%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SYO680-1 : TPTP v8.1.0. Released v7.3.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 21 19:55:30 EDT 2022 % Result : Unsatisfiable 0.18s 0.42s % Output : Refutation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO680-1 : TPTP v8.1.0. Released v7.3.0. % 0.07/0.12 % Command : run_spass %d %s % 0.13/0.32 % Computer : n026.cluster.edu % 0.13/0.32 % Model : x86_64 x86_64 % 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.32 % Memory : 8042.1875MB % 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.32 % CPULimit : 300 % 0.13/0.32 % WCLimit : 600 % 0.13/0.32 % DateTime : Sat Jul 9 09:35:40 EDT 2022 % 0.13/0.32 % CPUTime : % 0.18/0.42 % 0.18/0.42 SPASS V 3.9 % 0.18/0.42 SPASS beiseite: Proof found. % 0.18/0.42 % SZS status Theorem % 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.18/0.42 SPASS derived 93 clauses, backtracked 0 clauses, performed 0 splits and kept 80 clauses. % 0.18/0.42 SPASS allocated 63224 KBytes. % 0.18/0.42 SPASS spent 0:00:00.09 on the problem. % 0.18/0.42 0:00:00.04 for the input. % 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation. % 0.18/0.42 0:00:00.00 for inferences. % 0.18/0.42 0:00:00.00 for the backtracking. % 0.18/0.42 0:00:00.02 for the reduction. % 0.18/0.42 % 0.18/0.42 % 0.18/0.42 Here is a proof with depth 5, length 75 : % 0.18/0.42 % SZS output start Refutation % 0.18/0.42 1[0:Inp] || E(0,f(u)) E(0,f(suc(u))) -> iLEQ(suc(u),suc(u))*. % 0.18/0.42 2[0:Inp] || -> LE(f(u),s(s(s(s(0)))))*. % 0.18/0.42 3[0:Inp] || E(s(0),f(u)) E(s(0),f(suc(u)))*+ -> iLEQ(suc(u),suc(u))*. % 0.18/0.42 4[0:Inp] || LE(f(suc(u)),s(0))* -> E(0,f(suc(u))) LE(f(u),0). % 0.18/0.42 5[0:Inp] || E(s(s(0)),f(u)) E(s(s(0)),f(suc(u)))*+ -> iLEQ(suc(u),suc(u))*. % 0.18/0.42 6[0:Inp] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(0)),f(u)) E(s(s(0)),f(w)) E(s(s(0)),f(v)) E(s(s(0)),f(suc(w)))*+ E(s(s(0)),f(suc(u)))* E(s(s(0)),f(suc(v)))* -> . % 0.18/0.42 7[0:Inp] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(s(0))),f(u)) E(s(s(s(0))),f(v)) E(s(s(s(0))),f(w)) E(s(s(s(0))),f(suc(u)))*+ E(s(s(s(0))),f(suc(w)))* E(s(s(s(0))),f(suc(v)))* -> . % 0.18/0.42 8[0:Inp] || LE(f(u),s(s(0)))* -> LE(f(u),s(0)) E(s(0),f(u)). % 0.18/0.42 9[0:Inp] || LE(f(z__dfg),0)* -> . % 0.18/0.42 10[0:Inp] || LE(f(suc(u)),s(s(s(0))))* -> LE(f(u),s(s(0))) E(s(s(0)),f(suc(u))). % 0.18/0.42 11[0:Inp] || E(0,f(u)) E(0,f(v)) E(0,f(w)) E(0,f(suc(u)))+ E(0,f(suc(v))) E(0,f(suc(w))) iLEQ(suc(u),suc(w))* iLEQ(suc(w),suc(v))* -> . % 0.18/0.42 