## TPTP Problem File: SYN493+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN493+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=021
% 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-4-1-8-3-1-021.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       :  118 (   0 equ)
%            Maximal formula atoms :  118 ( 118 avg)
%            Number of connectives :  165 (  48   ~;  53   |;  51   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (  27 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   16 (  16 usr;  12 prp; 0-1 aty)
%            Number of functors    :   11 (  11 usr;  11 con; 0-0 aty)
%            Number of variables   :   13 (  13   !;   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
& ~ c0_1(a39)
& ~ c1_1(a39)
& ~ c2_1(a39) ) )
& ( ~ hskp1
| ( ndr1_0
& c3_1(a41)
& ~ c2_1(a41)
& ~ c0_1(a41) ) )
& ( ~ hskp2
| ( ndr1_0
& ~ c0_1(a43)
& c3_1(a43)
& ~ c1_1(a43) ) )
& ( ~ hskp3
| ( ndr1_0
& c3_1(a48)
& c0_1(a48)
& ~ c1_1(a48) ) )
& ( ~ hskp4
| ( ndr1_0
& ~ c0_1(a38)
& ~ c1_1(a38)
& c2_1(a38) ) )
& ( ~ hskp5
| ( ndr1_0
& ~ c0_1(a40)
& ~ c2_1(a40)
& c1_1(a40) ) )
& ( ~ hskp6
| ( ndr1_0
& c3_1(a42)
& ~ c0_1(a42)
& c2_1(a42) ) )
& ( ~ hskp7
| ( ndr1_0
& c1_1(a44)
& c0_1(a44)
& c3_1(a44) ) )
& ( ~ hskp8
| ( ndr1_0
& c3_1(a45)
& c2_1(a45)
& c1_1(a45) ) )
& ( ~ hskp9
| ( ndr1_0
& c0_1(a46)
& c1_1(a46)
& c3_1(a46) ) )
& ( ~ hskp10
| ( ndr1_0
& c3_1(a47)
& ~ c0_1(a47)
& c1_1(a47) ) )
& ( hskp4
| hskp0
| ! [U] :
( ndr1_0
=> ( c1_1(U)
| ~ c2_1(U)
| c0_1(U) ) ) )
& ( hskp5
| hskp1
| ! [V] :
( ndr1_0
=> ( c0_1(V)
| c2_1(V)
| c3_1(V) ) ) )
& ( hskp6
| hskp2
| hskp7 )
& ( ! [W] :
( ndr1_0
=> ( ~ c0_1(W)
| ~ c1_1(W)
| ~ c3_1(W) ) )
| ! [X] :
( ndr1_0
=> ( c0_1(X)
| c2_1(X)
| c1_1(X) ) )
| hskp8 )
& ( ! [Y] :
( ndr1_0
=> ( c1_1(Y)
| c2_1(Y)
| ~ c3_1(Y) ) )
| ! [Z] :
( ndr1_0
=> ( ~ c3_1(Z)
| c0_1(Z)
| c1_1(Z) ) )
| ! [X1] :
( ndr1_0
=> ( ~ c2_1(X1)
| ~ c0_1(X1)
| ~ c1_1(X1) ) ) )
& ( ! [X2] :
( ndr1_0
=> ( c0_1(X2)
| ~ c1_1(X2)
| c3_1(X2) ) )
| hskp9
| ! [X3] :
( ndr1_0
=> ( ~ c2_1(X3)
| ~ c1_1(X3)
| ~ c0_1(X3) ) ) )
& ( hskp10
| ! [X4] :
( ndr1_0
=> ( ~ c2_1(X4)
| ~ c3_1(X4)
| c0_1(X4) ) )
| ! [X5] :
( ndr1_0
=> ( ~ c3_1(X5)
| ~ c1_1(X5)
| c2_1(X5) ) ) )
& ( ! [X6] :
( ndr1_0
=> ( ~ c2_1(X6)
| ~ c1_1(X6)
| c0_1(X6) ) )
| hskp3
| ! [X7] :
( ndr1_0
=> ( ~ c2_1(X7)
| ~ c1_1(X7)
| ~ c0_1(X7) ) ) ) ) ).

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