TSTP Solution File: MGT027+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 : 600s
% DateTime : Sun Jul 17 22:26:16 EDT 2022
% Result : Theorem 0.37s 0.55s
% Output : Refutation 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.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 : 600
% 0.12/0.34 % DateTime : Thu Jun 9 11:50:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.37/0.55
% 0.37/0.55 SPASS V 3.9
% 0.37/0.55 SPASS beiseite: Proof found.
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.55 SPASS derived 650 clauses, backtracked 91 clauses, performed 7 splits and kept 443 clauses.
% 0.37/0.55 SPASS allocated 98466 KBytes.
% 0.37/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.37/0.55 0:00:00.03 for the input.
% 0.37/0.55 0:00:00.03 for the FLOTTER CNF translation.
% 0.37/0.55 0:00:00.01 for inferences.
% 0.37/0.55 0:00:00.00 for the backtracking.
% 0.37/0.55 0:00:00.09 for the reduction.
% 0.37/0.55
% 0.37/0.55
% 0.37/0.55 Here is a proof with depth 9, length 112 :
% 0.37/0.55 % SZS output start Refutation
% 0.37/0.55 1[0:Inp] || -> environment(skc1)*.
% 0.37/0.55 2[0:Inp] || -> stable(skc1)*.
% 0.37/0.55 3[0:Inp] || -> greater(cardinality_at_time(first_movers,skf2(u)),zero)*l.
% 0.37/0.55 4[0:Inp] || greater(u,v) -> greater_or_equal(u,v)*.
% 0.37/0.55 6[0:Inp] || contracts_from(u,first_movers)* greater(u,appear(efficient_producers,skc1))*+ -> .
% 0.37/0.55 7[0:Inp] || greater_or_equal(u,v)* -> equal(u,v) greater(u,v).
% 0.37/0.55 8[0:Inp] stable(u) environment(u) || -> in_environment(u,appear(efficient_producers,u))*.
% 0.37/0.55 9[0:Inp] || greater(u,v)* greater(v,w)* -> greater(u,w)*.
% 0.37/0.55 10[0:Inp] stable(u) environment(u) || -> greater(skf4(u),appear(efficient_producers,u))*r.
% 0.37/0.55 11[0:Inp] stable(u) environment(u) || in_environment(u,v)*+ -> contracts_from(v,first_movers) greater_or_equal(skf2(v),v)*.
% 0.37/0.55 12[0:Inp] stable(u) environment(u) || greater(v,w)*+ in_environment(u,w)* -> in_environment(u,v)*.
% 0.37/0.55 13[0:Inp] environment(u) || in_environment(u,v) greater_or_equal(v,appear(efficient_producers,u))* -> greater(cardinality_at_time(efficient_producers,v),zero).
% 0.37/0.55 14[0:Inp] stable(u) environment(u) || in_environment(u,v)* greater(zero,growth_rate(first_movers,skf2(v)))*r+ -> contracts_from(v,first_movers).
% 0.37/0.55 15[0:Inp] stable(u) environment(u) || greater_or_equal(v,skf4(u)) subpopulations(first_movers,efficient_producers,u,v)* -> greater(zero,growth_rate(first_movers,v)).
% 0.37/0.55 16[0:Inp] environment(u) || in_environment(u,v) greater(cardinality_at_time(first_movers,v),zero) greater(cardinality_at_time(efficient_producers,v),zero) -> subpopulations(first_movers,efficient_producers,u,v)*.
% 0.37/0.55 19[0:Res:2.0,12.1] environment(skc1) || in_environment(skc1,u)* greater(v,u)* -> in_environment(skc1,v)*.
% 0.37/0.55 20[0:Res:2.0,10.1] environment(skc1) || -> greater(skf4(skc1),appear(efficient_producers,skc1))*r.
% 0.37/0.55 22[0:Res:2.0,8.1] environment(skc1) || -> in_environment(skc1,appear(efficient_producers,skc1))*.
% 0.37/0.55 25[0:Res:1.0,14.0] stable(skc1) || greater(zero,growth_rate(first_movers,skf2(u)))*r in_environment(skc1,u) -> contracts_from(u,first_movers).
% 0.37/0.55 31[0:MRR:22.0,1.0] || -> in_environment(skc1,appear(efficient_producers,skc1))*.
% 0.37/0.55 32[0:MRR:20.0,1.0] || -> greater(skf4(skc1),appear(efficient_producers,skc1))*r.
