## TPTP Problem File: SYN539+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN539+1 : TPTP v8.1.0. Released v2.1.0.
% Domain   : Syntactic (Translated)
% Problem  : ALC, N=5, R=1, L=40, K=3, D=2, P=0, Index=036
% 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-5-1-40-3-2-036.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v4.1.0, 0.17 v4.0.1, 0.00 v3.2.0, 0.25 v3.1.0, 0.17 v2.7.0, 0.50 v2.6.0, 0.25 v2.5.0, 0.00 v2.4.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  370 (   0 equ)
%            Maximal formula atoms :  370 ( 370 avg)
%            Number of connectives :  506 ( 137   ~; 148   |; 168   &)
%                                         (   0 <=>;  53  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   43 (  43 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   53 (  53 usr;  53 con; 0-0 aty)
%            Number of variables   :   53 (  53   !;   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
| ( ndr1_0
& c2_1(a587)
& c3_1(a587)
& c5_1(a587) ) )
& ( ( ndr1_0
& ndr1_1(a588)
& ~ c1_2(a588,a589)
& c2_2(a588,a589)
& c3_2(a588,a589)
& ndr1_1(a588)
& ~ c4_2(a588,a590)
& c2_2(a588,a590)
& c1_2(a588,a590)
& ndr1_1(a588)
& c5_2(a588,a591)
& ~ c2_2(a588,a591) )
| ~ c2_0
| ! [U] :
( ndr1_0
=> ( c2_1(U)
| c5_1(U)
| ~ c3_1(U) ) ) )
& ( ~ c3_0
| ~ c1_0
| ~ c4_0 )
& ( ( ndr1_0
& ~ c3_1(a592)
& ! [V] :
( ndr1_1(a592)
=> ( c5_2(a592,V)
| c4_2(a592,V)
| ~ c1_2(a592,V) ) )
& ~ c4_1(a592) )
| ( ndr1_0
& ! [W] :
( ndr1_1(a593)
=> ( ~ c4_2(a593,W)
| c5_2(a593,W)
| ~ c1_2(a593,W) ) )
& c2_1(a593)
& ~ c5_1(a593) )
| ( ndr1_0
& c1_1(a594)
& c4_1(a594) ) )
& ( ~ c5_0
| ! [X] :
( ndr1_0
=> ( ( ndr1_1(X)
& ~ c4_2(X,a595)
& ~ c1_2(X,a595) )
| ~ c1_1(X)
| ! [Y] :
( ndr1_1(X)
=> ( c2_2(X,Y)
| ~ c5_2(X,Y) ) ) ) ) )
& ( ! [Z] :
( ndr1_0
=> ( c2_1(Z)
| ! [X1] :
( ndr1_1(Z)
=> ( ~ c2_2(Z,X1)
| c3_2(Z,X1) ) )
| c1_1(Z) ) )
| c2_0
| ( ndr1_0
& ! [X2] :
( ndr1_1(a596)
=> ( c3_2(a596,X2)
| ~ c4_2(a596,X2)
| ~ c1_2(a596,X2) ) )
& ndr1_1(a596)
& c5_2(a596,a597)
& ~ c2_2(a596,a597)
& ~ c1_2(a596,a597)
& ndr1_1(a596)
& c1_2(a596,a598)
& ~ c4_2(a596,a598)
& c2_2(a596,a598) ) )
& ( ! [X3] :
( ndr1_0
=> ( ( ndr1_1(X3)
& c2_2(X3,a599)
& ~ c3_2(X3,a599)
& ~ c5_2(X3,a599) )
| ( ndr1_1(X3)
& c1_2(X3,a600)
& ~ c3_2(X3,a600)
& c2_2(X3,a600) )
| c2_1(X3) ) )
| ! [X4] :
( ndr1_0
=> ( ~ c3_1(X4)
| c2_1(X4)
| ( ndr1_1(X4)
& c4_2(X4,a601)
& c2_2(X4,a601)
& c5_2(X4,a601) ) ) )
| c2_0 )
& ( c1_0
| ! [X5] :
( ndr1_0
=> ( ( ndr1_1(X5)
& ~ c2_2(X5,a602)
