## TPTP Problem File: SYN529+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN529+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=033
% 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-5-1-25-3-2-033.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 v2.4.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  242 (   0 equ)
%            Maximal formula atoms :  242 ( 242 avg)
%            Number of connectives :  314 (  73   ~;  84   |; 132   &)
%                                         (   0 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   36 (  36 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   43 (  43 usr;  43 con; 0-0 aty)
%            Number of variables   :   25 (  25   !;   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,
~ ( ( c2_0
| ~ c5_0 )
& ( ~ c4_0
| ~ c3_0
| ~ c2_0 )
& ( c4_0
| ( ndr1_0
& ndr1_1(a314)
& ~ c3_2(a314,a315)
& ~ c2_2(a314,a315)
& ~ c1_2(a314,a315)
& c4_1(a314)
& ! [U] :
( ndr1_1(a314)
=> ( ~ c1_2(a314,U)
| c4_2(a314,U)
| c3_2(a314,U) ) ) )
| ! [V] :
( ndr1_0
=> ( ! [W] :
( ndr1_1(V)
=> ( c4_2(V,W)
| c3_2(V,W)
| c1_2(V,W) ) )
| ~ c4_1(V)
| c5_1(V) ) ) )
& ( ( ndr1_0
& ~ c4_1(a316)
& ndr1_1(a316)
& c3_2(a316,a317)
& ~ c4_2(a316,a317)
& c2_2(a316,a317)
& c1_1(a316) )
| ( ndr1_0
& ndr1_1(a318)
& c4_2(a318,a319)
& c2_2(a318,a319)
& ndr1_1(a318)
& c2_2(a318,a320)
& ~ c4_2(a318,a320) )
| ~ c4_0 )
& ( ! [X] :
( ndr1_0
=> ( ! [Y] :
( ndr1_1(X)
=> ( ~ c4_2(X,Y)
| c2_2(X,Y)
| ~ c3_2(X,Y) ) )
| ( ndr1_1(X)
& ~ c1_2(X,a321)
& c5_2(X,a321)
& ~ c2_2(X,a321) )
| ~ c2_1(X) ) )
| c4_0
| ( ndr1_0
& c3_1(a322)
& ndr1_1(a322)
& ~ c4_2(a322,a323)
& c5_2(a322,a323)
& ~ c1_2(a322,a323) ) )
& ( ! [Z] :
( ndr1_0
=> ( c1_1(Z)
| c5_1(Z) ) )
| ! [X1] :
( ndr1_0
=> ( ~ c2_1(X1)
| c4_1(X1) ) )
| ! [X2] :
( ndr1_0
=> ( c4_1(X2)
| ! [X3] :
( ndr1_1(X2)
=> ( c5_2(X2,X3)
| c4_2(X2,X3) ) )
| c2_1(X2) ) ) )
& ( c2_0
| ~ c3_0 )
& ( c5_0
| ( ndr1_0
& ! [X4] :
( ndr1_1(a324)
=> ( c3_2(a324,X4)
| c2_2(a324,X4)
| ~ c4_2(a324,X4) ) )
& ndr1_1(a324)
& c1_2(a324,a325)
& c5_2(a324,a325)
& ! [X5] :
( ndr1_1(a324)
=> ( c3_2(a324,X5)
| c1_2(a324,X5) ) ) )
| ( ndr1_0
& c2_1(a326)
& c4_1(a326)
& ndr1_1(a326)
& ~ c2_2(a326,a327)
& ~ c5_2(a326,a327)
& c3_2(a326,a327) ) )
& ( ( ndr1_0
& ~ c2_1(a328)
& c5_1(a328) )
| c4_0
| ( ndr1_0
& ndr1_1(a329)
& ~ c2_2(a329,a330)
& ! [X6] :
( ndr1_1(a329)
=> ( ~ c4_2(a329,X6)
| ~ c5_2(a329,X6)
| c1_2(a329,X6) ) )
& c1_1(a329) ) )
& ( ~ c4_0
