## TPTP Problem File: SYN434+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN434+1 : TPTP v8.1.0. Released v2.1.0.
% Domain   : Syntactic (Translated)
% Problem  : ALC, N=4, R=1, L=40, K=3, D=1, P=0, Index=037
% 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-4-1-40-3-1-037.dfg [Wei97]

% Status   : CounterSatisfiable
% Rating   : 0.00 v5.5.0, 0.40 v5.3.0, 0.50 v5.0.0, 0.33 v4.1.0, 0.50 v4.0.1, 0.33 v3.7.0, 0.00 v3.5.0, 0.25 v3.4.0, 0.33 v3.3.0, 0.17 v3.2.0, 0.25 v3.1.0, 0.50 v2.6.0, 0.25 v2.5.0, 0.33 v2.2.1, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  564 (   0 equ)
%            Maximal formula atoms :  564 ( 564 avg)
%            Number of connectives :  782 ( 219   ~; 252   |; 251   &)
%                                         (   0 <=>;  60  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  101 ( 101 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   58 (  58 usr;  54 prp; 0-1 aty)
%            Number of functors    :   53 (  53 usr;  53 con; 0-0 aty)
%            Number of variables   :   60 (  60   !;   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,
~ ( ( ~ hskp0
| ( ndr1_0
& ~ c1_1(a223)
& ~ c2_1(a223)
& ~ c3_1(a223) ) )
& ( ~ hskp1
| ( ndr1_0
& c1_1(a226)
& c3_1(a226)
& ~ c2_1(a226) ) )
& ( ~ hskp2
| ( ndr1_0
& ~ c3_1(a227)
& c1_1(a227)
& ~ c0_1(a227) ) )
& ( ~ hskp3
| ( ndr1_0
& c1_1(a228)
& ~ c3_1(a228)
& ~ c0_1(a228) ) )
& ( ~ hskp4
| ( ndr1_0
& ~ c0_1(a229)
& c2_1(a229)
& ~ c1_1(a229) ) )
& ( ~ hskp5
| ( ndr1_0
& c1_1(a230)
& c3_1(a230)
& ~ c0_1(a230) ) )
& ( ~ hskp6
| ( ndr1_0
& c2_1(a233)
& ~ c1_1(a233)
& ~ c0_1(a233) ) )
& ( ~ hskp7
| ( ndr1_0
& ~ c3_1(a234)
& c0_1(a234)
& ~ c1_1(a234) ) )
& ( ~ hskp8
| ( ndr1_0
& c2_1(a238)
& c0_1(a238)
& ~ c3_1(a238) ) )
& ( ~ hskp9
| ( ndr1_0
& ~ c2_1(a239)
& ~ c1_1(a239)
& ~ c3_1(a239) ) )
& ( ~ hskp10
| ( ndr1_0
& c1_1(a240)
& c0_1(a240)
& ~ c3_1(a240) ) )
& ( ~ hskp11
| ( ndr1_0
& c0_1(a243)
& c1_1(a243)
& ~ c2_1(a243) ) )
& ( ~ hskp12
| ( ndr1_0
& ~ c0_1(a245)
& c3_1(a245)
& ~ c1_1(a245) ) )
& ( ~ hskp13
| ( ndr1_0
& c1_1(a246)
& ~ c3_1(a246)
& ~ c2_1(a246) ) )
& ( ~ hskp14
| ( ndr1_0
& c2_1(a249)
& c0_1(a249)
& ~ c1_1(a249) ) )
& ( ~ hskp15
| ( ndr1_0
& ~ c3_1(a252)
& c0_1(a252)
& ~ c2_1(a252) ) )
& ( ~ hskp16
| ( ndr1_0
& c3_1(a253)
& ~ c2_1(a253)
& ~ c1_1(a253) ) )
& ( ~ hskp17
| ( ndr1_0
& c2_1(a255)
& c3_1(a255)
& ~ c1_1(a255) ) )
& ( ~ hskp18
