TSTP Solution File: SWV036+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV036+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 21:41:03 EDT 2022
% Result : Theorem 2.49s 2.71s
% Output : Refutation 2.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV036+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.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 16:26:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.49/2.71
% 2.49/2.71 SPASS V 3.9
% 2.49/2.71 SPASS beiseite: Proof found.
% 2.49/2.71 % SZS status Theorem
% 2.49/2.71 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.49/2.71 SPASS derived 7578 clauses, backtracked 1813 clauses, performed 20 splits and kept 5438 clauses.
% 2.49/2.71 SPASS allocated 91325 KBytes.
% 2.49/2.71 SPASS spent 0:00:02.37 on the problem.
% 2.49/2.71 0:00:00.04 for the input.
% 2.49/2.71 0:00:00.08 for the FLOTTER CNF translation.
% 2.49/2.71 0:00:00.04 for inferences.
% 2.49/2.71 0:00:00.07 for the backtracking.
% 2.49/2.71 0:00:02.02 for the reduction.
% 2.49/2.71
% 2.49/2.71
% 2.49/2.71 Here is a proof with depth 4, length 194 :
% 2.49/2.71 % SZS output start Refutation
% 2.49/2.71 1[0:Inp] || -> SkC1*.
% 2.49/2.71 2[0:Inp] || -> SkC2*.
% 2.49/2.71 3[0:Inp] || -> SkC3*.
% 2.49/2.71 9[0:Inp] || -> equal(init,s_best7_init)**.
% 2.49/2.71 10[0:Inp] || -> equal(init,s_sworst7_init)**.
% 2.49/2.71 11[0:Inp] || -> equal(init,s_worst7_init)**.
% 2.49/2.71 12[0:Inp] || -> leq(n0,s_best7)*r.
% 2.49/2.71 13[0:Inp] || -> leq(n0,s_sworst7)*r.
% 2.49/2.71 14[0:Inp] || -> leq(n0,s_worst7)*r.
% 2.49/2.71 15[0:Inp] || -> leq(n2,pv1388)*r.
% 2.49/2.71 16[0:Inp] || -> leq(s_best7,n3)*r.
% 2.49/2.71 17[0:Inp] || -> leq(s_sworst7,n3)*r.
% 2.49/2.71 18[0:Inp] || -> leq(s_worst7,n3)*r.
% 2.49/2.71 19[0:Inp] || -> leq(pv1388,n3)*r.
% 2.49/2.71 30[0:Inp] || -> gt(n2,n0)*l.
% 2.49/2.71 34[0:Inp] || -> gt(n2,n1)*r.
% 2.49/2.71 42[0:Inp] || -> equal(succ(n0),n1)**.
% 2.49/2.71 43[0:Inp] || gt(u,u)* -> .
% 2.49/2.71 73[0:Inp] || gt(loopcounter,n1) -> equal(init,pvar1400_init)**.
% 2.49/2.71 74[0:Inp] || gt(loopcounter,n1) -> equal(init,pvar1401_init)**.
% 2.49/2.71 75[0:Inp] || gt(loopcounter,n1) -> equal(init,pvar1402_init)**.
% 2.49/2.71 81[0:Inp] || gt(u,v)* -> leq(v,u).
% 2.49/2.71 90[0:Inp] || leq(u,v)*+ -> gt(succ(v),u)*.
% 2.49/2.71 113[0:Inp] || leq(u,v)* -> gt(v,u) equal(u,v).
% 2.49/2.71 118[0:Inp] || gt(u,v)* gt(v,w)* -> gt(u,w)*.
% 2.49/2.71 119[0:Inp] || leq(u,v)* leq(v,w)* -> leq(u,w)*.
% 2.49/2.71 124[0:Inp] || SkC2 leq(n0,u) leq(u,n3) -> equal(a_select2(s_values7_init,u),init)**.
% 2.49/2.71 129[0:Inp] || leq(u,n3)* leq(n0,u) -> equal(u,n3) equal(u,n2) equal(u,n1)* equal(u,n0).
