TSTP Solution File: GRP292-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP292-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Sat Jul 16 11:46:43 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP292-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 10:41:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 688 clauses, backtracked 202 clauses, performed 8 splits and kept 496 clauses.
% 0.20/0.47 SPASS allocated 63530 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.20/0.47 0:00:00.03 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.01 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.04 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 5, length 217 :
% 0.20/0.47 % SZS output start Refutation
% 0.20/0.47 1[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.47 2[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.47 3[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.47 4[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.47 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.47 9[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.47 11[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 12[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.47 13[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 14[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 15[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 16[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 17[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.47 18[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.20/0.47 19[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.47 20[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.47 21[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c5) equal(inverse(x),sk_c7) equal(multiply(u,v),sk_c6)**+ equal(multiply(v,sk_c5),sk_c6)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 22[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.47 23[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.47 24[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.47 25[1:Spt:21.0,21.3,21.4] || equal(inverse(u),v) equal(multiply(u,v),sk_c6)**+ equal(multiply(v,sk_c5),sk_c6)** -> .
% 0.20/0.47 26[2:Spt:1.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.47 29[3:Spt:3.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.20/0.47 33[4:Spt:2.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.20/0.47 35[4:SpL:33.0,25.1] || equal(inverse(sk_c3),sk_c4) equal(sk_c6,sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.20/0.47 36[4:Obv:35.1] || equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.20/0.47 37[4:Rew:29.0,36.0] || equal(sk_c4,sk_c4) equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.20/0.47 38[4:Obv:37.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.20/0.47 39[4:MRR:20.1,38.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.47 40[4:MRR:12.1,38.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 41[4:MRR:16.0,38.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 59[3:SpR:29.0,23.0] || -> equal(multiply(sk_c4,sk_c3),identity)**.
% 0.20/0.47 60[4:SpR:39.0,23.0] || -> equal(multiply(sk_c5,sk_c2),identity)**.
% 0.20/0.47 61[4:SpR:40.0,23.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.20/0.47 62[1:SpL:23.0,25.1] || equal(inverse(inverse(u)),u) equal(identity,sk_c6) equal(multiply(u,sk_c5),sk_c6)** -> .
% 0.20/0.47 66[4:SpL:60.0,25.1] || equal(inverse(sk_c5),sk_c2) equal(identity,sk_c6) equal(multiply(sk_c2,sk_c5),sk_c6)** -> .
% 0.20/0.47 67[4:Rew:41.0,66.2] || equal(inverse(sk_c5),sk_c2)** equal(identity,sk_c6) equal(sk_c6,sk_c6) -> .
% 0.20/0.47 68[4:Obv:67.2] || equal(inverse(sk_c5),sk_c2)** equal(identity,sk_c6) -> .
% 0.20/0.47 77[0:SpR:23.0,24.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.47 80[3:SpR:59.0,24.0] || -> equal(multiply(sk_c4,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.20/0.47 81[4:SpR:60.0,24.0] || -> equal(multiply(sk_c5,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.20/0.47 84[3:Rew:22.0,80.0] || -> equal(multiply(sk_c4,multiply(sk_c3,u)),u)**.
% 0.20/0.47 85[4:Rew:22.0,81.0] || -> equal(multiply(sk_c5,multiply(sk_c2,u)),u)**.
% 0.20/0.47 87[0:Rew:22.0,77.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.47 91[4:SpR:33.0,84.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.20/0.47 100[4:SpR:41.0,85.0] || -> equal(multiply(sk_c5,sk_c6),sk_c5)**.
% 0.20/0.47 102[4:Rew:26.0,100.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 111[4:Rew:102.0,60.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.20/0.47 112[4:Rew:102.0,68.0] || equal(inverse(sk_c7),sk_c2)** equal(identity,sk_c6) -> .
% 0.20/0.47 145[0:SpR:87.0,87.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.47 148[0:SpR:23.0,87.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.47 154[4:SpR:91.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.20/0.47 155[4:SpR:61.0,87.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.20/0.47 157[4:SpR:111.0,87.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c2)**.
% 0.20/0.47 165[4:Rew:23.0,154.0] || -> equal(identity,sk_c6)**.
% 0.20/0.47 174[4:Rew:165.0,112.1] || equal(inverse(sk_c7),sk_c2)** equal(sk_c6,sk_c6) -> .
% 0.20/0.47 185[4:Rew:165.0,155.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c1)**.
% 0.20/0.47 186[4:Rew:185.0,157.0,165.0,157.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.47 192[4:Rew:165.0,148.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.20/0.47 196[4:Rew:145.0,192.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 197[4:Rew:196.0,185.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.47 201[4:Obv:174.1] || equal(inverse(sk_c7),sk_c2)** -> .
% 0.20/0.47 202[4:Rew:197.0,201.0,186.0,201.0] || equal(sk_c1,sk_c1)* -> .
