## TPTP Problem File: SYN540+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN540+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=084
% 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-5-1-40-3-2-084.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v5.5.0, 0.10 v5.4.0, 0.00 v4.1.0, 0.50 v4.0.1, 0.33 v3.7.0, 0.00 v3.5.0, 0.25 v3.4.0, 0.00 v3.2.0, 0.25 v3.1.0, 0.67 v2.6.0, 0.50 v2.5.0, 0.33 v2.4.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  319 (   0 equ)
%            Maximal formula atoms :  319 ( 319 avg)
%            Number of connectives :  439 ( 121   ~; 124   |; 148   &)
%                                         (   0 <=>;  46  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   45 (  45 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   44 (  44 usr;  44 con; 0-0 aty)
%            Number of variables   :   46 (  46   !;   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,
~ ( ( ! [U] :
( ndr1_0
=> ( c2_1(U)
| ( ndr1_1(U)
& c5_2(U,a681)
& ~ c1_2(U,a681)
& c4_2(U,a681) )
| ! [V] :
( ndr1_1(U)
=> ( c2_2(U,V)
| ~ c4_2(U,V)
| c1_2(U,V) ) ) ) )
| c1_0
| c4_0 )
& ( ! [W] :
( ndr1_0
=> ( ! [X] :
( ndr1_1(W)
=> ( ~ c2_2(W,X)
| c5_2(W,X) ) )
| ( ndr1_1(W)
& c1_2(W,a682)
& ~ c4_2(W,a682) )
| ! [Y] :
( ndr1_1(W)
=> ( ~ c4_2(W,Y)
| ~ c2_2(W,Y)
| c3_2(W,Y) ) ) ) )
| ! [Z] :
( ndr1_0
=> ( ~ c4_1(Z)
| c5_1(Z) ) )
| c4_0 )
& ( ! [X1] :
( ndr1_0
=> ( ( ndr1_1(X1)
& c4_2(X1,a683)
& c1_2(X1,a683) )
| ( ndr1_1(X1)
& c1_2(X1,a684)
& ~ c2_2(X1,a684) ) ) )
| c3_0
| ( ndr1_0
& ~ c1_1(a685)
& ndr1_1(a685)
& ~ c3_2(a685,a686)
& ~ c5_2(a685,a686)
& ~ c4_2(a685,a686)
& ! [X2] :
( ndr1_1(a685)
=> ( c1_2(a685,X2)
| ~ c2_2(a685,X2) ) ) ) )
& ( ( ndr1_0
& ! [X3] :
( ndr1_1(a687)
=> ( ~ c2_2(a687,X3)
| ~ c1_2(a687,X3)
| ~ c4_2(a687,X3) ) )
& ~ c1_1(a687)
& ndr1_1(a687)
& c4_2(a687,a688)
& c2_2(a687,a688)
& ~ c5_2(a687,a688) )
| c4_0
| ( ndr1_0
& ndr1_1(a689)
& ~ c1_2(a689,a690)
& c2_2(a689,a690)
& c3_2(a689,a690)
& ! [X4] :
( ndr1_1(a689)
=> ( c3_2(a689,X4)
| ~ c5_2(a689,X4)
| ~ c4_2(a689,X4) ) )
& ndr1_1(a689)
& c5_2(a689,a691)
& ~ c4_2(a689,a691)
& c1_2(a689,a691) ) )
& ( ( ndr1_0
& ~ c1_1(a692)
& ~ c4_1(a692)
& ! [X5] :
( ndr1_1(a692)
