## TPTP Problem File: SYN537+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN537+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=014
% 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-5-1-40-3-2-014.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v4.1.0, 0.17 v4.0.1, 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       :  293 (   0 equ)
%            Maximal formula atoms :  293 ( 293 avg)
%            Number of connectives :  413 ( 121   ~; 114   |; 140   &)
%                                         (   0 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   41 (  41 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   17 (  17 usr;   6 prp; 0-2 aty)
%            Number of functors    :   41 (  41 usr;  41 con; 0-0 aty)
%            Number of variables   :   38 (  38   !;   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
=> ( c1_1(U)
| ( ndr1_1(U)
& c2_2(U,a640)
& ~ c5_2(U,a640)
& c3_2(U,a640) )
| ! [V] :
( ndr1_1(U)
=> ( ~ c2_2(U,V)
| ~ c1_2(U,V)
| c3_2(U,V) ) ) ) )
| ! [W] :
( ndr1_0
=> ( ~ c1_1(W)
| ~ c5_1(W)
| c3_1(W) ) )
| ~ c5_0 )
& ( ~ c3_0
| ~ c4_0
| ( ndr1_0
& ndr1_1(a641)
& ~ c1_2(a641,a642)
& ~ c3_2(a641,a642)
& ! [X] :
( ndr1_1(a641)
=> ( ~ c4_2(a641,X)
| ~ c5_2(a641,X)
| c3_2(a641,X) ) ) ) )
& ( ~ c4_0
| ~ c1_0
| ~ c2_0 )
& ( ( ndr1_0
& ndr1_1(a643)
& ~ c2_2(a643,a644)
& c5_2(a643,a644)
& ~ c1_1(a643)
& c4_1(a643) )
| ( ndr1_0
& ~ c1_1(a645)
& ndr1_1(a645)
& c3_2(a645,a646)
& c2_2(a645,a646)
& ~ c5_2(a645,a646)
& ~ c2_1(a645) )
| ~ c3_0 )
& ( ! [Y] :
( ndr1_0
=> ( ~ c3_1(Y)
| ~ c1_1(Y)
| ~ c4_1(Y) ) )
| ~ c2_0
| c1_0 )
& ( ! [Z] :
( ndr1_0
=> ( ! [X1] :
( ndr1_1(Z)
=> ( ~ c4_2(Z,X1)
| ~ c1_2(Z,X1)
| ~ c3_2(Z,X1) ) )
| c1_1(Z)
| c2_1(Z) ) )
| ~ c3_0
| c1_0 )
& ( c5_0
| ~ c4_0 )
& ( c3_0
| c5_0
| ! [X2] :
( ndr1_0
=> ( ( ndr1_1(X2)
& c5_2(X2,a647)
& ~ c2_2(X2,a647)
& ~ c1_2(X2,a647) )
| c1_1(X2)
| ~ c2_1(X2) ) ) )
& ( c4_0
| ! [X3] :
( ndr1_0
=> ( ! [X4] :
( ndr1_1(X3)
=> ( ~ c1_2(X3,X4)
| c4_2(X3,X4) ) )
| c1_1(X3)
| ! [X5] :
( ndr1_1(X3)
=> ( c3_2(X3,X5)
| ~ c1_2(X3,X5)
| c5_2(X3,X5) ) ) ) )
| ( ndr1_0
& ~ c3_1(a648)
& ! [X6] :
( ndr1_1(a648)
=> ( ~ c1_2(a648,X6)
| ~ c3_2(a648,X6) ) )
& ! [X7] :
( ndr1_1(a648)
=> ( ~ c5_2(a648,X7)
| c4_2(a648,X7)
| ~ c2_2(a648,X7) ) ) ) )
& ( ! [X8] :
( ndr1_0
=> ( ~ c4_1(X8)
| ( ndr1_1(X8)
& c4_2(X8,a649)
& c1_2(X8,a649)
& ~ c5_2(X8,a649) )
| ( ndr1_1(X8)
& c5_2(X8,a650)
& ~ c3_2(X8,a650)
& c4_2(X8,a650) ) ) )
| c3_0 )
& ( ( ndr1_0
& ndr1_1(a651)
& ~ c5_2(a651,a652)
& c1_2(a651,a652)
& ~ c2_2(a651,a652)
& ! [X9] :
( ndr1_1(a651)
=> ( ~ c1_2(a651,X9)
| c5_2(a651,X9)
| c3_2(a651,X9) ) ) )
| ~ c5_0
| ~ c1_0 )
& ( ! [X10] :
( ndr1_0
=> ( c5_1(X10)
| c1_1(X10) ) )
| ( ndr1_0
& ! [X11] :
( ndr1_1(a653)
=> ( c3_2(a653,X11)
| c1_2(a653,X11) ) )
& ~ c4_1(a653)
& ~ c1_1(a653) )
| ~ c4_0 )
& ( ( ndr1_0
& ndr1_1(a654)
& c5_2(a654,a655)
& ~ c4_2(a654,a655)
& c3_2(a654,a655)
& ~ c1_1(a654)
& ~ c5_1(a654) )
| ! [X12] :
