~x12 \<or> ~x11"
+  and "~x12 \<or> ~x38"
+  and "~x44 \<or> ~x11"
+  and "~x44 \<or> ~x38"
+  and "~x11 \<or> ~x38"
+  and "~x13 \<or> ~x45"
+  and "~x13 \<or> ~x12"
+  and "~x13 \<or> ~x39"
+  and "~x45 \<or> ~x12"
+  and "~x45 \<or> ~x39"
+  and "~x12 \<or> ~x39"
+  and "~x14 \<or> ~x46"
+  and "~x14 \<or> ~x13"
+  and "~x14 \<or> ~x40"
+  and "~x46 \<or> ~x13"
+  and "~x46 \<or> ~x40"
+  and "~x13 \<or> ~x40"
+  and "~x47 \<or> ~x14"
+  and "~x47 \<or> ~x41"
+  and "~x14 \<or> ~x41"
+  and "~x15 \<or> ~x48"
+  and "~x15 \<or> ~x42"
+  and "~x48 \<or> ~x42"
+  and "~x16 \<or> ~x49"
+  and "~x16 \<or> ~x15"
+  and "~x16 \<or> ~x43"
+  and "~x49 \<or> ~x15"
+  and "~x49 \<or> ~x43"
+  and "~x15 \<or> ~x43"
+  and "~x17 \<or> ~x50"
+  and "~x17 \<or> ~x16"
+  and "~x17 \<or> ~x44"
+  and "~x50 \<or> ~x16"
+  and "~x50 \<or> ~x44"
+  and "~x16 \<or> ~x44"
+  and "~x18 \<or> ~x51"
+  and "~x18 \<or> ~x17"
+  and "~x18 \<or> ~x45"
+  and "~x51 \<or> ~x17"
+  and "~x51 \<or> ~x45"
+  and "~x17 \<or> ~x45"
+  and "~x19 \<or> ~x52"
+  and "~x19 \<or> ~x18"
+  and "~x19 \<or> ~x46"
+  and "~x52 \<or> ~x18"
+  and "~x52 \<or> ~x46"
+  and "~x18 \<or> ~x46"
+  and "~x53 \<or> ~x19"
+  and "~x53 \<or> ~x47"
+  and "~x19 \<or> ~x47"
+  and "~x20 \<or> ~x54"
+  and "~x20 \<or> ~x48"
+  and "~x54 \<or> ~x48"
+  and "~x21 \<or> ~x55"
+  and "~x21 \<or> ~x20"
+  and "~x21 \<or> ~x49"
+  and "~x55 \<or> ~x20"
+  and "~x55 \<or> ~x49"
+  and "~x20 \<or> ~x49"
+  and "~x22 \<or> ~x56"
+  and "~x22 \<or> ~x21"
+  and "~x22 \<or> ~x50"
+  and "~x56 \<or> ~x21"
+  and "~x56 \<or> ~x50"
+  and "~x21 \<or> ~x50"
+  and "~x23 \<or> ~x57"
+  and "~x23 \<or> ~x22"
+  and "~x23 \<or> ~x51"
+  and "~x57 \<or> ~x22"
+  and "~x57 \<or> ~x51"
+  and "~x22 \<or> ~x51"
+  and "~x24 \<or> ~x58"
+  and "~x24 \<or> ~x23"
+  and "~x24 \<or> ~x52"
+  and "~x58 \<or> ~x23"
+  and "~x58 \<or> ~x52"
+  and "~x23 \<or> ~x52"
+  and "~x59 \<or> ~x24"
+  and "~x59 \<or> ~x53"
+  and "~x24 \<or> ~x53"
+  and "~x25 \<or> ~x54"
+  and "~x26 \<or> ~x25"
+  and "~x26 \<or> ~x55"
+  and "~x25 \<or> ~x55"
+  and "~x27 \<or> ~x26"
+  and "~x27 \<or> ~x56"
+  and "~x26 \<or> ~x56"
+  and "~x28 \<or> ~x27"
+  and "~x28 \<or> ~x57"
+  and "~x27 \<or> ~x57"
+  and "~x29 \<or> ~x28"
+  and "~x29 \<or> ~x58"
+  and "~x28 \<or> ~x58"
   shows False
-  using assms by smt
+  using assms by smt (* smt2 FIXME: THM 0 *)
 
 lemma "\<forall>x::int. P x \<longrightarrow> (\<forall>y::int. P x \<or> P y)"
-  by smt
+  by smt2
 
