TSTP Solution File: MGT020+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : MGT020+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 : n006.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 09:06:47 EDT 2023
% Result : Theorem 61.58s 61.66s
% Output : CNFRefutation 61.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT020+1 : 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 : n006.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 06:33:06 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 61.58/61.65 %-------------------------------------------
% 61.58/61.65 % File :CSE---1.6
% 61.58/61.65 % Problem :theBenchmark
% 61.58/61.65 % Transform :cnf
% 61.58/61.65 % Format :tptp:raw
% 61.58/61.65 % Command :java -jar mcs_scs.jar %d %s
% 61.58/61.65
% 61.58/61.65 % Result :Theorem 61.030000s
% 61.58/61.65 % Output :CNFRefutation 61.030000s
% 61.58/61.65 %-------------------------------------------
% 61.58/61.65 %--------------------------------------------------------------------------
% 61.58/61.65 % File : MGT020+1 : TPTP v8.1.2. Released v2.0.0.
% 61.58/61.65 % Domain : Management (Organisation Theory)
% 61.58/61.65 % Problem : First movers exceeds efficient producers disbanding rate
% 61.58/61.65 % Version : [PB+94] axioms.
% 61.58/61.65 % English :
% 61.58/61.65
% 61.58/61.65 % Refs : [PM93] Peli & Masuch (1993), The Logic of Propogation Strateg
% 61.58/61.65 % : [PM94] Peli & Masuch (1994), The Logic of Propogation Strateg
% 61.58/61.65 % : [PB+94] Peli et al. (1994), A Logical Approach to Formalizing
% 61.58/61.65 % : [Kam95] Kamps (1995), Email to G. Sutcliffe
% 61.58/61.65 % Source : [Kam95]
% 61.58/61.65 % Names : LEMMA 2 [PM93]
% 61.58/61.65 % : L2 [PB+94]
% 61.58/61.65
% 61.58/61.65 % Status : Theorem
% 61.58/61.65 % Rating : 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
% 61.58/61.65 % Syntax : Number of formulae : 11 ( 0 unt; 0 def)
% 61.58/61.65 % Number of atoms : 42 ( 1 equ)
% 61.58/61.65 % Maximal formula atoms : 7 ( 3 avg)
% 61.58/61.65 % Number of connectives : 33 ( 2 ~; 1 |; 16 &)
% 61.58/61.65 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 61.58/61.65 % Maximal formula depth : 10 ( 6 avg)
% 61.58/61.65 % Maximal term depth : 3 ( 1 avg)
% 61.58/61.65 % Number of predicates : 7 ( 6 usr; 0 prp; 1-4 aty)
% 61.58/61.65 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% 61.58/61.65 % Number of variables : 26 ( 26 !; 0 ?)
% 61.58/61.65 % SPC : FOF_THM_RFO_SEQ
% 61.58/61.65
% 61.58/61.65 % Comments : Same as version with [PM93] axioms.
% 61.58/61.65 %--------------------------------------------------------------------------
% 61.58/61.65 %----Subsitution axioms
% 61.58/61.65 %----Problem axioms
% 61.58/61.65 %----L3. The difference between the disbanding rates of first movers and
% 61.58/61.65 %----efficient producers does not decrease.
% 61.58/61.65 fof(l3,axiom,
% 61.58/61.65 ! [E,T] :
% 61.58/61.65 ( ( environment(E)
% 61.58/61.65 & subpopulations(first_movers,efficient_producers,E,T) )
% 61.58/61.65 => ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ).
% 61.58/61.65
% 61.58/61.65 %----MP. The initial time point of the environment is the earliest time,
% 61.58/61.65 %----when both FM and EP are present in the environment.
% 61.58/61.65 fof(mp_earliest_time_point,axiom,
% 61.58/61.65 ! [E,T] :
% 61.58/61.65 ( environment(E)
% 61.58/61.65 => ( ( in_environment(E,initial_FM_EP(E))
% 61.58/61.65 => subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) )
% 61.58/61.65 & ( subpopulations(first_movers,efficient_producers,E,T)
% 61.58/61.65 => greater_or_equal(T,initial_FM_EP(E)) ) ) ) ).
