%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : MGT058-1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n028.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 06:19:57 AM UTC 2026 % Result : Unsatisfiable 0.22s 0.49s % Output : Refutation 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT058-1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_spass %d %s % 0.09/0.36 % Computer : n028.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Mon Sep 7 13:34:32 UTC 2026 % 0.13/0.36 % CPUTime : % 0.22/0.49 % 0.22/0.49 SPASS V 3.9 % 0.22/0.49 SPASS beiseite: Proof found. % 0.22/0.49 % SZS status Theorem % 0.22/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.22/0.49 SPASS derived 66 clauses, backtracked 17 clauses, performed 2 splits and kept 86 clauses. % 0.22/0.49 SPASS allocated 75657 KBytes. % 0.22/0.49 SPASS spent 0:00:00.11 on the problem. % 0.22/0.49 0:00:00.06 for the input. % 0.22/0.49 0:00:00.00 for the FLOTTER CNF translation. % 0.22/0.49 0:00:00.00 for inferences. % 0.22/0.49 0:00:00.00 for the backtracking. % 0.22/0.49 0:00:00.00 for the reduction. % 0.22/0.49 % 0.22/0.49 % 0.22/0.49 Here is a proof with depth 5, length 52 : % 0.22/0.49 % SZS output start Refutation % 0.22/0.49 1[0:Inp] fragile_position(u) || smaller_or_equal(age(u,v),sigma)* -> positional_advantage(u,v). % 0.22/0.49 7[0:Inp] robust_position(u) || positional_advantage(u,v) smaller_or_equal(age(u,v),tau)* -> . % 0.22/0.49 14[0:Inp] || -> equal(age(sk3,sk4),zero)**. % 0.22/0.49 15[0:Inp] || -> greater_or_equal(sigma,zero)*. % 0.22/0.49 16[0:Inp] || -> greater_or_equal(tau,zero)*. % 0.22/0.49 17[0:Inp] || -> fragile_position(sk3)*. % 0.22/0.49 18[0:Inp] || -> robust_position(sk3)*. % 0.22/0.49 20[0:Inp] || smaller(u,v)* -> smaller_or_equal(u,v). % 0.22/0.49 21[0:Inp] || equal(u,v) -> smaller_or_equal(u,v)*. % 0.22/0.49 22[0:Inp] || greater_or_equal(u,v)* -> equal(u,v) greater(u,v). % 0.22/0.49 26[0:Inp] || greater(u,v) -> smaller(v,u)*. % 0.22/0.49 31[0:Res:18.0,7.0] || positional_advantage(sk3,u) smaller_or_equal(age(sk3,u),tau)* -> . % 0.22/0.49 33[0:Res:17.0,1.0] || smaller_or_equal(age(sk3,u),sigma)* -> positional_advantage(sk3,u). % 0.22/0.49 34[0:Res:16.0,22.0] || -> equal(zero,tau) greater(tau,zero)*r. % 0.22/0.49 35[0:Res:15.0,22.0] || -> equal(zero,sigma) greater(sigma,zero)*r. % 0.22/0.49 36[0:Res:14.0,21.0] || -> smaller_or_equal(age(sk3,sk4),zero)*. % 0.22/0.49 40[0:Rew:14.0,36.0] || -> smaller_or_equal(zero,zero)*. % 0.22/0.49 44[1:Spt:35.0] || -> equal(zero,sigma)**. % 0.22/0.49 46[1:Rew:44.0,40.0] || -> smaller_or_equal(sigma,sigma)*. % 0.22/0.49 49[1:Rew:44.0,14.0] || -> equal(age(sk3,sk4),sigma)**. % 