(* Why driver for first-order tptp provers *)

printer "tptp-tff1"
filename "%f-%t-%g.p"

valid   "PROOF-FOUND"
timeout "Zenon error: could not find a proof within the time limit"
outofmemory "Zenon error: could not find a proof within the memory size limit"
unknown "NO-PROOF" "no proof found"
time "why3cpulimit time : %s s"

(* to be improved *)

(* Performed introductions depending on whether counterexamples are
   requested, as said by the meta "get_counterexmp". When this meta
   set, this transformation introduces the model variables that are
   still embedded in the goal. When it is not set, it removes all
   these unused-ce-related variables, even in the context.  *)
transformation "counterexamples_dependent_intros"

transformation "inline_trivial"

transformation "eliminate_builtin"
transformation "eliminate_definition"
transformation "eliminate_inductive"
transformation "eliminate_if"
transformation "eliminate_epsilon"
transformation "eliminate_algebraic"
transformation "eliminate_literal"
transformation "eliminate_let"

theory BuiltIn
  syntax predicate (=)  "(%1 = %2)"
  syntax type int  "$int"
  syntax type real "$real"
  meta "eliminate_algebraic" "no_index"
end


theory int.Int
  syntax function zero "0"
  syntax function one  "1"

  syntax function (+)  "$sum(%1,%2)"
  syntax function (-)  "$difference(%1,%2)"
  syntax function (*)  "$product(%1,%2)"
  syntax function (-_) "$uminus(%1)"

  syntax predicate (<=) "$lesseq(%1,%2)"
  syntax predicate (<)  "$less(%1,%2)"
  syntax predicate (>=) "$greatereq(%1,%2)"
  syntax predicate (>)  "$greater(%1,%2)"

  remove prop MulComm.Comm
  remove prop MulAssoc.Assoc
  remove prop Unit_def_l
  remove prop Unit_def_r
  remove prop Inv_def_l
  remove prop Inv_def_r
  remove prop Assoc
  remove prop Mul_distr_l
  remove prop Mul_distr_r
  remove prop Comm
  remove prop Unitary
  remove prop Refl
  remove prop Trans
  remove prop Antisymm
  remove prop Total
  remove prop NonTrivialRing
  remove prop CompatOrderAdd
  remove prop ZeroLessOne
end

theory real.Real
  syntax function zero "0.0"
  syntax function one  "1.0"

  syntax function (+)  "$sum(%1,%2)"
  syntax function (-)  "$difference(%1,%2)"
  syntax function (*)  "$product(%1,%2)"
  syntax function (-_) "$uminus(%1)"

  syntax function (/)  "$quotient(%1,%2)"
  syntax function inv  "$quotient(1.0,%1)"

  syntax predicate (<=) "$lesseq(%1,%2)"
  syntax predicate (<)  "$less(%1,%2)"
  syntax predicate (>=) "$greatereq(%1,%2)"
  syntax predicate (>)  "$greater(%1,%2)"

  remove prop MulComm.Comm
  remove prop MulAssoc.Assoc
  remove prop Unit_def_l
  remove prop Unit_def_r
  remove prop Inv_def_l
  remove prop Inv_def_r
  remove prop Assoc
  remove prop Mul_distr_l
  remove prop Mul_distr_r
  remove prop Comm
  remove prop Unitary
  remove prop Inverse
  remove prop Refl
  remove prop Trans
  remove prop Antisymm
  remove prop Total
  remove prop NonTrivialRing
  remove prop CompatOrderAdd
  remove prop ZeroLessOne
end

theory int.EuclideanDivision
  syntax function div "$quotient_e(%1,%2)"
  syntax function mod "$remainder_e(%1,%2)"

  remove prop Div_mod
  remove prop Div_bound
  remove prop Mod_bound
  remove prop Mod_1
  remove prop Div_1
  remove prop Div_inf
  remove prop Div_inf_neg
  remove prop Mod_0
  remove prop Div_1_left
  remove prop Div_minus1_left
  remove prop Mod_1_left
  remove prop Mod_minus1_left
end

theory tptp.Univ
  syntax type iType "$i"
end

theory tptp.IntTrunc
  syntax function floor    "$floor(%1)"
  syntax function ceiling  "$ceiling(%1)"
  syntax function truncate "$truncate(%1)"
  syntax function round    "$round(%1)"

  syntax function to_int   "$to_int(%1)"

  syntax predicate is_int  "$is_int(%1)"
  syntax predicate is_rat  "$is_rat(%1)"
end

