TSTP Solution File: SWV096+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV096+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 21:41:16 EDT 2022
% Result : Theorem 2.88s 3.04s
% Output : Refutation 2.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV096+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 01:16:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.88/3.04
% 2.88/3.04 SPASS V 3.9
% 2.88/3.04 SPASS beiseite: Proof found.
% 2.88/3.04 % SZS status Theorem
% 2.88/3.04 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.88/3.04 SPASS derived 7133 clauses, backtracked 1198 clauses, performed 8 splits and kept 4535 clauses.
% 2.88/3.04 SPASS allocated 92132 KBytes.
% 2.88/3.04 SPASS spent 0:00:02.68 on the problem.
% 2.88/3.04 0:00:00.04 for the input.
% 2.88/3.04 0:00:00.09 for the FLOTTER CNF translation.
% 2.88/3.04 0:00:00.05 for inferences.
% 2.88/3.04 0:00:00.05 for the backtracking.
% 2.88/3.04 0:00:02.25 for the reduction.
% 2.88/3.04
% 2.88/3.04
% 2.88/3.04 Here is a proof with depth 3, length 163 :
% 2.88/3.04 % SZS output start Refutation
% 2.88/3.04 2[0:Inp] || -> leq(n0,skc3)*r.
% 2.88/3.04 3[0:Inp] || -> leq(n0,pv5)*r.
% 2.88/3.04 15[0:Inp] || -> gt(n0,tptp_minus_1)*r.
% 2.88/3.04 23[0:Inp] || -> gt(n1,n0)*l.
% 2.88/3.04 30[0:Inp] || -> gt(n2,n1)*l.
% 2.88/3.04 41[0:Inp] || -> leq(u,u)*.
% 2.88/3.04 42[0:Inp] || -> equal(succ(n0),n1)**.
% 2.88/3.04 43[0:Inp] || gt(u,u)* -> .
% 2.88/3.04 45[0:Inp] || -> equal(succ(tptp_minus_1),n0)**.
% 2.88/3.04 47[0:Inp] || -> leq(skc2,minus(pv5,n1))*r.
% 2.88/3.04 48[0:Inp] || -> equal(a_select2(rho_defuse,n0),use)**.
% 2.88/3.04 49[0:Inp] || -> equal(a_select2(rho_defuse,n1),use)**.
% 2.88/3.04 50[0:Inp] || -> equal(a_select2(rho_defuse,n2),use)**.
% 2.88/3.04 51[0:Inp] || -> equal(a_select2(sigma_defuse,n0),use)**.
% 2.88/3.04 52[0:Inp] || -> equal(a_select2(sigma_defuse,n1),use)**.
% 2.88/3.04 53[0:Inp] || -> equal(a_select2(sigma_defuse,n2),use)**.
% 2.88/3.04 54[0:Inp] || -> equal(a_select2(sigma_defuse,n3),use)**.
% 2.88/3.04 55[0:Inp] || -> equal(a_select2(sigma_defuse,n4),use)**.
% 2.88/3.04 56[0:Inp] || -> equal(a_select2(sigma_defuse,n5),use)**.
% 2.88/3.04 57[0:Inp] || -> equal(a_select2(xinit_defuse,n3),use)**.
% 2.88/3.04 58[0:Inp] || -> equal(a_select2(xinit_defuse,n4),use)**.
% 2.88/3.04 59[0:Inp] || -> equal(a_select2(xinit_defuse,n5),use)**.
% 2.88/3.04 60[0:Inp] || -> equal(a_select2(xinit_mean_defuse,n0),use)**.
% 2.88/3.04 61[0:Inp] || -> equal(a_select2(xinit_mean_defuse,n1),use)**.
% 2.88/3.04 62[0:Inp] || -> equal(a_select2(xinit_mean_defuse,n2),use)**.
% 2.88/3.04 63[0:Inp] || -> equal(a_select2(xinit_mean_defuse,n3),use)**.
