## TPTP Problem File: SYN454+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN454+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=046
% 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-4-1-60-3-1-046.dfg [Wei97]

% Status   : Theorem
% Rating   : 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.22 v5.3.0, 0.27 v5.2.0, 0.00 v4.1.0, 0.39 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       :  576 (   0 equ)
%            Maximal formula atoms :  576 ( 576 avg)
%            Number of connectives :  780 ( 205   ~; 313   |; 179   &)
%                                         (   0 <=>;  83  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   93 (  93 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   35 (  35 usr;  31 prp; 0-1 aty)
%            Number of functors    :   30 (  30 usr;  30 con; 0-0 aty)
%            Number of variables   :   83 (  83   !;   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
& ~ c1_1(a96)
& ~ c2_1(a96)
& ~ c3_1(a96) ) )
& ( ~ hskp1
| ( ndr1_0
& c2_1(a97)
& c3_1(a97)
& ~ c1_1(a97) ) )
& ( ~ hskp2
| ( ndr1_0
& c1_1(a98)
& ~ c0_1(a98)
& ~ c3_1(a98) ) )
& ( ~ hskp3
| ( ndr1_0
& c2_1(a99)
& ~ c1_1(a99)
& ~ c3_1(a99) ) )
& ( ~ hskp4
| ( ndr1_0
& c2_1(a100)
& ~ c0_1(a100)
& ~ c1_1(a100) ) )
& ( ~ hskp5
| ( ndr1_0
& c3_1(a101)
& ~ c1_1(a101)
& ~ c2_1(a101) ) )
& ( ~ hskp6
| ( ndr1_0
& c1_1(a102)
& c2_1(a102)
& ~ c3_1(a102) ) )
& ( ~ hskp7
| ( ndr1_0
& c0_1(a103)
& ~ c1_1(a103)
& ~ c3_1(a103) ) )
& ( ~ hskp8
| ( ndr1_0
& ~ c0_1(a104)
& ~ c2_1(a104)
& ~ c3_1(a104) ) )
& ( ~ hskp9
| ( ndr1_0
& c0_1(a105)
& c2_1(a105)
& ~ c1_1(a105) ) )
& ( ~ hskp10
| ( ndr1_0
& c1_1(a106)
& c3_1(a106)
& ~ c2_1(a106) ) )
& ( ~ hskp11
| ( ndr1_0
& c2_1(a109)
& ~ c0_1(a109)
& ~ c3_1(a109) ) )
& ( ~ hskp12
| ( ndr1_0
& c2_1(a110)
& c3_1(a110)
& ~ c0_1(a110) ) )
& ( ~ hskp13
| ( ndr1_0
& c0_1(a112)
& c3_1(a112)
& ~ c1_1(a112) ) )
& ( ~ hskp14
| ( ndr1_0
& c0_1(a115)
& ~ c2_1(a115)
& ~ c3_1(a115) ) )
& ( ~ hskp15
| ( ndr1_0
& c1_1(a116)
& c3_1(a116)
& ~ c0_1(a116) ) )
& ( ~ hskp16
| ( ndr1_0
& c1_1(a118)
& ~ c2_1(a118)
& ~ c3_1(a118) ) )
& ( ~ hskp17
| ( ndr1_0
& ~ c0_1(a124)
& ~ c1_1(a124)
& ~ c3_1(a124) ) )
& ( ~ hskp18
| ( ndr1_0
& c0_1(a125)
& c1_1(a125)
& ~ c3_1(a125) ) )
& ( ~ hskp19
| ( ndr1_0
& c0_1(a127)
& c2_1(a127)
& ~ c3_1(a127) ) )
& ( ~ hskp20
| ( ndr1_0
& c0_1(a133)
& c3_1(a133)
& ~ c2_1(a133) ) )
& ( ~ hskp21
