{-# OPTIONS_GHC -w #-}
{-# OPTIONS -XMagicHash -XBangPatterns -XTypeSynonymInstances -XFlexibleInstances -cpp #-}
#if __GLASGOW_HASKELL__ >= 710
{-# OPTIONS_GHC -XPartialTypeSignatures #-}
#endif
{-# OPTIONS_GHC -w #-}
{-
Copyright (C) HyLoRes 2002-2007. See AUTHORS file

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307,
USA.
-}

module HyLo.InputFile.Parser ( parse,
                               initParseState,
                               ParseState,
                               QueryType(..),
                               RelProperty(..),
                               ParseOutput(..), RelInfo, ProverInfo,InferenceTask,
                               relations, provers, theory, tasks)

where

import Control.Monad.State

import HyLo.InputFile.Lexer ( Token(..), FilePos, line, col )

import HyLo.Signature.String ( StringSignature,
                               PropSymbol(..),
                               NomSymbol(..),
                               RelSymbol(..))

import HyLo.Signature ( Signature,
                        emptySignature,
                        addNomToSig,
                        addPropToSig,
                        addRelToSig,
                        isNomInSig,
                        isPropInSig,
                        isRelInSig)

-- since ghc 6.10, "Down" is defined in GHC.Exts, that is included
-- (unqualified) in the parser. we need to use Formula.Down instead of
-- simply Down to avoid ambiguities...
import HyLo.Formula as Formula ( Formula(..), Where(..), CountOp(..) )
import qualified Data.Array as Happy_Data_Array
import qualified Data.Bits as Bits
import qualified GHC.Exts as Happy_GHC_Exts
import Control.Applicative(Applicative(..))
import Control.Monad (ap)

-- parser produced by Happy Version 1.19.9

newtype HappyAbsSyn  = HappyAbsSyn HappyAny
#if __GLASGOW_HASKELL__ >= 607
type HappyAny = Happy_GHC_Exts.Any
#else
type HappyAny = forall a . a
#endif
happyIn4 :: (ParseOutput) -> (HappyAbsSyn )
happyIn4 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn4 #-}
happyOut4 :: (HappyAbsSyn ) -> (ParseOutput)
happyOut4 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut4 #-}
happyIn5 :: ([RelInfo]) -> (HappyAbsSyn )
happyIn5 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn5 #-}
happyOut5 :: (HappyAbsSyn ) -> ([RelInfo])
happyOut5 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut5 #-}
happyIn6 :: (String) -> (HappyAbsSyn )
happyIn6 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn6 #-}
happyOut6 :: (HappyAbsSyn ) -> (String)
happyOut6 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut6 #-}
happyIn7 :: ([Formula NomSymbol PropSymbol RelSymbol]) -> (HappyAbsSyn )
happyIn7 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn7 #-}
happyOut7 :: (HappyAbsSyn ) -> ([Formula NomSymbol PropSymbol RelSymbol])
happyOut7 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut7 #-}
happyIn8 :: ([InferenceTask]) -> (HappyAbsSyn )
happyIn8 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn8 #-}
happyOut8 :: (HappyAbsSyn ) -> ([InferenceTask])
happyOut8 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut8 #-}
happyIn9 :: (InferenceTask) -> (HappyAbsSyn )
happyIn9 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn9 #-}
happyOut9 :: (HappyAbsSyn ) -> (InferenceTask)
happyOut9 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut9 #-}
happyIn10 :: (Maybe String) -> (HappyAbsSyn )
happyIn10 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn10 #-}
happyOut10 :: (HappyAbsSyn ) -> (Maybe String)
happyOut10 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut10 #-}
happyIn11 :: ([ProverInfo]) -> (HappyAbsSyn )
happyIn11 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn11 #-}
happyOut11 :: (HappyAbsSyn ) -> ([ProverInfo])
happyOut11 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut11 #-}
happyIn12 :: ([ProverInfo]) -> (HappyAbsSyn )
happyIn12 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn12 #-}
happyOut12 :: (HappyAbsSyn ) -> ([ProverInfo])
happyOut12 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut12 #-}
happyIn13 :: ([(String,String)]) -> (HappyAbsSyn )
happyIn13 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn13 #-}
happyOut13 :: (HappyAbsSyn ) -> ([(String,String)])
happyOut13 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut13 #-}
happyIn14 :: (String) -> (HappyAbsSyn )
happyIn14 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn14 #-}
happyOut14 :: (HappyAbsSyn ) -> (String)
happyOut14 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut14 #-}
happyIn15 :: ([RelInfo]) -> (HappyAbsSyn )
happyIn15 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn15 #-}
happyOut15 :: (HappyAbsSyn ) -> ([RelInfo])
happyOut15 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut15 #-}
happyIn16 :: ([RelInfo]) -> (HappyAbsSyn )
happyIn16 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn16 #-}
happyOut16 :: (HappyAbsSyn ) -> ([RelInfo])
happyOut16 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut16 #-}
happyIn17 :: ([RelInfo]) -> (HappyAbsSyn )
happyIn17 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn17 #-}
happyOut17 :: (HappyAbsSyn ) -> ([RelInfo])
happyOut17 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut17 #-}
happyIn18 :: ([RelProperty]) -> (HappyAbsSyn )
happyIn18 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn18 #-}
happyOut18 :: (HappyAbsSyn ) -> ([RelProperty])
happyOut18 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut18 #-}
happyIn19 :: (RelProperty) -> (HappyAbsSyn )
happyIn19 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn19 #-}
happyOut19 :: (HappyAbsSyn ) -> (RelProperty)
happyOut19 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut19 #-}
happyIn20 :: (RelProperty) -> (HappyAbsSyn )
happyIn20 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn20 #-}
happyOut20 :: (HappyAbsSyn ) -> (RelProperty)
happyOut20 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut20 #-}
happyIn21 :: ([String]) -> (HappyAbsSyn )
happyIn21 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn21 #-}
happyOut21 :: (HappyAbsSyn ) -> ([String])
happyOut21 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut21 #-}
happyIn22 :: ([Formula NomSymbol PropSymbol RelSymbol]) -> (HappyAbsSyn )
happyIn22 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn22 #-}
happyOut22 :: (HappyAbsSyn ) -> ([Formula NomSymbol PropSymbol RelSymbol])
happyOut22 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut22 #-}
happyIn23 :: (Formula NomSymbol PropSymbol RelSymbol) -> (HappyAbsSyn )
happyIn23 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn23 #-}
happyOut23 :: (HappyAbsSyn ) -> (Formula NomSymbol PropSymbol RelSymbol)
happyOut23 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut23 #-}
happyIn24 :: (CountOp) -> (HappyAbsSyn )
happyIn24 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn24 #-}
happyOut24 :: (HappyAbsSyn ) -> (CountOp)
happyOut24 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut24 #-}
happyIn25 :: (RelSymbol) -> (HappyAbsSyn )
happyIn25 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn25 #-}
happyOut25 :: (HappyAbsSyn ) -> (RelSymbol)
happyOut25 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut25 #-}
happyIn26 :: (NomSymbol) -> (HappyAbsSyn )
happyIn26 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyIn26 #-}
happyOut26 :: (HappyAbsSyn ) -> (NomSymbol)
happyOut26 x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOut26 #-}
happyInTok :: ((Token, FilePos)) -> (HappyAbsSyn )
happyInTok x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyInTok #-}
happyOutTok :: (HappyAbsSyn ) -> ((Token, FilePos))
happyOutTok x = Happy_GHC_Exts.unsafeCoerce# x
{-# INLINE happyOutTok #-}


happyExpList :: HappyAddr
happyExpList = HappyA# 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{-# NOINLINE happyExpListPerState #-}
happyExpListPerState st =
    token_strs_expected
  where token_strs = ["error","%dummy","%start_parse","Input","Signature","Variable","Theory","Queries","Query","File","ProverSpecific","ProverList","OptionsList","Value","AutomaticSignature","ContentSignature","RelationList","RelPropertyList","UnaryRelProperty","BinaryRelProperty","VariableList","Formulas","Formula","CountSymbol","Rel","PropVar","signature","propositions","nominals","relations","reflexive","universal","difference","transitive","symmetric","functional","injective","inverseof","subsetof","equals","tclosureof","trclosureof","automatic","proverparameters","prover","theory","query","valid","satisfiable","retrieve","count","integer","variable","label","file","':'","down","greaterEqual","lowerEqual","greater","lower","equal","nonEqual","prop","nom","true","false","neg","and","or","dimp","imp","box","ibox","ubox","dbox","dia","idia","udia","ddia","'('","')'","';'","'.'","','","'{'","'}'","'<'","'>'","'['","']'","'='","%eof"]
        bit_start = st * 93
        bit_end = (st + 1) * 93
        read_bit = readArrayBit happyExpList
        bits = map read_bit [bit_start..bit_end - 1]
        bits_indexed = zip bits [0..92]
        token_strs_expected = concatMap f bits_indexed
        f (False, _) = []
        f (True, nr) = [token_strs !! nr]