| ( ndr1_0
& c2_1(a263)
& c1_1(a263)
& ~ c3_1(a263) ) )
& ( ~ hskp19
| ( ndr1_0
& c0_1(a264)
& ~ c2_1(a264)
& ~ c1_1(a264) ) )
& ( ~ hskp20
| ( ndr1_0
& ~ c1_1(a268)
& ~ c3_1(a268)
& ~ c2_1(a268) ) )
& ( ~ hskp21
| ( ndr1_0
& ~ c0_1(a271)
& ~ c1_1(a271)
& ~ c2_1(a271) ) )
& ( ~ hskp22
| ( ndr1_0
& ~ c3_1(a277)
& c1_1(a277)
& ~ c2_1(a277) ) )
& ( ~ hskp23
| ( ndr1_0
& ~ c1_1(a278)
& c2_1(a278)
& ~ c0_1(a278) ) )
& ( ~ hskp24
| ( ndr1_0
& ~ c2_1(a281)
& c0_1(a281)
& ~ c1_1(a281) ) )
& ( ~ hskp25
| ( ndr1_0
& ~ c2_1(a224)
& ~ c1_1(a224)
& c0_1(a224) ) )
& ( ~ hskp26
| ( ndr1_0
& ~ c0_1(a225)
& c3_1(a225)
& c2_1(a225) ) )
& ( ~ hskp27
| ( ndr1_0
& c1_1(a231)
& c2_1(a231)
& c0_1(a231) ) )
& ( ~ hskp28
| ( ndr1_0
& ~ c3_1(a232)
& c0_1(a232)
& c2_1(a232) ) )
& ( ~ hskp29
| ( ndr1_0
& ~ c2_1(a235)
& ~ c3_1(a235)
& c0_1(a235) ) )
& ( ~ hskp30
| ( ndr1_0
& ~ c2_1(a236)
& c0_1(a236)
& c1_1(a236) ) )
& ( ~ hskp31
| ( ndr1_0
& ~ c0_1(a237)
& c2_1(a237)
& c3_1(a237) ) )
& ( ~ hskp32
| ( ndr1_0
& ~ c0_1(a242)
& ~ c2_1(a242)
& c1_1(a242) ) )
& ( ~ hskp33
| ( ndr1_0
& ~ c3_1(a244)
& ~ c1_1(a244)
& c0_1(a244) ) )
& ( ~ hskp34
| ( ndr1_0
& c3_1(a247)
& c0_1(a247)
& c1_1(a247) ) )
& ( ~ hskp35
| ( ndr1_0
& ~ c1_1(a248)
& ~ c3_1(a248)
& c0_1(a248) ) )
& ( ~ hskp36
| ( ndr1_0
& ~ c3_1(a250)
& ~ c2_1(a250)
& c1_1(a250) ) )
& ( ~ hskp37
| ( ndr1_0
& ~ c1_1(a251)
& ~ c0_1(a251)
& c3_1(a251) ) )
& ( ~ hskp38
| ( ndr1_0
& c2_1(a254)
& ~ c0_1(a254)
& c3_1(a254) ) )
& ( ~ hskp39
| ( ndr1_0
& c3_1(a256)
& c2_1(a256)
& c1_1(a256) ) )
& ( ~ hskp40
| ( ndr1_0
& ~ c3_1(a257)
& ~ c1_1(a257)
& c2_1(a257) ) )
& ( ~ hskp41
| ( ndr1_0
& c2_1(a258)
& c0_1(a258)
& c1_1(a258) ) )
& ( ~ hskp42
| ( ndr1_0
& ~ c2_1(a260)
& ~ c0_1(a260)
& c3_1(a260) ) )
& ( ~ hskp43
| ( ndr1_0
& c2_1(a261)
& c1_1(a261)
& c0_1(a261) ) )
& ( ~ hskp44
| ( ndr1_0
& ~ c0_1(a262)
& ~ c1_1(a262)
& c3_1(a262) ) )
& ( ~ hskp45
| ( ndr1_0
& c0_1(a265)
& ~ c3_1(a265)
& c1_1(a265) ) )
& ( ~ hskp46
| ( ndr1_0
& c0_1(a266)
& c1_1(a266)
& c3_1(a266) ) )
& ( ~ hskp47
| ( ndr1_0
& c1_1(a269)
& c3_1(a269)
& c0_1(a269) ) )
& ( ~ hskp48
| ( ndr1_0
& ~ c0_1(a270)
& ~ c3_1(a270)
& c1_1(a270) ) )
& ( ~ hskp49
| ( ndr1_0
& ~ c2_1(a272)
& ~ c1_1(a272)
& c3_1(a272) ) )
& ( ~ hskp50
| ( ndr1_0
& c3_1(a273)
& c1_1(a273)
& c2_1(a273) ) )
& ( ~ hskp51
| ( ndr1_0
& ~ c1_1(a276)
& ~ c2_1(a276)
& c3_1(a276) ) )
& ( ~ hskp52
| ( ndr1_0
& c0_1(a279)
