%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : MGT028-1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n031.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 06:19:49 AM UTC 2026 % Result : Unsatisfiable 0.34s 0.63s % Output : Refutation 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.05 % Problem : MGT028-1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.06 % Command : run_spass %d %s % 0.18/0.44 % Computer : n031.cluster.edu % 0.18/0.44 % Model : x86_64 x86_64 % 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.44 % Memory : 8046.5625MB % 0.18/0.44 % OS : Linux 6.8.0-71-generic % 0.18/0.44 % CPULimit : 300 % 0.18/0.44 % WCLimit : 300 % 0.18/0.44 % DateTime : Mon Sep 7 12:18:26 UTC 2026 % 0.18/0.45 % CPUTime : % 0.34/0.63 % 0.34/0.63 SPASS V 3.9 % 0.34/0.63 SPASS beiseite: Proof found. % 0.34/0.63 % SZS status Theorem % 0.34/0.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.34/0.63 SPASS derived 62 clauses, backtracked 21 clauses, performed 4 splits and kept 76 clauses. % 0.34/0.63 SPASS allocated 75710 KBytes. % 0.34/0.63 SPASS spent 0:00:00.17 on the problem. % 0.34/0.63 0:00:00.10 for the input. % 0.34/0.63 0:00:00.00 for the FLOTTER CNF translation. % 0.34/0.63 0:00:00.00 for inferences. % 0.34/0.63 0:00:00.00 for the backtracking. % 0.34/0.63 0:00:00.01 for the reduction. % 0.34/0.63 % 0.34/0.63 % 0.34/0.63 Here is a proof with depth 7, length 80 : % 0.34/0.63 % SZS output start Refutation % 0.34/0.63 1[0:Inp] stable(u) environment(u) || in_environment(u,v) -> greater(sk2(u),appear(efficient_producers,u)) subpopulations(first_movers,efficient_producers,u,sk1(v,u))*. % 0.34/0.63 2[0:Inp] stable(u) environment(u) || in_environment(u,v)+ -> greater(sk2(u),appear(efficient_producers,u))* greater_or_equal(sk1(v,u),v)*. % 0.34/0.63 3[0:Inp] stable(u) environment(u) || in_environment(u,v) greater_or_equal(w,sk2(u)) subpopulations(first_movers,efficient_producers,u,w)* -> greater(zero,growth_rate(first_movers,w))* subpopulations(first_movers,efficient_producers,u,sk1(v,u))*. % 0.34/0.63 4[0:Inp] stable(u) environment(u) || in_environment(u,v) greater_or_equal(w,sk2(u)) subpopulations(first_movers,efficient_producers,u,w)*+ -> greater(zero,growth_rate(first_movers,w))* greater_or_equal(sk1(v,u),v)*. % 0.34/0.63 5[0:Inp] stable(u) environment(u) || in_environment(u,v) greater(zero,growth_rate(first_movers,sk1(v,u)))*+ -> greater(sk2(u),appear(efficient_producers,u))*. % 0.34/0.63 6[0:Inp] stable(u) environment(u) || in_environment(u,v) greater_or_equal(w,sk2(u)) greater(zero,growth_rate(first_movers,sk1(v,u)))* subpopulations(first_movers,efficient_producers,u,w)* -> greater(zero,growth_rate(first_movers,w))*. % 0.34/0.63 7[0:Inp] stable(u) environment(u) || -> in_environment(u,sk3(u))*. % 0.34/0.63 9[0:Inp] stable(u) environment(u) || greater_or_equal(v,sk3(u)) subpopulations(first_movers,efficient_producers,u,v)*+ -> greater(zero,growth_rate(first_movers,v))*. % 0.34/0.63 10[0:Inp] || -> environment(sk4)*. % 0.34/0.63 11[0:Inp] || -> stable(sk4)*. % 0.34/0.63 12[0:Inp] || greater(u,appear(efficient_producers,sk4)) -> subpopulations(first_movers,efficient_producers,sk4,sk5(u))*. % 