% 0.20/0.47 203[4:Obv:202.0] || -> .
% 0.20/0.47 210[4:Spt:203.0,2.0,33.0] || equal(multiply(sk_c3,sk_c4),sk_c6)** -> .
% 0.20/0.47 211[4:Spt:203.0,2.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.47 213[0:Rew:145.0,148.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.47 214[4:MRR:18.1,210.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.47 216[4:MRR:14.0,210.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 226[2:SpR:26.0,87.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.20/0.47 238[4:SpR:216.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.47 240[4:Rew:26.0,238.0,214.0,238.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 246[4:Rew:240.0,62.2] || equal(inverse(inverse(u)),u) equal(identity,sk_c6) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 250[4:Rew:240.0,226.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.47 257[4:Rew:23.0,250.0] || -> equal(identity,sk_c6)**.
% 0.20/0.47 260[4:Rew:257.0,23.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.47 262[4:Rew:257.0,213.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 271[4:Rew:257.0,246.1] || equal(inverse(inverse(u)),u) equal(sk_c6,sk_c6) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 272[4:Obv:271.1] || equal(inverse(inverse(u)),u) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 306[4:SpR:260.0,87.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.20/0.47 316[4:Rew:262.0,306.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.47 318[4:Rew:316.0,272.0] || equal(u,u) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 320[4:Obv:318.0] || equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 321[4:UnC:320.0,260.0] || -> .
% 0.20/0.47 323[3:Spt:321.0,3.0,29.0] || equal(inverse(sk_c3),sk_c4)** -> .
% 0.20/0.47 324[3:Spt:321.0,3.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.47 325[3:MRR:19.0,323.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.47 327[3:MRR:15.0,323.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 340[3:SpR:327.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.47 342[3:Rew:26.0,340.0,325.0,340.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 347[3:Rew:342.0,226.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.47 350[3:Rew:342.0,62.2] || equal(inverse(inverse(u)),u) equal(identity,sk_c6) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 357[3:Rew:23.0,347.0] || -> equal(identity,sk_c6)**.
% 0.20/0.47 358[3:Rew:357.0,213.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 361[3:Rew:357.0,23.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.47 368[3:Rew:357.0,350.1] || equal(inverse(inverse(u)),u) equal(sk_c6,sk_c6) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 369[3:Obv:368.1] || equal(inverse(inverse(u)),u) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 395[3:SpR:361.0,87.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.20/0.47 402[3:Rew:358.0,395.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.47 404[3:Rew:402.0,369.0] || equal(u,u) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 406[3:Obv:404.0] || equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.47 407[3:UnC:406.0,361.0] || -> .
% 0.20/0.47 409[2:Spt:407.0,1.0,26.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.47 410[2:Spt:407.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.47 411[2:MRR:17.1,409.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.47 412[2:MRR:9.1,409.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 413[2:MRR:13.0,409.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 414[2:MRR:5.0,409.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.47 423[2:SpR:413.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.47 425[2:Rew:411.0,423.0] || -> equal(multiply(sk_c5,sk_c6),sk_c5)**.
% 0.20/0.47 426[2:Rew:425.0,409.0] || equal(sk_c5,sk_c7)** -> .
% 0.20/0.47 428[2:SpR:414.0,87.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.47 430[2:Rew:410.0,428.0,412.0,428.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 431[2:MRR:430.0,426.0] || -> .
% 0.20/0.47 432[1:Spt:431.0,21.1,21.2,21.5,21.6,21.7,21.8] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.47 434[2:Spt:1.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.47 435[2:Rew:434.0,432.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(sk_c7,sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.20/0.47 437[2:Obv:435.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.20/0.47 440[2:SpR:434.0,87.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.20/0.47 442[3:Spt:3.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.20/0.47 445[4:Spt:4.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.47 447[4:SpR:445.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.20/0.47 452[5:Spt:2.0] || -> equal(multiply(sk_c3,sk_c4),sk_c6)**.
% 0.20/0.47 454[5:SpR:452.0,87.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c4)**.
% 0.20/0.47 456[5:Rew:442.0,454.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.20/0.47 458[5:SpR:456.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.20/0.48 460[5:Rew:23.0,458.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 462[5:Rew:460.0,213.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 463[5:Rew:460.0,23.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 468[5:Rew:462.0,434.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 471[5:Rew:462.0,437.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(sk_c5,sk_c7) -> .
% 0.20/0.48 478[5:Rew:468.0,471.4,468.0,471.2,468.0,471.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.20/0.48 479[5:Obv:478.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.20/0.48 480[5:Con:479.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.48 501[5:SpR:463.0,87.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.20/0.48 507[5:Rew:462.0,501.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.48 512[5:SpL:463.0,480.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.48 519[5:Obv:512.1] || equal(inverse(inverse(sk_c7)),sk_c7)** -> .
