## TPTP Problem File: SYN455+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN455+1 : TPTP v8.1.0. Released v2.1.0.
% Domain   : Syntactic (Translated)
% Problem  : ALC, N=4, R=1, L=60, K=3, D=1, P=0, Index=056
% 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-4-1-60-3-1-056.dfg [Wei97]

% Status   : Theorem
% Rating   : 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.33 v5.3.0, 0.27 v5.2.0, 0.00 v5.0.0, 0.25 v4.1.0, 0.44 v4.0.1, 0.42 v4.0.0, 0.45 v3.7.0, 0.67 v3.5.0, 0.38 v3.4.0, 0.25 v3.3.0, 0.22 v3.2.0, 0.33 v3.1.0, 0.67 v2.7.0, 0.33 v2.6.0, 0.00 v2.5.0, 0.33 v2.4.0, 0.33 v2.2.1, 0.50 v2.2.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  603 (   0 equ)
%            Maximal formula atoms :  603 ( 603 avg)
%            Number of connectives :  811 ( 209   ~; 329   |; 183   &)
%                                         (   0 <=>;  90  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   96 (  96 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   36 (  36 usr;  32 prp; 0-1 aty)
%            Number of functors    :   31 (  31 usr;  31 con; 0-0 aty)
%            Number of variables   :   90 (  90   !;   0   ?)
% SPC      : FOF_THM_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
& ~ c0_1(a901)
& ~ c1_1(a901)
& ~ c3_1(a901) ) )
& ( ~ hskp1
| ( ndr1_0
& c0_1(a902)
& c2_1(a902)
& ~ c1_1(a902) ) )
& ( ~ hskp2
| ( ndr1_0
& c0_1(a903)
& ~ c2_1(a903)
& ~ c3_1(a903) ) )
& ( ~ hskp3
| ( ndr1_0
& c0_1(a904)
& ~ c1_1(a904)
& ~ c2_1(a904) ) )
& ( ~ hskp4
| ( ndr1_0
& c3_1(a905)
& ~ c0_1(a905)
& ~ c2_1(a905) ) )
& ( ~ hskp5
| ( ndr1_0
& c0_1(a906)
& c2_1(a906)
& ~ c3_1(a906) ) )
& ( ~ hskp6
| ( ndr1_0
& c0_1(a907)
& c1_1(a907)
& ~ c2_1(a907) ) )
& ( ~ hskp7
| ( ndr1_0
& c1_1(a908)
& ~ c2_1(a908)
& ~ c3_1(a908) ) )
& ( ~ hskp8
| ( ndr1_0
& c1_1(a909)
& ~ c0_1(a909)
& ~ c3_1(a909) ) )
& ( ~ hskp9
| ( ndr1_0
& c2_1(a910)
& ~ c1_1(a910)
& ~ c3_1(a910) ) )
& ( ~ hskp10
| ( ndr1_0
& c1_1(a912)
& c2_1(a912)
& ~ c0_1(a912) ) )
& ( ~ hskp11
| ( ndr1_0
& c0_1(a914)
& c3_1(a914)
& ~ c2_1(a914) ) )
& ( ~ hskp12
| ( ndr1_0
& c1_1(a917)
