## TPTP Problem File: SYN525+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN525+1 : TPTP v8.1.0. Released v2.1.0.
% Domain   : Syntactic (Translated)
% Problem  : ALC, N=5, R=1, L=20, 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-5-1-20-3-2-094.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v6.0.0, 0.17 v5.5.0, 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       :  196 (   0 equ)
%            Maximal formula atoms :  196 ( 196 avg)
%            Number of connectives :  262 (  67   ~;  70   |; 100   &)
%                                         (   0 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (  26 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   :   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,
~ ( ( ( ndr1_0
& c3_1(a188)
& ndr1_1(a188)
& ~ c4_2(a188,a189)
& c3_2(a188,a189)
& c5_2(a188,a189)
& ! [U] :
( ndr1_1(a188)
=> ( ~ c3_2(a188,U)
| c1_2(a188,U)
| ~ c4_2(a188,U) ) ) )
| ~ c4_0
| ( ndr1_0
& ! [V] :
( ndr1_1(a190)
=> ( c3_2(a190,V)
| c5_2(a190,V) ) )
& c4_1(a190)
& ~ c2_1(a190) ) )
& ( ( ndr1_0
& ~ c3_1(a191)
& c5_1(a191)
& c2_1(a191) )
| ( ndr1_0
& ndr1_1(a192)
& ~ c1_2(a192,a193)
& ~ c4_2(a192,a193)
& c5_2(a192,a193)
& ~ c5_1(a192)
& ndr1_1(a192)
& c3_2(a192,a194)
& c5_2(a192,a194) )
| c1_0 )
& ( ( ndr1_0
& ~ c2_1(a195)
& ~ c1_1(a195)
& ! [W] :
( ndr1_1(a195)
=> ( c2_2(a195,W)
| c3_2(a195,W)
| c1_2(a195,W) ) ) )
| ( ndr1_0
& ! [X] :
( ndr1_1(a196)
=> ( ~ c4_2(a196,X)
| ~ c1_2(a196,X)
| ~ c3_2(a196,X) ) )
& ! [Y] :
( ndr1_1(a196)
=> ( c5_2(a196,Y)
| c1_2(a196,Y) ) )
& c4_1(a196) ) )
& ( ! [Z] :
( ndr1_0
=> ( ( ndr1_1(Z)
& c1_2(Z,a197)
& c4_2(Z,a197) )
| c3_1(Z)
| ( ndr1_1(Z)
& ~ c2_2(Z,a198)
& ~ c4_2(Z,a198)
& ~ c3_2(Z,a198) ) ) )
| ~ c4_0
| ! [X1] :
( ndr1_0
=> ( ~ c1_1(X1)
| ~ c5_1(X1) ) ) )
& ( ( ndr1_0
& ~ c2_1(a199)
& ~ c5_1(a199)
& c3_1(a199) )
| ~ c2_0
| ~ c5_0 )
& ( c4_0
| ( ndr1_0
& ! [X2] :
( ndr1_1(a200)
=> ( ~ c2_2(a200,X2)
| c1_2(a200,X2)
| c4_2(a200,X2) ) )
& c3_1(a200)
& ! [X3] :
( ndr1_1(a200)
=> ( c3_2(a200,X3)
| c5_2(a200,X3)
| ~ c1_2(a200,X3) ) ) )
| ( ndr1_0
& ! [X4] :
( ndr1_1(a201)
=> ( ~ c2_2(a201,X4)
| ~ c1_2(a201,X4)
| c5_2(a201,X4) ) )
& ~ c5_1(a201)
& c2_1(a201) ) )
& ( c4_0
| ( ndr1_0
& ~ c2_1(a202)
& ~ c3_1(a202) )
| ( ndr1_0
& c2_1(a203)
& ! [X5] :
( ndr1_1(a203)
=> ~ c4_2(a203,X5) )
& ndr1_1(a203)
& c2_2(a203,a204)
& c5_2(a203,a204)
& ~ c3_2(a203,a204) ) )
& ( ! [X6] :
( ndr1_0
=> ( c2_1(X6)
| ~ c4_1(X6)
| ( ndr1_1(X6)
& c4_2(X6,a205)
& ~ c5_2(X6,a205)
& ~ c2_2(X6,a205) ) ) )
| c3_0
| ! [X7] :
( ndr1_0
=> ( c2_1(X7)
| ~ c1_1(X7)
| ~ c3_1(X7) ) ) )
& ( c2_0
| ( ndr1_0
& c1_1(a206)
& ndr1_1(a206)
& c2_2(a206,a207)
& ~ c4_2(a206,a207)
& ndr1_1(a206)
& c3_2(a206,a208)
& ~ c2_2(a206,a208)
& ~ c1_2(a206,a208) )
| ~ c5_0 )
& ( ~ c2_0
| ! [X8] :
( ndr1_0
=> ( ( ndr1_1(X8)
& ~ c4_2(X8,a209)
& ~ c5_2(X8,a209)
& ~ c3_2(X8,a209) )
| ~ c3_1(X8)
| ! [X9] :
( ndr1_1(X8)
=> ( c3_2(X8,X9)
| c2_2(X8,X9)
| c4_2(X8,X9) ) ) ) ) )
& ( ( ndr1_0
& ! [X10] :
( ndr1_1(a210)
=> ( c3_2(a210,X10)
| c4_2(a210,X10)
| c2_2(a210,X10) ) )
& c1_1(a210)
& ndr1_1(a210)
& ~ c3_2(a210,a211)
& c4_2(a210,a211)
& ~ c5_2(a210,a211) )
| c5_0
| ( ndr1_0
& ndr1_1(a212)
& c4_2(a212,a213)
& ~ c1_2(a212,a213)
& c3_2(a212,a213)
& ~ c2_1(a212)
& ndr1_1(a212)
& ~ c4_2(a212,a214)
& c1_2(a212,a214)
& c5_2(a212,a214) ) )
& ( ! [X11] :
( ndr1_0
=> ( ~ c3_1(X11)
| ~ c4_1(X11)
| c1_1(X11) ) )
| ~ c2_0
| c4_0 )
& ( ( ndr1_0
& ~ c5_1(a215)
& ~ c3_1(a215) )
| c3_0
| ( ndr1_0
& c1_1(a216)
& c2_1(a216)
& ~ c4_1(a216) ) )
& ( ~ c4_0
| ! [X12] :
( ndr1_0
=> ( ~ c3_1(X12)
| c1_1(X12) ) )
| ! [X13] :
( ndr1_0
=> ( c3_1(X13)
| c2_1(X13)
| ! [X14] :
( ndr1_1(X13)
=> ( c4_2(X13,X14)
| ~ c3_2(X13,X14) ) ) ) ) )
& ( ! [X15] :
( ndr1_0
=> ( ! [X16] :
( ndr1_1(X15)
=> ( ~ c5_2(X15,X16)
| c1_2(X15,X16)
| c2_2(X15,X16) ) )
| ( ndr1_1(X15)
& ~ c4_2(X15,a217)
& c5_2(X15,a217)
& c1_2(X15,a217) )
| c4_1(X15) ) )
| ! [X17] :
( ndr1_0
=> ( ! [X18] :
( ndr1_1(X17)
=> ( c1_2(X17,X18)
| c5_2(X17,X18)
| c4_2(X17,X18) ) )
| c1_1(X17) ) ) )
& ( ~ c2_0
| ! [X19] :
( ndr1_0
=> ( ~ c2_1(X19)
| ~ c5_1(X19) ) )
| c5_0 ) ) ).

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