happyActOffsets :: HappyAddr
happyActOffsets = HappyA# "\x03\x00\x03\x00\xc6\xff\xce\xff\x26\x00\xe5\xff\x00\x00\x00\x00\xe9\xff\xfa\xff\x1a\x00\x00\x00\x35\x00\x35\x00\x35\x00\x48\x00\x5b\x00\x30\x00\x40\x00\x5a\x00\x00\x00\x00\x00\x00\x00\x5e\x00\xf6\xff\x65\x00\x3b\x00\x54\x00\x35\x00\x3b\x00\x3b\x00\x35\x00\x94\x00\x0d\x01\x70\x00\xe6\xff\x00\x00\x1a\x01\x7a\x00\x79\x00\x95\x00\x00\x00\x00\x00\x00\x00\x00\x00\x7e\x00\x00\x00\x87\x00\x99\x00\x9d\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x35\x00\xf8\xff\x05\x00\x35\x00\x35\x00\x35\x00\x00\x00\xa2\x00\x00\x00\x8b\x00\x34\x00\xb6\x00\xbe\x00\x0d\x00\x0c\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x20\x00\xc2\x00\x00\x00\x00\x00\xe6\xff\xe6\xff\xe6\xff\xe6\xff\xe6\xff\xe6\xff\xe6\xff\xe6\xff\xe6\xff\xe6\xff\x53\x00\x53\x00\xa3\x00\x00\x00\x00\x00\x00\x00\xa9\x00\x38\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xe6\xff\xb2\x00\x00\x00\x00\x00\xba\x00\x56\x00\xe6\xff\x08\x00\xe6\xff\xe6\xff\xe6\xff\xe6\xff\xe6\xff\x00\x00\xb5\x00\xb5\x00\xb5\x00\xb5\x00\xc0\x00\x00\x00\x00\x00\x00\x00\x58\x00\x00\x00\x58\x00\x00\x00\x7e\x00\x7e\x00\xc1\x00\x58\x00\x00\x00\x00\x00\xf4\x00\xf5\x00\xc4\x00\xcc\x00\x13\x01\xd0\x00\xd4\x00\xd8\x00\x00\x00\x93\x00\xf8\x00\xe9\x00\x00\x00\xde\x00\xe6\xff\x00\x00\xe6\xff\xe6\xff\xe6\xff\xe6\xff\x00\x00\x00\x00\xe6\xff\xe6\xff\x93\x00\x93\x00\x00\x00\x00\x00\x3c\x00\x4a\x00\x93\x00\xe6\xff\xe0\x00\xe4\x00\xf9\x00\x00\x00\xfa\x00\x58\x00\x00\x00\x00\x00\x00\x00\xf1\x00\xfc\x00\xe6\xff\xe6\xff\xe6\xff\xe6\xff\x93\x00\x00\x00\x00\x00\xfd\x00\xfe\x00\x00\x01\x01\x01\x21\x01\x2c\x00\x00\x00\x04\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x58\x00\x00\x00\x00\x00"#

happyGotoOffsets :: HappyAddr
happyGotoOffsets = HappyA# "\x37\x01\x00\x00\x00\x00\x00\x00\x8e\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x8f\x00\x01\x00\x1f\x00\x31\x01\x39\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x34\x01\x00\x00\x90\x00\x35\x01\x36\x01\x2b\x00\x3b\x01\x7c\x00\x00\x00\x82\x00\x00\x00\xb8\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x18\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x42\x01\x43\x01\x44\x01\x45\x01\x46\x01\x47\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x38\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xaf\x00\xb3\x00\xb7\x00\xbb\x00\xbf\x00\xc3\x00\xc7\x00\xcb\x00\xcf\x00\xd3\x00\x3a\x01\x3c\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xd7\x00\x00\x00\x00\x00\x00\x00\x00\x00\x3d\x01\xdb\x00\x3f\x01\xdf\x00\xe3\x00\xe7\x00\xeb\x00\x8d\x00\x00\x00\x4a\x01\x4c\x01\x4f\x01\x50\x01\x00\x00\x00\x00\x00\x00\x00\x00\x33\x00\x00\x00\x3e\x00\x00\x00\x1b\x01\x1e\x01\x00\x00\x91\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xef\x00\x00\x00\xf3\x00\xf7\x00\xfb\x00\xff\x00\x00\x00\x00\x00\x03\x01\x07\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x0b\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x55\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x92\x00\x97\x00\x9c\x00\xa1\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x51\x01\x47\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x69\x00\x00\x00\x00\x00"#

happyAdjustOffset :: Happy_GHC_Exts.Int# -> Happy_GHC_Exts.Int#
happyAdjustOffset off = off

happyDefActions :: HappyAddr
happyDefActions = HappyA# "\x00\x00\x00\x00\x00\x00\x00\x00\xe3\xff\x00\x00\xfd\xff\xfc\xff\x00\x00\x00\x00\x00\x00\xe4\xff\xdf\xff\xc7\xff\xc7\xff\xef\xff\x00\x00\x00\x00\xc6\xff\x00\x00\xfb\xff\xfa\xff\xf9\xff\x00\x00\xde\xff\x00\x00\xe3\xff\x00\x00\xdf\xff\xe3\xff\xe3\xff\xc7\xff\xed\xff\xf7\xff\x00\x00\xc4\xff\xfe\xff\xf7\xff\x00\x00\x00\x00\x00\x00\xc5\xff\xe2\xff\xe1\xff\xdd\xff\xda\xff\xe0\xff\x00\x00\xd9\xff\xd8\xff\xd3\xff\xd5\xff\xd4\xff\xd2\xff\xd1\xff\xd0\xff\xcf\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xee\xff\x00\x00\xf6\xff\x00\x00\xc3\xff\x00\x00\x00\x00\x9a\xff\x00\x00\xa4\xff\xa3\xff\xa2\xff\xa1\xff\xa0\xff\x9f\xff\x9b\xff\xbf\xff\xc1\xff\xc0\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x9c\xff\x9e\xff\x9d\xff\x00\x00\x00\x00\xb9\xff\xba\xff\xbb\xff\xbc\xff\xb5\xff\xb6\xff\xb7\xff\xb8\xff\xb0\xff\x00\x00\x00\x00\x9a\xff\x9b\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xc4\xff\xf8\xff\xf1\xff\xf1\xff\xf1\xff\xf1\xff\x00\x00\xc8\xff\xc9\xff\xcc\xff\xc7\xff\xce\xff\xc7\xff\xca\xff\xda\xff\xda\xff\xdc\xff\xdf\xff\xd7\xff\xd6\xff\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\xc2\xff\xb1\xff\xb2\xff\xae\xff\xaf\xff\x00\x00\x00\x00\xac\xff\x00\x00\x00\x00\x00\x00\x00\x00\xad\xff\xa5\xff\x00\x00\x00\x00\xb3\xff\xb4\xff\xa8\xff\xa9\xff\x00\x00\x00\x00\xa7\xff\x00\x00\x00\x00\x00\x00\x00\x00\xf0\xff\x00\x00\xeb\xff\xcb\xff\xcd\xff\xdb\xff\x00\x00\x00\x00\xc4\xff\xc4\xff\xc4\xff\xc4\xff\xa6\xff\xaa\xff\xab\xff\x00\x00\x00\x00\x00\x00\x00\x00\xed\xff\x00\x00\xe8\xff\xea\xff\xe7\xff\xe6\xff\xe5\xff\xec\xff\xf2\xff\xf3\xff\xf4\xff\xf5\xff\xeb\xff\xe9\xff"#

happyCheck :: HappyAddr
happyCheck = HappyA# "\xff\xff\x1b\x00\x3c\x00\x02\x00\x01\x00\x1f\x00\x20\x00\x21\x00\x22\x00\x23\x00\x24\x00\x25\x00\x26\x00\x27\x00\x28\x00\x29\x00\x2a\x00\x43\x00\x11\x00\x1b\x00\x1e\x00\x2f\x00\x30\x00\x31\x00\x32\x00\x33\x00\x34\x00\x35\x00\x36\x00\x37\x00\x26\x00\x27\x00\x1b\x00\x02\x00\x3d\x00\x1b\x00\x3e\x00\x3c\x00\x40\x00\x1b\x00\x02\x00\x03\x00\x04\x00\x26\x00\x27\x00\x02\x00\x26\x00\x27\x00\x11\x00\x3b\x00\x26\x00\x27\x00\x3c\x00\x02\x00\x3c\x00\x11\x00\x2b\x00\x2c\x00\x2d\x00\x2e\x00\x11\x00\x02\x00\x03\x00\x04\x00\x02\x00\x3c\x00\x3a\x00\x37\x00\x11\x00\x38\x00\x39\x00\x1b\x00\x1c\x00\x02\x00\x3d\x00\x2b\x00\x2c\x00\x2d\x00\x2e\x00\x11\x00\x1b\x00\x0a\x00\x26\x00\x27\x00\x28\x00\x29\x00\x3c\x00\x02\x00\x38\x00\x39\x00\x12\x00\x26\x00\x27\x00\x3d\x00\x09\x00\x2b\x00\x2c\x00\x2d\x00\x2e\x00\x2b\x00\x2c\x00\x2d\x00\x2e\x00\x2b\x00\x2c\x00\x2d\x00\x2e\x00\x02\x00\x3c\x00\x39\x00\x1b\x00\x14\x00\x38\x00\x1b\x00\x09\x00\x1b\x00\x38\x00\x2b\x00\x2c\x00\x2d\x00\x2e\x00\x26\x00\x27\x00\x3b\x00\x26\x00\x27\x00\x26\x00\x27\x00\x04\x00\x05\x00\x38\x00\x05\x00\x06\x00\x07\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x0c\x00\x0d\x00\x0e\x00\x0f\x00\x10\x00\x01\x00\x3c\x00\x02\x00\x02\x00\x02\x00\x12\x00\x13\x00\x14\x00\x3d\x00\x16\x00\x0b\x00\x0c\x00\x3d\x00\x0d\x00\x0d\x00\x0d\x00\x12\x00\x13\x00\x14\x00\x3d\x00\x16\x00\x12\x00\x13\x00\x14\x00\x13\x00\x16\x00\x12\x00\x13\x00\x14\x00\x3c\x00\x16\x00\x12\x00\x13\x00\x14\x00\x37\x00\x16\x00\x12\x00\x13\x00\x14\x00\x3d\x00\x16\x00\x16\x00\x17\x00\x18\x00\x19\x00\x04\x00\x05\x00\x2b\x00\x2c\x00\x2d\x00\x2e\x00\x13\x00\x14\x00\x3d\x00\x16\x00\x13\x00\x14\x00\x3d\x00\x16\x00\x13\x00\x14\x00\x37\x00\x16\x00\x13\x00\x14\x00\x1a\x00\x16\x00\x13\x00\x14\x00\x3b\x00\x16\x00\x13\x00\x14\x00\x3b\x00\x16\x00\x13\x00\x14\x00\x1e\x00\x16\x00\x13\x00\x14\x00\x1e\x00\x16\x00\x13\x00\x14\x00\x41\x00\x16\x00\x13\x00\x14\x00\x3f\x00\x16\x00\x13\x00\x14\x00\x3a\x00\x16\x00\x13\x00\x14\x00\x3b\x00\x16\x00\x13\x00\x14\x00\x3a\x00\x16\x00\x13\x00\x14\x00\x38\x00\x16\x00\x13\x00\x14\x00\x3b\x00\x16\x00\x13\x00\x14\x00\x3c\x00\x16\x00\x13\x00\x14\x00\x38\x00\x16\x00\x13\x00\x14\x00\x38\x00\x16\x00\x13\x00\x14\x00\x38\x00\x16\x00\x13\x00\x14\x00\x38\x00\x16\x00\x13\x00\x14\x00\x2b\x00\x16\x00\x13\x00\x14\x00\x3a\x00\x16\x00\x13\x00\x14\x00\x3c\x00\x16\x00\x13\x00\x14\x00\x3c\x00\x16\x00\x15\x00\x2b\x00\x2c\x00\x2d\x00\x0e\x00\x0f\x00\x10\x00\x0e\x00\x0f\x00\x10\x00\x0e\x00\x0f\x00\x10\x00\x15\x00\x1d\x00\x3d\x00\x3d\x00\x42\x00\x13\x00\x3c\x00\x3c\x00\x00\x00\x07\x00\x3d\x00\x3d\x00\x3d\x00\x03\x00\x3d\x00\x3d\x00\x3b\x00\x0c\x00\x0c\x00\x0c\x00\x08\x00\x02\x00\x02\x00\x02\x00\x02\x00\x02\x00\x02\x00\xff\xff\xff\xff\xff\xff\xff\xff\x16\x00\x15\x00\x06\x00\x15\x00\x06\x00\x16\x00\x15\x00\x06\x00\x06\x00\xff\xff\xff\xff\x08\x00\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"#