| ( ndr1_0
& ndr1_1(a331)
& c1_2(a331,a332)
& c2_2(a331,a332)
& ~ c5_2(a331,a332)
& c5_1(a331)
& c3_1(a331) )
| ( ndr1_0
& ~ c3_1(a333) ) )
& ( ! [X7] :
( ndr1_0
=> ( c3_1(X7)
| ( ndr1_1(X7)
& c4_2(X7,a334)
& c2_2(X7,a334) )
| c5_1(X7) ) )
| c1_0 )
& ( ( ndr1_0
& ndr1_1(a335)
& c4_2(a335,a336)
& c5_2(a335,a336)
& c2_2(a335,a336)
& ndr1_1(a335)
& c1_2(a335,a337)
& c5_2(a335,a337)
& ~ c3_2(a335,a337) )
| c4_0
| c5_0 )
& ( ~ c5_0
| ( ndr1_0
& c1_1(a338)
& c4_1(a338)
& ndr1_1(a338)
& c1_2(a338,a339)
& ~ c3_2(a338,a339)
& ~ c4_2(a338,a339) )
| ! [X8] :
( ndr1_0
=> ( ! [X9] :
( ndr1_1(X8)
=> ( ~ c3_2(X8,X9)
| c2_2(X8,X9)
| c1_2(X8,X9) ) )
| ( ndr1_1(X8)
& ~ c4_2(X8,a340)
& ~ c1_2(X8,a340)
& c2_2(X8,a340) )
| ( ndr1_1(X8)
& c2_2(X8,a341)
& c4_2(X8,a341)
& c3_2(X8,a341) ) ) ) )
& ( c3_0
| c5_0
| ~ c1_0 )
& ( c4_0
| ! [X10] :
( ndr1_0
=> ( ( ndr1_1(X10)
& c5_2(X10,a342)
& c2_2(X10,a342) )
| ~ c4_1(X10)
| c5_1(X10) ) ) )
& ( ~ c3_0
| ~ c5_0
| c4_0 )
& ( ! [X11] :
( ndr1_0
=> ( ! [X12] :
( ndr1_1(X11)
=> ( c4_2(X11,X12)
| c3_2(X11,X12)
| c2_2(X11,X12) ) )
| c3_1(X11)
| ~ c2_1(X11) ) )
| c5_0 )
& ( ( ndr1_0
& ~ c1_1(a343)
& c2_1(a343) )
| c3_0 )
& ( ( ndr1_0
& ndr1_1(a344)
& c3_2(a344,a345)
& ~ c1_2(a344,a345)
& ~ c2_1(a344)
& ! [X13] :
( ndr1_1(a344)
=> ( ~ c2_2(a344,X13)
| ~ c1_2(a344,X13)
| ~ c5_2(a344,X13) ) ) )
| c5_0
| ( ndr1_0
& c4_1(a346)
& ndr1_1(a346)
& ~ c5_2(a346,a347)
& c1_2(a346,a347)
& c3_1(a346) ) )
& ( ( ndr1_0
& ~ c3_1(a348)
& ! [X14] :
( ndr1_1(a348)
=> ( c5_2(a348,X14)
| ~ c4_2(a348,X14)
| ~ c2_2(a348,X14) ) )
& ndr1_1(a348)
& ~ c5_2(a348,a349)
& c2_2(a348,a349) )
| ! [X15] :
( ndr1_0
=> ( ( ndr1_1(X15)
& c2_2(X15,a350)
& ~ c3_2(X15,a350)
& ~ c1_2(X15,a350) )
| ~ c3_1(X15)
| ! [X16] :
( ndr1_1(X15)
=> ( c1_2(X15,X16)
| ~ c4_2(X15,X16)
| c5_2(X15,X16) ) ) ) ) )
& ( c4_0
| ~ c1_0
| ~ c5_0 )
& ( ( ndr1_0
& ~ c1_1(a351)
& ndr1_1(a351)
& c2_2(a351,a352)
& ~ c1_2(a351,a352)
& ~ c4_2(a351,a352)
& c4_1(a351) )
| c3_0
| ( ndr1_0
& ! [X17] :
( ndr1_1(a353)
=> ( ~ c2_2(a353,X17)
| c3_2(a353,X17)
| ~ c5_2(a353,X17) ) )
& ndr1_1(a353)
& c2_2(a353,a354)
& c3_2(a353,a354)
& ! [X18] :
( ndr1_1(a353)
=> ( ~ c1_2(a353,X18)
| ~ c4_2(a353,X18)
| c3_2(a353,X18) ) ) ) )
& ( ( ndr1_0
& ndr1_1(a355)
& ~ c4_2(a355,a356)
& ~ c5_2(a355,a356)
& ! [X19] :
( ndr1_1(a355)
=> ( c3_2(a355,X19)
| ~ c1_2(a355,X19) ) )
& ~ c3_1(a355) )
| c2_0
| c5_0 ) ) ).

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