%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : MGT020+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n028.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 58.58s 58.72s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.05 % Problem : MGT020+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.05 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.17/0.43 % Computer : n028.cluster.edu % 0.17/0.43 % Model : x86_64 x86_64 % 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.43 % Memory : 8046.5625MB % 0.17/0.43 % OS : Linux 6.8.0-71-generic % 0.17/0.43 % CPULimit : 300 % 0.17/0.43 % WCLimit : 300 % 0.17/0.43 % DateTime : Mon Sep 7 12:02:47 UTC 2026 % 0.17/0.44 % CPUTime : % 0.43/0.64 start to proof:theBenchmark % 58.58/58.71 %------------------------------------------- % 58.58/58.71 % File :CSE---1.7 % 58.58/58.71 % Problem :theBenchmark % 58.58/58.71 % Transform :cnf % 58.58/58.71 % Format :tptp:raw % 58.58/58.71 % Command :java -jar mcs_scs.jar %d %s % 58.58/58.71 % 58.58/58.71 % Result :Theorem 58.053754s % 58.58/58.71 % Output :CNFRefutation 58.053754s % 58.58/58.71 %------------------------------------------- % 58.58/58.72 %-------------------------------------------------------------------------- % 58.58/58.72 % File : MGT020+1 : TPTP v9.3.0. Released v2.0.0. % 58.58/58.72 % Domain : Management (Organisation Theory) % 58.58/58.72 % Problem : First movers exceeds efficient producers disbanding rate % 58.58/58.72 % Version : [PB+94] axioms. % 58.58/58.72 % English : % 58.58/58.72 % 58.58/58.72 % Refs : [PM93] Peli & Masuch (1993), The Logic of Propogation Strateg % 58.58/58.72 % : [PM94] Peli & Masuch (1994), The Logic of Propogation Strateg % 58.58/58.72 % : [PB+94] Peli et al. (1994), A Logical Approach to Formalizing % 58.58/58.72 % : [Kam95] Kamps (1995), Email to G. Sutcliffe % 58.58/58.72 % Source : [Kam95] % 58.58/58.72 % Names : LEMMA 2 [PM93] % 58.58/58.72 % : L2 [PB+94] % 58.58/58.72 % 58.58/58.72 % Status : Theorem % 58.58/58.72 % Rating : 0.13 v9.3.0, 0.15 v9.1.0, 0.09 v9.0.0, 0.14 v8.2.0, 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.1.0, 0.13 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.0, 0.08 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.14 v3.2.0, 0.18 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.38 v2.4.0, 0.00 v2.1.0 % 58.58/58.72 % Syntax : Number of formulae : 11 ( 0 unt; 0 def) % 58.58/58.72 % Number of atoms : 42 ( 1 equ) % 58.58/58.72 % Maximal formula atoms : 7 ( 3 avg) % 58.58/58.72 % Number of connectives : 33 ( 2 ~; 1 |; 16 &) % 58.58/58.72 % ( 0 <=>; 14 =>; 0 <=; 0 <~>) % 58.58/58.72 % Maximal formula depth : 10 ( 6 avg) % 58.58/58.72 % Maximal term depth : 3 ( 1 avg) % 58.58/58.72 % Number of predicates : 7 ( 6 usr; 0 prp; 1-4 aty) % 58.58/58.72 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty) % 58.58/58.72 % Number of variables : 26 ( 26 !; 0 ?) % 58.58/58.72 % SPC : FOF_THM_RFO_SEQ % 58.58/58.72 % 58.58/58.72 % Comments : Same as version with [PM93] axioms. % 58.58/58.72 %-------------------------------------------------------------------------- % 58.58/58.72 %----Subsitution axioms % 58.58/58.72 %----Problem axioms % 58.58/58.72 %----L3. The difference between the disbanding rates of first movers and % 58.58/58.72 %----efficient producers does not decrease. % 58.58/58.72 fof(l3,axiom, % 58.58/58.72 ! [E,T] : % 58.58/58.72 ( ( environment(E) % 58.58/58.72 & subpopulations(first_movers,efficient_producers,E,T) ) % 