TSTP Solution File: SWV157+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV157+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 21:41:28 EDT 2022
% Result : Theorem 27.86s 28.10s
% Output : Refutation 28.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV157+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 13:15:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 27.86/28.10
% 27.86/28.10 SPASS V 3.9
% 27.86/28.10 SPASS beiseite: Proof found.
% 27.86/28.10 % SZS status Theorem
% 27.86/28.10 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.86/28.10 SPASS derived 15791 clauses, backtracked 2369 clauses, performed 8 splits and kept 10468 clauses.
% 27.86/28.10 SPASS allocated 100749 KBytes.
% 27.86/28.10 SPASS spent 0:0:27.75 on the problem.
% 27.86/28.10 0:00:00.04 for the input.
% 27.86/28.10 0:00:00.07 for the FLOTTER CNF translation.
% 27.86/28.10 0:00:00.16 for inferences.
% 27.86/28.10 0:00:00.62 for the backtracking.
% 27.86/28.10 0:0:26.66 for the reduction.
% 27.86/28.10
% 27.86/28.10
% 27.86/28.10 Here is a proof with depth 4, length 96 :
% 27.86/28.10 % SZS output start Refutation
% 27.86/28.10 2[0:Inp] || -> leq(n0,skc1)*r.
% 27.86/28.10 4[0:Inp] || -> leq(n0,pv47)*r.
% 27.86/28.10 6[0:Inp] || -> leq(pv47,n4)*l.
% 27.86/28.10 7[0:Inp] || -> leq(skc1,pv47)*l.
% 27.86/28.10 29[0:Inp] || -> gt(n1,n0)*l.
% 27.86/28.10 44[0:Inp] || -> leq(u,u)*.
% 27.86/28.10 45[0:Inp] || equal(skc1,pv47)** -> .
% 27.86/28.10 46[0:Inp] || -> equal(succ(n0),n1)**.
% 27.86/28.10 51[0:Inp] || -> equal(succ(succ(n0)),n2)**.
% 27.86/28.10 68[0:Inp] || -> equal(pred(succ(u)),u)**.
% 27.86/28.10 70[0:Inp] || -> equal(succ(succ(succ(n0))),n3)**.
% 27.86/28.10 77[0:Inp] || -> equal(succ(succ(succ(succ(n0)))),n4)**.
% 27.86/28.10 82[0:Inp] || gt(u,v)* -> leq(v,u).
% 27.86/28.10 89[0:Inp] || gt(u,v)*+ -> leq(v,pred(u))*.
% 27.86/28.10 111[0:Inp] || leq(u,v)* -> gt(v,u) equal(u,v).
% 27.86/28.10 115[0:Inp] || leq(u,n0)*+ leq(n0,u)* -> equal(u,n0).
% 27.86/28.10 117[0:Inp] || leq(u,v)* leq(v,w)* -> leq(u,w)*.
% 27.86/28.10 121[0:Inp] || leq(u,n1)* leq(n0,u) -> equal(u,n1) equal(u,n0).
% 27.86/28.10 123[0:Inp] || leq(u,n2)*+ leq(n0,u) -> equal(u,n2) equal(u,n1)* equal(u,n0).
% 27.86/28.10 131[0:Inp] || leq(u,n4)*+ leq(n0,u) -> equal(u,n4) equal(u,n3)* equal(u,n2) equal(u,n1) equal(u,n0).
% 27.86/28.10 150[0:Inp] || -> equal(sum__dfg(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x__dfg,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))),pv84)**.
% 27.86/28.10 158[0:Inp] || equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,skc1)),minus(a_select2(x__dfg,pv10),a_select2(mu,skc1))),tptp_minus_2),times(a_select2(sigma,skc1),a_select2(sigma,skc1)))),a_select2(rho,skc1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,skc1))),sum__dfg(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x__dfg,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))),a_select3(q,pv10,skc1))** -> .
% 27.86/28.10 159[0:Inp] || leq(n0,u) leq(u,pred(pv47)) -> equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,u)),minus(a_select2(x__dfg,pv10),a_select2(mu,u))),tptp_minus_2),times(a_select2(sigma,u),a_select2(sigma,u)))),a_select2(rho,u)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,u))),sum__dfg(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x__dfg,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))),a_select3(q,pv10,u))**.
% 27.86/28.10 160[0:Rew:46.0,51.0] || -> equal(succ(n1),n2)**.
