Module `Micromega_plugin.Micromega`

type __ = Stdlib.Obj.t
type unit0 = | Tt

val negb : bool -> bool

type nat = | O | S of nat
type ('a, 'b) sum = | Inl of 'a | Inr of 'b

val fst : ('a1 * 'a2) -> 'a1
val snd : ('a1 * 'a2) -> 'a2
val app : 'a1 list -> 'a1 list -> 'a1 list

type comparison = | Eq | Lt | Gt

val compOpp : comparison -> comparison
val add : nat -> nat -> nat
val nth : nat -> 'a1 list -> 'a1 -> 'a1
val rev_append : 'a1 list -> 'a1 list -> 'a1 list
val map : ('a1 -> 'a2) -> 'a1 list -> 'a2 list
val fold_left : ('a1 -> 'a2 -> 'a1) -> 'a2 list -> 'a1 -> 'a1
val fold_right : ('a2 -> 'a1 -> 'a1) -> 'a1 -> 'a2 list -> 'a1

type positive = | XI of positive | XO of positive | XH
type n = | N0 | Npos of positive
type z = | Z0 | Zpos of positive | Zneg of positive

module Pos : sig ... end

module Coq_Pos : sig ... end

module N : sig ... end

val pow_pos : ('a1 -> 'a1 -> 'a1) -> 'a1 -> positive -> 'a1

module Z : sig ... end

val zeq_bool : z -> z -> bool

type 'c pExpr = | PEc of 'c | PEX of positive | PEadd of 'c pExpr * 'c pExpr | PEsub of 'c pExpr * 'c pExpr | PEmul of 'c pExpr * 'c pExpr | PEopp of 'c pExpr | PEpow of 'c pExpr * n
type 'c pol = | Pc of 'c | Pinj of positive * 'c pol | PX of 'c pol * positive * 'c pol

val p0 : 'a1 -> 'a1 pol
val p1 : 'a1 -> 'a1 pol
val peq : ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> bool
val mkPinj : positive -> 'a1 pol -> 'a1 pol
val mkPinj_pred : positive -> 'a1 pol -> 'a1 pol
val mkPX : 'a1 -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol
val mkXi : 'a1 -> 'a1 -> positive -> 'a1 pol
val mkX : 'a1 -> 'a1 -> 'a1 pol
val popp : ('a1 -> 'a1) -> 'a1 pol -> 'a1 pol
val paddC : ('a1 -> 'a1 -> 'a1) -> 'a1 pol -> 'a1 -> 'a1 pol
val psubC : ('a1 -> 'a1 -> 'a1) -> 'a1 pol -> 'a1 -> 'a1 pol
val paddI : ('a1 -> 'a1 -> 'a1) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol
val psubI : ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol
val paddX : 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol
val psubX : 'a1 -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol
val padd : 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol
val psub : 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol
val pmulC_aux : 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 -> 'a1 pol
val pmulC : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 -> 'a1 pol
val pmulI : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol
val pmul : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol
val psquare : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol
val mk_X : 'a1 -> 'a1 -> positive -> 'a1 pol
val ppow_pos : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> 'a1 pol -> positive -> 'a1 pol
val ppow_N : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> n -> 'a1 pol
val norm_aux : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> 'a1 pol

type kind = | IsProp | IsBool
type 'a trace = | Null | Push of 'a * 'a trace | Merge of 'a trace * 'a trace
type ('tA, 'tX, 'aA, 'aF) gFormula = | TT of kind | FF of kind | X of kind * 'tX | A of kind * 'tA * 'aA | AND of kind * ('tA, 'tX, 'aA, 'aF) gFormula * ('tA, 'tX, 'aA, 'aF) gFormula | OR of kind * ('tA, 'tX, 'aA, 'aF) gFormula * ('tA, 'tX, 'aA, 'aF) gFormula | NOT of kind * ('tA, 'tX, 'aA, 'aF) gFormula | IMPL of kind * ('tA, 'tX, 'aA, 'aF) gFormula * 'aF option * ('tA, 'tX, 'aA, 'aF) gFormula | IFF of kind * ('tA, 'tX, 'aA, 'aF) gFormula * ('tA, 'tX, 'aA, 'aF) gFormula | EQ of ('tA, 'tX, 'aA, 'aF) gFormula * ('tA, 'tX, 'aA, 'aF) gFormula

