TSTP Solution File: GRP294-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP294-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 : Sat Jul 16 11:46:43 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP294-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 08:52:39 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 570 clauses, backtracked 262 clauses, performed 10 splits and kept 519 clauses.
% 0.21/0.47 SPASS allocated 63503 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.47 0:00:00.04 for the input.
% 0.21/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.00 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.05 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 3, length 256 :
% 0.21/0.47 % SZS output start Refutation
% 0.21/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.21/0.47 3[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.21/0.47 7[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 8[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 10[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 12[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.47 13[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 14[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 15[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.47 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.21/0.47 17[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.21/0.47 18[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.21/0.47 21[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c2,sk_c7),sk_c5).
% 0.21/0.47 22[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 23[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 25[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 26[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 27[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.47 28[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 29[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 30[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.47 31[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c5)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.47 35[1:Spt:31.0,31.4] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c5),sk_c6)** -> .
% 0.21/0.47 36[2:Spt:16.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 38[3:Spt:19.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.47 44[4:Spt:20.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.47 46[4:SpL:44.0,35.1] || equal(inverse(sk_c4),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.21/0.47 47[4:Obv:46.1] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.21/0.47 48[4:Rew:38.0,47.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.47 49[4:Obv:48.0] || -> .
% 0.21/0.47 50[4:Spt:49.0,20.0,44.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.21/0.47 51[4:Spt:49.0,20.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 52[4:MRR:30.1,50.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 53[4:MRR:15.1,50.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 54[4:MRR:25.0,50.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 55[4:MRR:10.0,50.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 56[4:MRR:5.0,50.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 66[3:SpR:38.0,33.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.21/0.47 70[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c5)),sk_c6)** equal(sk_c6,identity) -> .
% 0.21/0.47 78[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.47 81[0:Rew:32.0,78.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.47 96[0:SpR:81.0,81.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.47 99[2:SpR:36.0,81.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.21/0.47 100[4:SpR:54.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 101[4:SpR:55.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.21/0.47 103[0:SpR:33.0,81.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.47 104[4:SpR:56.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.21/0.47 114[4:Rew:51.0,100.0,52.0,100.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 116[4:Rew:114.0,36.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.47 123[4:Rew:114.0,50.0] || equal(multiply(sk_c4,sk_c5),sk_c7)** -> .
% 0.21/0.47 124[4:Rew:114.0,66.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.21/0.47 137[4:Rew:53.0,101.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.47 138[4:Rew:116.0,137.0,114.0,137.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 143[4:Rew:138.0,104.0,114.0,104.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.47 144[4:Rew:33.0,143.0] || -> equal(identity,sk_c7)**.
% 0.21/0.47 145[4:Rew:144.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.47 149[4:Rew:144.0,124.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.21/0.47 162[4:Rew:145.0,149.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.47 174[4:Rew:145.0,123.0,162.0,123.0,138.0,123.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.47 175[4:Obv:174.0] || -> .
% 0.21/0.47 198[3:Spt:175.0,19.0,38.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.21/0.47 199[3:Spt:175.0,19.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 200[0:Rew:96.0,103.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.47 201[3:MRR:29.0,198.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 202[3:MRR:14.0,198.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 203[3:MRR:24.0,198.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 204[3:MRR:9.0,198.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 207[3:SpR:199.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.47 217[3:SpR:203.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 219[3:Rew:199.0,217.0,201.0,217.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 221[3:Rew:219.0,36.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.47 223[3:Rew:219.0,99.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.21/0.47 226[3:Rew:219.0,204.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.47 228[3:Rew:219.0,70.0] || equal(inverse(inverse(sk_c5)),sk_c7)** equal(sk_c6,identity) -> .
% 0.21/0.47 231[3:Rew:219.0,207.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.21/0.47 233[3:Rew:33.0,231.0] || -> equal(identity,sk_c5)**.
% 0.21/0.47 237[3:Rew:233.0,200.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.47 238[3:Rew:237.0,223.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.47 243[3:Rew:219.0,228.1,233.0,228.1] || equal(inverse(inverse(sk_c5)),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.21/0.47 256[3:SpR:226.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.47 258[3:Rew:221.0,256.0,202.0,256.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 266[3:Rew:258.0,243.0] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.21/0.47 280[3:Rew:238.0,266.0,238.0,266.0] || equal(sk_c7,sk_c7) equal(sk_c5,sk_c7)** -> .
% 0.21/0.47 281[3:Obv:280.0] || equal(sk_c5,sk_c7)** -> .
% 0.21/0.47 282[3:Rew:258.0,281.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.47 283[3:Obv:282.0] || -> .
% 0.21/0.47 284[2:Spt:283.0,16.0,36.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.21/0.47 285[2:Spt:283.0,16.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 286[2:MRR:26.1,284.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 288[2:MRR:21.0,284.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 290[2:MRR:1.0,284.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 299[2:SpR:288.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 301[2:Rew:285.0,299.0,286.0,299.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 303[2:Rew:301.0,284.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.21/0.47 307[2:Rew:301.0,290.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.47 312[2:Rew:307.0,303.0] || equal(sk_c5,sk_c5)* -> .