% 0.37/0.55 34[0:MRR:19.0,1.0] || greater(u,v)*+ in_environment(skc1,v)* -> in_environment(skc1,u)*.
% 0.37/0.55 35[0:MRR:25.0,2.0] || in_environment(skc1,u) greater(zero,growth_rate(first_movers,skf2(u)))*r -> contracts_from(u,first_movers).
% 0.37/0.55 37[0:Res:32.0,6.0] || contracts_from(skf4(skc1),first_movers)* -> .
% 0.37/0.55 41[0:NCh:9.2,9.1,6.1,32.0] || contracts_from(u,first_movers)* greater(u,skf4(skc1)) -> .
% 0.37/0.55 42[0:NCh:9.2,9.1,6.1,32.0] || contracts_from(u,first_movers)* equal(u,skf4(skc1)) -> .
% 0.37/0.55 46[0:Res:32.0,34.0] || in_environment(skc1,appear(efficient_producers,skc1))* -> in_environment(skc1,skf4(skc1)).
% 0.37/0.55 50[0:NCh:9.2,9.1,34.0,32.0] || greater(u,skf4(skc1)) in_environment(skc1,appear(efficient_producers,skc1))* -> in_environment(skc1,u)*.
% 0.37/0.55 51[0:NCh:9.2,9.1,34.0,32.0] || equal(u,skf4(skc1)) in_environment(skc1,appear(efficient_producers,skc1))* -> in_environment(skc1,u)*.
% 0.37/0.55 52[0:MRR:46.0,31.0] || -> in_environment(skc1,skf4(skc1))*.
% 0.37/0.55 53[0:MRR:51.1,31.0] || equal(u,skf4(skc1)) -> in_environment(skc1,u)*.
% 0.37/0.55 54[0:MRR:50.1,31.0] || greater(u,skf4(skc1)) -> in_environment(skc1,u)*.
% 0.37/0.55 69[0:Res:54.1,11.2] stable(skc1) environment(skc1) || greater(u,skf4(skc1)) -> contracts_from(u,first_movers) greater_or_equal(skf2(u),u)*.
% 0.37/0.55 70[0:Res:53.1,11.2] stable(skc1) environment(skc1) || equal(u,skf4(skc1)) -> contracts_from(u,first_movers) greater_or_equal(skf2(u),u)*.
% 0.37/0.55 71[0:Res:52.0,11.2] stable(skc1) environment(skc1) || -> contracts_from(skf4(skc1),first_movers) greater_or_equal(skf2(skf4(skc1)),skf4(skc1))*.
% 0.37/0.55 74[0:SSi:71.1,71.0,2.0,1.0,2.0,1.0] || -> contracts_from(skf4(skc1),first_movers) greater_or_equal(skf2(skf4(skc1)),skf4(skc1))*.
% 0.37/0.55 75[0:MRR:74.0,37.0] || -> greater_or_equal(skf2(skf4(skc1)),skf4(skc1))*.
% 0.37/0.55 76[0:SSi:70.1,70.0,2.0,1.0,2.0,1.0] || equal(u,skf4(skc1)) -> contracts_from(u,first_movers) greater_or_equal(skf2(u),u)*.
% 0.37/0.55 77[0:MRR:76.1,42.0] || equal(u,skf4(skc1)) -> greater_or_equal(skf2(u),u)*.
% 0.37/0.55 79[0:SSi:69.1,69.0,2.0,1.0,2.0,1.0] || greater(u,skf4(skc1)) -> contracts_from(u,first_movers) greater_or_equal(skf2(u),u)*.
% 0.37/0.55 80[0:MRR:79.1,41.0] || greater(u,skf4(skc1)) -> greater_or_equal(skf2(u),u)*.
% 0.37/0.55 84[0:Res:75.0,7.0] || -> equal(skf2(skf4(skc1)),skf4(skc1)) greater(skf2(skf4(skc1)),skf4(skc1))*l.
% 0.37/0.55 85[0:Res:77.1,7.0] || equal(u,skf4(skc1))*+ -> equal(skf2(u),u) greater(skf2(u),u)*l.
% 0.37/0.55 87[0:Res:80.1,7.0] || greater(u,skf4(skc1))*+ -> equal(skf2(u),u) greater(skf2(u),u)*l.
% 0.37/0.55 104[0:Res:84.1,34.0] || in_environment(skc1,skf4(skc1)) -> equal(skf2(skf4(skc1)),skf4(skc1)) in_environment(skc1,skf2(skf4(skc1)))*.