% 27.86/28.10 163[0:Rew:160.0,70.0,46.0,70.0] || -> equal(succ(n2),n3)**.
% 27.86/28.10 165[0:Rew:163.0,77.0,160.0,77.0,46.0,77.0] || -> equal(succ(n3),n4)**.
% 27.86/28.10 173[0:Rew:150.0,158.0] || equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,skc1)),minus(a_select2(x__dfg,pv10),a_select2(mu,skc1))),tptp_minus_2),times(a_select2(sigma,skc1),a_select2(sigma,skc1)))),a_select2(rho,skc1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,skc1))),pv84),a_select3(q,pv10,skc1))** -> .
% 27.86/28.10 174[0:Rew:150.0,159.2] || leq(u,pred(pv47)) leq(n0,u) -> equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,u)),minus(a_select2(x__dfg,pv10),a_select2(mu,u))),tptp_minus_2),times(a_select2(sigma,u),a_select2(sigma,u)))),a_select2(rho,u)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,u))),pv84),a_select3(q,pv10,u))**.
% 27.86/28.10 199[0:Res:7.0,111.0] || -> equal(skc1,pv47) gt(pv47,skc1)*r.
% 27.86/28.10 289[0:Res:6.0,131.1] || leq(n0,pv47) -> equal(pv47,n0) equal(n1,pv47) equal(pv47,n2) equal(n3,pv47)** equal(pv47,n4).
% 27.86/28.10 361[0:MRR:199.0,45.0] || -> gt(pv47,skc1)*r.
% 27.86/28.10 362[0:MRR:289.0,4.0] || -> equal(pv47,n4) equal(n3,pv47)** equal(pv47,n2) equal(n1,pv47) equal(pv47,n0).
% 27.86/28.10 452[1:Spt:362.0] || -> equal(pv47,n4)**.
% 27.86/28.10 508[1:Rew:452.0,361.0] || -> gt(n4,skc1)*r.
% 27.86/28.10 541[1:Rew:452.0,174.0] || leq(u,pred(n4)) leq(n0,u) -> equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,u)),minus(a_select2(x__dfg,pv10),a_select2(mu,u))),tptp_minus_2),times(a_select2(sigma,u),a_select2(sigma,u)))),a_select2(rho,u)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,u))),pv84),a_select3(q,pv10,u))**.
% 27.86/28.10 667[0:SpR:46.0,68.0] || -> equal(pred(n1),n0)**.
% 27.86/28.10 668[0:SpR:160.0,68.0] || -> equal(pred(n2),n1)**.
% 27.86/28.10 669[0:SpR:163.0,68.0] || -> equal(pred(n3),n2)**.
% 27.86/28.10 670[0:SpR:165.0,68.0] || -> equal(pred(n4),n3)**.
% 27.86/28.10 673[1:Rew:670.0,541.0] || leq(u,n3) leq(n0,u) -> equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,u)),minus(a_select2(x__dfg,pv10),a_select2(mu,u))),tptp_minus_2),times(a_select2(sigma,u),a_select2(sigma,u)))),a_select2(rho,u)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,u))),pv84),a_select3(q,pv10,u))**.
% 27.86/28.10 2792[0:Res:29.0,82.0] || -> leq(n0,n1)*r.
% 27.86/28.10 3083[1:Res:508.0,89.0] || -> leq(skc1,pred(n4))*r.
% 27.86/28.10 3205[1:Rew:670.0,3083.0] || -> leq(skc1,n3)*l.
% 27.86/28.10 11884[1:SpL:673.2,173.0] || leq(skc1,n3) leq(n0,skc1) equal(a_select3(q,pv10,skc1),a_select3(q,pv10,skc1))* -> .
% 27.86/28.10 11885[1:Obv:11884.2] || leq(skc1,n3)*l leq(n0,skc1) -> .
% 27.86/28.10 11886[1:MRR:11885.0,11885.1,3205.0,2.0] || -> .
% 27.86/28.10 11887[1:Spt:11886.0,362.0,452.0] || equal(pv47,n4)** -> .
% 27.86/28.10 11888[1:Spt:11886.0,362.1,362.2,362.3,362.4] || -> equal(n3,pv47)** equal(pv47,n2) equal(n1,pv47) equal(pv47,n0).
