--- a/src/HOL/ex/svc_test.thy Sun Oct 01 12:07:57 2006 +0200
+++ b/src/HOL/ex/svc_test.thy Sun Oct 01 18:29:23 2006 +0200
@@ -7,10 +7,245 @@
imports SVC_Oracle
begin
-syntax
- "<->" :: "[bool, bool] => bool" (infixr 25)
+subsubsection {* Propositional Logic *}
+
+text {*
+ @{text "blast"}'s runtime for this type of problem appears to be exponential
+ in its length, though @{text "fast"} manages.
+*}
+lemma "P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P=P"
+ by (tactic {* svc_tac 1 *})
+
+
+subsection {* Some big tautologies supplied by John Harrison *}
+
+text {*
+ @{text "auto"} manages; @{text "blast"} and @{text "fast"} take a minute or more.
+*}
+lemma puz013_1: "~(~v12 &
+ v0 &
+ v10 &
+ (v4 | v5) &
+ (v9 | v2) &
+ (v8 | v1) &
+ (v7 | v0) &
+ (v3 | v12) &
+ (v11 | v10) &
+ (~v12 | ~v6 | v7) &
+ (~v10 | ~v3 | v1) &
+ (~v10 | ~v0 | ~v4 | v11) &
+ (~v5 | ~v2 | ~v8) &
+ (~v12 | ~v9 | ~v7) &
+ (~v0 | ~v1 | v4) &
+ (~v4 | v7 | v2) &
+ (~v12 | ~v3 | v8) &
+ (~v4 | v5 | v6) &
+ (~v7 | ~v8 | v9) &
+ (~v10 | ~v11 | v12))"
+ by (tactic {* svc_tac 1 *})
+
+lemma dk17_be:
+ "(GE17 <-> ~IN4 & ~IN3 & ~IN2 & ~IN1) &
+ (GE0 <-> GE17 & ~IN5) &
+ (GE22 <-> ~IN9 & ~IN7 & ~IN6 & IN0) &
+ (GE19 <-> ~IN5 & ~IN4 & ~IN3 & ~IN0) &
+ (GE20 <-> ~IN7 & ~IN6) &
+ (GE18 <-> ~IN6 & ~IN2 & ~IN1 & ~IN0) &
+ (GE21 <-> IN9 & ~IN7 & IN6 & ~IN0) &
+ (GE23 <-> GE22 & GE0) &
+ (GE25 <-> ~IN9 & ~IN7 & IN6 & ~IN0) &
+ (GE26 <-> IN9 & ~IN7 & ~IN6 & IN0) &
+ (GE2 <-> GE20 & GE19) &
+ (GE1 <-> GE18 & ~IN7) &
+ (GE24 <-> GE23 | GE21 & GE0) &
+ (GE5 <-> ~IN5 & IN4 | IN5 & ~IN4) &
+ (GE6 <-> GE0 & IN7 & ~IN6 & ~IN0) &
+ (GE12 <-> GE26 & GE0 | GE25 & GE0) &
+ (GE14 <-> GE2 & IN8 & ~IN2 & IN1) &
+ (GE27 <-> ~IN8 & IN5 & ~IN4 & ~IN3) &
+ (GE9 <-> GE1 & ~IN5 & ~IN4 & IN3) &
+ (GE7 <-> GE24 | GE2 & IN2 & ~IN1) &
+ (GE10 <-> GE6 | GE5 & GE1 & ~IN3) &
+ (GE15 <-> ~IN8 | IN9) &
+ (GE16 <-> GE12 | GE14 & ~IN9) &
+ (GE4 <->
+ GE5 & GE1 & IN8 & ~IN3 |
+ GE0 & ~IN7 & IN6 & ~IN0 |
+ GE2 & IN2 & ~IN1) &
+ (GE13 <-> GE27 & GE1) &
+ (GE11 <-> GE9 | GE6 & ~IN8) &
+ (GE8 <-> GE1 & ~IN5 & IN4 & ~IN3 | GE2 & ~IN2 & IN1) &
+ (OUT0 <-> GE7 & ~IN8) &
+ (OUT1 <-> GE7 & IN8) &
+ (OUT2 <-> GE8 & ~IN9 | GE10 & IN8) &
+ (OUT3 <-> GE8 & IN9 & ~IN8 | GE11 & ~IN9 | GE12 & ~IN8) &
+ (OUT4 <-> GE11 & IN9 | GE12 & IN8) &
+ (OUT5 <-> GE14 & IN9) &
+ (OUT6 <-> GE13 & ~IN9) &
+ (OUT7 <-> GE13 & IN9) &
+ (OUT8 <-> GE9 & ~IN8 | GE15 & GE6 | GE4 & IN9) &
+ (OUT9 <-> GE9 & IN8 | ~GE15 & GE10 | GE16) &
