TPTP Problem File: SWV421-1.105.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SWV421-1.105 : TPTP v8.1.0. Released v3.5.0.
% Domain   : Software Verification
% Problem  : Mutex algorithm first process access B k=105
% Version  : Especial.
% English  : Model checking of an Mutex algorithm. The property to check is
%            that if the first process asks for access to the critical section,
%            it will be eventually granted.

% Refs     : [CC+02] Cimatti et al (2002), NuSmv 2 An OpenSource Tool for S
%          : [NV07a] Navarro (2007), Email to Geoff Sutcliffe
%          : [NV07b] Navarro & Voronkov (2007), Encodings of Bounded LTL Mo
% Source   : [NV07a]
% Names    : example_cmu/mutex.smv (property 2) [CC+02]
%          : mutex1b-k105 [NV07a]

% Status   : Unsatisfiable
% Rating   : 0.00 v7.3.0, 0.40 v7.2.0, 0.44 v7.1.0, 0.29 v7.0.0, 0.43 v6.4.0, 0.17 v6.3.0, 0.00 v6.2.0, 0.50 v6.1.0, 0.62 v6.0.0, 0.50 v5.5.0, 0.20 v5.4.0, 0.00 v5.0.0, 0.50 v4.1.0, 0.20 v4.0.1, 0.40 v3.7.0, 0.25 v3.5.0
% Syntax   : Number of clauses     :  185 ( 109 unt;  20 nHn; 182 RR)
%            Number of literals    :  455 (   0 equ; 123 neg)
%            Maximal clause size   :  106 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   31 (  31 usr;   1 prp; 0-2 aty)
%            Number of functors    :  113 ( 113 usr; 113 con; 0-0 aty)
%            Number of variables   :  112 (   0 sgn)
% SPC      : CNF_UNS_EPR_NEQ_NHN

% Comments : When solved by Darwin there seems to be two trendlines with
%            different difficulty:
%              An "easy" one when k = 0, 3 (mod 4)
%              A "hard" one when k = 1, 2 (mod 4)
%            Darwin run times seem to have a growth of order k^3.
%          : Translated from [CC+02] using [NV07b]
%------------------------------------------------------------------------------
cnf(bound1,axiom,
    succ(s0,s1) ).

cnf(bound2,axiom,
    succ(s1,s2) ).

cnf(bound3,axiom,
    succ(s2,s3) ).

cnf(bound4,axiom,
    succ(s3,s4) ).

cnf(bound5,axiom,
    succ(s4,s5) ).

cnf(bound6,axiom,
    succ(s5,s6) ).

cnf(bound7,axiom,
    succ(s6,s7) ).

cnf(bound8,axiom,
    succ(s7,s8) ).

cnf(bound9,axiom,
    succ(s8,s9) ).

cnf(bound10,axiom,
    succ(s9,s10) ).

cnf(bound11,axiom,
    succ(s10,s11) ).

cnf(bound12,axiom,
    succ(s11,s12) ).

cnf(bound13,axiom,
    succ(s12,s13) ).

cnf(bound14,axiom,
    succ(s13,s14) ).

cnf(bound15,axiom,
    succ(s14,s15) ).

cnf(bound16,axiom,
    succ(s15,s16) ).

cnf(bound17,axiom,
    succ(s16,s17) ).

cnf(bound18,axiom,
    succ(s17,s18) ).

cnf(bound19,axiom,
    succ(s18,s19) ).

cnf(bound20,axiom,
    succ(s19,s20) ).

cnf(bound21,axiom,
    succ(s20,s21) ).

cnf(bound22,axiom,
    succ(s21,s22) ).

cnf(bound23,axiom,
    succ(s22,s23) ).

cnf(bound24,axiom,
    succ(s23,s24) ).

cnf(bound25,axiom,
    succ(s24,s25) ).

cnf(bound26,axiom,
    succ(s25,s26) ).

cnf(bound27,axiom,
    succ(s26,s27) ).

cnf(bound28,axiom,
    succ(s27,s28) ).

cnf(bound29,axiom,
    succ(s28,s29) ).

cnf(bound30,axiom,
    succ(s29,s30) ).

cnf(bound31,axiom,
    succ(s30,s31) ).

cnf(bound32,axiom,
    succ(s31,s32) ).

