TPTP Problem File: SYN539+1.p

View Solutions - Solve Problem

%--------------------------------------------------------------------------
% File     : SYN539+1 : TPTP v8.1.0. Released v2.1.0.
% Domain   : Syntactic (Translated)
% Problem  : ALC, N=5, R=1, L=40, K=3, D=2, P=0, Index=036
% 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-5-1-40-3-2-036.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       :  370 (   0 equ)
%            Maximal formula atoms :  370 ( 370 avg)
%            Number of connectives :  506 ( 137   ~; 148   |; 168   &)
%                                         (   0 <=>;  53  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   43 (  43 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   53 (  53 usr;  53 con; 0-0 aty)
%            Number of variables   :   53 (  53   !;   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,
    ~ ( ( c4_0
        | ( ndr1_0
          & c2_1(a587)
          & c3_1(a587)
          & c5_1(a587) ) )
      & ( ( ndr1_0
          & ndr1_1(a588)
          & ~ c1_2(a588,a589)
          & c2_2(a588,a589)
          & c3_2(a588,a589)
          & ndr1_1(a588)
          & ~ c4_2(a588,a590)
          & c2_2(a588,a590)
          & c1_2(a588,a590)
          & ndr1_1(a588)
          & c5_2(a588,a591)
          & ~ c2_2(a588,a591) )
        | ~ c2_0
        | ! [U] :
            ( ndr1_0
           => ( c2_1(U)
              | c5_1(U)
              | ~ c3_1(U) ) ) )
      & ( ~ c3_0
        | ~ c1_0
        | ~ c4_0 )
      & ( ( ndr1_0
          & ~ c3_1(a592)
          & ! [V] :
              ( ndr1_1(a592)
             => ( c5_2(a592,V)
                | c4_2(a592,V)
                | ~ c1_2(a592,V) ) )
          & ~ c4_1(a592) )
        | ( ndr1_0
          & ! [W] :
              ( ndr1_1(a593)
             => ( ~ c4_2(a593,W)
                | c5_2(a593,W)
                | ~ c1_2(a593,W) ) )
          & c2_1(a593)
          & ~ c5_1(a593) )
        | ( ndr1_0
          & c1_1(a594)
          & c4_1(a594) ) )
      & ( ~ c5_0
        | ! [X] :
            ( ndr1_0
           => ( ( ndr1_1(X)
                & ~ c4_2(X,a595)
                & ~ c1_2(X,a595) )
              | ~ c1_1(X)
              | ! [Y] :
                  ( ndr1_1(X)
                 => ( c2_2(X,Y)
                    | ~ c5_2(X,Y) ) ) ) ) )
      & ( ! [Z] :
            ( ndr1_0
           => ( c2_1(Z)
              | ! [X1] :
                  ( ndr1_1(Z)
                 => ( ~ c2_2(Z,X1)
                    | c3_2(Z,X1) ) )
              | c1_1(Z) ) )
        | c2_0
        | ( ndr1_0
          & ! [X2] :
              ( ndr1_1(a596)
             => ( c3_2(a596,X2)
                | ~ c4_2(a596,X2)
                | ~ c1_2(a596,X2) ) )
          & ndr1_1(a596)
          & c5_2(a596,a597)
          & ~ c2_2(a596,a597)
          & ~ c1_2(a596,a597)
          & ndr1_1(a596)
          & c1_2(a596,a598)
          & ~ c4_2(a596,a598)
          & c2_2(a596,a598) ) )
      & ( ! [X3] :
            ( ndr1_0
           => ( ( ndr1_1(X3)
                & c2_2(X3,a599)
                & ~ c3_2(X3,a599)
                & ~ c5_2(X3,a599) )
              | ( ndr1_1(X3)
