%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : MGT030+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:19:50 AM UTC 2026 % Result : Theorem 0.22s 0.52s % Output : Refutation 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT030+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : run_spass %d %s % 0.08/0.35 % Computer : n004.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Mon Sep 7 12:18:00 UTC 2026 % 0.08/0.36 % CPUTime : % 0.22/0.52 % 0.22/0.52 SPASS V 3.9 % 0.22/0.52 SPASS beiseite: Proof found. % 0.22/0.52 % SZS status Theorem % 0.22/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.22/0.52 SPASS derived 47 clauses, backtracked 9 clauses, performed 2 splits and kept 57 clauses. % 0.22/0.52 SPASS allocated 97655 KBytes. % 0.22/0.52 SPASS spent 0:00:00.15 on the problem. % 0.22/0.52 0:00:00.06 for the input. % 0.22/0.52 0:00:00.04 for the FLOTTER CNF translation. % 0.22/0.52 0:00:00.00 for inferences. % 0.22/0.52 0:00:00.00 for the backtracking. % 0.22/0.52 0:00:00.00 for the reduction. % 0.22/0.52 % 0.22/0.52 % 0.22/0.52 Here is a proof with depth 4, length 41 : % 0.22/0.52 % SZS output start Refutation % 0.22/0.52 1[0:Inp] || -> environment(skc1)*. % 0.22/0.52 2[0:Inp] || -> stable(skc1)*. % 0.22/0.52 3[0:Inp] SkP0(u) || -> in_environment(u,skf5(u))*. % 0.22/0.52 4[0:Inp] || greater(growth_rate(efficient_producers,skf4(u)),growth_rate(first_movers,skf4(u)))* -> . % 0.22/0.52 5[0:Inp] || greater(growth_rate(efficient_producers,skf5(u)),growth_rate(first_movers,skf5(u)))* -> . % 0.22/0.52 6[0:Inp] stable(u) environment(u) || -> in_environment(u,skf8(u))*. % 0.22/0.52 7[0:Inp] || greater(growth_rate(efficient_producers,skf6(u,v)),growth_rate(first_movers,skf6(u,v)))* -> . % 0.22/0.52 8[0:Inp] environment(u) || in_environment(u,v) -> SkP0(u) greater_or_equal(skf6(v,u),v)*. % 0.22/0.52 9[0:Inp] || in_environment(skc1,u) -> greater(skf4(u),u) greater(growth_rate(efficient_producers,u),growth_rate(first_movers,u))*. % 0.22/0.52 10[0:Inp] environment(u) || in_environment(u,v) -> SkP0(u) subpopulations(first_movers,efficient_producers,u,skf6(v,u))*. % 0.22/0.52 11[0:Inp] || in_environment(skc1,u) -> greater(growth_rate(efficient_producers,u),growth_rate(first_movers,u))* subpopulations(first_movers,efficient_producers,skc1,skf4(u)). % 0.22/0.52 12[0:Inp] SkP0(u) || greater(v,skf5(u)) subpopulations(first_movers,efficient_producers,u,v)*+ -> greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v))*. % 0.22/0.52 13[0:Inp] stable(u) environment(u) || greater_or_equal(v,skf8(u)) subpopulations(first_movers,efficient_producers,u,v)*+ -> greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v))*. % 0.22/0.52 15[0:Res:2.0,6.1] environment(skc1) || -> in_environment(skc1,skf8(skc1))*. % 0.22/0.52 