% 2.49/2.71 161[0:Inp] || equal(init,s_best7_init) equal(init,s_sworst7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_sworst7) leq(n0,s_worst7) leq(s_best7,n3) leq(s_sworst7,n3) leq(s_worst7,n3) SkC1 SkC2 SkC3 -> gt(loopcounter,n1) SkC5*.
% 2.49/2.71 164[0:Inp] || equal(init,pvar1400_init) equal(init,pvar1401_init) equal(init,pvar1402_init) equal(init,s_best7_init) equal(init,s_sworst7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_sworst7) leq(n0,s_worst7) leq(s_best7,n3) leq(s_sworst7,n3) leq(s_worst7,n3) SkC1 SkC2 SkC3 -> SkC5*.
% 2.49/2.71 166[0:Inp] || equal(init,init) equal(init,s_best7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(a_select2(s_values7_init,s_worst7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC4 -> gt(loopcounter,n1) SkC0.
% 2.49/2.71 167[0:Inp] || equal(init,init) equal(init,s_sworst7_init) equal(init,s_worst7_init) leq(n0,s_sworst7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_sworst7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(init,s_best7_init) equal(a_select2(s_values7_init,s_best7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC0 -> gt(loopcounter,n1).
% 2.49/2.71 168[0:Inp] || equal(init,init) equal(init,s_best7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(init,s_sworst7_init) equal(a_select2(s_values7_init,s_sworst7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC5 -> gt(loopcounter,n1) SkC4.
% 2.49/2.71 169[0:Inp] || equal(init,pvar1400_init) equal(init,pvar1401_init) equal(init,pvar1402_init) equal(init,init) equal(init,s_best7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(a_select2(s_values7_init,s_worst7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC4 -> SkC0.
% 2.49/2.71 170[0:Inp] || equal(init,pvar1400_init) equal(init,pvar1401_init) equal(init,pvar1402_init) equal(init,init) equal(init,s_sworst7_init) equal(init,s_worst7_init) leq(n0,s_sworst7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_sworst7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(init,s_best7_init) equal(a_select2(s_values7_init,s_best7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC0 -> .
% 2.49/2.71 171[0:Inp] || equal(init,pvar1400_init) equal(init,pvar1401_init) equal(init,pvar1402_init) equal(init,init) equal(init,s_best7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(init,s_sworst7_init) equal(a_select2(s_values7_init,s_sworst7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC5 -> SkC4.
% 2.49/2.71 172[0:Rew:11.0,10.0] || -> equal(s_worst7_init,s_sworst7_init)**.
% 2.49/2.71 173[0:Rew:172.0,11.0] || -> equal(init,s_sworst7_init)**.
% 2.49/2.71 174[0:Rew:9.0,173.0] || -> equal(s_sworst7_init,s_best7_init)**.
% 2.49/2.71 175[0:Rew:174.0,172.0] || -> equal(s_worst7_init,s_best7_init)**.
% 2.49/2.71 189[0:Rew:9.0,75.1] || gt(loopcounter,n1) -> equal(pvar1402_init,s_best7_init)**.
% 2.49/2.71 190[0:Rew:9.0,74.1] || gt(loopcounter,n1) -> equal(pvar1401_init,s_best7_init)**.
% 2.49/2.71 191[0:Rew:9.0,73.1] || gt(loopcounter,n1) -> equal(pvar1400_init,s_best7_init)**.
% 2.49/2.71 192[0:Rew:9.0,124.3] || SkC2 leq(n0,u) leq(u,n3) -> equal(a_select2(s_values7_init,u),s_best7_init)**.
% 2.49/2.71 193[0:MRR:192.0,2.0] || leq(u,n3) leq(n0,u) -> equal(a_select2(s_values7_init,u),s_best7_init)**.
% 2.49/2.71 207[0:Rew:9.0,161.2,175.0,161.2,9.0,161.1,174.0,161.1,9.0,161.0] || equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) leq(n0,s_best7) leq(n0,s_sworst7) leq(n0,s_worst7) leq(s_best7,n3) leq(s_sworst7,n3) leq(s_worst7,n3) SkC1 SkC2 SkC3 -> gt(loopcounter,n1) SkC5*.
