TSTP Solution File: GRP267-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP267-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 11:46:36 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP267-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 : Tue Jun 14 05:10:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 410 clauses, backtracked 123 clauses, performed 7 splits and kept 286 clauses.
% 0.19/0.43 SPASS allocated 63405 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.43 0:00:00.03 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.03 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 4, length 161 :
% 0.19/0.43 % SZS output start Refutation
% 0.19/0.43 1[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.19/0.43 2[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.43 4[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.43 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.43 7[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.43 8[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.43 9[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.43 10[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.43 11[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.43 12[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.43 13[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.19/0.43 14[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.19/0.43 15[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.19/0.43 16[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.19/0.43 17[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.19/0.43 18[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.19/0.43 19[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.43 20[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.43 21[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.43 22[0:Inp] || equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(v,sk_c6),sk_c7)** equal(inverse(v),sk_c6) equal(multiply(sk_c7,w),sk_c6)** equal(multiply(x,sk_c7),w)* equal(inverse(x),sk_c7) equal(multiply(y,sk_c8),sk_c7)** equal(inverse(y),sk_c8) equal(inverse(sk_c6),sk_c7) -> .
% 0.19/0.43 23[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.43 24[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.43 25[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.43 26[0:Con:22.7] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c8) equal(inverse(sk_c6),sk_c7) equal(multiply(u,sk_c7),x)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,x),sk_c6)** -> .
% 0.19/0.43 27[1:Spt:26.2,26.6] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.19/0.43 30[2:Spt:20.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.43 34[3:Spt:10.1] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.43 36[3:SpL:34.0,27.1] || equal(inverse(sk_c5),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.19/0.43 37[3:Obv:36.1] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.43 38[3:Rew:30.0,37.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.43 39[3:Obv:38.0] || -> .
% 0.19/0.43 40[3:Spt:39.0,10.1,34.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.19/0.43 41[3:Spt:39.0,10.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.43 43[3:MRR:4.1,40.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.43 47[3:MRR:1.0,40.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.43 55[3:SpL:47.0,27.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.19/0.43 56[3:Obv:55.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.43 57[3:Rew:43.0,56.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.43 58[3:Obv:57.0] || -> .
% 0.19/0.43 59[2:Spt:58.0,20.0,30.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.43 60[2:Spt:58.0,20.1] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.43 62[2:MRR:5.0,59.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.43 66[2:MRR:2.0,59.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.43 74[2:SpL:66.0,27.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.19/0.43 75[2:Obv:74.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.43 76[2:Rew:62.0,75.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.43 77[2:Obv:76.0] || -> .
% 0.19/0.43 78[1:Spt:77.0,26.0,26.1,26.3,26.4,26.5,26.7] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(sk_c6),sk_c7) equal(multiply(u,sk_c7),w)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,w),sk_c6)** -> .
% 0.19/0.43 79[1:EqR:78.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(sk_c6),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.19/0.43 81[2:Spt:21.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.43 84[2:Rew:81.0,79.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(sk_c7,sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.19/0.43 85[2:Obv:84.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.19/0.43 89[3:Spt:11.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.43 91[4:Spt:19.1] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.19/0.43 94[2:SpR:81.0,24.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.19/0.43 95[3:SpR:89.0,24.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.43 101[0:SpR:24.0,25.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.43 107[0:Rew:23.0,101.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.43 113[0:SpR:107.0,107.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.43 116[0:SpR:24.0,107.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.43 120[3:SpR:95.0,107.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.19/0.43 126[0:Rew:113.0,116.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.43 127[3:Rew:126.0,120.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.19/0.43 129[3:SpR:127.0,24.0] || -> equal(multiply(sk_c5,sk_c8),identity)**.
% 0.19/0.43 132[4:Rew:91.0,129.0] || -> equal(sk_c7,identity)**.
% 0.19/0.43 133[4:Rew:132.0,81.0] || -> equal(inverse(sk_c6),identity)**.
% 0.19/0.43 135[4:Rew:132.0,94.0] || -> equal(multiply(identity,sk_c6),identity)**.
% 0.19/0.43 138[4:Rew:132.0,85.0] || equal(inverse(u),identity) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.19/0.43 143[4:Rew:23.0,135.0] || -> equal(identity,sk_c6)**.
% 0.19/0.43 144[4:Rew:143.0,23.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.43 148[4:Rew:143.0,126.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.43 149[4:Rew:143.0,132.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.43 150[4:Rew:143.0,133.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.43 157[4:Rew:148.0,138.3,144.0,138.3,149.0,138.3,148.0,138.2,149.0,138.2,143.0,138.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(v,sk_c6) equal(u,sk_c6) -> .
% 0.19/0.43 158[4:Con:157.0] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.19/0.43 261[4:SpL:150.0,158.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.19/0.43 263[4:Obv:261.1] || -> .
% 0.19/0.43 264[4:Spt:263.0,19.1,91.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.19/0.43 265[4:Spt:263.0,19.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.43 266[4:Rew:129.0,264.0] || equal(sk_c7,identity)** -> .
% 0.19/0.43 269[3:Rew:129.0,10.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c7,identity).