17[0:Res:1.0,10.0] || in_environment(skc1,u) -> SkP0(skc1) subpopulations(first_movers,efficient_producers,skc1,skf6(u,skc1))*. % 0.22/0.52 18[0:Res:1.0,8.0] || in_environment(skc1,u) -> SkP0(skc1) greater_or_equal(skf6(u,skc1),u)*. % 0.22/0.52 23[0:Res:12.3,4.0] SkP0(u) || greater(skf4(v),skf5(u)) subpopulations(first_movers,efficient_producers,u,skf4(v))* -> . % 0.22/0.52 24[0:Res:9.2,5.0] || in_environment(skc1,skf5(u)) -> greater(skf4(skf5(u)),skf5(u))*. % 0.22/0.52 27[0:MRR:15.0,1.0] || -> in_environment(skc1,skf8(skc1))*. % 0.22/0.52 35[1:Spt:18.0,18.2] || in_environment(skc1,u) -> greater_or_equal(skf6(u,skc1),u)*. % 0.22/0.52 36[2:Spt:17.0,17.2] || in_environment(skc1,u) -> subpopulations(first_movers,efficient_producers,skc1,skf6(u,skc1))*. % 0.22/0.52 41[0:Res:11.1,5.0] || in_environment(skc1,skf5(u)) -> subpopulations(first_movers,efficient_producers,skc1,skf4(skf5(u)))*. % 0.22/0.52 44[0:Res:41.1,23.2] SkP0(skc1) || in_environment(skc1,skf5(u)) greater(skf4(skf5(u)),skf5(skc1))* -> . % 0.22/0.52 52[2:Res:36.1,13.3] stable(skc1) environment(skc1) || in_environment(skc1,u) greater_or_equal(skf6(u,skc1),skf8(skc1)) -> greater(growth_rate(efficient_producers,skf6(u,skc1)),growth_rate(first_movers,skf6(u,skc1)))*. % 0.22/0.52 57[2:SSi:52.1,52.0,2.0,1.0,2.0,1.0] || in_environment(skc1,u) greater_or_equal(skf6(u,skc1),skf8(skc1)) -> greater(growth_rate(efficient_producers,skf6(u,skc1)),growth_rate(first_movers,skf6(u,skc1)))*. % 0.22/0.52 58[2:MRR:57.2,7.0] || in_environment(skc1,u) greater_or_equal(skf6(u,skc1),skf8(skc1))* -> . % 0.22/0.52 67[2:Res:35.1,58.1] || in_environment(skc1,skf8(skc1))* in_environment(skc1,skf8(skc1))* -> . % 0.22/0.52 69[2:Obv:67.0] || in_environment(skc1,skf8(skc1))* -> . % 0.22/0.52 70[2:MRR:69.0,27.0] || -> . % 0.22/0.52 78[2:Spt:70.0,17.1] || -> SkP0(skc1)*. % 0.22/0.52 79[2:MRR:44.0,78.0] || in_environment(skc1,skf5(u)) greater(skf4(skf5(u)),skf5(skc1))* -> . % 0.22/0.52 82[2:Res:24.1,79.1] || in_environment(skc1,skf5(skc1))* in_environment(skc1,skf5(skc1))* -> . % 0.22/0.52 83[2:Obv:82.0] || in_environment(skc1,skf5(skc1))* -> . % 0.22/0.52 87[2:Res:3.1,83.0] SkP0(skc1) || -> . % 0.22/0.52 88[2:SSi:87.0,2.0,1.0,78.0] || -> . % 0.22/0.52 89[1:Spt:88.0,18.1] || -> SkP0(skc1)*. % 0.22/0.52 90[1:MRR:44.0,89.0] || in_environment(skc1,skf5(u)) greater(skf4(skf5(u)),skf5(skc1))* -> . % 0.22/0.52 93[1:Res:24.1,90.1] || in_environment(skc1,skf5(skc1))* in_environment(skc1,skf5(skc1))* -> . % 0.22/0.52 94[1:Obv:93.0] || in_environment(skc1,skf5(skc1))* -> . % 0.22/0.52 95[1:Res:3.1,94.0] SkP0(skc1) || -> . % 0.22/0.52 96[1:SSi:95.0,2.0,1.0,89.0] || -> . % 0.22/0.52 % SZS output end Refutation % 0.22/0.52 Formulae used in the proof : prove_l12 l1 mp_earliest_time_growth_rate_exceeds % 0.22/0.52 %------------------------------------------------------------------------------