theory tptp.IntDivT
  syntax function div_t "$quotient_t(%1,%2)"
  syntax function mod_t "$remainder_t(%1,%2)"
end

theory tptp.IntDivF
  syntax function div_f "$quotient_f(%1,%2)"
  syntax function mod_f "$remainder_f(%1,%2)"
end

theory tptp.Rat
  syntax type rat "$rat"

  syntax function zero "0/1"
  syntax function one  "1/1"

  syntax function (+)  "$sum(%1,%2)"
  syntax function (-)  "$difference(%1,%2)"
  syntax function (*)  "$product(%1,%2)"
  syntax function (-_) "$uminus(%1)"

  syntax function (/)  "$quotient(%1,%2)"
  syntax function inv  "$quotient(1/1,%1)"

  syntax predicate (<=) "$lesseq(%1,%2)"
  syntax predicate (<)  "$less(%1,%2)"
  syntax predicate (>=) "$greatereq(%1,%2)"
  syntax predicate (>)  "$greater(%1,%2)"

  syntax function to_rat   "$to_rat(%1)"

  syntax predicate is_int  "$is_int(%1)"
  syntax predicate is_rat  "$is_rat(%1)"

  remove prop MulComm.Comm
  remove prop MulAssoc.Assoc
  remove prop Unit_def_l
  remove prop Unit_def_r
  remove prop Inv_def_l
  remove prop Inv_def_r
  remove prop Assoc
  remove prop Mul_distr_l
  remove prop Mul_distr_r
  remove prop Comm
  remove prop Unitary
  remove prop Refl
  remove prop Trans
  remove prop Antisymm
  remove prop Total
  remove prop NonTrivialRing
  remove prop CompatOrderAdd
  remove prop ZeroLessOne
end

theory tptp.RatTrunc
  syntax function floor    "$floor(%1)"
  syntax function ceiling  "$ceiling(%1)"
  syntax function truncate "$truncate(%1)"
  syntax function round    "$round(%1)"

  syntax function to_int   "$to_int(%1)"
end

theory tptp.RatDivE
  syntax function div "$quotient_e(%1,%2)"
  syntax function mod "$remainder_e(%1,%2)"
end

theory tptp.RatDivT
  syntax function div_t "$quotient_t(%1,%2)"
  syntax function mod_t "$remainder_t(%1,%2)"
end

theory tptp.RatDivF
  syntax function div_f "$quotient_f(%1,%2)"
  syntax function mod_f "$remainder_f(%1,%2)"
end

theory tptp.Real
  syntax function to_real "$to_real(%1)"
end

theory real.FromInt
  syntax function from_int "$to_real(%1)"

  remove prop Zero
  remove prop One
  remove prop Add
  remove prop Sub
  remove prop Mul
  remove prop Neg
end

theory real.Truncate
  syntax function floor    "$to_int(%1)"
  syntax function ceil     "$to_int($ceiling(%1))"
  syntax function truncate "$to_int($truncate(%1))"

  remove prop Truncate_int
  remove prop Truncate_down_pos
  remove prop Truncate_up_neg
  remove prop Real_of_truncate
  remove prop Truncate_monotonic
  remove prop Truncate_monotonic_int1
  remove prop Truncate_monotonic_int2
  remove prop Floor_int
  remove prop Ceil_int
  remove prop Floor_down
  remove prop Ceil_up
  remove prop Floor_monotonic
  remove prop Ceil_monotonic
end

theory tptp.RealTrunc
  syntax function floor    "$floor(%1)"
  syntax function ceiling  "$ceiling(%1)"
  syntax function truncate "$truncate(%1)"
  syntax function round    "$round(%1)"

  syntax function to_int   "$to_int(%1)"

  syntax predicate is_int  "$is_int(%1)"
  syntax predicate is_rat  "$is_rat(%1)"
end

theory tptp.RealDivE
  syntax function div "$quotient_e(%1,%2)"
  syntax function mod "$remainder_e(%1,%2)"
end

theory tptp.RealDivT
  syntax function div_t "$quotient_t(%1,%2)"
  syntax function mod_t "$remainder_t(%1,%2)"
end

theory tptp.RealDivF
  syntax function div_f "$quotient_f(%1,%2)"
  syntax function mod_f "$remainder_f(%1,%2)"
end

theory tptp.IntToRat
  syntax function to_rat   "$to_rat(%1)"
end

theory tptp.IntToReal
  syntax function to_real "$to_real(%1)"
end

theory tptp.RealToRat
  syntax function to_rat   "$to_rat(%1)"
end

theory tptp.RatToReal
  syntax function to_real "$to_real(%1)"
end
