## TPTP Problem File: SYN532+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN532+1 : TPTP v8.1.0. Released v2.1.0.
% Domain   : Syntactic (Translated)
% Problem  : ALC, N=5, R=1, L=25, K=3, D=2, P=0, Index=042
% 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-5-1-25-3-2-042.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v5.5.0, 0.10 v5.4.0, 0.20 v5.3.0, 0.00 v4.1.0, 0.17 v4.0.1, 0.00 v2.7.0, 0.17 v2.6.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  190 (   0 equ)
%            Maximal formula atoms :  190 ( 190 avg)
%            Number of connectives :  255 (  66   ~;  65   |; 104   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (  31 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   32 (  32 usr;  32 con; 0-0 aty)
%            Number of variables   :   20 (  20   !;   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,
~ ( ( ~ c3_0
| c5_0
| ( ndr1_0
& ! [U] :
( ndr1_1(a411)
=> ( c1_2(a411,U)
| c3_2(a411,U)
| c5_2(a411,U) ) )
& c2_1(a411)
& c1_1(a411) ) )
& ( ! [V] :
( ndr1_0
=> ( c5_1(V)
| ~ c3_1(V) ) )
| ~ c3_0
| ~ c4_0 )
& ( ! [W] :
( ndr1_0
=> ~ c2_1(W) )
| ( ndr1_0
& ~ c4_1(a412)
& ! [X] :
( ndr1_1(a412)
=> ( ~ c2_2(a412,X)
| c3_2(a412,X) ) )
& ~ c2_1(a412) )
| ( ndr1_0
& ~ c2_1(a413)
& ndr1_1(a413)
& ~ c3_2(a413,a414)
& ~ c5_2(a413,a414)
& c1_2(a413,a414)
& ! [Y] :
( ndr1_1(a413)
=> ( c5_2(a413,Y)
| ~ c1_2(a413,Y) ) ) ) )
& ( ~ c4_0
| ~ c5_0
| ( ndr1_0
& c2_1(a415)
& ~ c4_1(a415)
& c5_1(a415) ) )
& ( ( ndr1_0
& ! [Z] :
( ndr1_1(a416)
=> ( ~ c5_2(a416,Z)
| ~ c2_2(a416,Z) ) )
& c2_1(a416)
& ! [X1] :
( ndr1_1(a416)
=> c5_2(a416,X1) ) )
| ! [X2] :
( ndr1_0
=> ( ( ndr1_1(X2)
& ~ c4_2(X2,a417)
& c2_2(X2,a417) )
| ~ c2_1(X2) ) )
| ( ndr1_0
& c2_1(a418)
& ndr1_1(a418)
& c4_2(a418,a419)
& ~ c5_2(a418,a419)
& ~ c3_2(a418,a419) ) )
& ( ( ndr1_0
& ndr1_1(a420)
& ~ c4_2(a420,a421)
& c1_2(a420,a421)
& c4_1(a420)
& c5_1(a420) )
| c4_0 )
& ( ! [X3] :
( ndr1_0
=> ( ! [X4] :
( ndr1_1(X3)
=> ( ~ c4_2(X3,X4)
| ~ c2_2(X3,X4)
| c5_2(X3,X4) ) )
| ! [X5] :
( ndr1_1(X3)
=> ( ~ c2_2(X3,X5)
| ~ c3_2(X3,X5)
| c1_2(X3,X5) ) ) ) )
| c4_0
| ~ c3_0 )
& ( ~ c1_0
| ~ c3_0
| ~ c5_0 )
& ( c1_0
| ~ c4_0
| c5_0 )
& ( c5_0
| ~ c3_0
| c2_0 )
& ( c1_0
| ( ndr1_0
& ~ c2_1(a422)
& ndr1_1(a422)
& c1_2(a422,a423)
& c5_2(a422,a423)
& ~ c2_2(a422,a423)
& ~ c4_1(a422) )
| ~ c3_0 )
& ( c5_0
| ! [X6] :
( ndr1_0
=> ( c2_1(X6)
| c3_1(X6)
| ( ndr1_1(X6)
& c2_2(X6,a424)
& ~ c3_2(X6,a424)
& ~ c5_2(X6,a424) ) ) )
| ! [X7] :
( ndr1_0
=> ( c5_1(X7)
| c2_1(X7)
| ~ c4_1(X7) ) ) )
& ( c4_0
| ~ c3_0
| c1_0 )
& ( ( ndr1_0
& ndr1_1(a425)
& ~ c2_2(a425,a426)
& c4_2(a425,a426)
& ~ c5_2(a425,a426)
& ~ c3_1(a425)
& ndr1_1(a425)
& ~ c5_2(a425,a427)
& ~ c3_2(a425,a427)
& c2_2(a425,a427) )
| ! [X8] :
( ndr1_0
=> ( ( ndr1_1(X8)
& ~ c4_2(X8,a428)
& ~ c3_2(X8,a428) )
| ( ndr1_1(X8)
& c1_2(X8,a429)
& ~ c4_2(X8,a429)
& ~ c5_2(X8,a429) )
| ( ndr1_1(X8)
& c1_2(X8,a430)
& ~ c4_2(X8,a430)
& c5_2(X8,a430) ) ) )
| ( ndr1_0
& c3_1(a431)
& ~ c1_1(a431) ) )
& ( c1_0
| ( ndr1_0
& ! [X9] :
( ndr1_1(a432)
=> ( ~ c2_2(a432,X9)
| c5_2(a432,X9)
| c4_2(a432,X9) ) )
& ~ c1_1(a432)
& ndr1_1(a432)
& ~ c3_2(a432,a433)
& ~ c2_2(a432,a433) )
| c5_0 )
& ( ~ c3_0
| c1_0 )
& ( ( ndr1_0
& ! [X10] :
( ndr1_1(a434)
=> ( ~ c4_2(a434,X10)
| c2_2(a434,X10)
| ~ c3_2(a434,X10) ) )
& ndr1_1(a434)
& c5_2(a434,a435)
& c4_2(a434,a435)
& c3_2(a434,a435)
& ndr1_1(a434)
& ~ c5_2(a434,a436)
& c3_2(a434,a436) )
| ( ndr1_0
& c4_1(a437) )
| ( ndr1_0
& ~ c5_1(a438)
& c1_1(a438)
& c2_1(a438) ) )
& ( ( ndr1_0
& c5_1(a439)
& ! [X11] :
( ndr1_1(a439)
=> ( c5_2(a439,X11)
| c3_2(a439,X11) ) ) )
| c3_0 )
& ( c5_0
| c1_0
| ( ndr1_0
& ! [X12] :
( ndr1_1(a440)
=> ( c2_2(a440,X12)
| ~ c3_2(a440,X12)
| c4_2(a440,X12) ) )
& ~ c5_1(a440)
& c4_1(a440) ) )
& ( ( ndr1_0
& ndr1_1(a441)
& c3_2(a441,a442)
& ~ c1_2(a441,a442)
& ! [X13] :
( ndr1_1(a441)
=> ( c5_2(a441,X13)
| ~ c4_2(a441,X13) ) )
& c2_1(a441) )
| ! [X14] :
( ndr1_0
=> ( c5_1(X14)
| c2_1(X14)
| ~ c1_1(X14) ) )
| c4_0 ) ) ).

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