58.58/58.72 => ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ). % 58.58/58.72 % 58.58/58.72 %----MP. The initial time point of the environment is the earliest time, % 58.58/58.72 %----when both FM and EP are present in the environment. % 58.58/58.72 fof(mp_earliest_time_point,axiom, % 58.58/58.72 ! [E,T] : % 58.58/58.72 ( environment(E) % 58.58/58.72 => ( ( in_environment(E,initial_FM_EP(E)) % 58.58/58.72 => subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) ) % 58.58/58.72 & ( subpopulations(first_movers,efficient_producers,E,T) % 58.58/58.72 => greater_or_equal(T,initial_FM_EP(E)) ) ) ) ). % 58.58/58.72 % 58.58/58.72 %----MP. If f1(x1) > f2(x1) and f1(x)-f2(x) does not decrease on [x1,x2] % 58.58/58.72 %----then f1(x2) > f2(x2). % 58.58/58.72 %----INSTANTIATION: f1(x) = disbanding_rate(first_movers,x) ; % 58.58/58.72 %----f2(x) = disbanding_rate(efficient_producers,x) % 58.58/58.72 fof(mp_positive_function_difference,axiom, % 58.58/58.72 ! [E,T,T1,T2] : % 58.58/58.72 ( ( environment(E) % 58.58/58.72 & greater_or_equal(T,T1) % 58.58/58.72 & greater_or_equal(T2,T) % 58.58/58.72 & subpopulations(first_movers,efficient_producers,E,T2) % 58.58/58.72 & greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1)) ) % 58.58/58.72 => ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) % 58.58/58.72 => greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ) ) ). % 58.58/58.72 % 58.58/58.72 %----MP. If FM and EP are non-empty subpopulations at a time -point in the % 58.58/58.72 %----environment, then this time point occurs while the environment % 58.58/58.72 %----persists. % 58.58/58.72 fof(mp_time_point_occurs,axiom, % 58.58/58.72 ! [E,T] : % 58.58/58.72 ( ( environment(E) % 58.58/58.72 & subpopulations(first_movers,efficient_producers,E,T) ) % 58.58/58.72 => in_environment(E,T) ) ). % 58.58/58.72 % 58.58/58.72 %----MP. The initial time of an environment cannot precede the opening of % 58.58/58.72 %----this environment. % 58.58/58.72 fof(mp_initial_time,axiom, % 58.58/58.72 ! [E] : % 58.58/58.72 ( environment(E) % 58.58/58.72 => greater_or_equal(initial_FM_EP(E),start_time(E)) ) ). % 58.58/58.72 % 58.58/58.72 %----MP. If time point T1 occurs after the opening of the environment, and % 58.58/58.72 %----a later time point T2 occurs before the environment ends, then T1 also % 58.58/58.72 %----occurs before the end of the environment. % 58.58/58.72 fof(mp_times_in_order,axiom, % 58.58/58.72 ! [E,T1,T2] : % 58.58/58.72 ( ( environment(E) % 58.58/58.72 & greater_or_equal(T1,start_time(E)) % 58.58/58.72 & greater(T2,T1) % 58.58/58.72 & in_environment(E,T2) ) % 58.58/58.72 => in_environment(E,T1) ) ). % 58.58/58.72 % 58.58/58.72 %----MP. inequality % 58.58/58.72 fof(mp_greater_transitivity,axiom, % 58.58/58.72 ! [X,Y,Z] : % 58.58/58.72 ( ( greater(X,Y) % 58.58/58.72 & greater(Y,Z) ) % 58.58/58.72 => greater(X,Z) ) ). % 58.58/58.72 % 58.58/58.72 %----MP. on "greater or equal to" % 58.58/58.72 fof(mp_greater_or_equal,axiom, % 58.58/58.72 ! [X,Y] : % 58.58/58.72 ( greater_or_equal(X,Y) % 58.58/58.72 => ( greater(X,Y) % 58.58/58.72 | X = Y ) ) ). % 58.58/58.72 % 58.58/58.72 %----A8. The disbanding rate of first movers exceeds the disbanding rate % 58.58/58.72 %----of efficient producers initially. % 58.58/58.72 fof(a8,hypothesis, % 58.58/58.72 ! [E] : % 58.58/58.72 ( environment(E) % 58.58/58.72 => greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ) ). % 58.58/58.72 % 58.58/58.72 %----A10. If