## TPTP Problem File: SYN535+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN535+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=094
% 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-5-1-25-3-2-094.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v4.1.0, 0.17 v4.0.1, 0.00 v2.4.0, 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 :  269 (  75   ~;  74   |;  96   &)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (  32 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;  28 con; 0-0 aty)
%            Number of variables   :   24 (  24   !;   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,
~ ( ( c4_0
| c1_0 )
& ( ~ c3_0
| ! [U] :
( ndr1_0
=> ( c4_1(U)
| c5_1(U) ) )
| c5_0 )
& ( c1_0
| ( ndr1_0
& ~ c2_1(a492)
& ndr1_1(a492)
& ~ c5_2(a492,a493)
& ~ c3_2(a492,a493)
& ~ c2_2(a492,a493)
& c5_1(a492) )
| ( ndr1_0
& ~ c3_1(a494)
& ~ c4_1(a494)
& ! [V] :
( ndr1_1(a494)
=> ( c3_2(a494,V)
| c1_2(a494,V)
| ~ c4_2(a494,V) ) ) ) )
& ( c3_0
| ( ndr1_0
& ndr1_1(a495)
& c4_2(a495,a496)
& ~ c5_2(a495,a496)
& c2_2(a495,a496)
& c2_1(a495)
& ! [W] :
( ndr1_1(a495)
=> ( ~ c5_2(a495,W)
| ~ c3_2(a495,W) ) ) ) )
& ( c3_0
| ~ c5_0
| c1_0 )
& ( ! [X] :
( ndr1_0
=> ( ! [Y] :
( ndr1_1(X)
=> ( c2_2(X,Y)
| c1_2(X,Y) ) )
| ( ndr1_1(X)
& c5_2(X,a497)
& c1_2(X,a497)
& c3_2(X,a497) )
| c3_1(X) ) )
| c3_0
| ( ndr1_0
& ! [Z] :
( ndr1_1(a498)
=> ( ~ c4_2(a498,Z)
| c3_2(a498,Z) ) )
& c4_1(a498) ) )
& ( c1_0
| ( ndr1_0
& ~ c4_1(a499) ) )
& ( c3_0
| ~ c4_0
| ~ c1_0 )
& ( ~ c2_0
| ( ndr1_0
& ~ c2_1(a500)
& ndr1_1(a500)
& c1_2(a500,a501)
& ~ c2_2(a500,a501)
& ~ c3_2(a500,a501)
& c3_1(a500) )
| ! [X1] :
( ndr1_0
=> ( c5_1(X1)
| ! [X2] :
( ndr1_1(X1)
=> ( c3_2(X1,X2)
| c1_2(X1,X2)
| ~ c4_2(X1,X2) ) )
| ( ndr1_1(X1)
& ~ c2_2(X1,a502)
& ~ c3_2(X1,a502)
& c5_2(X1,a502) ) ) ) )
& ( ! [X3] :
( ndr1_0
=> ( ~ c3_1(X3)
| c2_1(X3)
| ~ c1_1(X3) ) )
| c2_0
| ( ndr1_0
& ndr1_1(a503)
& c4_2(a503,a504)
& ~ c2_2(a503,a504)
& ~ c5_2(a503,a504)
& ! [X4] :
( ndr1_1(a503)
=> ( ~ c3_2(a503,X4)
| c1_2(a503,X4)
| ~ c5_2(a503,X4) ) )
& ndr1_1(a503)
& ~ c3_2(a503,a505)
& ~ c5_2(a503,a505)
& ~ c2_2(a503,a505) ) )
& ( ! [X5] :
( ndr1_0
=> ( c4_1(X5)
| ( ndr1_1(X5)
& c4_2(X5,a506)
& c5_2(X5,a506)
& ~ c3_2(X5,a506) )
| ~ c5_1(X5) ) )
| ( ndr1_0
& ! [X6] :
( ndr1_1(a507)
=> ( ~ c2_2(a507,X6)
| ~ c3_2(a507,X6)
| ~ c5_2(a507,X6) ) )
& ~ c4_1(a507)
& c3_1(a507) )
| ( ndr1_0
& c5_1(a508)
& c1_1(a508) ) )
& ( c3_0
| c4_0
| ~ c5_0 )
& ( ( ndr1_0
& ! [X7] :
( ndr1_1(a509)
=> ( c4_2(a509,X7)
| ~ c2_2(a509,X7)
| c5_2(a509,X7) ) )
& ~ c2_1(a509) )
| ! [X8] :
( ndr1_0
=> ( ( ndr1_1(X8)
& ~ c2_2(X8,a510)
& ~ c3_2(X8,a510) )
| ~ c3_1(X8)
| c2_1(X8) ) )
| ! [X9] :
( ndr1_0
=> ( c3_1(X9)
| ! [X10] :
( ndr1_1(X9)
=> ( ~ c4_2(X9,X10)
| ~ c3_2(X9,X10) ) ) ) ) )
& ( ( ndr1_0
& ! [X11] :
( ndr1_1(a511)
=> ( c2_2(a511,X11)
| c4_2(a511,X11)
| ~ c3_2(a511,X11) ) )
& ~ c3_1(a511)
& ~ c2_1(a511) )
| ~ c4_0
| ( ndr1_0
& c4_1(a512)
& ~ c3_1(a512)
& c1_1(a512) ) )
& ( ~ c2_0
| ~ c5_0 )
& ( ~ c4_0
| ! [X12] :
( ndr1_0
=> ( ~ c4_1(X12)
| ~ c3_1(X12)
| ! [X13] :
( ndr1_1(X12)
=> ( ~ c4_2(X12,X13)
| ~ c5_2(X12,X13) ) ) ) )
| ~ c5_0 )
& ( ( ndr1_0
& ~ c4_1(a513)
& c1_1(a513)
& c3_1(a513) )
| c2_0
| ( ndr1_0
& c1_1(a514)
& ndr1_1(a514)
& ~ c5_2(a514,a515)
& c3_2(a514,a515)
& c2_2(a514,a515)
& ! [X14] :
( ndr1_1(a514)
=> ( ~ c4_2(a514,X14)
| c5_2(a514,X14)
| c3_2(a514,X14) ) ) ) )
& ( ~ c1_0
| ( ndr1_0
& c3_1(a516)
& ! [X15] :
( ndr1_1(a516)
=> ( ~ c4_2(a516,X15)
| c3_2(a516,X15)
| c5_2(a516,X15) ) )
& ~ c1_1(a516) ) )
& ( ~ c2_0
| ! [X16] :
( ndr1_0
=> c5_1(X16) )
| ! [X17] :
( ndr1_0
=> ( ~ c4_1(X17)
| ~ c1_1(X17)
| ! [X18] :
( ndr1_1(X17)
=> ( ~ c3_2(X17,X18)
| c5_2(X17,X18)
| ~ c1_2(X17,X18) ) ) ) ) )
& ( ( ndr1_0
& ~ c2_1(a517)
& c4_1(a517)
& ndr1_1(a517)
& c3_2(a517,a518)
& ~ c4_2(a517,a518)
& c5_2(a517,a518) )
| ( ndr1_0
& ~ c2_1(a519)
& c1_1(a519) )
| ~ c2_0 ) ) ).

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