% 2.49/2.71 208[0:Obv:207.2] || leq(n0,s_best7) leq(n0,s_sworst7) leq(n0,s_worst7) leq(s_best7,n3) leq(s_sworst7,n3) leq(s_worst7,n3) SkC1 SkC2 SkC3 -> gt(loopcounter,n1) SkC5*.
% 2.49/2.71 209[0:MRR:208.0,208.1,208.2,208.3,208.4,208.5,208.6,208.7,208.8,12.0,13.0,14.0,16.0,17.0,18.0,1.0,2.0,3.0] || -> SkC5* gt(loopcounter,n1).
% 2.49/2.71 210[0:Rew:9.0,164.5,175.0,164.5,9.0,164.4,174.0,164.4,9.0,164.3,9.0,164.2,9.0,164.1,9.0,164.0] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) leq(n0,s_best7) leq(n0,s_sworst7) leq(n0,s_worst7) leq(s_best7,n3) leq(s_sworst7,n3) leq(s_worst7,n3) SkC1 SkC2 SkC3 -> SkC5*.
% 2.49/2.71 211[0:Obv:210.5] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) leq(n0,s_best7) leq(n0,s_sworst7) leq(n0,s_worst7) leq(s_best7,n3) leq(s_sworst7,n3) leq(s_worst7,n3) SkC1 SkC2 SkC3 -> SkC5*.
% 2.49/2.71 212[0:MRR:211.3,211.4,211.5,211.6,211.7,211.8,211.9,211.10,211.11,12.0,13.0,14.0,16.0,17.0,18.0,1.0,2.0,3.0] || equal(pvar1402_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1400_init,s_best7_init) -> SkC5*.
% 2.49/2.71 213[0:Obv:166.0] || equal(init,s_best7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(a_select2(s_values7_init,s_worst7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC4 -> gt(loopcounter,n1) SkC0.
% 2.49/2.71 214[0:Rew:193.2,213.12,9.0,213.12,193.2,213.11,9.0,213.11,9.0,213.1,175.0,213.1,9.0,213.0] || equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) SkC4* -> gt(loopcounter,n1) SkC0.
% 2.49/2.71 215[0:Obv:214.12] || leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 SkC4* -> gt(loopcounter,n1) SkC0.
% 2.49/2.71 216[0:MRR:215.0,215.1,215.3,215.4,215.5,215.6,215.7,215.8,12.0,14.0,16.0,18.0,19.0,1.0,2.0,3.0] || leq(n0,pv1388) SkC4* -> gt(loopcounter,n1) SkC0.
% 2.49/2.71 217[0:Obv:167.0] || equal(init,s_sworst7_init) equal(init,s_worst7_init) leq(n0,s_sworst7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_sworst7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(init,s_best7_init) equal(a_select2(s_values7_init,s_best7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC0 -> gt(loopcounter,n1).
% 2.49/2.71 218[0:Rew:193.2,217.13,9.0,217.13,9.0,217.12,9.0,217.11,9.0,217.1,175.0,217.1,9.0,217.0,174.0,217.0] || equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) leq(n0,s_sworst7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_sworst7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(s_best7_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** equal(s_best7_init,s_best7_init) SkC0 -> gt(loopcounter,n1).
% 2.49/2.71 219[0:Obv:218.13] || leq(n0,s_sworst7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_sworst7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(a_select2(s_values7_init,s_best7),s_best7_init)** SkC0 -> gt(loopcounter,n1).
% 2.49/2.71 220[0:MRR:219.0,219.1,219.3,219.4,219.5,219.6,219.7,219.8,13.0,14.0,17.0,18.0,19.0,1.0,2.0,3.0] || leq(n0,pv1388) equal(a_select2(s_values7_init,s_best7),s_best7_init)** SkC0 -> gt(loopcounter,n1).
% 2.49/2.71 221[0:Obv:168.0] || equal(init,s_best7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(init,s_sworst7_init) equal(a_select2(s_values7_init,s_sworst7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC5 -> gt(loopcounter,n1) SkC4.