0.34/0.63 13[0:Inp] || greater(u,appear(efficient_producers,sk4))*+ -> greater_or_equal(sk5(u),u)*. % 0.34/0.63 14[0:Inp] || greater(u,appear(efficient_producers,sk4)) greater(zero,growth_rate(first_movers,sk5(u)))* -> . % 0.34/0.63 20[0:Res:11.0,9.1] environment(sk4) || subpopulations(first_movers,efficient_producers,sk4,u) greater_or_equal(u,sk3(sk4)) -> greater(zero,growth_rate(first_movers,u))*. % 0.34/0.63 22[0:Res:11.0,2.1] environment(sk4) || in_environment(sk4,u) -> greater_or_equal(sk1(u,sk4),u)* greater(sk2(sk4),appear(efficient_producers,sk4))*. % 0.34/0.63 23[0:Res:11.0,7.1] environment(sk4) || -> in_environment(sk4,sk3(sk4))*. % 0.34/0.63 24[0:Res:10.0,6.0] stable(sk4) || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* subpopulations(first_movers,efficient_producers,sk4,v) greater_or_equal(v,sk2(sk4)) -> greater(zero,growth_rate(first_movers,v))*. % 0.34/0.63 25[0:Res:10.0,3.0] stable(sk4) || in_environment(sk4,u) subpopulations(first_movers,efficient_producers,sk4,v) greater_or_equal(v,sk2(sk4)) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))* greater(zero,growth_rate(first_movers,v))*. % 0.34/0.63 26[0:Res:10.0,4.0] stable(sk4) || in_environment(sk4,u) subpopulations(first_movers,efficient_producers,sk4,v) greater_or_equal(v,sk2(sk4)) -> greater_or_equal(sk1(u,sk4),u)* greater(zero,growth_rate(first_movers,v))*. % 0.34/0.63 27[0:Res:10.0,5.0] stable(sk4) || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* -> greater(sk2(sk4),appear(efficient_producers,sk4)). % 0.34/0.63 28[0:Res:10.0,1.0] stable(sk4) || in_environment(sk4,u) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))* greater(sk2(sk4),appear(efficient_producers,sk4)). % 0.34/0.63 33[0:MRR:23.0,10.0] || -> in_environment(sk4,sk3(sk4))*. % 0.34/0.63 34[0:MRR:22.0,10.0] || in_environment(sk4,u)+ -> greater(sk2(sk4),appear(efficient_producers,sk4))* greater_or_equal(sk1(u,sk4),u)*. % 0.34/0.63 35[0:MRR:20.0,10.0] || greater_or_equal(u,sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*. % 0.34/0.63 37[0:MRR:28.0,11.0] || in_environment(sk4,u) -> greater(sk2(sk4),appear(efficient_producers,sk4)) subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))*. % 0.34/0.63 38[0:MRR:27.0,11.0] || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* -> greater(sk2(sk4),appear(efficient_producers,sk4)). % 0.34/0.63 39[0:MRR:26.0,11.0] || greater_or_equal(u,sk2(sk4)) in_environment(sk4,v) subpopulations(first_movers,efficient_producers,sk4,u)+ -> greater(zero,growth_rate(first_movers,u))* greater_or_equal(sk1(v,sk4),v)*. % 0.34/0.63 40[0:MRR:25.0,11.0] || greater_or_equal(u,sk2(sk4)) in_environment(sk4,v) subpopulations(first_movers,efficient_producers,sk4,u)+ -> greater(zero,growth_rate(first_movers,u))* subpopulations(first_movers,efficient_producers,sk4,sk1(v,sk4))*. % 0.34/0.63 41[0:MRR:24.0,11.0] || greater_or_equal(u,sk2(sk4)) in_environment(sk4,v) greater(zero,growth_rate(first_movers,sk1(v,sk4)))*+ subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*. % 0.34/0.63 44[1:Spt:39.0,39.2,39.3] || greater_or_equal(u,sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*. % 