TSTP Solution File: GRP357-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP357-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:47:00 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP357-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.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 : Mon Jun 13 14:54:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 968 clauses, backtracked 353 clauses, performed 10 splits and kept 800 clauses.
% 0.19/0.47 SPASS allocated 63732 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 4, length 394 :
% 0.19/0.47 % SZS output start Refutation
% 0.19/0.47 1[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.19/0.47 2[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.19/0.47 3[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.19/0.47 4[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.19/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.19/0.47 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.19/0.47 7[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 8[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.47 9[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c8),sk_c6)**.
% 0.19/0.47 10[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 11[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c8),sk_c6)**.
% 0.19/0.47 13[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.19/0.47 16[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.19/0.47 17[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 18[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 19[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 22[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 23[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 25[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.19/0.47 26[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.47 27[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.47 28[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.19/0.47 29[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.47 30[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.47 31[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(inverse(sk_c8),sk_c6) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),y)* equal(multiply(x,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.19/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.47 35[1:Spt:31.0,31.4,31.7] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.19/0.47 36[2:Spt:7.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.19/0.47 38[3:Spt:1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.19/0.47 42[4:Spt:19.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 45[1:SpL:32.0,35.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.47 46[5:Spt:13.1] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 48[5:SpL:46.0,35.1] || equal(inverse(sk_c1),sk_c2) equal(sk_c8,sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.47 49[5:Obv:48.1] || equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.47 50[5:Rew:42.0,49.0] || equal(sk_c2,sk_c2) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.47 51[5:Obv:50.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.47 52[5:MRR:30.1,51.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 53[5:MRR:27.1,51.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 54[5:MRR:29.1,51.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 55[5:MRR:28.1,51.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 56[5:MRR:26.1,51.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.47 57[5:MRR:25.1,51.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 77[2:SpR:36.0,33.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.19/0.47 86[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.47 93[0:Rew:32.0,86.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.47 115[0:SpR:93.0,93.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.47 117[3:SpR:38.0,93.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c6)**.
% 0.19/0.47 118[0:SpR:32.0,93.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.19/0.47 119[0:SpR:33.0,93.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 121[5:SpR:54.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 122[5:SpR:56.0,93.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.19/0.47 123[2:SpR:77.0,93.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c8)**.
% 0.19/0.47 136[5:Rew:55.0,121.0,52.0,121.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 138[5:Rew:136.0,36.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 139[5:Rew:136.0,38.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 142[5:Rew:136.0,53.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 146[5:Rew:136.0,57.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 148[5:Rew:136.0,77.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.47 152[5:Rew:136.0,45.1] || equal(inverse(identity),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.47 174[5:Rew:146.0,122.0,142.0,122.0,136.0,122.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 175[5:Rew:174.0,138.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 176[5:Rew:174.0,139.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 178[5:Rew:174.0,148.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.47 179[5:Rew:176.0,178.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 203[5:Rew:179.0,119.0] || -> equal(multiply(inverse(inverse(u)),sk_c7),u)**.
% 0.19/0.47 214[5:Rew:115.0,203.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 237[5:Rew:214.0,152.2,136.0,152.2,175.0,152.0,179.0,152.0] || equal(sk_c7,u)* equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.19/0.47 238[5:Obv:237.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 239[5:UnC:238.0,93.0] || -> .
% 0.19/0.47 248[5:Spt:239.0,13.1,46.0] || equal(multiply(sk_c1,sk_c2),sk_c8)** -> .
% 0.19/0.47 249[5:Spt:239.0,13.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 250[0:Rew:115.0,119.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.47 252[2:Rew:250.0,123.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.47 253[5:MRR:18.1,248.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 255[5:MRR:17.1,248.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 256[5:MRR:16.1,248.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 264[5:SpR:249.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.47 266[5:Rew:36.0,264.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.47 291[5:SpR:255.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 293[5:Rew:253.0,291.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 294[5:Rew:256.0,293.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 296[5:Rew:294.0,36.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 300[5:Rew:294.0,77.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.47 303[5:Rew:294.0,117.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.47 313[5:Rew:294.0,45.1] || equal(inverse(identity),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.47 321[5:Rew:300.0,303.0,296.0,303.0] || -> equal(identity,sk_c6)**.
% 0.19/0.47 323[5:Rew:321.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.47 326[5:Rew:321.0,250.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.47 328[5:Rew:323.0,266.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 329[5:Rew:328.0,296.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 333[5:Rew:328.0,321.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 336[5:Rew:328.0,326.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 359[5:Rew:336.0,313.2,294.0,313.2,329.0,313.0,333.0,313.0] || equal(sk_c7,u)* equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.19/0.47 360[5:Obv:359.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 361[5:UnC:360.0,93.0] || -> .