% 2.88/3.04 64[0:Inp] || -> equal(a_select2(xinit_mean_defuse,n4),use)**.
% 2.88/3.04 65[0:Inp] || -> equal(a_select2(xinit_mean_defuse,n5),use)**.
% 2.88/3.04 66[0:Inp] || -> equal(a_select2(xinit_noise_defuse,n0),use)**.
% 2.88/3.04 67[0:Inp] || -> equal(a_select2(xinit_noise_defuse,n1),use)**.
% 2.88/3.04 68[0:Inp] || -> equal(a_select2(xinit_noise_defuse,n2),use)**.
% 2.88/3.04 69[0:Inp] || -> equal(a_select2(xinit_noise_defuse,n3),use)**.
% 2.88/3.04 70[0:Inp] || -> equal(a_select2(xinit_noise_defuse,n4),use)**.
% 2.88/3.04 71[0:Inp] || -> equal(a_select2(xinit_noise_defuse,n5),use)**.
% 2.88/3.04 72[0:Inp] || -> leq(pv5,minus(n999,n1))*r.
% 2.88/3.04 74[0:Inp] || -> equal(succ(succ(n0)),n2)**.
% 2.88/3.04 91[0:Inp] || -> equal(pred(succ(u)),u)**.
% 2.88/3.04 93[0:Inp] || -> equal(a_select3(u_defuse,n0,n0),use)**.
% 2.88/3.04 94[0:Inp] || -> equal(a_select3(u_defuse,n1,n0),use)**.
% 2.88/3.04 95[0:Inp] || -> equal(a_select3(u_defuse,n2,n0),use)**.
% 2.88/3.04 101[0:Inp] || -> equal(minus(u,n1),pred(u))**.
% 2.88/3.04 108[0:Inp] || gt(u,v)* -> leq(v,u).
% 2.88/3.04 116[0:Inp] || leq(u,v)*+ -> leq(u,succ(v))*.
% 2.88/3.04 136[0:Inp] || leq(u,v) -> leq(succ(u),succ(v))*.
% 2.88/3.04 138[0:Inp] || leq(u,v)* -> gt(v,u) equal(u,v).
% 2.88/3.04 142[0:Inp] || leq(u,n0)*+ leq(n0,u)* -> equal(u,n0).
% 2.88/3.04 143[0:Inp] || gt(u,v)* gt(v,w)* -> gt(u,w)*.
% 2.88/3.04 144[0:Inp] || leq(u,v)* leq(v,w)* -> leq(u,w)*.
% 2.88/3.04 148[0:Inp] || leq(u,n1)* leq(n0,u) -> equal(u,n1) equal(u,n0).
% 2.88/3.04 150[0:Inp] || leq(u,n2)* leq(n0,u) -> equal(u,n2) equal(u,n1) equal(u,n0).
% 2.88/3.04 158[0:Inp] || leq(n0,u) leq(u,n2) leq(v,minus(pv5,n1)) leq(n0,v) -> equal(a_select3(z_defuse,u,v),use)**.
% 2.88/3.04 159[0:Inp] || leq(n0,u) leq(u,n2) leq(v,minus(pv5,n1)) leq(n0,v) -> equal(a_select3(u_defuse,u,v),use)**.