| ( ndr1_0
& c3_1(a145)
& ~ c0_1(a145)
& ~ c2_1(a145) ) )
& ( ~ hskp22
| ( ndr1_0
& c3_1(a149)
& ~ c0_1(a149)
& ~ c1_1(a149) ) )
& ( ~ hskp23
| ( ndr1_0
& c0_1(a152)
& c1_1(a152)
& ~ c2_1(a152) ) )
& ( ~ hskp24
| ( ndr1_0
& c1_1(a153)
& ~ c0_1(a153)
& ~ c2_1(a153) ) )
& ( ~ hskp25
| ( ndr1_0
& c0_1(a159)
& ~ c1_1(a159)
& ~ c2_1(a159) ) )
& ( ~ hskp26
| ( ndr1_0
& c0_1(a94)
& c1_1(a94)
& c2_1(a94) ) )
& ( ~ hskp27
| ( ndr1_0
& c0_1(a95)
& c2_1(a95)
& c3_1(a95) ) )
& ( ~ hskp28
| ( ndr1_0
& c0_1(a142)
& c1_1(a142)
& c3_1(a142) ) )
& ( ~ hskp29
| ( ndr1_0
& c1_1(a165)
& c2_1(a165)
& c3_1(a165) ) )
& ( ! [U] :
( ndr1_0
=> ( c0_1(U)
| c1_1(U)
| c2_1(U) ) )
| ! [V] :
( ndr1_0
=> ( c0_1(V)
| ~ c1_1(V)
| ~ c3_1(V) ) )
| ! [W] :
( ndr1_0
=> ( c1_1(W)
| c3_1(W)
| ~ c2_1(W) ) ) )
& ( ! [X] :
( ndr1_0
=> ( c0_1(X)
| c1_1(X)
| c2_1(X) ) )
| hskp26
| hskp27 )
& ( ! [Y] :
( ndr1_0
=> ( c0_1(Y)
| c1_1(Y)
| c3_1(Y) ) )
| ! [Z] :
( ndr1_0
=> ( c2_1(Z)
| ~ c0_1(Z)
| ~ c1_1(Z) ) )
| hskp0 )
& ( ! [X1] :
( ndr1_0
=> ( c0_1(X1)
| c1_1(X1)
| ~ c2_1(X1) ) )
| ! [X2] :
( ndr1_0
=> ( ~ c0_1(X2)
| ~ c2_1(X2)
| ~ c3_1(X2) ) )
| hskp1 )
& ( ! [X3] :
( ndr1_0
=> ( c0_1(X3)
| c1_1(X3)
| ~ c3_1(X3) ) )
| hskp2
| hskp3 )
& ( ! [X4] :
( ndr1_0
=> ( c0_1(X4)
| c1_1(X4)
| ~ c3_1(X4) ) )
| hskp4
| hskp5 )
& ( ! [X5] :
( ndr1_0
=> ( c0_1(X5)
| c2_1(X5)
| c3_1(X5) ) )
| ! [X6] :
( ndr1_0
=> ( c0_1(X6)
| c2_1(X6)
| ~ c1_1(X6) ) )
| hskp6 )
& ( ! [X7] :
( ndr1_0
=> ( c0_1(X7)
| c2_1(X7)
| ~ c1_1(X7) ) )
| ! [X8] :
( ndr1_0
=> ( c0_1(X8)
| ~ c2_1(X8)
| ~ c3_1(X8) ) )
| hskp7 )
& ( ! [X9] :
( ndr1_0
=> ( c0_1(X9)
| c2_1(X9)
| ~ c3_1(X9) ) )
| ! [X10] :
( ndr1_0
=> ( c0_1(X10)
| ~ c2_1(X10)
| ~ c3_1(X10) ) )
| ! [X11] :
( ndr1_0
=> ( c1_1(X11)
| c3_1(X11)
| ~ c0_1(X11) ) ) )
& ( ! [X12] :
( ndr1_0
=> ( c0_1(X12)
| c2_1(X12)
| ~ c3_1(X12) ) )
| ! [X13] :
( ndr1_0
=> ( ~ c0_1(X13)
| ~ c1_1(X13)
| ~ c3_1(X13) ) )
| hskp8 )
& ( ! [X14] :
( ndr1_0
=> ( c0_1(X14)
| c3_1(X14)
| ~ c1_1(X14) ) )
| ! [X15] :
( ndr1_0
=> ( c2_1(X15)
| c3_1(X15)
| ~ c0_1(X15) ) )
| hskp9 )
& ( ! [X16] :
( ndr1_0
=> ( c0_1(X16)
| c3_1(X16)
| ~ c1_1(X16) ) )
| ! [X17] :
( ndr1_0
=> ( c2_1(X17)
| ~ c0_1(X17)
| ~ c3_1(X17) ) )
| ! [X18] :
( ndr1_0
=> ( c2_1(X18)
| ~ c1_1(X18)
| ~ c3_1(X18) ) ) )
& ( ! [X19] :
( ndr1_0
=> ( c0_1(X19)
| c3_1(X19)
| ~ c2_1(X19) ) )
| ! [X20] :
( ndr1_0
=> ( c0_1(X20)
| ~ c1_1(X20)
| ~ c2_1(X20) ) )
