header {* Demonstrating the interface SVC *}
theory svc_test
imports SVC_Oracle
begin
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. *}
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