## TPTP Problem File: SYN534+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN534+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=090
% 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-5-1-25-3-2-090.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       :  186 (   0 equ)
%            Maximal formula atoms :  186 ( 186 avg)
%            Number of connectives :  252 (  67   ~;  83   |;  74   &)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (  30 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  21 con; 0-0 aty)
%            Number of variables   :   28 (  28   !;   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
| ( ndr1_0
& ~ c2_1(a471)
& ~ c4_1(a471) )
| ~ c1_0 )
& ( ~ c3_0
| ! [U] :
( ndr1_0
=> ( c3_1(U)
| c5_1(U) ) )
| c1_0 )
& ( c3_0
| c1_0
| ~ c5_0 )
& ( ( ndr1_0
& ~ c1_1(a472)
& c5_1(a472)
& ndr1_1(a472)
& ~ c5_2(a472,a473)
& ~ c3_2(a472,a473) )
| ( ndr1_0
& ! [V] :
( ndr1_1(a474)
=> ( c4_2(a474,V)
| ~ c3_2(a474,V) ) )
& ! [W] :
( ndr1_1(a474)
=> ( ~ c5_2(a474,W)
| c1_2(a474,W)
| ~ c4_2(a474,W) ) )
& ndr1_1(a474)
& ~ c5_2(a474,a475)
& c2_2(a474,a475) ) )
& ( ~ c2_0
| ~ c3_0 )
& ( c4_0
| ~ c2_0
| ! [X] :
( ndr1_0
=> ( ! [Y] :
( ndr1_1(X)
=> ( c3_2(X,Y)
| ~ c4_2(X,Y)
| c5_2(X,Y) ) )
| ~ c3_1(X)
| ( ndr1_1(X)
& ~ c3_2(X,a476)
& ~ c1_2(X,a476)
& ~ c5_2(X,a476) ) ) ) )
& ( ! [Z] :
( ndr1_0
=> ( c2_1(Z)
| ~ c4_1(Z)
| ~ c1_1(Z) ) )
| ! [X1] :
( ndr1_0
=> ( c5_1(X1)
| ( ndr1_1(X1)
& ~ c2_2(X1,a477)
& c5_2(X1,a477)
& c1_2(X1,a477) )
| ~ c2_1(X1) ) )
| ( ndr1_0
& ~ c2_1(a478)
& ! [X2] :
( ndr1_1(a478)
=> ( ~ c2_2(a478,X2)
| ~ c1_2(a478,X2)
| ~ c4_2(a478,X2) ) )
& c1_1(a478) ) )
& ( c4_0
| ( ndr1_0
& c5_1(a479)
& ! [X3] :
( ndr1_1(a479)
=> ( ~ c1_2(a479,X3)
| ~ c5_2(a479,X3)
| ~ c2_2(a479,X3) ) ) )
| ~ c3_0 )
& ( ( ndr1_0
& ndr1_1(a480)
& ~ c4_2(a480,a481)
& c1_2(a480,a481)
& c2_2(a480,a481)
& ~ c5_1(a480) )
| c5_0
| ! [X4] :
( ndr1_0
=> ( c2_1(X4)
| ! [X5] :
( ndr1_1(X4)
=> ( ~ c5_2(X4,X5)
| ~ c3_2(X4,X5)
| c4_2(X4,X5) ) )
| ! [X6] :
( ndr1_1(X4)
=> ( ~ c5_2(X4,X6)
| c2_2(X4,X6)
| ~ c4_2(X4,X6) ) ) ) ) )
& ( ! [X7] :
( ndr1_0
=> ( ! [X8] :
( ndr1_1(X7)
=> ( ~ c1_2(X7,X8)
| ~ c4_2(X7,X8)
| ~ c2_2(X7,X8) ) )
| c4_1(X7)
| ! [X9] :
( ndr1_1(X7)
=> ( c1_2(X7,X9)
| c5_2(X7,X9)
| ~ c4_2(X7,X9) ) ) ) )
| ! [X10] :
( ndr1_0
=> ( c1_1(X10)
| ( ndr1_1(X10)
& c3_2(X10,a482)
& c1_2(X10,a482)
& ~ c4_2(X10,a482) )
| ~ c2_1(X10) ) )
| ~ c3_0 )
& ( c5_0
| c1_0 )
& ( ! [X11] :
( ndr1_0
=> ( ( ndr1_1(X11)
& c3_2(X11,a483)
& c2_2(X11,a483)
& c1_2(X11,a483) )
| ~ c2_1(X11) ) )
| c4_0
| ~ c2_0 )
& ( ( ndr1_0
& ! [X12] :
( ndr1_1(a484)
=> c4_2(a484,X12) )
& ~ c3_1(a484)
& ~ c1_1(a484) )
| ( ndr1_0
& ndr1_1(a485)
& c3_2(a485,a486)
& c2_2(a485,a486)
& c5_2(a485,a486)
& c2_1(a485)
& c4_1(a485) )
| c2_0 )
& ( ! [X13] :
( ndr1_0
=> ( c1_1(X13)
| ~ c3_1(X13)
| ! [X14] :
( ndr1_1(X13)
=> ( ~ c1_2(X13,X14)
| c5_2(X13,X14)
| ~ c3_2(X13,X14) ) ) ) )
| ~ c5_0
| c2_0 )
& ( ! [X15] :
( ndr1_0
=> ( ! [X16] :
( ndr1_1(X15)
=> ( ~ c2_2(X15,X16)
| ~ c5_2(X15,X16)
| ~ c4_2(X15,X16) ) )
| c4_1(X15)
| c1_1(X15) ) )
| ! [X17] :
( ndr1_0
=> c2_1(X17) )
| c4_0 )
& ( c3_0
| ! [X18] :
( ndr1_0
=> ( c1_1(X18)
| c3_1(X18) ) )
| c5_0 )
& ( ~ c5_0
| ( ndr1_0
& ! [X19] :
( ndr1_1(a487)
=> ( ~ c2_2(a487,X19)
| c4_2(a487,X19)
| ~ c5_2(a487,X19) ) )
& ~ c2_1(a487) )
| ( ndr1_0
& c4_1(a488)
& ! [X20] :
( ndr1_1(a488)
=> ( c1_2(a488,X20)
| c4_2(a488,X20) ) )
& c2_1(a488) ) )
& ( c3_0
| ~ c5_0
| ! [X21] :
( ndr1_0
=> ( c2_1(X21)
| ( ndr1_1(X21)
& c3_2(X21,a489)
& c5_2(X21,a489)
& ~ c2_2(X21,a489) )
| ( ndr1_1(X21)
& c1_2(X21,a490)
& ~ c3_2(X21,a490) ) ) ) )
& ( ! [X22] :
( ndr1_0
=> ( ~ c3_1(X22)
| c4_1(X22)
| ~ c5_1(X22) ) )
| c5_0
| ~ c2_0 )
& ( ( ndr1_0
& c3_1(a491)
& c5_1(a491) )
| c3_0 ) ) ).

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