%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n019.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 01:08:10 PM UTC 2026 % Result : Theorem 0.21s 0.53s % Output : Refutation 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_spass %d %s % 0.10/0.36 % Computer : n019.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 23:56:53 UTC 2026 % 0.10/0.36 % CPUTime : % 0.21/0.53 % 0.21/0.53 SPASS V 3.9 % 0.21/0.53 SPASS beiseite: Proof found. % 0.21/0.53 % SZS status Theorem % 0.21/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.21/0.53 SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses. % 0.21/0.53 SPASS allocated 85108 KBytes. % 0.21/0.53 SPASS spent 0:00:00.15 on the problem. % 0.21/0.53 0:00:00.06 for the input. % 0.21/0.53 0:00:00.04 for the FLOTTER CNF translation. % 0.21/0.53 0:00:00.00 for inferences. % 0.21/0.53 0:00:00.00 for the backtracking. % 0.21/0.53 0:00:00.00 for the reduction. % 0.21/0.53 % 0.21/0.53 % 0.21/0.53 Here is a proof with depth 1, length 9 : % 0.21/0.53 % SZS output start Refutation % 0.21/0.53 2[0:Inp] || -> r1(u,skf2(u))*r. % 0.21/0.53 3[0:Inp] || -> r1(skf2(u),skf3(u))*l. % 0.21/0.53 4[0:Inp] || p1(skf3(u))* r1(skc1,u) -> . % 0.21/0.53 5[0:Inp] || r1(skc1,u) r1(skf2(u),v)*+ -> p1(v)*. % 0.21/0.53 6[0:Inp] || r1(u,v)* r1(v,w)* -> r1(u,w)*. % 0.21/0.53 7[0:OCh:6.1,6.0,3.0,2.0] || -> r1(u,skf3(u))*r. % 0.21/0.53 11[0:Res:3.0,5.1] || r1(skc1,u) -> p1(skf3(u))*. % 0.21/0.53 15[0:MRR:11.1,4.0] || r1(skc1,u)* -> . % 0.21/0.53 16[0:UnC:15.0,7.0] || -> . % 0.21/0.53 % SZS output end Refutation % 0.21/0.53 Formulae used in the proof : main reflexivity transitivity % 0.21/0.53 %------------------------------------------------------------------------------