& c3_2(X5,a602) )
| ( ndr1_1(X5)
& c5_2(X5,a603)
& c3_2(X5,a603)
& ~ c4_2(X5,a603) )
| ( ndr1_1(X5)
& c4_2(X5,a604)
& c3_2(X5,a604)
& ~ c1_2(X5,a604) ) ) )
| ! [X6] :
( ndr1_0
=> ( ! [X7] :
( ndr1_1(X6)
=> ( c4_2(X6,X7)
| c1_2(X6,X7)
| ~ c5_2(X6,X7) ) )
| ~ c1_1(X6) ) ) )
& ( ~ c1_0
| ( ndr1_0
& ! [X8] :
( ndr1_1(a605)
=> ( ~ c3_2(a605,X8)
| c2_2(a605,X8) ) )
& ! [X9] :
( ndr1_1(a605)
=> ( c5_2(a605,X9)
| c3_2(a605,X9)
| ~ c1_2(a605,X9) ) ) )
| ! [X10] :
( ndr1_0
=> ( ! [X11] :
( ndr1_1(X10)
=> ( c4_2(X10,X11)
| c5_2(X10,X11) ) )
| c3_1(X10) ) ) )
& ( ! [X12] :
( ndr1_0
=> ( ( ndr1_1(X12)
& c4_2(X12,a606)
& c3_2(X12,a606) )
| ~ c3_1(X12)
| ! [X13] :
( ndr1_1(X12)
=> ( ~ c2_2(X12,X13)
| c3_2(X12,X13)
| c5_2(X12,X13) ) ) ) )
| c5_0 )
& ( ! [X14] :
( ndr1_0
=> ( c4_1(X14)
| ( ndr1_1(X14)
& ~ c1_2(X14,a607)
& c4_2(X14,a607)
& c3_2(X14,a607) )
| c2_1(X14) ) )
| ~ c2_0
| c5_0 )
& ( ! [X15] :
( ndr1_0
=> ( ~ c1_1(X15)
| ! [X16] :
( ndr1_1(X15)
=> ( c5_2(X15,X16)
| c4_2(X15,X16) ) )
| ~ c3_1(X15) ) )
| ( ndr1_0
& ! [X17] :
( ndr1_1(a608)
=> ( ~ c3_2(a608,X17)
| c2_2(a608,X17) ) )
& ! [X18] :
( ndr1_1(a608)
=> ( ~ c2_2(a608,X18)
| ~ c5_2(a608,X18) ) )
& ndr1_1(a608)
& c5_2(a608,a609)
& ~ c4_2(a608,a609) )
| ! [X19] :
( ndr1_0
=> ( c5_1(X19)
| ( ndr1_1(X19)
& c2_2(X19,a610)
& c3_2(X19,a610)
& ~ c1_2(X19,a610) )
| c1_1(X19) ) ) )
& ( ~ c4_0
| ~ c2_0
| ( ndr1_0
& ndr1_1(a611)
& c5_2(a611,a612)
& ~ c1_2(a611,a612)
& ! [X20] :
( ndr1_1(a611)
=> ( c5_2(a611,X20)
| ~ c3_2(a611,X20)
| c2_2(a611,X20) ) )
& ~ c1_1(a611) ) )
& ( ~ c3_0
| ! [X21] :
( ndr1_0
=> ( ~ c3_1(X21)
| c5_1(X21) ) )
| ( ndr1_0
& ~ c3_1(a613)
& ndr1_1(a613)
& c1_2(a613,a614)
& ~ c4_2(a613,a614)
& ~ c3_2(a613,a614)
& ! [X22] :
( ndr1_1(a613)
=> ( ~ c2_2(a613,X22)
| c1_2(a613,X22) ) ) ) )
& ( ( ndr1_0
& ~ c1_1(a615)
& ! [X23] :
( ndr1_1(a615)
=> ( ~ c5_2(a615,X23)
| ~ c2_2(a615,X23)
| ~ c3_2(a615,X23) ) )
& ! [X24] :
( ndr1_1(a615)
=> ( ~ c2_2(a615,X24)
| c3_2(a615,X24)
| c1_2(a615,X24) ) ) )
| ~ c1_0
| ~ c3_0 )
& ( c4_0
| ~ c5_0
| ( ndr1_0
& ~ c3_1(a616)
& c1_1(a616)
& ~ c2_1(a616) ) )
& ( ~ c2_0
| ! [X25] :
( ndr1_0
=> ( ( ndr1_1(X25)
& c4_2(X25,a617)
& ~ c1_2(X25,a617) )
| c1_1(X25)
| ! [X26] :
( ndr1_1(X25)
=> ( ~ c5_2(X25,X26)
| c2_2(X25,X26)
| ~ c1_2(X25,X26) ) ) ) ) )
& ( ! [X27] :
( ndr1_0
=> ( c1_1(X27)
| ( ndr1_1(X27)
& ~ c4_2(X27,a618)
& ~ c3_2(X27,a618)
& ~ c2_2(X27,a618) )
| ~ c2_1(X27) ) )
| c2_0
| c4_0 )
& ( ~ c5_0
| ( ndr1_0
& c4_1(a619)
& c1_1(a619)
& c5_1(a619) )
| c1_0 )
& ( c4_0
