TSTP Solution File: MGT027+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : MGT027+1 : 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 : n021.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 09:06:51 EDT 2023
% Result : Theorem 120.72s 120.74s
% Output : CNFRefutation 120.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT027+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 06:34:28 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.58 start to proof:theBenchmark
% 120.72/120.73 %-------------------------------------------
% 120.72/120.73 % File :CSE---1.6
% 120.72/120.73 % Problem :theBenchmark
% 120.72/120.73 % Transform :cnf
% 120.72/120.73 % Format :tptp:raw
% 120.72/120.73 % Command :java -jar mcs_scs.jar %d %s
% 120.72/120.73
% 120.72/120.73 % Result :Theorem 120.100000s
% 120.72/120.73 % Output :CNFRefutation 120.100000s
% 120.72/120.73 %-------------------------------------------
% 120.72/120.74 %--------------------------------------------------------------------------
% 120.72/120.74 % File : MGT027+1 : TPTP v8.1.2. Released v2.0.0.
% 120.72/120.74 % Domain : Management (Organisation Theory)
% 120.72/120.74 % Problem : The FM set contracts in stable environments
% 120.72/120.74 % Version : [PB+94] axioms : Reduced & Augmented > Complete.
% 120.72/120.74 % English : The first mover set begins to contract past a certain time
% 120.72/120.74 % in stable environments.
% 120.72/120.74
% 120.72/120.74 % Refs : [PM93] Peli & Masuch (1993), The Logic of Propogation Strateg
% 120.72/120.74 % : [PM94] Peli & Masuch (1994), The Logic of Propogation Strateg
% 120.72/120.74 % : [Kam95] Kamps (1995), Email to G. Sutcliffe
% 120.72/120.74 % Source : [Kam95]
% 120.72/120.74 % Names :
% 120.72/120.74
% 120.72/120.74 % Status : Theorem
% 120.72/120.74 % Rating : 0.11 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.17 v7.3.0, 0.21 v7.2.0, 0.17 v7.1.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.17 v6.2.0, 0.16 v6.1.0, 0.17 v6.0.0, 0.09 v5.5.0, 0.15 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.17 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.25 v2.4.0, 0.25 v2.3.0, 0.33 v2.2.1, 0.00 v2.1.0
% 120.72/120.74 % Syntax : Number of formulae : 9 ( 0 unt; 0 def)
% 120.72/120.74 % Number of atoms : 40 ( 1 equ)
% 120.72/120.74 % Maximal formula atoms : 7 ( 4 avg)
% 120.72/120.74 % Number of connectives : 31 ( 0 ~; 1 |; 19 &)
% 120.72/120.74 % ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% 120.72/120.74 % Maximal formula depth : 10 ( 7 avg)
% 120.72/120.74 % Maximal term depth : 2 ( 1 avg)
% 120.72/120.74 % Number of predicates : 8 ( 7 usr; 0 prp; 1-4 aty)
% 120.72/120.74 % Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% 120.72/120.74 % Number of variables : 21 ( 19 !; 2 ?)
% 120.72/120.74 % SPC : FOF_THM_RFO_SEQ
% 120.72/120.74
% 120.72/120.74 % Comments :
% 120.72/120.74 %--------------------------------------------------------------------------
% 120.72/120.74 %----Subsitution axioms
% 120.72/120.74 %----Problem axioms
% 120.72/120.74 %----MP on "contracts from"
% 120.72/120.74 fof(mp_contracts_from,axiom,
% 120.72/120.74 ! [E,To] :
% 120.72/120.74 ( ( environment(E)
% 120.72/120.74 & stable(E)
% 120.72/120.74 & in_environment(E,To)
% 120.72/120.74 & ! [T] :
% 120.72/120.74 ( ( greater(cardinality_at_time(first_movers,T),zero)
% 120.72/120.74 & greater_or_equal(T,To) )
% 120.72/120.74 => greater(zero,growth_rate(first_movers,T)) ) )
% 120.72/120.74 => contracts_from(To,first_movers) ) ).
% 120.72/120.74
% 120.72/120.74 %----MP. If FM and EP have members in the environment, then they are
% 120.72/120.74 %----non-empty subpopulations.
