## TPTP Problem File: SYN495+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN495+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=065
% 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-4-1-8-3-1-065.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v4.1.0, 0.17 v4.0.1, 0.00 v3.1.0, 0.17 v2.6.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  127 (   0 equ)
%            Maximal formula atoms :  127 ( 127 avg)
%            Number of connectives :  174 (  48   ~;  45   |;  75   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (  33 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   22 (  22 usr;  18 prp; 0-1 aty)
%            Number of functors    :   17 (  17 usr;  17 con; 0-0 aty)
%            Number of variables   :    6 (   6   !;   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(a61)
& c1_1(a61)
& ~ c2_1(a61) ) )
& ( ~ hskp1
| ( ndr1_0
& c0_1(a66)
& c1_1(a66)
& ~ c3_1(a66) ) )
& ( ~ hskp2
| ( ndr1_0
& ~ c0_1(a69)
& c3_1(a69)
& ~ c2_1(a69) ) )
& ( ~ hskp3
| ( ndr1_0
& c0_1(a71)
& c3_1(a71)
& ~ c1_1(a71) ) )
& ( ~ hskp4
| ( ndr1_0
& c1_1(a73)
& c0_1(a73)
& ~ c2_1(a73) ) )
& ( ~ hskp5
| ( ndr1_0
& ~ c0_1(a75)
& c2_1(a75)
& ~ c1_1(a75) ) )
& ( ~ hskp6
| ( ndr1_0
& c0_1(a76)
& c1_1(a76)
& ~ c2_1(a76) ) )
& ( ~ hskp7
| ( ndr1_0
& ~ c2_1(a77)
& c3_1(a77)
& ~ c0_1(a77) ) )
& ( ~ hskp8
| ( ndr1_0
& ~ c1_1(a62)
& c3_1(a62)
& c0_1(a62) ) )
& ( ~ hskp9
| ( ndr1_0
& c2_1(a63)
& ~ c1_1(a63)
& c3_1(a63) ) )
& ( ~ hskp10
| ( ndr1_0
& ~ c3_1(a64)
& ~ c2_1(a64)
& c0_1(a64) ) )
& ( ~ hskp11
| ( ndr1_0
& ~ c1_1(a65)
& ~ c0_1(a65)
& c2_1(a65) ) )
& ( ~ hskp12
| ( ndr1_0
& ~ c3_1(a67)
& ~ c2_1(a67)
& c1_1(a67) ) )
& ( ~ hskp13
| ( ndr1_0
& ~ c1_1(a68)
& c2_1(a68)
& c0_1(a68) ) )
& ( ~ hskp14
| ( ndr1_0
& ~ c0_1(a70)
& c3_1(a70)
& c1_1(a70) ) )
& ( ~ hskp15
| ( ndr1_0
& c1_1(a72)
& c3_1(a72)
& c0_1(a72) ) )
& ( ~ hskp16
| ( ndr1_0
& ~ c1_1(a74)
& c2_1(a74)
& c3_1(a74) ) )
& ( hskp0
| ! [U] :
( ndr1_0
=> ( c2_1(U)
| c1_1(U)
| c3_1(U) ) )
| hskp8 )
& ( hskp9
| ! [V] :
( ndr1_0
=> ( c3_1(V)
| ~ c0_1(V)
| ~ c1_1(V) ) )
| hskp10 )
& ( hskp11
| hskp1
| hskp12 )
& ( hskp13
| hskp2
| hskp14 )
& ( hskp3
| ! [W] :
( ndr1_0
=> ( c0_1(W)
| ~ c1_1(W)
| ~ c3_1(W) ) )
| hskp15 )
& ( hskp4
| ! [X] :
( ndr1_0
=> ( c1_1(X)
| c0_1(X)
| ~ c3_1(X) ) )
| ! [Y] :
( ndr1_0
=> ( c1_1(Y)
| ~ c0_1(Y)
| ~ c2_1(Y) ) ) )
& ( hskp16
| hskp5
| hskp6 )
& ( hskp7
| ! [Z] :
( ndr1_0
=> ( c0_1(Z)
| ~ c3_1(Z)
| c1_1(Z) ) )
| hskp12 ) ) ).

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