## TPTP Problem File: SYN524+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN524+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=086
% 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-5-1-20-3-2-086.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       :  216 (   0 equ)
%            Maximal formula atoms :  216 ( 216 avg)
%            Number of connectives :  291 (  76   ~;  85   |;  99   &)
%                                         (   0 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (  28 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   31 (  31 usr;  31 con; 0-0 aty)
%            Number of variables   :   31 (  31   !;   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,
~ ( ( ! [U] :
( ndr1_0
=> ( ( ndr1_1(U)
& ~ c3_2(U,a157)
& c2_2(U,a157) )
| ~ c5_1(U)
| ! [V] :
( ndr1_1(U)
=> ( c1_2(U,V)
| c5_2(U,V) ) ) ) )
| c1_0
| ( ndr1_0
& c3_1(a158)
& c5_1(a158)
& ! [W] :
( ndr1_1(a158)
=> ( c1_2(a158,W)
| c5_2(a158,W)
| c4_2(a158,W) ) ) ) )
& ( ~ c1_0
| ( ndr1_0
& ~ c2_1(a159)
& ~ c3_1(a159)
& ndr1_1(a159)
& ~ c3_2(a159,a160)
& ~ c5_2(a159,a160) )
| ! [X] :
( ndr1_0
=> ( c1_1(X)
| c3_1(X)
| ! [Y] :
( ndr1_1(X)
=> ( ~ c5_2(X,Y)
| c2_2(X,Y) ) ) ) ) )
& ( ( ndr1_0
& ~ c3_1(a161)
& ndr1_1(a161)
& c3_2(a161,a162)
& c5_2(a161,a162)
& c1_2(a161,a162)
& c4_1(a161) )
| ! [Z] :
( ndr1_0
=> ( c2_1(Z)
| ! [X1] :
( ndr1_1(Z)
=> ( ~ c4_2(Z,X1)
| ~ c1_2(Z,X1) ) )
| c1_1(Z) ) )
| ( ndr1_0
& c3_1(a163)
& ndr1_1(a163)
& ~ c1_2(a163,a164)
& c5_2(a163,a164)
& ~ c3_2(a163,a164)
& ~ c2_1(a163) ) )
& ( ~ c5_0
| ( ndr1_0
& c1_1(a165)
& ndr1_1(a165)
& c1_2(a165,a166)
& c3_2(a165,a166)
& ~ c5_2(a165,a166)
& ! [X2] :
( ndr1_1(a165)
=> ( c5_2(a165,X2)
| ~ c3_2(a165,X2)
| c4_2(a165,X2) ) ) ) )
& ( ~ c2_0
| ! [X3] :
( ndr1_0
=> ( ~ c5_1(X3)
| ~ c2_1(X3)
| c1_1(X3) ) )
| ( ndr1_0
& ! [X4] :
( ndr1_1(a167)
=> ( ~ c2_2(a167,X4)
| ~ c1_2(a167,X4)
| c4_2(a167,X4) ) )
& ! [X5] :
( ndr1_1(a167)
=> ( ~ c3_2(a167,X5)
| ~ c1_2(a167,X5) ) )
& ndr1_1(a167)
& c2_2(a167,a168)
& c3_2(a167,a168)
& c4_2(a167,a168) ) )
& ( ( ndr1_0
& c3_1(a169)
& ! [X6] :
( ndr1_1(a169)
=> ( c2_2(a169,X6)
| c3_2(a169,X6)
| c5_2(a169,X6) ) ) )
| ( ndr1_0
& ~ c1_1(a170)
& ~ c3_1(a170) )
| ( ndr1_0
& ~ c4_1(a171)
& ndr1_1(a171)
& ~ c1_2(a171,a172)
