## TPTP Problem File: SYN490+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN490+1 : TPTP v8.1.0. Released v2.1.0.
% Domain   : Syntactic (Translated)
% Problem  : ALC, N=4, R=1, L=8, K=3, D=1, P=0, Index=003
% 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-4-1-8-3-1-003.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v4.1.0, 0.17 v4.0.1, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  121 (   0 equ)
%            Maximal formula atoms :  121 ( 121 avg)
%            Number of connectives :  166 (  46   ~;  48   |;  63   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (  29 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   19 (  19 usr;  15 prp; 0-1 aty)
%            Number of functors    :   14 (  14 usr;  14 con; 0-0 aty)
%            Number of variables   :    9 (   9   !;   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,
~ ( ( ~ hskp0
| ( ndr1_0
& ~ c3_1(a2)
& c0_1(a2)
& ~ c1_1(a2) ) )
& ( ~ hskp1
| ( ndr1_0
& ~ c3_1(a4)
& c1_1(a4)
& ~ c2_1(a4) ) )
& ( ~ hskp2
| ( ndr1_0
& c1_1(a5)
& c0_1(a5)
& ~ c2_1(a5) ) )
& ( ~ hskp3
| ( ndr1_0
& c1_1(a8)
& c3_1(a8)
& ~ c0_1(a8) ) )
& ( ~ hskp4
| ( ndr1_0
& c1_1(a11)
& c2_1(a11)
& ~ c0_1(a11) ) )
& ( ~ hskp5
| ( ndr1_0
& ~ c1_1(a12)
& ~ c0_1(a12)
& ~ c2_1(a12) ) )
& ( ~ hskp6
| ( ndr1_0
& ~ c0_1(a14)
& c1_1(a14)
& ~ c2_1(a14) ) )
& ( ~ hskp7
| ( ndr1_0
& c3_1(a1)
& c0_1(a1)
& c1_1(a1) ) )
& ( ~ hskp8
| ( ndr1_0
& ~ c3_1(a3)
& ~ c1_1(a3)
& c2_1(a3) ) )
& ( ~ hskp9
| ( ndr1_0
& c1_1(a6)
& c3_1(a6)
& c2_1(a6) ) )
& ( ~ hskp10
| ( ndr1_0
& ~ c2_1(a7)
& ~ c1_1(a7)
& c3_1(a7) ) )
& ( ~ hskp11
| ( ndr1_0
& c1_1(a9)
& c2_1(a9)
& c3_1(a9) ) )
& ( ~ hskp12
| ( ndr1_0
& ~ c1_1(a10)
& ~ c2_1(a10)
& c3_1(a10) ) )
& ( ~ hskp13
| ( ndr1_0
& c3_1(a15)
& c1_1(a15)
& c2_1(a15) ) )
& ( hskp7
| hskp0
| hskp8 )
& ( ! [U] :
( ndr1_0
=> ( ~ c1_1(U)
| c0_1(U)
| ~ c2_1(U) ) )
| hskp1
| ! [V] :
( ndr1_0
=> ( ~ c2_1(V)
| c1_1(V)
| c3_1(V) ) ) )
& ( ! [W] :
( ndr1_0
=> ( ~ c3_1(W)
| ~ c2_1(W)
| c1_1(W) ) )
| hskp2
| hskp9 )
& ( hskp10
| hskp3
| hskp11 )
& ( ! [X] :
( ndr1_0
=> ( ~ c3_1(X)
| ~ c1_1(X)
| ~ c2_1(X) ) )
| hskp12
| ! [Y] :
( ndr1_0
=> ( c2_1(Y)
| ~ c3_1(Y)
| c0_1(Y) ) ) )
& ( hskp4
| ! [Z] :
( ndr1_0
=> ( ~ c0_1(Z)
| ~ c1_1(Z)
| c2_1(Z) ) )
| ! [X1] :
( ndr1_0
=> ( ~ c0_1(X1)
| c1_1(X1)
| ~ c3_1(X1) ) ) )
& ( hskp5
| ! [X2] :
( ndr1_0
=> ( c2_1(X2)
| c0_1(X2)
| c1_1(X2) ) )
| hskp3 )
& ( ! [X3] :
( ndr1_0
=> ( c0_1(X3)
| c2_1(X3)
| c3_1(X3) ) )
| hskp6
| hskp13 ) ) ).

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