## TPTP Problem File: SYN522+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN522+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=051
% 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-5-1-20-3-2-051.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, 0.00 v2.7.0, 0.17 v2.6.0, 0.00 v2.4.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  226 (   0 equ)
%            Maximal formula atoms :  226 ( 226 avg)
%            Number of connectives :  304 (  79   ~;  79   |; 118   &)
%                                         (   0 <=>;  28  =>;   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    :   37 (  37 usr;  37 con; 0-0 aty)
%            Number of variables   :   28 (  28   !;   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
=> ( ! [V] :
( ndr1_1(U)
=> ( c2_2(U,V)
| ~ c5_2(U,V)
| c3_2(U,V) ) )
| ( ndr1_1(U)
& c4_2(U,a104)
& c3_2(U,a104)
& ~ c1_2(U,a104) )
| ( ndr1_1(U)
& ~ c4_2(U,a105)
& ~ c3_2(U,a105)
& c2_2(U,a105) ) ) )
| ( ndr1_0
& ~ c5_1(a106)
& ndr1_1(a106)
& c1_2(a106,a107)
& c4_2(a106,a107)
& c2_2(a106,a107) )
| ( ndr1_0
& c3_1(a108)
& ~ c4_1(a108)
& ! [W] :
( ndr1_1(a108)
=> ( c4_2(a108,W)
| c2_2(a108,W)
| c1_2(a108,W) ) ) ) )
& ( ( ndr1_0
& ~ c1_1(a109)
& c3_1(a109) )
| ( ndr1_0
& ~ c4_1(a110)
& ~ c3_1(a110)
& ! [X] :
( ndr1_1(a110)
=> ( c1_2(a110,X)
| c5_2(a110,X) ) ) )
| ! [Y] :
( ndr1_0
=> ( ~ c5_1(Y)
| ! [Z] :
( ndr1_1(Y)
=> ( ~ c5_2(Y,Z)
| ~ c1_2(Y,Z)
| ~ c3_2(Y,Z) ) )
| ~ c3_1(Y) ) ) )
& ( ! [X1] :
( ndr1_0
=> ( ( ndr1_1(X1)
& c5_2(X1,a111)
& ~ c3_2(X1,a111)
& c2_2(X1,a111) )
| ! [X2] :
( ndr1_1(X1)
=> ( c1_2(X1,X2)
| c4_2(X1,X2)
| ~ c2_2(X1,X2) ) )
| ~ c4_1(X1) ) )
| ~ c1_0
| ( ndr1_0
& ! [X3] :
( ndr1_1(a112)
=> ( c5_2(a112,X3)
| c1_2(a112,X3) ) )
& ! [X4] :
( ndr1_1(a112)
=> ( c1_2(a112,X4)
| c5_2(a112,X4) ) )
& ndr1_1(a112)
& c2_2(a112,a113)
& ~ c5_2(a112,a113)
& ~ c3_2(a112,a113) ) )
& ( ~ c1_0
| c5_0
| ! [X5] :
( ndr1_0
=> ( ~ c3_1(X5)
| ~ c4_1(X5)
| ! [X6] :
( ndr1_1(X5)
=> ( c4_2(X5,X6)
| c5_2(X5,X6) ) ) ) ) )
& ( c2_0
| ( ndr1_0
& ~ c1_1(a114)
& ! [X7] :
( ndr1_1(a114)
=> ( ~ c3_2(a114,X7)
| c5_2(a114,X7) ) )
& ! [X8] :
( ndr1_1(a114)
=> ( c1_2(a114,X8)
| c5_2(a114,X8)
| c4_2(a114,X8) ) ) ) )
& ( ~ c3_0
| ! [X9] :
( ndr1_0
=> ( ( ndr1_1(X9)
& c2_2(X9,a115)
& c5_2(X9,a115)
& ~ c4_2(X9,a115) )
| ( ndr1_1(X9)
& c5_2(X9,a116)
& ~ c2_2(X9,a116)
& c1_2(X9,a116) )