12[0:Inp] || LE(f(u),s(s(s(s(0)))))* -> E(s(s(s(0))),f(u)) LE(f(u),s(s(s(0)))). % 0.18/0.42 13[0:Inp] || LE(f(u),s(s(s(0))))* -> LE(f(u),s(s(0))) E(s(s(0)),f(u)). % 0.18/0.42 14[0:Inp] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(0),f(v)) E(s(0),f(w)) E(s(0),f(u)) E(s(0),f(suc(v)))*+ E(s(0),f(suc(w)))* E(s(0),f(suc(u)))* -> . % 0.18/0.42 15[0:Inp] || LE(f(suc(u)),s(s(s(s(0)))))* -> E(s(s(s(0))),f(suc(u))) LE(f(u),s(s(s(0)))). % 0.18/0.42 16[0:Inp] || E(s(s(s(0))),f(u)) E(s(s(s(0))),f(suc(u)))*+ -> iLEQ(suc(u),suc(u))*. % 0.18/0.42 17[0:Inp] || LE(f(u),s(0))* -> E(0,f(u)) LE(f(u),0). % 0.18/0.42 18[0:Inp] || LE(f(suc(u)),s(s(0)))* -> LE(f(u),s(0)) E(s(0),f(suc(u))). % 0.18/0.42 19[0:MRR:12.0,2.0] || -> LE(f(u),s(s(s(0)))) E(s(s(s(0))),f(u))*. % 0.18/0.42 20[0:MRR:15.0,2.0] || -> LE(f(u),s(s(s(0)))) E(s(s(s(0))),f(suc(u)))*. % 0.18/0.42 22[0:Res:20.1,16.1] || E(s(s(s(0))),f(u))* -> LE(f(u),s(s(s(0)))) iLEQ(suc(u),suc(u))*. % 0.18/0.42 23[0:MRR:22.0,19.1] || -> LE(f(u),s(s(s(0))))* iLEQ(suc(u),suc(u))*. % 0.18/0.42 38[0:Res:20.1,7.5] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(s(0))),f(u))* E(s(s(s(0))),f(v)) E(s(s(s(0))),f(w)) E(s(s(s(0))),f(suc(w)))* E(s(s(s(0))),f(suc(v)))* -> LE(f(u),s(s(s(0)))). % 0.18/0.42 39[0:MRR:38.2,19.1] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(s(0))),f(v)) E(s(s(s(0))),f(w)) E(s(s(s(0))),f(suc(w)))*+ E(s(s(s(0))),f(suc(v)))* -> LE(f(u),s(s(s(0))))*. % 0.18/0.42 41[0:Res:20.1,39.4] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(s(0))),f(v)) E(s(s(s(0))),f(w))* E(s(s(s(0))),f(suc(v)))* -> LE(f(w),s(s(s(0)))) LE(f(u),s(s(s(0))))*. % 0.18/0.42 42[0:MRR:41.3,19.1] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(s(0))),f(v)) E(s(s(s(0))),f(suc(v)))*+ -> LE(f(w),s(s(s(0))))* LE(f(u),s(s(s(0))))*. % 0.18/0.42 44[0:Res:20.1,42.3] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(s(0))),f(v))* -> LE(f(v),s(s(s(0)))) LE(f(w),s(s(s(0))))* LE(f(u),s(s(s(0))))*. % 0.18/0.42 45[0:MRR:44.2,19.1] || iLEQ(suc(u),suc(v))*+ iLEQ(suc(v),suc(w))* -> LE(f(v),s(s(s(0))))* LE(f(w),s(s(s(0))))* LE(f(u),s(s(s(0))))*. % 0.18/0.42 50[0:Res:23.1,45.0] || iLEQ(suc(u),suc(v))* -> LE(f(u),s(s(s(0))))* LE(f(u),s(s(s(0))))* LE(f(v),s(s(s(0))))* LE(f(u),s(s(s(0))))*. % 0.18/0.42 56[0:Obv:50.2] || iLEQ(suc(u),suc(v))*+ -> LE(f(v),s(s(s(0))))* LE(f(u),s(s(s(0))))*. % 0.18/0.42 64[0:Res:23.1,56.0] || -> LE(f(u),s(s(s(0))))* LE(f(u),s(s(s(0))))* LE(f(u),s(s(s(0))))*. % 0.18/0.42 70[0:Obv:64.1] || -> LE(f(u),s(s(s(0))))*. % 0.18/0.42 71[0:MRR:13.0,70.0] || -> LE(f(u),s(s(0))) E(s(s(0)),f(u))*. % 