& c3_2(a171,a172)
& ! [X7] :
( ndr1_1(a171)
=> ( ~ c4_2(a171,X7)
| ~ c5_2(a171,X7) ) ) ) )
& ( ~ c5_0
| ! [X8] :
( ndr1_0
=> ( ndr1_1(X8)
& ~ c5_2(X8,a173)
& ~ c3_2(X8,a173) ) )
| ! [X9] :
( ndr1_0
=> ( ! [X10] :
( ndr1_1(X9)
=> ( c2_2(X9,X10)
| c5_2(X9,X10)
| c4_2(X9,X10) ) )
| ~ c2_1(X9)
| ~ c5_1(X9) ) ) )
& ( c3_0
| ~ c4_0
| c2_0 )
& ( ~ c4_0
| ! [X11] :
( ndr1_0
=> ( c1_1(X11)
| ~ c3_1(X11)
| ( ndr1_1(X11)
& ~ c2_2(X11,a174)
& ~ c5_2(X11,a174)
& ~ c1_2(X11,a174) ) ) )
| ( ndr1_0
& c1_1(a175)
& c2_1(a175)
& ! [X12] :
( ndr1_1(a175)
=> ( c2_2(a175,X12)
| ~ c3_2(a175,X12)
| c4_2(a175,X12) ) ) ) )
& ( ! [X13] :
( ndr1_0
=> ( c4_1(X13)
| ~ c5_1(X13)
| ~ c2_1(X13) ) )
| c3_0
| ! [X14] :
( ndr1_0
=> ( ( ndr1_1(X14)
& ~ c4_2(X14,a176)
& c2_2(X14,a176) )
| ( ndr1_1(X14)
& c2_2(X14,a177)
& c4_2(X14,a177)
& c3_2(X14,a177) )
| ~ c1_1(X14) ) ) )
& ( ~ c2_0
| ( ndr1_0
& c4_1(a178)
& ndr1_1(a178)
& ~ c4_2(a178,a179)
& c5_2(a178,a179)
& ! [X15] :
( ndr1_1(a178)
=> ( c4_2(a178,X15)
| c3_2(a178,X15) ) ) )
| ~ c3_0 )
& ( ~ c2_0
| ~ c3_0
| ! [X16] :
( ndr1_0
=> ( ~ c4_1(X16)
| ~ c5_1(X16)
| ~ c3_1(X16) ) ) )
& ( ( ndr1_0
& c2_1(a180)
& ! [X17] :
( ndr1_1(a180)
=> ( ~ c5_2(a180,X17)
| c4_2(a180,X17)
| ~ c1_2(a180,X17) ) )
& c3_1(a180) )
| ~ c3_0 )
& ( ( ndr1_0
& ~ c4_1(a181)
& ! [X18] :
( ndr1_1(a181)
=> ( ~ c1_2(a181,X18)
| c5_2(a181,X18)
| c3_2(a181,X18) ) )
& c1_1(a181) )
| c4_0
| c2_0 )
& ( c3_0
| ! [X19] :
( ndr1_0
=> ( ~ c1_1(X19)
| ~ c4_1(X19)
| ! [X20] :
( ndr1_1(X19)
=> ( ~ c4_2(X19,X20)
| ~ c3_2(X19,X20)
| ~ c1_2(X19,X20) ) ) ) )
| ! [X21] :
( ndr1_0
=> ( c1_1(X21)
| ( ndr1_1(X21)
& ~ c3_2(X21,a182)
& ~ c2_2(X21,a182)
& c5_2(X21,a182) )
| ! [X22] :
( ndr1_1(X21)
=> ( c2_2(X21,X22)
| c1_2(X21,X22)
| ~ c3_2(X21,X22) ) ) ) ) )
& ( c1_0
| c5_0
| ( ndr1_0
& ndr1_1(a183)
& c1_2(a183,a184)
& ~ c5_2(a183,a184)
& c2_1(a183)
& ! [X23] :
( ndr1_1(a183)
=> ( c3_2(a183,X23)
| c2_2(a183,X23) ) ) ) )
& ( c3_0
| ! [X24] :
( ndr1_0
=> ( ( ndr1_1(X24)
& ~ c2_2(X24,a185)
& ~ c3_2(X24,a185) )
| ~ c3_1(X24)
| ( ndr1_1(X24)
& ~ c1_2(X24,a186)
& c4_2(X24,a186) ) ) ) )
& ( ! [X25] :
( ndr1_0
=> ( ( ndr1_1(X25)
& c1_2(X25,a187)
& ~ c5_2(X25,a187)
& c2_2(X25,a187) )
| ~ c2_1(X25) ) )
| ~ c1_0
| c5_0 ) ) ).

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