| ~ c3_0
| c1_0 )
& ( ~ c5_0
| ~ c1_0
| ( ndr1_0
& ~ c4_1(a620) ) )
& ( ! [X28] :
( ndr1_0
=> c2_1(X28) )
| c2_0
| ! [X29] :
( ndr1_0
=> ( ~ c2_1(X29)
| ( ndr1_1(X29)
& c1_2(X29,a621)
& c4_2(X29,a621)
& ~ c2_2(X29,a621) )
| ( ndr1_1(X29)
& ~ c1_2(X29,a622)
& c5_2(X29,a622) ) ) ) )
& ( ~ c4_0
| ! [X30] :
( ndr1_0
=> ( ~ c2_1(X30)
| ! [X31] :
( ndr1_1(X30)
=> ( c2_2(X30,X31)
| ~ c1_2(X30,X31)
| ~ c4_2(X30,X31) ) )
| c4_1(X30) ) )
| ~ c3_0 )
& ( ~ c4_0
| ~ c1_0
| ! [X32] :
( ndr1_0
=> ( ( ndr1_1(X32)
& ~ c3_2(X32,a623) )
| ~ c3_1(X32)
| ! [X33] :
( ndr1_1(X32)
=> ( ~ c4_2(X32,X33)
| c1_2(X32,X33)
| ~ c2_2(X32,X33) ) ) ) ) )
& ( ( ndr1_0
& ! [X34] :
( ndr1_1(a624)
=> ( c3_2(a624,X34)
| c2_2(a624,X34)
| c5_2(a624,X34) ) )
& ndr1_1(a624)
& c3_2(a624,a625)
& ~ c1_2(a624,a625)
& ~ c2_2(a624,a625)
& ndr1_1(a624)
& c5_2(a624,a626)
& ~ c3_2(a624,a626)
& c4_2(a624,a626) )
| c2_0
| ! [X35] :
( ndr1_0
=> ( ~ c3_1(X35)
| ( ndr1_1(X35)
& ~ c2_2(X35,a627)
& c1_2(X35,a627) )
| ! [X36] :
( ndr1_1(X35)
=> ( ~ c5_2(X35,X36)
| ~ c1_2(X35,X36)
| ~ c3_2(X35,X36) ) ) ) ) )
& ( ! [X37] :
( ndr1_0
=> ( ! [X38] :
( ndr1_1(X37)
=> ( c2_2(X37,X38)
| ~ c1_2(X37,X38)
| c3_2(X37,X38) ) )
| ( ndr1_1(X37)
& c4_2(X37,a628)
& ~ c1_2(X37,a628)
& ~ c5_2(X37,a628) )
| ~ c4_1(X37) ) )
| ( ndr1_0
& ndr1_1(a629)
& ~ c2_2(a629,a630)
& ~ c5_2(a629,a630)
& ~ c2_1(a629)
& c3_1(a629) )
| ~ c3_0 )
& ( ~ c4_0
| ( ndr1_0
& c1_1(a631)
& ~ c3_1(a631) ) )
& ( ! [X39] :
( ndr1_0
=> ( ! [X40] :
( ndr1_1(X39)
=> ( c3_2(X39,X40)
| ~ c1_2(X39,X40)
| c5_2(X39,X40) ) )
| c2_1(X39)
| ( ndr1_1(X39)
& ~ c2_2(X39,a632)
& ~ c3_2(X39,a632) ) ) )
| c3_0
| ( ndr1_0
& ~ c3_1(a633)
& ! [X41] :
( ndr1_1(a633)
=> ( c1_2(a633,X41)
| ~ c3_2(a633,X41) ) )
& ~ c1_1(a633) ) )
& ( ( ndr1_0
& ~ c2_1(a634) )
| ! [X42] :
( ndr1_0
=> ( ( ndr1_1(X42)
& ~ c2_2(X42,a635) )
| ~ c5_1(X42)
| ! [X43] :
( ndr1_1(X42)
=> ( c2_2(X42,X43)
| ~ c1_2(X42,X43) ) ) ) )
| c1_0 )
& ( c3_0
| ~ c1_0
| c5_0 )
& ( ~ c5_0
| ~ c2_0
| ! [X44] :
( ndr1_0
=> ( ! [X45] :
( ndr1_1(X44)
=> ( c1_2(X44,X45)
| ~ c2_2(X44,X45) ) )
| ! [X46] :
( ndr1_1(X44)
=> ( c4_2(X44,X46)
| ~ c2_2(X44,X46) ) )
| ( ndr1_1(X44)
& c2_2(X44,a636)
& ~ c3_2(X44,a636) ) ) ) )
& c5_0
& ( c3_0
| ( ndr1_0
& ~ c3_1(a637)
& ~ c2_1(a637)
& ndr1_1(a637)
& c1_2(a637,a638)
& ~ c4_2(a637,a638) ) )
& ( ! [X47] :
( ndr1_0
=> ( ( ndr1_1(X47)
& ~ c1_2(X47,a639)
& ~ c2_2(X47,a639)
& c5_2(X47,a639) )
| ~ c5_1(X47)
| c3_1(X47) ) )
| c4_0 ) ) ).

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