%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : MGT023+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 : n001.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 117.12s 117.29s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT023+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 % 0.09/0.35 % Computer : n001.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Mon Sep 7 12:11:22 UTC 2026 % 0.09/0.35 % CPUTime : % 0.25/0.52 start to proof:theBenchmark % 117.12/117.28 %------------------------------------------- % 117.12/117.28 % File :CSE---1.7 % 117.12/117.28 % Problem :theBenchmark % 117.12/117.28 % Transform :cnf % 117.12/117.28 % Format :tptp:raw % 117.12/117.28 % Command :java -jar mcs_scs.jar %d %s % 117.12/117.28 % 117.12/117.28 % Result :Theorem 116.774312s % 117.12/117.28 % Output :CNFRefutation 116.774312s % 117.12/117.28 %------------------------------------------- % 117.12/117.28 %-------------------------------------------------------------------------- % 117.12/117.28 % File : MGT023+1 : TPTP v9.3.0. Released v2.0.0. % 117.12/117.28 % Domain : Management (Organisation Theory) % 117.12/117.28 % Problem : Stable environments have a critical point. % 117.12/117.28 % Version : [PB+94] axioms : Reduced & Augmented > Complete. % 117.12/117.28 % English : % 117.12/117.28 % 117.12/117.28 % Refs : [PM93] Peli & Masuch (1993), The Logic of Propogation Strateg % 117.12/117.28 % : [PM94] Peli & Masuch (1994), The Logic of Propogation Strateg % 117.12/117.28 % : [Kam95] Kamps (1995), Email to G. Sutcliffe % 117.12/117.28 % Source : [Kam95] % 117.12/117.28 % Names : % 117.12/117.28 % 117.12/117.28 % Status : Theorem % 117.12/117.28 % Rating : 0.04 v9.3.0, 0.09 v9.1.0, 0.06 v9.0.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.04 v5.3.0, 0.07 v5.2.0, 0.00 v5.0.0, 0.04 v3.7.0, 0.00 v3.4.0, 0.05 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.25 v2.4.0, 0.00 v2.1.0 % 117.12/117.28 % Syntax : Number of formulae : 3 ( 0 unt; 0 def) % 117.12/117.28 % Number of atoms : 17 ( 1 equ) % 117.12/117.28 % Maximal formula atoms : 7 ( 5 avg) % 117.12/117.28 % Number of connectives : 16 ( 2 ~; 0 |; 9 &) % 117.12/117.28 % ( 0 <=>; 5 =>; 0 <=; 0 <~>) % 117.12/117.28 % Maximal formula depth : 10 ( 8 avg) % 117.12/117.28 % Maximal term depth : 2 ( 1 avg) % 117.12/117.28 % Number of predicates : 6 ( 5 usr; 0 prp; 1-4 aty) % 117.12/117.28 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty) % 117.12/117.28 % Number of variables : 7 ( 6 !; 1 ?) % 117.12/117.28 % SPC : FOF_THM_RFO_SEQ % 117.12/117.28 % 117.12/117.28 % Comments : % 117.12/117.28 %-------------------------------------------------------------------------- % 117.12/117.28 %----Subsitution axioms % 117.12/117.28 %----Problem axioms % 117.12/117.28 %----D1=>. A time point is the critical point of an environmental patch, % 117.12/117.28 %----if and only if, it is the earliest time past which the growth rate of % 117.12/117.28 %----efficient producers permanently exceeds growth rate of first movers. % 117.12/117.28 fof(d1,hypothesis, % 117.12/117.29 ! [E,To] : % 117.12/117.29 ( ( environment(E) % 117.12/117.29 & ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To)) % 117.12/117.29 & in_environment(E,To) % 117.12/117.29 & ! [T] : % 117.12/117.29 ( ( subpopulations(first_movers,efficient_producers,E,T) % 