%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:04:16 AM UTC 2026 % Result : Theorem 0.23s 0.53s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.08/0.35 % Computer : n016.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Mon Sep 7 12:07:02 UTC 2026 % 0.08/0.35 % CPUTime : % 0.23/0.52 start to proof:theBenchmark % 0.23/0.52 %------------------------------------------- % 0.23/0.52 % File :CSE---1.7 % 0.23/0.52 % Problem :theBenchmark % 0.23/0.52 % Transform :cnf % 0.23/0.52 % Format :tptp:raw % 0.23/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.23/0.52 % 0.23/0.52 % Result :Theorem 0.022341s % 0.23/0.52 % Output :CNFRefutation 0.022341s % 0.23/0.52 %------------------------------------------- % 0.23/0.53 %-------------------------------------------------------------------------- % 0.23/0.53 % File : MGT021+1 : TPTP v9.3.0. Released v2.0.0. % 0.23/0.53 % Domain : Management (Organisation Theory) % 0.23/0.53 % Problem : Difference between disbanding rates does not decrease % 0.23/0.53 % Version : [PB+94] axioms. % 0.23/0.53 % English : The difference between the disbanding rates of first movers % 0.23/0.53 % and efficient producers does not decrease with time. % 0.23/0.53 % 0.23/0.53 % Refs : [PM93] Peli & Masuch (1993), The Logic of Propogation Strateg % 0.23/0.53 % : [PM94] Peli & Masuch (1994), The Logic of Propogation Strateg % 0.23/0.53 % : [PB+94] Peli et al. (1994), A Logical Approach to Formalizing % 0.23/0.53 % : [Kam95] Kamps (1995), Email to G. Sutcliffe % 0.23/0.53 % Source : [Kam95] % 0.23/0.53 % Names : LEMMA 3 [PM93] % 0.23/0.53 % : L3 [PB+94] % 0.23/0.53 % 0.23/0.53 % Status : Theorem % 0.23/0.53 % Rating : 0.04 v9.3.0, 0.09 v9.1.0, 0.06 v9.0.0, 0.08 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.04 v5.3.0, 0.11 v5.2.0, 0.00 v3.2.0, 0.09 v3.1.0, 0.00 v2.5.0, 0.12 v2.4.0, 0.25 v2.3.0, 0.33 v2.2.1, 0.00 v2.1.0 % 0.23/0.53 % Syntax : Number of formulae : 7 ( 0 unt; 0 def) % 0.23/0.53 % Number of atoms : 27 ( 1 equ) % 0.23/0.53 % Maximal formula atoms : 7 ( 3 avg) % 0.23/0.53 % Number of connectives : 24 ( 4 ~; 1 |; 8 &) % 0.23/0.53 % ( 0 <=>; 11 =>; 0 <=; 0 <~>) % 0.23/0.53 % Maximal formula depth : 7 ( 5 avg) % 0.23/0.53 % Maximal term depth : 3 ( 1 avg) % 0.23/0.53 % Number of predicates : 9 ( 8 usr; 0 prp; 1-4 aty) % 0.23/0.53 % Number of functors : 8 ( 8 usr; 3 con; 0-2 aty) % 0.23/0.53 % Number of variables : 13 ( 13 !; 0 ?) % 0.23/0.53 % SPC : FOF_THM_RFO_SEQ % 0.23/0.53 % 0.23/0.53 % Comments : Same as version with [PM93] axioms. % 0.23/0.53 %-------------------------------------------------------------------------- % 0.23/0.53 %----Subsitution axioms % 0.23/0.53 %----Problem axioms % 0.23/0.53 %----MP. If first movers and efficient producers are present in an % 0.23/0.53 %----environment at a certain point of time, then this time-point belongs % 0.23/0.53 %----to the the environment. % 0.23/0.53 fof(mp_time_point_in_environment,axiom, % 0.23/0.53 ! [E,T] : % 0.23/0.53 ( ( environment(E) % 0.23/0.53 & subpopulations(first_movers,efficient_producers,E,T) ) % 