Goal:
  
  __p3 : Prop
  __p2 : Prop
  __p1 : Prop
  __x8 : Z
  __x7 : Z
  __x6 : Z
  __x5 : Z
  __x4 : Z
  __x3 : Z
  __x2 : Z
  __x1 : Z
  __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] : list ZMicromega.ZArithProof
  __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)) : VarMap.t Z
  __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)))))
       : Tauto.BFormula (RingMicromega.Formula Z) Tauto.isProp
  ============================
   (__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:
exact
(ZMicromega.ZTautoChecker_sound __ff __wit
   (eq_refl <: ZMicromega.ZTautoChecker __ff __wit = true)
   (VarMap.find 0 __varmap))