                & c1_2(X3,a600)
                & ~ c3_2(X3,a600)
                & c2_2(X3,a600) )
              | c2_1(X3) ) )
        | ! [X4] :
            ( ndr1_0
           => ( ~ c3_1(X4)
              | c2_1(X4)
              | ( ndr1_1(X4)
                & c4_2(X4,a601)
                & c2_2(X4,a601)
                & c5_2(X4,a601) ) ) )
        | c2_0 )
      & ( c1_0
        | ! [X5] :
            ( ndr1_0
           => ( ( ndr1_1(X5)
                & ~ c2_2(X5,a602)
                & c3_2(X5,a602) )
              | ( ndr1_1(X5)
                & c5_2(X5,a603)
                & c3_2(X5,a603)
                & ~ c4_2(X5,a603) )
              | ( ndr1_1(X5)
                & c4_2(X5,a604)
                & c3_2(X5,a604)
                & ~ c1_2(X5,a604) ) ) )
        | ! [X6] :
            ( ndr1_0
           => ( ! [X7] :
                  ( ndr1_1(X6)
                 => ( c4_2(X6,X7)
                    | c1_2(X6,X7)
                    | ~ c5_2(X6,X7) ) )
              | ~ c1_1(X6) ) ) )
      & ( ~ c1_0
        | ( ndr1_0
          & ! [X8] :
              ( ndr1_1(a605)
             => ( ~ c3_2(a605,X8)
                | c2_2(a605,X8) ) )
          & ! [X9] :
              ( ndr1_1(a605)
             => ( c5_2(a605,X9)
                | c3_2(a605,X9)
                | ~ c1_2(a605,X9) ) ) )
        | ! [X10] :
            ( ndr1_0
           => ( ! [X11] :
                  ( ndr1_1(X10)
                 => ( c4_2(X10,X11)
                    | c5_2(X10,X11) ) )
              | c3_1(X10) ) ) )
      & ( ! [X12] :
            ( ndr1_0
           => ( ( ndr1_1(X12)
                & c4_2(X12,a606)
                & c3_2(X12,a606) )
              | ~ c3_1(X12)
              | ! [X13] :
                  ( ndr1_1(X12)
                 => ( ~ c2_2(X12,X13)
                    | c3_2(X12,X13)
                    | c5_2(X12,X13) ) ) ) )
        | c5_0 )
      & ( ! [X14] :
            ( ndr1_0
           => ( c4_1(X14)
              | ( ndr1_1(X14)
                & ~ c1_2(X14,a607)
                & c4_2(X14,a607)
                & c3_2(X14,a607) )
              | c2_1(X14) ) )
        | ~ c2_0
        | c5_0 )
      & ( ! [X15] :
            ( ndr1_0
           => ( ~ c1_1(X15)
              | ! [X16] :
                  ( ndr1_1(X15)
                 => ( c5_2(X15,X16)
                    | c4_2(X15,X16) ) )
              | ~ c3_1(X15) ) )
        | ( ndr1_0
          & ! [X17] :
              ( ndr1_1(a608)
             => ( ~ c3_2(a608,X17)
                | c2_2(a608,X17) ) )
          & ! [X18] :
              ( ndr1_1(a608)
             => ( ~ c2_2(a608,X18)
                | ~ c5_2(a608,X18) ) )
          & ndr1_1(a608)
          & c5_2(a608,a609)
          & ~ c4_2(a608,a609) )
        | ! [X19] :
            ( ndr1_0
           => ( c5_1(X19)
              | ( ndr1_1(X19)
                & c2_2(X19,a610)
                & c3_2(X19,a610)
                & ~ c1_2(X19,a610) )
              | c1_1(X19) ) ) )
      & ( ~ c4_0
        | ~ c2_0
        | ( ndr1_0
          & ndr1_1(a611)
          & c5_2(a611,a612)
          & ~ c1_2(a611,a612)
          & ! [X20] :
              ( ndr1_1(a611)