happyTable :: HappyAddr
happyTable = HappyA# "\x00\x00\x47\x00\x05\x00\x12\x00\x03\x00\x48\x00\x49\x00\x4a\x00\x4b\x00\x4c\x00\x4d\x00\x4e\x00\x4f\x00\x50\x00\x51\x00\x52\x00\x53\x00\xff\xff\x17\x00\x15\x00\x1c\x00\x54\x00\x55\x00\x56\x00\x57\x00\x58\x00\x59\x00\x5a\x00\x5b\x00\x5c\x00\x16\x00\x17\x00\x15\x00\x12\x00\x10\x00\x60\x00\x5d\x00\x0f\x00\x5e\x00\x70\x00\x09\x00\x0a\x00\x0b\x00\x16\x00\x17\x00\x12\x00\x61\x00\x62\x00\x13\x00\x1d\x00\x71\x00\x72\x00\x86\x00\x12\x00\x0e\x00\x0c\x00\xbd\xff\xbd\xff\xbd\xff\xbd\xff\x29\x00\x09\x00\x0a\x00\x0b\x00\x12\x00\x84\x00\x9c\x00\x73\x00\x8e\x00\xbd\xff\xbd\xff\x15\x00\xc8\x00\xc5\x00\xbd\xff\xbe\xff\xbe\xff\xbe\xff\xbe\xff\x8d\x00\x15\x00\xc6\x00\x16\x00\x17\x00\xc9\x00\xca\x00\x0d\x00\xb6\x00\xbe\xff\xbe\xff\x12\x00\x16\x00\x17\x00\xbe\xff\xb7\x00\x76\x00\x77\x00\x78\x00\x79\x00\x76\x00\x77\x00\x78\x00\x79\x00\x76\x00\x77\x00\x78\x00\x79\x00\xb6\x00\x21\x00\x7a\x00\x60\x00\x23\x00\xa3\x00\x70\x00\xd0\x00\x15\x00\xbf\x00\x76\x00\x77\x00\x78\x00\x79\x00\x61\x00\x62\x00\x20\x00\x71\x00\x9f\x00\x16\x00\x17\x00\x24\x00\x25\x00\xbe\x00\x33\x00\x34\x00\x35\x00\x36\x00\x37\x00\x38\x00\x39\x00\x3a\x00\x3b\x00\x3c\x00\x3d\x00\x3e\x00\x05\x00\x2e\x00\x18\x00\x18\x00\x18\x00\x42\x00\x43\x00\x44\x00\x1f\x00\x45\x00\x06\x00\x07\x00\x1e\x00\x19\x00\x2c\x00\xb5\x00\x95\x00\x43\x00\x44\x00\x1b\x00\x45\x00\xc2\x00\x43\x00\x44\x00\x29\x00\x45\x00\xc1\x00\x43\x00\x44\x00\x24\x00\x45\x00\xc0\x00\x43\x00\x44\x00\x41\x00\x45\x00\xbf\x00\x43\x00\x44\x00\x40\x00\x45\x00\x7c\x00\x7d\x00\x7e\x00\x7f\x00\x41\x00\x25\x00\x76\x00\x77\x00\x78\x00\x79\x00\x6c\x00\x44\x00\x8a\x00\x45\x00\x6b\x00\x44\x00\x7b\x00\x45\x00\x6a\x00\x44\x00\x3f\x00\x45\x00\x69\x00\x44\x00\x75\x00\x45\x00\x68\x00\x44\x00\x89\x00\x45\x00\x67\x00\x44\x00\x88\x00\x45\x00\x66\x00\x44\x00\x74\x00\x45\x00\x65\x00\x44\x00\x6e\x00\x45\x00\x64\x00\x44\x00\xa5\x00\x45\x00\x63\x00\x44\x00\xa4\x00\x45\x00\xa1\x00\x44\x00\xa1\x00\x45\x00\x9c\x00\x44\x00\x92\x00\x45\x00\x99\x00\x44\x00\xa0\x00\x45\x00\x98\x00\x44\x00\x90\x00\x45\x00\x97\x00\x44\x00\x8b\x00\x45\x00\x96\x00\x44\x00\xb3\x00\x45\x00\xab\x00\x44\x00\xb2\x00\x45\x00\xaa\x00\x44\x00\xb0\x00\x45\x00\xa9\x00\x44\x00\xaf\x00\x45\x00\xa8\x00\x44\x00\xae\x00\x45\x00\xa7\x00\x44\x00\x76\x00\x45\x00\xa6\x00\x44\x00\xad\x00\x45\x00\xa5\x00\x44\x00\xbc\x00\x45\x00\xbc\x00\x44\x00\xbb\x00\x45\x00\x27\x00\x76\x00\x77\x00\x78\x00\x2f\x00\x30\x00\x31\x00\x8c\x00\x30\x00\x31\x00\x8b\x00\x30\x00\x31\x00\x27\x00\xb1\x00\xb5\x00\xb4\x00\xc5\x00\x29\x00\xba\x00\xb9\x00\x03\x00\x10\x00\xc4\x00\xcf\x00\xce\x00\x21\x00\xcd\x00\xcc\x00\xd0\x00\x2e\x00\x2b\x00\x2a\x00\x27\x00\x86\x00\x84\x00\x82\x00\x81\x00\x80\x00\x7f\x00\x00\x00\x00\x00\x00\x00\x00\x00\x6e\x00\x62\x00\x94\x00\x5e\x00\x93\x00\x9d\x00\x9a\x00\x92\x00\x90\x00\x00\x00\x00\x00\xca\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"#

happyReduceArr = Happy_Data_Array.array (1, 101) [
        (1 , happyReduce_1),
        (2 , happyReduce_2),
        (3 , happyReduce_3),
        (4 , happyReduce_4),
        (5 , happyReduce_5),
        (6 , happyReduce_6),
        (7 , happyReduce_7),
        (8 , happyReduce_8),
        (9 , happyReduce_9),
        (10 , happyReduce_10),
        (11 , happyReduce_11),
        (12 , happyReduce_12),
        (13 , happyReduce_13),
        (14 , happyReduce_14),
        (15 , happyReduce_15),
        (16 , happyReduce_16),
        (17 , happyReduce_17),
        (18 , happyReduce_18),
        (19 , happyReduce_19),
        (20 , happyReduce_20),
        (21 , happyReduce_21),
        (22 , happyReduce_22),
        (23 , happyReduce_23),
        (24 , happyReduce_24),
        (25 , happyReduce_25),
        (26 , happyReduce_26),
        (27 , happyReduce_27),
        (28 , happyReduce_28),
        (29 , happyReduce_29),
        (30 , happyReduce_30),
        (31 , happyReduce_31),
        (32 , happyReduce_32),
        (33 , happyReduce_33),
        (34 , happyReduce_34),
        (35 , happyReduce_35),
        (36 , happyReduce_36),
        (37 , happyReduce_37),
        (38 , happyReduce_38),
        (39 , happyReduce_39),
        (40 , happyReduce_40),
        (41 , happyReduce_41),
        (42 , happyReduce_42),
        (43 , happyReduce_43),
        (44 , happyReduce_44),
        (45 , happyReduce_45),
        (46 , happyReduce_46),
        (47 , happyReduce_47),
        (48 , happyReduce_48),
        (49 , happyReduce_49),
        (50 , happyReduce_50),
        (51 , happyReduce_51),
        (52 , happyReduce_52),
        (53 , happyReduce_53),
        (54 , happyReduce_54),
        (55 , happyReduce_55),
        (56 , happyReduce_56),
        (57 , happyReduce_57),
        (58 , happyReduce_58),
        (59 , happyReduce_59),
        (60 , happyReduce_60),
        (61 , happyReduce_61),
        (62 , happyReduce_62),
        (63 , happyReduce_63),
        (64 , happyReduce_64),
        (65 , happyReduce_65),
        (66 , happyReduce_66),
        (67 , happyReduce_67),
        (68 , happyReduce_68),
        (69 , happyReduce_69),
        (70 , happyReduce_70),
        (71 , happyReduce_71),
        (72 , happyReduce_72),
        (73 , happyReduce_73),
        (74 , happyReduce_74),
        (75 , happyReduce_75),
        (76 , happyReduce_76),
        (77 , happyReduce_77),
        (78 , happyReduce_78),
        (79 , happyReduce_79),
        (80 , happyReduce_80),
        (81 , happyReduce_81),
        (82 , happyReduce_82),
        (83 , happyReduce_83),
        (84 , happyReduce_84),
        (85 , happyReduce_85),
        (86 , happyReduce_86),
        (87 , happyReduce_87),
        (88 , happyReduce_88),
        (89 , happyReduce_89),
        (90 , happyReduce_90),
        (91 , happyReduce_91),
        (92 , happyReduce_92),
        (93 , happyReduce_93),
        (94 , happyReduce_94),
        (95 , happyReduce_95),
        (96 , happyReduce_96),
        (97 , happyReduce_97),
        (98 , happyReduce_98),
        (99 , happyReduce_99),
        (100 , happyReduce_100),
        (101 , happyReduce_101)
        ]

