## TPTP Problem File: SYN521+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN521+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=049
% 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-5-1-20-3-2-049.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 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  182 (   0 equ)
%            Maximal formula atoms :  182 ( 182 avg)
%            Number of connectives :  254 (  73   ~;  57   |; 105   &)
%                                         (   0 <=>;  19  =>;   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    :   34 (  34 usr;  34 con; 0-0 aty)
%            Number of variables   :   19 (  19   !;   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
& ndr1_1(a70)
& c4_2(a70,a71)
& ~ c2_2(a70,a71)
& c1_2(a70,a71)
& ndr1_1(a70)
& ~ c5_2(a70,a72)
& ~ c2_2(a70,a72)
& ~ c3_2(a70,a72)
& ndr1_1(a70)
& ~ c5_2(a70,a73)
& ~ c4_2(a70,a73) )
| ~ c4_0 )
& ( ~ c5_0
| ~ c2_0 )
& ( c3_0
| ( ndr1_0
& ndr1_1(a74)
& ~ c2_2(a74,a75)
& c5_2(a74,a75)
& ~ c1_2(a74,a75)
& ~ c2_1(a74) ) )
& ( ( ndr1_0
& c1_1(a76)
& c3_1(a76) )
| ~ c4_0
| c1_0 )
& ( ! [U] :
( ndr1_0
=> ( c4_1(U)
| c2_1(U)
| ! [V] :
( ndr1_1(U)
=> ( ~ c1_2(U,V)
| ~ c3_2(U,V)
| ~ c5_2(U,V) ) ) ) )
| c5_0 )
& ( ! [W] :
( ndr1_0
=> ( ! [X] :
( ndr1_1(W)
=> ( c4_2(W,X)
| c1_2(W,X) ) )
| ~ c1_1(W) ) )
| ( ndr1_0
& ~ c3_1(a77)
& ndr1_1(a77)
& ~ c5_2(a77,a78)
& ~ c3_2(a77,a78)
& ndr1_1(a77)
& ~ c5_2(a77,a79)
& ~ c2_2(a77,a79)
& c3_2(a77,a79) )
| c3_0 )
& ( ( ndr1_0
& ~ c2_1(a80)
& c4_1(a80)
& ~ c3_1(a80) )
| ! [Y] :
( ndr1_0
=> ( ! [Z] :
( ndr1_1(Y)
=> ( c4_2(Y,Z)
| c2_2(Y,Z) ) )
| c1_1(Y)
| ( ndr1_1(Y)
& c4_2(Y,a81)
& c1_2(Y,a81)
& ~ c5_2(Y,a81) ) ) )
| ~ c1_0 )
& ( ~ c3_0
| ( ndr1_0
& ndr1_1(a82)
& c4_2(a82,a83)
& ~ c5_2(a82,a83)
& ndr1_1(a82)
& ~ c2_2(a82,a84)
& ~ c4_2(a82,a84)
& ~ c5_2(a82,a84)
& c1_1(a82) ) )
& ( ! [X1] :
( ndr1_0
=> ( ! [X2] :
( ndr1_1(X1)
=> ( ~ c3_2(X1,X2)
| ~ c5_2(X1,X2)
| c1_2(X1,X2) ) )
| ~ c1_1(X1)
| c4_1(X1) ) )
| c2_0
| ~ c4_0 )
& ( c4_0
| ~ c2_0
| ( ndr1_0
& ndr1_1(a85)
& ~ c3_2(a85,a86)
& ~ c1_2(a85,a86)
& ndr1_1(a85)
& ~ c3_2(a85,a87)
& c4_2(a85,a87)
& c5_2(a85,a87)
& c5_1(a85) ) )
& ( ( ndr1_0
& c1_1(a88)
& ! [X3] :
( ndr1_1(a88)
=> ( c5_2(a88,X3)
| c2_2(a88,X3) ) )
& ndr1_1(a88)
& ~ c2_2(a88,a89)
& ~ c5_2(a88,a89)
& c4_2(a88,a89) )
| ( ndr1_0
& ~ c4_1(a90)
& ~ c3_1(a90)
& ~ c2_1(a90) )
| ! [X4] :
( ndr1_0
=> ( ! [X5] :
( ndr1_1(X4)
=> ( ~ c3_2(X4,X5)
| c5_2(X4,X5)
| ~ c1_2(X4,X5) ) )
| ( ndr1_1(X4)
& ~ c2_2(X4,a91)
& ~ c4_2(X4,a91)
& ~ c1_2(X4,a91) )
| ( ndr1_1(X4)
& c1_2(X4,a92)
& c5_2(X4,a92) ) ) ) )
& ( c4_0
| ( ndr1_0
& ndr1_1(a93)
& ~ c1_2(a93,a94)
& c2_2(a93,a94)
& ~ c4_2(a93,a94)
& c4_1(a93)
& c3_1(a93) )
| ( ndr1_0
& ndr1_1(a95)
& ~ c4_2(a95,a96)
& c1_2(a95,a96)
& c5_2(a95,a96)
& ! [X6] :
( ndr1_1(a95)
=> ( c5_2(a95,X6)
| ~ c1_2(a95,X6)
| ~ c3_2(a95,X6) ) ) ) )
& ( ~ c5_0
| ( ndr1_0
& ndr1_1(a97)
& c5_2(a97,a98)
& ~ c2_2(a97,a98)
& ndr1_1(a97)
& ~ c2_2(a97,a99)
& ~ c1_2(a97,a99)
& c5_2(a97,a99)
& ! [X7] :
( ndr1_1(a97)
=> ( c3_2(a97,X7)
| c2_2(a97,X7)
| c1_2(a97,X7) ) ) )
| ( ndr1_0
& ! [X8] :
( ndr1_1(a100)
=> ( ~ c4_2(a100,X8)
| ~ c3_2(a100,X8)
| ~ c2_2(a100,X8) ) )
& c4_1(a100)
& c2_1(a100) ) )
& ( ( ndr1_0
& ! [X9] :
( ndr1_1(a101)
=> ( ~ c2_2(a101,X9)
| ~ c5_2(a101,X9) ) )
& ! [X10] :
( ndr1_1(a101)
=> ( ~ c1_2(a101,X10)
| c3_2(a101,X10)
| ~ c5_2(a101,X10) ) ) )
| c3_0
| ( ndr1_0
& c2_1(a102)
& ndr1_1(a102)
& c1_2(a102,a103)
& ~ c5_2(a102,a103)
& ! [X11] :
( ndr1_1(a102)
=> ( ~ c1_2(a102,X11)
| ~ c5_2(a102,X11)
| ~ c3_2(a102,X11) ) ) ) )
& ( ~ c1_0
| ! [X12] :
( ndr1_0
=> ( ! [X13] :
( ndr1_1(X12)
=> ( c4_2(X12,X13)
| c3_2(X12,X13)
| ~ c5_2(X12,X13) ) )
| ~ c4_1(X12) ) )
| c3_0 ) ) ).

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