%------------------------------------------------------------------------------ % 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 : 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 06:19:57 AM UTC 2026 % Result : Theorem 0.23s 0.52s % Output : Refutation 0.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT058+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_spass %d %s % 0.07/0.34 % Computer : n004.cluster.edu % 0.07/0.34 % Model : x86_64 x86_64 % 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.34 % Memory : 8046.5625MB % 0.07/0.34 % OS : Linux 6.8.0-71-generic % 0.07/0.34 % CPULimit : 300 % 0.07/0.34 % WCLimit : 300 % 0.07/0.34 % DateTime : Mon Sep 7 13:31:15 UTC 2026 % 0.07/0.35 % CPUTime : % 0.23/0.52 % 0.23/0.52 SPASS V 3.9 % 0.23/0.52 SPASS beiseite: Proof found. % 0.23/0.52 % SZS status Theorem % 0.23/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.23/0.52 SPASS derived 63 clauses, backtracked 17 clauses, performed 2 splits and kept 87 clauses. % 0.23/0.52 SPASS allocated 97834 KBytes. % 0.23/0.52 SPASS spent 0:00:00.16 on the problem. % 0.23/0.52 0:00:00.06 for the input. % 0.23/0.52 0:00:00.05 for the FLOTTER CNF translation. % 0.23/0.52 0:00:00.00 for inferences. % 0.23/0.52 0:00:00.00 for the backtracking. % 0.23/0.52 0:00:00.00 for the reduction. % 0.23/0.52 % 0.23/0.52 % 0.23/0.52 Here is a proof with depth 5, length 54 : % 0.23/0.52 % SZS output start Refutation % 0.23/0.52 2[0:Inp] || -> fragile_position(skc2)*. % 0.23/0.52 3[0:Inp] || -> robust_position(skc2)*. % 0.23/0.52 4[0:Inp] || -> greater_or_equal(tau,zero)*. % 0.23/0.52 5[0:Inp] || -> greater_or_equal(sigma,zero)*. % 0.23/0.52 6[0:Inp] || -> equal(age(skc2,skc3),zero)**. % 0.23/0.52 7[0:Inp] || smaller(u,v)* -> smaller_or_equal(u,v). % 0.23/0.52 8[0:Inp] || equal(u,v) -> smaller_or_equal(u,v)*. % 0.23/0.52 12[0:Inp] || greater(u,v) -> smaller(v,u)*. % 0.23/0.52 16[0:Inp] || greater_or_equal(u,v)* -> equal(u,v) greater(u,v). % 0.23/0.52 20[0:Inp] fragile_position(u) || smaller_or_equal(age(u,v),sigma)* -> positional_advantage(u,v). % 0.23/0.52 26[0:Inp] robust_position(u) || positional_advantage(u,v) smaller_or_equal(age(u,v),tau)* -> . % 0.23/0.52 31[0:Res:3.0,26.0] || positional_advantage(skc2,u) smaller_or_equal(age(skc2,u),tau)* -> . % 0.23/0.52 33[0:Res:2.0,20.0] || smaller_or_equal(age(skc2,u),sigma)* -> positional_advantage(skc2,u). % 0.23/0.52 34[0:Res:5.0,16.0] || -> equal(zero,sigma) greater(sigma,zero)*r. % 0.23/0.52 35[0:Res:4.0,16.0] || -> equal(zero,tau) greater(tau,zero)*r. % 0.23/0.52 36[0:Res:6.0,8.0] || -> smaller_or_equal(age(skc2,skc3),zero)*. % 0.23/0.52 40[0:Rew:6.0,36.0] || -> smaller_or_equal(zero,zero)*. % 0.23/0.52 44[1:Spt:35.0] || -> equal(zero,tau)**. % 0.23/0.52 46[1:Rew:44.0,40.0] || -> smaller_or_equal(tau,tau)*. % 0.23/0.52 