TSTP Solution File: MGT036+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : MGT036+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:06:56 EDT 2023
% Result : Theorem 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 06:25:49 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % File :CSE---1.6
% 0.19/0.62 % Problem :theBenchmark
% 0.19/0.62 % Transform :cnf
% 0.19/0.62 % Format :tptp:raw
% 0.19/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.62
% 0.19/0.62 % Result :Theorem 0.000000s
% 0.19/0.62 % Output :CNFRefutation 0.000000s
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 % File : MGT036+2 : TPTP v8.1.2. Released v2.0.0.
% 0.19/0.62 % Domain : Management (Organisation Theory)
% 0.19/0.62 % Problem : First movers never outcompete efficient producers.
% 0.19/0.62 % Version : [PM93] axioms.
% 0.19/0.62 % English :
% 0.19/0.62
% 0.19/0.62 % Refs : [PM93] Peli & Masuch (1993), The Logic of Propogation Strateg
% 0.19/0.62 % : [PM94] Peli & Masuch (1994), The Logic of Propogation Strateg
% 0.19/0.62 % : [PB+94] Peli et al. (1994), A Logical Approach to Formalizing
% 0.19/0.62 % Source : [PM93]
% 0.19/0.62 % Names : THEOREM 5 [PM93]
% 0.19/0.62 % : T5 [PB+94]
% 0.19/0.62
% 0.19/0.62 % Status : Theorem
% 0.19/0.62 % Rating : 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.12 v5.4.0, 0.09 v5.3.0, 0.17 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v3.7.0, 0.00 v2.1.0
% 0.19/0.62 % Syntax : Number of formulae : 7 ( 1 unt; 0 def)
% 0.19/0.62 % Number of atoms : 24 ( 0 equ)
% 0.19/0.62 % Maximal formula atoms : 5 ( 3 avg)
% 0.19/0.62 % Number of connectives : 21 ( 4 ~; 0 |; 9 &)
% 0.19/0.62 % ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.62 % Maximal formula depth : 10 ( 6 avg)
% 0.19/0.62 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.62 % Number of predicates : 6 ( 6 usr; 0 prp; 1-4 aty)
% 0.19/0.62 % Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.19/0.62 % Number of variables : 20 ( 20 !; 0 ?)
% 0.19/0.62 % SPC : FOF_THM_RFO_NEQ
% 0.19/0.62
% 0.19/0.62 % Comments :
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 %----MP. The "pop" predicate is symmetric: if S1 and S2 are subpopulations,
% 0.19/0.62 %----then S2 and S1 are also subpopulations.
% 0.19/0.62 fof(mp_symmetry_of_subpopulations,axiom,
% 0.19/0.62 ! [E,S1,S2,T] :
% 0.19/0.62 ( ( environment(E)
% 0.19/0.62 & subpopulations(S1,S2,E,T) )
% 0.19/0.62 => subpopulations(S2,S1,E,T) ) ).
% 0.19/0.62
% 0.19/0.62 %----MP. The time points when FM and EP are present in the environment
% 0.19/0.62 %----occur during the environment sustains.
% 0.19/0.62 fof(mp_time_point_occur,axiom,
% 0.19/0.62 ! [E,T] :
% 0.19/0.62 ( ( environment(E)
% 0.19/0.62 & subpopulations(first_movers,efficient_producers,E,T) )
% 0.19/0.62 => in_environment(E,T) ) ).
% 0.19/0.62
% 0.19/0.62 %----MP. on "greater or equal to"
% 0.19/0.62 fof(mp_growth_rate_relationships,axiom,
% 0.19/0.62 ! [E,S1,S2,T] :
% 0.19/0.62 ( ( ( environment(E)
% 0.19/0.62 & subpopulations(S1,S2,E,T) )
% 0.19/0.62 => greater_or_equal(growth_rate(S1,T),zero) )
% 0.19/0.62 <=> ~ greater(zero,growth_rate(S1,T)) ) ).
% 0.19/0.62
% 0.19/0.62 %----D2. A subpopulation outcompetes an other in an environment at a
% 0.19/0.62 %----certain time, if and only if, it has non-negative growth rate while
% 0.19/0.62 %----the other subpopulation has negative growth rate.
