Goal:
  
  __p3 : Prop
  __p2 : Prop
  __p1 : Prop
  __x8 : Z
  __x7 : Z
  __x6 : Z
  __x5 : Z
  __x4 : Z
  __x3 : Z
  __x2 : Z
  __x1 : Z
  ============================
   (let __wit :=
      [ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 6)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
               (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                  (RingMicromega.PsatzIn Z 2)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 5)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
               (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                  (RingMicromega.PsatzIn Z 2)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 5)
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                  (RingMicromega.PsatzIn Z 4))
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 1)
                  (RingMicromega.PsatzIn Z 0)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 6)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 5)
               (RingMicromega.PsatzAdd
                  (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                     (RingMicromega.PsatzIn Z 4))
                  (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 1)
                     (RingMicromega.PsatzIn Z 0))))) ZMicromega.DoneProof] in
    let __varmap :=
      VarMap.Branch
        (VarMap.Branch (VarMap.Branch VarMap.Empty __x8 (VarMap.Elt __x7))
           __x2 (VarMap.Branch (VarMap.Elt __x6) __x4 VarMap.Empty)) __x1
        (VarMap.Branch (VarMap.Branch VarMap.Empty __x8 (VarMap.Elt __x8))
           __x3 (VarMap.Elt __x5)) in
    let __ff :=
      Tauto.IMPL
        (Tauto.OR
           (Tauto.AND (Tauto.X Tauto.isProp __p1)
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX 1;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs :=
                     EnvRing.PEadd (EnvRing.PEX 6)
                       (EnvRing.PEadd (EnvRing.PEX 12) (EnvRing.PEX 13))
                 |} tt))
           (Tauto.AND (Tauto.X Tauto.isProp __p2)
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX 1;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs := EnvRing.PEc 0
                 |} tt))) None
        (Tauto.IMPL
           (Tauto.OR
              (Tauto.AND (Tauto.X Tauto.isProp __p3)
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs := EnvRing.PEX 3;
                      RingMicromega.Fop := RingMicromega.OpEq;
                      RingMicromega.Frhs :=
                        EnvRing.PEadd (EnvRing.PEX 7)
                          (EnvRing.PEadd (EnvRing.PEX 12) (EnvRing.PEX 13))
                    |} tt))
              (Tauto.AND
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs :=
                        EnvRing.PEadd (EnvRing.PEX 7)
                          (EnvRing.PEadd (EnvRing.PEX 12) (EnvRing.PEX 13));
                      RingMicromega.Fop := RingMicromega.OpLe;
                      RingMicromega.Frhs := EnvRing.PEc 0
                    |} tt)
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs := EnvRing.PEX 3;
                      RingMicromega.Fop := RingMicromega.OpEq;
                      RingMicromega.Frhs := EnvRing.PEc 0
                    |} tt))) None
           (Tauto.IMPL
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEc 0;
                   RingMicromega.Fop := RingMicromega.OpLe;
                   RingMicromega.Frhs := EnvRing.PEX 10
                 |} tt) None
              (Tauto.IMPL
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs := EnvRing.PEX 1;
                      RingMicromega.Fop := RingMicromega.OpEq;
                      RingMicromega.Frhs :=
                        EnvRing.PEadd (EnvRing.PEX 10) (EnvRing.PEc 1)
                    |} tt) None
                 (Tauto.IMPL
                    (Tauto.A Tauto.isProp
                       {|
                         RingMicromega.Flhs :=
                           EnvRing.PEadd (EnvRing.PEX 6) (EnvRing.PEX 2);
                         RingMicromega.Fop := RingMicromega.OpLe;
                         RingMicromega.Frhs := EnvRing.PEX 7
                       |} tt) None
                    (Tauto.A Tauto.isProp
                       {|
                         RingMicromega.Flhs :=
                           EnvRing.PEadd (EnvRing.PEX 1) (EnvRing.PEX 2);
                         RingMicromega.Fop := RingMicromega.OpLe;
                         RingMicromega.Frhs := EnvRing.PEX 3
                       |} tt))))) in
    __p1 /\ __x1 = __x4 + (__x7 + __x8) \/ __p2 /\ __x1 = 0 ->
    __p3 /\ __x3 = __x5 + (__x7 + __x8) \/
    __x5 + (__x7 + __x8) <= 0 /\ __x3 = 0 ->
    0 <= __x6 ->
    __x1 = __x6 + 1 -> __x4 + __x2 <= __x5 -> __x1 + __x2 <= __x3)


DEBUG:Going to execute:
let __wit := fresh "__wit" in
           let __varmap := fresh "__varmap" in
           let __ff := fresh "__ff" in
           intros __wit __varmap __ff; exact
            (ZMicromega.ZTautoChecker_sound __ff __wit
               (eq_refl <: ZMicromega.ZTautoChecker __ff __wit = true)
               (VarMap.find 0 __varmap))