             => ( c5_2(a611,X20)
                | ~ c3_2(a611,X20)
                | c2_2(a611,X20) ) )
          & ~ c1_1(a611) ) )
      & ( ~ c3_0
        | ! [X21] :
            ( ndr1_0
           => ( ~ c3_1(X21)
              | c5_1(X21) ) )
        | ( ndr1_0
          & ~ c3_1(a613)
          & ndr1_1(a613)
          & c1_2(a613,a614)
          & ~ c4_2(a613,a614)
          & ~ c3_2(a613,a614)
          & ! [X22] :
              ( ndr1_1(a613)
             => ( ~ c2_2(a613,X22)
                | c1_2(a613,X22) ) ) ) )
      & ( ( ndr1_0
          & ~ c1_1(a615)
          & ! [X23] :
              ( ndr1_1(a615)
             => ( ~ c5_2(a615,X23)
                | ~ c2_2(a615,X23)
                | ~ c3_2(a615,X23) ) )
          & ! [X24] :
              ( ndr1_1(a615)
             => ( ~ c2_2(a615,X24)
                | c3_2(a615,X24)
                | c1_2(a615,X24) ) ) )
        | ~ c1_0
        | ~ c3_0 )
      & ( c4_0
        | ~ c5_0
        | ( ndr1_0
          & ~ c3_1(a616)
          & c1_1(a616)
          & ~ c2_1(a616) ) )
      & ( ~ c2_0
        | ! [X25] :
            ( ndr1_0
           => ( ( ndr1_1(X25)
                & c4_2(X25,a617)
                & ~ c1_2(X25,a617) )
              | c1_1(X25)
              | ! [X26] :
                  ( ndr1_1(X25)
                 => ( ~ c5_2(X25,X26)
                    | c2_2(X25,X26)
                    | ~ c1_2(X25,X26) ) ) ) ) )
      & ( ! [X27] :
            ( ndr1_0
           => ( c1_1(X27)
              | ( ndr1_1(X27)
                & ~ c4_2(X27,a618)
                & ~ c3_2(X27,a618)
                & ~ c2_2(X27,a618) )
              | ~ c2_1(X27) ) )
        | c2_0
        | c4_0 )
      & ( ~ c5_0
        | ( ndr1_0
          & c4_1(a619)
          & c1_1(a619)
          & c5_1(a619) )
        | c1_0 )
      & ( c4_0
        | ~ c3_0
        | c1_0 )
      & ( ~ c5_0
        | ~ c1_0
        | ( ndr1_0
          & ~ c4_1(a620) ) )
      & ( ! [X28] :
            ( ndr1_0
           => c2_1(X28) )
        | c2_0
        | ! [X29] :
            ( ndr1_0
           => ( ~ c2_1(X29)
              | ( ndr1_1(X29)
                & c1_2(X29,a621)
                & c4_2(X29,a621)
                & ~ c2_2(X29,a621) )
              | ( ndr1_1(X29)
                & ~ c1_2(X29,a622)
                & c5_2(X29,a622) ) ) ) )
      & ( ~ c4_0
        | ! [X30] :
            ( ndr1_0
           => ( ~ c2_1(X30)
              | ! [X31] :
                  ( ndr1_1(X30)
                 => ( c2_2(X30,X31)
                    | ~ c1_2(X30,X31)
                    | ~ c4_2(X30,X31) ) )
              | c4_1(X30) ) )
        | ~ c3_0 )
      & ( ~ c4_0
        | ~ c1_0
        | ! [X32] :
            ( ndr1_0
           => ( ( ndr1_1(X32)
                & ~ c3_2(X32,a623) )
              | ~ c3_1(X32)
              | ! [X33] :
                  ( ndr1_1(X32)
                 => ( ~ c4_2(X32,X33)
                    | c1_2(X32,X33)
                    | ~ c2_2(X32,X33) ) ) ) ) )
      & ( ( ndr1_0
          & ! [X34] :
              ( ndr1_1(a624)
             => ( c3_2(a624,X34)
                | c2_2(a624,X34)