0.23/0.53 => in_environment(E,T) ) ). % 0.23/0.53 % 0.23/0.53 %----MP. If first movers and efficient producers are present in an % 0.23/0.53 %----environment at a certain point of time, then then the environment % 0.23/0.53 %----is not empty at this time. % 0.23/0.53 fof(mp_environment_not_empty,axiom, % 0.23/0.53 ! [E,T] : % 0.23/0.53 ( ( environment(E) % 0.23/0.53 & subpopulations(first_movers,efficient_producers,E,T) ) % 0.23/0.53 => greater(number_of_organizations(E,T),zero) ) ). % 0.23/0.53 % 0.23/0.53 %----MP. If something increases, then it does not decrease. % 0.23/0.53 fof(mp_increase_not_decrease,axiom, % 0.23/0.53 ! [X] : % 0.23/0.53 ( increases(X) % 0.23/0.53 => ~ decreases(X) ) ). % 0.23/0.53 % 0.23/0.53 %----MP. on "greater or equal to" % 0.23/0.53 fof(mp_greater_or_equal,axiom, % 0.23/0.53 ! [X,Y] : % 0.23/0.53 ( greater_or_equal(X,Y) % 0.23/0.53 => ( greater(X,Y) % 0.23/0.53 | X = Y ) ) ). % 0.23/0.53 % 0.23/0.53 %----A3. Resource availability decreases until equilibrium is reached. % 0.23/0.53 fof(a3,hypothesis, % 0.23/0.53 ! [E,T] : % 0.23/0.53 ( ( environment(E) % 0.23/0.53 & in_environment(E,T) % 0.23/0.53 & greater(number_of_organizations(E,T),zero) ) % 0.23/0.53 => ( ( greater(equilibrium(E),T) % 0.23/0.53 => decreases(resources(E,T)) ) % 0.23/0.53 & ( ~ greater(equilibrium(E),T) % 0.23/0.53 => constant(resources(E,T)) ) ) ) ). % 0.23/0.53 % 0.23/0.53 %----L4. A decreasing resource availability affects the disbanding rate of % 0.23/0.53 %----first movers more than the disbanding rate of efficient producers. % 0.23/0.53 fof(l4,hypothesis, % 0.23/0.53 ! [E,T] : % 0.23/0.53 ( ( environment(E) % 0.23/0.53 & subpopulations(first_movers,efficient_producers,E,T) ) % 0.23/0.53 => ( ( decreases(resources(E,T)) % 0.23/0.53 => increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) % 0.23/0.53 & ( constant(resources(E,T)) % 0.23/0.53 => ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ) ). % 0.23/0.53 % 0.23/0.53 %----GOAL: L3. The difference between the disbanding rates of first movers % 0.23/0.53 %----and efficient producers does not decrease. % 0.23/0.53 fof(prove_l3,conjecture, % 0.23/0.53 ! [E,T] : % 0.23/0.53 ( ( environment(E) % 0.23/0.53 & subpopulations(first_movers,efficient_producers,E,T) ) % 0.23/0.53 => ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ). % 0.23/0.53 % 0.23/0.53 %-------------------------------------------------------------------------- % 0.23/0.53 %------------------------------------------- % 0.23/0.53 % Proof found % 0.23/0.53 % SZS status Theorem for theBenchmark % 0.23/0.53 % SZS output start Proof % 0.23/0.53 %ClaNum:37(EqnAxiom:26) % 0.23/0.53 %VarNum:50(SingletonVarNum:15) % 0.23/0.53 %MaxLitNum:5 % 0.23/0.53 %MaxfuncDepth:2 % 0.23/0.53 %SharedTerms:11 % 0.23/0.53 %goalClause: 27 28 29 % 0.23/0.53 %singleGoalClaCount:3 % 0.23/0.53 [27]P1(a1) % 0.23/0.53 [29]P4(a6,a4,a1,a7) % 0.23/0.53 [28]P2(f3(f2(a6,a7),f2(a4,a7))) % 0.23/0.53 [30]~P2(x301)+~P5(x301) % 0.23/0.53 [31]P6(x311,x312)+~P7(x311,x312)+E(x311,x312) % 