TPTP Problem File: SYN541+1.p

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%--------------------------------------------------------------------------
% File     : SYN541+1 : TPTP v8.1.0. Released v2.1.0.
% Domain   : Syntactic (Translated)
% Problem  : ALC, N=5, R=1, L=45, K=3, D=2, P=0, Index=096
% Version  : Especial.
% English  :

% Refs     : [OS95]  Ohlbach & Schmidt (1995), Functional Translation and S
%          : [HS97]  Hustadt & Schmidt (1997), On Evaluating Decision Proce
%          : [Wei97] Weidenbach (1997), Email to G. Sutcliffe
% Source   : [Wei97]
% Names    : alc-5-1-45-3-2-096.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v4.1.0, 0.17 v4.0.1, 0.00 v3.2.0, 0.25 v3.1.0, 0.17 v2.7.0, 0.50 v2.6.0, 0.25 v2.5.0, 0.00 v2.4.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  368 (   0 equ)
%            Maximal formula atoms :  368 ( 368 avg)
%            Number of connectives :  500 ( 133   ~; 146   |; 167   &)
%                                         (   0 <=>;  54  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   47 (  47 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   50 (  50 usr;  50 con; 0-0 aty)
%            Number of variables   :   54 (  54   !;   0   ?)
% SPC      : FOF_CSA_EPR_NEQ

% Comments : These ALC problems have been translated from propositional
%            multi-modal K logic formulae generated according to the scheme
%            described in [HS97], using the optimized functional translation
%            described in [OS95]. The finite model property holds, the
%            Herbrand Universe is finite, they are decidable (the complexity
%            is PSPACE-complete), resolution + subsumption + condensing is a
%            decision procedure, and the translated formulae belong to the
%            (CNF-translation of the) Bernays-Schoenfinkel class [Wei97].
%--------------------------------------------------------------------------
fof(co1,conjecture,
    ~ ( ( ~ c5_0
        | ( ndr1_0
          & ~ c4_1(a725)
          & c5_1(a725)
          & c2_1(a725) )
        | c4_0 )
      & ( c5_0
        | ~ c4_0
        | ! [U] :
            ( ndr1_0
           => ( c2_1(U)
              | ! [V] :
                  ( ndr1_1(U)
                 => ( ~ c2_2(U,V)
                    | c4_2(U,V)
                    | c1_2(U,V) ) ) ) ) )
      & ( c5_0
        | c1_0
        | ! [W] :
            ( ndr1_0
           => ( ! [X] :
                  ( ndr1_1(W)
                 => ( ~ c2_2(W,X)
                    | ~ c5_2(W,X) ) )
              | ! [Y] :
                  ( ndr1_1(W)
                 => ( ~ c5_2(W,Y)
                    | ~ c1_2(W,Y)
                    | ~ c2_2(W,Y) ) ) ) ) )
      & ( ( ndr1_0
          & ! [Z] :
              ( ndr1_1(a726)
             => ( ~ c5_2(a726,Z)
                | c3_2(a726,Z) ) )
          & ndr1_1(a726)
          & c2_2(a726,a727)
          & ~ c5_2(a726,a727)
          & c4_2(a726,a727)
          & ndr1_1(a726)
          & ~ c4_2(a726,a728)
          & c2_2(a726,a728) )
        | ~ c3_0
        | ( ndr1_0
          & ! [X1] :
              ( ndr1_1(a729)
             => ( ~ c5_2(a729,X1)
                | c4_2(a729,X1)
                | ~ c1_2(a729,X1) ) )
          & ! [X2] :
              ( ndr1_1(a729)
             => ( ~ c4_2(a729,X2)
                | ~ c1_2(a729,X2) ) )
          & c4_1(a729) ) )
      & ( ! [X3] :
            ( ndr1_0