cnf(bound33,axiom,
    succ(s32,s33) ).

cnf(bound34,axiom,
    succ(s33,s34) ).

cnf(bound35,axiom,
    succ(s34,s35) ).

cnf(bound36,axiom,
    succ(s35,s36) ).

cnf(bound37,axiom,
    succ(s36,s37) ).

cnf(bound38,axiom,
    succ(s37,s38) ).

cnf(bound39,axiom,
    succ(s38,s39) ).

cnf(bound40,axiom,
    succ(s39,s40) ).

cnf(bound41,axiom,
    succ(s40,s41) ).

cnf(bound42,axiom,
    succ(s41,s42) ).

cnf(bound43,axiom,
    succ(s42,s43) ).

cnf(bound44,axiom,
    succ(s43,s44) ).

cnf(bound45,axiom,
    succ(s44,s45) ).

cnf(bound46,axiom,
    succ(s45,s46) ).

cnf(bound47,axiom,
    succ(s46,s47) ).

cnf(bound48,axiom,
    succ(s47,s48) ).

cnf(bound49,axiom,
    succ(s48,s49) ).

cnf(bound50,axiom,
    succ(s49,s50) ).

cnf(bound51,axiom,
    succ(s50,s51) ).

cnf(bound52,axiom,
    succ(s51,s52) ).

cnf(bound53,axiom,
    succ(s52,s53) ).

cnf(bound54,axiom,
    succ(s53,s54) ).

cnf(bound55,axiom,
    succ(s54,s55) ).

cnf(bound56,axiom,
    succ(s55,s56) ).

cnf(bound57,axiom,
    succ(s56,s57) ).

cnf(bound58,axiom,
    succ(s57,s58) ).

cnf(bound59,axiom,
    succ(s58,s59) ).

cnf(bound60,axiom,
    succ(s59,s60) ).

cnf(bound61,axiom,
    succ(s60,s61) ).

cnf(bound62,axiom,
    succ(s61,s62) ).

cnf(bound63,axiom,
    succ(s62,s63) ).

cnf(bound64,axiom,
    succ(s63,s64) ).

cnf(bound65,axiom,
    succ(s64,s65) ).

cnf(bound66,axiom,
    succ(s65,s66) ).

cnf(bound67,axiom,
    succ(s66,s67) ).

cnf(bound68,axiom,
    succ(s67,s68) ).

cnf(bound69,axiom,
    succ(s68,s69) ).

cnf(bound70,axiom,
    succ(s69,s70) ).

cnf(bound71,axiom,
    succ(s70,s71) ).

cnf(bound72,axiom,
    succ(s71,s72) ).

cnf(bound73,axiom,
    succ(s72,s73) ).

cnf(bound74,axiom,
    succ(s73,s74) ).

cnf(bound75,axiom,
    succ(s74,s75) ).

cnf(bound76,axiom,
    succ(s75,s76) ).

cnf(bound77,axiom,
    succ(s76,s77) ).

cnf(bound78,axiom,
    succ(s77,s78) ).

cnf(bound79,axiom,
    succ(s78,s79) ).

cnf(bound80,axiom,
    succ(s79,s80) ).

cnf(bound81,axiom,
    succ(s80,s81) ).

cnf(bound82,axiom,
    succ(s81,s82) ).

cnf(bound83,axiom,
    succ(s82,s83) ).

cnf(bound84,axiom,
    succ(s83,s84) ).

cnf(bound85,axiom,
    succ(s84,s85) ).

cnf(bound86,axiom,
    succ(s85,s86) ).

cnf(bound87,axiom,
    succ(s86,s87) ).

cnf(bound88,axiom,
    succ(s87,s88) ).

cnf(bound89,axiom,
    succ(s88,s89) ).

cnf(bound90,axiom,
    succ(s89,s90) ).

cnf(bound91,axiom,
    succ(s90,s91) ).

cnf(bound92,axiom,
    succ(s91,s92) ).

cnf(bound93,axiom,
    succ(s92,s93) ).

cnf(bound94,axiom,
    succ(s93,s94) ).

cnf(bound95,axiom,
    succ(s94,s95) ).

cnf(bound96,axiom,
    succ(s95,s96) ).