% 27.86/28.10 11894[2:Spt:11888.0] || -> equal(n3,pv47)**.
% 27.86/28.10 11897[2:Rew:11894.0,669.0] || -> equal(pred(pv47),n2)**.
% 27.86/28.10 12664[2:Rew:11897.0,174.0] || leq(u,n2) leq(n0,u) -> equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,u)),minus(a_select2(x__dfg,pv10),a_select2(mu,u))),tptp_minus_2),times(a_select2(sigma,u),a_select2(sigma,u)))),a_select2(rho,u)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,u))),pv84),a_select3(q,pv10,u))**.
% 27.86/28.10 13295[0:NCh:117.2,117.0,7.0,115.0] || equal(pv47,n0) leq(n0,skc1)*r -> equal(skc1,n0).
% 27.86/28.10 13297[0:NCh:117.2,117.0,7.0,121.0] || equal(n1,pv47) leq(n0,skc1)*r -> equal(skc1,n1) equal(skc1,n0).
% 27.86/28.10 13299[0:NCh:117.2,117.0,7.0,123.0] || equal(pv47,n2) leq(n0,skc1)*r -> equal(skc1,n2) equal(skc1,n1) equal(skc1,n0).
% 27.86/28.10 13302[0:MRR:13295.1,2.0] || equal(pv47,n0) -> equal(skc1,n0)**.
% 27.86/28.10 13303[0:MRR:13297.1,2.0] || equal(n1,pv47) -> equal(skc1,n1)** equal(skc1,n0).
% 27.86/28.10 13329[0:SpL:13302.1,45.0] || equal(pv47,n0)** equal(pv47,n0)** -> .
% 27.86/28.10 13330[0:Obv:13329.0] || equal(pv47,n0)** -> .
% 27.86/28.10 13391[0:Res:361.0,89.0] || -> leq(skc1,pred(pv47))*r.
% 27.86/28.10 13401[2:Rew:11897.0,13391.0] || -> leq(skc1,n2)*l.
% 27.86/28.10 15137[2:SpL:12664.2,173.0] || leq(skc1,n2) leq(n0,skc1) equal(a_select3(q,pv10,skc1),a_select3(q,pv10,skc1))* -> .
% 27.86/28.10 15138[2:Obv:15137.2] || leq(skc1,n2)*l leq(n0,skc1) -> .
% 27.86/28.10 15139[2:MRR:15138.0,15138.1,13401.0,2.0] || -> .
% 27.86/28.10 15140[2:Spt:15139.0,11888.0,11894.0] || equal(n3,pv47)** -> .
% 27.86/28.10 15141[2:Spt:15139.0,11888.1,11888.2,11888.3] || -> equal(pv47,n2) equal(n1,pv47)** equal(pv47,n0).
% 27.86/28.10 15143[2:MRR:15141.2,13330.0] || -> equal(pv47,n2) equal(n1,pv47)**.
% 27.86/28.10 15145[0:MRR:13299.1,2.0] || equal(pv47,n2) -> equal(skc1,n2) equal(skc1,n1)** equal(skc1,n0).
% 27.86/28.10 15380[3:Spt:15143.1] || -> equal(n1,pv47)**.
% 27.86/28.10 15383[3:Rew:15380.0,667.0] || -> equal(pred(pv47),n0)**.
% 27.86/28.10 15923[3:Rew:15380.0,13303.1] || equal(n1,pv47) -> equal(skc1,pv47)** equal(skc1,n0).
% 27.86/28.10 15986[3:Rew:15383.0,174.0] || leq(u,n0) leq(n0,u) -> equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,u)),minus(a_select2(x__dfg,pv10),a_select2(mu,u))),tptp_minus_2),times(a_select2(sigma,u),a_select2(sigma,u)))),a_select2(rho,u)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,u))),pv84),a_select3(q,pv10,u))**.
% 28.29/28.48 15987[3:Rew:15380.0,15923.0] || equal(pv47,pv47) -> equal(skc1,pv47)** equal(skc1,n0).
% 28.29/28.48 15988[3:Obv:15987.0] || -> equal(skc1,pv47)** equal(skc1,n0).
% 28.29/28.48 15989[3:MRR:15988.0,45.0] || -> equal(skc1,n0)**.