 lemma
   assumes "(\<forall>x y. P x y = x)"
   shows "(\<exists>y. P x y) = P x c"
-  using assms by smt
+  using assms by smt (* smt2 FIXME: Option *)
 
 lemma
   assumes "(\<forall>x y. P x y = x)"
   and "(\<forall>x. \<exists>y. P x y) = (\<forall>x. P x c)"
   shows "(EX y. P x y) = P x c"
-  using assms by smt
+  using assms by smt (* smt2 FIXME: Option *)
 
 lemma
   assumes "if P x then \<not>(\<exists>y. P y) else (\<forall>y. \<not>P y)"
   shows "P x \<longrightarrow> P y"
-  using assms by smt
+  using assms by smt2
 
 
 section {* Arithmetic *}
 
 subsection {* Linear arithmetic over integers and reals *}
 
-lemma "(3::int) = 3" by smt
+lemma "(3::int) = 3" by smt2
 
-lemma "(3::real) = 3" by smt
+lemma "(3::real) = 3" by smt2
 
-lemma "(3 :: int) + 1 = 4" by smt
+lemma "(3 :: int) + 1 = 4" by smt2
 
-lemma "x + (y + z) = y + (z + (x::int))" by smt
+lemma "x + (y + z) = y + (z + (x::int))" by smt2
 
-lemma "max (3::int) 8 > 5" by smt
+lemma "max (3::int) 8 > 5" by smt2
 
-lemma "abs (x :: real) + abs y \<ge> abs (x + y)" by smt
+lemma "abs (x :: real) + abs y \<ge> abs (x + y)" by smt2
 
-lemma "P ((2::int) < 3) = P True" by smt
+lemma "P ((2::int) < 3) = P True" by smt2
 
-lemma "x + 3 \<ge> 4 \<or> x < (1::int)" by smt
+lemma "x + 3 \<ge> 4 \<or> x < (1::int)" by smt2
 
 lemma
   assumes "x \<ge> (3::int)" and "y = x + 4"
   shows "y - x > 0"
-  using assms by smt
+  using assms by smt2
 
-lemma "let x = (2 :: int) in x + x \<noteq> 5" by smt
+lemma "let x = (2 :: int) in x + x \<noteq> 5" by smt2
 
 lemma
   fixes x :: real
   assumes "3 * x + 7 * a < 4" and "3 < 2 * x"
   shows "a < 0"
-  using assms by smt
+  using assms by smt2
 
-lemma "(0 \<le> y + -1 * x \<or> \<not> 0 \<le> x \<or> 0 \<le> (x::int)) = (\<not> False)" by smt
+lemma "(0 \<le> y + -1 * x \<or> \<not> 0 \<le> x \<or> 0 \<le> (x::int)) = (\<not> False)" by smt2
 
 lemma "
-  (n < m & m < n') | (n < m & m = n') | (n < n' & n' < m) |
-  (n = n' & n' < m) | (n = m & m < n') |
-  (n' < m & m < n) | (n' < m & m = n) |
-  (n' < n & n < m) | (n' = n & n < m) | (n' = m & m < n) |
-  (m < n & n < n') | (m < n & n' = n) | (m < n' & n' < n) |
-  (m = n & n < n') | (m = n' & n' < n) |
-  (n' = m & m = (n::int))"
-  by smt
+  (n < m \<and> m < n') \<or> (n < m \<and> m = n') \<or> (n < n' \<and> n' < m) \<or>
+  (n = n' \<and> n' < m) \<or> (n = m \<and> m < n') \<or>
+  (n' < m \<and> m < n) \<or> (n' < m \<and> m = n) \<or>
+  (n' < n \<and> n < m) \<or> (n' = n \<and> n < m) \<or> (n' = m \<and> m < n) \<or>
+  (m < n \<and> n < n') \<or> (m < n \<and> n' = n) \<or> (m < n' \<and> n' < n) \<or>
+  (m = n \<and> n < n') \<or> (m = n' \<and> n' < n) \<or>
+  (n' = m \<and> m = (n::int))"
+  by smt2
 
 text{*
 The following example was taken from HOL/ex/PresburgerEx.thy, where it says:
@@ -320,175 +322,173 @@
 lemma "\<lbrakk> x3 = abs x2 - x1; x4 = abs x3 - x2; x5 = abs x4 - x3;
          x6 = abs x5 - x4; x7 = abs x6 - x5; x8 = abs x7 - x6;
          x9 = abs x8 - x7; x10 = abs x9 - x8; x11 = abs x10 - x9 \<rbrakk>
- \<Longrightarrow> x1 = x10 & x2 = (x11::int)"
-  by smt
+ \<Longrightarrow> x1 = x10 \<and> x2 = (x11::int)"
+  by smt2
 