cnf(bound97,axiom,
    succ(s96,s97) ).

cnf(bound98,axiom,
    succ(s97,s98) ).

cnf(bound99,axiom,
    succ(s98,s99) ).

cnf(bound100,axiom,
    succ(s99,s100) ).

cnf(bound101,axiom,
    succ(s100,s101) ).

cnf(bound102,axiom,
    succ(s101,s102) ).

cnf(bound103,axiom,
    succ(s102,s103) ).

cnf(bound104,axiom,
    succ(s103,s104) ).

cnf(bound105,axiom,
    last(s104) ).

cnf(bound106,axiom,
    ( ~ succ(X,Y)
    | trans(X,Y) ) ).

cnf(bound107,axiom,
    ( ~ loop
    | trans(s104,s0)
    | trans(s104,s1)
    | trans(s104,s2)
    | trans(s104,s3)
    | trans(s104,s4)
    | trans(s104,s5)
    | trans(s104,s6)
    | trans(s104,s7)
    | trans(s104,s8)
    | trans(s104,s9)
    | trans(s104,s10)
    | trans(s104,s11)
    | trans(s104,s12)
    | trans(s104,s13)
    | trans(s104,s14)
    | trans(s104,s15)
    | trans(s104,s16)
    | trans(s104,s17)
    | trans(s104,s18)
    | trans(s104,s19)
    | trans(s104,s20)
    | trans(s104,s21)
    | trans(s104,s22)
    | trans(s104,s23)
    | trans(s104,s24)
    | trans(s104,s25)
    | trans(s104,s26)
    | trans(s104,s27)
    | trans(s104,s28)
    | trans(s104,s29)
    | trans(s104,s30)
    | trans(s104,s31)
    | trans(s104,s32)
    | trans(s104,s33)
    | trans(s104,s34)
    | trans(s104,s35)
    | trans(s104,s36)
    | trans(s104,s37)
    | trans(s104,s38)
    | trans(s104,s39)
    | trans(s104,s40)
    | trans(s104,s41)
    | trans(s104,s42)
    | trans(s104,s43)
    | trans(s104,s44)
    | trans(s104,s45)
    | trans(s104,s46)
    | trans(s104,s47)
    | trans(s104,s48)
    | trans(s104,s49)
    | trans(s104,s50)
    | trans(s104,s51)
    | trans(s104,s52)
    | trans(s104,s53)
    | trans(s104,s54)
    | trans(s104,s55)
    | trans(s104,s56)
    | trans(s104,s57)
    | trans(s104,s58)
    | trans(s104,s59)
    | trans(s104,s60)
    | trans(s104,s61)
    | trans(s104,s62)
    | trans(s104,s63)
    | trans(s104,s64)
    | trans(s104,s65)
    | trans(s104,s66)
    | trans(s104,s67)
    | trans(s104,s68)
    | trans(s104,s69)
    | trans(s104,s70)
    | trans(s104,s71)
    | trans(s104,s72)
    | trans(s104,s73)
    | trans(s104,s74)
    | trans(s104,s75)
    | trans(s104,s76)
    | trans(s104,s77)
    | trans(s104,s78)
    | trans(s104,s79)
    | trans(s104,s80)
    | trans(s104,s81)
    | trans(s104,s82)
    | trans(s104,s83)
    | trans(s104,s84)
    | trans(s104,s85)
    | trans(s104,s86)
    | trans(s104,s87)
    | trans(s104,s88)
    | trans(s104,s89)
    | trans(s104,s90)
    | trans(s104,s91)
    | trans(s104,s92)
    | trans(s104,s93)
    | trans(s104,s94)
    | trans(s104,s95)
    | trans(s104,s96)
    | trans(s104,s97)
    | trans(s104,s98)
    | trans(s104,s99)
    | trans(s104,s100)
    | trans(s104,s101)
    | trans(s104,s102)
    | trans(s104,s103)
    | trans(s104,s104) ) ).

cnf(m_main_1,axiom,
    ( m_main_v_state1(X,c_n1)
    | m_main_v_state1(X,c_t1)
    | m_main_v_state1(X,c_c1) ) ).

cnf(m_main_2,axiom,
    ( ~ m_main_v_state1(X,c_n1)
    | ~ m_main_v_state1(X,c_t1) ) ).