FM and EP are present in the environment at time-points t1 % 58.58/58.72 %----and t2, then they are present during the time-interval between % 58.58/58.72 %----t1 and t2. % 58.58/58.72 fof(a10,hypothesis, % 58.58/58.72 ! [E,T1,T2,T] : % 58.58/58.72 ( ( environment(E) % 58.58/58.72 & subpopulations(first_movers,efficient_producers,E,T1) % 58.58/58.72 & subpopulations(first_movers,efficient_producers,E,T2) % 58.58/58.72 & greater_or_equal(T,T1) % 58.58/58.72 & greater_or_equal(T2,T) ) % 58.58/58.72 => subpopulations(first_movers,efficient_producers,E,T) ) ). % 58.58/58.72 % 58.58/58.72 %----GOAL: L2. The disbanding rate of first movers exceeds the disbanding % 58.58/58.72 %----rate of efficient producers. % 58.58/58.72 fof(prove_l2,conjecture, % 58.58/58.72 ! [E,T] : % 58.58/58.72 ( ( environment(E) % 58.58/58.72 & subpopulations(first_movers,efficient_producers,E,T) ) % 58.58/58.72 => greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ) ). % 58.58/58.72 % 58.58/58.72 %-------------------------------------------------------------------------- % 58.58/58.72 %------------------------------------------- % 58.58/58.72 % Proof found % 58.58/58.72 % SZS status Theorem for theBenchmark % 58.58/58.72 % SZS output start Proof % 58.58/58.72 %ClaNum:35(EqnAxiom:21) % 58.58/58.72 %VarNum:71(SingletonVarNum:25) % 58.58/58.72 %MaxLitNum:7 % 58.58/58.72 %MaxfuncDepth:2 % 58.58/58.72 %SharedTerms:9 % 58.58/58.72 %goalClause: 22 23 24 % 58.58/58.72 %singleGoalClaCount:3 % 58.58/58.72 [22]P1(a1) % 58.58/58.72 [23]P3(a5,a2,a1,a6) % 58.58/58.72 [24]~P4(f3(a5,a6),f3(a2,a6)) % 58.58/58.72 [25]~P1(x251)+P5(f7(x251),f8(x251)) % 58.58/58.72 [28]~P1(x281)+P4(f3(a5,f7(x281)),f3(a2,f7(x281))) % 58.58/58.72 [30]~P1(x301)+~P6(x301,f7(x301))+P3(a5,a2,x301,f7(x301)) % 58.58/58.72 [26]P4(x261,x262)+~P5(x261,x262)+E(x261,x262) % 58.58/58.72 [31]~P1(x311)+P6(x311,x312)+~P3(a5,a2,x311,x312) % 58.58/58.72 [32]~P1(x322)+~P3(a5,a2,x322,x321)+P5(x321,f7(x322)) % 58.58/58.72 [33]~P1(x331)+~P3(a5,a2,x331,x332)+~P2(f4(f3(a5,x332),f3(a2,x332))) % 58.58/58.72 [27]~P4(x271,x273)+P4(x271,x272)+~P4(x273,x272) % 58.58/58.72 [29]~P1(x291)+~P4(x293,x292)+P6(x291,x292)+~P6(x291,x293)+~P5(x292,f8(x291)) % 58.58/58.72 [35]~P1(x351)+~P5(x352,x353)+~P5(x354,x352)+~P3(a5,a2,x351,x354)+~P3(a5,a2,x351,x353)+P3(a5,a2,x351,x352) % 58.58/58.72 [34]~P5(x341,x342)+~P5(x342,x344)+~P1(x343)+~P3(a5,a2,x343,x341)+~P4(f3(a5,x344),f3(a2,x344))+P4(f3(a5,x341),f3(a2,x341))+P2(f4(f3(a5,x342),f3(a2,x342))) % 58.58/58.72 %EqnAxiom % 58.58/58.72 [1]E(x11,x11) % 58.58/58.72 [2]E(x22,x21)+~E(x21,x22) % 58.58/58.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 58.58/58.72 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 58.58/58.72 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 58.58/58.72 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63)) % 58.58/58.72 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72)) % 58.58/58.72 [8]~E(x81,x82)+E(f7(x81),f7(x82)) % 58.58/58.72 [9]~E(x91,x92)+E(f8(x91),f8(x92)) % 58.58/58.72 [10]~P1(x101)+P1(x102)+~E(x101,x102) % 58.58/58.72 [11]P3(x112,x113,x114,x115)+~E(x111,x112)+~P3(x111,x113,x114,x115) % 58.58/58.72 [12]P3(x123,x122,x124,x125)+~E(x121,x122)+~P3(x123,x121,x124,x125) % 58.58/58.72 [13]P3(x133,x134,x132,x135)+~E(x131,x132)+~P3(x133,x134,x131,x135) % 58.58/58.72 [14]P3(x143,x144,x145,x142)+~E(x141,x142)+~P3(x143,x144,x145,x141) % 58.58/58.72 [15]P4(x152,x153)+~E(x151,x152)+~P4(x151,x153) % 58.58/58.72 [16]P4(x163,x162)+~E(x161,x162)+~P4(x163,x161) % 58.58/58.72 [17]P5(x172,x173)+~E(x171,x172)+~P5(x171,x173) % 58.58/58.72 [18]P5(x183,x182)+~E(x181,x182)+~P5(x183,x181) % 58.58/58.72 [19]~P2(x191)+P2(x192)+~E(x191,x192) % 58.58/58.72 [20]P6(x202,x203)+~E(x201,x202)+~P6(x201,x203) % 58.58/58.72 [21]P6(x213,x212)+~E(x211,x212)+~P6(x213,x211) % 58.58/58.72 % 58.58/58.72 %------------------------------------------- % 58.58/58.73 cnf(36,plain, % 58.58/58.73 (P6(a1,a6)), % 58.58/58.73 inference(scs_inference,[],[22,23,31])). % 58.58/58.73 cnf(82,plain, % 58.58/58.73 (~E(a1,x821)+P5(f7(x821),f8(x821))), % 58.58/58.73 inference(scs_inference,[],[22,25,10])). % 58.58/58.73 cnf(83,plain, % 58.58/58.73 (P5(f7(a1),f8(a1))), % 58.58/58.73 inference(equality_inference,[],[82])). % 58.58/58.73 cnf(249,plain, % 58.58/58.73 (~E(a1,x2491)+P4(f3(a5,f7(x2491)),f3(a2,f7(x2491)))), % 58.58/58.73 inference(scs_inference,[],[22,28,10])). % 58.58/58.73 cnf(250,plain, % 58.58/58.73 (P4(f3(a5,f7(a1)),f3(a2,f7(a1)))), % 58.58/58.73 inference(equality_inference,[],[249])). % 58.58/58.73 cnf(259,plain, % 58.58/58.73 (~E(f7(a1),a6)+~E(f3(a2,f7(a1)),f3(a2,a6))), % 58.58/58.73 inference(scs_inference,[],[24,250,16,15,5])). % 58.58/58.73 cnf(311,plain, % 58.58/58.73 (~E(f3(a2,a6),f3(a2,f7(a1)))+~E(f7(a1),a6)), % 58.58/58.73 inference(scs_inference,[],[259,2])). % 58.58/58.73 cnf(327,plain, % 58.58/58.73 (~E(a6,f7(a1))+~E(f3(a2,a6),f3(a2,f7(a1)))), % 58.58/58.73 inference(scs_inference,[],[311,2])). % 58.58/58.73 cnf(343,plain, % 58.58/58.73 (~E(a6,f7(a1))), % 58.58/58.73 inference(scs_inference,[],[327,5])). % 58.58/58.73 cnf(455,plain, % 58.58/58.73 (P5(a6,f7(a1))+~P3(a5,a2,a1,a6)), % 58.58/58.73 inference(scs_inference,[],[23,22,32,10])). % 58.58/58.73 cnf(456,plain, % 58.58/58.73 (P5(a6,f7(a1))), % 58.58/58.73 inference(scs_inference,[],[23,455])). % 58.58/58.73 cnf(459,plain, % 58.58/58.73 (P6(a1,f7(a1))), % 58.58/58.73 inference(scs_inference,[],[36,23,22,83,343,455,26,29])). % 58.58/58.73 cnf(473,plain, % 58.58/58.73 (P5(a6,x4731)+~E(f7(a1),x4731)), % 58.58/58.73 inference(scs_inference,[],[459,456,17,21,20,18])). % 58.58/58.73 cnf(496,plain, % 58.58/58.73 (~P6(a1,f7(a1))+P3(a5,a2,a1,f7(a1))), % 58.58/58.73 inference(scs_inference,[],[459,22,30,10])). % 58.58/58.73 cnf(497,plain, % 58.58/58.73 (P3(a5,a2,a1,f7(a1))), % 58.58/58.73 inference(scs_inference,[],[459,496])). % 58.58/58.73 cnf(529,plain, % 58.58/58.73 (E(f7(x5291),f7(x5292))+~E(x5292,x5291)), % 58.58/58.73 inference(scs_inference,[],[2,8])). % 58.58/58.73 cnf(829,plain, % 58.58/58.73 (~E(a1,x8291)+P5(a6,f7(x8291))), % 58.58/58.73 inference(scs_inference,[],[473,8])). % 58.58/58.73 cnf(833,plain, % 58.58/58.73 (~E(x8331,a1)+P5(a6,f7(x8331))), % 58.58/58.73 inference(scs_inference,[],[473,529])). % 58.58/58.73 cnf(982,plain, % 58.58/58.73 (~P5(f7(x9821),f7(a1))+~E(a1,x9821)+P2(f4(f3(a5,f7(x9821)),f3(a2,f7(x9821))))), % 58.58/58.73 inference(scs_inference,[],[250,24,23,22,829,34])). % 58.58/58.73 cnf(993,plain, % 58.58/58.73 (~P5(f7(x9931),f7(a1))+~E(x9931,a1)+P2(f4(f3(a5,f7(x9931)),f3(a2,f7(x9931))))), % 58.58/58.73 inference(scs_inference,[],[250,24,23,22,833,34])). % 58.58/58.73 cnf(1477,plain, % 58.58/58.73 ($false), % 58.58/58.73 inference(scs_inference,[],[22,497,456,250,24,23,32,33,982,993,34]), % 58.58/58.73 ['proof']). % 58.58/58.73 % SZS output end Proof % 58.58/58.73 % Total time :58.053754s %------------------------------------------------------------------------------