 
-lemma "let P = 2 * x + 1 > x + (x::real) in P \<or> False \<or> P" by smt
+lemma "let P = 2 * x + 1 > x + (x::real) in P \<or> False \<or> P" by smt2
 
 lemma "x + (let y = x mod 2 in 2 * y + 1) \<ge> x + (1::int)"
-  using [[z3_with_extensions]]
-  by smt
+  using [[z3_new_extensions]]
+  by smt2
 
 lemma "x + (let y = x mod 2 in y + y) < x + (3::int)"
-  using [[z3_with_extensions]]
-  by smt
+  using [[z3_new_extensions]]
+  by smt2
 
 lemma
   assumes "x \<noteq> (0::real)"
-  shows "x + x \<noteq> (let P = (abs x > 1) in if P \<or> \<not>P then 4 else 2) * x"
-  using assms by smt
+  shows "x + x \<noteq> (let P = (abs x > 1) in if P \<or> \<not> P then 4 else 2) * x"
+  using assms [[z3_new_extensions]] by smt2
 
 lemma
   assumes "(n + m) mod 2 = 0" and "n mod 4 = 3"
-  shows "n mod 2 = 1 & m mod 2 = (1::int)"
-  using assms [[z3_with_extensions]] by smt
-
+  shows "n mod 2 = 1 \<and> m mod 2 = (1::int)"
+  using assms [[z3_new_extensions]] by smt2
 
 
 subsection {* Linear arithmetic with quantifiers *}
 
-lemma "~ (\<exists>x::int. False)" by smt
+lemma "~ (\<exists>x::int. False)" by smt2
 
-lemma "~ (\<exists>x::real. False)" by smt
+lemma "~ (\<exists>x::real. False)" by smt2
 
 lemma "\<exists>x::int. 0 < x"
-  using [[smt_oracle=true]] (* no Z3 proof *)
-  by smt
+  using [[smt2_oracle=true]] (* no Z3 proof *)
+  by smt2
 
 lemma "\<exists>x::real. 0 < x"
-  using [[smt_oracle=true]] (* no Z3 proof *)
-  by smt
+  using [[smt2_oracle=true]] (* no Z3 proof *)
+  by smt2
 
 lemma "\<forall>x::int. \<exists>y. y > x"
-  using [[smt_oracle=true]] (* no Z3 proof *)
-  by smt
+  using [[smt2_oracle=true]] (* no Z3 proof *)
+  by smt2
 
-lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y" by smt
+lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y" by smt2
 
-lemma "\<exists>x::int. \<forall>y. x < y \<longrightarrow> y < 0 \<or> y >= 0" by smt
+lemma "\<exists>x::int. \<forall>y. x < y \<longrightarrow> y < 0 \<or> y >= 0" by smt2
 
-lemma "\<forall>x y::int. x < y \<longrightarrow> (2 * x + 1) < (2 * y)" by smt
+lemma "\<forall>x y::int. x < y \<longrightarrow> (2 * x + 1) < (2 * y)" by smt2
 
-lemma "\<forall>x y::int. (2 * x + 1) \<noteq> (2 * y)" by smt
+lemma "\<forall>x y::int. (2 * x + 1) \<noteq> (2 * y)" by smt2
 
-lemma "\<forall>x y::int. x + y > 2 \<or> x + y = 2 \<or> x + y < 2" by smt
+lemma "\<forall>x y::int. x + y > 2 \<or> x + y = 2 \<or> x + y < 2" by smt2
 
-lemma "\<forall>x::int. if x > 0 then x + 1 > 0 else 1 > x" by smt
+lemma "\<forall>x::int. if x > 0 then x + 1 > 0 else 1 > x" by smt2
 
-lemma "if (ALL x::int. x < 0 \<or> x > 0) then False else True" by smt
+lemma "if (ALL x::int. x < 0 \<or> x > 0) then False else True" by smt2
 
-lemma "(if (ALL x::int. x < 0 \<or> x > 0) then -1 else 3) > (0::int)" by smt
+lemma "(if (ALL x::int. x < 0 \<or> x > 0) then -1 else 3) > (0::int)" by smt2
 
-lemma "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))" by smt
+lemma "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))" by smt2
 
-lemma "\<exists>x::int. \<forall>x y. 0 < x \<and> 0 < y \<longrightarrow> (0::int) < x + y" by smt
+lemma "\<exists>x::int. \<forall>x y. 0 < x \<and> 0 < y \<longrightarrow> (0::int) < x + y" by smt2
 