=> ( c4_2(a692,X5)
| ~ c3_2(a692,X5)
| c2_2(a692,X5) ) ) )
| ( ndr1_0
& c2_1(a693)
& ~ c5_1(a693)
& ! [X6] :
( ndr1_1(a693)
=> ( c2_2(a693,X6)
| ~ c1_2(a693,X6) ) ) )
| c3_0 )
& ( ~ c1_0
| c2_0 )
& ( c2_0
| c5_0
| ! [X7] :
( ndr1_0
=> ( ~ c5_1(X7)
| c2_1(X7)
| c1_1(X7) ) ) )
& ( c2_0
| c3_0
| ~ c5_0 )
& ( c4_0
| ( ndr1_0
& ~ c3_1(a694)
& ~ c1_1(a694)
& ! [X8] :
( ndr1_1(a694)
=> ( c2_2(a694,X8)
| c4_2(a694,X8)
| c3_2(a694,X8) ) ) ) )
& ( c1_0
| ~ c2_0
| ~ c4_0 )
& ( ~ c3_0
| ! [X9] :
( ndr1_0
=> ( ~ c5_1(X9)
| ~ c3_1(X9)
| c4_1(X9) ) ) )
& ( ! [X10] :
( ndr1_0
=> ( ! [X11] :
( ndr1_1(X10)
=> ( ~ c1_2(X10,X11)
| ~ c2_2(X10,X11) ) )
| ( ndr1_1(X10)
& c3_2(X10,a695)
& c2_2(X10,a695) )
| ! [X12] :
( ndr1_1(X10)
=> ( ~ c2_2(X10,X12)
| c3_2(X10,X12)
| ~ c4_2(X10,X12) ) ) ) )
| c2_0 )
& ( ! [X13] :
( ndr1_0
=> ( ! [X14] :
( ndr1_1(X13)
=> ( ~ c3_2(X13,X14)
| c1_2(X13,X14) ) )
| c4_1(X13) ) )
| ~ c1_0
| ( ndr1_0
& c2_1(a696)
& c5_1(a696) ) )
& ( ~ c4_0
| ( ndr1_0
& c5_1(a697)
& ~ c2_1(a697)
& ~ c4_1(a697) ) )
& ( c5_0
| ( ndr1_0
& c3_1(a698)
& ndr1_1(a698)
& ~ c4_2(a698,a699)
& ~ c1_2(a698,a699)
& ! [X15] :
( ndr1_1(a698)
=> ( c5_2(a698,X15)
| c1_2(a698,X15)
| c4_2(a698,X15) ) ) ) )
& ( c4_0
| ( ndr1_0
& ~ c5_1(a700)
& ndr1_1(a700)
& ~ c1_2(a700,a701)
& ~ c4_2(a700,a701)
& ~ c2_2(a700,a701)
& ~ c3_1(a700) )
| ~ c1_0 )
& ( ( ndr1_0
& ! [X16] :
( ndr1_1(a702)
=> ( c4_2(a702,X16)
| ~ c1_2(a702,X16) ) )
& ! [X17] :
( ndr1_1(a702)
=> ( ~ c5_2(a702,X17)
| c1_2(a702,X17) ) )
& ! [X18] :
( ndr1_1(a702)
=> ( ~ c5_2(a702,X18)
| c1_2(a702,X18)
| ~ c2_2(a702,X18) ) ) )
| c1_0 )
& ( c3_0
| ! [X19] :
( ndr1_0
=> ( c5_1(X19)
| ( ndr1_1(X19)
& ~ c1_2(X19,a703)
& ~ c3_2(X19,a703) ) ) )
| ~ c5_0 )
& ( ! [X20] :
( ndr1_0
=> ( ! [X21] :
( ndr1_1(X20)
=> ( c1_2(X20,X21)
| ~ c2_2(X20,X21) ) )
| c1_1(X20) ) )
| c4_0 )
& ( c2_0
| ~ c4_0 )
& ( ~ c5_0
| ~ c1_0
| c4_0 )
& ( ~ c2_0
| ~ c1_0 )
& ( ! [X22] :
( ndr1_0
=> ( ! [X23] :
( ndr1_1(X22)
=> ( ~ c3_2(X22,X23)
| ~ c2_2(X22,X23) ) )
| c3_1(X22) ) )
| ( ndr1_0
& ndr1_1(a704)
& c3_2(a704,a705)
& c4_2(a704,a705)
& c1_2(a704,a705)
& ~ c4_1(a704)
& ~ c5_1(a704) )
| ~ c2_0 )
& ( ~ c3_0
| ( ndr1_0
& ~ c4_1(a706)
& ndr1_1(a706)
& ~ c1_2(a706,a707)