% 120.72/120.74 fof(mp_non_empty_fm_and_ep,axiom,
% 120.72/120.74 ! [E,T] :
% 120.72/120.74 ( ( environment(E)
% 120.72/120.74 & in_environment(E,T)
% 120.72/120.74 & greater(cardinality_at_time(first_movers,T),zero)
% 120.72/120.74 & greater(cardinality_at_time(efficient_producers,T),zero) )
% 120.72/120.74 => subpopulations(first_movers,efficient_producers,E,T) ) ).
% 120.72/120.74
% 120.72/120.74 %----MP. Stable environments are long.
% 120.72/120.74 fof(mp_long_stable_environments,axiom,
% 120.72/120.74 ! [E,T1,T2] :
% 120.72/120.74 ( ( environment(E)
% 120.72/120.74 & stable(E)
% 120.72/120.74 & in_environment(E,T1)
% 120.72/120.74 & greater(T2,T1) )
% 120.72/120.74 => in_environment(E,T2) ) ).
% 120.72/120.74
% 120.72/120.74 %----MP. Efficient producers appear in stable environments.
% 120.72/120.74 fof(mp_EP_in_stable_environments,axiom,
% 120.72/120.74 ! [E] :
% 120.72/120.74 ( ( environment(E)
% 120.72/120.74 & stable(E) )
% 120.72/120.74 => in_environment(E,appear(efficient_producers,E)) ) ).
% 120.72/120.74
% 120.72/120.74 %----MP. inequality
% 120.72/120.74 fof(mp_greater_transitivity,axiom,
% 120.72/120.74 ! [X,Y,Z] :
% 120.72/120.74 ( ( greater(X,Y)
% 120.72/120.74 & greater(Y,Z) )
% 120.72/120.74 => greater(X,Z) ) ).
% 120.72/120.74
% 120.72/120.74 %----MP. on "greater or equal to"
% 120.72/120.74 fof(mp_greater_or_equal,axiom,
% 120.72/120.74 ! [X,Y] :
% 120.72/120.74 ( greater_or_equal(X,Y)
% 120.72/120.74 <=> ( greater(X,Y)
% 120.72/120.74 | X = Y ) ) ).
% 120.72/120.74
% 120.72/120.74 %----T6. Once appeared in an environment, efficient producers do not
% 120.72/120.74 %----disappear.
% 120.72/120.74 fof(t6,hypothesis,
% 120.72/120.74 ! [E,T] :
% 120.72/120.74 ( ( environment(E)
% 120.72/120.74 & in_environment(E,T)
% 120.72/120.74 & greater_or_equal(T,appear(efficient_producers,E)) )
% 120.72/120.74 => greater(cardinality_at_time(efficient_producers,T),zero) ) ).
% 120.72/120.74
% 120.72/120.74 %----L10. First movers have negative growth rate past a certain point of
% 120.72/120.74 %----time (also after the appearence of efficient producers) in stable
% 120.72/120.74 %----environments.
% 120.72/120.74 fof(l10,hypothesis,
% 120.72/120.74 ! [E] :
% 120.72/120.74 ( ( environment(E)
% 120.72/120.74 & stable(E) )
% 120.72/120.74 => ? [To] :
% 120.72/120.74 ( greater(To,appear(efficient_producers,E))
% 120.72/120.74 & ! [T] :
% 120.72/120.74 ( ( subpopulations(first_movers,efficient_producers,E,T)
% 120.72/120.74 & greater_or_equal(T,To) )
% 120.72/120.74 => greater(zero,growth_rate(first_movers,T)) ) ) ) ).
% 120.72/120.74
% 120.72/120.74 %----GOAL: L9. The first mover set begins to contract past a certain time
% 120.72/120.74 %----in stable environments.
% 120.72/120.74 fof(prove_l9,conjecture,
% 120.72/120.74 ! [E] :
% 120.72/120.74 ( ( environment(E)
% 120.72/120.74 & stable(E) )
% 120.72/120.74 => ? [To] :
% 120.72/120.74 ( greater(To,appear(efficient_producers,E))
% 120.72/120.74 & contracts_from(To,first_movers) ) ) ).