% 0.19/0.62 fof(d2,hypothesis,
% 0.19/0.62 ! [E,S1,S2,T] :
% 0.19/0.62 ( ( environment(E)
% 0.19/0.62 & subpopulations(S1,S2,E,T) )
% 0.19/0.62 => ( ( greater_or_equal(growth_rate(S2,T),zero)
% 0.19/0.62 & greater(zero,growth_rate(S1,T)) )
% 0.19/0.62 <=> outcompetes(S2,S1,T) ) ) ).
% 0.19/0.62
% 0.19/0.62 %----A2. Efficient producers are more resilient than first movers.
% 0.19/0.62 fof(a2,hypothesis,
% 0.19/0.62 greater(resilience(efficient_producers),resilience(first_movers)) ).
% 0.19/0.62
% 0.19/0.62 %----A13. If a less resilient organizational group does not decrease in a
% 0.19/0.62 %----given environment, then a more resilient organizational group does not
% 0.19/0.62 %----decrease either in the same environment.
% 0.19/0.62 fof(a13,hypothesis,
% 0.19/0.62 ! [E,S1,S2,T] :
% 0.19/0.62 ( ( environment(E)
% 0.19/0.62 & in_environment(E,T)
% 0.19/0.62 & ~ greater(zero,growth_rate(S1,T))
% 0.19/0.62 & greater(resilience(S2),resilience(S1)) )
% 0.19/0.62 => ~ greater(zero,growth_rate(S2,T)) ) ).
% 0.19/0.62
% 0.19/0.62 %----GOAL: T5. First movers never outcompete efficient producers.
% 0.19/0.62 fof(prove_t5,conjecture,
% 0.19/0.62 ! [E,T] :
% 0.19/0.62 ( ( environment(E)
% 0.19/0.62 & subpopulations(first_movers,efficient_producers,E,T) )
% 0.19/0.62 => ~ outcompetes(first_movers,efficient_producers,T) ) ).
% 0.19/0.62
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark
% 0.19/0.62 % SZS output start Proof
% 0.19/0.63 %ClaNum:14(EqnAxiom:0)
% 0.19/0.63 %VarNum:77(SingletonVarNum:35)
% 0.19/0.63 %MaxLitNum:5
% 0.19/0.63 %MaxfuncDepth:1
% 0.19/0.63 %SharedTerms:11
% 0.19/0.63 %goalClause: 1 3 4
% 0.19/0.63 %singleGoalClaCount:3
% 0.19/0.63 [1]P1(a1)
% 0.19/0.63 [3]P3(a4,a2,a5)
% 0.19/0.63 [4]P6(a4,a2,a1,a5)
% 0.19/0.63 [2]P2(f3(a2),f3(a4))
% 0.19/0.63 [6]~P2(a7,f6(x61,x62))+~P4(f6(x61,x62),a7)
% 0.19/0.63 [5]P1(x51)+~P2(a7,f6(x52,x53))
% 0.19/0.63 [8]P6(x81,x82,x83,x84)+~P2(a7,f6(x81,x84))
% 0.19/0.63 [9]~P1(x91)+P5(x91,x92)+~P6(a4,a2,x91,x92)
% 0.19/0.63 [14]~P1(x143)+~P6(x142,x141,x143,x144)+P6(x141,x142,x143,x144)
% 0.19/0.63 [10]~P6(x101,x104,x103,x102)+~P1(x103)+P2(a7,f6(x101,x102))+P4(f6(x101,x102),a7)
% 0.19/0.63 [11]~P6(x111,x114,x113,x112)+~P3(x114,x111,x112)+~P1(x113)+P2(a7,f6(x111,x112))
% 0.19/0.63 [12]~P6(x124,x121,x123,x122)+~P3(x121,x124,x122)+~P1(x123)+P4(f6(x121,x122),a7)
% 0.19/0.63 [7]~P5(x73,x72)+~P1(x73)+~P2(f3(x74),f3(x71))+P2(a7,f6(x71,x72))+~P2(a7,f6(x74,x72))
% 0.19/0.63 [13]~P6(x132,x131,x134,x133)+P3(x131,x132,x133)+~P1(x134)+~P2(a7,f6(x132,x133))+~P4(f6(x131,x133),a7)
% 0.19/0.63 %EqnAxiom
% 0.19/0.63
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 cnf(26,plain,
% 0.19/0.63 ($false),
% 0.19/0.63 inference(scs_inference,[],[1,3,4,2,9,14,12,11,7,5,8,6]),
% 0.19/0.63 ['proof']).
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------