& c3_1(a279)
& c2_1(a279) ) )
& ( hskp0
| hskp25
| hskp26 )
& ( ! [U] :
( ndr1_0
=> ( c1_1(U)
| c0_1(U)
| ~ c2_1(U) ) )
| ! [V] :
( ndr1_0
=> ( c0_1(V)
| c3_1(V)
| ~ c2_1(V) ) )
| hskp1 )
& ( hskp2
| hskp3
| hskp4 )
& ( ! [W] :
( ndr1_0
=> ( ~ c0_1(W)
| ~ c1_1(W)
| c2_1(W) ) )
| hskp5
| ! [X] :
( ndr1_0
=> ( ~ c2_1(X)
| c3_1(X)
| ~ c1_1(X) ) ) )
& ( ! [Y] :
( ndr1_0
=> ( ~ c0_1(Y)
| c3_1(Y)
| ~ c2_1(Y) ) )
| hskp27
| hskp28 )
& ( ! [Z] :
( ndr1_0
=> ( ~ c2_1(Z)
| c3_1(Z)
| c1_1(Z) ) )
| ! [X1] :
( ndr1_0
=> ( ~ c3_1(X1)
| c0_1(X1)
| c2_1(X1) ) )
| ! [X2] :
( ndr1_0
=> ( c3_1(X2)
| c0_1(X2)
| c2_1(X2) ) ) )
& ( ! [X3] :
( ndr1_0
=> ( c0_1(X3)
| ~ c2_1(X3)
| c1_1(X3) ) )
| hskp6
| ! [X4] :
( ndr1_0
=> ( c3_1(X4)
| ~ c2_1(X4)
| ~ c1_1(X4) ) ) )
& ( ! [X5] :
( ndr1_0
=> ( c1_1(X5)
| c3_1(X5)
| c2_1(X5) ) )
| ! [X6] :
( ndr1_0
=> ( c3_1(X6)
| ~ c0_1(X6)
| ~ c2_1(X6) ) )
| ! [X7] :
( ndr1_0
=> ( c0_1(X7)
| c2_1(X7)
| ~ c1_1(X7) ) ) )
& ( ! [X8] :
( ndr1_0
=> ( ~ c1_1(X8)
| ~ c0_1(X8)
| ~ c2_1(X8) ) )
| ! [X9] :
( ndr1_0
=> ( c0_1(X9)
| c1_1(X9)
| ~ c3_1(X9) ) )
| hskp7 )
& ( ! [X10] :
( ndr1_0
=> ( c1_1(X10)
| c2_1(X10)
| c0_1(X10) ) )
| ! [X11] :
( ndr1_0
=> ( ~ c1_1(X11)
| ~ c3_1(X11)
| c2_1(X11) ) )
| hskp29 )
& ( hskp30
| ! [X12] :
( ndr1_0
=> ( ~ c1_1(X12)
| ~ c2_1(X12)
| c3_1(X12) ) ) )
& ( hskp31
| ! [X13] :
( ndr1_0
=> ( c1_1(X13)
| c0_1(X13)
| ~ c2_1(X13) ) )
| hskp8 )
& ( ! [X14] :
( ndr1_0
=> ( ~ c2_1(X14)
| c3_1(X14)
| ~ c0_1(X14) ) )
| ! [X15] :
( ndr1_0
=> ( c1_1(X15)
| ~ c0_1(X15)
| c2_1(X15) ) )
| hskp9 )
& ( hskp10
| ! [X16] :
( ndr1_0
=> ( c3_1(X16)
| c1_1(X16)
| c2_1(X16) ) )
| hskp8 )
& ( hskp32
| ! [X17] :
( ndr1_0
=> ( ~ c3_1(X17)
| ~ c1_1(X17)
| ~ c2_1(X17) ) )
| hskp11 )
& ( ! [X18] :
( ndr1_0
=> ( ~ c1_1(X18)
| ~ c0_1(X18)
| ~ c2_1(X18) ) )
| ! [X19] :
( ndr1_0
=> ( c0_1(X19)
| ~ c1_1(X19)
| ~ c2_1(X19) ) )
| ! [X20] :
( ndr1_0
=> ( ~ c3_1(X20)
| c0_1(X20)
| c1_1(X20) ) ) )
& ( hskp33
| ! [X21] :
( ndr1_0
=> ( c3_1(X21)
| ~ c2_1(X21)
| c1_1(X21) ) )
| hskp12 )
& ( ! [X22] :
( ndr1_0
=> ( c1_1(X22)
| ~ c2_1(X22)
| ~ c3_1(X22) ) )
| hskp13
| hskp34 )
& ( ! [X23] :
( ndr1_0
=> ( ~ c2_1(X23)
| c3_1(X23)
| c1_1(X23) ) )
| ! [X24] :
( ndr1_0
=> ( c0_1(X24)
| c1_1(X24)
| ~ c3_1(X24) ) )
| hskp35 )
& ( ! [X25] :
( ndr1_0
=> ( ~ c0_1(X25)
| c2_1(X25)
| ~ c1_1(X25) ) )
| ! [X26] :
( ndr1_0
=> ( c1_1(X26)
| c0_1(X26)
| ~ c3_1(X26) ) )