% 120.72/120.74
% 120.72/120.74 %--------------------------------------------------------------------------
% 120.72/120.74 %-------------------------------------------
% 120.72/120.74 % Proof found
% 120.72/120.74 % SZS status Theorem for theBenchmark
% 120.72/120.74 % SZS output start Proof
% 120.72/120.74 %ClaNum:42(EqnAxiom:26)
% 120.72/120.74 %VarNum:80(SingletonVarNum:27)
% 120.72/120.74 %MaxLitNum:5
% 120.72/120.74 %MaxfuncDepth:2
% 120.72/120.74 %SharedTerms:7
% 120.72/120.74 %goalClause: 27 28 35
% 120.72/120.74 %singleGoalClaCount:2
% 120.72/120.74 [27]P1(a1)
% 120.72/120.74 [28]P3(a1)
% 120.72/120.74 [35]~P2(x351,a7)+~P5(x351,f3(a2,a1))
% 120.72/120.74 [29]~E(x291,x292)+P4(x291,x292)
% 120.72/120.74 [30]~P5(x301,x302)+P4(x301,x302)
% 120.72/120.74 [32]~P1(x321)+~P3(x321)+P6(x321,f3(a2,x321))
% 120.72/120.74 [33]~P1(x331)+~P3(x331)+P5(f5(x331),f3(a2,x331))
% 120.72/120.74 [31]P5(x311,x312)+~P4(x311,x312)+E(x311,x312)
% 120.72/120.74 [34]~P5(x341,x343)+P5(x341,x342)+~P5(x343,x342)
% 120.72/120.74 [38]~P6(x382,x381)+~P1(x382)+~P4(x381,f3(a2,x382))+P5(f4(a2,x381),a8)
% 120.72/120.74 [37]~P1(x372)+~P3(x372)+~P6(x372,x371)+P4(f6(x372,x371),x371)+P2(x371,a7)
% 120.72/120.74 [41]~P1(x411)+~P6(x411,x412)+P7(a7,a2,x411,x412)+~P5(f4(a7,x412),a8)+~P5(f4(a2,x412),a8)
% 120.72/120.74 [42]~P3(x422)+~P1(x422)+~P4(x421,f5(x422))+~P7(a7,a2,x422,x421)+P5(a8,f9(a7,x421))
% 120.72/120.74 [39]~P1(x392)+~P3(x392)+~P6(x392,x391)+P2(x391,a7)+P5(f4(a7,f6(x392,x391)),a8)
% 120.72/120.74 [40]~P3(x402)+~P6(x402,x401)+~P1(x402)+P2(x401,a7)+~P5(a8,f9(a7,f6(x402,x401)))
% 120.72/120.74 [36]~P1(x361)+~P3(x361)+~P5(x362,x363)+P6(x361,x362)+~P6(x361,x363)
% 120.72/120.74 %EqnAxiom
% 120.72/120.74 [1]E(x11,x11)
% 120.72/120.74 [2]E(x22,x21)+~E(x21,x22)
% 120.72/120.74 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 120.72/120.74 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 120.72/120.74 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 120.72/120.74 [6]~E(x61,x62)+E(f5(x61),f5(x62))
% 120.72/120.74 [7]~E(x71,x72)+E(f4(x71,x73),f4(x72,x73))
% 120.72/120.74 [8]~E(x81,x82)+E(f4(x83,x81),f4(x83,x82))
% 120.72/120.74 [9]~E(x91,x92)+E(f9(x91,x93),f9(x92,x93))
% 120.72/120.74 [10]~E(x101,x102)+E(f9(x103,x101),f9(x103,x102))
% 120.72/120.74 [11]~E(x111,x112)+E(f6(x111,x113),f6(x112,x113))
% 120.72/120.74 [12]~E(x121,x122)+E(f6(x123,x121),f6(x123,x122))
% 120.72/120.74 [13]~P1(x131)+P1(x132)+~E(x131,x132)
% 120.72/120.74 [14]~P3(x141)+P3(x142)+~E(x141,x142)
% 120.72/120.74 [15]P4(x152,x153)+~E(x151,x152)+~P4(x151,x153)
% 120.72/120.74 [16]P4(x163,x162)+~E(x161,x162)+~P4(x163,x161)
% 120.72/120.74 [17]P6(x172,x173)+~E(x171,x172)+~P6(x171,x173)
% 120.72/120.74 [18]P6(x183,x182)+~E(x181,x182)+~P6(x183,x181)
% 120.72/120.74 [19]P5(x192,x193)+~E(x191,x192)+~P5(x191,x193)
% 120.72/120.74 [20]P5(x203,x202)+~E(x201,x202)+~P5(x203,x201)
% 120.72/120.74 [21]P2(x212,x213)+~E(x211,x212)+~P2(x211,x213)
% 120.72/120.74 [22]P2(x223,x222)+~E(x221,x222)+~P2(x223,x221)
% 120.72/120.74 [23]P7(x232,x233,x234,x235)+~E(x231,x232)+~P7(x231,x233,x234,x235)
% 120.72/120.74 [24]P7(x243,x242,x244,x245)+~E(x241,x242)+~P7(x243,x241,x244,x245)
% 120.72/120.74 [25]P7(x253,x254,x252,x255)+~E(x251,x252)+~P7(x253,x254,x251,x255)
% 120.72/120.74 [26]P7(x263,x264,x265,x262)+~E(x261,x262)+~P7(x263,x264,x265,x261)
% 120.72/120.74
% 120.72/120.74 %-------------------------------------------
% 120.72/120.75 cnf(43,plain,
% 120.72/120.75 (~E(a1,x431)+P3(x431)),
% 120.72/120.75 inference(scs_inference,[],[28,14])).