& c3_1(a917)
& ~ c2_1(a917) ) )
& ( ~ hskp13
| ( ndr1_0
& c2_1(a921)
& ~ c0_1(a921)
& ~ c3_1(a921) ) )
& ( ~ hskp14
| ( ndr1_0
& c3_1(a923)
& ~ c0_1(a923)
& ~ c1_1(a923) ) )
& ( ~ hskp15
| ( ndr1_0
& c2_1(a924)
& ~ c0_1(a924)
& ~ c1_1(a924) ) )
& ( ~ hskp16
| ( ndr1_0
& c1_1(a926)
& c2_1(a926)
& ~ c3_1(a926) ) )
& ( ~ hskp17
| ( ndr1_0
& ~ c1_1(a936)
& ~ c2_1(a936)
& ~ c3_1(a936) ) )
& ( ~ hskp18
| ( ndr1_0
& c1_1(a937)
& ~ c0_1(a937)
& ~ c2_1(a937) ) )
& ( ~ hskp19
| ( ndr1_0
& c2_1(a938)
& c3_1(a938)
& ~ c0_1(a938) ) )
& ( ~ hskp20
| ( ndr1_0
& c0_1(a939)
& ~ c1_1(a939)
& ~ c3_1(a939) ) )
& ( ~ hskp21
| ( ndr1_0
& ~ c0_1(a946)
& ~ c2_1(a946)
& ~ c3_1(a946) ) )
& ( ~ hskp22
| ( ndr1_0
& c2_1(a949)
& c3_1(a949)
& ~ c1_1(a949) ) )
& ( ~ hskp23
| ( ndr1_0
& c1_1(a954)
& c3_1(a954)
& ~ c0_1(a954) ) )
& ( ~ hskp24
| ( ndr1_0
& ~ c0_1(a959)
& ~ c1_1(a959)
& ~ c2_1(a959) ) )
& ( ~ hskp25
| ( ndr1_0
& c0_1(a960)
& c3_1(a960)
& ~ c1_1(a960) ) )
& ( ~ hskp26
| ( ndr1_0
& c0_1(a979)
& c1_1(a979)
& ~ c3_1(a979) ) )
& ( ~ hskp27
| ( ndr1_0
& c1_1(a900)
& c2_1(a900)
& c3_1(a900) ) )
& ( ~ hskp28
| ( ndr1_0
& c0_1(a916)
& c1_1(a916)
& c3_1(a916) ) )
& ( ~ hskp29
| ( ndr1_0
& c0_1(a933)
& c2_1(a933)
& c3_1(a933) ) )
& ( ~ hskp30
| ( ndr1_0
& c0_1(a942)
& c1_1(a942)
& c2_1(a942) ) )
& ( ! [U] :
( ndr1_0
=> ( c0_1(U)
| c1_1(U)
| c2_1(U) ) )
| ! [V] :
( ndr1_0
=> ( c0_1(V)
| c2_1(V)
| ~ c3_1(V) ) )
| ! [W] :
( ndr1_0
=> ( ~ c0_1(W)
| ~ c1_1(W)
| ~ c3_1(W) ) ) )
& ( ! [X] :
( ndr1_0
=> ( c0_1(X)
| c1_1(X)
| c2_1(X) ) )
| ! [Y] :
( ndr1_0
=> ( c0_1(Y)
| c3_1(Y)
| ~ c2_1(Y) ) )
| ! [Z] :
( ndr1_0
=> ( c1_1(Z)
| c3_1(Z)
| ~ c0_1(Z) ) ) )
& ( ! [X1] :
( ndr1_0
=> ( c0_1(X1)
| c1_1(X1)
| c2_1(X1) ) )
| ! [X2] :
( ndr1_0
=> ( c0_1(X2)
| ~ c1_1(X2)
| ~ c3_1(X2) ) )
| hskp27 )
& ( ! [X3] :
( ndr1_0
=> ( c0_1(X3)
| c1_1(X3)
| c2_1(X3) ) )
| ! [X4] :
( ndr1_0
=> ( c2_1(X4)
| ~ c0_1(X4)
| ~ c3_1(X4) ) )
| hskp0 )
& ( ! [X5] :
( ndr1_0
=> ( c0_1(X5)
| c1_1(X5)
| c2_1(X5) ) )
| ! [X6] :
( ndr1_0
=> ( c3_1(X6)
| ~ c0_1(X6)
| ~ c2_1(X6) ) )
| ! [X7] :
( ndr1_0
