%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n013.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 1.65s 1.92s % Output : Refutation 1.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0. % 0.00/0.03 % Command : run_spass %d %s % 0.09/0.35 % Computer : n013.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sun Sep 6 01:01:20 UTC 2026 % 0.12/0.36 % CPUTime : % 1.65/1.92 % 1.65/1.92 SPASS V 3.9 % 1.65/1.92 SPASS beiseite: Proof found. % 1.65/1.92 % SZS status Theorem % 1.65/1.92 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 1.65/1.92 SPASS derived 3551 clauses, backtracked 0 clauses, performed 0 splits and kept 636 clauses. % 1.65/1.92 SPASS allocated 88433 KBytes. % 1.65/1.92 SPASS spent 0:00:01.54 on the problem. % 1.65/1.92 0:00:00.03 for the input. % 1.65/1.92 0:00:00.02 for the FLOTTER CNF translation. % 1.65/1.92 0:00:00.03 for inferences. % 1.65/1.92 0:00:00.00 for the backtracking. % 1.65/1.92 0:00:01.43 for the reduction. % 1.65/1.92 % 1.65/1.92 % 1.65/1.92 Here is a proof with depth 3, length 28 : % 1.65/1.92 % SZS output start Refutation % 1.65/1.92 1[0:Inp] || -> a62__a61_(u,u)*. % 1.65/1.92 2[0:Inp] || -> a62__a61_(u,0)*. % 1.65/1.92 3[0:Inp] || -> equal(a43_(u,0),u)**. % 1.65/1.92 4[0:Inp] || -> equal(a43_(u,1),1)**. % 1.65/1.92 5[0:Inp] || -> equal(a43_(u,v),a43_(v,u))*. % 1.65/1.92 6[0:Inp] || equal(a61__a61__a62_(a61__a61__a62_(skc1,1),1),skc1)** -> . % 1.65/1.92 9[0:Inp] || a62__a61_(u,v)*+ a62__a61_(v,u)* -> equal(v,u). % 1.65/1.92 10[0:Inp] || a62__a61_(a43_(u,v),w)*+ -> a62__a61_(v,a61__a61__a62_(u,w))*. % 1.65/1.92 11[0:Inp] || a62__a61_(u,a61__a61__a62_(v,w))*+ -> a62__a61_(a43_(v,u),w)*. % 1.65/1.92 12[0:Inp] || a62__a61_(u,v) -> a62__a61_(a43_(u,w),a43_(v,w))*. % 1.65/1.92 15[0:Inp] || -> equal(a61__a61__a62_(a61__a61__a62_(u,v),v),a61__a61__a62_(a61__a61__a62_(v,u),u))*. % 1.65/1.92 16[0:Rew:15.0,6.0] || equal(a61__a61__a62_(a61__a61__a62_(1,skc1),skc1),skc1)** -> . % 1.65/1.92 18[0:Res:9.2,16.0] || a62__a61_(skc1,a61__a61__a62_(a61__a61__a62_(1,skc1),skc1)) a62__a61_(a61__a61__a62_(a61__a61__a62_(1,skc1),skc1),skc1)*l -> . % 1.65/1.92 21[0:SpR:5.0,4.0] || -> equal(a43_(1,u),1)**. % 1.65/1.92 22[0:SpR:5.0,3.0] || -> equal(a43_(0,u),u)**. % 1.65/1.92 394[0:Res:2.0,9.0] || a62__a61_(0,u)* -> equal(0,u). % 1.65/1.92 4200[0:SpR:22.0,12.1] || a62__a61_(u,0) -> a62__a61_(a43_(u,v),v)*l. % 1.65/1.92 4277[0:MRR:4200.0,2.0] || -> a62__a61_(a43_(u,v),v)*l. % 1.65/1.92 4288[0:SpR:21.0,4277.0] || -> a62__a61_(1,u)*. % 1.65/1.92 4338[0:Res:1.0,11.0] || -> a62__a61_(a43_(u,a61__a61__a62_(u,v)),v)*l. % 1.65/1.92 4609[0:SpL:21.0,10.0] || a62__a61_(1,u) -> a62__a61_(v,a61__a61__a62_(1,u))*. % 1.65/1.92 4641[0:Res:4277.0,10.0] || -> a62__a61_(u,a61__a61__a62_(v,u))*r. % 1.65/1.92 4659[0:MRR:18.0,4641.0] || a62__a61_(a61__a61__a62_(a61__a61__a62_(1,skc1),skc1),skc1)*l -> . % 1.65/1.92 4660[0:MRR:4609.0,4288.0] || -> a62__a61_(u,a61__a61__a62_(1,v))*. % 1.65/1.92 4930[0:SpR:22.0,4338.0] || -> a62__a61_(a61__a61__a62_(0,u),u)*l. % 1.65/1.92 5483[0:Res:4660.0,394.0] || -> equal(a61__a61__a62_(1,u),0)**. % 1.65/1.92 5513[0:Rew:5483.0,4659.0] || a62__a61_(a61__a61__a62_(0,skc1),skc1)*l -> . % 1.65/1.92 5524[0:MRR:5513.0,4930.0] || -> . % 1.65/1.92 % SZS output end Refutation % 1.65/1.92 Formulae used in the proof : sos_04 sos_08 sos_03 sos_12 sos_02 goals_14 sos_06 sos_07 sos_09 sos_13 % 1.65/1.92 %------------------------------------------------------------------------------