diff -r 3728dba101f1 -r bd3b60f9a343 src/HOL/ex/svc_test.thy --- 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