% 61.58/61.65
% 61.58/61.66 %----MP. If f1(x1) > f2(x1) and f1(x)-f2(x) does not decrease on [x1,x2]
% 61.58/61.66 %----then f1(x2) > f2(x2).
% 61.58/61.66 %----INSTANTIATION: f1(x) = disbanding_rate(first_movers,x) ;
% 61.58/61.66 %----f2(x) = disbanding_rate(efficient_producers,x)
% 61.58/61.66 fof(mp_positive_function_difference,axiom,
% 61.58/61.66 ! [E,T,T1,T2] :
% 61.58/61.66 ( ( environment(E)
% 61.58/61.66 & greater_or_equal(T,T1)
% 61.58/61.66 & greater_or_equal(T2,T)
% 61.58/61.66 & subpopulations(first_movers,efficient_producers,E,T2)
% 61.58/61.66 & greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1)) )
% 61.58/61.66 => ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
% 61.58/61.66 => greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ) ) ).
% 61.58/61.66
% 61.58/61.66 %----MP. If FM and EP are non-empty subpopulations at a time -point in the
% 61.58/61.66 %----environment, then this time point occurs while the environment
% 61.58/61.66 %----persists.
% 61.58/61.66 fof(mp_time_point_occurs,axiom,
% 61.58/61.66 ! [E,T] :
% 61.58/61.66 ( ( environment(E)
% 61.58/61.66 & subpopulations(first_movers,efficient_producers,E,T) )
% 61.58/61.66 => in_environment(E,T) ) ).
% 61.58/61.66
% 61.58/61.66 %----MP. The initial time of an environment cannot precede the opening of
% 61.58/61.66 %----this environment.
% 61.58/61.66 fof(mp_initial_time,axiom,
% 61.58/61.66 ! [E] :
% 61.58/61.66 ( environment(E)
% 61.58/61.66 => greater_or_equal(initial_FM_EP(E),start_time(E)) ) ).
% 61.58/61.66
% 61.58/61.66 %----MP. If time point T1 occurs after the opening of the environment, and
% 61.58/61.66 %----a later time point T2 occurs before the environment ends, then T1 also
% 61.58/61.66 %----occurs before the end of the environment.
% 61.58/61.66 fof(mp_times_in_order,axiom,
% 61.58/61.66 ! [E,T1,T2] :
% 61.58/61.66 ( ( environment(E)
% 61.58/61.66 & greater_or_equal(T1,start_time(E))
% 61.58/61.66 & greater(T2,T1)
% 61.58/61.66 & in_environment(E,T2) )
% 61.58/61.66 => in_environment(E,T1) ) ).
% 61.58/61.66
% 61.58/61.66 %----MP. inequality
% 61.58/61.66 fof(mp_greater_transitivity,axiom,
% 61.58/61.66 ! [X,Y,Z] :
% 61.58/61.66 ( ( greater(X,Y)
% 61.58/61.66 & greater(Y,Z) )
% 61.58/61.66 => greater(X,Z) ) ).
% 61.58/61.66
% 61.58/61.66 %----MP. on "greater or equal to"
% 61.58/61.66 fof(mp_greater_or_equal,axiom,
% 61.58/61.66 ! [X,Y] :
% 61.58/61.66 ( greater_or_equal(X,Y)
% 61.58/61.66 => ( greater(X,Y)
% 61.58/61.66 | X = Y ) ) ).
% 61.58/61.66
% 61.58/61.66 %----A8. The disbanding rate of first movers exceeds the disbanding rate
% 61.58/61.66 %----of efficient producers initially.
% 61.58/61.66 fof(a8,hypothesis,
% 61.58/61.66 ! [E] :
% 61.58/61.66 ( environment(E)
% 61.58/61.66 => greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ) ).
% 61.58/61.66
% 61.58/61.66 %----A10. If FM and EP are present in the environment at time-points t1
% 61.58/61.66 %----and t2, then they are present during the time-interval between
% 61.58/61.66 %----t1 and t2.