% 28.29/28.48 15991[3:Rew:15989.0,173.0] || equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,n0)),minus(a_select2(x__dfg,pv10),a_select2(mu,n0))),tptp_minus_2),times(a_select2(sigma,n0),a_select2(sigma,n0)))),a_select2(rho,n0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,n0))),pv84),a_select3(q,pv10,n0))** -> .
% 28.29/28.48 18683[3:SpL:15986.2,15991.0] || leq(n0,n0) leq(n0,n0) equal(a_select3(q,pv10,n0),a_select3(q,pv10,n0))* -> .
% 28.29/28.48 18684[3:Obv:18683.2] || leq(n0,n0)* -> .
% 28.29/28.48 18685[3:MRR:18684.0,44.0] || -> .
% 28.29/28.48 18686[3:Spt:18685.0,15143.1,15380.0] || equal(n1,pv47)** -> .
% 28.29/28.48 18687[3:Spt:18685.0,15143.0] || -> equal(pv47,n2)**.
% 28.29/28.48 18812[3:Rew:18687.0,45.0] || equal(skc1,n2)** -> .
% 28.29/28.48 18847[3:Rew:18687.0,15145.0] || equal(n2,n2) -> equal(skc1,n2) equal(skc1,n1)** equal(skc1,n0).
% 28.29/28.48 18848[3:Obv:18847.0] || -> equal(skc1,n2) equal(skc1,n1)** equal(skc1,n0).
% 28.29/28.48 18849[3:MRR:18848.0,18812.0] || -> equal(skc1,n1)** equal(skc1,n0).
% 28.29/28.48 18994[3:Rew:668.0,174.0,18687.0,174.0] || leq(u,n1) leq(n0,u) -> equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,u)),minus(a_select2(x__dfg,pv10),a_select2(mu,u))),tptp_minus_2),times(a_select2(sigma,u),a_select2(sigma,u)))),a_select2(rho,u)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,u))),pv84),a_select3(q,pv10,u))**.
% 28.29/28.48 19153[4:Spt:18849.0] || -> equal(skc1,n1)**.
% 28.29/28.48 19301[4:Rew:19153.0,173.0] || equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,n1)),minus(a_select2(x__dfg,pv10),a_select2(mu,n1))),tptp_minus_2),times(a_select2(sigma,n1),a_select2(sigma,n1)))),a_select2(rho,n1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,n1))),pv84),a_select3(q,pv10,n1))** -> .
% 28.29/28.48 21078[4:SpL:18994.2,19301.0] || leq(n1,n1) leq(n0,n1) equal(a_select3(q,pv10,n1),a_select3(q,pv10,n1))* -> .
% 28.29/28.48 21079[4:Obv:21078.2] || leq(n1,n1)* leq(n0,n1) -> .
% 28.29/28.48 21080[4:MRR:21079.0,21079.1,44.0,2792.0] || -> .
% 28.29/28.48 21081[4:Spt:21080.0,18849.0,19153.0] || equal(skc1,n1)** -> .
% 28.29/28.48 21082[4:Spt:21080.0,18849.1] || -> equal(skc1,n0)**.
% 28.29/28.48 21299[4:Rew:21082.0,173.0] || equal(divide(divide(times(exp(divide(divide(times(minus(a_select2(x__dfg,pv10),a_select2(mu,n0)),minus(a_select2(x__dfg,pv10),a_select2(mu,n0))),tptp_minus_2),times(a_select2(sigma,n0),a_select2(sigma,n0)))),a_select2(rho,n0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,n0))),pv84),a_select3(q,pv10,n0))** -> .
% 28.29/28.48 21399[4:SpL:18994.2,21299.0] || leq(n0,n1) leq(n0,n0) equal(a_select3(q,pv10,n0),a_select3(q,pv10,n0))* -> .
% 28.29/28.48 21400[4:Obv:21399.2] || leq(n0,n1)*r leq(n0,n0) -> .
% 28.29/28.48 21401[4:MRR:21400.0,21400.1,2792.0,44.0] || -> .
% 28.29/28.48 % SZS output end Refutation
% 28.29/28.48 Formulae used in the proof : cl5_nebula_norm_0007 gt_1_0 reflexivity_leq successor_1 successor_2 pred_succ successor_3 successor_4 leq_gt1 leq_gt_pred leq_gt2 finite_domain_0 transitivity_leq finite_domain_1 finite_domain_2 finite_domain_4
% 28.29/28.48
%------------------------------------------------------------------------------