% 0.21/0.47 313[2:Obv:312.0] || -> .
% 0.21/0.47 325[1:Spt:313.0,31.1,31.2,31.3,31.5,31.6,31.7,31.8,31.9,31.10] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.47 327[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.47 328[2:Rew:327.0,325.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.21/0.47 330[2:Obv:328.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.21/0.47 333[2:SpR:327.0,81.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.21/0.47 335[3:Spt:18.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.47 336[3:SpR:335.0,81.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.21/0.47 338[4:Spt:19.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.47 341[5:Spt:17.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.47 343[5:SpR:341.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.21/0.47 345[5:Rew:327.0,343.0,335.0,343.0] || -> equal(sk_c6,sk_c5)**.
% 0.21/0.47 347[5:Rew:345.0,335.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.47 348[5:Rew:345.0,338.0] || -> equal(inverse(sk_c4),sk_c5)**.
% 0.21/0.47 349[5:Rew:345.0,341.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.21/0.47 351[5:Rew:345.0,330.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c5) equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.21/0.47 354[5:Rew:345.0,10.0] || -> equal(multiply(sk_c4,sk_c5),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 356[5:Rew:345.0,15.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c5)**.
% 0.21/0.47 358[5:Rew:345.0,333.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.21/0.47 362[5:Rew:33.0,358.0] || -> equal(identity,sk_c7)**.
% 0.21/0.47 363[5:Rew:362.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.47 364[5:Rew:362.0,200.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.47 365[5:Rew:362.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.21/0.47 370[5:Rew:364.0,354.1,345.0,354.1] || -> equal(multiply(sk_c4,sk_c5),sk_c5)** equal(sk_c1,sk_c5).
% 0.21/0.47 371[5:Rew:370.1,356.0] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c5)**.
% 0.21/0.47 374[5:Rew:345.0,351.7,363.0,351.7,363.0,351.6,364.0,351.5,345.0,351.5,364.0,351.4,345.0,351.3,345.0,351.0] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(multiply(u,sk_c5),sk_c7)** equal(v,sk_c5) equal(w,sk_c5) equal(sk_c5,sk_c5) equal(sk_c5,sk_c5) -> .
% 0.21/0.47 375[5:Obv:374.7] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(multiply(u,sk_c5),sk_c7)** equal(v,sk_c5) equal(w,sk_c5) -> .
% 0.21/0.47 376[5:Con:375.2] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7)** equal(multiply(u,sk_c5),sk_c7)** equal(v,sk_c5) -> .
% 0.21/0.47 392[5:SpR:347.0,365.0] || -> equal(multiply(sk_c5,sk_c3),sk_c7)**.
% 0.21/0.47 393[5:SpR:348.0,365.0] || -> equal(multiply(sk_c5,sk_c4),sk_c7)**.
% 0.21/0.47 403[5:SpR:392.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c3)**.
% 0.21/0.47 405[5:Rew:364.0,403.0] || -> equal(inverse(sk_c5),sk_c3)**.
% 0.21/0.47 406[5:Rew:405.0,371.0] || -> equal(sk_c3,sk_c7) equal(multiply(sk_c4,sk_c5),sk_c5)**.
% 0.21/0.47 412[5:SpR:393.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c4)**.
% 0.21/0.47 414[5:Rew:405.0,412.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.21/0.47 415[5:Rew:364.0,414.0] || -> equal(sk_c4,sk_c3)**.
% 0.21/0.47 419[5:Rew:415.0,406.1] || -> equal(sk_c3,sk_c7) equal(multiply(sk_c3,sk_c5),sk_c5)**.
% 0.21/0.47 422[5:Rew:349.0,419.1] || -> equal(sk_c3,sk_c7)** equal(sk_c5,sk_c7).
% 0.21/0.47 427[6:Spt:422.1] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 429[6:Rew:427.0,347.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.47 430[6:Rew:427.0,349.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.47 435[6:Rew:427.0,376.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7)** equal(multiply(u,sk_c5),sk_c7)** equal(v,sk_c5) -> .
% 0.21/0.47 438[6:Rew:364.0,430.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.47 440[6:Rew:438.0,429.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.47 448[6:Rew:427.0,435.3,364.0,435.2,427.0,435.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.47 449[6:Con:448.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.47 460[6:SpL:440.0,449.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.47 461[6:Obv:460.1] || -> .
% 0.21/0.47 462[6:Spt:461.0,422.1,427.0] || equal(sk_c5,sk_c7)** -> .
% 0.21/0.47 463[6:Spt:461.0,422.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.47 469[6:Rew:463.0,349.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.47 470[6:Rew:363.0,469.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 471[6:MRR:470.0,462.0] || -> .