% 61.58/61.66 fof(a10,hypothesis,
% 61.58/61.66 ! [E,T1,T2,T] :
% 61.58/61.66 ( ( environment(E)
% 61.58/61.66 & subpopulations(first_movers,efficient_producers,E,T1)
% 61.58/61.66 & subpopulations(first_movers,efficient_producers,E,T2)
% 61.58/61.66 & greater_or_equal(T,T1)
% 61.58/61.66 & greater_or_equal(T2,T) )
% 61.58/61.66 => subpopulations(first_movers,efficient_producers,E,T) ) ).
% 61.58/61.66
% 61.58/61.66 %----GOAL: L2. The disbanding rate of first movers exceeds the disbanding
% 61.58/61.66 %----rate of efficient producers.
% 61.58/61.66 fof(prove_l2,conjecture,
% 61.58/61.66 ! [E,T] :
% 61.58/61.66 ( ( environment(E)
% 61.58/61.66 & subpopulations(first_movers,efficient_producers,E,T) )
% 61.58/61.66 => greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ) ).
% 61.58/61.66
% 61.58/61.66 %--------------------------------------------------------------------------
% 61.58/61.66 %-------------------------------------------
% 61.58/61.66 % Proof found
% 61.58/61.66 % SZS status Theorem for theBenchmark
% 61.58/61.66 % SZS output start Proof
% 61.58/61.66 %ClaNum:35(EqnAxiom:21)
% 61.58/61.66 %VarNum:71(SingletonVarNum:25)
% 61.58/61.66 %MaxLitNum:7
% 61.58/61.66 %MaxfuncDepth:2
% 61.58/61.66 %SharedTerms:9
% 61.58/61.66 %goalClause: 22 23 24
% 61.58/61.66 %singleGoalClaCount:3
% 61.58/61.66 [22]P1(a1)
% 61.58/61.66 [23]P3(a5,a2,a1,a6)
% 61.58/61.66 [24]~P4(f3(a5,a6),f3(a2,a6))
% 61.58/61.66 [25]~P1(x251)+P5(f7(x251),f8(x251))
% 61.58/61.66 [28]~P1(x281)+P4(f3(a5,f7(x281)),f3(a2,f7(x281)))
% 61.58/61.66 [30]~P1(x301)+~P6(x301,f7(x301))+P3(a5,a2,x301,f7(x301))
% 61.58/61.66 [26]P4(x261,x262)+~P5(x261,x262)+E(x261,x262)
% 61.58/61.66 [31]~P1(x311)+P6(x311,x312)+~P3(a5,a2,x311,x312)
% 61.58/61.66 [32]~P1(x322)+~P3(a5,a2,x322,x321)+P5(x321,f7(x322))
% 61.58/61.66 [33]~P1(x331)+~P3(a5,a2,x331,x332)+~P2(f4(f3(a5,x332),f3(a2,x332)))
% 61.58/61.66 [27]~P4(x271,x273)+P4(x271,x272)+~P4(x273,x272)
% 61.58/61.66 [29]~P1(x291)+~P4(x293,x292)+P6(x291,x292)+~P6(x291,x293)+~P5(x292,f8(x291))
% 61.58/61.66 [35]~P1(x351)+~P5(x352,x353)+~P5(x354,x352)+~P3(a5,a2,x351,x354)+~P3(a5,a2,x351,x353)+P3(a5,a2,x351,x352)
% 61.58/61.66 [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)))
% 61.58/61.66 %EqnAxiom
% 61.58/61.66 [1]E(x11,x11)
% 61.58/61.66 [2]E(x22,x21)+~E(x21,x22)
% 61.58/61.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 61.58/61.66 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 61.58/61.66 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 61.58/61.66 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 61.58/61.66 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 61.58/61.66 [8]~E(x81,x82)+E(f7(x81),f7(x82))