| ! [X21] :
( ndr1_0
=> ( c0_1(X21)
| ~ c1_1(X21)
| ~ c3_1(X21) ) ) )
& ( ! [X22] :
( ndr1_0
=> ( c0_1(X22)
| c3_1(X22)
| ~ c2_1(X22) ) )
| ! [X23] :
( ndr1_0
=> ( c1_1(X23)
| c2_1(X23)
| c3_1(X23) ) )
| ! [X24] :
( ndr1_0
=> ( c2_1(X24)
| c3_1(X24)
| ~ c1_1(X24) ) ) )
& ( ! [X25] :
( ndr1_0
=> ( c0_1(X25)
| c3_1(X25)
| ~ c2_1(X25) ) )
| ! [X26] :
( ndr1_0
=> ( c1_1(X26)
| c3_1(X26)
| ~ c2_1(X26) ) )
| hskp10 )
& ( ! [X27] :
( ndr1_0
=> ( c0_1(X27)
| ~ c1_1(X27)
| ~ c2_1(X27) ) )
| ! [X28] :
( ndr1_0
=> ( c2_1(X28)
| ~ c0_1(X28)
| ~ c3_1(X28) ) )
| ! [X29] :
( ndr1_0
=> ( ~ c0_1(X29)
| ~ c1_1(X29)
| ~ c2_1(X29) ) ) )
& ( ! [X30] :
( ndr1_0
=> ( c0_1(X30)
| ~ c1_1(X30)
| ~ c2_1(X30) ) )
| ! [X31] :
( ndr1_0
=> ( ~ c0_1(X31)
| ~ c2_1(X31)
| ~ c3_1(X31) ) )
| hskp1 )
& ( ! [X32] :
( ndr1_0
=> ( c0_1(X32)
| ~ c1_1(X32)
| ~ c2_1(X32) ) )
| hskp26
| hskp11 )
& ( ! [X33] :
( ndr1_0
=> ( c0_1(X33)
| ~ c1_1(X33)
| ~ c3_1(X33) ) )
| ! [X34] :
( ndr1_0
=> ( c1_1(X34)
| c3_1(X34)
| ~ c0_1(X34) ) )
| hskp12 )
& ( ! [X35] :
( ndr1_0
=> ( c1_1(X35)
| c2_1(X35)
| c3_1(X35) ) )
| ! [X36] :
( ndr1_0
=> ( ~ c0_1(X36)
| ~ c2_1(X36)
| ~ c3_1(X36) ) )
| hskp3 )
& ( ! [X37] :
( ndr1_0
=> ( c1_1(X37)
| c2_1(X37)
| c3_1(X37) ) )
| hskp13
| hskp3 )
& ( ! [X38] :
( ndr1_0
=> ( c1_1(X38)
| c2_1(X38)
| c3_1(X38) ) )
| hskp1 )
& ( ! [X39] :
( ndr1_0
=> ( c1_1(X39)
| c2_1(X39)
| ~ c0_1(X39) ) )
| ! [X40] :
( ndr1_0
=> ( c1_1(X40)
| c2_1(X40)
| ~ c3_1(X40) ) )
| ! [X41] :
( ndr1_0
=> ( c2_1(X41)
| ~ c1_1(X41)
| ~ c3_1(X41) ) ) )
& ( ! [X42] :
( ndr1_0
=> ( c1_1(X42)
| c2_1(X42)
| ~ c0_1(X42) ) )
| ! [X43] :
( ndr1_0
=> ( c1_1(X43)
| c2_1(X43)
| ~ c3_1(X43) ) )
| hskp14 )
& ( ! [X44] :
( ndr1_0
=> ( c1_1(X44)
| c2_1(X44)
| ~ c0_1(X44) ) )
| ! [X45] :
( ndr1_0
=> ( c2_1(X45)
| ~ c0_1(X45)
| ~ c3_1(X45) ) )
| hskp15 )
& ( ! [X46] :
( ndr1_0
=> ( c1_1(X46)
| c2_1(X46)
| ~ c3_1(X46) ) )
| ! [X47] :
( ndr1_0
=> ( c2_1(X47)
| ~ c0_1(X47)
| ~ c1_1(X47) ) )
| ! [X48] :
( ndr1_0
=> ( ~ c0_1(X48)
| ~ c1_1(X48)
| ~ c3_1(X48) ) ) )
& ( ! [X49] :
( ndr1_0
=> ( c1_1(X49)
| c3_1(X49)
| ~ c0_1(X49) ) )
| ! [X50] :
( ndr1_0
=> ( c1_1(X50)
| ~ c0_1(X50)
| ~ c2_1(X50) ) ) )
& ( ! [X51] :
( ndr1_0
=> ( c1_1(X51)
| c3_1(X51)
| ~ c2_1(X51) ) )
| ! [X52] :
( ndr1_0
=> ( c3_1(X52)
| ~ c0_1(X52)
| ~ c1_1(X52) ) )
| hskp10 )
& ( ! [X53] :
( ndr1_0
=> ( c1_1(X53)
| ~ c0_1(X53)
| ~ c3_1(X53) ) )
| ! [X54] :
( ndr1_0
