## TPTP Problem File: SYN530+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN530+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=034
% 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-5-1-25-3-2-034.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       :  195 (   0 equ)
%            Maximal formula atoms :  195 ( 195 avg)
%            Number of connectives :  267 (  73   ~;  75   |;  96   &)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (  29 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   30 (  30 usr;  30 con; 0-0 aty)
%            Number of variables   :   23 (  23   !;   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
=> ( ~ c5_1(U)
| ~ c1_1(U) ) )
| ( ndr1_0
& ndr1_1(a357)
& ~ c5_2(a357,a358)
& ~ c1_2(a357,a358)
& c3_2(a357,a358)
& ~ c2_1(a357)
& ~ c5_1(a357) )
| ( ndr1_0
& ~ c3_1(a359)
& ~ c5_1(a359) ) )
& ( c5_0
| ( ndr1_0
& ~ c5_1(a360)
& c3_1(a360) )
| c1_0 )
& ( ( ndr1_0
& ! [V] :
( ndr1_1(a361)
=> ( c2_2(a361,V)
| c3_2(a361,V) ) )
& ! [W] :
( ndr1_1(a361)
=> ( c2_2(a361,W)
| ~ c1_2(a361,W)
| c3_2(a361,W) ) )
& ~ c1_1(a361) )
| ~ c1_0
| ~ c5_0 )
& ( ~ c2_0
| ! [X] :
( ndr1_0
=> ( ! [Y] :
( ndr1_1(X)
=> ( c4_2(X,Y)
| ~ c5_2(X,Y)
| ~ c1_2(X,Y) ) )
| ! [Z] :
( ndr1_1(X)
=> ( c5_2(X,Z)
| c3_2(X,Z)
| ~ c4_2(X,Z) ) )
| ! [X1] :
( ndr1_1(X)
=> ( c1_2(X,X1)
| ~ c5_2(X,X1)
| ~ c4_2(X,X1) ) ) ) )
| ! [X2] :
( ndr1_0
=> ( ( ndr1_1(X2)
& ~ c1_2(X2,a362) )
| ~ c4_1(X2) ) ) )
& ( ( ndr1_0
& ndr1_1(a363)
& ~ c4_2(a363,a364)
& ~ c2_2(a363,a364)
& ~ c5_2(a363,a364)
& ~ c4_1(a363)
& ! [X3] :
( ndr1_1(a363)
=> ( c1_2(a363,X3)
| ~ c3_2(a363,X3) ) ) )
| c3_0
| ~ c1_0 )
& ( ! [X4] :
( ndr1_0
=> ( c5_1(X4)
| ( ndr1_1(X4)
& ~ c1_2(X4,a365)
& c3_2(X4,a365) )
| ! [X5] :
( ndr1_1(X4)
=> ( c2_2(X4,X5)
| ~ c3_2(X4,X5)
| c1_2(X4,X5) ) ) ) )
| c5_0
| ! [X6] :
( ndr1_0
=> ( ( ndr1_1(X6)
& ~ c2_2(X6,a366)
& ~ c1_2(X6,a366) )
| ~ c2_1(X6)
| ( ndr1_1(X6)
& ~ c4_2(X6,a367)
& c3_2(X6,a367)
& c2_2(X6,a367) ) ) ) )
& ( c5_0
| c2_0
| ! [X7] :
( ndr1_0
=> ( c3_1(X7)
| c4_1(X7)
| ( ndr1_1(X7)
& ~ c4_2(X7,a368)
& ~ c2_2(X7,a368)
& c1_2(X7,a368) ) ) ) )
& ( ~ c3_0
| c4_0
| c5_0 )
& ( ! [X8] :
( ndr1_0
=> ( c5_1(X8)
| ~ c1_1(X8)
| c4_1(X8) ) )
| c3_0
| ( ndr1_0
& ~ c3_1(a369)
& c4_1(a369) ) )
& ( ! [X9] :
( ndr1_0
=> ( ( ndr1_1(X9)
& c3_2(X9,a370)
& c1_2(X9,a370)
& ~ c5_2(X9,a370) )
| c5_1(X9)
| c4_1(X9) ) )
| c4_0 )
& ( c1_0
| ( ndr1_0
& ! [X10] :
( ndr1_1(a371)
=> ( ~ c5_2(a371,X10)
| c4_2(a371,X10)
| ~ c1_2(a371,X10) ) )
& ndr1_1(a371)
& ~ c1_2(a371,a372)
& c4_2(a371,a372)
& ~ c2_2(a371,a372)
& ndr1_1(a371)
& ~ c1_2(a371,a373)
& c2_2(a371,a373) )
| c2_0 )
& ( c4_0
| ~ c2_0 )
& ( c5_0
| ~ c4_0 )
& ( ~ c1_0
| ! [X11] :
( ndr1_0
=> ( c5_1(X11)
| ( ndr1_1(X11)
& c3_2(X11,a374)
& ~ c1_2(X11,a374)
& c5_2(X11,a374) )
| ( ndr1_1(X11)
& c4_2(X11,a375)
& c1_2(X11,a375) ) ) )
| ~ c5_0 )
& ( ! [X12] :
( ndr1_0
=> ( c1_1(X12)
| ! [X13] :
( ndr1_1(X12)
=> ( c1_2(X12,X13)
| ~ c3_2(X12,X13) ) )
| ( ndr1_1(X12)
& c1_2(X12,a376)
& c3_2(X12,a376)
& ~ c4_2(X12,a376) ) ) )
| ~ c2_0
| ~ c4_0 )
& ( ~ c2_0
| ( ndr1_0
& c3_1(a377)
& ~ c1_1(a377) ) )
& ( ~ c3_0
| ! [X14] :
( ndr1_0
=> ( c3_1(X14)
| ! [X15] :
( ndr1_1(X14)
=> ( ~ c2_2(X14,X15)
| ~ c3_2(X14,X15) ) ) ) )
| ( ndr1_0
& c3_1(a378)
& ndr1_1(a378)
& ~ c1_2(a378,a379)
& c2_2(a378,a379)
& ~ c4_2(a378,a379)
& ~ c5_1(a378) ) )
& ( ~ c1_0
| ! [X16] :
( ndr1_0
=> ( ( ndr1_1(X16)
& c2_2(X16,a380)
& ~ c5_2(X16,a380)
& ~ c3_2(X16,a380) )
| ( ndr1_1(X16)
& ~ c3_2(X16,a381)
& c4_2(X16,a381)
& ~ c2_2(X16,a381) )
| ~ c2_1(X16) ) ) )
& ( c4_0
| ( ndr1_0
& c4_1(a382)
& c1_1(a382)
& c5_1(a382) )
| ( ndr1_0
& ndr1_1(a383)
& ~ c5_2(a383,a384)
& ~ c1_2(a383,a384)
& ~ c3_1(a383)
& c1_1(a383) ) )
& ( ~ c1_0
| c4_0
| ( ndr1_0
& c4_1(a385)
& c5_1(a385) ) )
& ( ( ndr1_0
& c3_1(a386) )
| ~ c1_0
| ! [X17] :
( ndr1_0
=> ( c5_1(X17)
| c4_1(X17) ) ) ) ) ).

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