% 61.58/61.66 [9]~E(x91,x92)+E(f8(x91),f8(x92))
% 61.58/61.66 [10]~P1(x101)+P1(x102)+~E(x101,x102)
% 61.58/61.66 [11]P3(x112,x113,x114,x115)+~E(x111,x112)+~P3(x111,x113,x114,x115)
% 61.58/61.66 [12]P3(x123,x122,x124,x125)+~E(x121,x122)+~P3(x123,x121,x124,x125)
% 61.58/61.66 [13]P3(x133,x134,x132,x135)+~E(x131,x132)+~P3(x133,x134,x131,x135)
% 61.58/61.66 [14]P3(x143,x144,x145,x142)+~E(x141,x142)+~P3(x143,x144,x145,x141)
% 61.58/61.66 [15]P4(x152,x153)+~E(x151,x152)+~P4(x151,x153)
% 61.58/61.66 [16]P4(x163,x162)+~E(x161,x162)+~P4(x163,x161)
% 61.58/61.66 [17]P5(x172,x173)+~E(x171,x172)+~P5(x171,x173)
% 61.58/61.66 [18]P5(x183,x182)+~E(x181,x182)+~P5(x183,x181)
% 61.58/61.66 [19]~P2(x191)+P2(x192)+~E(x191,x192)
% 61.58/61.66 [20]P6(x202,x203)+~E(x201,x202)+~P6(x201,x203)
% 61.58/61.66 [21]P6(x213,x212)+~E(x211,x212)+~P6(x213,x211)
% 61.58/61.66
% 61.58/61.66 %-------------------------------------------
% 61.58/61.66 cnf(36,plain,
% 61.58/61.66 (P6(a1,a6)),
% 61.58/61.66 inference(scs_inference,[],[22,23,31])).
% 61.58/61.66 cnf(37,plain,
% 61.58/61.66 (P4(f3(a5,f7(a1)),f3(a2,f7(a1)))),
% 61.58/61.66 inference(scs_inference,[],[22,23,31,28])).
% 61.58/61.66 cnf(38,plain,
% 61.58/61.66 (P5(f7(a1),f8(a1))),
% 61.58/61.66 inference(scs_inference,[],[22,23,31,28,25])).
% 61.58/61.66 cnf(58,plain,
% 61.58/61.66 (P5(a6,f7(a1))),
% 61.58/61.66 inference(scs_inference,[],[22,23,32])).
% 61.58/61.66 cnf(62,plain,
% 61.58/61.66 (~E(a1,x621)+P1(x621)),
% 61.58/61.66 inference(scs_inference,[],[22,23,32,33,10])).
% 61.58/61.66 cnf(65,plain,
% 61.58/61.66 (~P5(a6,a6)),
% 61.58/61.66 inference(scs_inference,[],[22,23,24,38,37,32,33,10,35,34])).
% 61.58/61.66 cnf(69,plain,
% 61.58/61.66 (P6(a1,f7(a1))+~P4(a6,f7(a1))),
% 61.58/61.66 inference(scs_inference,[],[22,23,24,38,37,36,32,33,10,35,34,26,29])).
% 61.58/61.66 cnf(84,plain,
% 61.58/61.66 (P3(a5,a2,a1,f7(a1))),
% 61.58/61.66 inference(scs_inference,[],[58,65,22,18,2,17,26,69,30])).
% 61.58/61.66 cnf(113,plain,
% 61.58/61.66 (P5(f7(a1),f7(a1))),
% 61.58/61.66 inference(scs_inference,[],[84,22,32])).
% 61.58/61.66 cnf(348,plain,
% 61.58/61.66 (~P2(f4(f3(a5,f7(a1)),f3(a2,f7(a1))))),
% 61.58/61.66 inference(scs_inference,[],[84,62,33])).
% 61.58/61.66 cnf(349,plain,
% 61.58/61.66 (P2(f4(f3(a5,f7(a1)),f3(a2,f7(a1))))),
% 61.58/61.66 inference(scs_inference,[],[37,24,23,58,113,62,34])).
% 61.58/61.66 cnf(1361,plain,
% 61.58/61.66 ($false),
% 61.58/61.66 inference(scs_inference,[],[348,349]),
% 61.58/61.66 ['proof']).
% 61.58/61.66 % SZS output end Proof
% 61.58/61.66 % Total time :61.030000s
%------------------------------------------------------------------------------