val mapX : (kind -> 'a2 -> 'a2) -> kind -> ('a1, 'a2, 'a3, 'a4) gFormula -> ('a1, 'a2, 'a3, 'a4) gFormula
val foldA : ('a5 -> 'a3 -> 'a5) -> kind -> ('a1, 'a2, 'a3, 'a4) gFormula -> 'a5 -> 'a5
val cons_id : 'a1 option -> 'a1 list -> 'a1 list
val ids_of_formula : kind -> ('a1, 'a2, 'a3, 'a4) gFormula -> 'a4 list
val collect_annot : kind -> ('a1, 'a2, 'a3, 'a4) gFormula -> 'a3 list

type rtyp = __
type eKind = __
type 'a bFormula = ('a, eKind, unit0, unit0) gFormula

val map_bformula : kind -> ('a1 -> 'a2) -> ('a1, 'a3, 'a4, 'a5) gFormula -> ('a2, 'a3, 'a4, 'a5) gFormula

type ('x, 'annot) clause = ('x * 'annot) list
type ('x, 'annot) cnf = ('x, 'annot) clause list

val cnf_tt : ('a1, 'a2) cnf
val cnf_ff : ('a1, 'a2) cnf
val add_term : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1 * 'a2) -> ('a1, 'a2) clause -> ('a1, 'a2) clause option
val or_clause : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1, 'a2) clause -> ('a1, 'a2) clause -> ('a1, 'a2) clause option
val xor_clause_cnf : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1, 'a2) clause -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf
val or_clause_cnf : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1, 'a2) clause -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf
val or_cnf : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf
val and_cnf : ('a1, 'a2) cnf -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf

type ('term, 'annot, 'tX, 'aF) tFormula = ('term, 'tX, 'annot, 'aF) gFormula

val is_cnf_tt : ('a1, 'a2) cnf -> bool
val is_cnf_ff : ('a1, 'a2) cnf -> bool
val and_cnf_opt : ('a1, 'a2) cnf -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf
val or_cnf_opt : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf
val mk_and : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> (bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf) -> kind -> bool -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf
val mk_or : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> (bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf) -> kind -> bool -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf
val mk_impl : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> (bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf) -> kind -> bool -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf
val mk_iff : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> (bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf) -> kind -> bool -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf
val is_bool : kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> bool option
val xcnf : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a3 -> ('a2, 'a3) cnf) -> ('a1 -> 'a3 -> ('a2, 'a3) cnf) -> bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf
val radd_term : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1 * 'a2) -> ('a1, 'a2) clause -> (('a1, 'a2) clause, 'a2 trace) sum
val ror_clause : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1 * 'a2) list -> ('a1, 'a2) clause -> (('a1, 'a2) clause, 'a2 trace) sum
val xror_clause_cnf : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1 * 'a2) list -> ('a1, 'a2) clause list -> ('a1, 'a2) clause list * 'a2 trace
val ror_clause_cnf : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1 * 'a2) list -> ('a1, 'a2) clause list -> ('a1, 'a2) clause list * 'a2 trace
val ror_cnf : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1, 'a2) clause list -> ('a1, 'a2) clause list -> ('a1, 'a2) cnf * 'a2 trace
val ror_cnf_opt : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf -> ('a1, 'a2) cnf * 'a2 trace
val ratom : ('a1, 'a2) cnf -> 'a2 -> ('a1, 'a2) cnf * 'a2 trace
val rxcnf_and : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> (bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf * 'a3 trace) -> bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf * 'a3 trace
val rxcnf_or : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> (bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf * 'a3 trace) -> bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf * 'a3 trace
val rxcnf_impl : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> (bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf * 'a3 trace) -> bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf * 'a3 trace
val rxcnf_iff : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> (bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf * 'a3 trace) -> bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf * 'a3 trace
val rxcnf : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a3 -> ('a2, 'a3) cnf) -> ('a1 -> 'a3 -> ('a2, 'a3) cnf) -> bool -> kind -> ('a1, 'a3, 'a4, 'a5) tFormula -> ('a2, 'a3) cnf * 'a3 trace

type ('term, 'annot, 'tX) to_constrT = { mkTT : kind -> 'tX; mkFF : kind -> 'tX; mkA : kind -> 'term -> 'annot -> 'tX; mkAND : kind -> 'tX -> 'tX -> 'tX; mkOR : kind -> 'tX -> 'tX -> 'tX; mkIMPL : kind -> 'tX -> 'tX -> 'tX; mkIFF : kind -> 'tX -> 'tX -> 'tX; mkNOT : kind -> 'tX -> 'tX; mkEQ : 'tX -> 'tX -> 'tX; }