+ (OUT10 <-> GE7) &
+ (WRES0 <-> ~IN5 & ~IN4 & ~IN3 & ~IN2 & ~IN1) &
+ (WRES1 <-> ~IN7 & ~IN6 & ~IN2 & ~IN1 & ~IN0) &
+ (WRES2 <-> ~IN7 & ~IN6 & ~IN5 & ~IN4 & ~IN3 & ~IN0) &
+ (WRES5 <-> ~IN5 & IN4 | IN5 & ~IN4) &
+ (WRES6 <-> WRES0 & IN7 & ~IN6 & ~IN0) &
+ (WRES9 <-> WRES1 & ~IN5 & ~IN4 & IN3) &
+ (WRES7 <->
+ WRES0 & ~IN9 & ~IN7 & ~IN6 & IN0 |
+ WRES0 & IN9 & ~IN7 & IN6 & ~IN0 |
+ WRES2 & IN2 & ~IN1) &
+ (WRES10 <-> WRES6 | WRES5 & WRES1 & ~IN3) &
+ (WRES12 <->
+ WRES0 & IN9 & ~IN7 & ~IN6 & IN0 |
+ WRES0 & ~IN9 & ~IN7 & IN6 & ~IN0) &
+ (WRES14 <-> WRES2 & IN8 & ~IN2 & IN1) &
+ (WRES15 <-> ~IN8 | IN9) &
+ (WRES4 <->
+ WRES5 & WRES1 & IN8 & ~IN3 |
+ WRES2 & IN2 & ~IN1 |
+ WRES0 & ~IN7 & IN6 & ~IN0) &
+ (WRES13 <-> WRES1 & ~IN8 & IN5 & ~IN4 & ~IN3) &
+ (WRES11 <-> WRES9 | WRES6 & ~IN8) &
+ (WRES8 <-> WRES1 & ~IN5 & IN4 & ~IN3 | WRES2 & ~IN2 & IN1)
+ --> (OUT10 <-> WRES7) &
+ (OUT9 <-> WRES9 & IN8 | WRES12 | WRES14 & ~IN9 | ~WRES15 & WRES10) &
+ (OUT8 <-> WRES9 & ~IN8 | WRES15 & WRES6 | WRES4 & IN9) &
+ (OUT7 <-> WRES13 & IN9) &
+ (OUT6 <-> WRES13 & ~IN9) &
+ (OUT5 <-> WRES14 & IN9) &
+ (OUT4 <-> WRES11 & IN9 | WRES12 & IN8) &
+ (OUT3 <-> WRES8 & IN9 & ~IN8 | WRES11 & ~IN9 | WRES12 & ~IN8) &
+ (OUT2 <-> WRES8 & ~IN9 | WRES10 & IN8) &
+ (OUT1 <-> WRES7 & IN8) &
+ (OUT0 <-> WRES7 & ~IN8)"
+ by (tactic {* svc_tac 1 *})
+
+text {* @{text "fast"} only takes a couple of seconds. *}
-translations
- "x <-> y" => "x = y"
+lemma sqn_be: "(GE0 <-> IN6 & IN1 | ~IN6 & ~IN1) &
+ (GE8 <-> ~IN3 & ~IN1) &
+ (GE5 <-> IN6 | IN5) &
+ (GE9 <-> ~GE0 | IN2 | ~IN5) &
+ (GE1 <-> IN3 | ~IN0) &
+ (GE11 <-> GE8 & IN4) &
+ (GE3 <-> ~IN4 | ~IN2) &
+ (GE34 <-> ~GE5 & IN4 | ~GE9) &
+ (GE2 <-> ~IN4 & IN1) &
+ (GE14 <-> ~GE1 & ~IN4) &
+ (GE19 <-> GE11 & ~GE5) &
+ (GE13 <-> GE8 & ~GE3 & ~IN0) &
+ (GE20 <-> ~IN5 & IN2 | GE34) &
+ (GE12 <-> GE2 & ~IN3) &
+ (GE27 <-> GE14 & IN6 | GE19) &
+ (GE10 <-> ~IN6 | IN5) &
+ (GE28 <-> GE13 | GE20 & ~GE1) &
+ (GE6 <-> ~IN5 | IN6) &
+ (GE15 <-> GE2 & IN2) &
+ (GE29 <-> GE27 | GE12 & GE5) &
+ (GE4 <-> IN3 & ~IN0) &
+ (GE21 <-> ~GE10 & ~IN1 | ~IN5 & ~IN2) &
+ (GE30 <-> GE28 | GE14 & IN2) &
+ (GE31 <-> GE29 | GE15 & ~GE6) &
+ (GE7 <-> ~IN6 | ~IN5) &
+ (GE17 <-> ~GE3 & ~IN1) &
+ (GE18 <-> GE4 & IN2) &
+ (GE16 <-> GE2 & IN0) &
+ (GE23 <-> GE19 | GE9 & ~GE1) &
+ (GE32 <-> GE15 & ~IN6 & ~IN0 | GE21 & GE4 & ~IN4 | GE30 | GE31) &
+ (GE33 <->
+ GE18 & ~GE6 & ~IN4 |
+ GE17 & ~GE7 & IN3 |
+ ~GE7 & GE4 & ~GE3 |
+ GE11 & IN5 & ~IN0) &
