TSTP Solution File: MGT036+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n015.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 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:26:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 0.20/0.59 %-------------------------------------------
% 0.20/0.59 % File :CSE---1.6
% 0.20/0.59 % Problem :theBenchmark
% 0.20/0.59 % Transform :cnf
% 0.20/0.59 % Format :tptp:raw
% 0.20/0.59 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.59
% 0.20/0.59 % Result :Theorem 0.000000s
% 0.20/0.59 % Output :CNFRefutation 0.000000s
% 0.20/0.59 %-------------------------------------------
% 0.20/0.60 %--------------------------------------------------------------------------
% 0.20/0.60 % File : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.20/0.60 % Domain : Management (Organisation Theory)
% 0.20/0.60 % Problem : First movers never outcompete efficient producers.
% 0.20/0.60 % Version : [PM93] axioms.
% 0.20/0.60 % English :
% 0.20/0.60
% 0.20/0.60 % Refs : [PM93] Peli & Masuch (1993), The Logic of Propogation Strateg
% 0.20/0.60 % : [PM94] Peli & Masuch (1994), The Logic of Propogation Strateg
% 0.20/0.60 % Source : [PM93]
% 0.20/0.60 % Names : THEOREM 5* [PM93]
% 0.20/0.60
% 0.20/0.60 % Status : Theorem
% 0.20/0.60 % Rating : 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.04 v5.3.0, 0.13 v5.2.0, 0.00 v2.1.0
% 0.20/0.60 % Syntax : Number of formulae : 4 ( 0 unt; 0 def)
% 0.20/0.60 % Number of atoms : 15 ( 0 equ)
% 0.20/0.60 % Maximal formula atoms : 5 ( 3 avg)
% 0.20/0.60 % Number of connectives : 11 ( 0 ~; 0 |; 8 &)
% 0.20/0.60 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.60 % Maximal formula depth : 8 ( 7 avg)
% 0.20/0.60 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.60 % Number of predicates : 5 ( 5 usr; 0 prp; 1-4 aty)
% 0.20/0.60 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 0.20/0.60 % Number of variables : 12 ( 8 !; 4 ?)
% 0.20/0.60 % SPC : FOF_THM_RFO_NEQ
% 0.20/0.60
% 0.20/0.60 % Comments :
% 0.20/0.60 %--------------------------------------------------------------------------
% 0.20/0.60 %----MP. The "pop" predicate is symmetric: if S1 and S2 are subpopulations,
% 0.20/0.60 %----then S2 and S1 are also subpopulations.
% 0.20/0.60 fof(mp_symmetry_of_subpopulations,axiom,
% 0.20/0.60 ! [E,S1,S2,T] :
% 0.20/0.60 ( ( environment(E)
% 0.20/0.60 & subpopulations(S1,S2,E,T) )
% 0.20/0.60 => subpopulations(S2,S1,E,T) ) ).
% 0.20/0.60
% 0.20/0.60 %----D2. A subpopulation outcompetes an other in an environment at a
% 0.20/0.60 %----certain time, if and only if, it has non-negative growth rate while
% 0.20/0.60 %----the other subpopulation has negative growth rate.
% 0.20/0.60 fof(d2,hypothesis,
% 0.20/0.60 ! [E,S1,S2,T] :
% 0.20/0.60 ( ( environment(E)
% 0.20/0.60 & subpopulations(S1,S2,E,T) )
% 0.20/0.60 => ( ( greater_or_equal(growth_rate(S2,T),zero)
% 0.20/0.60 & greater(zero,growth_rate(S1,T)) )
% 0.20/0.60 <=> outcompetes(S2,S1,T) ) ) ).
% 0.20/0.60
% 0.20/0.60 %----A13*: Efficient producers may decrease in members even when the first
% 0.20/0.60 %----mover subpopulation grows or stagnates.
% 0.20/0.60 fof(a13_star,hypothesis,
% 0.20/0.60 ? [E,T] :
% 0.20/0.60 ( environment(E)
% 0.20/0.60 & subpopulations(first_movers,efficient_producers,E,T)
% 0.20/0.60 & greater_or_equal(growth_rate(first_movers,T),zero)
% 0.20/0.60 & greater(zero,growth_rate(efficient_producers,T)) ) ).
% 0.20/0.60
% 0.20/0.60 %----GOAL: T5*. First movers may outcompete efficient producers in some
% 0.20/0.60 %----environments.
% 0.20/0.60 fof(prove_t5_star,conjecture,
% 0.20/0.60 ? [E,T] :
% 0.20/0.60 ( environment(E)
% 0.20/0.60 & subpopulations(first_movers,efficient_producers,E,T)
% 0.20/0.60 & outcompetes(first_movers,efficient_producers,T) ) ).
% 0.20/0.60
% 0.20/0.60 %--------------------------------------------------------------------------
% 0.20/0.60 %-------------------------------------------
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark
% 0.20/0.60 % SZS output start Proof
% 0.20/0.60 %ClaNum:9(EqnAxiom:0)
% 0.20/0.60 %VarNum:45(SingletonVarNum:18)
% 0.20/0.60 %MaxLitNum:5
% 0.20/0.60 %MaxfuncDepth:1
% 0.20/0.60 %SharedTerms:11
% 0.20/0.60 %goalClause: 5
% 0.20/0.60 [1]P1(a1)
% 0.20/0.60 [4]P4(a6,a2,a1,a4)
% 0.20/0.60 [2]P2(a3,f5(a2,a4))
% 0.20/0.60 [3]P3(f5(a6,a4),a3)
% 0.20/0.60 [5]~P1(x51)+~P4(a6,a2,x51,x52)+~P5(a6,a2,x52)
% 0.20/0.60 [9]~P1(x93)+~P4(x92,x91,x93,x94)+P4(x91,x92,x93,x94)
% 0.20/0.60 [6]~P4(x61,x64,x63,x62)+~P5(x64,x61,x62)+~P1(x63)+P2(a3,f5(x61,x62))
% 0.20/0.60 [7]~P4(x74,x71,x73,x72)+~P5(x71,x74,x72)+~P1(x73)+P3(f5(x71,x72),a3)
% 0.20/0.60 [8]~P4(x82,x81,x84,x83)+P5(x81,x82,x83)+~P1(x84)+~P2(a3,f5(x82,x83))+~P3(f5(x81,x83),a3)
% 0.20/0.60 %EqnAxiom
% 0.20/0.60
% 0.20/0.60 %-------------------------------------------
% 0.20/0.60 cnf(12,plain,
% 0.20/0.60 ($false),
% 0.20/0.60 inference(scs_inference,[],[1,4,2,3,9,5,8]),
% 0.20/0.60 ['proof']).
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time :0.000000s
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