           => ( ~ c4_1(X3)
              | ( ndr1_1(X3)
                & ~ c2_2(X3,a730)
                & ~ c3_2(X3,a730) )
              | ~ c3_1(X3) ) )
        | ~ c3_0
        | ~ c5_0 )
      & ndr1_0
      & c2_1(a731)
      & c4_1(a731)
      & ( c3_0
        | ( ndr1_0
          & ndr1_1(a732)
          & c4_2(a732,a733)
          & ~ c3_2(a732,a733)
          & ~ c2_1(a732) )
        | ! [X4] :
            ( ndr1_0
           => ( c2_1(X4)
              | ~ c5_1(X4) ) ) )
      & ( ( ndr1_0
          & ~ c5_1(a734)
          & c4_1(a734) )
        | ! [X5] :
            ( ndr1_0
           => ( ( ndr1_1(X5)
                & ~ c5_2(X5,a735)
                & c1_2(X5,a735)
                & c4_2(X5,a735) )
              | ~ c4_1(X5)
              | c5_1(X5) ) ) )
      & ( ~ c1_0
        | c2_0
        | ( ndr1_0
          & ndr1_1(a736)
          & c5_2(a736,a737)
          & ~ c4_2(a736,a737)
          & ~ c3_2(a736,a737)
          & c4_1(a736)
          & ~ c3_1(a736) ) )
      & ( c4_0
        | ! [X6] :
            ( ndr1_0
           => ( ~ c1_1(X6)
              | c4_1(X6)
              | c3_1(X6) ) )
        | ( ndr1_0
          & ndr1_1(a738)
          & ~ c4_2(a738,a739)
          & ~ c1_2(a738,a739)
          & ~ c5_2(a738,a739)
          & ndr1_1(a738)
          & c1_2(a738,a740)
          & ~ c5_2(a738,a740) ) )
      & ( ( ndr1_0
          & c2_1(a741)
          & c3_1(a741)
          & ~ c4_1(a741) )
        | ~ c4_0 )
      & ( ( ndr1_0
          & ndr1_1(a742)
          & ~ c4_2(a742,a743)
          & ~ c1_2(a742,a743)
          & c2_2(a742,a743)
          & ! [X7] :
              ( ndr1_1(a742)
             => ( c4_2(a742,X7)
                | c1_2(a742,X7)
                | c3_2(a742,X7) ) )
          & c3_1(a742) )
        | ( ndr1_0
          & c3_1(a744)
          & ndr1_1(a744)
          & c3_2(a744,a745)
          & ~ c4_2(a744,a745)
          & c1_2(a744,a745)
          & ~ c5_1(a744) )
        | ! [X8] :
            ( ndr1_0
           => ( ( ndr1_1(X8)
                & c5_2(X8,a746)
                & c1_2(X8,a746) )
              | ! [X9] :
                  ( ndr1_1(X8)
                 => ( ~ c5_2(X8,X9)
                    | ~ c3_2(X8,X9)
                    | ~ c1_2(X8,X9) ) )
              | ~ c5_1(X8) ) ) )
      & ( ( ndr1_0
          & ndr1_1(a747)
          & ~ c4_2(a747,a748)
          & ~ c2_2(a747,a748)
          & ~ c3_2(a747,a748)
          & ! [X10] :
              ( ndr1_1(a747)
             => ( c1_2(a747,X10)
                | ~ c3_2(a747,X10) ) )
          & ndr1_1(a747)
          & ~ c2_2(a747,a749)
          & c3_2(a747,a749)
          & ~ c4_2(a747,a749) )
        | ~ c4_0
        | c5_0 )
      & ( ~ c4_0
        | c1_0 )
      & ( c2_0
        | ( ndr1_0
          & ~ c2_1(a750)
          & ndr1_1(a750)
          & c4_2(a750,a751)
          & ~ c1_2(a750,a751)
          & c2_2(a750,a751)
          & ! [X11] :
              ( ndr1_1(a750)
             => ( ~ c2_2(a750,X11)
                | ~ c1_2(a750,X11) ) ) )
        | ! [X12] :
            ( ndr1_0
           => ( ( ndr1_1(X12)
                & c3_2(X12,a752)
                & c5_2(X12,a752) )
              | ! [X13] :
                  ( ndr1_1(X12)
                 => ( ~ c4_2(X12,X13)
                    | c3_2(X12,X13)
                    | ~ c5_2(X12,X13) ) )
              | ! [X14] :
                  ( ndr1_1(X12)
