TSTP Solution File: GRP347-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP347-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:46:57 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
% 0.03/0.12 % Problem : GRP347-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 08:08:07 EDT 2022
% 0.13/0.34 % 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 783 clauses, backtracked 362 clauses, performed 12 splits and kept 654 clauses.
% 0.20/0.47 SPASS allocated 63598 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.04 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 0:00:00.06 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 4, length 327 :
% 0.20/0.47 % SZS output start Refutation
% 0.20/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c5),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c5).
% 0.20/0.47 2[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c5).
% 0.20/0.47 4[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(multiply(sk_c6,sk_c7),sk_c5).
% 0.20/0.47 6[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 7[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.47 8[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 9[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 10[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.47 12[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 13[0:Inp] || -> equal(multiply(sk_c6,sk_c5),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 14[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 15[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 16[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 17[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 18[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 19[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.47 20[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.47 21[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 22[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.47 23[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.47 25[0:Inp] || -> equal(multiply(sk_c6,sk_c5),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 26[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 31[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(inverse(sk_c6),sk_c5) equal(multiply(u,sk_c7),sk_c5)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(x,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c5),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c5) -> .
% 0.20/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.47 35[1:Spt:31.3,31.8] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.20/0.47 36[2:Spt:2.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 38[3:Spt:8.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 40[4:Spt:20.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.47 44[5:Spt:14.1] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 46[5:SpL:44.0,35.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.47 47[5:Obv:46.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.20/0.47 48[5:Rew:38.0,47.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.47 49[5:Obv:48.0] || -> .
% 0.20/0.47 50[5:Spt:49.0,14.1,44.0] || equal(multiply(sk_c1,sk_c6),sk_c7)** -> .
% 0.20/0.47 51[5:Spt:49.0,14.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.20/0.47 52[5:MRR:18.1,50.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.47 53[5:MRR:16.1,50.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.47 54[5:MRR:17.1,50.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.47 55[5:MRR:15.1,50.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 67[3:SpR:38.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.20/0.47 68[4:SpR:40.0,33.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.20/0.47 69[5:SpR:51.0,33.0] || -> equal(multiply(sk_c5,sk_c6),identity)**.
% 0.20/0.47 70[5:SpR:52.0,33.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.47 71[5:SpR:53.0,33.0] || -> equal(multiply(sk_c6,sk_c3),identity)**.
% 0.20/0.47 72[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(identity,sk_c7) -> .
% 0.20/0.47 73[5:Rew:51.0,72.0] || equal(inverse(sk_c5),sk_c7)** equal(identity,sk_c7) -> .
% 0.20/0.47 80[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.47 83[0:Rew:32.0,80.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.47 89[4:SpR:68.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.20/0.47 90[4:Rew:32.0,89.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.20/0.47 92[5:SpR:69.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(identity,u))**.
% 0.20/0.47 94[5:Rew:32.0,92.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.20/0.47 111[5:SpR:68.0,94.0] || -> equal(multiply(sk_c5,identity),sk_c2)**.
% 0.20/0.47 112[5:SpR:71.0,94.0] || -> equal(multiply(sk_c5,identity),sk_c3)**.
% 0.20/0.47 113[5:SpR:90.0,94.0] || -> equal(multiply(sk_c2,u),multiply(sk_c5,u))**.
% 0.20/0.47 114[5:Rew:111.0,112.0] || -> equal(sk_c2,sk_c3)**.
% 0.20/0.47 119[5:Rew:114.0,113.0] || -> equal(multiply(sk_c3,u),multiply(sk_c5,u))**.
% 0.20/0.47 120[5:Rew:119.0,55.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.47 123[5:Rew:69.0,120.0] || -> equal(identity,sk_c7)**.
% 0.20/0.47 124[5:Rew:123.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 126[5:Rew:123.0,67.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.20/0.47 128[5:Rew:123.0,70.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.20/0.47 130[5:Rew:123.0,73.1] || equal(inverse(sk_c5),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.47 137[5:Rew:124.0,126.0] || -> equal(sk_c1,sk_c7)**.