| hskp14 )
& ( ! [X27] :
( ndr1_0
=> ( c3_1(X27)
| ~ c0_1(X27)
| ~ c2_1(X27) ) )
| hskp36
| hskp37 )
& ( hskp15
| ! [X28] :
( ndr1_0
=> ( c1_1(X28)
| c3_1(X28)
| c2_1(X28) ) )
| hskp16 )
& ( hskp38
| ! [X29] :
( ndr1_0
=> ( ~ c3_1(X29)
| ~ c2_1(X29)
| ~ c1_1(X29) ) )
| ! [X30] :
( ndr1_0
=> ( ~ c0_1(X30)
| ~ c3_1(X30)
| ~ c1_1(X30) ) ) )
& ( ! [X31] :
( ndr1_0
=> ( c2_1(X31)
| c0_1(X31)
| ~ c1_1(X31) ) )
| ! [X32] :
( ndr1_0
=> ( c2_1(X32)
| ~ c3_1(X32)
| ~ c0_1(X32) ) )
| ! [X33] :
( ndr1_0
=> ( c3_1(X33)
| ~ c1_1(X33)
| c0_1(X33) ) ) )
& ( hskp17
| hskp39
| hskp40 )
& ( hskp41
| hskp2
| hskp42 )
& ( hskp43
| hskp44
| ! [X34] :
( ndr1_0
=> ( c0_1(X34)
| c1_1(X34)
| ~ c3_1(X34) ) ) )
& ( hskp18
| ! [X35] :
( ndr1_0
=> ( c2_1(X35)
| c3_1(X35)
| ~ c1_1(X35) ) )
| ! [X36] :
( ndr1_0
=> ( ~ c3_1(X36)
| c0_1(X36)
| c2_1(X36) ) ) )
& ( ! [X37] :
( ndr1_0
=> ( c3_1(X37)
| ~ c1_1(X37)
| ~ c0_1(X37) ) )
| ! [X38] :
( ndr1_0
=> ( ~ c3_1(X38)
| ~ c1_1(X38)
| ~ c2_1(X38) ) )
| ! [X39] :
( ndr1_0
=> ( ~ c0_1(X39)
| ~ c3_1(X39)
| c1_1(X39) ) ) )
& ( hskp19
| hskp45
| hskp46 )
& ( ! [X40] :
( ndr1_0
=> ( c3_1(X40)
| ~ c1_1(X40)
| c2_1(X40) ) )
| hskp16
| ! [X41] :
( ndr1_0
=> ( ~ c0_1(X41)
| ~ c1_1(X41)
| c3_1(X41) ) ) )
& ( ! [X42] :
( ndr1_0
=> ( c0_1(X42)
| ~ c1_1(X42)
| c2_1(X42) ) )
| ! [X43] :
( ndr1_0
=> ( ~ c2_1(X43)
| c1_1(X43)
| c0_1(X43) ) )
| ! [X44] :
( ndr1_0
=> ( c3_1(X44)
| c0_1(X44)
| c2_1(X44) ) ) )
& ( hskp20
| hskp47
| hskp48 )
& ( hskp21
| ! [X45] :
( ndr1_0
=> ( c1_1(X45)
| ~ c2_1(X45)
| ~ c0_1(X45) ) )
| ! [X46] :
( ndr1_0
=> ( c3_1(X46)
| c2_1(X46)
| c1_1(X46) ) ) )
& ( hskp49
| hskp50
| hskp13 )
& ( hskp40
| ! [X47] :
( ndr1_0
=> ( c1_1(X47)
| c3_1(X47)
| ~ c0_1(X47) ) )
| ! [X48] :
( ndr1_0
=> ( ~ c3_1(X48)
| c2_1(X48)
| ~ c0_1(X48) ) ) )
& ( ! [X49] :
( ndr1_0
=> ( ~ c1_1(X49)
| ~ c3_1(X49)
| c2_1(X49) ) )
| hskp51
| ! [X50] :
( ndr1_0
=> ( c1_1(X50)
| c0_1(X50)
| ~ c3_1(X50) ) ) )
& ( ! [X51] :
( ndr1_0
=> ( ~ c2_1(X51)
| c1_1(X51)
| ~ c0_1(X51) ) )
| ! [X52] :
( ndr1_0
=> ( c3_1(X52)
| ~ c2_1(X52)
| ~ c0_1(X52) ) )
| hskp22 )
& ( hskp23
| hskp52
| hskp30 )
& ( ! [X53] :
( ndr1_0
=> ( ~ c2_1(X53)
| ~ c3_1(X53)
| c0_1(X53) ) )
| hskp24
| ! [X54] :
( ndr1_0
=> ( c2_1(X54)
| ~ c0_1(X54)
| c1_1(X54) ) ) ) ) ).

%--------------------------------------------------------------------------
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