%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : MGT022-2 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n027.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 06:19:48 AM UTC 2026 % Result : Unsatisfiable 0.14s 0.48s % Output : Refutation 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT022-2 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_spass %d %s % 0.10/0.36 % Computer : n027.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Mon Sep 7 12:08:45 UTC 2026 % 0.10/0.36 % CPUTime : % 0.14/0.48 % 0.14/0.48 SPASS V 3.9 % 0.14/0.48 SPASS beiseite: Proof found. % 0.14/0.48 % SZS status Theorem % 0.14/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.14/0.48 SPASS derived 13 clauses, backtracked 11 clauses, performed 2 splits and kept 26 clauses. % 0.14/0.48 SPASS allocated 75628 KBytes. % 0.14/0.48 SPASS spent 0:00:00.10 on the problem. % 0.14/0.48 0:00:00.06 for the input. % 0.14/0.48 0:00:00.00 for the FLOTTER CNF translation. % 0.14/0.48 0:00:00.00 for inferences. % 0.14/0.48 0:00:00.00 for the backtracking. % 0.14/0.48 0:00:00.00 for the reduction. % 0.14/0.48 % 0.14/0.48 % 0.14/0.48 Here is a proof with depth 2, length 24 : % 0.14/0.48 % SZS output start Refutation % 0.14/0.48 1[0:Inp] decreases(u) constant(u) || -> . % 0.14/0.48 2[0:Inp] environment(u) || decreases(resources(u,v)) greater(resilience(w),resilience(x)) subpopulations(x,w,u,v)* -> increases(difference(disbanding_rate(x,v),disbanding_rate(w,v)))*. % 0.14/0.48 3[0:Inp] environment(u) || constant(resources(u,v)) greater(resilience(w),resilience(x)) subpopulations(x,w,u,v)* -> constant(difference(disbanding_rate(x,v),disbanding_rate(w,v)))*. % 0.14/0.48 4[0:Inp] || -> greater(resilience(efficient_producers),resilience(first_movers))*. % 0.14/0.48 5[0:Inp] || -> environment(sk1)*. % 0.14/0.48 6[0:Inp] || -> subpopulations(first_movers,efficient_producers,sk1,sk2)*. % 0.14/0.48 7[0:Inp] || -> constant(resources(sk1,sk2))* decreases(resources(sk1,sk2)). % 0.14/0.48 8[0:Inp] || -> decreases(resources(sk1,sk2)) decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*. % 0.14/0.48 9[0:Inp] || increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))* -> constant(resources(sk1,sk2)). % 0.14/0.48 13[0:Res:6.0,3.1] environment(sk1) || greater(resilience(efficient_producers),resilience(first_movers)) constant(resources(sk1,sk2)) -> constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*. % 0.14/0.48 14[0:Res:6.0,2.1] environment(sk1) || greater(resilience(efficient_producers),resilience(first_movers)) decreases(resources(sk1,sk2)) -> increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*. % 0.14/0.48 15[0:MRR:14.0,14.1,5.0,4.0] || decreases(resources(sk1,sk2)) -> increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*. % 0.14/0.48 16[0:MRR:13.0,13.1,5.0,4.0] || constant(resources(sk1,sk2)) -> constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*. % 0.14/0.48 32[1:Spt:7.0] || -> constant(resources(sk1,sk2))*. % 0.14/0.48 33[1:MRR:16.0,32.0] || -> constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*. % 0.14/0.48 34[2:Spt:8.0] || -> decreases(resources(sk1,sk2))*. % 0.14/0.48 37[2:EmS:1.0,1.1,34.0,32.0] || -> . % 0.14/0.48 38[2:Spt:37.0,8.0,34.0] || decreases(resources(sk1,sk2))* -> . % 0.14/0.48 39[2:Spt:37.0,8.1] || -> decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*. % 0.14/0.48 40[2:EmS:1.0,1.1,39.0,33.0] || -> . % 0.14/0.48 41[1:Spt:40.0,7.0,32.0] || constant(resources(sk1,sk2))* -> . % 0.14/0.48 42[1:Spt:40.0,7.1] || -> decreases(resources(sk1,sk2))*. % 0.14/0.48 43[1:MRR:15.0,42.0] || -> increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*. % 0.14/0.48 44[1:MRR:9.0,9.1,43.0,41.0] || -> . % 0.14/0.48 % SZS output end Refutation % 0.14/0.48 Formulae used in the proof : mp_constant_not_decrease_1 a6_2 a6_3 a2_4 prove_l4_5 prove_l4_6 prove_l4_7 prove_l4_8 prove_l4_9 % 0.14/0.48 %------------------------------------------------------------------------------