cnf(m_main_3,axiom,
    ( ~ m_main_v_state1(X,c_n1)
    | ~ m_main_v_state1(X,c_c1) ) ).

cnf(m_main_4,axiom,
    ( ~ m_main_v_state1(X,c_t1)
    | ~ m_main_v_state1(X,c_c1) ) ).

cnf(m_main_5,axiom,
    ( m_main_v_state2(X,c_n2)
    | m_main_v_state2(X,c_t2)
    | m_main_v_state2(X,c_c2) ) ).

cnf(m_main_6,axiom,
    ( ~ m_main_v_state2(X,c_n2)
    | ~ m_main_v_state2(X,c_t2) ) ).

cnf(m_main_7,axiom,
    ( ~ m_main_v_state2(X,c_n2)
    | ~ m_main_v_state2(X,c_c2) ) ).

cnf(m_main_8,axiom,
    ( ~ m_main_v_state2(X,c_t2)
    | ~ m_main_v_state2(X,c_c2) ) ).

cnf(m_main_9,axiom,
    ( m_main_v_turn(X,c_1)
    | m_main_v_turn(X,c_2) ) ).

cnf(m_main_10,axiom,
    ( ~ m_main_v_turn(X,c_1)
    | ~ m_main_v_turn(X,c_2) ) ).

cnf(m_main_11,axiom,
    m_main_v_state1(s0,c_n1) ).

cnf(m_main_12,axiom,
    m_main_v_state2(s0,c_n2) ).

cnf(m_main_13,axiom,
    m_main_v_turn(s0,c_1) ).

cnf(m_main_14,axiom,
    ( m_main_v_state1(X,c_n1)
    | ~ node1(X) ) ).

cnf(m_main_15,axiom,
    ( m_main_v_state2(X,c_t2)
    | ~ node1(X) ) ).

cnf(m_main_16,axiom,
    ( m_main_v_state1(X,c_n1)
    | ~ node2(X) ) ).

cnf(m_main_17,axiom,
    ( m_main_v_state2(X,c_n2)
    | ~ node2(X) ) ).

cnf(m_main_18,axiom,
    ( m_main_v_state1(X,c_n1)
    | ~ node3(X) ) ).

cnf(m_main_19,axiom,
    ( m_main_v_state2(X,c_c2)
    | ~ node3(X) ) ).

cnf(m_main_20,axiom,
    ( m_main_v_state1(X,c_t1)
    | ~ node4(X) ) ).

cnf(m_main_21,axiom,
    ( m_main_v_state2(X,c_n2)
    | ~ node4(X) ) ).

cnf(m_main_22,axiom,
    ( m_main_v_state1(X,c_t1)
    | ~ node5(X) ) ).

cnf(m_main_23,axiom,
    ( m_main_v_state2(X,c_t2)
    | ~ node5(X) ) ).

cnf(m_main_24,axiom,
    ( m_main_v_turn(X,c_1)
    | ~ node5(X) ) ).

cnf(m_main_25,axiom,
    ( m_main_v_state1(Y,V)
    | ~ m_main_v_state1(X,V)
    | ~ node6(X,Y) ) ).

cnf(m_main_26,axiom,
    ( ~ m_main_v_state1(Y,V)
    | m_main_v_state1(X,V)
    | ~ node6(X,Y) ) ).

cnf(m_main_27,axiom,
    ( ~ m_main_v_state1(X,c_n1)
    | ~ m_main_v_state2(X,c_t2)
    | m_main_v_state1(Y,c_t1)
    | ~ node7(X,Y) ) ).

cnf(m_main_28,axiom,
    ( node1(X)
    | ~ m_main_v_state1(X,c_n1)
    | ~ m_main_v_state2(X,c_n2)
    | m_main_v_state1(Y,c_t1)
    | ~ node7(X,Y) ) ).

cnf(m_main_29,axiom,
    ( node1(X)
    | node2(X)
    | ~ m_main_v_state1(X,c_n1)
    | ~ m_main_v_state2(X,c_c2)
    | m_main_v_state1(Y,c_t1)
    | ~ node7(X,Y) ) ).