% 120.72/120.75 cnf(45,plain,
% 120.72/120.75 (P5(f5(a1),f3(a2,a1))),
% 120.72/120.75 inference(scs_inference,[],[27,28,14,32,33])).
% 120.72/120.75 cnf(47,plain,
% 120.72/120.75 (~P2(f5(a1),a7)),
% 120.72/120.75 inference(scs_inference,[],[27,28,14,32,33,35])).
% 120.72/120.75 cnf(51,plain,
% 120.72/120.75 (P6(a1,f5(a1))),
% 120.72/120.75 inference(scs_inference,[],[27,28,14,32,33,35,38,36])).
% 120.72/120.75 cnf(56,plain,
% 120.72/120.75 (P4(f5(a1),f3(a2,a1))),
% 120.72/120.75 inference(scs_inference,[],[45,30])).
% 120.72/120.75 cnf(58,plain,
% 120.72/120.75 (P5(f4(a2,f5(a1)),a8)),
% 120.72/120.75 inference(scs_inference,[],[27,45,51,30,38])).
% 120.72/120.75 cnf(61,plain,
% 120.72/120.75 (P4(f6(a1,f5(a1)),f5(a1))),
% 120.72/120.75 inference(scs_inference,[],[27,28,45,47,51,30,38,22,37])).
% 120.72/120.75 cnf(66,plain,
% 120.72/120.75 (~P2(x661,a7)+~E(x661,f5(a1))),
% 120.72/120.75 inference(scs_inference,[],[47,21])).
% 120.72/120.75 cnf(72,plain,
% 120.72/120.75 (~E(a1,x721)+P1(x721)),
% 120.72/120.75 inference(scs_inference,[],[27,13])).
% 120.72/120.75 cnf(76,plain,
% 120.72/120.75 (E(f6(a1,f5(a1)),f5(a1))+P5(f6(a1,f5(a1)),f5(a1))),
% 120.72/120.75 inference(scs_inference,[],[61,31])).
% 120.72/120.75 cnf(80,plain,
% 120.72/120.75 (E(f6(a1,f5(a1)),f5(a1))+P5(f6(a1,f5(a1)),f3(a2,a1))),
% 120.72/120.75 inference(scs_inference,[],[45,61,58,31,30,34])).
% 120.72/120.75 cnf(82,plain,
% 120.72/120.75 (E(f6(a1,f5(a1)),f5(a1))+~P2(f6(a1,f5(a1)),a7)),
% 120.72/120.75 inference(scs_inference,[],[45,61,58,31,30,34,35])).
% 120.72/120.75 cnf(86,plain,
% 120.72/120.75 (P6(a1,x861)+~P5(x861,f5(a1))),
% 120.72/120.75 inference(scs_inference,[],[51,28,27,36])).
% 120.72/120.75 cnf(112,plain,
% 120.72/120.75 (~E(f6(a1,f5(a1)),x1121)+~P7(a7,a2,a1,x1121)+P5(a8,f9(a7,x1121))),
% 120.72/120.75 inference(scs_inference,[],[61,28,27,15,42])).
% 120.72/120.75 cnf(120,plain,
% 120.72/120.75 (P5(a8,f9(a7,f6(a1,f5(a1))))+~P7(a7,a2,a1,f6(a1,f5(a1)))),
% 120.72/120.75 inference(equality_inference,[],[112])).