% 2.88/3.04 186[0:Inp] || equal(a_select2(rho_defuse,n0),use) equal(a_select2(rho_defuse,n1),use) equal(a_select2(rho_defuse,n2),use) equal(a_select2(sigma_defuse,n0),use) equal(a_select2(sigma_defuse,n1),use) equal(a_select2(sigma_defuse,n2),use) equal(a_select2(sigma_defuse,n3),use) equal(a_select2(sigma_defuse,n4),use) equal(a_select2(sigma_defuse,n5),use) equal(a_select3(u_defuse,n0,n0),use) equal(a_select3(u_defuse,n1,n0),use) equal(a_select3(u_defuse,n2,n0),use)** equal(a_select2(xinit_defuse,n3),use) equal(a_select2(xinit_defuse,n4),use) equal(a_select2(xinit_defuse,n5),use) equal(a_select2(xinit_mean_defuse,n0),use) equal(a_select2(xinit_mean_defuse,n1),use) equal(a_select2(xinit_mean_defuse,n2),use) equal(a_select2(xinit_mean_defuse,n3),use) equal(a_select2(xinit_mean_defuse,n4),use) equal(a_select2(xinit_mean_defuse,n5),use) equal(a_select2(xinit_noise_defuse,n0),use) equal(a_select2(xinit_noise_defuse,n1),use) equal(a_select2(xinit_noise_defuse,n2),use) equal(a_select2(xinit_noise_defuse,n3),use) equal(a_select2(xinit_noise_defuse,n4),use) equal(a_select2(xinit_noise_defuse,n5),use) leq(n0,pv5) leq(pv5,minus(n999,n1)) -> leq(n0,skc2).
% 2.88/3.04 187[0:Inp] || equal(a_select2(rho_defuse,n0),use) equal(a_select2(rho_defuse,n1),use) equal(a_select2(rho_defuse,n2),use) equal(a_select2(sigma_defuse,n0),use) equal(a_select2(sigma_defuse,n1),use) equal(a_select2(sigma_defuse,n2),use) equal(a_select2(sigma_defuse,n3),use) equal(a_select2(sigma_defuse,n4),use) equal(a_select2(sigma_defuse,n5),use) equal(a_select3(u_defuse,n0,n0),use) equal(a_select3(u_defuse,n1,n0),use) equal(a_select3(u_defuse,n2,n0),use)** equal(a_select2(xinit_defuse,n3),use) equal(a_select2(xinit_defuse,n4),use) equal(a_select2(xinit_defuse,n5),use) equal(a_select2(xinit_mean_defuse,n0),use) equal(a_select2(xinit_mean_defuse,n1),use) equal(a_select2(xinit_mean_defuse,n2),use) equal(a_select2(xinit_mean_defuse,n3),use) equal(a_select2(xinit_mean_defuse,n4),use) equal(a_select2(xinit_mean_defuse,n5),use) equal(a_select2(xinit_noise_defuse,n0),use) equal(a_select2(xinit_noise_defuse,n1),use) equal(a_select2(xinit_noise_defuse,n2),use) equal(a_select2(xinit_noise_defuse,n3),use) equal(a_select2(xinit_noise_defuse,n4),use) equal(a_select2(xinit_noise_defuse,n5),use) leq(n0,pv5) leq(pv5,minus(n999,n1)) -> leq(skc3,n2).
% 2.88/3.04 188[0:Inp] || equal(a_select3(u_defuse,skc3,skc2),use) equal(a_select3(z_defuse,skc3,skc2),use)** equal(a_select2(rho_defuse,n0),use) equal(a_select2(rho_defuse,n1),use) equal(a_select2(rho_defuse,n2),use) equal(a_select2(sigma_defuse,n0),use) equal(a_select2(sigma_defuse,n1),use) equal(a_select2(sigma_defuse,n2),use) equal(a_select2(sigma_defuse,n3),use) equal(a_select2(sigma_defuse,n4),use) equal(a_select2(sigma_defuse,n5),use) equal(a_select3(u_defuse,n0,n0),use) equal(a_select3(u_defuse,n1,n0),use) equal(a_select3(u_defuse,n2,n0),use) equal(a_select2(xinit_defuse,n3),use) equal(a_select2(xinit_defuse,n4),use) equal(a_select2(xinit_defuse,n5),use) equal(a_select2(xinit_mean_defuse,n0),use) equal(a_select2(xinit_mean_defuse,n1),use) equal(a_select2(xinit_mean_defuse,n2),use) equal(a_select2(xinit_mean_defuse,n3),use) equal(a_select2(xinit_mean_defuse,n4),use) equal(a_select2(xinit_mean_defuse,n5),use) equal(a_select2(xinit_noise_defuse,n0),use) equal(a_select2(xinit_noise_defuse,n1),use) equal(a_select2(xinit_noise_defuse,n2),use) equal(a_select2(xinit_noise_defuse,n3),use) equal(a_select2(xinit_noise_defuse,n4),use) equal(a_select2(xinit_noise_defuse,n5),use) leq(n0,pv5) leq(pv5,minus(n999,n1)) -> .