-lemma "\<exists>u::int. \<forall>(x::int) y::real. 0 < x \<and> 0 < y \<longrightarrow> -1 < x" by smt
+lemma "\<exists>u::int. \<forall>(x::int) y::real. 0 < x \<and> 0 < y \<longrightarrow> -1 < x" by smt2
 
-lemma "\<exists>x::int. (\<forall>y. y \<ge> x \<longrightarrow> y > 0) \<longrightarrow> x > 0" by smt
+lemma "\<exists>x::int. (\<forall>y. y \<ge> x \<longrightarrow> y > 0) \<longrightarrow> x > 0" by smt2
 
-lemma "\<forall>x::int. SMT.trigger [[SMT.pat x]] (x < a \<longrightarrow> 2 * x < 2 * a)" by smt
+lemma "\<forall>x::int. SMT2.trigger [[SMT2.pat x]] (x < a \<longrightarrow> 2 * x < 2 * a)" by smt2
 
-lemma "\<forall>(a::int) b::int. 0 < b \<or> b < 1" by smt
+lemma "\<forall>(a::int) b::int. 0 < b \<or> b < 1" by smt2
 
 
 subsection {* Non-linear arithmetic over integers and reals *}
 
 lemma "a > (0::int) \<Longrightarrow> a*b > 0 \<Longrightarrow> b > 0"
-  using [[smt_oracle, z3_with_extensions]]
-  by smt
+  using [[smt2_oracle, z3_new_extensions]]
+  by smt2
 
 lemma  "(a::int) * (x + 1 + y) = a * x + a * (y + 1)"
-  using [[z3_with_extensions]]
-  by smt
+  using [[z3_new_extensions]]
+  by smt2
 
 lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)"
-  using [[z3_with_extensions]]
-  by smt
+  using [[z3_new_extensions]]
+  by smt2
 
 lemma
   "(U::int) + (1 + p) * (b + e) + p * d =
    U + (2 * (1 + p) * (b + e) + (1 + p) * d + d * p) - (1 + p) * (b + d + e)"
-  using [[z3_with_extensions]]
-  by smt
+  using [[z3_new_extensions]]
+  by smt2
 
-lemma [z3_rule]:
+lemma [z3_rule, z3_new_rule]:
   fixes x :: "int"
   assumes "x * y \<le> 0" and "\<not> y \<le> 0" and "\<not> x \<le> 0"
   shows False
   using assms by (metis mult_le_0_iff)
 
 lemma "x * y \<le> (0 :: int) \<Longrightarrow> x \<le> 0 \<or> y \<le> 0"
-  using [[z3_with_extensions]]
-  by smt
-
+  using [[z3_with_extensions]] [[z3_new_extensions]]
+  by smt (* smt2 FIXME: "th-lemma" tactic fails *)
 
 
 subsection {* Linear arithmetic for natural numbers *}
 
-lemma "2 * (x::nat) ~= 1" by smt
+lemma "2 * (x::nat) ~= 1" by smt2
 
-lemma "a < 3 \<Longrightarrow> (7::nat) > 2 * a" by smt
+lemma "a < 3 \<Longrightarrow> (7::nat) > 2 * a" by smt2
 
-lemma "let x = (1::nat) + y in x - y > 0 * x" by smt
+lemma "let x = (1::nat) + y in x - y > 0 * x" by smt2
 
 lemma
   "let x = (1::nat) + y in
    let P = (if x > 0 then True else False) in
    False \<or> P = (x - 1 = y) \<or> (\<not>P \<longrightarrow> False)"
-  by smt
+  by smt2
 
-lemma "int (nat \<bar>x::int\<bar>) = \<bar>x\<bar>" by smt
+lemma "int (nat \<bar>x::int\<bar>) = \<bar>x\<bar>" by smt2
 
 definition prime_nat :: "nat \<Rightarrow> bool" where
   "prime_nat p = (1 < p \<and> (\<forall>m. m dvd p --> m = 1 \<or> m = p))"
-lemma "prime_nat (4*m + 1) \<Longrightarrow> m \<ge> (1::nat)" by (smt prime_nat_def)
+lemma "prime_nat (4*m + 1) \<Longrightarrow> m \<ge> (1::nat)" by (smt2 prime_nat_def)
 
 
 section {* Pairs *}
 
 lemma "fst (x, y) = a \<Longrightarrow> x = a"
   using fst_conv
-  by smt
+  by smt2
 
 lemma "p1 = (x, y) \<and> p2 = (y, x) \<Longrightarrow> fst p1 = snd p2"
   using fst_conv snd_conv
-  by smt
+  by smt2
 
 
 section {* Higher-order problems and recursion *}
 
 lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> (f (i1 := v1, i2 := v2)) i = f i"
   using fun_upd_same fun_upd_apply
-  by smt
+  by smt2
 
 lemma "(f g (x::'a::type) = (g x \<and> True)) \<or> (f g x = True) \<or> (g x = True)"
-  by smt
+  by smt2
 
