Goal:
    __p2 : Prop  __p1 : Prop  __x3 : Z  __x2 : Z  __x1 : Z
  ============================
   (let __wit :=
      (ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 1)
                  (RingMicromega.PsatzIn Z 0)))) ZMicromega.DoneProof
       :: ZMicromega.RatProof
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                  (RingMicromega.PsatzIn Z 0))) ZMicromega.DoneProof :: nil)%list
      in
    let __varmap := VarMap.Branch (VarMap.Elt __x2) __x1 (VarMap.Elt __x3) 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.PEsub (EnvRing.PEX 2)
                       (EnvRing.PEadd (EnvRing.PEX 3) (EnvRing.PEc 1%Z))
                 |} 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%Z
                 |} tt))) None
        (Tauto.IMPL
           (Tauto.A Tauto.isProp
              {|
                RingMicromega.Flhs := EnvRing.PEc 0%Z;
                RingMicromega.Fop := RingMicromega.OpLe;
                RingMicromega.Frhs := EnvRing.PEX 3
              |} tt) None
           (Tauto.IMPL
              (Tauto.NOT
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs := EnvRing.PEX 2;
                      RingMicromega.Fop := RingMicromega.OpLe;
                      RingMicromega.Frhs := EnvRing.PEX 3
                    |} tt)) None
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX 1;
                   RingMicromega.Fop := RingMicromega.OpLt;
                   RingMicromega.Frhs := EnvRing.PEX 2
                 |} tt))) in
    __p1 /\ __x1 = (__x2 - (__x3 + 1))%Z \/ __p2 /\ __x1 = 0%Z ->
    (0 <= __x3)%Z -> ((__x2 <= __x3)%Z -> False) -> (__x1 < __x2)%Z)


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