% 0.37/0.55 110[0:MRR:104.0,104.1,52.0,53.0] || -> in_environment(skc1,skf2(skf4(skc1)))*.
% 0.37/0.55 111[0:Res:110.0,11.2] stable(skc1) environment(skc1) || -> contracts_from(skf2(skf4(skc1)),first_movers) greater_or_equal(skf2(skf2(skf4(skc1))),skf2(skf4(skc1)))*.
% 0.37/0.55 112[0:SSi:111.1,111.0,2.0,1.0,2.0,1.0] || -> contracts_from(skf2(skf4(skc1)),first_movers) greater_or_equal(skf2(skf2(skf4(skc1))),skf2(skf4(skc1)))*.
% 0.37/0.55 113[0:Res:4.1,13.2] environment(u) || greater(v,appear(efficient_producers,u))*+ in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 0.37/0.55 153[0:Res:16.4,15.3] environment(u) stable(u) environment(u) || in_environment(u,v) greater(cardinality_at_time(first_movers,v),zero) greater(cardinality_at_time(efficient_producers,v),zero) greater_or_equal(v,skf4(u))* -> greater(zero,growth_rate(first_movers,v)).
% 0.37/0.55 154[0:Obv:153.0] stable(u) environment(u) || in_environment(u,v) greater(cardinality_at_time(first_movers,v),zero) greater(cardinality_at_time(efficient_producers,v),zero) greater_or_equal(v,skf4(u))* -> greater(zero,growth_rate(first_movers,v)).
% 0.37/0.55 250[0:NCh:9.2,9.1,113.1,32.0] environment(skc1) || greater(u,skf4(skc1)) in_environment(skc1,u) -> greater(cardinality_at_time(efficient_producers,u),zero)*l.
% 0.37/0.55 251[0:NCh:9.2,9.1,113.1,32.0] environment(skc1) || equal(u,skf4(skc1)) in_environment(skc1,u) -> greater(cardinality_at_time(efficient_producers,u),zero)*l.
% 0.37/0.55 252[0:NCh:9.2,9.1,113.1,10.2] environment(u) stable(u) environment(u) || greater(v,skf4(u)) in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 0.37/0.55 256[0:SSi:251.0,2.0,1.0] || equal(u,skf4(skc1)) in_environment(skc1,u) -> greater(cardinality_at_time(efficient_producers,u),zero)*l.
% 0.37/0.55 257[0:MRR:256.1,53.1] || equal(u,skf4(skc1)) -> greater(cardinality_at_time(efficient_producers,u),zero)*l.
% 0.37/0.55 260[0:SSi:250.0,2.0,1.0] || greater(u,skf4(skc1)) in_environment(skc1,u) -> greater(cardinality_at_time(efficient_producers,u),zero)*l.
% 0.37/0.55 261[0:MRR:260.1,54.1] || greater(u,skf4(skc1)) -> greater(cardinality_at_time(efficient_producers,u),zero)*l.
% 0.37/0.55 264[0:Obv:252.0] stable(u) environment(u) || greater(v,skf4(u))+ in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 0.37/0.55 350[0:Res:75.0,154.5] stable(skc1) environment(skc1) || in_environment(skc1,skf2(skf4(skc1))) greater(cardinality_at_time(first_movers,skf2(skf4(skc1))),zero) greater(cardinality_at_time(efficient_producers,skf2(skf4(skc1))),zero) -> greater(zero,growth_rate(first_movers,skf2(skf4(skc1))))*r.
% 0.37/0.55 354[0:SSi:350.1,350.0,2.0,1.0,2.0,1.0] || in_environment(skc1,skf2(skf4(skc1))) greater(cardinality_at_time(first_movers,skf2(skf4(skc1))),zero) greater(cardinality_at_time(efficient_producers,skf2(skf4(skc1))),zero) -> greater(zero,growth_rate(first_movers,skf2(skf4(skc1))))*r.
% 0.37/0.55 355[0:MRR:354.0,354.1,110.0,3.0] || greater(cardinality_at_time(efficient_producers,skf2(skf4(skc1))),zero) -> greater(zero,growth_rate(first_movers,skf2(skf4(skc1))))*r.
% 0.37/0.55 502[0:Res:84.1,87.0] || -> equal(skf2(skf4(skc1)),skf4(skc1)) equal(skf2(skf2(skf4(skc1))),skf2(skf4(skc1))) greater(skf2(skf2(skf4(skc1))),skf2(skf4(skc1)))*l.