% 120.72/120.75 cnf(162,plain,
% 120.72/120.75 (~P2(f6(a1,f5(a1)),a7)),
% 120.72/120.75 inference(scs_inference,[],[82,66])).
% 120.72/120.75 cnf(165,plain,
% 120.72/120.75 (P4(x1651,f3(a2,a1))+~E(f5(a1),x1651)),
% 120.72/120.75 inference(scs_inference,[],[56,162,22,21,15])).
% 120.72/120.75 cnf(170,plain,
% 120.72/120.75 (P6(a1,x1701)+~E(f5(a1),x1701)),
% 120.72/120.75 inference(scs_inference,[],[51,18])).
% 120.72/120.75 cnf(276,plain,
% 120.72/120.75 (~P5(a8,f9(a7,f6(a1,f5(a1))))),
% 120.72/120.75 inference(scs_inference,[],[51,47,27,43,40])).
% 120.72/120.75 cnf(285,plain,
% 120.72/120.75 (P5(f4(a7,f6(a1,f5(a1))),a8)),
% 120.72/120.75 inference(scs_inference,[],[47,28,51,72,39])).
% 120.72/120.75 cnf(363,plain,
% 120.72/120.75 (E(f5(a1),f6(a1,f5(a1)))+P5(f6(a1,f5(a1)),f5(a1))),
% 120.72/120.75 inference(scs_inference,[],[2,76])).
% 120.72/120.75 cnf(368,plain,
% 120.72/120.75 (E(f5(a1),f6(a1,f5(a1)))+P5(f6(a1,f5(a1)),f3(a2,a1))),
% 120.72/120.75 inference(scs_inference,[],[2,80])).
% 120.72/120.75 cnf(369,plain,
% 120.72/120.75 (P4(f6(a1,f5(a1)),f3(a2,a1))+E(f5(a1),f6(a1,f5(a1)))),
% 120.72/120.75 inference(scs_inference,[],[368,30])).
% 120.72/120.75 cnf(749,plain,
% 120.72/120.75 (P5(f6(a1,f5(a1)),f5(a1))+P6(a1,f6(a1,f5(a1)))),
% 120.72/120.75 inference(scs_inference,[],[170,363])).
% 120.72/120.75 cnf(750,plain,
% 120.72/120.75 (P6(a1,f6(a1,f5(a1)))),
% 120.72/120.75 inference(scs_inference,[],[749,86])).
% 120.72/120.75 cnf(755,plain,
% 120.72/120.75 (P6(x7551,f6(a1,f5(a1)))+~E(a1,x7551)),
% 120.72/120.75 inference(scs_inference,[],[750,17])).
% 120.72/120.75 cnf(1410,plain,
% 120.72/120.75 (P4(f6(a1,f5(a1)),f3(a2,a1))),
% 120.72/120.75 inference(scs_inference,[],[165,369])).
% 120.72/120.75 cnf(1743,plain,
% 120.72/120.75 (P5(f4(a2,f6(a1,f5(a1))),a8)),
% 120.72/120.75 inference(scs_inference,[],[1410,27,755,38])).
% 120.72/120.75 cnf(1744,plain,
% 120.72/120.75 (~E(x17441,a1)+P6(x17441,f6(a1,f5(a1)))),
% 120.72/120.75 inference(scs_inference,[],[755,2])).
% 120.72/120.75 cnf(2144,plain,
% 120.72/120.75 (~P7(a7,a2,a1,f6(a1,f5(a1)))),
% 120.72/120.75 inference(scs_inference,[],[276,120])).
% 120.72/120.75 cnf(2200,plain,
% 120.72/120.75 (~P5(f4(a7,f6(a1,f5(a1))),a8)+~P5(f4(a2,f6(a1,f5(a1))),a8)),
% 120.72/120.75 inference(scs_inference,[],[2144,27,1744,41])).
% 120.72/120.75 cnf(3255,plain,
% 120.72/120.75 ($false),
% 120.72/120.75 inference(scs_inference,[],[285,1743,2200]),
% 120.72/120.75 ['proof']).
% 120.72/120.75 % SZS output end Proof
% 120.72/120.75 % Total time :120.100000s
%------------------------------------------------------------------------------