val aformula : ('a1, 'a2, 'a3) to_constrT -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> 'a3
val is_X : kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> 'a3 option
val abs_and : ('a1, 'a2, 'a3) to_constrT -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> (kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula) -> ('a1, 'a3, 'a2, 'a4) gFormula
val abs_or : ('a1, 'a2, 'a3) to_constrT -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> (kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula) -> ('a1, 'a3, 'a2, 'a4) gFormula
val abs_not : ('a1, 'a2, 'a3) to_constrT -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> (kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula) -> ('a1, 'a3, 'a2, 'a4) gFormula
val mk_arrow : 'a4 option -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula
val abst_simpl : ('a1, 'a2, 'a3) to_constrT -> ('a2 -> bool) -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula
val abst_and : ('a1, 'a2, 'a3) to_constrT -> (bool -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula) -> bool -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula
val abst_or : ('a1, 'a2, 'a3) to_constrT -> (bool -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula) -> bool -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula
val abst_impl : ('a1, 'a2, 'a3) to_constrT -> (bool -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula) -> bool -> 'a4 option -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula
val or_is_X : kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> bool
val abs_iff : ('a1, 'a2, 'a3) to_constrT -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula
val abst_iff : ('a1, 'a2, 'a3) to_constrT -> ('a2 -> bool) -> (bool -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula) -> bool -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula
val abst_eq : ('a1, 'a2, 'a3) to_constrT -> ('a2 -> bool) -> (bool -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula) -> bool -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula
val abst_form : ('a1, 'a2, 'a3) to_constrT -> ('a2 -> bool) -> bool -> kind -> ('a1, 'a2, 'a3, 'a4) tFormula -> ('a1, 'a2, 'a3, 'a4) tFormula
val cnf_checker : (('a1 * 'a2) list -> 'a3 -> bool) -> ('a1, 'a2) cnf -> 'a3 list -> bool
val tauto_checker : ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a3 -> ('a2, 'a3) cnf) -> ('a1 -> 'a3 -> ('a2, 'a3) cnf) -> (('a2 * 'a3) list -> 'a4 -> bool) -> ('a1, rtyp, 'a3, unit0) gFormula -> 'a4 list -> bool
val cneqb : ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool
val cltb : ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool

type 'c polC = 'c pol
type op1 = | Equal | NonEqual | Strict | NonStrict
type 'c nFormula = 'c polC * op1

val opMult : op1 -> op1 -> op1 option
val opAdd : op1 -> op1 -> op1 option

type 'c psatz = | PsatzIn of nat | PsatzSquare of 'c polC | PsatzMulC of 'c polC * 'c psatz | PsatzMulE of 'c psatz * 'c psatz | PsatzAdd of 'c psatz * 'c psatz | PsatzC of 'c | PsatzZ

val map_option : ('a1 -> 'a2 option) -> 'a1 option -> 'a2 option
val map_option2 : ('a1 -> 'a2 -> 'a3 option) -> 'a1 option -> 'a2 option -> 'a3 option
val pexpr_times_nformula : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 polC -> 'a1 nFormula -> 'a1 nFormula option
val nformula_times_nformula : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> 'a1 nFormula -> 'a1 nFormula option
val nformula_plus_nformula : 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> 'a1 nFormula -> 'a1 nFormula option
val eval_Psatz : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz -> 'a1 nFormula option
val check_inconsistent : 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> bool
val check_normalised_formulas : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz -> bool

type op2 = | OpEq | OpNEq | OpLe | OpGe | OpLt | OpGt
type 't formula = { flhs : 't pExpr; fop : op2; frhs : 't pExpr; }

val norm : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> 'a1 pol
val psub0 : 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol
val padd0 : 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol
val popp0 : ('a1 -> 'a1) -> 'a1 pol -> 'a1 pol
val normalise : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 nFormula
val xnormalise : ('a1 -> 'a1) -> 'a1 nFormula -> 'a1 nFormula list
val xnegate : ('a1 -> 'a1) -> 'a1 nFormula -> 'a1 nFormula list
val cnf_of_list : 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a2 -> ('a1 nFormula, 'a2) cnf
val cnf_normalise : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a2 -> ('a1 nFormula, 'a2) cnf
val cnf_negate : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a2 -> ('a1 nFormula, 'a2) cnf
val xdenorm : positive -> 'a1 pol -> 'a1 pExpr
val denorm : 'a1 pol -> 'a1 pExpr
val map_PExpr : ('a2 -> 'a1) -> 'a2 pExpr -> 'a1 pExpr
val map_Formula : ('a2 -> 'a1) -> 'a2 formula -> 'a1 formula
val simpl_cone : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 psatz -> 'a1 psatz