=> ( c3_1(X7)
| ~ c1_1(X7)
| ~ c2_1(X7) ) ) )
& ( ! [X8] :
( ndr1_0
=> ( c0_1(X8)
| c1_1(X8)
| c2_1(X8) ) )
| hskp1
| hskp2 )
& ( ! [X9] :
( ndr1_0
=> ( c0_1(X9)
| c1_1(X9)
| c3_1(X9) ) )
| ! [X10] :
( ndr1_0
=> ( c0_1(X10)
| c2_1(X10)
| c3_1(X10) ) )
| ! [X11] :
( ndr1_0
=> ( c2_1(X11)
| c3_1(X11)
| ~ c0_1(X11) ) ) )
& ( ! [X12] :
( ndr1_0
=> ( c0_1(X12)
| c1_1(X12)
| c3_1(X12) ) )
| ! [X13] :
( ndr1_0
=> ( c0_1(X13)
| ~ c1_1(X13)
| ~ c2_1(X13) ) )
| ! [X14] :
( ndr1_0
=> ( c2_1(X14)
| c3_1(X14)
| ~ c0_1(X14) ) ) )
& ( ! [X15] :
( ndr1_0
=> ( c0_1(X15)
| c1_1(X15)
| ~ c2_1(X15) ) )
| hskp3
| hskp4 )
& ( ! [X16] :
( ndr1_0
=> ( c0_1(X16)
| c1_1(X16)
| ~ c3_1(X16) ) )
| ! [X17] :
( ndr1_0
=> ( ~ c1_1(X17)
| ~ c2_1(X17)
| ~ c3_1(X17) ) )
| hskp5 )
& ( ! [X18] :
( ndr1_0
=> ( c0_1(X18)
| c1_1(X18)
| ~ c3_1(X18) ) )
| hskp6
| hskp7 )
& ( ! [X19] :
( ndr1_0
=> ( c0_1(X19)
| c2_1(X19)
| c3_1(X19) ) )
| ! [X20] :
( ndr1_0
=> ( c0_1(X20)
| ~ c1_1(X20)
| ~ c3_1(X20) ) )
| hskp8 )
& ( ! [X21] :
( ndr1_0
=> ( c0_1(X21)
| c2_1(X21)
| c3_1(X21) ) )
| ! [X22] :
( ndr1_0
=> ( c1_1(X22)
| c2_1(X22)
| ~ c0_1(X22) ) )
| hskp9 )
& ( ! [X23] :
( ndr1_0
=> ( c0_1(X23)
| c2_1(X23)
| c3_1(X23) ) )
| hskp27
| hskp10 )
& ( ! [X24] :
( ndr1_0
=> ( c0_1(X24)
| c3_1(X24)
| ~ c1_1(X24) ) )
| hskp6
| hskp11 )
& ( ! [X25] :
( ndr1_0
=> ( c0_1(X25)
| c3_1(X25)
| ~ c2_1(X25) ) )
| ! [X26] :
( ndr1_0
=> ( c0_1(X26)
| ~ c2_1(X26)
| ~ c3_1(X26) ) )
| hskp5 )
& ( ! [X27] :
( ndr1_0
=> ( c0_1(X27)
| c3_1(X27)
| ~ c2_1(X27) ) )
| hskp28
| hskp12 )
& ( ! [X28] :
( ndr1_0
=> ( c0_1(X28)
| c3_1(X28)
| ~ c2_1(X28) ) )
| hskp2
| hskp0 )
& ( ! [X29] :
( ndr1_0
=> ( c0_1(X29)
| ~ c1_1(X29)
| ~ c2_1(X29) ) )
| ! [X30] :
( ndr1_0
=> ( c1_1(X30)
| c3_1(X30)
| ~ c2_1(X30) ) )
| ! [X31] :
( ndr1_0
=> ( c2_1(X31)
| ~ c1_1(X31)
| ~ c3_1(X31) ) ) )
& ( ! [X32] :
( ndr1_0
=> ( c0_1(X32)
| ~ c1_1(X32)
| ~ c2_1(X32) ) )
| hskp3
| hskp13 )
& ( ! [X33] :
( ndr1_0
=> ( c0_1(X33)
| ~ c1_1(X33)
| ~ c2_1(X33) ) )
| hskp7
| hskp14 )
& ( ! [X34] :
( ndr1_0
=> ( c0_1(X34)
| ~ c2_1(X34)
| ~ c3_1(X34) ) )