% 0.20/0.47 138[5:Rew:137.0,38.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.47 140[5:Rew:124.0,128.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.47 142[5:Rew:140.0,54.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.47 150[5:Rew:124.0,142.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 174[5:Obv:130.1] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.20/0.47 175[5:Rew:138.0,174.0,150.0,174.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.47 176[5:Obv:175.0] || -> .
% 0.20/0.47 179[4:Spt:176.0,20.1,40.0] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.20/0.47 180[4:Spt:176.0,20.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.20/0.47 181[4:MRR:24.1,179.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.47 182[4:MRR:22.1,179.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.47 183[4:MRR:23.0,179.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.47 184[4:MRR:21.0,179.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 185[4:MRR:19.0,179.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.47 196[4:SpR:183.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.20/0.47 200[4:SpL:184.0,35.1] || equal(inverse(sk_c3),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.47 201[4:Obv:200.1] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.47 202[4:Rew:182.0,201.0] || equal(sk_c7,sk_c6)** -> .
% 0.20/0.47 210[4:SpR:180.0,33.0] || -> equal(multiply(sk_c5,sk_c6),identity)**.
% 0.20/0.47 212[4:SpR:181.0,33.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.47 231[0:SpR:83.0,83.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.47 233[4:SpR:184.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.47 239[2:SpR:36.0,83.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.47 244[0:SpR:33.0,83.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.47 249[4:Rew:36.0,233.0,182.0,233.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 253[4:Rew:249.0,185.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.20/0.47 254[4:Rew:249.0,210.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.20/0.47 256[4:Rew:249.0,196.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.47 260[4:Rew:253.0,254.0] || -> equal(identity,sk_c7)**.
% 0.20/0.47 262[4:Rew:260.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 264[4:Rew:260.0,212.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.20/0.47 271[4:Rew:262.0,264.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.47 300[4:Rew:262.0,256.0,271.0,256.0,262.0,256.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.47 302[4:Rew:300.0,253.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 303[4:MRR:302.0,202.0] || -> .
% 0.20/0.47 308[3:Spt:303.0,8.1,38.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.20/0.47 309[3:Spt:303.0,8.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.20/0.47 310[3:Rew:309.0,239.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.20/0.47 311[0:Rew:231.0,244.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.47 312[3:MRR:12.1,308.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.47 313[3:MRR:10.1,308.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.47 314[3:MRR:11.0,308.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.47 315[3:MRR:9.0,308.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 319[3:SpR:309.0,83.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.20/0.47 321[3:SpR:312.0,83.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.20/0.47 329[3:SpR:314.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.20/0.47 333[3:SpR:310.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.47 337[3:SpR:315.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.47 338[3:SpR:315.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.47 339[3:SpL:315.0,35.1] || equal(inverse(sk_c3),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.47 340[3:Rew:36.0,338.0,313.0,338.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 346[3:Rew:340.0,329.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.47 349[3:Rew:340.0,319.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.47 352[3:Rew:340.0,333.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.47 354[3:Obv:339.1] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.47 355[3:Rew:313.0,354.0] || equal(sk_c7,sk_c6)** -> .
% 0.20/0.47 357[3:Rew:349.0,352.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 359[3:Rew:357.0,337.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),u)**.
% 0.20/0.47 361[3:Rew:357.0,346.0] || -> equal(multiply(sk_c4,u),multiply(sk_c6,u))**.
% 0.20/0.47 362[3:Rew:357.0,321.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.47 366[3:Rew:362.0,361.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.47 370[3:Rew:366.0,359.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.47 374[3:Rew:370.0,315.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 375[3:MRR:374.0,355.0] || -> .
% 0.20/0.47 376[2:Spt:375.0,2.1,36.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.47 377[2:Spt:375.0,2.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.20/0.47 378[2:MRR:6.1,376.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.47 380[2:Rew:377.0,72.0] || equal(inverse(sk_c5),sk_c7)** equal(identity,sk_c7) -> .