                 => ( ~ c4_2(X12,X14)
                    | ~ c1_2(X12,X14)
                    | ~ c3_2(X12,X14) ) ) ) ) )
      & ( ~ c4_0
        | c3_0
        | ! [X15] :
            ( ndr1_0
           => ( ! [X16] :
                  ( ndr1_1(X15)
                 => ( ~ c3_2(X15,X16)
                    | ~ c2_2(X15,X16) ) )
              | c4_1(X15)
              | c5_1(X15) ) ) )
      & ( ~ c4_0
        | ! [X17] :
            ( ndr1_0
           => ( ( ndr1_1(X17)
                & c2_2(X17,a753)
                & ~ c5_2(X17,a753)
                & ~ c1_2(X17,a753) )
              | ~ c2_1(X17)
              | ~ c1_1(X17) ) )
        | ! [X18] :
            ( ndr1_0
           => ( ~ c5_1(X18)
              | c3_1(X18)
              | ! [X19] :
                  ( ndr1_1(X18)
                 => ( ~ c3_2(X18,X19)
                    | c2_2(X18,X19)
                    | ~ c1_2(X18,X19) ) ) ) ) )
      & ( ~ c2_0
        | c3_0 )
      & ( ! [X20] :
            ( ndr1_0
           => ( c1_1(X20)
              | ( ndr1_1(X20)
                & c3_2(X20,a754)
                & ~ c5_2(X20,a754) )
              | ! [X21] :
                  ( ndr1_1(X20)
                 => ( ~ c4_2(X20,X21)
                    | c3_2(X20,X21)
                    | c5_2(X20,X21) ) ) ) )
        | c4_0
        | c2_0 )
      & ( ! [X22] :
            ( ndr1_0
           => ( ( ndr1_1(X22)
                & c3_2(X22,a755)
                & ~ c4_2(X22,a755) )
              | c4_1(X22)
              | ( ndr1_1(X22)
                & c1_2(X22,a756)
                & c5_2(X22,a756)
                & ~ c4_2(X22,a756) ) ) )
        | ~ c2_0
        | c1_0 )
      & ( ~ c2_0
        | ( ndr1_0
          & c4_1(a757)
          & ~ c1_1(a757) ) )
      & ( c4_0
        | ~ c5_0 )
      & ( c1_0
        | ! [X23] :
            ( ndr1_0
           => ( ~ c2_1(X23)
              | ! [X24] :
                  ( ndr1_1(X23)
                 => ( c1_2(X23,X24)
                    | ~ c4_2(X23,X24) ) )
              | ! [X25] :
                  ( ndr1_1(X23)
                 => ( ~ c2_2(X23,X25)
                    | c4_2(X23,X25)
                    | c5_2(X23,X25) ) ) ) ) )
      & ( ! [X26] :
            ( ndr1_0
           => ( ! [X27] :
                  ( ndr1_1(X26)
                 => ( c1_2(X26,X27)
                    | ~ c4_2(X26,X27) ) )
              | ( ndr1_1(X26)
                & c5_2(X26,a758)
                & ~ c2_2(X26,a758) )
              | c1_1(X26) ) )
        | ( ndr1_0
          & c3_1(a759)
          & ndr1_1(a759)
          & ~ c1_2(a759,a760)
          & ~ c3_2(a759,a760)
          & c4_2(a759,a760)
          & ! [X28] :
              ( ndr1_1(a759)
             => ( ~ c5_2(a759,X28)
                | ~ c2_2(a759,X28)
                | c1_2(a759,X28) ) ) ) )
      & ( ! [X29] :
            ( ndr1_0
           => ( ~ c5_1(X29)
              | ! [X30] :
                  ( ndr1_1(X29)
                 => ( ~ c1_2(X29,X30)
                    | ~ c2_2(X29,X30) ) )
              | ~ c2_1(X29) ) )
        | ~ c3_0
        | ! [X31] :
            ( ndr1_0
           => ( ~ c3_1(X31)
              | ( ndr1_1(X31)
                & c3_2(X31,a761)
                & ~ c1_2(X31,a761)
                & c5_2(X31,a761) ) ) ) )
      & ( ! [X32] :
            ( ndr1_0
           => ( ! [X33] :
                  ( ndr1_1(X32)
                 => ( ~ c1_2(X32,X33)