& ~ c5_2(a706,a707)
& ! [X24] :
( ndr1_1(a706)
=> ( ~ c5_2(a706,X24)
| c2_2(a706,X24)
| ~ c3_2(a706,X24) ) ) )
| ! [X25] :
( ndr1_0
=> ( ( ndr1_1(X25)
& c2_2(X25,a708)
& ~ c5_2(X25,a708)
& c1_2(X25,a708) )
| c5_1(X25)
| ~ c4_1(X25) ) ) )
& ( c4_0
| ! [X26] :
( ndr1_0
=> ( ( ndr1_1(X26)
& ~ c1_2(X26,a709)
& c2_2(X26,a709)
& c4_2(X26,a709) )
| ~ c2_1(X26) ) )
| c5_0 )
& ( ( ndr1_0
& c1_1(a710)
& ! [X27] :
( ndr1_1(a710)
=> ( ~ c3_2(a710,X27)
| ~ c5_2(a710,X27)
| c4_2(a710,X27) ) ) )
| c3_0
| ! [X28] :
( ndr1_0
=> ( ( ndr1_1(X28)
& c4_2(X28,a711)
& ~ c2_2(X28,a711) )
| ! [X29] :
( ndr1_1(X28)
=> ( c2_2(X28,X29)
| c1_2(X28,X29) ) )
| ~ c4_1(X28) ) ) )
& ( ~ c5_0
| ! [X30] :
( ndr1_0
=> ( ( ndr1_1(X30)
& c3_2(X30,a712)
& ~ c5_2(X30,a712)
& c1_2(X30,a712) )
| ! [X31] :
( ndr1_1(X30)
=> ( ~ c1_2(X30,X31)
| c4_2(X30,X31)
| ~ c3_2(X30,X31) ) )
| ~ c4_1(X30) ) )
| ~ c4_0 )
& ( ~ c3_0
| c1_0
| ( ndr1_0
& ~ c3_1(a713)
& ! [X32] :
( ndr1_1(a713)
=> c2_2(a713,X32) )
& ndr1_1(a713)
& ~ c1_2(a713,a714)
& ~ c2_2(a713,a714)
& ~ c3_2(a713,a714) ) )
& ( ~ c3_0
| ( ndr1_0
& ~ c3_1(a715)
& ndr1_1(a715)
& ~ c5_2(a715,a716)
& ~ c4_2(a715,a716)
& ~ c2_2(a715,a716) )
| ! [X33] :
( ndr1_0
=> ( ! [X34] :
( ndr1_1(X33)
=> ( c2_2(X33,X34)
| ~ c3_2(X33,X34) ) )
| c2_1(X33)
| ! [X35] :
( ndr1_1(X33)
=> ( c3_2(X33,X35)
| ~ c2_2(X33,X35) ) ) ) ) )
& ( ( ndr1_0
& c4_1(a717)
& ndr1_1(a717)
& c5_2(a717,a718)
& c1_2(a717,a718) )
| ~ c3_0
| ( ndr1_0
& ndr1_1(a719)
& c4_2(a719,a720)
& c2_2(a719,a720)
& ~ c2_1(a719)
& ndr1_1(a719)
& c4_2(a719,a721)
& ~ c5_2(a719,a721)
& c1_2(a719,a721) ) )
& ( ( ndr1_0
& ! [X36] :
( ndr1_1(a722)
=> ( ~ c1_2(a722,X36)
| ~ c5_2(a722,X36)
| ~ c4_2(a722,X36) ) )
& ! [X37] :
( ndr1_1(a722)
=> ( c1_2(a722,X37)
| ~ c2_2(a722,X37)
| ~ c3_2(a722,X37) ) )
& c3_1(a722) )
| c1_0
| ( ndr1_0
& ndr1_1(a723)
& c4_2(a723,a724)
& c2_2(a723,a724)
& ~ c5_2(a723,a724)
& ! [X38] :
( ndr1_1(a723)
=> ( ~ c4_2(a723,X38)
| ~ c5_2(a723,X38)
| ~ c2_2(a723,X38) ) ) ) )
& ( ! [X39] :
( ndr1_0
=> ( ! [X40] :
( ndr1_1(X39)
=> ( ~ c1_2(X39,X40)
| c5_2(X39,X40)
| ~ c4_2(X39,X40) ) )
| c4_1(X39)
| ~ c1_1(X39) ) )
| ~ c3_0 ) ) ).

%--------------------------------------------------------------------------
```