% 2.49/2.71 222[0:Rew:193.2,221.13,9.0,221.13,9.0,221.12,9.0,221.11,174.0,221.11,9.0,221.1,175.0,221.1,9.0,221.0] || equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(s_best7_init,s_best7_init) equal(a_select2(s_values7_init,s_sworst7),s_best7_init)** equal(s_best7_init,s_best7_init) SkC5 -> gt(loopcounter,n1) SkC4.
% 2.49/2.71 223[0:Obv:222.13] || leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(a_select2(s_values7_init,s_sworst7),s_best7_init)** SkC5 -> gt(loopcounter,n1) SkC4.
% 2.49/2.71 224[0:MRR:223.0,223.1,223.3,223.4,223.5,223.6,223.7,223.8,223.10,12.0,14.0,16.0,18.0,19.0,1.0,2.0,3.0,209.1] || leq(n0,pv1388) equal(a_select2(s_values7_init,s_sworst7),s_best7_init)** -> gt(loopcounter,n1) SkC4.
% 2.49/2.71 225[0:Obv:169.3] || equal(init,pvar1400_init) equal(init,pvar1401_init) equal(init,pvar1402_init) equal(init,s_best7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(a_select2(s_values7_init,s_worst7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC4 -> SkC0.
% 2.49/2.71 226[0:Rew:193.2,225.15,9.0,225.15,193.2,225.14,9.0,225.14,9.0,225.4,175.0,225.4,9.0,225.3,9.0,225.2,9.0,225.1,9.0,225.0] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) SkC4* -> SkC0.
% 2.49/2.71 227[0:Obv:226.15] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 SkC4* -> SkC0.
% 2.49/2.71 228[0:MRR:227.3,227.4,227.6,227.7,227.8,227.9,227.10,227.11,12.0,14.0,16.0,18.0,19.0,1.0,2.0,3.0] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) leq(n0,pv1388) SkC4* -> SkC0.
% 2.49/2.71 229[0:Obv:170.3] || equal(init,pvar1400_init) equal(init,pvar1401_init) equal(init,pvar1402_init) equal(init,s_sworst7_init) equal(init,s_worst7_init) leq(n0,s_sworst7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_sworst7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(init,s_best7_init) equal(a_select2(s_values7_init,s_best7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC0 -> .
% 2.49/2.71 230[0:Rew:193.2,229.16,9.0,229.16,9.0,229.15,9.0,229.14,9.0,229.4,175.0,229.4,9.0,229.3,174.0,229.3,9.0,229.2,9.0,229.1,9.0,229.0] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) leq(n0,s_sworst7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_sworst7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(s_best7_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** equal(s_best7_init,s_best7_init) SkC0 -> .
% 2.49/2.71 231[0:Obv:230.16] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) leq(n0,s_sworst7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_sworst7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(a_select2(s_values7_init,s_best7),s_best7_init)** SkC0 -> .
% 2.49/2.71 232[0:MRR:231.3,231.4,231.6,231.7,231.8,231.9,231.10,231.11,13.0,14.0,17.0,18.0,19.0,1.0,2.0,3.0] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) leq(n0,pv1388) equal(a_select2(s_values7_init,s_best7),s_best7_init)** SkC0 -> .
% 2.49/2.71 233[0:Obv:171.3] || equal(init,pvar1400_init) equal(init,pvar1401_init) equal(init,pvar1402_init) equal(init,s_best7_init) equal(init,s_worst7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(init,s_sworst7_init) equal(a_select2(s_values7_init,s_sworst7),init) equal(a_select2(s_values7_init,pv1388),init)** SkC5 -> SkC4.
% 2.49/2.71 234[0:Rew:193.2,233.16,9.0,233.16,9.0,233.15,9.0,233.14,174.0,233.14,9.0,233.4,175.0,233.4,9.0,233.3,9.0,233.2,9.0,233.1,9.0,233.0] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(s_best7_init,s_best7_init) equal(a_select2(s_values7_init,s_sworst7),s_best7_init)** equal(s_best7_init,s_best7_init) SkC5 -> SkC4.
