%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n011.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 01:08:40 PM UTC 2026 % Result : Theorem 0.13s 5.60s % Output : Refutation 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0. % 0.00/0.03 % Command : run_spass %d %s % 0.09/0.36 % Computer : n011.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 : Sun Sep 6 01:05:29 UTC 2026 % 0.09/0.36 % CPUTime : % 0.13/5.60 % 0.13/5.60 SPASS V 3.9 % 0.13/5.60 SPASS beiseite: Proof found. % 0.13/5.60 % SZS status Theorem % 0.13/5.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.13/5.60 SPASS derived 5886 clauses, backtracked 0 clauses, performed 0 splits and kept 1340 clauses. % 0.13/5.60 SPASS allocated 90599 KBytes. % 0.13/5.60 SPASS spent 0:00:05.15 on the problem. % 0.13/5.60 0:00:00.06 for the input. % 0.13/5.60 0:00:00.04 for the FLOTTER CNF translation. % 0.13/5.60 0:00:00.11 for inferences. % 0.13/5.60 0:00:00.00 for the backtracking. % 0.13/5.60 0:00:04.90 for the reduction. % 0.13/5.60 % 0.13/5.60 % 0.13/5.60 Here is a proof with depth 6, length 35 : % 0.13/5.60 % SZS output start Refutation % 0.13/5.60 1[0:Inp] || -> a62__a61_(u,u)*. % 0.13/5.60 2[0:Inp] || -> a62__a61_(u,0)*. % 0.13/5.60 3[0:Inp] || -> equal(a43_(u,0),u)**. % 0.13/5.60 4[0:Inp] || -> equal(a43_(u,1),1)**. % 0.13/5.60 5[0:Inp] || -> equal(a43_(u,v),a43_(v,u))*. % 0.13/5.60 6[0:Inp] || equal(a61__a61__a62_(a61__a61__a62_(skc1,1),1),skc1)** -> . % 0.13/5.60 7[0:Inp] || -> equal(a61__a61__a62_(a61__a61__a62_(a61__a61__a62_(u,1),u),u),0)**. % 0.13/5.60 9[0:Inp] || a62__a61_(u,v)* a62__a61_(v,w)* -> a62__a61_(u,w)*. % 0.13/5.60 10[0:Inp] || a62__a61_(u,v)*+ a62__a61_(v,u)* -> equal(v,u). % 0.13/5.60 11[0:Inp] || a62__a61_(a43_(u,v),w)*+ -> a62__a61_(v,a61__a61__a62_(u,w))*. % 0.13/5.60 12[0:Inp] || a62__a61_(u,a61__a61__a62_(v,w))*+ -> a62__a61_(a43_(v,u),w)*. % 0.13/5.60 13[0:Inp] || a62__a61_(u,v) -> a62__a61_(a43_(u,w),a43_(v,w))*. % 0.13/5.60 15[0:Inp] || a62__a61_(u,v) -> a62__a61_(a61__a61__a62_(w,u),a61__a61__a62_(w,v))*. % 0.13/5.60 17[0:Res:10.2,6.0] || a62__a61_(skc1,a61__a61__a62_(a61__a61__a62_(skc1,1),1)) a62__a61_(a61__a61__a62_(a61__a61__a62_(skc1,1),1),skc1)*l -> . % 0.13/5.60 20[0:SpR:5.0,4.0] || -> equal(a43_(1,u),1)**. % 0.13/5.60 21[0:SpR:5.0,3.0] || -> equal(a43_(0,u),u)**. % 0.13/5.60 3768[0:SpR:21.0,13.1] || a62__a61_(u,0) -> a62__a61_(a43_(u,v),v)*l. % 0.13/5.60 3841[0:MRR:3768.0,2.0] || -> a62__a61_(a43_(u,v),v)*l. % 0.13/5.60 3852[0:SpR:20.0,3841.0] || -> a62__a61_(1,u)*. % 0.13/5.60 3883[0:Res:3852.0,10.0] || a62__a61_(u,1)* -> equal(u,1). % 0.13/5.60 3898[0:SpL:7.0,12.0] || a62__a61_(u,0) -> a62__a61_(a43_(a61__a61__a62_(a61__a61__a62_(v,1),v),u),v)*l. % 0.13/5.60 3900[0:Res:1.0,12.0] || -> a62__a61_(a43_(u,a61__a61__a62_(u,v)),v)*l. % 0.13/5.60 3922[0:MRR:3898.0,2.0] || -> a62__a61_(a43_(a61__a61__a62_(a61__a61__a62_(u,1),u),v),u)*l. % 0.13/5.60 4187[0:Res:1.0,11.0] || -> a62__a61_(u,a61__a61__a62_(v,a43_(v,u)))*r. % 0.13/5.60 4189[0:Res:3841.0,11.0] || -> a62__a61_(u,a61__a61__a62_(v,u))*r. % 0.13/5.60 4594[0:Res:3900.0,3883.0] || -> equal(a43_(u,a61__a61__a62_(u,1)),1)**. % 0.13/5.60 5042[0:SpR:5.0,4187.0] || -> a62__a61_(u,a61__a61__a62_(v,a43_(u,v)))*r. % 0.13/5.60 5175[0:SpR:3.0,3922.0] || -> a62__a61_(a61__a61__a62_(a61__a61__a62_(u,1),u),u)*l. % 0.13/5.60 8157[0:Res:5175.0,10.0] || a62__a61_(u,a61__a61__a62_(a61__a61__a62_(u,1),u))*r -> equal(a61__a61__a62_(a61__a61__a62_(u,1),u),u). % 0.13/5.60 8182[0:MRR:8157.0,4189.0] || -> equal(a61__a61__a62_(a61__a61__a62_(u,1),u),u)**. % 0.13/5.60 8584[0:SpR:4594.0,5042.0] || -> a62__a61_(u,a61__a61__a62_(a61__a61__a62_(u,1),1))*r. % 0.13/5.60 8658[0:MRR:17.0,8584.0] || a62__a61_(a61__a61__a62_(a61__a61__a62_(skc1,1),1),skc1)*l -> . % 0.13/5.60 8890[0:NCh:9.2,9.0,8658.0,15.1] || equal(a61__a61__a62_(a61__a61__a62_(skc1,1),u),skc1)** a62__a61_(1,u) -> . % 0.13/5.60 8894[0:MRR:8890.1,3852.0] || equal(a61__a61__a62_(a61__a61__a62_(skc1,1),u),skc1)** -> . % 0.13/5.60 8895[0:UnC:8894.0,8182.0] || -> . % 0.13/5.60 % SZS output end Refutation % 0.13/5.60 Formulae used in the proof : sos_04 sos_08 sos_03 sos_12 sos_02 goals_14 sos_13 sos_05 sos_06 sos_07 sos_09 sos_11 % 0.13/5.60 %------------------------------------------------------------------------------