0.23/0.54 [34]~P1(x341)+P8(x341,x342)+~P4(a6,a4,x341,x342) % 0.23/0.54 [35]~P1(x351)+~P4(a6,a4,x351,x352)+P6(f9(x351,x352),a10) % 0.23/0.54 [36]~P1(x362)+~P4(a6,a4,x362,x361)+~P2(f8(x362,x361))+P5(f3(f2(a6,x361),f2(a4,x361))) % 0.23/0.54 [37]~P1(x371)+~P4(a6,a4,x371,x372)+~P3(f8(x371,x372))+~P2(f3(f2(a6,x372),f2(a4,x372))) % 0.23/0.54 [32]~P1(x321)+~P8(x321,x322)+P6(f5(x321),x322)+~P6(f9(x321,x322),a10)+P3(f8(x321,x322)) % 0.23/0.54 [33]~P1(x331)+~P8(x331,x332)+~P6(f5(x331),x332)+~P6(f9(x331,x332),a10)+P2(f8(x331,x332)) % 0.23/0.54 %EqnAxiom % 0.23/0.54 [1]E(x11,x11) % 0.23/0.54 [2]E(x22,x21)+~E(x21,x22) % 0.23/0.54 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.23/0.54 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.23/0.54 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.23/0.54 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.23/0.54 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.23/0.54 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83)) % 0.23/0.54 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92)) % 0.23/0.54 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103)) % 0.23/0.54 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112)) % 0.23/0.54 [12]~E(x121,x122)+E(f5(x121),f5(x122)) % 0.23/0.54 [13]~P1(x131)+P1(x132)+~E(x131,x132) % 0.23/0.54 [14]~P2(x141)+P2(x142)+~E(x141,x142) % 0.23/0.54 [15]P4(x152,x153,x154,x155)+~E(x151,x152)+~P4(x151,x153,x154,x155) % 0.23/0.54 [16]P4(x163,x162,x164,x165)+~E(x161,x162)+~P4(x163,x161,x164,x165) % 0.23/0.54 [17]P4(x173,x174,x172,x175)+~E(x171,x172)+~P4(x173,x174,x171,x175) % 0.23/0.54 [18]P4(x183,x184,x185,x182)+~E(x181,x182)+~P4(x183,x184,x185,x181) % 0.23/0.54 [19]~P5(x191)+P5(x192)+~E(x191,x192) % 0.23/0.54 [20]P6(x202,x203)+~E(x201,x202)+~P6(x201,x203) % 0.23/0.54 [21]P6(x213,x212)+~E(x211,x212)+~P6(x213,x211) % 0.23/0.54 [22]P8(x222,x223)+~E(x221,x222)+~P8(x221,x223) % 0.23/0.54 [23]P8(x233,x232)+~E(x231,x232)+~P8(x233,x231) % 0.23/0.54 [24]P7(x242,x243)+~E(x241,x242)+~P7(x241,x243) % 0.23/0.54 [25]P7(x253,x252)+~E(x251,x252)+~P7(x253,x251) % 0.23/0.54 [26]~P3(x261)+P3(x262)+~E(x261,x262) % 0.23/0.54 % 0.23/0.54 %------------------------------------------- % 0.23/0.54 cnf(38,plain, % 0.23/0.54 (P8(a1,a7)), % 0.23/0.54 inference(scs_inference,[],[27,29,34])). % 0.23/0.54 cnf(40,plain, % 0.23/0.54 (~P3(f8(a1,a7))), % 0.23/0.54 inference(scs_inference,[],[27,29,28,34,37])). % 0.23/0.54 cnf(54,plain, % 0.23/0.54 (~P2(f8(a1,a7))), % 0.23/0.54 inference(scs_inference,[],[28,29,27,30,36])). % 0.23/0.54 cnf(65,plain, % 0.23/0.54 (~E(x651,a1)+P1(x651)), % 0.23/0.54 inference(scs_inference,[],[27,13,2])). % 0.23/0.54 cnf(84,plain, % 0.23/0.54 (P6(f9(a1,a7),a10)), % 0.23/0.54 inference(scs_inference,[],[29,35,65])). % 0.23/0.54 cnf(87,plain, % 0.23/0.54 ($false), % 0.23/0.54 inference(scs_inference,[],[27,38,84,54,40,32,33]), % 0.23/0.54 ['proof']). % 0.23/0.54 % SZS output end Proof % 0.23/0.54 % Total time :0.022341s %------------------------------------------------------------------------------