| ! [X35] :
( ndr1_0
=> ( ~ c1_1(X35)
| ~ c2_1(X35)
| ~ c3_1(X35) ) )
| hskp15 )
& ( ! [X36] :
( ndr1_0
=> ( c0_1(X36)
| ~ c2_1(X36)
| ~ c3_1(X36) ) )
| hskp28
| hskp16 )
& ( ! [X37] :
( ndr1_0
=> ( c0_1(X37)
| ~ c2_1(X37)
| ~ c3_1(X37) ) )
| hskp7
| hskp13 )
& ( ! [X38] :
( ndr1_0
=> ( c1_1(X38)
| c2_1(X38)
| c3_1(X38) ) )
| hskp11
| hskp27 )
& ( ! [X39] :
( ndr1_0
=> ( c1_1(X39)
| c2_1(X39)
| c3_1(X39) ) )
| hskp27
| hskp9 )
& ( ! [X40] :
( ndr1_0
=> ( c1_1(X40)
| c2_1(X40)
| ~ c0_1(X40) ) )
| ! [X41] :
( ndr1_0
=> ( c1_1(X41)
| ~ c0_1(X41)
| ~ c3_1(X41) ) )
| hskp29 )
& ( ! [X42] :
( ndr1_0
=> ( c1_1(X42)
| c2_1(X42)
| ~ c0_1(X42) ) )
| ! [X43] :
( ndr1_0
=> ( ~ c0_1(X43)
| ~ c1_1(X43)
| ~ c3_1(X43) ) )
| hskp15 )
& ( ! [X44] :
( ndr1_0
=> ( c1_1(X44)
| c2_1(X44)
| ~ c0_1(X44) ) )
| hskp12
| hskp17 )
& ( ! [X45] :
( ndr1_0
=> ( c1_1(X45)
| c2_1(X45)
| ~ c0_1(X45) ) )
| hskp18
| hskp19 )
& ( ! [X46] :
( ndr1_0
=> ( c1_1(X46)
| c2_1(X46)
| ~ c3_1(X46) ) )
| hskp20
| hskp18 )
& ( ! [X47] :
( ndr1_0
=> ( c1_1(X47)
| c3_1(X47)
| ~ c0_1(X47) ) )
| ! [X48] :
( ndr1_0
=> ( ~ c0_1(X48)
| ~ c2_1(X48)
| ~ c3_1(X48) ) )
| hskp9 )
& ( ! [X49] :
( ndr1_0
=> ( c1_1(X49)
| c3_1(X49)
| ~ c0_1(X49) ) )
| hskp30
| hskp7 )
& ( ! [X50] :
( ndr1_0
=> ( c1_1(X50)
| ~ c0_1(X50)
| ~ c2_1(X50) ) )
| ! [X51] :
( ndr1_0
=> ( c2_1(X51)
| c3_1(X51)
| ~ c1_1(X51) ) )
| hskp27 )
& ( ! [X52] :
( ndr1_0
=> ( c1_1(X52)
| ~ c0_1(X52)
| ~ c2_1(X52) ) )
| ! [X53] :
( ndr1_0
=> ( c2_1(X53)
| ~ c0_1(X53)
| ~ c1_1(X53) ) )
| hskp0 )
& ( ! [X54] :
( ndr1_0
=> ( c1_1(X54)
| ~ c0_1(X54)
| ~ c3_1(X54) ) )
| ! [X55] :
( ndr1_0
=> ( c2_1(X55)
| c3_1(X55)
| ~ c1_1(X55) ) )
| hskp21 )
& ( ! [X56] :
( ndr1_0
=> ( c1_1(X56)
| ~ c0_1(X56)
| ~ c3_1(X56) ) )
| ! [X57] :
( ndr1_0
=> ( ~ c0_1(X57)
| ~ c1_1(X57)
| ~ c3_1(X57) ) )
| hskp1 )
& ( ! [X58] :
( ndr1_0
=> ( c1_1(X58)
| ~ c0_1(X58)
| ~ c3_1(X58) ) )
| hskp28 )
& ( ! [X59] :
( ndr1_0
=> ( c2_1(X59)
| c3_1(X59)
| ~ c0_1(X59) ) )
| ! [X60] :
( ndr1_0
=> ( c2_1(X60)
| ~ c1_1(X60)
| ~ c3_1(X60) ) )
| hskp22 )
& ( ! [X61] :
( ndr1_0