happy_n_terms = 68 :: Int
happy_n_nonterms = 23 :: Int

happyReduce_1 = happyReduce 7# 0# happyReduction_1
happyReduction_1 (happy_x_7 `HappyStk`
        happy_x_6 `HappyStk`
        happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut5 happy_x_3 of { happy_var_3 ->
        case happyOut11 happy_x_5 of { happy_var_5 ->
        case happyOut7 happy_x_6 of { happy_var_6 ->
        case happyOut8 happy_x_7 of { happy_var_7 ->
        happyIn4
                 (PO{relations = happy_var_3,
               provers   = happy_var_5,
               theory    = happy_var_6,
               tasks     = happy_var_7}
        ) `HappyStk` happyRest}}}}

happyReduce_2 = happySpecReduce_1  1# happyReduction_2
happyReduction_2 happy_x_1
         =  case happyOut15 happy_x_1 of { happy_var_1 ->
        happyIn5
                 (happy_var_1
        )}

happyReduce_3 = happySpecReduce_1  1# happyReduction_3
happyReduction_3 happy_x_1
         =  case happyOut16 happy_x_1 of { happy_var_1 ->
        happyIn5
                 (happy_var_1
        )}

happyReduce_4 = happySpecReduce_1  2# happyReduction_4
happyReduction_4 happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenVariable happy_var_1,  _)) ->
        happyIn6
                 (happy_var_1
        )}

happyReduce_5 = happySpecReduce_1  2# happyReduction_5
happyReduction_5 happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenProp happy_var_1  ,    _)) ->
        happyIn6
                 (let PropSymbol x = happy_var_1 in x
        )}

happyReduce_6 = happySpecReduce_1  2# happyReduction_6
happyReduction_6 happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenNom happy_var_1   ,    _)) ->
        happyIn6
                 (let NomSymbol x  = happy_var_1 in x
        )}

happyReduce_7 = happyReduce 4# 3# happyReduction_7
happyReduction_7 (happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut22 happy_x_3 of { happy_var_3 ->
        happyIn7
                 (happy_var_3
        ) `HappyStk` happyRest}

happyReduce_8 = happySpecReduce_0  4# happyReduction_8
happyReduction_8  =  happyIn8
                 ([]
        )

happyReduce_9 = happySpecReduce_2  4# happyReduction_9
happyReduction_9 happy_x_2
        happy_x_1
         =  case happyOut9 happy_x_1 of { happy_var_1 ->
        case happyOut8 happy_x_2 of { happy_var_2 ->
        happyIn8
                 (happy_var_1:happy_var_2
        )}}

happyReduce_10 = happyReduce 8# 5# happyReduction_10
happyReduction_10 (happy_x_8 `HappyStk`
        happy_x_7 `HappyStk`
        happy_x_6 `HappyStk`
        happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut10 happy_x_4 of { happy_var_4 ->
        case happyOut22 happy_x_7 of { happy_var_7 ->
        happyIn9
                 ((Valid,       happy_var_4, happy_var_7)
        ) `HappyStk` happyRest}}

happyReduce_11 = happyReduce 8# 5# happyReduction_11
happyReduction_11 (happy_x_8 `HappyStk`
        happy_x_7 `HappyStk`
        happy_x_6 `HappyStk`
        happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut10 happy_x_4 of { happy_var_4 ->
        case happyOut22 happy_x_7 of { happy_var_7 ->
        happyIn9
                 ((Satisfiable, happy_var_4, happy_var_7)
        ) `HappyStk` happyRest}}

happyReduce_12 = happyReduce 8# 5# happyReduction_12
happyReduction_12 (happy_x_8 `HappyStk`
        happy_x_7 `HappyStk`
        happy_x_6 `HappyStk`
        happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut10 happy_x_4 of { happy_var_4 ->
        case happyOut22 happy_x_7 of { happy_var_7 ->
        happyIn9
                 ((Retrieve,    happy_var_4, happy_var_7)
        ) `HappyStk` happyRest}}

happyReduce_13 = happyReduce 8# 5# happyReduction_13
happyReduction_13 (happy_x_8 `HappyStk`
        happy_x_7 `HappyStk`
        happy_x_6 `HappyStk`
        happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut10 happy_x_4 of { happy_var_4 ->
        case happyOut22 happy_x_7 of { happy_var_7 ->
        happyIn9
                 ((Counting,    happy_var_4, happy_var_7)
        ) `HappyStk` happyRest}}

happyReduce_14 = happySpecReduce_0  6# happyReduction_14
happyReduction_14  =  happyIn10
                 (Nothing
        )

happyReduce_15 = happySpecReduce_2  6# happyReduction_15
happyReduction_15 happy_x_2
        happy_x_1
         =  case happyOutTok happy_x_2 of { ((TokenFile happy_var_2,      _)) ->
        happyIn10
                 (Just happy_var_2
        )}

happyReduce_16 = happySpecReduce_0  7# happyReduction_16
happyReduction_16  =  happyIn11
                 ([]
        )

happyReduce_17 = happyReduce 4# 7# happyReduction_17
happyReduction_17 (happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut12 happy_x_3 of { happy_var_3 ->
        happyIn11
                 (happy_var_3
        ) `HappyStk` happyRest}

happyReduce_18 = happySpecReduce_0  8# happyReduction_18
happyReduction_18  =  happyIn12
                 ([]
        )

happyReduce_19 = happyReduce 8# 8# happyReduction_19
happyReduction_19 (happy_x_8 `HappyStk`
        happy_x_7 `HappyStk`
        happy_x_6 `HappyStk`
        happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut6 happy_x_3 of { happy_var_3 ->
        case happyOut13 happy_x_6 of { happy_var_6 ->
        case happyOut12 happy_x_8 of { happy_var_8 ->
        happyIn12
                 ((happy_var_3,happy_var_6):happy_var_8
        ) `HappyStk` happyRest}}}

happyReduce_20 = happySpecReduce_0  9# happyReduction_20
happyReduction_20  =  happyIn13
                 ([]
        )

happyReduce_21 = happySpecReduce_3  9# happyReduction_21
happyReduction_21 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut6 happy_x_1 of { happy_var_1 ->
        case happyOut14 happy_x_3 of { happy_var_3 ->
        happyIn13
                 ([(happy_var_1,happy_var_3)]
        )}}

happyReduce_22 = happyReduce 5# 9# happyReduction_22
happyReduction_22 (happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut6 happy_x_1 of { happy_var_1 ->
        case happyOut14 happy_x_3 of { happy_var_3 ->
        case happyOut13 happy_x_5 of { happy_var_5 ->
        happyIn13
                 ((happy_var_1,happy_var_3): happy_var_5
        ) `HappyStk` happyRest}}}

happyReduce_23 = happySpecReduce_1  10# happyReduction_23
happyReduction_23 happy_x_1
         =  case happyOut6 happy_x_1 of { happy_var_1 ->
        happyIn14
                 (happy_var_1
        )}

happyReduce_24 = happySpecReduce_1  10# happyReduction_24
happyReduction_24 happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenLabel happy_var_1,     _)) ->
        happyIn14
                 (happy_var_1
        )}

happyReduce_25 = happySpecReduce_1  10# happyReduction_25
happyReduction_25 happy_x_1
         =  happyIn14
                 ("true"
        )

happyReduce_26 = happySpecReduce_1  10# happyReduction_26
happyReduction_26 happy_x_1
         =  happyIn14
                 ("false"
        )

happyReduce_27 = happyMonadReduce 1# 11# happyReduction_27
happyReduction_27 (happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((( putType Automatic >>= \s -> return []))
        ) (\r -> happyReturn (happyIn15 r))

happyReduce_28 = happyMonadReduce 0# 12# happyReduction_28
happyReduction_28 (happyRest) tk
         = happyThen ((( putType NotAutomatic >>= \s -> return []))
        ) (\r -> happyReturn (happyIn16 r))

happyReduce_29 = happyMonadReduce 5# 12# happyReduction_29
happyReduction_29 (happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOut21 happy_x_3 of { happy_var_3 ->
        case happyOut16 happy_x_5 of { happy_var_5 ->
        ( getSig >>= \s -> putSig (foldr addPToSig s happy_var_3)
             >>= \s -> putType NotAutomatic
             >>= \s -> return happy_var_5)}})
        ) (\r -> happyReturn (happyIn16 r))

happyReduce_30 = happyMonadReduce 5# 12# happyReduction_30
happyReduction_30 (happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOut21 happy_x_3 of { happy_var_3 ->
        case happyOut16 happy_x_5 of { happy_var_5 ->
        ( getSig >>= \s -> putSig (foldr addNToSig s happy_var_3)
             >>= \s -> putType NotAutomatic
             >>= \s -> return happy_var_5)}})
        ) (\r -> happyReturn (happyIn16 r))