% 2.49/2.71 235[0:Obv:234.16] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) leq(n0,s_best7) leq(n0,s_worst7) leq(n0,pv1388) leq(s_best7,n3) leq(s_worst7,n3) leq(pv1388,n3) SkC1 SkC2 SkC3 equal(a_select2(s_values7_init,s_sworst7),s_best7_init)** SkC5 -> SkC4.
% 2.49/2.71 236[0:MRR:235.3,235.4,235.6,235.7,235.8,235.9,235.10,235.11,235.13,12.0,14.0,16.0,18.0,19.0,1.0,2.0,3.0,212.3] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) leq(n0,pv1388) equal(a_select2(s_values7_init,s_sworst7),s_best7_init)** -> SkC4.
% 2.49/2.71 286[0:Res:19.0,129.1] || leq(n0,pv1388) -> equal(n3,pv1388) equal(pv1388,n2) equal(n1,pv1388)** equal(pv1388,n0).
% 2.49/2.71 315[0:Res:18.0,113.0] || -> gt(n3,s_worst7)*l equal(n3,s_worst7).
% 2.49/2.71 376[0:Res:17.0,113.0] || -> gt(n3,s_sworst7)*l equal(n3,s_sworst7).
% 2.49/2.71 409[0:Res:17.0,193.1] || leq(n0,s_sworst7) -> equal(a_select2(s_values7_init,s_sworst7),s_best7_init)**.
% 2.49/2.71 431[0:MRR:409.0,13.0] || -> equal(a_select2(s_values7_init,s_sworst7),s_best7_init)**.
% 2.49/2.71 432[0:Rew:431.0,236.4] || equal(pvar1400_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1402_init,s_best7_init) leq(n0,pv1388) equal(s_best7_init,s_best7_init) -> SkC4*.
% 2.49/2.71 433[0:Rew:431.0,224.1] || leq(n0,pv1388) equal(s_best7_init,s_best7_init) -> gt(loopcounter,n1) SkC4*.
% 2.49/2.71 437[0:Obv:433.1] || leq(n0,pv1388) -> SkC4* gt(loopcounter,n1).
% 2.49/2.71 438[0:MRR:216.1,437.2] || leq(n0,pv1388) -> SkC0* gt(loopcounter,n1).
% 2.49/2.71 439[0:MRR:220.2,438.2] || leq(n0,pv1388) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> gt(loopcounter,n1).
% 2.49/2.71 444[0:Obv:432.4] || leq(n0,pv1388) equal(pvar1402_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1400_init,s_best7_init) -> SkC4*.
% 2.49/2.71 445[0:MRR:228.4,444.4] || leq(n0,pv1388) equal(pvar1402_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1400_init,s_best7_init) -> SkC0*.
% 2.49/2.71 446[0:MRR:232.5,445.4] || leq(n0,pv1388) equal(pvar1402_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1400_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.49/2.71 505[1:Spt:286.1] || -> equal(n3,pv1388)**.
% 2.49/2.71 573[1:Rew:505.0,193.0] || leq(u,pv1388) leq(n0,u) -> equal(a_select2(s_values7_init,u),s_best7_init)**.
% 2.49/2.71 623[1:Rew:505.0,18.0] || -> leq(s_worst7,pv1388)*r.
% 2.49/2.71 625[1:Rew:505.0,16.0] || -> leq(s_best7,pv1388)*r.
% 2.49/2.71 729[2:Spt:439.0] || leq(n0,pv1388)*r -> .
% 2.49/2.71 884[2:NCh:119.2,119.1,623.0,729.0] || leq(n0,s_worst7)*r -> .
% 2.49/2.71 887[2:MRR:884.0,14.0] || -> .
% 2.55/2.75 888[2:Spt:887.0,439.0,729.0] || -> leq(n0,pv1388)*r.
% 2.55/2.75 889[2:Spt:887.0,439.1,439.2] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> gt(loopcounter,n1).
% 2.55/2.75 901[2:MRR:446.0,888.0] || equal(pvar1402_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1400_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 930[3:Spt:190.0] || gt(loopcounter,n1)*r -> .