0.22/0.49 50[1:Rew:44.0,34.0] || -> equal(tau,sigma) greater(tau,zero)*r. % 0.22/0.49 51[1:Rew:44.0,50.1] || -> equal(tau,sigma) greater(tau,sigma)*l. % 0.22/0.49 54[1:SpL:49.0,33.0] || smaller_or_equal(sigma,sigma) -> positional_advantage(sk3,sk4)*. % 0.22/0.49 56[1:MRR:54.0,46.0] || -> positional_advantage(sk3,sk4)*. % 0.22/0.49 59[1:SpL:49.0,31.1] || positional_advantage(sk3,sk4)* smaller_or_equal(sigma,tau) -> . % 0.22/0.49 61[1:MRR:59.0,56.0] || smaller_or_equal(sigma,tau)* -> . % 0.22/0.49 63[1:Res:21.1,61.0] || equal(tau,sigma)** -> . % 0.22/0.49 64[1:MRR:51.0,63.0] || -> greater(tau,sigma)*l. % 0.22/0.49 66[0:Res:26.1,20.0] || greater(u,v) -> smaller_or_equal(v,u)*. % 0.22/0.49 71[1:Res:66.1,61.0] || greater(tau,sigma)*l -> . % 0.22/0.49 72[1:MRR:71.0,64.0] || -> . % 0.22/0.49 73[1:Spt:72.0,35.0,44.0] || equal(zero,sigma)** -> . % 0.22/0.49 74[1:Spt:72.0,35.1] || -> greater(sigma,zero)*r. % 0.22/0.49 75[2:Spt:34.0] || -> equal(zero,tau)**. % 0.22/0.49 76[2:Rew:75.0,74.0] || -> greater(sigma,tau)*r. % 0.22/0.49 79[2:Rew:75.0,40.0] || -> smaller_or_equal(tau,tau)*. % 0.22/0.49 82[2:Rew:75.0,14.0] || -> equal(age(sk3,sk4),tau)**. % 0.22/0.49 85[2:SpL:82.0,33.0] || smaller_or_equal(tau,sigma) -> positional_advantage(sk3,sk4)*. % 0.22/0.49 87[2:SpL:82.0,31.1] || positional_advantage(sk3,sk4)* smaller_or_equal(tau,tau) -> . % 0.22/0.49 89[2:MRR:87.1,79.0] || positional_advantage(sk3,sk4)* -> . % 0.22/0.49 90[2:MRR:85.1,89.0] || smaller_or_equal(tau,sigma)* -> . % 0.22/0.49 95[2:Res:66.1,90.0] || greater(sigma,tau)*r -> . % 0.22/0.49 96[2:MRR:95.0,76.0] || -> . % 0.22/0.49 97[2:Spt:96.0,34.0,75.0] || equal(zero,tau)** -> . % 0.22/0.49 98[2:Spt:96.0,34.1] || -> greater(tau,zero)*r. % 0.22/0.49 100[0:SpL:14.0,33.0] || smaller_or_equal(zero,sigma) -> positional_advantage(sk3,sk4)*. % 0.22/0.49 102[0:SpL:14.0,31.1] || positional_advantage(sk3,sk4)* smaller_or_equal(zero,tau) -> . % 0.22/0.49 108[0:Res:100.1,102.0] || smaller_or_equal(zero,sigma) smaller_or_equal(zero,tau)* -> . % 0.22/0.49 110[0:Res:66.1,108.1] || greater(tau,zero) smaller_or_equal(zero,sigma)* -> . % 0.22/0.49 111[2:MRR:110.0,98.0] || smaller_or_equal(zero,sigma)* -> . % 0.22/0.49 113[2:Res:66.1,111.0] || greater(sigma,zero)*r -> . % 0.22/0.49 114[2:MRR:113.0,74.0] || -> . % 0.22/0.49 % SZS output end Refutation % 0.22/0.49 Formulae used in the proof : definition_3_30 definition_4_36 lemma_10_43 lemma_10_44 lemma_10_45 lemma_10_46 lemma_10_47 definition_smaller_or_equal_2 definition_smaller_or_equal_3 definition_greater_or_equal_4 definition_smaller_8 % 0.22/0.49 %------------------------------------------------------------------------------