happyReduce_31 = happyMonadReduce 5# 12# happyReduction_31
happyReduction_31 (happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOut17 happy_x_3 of { happy_var_3 ->
        case happyOut16 happy_x_5 of { happy_var_5 ->
        ( getSig >>= \s -> putSig (foldr (addRToSig . fst) s happy_var_3)
             >>= \s -> putType NotAutomatic
             >>= \s -> return (happy_var_3++happy_var_5))}})
        ) (\r -> happyReturn (happyIn16 r))

happyReduce_32 = happySpecReduce_0  13# happyReduction_32
happyReduction_32  =  happyIn17
                 ([]
        )

happyReduce_33 = happySpecReduce_1  13# happyReduction_33
happyReduction_33 happy_x_1
         =  case happyOut6 happy_x_1 of { happy_var_1 ->
        happyIn17
                 ([(happy_var_1, [])]
        )}

happyReduce_34 = happySpecReduce_3  13# happyReduction_34
happyReduction_34 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut6 happy_x_1 of { happy_var_1 ->
        case happyOut17 happy_x_3 of { happy_var_3 ->
        happyIn17
                 ((happy_var_1, []):happy_var_3
        )}}

happyReduce_35 = happyReduce 5# 13# happyReduction_35
happyReduction_35 (happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut6 happy_x_1 of { happy_var_1 ->
        case happyOut18 happy_x_4 of { happy_var_4 ->
        happyIn17
                 ([(happy_var_1, happy_var_4)]
        ) `HappyStk` happyRest}}

happyReduce_36 = happyReduce 7# 13# happyReduction_36
happyReduction_36 (happy_x_7 `HappyStk`
        happy_x_6 `HappyStk`
        happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut6 happy_x_1 of { happy_var_1 ->
        case happyOut18 happy_x_4 of { happy_var_4 ->
        case happyOut17 happy_x_7 of { happy_var_7 ->
        happyIn17
                 ((happy_var_1 , happy_var_4):happy_var_7
        ) `HappyStk` happyRest}}}

happyReduce_37 = happySpecReduce_0  14# happyReduction_37
happyReduction_37  =  happyIn18
                 ([]
        )

happyReduce_38 = happySpecReduce_1  14# happyReduction_38
happyReduction_38 happy_x_1
         =  case happyOut19 happy_x_1 of { happy_var_1 ->
        happyIn18
                 ([happy_var_1]
        )}

happyReduce_39 = happySpecReduce_1  14# happyReduction_39
happyReduction_39 happy_x_1
         =  case happyOut20 happy_x_1 of { happy_var_1 ->
        happyIn18
                 ([happy_var_1]
        )}

happyReduce_40 = happySpecReduce_3  14# happyReduction_40
happyReduction_40 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut19 happy_x_1 of { happy_var_1 ->
        case happyOut18 happy_x_3 of { happy_var_3 ->
        happyIn18
                 (happy_var_1:happy_var_3
        )}}

happyReduce_41 = happySpecReduce_3  14# happyReduction_41
happyReduction_41 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut20 happy_x_1 of { happy_var_1 ->
        case happyOut18 happy_x_3 of { happy_var_3 ->
        happyIn18
                 (happy_var_1:happy_var_3
        )}}

happyReduce_42 = happySpecReduce_1  15# happyReduction_42
happyReduction_42 happy_x_1
         =  happyIn19
                 (Universal
        )

happyReduce_43 = happySpecReduce_1  15# happyReduction_43
happyReduction_43 happy_x_1
         =  happyIn19
                 (Difference
        )

happyReduce_44 = happySpecReduce_1  15# happyReduction_44
happyReduction_44 happy_x_1
         =  happyIn19
                 (Reflexive
        )

happyReduce_45 = happySpecReduce_1  15# happyReduction_45
happyReduction_45 happy_x_1
         =  happyIn19
                 (Transitive
        )

happyReduce_46 = happySpecReduce_1  15# happyReduction_46
happyReduction_46 happy_x_1
         =  happyIn19
                 (Symmetric
        )

happyReduce_47 = happySpecReduce_1  15# happyReduction_47
happyReduction_47 happy_x_1
         =  happyIn19
                 (Functional
        )

happyReduce_48 = happySpecReduce_1  15# happyReduction_48
happyReduction_48 happy_x_1
         =  happyIn19
                 (Injective
        )

happyReduce_49 = happySpecReduce_2  16# happyReduction_49
happyReduction_49 happy_x_2
        happy_x_1
         =  case happyOut6 happy_x_2 of { happy_var_2 ->
        happyIn20
                 (SubsetOf [happy_var_2]
        )}

happyReduce_50 = happyReduce 4# 16# happyReduction_50
happyReduction_50 (happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut21 happy_x_3 of { happy_var_3 ->
        happyIn20
                 (SubsetOf happy_var_3
        ) `HappyStk` happyRest}

happyReduce_51 = happySpecReduce_2  16# happyReduction_51
happyReduction_51 happy_x_2
        happy_x_1
         =  case happyOut6 happy_x_2 of { happy_var_2 ->
        happyIn20
                 (Equals [happy_var_2]
        )}

happyReduce_52 = happyReduce 4# 16# happyReduction_52
happyReduction_52 (happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut21 happy_x_3 of { happy_var_3 ->
        happyIn20
                 (Equals happy_var_3
        ) `HappyStk` happyRest}

happyReduce_53 = happySpecReduce_2  16# happyReduction_53
happyReduction_53 happy_x_2
        happy_x_1
         =  case happyOut6 happy_x_2 of { happy_var_2 ->
        happyIn20
                 (InverseOf happy_var_2
        )}

happyReduce_54 = happySpecReduce_2  16# happyReduction_54
happyReduction_54 happy_x_2
        happy_x_1
         =  case happyOut6 happy_x_2 of { happy_var_2 ->
        happyIn20
                 (TClosureOf happy_var_2
        )}

happyReduce_55 = happySpecReduce_2  16# happyReduction_55
happyReduction_55 happy_x_2
        happy_x_1
         =  case happyOut6 happy_x_2 of { happy_var_2 ->
        happyIn20
                 (TRClosureOf happy_var_2
        )}

happyReduce_56 = happySpecReduce_0  17# happyReduction_56
happyReduction_56  =  happyIn21
                 ([]
        )

happyReduce_57 = happySpecReduce_1  17# happyReduction_57
happyReduction_57 happy_x_1
         =  case happyOut6 happy_x_1 of { happy_var_1 ->
        happyIn21
                 ([happy_var_1]
        )}

happyReduce_58 = happySpecReduce_3  17# happyReduction_58
happyReduction_58 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut6 happy_x_1 of { happy_var_1 ->
        case happyOut21 happy_x_3 of { happy_var_3 ->
        happyIn21
                 (happy_var_1:happy_var_3
        )}}

happyReduce_59 = happySpecReduce_0  18# happyReduction_59
happyReduction_59  =  happyIn22
                 ([]
        )

happyReduce_60 = happySpecReduce_1  18# happyReduction_60
happyReduction_60 happy_x_1
         =  case happyOut23 happy_x_1 of { happy_var_1 ->
        happyIn22
                 ([happy_var_1]
        )}

happyReduce_61 = happySpecReduce_3  18# happyReduction_61
happyReduction_61 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_1 of { happy_var_1 ->
        case happyOut22 happy_x_3 of { happy_var_3 ->
        happyIn22
                 (happy_var_1:happy_var_3
        )}}

happyReduce_62 = happySpecReduce_1  19# happyReduction_62
happyReduction_62 happy_x_1
         =  happyIn23
                 (Top
        )

happyReduce_63 = happySpecReduce_1  19# happyReduction_63
happyReduction_63 happy_x_1
         =  happyIn23
                 (Bot
        )

happyReduce_64 = happyMonadReduce 1# 19# happyReduction_64
happyReduction_64 (happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOutTok happy_x_1 of { ((TokenNom happy_var_1   ,    _)) ->
        ( get >>= \s -> if (isAutomatic s)
                    then return (Nom happy_var_1)
                    else if (isNomInSig happy_var_1 (pSig s))
                    then return (Nom happy_var_1)
                    else (error $ (show happy_var_1) ++ " not in Sig as Nominal"))})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_65 = happyMonadReduce 1# 19# happyReduction_65
happyReduction_65 (happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOutTok happy_x_1 of { ((TokenProp happy_var_1  ,    _)) ->
        ( get >>= \s -> if (isAutomatic s)
                    then return (Prop happy_var_1)
                    else if (isPropInSig happy_var_1 (pSig s))
                    then return (Prop happy_var_1)
                    else (error $ (show happy_var_1) ++ " not in Sig as Prop"))})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_66 = happyMonadReduce 1# 19# happyReduction_66
happyReduction_66 (happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOutTok happy_x_1 of { ((TokenVariable happy_var_1,  _)) ->
        ( getSig >>= \s -> if (isNomInSig (NomSymbol happy_var_1) s)
                       then return (Nom (NomSymbol happy_var_1))
                       else if (isPropInSig (PropSymbol happy_var_1) s)
                       then return (Prop (PropSymbol happy_var_1))
                       else if (isRelInSig (RelSymbol happy_var_1) s)
                       then error (happy_var_1 ++ " defined as Rel")
                       else (error $ "Symbol not in Sig : " ++ happy_var_1))})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_67 = happySpecReduce_2  19# happyReduction_67
happyReduction_67 happy_x_2
        happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenDia happy_var_1   ,    _)) ->
        case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (Diam happy_var_1 happy_var_2
        )}}

happyReduce_68 = happySpecReduce_2  19# happyReduction_68
happyReduction_68 happy_x_2
        happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenIDia happy_var_1  ,    _)) ->
        case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (IDiam happy_var_1 happy_var_2
        )}}

happyReduce_69 = happySpecReduce_2  19# happyReduction_69
happyReduction_69 happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (E happy_var_2
        )}