49[1:Rew:44.0,6.0] || -> equal(age(skc2,skc3),tau)**. % 0.23/0.52 50[1:Rew:44.0,34.0] || -> equal(tau,sigma) greater(sigma,zero)*r. % 0.23/0.52 51[1:Rew:44.0,50.1] || -> equal(tau,sigma) greater(sigma,tau)*r. % 0.23/0.52 54[1:SpL:49.0,33.0] || smaller_or_equal(tau,sigma) -> positional_advantage(skc2,skc3)*. % 0.23/0.52 55[0:Res:8.1,33.0] || equal(age(skc2,u),sigma)** -> positional_advantage(skc2,u). % 0.23/0.52 56[1:SpL:49.0,55.0] || equal(tau,sigma) -> positional_advantage(skc2,skc3)*. % 0.23/0.52 58[1:SpL:49.0,31.1] || positional_advantage(skc2,skc3)* smaller_or_equal(tau,tau) -> . % 0.23/0.52 60[1:MRR:58.1,46.0] || positional_advantage(skc2,skc3)* -> . % 0.23/0.52 61[1:MRR:54.1,60.0] || smaller_or_equal(tau,sigma)* -> . % 0.23/0.52 62[1:MRR:56.1,60.0] || equal(tau,sigma)** -> . % 0.23/0.52 63[1:MRR:51.0,62.0] || -> greater(sigma,tau)*r. % 0.23/0.52 67[0:Res:12.1,7.0] || greater(u,v) -> smaller_or_equal(v,u)*. % 0.23/0.52 72[1:Res:67.1,61.0] || greater(sigma,tau)*r -> . % 0.23/0.52 73[1:MRR:72.0,63.0] || -> . % 0.23/0.52 74[1:Spt:73.0,35.0,44.0] || equal(zero,tau)** -> . % 0.23/0.52 75[1:Spt:73.0,35.1] || -> greater(tau,zero)*r. % 0.23/0.52 76[2:Spt:34.0] || -> equal(zero,sigma)**. % 0.23/0.52 77[2:Rew:76.0,75.0] || -> greater(tau,sigma)*l. % 0.23/0.52 80[2:Rew:76.0,40.0] || -> smaller_or_equal(sigma,sigma)*. % 0.23/0.52 83[2:Rew:76.0,6.0] || -> equal(age(skc2,skc3),sigma)**. % 0.23/0.52 86[2:SpL:83.0,33.0] || smaller_or_equal(sigma,sigma) -> positional_advantage(skc2,skc3)*. % 0.23/0.52 88[2:SpL:83.0,31.1] || positional_advantage(skc2,skc3)* smaller_or_equal(sigma,tau) -> . % 0.23/0.52 90[2:MRR:86.0,80.0] || -> positional_advantage(skc2,skc3)*. % 0.23/0.52 92[2:MRR:88.0,90.0] || smaller_or_equal(sigma,tau)* -> . % 0.23/0.52 94[2:Res:67.1,92.0] || greater(tau,sigma)*l -> . % 0.23/0.52 95[2:MRR:94.0,77.0] || -> . % 0.23/0.52 96[2:Spt:95.0,34.0,76.0] || equal(zero,sigma)** -> . % 0.23/0.52 97[2:Spt:95.0,34.1] || -> greater(sigma,zero)*r. % 0.23/0.52 99[0:SpL:6.0,33.0] || smaller_or_equal(zero,sigma) -> positional_advantage(skc2,skc3)*. % 0.23/0.52 101[0:SpL:6.0,31.1] || positional_advantage(skc2,skc3)* smaller_or_equal(zero,tau) -> . % 0.23/0.52 103[0:Res:99.1,101.0] || smaller_or_equal(zero,sigma) smaller_or_equal(zero,tau)* -> . % 0.23/0.52 106[0:Res:67.1,103.1] || greater(tau,zero) smaller_or_equal(zero,sigma)* -> . % 0.23/0.52 107[1:MRR:106.0,75.0] || smaller_or_equal(zero,sigma)* -> . % 0.23/0.52 109[1:Res:67.1,107.0] || greater(sigma,zero)*r -> . % 0.23/0.52 110[2:MRR:109.0,97.0] || -> . % 0.23/0.52 % SZS output end Refutation % 0.23/0.52 Formulae used in the proof : lemma_10 definition_smaller_or_equal definition_smaller definition_greater_or_equal definition_3 definition_4 % 0.23/0.52 %------------------------------------------------------------------------------