% 0.19/0.47 367[4:Spt:361.0,19.0,42.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.19/0.47 368[4:Spt:361.0,19.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 369[4:MRR:24.1,367.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 371[4:MRR:23.0,367.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 372[4:MRR:22.0,367.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 377[4:SpR:368.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.47 379[4:Rew:36.0,377.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.47 397[4:SpR:371.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 399[4:Rew:369.0,397.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 400[4:Rew:372.0,399.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 403[4:Rew:400.0,252.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.47 404[4:Rew:400.0,36.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 407[4:Rew:400.0,77.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.47 409[4:Rew:400.0,117.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.47 418[4:Rew:400.0,45.1] || equal(inverse(identity),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.47 425[4:Rew:407.0,409.0,404.0,409.0] || -> equal(identity,sk_c6)**.
% 0.19/0.47 426[4:Rew:425.0,250.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.47 431[4:Rew:426.0,379.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 432[4:Rew:431.0,403.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 435[4:Rew:431.0,425.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 436[4:Rew:431.0,426.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 458[4:Rew:436.0,418.2,400.0,418.2,432.0,418.0,435.0,418.0] || equal(sk_c7,u)* equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.19/0.47 459[4:Obv:458.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 460[4:UnC:459.0,93.0] || -> .
% 0.19/0.47 466[3:Spt:460.0,1.1,38.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.19/0.47 467[3:Spt:460.0,1.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 468[3:MRR:6.1,466.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 469[3:MRR:3.1,466.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 470[3:MRR:5.1,466.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 471[3:MRR:4.1,466.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 472[3:MRR:2.1,466.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.47 476[3:SpR:467.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.47 478[3:Rew:36.0,476.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.47 493[3:SpR:470.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 495[3:Rew:468.0,493.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 496[3:Rew:471.0,495.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 497[3:Rew:496.0,467.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 498[3:Rew:496.0,36.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 501[3:Rew:496.0,469.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 502[3:Rew:496.0,77.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.47 507[3:Rew:496.0,471.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.19/0.47 508[3:Rew:496.0,472.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 511[3:Rew:496.0,45.1] || equal(inverse(identity),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.47 520[3:Rew:496.0,511.2] || equal(inverse(identity),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.47 552[3:SpR:507.0,93.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.19/0.47 554[3:Rew:502.0,552.0,498.0,552.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 555[3:Rew:554.0,502.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 557[3:Rew:554.0,250.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 560[3:Rew:554.0,520.0] || equal(inverse(sk_c5),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.47 567[3:SpR:508.0,93.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.19/0.47 569[3:Rew:497.0,567.0,501.0,567.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 570[3:Rew:569.0,498.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 572[3:Rew:569.0,478.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 579[3:Rew:569.0,555.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 581[3:Rew:572.0,579.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 585[3:Rew:581.0,557.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 588[3:Rew:581.0,560.0] || equal(inverse(sk_c7),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.47 612[3:Rew:585.0,588.2,570.0,588.0] || equal(sk_c7,u)* equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.19/0.47 613[3:Obv:612.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 614[3:UnC:613.0,496.0] || -> .
% 0.19/0.47 617[2:Spt:614.0,7.0,36.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.19/0.47 618[2:Spt:614.0,7.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 619[2:MRR:12.1,617.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 620[2:MRR:9.1,617.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 621[2:MRR:11.0,617.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 622[2:MRR:10.0,617.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 623[2:MRR:8.0,617.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.47 625[2:SpR:618.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.47 632[2:SpR:621.0,93.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 634[2:Rew:619.0,632.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.47 635[2:Rew:622.0,634.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 636[2:Rew:635.0,618.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 637[2:Rew:635.0,619.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.47 638[2:Rew:635.0,620.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 639[2:Rew:635.0,617.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.19/0.47 640[2:Rew:635.0,621.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.47 641[2:Rew:635.0,625.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.19/0.47 642[2:Rew:635.0,622.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.19/0.47 643[2:Rew:635.0,623.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.48 671[2:SpR:642.0,93.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.19/0.48 673[2:Rew:33.0,671.0] || -> equal(identity,sk_c5)**.