% 0.39/0.56 519[0:MRR:502.0,85.0] || -> equal(skf2(skf2(skf4(skc1))),skf2(skf4(skc1))) greater(skf2(skf2(skf4(skc1))),skf2(skf4(skc1)))*l.
% 0.39/0.56 521[0:Res:519.1,34.0] || in_environment(skc1,skf2(skf4(skc1))) -> equal(skf2(skf2(skf4(skc1))),skf2(skf4(skc1))) in_environment(skc1,skf2(skf2(skf4(skc1))))*.
% 0.39/0.56 527[0:NCh:9.2,9.0,519.1,6.1] || contracts_from(skf2(skf2(skf4(skc1))),first_movers)* greater(skf2(skf4(skc1)),appear(efficient_producers,skc1)) -> equal(skf2(skf2(skf4(skc1))),skf2(skf4(skc1))).
% 0.39/0.56 543[0:MRR:521.0,110.0] || -> equal(skf2(skf2(skf4(skc1))),skf2(skf4(skc1))) in_environment(skc1,skf2(skf2(skf4(skc1))))*.
% 0.39/0.56 546[1:Spt:543.0] || -> equal(skf2(skf2(skf4(skc1))),skf2(skf4(skc1)))**.
% 0.39/0.56 547[1:Rew:546.0,112.1] || -> contracts_from(skf2(skf4(skc1)),first_movers) greater_or_equal(skf2(skf4(skc1)),skf2(skf4(skc1)))*.
% 0.39/0.56 556[1:SpL:546.0,35.1] || in_environment(skc1,skf2(skf4(skc1))) greater(zero,growth_rate(first_movers,skf2(skf4(skc1))))*r -> contracts_from(skf2(skf4(skc1)),first_movers).
% 0.39/0.56 558[1:MRR:556.0,110.0] || greater(zero,growth_rate(first_movers,skf2(skf4(skc1))))*r -> contracts_from(skf2(skf4(skc1)),first_movers).
% 0.39/0.56 564[2:Spt:547.0] || -> contracts_from(skf2(skf4(skc1)),first_movers)*.
% 0.39/0.56 565[2:Res:564.0,41.0] || greater(skf2(skf4(skc1)),skf4(skc1))*l -> .
% 0.39/0.56 566[2:Res:564.0,42.0] || equal(skf2(skf4(skc1)),skf4(skc1))** -> .
% 0.39/0.56 567[2:MRR:84.0,566.0] || -> greater(skf2(skf4(skc1)),skf4(skc1))*l.
% 0.39/0.56 573[2:MRR:565.0,567.0] || -> .
% 0.39/0.56 574[2:Spt:573.0,547.0,564.0] || contracts_from(skf2(skf4(skc1)),first_movers)* -> .
% 0.39/0.56 575[2:Spt:573.0,547.1] || -> greater_or_equal(skf2(skf4(skc1)),skf2(skf4(skc1)))*.
% 0.39/0.56 576[2:MRR:558.1,574.0] || greater(zero,growth_rate(first_movers,skf2(skf4(skc1))))*r -> .
% 0.39/0.56 577[2:MRR:355.1,576.0] || greater(cardinality_at_time(efficient_producers,skf2(skf4(skc1))),zero)*l -> .
% 0.39/0.56 581[2:Res:257.1,577.0] || equal(skf2(skf4(skc1)),skf4(skc1))** -> .
% 0.39/0.56 583[2:NCh:9.2,9.0,577.0,261.1] || equal(zero,zero) greater(skf2(skf4(skc1)),skf4(skc1))*l -> .
% 0.39/0.56 586[2:MRR:84.0,581.0] || -> greater(skf2(skf4(skc1)),skf4(skc1))*l.
% 0.39/0.56 593[2:Obv:583.0] || greater(skf2(skf4(skc1)),skf4(skc1))*l -> .
% 0.39/0.56 594[2:MRR:593.0,586.0] || -> .
% 0.39/0.56 596[1:Spt:594.0,543.0,546.0] || equal(skf2(skf2(skf4(skc1))),skf2(skf4(skc1)))** -> .
% 0.39/0.56 597[1:Spt:594.0,543.1] || -> in_environment(skc1,skf2(skf2(skf4(skc1))))*.
% 0.39/0.56 601[1:MRR:527.2,596.0] || contracts_from(skf2(skf2(skf4(skc1))),first_movers)* greater(skf2(skf4(skc1)),appear(efficient_producers,skc1)) -> .