117.12/117.29 & greater(T,To) ) % 117.12/117.29 => greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) % 117.12/117.29 => To = critical_point(E) ) ). % 117.12/117.29 % 117.12/117.29 %----L12. There is an earliest time point, past which FM's growth rate % 117.12/117.29 %----exceeds EP's growth rate. % 117.12/117.29 fof(l12,hypothesis, % 117.12/117.29 ! [E] : % 117.12/117.29 ( ( environment(E) % 117.12/117.29 & stable(E) ) % 117.12/117.29 => ? [To] : % 117.12/117.29 ( in_environment(E,To) % 117.12/117.29 & ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To)) % 117.12/117.29 & ! [T] : % 117.12/117.29 ( ( subpopulations(first_movers,efficient_producers,E,T) % 117.12/117.29 & greater(T,To) ) % 117.12/117.29 => greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ) ). % 117.12/117.29 % 117.12/117.29 %----GOAL: L5. Stable environments have a critical point. % 117.12/117.29 fof(prove_l5,conjecture, % 117.12/117.29 ! [E] : % 117.12/117.29 ( ( environment(E) % 117.12/117.29 & stable(E) ) % 117.12/117.29 => in_environment(E,critical_point(E)) ) ). % 117.12/117.29 % 117.12/117.29 %-------------------------------------------------------------------------- % 117.12/117.29 %------------------------------------------- % 117.12/117.29 % Proof found % 117.12/117.29 % SZS status Theorem for theBenchmark % 117.12/117.29 % SZS output start Proof % 117.12/117.29 %ClaNum:28(EqnAxiom:19) % 117.12/117.29 %VarNum:47(SingletonVarNum:10) % 117.12/117.29 %MaxLitNum:5 % 117.12/117.29 %MaxfuncDepth:2 % 117.12/117.29 %SharedTerms:7 % 117.12/117.29 %goalClause: 20 21 22 % 117.12/117.29 %singleGoalClaCount:3 % 117.12/117.29 [20]P1(a1) % 117.12/117.29 [21]P2(a1) % 117.12/117.29 [22]~P3(a1,f2(a1)) % 117.12/117.29 [23]~P1(x231)+~P2(x231)+P3(x231,f3(x231)) % 117.12/117.29 [25]~P2(x251)+~P1(x251)+~P4(f6(a5,f3(x251)),f6(a7,f3(x251))) % 117.12/117.29 [24]~P1(x242)+~P3(x242,x241)+P4(f4(x242,x241),x241)+E(x241,f2(x242))+P4(f6(a5,x241),f6(a7,x241)) % 117.12/117.29 [27]~P1(x272)+~P3(x272,x271)+E(x271,f2(x272))+P5(a7,a5,x272,f4(x272,x271))+P4(f6(a5,x271),f6(a7,x271)) % 117.12/117.29 [28]~P2(x282)+~P1(x282)+~P4(x281,f3(x282))+~P5(a7,a5,x282,x281)+P4(f6(a5,x281),f6(a7,x281)) % 117.12/117.29 [26]~P1(x262)+~P3(x262,x261)+E(x261,f2(x262))+P4(f6(a5,x261),f6(a7,x261))+~P4(f6(a5,f4(x262,x261)),f6(a7,f4(x262,x261))) % 117.12/117.29 %EqnAxiom % 117.12/117.29 [1]E(x11,x11) % 117.12/117.29 [2]E(x22,x21)+~E(x21,x22) % 117.12/117.29 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 117.12/117.29 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 117.12/117.29 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 117.12/117.29 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63)) % 117.12/117.29 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72)) % 117.12/117.29 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83)) % 117.12/117.29 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92)) % 117.12/117.29 [10]~P1(x101)+P1(x102)+~E(x101,x102) % 117.12/117.29 [11]~P2(x111)+P2(x112)+~E(x111,x112) % 117.12/117.29 [12]P3(x122,x123)+~E(x121,x122)+~P3(x121,x123) % 117.12/117.29 [13]P3(x133,x132)+~E(x131,x132)+~P3(x133,x131) % 117.12/117.29 [14]P4(x142,x143)+~E(x141,x142)+~P4(x141,x143) % 117.12/117.29 [15]P4(x153,x152)+~E(x151,x152)+~P4(x153,x151) % 117.12/117.29 [16]P5(x162,x163,x164,x165)+~E(x161,x162)+~P5(x161,x163,x164,x165) % 117.12/117.29 [17]P5(x173,x172,x174,x175)+~E(x171,x172)+~P5(x173,x171,x174,x175) % 117.12/117.29 [18]P5(x183,x184,x182,x185)+~E(x181,x182)+~P5(x183,x184,x181,x185) % 117.12/117.29 [19]P5(x193,x194,x195,x192)+~E(x191,x192)+~P5(x193,x194,x195,x191) % 117.12/117.29 % 117.12/117.29 %------------------------------------------- % 117.12/117.29 cnf(37,plain, % 117.12/117.29 (~E(x371,a1)+P1(x371)), % 117.12/117.29 inference(scs_inference,[],[20,10,2])). % 117.12/117.29 cnf(39,plain, % 117.12/117.29 (~E(x391,a1)+P2(x391)), % 117.12/117.29 inference(scs_inference,[],[21,11,2])). % 117.12/117.29 cnf(41,plain, % 117.12/117.29 (P3(a1,f3(a1))), % 117.12/117.29 inference(scs_inference,[],[20,23,39])). % 117.12/117.29 cnf(42,plain, % 117.12/117.29 (~E(f3(a1),f2(a1))), % 117.12/117.29 inference(scs_inference,[],[22,41,13])). % 117.12/117.29 cnf(48,plain, % 117.12/117.29 (P4(x481,f3(a1))+~E(f4(a1,f3(a1)),x481)+P4(f6(a5,f3(a1)),f6(a7,f3(a1)))), % 117.12/117.29 inference(scs_inference,[],[42,20,41,14,24])). % 117.12/117.29 cnf(49,plain, % 117.12/117.29 (P4(f4(a1,f3(a1)),f3(a1))+P4(f6(a5,f3(a1)),f6(a7,f3(a1)))), % 117.12/117.29 inference(equality_inference,[],[48])). % 117.12/117.29 cnf(50,plain, % 117.12/117.29 (P4(f4(a1,f3(a1)),f3(a1))), % 117.12/117.29 inference(scs_inference,[],[20,21,49,25])). % 117.12/117.29 cnf(51,plain, % 117.12/117.29 (P4(x511,f3(a1))+~E(f4(a1,f3(a1)),x511)), % 117.12/117.29 inference(scs_inference,[],[50,14])). % 117.12/117.29 cnf(57,plain, % 117.12/117.29 (P5(x571,a5,a1,f4(a1,f3(a1)))+~E(a7,x571)+P4(f6(a5,f3(a1)),f6(a7,f3(a1)))), % 117.12/117.29 inference(scs_inference,[],[42,20,41,16,27])). % 117.12/117.29 cnf(58,plain, % 117.12/117.29 (P4(f6(a5,f3(a1)),f6(a7,f3(a1)))+P5(a7,a5,a1,f4(a1,f3(a1)))), % 117.12/117.29 inference(equality_inference,[],[57])). % 117.12/117.29 cnf(59,plain, % 117.12/117.29 (P5(a7,a5,a1,f4(a1,f3(a1)))), % 117.12/117.29 inference(scs_inference,[],[20,21,58,25])). % 117.12/117.29 cnf(63,plain, % 117.12/117.29 (P5(a7,a5,a1,x631)+~E(f4(a1,f3(a1)),x631)), % 117.12/117.29 inference(scs_inference,[],[59,16,17,18,19])). % 117.12/117.29 cnf(69,plain, % 117.12/117.29 (~P4(f6(a5,f3(a1)),f6(a7,f3(a1)))), % 117.12/117.29 inference(scs_inference,[],[21,37,25])). % 117.12/117.29 cnf(72,plain, % 117.12/117.29 (~E(f4(a1,f3(a1)),f3(a1))+~P4(f3(a1),f3(a1))), % 117.12/117.29 inference(scs_inference,[],[21,20,69,28,63])). % 117.12/117.29 cnf(76,plain, % 117.12/117.29 (~E(f4(a1,f3(a1)),f3(a1))), % 117.12/117.29 inference(scs_inference,[],[72,51])). % 117.12/117.29 cnf(80,plain, % 117.12/117.29 (~P4(f6(a5,f4(a1,f3(a1))),f6(a7,f4(a1,f3(a1))))), % 117.12/117.29 inference(scs_inference,[],[69,42,41,37,26])). % 117.12/117.29 cnf(858,plain, % 117.12/117.29 (~E(a1,x8581)+P1(x8581)), % 117.12/117.29 inference(scs_inference,[],[20,76,22,2,12,10])). % 117.12/117.29 cnf(912,plain, % 117.12/117.29 (P4(f6(a5,f4(a1,f3(a1))),f6(a7,f4(a1,f3(a1))))), % 117.12/117.29 inference(scs_inference,[],[50,21,59,858,28])). % 117.12/117.29 cnf(990,plain, % 117.12/117.29 ($false), % 117.12/117.29 inference(scs_inference,[],[80,912]), % 117.12/117.29 ['proof']). % 117.12/117.29 % SZS output end Proof % 117.12/117.29 % Total time :116.774312s %------------------------------------------------------------------------------