% 0.19/0.48 674[2:Rew:673.0,250.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.48 678[2:Rew:673.0,33.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.48 684[2:SpR:643.0,93.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.19/0.48 686[2:Rew:636.0,684.0,638.0,684.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 688[2:Rew:686.0,639.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.48 689[2:Rew:686.0,641.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.48 691[2:Rew:678.0,689.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.48 692[2:Rew:691.0,640.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.48 694[2:Rew:691.0,674.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 701[2:Rew:694.0,692.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.48 707[2:Rew:701.0,637.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 711[2:MRR:707.0,688.0] || -> .
% 0.19/0.48 720[1:Spt:711.0,31.1,31.2,31.3,31.5,31.6,31.8,31.9,31.10] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c6) equal(multiply(u,sk_c8),w)*+ equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,w),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.19/0.48 721[1:EqR:720.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c6) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.19/0.48 723[2:Spt:7.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.19/0.48 726[2:Rew:723.0,721.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c6,sk_c6) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.19/0.48 727[2:Obv:726.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.19/0.48 732[3:Spt:1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.19/0.48 735[3:Rew:732.0,727.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) equal(sk_c8,sk_c8) -> .
% 0.19/0.48 736[3:Obv:735.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.19/0.48 740[3:SpR:732.0,93.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c6)**.
% 0.19/0.48 742[4:Spt:19.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.48 745[5:Spt:25.1] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.48 752[6:Spt:13.1] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.48 754[6:SpR:752.0,93.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.19/0.48 756[6:Rew:742.0,754.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.19/0.48 758[0:SpR:33.0,93.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.48 760[2:SpR:723.0,33.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.19/0.48 761[4:SpR:742.0,33.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.19/0.48 762[0:Rew:250.0,758.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.48 766[6:SpR:756.0,93.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.19/0.48 768[6:Rew:33.0,766.0] || -> equal(sk_c8,identity)**.
% 0.19/0.48 769[6:Rew:768.0,723.0] || -> equal(inverse(identity),sk_c6)**.
% 0.19/0.48 770[6:Rew:768.0,732.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.19/0.48 776[6:Rew:768.0,736.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(multiply(identity,sk_c7),sk_c6) -> .
% 0.19/0.48 783[6:Rew:768.0,760.0] || -> equal(multiply(sk_c6,identity),identity)**.
% 0.19/0.48 784[6:Rew:769.0,118.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.48 785[6:Rew:250.0,783.0] || -> equal(identity,sk_c6)**.
% 0.19/0.48 788[6:Rew:785.0,250.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.48 790[6:Rew:785.0,768.0] || -> equal(sk_c8,sk_c6)**.
% 0.19/0.48 791[6:Rew:785.0,769.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.19/0.48 792[6:Rew:785.0,770.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.19/0.48 795[6:Rew:788.0,792.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 796[6:Rew:795.0,785.0] || -> equal(identity,sk_c7)**.
% 0.19/0.48 797[6:Rew:795.0,790.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 798[6:Rew:795.0,791.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 799[6:Rew:795.0,784.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 800[6:Rew:795.0,788.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 820[6:Rew:796.0,776.4,800.0,776.4,795.0,776.4,800.0,776.3,799.0,776.3,797.0,776.3,800.0,776.2,797.0,776.2,797.0,776.1,797.0,776.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(v,sk_c7) equal(u,sk_c7) equal(sk_c7,sk_c7) -> .
% 0.19/0.48 821[6:Obv:820.4] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(v,sk_c7) equal(u,sk_c7) -> .
% 0.19/0.48 822[6:Con:821.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.48 841[0:SpR:762.0,93.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.48 883[6:SpL:798.0,822.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 885[6:Obv:883.1] || -> .
% 0.19/0.48 886[6:Spt:885.0,13.1,752.0] || equal(multiply(sk_c1,sk_c2),sk_c8)** -> .
% 0.19/0.48 887[6:Spt:885.0,13.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.48 888[6:MRR:18.1,886.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 890[6:MRR:17.1,886.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.48 891[6:MRR:16.1,886.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.48 900[6:SpR:887.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.48 902[6:Rew:723.0,900.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.48 904[6:SpR:888.0,762.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.48 907[6:Rew:723.0,904.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.48 909[6:Rew:907.0,890.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.48 910[6:Rew:760.0,909.0] || -> equal(identity,sk_c5)**.
% 0.19/0.48 911[6:Rew:910.0,760.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.48 912[6:Rew:910.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.48 913[6:Rew:910.0,761.0] || -> equal(multiply(sk_c2,sk_c1),sk_c5)**.