( ndr1_0
=> ! [X13] :
( ndr1_1(X12)
=> ( c5_2(X12,X13)
| ~ c4_2(X12,X13)
| c1_2(X12,X13) ) ) )
| ~ c2_0 )
& ( ~ c1_0
| ! [X14] :
( ndr1_0
=> ( ~ c3_1(X14)
| ! [X15] :
( ndr1_1(X14)
=> ( ~ c4_2(X14,X15)
| ~ c1_2(X14,X15)
| c3_2(X14,X15) ) ) ) )
| ~ c4_0 )
& ( c5_0
| ! [X16] :
( ndr1_0
=> ( c5_1(X16)
| ~ c2_1(X16)
| ( ndr1_1(X16)
& ~ c2_2(X16,a656)
& ~ c1_2(X16,a656)
& ~ c3_2(X16,a656) ) ) ) )
& ( ! [X17] :
( ndr1_0
=> ( c2_1(X17)
| ( ndr1_1(X17)
& ~ c4_2(X17,a657)
& ~ c1_2(X17,a657)
& ~ c5_2(X17,a657) ) ) )
| ! [X18] :
( ndr1_0
=> ( c4_1(X18)
| ( ndr1_1(X18)
& c4_2(X18,a658)
& c5_2(X18,a658) )
| ! [X19] :
( ndr1_1(X18)
=> ( c5_2(X18,X19)
| ~ c2_2(X18,X19)
| c1_2(X18,X19) ) ) ) )
| c3_0 )
& ( ( ndr1_0
& ! [X20] :
( ndr1_1(a659)
=> ( c5_2(a659,X20)
| ~ c1_2(a659,X20)
| ~ c3_2(a659,X20) ) )
& ~ c1_1(a659)
& c2_1(a659) )
| c5_0 )
& ( ( ndr1_0
& ~ c4_1(a660)
& ndr1_1(a660)
& ~ c4_2(a660,a661)
& c2_2(a660,a661)
& ~ c3_2(a660,a661)
& ndr1_1(a660)
& ~ c4_2(a660,a662)
& ~ c5_2(a660,a662)
& ~ c2_2(a660,a662) )
| c4_0
| c2_0 )
& ( c5_0
| ( ndr1_0
& ! [X21] :
( ndr1_1(a663)
=> ( c4_2(a663,X21)
| c1_2(a663,X21)
| c2_2(a663,X21) ) )
& c4_1(a663)
& ndr1_1(a663)
& ~ c5_2(a663,a664)
& c1_2(a663,a664) )
| ~ c3_0 )
& ( ( ndr1_0
& ~ c5_1(a665)
& c3_1(a665)
& ! [X22] :
( ndr1_1(a665)
=> ( c5_2(a665,X22)
| ~ c1_2(a665,X22) ) ) )
| c2_0
| c4_0 )
& ( c2_0
| ( ndr1_0
& ~ c1_1(a666)
& c3_1(a666)
& ! [X23] :
( ndr1_1(a666)
=> ( c3_2(a666,X23)
| ~ c5_2(a666,X23) ) ) )
| ( ndr1_0
& ~ c4_1(a667)
& ndr1_1(a667)
& ~ c4_2(a667,a668)
& ~ c1_2(a667,a668) ) )
& ( ( ndr1_0
& ! [X24] :
( ndr1_1(a669)
=> ( c3_2(a669,X24)
| ~ c4_2(a669,X24)
| c2_2(a669,X24) ) )
& ~ c1_1(a669)
& ndr1_1(a669)
& ~ c5_2(a669,a670)
& c1_2(a669,a670)
& ~ c2_2(a669,a670) )
| ~ c5_0 )
& ~ c3_0
& ( c5_0
| c1_0
| ( ndr1_0
& ! [X25] :
( ndr1_1(a671)
=> ( c5_2(a671,X25)
| ~ c2_2(a671,X25) ) )
& ~ c5_1(a671)
& ! [X26] :
( ndr1_1(a671)
=> ( ~ c4_2(a671,X26)
| c5_2(a671,X26)
| ~ c1_2(a671,X26) ) ) ) )
& ( c4_0
| ( ndr1_0
& ~ c5_1(a672)
& ! [X27] :
( ndr1_1(a672)
=> ( c1_2(a672,X27)
| c4_2(a672,X27)
| ~ c5_2(a672,X27) ) )
& ~ c1_1(a672) )
| ! [X28] :
( ndr1_0
=> ( c2_1(X28)
| ( ndr1_1(X28)
& ~ c5_2(X28,a673)
& ~ c4_2(X28,a673)
& ~ c1_2(X28,a673) )
| ~ c3_1(X28) ) ) )
& ( ~ c2_0
| ( ndr1_0
& c4_1(a674)
& c2_1(a674) ) )
& c1_0
& ( ( ndr1_0
& c3_1(a675)
& c5_1(a675) )
| ! [X29] :
( ndr1_0
=> ( c5_1(X29)
| ! [X30] :
( ndr1_1(X29)
=> ( ~ c2_2(X29,X30)
| c1_2(X29,X30)
| ~ c4_2(X29,X30) ) )
| ~ c1_1(X29) ) )
| ~ c5_0 )
& ( ~ c2_0
| ~ c5_0
| ( ndr1_0
& ndr1_1(a676)
& ~ c4_2(a676,a677)
& ~ c2_2(a676,a677)
& ~ c3_2(a676,a677)
& c3_1(a676)
& c4_1(a676) ) )
& ( ( ndr1_0
& ~ c2_1(a678)
& ~ c4_1(a678) )
| ( ndr1_0
& ~ c4_1(a679)
& ! [X31] :
( ndr1_1(a679)
=> ( c1_2(a679,X31)
| c5_2(a679,X31)
| c3_2(a679,X31) ) )
& ~ c5_1(a679) )
| ( ndr1_0
& ! [X32] :
( ndr1_1(a680)
=> ( ~ c1_2(a680,X32)
| c2_2(a680,X32) ) )
& ~ c3_1(a680) ) ) ) ).

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