% 0.20/0.48 520[5:Rew:507.0,519.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.48 521[5:Obv:520.0] || -> .
% 0.20/0.48 522[5:Spt:521.0,2.0,452.0] || equal(multiply(sk_c3,sk_c4),sk_c6)** -> .
% 0.20/0.48 523[5:Spt:521.0,2.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 524[5:MRR:18.1,522.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 526[5:MRR:14.0,522.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 546[5:SpR:526.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 548[5:Rew:434.0,546.0,524.0,546.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 554[5:Rew:548.0,447.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.48 555[5:Rew:548.0,440.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.48 563[5:Rew:23.0,555.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 565[5:Rew:563.0,213.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 567[5:Rew:563.0,23.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 568[5:Rew:565.0,554.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.48 621[5:SpR:442.0,567.0] || -> equal(multiply(sk_c4,sk_c3),sk_c6)**.
% 0.20/0.48 624[5:SpR:568.0,567.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.20/0.48 630[5:SpR:621.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c3)**.
% 0.20/0.48 632[5:Rew:565.0,630.0,568.0,630.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.48 634[5:Rew:632.0,522.0] || equal(multiply(sk_c7,sk_c4),sk_c6)** -> .
% 0.20/0.48 637[5:Rew:624.0,634.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.48 638[5:Obv:637.0] || -> .
% 0.20/0.48 641[4:Spt:638.0,4.0,445.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.20/0.48 642[4:Spt:638.0,4.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 643[4:MRR:20.1,641.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 644[4:MRR:12.1,641.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 645[4:MRR:16.0,641.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 647[4:Rew:642.0,437.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.48 648[4:Obv:647.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.20/0.48 664[4:SpR:645.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 666[4:Rew:434.0,664.0,643.0,664.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 671[4:Rew:666.0,440.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.48 674[4:Rew:666.0,648.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.20/0.48 679[4:Rew:23.0,671.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 680[4:Rew:679.0,213.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 682[4:Rew:679.0,23.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 687[4:Rew:666.0,674.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.20/0.48 688[4:Con:687.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.48 718[4:SpR:644.0,682.0] || -> equal(multiply(sk_c7,sk_c1),sk_c6)**.
% 0.20/0.48 729[4:SpR:718.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c1)**.
% 0.20/0.48 731[4:Rew:680.0,729.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.48 794[4:SpL:682.0,688.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.48 800[4:Obv:794.1] || equal(inverse(inverse(sk_c7)),sk_c7)** -> .
% 0.20/0.48 801[4:Rew:644.0,800.0,731.0,800.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.48 802[4:Obv:801.0] || -> .
% 0.20/0.48 803[3:Spt:802.0,3.0,442.0] || equal(inverse(sk_c3),sk_c4)** -> .
% 0.20/0.48 804[3:Spt:802.0,3.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 805[3:MRR:19.0,803.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 806[3:MRR:11.0,803.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 807[3:MRR:15.0,803.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 809[3:Rew:804.0,437.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.48 810[3:Obv:809.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.20/0.48 824[3:SpR:807.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 826[3:Rew:434.0,824.0,805.0,824.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 831[3:Rew:826.0,440.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.48 833[3:Rew:826.0,810.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.20/0.48 838[3:Rew:23.0,831.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 840[3:Rew:838.0,213.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 842[3:Rew:838.0,23.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 846[3:Rew:826.0,833.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.20/0.48 847[3:Con:846.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.20/0.48 887[3:SpR:806.0,842.0] || -> equal(multiply(sk_c7,sk_c1),sk_c6)**.
% 0.20/0.48 894[3:SpR:887.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c1)**.
% 0.20/0.48 896[3:Rew:840.0,894.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.48 976[3:SpL:842.0,847.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.48 982[3:Obv:976.1] || equal(inverse(inverse(sk_c7)),sk_c7)** -> .
% 0.20/0.48 983[3:Rew:806.0,982.0,896.0,982.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.48 984[3:Obv:983.0] || -> .
% 0.20/0.48 985[2:Spt:984.0,1.0,434.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.48 986[2:Spt:984.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.48 987[2:MRR:17.1,985.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.20/0.48 988[2:MRR:9.1,985.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.48 989[2:MRR:13.0,985.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.48 990[2:MRR:5.0,985.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.48 999[2:SpR:989.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.48 1001[2:Rew:987.0,999.0] || -> equal(multiply(sk_c5,sk_c6),sk_c5)**.
% 0.20/0.48 1002[2:Rew:1001.0,985.0] || equal(sk_c5,sk_c7)** -> .
% 0.20/0.48 1004[2:SpR:990.0,87.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.48 1006[2:Rew:986.0,1004.0,988.0,1004.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.48 1007[2:MRR:1006.0,1002.0] || -> .
% 0.20/0.48 % SZS output end Refutation
% 0.20/0.48 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_9 prove_this_11 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 left_identity left_inverse associativity
% 0.20/0.48
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