% 0.20/0.47 382[2:MRR:5.1,376.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.47 384[2:MRR:1.1,376.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.47 392[2:SpR:382.0,83.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.20/0.47 394[2:Rew:378.0,392.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.20/0.47 404[2:SpR:384.0,83.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.20/0.47 406[2:Rew:377.0,404.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.20/0.47 412[2:SpR:394.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.20/0.47 414[2:Rew:33.0,412.0] || -> equal(identity,sk_c5)**.
% 0.20/0.47 415[2:Rew:414.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.47 418[2:Rew:414.0,311.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.47 419[2:Rew:414.0,380.1] || equal(inverse(sk_c5),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.20/0.47 420[2:Rew:415.0,406.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 425[2:Rew:420.0,382.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.20/0.47 431[2:Rew:420.0,418.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.47 434[2:Rew:431.0,425.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.47 435[2:Rew:434.0,378.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.47 446[2:Rew:420.0,419.1,435.0,419.0,420.0,419.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.47 447[2:Obv:446.1] || -> .
% 0.20/0.47 448[1:Spt:447.0,31.0,31.1,31.2,31.4,31.5,31.6,31.7,31.9,31.10] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(inverse(sk_c6),sk_c5) equal(multiply(u,sk_c7),sk_c5)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c5) -> .
% 0.20/0.47 450[2:Spt:2.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.47 451[2:Rew:450.0,448.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(inverse(sk_c6),sk_c5) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7)** equal(sk_c5,sk_c5) -> .
% 0.20/0.47 453[2:Obv:451.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(inverse(sk_c6),sk_c5) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.47 456[2:SpR:450.0,83.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.47 458[3:Spt:20.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.20/0.47 460[3:Rew:458.0,453.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(sk_c5,sk_c5) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.47 461[3:Rew:458.0,456.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.20/0.47 462[3:Obv:460.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.47 464[3:SpR:458.0,83.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.20/0.47 466[4:Spt:7.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.47 468[4:Rew:466.0,462.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.20/0.47 469[4:Obv:468.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c7),sk_c5)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c6)** -> .
% 0.20/0.47 471[4:SpR:466.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.47 472[4:SpR:466.0,83.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.20/0.47 474[4:Rew:458.0,472.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.20/0.47 475[5:Spt:12.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.47 476[5:SpR:475.0,83.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.20/0.47 481[6:Spt:10.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.47 482[6:SpR:481.0,83.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.47 484[7:Spt:11.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.47 486[7:SpR:484.0,83.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.20/0.47 488[7:Rew:475.0,486.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.20/0.47 489[8:Spt:9.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 491[8:SpR:489.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.47 493[8:Rew:450.0,491.0,481.0,491.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 495[8:Rew:493.0,458.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.47 500[8:Rew:493.0,471.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.47 502[8:Rew:493.0,464.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.47 503[8:Rew:493.0,469.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c6)** -> .
% 0.20/0.47 508[8:Rew:493.0,488.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.47 510[8:Rew:502.0,500.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 511[8:Rew:510.0,508.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 514[8:Rew:510.0,476.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.47 520[8:Rew:511.0,510.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.47 526[8:Rew:493.0,503.5,511.0,503.4,511.0,503.3,511.0,503.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c6)** equal(multiply(w,sk_c6),sk_c6)** -> .
% 0.20/0.47 527[8:Con:526.1] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.20/0.47 550[8:SpR:514.0,311.0] || -> equal(identity,sk_c4)**.
% 0.20/0.47 553[8:Rew:550.0,311.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.20/0.47 555[8:Rew:550.0,33.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.20/0.47 561[8:SpR:481.0,555.0] || -> equal(multiply(sk_c6,sk_c3),sk_c4)**.
