%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n009.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 : Mon Sep 7 01:08:13 PM UTC 2026 % Result : Theorem 0.22s 0.53s % Output : Refutation 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_spass %d %s % 0.10/0.36 % Computer : n009.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 : Sat Sep 5 09:50:36 UTC 2026 % 0.10/0.36 % CPUTime : % 0.22/0.53 % 0.22/0.53 SPASS V 3.9 % 0.22/0.53 SPASS beiseite: Proof found. % 0.22/0.53 % SZS status Theorem % 0.22/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.22/0.53 SPASS derived 28 clauses, backtracked 0 clauses, performed 0 splits and kept 26 clauses. % 0.22/0.53 SPASS allocated 97632 KBytes. % 0.22/0.53 SPASS spent 0:00:00.15 on the problem. % 0.22/0.53 0:00:00.06 for the input. % 0.22/0.53 0:00:00.04 for the FLOTTER CNF translation. % 0.22/0.53 0:00:00.00 for inferences. % 0.22/0.53 0:00:00.00 for the backtracking. % 0.22/0.53 0:00:00.00 for the reduction. % 0.22/0.53 % 0.22/0.53 % 0.22/0.53 Here is a proof with depth 1, length 11 : % 0.22/0.53 % SZS output start Refutation % 0.22/0.53 7[0:Inp] || -> r1(u,skf5(u))*r. % 0.22/0.53 11[0:Inp] || r1(skc7,u) -> p2(skf5(u))* p1(skf5(u)). % 0.22/0.53 13[0:Inp] || p1(skf5(u)) p2(skf5(u))* r1(skc7,u) -> . % 0.22/0.53 14[0:Inp] p2(u) || r1(v,u)*+ r1(skc7,v)* -> p1(u)*. % 0.22/0.53 15[0:Inp] p1(u) || r1(v,u)*+ r1(skc7,v)* -> p2(u)*. % 0.22/0.53 28[0:Res:7.0,15.1] p1(skf5(u)) || r1(skc7,u) -> p2(skf5(u))*. % 0.22/0.53 37[0:MRR:28.0,11.2] || r1(skc7,u) -> p2(skf5(u))*. % 0.22/0.53 38[0:MRR:13.1,37.1] || p1(skf5(u))* r1(skc7,u) -> . % 0.22/0.53 45[0:Res:7.0,14.1] p2(skf5(u)) || r1(skc7,u) -> p1(skf5(u))*. % 0.22/0.53 53[0:MRR:45.0,45.2,37.1,38.0] || r1(skc7,u)* -> . % 0.22/0.53 54[0:UnC:53.0,7.0] || -> . % 0.22/0.53 % SZS output end Refutation % 0.22/0.53 Formulae used in the proof : main reflexivity transitivity % 0.22/0.53 %------------------------------------------------------------------------------