% 2.88/3.04 189[0:Rew:42.0,74.0] || -> equal(succ(n1),n2)**.
% 2.88/3.04 204[0:Rew:101.0,72.0] || -> leq(pv5,pred(n999))*r.
% 2.88/3.04 205[0:Rew:101.0,47.0] || -> leq(skc2,pred(pv5))*r.
% 2.88/3.04 206[0:Rew:101.0,158.2] || leq(u,n2) leq(v,pred(pv5)) leq(n0,v) leq(n0,u) -> equal(a_select3(z_defuse,u,v),use)**.
% 2.88/3.04 207[0:Rew:101.0,159.2] || leq(u,n2) leq(v,pred(pv5)) leq(n0,v) leq(n0,u) -> equal(a_select3(u_defuse,u,v),use)**.
% 2.88/3.04 208[0:Rew:101.0,186.28,71.0,186.26,70.0,186.25,69.0,186.24,68.0,186.23,67.0,186.22,66.0,186.21,65.0,186.20,64.0,186.19,63.0,186.18,62.0,186.17,61.0,186.16,60.0,186.15,59.0,186.14,58.0,186.13,57.0,186.12,95.0,186.11,94.0,186.10,93.0,186.9,56.0,186.8,55.0,186.7,54.0,186.6,53.0,186.5,52.0,186.4,51.0,186.3,50.0,186.2,49.0,186.1,48.0,186.0] || equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) leq(n0,pv5) leq(pv5,pred(n999))*r -> leq(n0,skc2).
% 2.88/3.04 209[0:Obv:208.26] || leq(n0,pv5) leq(pv5,pred(n999))*r -> leq(n0,skc2).
% 2.88/3.04 210[0:MRR:209.0,209.1,3.0,204.0] || -> leq(n0,skc2)*r.
% 2.88/3.04 211[0:Rew:101.0,187.28,71.0,187.26,70.0,187.25,69.0,187.24,68.0,187.23,67.0,187.22,66.0,187.21,65.0,187.20,64.0,187.19,63.0,187.18,62.0,187.17,61.0,187.16,60.0,187.15,59.0,187.14,58.0,187.13,57.0,187.12,95.0,187.11,94.0,187.10,93.0,187.9,56.0,187.8,55.0,187.7,54.0,187.6,53.0,187.5,52.0,187.4,51.0,187.3,50.0,187.2,49.0,187.1,48.0,187.0] || equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) leq(n0,pv5) leq(pv5,pred(n999))*r -> leq(skc3,n2).
% 2.88/3.04 212[0:Obv:211.26] || leq(n0,pv5) leq(pv5,pred(n999))*r -> leq(skc3,n2).
% 2.88/3.04 213[0:MRR:212.0,212.1,3.0,204.0] || -> leq(skc3,n2)*l.
% 2.88/3.04 214[0:Rew:101.0,188.30,71.0,188.28,70.0,188.27,69.0,188.26,68.0,188.25,67.0,188.24,66.0,188.23,65.0,188.22,64.0,188.21,63.0,188.20,62.0,188.19,61.0,188.18,60.0,188.17,59.0,188.16,58.0,188.15,57.0,188.14,95.0,188.13,94.0,188.12,93.0,188.11,56.0,188.10,55.0,188.9,54.0,188.8,53.0,188.7,52.0,188.6,51.0,188.5,50.0,188.4,49.0,188.3,48.0,188.2] || equal(a_select3(u_defuse,skc3,skc2),use) equal(a_select3(z_defuse,skc3,skc2),use)** equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) equal(use,use) leq(n0,pv5) leq(pv5,pred(n999)) -> .