0.34/0.63 45[2:Spt:34.1] || -> greater(sk2(sk4),appear(efficient_producers,sk4))*. % 0.34/0.63 46[2:Res:45.0,13.0] || -> greater_or_equal(sk5(sk2(sk4)),sk2(sk4))*. % 0.34/0.63 47[1:Res:44.2,14.1] || greater_or_equal(sk5(u),sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk5(u))* greater(u,appear(efficient_producers,sk4)) -> . % 0.34/0.63 48[1:MRR:47.1,12.1] || greater_or_equal(sk5(u),sk2(sk4))* greater(u,appear(efficient_producers,sk4)) -> . % 0.34/0.63 49[2:Res:46.0,48.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> . % 0.34/0.63 50[2:MRR:49.0,45.0] || -> . % 0.34/0.63 51[2:Spt:50.0,34.1,45.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> . % 0.34/0.63 52[2:Spt:50.0,34.0,34.2] || in_environment(sk4,u) -> greater_or_equal(sk1(u,sk4),u)*. % 0.34/0.63 53[2:MRR:37.1,51.0] || in_environment(sk4,u) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))*. % 0.34/0.63 54[2:MRR:38.2,51.0] || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* -> . % 0.34/0.63 65[2:Res:35.2,54.1] || greater_or_equal(sk1(u,sk4),sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))* in_environment(sk4,u) -> . % 0.34/0.63 67[2:MRR:65.1,53.1] || greater_or_equal(sk1(u,sk4),sk3(sk4))* in_environment(sk4,u) -> . % 0.34/0.63 68[2:Res:52.1,67.0] || in_environment(sk4,sk3(sk4))* in_environment(sk4,sk3(sk4))* -> . % 0.34/0.63 71[2:Obv:68.0] || in_environment(sk4,sk3(sk4))* -> . % 0.34/0.63 72[2:MRR:71.0,33.0] || -> . % 0.34/0.63 73[1:Spt:72.0,39.1,39.4] || in_environment(sk4,u) -> greater_or_equal(sk1(u,sk4),u)*. % 0.34/0.63 74[2:Spt:40.0,40.2,40.3] || greater_or_equal(u,sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*. % 0.34/0.63 75[2:Res:74.2,14.1] || greater_or_equal(sk5(u),sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk5(u))* greater(u,appear(efficient_producers,sk4)) -> . % 0.34/0.63 76[2:MRR:75.1,12.1] || greater_or_equal(sk5(u),sk2(sk4))* greater(u,appear(efficient_producers,sk4)) -> . % 0.34/0.63 77[3:Spt:37.1] || -> greater(sk2(sk4),appear(efficient_producers,sk4))*. % 0.34/0.63 78[3:Res:77.0,13.0] || -> greater_or_equal(sk5(sk2(sk4)),sk2(sk4))*. % 0.34/0.63 80[3:Res:78.0,76.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> . % 0.34/0.63 81[3:MRR:80.0,77.0] || -> . % 0.34/0.63 82[3:Spt:81.0,37.1,77.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> . % 0.34/0.63 83[3:Spt:81.0,37.0,37.2] || in_environment(sk4,u) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))*. % 0.34/0.63 85[3:MRR:38.2,82.0] || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* -> . % 0.34/0.63 89[3:Res:83.1,9.3] stable(sk4) environment(sk4) || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4)) -> greater(zero,growth_rate(first_movers,sk1(u,sk4)))*. % 0.34/0.63 90[3:SSi:89.1,89.0,11.0,10.0,11.0,10.0] || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4)) -> greater(zero,growth_rate(first_movers,sk1(u,sk4)))*. % 0.34/0.63 91[3:MRR:90.2,85.1] || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4))* -> . % 0.34/0.63 92[3:Res:73.1,91.1] || in_environment(sk4,sk3(sk4))* in_environment(sk4,sk3(sk4))* -> . % 