% 2.55/2.75 931[3:MRR:889.1,930.0] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 1109[0:NCh:118.2,118.1,43.0,34.0] || gt(n1,n2)*l -> .
% 2.55/2.75 1110[0:NCh:118.2,118.1,43.0,34.0] || equal(n1,n2)** -> .
% 2.55/2.75 4145[0:Res:30.0,81.0] || -> leq(n0,n2)*r.
% 2.55/2.75 7343[0:Res:15.0,113.0] || -> gt(pv1388,n2)*l equal(pv1388,n2).
% 2.55/2.75 7345[0:Res:15.0,90.0] || -> gt(succ(pv1388),n2)*l.
% 2.55/2.75 7553[3:SpL:573.2,931.0] || leq(s_best7,pv1388)*r leq(n0,s_best7) equal(s_best7_init,s_best7_init) -> .
% 2.55/2.75 7554[3:Obv:7553.2] || leq(s_best7,pv1388)*r leq(n0,s_best7) -> .
% 2.55/2.75 7555[3:MRR:7554.0,7554.1,625.0,12.0] || -> .
% 2.55/2.75 7556[3:Spt:7555.0,190.0,930.0] || -> gt(loopcounter,n1)*r.
% 2.55/2.75 7557[3:Spt:7555.0,190.1] || -> equal(pvar1401_init,s_best7_init)**.
% 2.55/2.75 7558[3:MRR:191.0,7556.0] || -> equal(pvar1400_init,s_best7_init)**.
% 2.55/2.75 7559[3:MRR:189.0,7556.0] || -> equal(pvar1402_init,s_best7_init)**.
% 2.55/2.75 7566[3:Rew:7558.0,901.2,7557.0,901.1,7559.0,901.0] || equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 7567[3:Obv:7566.2] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 7571[3:SpL:573.2,7567.0] || leq(s_best7,pv1388)*r leq(n0,s_best7) equal(s_best7_init,s_best7_init) -> .
% 2.55/2.75 7572[3:Obv:7571.2] || leq(s_best7,pv1388)*r leq(n0,s_best7) -> .
% 2.55/2.75 7573[3:MRR:7572.0,7572.1,625.0,12.0] || -> .
% 2.55/2.75 7574[1:Spt:7573.0,286.1,505.0] || equal(n3,pv1388)** -> .
% 2.55/2.75 7575[1:Spt:7573.0,286.0,286.2,286.3,286.4] || leq(n0,pv1388) -> equal(pv1388,n2) equal(n1,pv1388)** equal(pv1388,n0).
% 2.55/2.75 7612[2:Spt:7575.2] || -> equal(n1,pv1388)**.
% 2.55/2.75 7626[2:Rew:7612.0,1110.0] || equal(pv1388,n2)** -> .
% 2.55/2.75 7628[2:Rew:7612.0,1109.0] || gt(pv1388,n2)*l -> .
% 2.55/2.75 7740[2:MRR:7343.1,7626.0] || -> gt(pv1388,n2)*l.
% 2.55/2.75 7779[2:MRR:7628.0,7740.0] || -> .
% 2.55/2.75 7789[2:Spt:7779.0,7575.2,7612.0] || equal(n1,pv1388)** -> .
% 2.55/2.75 7790[2:Spt:7779.0,7575.0,7575.1,7575.3] || leq(n0,pv1388)*r -> equal(pv1388,n2) equal(pv1388,n0).
% 2.55/2.75 7791[3:Spt:7790.1] || -> equal(pv1388,n2)**.
% 2.55/2.75 7872[3:Rew:7791.0,446.0] || leq(n0,n2) equal(pvar1402_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1400_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 7874[3:Rew:7791.0,439.0] || leq(n0,n2) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> gt(loopcounter,n1).
% 2.55/2.75 7894[3:MRR:7874.0,4145.0] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> gt(loopcounter,n1).
% 2.55/2.75 7899[3:MRR:7872.0,4145.0] || equal(pvar1402_init,s_best7_init) equal(pvar1401_init,s_best7_init) equal(pvar1400_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 7961[4:Spt:376.1] || -> equal(n3,s_sworst7)**.