happyReduce_70 = happySpecReduce_2  19# happyReduction_70
happyReduction_70 happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (D happy_var_2
        )}

happyReduce_71 = happySpecReduce_2  19# happyReduction_71
happyReduction_71 happy_x_2
        happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenBox happy_var_1   ,    _)) ->
        case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (Box happy_var_1 happy_var_2
        )}}

happyReduce_72 = happySpecReduce_2  19# happyReduction_72
happyReduction_72 happy_x_2
        happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenIBox happy_var_1  ,    _)) ->
        case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (IBox happy_var_1 happy_var_2
        )}}

happyReduce_73 = happySpecReduce_2  19# happyReduction_73
happyReduction_73 happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (A happy_var_2
        )}

happyReduce_74 = happySpecReduce_2  19# happyReduction_74
happyReduction_74 happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (B happy_var_2
        )}

happyReduce_75 = happyMonadReduce 4# 19# happyReduction_75
happyReduction_75 (happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOut25 happy_x_2 of { happy_var_2 ->
        case happyOut23 happy_x_4 of { happy_var_4 ->
        ( getSig >>= \s -> if (isRelInSig happy_var_2 s)
                       then return (Diam happy_var_2 happy_var_4)
                       else (error $ (show happy_var_2) ++ " not in Sig as Relation"))}})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_76 = happyMonadReduce 4# 19# happyReduction_76
happyReduction_76 (happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOut25 happy_x_2 of { happy_var_2 ->
        case happyOut23 happy_x_4 of { happy_var_4 ->
        ( getSig >>= \s -> if (isRelInSig happy_var_2 s)
                       then return (Box happy_var_2 happy_var_4)
                       else (error $ (show happy_var_2) ++ " not in Sig as Relation"))}})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_77 = happySpecReduce_3  19# happyReduction_77
happyReduction_77 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_1 of { happy_var_1 ->
        case happyOut23 happy_x_3 of { happy_var_3 ->
        happyIn23
                 (happy_var_1 :<-->: happy_var_3
        )}}

happyReduce_78 = happySpecReduce_3  19# happyReduction_78
happyReduction_78 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_1 of { happy_var_1 ->
        case happyOut23 happy_x_3 of { happy_var_3 ->
        happyIn23
                 (happy_var_1 :-->: happy_var_3
        )}}

happyReduce_79 = happySpecReduce_2  19# happyReduction_79
happyReduction_79 happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (Neg happy_var_2
        )}

happyReduce_80 = happySpecReduce_3  19# happyReduction_80
happyReduction_80 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_1 of { happy_var_1 ->
        case happyOut23 happy_x_3 of { happy_var_3 ->
        happyIn23
                 (happy_var_1 :&: happy_var_3
        )}}

happyReduce_81 = happySpecReduce_3  19# happyReduction_81
happyReduction_81 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_1 of { happy_var_1 ->
        case happyOut23 happy_x_3 of { happy_var_3 ->
        happyIn23
                 (happy_var_1 :|: happy_var_3
        )}}

happyReduce_82 = happyMonadReduce 3# 19# happyReduction_82
happyReduction_82 (happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOutTok happy_x_1 of { ((TokenNom happy_var_1   ,    _)) ->
        case happyOut23 happy_x_3 of { happy_var_3 ->
        ( get >>= \s -> if (isAutomatic s)
                    then return (At happy_var_1 happy_var_3)
                    else if (isNomInSig happy_var_1 (pSig s))
                    then return (At happy_var_1 happy_var_3)
                    else (error $ (show happy_var_1) ++ " not defined as Nom in Sig"))}})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_83 = happyMonadReduce 3# 19# happyReduction_83
happyReduction_83 (happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOut26 happy_x_1 of { happy_var_1 ->
        case happyOut23 happy_x_3 of { happy_var_3 ->
        ( getSig >>= \s -> if (isNomInSig happy_var_1 s)
                       then return (At happy_var_1 happy_var_3)
                       else (error $ (show happy_var_1) ++ " not defined as Nom in Sig"))}})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_84 = happyMonadReduce 5# 19# happyReduction_84
happyReduction_84 (happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOutTok happy_x_3 of { ((TokenNom happy_var_3   ,    _)) ->
        case happyOut23 happy_x_4 of { happy_var_4 ->
        ( get >>= \s -> if (isAutomatic s)
                    then return (Formula.Down happy_var_3 happy_var_4)
                    else if (isNomInSig happy_var_3 (pSig s))
                    then return (Formula.Down happy_var_3 happy_var_4)
                    else (error $ (show happy_var_3) ++ " not defined as Nom in Sig"))}})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_85 = happyMonadReduce 5# 19# happyReduction_85
happyReduction_85 (happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOut26 happy_x_3 of { happy_var_3 ->
        case happyOut23 happy_x_4 of { happy_var_4 ->
        ( getSig >>= \s -> if (isNomInSig happy_var_3 s)
                       then return (Formula.Down happy_var_3 happy_var_4)
                       else (error $ (show happy_var_3) ++ " not defined as Nom in Sig"))}})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_86 = happyMonadReduce 4# 19# happyReduction_86
happyReduction_86 (happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOutTok happy_x_2 of { ((TokenNom happy_var_2   ,    _)) ->
        case happyOut23 happy_x_4 of { happy_var_4 ->
        ( get >>= \s -> if (isAutomatic s)
                    then return (Formula.Down happy_var_2 happy_var_4)
                    else if (isNomInSig happy_var_2 (pSig s))
                    then return (Formula.Down happy_var_2 happy_var_4)
                    else (error $ (show happy_var_2) ++ " not defined as Nom in Sig"))}})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_87 = happyMonadReduce 4# 19# happyReduction_87
happyReduction_87 (happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOut26 happy_x_2 of { happy_var_2 ->
        case happyOut23 happy_x_4 of { happy_var_4 ->
        ( getSig >>= \s -> if (isNomInSig happy_var_2 s)
                       then return (Formula.Down happy_var_2 happy_var_4)
                       else (error $ (show happy_var_2) ++ " not defined as Nom in Sig"))}})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_88 = happyReduce 4# 19# happyReduction_88
happyReduction_88 (happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest)
         = case happyOut24 happy_x_1 of { happy_var_1 ->
        case happyOutTok happy_x_2 of { ((TokenInteger happy_var_2,   _)) ->
        case happyOut23 happy_x_4 of { happy_var_4 ->
        happyIn23
                 (Count happy_var_1 Global     happy_var_2 happy_var_4
        ) `HappyStk` happyRest}}}

happyReduce_89 = happyMonadReduce 5# 19# happyReduction_89
happyReduction_89 (happy_x_5 `HappyStk`
        happy_x_4 `HappyStk`
        happy_x_3 `HappyStk`
        happy_x_2 `HappyStk`
        happy_x_1 `HappyStk`
        happyRest) tk
         = happyThen ((case happyOut24 happy_x_1 of { happy_var_1 ->
        case happyOutTok happy_x_2 of { ((TokenInteger happy_var_2,   _)) ->
        case happyOut25 happy_x_3 of { happy_var_3 ->
        case happyOut23 happy_x_5 of { happy_var_5 ->
        ( getSig >>= \s -> if (isRelInSig happy_var_3 s)
                       then return (Count happy_var_1 (Local happy_var_3) happy_var_2 happy_var_5)
                       else (error $ (show happy_var_3) ++ " not in Sig as Relation"))}}}})
        ) (\r -> happyReturn (happyIn23 r))

happyReduce_90 = happySpecReduce_3  19# happyReduction_90
happyReduction_90 happy_x_3
        happy_x_2
        happy_x_1
         =  case happyOut23 happy_x_2 of { happy_var_2 ->
        happyIn23
                 (happy_var_2
        )}

happyReduce_91 = happySpecReduce_1  20# happyReduction_91
happyReduction_91 happy_x_1
         =  happyIn24
                 (:>=:
        )

happyReduce_92 = happySpecReduce_1  20# happyReduction_92
happyReduction_92 happy_x_1
         =  happyIn24
                 (:<=:
        )

happyReduce_93 = happySpecReduce_1  20# happyReduction_93
happyReduction_93 happy_x_1
         =  happyIn24
                 (:>:
        )

happyReduce_94 = happySpecReduce_1  20# happyReduction_94
happyReduction_94 happy_x_1
         =  happyIn24
                 (:<:
        )

happyReduce_95 = happySpecReduce_1  20# happyReduction_95
happyReduction_95 happy_x_1
         =  happyIn24
                 (:=:
        )

happyReduce_96 = happySpecReduce_1  20# happyReduction_96
happyReduction_96 happy_x_1
         =  happyIn24
                 (:/=:
        )

happyReduce_97 = happySpecReduce_1  21# happyReduction_97
happyReduction_97 happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenProp happy_var_1  ,    _)) ->
        happyIn25
                 (let (PropSymbol l) = happy_var_1 in RelSymbol l
        )}

happyReduce_98 = happySpecReduce_1  21# happyReduction_98
happyReduction_98 happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenNom happy_var_1   ,    _)) ->
        happyIn25
                 (let (NomSymbol l) = happy_var_1 in RelSymbol l
        )}

happyReduce_99 = happySpecReduce_1  21# happyReduction_99
happyReduction_99 happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenVariable happy_var_1,  _)) ->
        happyIn25
                 (RelSymbol happy_var_1
        )}

happyReduce_100 = happySpecReduce_1  22# happyReduction_100
happyReduction_100 happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenProp happy_var_1  ,    _)) ->
        happyIn26
                 (let (PropSymbol l) = happy_var_1 in NomSymbol l
        )}

happyReduce_101 = happySpecReduce_1  22# happyReduction_101
happyReduction_101 happy_x_1
         =  case happyOutTok happy_x_1 of { ((TokenVariable happy_var_1,  _)) ->
        happyIn26
                 (NomSymbol happy_var_1
        )}