0.18/0.42 72[0:MRR:10.0,70.0] || -> LE(f(u),s(s(0))) E(s(s(0)),f(suc(u)))*. % 0.18/0.42 81[0:Res:72.1,5.1] || E(s(s(0)),f(u))* -> LE(f(u),s(s(0))) iLEQ(suc(u),suc(u))*. % 0.18/0.42 82[0:Res:72.1,6.5] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(0)),f(u)) E(s(s(0)),f(w))* E(s(s(0)),f(v)) E(s(s(0)),f(suc(u)))* E(s(s(0)),f(suc(v)))* -> LE(f(w),s(s(0))). % 0.18/0.42 83[0:MRR:81.0,71.1] || -> LE(f(u),s(s(0)))* iLEQ(suc(u),suc(u))*. % 0.18/0.42 84[0:MRR:82.3,71.1] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(0)),f(u)) E(s(s(0)),f(v)) E(s(s(0)),f(suc(u)))*+ E(s(s(0)),f(suc(v)))* -> LE(f(w),s(s(0)))*. % 0.18/0.42 91[0:Res:72.1,84.4] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(0)),f(u))* E(s(s(0)),f(v)) E(s(s(0)),f(suc(v)))* -> LE(f(u),s(s(0))) LE(f(w),s(s(0)))*. % 0.18/0.42 92[0:MRR:91.2,71.1] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(0)),f(v)) E(s(s(0)),f(suc(v)))*+ -> LE(f(u),s(s(0)))* LE(f(w),s(s(0)))*. % 0.18/0.42 94[0:Res:72.1,92.3] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(s(0)),f(v))* -> LE(f(v),s(s(0))) LE(f(u),s(s(0)))* LE(f(w),s(s(0)))*. % 0.18/0.42 95[0:MRR:94.2,71.1] || iLEQ(suc(u),suc(v))*+ iLEQ(suc(v),suc(w))* -> LE(f(v),s(s(0)))* LE(f(u),s(s(0)))* LE(f(w),s(s(0)))*. % 0.18/0.42 97[0:Res:83.1,95.0] || iLEQ(suc(u),suc(v))* -> LE(f(u),s(s(0)))* LE(f(u),s(s(0)))* LE(f(u),s(s(0)))* LE(f(v),s(s(0)))*. % 0.18/0.42 102[0:Obv:97.2] || iLEQ(suc(u),suc(v))*+ -> LE(f(u),s(s(0)))* LE(f(v),s(s(0)))*. % 0.18/0.42 112[0:Res:83.1,102.0] || -> LE(f(u),s(s(0)))* LE(f(u),s(s(0)))* LE(f(u),s(s(0)))*. % 0.18/0.42 117[0:Obv:112.1] || -> LE(f(u),s(s(0)))*. % 0.18/0.42 118[0:MRR:8.0,117.0] || -> LE(f(u),s(0)) E(s(0),f(u))*. % 0.18/0.42 119[0:MRR:18.0,117.0] || -> LE(f(u),s(0)) E(s(0),f(suc(u)))*. % 0.18/0.42 127[0:Res:119.1,3.1] || E(s(0),f(u)) -> LE(f(u),s(0)) iLEQ(suc(u),suc(u))*. % 0.18/0.42 128[0:Res:119.1,14.5] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(0),f(v)) E(s(0),f(w)) E(s(0),f(u)) E(s(0),f(suc(w)))* E(s(0),f(suc(u)))* -> LE(f(v),s(0)). % 0.18/0.42 129[0:MRR:127.0,118.1] || -> LE(f(u),s(0)) iLEQ(suc(u),suc(u))*. % 0.18/0.42 130[0:MRR:128.2,118.1] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(0),f(w)) E(s(0),f(u)) E(s(0),f(suc(w)))*+ E(s(0),f(suc(u)))* -> LE(f(v),s(0)). % 0.18/0.42 134[0:Res:119.1,130.4] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(0),f(w)) E(s(0),f(u)) E(s(0),f(suc(u)))* -> LE(f(w),s(0)) LE(f(v),s(0)). % 0.18/0.42 135[0:MRR:134.2,118.1] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(0),f(u)) E(s(0),f(suc(u)))*+ -> LE(f(w),s(0)) LE(f(v),s(0)). % 0.18/0.42 137[0:Res:119.1,135.3] || iLEQ(suc(u),suc(v))* iLEQ(suc(v),suc(w))* E(s(0),f(u)) -> LE(f(u),s(0)) LE(f(w),s(0)) LE(f(v),s(0)). % 0.18/0.42 138[0:MRR:137.2,118.1] || iLEQ(suc(u),suc(v))*+ iLEQ(suc(v),suc(w))* -> LE(f(u),s(0)) LE(f(w),s(0)) LE(f(v),s(0)). % 0.18/0.42 142[0:Res:129.1,138.0] || iLEQ(suc(u),suc(v))* -> LE(f(u),s(0)) LE(f(u),s(0)) LE(f(v),s(0)) LE(f(u),s(0)). % 0.18/0.42 145[0:Obv:142.2] || iLEQ(suc(u),suc(v))* -> LE(f(v),s(0)) LE(f(u),s(0)). % 0.18/0.42 148[0:Res:129.1,145.0] || -> LE(f(u),s(0))* LE(f(u),s(0))* LE(f(u),s(0))*. % 0.18/0.42 151[0:Obv:148.1] || -> LE(f(u),s(0))*. % 0.18/0.42 152[0:MRR:17.0,151.0] || -> E(0,f(u))* LE(f(u),0). % 0.18/0.42 153[0:MRR:4.0,151.0] || -> E(0,f(suc(u)))* LE(f(u),0). % 0.18/0.42 157[0:Res:153.0,11.3] || E(0,f(u)) E(0,f(v)) E(0,f(w)) E(0,f(suc(v))) E(0,f(suc(w))) iLEQ(suc(u),suc(w))* iLEQ(suc(w),suc(v))* -> LE(f(u),0). % 0.18/0.42 158[0:MRR:157.0,152.0] || E(0,f(u)) E(0,f(v)) E(0,f(suc(u)))+ E(0,f(suc(v))) iLEQ(suc(w),suc(v))* iLEQ(suc(v),suc(u))* -> LE(f(w),0). % 0.18/0.42 160[0:Res:153.0,158.2] || E(0,f(u)) E(0,f(v)) E(0,f(suc(v))) iLEQ(suc(w),suc(v))* iLEQ(suc(v),suc(u))* -> LE(f(u),0) LE(f(w),0). % 0.18/0.42 161[0:MRR:160.0,152.0] || E(0,f(u)) E(0,f(suc(u)))+ iLEQ(suc(v),suc(u))* iLEQ(suc(u),suc(w))* -> LE(f(w),0) LE(f(v),0). % 0.18/0.42 163[0:Res:153.0,161.1] || E(0,f(u)) iLEQ(suc(v),suc(u))* iLEQ(suc(u),suc(w))* -> LE(f(u),0) LE(f(w),0) LE(f(v),0). % 0.18/0.42 164[0:MRR:163.0,152.0] || iLEQ(suc(u),suc(v))*+ iLEQ(suc(v),suc(w))* -> LE(f(v),0) LE(f(w),0) LE(f(u),0). % 0.18/0.42 165[0:Res:1.2,164.0] || E(0,f(u)) E(0,f(suc(u))) iLEQ(suc(u),suc(v))* -> LE(f(u),0) LE(f(v),0) LE(f(u),0). % 0.18/0.42 166[0:Obv:165.3] || E(0,f(u)) E(0,f(suc(u))) iLEQ(suc(u),suc(v))* -> LE(f(v),0) LE(f(u),0). % 0.18/0.42 167[0:MRR:166.0,166.1,152.0,153.0] || iLEQ(suc(u),suc(v))* -> LE(f(v),0) LE(f(u),0). % 0.18/0.42 168[0:Res:1.2,167.0] || E(0,f(u)) E(0,f(suc(u)))* -> LE(f(u),0) LE(f(u),0). % 0.18/0.42 169[0:Obv:168.2] || E(0,f(u)) E(0,f(suc(u)))* -> LE(f(u),0). % 0.18/0.42 170[0:MRR:169.0,169.1,152.0,153.0] || -> LE(f(u),0)*. % 0.18/0.42 171[0:UnC:170.0,9.0] || -> . % 0.18/0.42 % SZS output end Refutation % 0.18/0.42 Formulae used in the proof : clause_109 clause_104 clause_91 clause_114 clause_5 clause_20 clause_71 clause_6 clause_66 clause_84 clause_144 clause_127 clause_51 clause_21 clause_102 clause_14 clause_96 clause_15 % 0.18/0.42 %------------------------------------------------------------------------------