% 0.19/0.48 914[6:Rew:910.0,250.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.48 917[6:Rew:914.0,891.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 919[6:Rew:917.0,723.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.48 920[6:Rew:917.0,745.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.48 923[6:Rew:917.0,740.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.48 924[6:Rew:917.0,886.0] || equal(multiply(sk_c1,sk_c2),sk_c7)** -> .
% 0.19/0.48 935[6:Rew:917.0,911.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.48 936[6:Rew:935.0,923.0,919.0,923.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.48 938[6:Rew:936.0,912.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.48 939[6:Rew:936.0,913.0] || -> equal(multiply(sk_c2,sk_c1),sk_c6)**.
% 0.19/0.48 940[6:Rew:936.0,914.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.48 944[6:Rew:938.0,902.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 952[6:Rew:944.0,938.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 953[6:Rew:944.0,939.0] || -> equal(multiply(sk_c2,sk_c1),sk_c7)**.
% 0.19/0.48 954[6:Rew:944.0,940.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 957[6:Rew:954.0,920.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.48 961[6:Rew:957.0,953.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.19/0.48 963[6:Rew:952.0,961.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.48 965[6:Rew:952.0,924.0,963.0,924.0,957.0,924.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 966[6:Obv:965.0] || -> .
% 0.19/0.48 980[5:Spt:966.0,25.1,745.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.48 981[5:Spt:966.0,25.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.48 982[5:MRR:30.1,980.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 984[5:MRR:29.1,980.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.48 985[5:MRR:28.1,980.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.48 987[5:Rew:981.0,736.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.48 988[5:Obv:987.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.48 994[5:SpR:981.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.48 996[5:Rew:723.0,994.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.48 1006[5:SpR:982.0,762.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.48 1009[5:Rew:723.0,1006.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.48 1011[5:Rew:1009.0,984.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.48 1012[5:Rew:760.0,1011.0] || -> equal(identity,sk_c5)**.
% 0.19/0.48 1013[5:Rew:1012.0,250.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.48 1015[5:Rew:1012.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.48 1016[5:Rew:1012.0,760.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.48 1019[5:Rew:1013.0,985.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 1021[5:Rew:1019.0,723.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.48 1023[5:Rew:1019.0,740.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.48 1030[5:Rew:1019.0,988.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.48 1035[5:Rew:1019.0,1016.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.48 1036[5:Rew:1035.0,1023.0,1021.0,1023.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.48 1038[5:Rew:1036.0,1013.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.48 1040[5:Rew:1036.0,1015.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.48 1044[5:Rew:1038.0,996.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 1046[5:Rew:1044.0,1021.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 1051[5:Rew:1044.0,1038.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 1053[5:Rew:1044.0,1040.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 1066[5:Rew:1051.0,1030.3,1053.0,1030.3,1019.0,1030.3,1051.0,1030.2,1019.0,1030.2,1019.0,1030.1] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(v,sk_c7) equal(u,sk_c7) -> .
% 0.19/0.48 1067[5:Con:1066.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.48 1147[5:SpL:1046.0,1067.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 1148[5:Obv:1147.1] || -> .
% 0.19/0.48 1149[4:Spt:1148.0,19.0,742.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.19/0.48 1150[4:Spt:1148.0,19.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.48 1151[4:MRR:24.1,1149.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 1153[4:MRR:23.0,1149.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.48 1154[4:MRR:22.0,1149.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.48 1156[4:Rew:1150.0,736.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.48 1157[4:Obv:1156.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.48 1163[4:SpR:1150.0,93.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.19/0.48 1165[4:Rew:723.0,1163.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.48 1175[4:SpR:1151.0,762.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.48 1178[4:Rew:723.0,1175.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.48 1180[4:Rew:1178.0,1153.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.48 1181[4:Rew:760.0,1180.0] || -> equal(identity,sk_c5)**.
% 0.19/0.48 1182[4:Rew:1181.0,760.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.48 1183[4:Rew:1181.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.48 1184[4:Rew:1181.0,250.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.48 1187[4:Rew:1184.0,1154.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 1189[4:Rew:1187.0,723.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.48 1192[4:Rew:1187.0,740.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.48 1199[4:Rew:1187.0,1157.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.48 1202[4:Rew:1187.0,1182.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.48 1203[4:Rew:1202.0,1192.0,1189.0,1192.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.48 1205[4:Rew:1203.0,1183.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.48 1206[4:Rew:1203.0,1184.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.48 1210[4:Rew:1205.0,1165.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 1212[4:Rew:1210.0,1189.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 1218[4:Rew:1210.0,1205.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 1219[4:Rew:1210.0,1206.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 1230[4:Rew:1219.0,1199.3,1218.0,1199.3,1187.0,1199.3,1219.0,1199.2,1187.0,1199.2,1187.0,1199.1] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(v,sk_c7) equal(u,sk_c7) -> .