happyNewToken action sts stk [] =
        happyDoAction 67# notHappyAtAll action sts stk []

happyNewToken action sts stk (tk:tks) =
        let cont i = happyDoAction i tk action sts stk tks in
        case tk of {
        (TokenSignature,    _) -> cont 1#;
        (TokenPropositions, _) -> cont 2#;
        (TokenNominals ,    _) -> cont 3#;
        (TokenRelations,    _) -> cont 4#;
        (TokenReflexive,    _) -> cont 5#;
        (TokenUniversal,    _) -> cont 6#;
        (TokenDifference,   _) -> cont 7#;
        (TokenTransitive,   _) -> cont 8#;
        (TokenSymmetric,    _) -> cont 9#;
        (TokenFunctional,   _) -> cont 10#;
        (TokenInjective,    _) -> cont 11#;
        (TokenInverseOf,    _) -> cont 12#;
        (TokenSubsetOf,     _) -> cont 13#;
        (TokenEquals,       _) -> cont 14#;
        (TokenTClosureOf   ,_) -> cont 15#;
        (TokenTRClosureOf,  _) -> cont 16#;
        (TokenAutomatic,    _) -> cont 17#;
        (TokenProverParameters, _) -> cont 18#;
        (TokenProver,       _) -> cont 19#;
        (TokenTheory,       _) -> cont 20#;
        (TokenQuery,        _) -> cont 21#;
        (TokenValid,        _) -> cont 22#;
        (TokenSatisfiable,  _) -> cont 23#;
        (TokenRetrieve,     _) -> cont 24#;
        (TokenCount,        _) -> cont 25#;
        (TokenInteger happy_dollar_dollar,   _) -> cont 26#;
        (TokenVariable happy_dollar_dollar,  _) -> cont 27#;
        (TokenLabel happy_dollar_dollar,     _) -> cont 28#;
        (TokenFile happy_dollar_dollar,      _) -> cont 29#;
        (TokenColon    ,    _) -> cont 30#;
        (TokenDown     ,    _) -> cont 31#;
        (TokenGE       ,    _) -> cont 32#;
        (TokenLE       ,    _) -> cont 33#;
        (TokenG        ,    _) -> cont 34#;
        (TokenL        ,    _) -> cont 35#;
        (TokenE        ,    _) -> cont 36#;
        (TokenNE       ,    _) -> cont 37#;
        (TokenProp happy_dollar_dollar  ,    _) -> cont 38#;
        (TokenNom happy_dollar_dollar   ,    _) -> cont 39#;
        (TokenTrue     ,    _) -> cont 40#;
        (TokenFalse    ,    _) -> cont 41#;
        (TokenNeg      ,    _) -> cont 42#;
        (TokenAnd      ,    _) -> cont 43#;
        (TokenOr       ,    _) -> cont 44#;
        (TokenDimp     ,    _) -> cont 45#;
        (TokenImp      ,    _) -> cont 46#;
        (TokenBox happy_dollar_dollar   ,    _) -> cont 47#;
        (TokenIBox happy_dollar_dollar  ,    _) -> cont 48#;
        (TokenUBox     ,    _) -> cont 49#;
        (TokenDBox     ,    _) -> cont 50#;
        (TokenDia happy_dollar_dollar   ,    _) -> cont 51#;
        (TokenIDia happy_dollar_dollar  ,    _) -> cont 52#;
        (TokenUDia     ,    _) -> cont 53#;
        (TokenDDia     ,    _) -> cont 54#;
        (TokenOB       ,    _) -> cont 55#;
        (TokenCB       ,    _) -> cont 56#;
        (TokenSC       ,    _) -> cont 57#;
        (TokenDot      ,    _) -> cont 58#;
        (TokenComma    ,    _) -> cont 59#;
        (TokenOC       ,    _) -> cont 60#;
        (TokenCC       ,    _) -> cont 61#;
        (TokenODia     ,    _) -> cont 62#;
        (TokenCDia     ,    _) -> cont 63#;
        (TokenOBox     ,    _) -> cont 64#;
        (TokenCBox     ,    _) -> cont 65#;
        (TokenEqual    ,    _) -> cont 66#;
        _ -> happyError' ((tk:tks), [])
        }

happyError_ explist 67# tk tks = happyError' (tks, explist)
happyError_ explist _ tk tks = happyError' ((tk:tks), explist)

happyThen :: () => State ParseState a -> (a -> State ParseState b) -> State ParseState b
happyThen = (>>=)
happyReturn :: () => a -> State ParseState a
happyReturn = (return)
happyThen1 m k tks = (>>=) m (\a -> k a tks)
happyReturn1 :: () => a -> b -> State ParseState a
happyReturn1 = \a tks -> (return) a
happyError' :: () => ([((Token, FilePos))], [String]) -> State ParseState a
happyError' = (\(tokens, _) -> happyError tokens)
parse tks = happySomeParser where
 happySomeParser = happyThen (happyParse 0# tks) (\x -> happyReturn (happyOut4 x))

happySeq = happyDontSeq


data ParseOutput = PO{relations :: [RelInfo],
                      provers   :: [ProverInfo],
                      theory    :: [Formula NomSymbol PropSymbol RelSymbol],
                      tasks     :: [InferenceTask]
                     } deriving (Show)

type RelInfo = (String,[RelProperty])
type ProverInfo = (String, [(String,String)])
type InferenceTask = (QueryType,
                      Maybe String,
                      [Formula NomSymbol PropSymbol RelSymbol])

data RelProperty   = Reflexive |
                     Symmetric |
                     Transitive |
                     Functional |
                     Injective |
                     Universal |
                     Difference |
                     --
                     InverseOf  String |
                     SubsetOf [String] |
                     Equals   [String] |
                     TClosureOf String |
                     TRClosureOf String
                     deriving (Eq, Show, Ord)

data QueryType = Valid | Satisfiable | Retrieve | Counting
                  deriving (Eq, Show)

data SignatureType = NotAutomatic | Automatic | NotSet deriving (Eq)

type ParseState = (StringSignature,SignatureType)

initParseState = (emptySignature, NotSet)

pSig = fst
pType = snd

isAutomatic s = (pType s) == Automatic


getSig :: State ParseState (StringSignature)
getSig = do
          state <- get
          return (fst state)

putSig :: StringSignature -> State ParseState ()
putSig s = do
            state <- get
            put (s,snd state)

getType :: State ParseState (SignatureType)
getType = do
           state <- get
           return (snd state)

putType :: SignatureType -> State ParseState ()
putType t = do
             state <- get
             put (fst state, t)

addPToSig l s =
  if (isNomInSig (NomSymbol l) s)
  then error $ l ++ " already declared as Nom"
  else if (isRelInSig (RelSymbol l) s)
  then error $ l ++ " already declared as Rel"
  else addPropToSig (PropSymbol l) s

addNToSig l s =
  if (isPropInSig (PropSymbol l) s)
  then error $ l ++ " already declared as Prop"
  else if (isRelInSig (RelSymbol l) s)
  then error $ l ++ " already declared as Rel"
  else addNomToSig (NomSymbol l) s

addRToSig l s =
  if (isPropInSig (PropSymbol l) s)
  then error $ l ++ " already declared as Prop"
  else if (isNomInSig (NomSymbol l) s)
  then error $ l ++ " already declared as Nom"
  else addRelToSig (RelSymbol l) s

happyError :: [(Token, FilePos)] -> a
happyError ((_, fp):_) = error ("Parse error near line " ++
                                   (show $ line fp) ++
                                   ", col. " ++
                                   (show $ col fp))
{-# LINE 1 "templates/GenericTemplate.hs" #-}
{-# LINE 1 "templates/GenericTemplate.hs" #-}
{-# LINE 1 "<built-in>" #-}
{-# LINE 1 "<command-line>" #-}
{-# LINE 10 "<command-line>" #-}
# 1 "/usr/include/stdc-predef.h" 1 3 4

# 17 "/usr/include/stdc-predef.h" 3 4














































{-# LINE 10 "<command-line>" #-}
{-# LINE 1 "/opt/ghc/8.6.3/lib/ghc-8.6.3/include/ghcversion.h" #-}















{-# LINE 10 "<command-line>" #-}
{-# LINE 1 "/tmp/ghc780_0/ghc_2.h" #-}






































































































































































































{-# LINE 10 "<command-line>" #-}
{-# LINE 1 "templates/GenericTemplate.hs" #-}
-- Id: GenericTemplate.hs,v 1.26 2005/01/14 14:47:22 simonmar Exp 













-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex.
#if __GLASGOW_HASKELL__ > 706
#define LT(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.<# m)) :: Bool)
#define GTE(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.>=# m)) :: Bool)
#define EQ(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.==# m)) :: Bool)
#else
#define LT(n,m) (n Happy_GHC_Exts.<# m)
#define GTE(n,m) (n Happy_GHC_Exts.>=# m)
#define EQ(n,m) (n Happy_GHC_Exts.==# m)
#endif
{-# LINE 43 "templates/GenericTemplate.hs" #-}

data Happy_IntList = HappyCons Happy_GHC_Exts.Int# Happy_IntList







{-# LINE 65 "templates/GenericTemplate.hs" #-}

{-# LINE 75 "templates/GenericTemplate.hs" #-}

{-# LINE 84 "templates/GenericTemplate.hs" #-}

infixr 9 `HappyStk`
data HappyStk a = HappyStk a (HappyStk a)

-----------------------------------------------------------------------------
-- starting the parse

happyParse start_state = happyNewToken start_state notHappyAtAll notHappyAtAll

-----------------------------------------------------------------------------
-- Accepting the parse

-- If the current token is 0#, it means we've just accepted a partial
-- parse (a %partial parser).  We must ignore the saved token on the top of
-- the stack in this case.
happyAccept 0# tk st sts (_ `HappyStk` ans `HappyStk` _) =
        happyReturn1 ans
happyAccept j tk st sts (HappyStk ans _) =
        (happyTcHack j (happyTcHack st)) (happyReturn1 ans)

