section {* 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