%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : LCL893+1 : TPTP v9.3.1. Released v5.5.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n017.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 01:08:39 PM UTC 2026 % Result : Theorem 0.22s 0.51s % Output : Refutation 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL893+1 : TPTP v9.3.1. Released v5.5.0. % 0.00/0.04 % Command : run_spass %d %s % 0.11/0.36 % Computer : n017.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Sun Sep 6 00:21:07 UTC 2026 % 0.11/0.36 % CPUTime : % 0.22/0.51 % 0.22/0.51 SPASS V 3.9 % 0.22/0.51 SPASS beiseite: Proof found. % 0.22/0.51 % SZS status Theorem % 0.22/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.22/0.51 SPASS derived 912 clauses, backtracked 0 clauses, performed 0 splits and kept 315 clauses. % 0.22/0.51 SPASS allocated 85905 KBytes. % 0.22/0.51 SPASS spent 0:00:00.13 on the problem. % 0.22/0.51 0:00:00.03 for the input. % 0.22/0.51 0:00:00.02 for the FLOTTER CNF translation. % 0.22/0.51 0:00:00.01 for inferences. % 0.22/0.51 0:00:00.00 for the backtracking. % 0.22/0.51 0:00:00.05 for the reduction. % 0.22/0.51 % 0.22/0.51 % 0.22/0.51 Here is a proof with depth 5, length 19 : % 0.22/0.51 % SZS output start Refutation % 0.22/0.51 2[0:Inp] || -> a62__a61_(u,0)*. % 0.22/0.51 3[0:Inp] || -> equal(h(skc1),skc1)**. % 0.22/0.51 4[0:Inp] || equal(skc1,0)** -> . % 0.22/0.51 5[0:Inp] || -> equal(a43_(u,0),u)**. % 0.22/0.51 7[0:Inp] || -> equal(a43_(u,v),a43_(v,u))*. % 0.22/0.51 8[0:Inp] || -> equal(a61__a61__a62_(h(u),u),h(u))**. % 0.22/0.51 11[0:Inp] || a62__a61_(u,v)*+ a62__a61_(v,u)* -> equal(v,u). % 0.22/0.51 12[0:Inp] || a62__a61_(a43_(u,v),w)*+ -> a62__a61_(v,a61__a61__a62_(u,w))*. % 0.22/0.51 14[0:Inp] || a62__a61_(u,v) -> a62__a61_(a43_(u,w),a43_(v,w))*. % 0.22/0.51 18[0:Res:11.2,4.0] || a62__a61_(skc1,0)*l a62__a61_(0,skc1) -> . % 0.22/0.51 20[0:MRR:18.0,2.0] || a62__a61_(0,skc1)*r -> . % 0.22/0.51 25[0:SpR:3.0,8.0] || -> equal(a61__a61__a62_(skc1,skc1),skc1)**. % 0.22/0.51 28[0:SpR:7.0,5.0] || -> equal(a43_(0,u),u)**. % 0.22/0.51 309[0:SpR:28.0,14.1] || a62__a61_(u,0) -> a62__a61_(a43_(u,v),v)*l. % 0.22/0.51 354[0:MRR:309.0,2.0] || -> a62__a61_(a43_(u,v),v)*l. % 0.22/0.51 359[0:SpR:7.0,354.0] || -> a62__a61_(a43_(u,v),u)*l. % 0.22/0.51 585[0:Res:359.0,12.0] || -> a62__a61_(u,a61__a61__a62_(v,v))*. % 0.22/0.51 1109[0:SpR:25.0,585.0] || -> a62__a61_(u,skc1)*. % 0.22/0.51 1141[0:UnC:1109.0,20.0] || -> . % 0.22/0.51 % SZS output end Refutation % 0.22/0.51 Formulae used in the proof : sos_09 goals_15 sos_03 sos_02 sos_14 sos_07 sos_08 sos_10 % 0.22/0.51 %------------------------------------------------------------------------------