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  
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