% 2.88/3.04 215[0:Obv:214.28] || equal(a_select3(u_defuse,skc3,skc2),use) equal(a_select3(z_defuse,skc3,skc2),use)** leq(n0,pv5) leq(pv5,pred(n999)) -> .
% 2.88/3.04 216[0:MRR:215.2,215.3,3.0,204.0] || equal(a_select3(z_defuse,skc3,skc2),use)** equal(a_select3(u_defuse,skc3,skc2),use) -> .
% 2.88/3.04 356[0:Res:3.0,148.0] || leq(pv5,n1)*l -> equal(pv5,n1) equal(pv5,n0).
% 2.88/3.04 389[0:Res:3.0,138.0] || -> gt(pv5,n0)*l equal(pv5,n0).
% 2.88/3.04 390[0:Res:3.0,136.0] || -> leq(succ(n0),succ(pv5))*r.
% 2.88/3.04 391[0:Res:3.0,116.0] || -> leq(n0,succ(pv5))*r.
% 2.88/3.04 454[0:Rew:42.0,390.0] || -> leq(n1,succ(pv5))*r.
% 2.88/3.04 513[1:Spt:356.1] || -> equal(pv5,n1)**.
% 2.88/3.04 514[1:Rew:513.0,206.1] || leq(u,n2) leq(v,pred(n1)) leq(n0,v) leq(n0,u) -> equal(a_select3(z_defuse,u,v),use)**.
% 2.88/3.04 522[1:Rew:513.0,205.0] || -> leq(skc2,pred(n1))*r.
% 2.88/3.04 523[1:Rew:513.0,454.0] || -> leq(n1,succ(n1))*r.
% 2.88/3.04 525[1:Rew:513.0,391.0] || -> leq(n0,succ(n1))*r.
% 2.88/3.04 588[1:Rew:513.0,3.0] || -> leq(n0,n1)*r.
% 2.88/3.04 599[1:Rew:189.0,523.0] || -> leq(n1,n2)*r.
% 2.88/3.04 601[1:Rew:189.0,525.0] || -> leq(n0,n2)*r.
% 2.88/3.04 851[0:SpR:45.0,91.0] || -> equal(pred(n0),tptp_minus_1)**.
% 2.88/3.04 852[0:SpR:42.0,91.0] || -> equal(pred(n1),n0)**.
% 2.88/3.04 859[1:Rew:852.0,522.0] || -> leq(skc2,n0)*l.
% 2.88/3.04 865[1:Rew:852.0,514.1] || leq(u,n2) leq(v,n0) leq(n0,v) leq(n0,u) -> equal(a_select3(z_defuse,u,v),use)**.
% 2.88/3.04 999[0:OCh:144.1,144.0,213.0,2.0] || -> leq(n0,n2)*r.
% 2.88/3.04 1352[0:NCh:143.2,143.1,43.0,15.0] || gt(tptp_minus_1,n0)*l -> .
% 2.88/3.04 1353[0:NCh:143.2,143.1,43.0,15.0] || equal(tptp_minus_1,n0)** -> .
% 2.88/3.04 3491[0:Res:30.0,108.0] || -> leq(n1,n2)*r.
% 2.88/3.04 3498[0:Res:23.0,108.0] || -> leq(n0,n1)*r.
% 2.88/3.04 3506[0:Res:15.0,108.0] || -> leq(tptp_minus_1,n0)*l.
% 2.88/3.04 5637[1:Res:859.0,142.0] || leq(n0,skc2)*r -> equal(skc2,n0).
% 2.88/3.04 5721[1:MRR:5637.0,210.0] || -> equal(skc2,n0)**.
% 2.88/3.04 5724[1:Rew:5721.0,216.0] || equal(a_select3(z_defuse,skc3,n0),use)** equal(a_select3(u_defuse,skc3,skc2),use) -> .