% 0.20/0.47 562[8:SpR:495.0,555.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.20/0.47 564[8:Rew:520.0,561.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.47 569[8:Rew:564.0,553.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.20/0.47 570[8:Rew:520.0,562.0,564.0,562.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.47 576[8:Rew:570.0,569.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 577[8:Rew:576.0,527.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.47 634[8:SpL:495.0,577.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.47 636[8:Obv:634.1] || -> .
% 0.20/0.47 637[8:Spt:636.0,9.1,489.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.20/0.47 638[8:Spt:636.0,9.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 676[7:SpR:488.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.20/0.47 678[7:Rew:33.0,676.0] || -> equal(identity,sk_c5)**.
% 0.20/0.47 679[7:Rew:678.0,311.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.47 680[7:Rew:678.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.47 684[7:Rew:679.0,466.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 685[7:Rew:679.0,461.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 698[8:Rew:684.0,637.0] || equal(multiply(sk_c3,sk_c6),sk_c6)** -> .
% 0.20/0.47 707[7:Rew:684.0,685.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 713[7:Rew:707.0,680.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.47 714[7:Rew:713.0,482.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.47 725[8:Rew:714.0,698.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.47 726[8:Obv:725.0] || -> .
% 0.20/0.47 740[7:Spt:726.0,11.1,484.0] || equal(multiply(sk_c4,sk_c7),sk_c5)** -> .
% 0.20/0.47 741[7:Spt:726.0,11.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 743[7:MRR:17.0,740.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 754[7:SpR:743.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.20/0.47 756[7:Rew:741.0,754.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.47 769[4:SpR:474.0,83.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.20/0.47 771[4:Rew:33.0,769.0] || -> equal(identity,sk_c7)**.
% 0.20/0.47 772[4:Rew:771.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.47 773[4:Rew:771.0,311.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.47 776[7:Rew:772.0,756.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 782[5:Rew:772.0,476.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.47 788[7:Rew:776.0,450.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.47 791[7:Rew:776.0,740.0] || equal(multiply(sk_c4,sk_c6),sk_c5)** -> .
% 0.20/0.47 796[7:Rew:776.0,773.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 797[7:Rew:796.0,788.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 811[7:Rew:782.0,791.0,797.0,791.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.47 812[7:Obv:811.0] || -> .
% 0.20/0.47 823[6:Spt:812.0,10.0,481.0] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.20/0.47 824[6:Spt:812.0,10.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 825[4:Rew:773.0,450.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 826[4:Rew:825.0,458.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.47 836[6:MRR:16.0,823.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 841[4:Rew:825.0,469.5,773.0,469.3,825.0,469.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c6)** -> .
% 0.20/0.47 843[6:SpR:824.0,83.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.20/0.47 845[6:Rew:772.0,843.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.47 846[6:Rew:845.0,836.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 851[6:Rew:846.0,773.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 855[6:Rew:846.0,841.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c6)** -> .
% 0.20/0.47 860[6:Rew:851.0,855.5,851.0,855.4,846.0,855.4] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) -> .
% 0.20/0.47 861[6:Con:860.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.47 910[6:SpL:826.0,861.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.47 911[6:Obv:910.1] || -> .
% 0.20/0.47 912[5:Spt:911.0,12.0,475.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.20/0.47 913[5:Spt:911.0,12.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 916[5:MRR:18.0,912.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 921[5:SpR:913.0,83.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.20/0.47 923[5:Rew:772.0,921.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.47 924[5:Rew:923.0,916.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 928[5:Rew:924.0,773.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 933[5:Rew:924.0,841.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c6)** -> .
% 0.20/0.47 938[5:Rew:928.0,933.5,928.0,933.4,924.0,933.4] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) -> .
% 0.20/0.47 939[5:Con:938.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.47 1003[5:SpL:826.0,939.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.47 1005[5:Obv:1003.1] || -> .
