%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SWV053+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n007.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 : Wed Jul 20 21:41:07 EDT 2022 % Result : Theorem 1.37s 1.64s % Output : Refutation 1.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV053+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.03/0.12 % Command : run_spass %d %s % 0.12/0.34 % Computer : n007.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Thu Jun 16 06:32:11 EDT 2022 % 0.12/0.34 % CPUTime : % 1.37/1.64 % 1.37/1.64 SPASS V 3.9 % 1.37/1.64 SPASS beiseite: Proof found. % 1.37/1.64 % SZS status Theorem % 1.37/1.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 1.37/1.64 SPASS derived 4777 clauses, backtracked 171 clauses, performed 3 splits and kept 2505 clauses. % 1.37/1.64 SPASS allocated 89525 KBytes. % 1.37/1.64 SPASS spent 0:00:01.27 on the problem. % 1.37/1.64 0:00:00.04 for the input. % 1.37/1.64 0:00:00.08 for the FLOTTER CNF translation. % 1.37/1.64 0:00:00.04 for inferences. % 1.37/1.64 0:00:00.01 for the backtracking. % 1.37/1.64 0:00:00.96 for the reduction. % 1.37/1.64 % 1.37/1.64 % 1.37/1.64 Here is a proof with depth 1, length 43 : % 1.37/1.64 % SZS output start Refutation % 1.37/1.64 1[0:Inp] || -> SkC0*. % 1.37/1.64 3[0:Inp] || -> leq(n0,pv10)*r. % 1.37/1.64 4[0:Inp] || -> leq(n0,pv12)*r. % 1.37/1.64 34[0:Inp] || -> equal(succ(n0),n1)**. % 1.37/1.64 37[0:Inp] || -> equal(succ(tptp_minus_1),n0)**. % 1.37/1.64 40[0:Inp] || -> leq(skc4,minus(pv10,n1))*r. % 1.37/1.64 41[0:Inp] || -> leq(pv10,minus(n135300,n1))*r. % 1.37/1.64 42[0:Inp] || -> leq(pv12,minus(n5,n1))*r. % 1.37/1.64 43[0:Inp] || -> equal(succ(succ(n0)),n2)**. % 1.37/1.64 60[0:Inp] || -> equal(pred(succ(u)),u)**. % 1.37/1.64 62[0:Inp] || -> equal(succ(succ(succ(n0))),n3)**. % 1.37/1.64 63[0:Inp] || -> equal(sum__dfg(n0,tptp_minus_1,u),n0)**. % 1.37/1.64 64[0:Inp] || -> equal(sum__dfg(n0,tptp_minus_1,u),tptp_float_0_0)**. % 1.37/1.64 67[0:Inp] || -> equal(minus(u,n1),pred(u))**. % 1.37/1.64 69[0:Inp] || -> equal(succ(succ(succ(succ(n0)))),n4)**. % 1.37/1.64 79[0:Inp] || -> equal(succ(succ(succ(succ(succ(n0))))),n5)**. % 1.37/1.64 121[0:Inp] || leq(u,minus(pv10,n1)) leq(n0,u) -> equal(sum__dfg(n0,minus(n5,n1),a_select3(q,u,v)),n1)**. % 1.37/1.64 146[0:Inp] || equal(sum__dfg(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10))))),n0)** leq(n0,pv10) leq(n0,pv12) leq(pv10,minus(n135300,n1)) leq(pv12,minus(n5,n1)) SkC0 -> leq(n0,skc4). % 1.37/1.64 151[0:Inp] || equal(sum__dfg(n0,minus(n5,n1),a_select3(q,skc4,skc5)),n1) equal(sum__dfg(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10))))),n0)** leq(n0,pv10) leq(n0,pv12) leq(pv10,minus(n135300,n1)) leq(pv12,minus(n5,n1)) SkC0 -> . % 1.37/1.64 152[0:Rew:34.0,43.0] || -> equal(succ(n1),n2)**. % 1.37/1.64 