% 2.88/3.04 5804[1:Rew:5721.0,5724.1] || equal(a_select3(z_defuse,skc3,n0),use)** equal(a_select3(u_defuse,skc3,n0),use) -> .
% 2.88/3.04 6237[0:Res:213.0,150.0] || leq(n0,skc3)*r -> equal(skc3,n2) equal(skc3,n1) equal(skc3,n0).
% 2.88/3.04 6319[0:MRR:6237.0,2.0] || -> equal(skc3,n2)** equal(skc3,n1) equal(skc3,n0).
% 2.88/3.04 7756[2:Spt:6319.0] || -> equal(skc3,n2)**.
% 2.88/3.04 7771[2:Rew:7756.0,5804.0] || equal(a_select3(z_defuse,n2,n0),use)** equal(a_select3(u_defuse,skc3,n0),use) -> .
% 2.88/3.04 7933[2:Rew:7756.0,7771.1] || equal(a_select3(z_defuse,n2,n0),use)** equal(a_select3(u_defuse,n2,n0),use) -> .
% 2.88/3.04 7934[2:Rew:95.0,7933.1] || equal(a_select3(z_defuse,n2,n0),use)** equal(use,use) -> .
% 2.88/3.04 7935[2:Obv:7934.1] || equal(a_select3(z_defuse,n2,n0),use)** -> .
% 2.88/3.04 7989[2:SpL:865.4,7935.0] || leq(n2,n2) leq(n0,n0) leq(n0,n0) leq(n0,n2) equal(use,use)* -> .
% 2.88/3.04 7993[2:Obv:7989.4] || leq(n2,n2)* leq(n0,n0) leq(n0,n2) -> .
% 2.88/3.04 7994[2:MRR:7993.0,7993.1,7993.2,41.0,41.0,601.0] || -> .
% 2.88/3.04 7998[2:Spt:7994.0,6319.0,7756.0] || equal(skc3,n2)** -> .
% 2.88/3.04 7999[2:Spt:7994.0,6319.1,6319.2] || -> equal(skc3,n1)** equal(skc3,n0).
% 2.88/3.04 8002[3:Spt:7999.0] || -> equal(skc3,n1)**.
% 2.88/3.04 8119[3:Rew:8002.0,5804.0] || equal(a_select3(z_defuse,n1,n0),use)** equal(a_select3(u_defuse,skc3,n0),use) -> .
% 2.88/3.04 8168[3:Rew:8002.0,8119.1] || equal(a_select3(z_defuse,n1,n0),use)** equal(a_select3(u_defuse,n1,n0),use) -> .
% 2.88/3.04 8169[3:Rew:94.0,8168.1] || equal(a_select3(z_defuse,n1,n0),use)** equal(use,use) -> .
% 2.88/3.04 8170[3:Obv:8169.1] || equal(a_select3(z_defuse,n1,n0),use)** -> .
% 2.88/3.04 8209[3:SpL:865.4,8170.0] || leq(n1,n2) leq(n0,n0) leq(n0,n0) leq(n0,n1) equal(use,use)* -> .
% 2.88/3.04 8210[3:Obv:8209.4] || leq(n1,n2)*r leq(n0,n0) leq(n0,n1) -> .
% 2.88/3.04 8211[3:MRR:8210.0,8210.1,8210.2,599.0,41.0,588.0] || -> .
% 2.88/3.04 8212[3:Spt:8211.0,7999.0,8002.0] || equal(skc3,n1)** -> .
% 2.88/3.04 8213[3:Spt:8211.0,7999.1] || -> equal(skc3,n0)**.
% 2.88/3.04 8282[3:Rew:8213.0,5804.1,8213.0,5804.0] || equal(a_select3(z_defuse,n0,n0),use)** equal(a_select3(u_defuse,n0,n0),use) -> .
% 2.88/3.04 8283[3:Rew:93.0,8282.1] || equal(a_select3(z_defuse,n0,n0),use)** equal(use,use) -> .