% 0.19/0.43 270[4:MRR:269.1,266.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.43 271[3:Rew:129.0,16.0] || -> equal(sk_c7,identity) equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.19/0.43 272[4:MRR:271.0,266.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.19/0.43 273[3:Rew:129.0,13.0] || -> equal(sk_c7,identity) equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.19/0.43 274[4:MRR:273.0,266.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.19/0.43 275[3:Rew:129.0,7.0] || -> equal(sk_c7,identity) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.43 276[4:MRR:275.0,266.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.43 288[4:SpR:272.0,107.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c7)**.
% 0.19/0.43 290[4:Rew:265.0,288.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.19/0.43 291[4:Rew:274.0,290.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.43 293[4:Rew:291.0,81.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.43 294[4:Rew:291.0,266.0] || equal(identity,sk_c6)** -> .
% 0.19/0.43 296[4:Rew:291.0,94.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.19/0.43 299[4:Rew:291.0,274.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.19/0.43 300[4:Rew:291.0,276.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.19/0.43 338[4:SpR:299.0,107.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c4)**.
% 0.19/0.43 340[4:Rew:296.0,338.0,293.0,338.0] || -> equal(identity,sk_c4)**.
% 0.19/0.44 341[4:Rew:340.0,294.0] || equal(sk_c4,sk_c6)** -> .
% 0.19/0.44 344[4:Rew:340.0,296.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.19/0.44 354[4:SpR:300.0,107.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c6)**.
% 0.19/0.44 356[4:Rew:270.0,354.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.19/0.44 357[4:Rew:344.0,356.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.44 358[4:MRR:357.0,341.0] || -> .
% 0.19/0.44 359[3:Spt:358.0,11.0,89.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.44 360[3:Spt:358.0,11.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.44 362[3:MRR:20.0,359.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.44 363[3:MRR:17.0,359.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.19/0.44 364[3:MRR:14.0,359.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.19/0.44 365[3:MRR:8.0,359.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.44 381[3:SpR:363.0,107.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c7)**.
% 0.19/0.44 383[3:Rew:362.0,381.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.19/0.44 384[3:Rew:364.0,383.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.44 385[3:Rew:384.0,81.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.44 387[3:Rew:384.0,94.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.19/0.44 391[3:Rew:384.0,364.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.19/0.44 392[3:Rew:384.0,365.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.19/0.44 395[3:Rew:384.0,85.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.19/0.44 400[3:Rew:384.0,395.3,384.0,395.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c6)** -> .
% 0.19/0.44 418[3:SpR:391.0,107.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c4)**.
% 0.19/0.44 420[3:Rew:387.0,418.0,385.0,418.0] || -> equal(identity,sk_c4)**.
% 0.19/0.44 421[3:Rew:420.0,387.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.19/0.44 422[3:Rew:420.0,126.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.44 423[3:Rew:420.0,23.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.44 430[3:SpR:392.0,107.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c6)**.
% 0.19/0.44 432[3:Rew:360.0,430.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.19/0.44 433[3:Rew:421.0,432.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.44 437[3:Rew:433.0,422.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.44 438[3:Rew:433.0,423.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.44 444[3:Rew:437.0,400.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.19/0.44 457[3:Rew:438.0,444.3,437.0,444.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(v,sk_c6) equal(u,sk_c6) -> .
% 0.19/0.44 458[3:Con:457.0] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.19/0.44 540[3:SpL:385.0,458.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.19/0.44 543[3:Obv:540.1] || -> .
% 0.19/0.44 544[2:Spt:543.0,21.0,81.0] || equal(inverse(sk_c6),sk_c7)** -> .
% 0.19/0.44 545[2:Spt:543.0,21.1] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.44 546[2:MRR:12.0,544.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.44 548[2:MRR:18.0,544.0] || -> equal(multiply(sk_c3,sk_c7),sk_c4)**.
% 0.19/0.44 549[2:MRR:15.0,544.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.19/0.44 550[2:MRR:9.0,544.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.44 559[2:SpR:548.0,107.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c7)**.
% 0.19/0.44 561[2:Rew:545.0,559.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.19/0.44 562[2:Rew:549.0,561.0] || -> equal(sk_c7,sk_c6)**.
% 0.19/0.44 563[2:Rew:562.0,545.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.19/0.44 564[2:Rew:562.0,544.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.19/0.44 565[2:Rew:562.0,548.0] || -> equal(multiply(sk_c3,sk_c6),sk_c4)**.
% 0.19/0.44 566[2:Rew:562.0,549.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.19/0.44 567[2:Rew:562.0,550.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.19/0.44 579[2:SpR:566.0,107.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c4)**.
% 0.19/0.44 581[2:Rew:24.0,579.0] || -> equal(identity,sk_c4)**.
% 0.19/0.44 583[2:Rew:581.0,126.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.44 584[2:Rew:581.0,24.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.19/0.44 589[2:SpR:567.0,107.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c6)**.
% 0.19/0.44 591[2:Rew:546.0,589.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.19/0.44 598[2:SpR:591.0,107.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.19/0.44 600[2:Rew:584.0,598.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.44 601[2:Rew:600.0,565.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.19/0.44 604[2:Rew:600.0,583.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.44 613[2:Rew:604.0,601.0] || -> equal(sk_c3,sk_c6)**.
% 0.19/0.44 615[2:Rew:613.0,563.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.44 617[2:MRR:615.0,564.0] || -> .
% 0.19/0.44 % SZS output end Refutation
% 0.19/0.44 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_5 prove_this_7 prove_this_8 prove_this_9 prove_this_10 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 prove_this_22 left_identity left_inverse associativity
% 0.19/0.44
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