=> ( c3_1(X54)
| ~ c0_1(X54)
| ~ c1_1(X54) ) )
| hskp16 )
& ( ! [X55] :
( ndr1_0
=> ( c1_1(X55)
| ~ c0_1(X55)
| ~ c3_1(X55) ) )
| hskp14
| hskp10 )
& ( ! [X56] :
( ndr1_0
=> ( c1_1(X56)
| ~ c0_1(X56)
| ~ c3_1(X56) ) )
| hskp16
| hskp8 )
& ( ! [X57] :
( ndr1_0
=> ( c1_1(X57)
| ~ c2_1(X57)
| ~ c3_1(X57) ) )
| hskp26
| hskp17 )
& ( ! [X58] :
( ndr1_0
=> ( c1_1(X58)
| ~ c2_1(X58)
| ~ c3_1(X58) ) )
| hskp18
| hskp14 )
& ( ! [X59] :
( ndr1_0
=> ( c1_1(X59)
| ~ c2_1(X59)
| ~ c3_1(X59) ) )
| hskp19
| hskp5 )
& ( ! [X60] :
( ndr1_0
=> ( c1_1(X60)
| ~ c2_1(X60)
| ~ c3_1(X60) ) )
| hskp13 )
& ( ! [X61] :
( ndr1_0
=> ( c1_1(X61)
| ~ c2_1(X61)
| ~ c3_1(X61) ) )
| hskp6
| hskp4 )
& ( ! [X62] :
( ndr1_0
=> ( c2_1(X62)
| c3_1(X62)
| ~ c0_1(X62) ) )
| ! [X63] :
( ndr1_0
=> ( ~ c0_1(X63)
| ~ c2_1(X63)
| ~ c3_1(X63) ) )
| hskp8 )
& ( ! [X64] :
( ndr1_0
=> ( c2_1(X64)
| c3_1(X64)
| ~ c0_1(X64) ) )
| hskp20
| hskp10 )
& ( ! [X65] :
( ndr1_0
=> ( c2_1(X65)
| c3_1(X65)
| ~ c0_1(X65) ) )
| hskp12
| hskp5 )
& ( ! [X66] :
( ndr1_0
=> ( c2_1(X66)
| c3_1(X66)
| ~ c0_1(X66) ) )
| hskp1
| hskp17 )
& ( ! [X67] :
( ndr1_0
=> ( c2_1(X67)
| c3_1(X67)
| ~ c1_1(X67) ) )
| ! [X68] :
( ndr1_0
=> ( c3_1(X68)
| ~ c1_1(X68)
| ~ c2_1(X68) ) )
| hskp5 )
& ( ! [X69] :
( ndr1_0
=> ( c2_1(X69)
| ~ c0_1(X69)
| ~ c1_1(X69) ) )
| ! [X70] :
( ndr1_0
=> ( c2_1(X70)
| ~ c1_1(X70)
| ~ c3_1(X70) ) )
| ! [X71] :
( ndr1_0
=> ( ~ c0_1(X71)
| ~ c1_1(X71)
| ~ c3_1(X71) ) ) )
& ( ! [X72] :
( ndr1_0
=> ( c2_1(X72)
| ~ c0_1(X72)
| ~ c1_1(X72) ) )
| hskp6
| hskp3 )
& ( ! [X73] :
( ndr1_0
=> ( c3_1(X73)
| ~ c1_1(X73)
| ~ c2_1(X73) ) )
| hskp28
| hskp18 )
& ( ! [X74] :
( ndr1_0
=> ( c3_1(X74)
| ~ c1_1(X74)
| ~ c2_1(X74) ) )
| hskp12
| hskp21 )
& ( ! [X75] :
( ndr1_0
=> ( ~ c0_1(X75)
| ~ c2_1(X75)
| ~ c3_1(X75) ) )
| hskp26
| hskp1 )
& ( ! [X76] :
( ndr1_0
=> ( ~ c1_1(X76)
| ~ c2_1(X76)
| ~ c3_1(X76) ) )
| hskp9
| hskp22 )
& ( ! [X77] :
( ndr1_0
=> ( ~ c1_1(X77)
| ~ c2_1(X77)
| ~ c3_1(X77) ) )
| hskp12
| hskp8 )
& ( hskp23
| hskp24
| hskp16 )
& ( hskp18
| hskp19
| hskp13 )
& ( hskp18
| hskp25
| hskp17 )
& ( hskp9
| hskp14
| hskp2 )
& ( hskp20
| hskp29
| hskp0 )
& ( hskp20
| hskp3
| hskp8 )
& ( hskp14
| hskp16
| hskp21 )
& ( hskp14
| hskp12
| hskp11 )
& ( hskp14
| hskp1
| hskp3 )
& ( hskp29
| hskp24
| hskp11 )
& ( hskp6
| hskp22
| hskp17 )
& ( hskp15
| hskp22
| hskp17 ) ) ).

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