-----------------------------------------------------------------------------
-- Arrays only: do the next action



happyDoAction i tk st
        = {- nothing -}


          case action of
                0#           -> {- nothing -}
                                     happyFail (happyExpListPerState ((Happy_GHC_Exts.I# (st)) :: Int)) i tk st
                -1#          -> {- nothing -}
                                     happyAccept i tk st
                n | LT(n,(0# :: Happy_GHC_Exts.Int#)) -> {- nothing -}

                                                   (happyReduceArr Happy_Data_Array.! rule) i tk st
                                                   where rule = (Happy_GHC_Exts.I# ((Happy_GHC_Exts.negateInt# ((n Happy_GHC_Exts.+# (1# :: Happy_GHC_Exts.Int#))))))
                n                 -> {- nothing -}


                                     happyShift new_state i tk st
                                     where new_state = (n Happy_GHC_Exts.-# (1# :: Happy_GHC_Exts.Int#))
   where off    = happyAdjustOffset (indexShortOffAddr happyActOffsets st)
         off_i  = (off Happy_GHC_Exts.+#  i)
         check  = if GTE(off_i,(0# :: Happy_GHC_Exts.Int#))
                  then EQ(indexShortOffAddr happyCheck off_i, i)
                  else False
         action
          | check     = indexShortOffAddr happyTable off_i
          | otherwise = indexShortOffAddr happyDefActions st




indexShortOffAddr (HappyA# arr) off =
        Happy_GHC_Exts.narrow16Int# i
  where
        i = Happy_GHC_Exts.word2Int# (Happy_GHC_Exts.or# (Happy_GHC_Exts.uncheckedShiftL# high 8#) low)
        high = Happy_GHC_Exts.int2Word# (Happy_GHC_Exts.ord# (Happy_GHC_Exts.indexCharOffAddr# arr (off' Happy_GHC_Exts.+# 1#)))
        low  = Happy_GHC_Exts.int2Word# (Happy_GHC_Exts.ord# (Happy_GHC_Exts.indexCharOffAddr# arr off'))
        off' = off Happy_GHC_Exts.*# 2#




{-# INLINE happyLt #-}
happyLt x y = LT(x,y)


readArrayBit arr bit =
    Bits.testBit (Happy_GHC_Exts.I# (indexShortOffAddr arr ((unbox_int bit) `Happy_GHC_Exts.iShiftRA#` 4#))) (bit `mod` 16)
  where unbox_int (Happy_GHC_Exts.I# x) = x






data HappyAddr = HappyA# Happy_GHC_Exts.Addr#


-----------------------------------------------------------------------------
-- HappyState data type (not arrays)

{-# LINE 180 "templates/GenericTemplate.hs" #-}

-----------------------------------------------------------------------------
-- Shifting a token

happyShift new_state 0# tk st sts stk@(x `HappyStk` _) =
     let i = (case Happy_GHC_Exts.unsafeCoerce# x of { (Happy_GHC_Exts.I# (i)) -> i }) in
--     trace "shifting the error token" $
     happyDoAction i tk new_state (HappyCons (st) (sts)) (stk)

happyShift new_state i tk st sts stk =
     happyNewToken new_state (HappyCons (st) (sts)) ((happyInTok (tk))`HappyStk`stk)

-- happyReduce is specialised for the common cases.

happySpecReduce_0 i fn 0# tk st sts stk
     = happyFail [] 0# tk st sts stk
happySpecReduce_0 nt fn j tk st@((action)) sts stk
     = happyGoto nt j tk st (HappyCons (st) (sts)) (fn `HappyStk` stk)

happySpecReduce_1 i fn 0# tk st sts stk
     = happyFail [] 0# tk st sts stk
happySpecReduce_1 nt fn j tk _ sts@((HappyCons (st@(action)) (_))) (v1`HappyStk`stk')
     = let r = fn v1 in
       happySeq r (happyGoto nt j tk st sts (r `HappyStk` stk'))

happySpecReduce_2 i fn 0# tk st sts stk
     = happyFail [] 0# tk st sts stk
happySpecReduce_2 nt fn j tk _ (HappyCons (_) (sts@((HappyCons (st@(action)) (_))))) (v1`HappyStk`v2`HappyStk`stk')
     = let r = fn v1 v2 in
       happySeq r (happyGoto nt j tk st sts (r `HappyStk` stk'))

happySpecReduce_3 i fn 0# tk st sts stk
     = happyFail [] 0# tk st sts stk
happySpecReduce_3 nt fn j tk _ (HappyCons (_) ((HappyCons (_) (sts@((HappyCons (st@(action)) (_))))))) (v1`HappyStk`v2`HappyStk`v3`HappyStk`stk')
     = let r = fn v1 v2 v3 in
       happySeq r (happyGoto nt j tk st sts (r `HappyStk` stk'))

happyReduce k i fn 0# tk st sts stk
     = happyFail [] 0# tk st sts stk
happyReduce k nt fn j tk st sts stk
     = case happyDrop (k Happy_GHC_Exts.-# (1# :: Happy_GHC_Exts.Int#)) sts of
         sts1@((HappyCons (st1@(action)) (_))) ->
                let r = fn stk in  -- it doesn't hurt to always seq here...
                happyDoSeq r (happyGoto nt j tk st1 sts1 r)

happyMonadReduce k nt fn 0# tk st sts stk
     = happyFail [] 0# tk st sts stk
happyMonadReduce k nt fn j tk st sts stk =
      case happyDrop k (HappyCons (st) (sts)) of
        sts1@((HappyCons (st1@(action)) (_))) ->
          let drop_stk = happyDropStk k stk in
          happyThen1 (fn stk tk) (\r -> happyGoto nt j tk st1 sts1 (r `HappyStk` drop_stk))

happyMonad2Reduce k nt fn 0# tk st sts stk
     = happyFail [] 0# tk st sts stk
happyMonad2Reduce k nt fn j tk st sts stk =
      case happyDrop k (HappyCons (st) (sts)) of
        sts1@((HappyCons (st1@(action)) (_))) ->
         let drop_stk = happyDropStk k stk

             off = happyAdjustOffset (indexShortOffAddr happyGotoOffsets st1)
             off_i = (off Happy_GHC_Exts.+#  nt)
             new_state = indexShortOffAddr happyTable off_i




          in
          happyThen1 (fn stk tk) (\r -> happyNewToken new_state sts1 (r `HappyStk` drop_stk))

happyDrop 0# l = l
happyDrop n (HappyCons (_) (t)) = happyDrop (n Happy_GHC_Exts.-# (1# :: Happy_GHC_Exts.Int#)) t

happyDropStk 0# l = l
happyDropStk n (x `HappyStk` xs) = happyDropStk (n Happy_GHC_Exts.-# (1#::Happy_GHC_Exts.Int#)) xs

-----------------------------------------------------------------------------
-- Moving to a new state after a reduction


happyGoto nt j tk st =
   {- nothing -}
   happyDoAction j tk new_state
   where off = happyAdjustOffset (indexShortOffAddr happyGotoOffsets st)
         off_i = (off Happy_GHC_Exts.+#  nt)
         new_state = indexShortOffAddr happyTable off_i




-----------------------------------------------------------------------------
-- Error recovery (0# is the error token)

-- parse error if we are in recovery and we fail again
happyFail explist 0# tk old_st _ stk@(x `HappyStk` _) =
     let i = (case Happy_GHC_Exts.unsafeCoerce# x of { (Happy_GHC_Exts.I# (i)) -> i }) in
--      trace "failing" $ 
        happyError_ explist i tk

{-  We don't need state discarding for our restricted implementation of
    "error".  In fact, it can cause some bogus parses, so I've disabled it
    for now --SDM

-- discard a state
happyFail  0# tk old_st (HappyCons ((action)) (sts)) 
                                                (saved_tok `HappyStk` _ `HappyStk` stk) =
--      trace ("discarding state, depth " ++ show (length stk))  $
        happyDoAction 0# tk action sts ((saved_tok`HappyStk`stk))
-}

-- Enter error recovery: generate an error token,
--                       save the old token and carry on.
happyFail explist i tk (action) sts stk =
--      trace "entering error recovery" $
        happyDoAction 0# tk action sts ( (Happy_GHC_Exts.unsafeCoerce# (Happy_GHC_Exts.I# (i))) `HappyStk` stk)

-- Internal happy errors:

notHappyAtAll :: a
notHappyAtAll = error "Internal Happy error\n"

-----------------------------------------------------------------------------
-- Hack to get the typechecker to accept our action functions


happyTcHack :: Happy_GHC_Exts.Int# -> a -> a
happyTcHack x y = y
{-# INLINE happyTcHack #-}


-----------------------------------------------------------------------------
-- Seq-ing.  If the --strict flag is given, then Happy emits 
--      happySeq = happyDoSeq
-- otherwise it emits
--      happySeq = happyDontSeq

happyDoSeq, happyDontSeq :: a -> b -> b
happyDoSeq   a b = a `seq` b
happyDontSeq a b = b

-----------------------------------------------------------------------------
-- Don't inline any functions from the template.  GHC has a nasty habit
-- of deciding to inline happyGoto everywhere, which increases the size of
-- the generated parser quite a bit.


{-# NOINLINE happyDoAction #-}
{-# NOINLINE happyTable #-}
{-# NOINLINE happyCheck #-}
{-# NOINLINE happyActOffsets #-}
{-# NOINLINE happyGotoOffsets #-}
{-# NOINLINE happyDefActions #-}

{-# NOINLINE happyShift #-}
{-# NOINLINE happySpecReduce_0 #-}
{-# NOINLINE happySpecReduce_1 #-}
{-# NOINLINE happySpecReduce_2 #-}
{-# NOINLINE happySpecReduce_3 #-}
{-# NOINLINE happyReduce #-}
{-# NOINLINE happyMonadReduce #-}
{-# NOINLINE happyGoto #-}
{-# NOINLINE happyFail #-}

-- end of Happy Template.