% 0.20/0.47 1006[4:Spt:1005.0,7.1,466.0] || equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.47 1007[4:Spt:1005.0,7.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 1008[4:MRR:19.1,1006.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.47 1009[4:MRR:13.0,1006.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 1010[4:MRR:25.0,1006.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 1025[4:SpR:1009.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.20/0.47 1027[4:Rew:1007.0,1025.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.47 1029[4:SpR:1010.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.47 1031[4:Rew:1008.0,1029.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.47 1036[4:SpR:1031.0,83.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.47 1038[4:Rew:461.0,1036.0,458.0,1036.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 1043[4:Rew:1038.0,1027.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.47 1045[4:Rew:1038.0,1006.0] || equal(multiply(sk_c6,sk_c5),sk_c6)** -> .
% 0.20/0.47 1052[4:Rew:1031.0,1043.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 1055[4:Rew:1052.0,1031.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.47 1060[4:Rew:1055.0,1045.0,1052.0,1045.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.47 1061[4:Obv:1060.0] || -> .
% 0.20/0.47 1069[3:Spt:1061.0,20.0,458.0] || equal(inverse(sk_c6),sk_c5)** -> .
% 0.20/0.47 1070[3:Spt:1061.0,20.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.47 1071[3:MRR:8.0,1069.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.47 1072[3:MRR:26.0,1069.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.20/0.47 1073[3:MRR:14.0,1069.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.20/0.47 1082[3:SpR:1072.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.20/0.47 1084[3:Rew:1070.0,1082.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.47 1086[3:SpR:1073.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c6)**.
% 0.20/0.47 1088[3:Rew:1071.0,1086.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.47 1090[3:SpR:1084.0,83.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.47 1092[3:Rew:456.0,1090.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 1093[3:Rew:1092.0,1071.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.47 1095[3:Rew:1092.0,1073.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.47 1096[3:Rew:1092.0,456.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.47 1100[3:Rew:1092.0,1088.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.47 1101[3:Rew:1084.0,1100.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 1102[3:Rew:1101.0,1069.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.20/0.47 1106[3:Rew:33.0,1096.0,1101.0,1096.0] || -> equal(identity,sk_c6)**.
% 0.20/0.47 1107[3:Rew:1106.0,311.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.47 1112[3:Rew:1107.0,1095.0] || -> equal(sk_c1,sk_c6)**.
% 0.20/0.47 1115[3:Rew:1112.0,1093.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.47 1117[3:MRR:1115.0,1102.0] || -> .
% 0.20/0.47 1124[2:Spt:1117.0,2.1,450.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.47 1125[2:Spt:1117.0,2.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.20/0.47 1126[2:MRR:6.1,1124.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.47 1127[2:MRR:4.1,1124.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.47 1128[2:MRR:5.1,1124.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.47 1129[2:MRR:3.1,1124.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.47 1130[2:MRR:1.1,1124.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.47 1131[2:SpR:1125.0,83.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.20/0.47 1135[2:SpR:1127.0,83.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.47 1138[2:SpR:1128.0,83.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.20/0.47 1140[2:Rew:1126.0,1138.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.20/0.47 1142[2:SpR:1129.0,83.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.47 1144[2:Rew:1127.0,1142.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.47 1145[2:Rew:1144.0,1124.0] || equal(sk_c5,sk_c6)** -> .
% 0.20/0.47 1147[2:SpR:1130.0,83.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.20/0.47 1149[2:Rew:1125.0,1147.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.20/0.47 1154[2:SpR:1140.0,83.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.20/0.47 1156[2:Rew:33.0,1154.0] || -> equal(identity,sk_c5)**.
% 0.20/0.47 1157[2:Rew:1156.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.47 1161[2:Rew:1157.0,1149.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.47 1164[2:Rew:1157.0,1131.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.47 1167[2:Rew:1161.0,1145.0] || equal(sk_c7,sk_c6)** -> .
% 0.20/0.48 1174[2:Rew:1164.0,1135.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.48 1178[2:Rew:1174.0,1129.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 1179[2:MRR:1178.0,1167.0] || -> .
% 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_6 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 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_31 left_identity left_inverse associativity
% 0.20/0.48
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