% 2.55/2.75 7971[4:Rew:7961.0,16.0] || -> leq(s_best7,s_sworst7)*r.
% 2.55/2.75 8068[4:Rew:7961.0,193.0] || leq(u,s_sworst7) leq(n0,u) -> equal(a_select2(s_values7_init,u),s_best7_init)**.
% 2.55/2.75 8217[5:Spt:191.0] || gt(loopcounter,n1)*r -> .
% 2.55/2.75 8221[5:MRR:7894.1,8217.0] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 8839[5:SpL:8068.2,8221.0] || leq(s_best7,s_sworst7)*r leq(n0,s_best7) equal(s_best7_init,s_best7_init) -> .
% 2.55/2.75 8840[5:Obv:8839.2] || leq(s_best7,s_sworst7)*r leq(n0,s_best7) -> .
% 2.55/2.75 8841[5:MRR:8840.0,8840.1,7971.0,12.0] || -> .
% 2.55/2.75 8842[5:Spt:8841.0,191.0,8217.0] || -> gt(loopcounter,n1)*r.
% 2.55/2.75 8843[5:Spt:8841.0,191.1] || -> equal(pvar1400_init,s_best7_init)**.
% 2.55/2.75 8844[5:MRR:189.0,8842.0] || -> equal(pvar1402_init,s_best7_init)**.
% 2.55/2.75 8845[5:MRR:190.0,8842.0] || -> equal(pvar1401_init,s_best7_init)**.
% 2.55/2.75 8852[5:Rew:8843.0,7899.2,8845.0,7899.1,8844.0,7899.0] || equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 8853[5:Obv:8852.2] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 8857[5:SpL:8068.2,8853.0] || leq(s_best7,s_sworst7)*r leq(n0,s_best7) equal(s_best7_init,s_best7_init) -> .
% 2.55/2.75 8858[5:Obv:8857.2] || leq(s_best7,s_sworst7)*r leq(n0,s_best7) -> .
% 2.55/2.75 8859[5:MRR:8858.0,8858.1,7971.0,12.0] || -> .
% 2.55/2.75 8860[4:Spt:8859.0,376.1,7961.0] || equal(n3,s_sworst7)** -> .
% 2.55/2.75 8861[4:Spt:8859.0,376.0] || -> gt(n3,s_sworst7)*l.
% 2.55/2.75 8877[5:Spt:315.1] || -> equal(n3,s_worst7)**.
% 2.55/2.75 8904[5:Rew:8877.0,16.0] || -> leq(s_best7,s_worst7)*r.
% 2.55/2.75 8990[5:Rew:8877.0,193.0] || leq(u,s_worst7) leq(n0,u) -> equal(a_select2(s_values7_init,u),s_best7_init)**.
% 2.55/2.75 9139[6:Spt:189.0] || gt(loopcounter,n1)*r -> .
% 2.55/2.75 9143[6:MRR:7894.1,9139.0] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 9552[6:SpL:8990.2,9143.0] || leq(s_best7,s_worst7)*r leq(n0,s_best7) equal(s_best7_init,s_best7_init) -> .
% 2.55/2.75 9553[6:Obv:9552.2] || leq(s_best7,s_worst7)*r leq(n0,s_best7) -> .
% 2.55/2.75 9554[6:MRR:9553.0,9553.1,8904.0,12.0] || -> .
% 2.55/2.75 9555[6:Spt:9554.0,189.0,9139.0] || -> gt(loopcounter,n1)*r.
% 2.55/2.75 9556[6:Spt:9554.0,189.1] || -> equal(pvar1402_init,s_best7_init)**.
% 2.55/2.75 9557[6:MRR:190.0,9555.0] || -> equal(pvar1401_init,s_best7_init)**.
% 2.55/2.75 9558[6:MRR:191.0,9555.0] || -> equal(pvar1400_init,s_best7_init)**.
% 2.55/2.75 9565[6:Rew:9558.0,7899.2,9557.0,7899.1,9556.0,7899.0] || equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 9566[6:Obv:9565.2] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 9570[6:SpL:8990.2,9566.0] || leq(s_best7,s_worst7)*r leq(n0,s_best7) equal(s_best7_init,s_best7_init) -> .