% 0.21/0.47 477[5:Spt:471.0,17.0,341.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.21/0.47 478[5:Spt:471.0,17.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 479[5:MRR:27.1,477.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 480[5:MRR:12.1,477.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 481[5:MRR:22.0,477.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 482[5:MRR:7.0,477.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 489[5:SpR:478.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.47 500[5:SpR:481.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 502[5:Rew:478.0,500.0,479.0,500.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 506[5:Rew:502.0,327.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.47 508[5:Rew:502.0,477.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.21/0.47 510[5:Rew:502.0,336.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.21/0.47 512[5:Rew:502.0,482.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.47 516[5:Rew:502.0,489.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.21/0.47 518[5:Rew:33.0,516.0] || -> equal(identity,sk_c5)**.
% 0.21/0.47 519[5:Rew:518.0,200.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.47 520[5:Rew:518.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.47 537[5:SpR:512.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.47 539[5:Rew:480.0,537.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.47 540[5:Rew:506.0,539.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.47 544[5:Rew:540.0,519.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.47 545[5:Rew:540.0,520.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.47 551[5:Rew:544.0,508.0] || equal(sk_c3,sk_c7)** -> .
% 0.21/0.47 558[5:Rew:545.0,510.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.47 587[5:SpR:558.0,544.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.47 589[5:MRR:587.0,551.0] || -> .
% 0.21/0.47 591[4:Spt:589.0,19.0,338.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.21/0.47 592[4:Spt:589.0,19.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.47 593[4:MRR:29.0,591.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.47 594[4:MRR:14.0,591.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.47 595[4:MRR:24.0,591.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.47 596[4:MRR:9.0,591.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.47 597[4:MRR:4.0,591.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.47 598[4:Rew:597.0,330.7,592.0,330.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c6,sk_c6) equal(sk_c5,sk_c5) -> .
% 0.21/0.47 599[4:Obv:598.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.47 603[4:SpR:592.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.47 615[4:SpR:595.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.47 617[4:Rew:592.0,615.0,593.0,615.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.47 620[4:Rew:617.0,327.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.47 622[4:Rew:617.0,333.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.21/0.47 625[4:Rew:617.0,596.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.47 627[4:Rew:617.0,599.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.47 629[4:Rew:617.0,603.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.21/0.48 631[4:Rew:33.0,629.0] || -> equal(identity,sk_c5)**.
% 0.21/0.48 633[4:Rew:631.0,200.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.48 636[4:Rew:633.0,622.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 640[4:Rew:617.0,627.5,617.0,627.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.21/0.48 641[4:Con:640.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** -> .
% 0.21/0.48 655[4:SpR:625.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.48 657[4:Rew:620.0,655.0,594.0,655.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 662[4:Rew:657.0,633.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.48 665[4:Rew:657.0,641.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.21/0.48 680[4:Con:665.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.21/0.48 681[4:Rew:662.0,680.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 745[4:SpL:636.0,681.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 747[4:Obv:745.1] || -> .
% 0.21/0.48 748[3:Spt:747.0,18.0,335.0] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.21/0.48 749[3:Spt:747.0,18.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.48 750[3:MRR:28.0,748.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.48 751[3:MRR:13.0,748.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 752[3:MRR:23.0,748.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.48 753[3:MRR:8.0,748.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 754[3:MRR:3.0,748.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 755[3:Rew:754.0,330.7,749.0,330.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c6,sk_c6) equal(sk_c5,sk_c5) -> .
% 0.21/0.48 756[3:Obv:755.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 760[3:SpR:749.0,81.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.48 770[3:SpR:752.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.48 772[3:Rew:749.0,770.0,750.0,770.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 774[3:Rew:772.0,327.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.48 776[3:Rew:772.0,333.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.21/0.48 778[3:Rew:772.0,753.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.48 780[3:Rew:772.0,756.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 782[3:Rew:772.0,760.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.21/0.48 784[3:Rew:33.0,782.0] || -> equal(identity,sk_c5)**.
% 0.21/0.48 785[3:Rew:784.0,200.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.48 789[3:Rew:785.0,776.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 793[3:Rew:772.0,780.5,772.0,780.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.21/0.48 794[3:Con:793.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** -> .
% 0.21/0.48 806[3:SpR:778.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.48 808[3:Rew:774.0,806.0,751.0,806.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 812[3:Rew:808.0,785.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.48 816[3:Rew:808.0,794.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.21/0.48 830[3:Con:816.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.21/0.48 831[3:Rew:812.0,830.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 860[3:SpL:789.0,831.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 862[3:Obv:860.1] || -> .
% 0.21/0.48 863[2:Spt:862.0,1.0,327.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.21/0.48 864[2:Spt:862.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 865[2:MRR:26.1,863.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.48 867[2:MRR:21.0,863.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.21/0.48 869[2:MRR:16.0,863.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.48 878[2:SpR:867.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.21/0.48 880[2:Rew:865.0,878.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.48 881[2:Rew:869.0,880.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 882[2:Rew:881.0,864.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.48 883[2:Rew:881.0,863.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.21/0.48 888[2:Rew:882.0,883.0] || equal(sk_c5,sk_c5)* -> .
% 0.21/0.48 889[2:Obv:888.0] || -> .
% 0.21/0.48 % SZS output end Refutation
% 0.21/0.48 Formulae used in the proof : prove_this_1 prove_this_3 prove_this_4 prove_this_5 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.21/0.48
%------------------------------------------------------------------------------