type q = { qnum : z; qden : positive; }

val qeq_bool : q -> q -> bool
val qle_bool : q -> q -> bool
val qplus : q -> q -> q
val qmult : q -> q -> q
val qopp : q -> q
val qminus : q -> q -> q
val qinv : q -> q
val qpower_positive : q -> positive -> q
val qpower : q -> z -> q

type 'a t = | Empty | Elt of 'a | Branch of 'a t * 'a * 'a t

val find : 'a1 -> 'a1 t -> positive -> 'a1
val singleton : 'a1 -> positive -> 'a1 -> 'a1 t
val vm_add : 'a1 -> positive -> 'a1 -> 'a1 t -> 'a1 t
val zeval_const : z pExpr -> z option

type zWitness = z psatz

val zWeakChecker : z nFormula list -> z psatz -> bool
val psub1 : z pol -> z pol -> z pol
val popp1 : z pol -> z pol
val padd1 : z pol -> z pol -> z pol
val normZ : z pExpr -> z pol
val zunsat : z nFormula -> bool
val zdeduce : z nFormula -> z nFormula -> z nFormula option
val xnnormalise : z formula -> z nFormula
val xnormalise0 : z nFormula -> z nFormula list
val cnf_of_list0 : 'a1 -> z nFormula list -> (z nFormula * 'a1) list list
val normalise0 : z formula -> 'a1 -> (z nFormula, 'a1) cnf
val xnegate0 : z nFormula -> z nFormula list
val negate : z formula -> 'a1 -> (z nFormula, 'a1) cnf
val cnfZ : kind -> (z formula, 'a1, 'a2, 'a3) tFormula -> (z nFormula, 'a1) cnf * 'a1 trace
val ceiling : z -> z -> z

type zArithProof = | DoneProof | RatProof of zWitness * zArithProof | CutProof of zWitness * zArithProof | SplitProof of z polC * zArithProof * zArithProof | EnumProof of zWitness * zWitness * zArithProof list | ExProof of positive * zArithProof

val zgcdM : z -> z -> z
val zgcd_pol : z polC -> z * z
val zdiv_pol : z polC -> z -> z polC
val makeCuttingPlane : z polC -> z polC * z
val genCuttingPlane : z nFormula -> ((z polC * z) * op1) option
val nformula_of_cutting_plane : ((z polC * z) * op1) -> z nFormula
val is_pol_Z0 : z polC -> bool
val eval_Psatz0 : z nFormula list -> zWitness -> z nFormula option
val valid_cut_sign : op1 -> bool
val bound_var : positive -> z formula
val mk_eq_pos : positive -> positive -> positive -> z formula
val max_var : positive -> z pol -> positive
val max_var_nformulae : z nFormula list -> positive
val zChecker : z nFormula list -> zArithProof -> bool
val zTautoChecker : z formula bFormula -> zArithProof list -> bool

type qWitness = q psatz

val qWeakChecker : q nFormula list -> q psatz -> bool
val qnormalise : q formula -> 'a1 -> (q nFormula, 'a1) cnf
val qnegate : q formula -> 'a1 -> (q nFormula, 'a1) cnf
val qunsat : q nFormula -> bool
val qdeduce : q nFormula -> q nFormula -> q nFormula option
val normQ : q pExpr -> q pol
val cnfQ : kind -> (q formula, 'a1, 'a2, 'a3) tFormula -> (q nFormula, 'a1) cnf * 'a1 trace
val qTautoChecker : q formula bFormula -> qWitness list -> bool

type rcst = | C0 | C1 | CQ of q | CZ of z | CPlus of rcst * rcst | CMinus of rcst * rcst | CMult of rcst * rcst | CPow of rcst * (z, nat) sum | CInv of rcst | COpp of rcst

val z_of_exp : (z, nat) sum -> z
val q_of_Rcst : rcst -> q

type rWitness = q psatz

val rWeakChecker : q nFormula list -> q psatz -> bool
val rnormalise : q formula -> 'a1 -> (q nFormula, 'a1) cnf
val rnegate : q formula -> 'a1 -> (q nFormula, 'a1) cnf
val runsat : q nFormula -> bool
val rdeduce : q nFormula -> q nFormula -> q nFormula option
val rTautoChecker : rcst formula bFormula -> rWitness list -> bool