0.34/0.63 95[3:Obv:92.0] || in_environment(sk4,sk3(sk4))* -> . % 0.34/0.65 96[3:MRR:95.0,33.0] || -> . % 0.34/0.65 97[2:Spt:96.0,40.1,40.4] || in_environment(sk4,u) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))*. % 0.34/0.65 98[2:Res:97.1,9.3] stable(sk4) environment(sk4) || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4)) -> greater(zero,growth_rate(first_movers,sk1(u,sk4)))*. % 0.34/0.65 101[2:SSi:98.1,98.0,11.0,10.0,11.0,10.0] || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4)) -> greater(zero,growth_rate(first_movers,sk1(u,sk4)))*. % 0.34/0.65 102[0:Res:35.2,38.1] || greater_or_equal(sk1(u,sk4),sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))* in_environment(sk4,u) -> greater(sk2(sk4),appear(efficient_producers,sk4)). % 0.34/0.65 103[2:MRR:102.1,97.1] || greater_or_equal(sk1(u,sk4),sk3(sk4))* in_environment(sk4,u) -> greater(sk2(sk4),appear(efficient_producers,sk4)). % 0.34/0.65 109[2:Res:73.1,103.0] || in_environment(sk4,sk3(sk4)) in_environment(sk4,sk3(sk4)) -> greater(sk2(sk4),appear(efficient_producers,sk4))*. % 0.34/0.65 111[2:Obv:109.0] || in_environment(sk4,sk3(sk4)) -> greater(sk2(sk4),appear(efficient_producers,sk4))*. % 0.34/0.65 112[2:MRR:111.0,33.0] || -> greater(sk2(sk4),appear(efficient_producers,sk4))*. % 0.34/0.65 114[2:Res:112.0,13.0] || -> greater_or_equal(sk5(sk2(sk4)),sk2(sk4))*. % 0.34/0.65 127[2:Res:101.2,41.2] || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4))* greater_or_equal(v,sk2(sk4)) in_environment(sk4,u) subpopulations(first_movers,efficient_producers,sk4,v) -> greater(zero,growth_rate(first_movers,v))*. % 0.34/0.65 128[2:Obv:127.0] || greater_or_equal(sk1(u,sk4),sk3(sk4))*+ greater_or_equal(v,sk2(sk4)) in_environment(sk4,u) subpopulations(first_movers,efficient_producers,sk4,v) -> greater(zero,growth_rate(first_movers,v))*. % 0.34/0.65 129[2:Res:73.1,128.0] || in_environment(sk4,sk3(sk4)) greater_or_equal(u,sk2(sk4)) in_environment(sk4,sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*. % 0.34/0.65 130[2:Obv:129.0] || greater_or_equal(u,sk2(sk4)) in_environment(sk4,sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*. % 0.34/0.65 131[2:MRR:130.1,33.0] || greater_or_equal(u,sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*. % 0.34/0.65 132[2:Res:131.2,14.1] || greater_or_equal(sk5(u),sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk5(u))* greater(u,appear(efficient_producers,sk4)) -> . % 0.34/0.65 133[2:MRR:132.1,12.1] || greater_or_equal(sk5(u),sk2(sk4))* greater(u,appear(efficient_producers,sk4)) -> . % 0.34/0.65 134[2:Res:114.0,133.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> . % 0.34/0.65 135[2:MRR:134.0,112.0] || -> . % 0.34/0.65 % SZS output end Refutation % 0.34/0.65 Formulae used in the proof : mp_first_movers_negative_growth_1 mp_first_movers_negative_growth_2 mp_first_movers_negative_growth_3 mp_first_movers_negative_growth_4 mp_first_movers_negative_growth_5 mp_first_movers_negative_growth_6 l11_7 l11_9 prove_l10_10 prove_l10_11 prove_l10_12 prove_l10_13 prove_l10_14 % 0.34/0.65 %------------------------------------------------------------------------------