% 2.55/2.75 9571[6:Obv:9570.2] || leq(s_best7,s_worst7)*r leq(n0,s_best7) -> .
% 2.55/2.75 9572[6:MRR:9571.0,9571.1,8904.0,12.0] || -> .
% 2.55/2.75 9573[5:Spt:9572.0,315.1,8877.0] || equal(n3,s_worst7)** -> .
% 2.55/2.75 9574[5:Spt:9572.0,315.0] || -> gt(n3,s_worst7)*l.
% 2.55/2.75 9584[6:Spt:190.0] || gt(loopcounter,n1)*r -> .
% 2.55/2.75 9588[6:MRR:7894.1,9584.0] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 10053[6:SpL:193.2,9588.0] || leq(s_best7,n3)*r leq(n0,s_best7) equal(s_best7_init,s_best7_init) -> .
% 2.55/2.75 10054[6:Obv:10053.2] || leq(s_best7,n3)*r leq(n0,s_best7) -> .
% 2.55/2.75 10055[6:MRR:10054.0,10054.1,16.0,12.0] || -> .
% 2.55/2.75 10056[6:Spt:10055.0,190.0,9584.0] || -> gt(loopcounter,n1)*r.
% 2.55/2.75 10057[6:Spt:10055.0,190.1] || -> equal(pvar1401_init,s_best7_init)**.
% 2.55/2.75 10058[6:MRR:191.0,10056.0] || -> equal(pvar1400_init,s_best7_init)**.
% 2.55/2.75 10059[6:MRR:189.0,10056.0] || -> equal(pvar1402_init,s_best7_init)**.
% 2.55/2.75 10066[6:Rew:10058.0,7899.2,10057.0,7899.1,10059.0,7899.0] || equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(s_best7_init,s_best7_init) equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 10067[6:Obv:10066.2] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> .
% 2.55/2.75 10071[6:SpL:193.2,10067.0] || leq(s_best7,n3)*r leq(n0,s_best7) equal(s_best7_init,s_best7_init) -> .
% 2.55/2.75 10072[6:Obv:10071.2] || leq(s_best7,n3)*r leq(n0,s_best7) -> .
% 2.55/2.75 10073[6:MRR:10072.0,10072.1,16.0,12.0] || -> .
% 2.55/2.75 10074[3:Spt:10073.0,7790.1,7791.0] || equal(pv1388,n2)** -> .
% 2.55/2.75 10075[3:Spt:10073.0,7790.0,7790.2] || leq(n0,pv1388)*r -> equal(pv1388,n0).
% 2.55/2.75 10535[4:Spt:439.0] || leq(n0,pv1388)*r -> .
% 2.55/2.75 10630[4:NCh:119.2,119.1,15.0,10535.0] || leq(n0,n2)*r -> .
% 2.55/2.75 10638[4:MRR:10630.0,4145.0] || -> .
% 2.55/2.75 10639[4:Spt:10638.0,439.0,10535.0] || -> leq(n0,pv1388)*r.
% 2.55/2.75 10640[4:Spt:10638.0,439.1,439.2] || equal(a_select2(s_values7_init,s_best7),s_best7_init)** -> gt(loopcounter,n1).
% 2.55/2.75 10641[4:MRR:10075.0,10639.0] || -> equal(pv1388,n0)**.
% 2.55/2.75 10654[4:Rew:10641.0,7345.0] || -> gt(succ(n0),n2)*l.
% 2.55/2.75 10693[4:Rew:42.0,10654.0] || -> gt(n1,n2)*l.
% 2.55/2.75 10694[4:MRR:10693.0,1109.0] || -> .
% 2.55/2.75 % SZS output end Refutation
% 2.55/2.75 Formulae used in the proof : gauss_init_0057 reflexivity_leq leq_succ_succ gt_2_0 gt_2_1 successor_1 irreflexivity_gt leq_gt1 leq_succ_gt_equiv leq_gt2 transitivity_gt transitivity_leq finite_domain_3
% 2.55/2.75
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