% 2.88/3.04 8284[3:Obv:8283.1] || equal(a_select3(z_defuse,n0,n0),use)** -> .
% 2.88/3.04 8377[3:SpL:865.4,8284.0] || leq(n0,n2) leq(n0,n0) leq(n0,n0) leq(n0,n0) equal(use,use)* -> .
% 2.88/3.04 8378[3:Obv:8377.4] || leq(n0,n2)*r leq(n0,n0) -> .
% 2.88/3.04 8379[3:MRR:8378.0,8378.1,601.0,41.0] || -> .
% 2.88/3.04 8380[1:Spt:8379.0,356.1,513.0] || equal(pv5,n1)** -> .
% 2.88/3.04 8381[1:Spt:8379.0,356.0,356.2] || leq(pv5,n1)*l -> equal(pv5,n0).
% 2.88/3.04 8558[2:Spt:389.1] || -> equal(pv5,n0)**.
% 2.88/3.04 8566[2:Rew:8558.0,205.0] || -> leq(skc2,pred(n0))*r.
% 2.88/3.04 8644[2:Rew:851.0,8566.0] || -> leq(skc2,tptp_minus_1)*l.
% 2.88/3.04 8913[2:Res:8644.0,138.0] || -> gt(tptp_minus_1,skc2)*r equal(skc2,tptp_minus_1).
% 2.88/3.04 8925[2:NCh:144.2,144.0,8644.0,142.0] || leq(tptp_minus_1,n0) leq(n0,skc2)*r -> equal(skc2,n0).
% 2.88/3.04 8942[2:MRR:8925.0,8925.1,3506.0,210.0] || -> equal(skc2,n0)**.
% 2.88/3.04 8959[2:Rew:8942.0,8913.0] || -> gt(tptp_minus_1,n0) equal(skc2,tptp_minus_1)**.
% 2.88/3.04 8968[2:Rew:8942.0,8959.1] || -> gt(tptp_minus_1,n0)*l equal(tptp_minus_1,n0).
% 2.88/3.04 8969[2:MRR:8968.0,8968.1,1352.0,1353.0] || -> .
% 2.88/3.04 8984[2:Spt:8969.0,389.1,8558.0] || equal(pv5,n0)** -> .
% 2.88/3.04 8985[2:Spt:8969.0,389.0] || -> gt(pv5,n0)*l.
% 2.88/3.04 9438[3:Spt:6319.0] || -> equal(skc3,n2)**.
% 2.88/3.04 9455[3:Rew:9438.0,216.0] || equal(a_select3(z_defuse,n2,skc2),use)** equal(a_select3(u_defuse,skc3,skc2),use) -> .
% 2.88/3.04 9616[3:Rew:9438.0,9455.1] || equal(a_select3(z_defuse,n2,skc2),use)** equal(a_select3(u_defuse,n2,skc2),use) -> .
% 2.88/3.04 9675[3:SpL:206.4,9616.0] || leq(n2,n2) leq(skc2,pred(pv5)) leq(n0,skc2) leq(n0,n2) equal(use,use) equal(a_select3(u_defuse,n2,skc2),use)** -> .
% 2.88/3.04 9676[3:Obv:9675.4] || leq(n2,n2) leq(skc2,pred(pv5)) leq(n0,skc2) leq(n0,n2) equal(a_select3(u_defuse,n2,skc2),use)** -> .
% 2.88/3.04 9677[3:Rew:207.4,9676.4] || leq(n2,n2) leq(skc2,pred(pv5))*r leq(n0,skc2) leq(n0,n2) equal(use,use) -> .
% 2.88/3.04 9678[3:Obv:9677.4] || leq(n2,n2) leq(skc2,pred(pv5))*r leq(n0,skc2) leq(n0,n2) -> .
% 2.88/3.04 9679[3:MRR:9678.0,9678.1,9678.2,9678.3,41.0,205.0,210.0,999.0] || -> .