=> ( c2_1(X61)
| c3_1(X61)
| ~ c0_1(X61) ) )
| ! [X62] :
( ndr1_0
=> ( c3_1(X62)
| ~ c0_1(X62)
| ~ c1_1(X62) ) )
| hskp0 )
& ( ! [X63] :
( ndr1_0
=> ( c2_1(X63)
| c3_1(X63)
| ~ c0_1(X63) ) )
| hskp6
| hskp14 )
& ( ! [X64] :
( ndr1_0
=> ( c2_1(X64)
| c3_1(X64)
| ~ c0_1(X64) ) )
| hskp1
| hskp23 )
& ( ! [X65] :
( ndr1_0
=> ( c2_1(X65)
| c3_1(X65)
| ~ c1_1(X65) ) )
| ! [X66] :
( ndr1_0
=> ( c2_1(X66)
| ~ c1_1(X66)
| ~ c3_1(X66) ) ) )
& ( ! [X67] :
( ndr1_0
=> ( c2_1(X67)
| c3_1(X67)
| ~ c1_1(X67) ) )
| ! [X68] :
( ndr1_0
=> ( c3_1(X68)
| ~ c0_1(X68)
| ~ c2_1(X68) ) )
| ! [X69] :
( ndr1_0
=> ( ~ c0_1(X69)
| ~ c1_1(X69)
| ~ c3_1(X69) ) ) )
& ( ! [X70] :
( ndr1_0
=> ( c2_1(X70)
| c3_1(X70)
| ~ c1_1(X70) ) )
| ! [X71] :
( ndr1_0
=> ( ~ c1_1(X71)
| ~ c2_1(X71)
| ~ c3_1(X71) ) )
| hskp16 )
& ( ! [X72] :
( ndr1_0
=> ( c2_1(X72)
| c3_1(X72)
| ~ c1_1(X72) ) )
| hskp30
| hskp9 )
& ( ! [X73] :
( ndr1_0
=> ( c2_1(X73)
| ~ c0_1(X73)
| ~ c1_1(X73) ) )
| hskp30
| hskp24 )
& ( ! [X74] :
( ndr1_0
=> ( c2_1(X74)
| ~ c0_1(X74)
| ~ c3_1(X74) ) )
| ! [X75] :
( ndr1_0
=> ( c3_1(X75)
| ~ c0_1(X75)
| ~ c1_1(X75) ) )
| hskp25 )
& ( ! [X76] :
( ndr1_0
=> ( c2_1(X76)
| ~ c0_1(X76)
| ~ c3_1(X76) ) )
| hskp1
| hskp10 )
& ( ! [X77] :
( ndr1_0
=> ( c2_1(X77)
| ~ c0_1(X77)
| ~ c3_1(X77) ) )
| hskp5
| hskp7 )
& ( ! [X78] :
( ndr1_0
=> ( c2_1(X78)
| ~ c1_1(X78)
| ~ c3_1(X78) ) )
| hskp25
| hskp21 )
& ( ! [X79] :
( ndr1_0
=> ( c2_1(X79)
| ~ c1_1(X79)
| ~ c3_1(X79) ) )
| hskp10
| hskp21 )
& ( ! [X80] :
( ndr1_0
=> ( c3_1(X80)
| ~ c0_1(X80)
| ~ c1_1(X80) ) )
| hskp27
| hskp13 )
& ( ! [X81] :
( ndr1_0
=> ( c3_1(X81)
| ~ c0_1(X81)
| ~ c2_1(X81) ) )
| hskp30
| hskp17 )
& ( ! [X82] :
( ndr1_0
=> ( c3_1(X82)
| ~ c1_1(X82)
| ~ c2_1(X82) ) )
| hskp20
| hskp8 )
& ( ! [X83] :
( ndr1_0
=> ( ~ c0_1(X83)
| ~ c2_1(X83)
| ~ c3_1(X83) ) )
| hskp23
| hskp15 )
& ( ! [X84] :
( ndr1_0
=> ( ~ c1_1(X84)
| ~ c2_1(X84)
| ~ c3_1(X84) ) )
| hskp11
| hskp12 )
& ( hskp26
| hskp5
| hskp21 )
& ( hskp20
| hskp14
| hskp4 )
& ( hskp12
| hskp13
| hskp21 ) ) ).

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