% 0.19/0.48 1231[4:Con:1230.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.48 1270[4:SpL:1212.0,1231.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 1271[4:Obv:1270.1] || -> .
% 0.19/0.48 1272[3:Spt:1271.0,1.1,732.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.19/0.48 1273[3:Spt:1271.0,1.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.48 1274[3:MRR:6.1,1272.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 1275[3:MRR:3.1,1272.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.48 1276[3:MRR:5.1,1272.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.48 1277[3:MRR:4.1,1272.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.48 1278[3:MRR:2.1,1272.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.48 1292[3:SpR:1274.0,762.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.48 1295[3:Rew:723.0,1292.0] || -> equal(sk_c4,sk_c6)**.
% 0.19/0.48 1297[3:Rew:1295.0,1276.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.48 1298[3:Rew:760.0,1297.0] || -> equal(identity,sk_c5)**.
% 0.19/0.48 1299[3:Rew:1298.0,250.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.48 1300[3:Rew:1298.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.48 1301[3:Rew:1298.0,760.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.48 1304[3:Rew:1299.0,1277.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 1305[3:Rew:1304.0,1273.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.48 1307[3:Rew:1304.0,723.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.48 1308[3:Rew:1304.0,1272.0] || equal(multiply(sk_c7,sk_c6),sk_c7)** -> .
% 0.19/0.48 1311[3:Rew:1304.0,1275.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.48 1312[3:Rew:1304.0,1278.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.48 1314[3:Rew:1304.0,1301.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.48 1329[3:SpR:1311.0,762.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.48 1332[3:Rew:1307.0,1329.0] || -> equal(sk_c3,sk_c6)**.
% 0.19/0.48 1334[3:Rew:1332.0,1312.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.19/0.48 1335[3:Rew:1314.0,1334.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.48 1337[3:Rew:1335.0,1299.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 1338[3:Rew:1335.0,1300.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 1342[3:Rew:1337.0,1305.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 1347[3:Rew:1342.0,1308.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.19/0.48 1354[3:Rew:1338.0,1347.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 1355[3:Obv:1354.0] || -> .
% 0.19/0.48 1360[2:Spt:1355.0,7.0,723.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.19/0.48 1361[2:Spt:1355.0,7.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.48 1362[2:MRR:12.1,1360.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 1363[2:MRR:9.1,1360.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.48 1364[2:MRR:11.0,1360.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.48 1365[2:MRR:10.0,1360.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.48 1366[2:MRR:8.0,1360.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.19/0.48 1371[2:SpR:1362.0,762.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.48 1374[2:Rew:1371.0,1360.0] || equal(sk_c4,sk_c6)** -> .
% 0.19/0.48 1377[2:SpR:1363.0,762.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.19/0.48 1378[2:SpR:1363.0,841.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),u)**.
% 0.19/0.48 1380[2:Rew:1371.0,1377.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.48 1382[2:Rew:1380.0,1364.0] || -> equal(multiply(sk_c3,sk_c8),sk_c5)**.
% 0.19/0.48 1384[2:Rew:1380.0,1374.0] || equal(sk_c3,sk_c6)** -> .
% 0.19/0.48 1388[2:Rew:1366.0,1382.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.48 1389[2:Rew:1388.0,1365.0] || -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.19/0.48 1390[2:Rew:1361.0,1389.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 1391[2:Rew:1390.0,1361.0] || -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.19/0.48 1393[2:Rew:1390.0,1384.0] || equal(sk_c3,sk_c7)** -> .
% 0.19/0.48 1402[2:SpR:1366.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.19/0.48 1403[2:SpR:1366.0,93.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.19/0.48 1405[2:Rew:1363.0,1403.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.48 1406[2:Rew:1391.0,1405.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 1407[2:Rew:1406.0,1363.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.48 1412[2:Rew:1406.0,1378.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.19/0.48 1414[2:Rew:1412.0,1402.0,1406.0,1402.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 1445[2:SpR:1414.0,250.0] || -> equal(identity,sk_c7)**.
% 0.19/0.48 1450[2:Rew:1445.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.48 1461[2:SpR:1407.0,1450.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.48 1463[2:Rew:1414.0,1461.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.48 1464[2:MRR:1463.0,1393.0] || -> .
% 0.19/0.48 % SZS output end Refutation
% 0.19/0.48 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_16 prove_this_17 prove_this_18 prove_this_19 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
% 0.19/0.48
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