                | c5_2(a624,X34) ) )
          & ndr1_1(a624)
          & c3_2(a624,a625)
          & ~ c1_2(a624,a625)
          & ~ c2_2(a624,a625)
          & ndr1_1(a624)
          & c5_2(a624,a626)
          & ~ c3_2(a624,a626)
          & c4_2(a624,a626) )
        | c2_0
        | ! [X35] :
            ( ndr1_0
           => ( ~ c3_1(X35)
              | ( ndr1_1(X35)
                & ~ c2_2(X35,a627)
                & c1_2(X35,a627) )
              | ! [X36] :
                  ( ndr1_1(X35)
                 => ( ~ c5_2(X35,X36)
                    | ~ c1_2(X35,X36)
                    | ~ c3_2(X35,X36) ) ) ) ) )
      & ( ! [X37] :
            ( ndr1_0
           => ( ! [X38] :
                  ( ndr1_1(X37)
                 => ( c2_2(X37,X38)
                    | ~ c1_2(X37,X38)
                    | c3_2(X37,X38) ) )
              | ( ndr1_1(X37)
                & c4_2(X37,a628)
                & ~ c1_2(X37,a628)
                & ~ c5_2(X37,a628) )
              | ~ c4_1(X37) ) )
        | ( ndr1_0
          & ndr1_1(a629)
          & ~ c2_2(a629,a630)
          & ~ c5_2(a629,a630)
          & ~ c2_1(a629)
          & c3_1(a629) )
        | ~ c3_0 )
      & ( ~ c4_0
        | ( ndr1_0
          & c1_1(a631)
          & ~ c3_1(a631) ) )
      & ( ! [X39] :
            ( ndr1_0
           => ( ! [X40] :
                  ( ndr1_1(X39)
                 => ( c3_2(X39,X40)
                    | ~ c1_2(X39,X40)
                    | c5_2(X39,X40) ) )
              | c2_1(X39)
              | ( ndr1_1(X39)
                & ~ c2_2(X39,a632)
                & ~ c3_2(X39,a632) ) ) )
        | c3_0
        | ( ndr1_0
          & ~ c3_1(a633)
          & ! [X41] :
              ( ndr1_1(a633)
             => ( c1_2(a633,X41)
                | ~ c3_2(a633,X41) ) )
          & ~ c1_1(a633) ) )
      & ( ( ndr1_0
          & ~ c2_1(a634) )
        | ! [X42] :
            ( ndr1_0
           => ( ( ndr1_1(X42)
                & ~ c2_2(X42,a635) )
              | ~ c5_1(X42)
              | ! [X43] :
                  ( ndr1_1(X42)
                 => ( c2_2(X42,X43)
                    | ~ c1_2(X42,X43) ) ) ) )
        | c1_0 )
      & ( c3_0
        | ~ c1_0
        | c5_0 )
      & ( ~ c5_0
        | ~ c2_0
        | ! [X44] :
            ( ndr1_0
           => ( ! [X45] :
                  ( ndr1_1(X44)
                 => ( c1_2(X44,X45)
                    | ~ c2_2(X44,X45) ) )
              | ! [X46] :
                  ( ndr1_1(X44)
                 => ( c4_2(X44,X46)
                    | ~ c2_2(X44,X46) ) )
              | ( ndr1_1(X44)
                & c2_2(X44,a636)
                & ~ c3_2(X44,a636) ) ) ) )
      & c5_0
      & ( c3_0
        | ( ndr1_0
          & ~ c3_1(a637)
          & ~ c2_1(a637)
          & ndr1_1(a637)
          & c1_2(a637,a638)
          & ~ c4_2(a637,a638) ) )
      & ( ! [X47] :
            ( ndr1_0
           => ( ( ndr1_1(X47)
                & ~ c1_2(X47,a639)
                & ~ c2_2(X47,a639)
                & c5_2(X47,a639) )
              | ~ c5_1(X47)
              | c3_1(X47) ) )
        | c4_0 ) ) ).

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