cnf(m_main_30,axiom,
    ( node1(X)
    | node2(X)
    | node3(X)
    | ~ m_main_v_state1(X,c_t1)
    | ~ m_main_v_state2(X,c_n2)
    | m_main_v_state1(Y,c_c1)
    | ~ node7(X,Y) ) ).

cnf(m_main_31,axiom,
    ( node1(X)
    | node2(X)
    | node3(X)
    | node4(X)
    | ~ m_main_v_state1(X,c_t1)
    | ~ m_main_v_state2(X,c_t2)
    | ~ m_main_v_turn(X,c_1)
    | m_main_v_state1(Y,c_c1)
    | ~ node7(X,Y) ) ).

cnf(m_main_32,axiom,
    ( node1(X)
    | node2(X)
    | node3(X)
    | node4(X)
    | node5(X)
    | ~ m_main_v_state1(X,c_c1)
    | m_main_v_state1(Y,c_n1)
    | ~ node7(X,Y) ) ).

cnf(m_main_33,axiom,
    ( node1(X)
    | node2(X)
    | node3(X)
    | node4(X)
    | node5(X)
    | m_main_v_state1(X,c_c1)
    | node6(X,Y)
    | ~ node7(X,Y) ) ).

cnf(m_main_34,axiom,
    ( ~ trans(X,Y)
    | node7(X,Y) ) ).

cnf(m_main_35,axiom,
    ( m_main_v_state2(X,c_n2)
    | ~ node8(X) ) ).

cnf(m_main_36,axiom,
    ( m_main_v_state1(X,c_t1)
    | ~ node8(X) ) ).

cnf(m_main_37,axiom,
    ( m_main_v_state2(X,c_n2)
    | ~ node9(X) ) ).

cnf(m_main_38,axiom,
    ( m_main_v_state1(X,c_n1)
    | ~ node9(X) ) ).

cnf(m_main_39,axiom,
    ( m_main_v_state2(X,c_n2)
    | ~ node10(X) ) ).

cnf(m_main_40,axiom,
    ( m_main_v_state1(X,c_c1)
    | ~ node10(X) ) ).

cnf(m_main_41,axiom,
    ( m_main_v_state2(X,c_t2)
    | ~ node11(X) ) ).

cnf(m_main_42,axiom,
    ( m_main_v_state1(X,c_n1)
    | ~ node11(X) ) ).

cnf(m_main_43,axiom,
    ( m_main_v_state2(X,c_t2)
    | ~ node12(X) ) ).

cnf(m_main_44,axiom,
    ( m_main_v_state1(X,c_t1)
    | ~ node12(X) ) ).

cnf(m_main_45,axiom,
    ( m_main_v_turn(X,c_2)
    | ~ node12(X) ) ).

cnf(m_main_46,axiom,
    ( m_main_v_state2(Y,V)
    | ~ m_main_v_state2(X,V)
    | ~ node13(X,Y) ) ).

cnf(m_main_47,axiom,
    ( ~ m_main_v_state2(Y,V)
    | m_main_v_state2(X,V)
    | ~ node13(X,Y) ) ).

cnf(m_main_48,axiom,
    ( ~ m_main_v_state2(X,c_n2)
    | ~ m_main_v_state1(X,c_t1)
    | m_main_v_state2(Y,c_t2)
    | ~ node14(X,Y) ) ).

cnf(m_main_49,axiom,
    ( node8(X)
    | ~ m_main_v_state2(X,c_n2)
    | ~ m_main_v_state1(X,c_n1)
    | m_main_v_state2(Y,c_t2)
    | ~ node14(X,Y) ) ).

cnf(m_main_50,axiom,
    ( node8(X)
    | node9(X)
    | ~ m_main_v_state2(X,c_n2)
    | ~ m_main_v_state1(X,c_c1)
    | m_main_v_state2(Y,c_t2)
    | ~ node14(X,Y) ) ).

cnf(m_main_51,axiom,
    ( node8(X)
    | node9(X)
    | node10(X)
    | ~ m_main_v_state2(X,c_t2)
    | ~ m_main_v_state1(X,c_n1)
    | m_main_v_state2(Y,c_c2)
    | ~ node14(X,Y) ) ).