                    | c5_2(X32,X33)
                    | c2_2(X32,X33) ) )
              | c5_1(X32) ) )
        | ! [X34] :
            ( ndr1_0
           => ( ( ndr1_1(X34)
                & c3_2(X34,a762)
                & c2_2(X34,a762) )
              | ~ c2_1(X34) ) ) )
      & ( ~ c4_0
        | ! [X35] :
            ( ndr1_0
           => ( c2_1(X35)
              | ! [X36] :
                  ( ndr1_1(X35)
                 => ( ~ c1_2(X35,X36)
                    | c3_2(X35,X36)
                    | ~ c2_2(X35,X36) ) )
              | ~ c1_1(X35) ) ) )
      & ( ! [X37] :
            ( ndr1_0
           => ( c3_1(X37)
              | ! [X38] :
                  ( ndr1_1(X37)
                 => ( ~ c5_2(X37,X38)
                    | ~ c2_2(X37,X38)
                    | c4_2(X37,X38) ) )
              | ~ c2_1(X37) ) )
        | c2_0
        | ( ndr1_0
          & ndr1_1(a763)
          & c1_2(a763,a764)
          & c2_2(a763,a764)
          & c5_2(a763,a764)
          & ! [X39] :
              ( ndr1_1(a763)
             => ( c2_2(a763,X39)
                | c5_2(a763,X39)
                | c4_2(a763,X39) ) )
          & ~ c2_1(a763) ) )
      & ( ~ c1_0
        | c4_0
        | ! [X40] :
            ( ndr1_0
           => ( c4_1(X40)
              | ! [X41] :
                  ( ndr1_1(X40)
                 => ( c2_2(X40,X41)
                    | c1_2(X40,X41)
                    | ~ c3_2(X40,X41) ) )
              | c3_1(X40) ) ) )
      & ( ~ c4_0
        | ( ndr1_0
          & c5_1(a765)
          & ! [X42] :
              ( ndr1_1(a765)
             => ( c1_2(a765,X42)
                | c2_2(a765,X42)
                | ~ c3_2(a765,X42) ) )
          & ~ c4_1(a765) )
        | ~ c3_0 )
      & ( ! [X43] :
            ( ndr1_0
           => ( ( ndr1_1(X43)
                & ~ c2_2(X43,a766)
                & c3_2(X43,a766)
                & ~ c1_2(X43,a766) )
              | c5_1(X43)
              | ! [X44] :
                  ( ndr1_1(X43)
                 => ( c3_2(X43,X44)
                    | ~ c5_2(X43,X44) ) ) ) )
        | c1_0
        | ( ndr1_0
          & ndr1_1(a767)
          & ~ c5_2(a767,a768)
          & c4_2(a767,a768)
          & c3_2(a767,a768)
          & ~ c4_1(a767)
          & c5_1(a767) ) )
      & ( ( ndr1_0
          & ndr1_1(a769)
          & c4_2(a769,a770)
          & c3_2(a769,a770)
          & ~ c2_2(a769,a770)
          & ~ c3_1(a769)
          & ! [X45] :
              ( ndr1_1(a769)
             => ( c1_2(a769,X45)
                | c3_2(a769,X45)
                | c4_2(a769,X45) ) ) )
        | ~ c1_0
        | ~ c3_0 )
      & ( c4_0
        | c1_0
        | ( ndr1_0
          & ! [X46] :
              ( ndr1_1(a771)
             => ( ~ c2_2(a771,X46)
                | c3_2(a771,X46)
                | ~ c5_2(a771,X46) ) )
          & c4_1(a771) ) )
      & ( c1_0
        | ( ndr1_0
          & c2_1(a772)
          & c5_1(a772)
          & ndr1_1(a772)
          & ~ c1_2(a772,a773)
          & ~ c4_2(a772,a773)
          & c5_2(a772,a773) )
        | ( ndr1_0
          & ! [X47] :
              ( ndr1_1(a774)
             => ( c1_2(a774,X47)
                | ~ c4_2(a774,X47) ) )
          & ! [X48] :
              ( ndr1_1(a774)
             => ( c2_2(a774,X48)
                | ~ c1_2(a774,X48) ) )
          & c3_1(a774) ) ) ) ).

%--------------------------------------------------------------------------