% 0.39/0.56 616[1:Res:597.0,11.2] stable(skc1) environment(skc1) || -> contracts_from(skf2(skf2(skf4(skc1))),first_movers) greater_or_equal(skf2(skf2(skf2(skf4(skc1)))),skf2(skf2(skf4(skc1))))*.
% 0.39/0.56 617[1:SSi:616.1,616.0,2.0,1.0,2.0,1.0] || -> contracts_from(skf2(skf2(skf4(skc1))),first_movers) greater_or_equal(skf2(skf2(skf2(skf4(skc1)))),skf2(skf2(skf4(skc1))))*.
% 0.39/0.56 643[2:Spt:617.0] || -> contracts_from(skf2(skf2(skf4(skc1))),first_movers)*.
% 0.39/0.56 645[2:MRR:601.0,643.0] || greater(skf2(skf4(skc1)),appear(efficient_producers,skc1))*r -> .
% 0.39/0.56 656[2:NCh:9.2,9.1,645.0,32.0] || equal(skf2(skf4(skc1)),skf4(skc1))** -> .
% 0.39/0.56 657[2:NCh:9.2,9.1,645.0,10.2] stable(skc1) environment(skc1) || greater(skf2(skf4(skc1)),skf4(skc1))*l -> .
% 0.39/0.56 659[2:MRR:84.0,656.0] || -> greater(skf2(skf4(skc1)),skf4(skc1))*l.
% 0.39/0.56 668[2:SSi:657.1,657.0,2.0,1.0,2.0,1.0] || greater(skf2(skf4(skc1)),skf4(skc1))*l -> .
% 0.39/0.56 669[2:MRR:668.0,659.0] || -> .
% 0.39/0.56 670[2:Spt:669.0,617.0,643.0] || contracts_from(skf2(skf2(skf4(skc1))),first_movers)* -> .
% 0.39/0.56 671[2:Spt:669.0,617.1] || -> greater_or_equal(skf2(skf2(skf2(skf4(skc1)))),skf2(skf2(skf4(skc1))))*.
% 0.39/0.56 684[3:Spt:84.0] || -> equal(skf2(skf4(skc1)),skf4(skc1))**.
% 0.39/0.56 696[3:Rew:684.0,596.0] || equal(skf2(skf4(skc1)),skf4(skc1))** -> .
% 0.39/0.56 717[3:Rew:684.0,696.0] || equal(skf4(skc1),skf4(skc1))* -> .
% 0.39/0.56 718[3:Obv:717.0] || -> .
% 0.39/0.56 730[3:Spt:718.0,84.0,684.0] || equal(skf2(skf4(skc1)),skf4(skc1))** -> .
% 0.39/0.56 731[3:Spt:718.0,84.1] || -> greater(skf2(skf4(skc1)),skf4(skc1))*l.
% 0.39/0.56 769[3:Res:731.0,264.2] stable(skc1) environment(skc1) || in_environment(skc1,skf2(skf4(skc1))) -> greater(cardinality_at_time(efficient_producers,skf2(skf4(skc1))),zero)*l.
% 0.39/0.56 786[3:SSi:769.1,769.0,2.0,1.0,2.0,1.0] || in_environment(skc1,skf2(skf4(skc1))) -> greater(cardinality_at_time(efficient_producers,skf2(skf4(skc1))),zero)*l.
% 0.39/0.56 787[3:MRR:786.0,110.0] || -> greater(cardinality_at_time(efficient_producers,skf2(skf4(skc1))),zero)*l.
% 0.39/0.56 788[3:MRR:355.0,787.0] || -> greater(zero,growth_rate(first_movers,skf2(skf4(skc1))))*r.
% 0.39/0.56 828[3:NCh:9.2,9.1,788.0,35.1] || in_environment(skc1,skf4(skc1)) equal(zero,zero) -> contracts_from(skf4(skc1),first_movers)*.
% 0.39/0.56 842[3:Obv:828.1] || in_environment(skc1,skf4(skc1)) -> contracts_from(skf4(skc1),first_movers)*.
% 0.39/0.56 843[3:MRR:842.0,842.1,52.0,37.0] || -> .
% 0.39/0.56 % SZS output end Refutation
% 0.39/0.56 Formulae used in the proof : prove_l9 mp_contracts_from l10 mp_EP_in_stable_environments mp_long_stable_environments mp_greater_or_equal mp_greater_transitivity t6 mp_non_empty_fm_and_ep
% 0.39/0.56
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