| ( ndr1_1(X9)
& c4_2(X9,a117)
& ~ c5_2(X9,a117)
& c3_2(X9,a117) ) ) )
| ! [X10] :
( ndr1_0
=> ( c2_1(X10)
| ~ c4_1(X10) ) ) )
& ( ~ c5_0
| c3_0
| ~ c1_0 )
& ( ( ndr1_0
& c5_1(a118)
& c1_1(a118)
& ~ c2_1(a118) )
| c1_0 )
& ( ~ c4_0
| c3_0
| ! [X11] :
( ndr1_0
=> ( ( ndr1_1(X11)
& ~ c3_2(X11,a119)
& c4_2(X11,a119)
& ~ c2_2(X11,a119) )
| c4_1(X11)
| ( ndr1_1(X11)
& c2_2(X11,a120)
& c5_2(X11,a120)
& ~ c1_2(X11,a120) ) ) ) )
& ( ~ c1_0
| ( ndr1_0
& ndr1_1(a121)
& c3_2(a121,a122)
& ~ c2_2(a121,a122)
& ! [X12] :
( ndr1_1(a121)
=> ( c3_2(a121,X12)
| ~ c1_2(a121,X12)
| ~ c4_2(a121,X12) ) )
& ! [X13] :
( ndr1_1(a121)
=> ( ~ c5_2(a121,X13)
| ~ c1_2(a121,X13)
| c3_2(a121,X13) ) ) ) )
& ( c4_0
| ( ndr1_0
& ndr1_1(a123)
& c1_2(a123,a124)
& ~ c2_2(a123,a124)
& c5_1(a123)
& ~ c1_1(a123) ) )
& ( ( ndr1_0
& ndr1_1(a125)
& ~ c3_2(a125,a126)
& ~ c5_2(a125,a126)
& c1_2(a125,a126)
& ~ c4_1(a125)
& ndr1_1(a125)
& ~ c4_2(a125,a127)
& ~ c3_2(a125,a127)
& ~ c2_2(a125,a127) )
| ( ndr1_0
& ndr1_1(a128)
& ~ c1_2(a128,a129)
& c4_2(a128,a129)
& c2_2(a128,a129)
& ~ c2_1(a128)
& c3_1(a128) )
| ( ndr1_0
& ! [X14] :
( ndr1_1(a130)
=> ( ~ c3_2(a130,X14)
| ~ c2_2(a130,X14)
| ~ c4_2(a130,X14) ) )
& ! [X15] :
( ndr1_1(a130)
=> ( c5_2(a130,X15)
| c2_2(a130,X15) ) )
& ~ c1_1(a130) ) )
& ( ! [X16] :
( ndr1_0
=> ( ( ndr1_1(X16)
& ~ c4_2(X16,a131)
& ~ c1_2(X16,a131) )
| c5_1(X16)
| ( ndr1_1(X16)
& c2_2(X16,a132)
& c5_2(X16,a132)
& c1_2(X16,a132) ) ) )
| c2_0
| ( ndr1_0
& ~ c5_1(a133)
& ~ c2_1(a133) ) )
& ( ( ndr1_0
& ! [X17] :
( ndr1_1(a134)
=> ( c4_2(a134,X17)
| ~ c5_2(a134,X17)
| c1_2(a134,X17) ) )
& ! [X18] :
( ndr1_1(a134)
=> ( ~ c2_2(a134,X18)
| ~ c3_2(a134,X18)
| ~ c1_2(a134,X18) ) )
& ~ c2_1(a134) )
| ( ndr1_0
& ~ c3_1(a135)
& ndr1_1(a135)
& ~ c3_2(a135,a136)
& ~ c1_2(a135,a136)
& c1_1(a135) )
| c4_0 )
& ( ( ndr1_0
& c4_1(a137)
& c1_1(a137) )
| ~ c3_0
| ~ c4_0 )
& ( ~ c2_0
| ! [X19] :
( ndr1_0
=> ( ( ndr1_1(X19)
& c5_2(X19,a138)
& ~ c4_2(X19,a138) )
| c5_1(X19)
| ! [X20] :
( ndr1_1(X19)
=> ( c5_2(X19,X20)
| c2_2(X19,X20)
| c3_2(X19,X20) ) ) ) )
| ~ c4_0 )
& c4_0
& ( ! [X21] :
( ndr1_0
=> ( ! [X22] :
( ndr1_1(X21)
=> ( c1_2(X21,X22)
| c2_2(X21,X22)
| c3_2(X21,X22) ) )
| ~ c4_1(X21)
| ~ c5_1(X21) ) )
| c3_0
| ( ndr1_0
& ndr1_1(a139)
& c2_2(a139,a140)
& c1_2(a139,a140)
& ~ c4_2(a139,a140)
& ~ c5_1(a139) ) ) ) ).

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