+ (GE25 <-> GE14 & ~GE6 | GE13 & ~GE5 | GE16 & ~IN5 | GE15 & GE1) &
+ (GE26 <->
+ GE12 & IN5 & ~IN2 |
+ GE10 & GE4 & IN1 |
+ GE17 & ~GE6 & IN0 |
+ GE2 & ~IN6) &
+ (GE24 <-> GE23 | GE16 & GE7) &
+ (OUT0 <->
+ GE6 & IN4 & ~IN1 & IN0 | GE18 & GE0 & ~IN5 | GE12 & ~GE10 | GE24) &
+ (OUT1 <-> GE26 | GE25 | ~GE5 & GE4 & GE3 | GE7 & ~GE1 & IN1) &
+ (OUT2 <-> GE33 | GE32) &
+ (WRES8 <-> ~IN3 & ~IN1) &
+ (WRES0 <-> IN6 & IN1 | ~IN6 & ~IN1) &
+ (WRES2 <-> ~IN4 & IN1) &
+ (WRES3 <-> ~IN4 | ~IN2) &
+ (WRES1 <-> IN3 | ~IN0) &
+ (WRES4 <-> IN3 & ~IN0) &
+ (WRES5 <-> IN6 | IN5) &
+ (WRES11 <-> WRES8 & IN4) &
+ (WRES9 <-> ~WRES0 | IN2 | ~IN5) &
+ (WRES10 <-> ~IN6 | IN5) &
+ (WRES6 <-> ~IN5 | IN6) &
+ (WRES7 <-> ~IN6 | ~IN5) &
+ (WRES12 <-> WRES2 & ~IN3) &
+ (WRES13 <-> WRES8 & ~WRES3 & ~IN0) &
+ (WRES14 <-> ~WRES1 & ~IN4) &
+ (WRES15 <-> WRES2 & IN2) &
+ (WRES17 <-> ~WRES3 & ~IN1) &
+ (WRES18 <-> WRES4 & IN2) &
+ (WRES19 <-> WRES11 & ~WRES5) &
+ (WRES20 <-> ~IN5 & IN2 | ~WRES5 & IN4 | ~WRES9) &
+ (WRES21 <-> ~WRES10 & ~IN1 | ~IN5 & ~IN2) &
+ (WRES16 <-> WRES2 & IN0)
+ --> (OUT2 <->
+ WRES11 & IN5 & ~IN0 |
+ ~WRES7 & WRES4 & ~WRES3 |
+ WRES12 & WRES5 |
+ WRES13 |
+ WRES14 & IN2 |
+ WRES14 & IN6 |
+ WRES15 & ~WRES6 |
+ WRES15 & ~IN6 & ~IN0 |
+ WRES17 & ~WRES7 & IN3 |
+ WRES18 & ~WRES6 & ~IN4 |
+ WRES20 & ~WRES1 |
+ WRES21 & WRES4 & ~IN4 |
+ WRES19) &
+ (OUT1 <->
+ ~WRES5 & WRES4 & WRES3 |
+ WRES7 & ~WRES1 & IN1 |
+ WRES2 & ~IN6 |
+ WRES10 & WRES4 & IN1 |
+ WRES12 & IN5 & ~IN2 |
+ WRES13 & ~WRES5 |
+ WRES14 & ~WRES6 |
+ WRES15 & WRES1 |
+ WRES16 & ~IN5 |
+ WRES17 & ~WRES6 & IN0) &
+ (OUT0 <->
+ WRES6 & IN4 & ~IN1 & IN0 |
+ WRES9 & ~WRES1 |
+ WRES12 & ~WRES10 |
+ WRES16 & WRES7 |
+ WRES18 & WRES0 & ~IN5 |
+ WRES19)"
+ by (tactic {* svc_tac 1 *})
+
+
+subsection {* Linear arithmetic *}
+
+lemma "x ~= 14 & x ~= 13 & x ~= 12 & x ~= 11 & x ~= 10 & x ~= 9 &
+ x ~= 8 & x ~= 7 & x ~= 6 & x ~= 5 & x ~= 4 & x ~= 3 &
+ x ~= 2 & x ~= 1 & 0 < x & x < 16 --> 15 = (x::int)"
+ by (tactic {* svc_tac 1 *})
+
+text {*merely to test polarity handling in the presence of biconditionals*}
+lemma "(x < (y::int)) = (x+1 <= y)"
+ by (tactic {* svc_tac 1 *})
+
+
+subsection {* Natural number examples requiring implicit "non-negative" assumptions *}
+
+lemma "(3::nat)*a <= 2 + 4*b + 6*c & 11 <= 2*a + b + 2*c &
+ a + 3*b <= 5 + 2*c --> 2 + 3*b <= 2*a + 6*c"
+ by (tactic {* svc_tac 1 *})
+
+lemma "(n::nat) < 2 ==> (n = 0) | (n = 1)"
+ by (tactic {* svc_tac 1 *})
end