% 2.88/3.04 9683[3:Spt:9679.0,6319.0,9438.0] || equal(skc3,n2)** -> .
% 2.88/3.04 9684[3:Spt:9679.0,6319.1,6319.2] || -> equal(skc3,n1)** equal(skc3,n0).
% 2.88/3.04 9687[4:Spt:9684.0] || -> equal(skc3,n1)**.
% 2.88/3.04 9804[4:Rew:9687.0,216.0] || equal(a_select3(z_defuse,n1,skc2),use)** equal(a_select3(u_defuse,skc3,skc2),use) -> .
% 2.88/3.04 9853[4:Rew:9687.0,9804.1] || equal(a_select3(z_defuse,n1,skc2),use)** equal(a_select3(u_defuse,n1,skc2),use) -> .
% 2.88/3.04 9914[4:SpL:206.4,9853.0] || leq(n1,n2) leq(skc2,pred(pv5)) leq(n0,skc2) leq(n0,n1) equal(use,use) equal(a_select3(u_defuse,n1,skc2),use)** -> .
% 2.88/3.04 9915[4:Obv:9914.4] || leq(n1,n2) leq(skc2,pred(pv5)) leq(n0,skc2) leq(n0,n1) equal(a_select3(u_defuse,n1,skc2),use)** -> .
% 2.88/3.04 9916[4:Rew:207.4,9915.4] || leq(n1,n2) leq(skc2,pred(pv5))*r leq(n0,skc2) leq(n0,n1) equal(use,use) -> .
% 2.88/3.07 9917[4:Obv:9916.4] || leq(n1,n2) leq(skc2,pred(pv5))*r leq(n0,skc2) leq(n0,n1) -> .
% 2.88/3.07 9918[4:MRR:9917.0,9917.1,9917.2,9917.3,3491.0,205.0,210.0,3498.0] || -> .
% 2.88/3.07 9919[4:Spt:9918.0,9684.0,9687.0] || equal(skc3,n1)** -> .
% 2.88/3.07 9920[4:Spt:9918.0,9684.1] || -> equal(skc3,n0)**.
% 2.88/3.07 10004[4:Rew:9920.0,216.1,9920.0,216.0] || equal(a_select3(z_defuse,n0,skc2),use)** equal(a_select3(u_defuse,n0,skc2),use) -> .
% 2.88/3.07 10161[4:SpL:206.4,10004.0] || leq(n0,n2) leq(skc2,pred(pv5)) leq(n0,skc2) leq(n0,n0) equal(use,use) equal(a_select3(u_defuse,n0,skc2),use)** -> .
% 2.88/3.07 10162[4:Obv:10161.4] || leq(n0,n2) leq(skc2,pred(pv5)) leq(n0,skc2) leq(n0,n0) equal(a_select3(u_defuse,n0,skc2),use)** -> .
% 2.88/3.07 10163[4:Rew:207.4,10162.4] || leq(n0,n2) leq(skc2,pred(pv5))*r leq(n0,skc2) leq(n0,n0) equal(use,use) -> .
% 2.88/3.07 10164[4:Obv:10163.4] || leq(n0,n2) leq(skc2,pred(pv5))*r leq(n0,skc2) leq(n0,n0) -> .
% 2.88/3.07 10165[4:MRR:10164.0,10164.1,10164.2,10164.3,999.0,205.0,210.0,41.0] || -> .
% 2.88/3.07 % SZS output end Refutation
% 2.88/3.07 Formulae used in the proof : quaternion_ds1_inuse_0008 gt_succ leq_succ_gt_equiv gt_0_tptp_minus_1 gt_1_0 gt_2_1 reflexivity_leq successor_1 irreflexivity_gt succ_tptp_minus_1 successor_2 pred_succ pred_minus_1 leq_gt1 leq_succ leq_succ_succ leq_gt2 finite_domain_0 transitivity_gt transitivity_leq finite_domain_1 finite_domain_2
% 2.88/3.07
%------------------------------------------------------------------------------