-lemma "id x = x \<and> id True = True" by (smt id_def)
+lemma "id x = x \<and> id True = True" by (smt id_def) (* smt2 FIXME: Option *)
 
 lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> ((f (i1 := v1)) (i2 := v2)) i = f i"
   using fun_upd_same fun_upd_apply
-  by smt
+  by smt2
 
 lemma
   "f (\<exists>x. g x) \<Longrightarrow> True"
   "f (\<forall>x. g x) \<Longrightarrow> True"
-  by smt+
+  by smt2+
 
-lemma True using let_rsp by smt
+lemma True using let_rsp by smt2
 
-lemma "le = op \<le> \<Longrightarrow> le (3::int) 42" by smt
+lemma "le = op \<le> \<Longrightarrow> le (3::int) 42" by smt2
 
-lemma "map (\<lambda>i::nat. i + 1) [0, 1] = [1, 2]" by (smt list.map)
+lemma "map (\<lambda>i::nat. i + 1) [0, 1] = [1, 2]" by (smt2 list.map)
 
 
-lemma "(ALL x. P x) | ~ All P" by smt
+lemma "(ALL x. P x) \<or> ~ All P" by smt2
 
 fun dec_10 :: "nat \<Rightarrow> nat" where
   "dec_10 n = (if n < 10 then n else dec_10 (n - 10))"
-lemma "dec_10 (4 * dec_10 4) = 6" by (smt dec_10.simps)
+lemma "dec_10 (4 * dec_10 4) = 6" by (smt2 dec_10.simps)
 
 
 axiomatization
@@ -505,35 +505,36 @@
    (eval_dioph ks (map (\<lambda>x. x mod 2) xs) mod 2 = l mod 2 \<and>
     eval_dioph ks (map (\<lambda>x. x div 2) xs) =
       (l - eval_dioph ks (map (\<lambda>x. x mod 2) xs)) div 2)"
-  using [[smt_oracle=true]] (*FIXME*)
-  using [[z3_with_extensions]]
-  by (smt eval_dioph_mod[where n=2] eval_dioph_div_mult[where n=2])
+  using [[smt2_oracle=true]] (*FIXME*)
+  using [[z3_new_extensions]]
+  by (smt2 eval_dioph_mod[where n=2] eval_dioph_div_mult[where n=2])
 
 
 context complete_lattice
 begin
 
 lemma
-  assumes "Sup { a | i::bool . True } \<le> Sup { b | i::bool . True }"
-  and     "Sup { b | i::bool . True } \<le> Sup { a | i::bool . True }"
-  shows   "Sup { a | i::bool . True } \<le> Sup { a | i::bool . True }"
-  using assms by (smt order_trans)
+  assumes "Sup {a | i::bool. True} \<le> Sup {b | i::bool. True}"
+  and "Sup {b | i::bool. True} \<le> Sup {a | i::bool. True}"
+  shows "Sup {a | i::bool. True} \<le> Sup {a | i::bool. True}"
+  using assms by (smt2 order_trans)
 
 end
 
 
-
 section {* Monomorphization examples *}
 
 definition Pred :: "'a \<Rightarrow> bool" where "Pred x = True"
-lemma poly_Pred: "Pred x \<and> (Pred [x] \<or> \<not>Pred[x])" by (simp add: Pred_def)
-lemma "Pred (1::int)" by (smt poly_Pred)
+
+lemma poly_Pred: "Pred x \<and> (Pred [x] \<or> \<not> Pred [x])" by (simp add: Pred_def)
+lemma "Pred (1::int)" by (smt2 poly_Pred)
 
 axiomatization g :: "'a \<Rightarrow> nat"
 axiomatization where
   g1: "g (Some x) = g [x]" and
   g2: "g None = g []" and
   g3: "g xs = length xs"
-lemma "g (Some (3::int)) = g (Some True)" by (smt g1 g2 g3 list.size)
+
+lemma "g (Some (3::int)) = g (Some True)" by (smt g1 g2 g3 list.size) (* smt2 FIXME: Option *)
 
 end