cnf(m_main_52,axiom,
    ( node8(X)
    | node9(X)
    | node10(X)
    | node11(X)
    | ~ m_main_v_state2(X,c_t2)
    | ~ m_main_v_state1(X,c_t1)
    | ~ m_main_v_turn(X,c_2)
    | m_main_v_state2(Y,c_c2)
    | ~ node14(X,Y) ) ).

cnf(m_main_53,axiom,
    ( node8(X)
    | node9(X)
    | node10(X)
    | node11(X)
    | node12(X)
    | ~ m_main_v_state2(X,c_c2)
    | m_main_v_state2(Y,c_n2)
    | ~ node14(X,Y) ) ).

cnf(m_main_54,axiom,
    ( node8(X)
    | node9(X)
    | node10(X)
    | node11(X)
    | node12(X)
    | m_main_v_state2(X,c_c2)
    | node13(X,Y)
    | ~ node14(X,Y) ) ).

cnf(m_main_55,axiom,
    ( ~ trans(X,Y)
    | node14(X,Y) ) ).

cnf(m_main_56,axiom,
    ( m_main_v_state1(X,c_n1)
    | ~ node15(X) ) ).

cnf(m_main_57,axiom,
    ( m_main_v_state2(X,c_t2)
    | ~ node15(X) ) ).

cnf(m_main_58,axiom,
    ( m_main_v_state2(X,c_n2)
    | ~ node16(X) ) ).

cnf(m_main_59,axiom,
    ( m_main_v_state1(X,c_t1)
    | ~ node16(X) ) ).

cnf(m_main_60,axiom,
    ( m_main_v_turn(Y,V)
    | ~ m_main_v_turn(X,V)
    | ~ node17(X,Y) ) ).

cnf(m_main_61,axiom,
    ( ~ m_main_v_turn(Y,V)
    | m_main_v_turn(X,V)
    | ~ node17(X,Y) ) ).

cnf(m_main_62,axiom,
    ( ~ m_main_v_state1(X,c_n1)
    | ~ m_main_v_state2(X,c_t2)
    | m_main_v_turn(Y,c_2)
    | ~ node18(X,Y) ) ).

cnf(m_main_63,axiom,
    ( node15(X)
    | ~ m_main_v_state2(X,c_n2)
    | ~ m_main_v_state1(X,c_t1)
    | m_main_v_turn(Y,c_1)
    | ~ node18(X,Y) ) ).

cnf(m_main_64,axiom,
    ( node15(X)
    | node16(X)
    | node17(X,Y)
    | ~ node18(X,Y) ) ).

cnf(m_main_65,axiom,
    ( ~ trans(X,Y)
    | node18(X,Y) ) ).

cnf(prpty1,negated_conjecture,
    ( ~ m_main_v_state1(X,c_c1)
    | ~ always19(X) ) ).

cnf(prpty2,negated_conjecture,
    ( always19(Y)
    | ~ trans(X,Y)
    | ~ always19(X) ) ).

cnf(prpty3,negated_conjecture,
    ( loop
    | ~ always19(X)
    | ~ last(X) ) ).

cnf(prpty4,negated_conjecture,
    ( m_main_v_state1(X,c_t1)
    | ~ node20(X) ) ).

cnf(prpty5,negated_conjecture,
    ( always19(X)
    | ~ node20(X) ) ).

cnf(prpty6,negated_conjecture,
    ( node20(X)
    | xuntil22(X)
    | ~ until21(X) ) ).

cnf(prpty7,negated_conjecture,
    ( until21(Y)
    | ~ succ(X,Y)
    | ~ xuntil22(X) ) ).

cnf(prpty8,negated_conjecture,
    ( loop
    | ~ last(X)
    | ~ xuntil22(X) ) ).

cnf(prpty9,negated_conjecture,
    ( until2p23(Y)
    | ~ trans(X,Y)
    | ~ last(X)
    | ~ xuntil22(X) ) ).

cnf(prpty10,negated_conjecture,
    ( node20(X)
    | xuntil2p24(X)
    | ~ until2p23(X) ) ).

cnf(prpty11,negated_conjecture,
    ( until2p23(Y)
    | ~ succ(X,Y)
    | ~ xuntil2p24(X) ) ).

cnf(prpty12,negated_conjecture,
    ( ~ last(X)
    | ~ xuntil2p24(X) ) ).

cnf(prpty13,negated_conjecture,
    until21(s0) ).

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