153[0:Rew:64.0,63.0] || -> equal(tptp_float_0_0,n0)**. % 1.37/1.64 154[0:Rew:153.0,64.0] || -> equal(sum__dfg(n0,tptp_minus_1,u),n0)**. % 1.37/1.64 155[0:Rew:152.0,62.0,34.0,62.0] || -> equal(succ(n2),n3)**. % 1.37/1.64 157[0:Rew:155.0,69.0,152.0,69.0,34.0,69.0] || -> equal(succ(n3),n4)**. % 1.37/1.64 160[0:Rew:157.0,79.0,155.0,79.0,152.0,79.0,34.0,79.0] || -> equal(succ(n4),n5)**. % 1.37/1.64 165[0:Rew:67.0,42.0] || -> leq(pv12,pred(n5))*r. % 1.37/1.64 166[0:Rew:67.0,41.0] || -> leq(pv10,pred(n135300))*r. % 1.37/1.64 167[0:Rew:67.0,40.0] || -> leq(skc4,pred(pv10))*r. % 1.37/1.64 169[0:Rew:67.0,121.2,67.0,121.0] || leq(u,pred(pv10)) leq(n0,u) -> equal(sum__dfg(n0,pred(n5),a_select3(q,u,v)),n1)**. % 1.37/1.64 172[0:Rew:67.0,146.4,67.0,146.3,67.0,146.0] || equal(sum__dfg(n0,pred(n0),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10))))),n0)** leq(n0,pv10) leq(n0,pv12) leq(pv10,pred(n135300)) leq(pv12,pred(n5)) SkC0 -> leq(n0,skc4). % 1.37/1.64 173[0:MRR:172.1,172.2,172.3,172.4,172.5,3.0,4.0,166.0,165.0,1.0] || equal(sum__dfg(n0,pred(n0),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10))))),n0)** -> leq(n0,skc4). % 1.37/1.64 174[0:Rew:67.0,151.5,67.0,151.4,67.0,151.1,67.0,151.0] || equal(sum__dfg(n0,pred(n5),a_select3(q,skc4,skc5)),n1) equal(sum__dfg(n0,pred(n0),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10))))),n0)** leq(n0,pv10) leq(n0,pv12) leq(pv10,pred(n135300)) leq(pv12,pred(n5)) SkC0 -> . % 1.37/1.64 175[0:MRR:174.2,174.3,174.4,174.5,174.6,3.0,4.0,166.0,165.0,1.0] || equal(sum__dfg(n0,pred(n0),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,pv71,n0),a_select2(x__dfg,pv10))))),n0)** equal(sum__dfg(n0,pred(n5),a_select3(q,skc4,skc5)),n1) -> . % 1.37/1.64 760[0:SpR:37.0,60.0] || -> equal(pred(n0),tptp_minus_1)**. % 1.37/1.64 765[0:SpR:160.0,60.0] || -> equal(pred(n5),n4)**. % 1.37/1.64 3478[0:Rew:765.0,169.2] || leq(u,pred(pv10)) leq(n0,u) -> equal(sum__dfg(n0,n4,a_select3(q,u,v)),n1)**. % 1.37/1.64 3479[0:Rew:154.0,173.0,760.0,173.0] || equal(n0,n0) -> leq(n0,skc4)*r. % 1.37/1.64 3480[0:Obv:3479.0] || -> leq(n0,skc4)*r. % 1.37/1.64 3481[0:Rew:765.0,175.1,154.0,175.0,760.0,175.0] || equal(n0,n0) equal(sum__dfg(n0,n4,a_select3(q,skc4,skc5)),n1)** -> . % 1.37/1.64 3482[0:Obv:3481.0] || equal(sum__dfg(n0,n4,a_select3(q,skc4,skc5)),n1)** -> . % 1.37/1.64 6504[0:SpL:3478.2,3482.0] || leq(skc4,pred(pv10))*r leq(n0,skc4) equal(n1,n1) -> . % 1.37/1.64 6505[0:Obv:6504.2] || leq(skc4,pred(pv10))*r leq(n0,skc4) -> . % 1.37/1.64 6506[0:MRR:6505.0,6505.1,167.0,3480.0] || -> . % 1.37/1.64 % SZS output end Refutation % 1.37/1.64 Formulae used in the proof : cl5_nebula_norm_0031 gt_succ leq_succ_gt_equiv successor_1 succ_tptp_minus_1 successor_2 pred_succ successor_3 sum_plus_base sum_plus_base_float pred_minus_1 successor_4 successor_5 % 1.37/1.64 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