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


DEBUG:Going to execute:
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))